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We present a hardware mechanism called HourGlass to predictably share data in
a multi-core system where cores are explicitly designated as critical or
non-critical. HourGlass is a time-based cache coherence protocol for
dual-critical multi-core systems that ensures worst-case latency (WCL) bounds
for memory requests originating from critical cores. Although HourGlass does
not provide either WCL or bandwidth guarantees for memory requests from
non-critical cores, it promotes the use of timers to improve its bandwidth
utilization while still maintaining WCL bounds for critical cores. This
encourages a trade-off between the WCL bounds for critical cores, and the
improved memory bandwidth for non-critical cores via timer configurations. We
evaluate HourGlass using gem5, and with multithreaded benchmark suites
including SPLASH-2, and synthetic workloads. Our results show that the WCL for
critical cores with HourGlass is always within the analytical WCL bounds, and
provides a tighter WCL bound on critical cores compared to the state-of-the-art
real-time cache coherence protocol. Further, we show that HourGlass enables a
trade-off between provable WCL bounds for critical cores, and improved
bandwidth utilization for non-critical cores. The average-case performance of
HourGlass is comparable to the state-of-the-art real-time cache coherence
protocol, and suffers a slowdown of 1.43x and 1.46x compared to the
conventional MSI and MESI protocols.
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In the present paper, we study the hemi-slant submanifolds of nearly Kaehler
manifolds. We study the integrability of distributions involved in the
definition of hemi-slant submanifolds. some results are worked out on totally
umbilical hemi-slant submanifolds. we study the cohomology class for hemi-slant
submanifolds of nearly Kaehler manifolds.
|
We consider a QED scattering ($AB\rightarrow AB$), in which $B$ is initially
entangled with a third particle ($C$) that does not participate directly in the
scattering. The effect of the scattering over $C$'s final state is evaluated
and we note coherence (off-diagonal) terms are created, which lead to non null
values for $\langle \sigma_x\rangle$ and $\langle \sigma_y\rangle$ that are, in
principle, measurable in a Stern-Gerlach apparatus. We chose a particular QED
scattering ($e^+e^-\rightarrow\mu^+\mu^-$) and found that $\langle
\sigma_x\rangle$ and $\langle \sigma_y\rangle$ are proportional to the total
cross section ($\sigma_{\text{total}}$) of the $AB$ scattering, besides being
maximal if $BC$'s initial state is taken as a Bell basis. Furthermore, we
calculated the initial and final mutual informations $I_{AC}$ and $I_{BC}$, and
noticed an increase (decrease) in $I_{AC}$ ($I_{BC}$), which indicates that,
after $AB$ interact, the total amount of correlations (quantum $+$ classical)
are distributed among the $3$ subsystems.
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Asteroid 99942 Apophis will pass near the Earth in April 2029. Expected to
miss our planet by a safe margin, that could change if Apophis' path was
perturbed by a collision with another asteroid in the interim. Though the
statistical chance of such a collision is minuscule, the high risk associated
with Apophis motivates us to examine even this very unlikely scenario. In this
work, we identify encounters between known asteroids and Apophis up to April
2029. Here we show that Apophis will encounter the 1300 meter diameter asteroid
4544 Xanthus in December 2026. Their Minimum Orbit Intersection Distance (MOID)
is less than 10,000 km, with Xanthus passing that closest point just four hours
after Apophis. Though a direct collision is ruled out, the encounter is close
enough that material accompanying Xanthus (if any) could strike Apophis. We
also identify other asteroid encounters that deserve monitoring.
|
This paper addresses the problem of learning fair Graph Neural Networks
(GNNs) under missing protected attributes. GNNs have achieved state-of-the-art
results in many relevant tasks where decisions might disproportionately impact
specific communities. However, existing work on fair GNNs assumes that either
protected attributes are fully-observed or that the missing data imputation is
fair. In practice, biases in the imputation will be propagated to the model
outcomes, leading them to overestimate the fairness of their predictions. We
address this challenge by proposing Better Fair than Sorry (BFtS), a fair
missing data imputation model for protected attributes used by fair GNNs. The
key design principle behind BFtS is that imputations should approximate the
worst-case scenario for the fair GNN -- i.e. when optimizing fairness is the
hardest. We implement this idea using a 3-player adversarial scheme where two
adversaries collaborate against the fair GNN. Experiments using synthetic and
real datasets show that BFtS often achieves a better fairness $\times$ accuracy
trade-off than existing alternatives.
|
Attack-awareness recognizes self-awareness for security systems regarding the
occurring attacks. More frequent and intense attacks on cloud and network
infrastructures are pushing security systems to the limit. With the end of
Moore's Law, merely scaling against these attacks is no longer economically
justified. Previous works have already dealt with the adoption of
Software-defined Networking and Network Function Virtualization in security
systems and used both approaches to optimize performance by the intelligent
placement of security functions. However, these works have not yet considered
the sequence in which traffic passes through these functions. In this work, we
make a case for the need to take this ordering into account by showing its
impact. We then propose a reordering framework and analyze what aspects are
necessary for modeling security service function chains and making decisions
regarding the order based on those models. We show the impact of the order and
validate our framework in an evaluation environment. The effect can extend to
multiple orders of magnitude, and the framework's evaluation proves the
feasibility of our concept.
|
AMI observations towards CIZA J2242+5301, in comparison with observations of
weak gravitational lensing and X-ray emission from the literature, are used to
investigate the behaviour of non-baryonic dark matter (NBDM) and gas during the
merger. Analysis of the Sunyaev-Zel'dovich (SZ) signal indicates the presence
of high pressure gas elongated perpendicularly to the X-ray and weak-lensing
morphologies which, given the merger-axis constraints in the literature,
implies that high pressure gas is pushed out into a linear structure during
core passing. Simulations in the literature closely matching the inferred
merger scenario show the formation of gas density and temperature structures
perpendicular to the merger axis. These SZ observations are challenging for
modified gravity theories in which NBDM is not the dominant contributor to
galaxy-cluster gravity.
|
In the context of Lorentz-Finsler spacetime theories the relativity principle
holds at a spacetime point if the indicatrix (observer space) is homogeneous.
We point out that in four spacetime dimensions there are just three kinematical
models which respect an exact form of the relativity principle and for which
all observers agree on the spacetime volume. They have necessarily affine
sphere indicatrices. For them every observer which looks at a flash of light
emitted by a point would observe, respectively, an expanding (a) sphere, (b)
tetrahedron, or (c) cone, with barycenter at the point. The first model
corresponds to Lorentzian relativity, the second one has been studied by
several authors though the relationship with affine spheres passed unnoticed,
and the last one has not been previously recognized and it is studied here in
some detail. The symmetry groups are $O^+(3,1)$, $R^3$, $O^+(2,1) \times R$,
respectively. In the second part, devoted to the general relativistic theory,
we show that the field equations can be obtained by gauging the Finsler
Lagrangian symmetry while avoiding direct use of Finslerian curvatures. We
construct some notable affine sphere spacetimes which in the appropriate
velocity limit return the Schwarzschild, Kerr-Schild, Kerr-de Sitter,
Kerr-Newman, Taub, and FLRW spacetimes, respectively.
|
Aging society has been becoming a global problem not only in advanced
countries. Under such circumstances, it is said that participation of elderly
people in social activities is highly desirable from various perspectives
including decrease of social welfare costs. Thus, we propose a mobile service
that notifies barrier information nearby users outside to lowers the anxiety of
elderly people and promote their social activities. There are barrier free maps
in some areas, but those are static and updated annually at the earliest.
However, there exist temporary barriers like road repairing and parked
bicycles, and also every barrier is not for every elder person. That is, the
elder people are under several conditions and wills to go out, so that a
barrier for an elder person is not necessarily the one for the other.
Therefore, we first collect the barrier information in the user participatory
manner and select the ones the user need to know, then timely provide them via
a mobile phone equipped with GPS. This paper shows the public experiment that
we conducted in Tokyo, and confirms the usability and the accuracy of the
information filtering.
|
The Regge behaviour of the scattering amplitudes in perturbative QCD is
governed in the generalized leading logarithmic approximation by the
contribution of the color--singlet compound states of Reggeized gluons. The
interaction between Reggeons is described by the effective hamiltonian, which
in the multi--color limit turns out to be identical to the hamiltonian of the
completely integrable one--dimensional XXX Heisenberg magnet of noncompact spin
$s=0$. The spectrum of the color singlet Reggeon compound states - perturbative
Pomerons and Odderons, is expressed by means of the Bethe Ansatz in terms of
the fundamental $Q-$function, which satisfies the Baxter equation for the XXX
Heisenberg magnet. The exact solution of the Baxter equation is known only in
the simplest case of the compound state of two Reggeons, the BFKL Pomeron. For
higher Reggeon states the method is developed which allows to find its general
solution as an asymptotic series in powers of the inverse conformal weight of
the Reggeon states. The quantization conditions for the conserved charges for
interacting Reggeons are established and an agreement with the results of
numerical solutions is observed. The asymptotic approximation of the energy of
the Reggeon states is defined based on the properties of the asymptotic series,
and the intercept of the three--Reggeon states, perturbative Odderon, is
estimated.
|
If the massive compact halo object (MACHO) fraction of the Galactic dark halo
is f ~ 20% as suggested by some microlensing experiments, then about 1.2% of
lensing events toward the Galactic bulge are due to MACHOs. For the 40% of
these that lie nearby (D_l < 4 kpc), measurement of their distance D_l would
distinguish them from bulge lenses, while measurement of their transverse
velocity v_l would distinguish them from disk lenses. Hence, it would be
possible to identify about 0.5%(f/20%) of all events as due to MACHOs. I show
that a planned experiment using the Space Interferometry Mission (SIM
PlanetQuest) could thereby detect 1 or 2 such events. This is at the margin of
what is required because of a small, but non-negligible background from
spheroid stars.
|
In the hindered magnetic dipole transitions of heavy quarkonia, the
coupled-channel effects originating from the coupling of quarkonia to a pair of
heavy and anti-heavy mesons can play a dominant role. Here, we study the
hindered magnetic dipole transitions between two $P$-wave bottomonia, $\chi_b(n
P)$ and $h_b(n^\prime P)$, with $n\neq n^\prime$. In these processes the
coupled-channel effects are expected to lead to partial widths much larger than
the quark model predictions. We estimate these partial widths which, however,
are very sensitive to unknown coupling constants related to the vertices
$\chi_{b0}(nP)B\bar B$. A measurement of the hindered M1 transitions can shed
light on the coupled-channel dynamics in these transitions and hence on the
size of the coupling constants. We also suggest to check the coupled-channel
effects by comparing results from quenched and fully dynamical lattice QCD
calculations.
|
In this exploratory article, we present a constructive method for scattering
points on the surface of $d$ dimensional spheres which we believe is new and of
interest. Indeed, the problem of uniformly distributing points on spheres is an
interesting and difficult problem with vast applications in fields as diverse
as crystallography, approximation theory, computational complexity, molecular
structure, and electrostatics.
|
In this paper we have considered the structure of the non-projectable
Horava-Melby-Thompson (HMT) gravity to find braneworld scenarios. A
relativistic scalar field is considered in the matter sector and we have shown
how to reduce the equations of motion to first-order differential equations. In
particular, we have studied thick brane solutions of both the dilatonic and
Randall-Sundrum types.
|
We investigate bounds on speed, non-adiabatic entropy production and
trade-off relation between them for classical stochastic processes with
time-independent transition rates. Our results show that the time required to
evolve from an initial to a desired target state is bounded from below by the
informational-theoretic $\infty$-R\'enyi divergence between these states,
divided by the total rate. Furthermore, we conjecture and provide extensive
numerical evidence for an information-theoretical bound on the non-adiabatic
entropy production and a novel dissipation-time trade-off relation that
outperforms previous bounds in some cases.
|
The asymptotic derivation of a new family of one-dimensional, weakly
nonlinear and weakly dispersive equations that model the flow of an ideal fluid
in an elastic vessel is presented. Dissipative effects due to the viscous
nature of the fluid are also taken into account. The new models validate by
asymptotic reasoning other non-dispersive systems of equations that are
commonly used, and improve other nonlinear and dispersive mathematical models
derived to describe the blood flow in elastic vessels. The new systems are
studied analytically in terms of their basic characteristic properties such as
the linear dispersion characteristics, symmetries, conservation laws and
solitary waves. Unidirectional model equations are also derived and analysed in
the case of vessels of constant radius. The capacity of the models to be used
in practical problems is being demonstrated by employing a particular system
with favourable properties to study the blood flow in a large artery. Two
different cases are considered: A vessel with constant radius and a tapered
vessel. Significant changes in the flow can be observed in the case of the
tapered vessel.
|
Learning with noisy labels is an active research area for image
classification. However, the effect of noisy labels on image retrieval has been
less studied. In this work, we propose a noise-resistant method for image
retrieval named Teacher-based Selection of Interactions, T-SINT, which
identifies noisy interactions, ie. elements in the distance matrix, and selects
correct positive and negative interactions to be considered in the retrieval
loss by using a teacher-based training setup which contributes to the
stability. As a result, it consistently outperforms state-of-the-art methods on
high noise rates across benchmark datasets with synthetic noise and more
realistic noise.
|
There have been significant research activities in recent years to automate
the design of channel encoders and decoders via deep learning. Due the
dimensionality challenge in channel coding, it is prohibitively complex to
design and train relatively large neural channel codes via deep learning
techniques. Consequently, most of the results in the literature are limited to
relatively short codes having less than 100 information bits. In this paper, we
construct ProductAEs, a computationally efficient family of deep-learning
driven (encoder, decoder) pairs, that aim at enabling the training of
relatively large channel codes (both encoders and decoders) with a manageable
training complexity. We build upon the ideas from classical product codes, and
propose constructing large neural codes using smaller code components. More
specifically, instead of directly training the encoder and decoder for a large
neural code of dimension $k$ and blocklength $n$, we provide a framework that
requires training neural encoders and decoders for the code parameters
$(n_1,k_1)$ and $(n_2,k_2)$ such that $n_1 n_2=n$ and $k_1 k_2=k$. Our training
results show significant gains, over all ranges of signal-to-noise ratio (SNR),
for a code of parameters $(225,100)$ and a moderate-length code of parameters
$(441,196)$, over polar codes under successive cancellation (SC) decoder.
Moreover, our results demonstrate meaningful gains over Turbo Autoencoder
(TurboAE) and state-of-the-art classical codes. This is the first work to
design product autoencoders and a pioneering work on training large channel
codes.
|
We have studied the correlation effects in Cs and Fr arising from the
interplay of the residual Coulomb interaction to all orders and the neutral
weak interaction which gives rise to the parity violating electric dipole
transition to first order, within the framework of the relativistic
coupled-cluster theory which circumvents the constrain of explicitly summing
over the intermediate states. We observe that, the contributions arising from
the perturbed doubly excited states are quite significant and hence, any
calculation should not be considered accurate unless it includes the perturbed
double excitations comprehensively. In this article, we have reported a
comparative study of various results related to the parity violation in Cs and
Fr.
|
We introduce the world's first SPAD family design in 130 nm SiGe BiCMOS
process. At 1.8um, we achieved the smallest pitch on record thanks to
guard-ring sharing techniques, while keeping a relatively high fill factor of
24.2%. 4x4 SPAD arrays with two parallel selective readout circuits were
designed to explore crosstalk and scalability. The SPAD family has a minimum
breakdown voltage of 11 V, a maximum PDP of 40.6% and a typical timing jitter
of 47 ps FWHM. The development of silicon SPADs in SiGe process paves the way
to Ge-on-Si SPADs for SWIR applications, and to cryogenic optical interfaces
for quantum applications.
|
In this article I review recent observations of the gaseous halos of galaxies
and the intergalactic medium at low redshift. In the first part I discuss
distribution, metal content, and physical properties of the Galactic
intermediate- and high-velocity clouds and the hot halo of the Milky Way.
Recent absorption and emission measurements show that the Galaxy's tidal
interaction with the Magellanic Clouds, the infall of low-metallicity gas, as
well as the circulation of gas as part of the galactic fountain contribute to
the observed distribution of gas in the halo of the Milky Way. In the second
part I give a short overview on the circumgalactic gaseous environment of other
nearby spiral galaxies. Multi-wavelength observations demonstrate that neutral
and ionized gaseous halos of galaxies are common, and that they extend deep
into intergalactic space. These studies suggest that the gaseous material
around spiral galaxies is tightly connected to the on-going hierarchical
formation and evolution of these galaxies. In the last part of this article I
summarize recent quasar absorption-line measurements of the local intergalactic
medium. In accordance with cosmological simulations, absorption-line studies in
the far-ultraviolet indicate that both the photoionized Ly alpha forest and the
shock-heated warm-hot intergalactic medium harbor a substantial fraction of the
baryons in the local Universe.
|
To search for optical variability on a wide range of timescales, we have
carried out photometric monitoring of two flat spectrum radio quasars, 3C 454.3
and 3C 279, plus one BL Lac, S5 0716+714, all of which have been exhibiting
remarkably high activity and pronounced variability at all wavelengths. CCD
magnitudes in B, V, R and I pass-bands were determined for $\sim$ 7000 new
optical observations from 114 nights made during 2011 - 2014, with an average
length of $\sim$ 4 h each, at seven optical telescopes: four in Bulgaria, one
in Greece, and two in India. We measured multiband optical flux and colour
variations on diverse timescales. Discrete correlation functions were computed
among B, V, R, and I observations, to search for any time delays. We found weak
correlations in some cases with no significant time lags. The structure
function method was used to estimate any characteristic time-scales of
variability. We also investigated the spectral energy distribution of the three
blazars using B, V, R, I, J and K pass-band data. We found that the sources
almost always follows a bluer-when-brighter trend. We discuss possible physical
causes of the observed spectral variability.
|
In this paper we discuss the invariant thermal Proca - Klein - Gordon
equation (PKG). We argue that for the thermal PKG equation the absolute
velocity is equal v = alpha*c, where alpha is the fine stucture constant for
electromagnetic interaction.
|
Large Language Models (LLMs) have demonstrated remarkable capabilities,
revolutionizing the integration of AI in daily life applications. However, they
are prone to hallucinations, generating claims that contradict established
facts, deviating from prompts, and producing inconsistent responses when the
same prompt is presented multiple times. Addressing these issues is challenging
due to the lack of comprehensive and easily assessable benchmark datasets. Most
existing datasets are small and rely on multiple-choice questions, which are
inadequate for evaluating the generative prowess of LLMs. To measure
hallucination in LLMs, this paper introduces a comprehensive benchmark dataset
comprising over 75,000 prompts across eight domains. These prompts are designed
to elicit definitive, concise, and informative answers. The dataset is divided
into two segments: one publicly available for testing and assessing LLM
performance and a hidden segment for benchmarking various LLMs. In our
experiments, we tested six LLMs-GPT-3.5, LLama 2, LLama 3, Gemini, Mixtral, and
Zephyr-revealing that overall factual hallucination ranges from 59% to 82% on
the public dataset and 57% to 76% in the hidden benchmark. Prompt misalignment
hallucination ranges from 6% to 95% in the public dataset and 17% to 94% in the
hidden counterpart. Average consistency ranges from 21% to 61% and 22% to 63%,
respectively. Domain-wise analysis shows that LLM performance significantly
deteriorates when asked for specific numeric information while performing
moderately with person, location, and date queries. Our dataset demonstrates
its efficacy and serves as a comprehensive benchmark for LLM performance
evaluation. Our dataset and LLMs responses are available at
\href{https://github.com/ashikiut/DefAn}{https://github.com/ashikiut/DefAn}.
|
A goal of Introductory Physics for Life Sciences (IPLS) curricula is to
prepare students to effectively use physical models and quantitative reasoning
in biological and medical settings. To assess whether this goal is being met,
we conducted a longitudinal study of the impact of IPLS on student work in
later biology and chemistry courses. We report here on one part of that study,
a comparison of written responses by students with different physics
backgrounds on a diffusion task administered in a senior biology capstone
course. We observed differences in student reasoning that were associated with
prior or concurrent enrollment in IPLS. In particular, we found that IPLS
students were more likely than non-IPLS students to reason quantitatively and
mechanistically about diffusive phenomena, and to successfully coordinate
between multiple representations of diffusive processes, even up to two years
after taking the IPLS course. Finally, we describe methodological challenges
encountered in both this task and other tasks used in our longitudinal study.
|
The first Pop III stars formed out of primordial, metal free gas, in
minihalos at z>20, and kickstarted the cosmic processes of reionizaton and
enrichment. While these stars are likely more massive than their enriched
counterparts, the current unknowns of their astrophysics include; when the
first Pop III stars ignited, how massive they were, and when and how the era of
the first stars ended. Investigating these questions requires an exploration of
a multi-dimensional parameter space, including the slope of the Pop III stellar
initial mass function (IMF) and the strength of the non-ionizing UV background.
In this work, we present a novel model which treats both the slope and maximum
mass of Pop III stars as truly free parameters while including the physics of
the fragmentation of primordial gas. Our results also hint at a non-universal
Pop III IMF which is dependent on the efficiency of primordial gas
fragmentation. Our relatively simple model reproduces the results from
hydrodynamic simulations, but with a computational efficiency which allows us
to investigate the observable differences between a wide range of potential Pop
III IMFs. In addition, the evolution of the number density of Pop III stars may
provide insight into the evolution of the H2 dissociating background. While the
slope of the Pop III IMF does not significantly affect the predicted number
density of the first stars, more top heavy IMFs produce Pop III star clusters
which are 2-3 magnitudes brighter than their more bottom heavy counterparts.
While the Pop III star clusters are too dim for direct detection by JWST, we
find they are within the reach of gravitational lensing.
|
Third generation gravitational wave (GW) detectors are expected to detect
millions of binary black hole (BBH) mergers during their operation period. A
small fraction of them ($\sim 1\%$) will be strongly lensed by intervening
galaxies and clusters, producing multiple observable copies of the GW signals.
The expected number of lensed events and the distribution of the time delay
between lensed events depend on the cosmology. We develop a Bayesian analysis
method for estimating cosmological parameters from the detected number of
lensed events and their time delay distribution. The expected constraints are
comparable to that obtained from other cosmological measurements, but probing a
different redshift regime ($z \sim 10$) that is not explored by other probes.
|
5G NR (New Radio) incorporates concepts of novel technologies such as
spectrum sharing, D2D communication, UDN, and massive MIMO. However, providing
security and identifying the security threats to these technologies occupies
the prime concern. This paper intends to provide an ample survey of security
issues and their countermeasures encompassed in the technologies of 5G NR.
Further, security concerns of each technology are defined mathematically.
Thereby defining the impact on the factors of security. Moreover, a methodology
is developed in which the influence on security due to artificially generated
rain and artificially generated dust on the wireless communication network is
studied. By doing so, an attacking scenario is identified, where a half-duplex
attack in D2D communication is attained. Half-duplex attack specifies the
attack solely on the downlink to spoof the allocated resources, with reduced
miss-rate. Thus, ultra-reliable and adequate advances are required to be
addressed to remove the obstacles that create a hindrance in achieving the
secured and authenticated communicating network
|
In a comment on the paper of Habib and Ryne, chao-dyn/9406010 and
Phys.Rev.Lett. vol.74, 70 (1995), I point out that the Iwasawa decomposition of
the symplectic group can be used to write down closed-form expressions for the
noncompact part of the group and thus to compute the Lyapunov exponents in
systems with more than two degrees of freedom using the cited method.
|
A systematic mathematical methodology for derivation of boundary layer
expansions is presented. An explicit calculation of boundary layer sizes is
given and proved to be coordinates system independent. It relies on asymptotic
properties of symbols of operators. Several examples, including the
quasigeostrophic model, are discussed.
|
Let $f$ be an $L^2$-normalized Hecke--Maass cuspidal newform of level $N$,
character $\chi$ and Laplace eigenvalue $\lambda$. Let $N_1$ denote the
smallest integer such that $N|N_1^2$ and $N_0$ denote the largest integer such
that $N_0^2 |N$. Let $M$ denote the conductor of $\chi$ and define $M_1=
M/\gcd(M,N_1)$. In this paper, we prove the bound $|f|_\infty$ $\ll_{\epsilon}$
$N_0^{1/6 + \epsilon} N_1^{1/3+\epsilon} M_1^{1/2} \lambda^{5/24+\epsilon}$,
which generalizes and strengthens previously known upper bounds for
$|f|_\infty$.
This is the first time a hybrid bound (i.e., involving both $N$ and
$\lambda$) has been established for $|f|_\infty$ in the case of non-squarefree
$N$. The only previously known bound in the non-squarefree case was in the
N-aspect; it had been shown by the author that $|f|_\infty \ll_{\lambda,
\epsilon} N^{5/12+\epsilon}$ provided $M=1$. The present result significantly
improves the exponent of $N$ in the above case. If $N$ is a squarefree integer,
our bound reduces to $|f|_\infty \ll_\epsilon N^{1/3 + \epsilon}\lambda^{5/24 +
\epsilon}$, which was previously proved by Templier.
The key new feature of the present work is a systematic use of p-adic
representation theoretic techniques and in particular a detailed study of
Whittaker newforms and matrix coefficients for $GL_2(F)$ where $F$ is a local
field.
|
In this work, conserved charges and fluxes at the future null infinity are
determined in the asymptotically flat spacetime for Chern-Simons modified
gravity. The flux-balance laws are used to constrain the memory effects. For
tensor memories, the Penrose's conformal completion method is used to analyze
the asymptotic structures and asymptotic symmetries, and then, conserved
charges for the Bondi-Metzner-Sachs algebra are constructed with the
Wald-Zoupas formalism. These charges take very similar forms to those in
Brans-Dicke theory. For the scalar memory, Chern-Simons modified gravity is
rewritten in the first-order formalism, and the scalar field is replaced by a
2-form field dual to it. With this dual formalism, the scalar memory is
described by the vacuum transition induced by the large gauge transformation of
the 2-form field.
|
This paper presents a novel ML-based methodology for geothermal exploration
towards PFA applications. Our methodology is provided through our open-source
ML framework, GeoThermalCloud
\url{https://github.com/SmartTensors/GeoThermalCloud.jl}. The GeoThermalCloud
uses a series of unsupervised, supervised, and physics-informed ML methods
available in SmartTensors AI platform \url{https://github.com/SmartTensors}.
Here, the presented analyses are performed using our unsupervised ML algorithm
called NMF$k$, which is available in the SmartTensors AI platform. Our ML
algorithm facilitates the discovery of new phenomena, hidden patterns, and
mechanisms that helps us to make informed decisions. Moreover, the
GeoThermalCloud enhances the collected PFA data and discovers signatures
representative of geothermal resources. Through GeoThermalCloud, we could
identify hidden patterns in the geothermal field data needed to discover blind
systems efficiently. Crucial geothermal signatures often overlooked in
traditional PFA are extracted using the GeoThermalCloud and analyzed by the
subject matter experts to provide ML-enhanced PFA, which is informative for
efficient exploration. We applied our ML methodology to various open-source
geothermal datasets within the U.S. (some of these are collected by past PFA
work). The results provide valuable insights into resource types within those
regions. This ML-enhanced workflow makes the GeoThermalCloud attractive for the
geothermal community to improve existing datasets and extract valuable
information often unnoticed during geothermal exploration.
|
The coexistence of electric dipoles and itinerant electrons in a solid was
postulated decades ago, before being experimentally established in several
'polar metals' during the last decade. Here, we report a concentration-driven
polar-to-nonpolar phase transition in electron-doped BaTiO_3. Comparing our
case with other polar metals, we find a particular threshold concentration (n*)
linked to the dipole density (n_d). The universal ratio n_d/n*=8(0.6) suggests
a common mechanism across different polar systems, possibly explained by a
dipolar Ruderman-Kittel-Kasuya-Yosida theory. Moreover, in BaTiO_3, we observe
enhanced thermopower and upturn on resistivity at low temperatures near n*,
resembling the Kondo effect. We argue that local electric dipoles act as
two-level-systems, whose fluctuations couple with surrounding electron clouds,
giving rise to a potential dipolar-counterpart of the Kondo effect. Our
findings unveil a mostly uncharted territory for exploring emerging physics
associated with electron-dipole correlations, encouraging further theoretical
work on dipolar-RKKY and Kondo interactions.
|
We propose a novel method for automatic program synthesis. P-Tree Programming
represents the program search space through a single probabilistic prototype
tree. From this prototype tree we form program instances which we evaluate on a
given problem. The error values from the evaluations are propagated through the
prototype tree. We use them to update the probability distributions that
determine the symbol choices of further instances. The iterative method is
applied to several symbolic regression benchmarks from the literature. It
outperforms standard Genetic Programming to a large extend. Furthermore, it
relies on a concise set of parameters which are held constant for all problems.
The algorithm can be employed for most of the typical computational
intelligence tasks such as classification, automatic program induction, and
symbolic regression.
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We consider a small stochastic perturbation of an optimal velocity
car-following model. We give a detailed analysis of behavior near the collision
singularity. We show that collision is impossible in a simplified model without
noise, and then we show that collision is asymptotically unlikely over large
time intervals in presence of small noise, with large time interval scaling
like a square of the reciprocal of the strength of the noise. Our calculations
depend on careful boundary-layer analyses.
|
In this article we discuss few new derivations of the so called Born's rule
for quantum probability in the context of the pilot wave theory proposed by de
Broglie in 1927.
|
B20 compounds are the playground for various non-trivial magnetic textures
such as skyrmions, which are topologically protected states. Recent
measurements on B20-MnGe indicate no clear consensus on its magnetic behavior,
which is characterized by the presence of either spin-spirals or 3-dimensional
objects interpreted to be a cubic lattice of hedgehogs and anti-hedgehogs.
Utilizing a massively parallel linear scaling all-electron density functional
algorithm, we find from full first-principles simulations on cells containing
thousands of atoms that upon increase of the compound volume, the state with
lowest energy switches across different magnetic phases: ferromagnetic,
spin-spiral, hedgehog and monopole.
|
In this study, we investigate the finite-temperature properties of the
spin-1/2 $J_1-J_2$ Heisenberg model on the kagome lattice using the
orthogonalized finite-temperature Lanczos method. Under a zero magnetic field,
the specific heat exhibits a double-peak structure, as $|J_2|$ increases.
Additionally, at approximately $J_2=0$, the magnetic entropy remains finite,
even at low temperatures. The finite-temperature magnetization curve reveals
the asymmetric melting behavior of the 1/3 plateau around $J_2=0$. As $|J_2|$
increases, the 1/3 plateau becomes more stable, exhibiting symmetric melting
behavior. Specifically, for $J_2 > 0$, the $\bf Q=0$ up-up-down structure is
stabilized, whereas for $J_2 < 0$, the $\sqrt{3} \times \sqrt{3}$ up-up-down
structure is stabilized.
|
Cooperation is challenging in biological systems, human societies, and
multi-agent systems in general. While a group can benefit when everyone
cooperates, it is tempting for each agent to act selfishly instead. Prior human
studies show that people can overcome such social dilemmas while choosing
interaction partners, i.e., strategic network rewiring. However, little is
known about how agents, including humans, can learn about cooperation from
strategic rewiring and vice versa. Here, we perform multi-agent reinforcement
learning simulations in which two agents play the Prisoner's Dilemma game
iteratively. Each agent has two policies: one controls whether to cooperate or
defect; the other controls whether to rewire connections with another agent.
This setting enables us to disentangle complex causal dynamics between
cooperation and network rewiring. We find that network rewiring facilitates
mutual cooperation even when one agent always offers cooperation, which is
vulnerable to free-riding. We then confirm that the network-rewiring effect is
exerted through agents' learning of ostracism, that is, connecting to
cooperators and disconnecting from defectors. However, we also find that
ostracism alone is not sufficient to make cooperation emerge. Instead,
ostracism emerges from the learning of cooperation, and existing cooperation is
subsequently reinforced due to the presence of ostracism. Our findings provide
insights into the conditions and mechanisms necessary for the emergence of
cooperation with network rewiring.
|
The Optical Gravitational Lensing Experiment identified over 1,800
carbon-rich Mira and semi-regular variables in the Small Magellanic Cloud.
Multi-epoch infrared photometry reveals that the semi-regulars and Miras follow
different sequences in color-color space when using colors sensitive to
molecular absorption bands. The dustiest Miras have the strongest pulsation
amplitudes and longest periods. Efforts to determine bolometric magnitudes
reveal possible systematic errors with published bolometric corrections.
|
Optical absorption in rhombohedral BiFeO$_3$ starts at photon energies below
the photoemission band gap of $\approx$ 3 eV calculated from first principles.
A shoulder at the absorption onset has so far been attributed to low-lying
electronic transitions or to oxygen vacancies. In this work optical spectra are
calculated ab initio to determine the nature of the optical transitions near
the absorption onset of pristine BiFeO$_3$, the effect of electron-hole
interaction, and the spectroscopic signatures of typical defects, i.e. doping
(excess electrons or holes), intrinsic defects (oxygen and bismuth vacancies),
and low-energy structural defects (ferroelectric domain walls).
|
Magneto resistance measurements coupled with positron lifetime measurements,
to characterize the vacancy type defects, have been carried out on the
topological insulator (TI) system Bi2Se3, of varying Se/Bi ratio. Pronounced
Shubnikov de Haas (SdH) oscillations are seen in nominal Bi2Se3.1 crystals for
measurements performed in magnetic fields up to 15 T in the 4 K to 10 K
temperature range, with field applied perpendicular to the (001) plane of the
crystal. The quantum oscillations, characteristic of 2D electronic structure,
are seen only in the crystals that have a lower concentration of Se vacancies,
as inferred from positron annihilation spectroscopy.
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Chiral anomaly or Adler-Bell-Jackiw anomaly in Weyl semimetals (WSMs) has a
significant impact on the electron transport behaviors, leading to remarkable
longitudinal or planar electrical and thermoelectric transport phenomena in the
presence of electromagnetic gauge fields. These phenomena are consequences of
the imbalanced chiral charge and energy induced by chiral anomaly in the
presence of parallel electric ($\mathbf{E}$) and magnetic ($\mathbf{B}$) fields
($\mathbf{E \cdot B }\neq 0$) or $(\mathbf{B \cdot \nabla }T\neq 0)$
($\mathbf{\nabla}T$ is the thermal gradient). We here propose another two
fascinating transport properties, namely, the nonlinear planar Nernst effect
and nonlinear planar thermal Hall effect induced by chiral anomaly in the
presence of $\mathbf{B \cdot \nabla}T\neq 0$ in WSMs. Using the semiclassical
Boltzmann transport theory, we derive the analytical expressions for the chiral
anomaly induced nonlinear Nernst and thermal Hall transport coefficients and
also evaluate the fundamental mathematical relations among them in the
nonlinear regime. The formulas we find in this current work are consistent with
that predicted for the nonlinear anomalous electrical and thermoelectric
effects induced by Berry curvature dipole recently. Additionally, in contrast
to the recent work, by utilizing the lattice Weyl Hamiltonian with intrinsic
chiral chemical potential, we find that the chiral anomaly induced nonlinear
planar effects can exist even for a pair of oppositely tilted or non-tilted
Weyl cones in both time reversal and inversion broken WSMs. The chiral anomaly
induced nonlinear planar effects predicted here along with the related
parameter dependencies are hence possible to be realized in realistic WSMs in
experiment.
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Let $A$ be a quaternion algebra over a number field $F$, and $\mathcal{O}$ be
an $O_F$-order of full rank in $A$. Let $K$ be a quadratic field extension of
$F$ that embeds into $A$, and $B$ be an $O_F$-order in $K$. Suppose that
$\mathcal{O}$ is a Bass order that is well-behaved at all the dyadic primes of
$F$. We provide a necessary and sufficient condition for $B$ to be optimally
spinor selective for the genus of $\mathcal{O}$. This partially generalizes
previous results on optimal (spinor) selectivity by C. Maclachlan [Optimal
embeddings in quaternion algebras. J. Number Theory, 128(10):2852-2860, 2008]
for Eichler orders of square-free levels, and independently by M. Arenas et al.
[On optimal embeddings and trees. J. Number Theory, 193:91-117, 2018] and by J.
Voight [Chapter 31, Quaternion algebras, volume 288 of Graduate Texts in
Mathematics. Springer-Verlag, 2021] for Eichler orders of arbitrary levels.
|
Low-energy spin excitations in any long-range ordered magnetic system in the
absence of magnetocrystalline anisotropy are gapless Goldstone modes emanating
from the ordering wave vectors. In helimagnets, these modes hybridize into the
so-called helimagnon excitations. Here we employ neutron spectroscopy supported
by theoretical calculations to investigate the magnetic excitation spectrum of
the isotropic Heisenberg helimagnet ZnCr2Se4 with a cubic spinel structure, in
which spin-3/2 magnetic Cr3+ ions are arranged in a geometrically frustrated
pyrochlore sublattice. Apart from the conventional Goldstone mode emanating
from the (0 0 q) ordering vector, low-energy magnetic excitations in the
single-domain proper-screw spiral phase show soft helimagnon modes with a small
energy gap of ~0.17 meV, emerging from two orthogonal wave vectors (q 0 0) and
(0 q 0) where no magnetic Bragg peaks are present. We term them
pseudo-Goldstone magnons, as they appear gapless within linear spin-wave theory
and only acquire a finite gap due to higher-order quantum-fluctuation
corrections. Our results are likely universal for a broad class of symmetric
helimagnets, opening up a new way of studying weak magnon-magnon interactions
with accessible spectroscopic methods.
|
We prove several relations between spectrum and dynamics including wave trace
expansion, sharp/improved Weyl laws, propagation of singularities and quantum
ergodicity for the sub-Riemannian (sR) Laplacian in the four dimensional
quasi-contact case. A key role in all results is played by the presence of
abnormal geodesics and represents the first such appearance of these in
sub-Riemannian spectral geometry.
|
In this paper we perform a numerical study on the interesting phenomenon of
soliton reflection of solid walls. We consider the 2D nonlinear Schrodinger
equation as the underlying mathematical model and we use an implicit-explicit
type Crank-Nicolson finite element scheme for its numerical solution. After
verifying the perfect reflection of the solitons on a vertical wall, we present
the imperfect reflection of a dark soliton on a diagonal wall.
|
The possibility of extending the Liouville Conformal Field Theory from values
of the central charge $c \geq 25$ to $c \leq 1$ has been debated for many years
in condensed matter physics as well as in string theory. It was only recently
proven that such an extension -- involving a real spectrum of critical
exponents as well as an analytic continuation of the DOZZ formula for
three-point couplings -- does give rise to a consistent theory. We show in this
Letter that this theory can be interpreted in terms of microscopic loop models.
We introduce in particular a family of geometrical operators, and, using an
efficient algorithm to compute three-point functions from the lattice, we show
that their operator algebra corresponds exactly to that of vertex operators
$V_{\hat{\alpha}}$ in $c \leq 1$ Liouville. We interpret geometrically the
limit $\hat{\alpha} \to 0$ of $V_{\hat{\alpha}}$ and explain why it is not the
identity operator (despite having conformal weight $\Delta=0$).
|
We present an exact calculation of the single-electron energies and
wave-functions for any bound state in a realistic Si-SiO2 spherical quantum
dot, including the material dependence of the electron effective mass. The
influence of dot radius, confinement barrier potential and barrier-to-dot
electron mass ratio on the electronic structure is investigated in detail. The
results show that the energy structure shifts down from some tens to some
hundreds meV compared to that obtained in the simplified model where the change
in effective mass is neglected. Our exact single-electron calculation is
finally used to verify the accuracy of the results obtained from a numerical
approximate method developed to treat many-electron systems.
|
We present a reciprocal-space pseudopotential scheme for calculating X-ray
absorption near-edge structure (XANES) spectra. The scheme incorporates a
recursive method to compute absorption cross section as a continued fraction.
The continued fraction formulation of absorption is advantageous in that it
permits the treatment of core-hole interaction through large supercells
(hundreds of atoms). The method is compared with recently developed
Bethe-Salpeter approach. The method is applied to the carbon K-edge in diamond
and to the silicon and oxygen K-edges in alpha-quartz for which polarized XANES
spectra were measured. Core-hole effects are investigated by varying the size
of the supercell, thus leading to information similar to that obtained from
cluster size analysis usually performed within multiple scattering
calculations.
|
The entanglement in one-dimensional Anderson model is studied. We show that
the pairwise entanglement measured by the average concurrence has a direct
relation to the localization length. The numerical study indicates that the
disorder significantly reduces the average entanglement, and entanglement
distribution clearly displays the entanglement localization. The maximal
pairwise entanglement exhibits a maximum as the disorder strength
increases,experiencing a transition from increase to decrease. The entanglement
between the center of localization and other site decreases exponentially along
the spatial direction. Finally,we study effects of disorder on dynamical
properties of entanglement.
|
In this paper, we consider the approximate weighted graph matching problem
and introduce stable and informative first and second order compatibility terms
suitable for inclusion into the popular integer quadratic program formulation.
Our approach relies on a rigorous analysis of stability of spectral signatures
based on the graph Laplacian. In the case of the first order term, we derive an
objective function that measures both the stability and informativeness of a
given spectral signature. By optimizing this objective, we design new spectral
node signatures tuned to a specific graph to be matched. We also introduce the
pairwise heat kernel distance as a stable second order compatibility term; we
justify its plausibility by showing that in a certain limiting case it
converges to the classical adjacency matrix-based second order compatibility
function. We have tested our approach on a set of synthetic graphs, the
widely-used CMU house sequence, and a set of real images. These experiments
show the superior performance of our first and second order compatibility terms
as compared with the commonly used ones.
|
We report on a time-domain search for pulsars in 44 steep spectrum radio
sources originally identified from recent imaging surveys. The time-domain
search was conducted at 327 MHz using the Ooty radio telescope, and utilized a
semi-coherent dedispersion scheme retaining the sensitivity even for
sub-millisecond periods up to reasonably high dispersion measures. No new
pulsars were found. We discuss the nature of these steep spectrum sources and
argue that majority of the sources in our sample should either be pulsars or a
new category of Galactic sources. Several possibilities that could hinder
detection of these sources as pulsars, including anomalously high scattering or
alignment of the rotation and magnetic axes, are discussed in detail, and we
suggest unconventional search methods to further probe these possibilities.
|
Transformers have made remarkable progress towards modeling long-range
dependencies within the medical image analysis domain. However, current
transformer-based models suffer from several disadvantages: (1) existing
methods fail to capture the important features of the images due to the naive
tokenization scheme; (2) the models suffer from information loss because they
only consider single-scale feature representations; and (3) the segmentation
label maps generated by the models are not accurate enough without considering
rich semantic contexts and anatomical textures. In this work, we present
CASTformer, a novel type of adversarial transformers, for 2D medical image
segmentation. First, we take advantage of the pyramid structure to construct
multi-scale representations and handle multi-scale variations. We then design a
novel class-aware transformer module to better learn the discriminative regions
of objects with semantic structures. Lastly, we utilize an adversarial training
strategy that boosts segmentation accuracy and correspondingly allows a
transformer-based discriminator to capture high-level semantically correlated
contents and low-level anatomical features. Our experiments demonstrate that
CASTformer dramatically outperforms previous state-of-the-art transformer-based
approaches on three benchmarks, obtaining 2.54%-5.88% absolute improvements in
Dice over previous models. Further qualitative experiments provide a more
detailed picture of the model's inner workings, shed light on the challenges in
improved transparency, and demonstrate that transfer learning can greatly
improve performance and reduce the size of medical image datasets in training,
making CASTformer a strong starting point for downstream medical image analysis
tasks.
|
The synthesis of water is one necessary step in the origin and development of
life. It is believed that pristine water is formed and grows on the surface of
icy dust grains in dark interstellar clouds. Until now, there has been no
experimental evidence whether this scenario is feasible or not. We present here
the first experimental evidence of water synthesis under interstellar
conditions. After D and O deposition on a water ice substrate (HO) held at 10
K, we observe production of HDO and DO. The water substrate itself has an
active role in water formation, which appears to be more complicated than
previously thought. Amorphous water ice layers are the matrices where complex
organic prebiotic species may be synthesized. This experiment opens up the
field of a little explored complex chemistry that could occur on interstellar
dust grains, believed to be the site of key processes leading to the molecular
diversity and complexity observed in our universe.
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While the members of the Type IIn category of supernovae are united by the
presence of strong multicomponent Balmer emission lines in their spectra, they
are quite heterogeneous with respect to other properties such as Balmer line
profiles, light curves, strength of radio emission, and intrinsic brightness.
We are now beginning to see variety among SNe IIn in their polarimetric
characteristics as well, some but not all of which may be due to inclination
angle effects. The increasing number of known "hybrid" SNe with IIn-like
emission lines suggests that circumstellar material may be more common around
all types of SNe than previously thought. Investigation of the correlations
between spectropolarimetric signatures and other IIn attributes will help us
address the question of classification of "interacting SNe" and the possibility
of distinguishing different groups within the diverse IIn subclass.
|
In this paper we discuss the solvability of Langevin equations with two
Hadamard fractional derivatives. The method of this discussion is to study the
solutions of the equivalent Volterra integral equation in terms of Mittag-
Leffler functions. The existence and uniqueness results are established by
using Schauder fixed point theorem and Banach fixed point theorem respectively.
An example is given to illustrate the main results.
|
We classify closed abelian subgroups of the automorphism group of any compact
classical simple Lie algebra whose centralizer has the same dimension as the
dimension of the subgroup, and describe Weyl groups of maximal abelian
subgroups.
|
We consider the Dynamic Map Visitation Problem (DMVP), in which a team of
agents must visit a collection of critical locations as quickly as possible, in
an environment that may change rapidly and unpredictably during the agents'
navigation. We apply recent formulations of time-varying graphs (TVGs) to DMVP,
shedding new light on the computational hierarchy $\mathcal{R} \supset
\mathcal{B} \supset \mathcal{P}$ of TVG classes by analyzing them in the
context of graph navigation. We provide hardness results for all three classes,
and for several restricted topologies, we show a separation between the classes
by showing severe inapproximability in $\mathcal{R}$, limited approximability
in $\mathcal{B}$, and tractability in $\mathcal{P}$. We also give topologies in
which DMVP in $\mathcal{R}$ is fixed parameter tractable, which may serve as a
first step toward fully characterizing the features that make DMVP difficult.
|
The magnetic state of the noncentrosymmetric antiferromagnet CeNiC$_2$ has
been studied by magnetic susceptibility, heat capacity, muon spin relaxation
($\mu$SR) and inelastic neutron scattering (INS) measurements. CeNiC$_2$
exhibits three magnetic phase transitions at $T_{N_1}$ = 20 K, $T_{N_2}$ = 10 K
and $T_{N_3}$ = 2.5 K. The presence of long range magnetic order below 20 K is
confirmed by the observation of oscillations in the $\mu$SR spectra between 10
and 20 K and a sharp increase in the muon depolarization rate. INS studies
reveal two well-defined crystal electric field (CEF) excitations around 8 and
30 meV. INS data have been analyzed using a CEF model and the wave functions
were evaluated. We also calculated the direction and magnitude of the ground
state moment using CEF wave functions and compare the results with that
proposed from the neutron diffraction. Our CEF model correctly predicts that
the moments order along the $b-$axis (or $y$-axis) and the observed magnetic
moment is 0.687(5) $\mu_B$, which is higher than the moment observed from the
neutron diffraction (0.25 $\mu_B$/Ce). We attribute the observed reduced moment
due to the Kondo screening effect.
|
This paper presents a programming language which includes paradigms that are
usually associated with declarative languages, such as sets, rules and search,
into an imperative (functional) language. Although these paradigms are
separately well known and are available under various programming environments,
the originality of the CLAIRE language comes from the tight integration, which
yields interesting run-time performances, and from the richness of this
combination, which yields new ways in which to express complex algorithmic
patterns with few elegant lines. To achieve the opposite goals of a high
abstraction level (conciseness and readability) and run-time performance
(CLAIRE is used as a C++ preprocessor), we have developed two kinds of
compiler: first, a pattern pre-processor handles iterations over both concrete
and abstract sets (data types and program fragments), in a completely
user-extensible manner; secondly, an inference compiler transforms a set of
logical rules into a set of functions (demons that are used through procedural
attachment).
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The development of luminescent organic radicals has resulted in materials
with excellent optical properties for near-infrared (NIR) emission.
Applications of light generation in this range span from bioimaging to
surveillance. Whilst the unpaired electron arrangements of radicals enable
efficient radiative transitions within the doublet-spin manifold in organic
light-emitting diodes (OLEDs), their performance is limited by non-radiative
pathways introduced in electroluminescence. Here, we present a host:guest
design for OLEDs that exploits energy transfer with demonstration of up to 9.6%
external quantum efficiency (EQE) for 800 nm emission. The
tris(2,4,6-trichlorophenyl)methyl-triphenylamine (TTM-TPA) radical guest is
energy-matched to the triplet state in a charge-transporting
anthracene-derivative host. We show from optical spectroscopy and
quantum-chemical modelling that reversible host-guest triplet-doublet energy
transfer allows efficient harvesting of host triplet excitons.
|
In the Randall-Sundrum model, we study top-antitop pair production and top
spin correlations at the Large Hadron Collider. In addition to the Standard
Model processes, there is a new contribution to the top-antitop pair production
process mediated by graviton Kaluza-Klein modes in the s-channel. We calculate
the density matrix for the top-antitop pair production including the new
contribution. With a reasonable parameter choice in the Randall-Sundrum model,
we find a sizable deviation of the top-antitop pair production cross section
and the top spin correlations from those in the Standard Model. In particular,
resonant productions of the graviton Kaluza-Klein modes give rise to a
remarkable enhancement of such a deviation.
|
This is the first of a series of papers dealing with the asymptotic behavior
of certain integrals occuring in the description of the spectrum of an
invariant elliptic operator on a compact Riemannian manifold carrying the
action of a compact, connected Lie group of isometries, and in the study of its
equivariant cohomology via the moment map.
|
The NRO-OVRO CO imaging survey showed that molecular gas was more
concentrated to the central kiloparsec in barred spiral galaxies than in their
unbarred counterparts. The result provided not only evidence for bar-driven gas
transport but also estimates on the mean rate of gas transfer and lower limits
to the lifetime of bars. Other lines of evidence for the bar-driven transport
of ISM in spiral galaxies are summarized. They are complementary with each
other.
|
We study the competition between field-induced transport and trapping in a
disordered medium by studying biased random walks on random combs and the
bond-diluted Bethe lattice above the percolation threshold. While it is known
that the drift velocity vanishes above a critical threshold, here our focus is
on fluctuations, characterized by the variance of the transit times. On the
random comb, the variance is calculated exactly for a given realization of
disorder using a 'forward transport' limit which prohibits backward movement
along the backbone but allows an arbitrary number of excursions into
random-length branches. The disorder-averaged variance diverges at an earlier
threshold of the bias, implying a regime of anomalous fluctuations, although
the velocity is nonzero. Our results are verified numerically using a Monte
Carlo procedure that is adapted to account for ultra-slow returns from long
branches. On the Bethe lattice, we derive an upper bound for the critical
threshold bias for anomalous fluctuations of the mean transit time averaged
over disorder realizations. Finally, as for the passage to the vanishing
velocity regime, it is shown that the transition to the anomalous fluctuation
regime can change from continuous to first order depending on the distribution
of branch lengths.
|
Domain randomization is an effective computer vision technique for improving
transferability of vision models across visually distinct domains exhibiting
similar content. Existing approaches, however, rely extensively on tweaking
complex and specialized simulation engines that are difficult to construct,
subsequently affecting their feasibility and scalability. This paper introduces
BehAVE, a video understanding framework that uniquely leverages the plethora of
existing commercial video games for domain randomization, without requiring
access to their simulation engines. Under BehAVE (1) the inherent rich visual
diversity of video games acts as the source of randomization and (2) player
behavior -- represented semantically via textual descriptions of actions --
guides the *alignment* of videos with similar content. We test BehAVE on 25
games of the first-person shooter (FPS) genre across various video and text
foundation models and we report its robustness for domain randomization. BehAVE
successfully aligns player behavioral patterns and is able to zero-shot
transfer them to multiple unseen FPS games when trained on just one FPS game.
In a more challenging setting, BehAVE manages to improve the zero-shot
transferability of foundation models to unseen FPS games (up to 22%) even when
trained on a game of a different genre (Minecraft). Code and dataset can be
found at https://github.com/nrasajski/BehAVE.
|
MediaWiki and Wikipedia authors usually use LaTeX to define mathematical
formulas in the wiki text markup. In the Wikimedia ecosystem, these formulas
were processed by a long cascade of web services and finally delivered to
users' browsers in rendered form for visually readable representation as SVG.
With the latest developments of supporting MathML Core in Chromium-based
browsers, MathML continues its path to be a de facto standard markup language
for mathematical notation in the web. Conveying formulas in MathML enables
semantic annotation and machine readability for extended interpretation of
mathematical content, in example for accessibility technologies.
With this work, we present WikiTexVC, a novel method for validating LaTeX
formulas from wiki texts and converting them to MathML, which is directly
integrated into MediaWiki. This mitigates the shortcomings of previously used
rendering methods in MediaWiki in terms of robustness, maintainability and
performance. In addition, there is no need for a multitude of web services
running in the background, but processing takes place directly within MediaWiki
instances. We validated this method with an extended dataset of over 300k
formulas which have been incorporated as automated tests to the MediaWiki
continuous integration instances. Furthermore, we conducted an evaluation with
423 formulas, comparing the tree edit distance for produced parse trees to
other MathML renderers. Our method has been made available Open Source and can
be used on German Wikipedia and is delivered with recent MediaWiki versions. As
a practical example of enabling semantic annotations within our method, we
present a new macro that adds content to formula disambiguation to facilitate
accessibility for visually impaired people.
|
In a type II superconductor the gap variation in the core of a vortex line
induces a local charge modulation. Accounting for metallic screening, we
determine the line charge of individual vortices and calculate the electric
field distribution in the half space above a field penetrated superconductor.
The resulting field is that of an atomic size dipole ${\bf d} \sim e a_{{\rm
B}} {\bf {\hat z}}$, $a_{{\rm B}} = \hbar^2/m e^2$ is the Bohr radius, acting
on a force microscope in the pico to femto Newton range.
|
We present numerical results on two- (2D) and three-dimensional (3D)
hydrodynamic core-collapse simulations of an 11.2$M_\odot$ star. By changing
numerical resolutions and seed perturbations systematically, we study how the
postbounce dynamics is different in 2D and 3D. The calculations were performed
with an energy-dependent treatment of the neutrino transport based on the
isotropic diffusion source approximation scheme, which we have updated to
achieve a very high computational efficiency. All the computed models in this
work including nine 3D models and fifteen 2D models exhibit the revival of the
stalled bounce shock, leading to the possibility of explosion. All of them are
driven by the neutrino-heating mechanism, which is fostered by neutrino-driven
convection and the standing-accretion-shock instability (SASI). Reflecting the
stochastic nature of multi-dimensional (multi-D) neutrino-driven explosions,
the blast morphology changes from models to models. However, we find that the
final fate of the multi-D models whether an explosion is obtained or not, is
little affected by the explosion stochasticity. In agreement with some previous
studies, higher numerical resolutions lead to slower onset of the shock revival
in both 3D and 2D. Based on the self-consistent supernova models leading to the
possibility of explosions, our results systematically show that the revived
shock expands more energetically in 2D than in 3D.
|
An outline of recent work on complex networks is given from the point of view
of a physicist. Motivation, achievements and goals are discussed with some of
the typical applications from a wide range of academic fields. An introduction
to the relevant literature and useful resources is also given.
|
Poisson's equation has been used in VLSI global placement for describing the
potential field caused by a given charge density distribution. Unlike previous
global placement methods that solve Poisson's equation numerically, in this
paper, we provide an analytical solution of the equation to calculate the
potential energy of an electrostatic system. The analytical solution is derived
based on the separation of variables method and an exact density function to
model the block distribution in the placement region, which is an infinite
series and converges absolutely. Using the analytical solution, we give a fast
computation scheme of Poisson's equation and develop an effective and efficient
global placement algorithm called Pplace. Experimental results show that our
Pplace achieves smaller placement wirelength than ePlace and NTUplace3. With
the pervasive applications of Poisson's equation in scientific fields, in
particular, our effective, efficient, and robust computation scheme for its
analytical solution can provide substantial impacts on these fields.
|
In this paper we consider the orbifold curve, which is a quotient of an
elliptic curve $\mathcal{E}$ by a cyclic group of order 4. We develop a
systematic way to obtain a Givental-type reconstruction of Gromov-Witten theory
of the orbifold curve via the product of the Gromov-Witten theories of a point.
This is done by employing mirror symmetry and certain results in FJRW theory.
In particular, we present the particular Givental's action giving the CY/LG
correspondence between the Gromov-Witten theory of the orbifold curve
$\mathcal{E} / \mathbb{Z}_4$ and FJRW theory of the pair defined by the
polynomial $x^4+y^4+z^2$ and the maximal group of diagonal symmetries. The
methods we have developed can easily be applied to other finite quotients of an
elliptic curve. Using Givental's action we also recover this FJRW theory via
the product of the Gromov-Witten theories of a point. Combined with the CY/LG
action we get a result in "pure" Gromov-Witten theory with the help of modern
mirror symmetry conjectures.
|
For a dominant algebraically stable rational self-map of the complex
projective plane of degree at least 2, we will consider three different
definitions of Fatou set and show the equivalence of them. Consequently, it
follows that all Fatou components are Stein. This is an improvement of an early
result by Fornaess and Sibony.
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Predicting the binding of viral peptides to the major histocompatibility
complex with machine learning can potentially extend the computational
immunology toolkit for vaccine development, and serve as a key component in the
fight against a pandemic. In this work, we adapt and extend USMPep, a recently
proposed, conceptually simple prediction algorithm based on recurrent neural
networks. Most notably, we combine regressors (binding affinity data) and
classifiers (mass spectrometry data) from qualitatively different data sources
to obtain a more comprehensive prediction tool. We evaluate the performance on
a recently released SARS-CoV-2 dataset with binding stability measurements.
USMPep not only sets new benchmarks on selected single alleles, but
consistently turns out to be among the best-performing methods or, for some
metrics, to be even the overall best-performing method for this task.
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Nutrition estimation is crucial for effective dietary management and overall
health and well-being. Existing methods often struggle with sub-optimal
accuracy and can be time-consuming. In this paper, we propose NuNet, a
transformer-based network designed for nutrition estimation that utilizes both
RGB and depth information from food images. We have designed and implemented a
multi-scale encoder and decoder, along with two types of feature fusion
modules, specialized for estimating five nutritional factors. These modules
effectively balance the efficiency and effectiveness of feature extraction with
flexible usage of our customized attention mechanisms and fusion strategies.
Our experimental study shows that NuNet outperforms its variants and existing
solutions significantly for nutrition estimation. It achieves an error rate of
15.65%, the lowest known to us, largely due to our multi-scale architecture and
fusion modules. This research holds practical values for dietary management
with huge potential for transnational research and deployment and could inspire
other applications involving multiple data types with varying degrees of
importance.
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For a dominant rational self-map on a smooth projective variety defined over
a number field, Kawaguchi and Silverman conjectured that the (first) dynamical
degree is equal to the arithmetic degree at a rational point whose forward
orbit is well-defined and Zariski dense. We prove this conjecture for
surjective endomorphisms on smooth projective surfaces. For surjective
endomorphisms on any smooth projective varieties, we show the existence of
rational points whose arithmetic degrees are equal to the dynamical degree.
Moreover, we prove that there exists a Zariski dense set of rational points
having disjoint orbits if the endomorphism is an automorphism.
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In this paper we study fluctuations of small noise multiscale diffusions
around their homogenized deterministic limit. We derive quantitative rates of
convergence of the fluctuation processes to the respective Gaussian limits in
the appropriate Wasserstein metric. We use tools from Malliavin analysis and in
particular a bound of the Wasserstein distance of the two distributions in
terms of the first and second order Malliavin derivative of the slow component.
The system we study is fully coupled and the derivation of the quantitative
rates of convergence depends on a very careful decomposition of the first and
second Malliavin derivatives of the slow and fast component with respect to
components that have different rates of convergence as measured by the strength
of the noise and timescale separation parameter.
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Given the widespread dissemination of inaccurate medical advice related to
the 2019 coronavirus pandemic (COVID-19), such as fake remedies, treatments and
prevention suggestions, misinformation detection has emerged as an open problem
of high importance and interest for the research community. Several works study
health misinformation detection, yet little attention has been given to the
perceived severity of misinformation posts. In this work, we frame health
misinformation as a risk assessment task. More specifically, we study the
severity of each misinformation story and how readers perceive this severity,
i.e., how harmful a message believed by the audience can be and what type of
signals can be used to recognize potentially malicious fake news and detect
refuted claims. To address our research questions, we introduce a new benchmark
dataset, accompanied by detailed data analysis. We evaluate several traditional
and state-of-the-art models and show there is a significant gap in performance
when applying traditional misinformation classification models to this task. We
conclude with open challenges and future directions.
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The goal of subspace learning is to find a $k$-dimensional subspace of
$\mathbb{R}^d$, such that the expected squared distance between instance
vectors and the subspace is as small as possible. In this paper we study
subspace learning in a partial information setting, in which the learner can
only observe $r \le d$ attributes from each instance vector. We propose several
efficient algorithms for this task, and analyze their sample complexity
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We present Hubble Space Telescope observations of active asteroid P/2020 O1
taken to examine its development for a year after perihelion. We find that the
mass loss peaks <~1 kg/s in 2020 August and then declines to nearly zero over
four months. Long-duration mass loss (~180 days) is consistent with a
sublimation origin, indicating that this object is likely an ice-bearing
main-belt comet. Equilibrium sublimation of water ice from an area as small as
1580 m^2 can supply the observed mass loss. Time-series photometry shows
tentative evidence for extremely rapid rotation (double-peaked period < 2 hr)
of the small nucleus (effective radius ~420 m). Ejection velocities of 0.1 mm
particles are comparable to the 0.3 m/s gravitational escape speed from the
nucleus, while larger particles are ejected at speeds less than the escape
velocity. These properties are consistent with the sublimation of near-surface
ice aided by centripetal acceleration. If water ice sublimation is confirmed,
P/2020 O1 would be the icy asteroid with the smallest semimajor axis (highest
temperature), setting new bounds on the distribution of ice in the asteroid
belt.
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The most promising mechanisms for the formation of Majorana bound states
(MBSs) in condensed matter systems involve one-dimensional systems (such as
semiconductor nanowires, magnetic chains, and quantum spin Hall insulator
(QSHI) edges) proximitized to superconducting materials. The choice between
each of these options involves trade-offs between several factors such as
reproducibility of results, system tunability, and robustness of the resulting
MBS. In this article, we propose that a combination of two of these systems,
namely a magnetic chain deposited on a QSHI edge in contact with a
superconducting surface, offers a better choice of tunability and MBS
robustness compared to magnetic chain deposited on bulk. We study how the QSHI
edge interacts with the magnetic chain, and see how the topological phase is
affected by edge proximity. We show that MBSs near the edge can be realized
with lower chemical potential and Zeeman field than the ones inside the bulk,
independently of the chain's magnetic order (ferromagnetic or spiral order).
Different magnetic orderings in the chain modify the overall phase diagram,
even suppressing the boundless topological phase found in the bulk for chains
located at the QSHI edge. Moreover, we quantify the "quality" of MBSs by
calculating the Majorana Polarization (MP) for different configurations. For
chains located at the edge, the MP is close to its maximum value already for
short chains. For chains located away from the edge, longer chains are needed
to attain the same quality as chains located at the edge. The MP also
oscillates in phase with the in-gap states, which is relatively unexpected as
peaks in the energy spectrum corresponds to stronger overlap of MBSs.
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We find all positive integer solutions in $x, y$ and $n$ of
$x^2+19^{2k+1}=4y^{n}$ for any non-negative integer $k$.
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Radar systems typically employ well-designed deterministic signals for target
sensing, while integrated sensing and communications (ISAC) systems have to
adopt random signals to convey useful information. This paper analyzes the
sensing and ISAC performance relying on random signaling in a multi-antenna
system. Towards this end, we define a new sensing performance metric, namely,
ergodic linear minimum mean square error (ELMMSE), which characterizes the
estimation error averaged over random ISAC signals. Then, we investigate a
data-dependent precoding (DDP) scheme to minimize the ELMMSE in sensing-only
scenarios, which attains the optimized performance at the cost of high
implementation overhead. To reduce the cost, we present an alternative
data-independent precoding (DIP) scheme by stochastic gradient projection
(SGP). Moreover, we shed light on the optimal structures of both sensing-only
DDP and DIP precoders. As a further step, we extend the proposed DDP and DIP
approaches to ISAC scenarios, which are solved via a tailored penalty-based
alternating optimization algorithm. Our numerical results demonstrate that the
proposed DDP and DIP methods achieve substantial performance gains over
conventional ISAC signaling schemes that treat the signal sample covariance
matrix as deterministic, which proves that random ISAC signals deserve
dedicated precoding designs.
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Cosmological parameter measurements from CMB experiments such as Planck,
ACTpol, SPTpol and other high resolution follow-ons fundamentally rely on the
accuracy of the assumed recombination model, or one with well prescribed
uncertainties. Deviations from the standard recombination history might suggest
new particle physics or modified atomic physics. Here we treat possible
perturbative fluctuations in the free electron fraction, $\Xe(z)$, by a
semi-blind expansion in densely-packed modes in redshift. From these we
construct parameter eigenmodes, which we rank order so that the lowest modes
provide the most power to probe the $\Xe(z)$ with CMB measurements. Since the
eigenmodes are effectively weighed by the fiducial $\Xe$ history, they are
localized around the differential visibility peak, allowing for an excellent
probe of hydrogen recombination, but a weaker probe of the higher redshift
helium recombination and the lower redshift highly neutral freeze-out tail. We
use an information-based criterion to truncate the mode hierarchy, and show
that with even a few modes the method goes a long way towards morphing a
fiducial older {\sc Recfast} $X_{\rm e,i} (z)$ into the new and improved {\sc
CosmoRec} and {\sc HyRec} $X_{\rm e,f} (z)$ in the hydrogen recombination
regime, though not well in the helium regime. Without such a correction, the
derived cosmic parameters are biased. We discuss an iterative approach for
updating the eigenmodes to further hone in on $X_{\rm e,f} (z)$ if large
deviations are indeed found. We also introduce control parameters that
downweight the attention on the visibility peak structure, e.g., focusing the
eigenmode probes more strongly on the $\Xe (z)$ freeze-out tail, as would be
appropriate when looking for the $\Xe$ signature of annihilating or decaying
elementary particles.
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With the proliferation of spatio-textual data, Top-k KNN spatial keyword
queries (TkQs), which return a list of objects based on a ranking function that
evaluates both spatial and textual relevance, have found many real-life
applications. Existing geo-textual indexes for TkQs use traditional retrieval
models like BM25 to compute text relevance and usually exploit a simple linear
function to compute spatial relevance, but its effectiveness is limited. To
improve effectiveness, several deep learning models have recently been
proposed, but they suffer severe efficiency issues. To the best of our
knowledge, there are no efficient indexes specifically designed to accelerate
the top-k search process for these deep learning models.
To tackle these issues, we propose a novel technique, which Learns to Index
the Spatio-Textual data for answering embedding based spatial keyword queries
(called LIST). LIST is featured with two novel components. Firstly, we propose
a lightweight and effective relevance model that is capable of learning both
textual and spatial relevance. Secondly, we introduce a novel machine learning
based Approximate Nearest Neighbor Search (ANNS) index, which utilizes a new
learning-to-cluster technique to group relevant queries and objects together
while separating irrelevant queries and objects. Two key challenges in building
an effective and efficient index are the absence of high-quality labels and
unbalanced clustering results. We develop a novel pseudo-label generation
technique to address the two challenges. Experimental results show that LIST
significantly outperforms state-of-the-art methods on effectiveness, with
improvements up to 19.21% and 12.79% in terms of NDCG@1 and Recall@10, and is
three orders of magnitude faster than the most effective baseline.
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Since its major release in 2006, the Unified Extensible Firmware Interface
(UEFI) has become the industry standard for interfacing a computer's hardware
and operating system, replacing BIOS. UEFI has higher privileged security
access to system resources than any other software component, including the
system kernel. Hence, identifying and characterizing vulnerabilities in UEFI is
extremely important for computer security. However, automated detection and
characterization of UEFI vulnerabilities is a challenging problem. Static
vulnerability analysis techniques are scalable but lack precision (reporting
many false positives), whereas symbolic analysis techniques are precise but are
hampered by scalability issues due to path explosion and the cost of constraint
solving. In this paper, we introduce a technique called STatic Analysis guided
Symbolic Execution (STASE), which integrates both analysis approaches to
leverage their strengths and minimize their weaknesses. We begin with a
rule-based static vulnerability analysis on LLVM bitcode to identify potential
vulnerability targets for symbolic execution. We then focus symbolic execution
on each target to achieve precise vulnerability detection and signature
generation. STASE relies on the manual specification of reusable vulnerability
rules and attacker-controlled inputs. However, it automates the generation of
harnesses that guide the symbolic execution process, addressing the usability
and scalability of symbolic execution, which typically requires manual harness
generation to reduce the state space. We implemented and applied STASE to the
implementations of UEFI code base. STASE detects and generates vulnerability
signatures for 5 out of 9 recently reported PixieFail vulnerabilities and 13
new vulnerabilities in Tianocore's EDKII codebase.
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An open issue in classical relativistic mechanics is the consistent treatment
of the dynamics of classical $N$-body systems of mutually-interacting
particles. This refers, in particular, to charged particles subject to EM
interactions, including both binary and self interactions (EM-interacting
$N$-body systems). In this paper it is shown that such a description can be
consistently obtained in the context of classical electrodynamics, for the case
of a $N$-body system of classical finite-size charged particles. A variational
formulation of the problem is presented, based on the $N$-body hybrid
synchronous Hamilton variational principle. Covariant Lagrangian and
Hamiltonian equations of motion for the dynamics of the interacting $N$-body
system are derived, which are proved to be delay-type ODEs. Then, a
representation in both standard Lagrangian and Hamiltonian forms is proved to
hold, the latter expressed by means of classical Poisson Brackets. The theory
developed retains both the covariance with respect to the Lorentz group and the
exact Hamiltonian structure of the problem, which is shown to be intrinsically
non-local. Different applications of the theory are investigated. The first one
concerns the development of a suitable Hamiltonian approximation of the exact
equations that retains finite delay-time effects characteristic of the binary
and self EM interactions. Second, basic consequences concerning the validity of
Dirac generator formalism are pointed out, with particular reference to the
instant-form representation of Poincar\`{e} generators. Finally, a discussion
is presented both on the validity and possible extension of the Dirac generator
formalism as well as the failure of the so-called Currie \textquotedblleft
no-interaction\textquotedblright\ theorem for the non-local Hamiltonian system
considered here.
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Development of efficient and high-performing electrolytes is crucial for
advancing energy storage technologies, particularly in batteries. Predicting
the performance of battery electrolytes rely on complex interactions between
the individual constituents. Consequently, a strategy that adeptly captures
these relationships and forms a robust representation of the formulation is
essential for integrating with machine learning models to predict properties
accurately. In this paper, we introduce a novel approach leveraging a
transformer-based molecular representation model to effectively and efficiently
capture the representation of electrolyte formulations. The performance of the
proposed approach is evaluated on two battery property prediction tasks and the
results show superior performance compared to the state-of-the-art methods.
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The first examples of exceptional terminal singularities are constructed.
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The Average Vector Field (AVF) method is a B-series scheme of the second
order. As a discrete gradient method it preserves exactly the energy integral
for any canonical Hamiltonian system. We present and discuss two locally exact
and energy-preserving modifications of the AVF method: AVF-LEX (of the third
order) and AVF-SLEX (of the fourth order). Applications to spherically
symmetric potentials are given, including a compact explicit expression for the
AVF scheme for the Coulomb-Kepler problem.
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We study the entanglement wedge cross-section (EWCS) in holographic massive
gravity theory, in which a first and second-order phase transition can occur.
We find that the mixed state entanglement measures, the EWCS and mutual
information (MI) can characterize the phase transitions. The EWCS and MI show
exactly the opposite behavior in the critical region, which suggests that the
EWCS captures distinct degrees of freedom from that of the MI. More
importantly, EWCS, MI and HEE all show the same scaling behavior in the
critical region. We give an analytical understanding of this phenomenon. By
comparing the quantum information behavior in the thermodynamic phase
transition of holographic superconductors, we analyze the relationship and
difference between them, and provide two mechanisms of quantum information
scaling behavior in the thermodynamic phase transition.
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As 3rd-person pronoun usage shifts to include novel forms, e.g., neopronouns,
we need more research on identity-inclusive NLP. Exclusion is particularly
harmful in one of the most popular NLP applications, machine translation (MT).
Wrong pronoun translations can discriminate against marginalized groups, e.g.,
non-binary individuals (Dev et al., 2021). In this ``reality check'', we study
how three commercial MT systems translate 3rd-person pronouns. Concretely, we
compare the translations of gendered vs. gender-neutral pronouns from English
to five other languages (Danish, Farsi, French, German, Italian), and vice
versa, from Danish to English. Our error analysis shows that the presence of a
gender-neutral pronoun often leads to grammatical and semantic translation
errors. Similarly, gender neutrality is often not preserved. By surveying the
opinions of affected native speakers from diverse languages, we provide
recommendations to address the issue in future MT research.
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In some problems there is information about the destination of a moving
object. An example is an airliner flying from an origin to a destination. Such
problems have three main components: an origin, a destination, and motion in
between. To emphasize that the motion trajectories end up at the destination,
we call them \textit{destination-directed trajectories}. The Markov sequence is
not flexible enough to model such trajectories. Given an initial density and an
evolution law, the future of a Markov sequence is determined probabilistically.
One class of conditionally Markov (CM) sequences, called the $CM_L$ sequence
(including the Markov sequence as a special case), has the following main
components: a joint endpoint density (i.e., an initial density and a final
density conditioned on the initial) and a Markov-like evolution law. This paper
proposes using the $CM_L$ sequence for modeling destination-directed
trajectories. It is demonstrated how the $CM_L$ sequence enjoys several
desirable properties for destination-directed trajectory modeling. Some
simulations of trajectory modeling and prediction are presented for
illustration.
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We show that Bertini theorems hold for $F$-signature and Hilbert--Kunz
multiplicity. In particular, if $X \subseteq \mathbb{P}^n$ is normal and
quasi-projective with $F$-signature greater than $\lambda$ (respectively the
Hilbert--Kunz multiplicity is less than $\lambda$) at all points $x \in X$,
then for a general hyperplane $H \subseteq \mathbb{P}^n$ the $F$-signature
(respectively Hilbert--Kunz multiplicity) of $X \cap H$ is greater than
$\lambda$ (respectively less than $\lambda$) at all points $x \in X \cap H$.
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Building and maintaining high-quality test sets remains a laborious and
expensive task. As a result, test sets in the real world are often not properly
kept up to date and drift from the production traffic they are supposed to
represent. The frequency and severity of this drift raises serious concerns
over the value of manually labeled test sets in the QA process. This paper
proposes a simple but effective technique that drastically reduces the effort
needed to construct and maintain a high-quality test set (reducing labeling
effort by 80-100% across a range of practical scenarios). This result
encourages a fundamental rethinking of the testing process by both
practitioners, who can use these techniques immediately to improve their
testing, and researchers who can help address many of the open questions raised
by this new approach.
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We find marginal and scalar solutions in cubic open string field theory by
using left-right splitting properties of a delta function. The marginal
solution represents a marginal deformation generated by a U(1) current, and it
is a generalized solution of the Wilson lines one given by the present authors.
The scalar solution has a well-defined universal Fock space expression, and it
is expressed as a singular gauge transform of the trivial vacuum. The expanded
theory around it is unable to be connected with the original theory by the
string field redefinition. Errors in hep-th/0112124 are corrected in this
paper.
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Pion-loop corrections for Compton scattering are calculated in a novel
approach based on the use of dispersion relations in a formalism obeying
unitarity. The basic framework is presented, including an application to
Compton scattering. In the approach the effects of the non-pole contribution
arising from pion dressing are expressed in terms of (half-off-shell) form
factors and the nucleon self-energy. These quantities are constructed through
the application of dispersion integrals to the pole contribution of loop
diagrams, the same as those included in the calculation of the amplitudes
through a K-matrix formalism. The prescription of minimal substitution is used
to restore gauge invariance. The resulting relativistic-covariant model
combines constraints from unitarity, causality, and crossing symmetry.
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The diagonal of a multivariate power series F is the univariate power series
Diag(F) generated by the diagonal terms of F. Diagonals form an important class
of power series; they occur frequently in number theory, theoretical physics
and enumerative combinatorics. We study algorithmic questions related to
diagonals in the case where F is the Taylor expansion of a bivariate rational
function. It is classical that in this case Diag(F) is an algebraic function.
We propose an algorithm that computes an annihilating polynomial for Diag(F).
Generically, it is its minimal polynomial and is obtained in time quasi-linear
in its size. We show that this minimal polynomial has an exponential size with
respect to the degree of the input rational function. We then address the
related problem of enumerating directed lattice walks. The insight given by our
study leads to a new method for expanding the generating power series of
bridges, excursions and meanders. We show that their first N terms can be
computed in quasi-linear complexity in N, without first computing a very large
polynomial equation.
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