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We consider the excitation of water in the Photon Dominated Region (PDR).
With the use of a three-dimensional escape probability method we compute the
level populations of ortho- and para-H_2O up to 350 K (i.e., 8 levels), as well
as line intensities for various transitions. Homogeneous and inhomogeneous
models are presented with densities of 10^4-10^5 cm^{-3} and the differences
between the resulting intensities are displayed. Density, temperature, and
abundance distributions inside the cloud are computed with the use of a
self-consistent physi-chemical (in)homogeneous model in order to reproduce the
line intensities observed with SWAS, and to make predictions for various lines
that HIFI will probe in the future. Line intensities vary from 10^{-13} erg
cm^{-2} s^{-1} sr^{-1} to a few times 10^{-6} erg cm^{-2} s^{-1} sr^{-1}. We
can reproduce the intensity for the 1_{10}-1_{01} line observed by the SWAS
satellite. It is found that the 2_{12}-1_{01} line is the strongest, whereas
the 3_{12}-2_{21} line is the weakest, in all the models. It is found that the
1_{10}-1_{01} line probes the total column, while higher excitation lines probe
the higher density gas (e.g., clumps).
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Moerdijk's site description for equivariant sheaf toposes on open topological
groupoids is used to give a proof for the (known, but apparently unpublished)
proposition that if H is a strictly full subgroupoid of an open topological
groupoid G, then the topos of equivariant sheaves on H is a subtopos of the
topos of equivariant sheaves on G. This proposition is then applied to the
study of quotient geometric theories and subtoposes. In particular, an
intrinsic characterization is given of those subgroupoids that are definable by
quotient theories.
|
The results of observations of the giant 1998 August 27 outburst in SGR
1900+14 are presented. A comparison is made of the two extremely intense events
on August 27, 1998 and March 5, 1979. The striking similarity between the
outbursts strongly implies a common nature. The observation of two giant
outbursts within 20 years from different sources suggests that such events
occur in an SGR once every 50-100 years.
|
Nowadays, owners and developers of deep learning models must consider
stringent privacy-preservation rules of their training data, usually
crowd-sourced and retaining sensitive information. The most widely adopted
method to enforce privacy guarantees of a deep learning model nowadays relies
on optimization techniques enforcing differential privacy. According to the
literature, this approach has proven to be a successful defence against several
models' privacy attacks, but its downside is a substantial degradation of the
models' performance. In this work, we compare the effectiveness of the
differentially-private stochastic gradient descent (DP-SGD) algorithm against
standard optimization practices with regularization techniques. We analyze the
resulting models' utility, training performance, and the effectiveness of
membership inference and model inversion attacks against the learned models.
Finally, we discuss differential privacy's flaws and limits and empirically
demonstrate the often superior privacy-preserving properties of dropout and
l2-regularization.
|
Statistical observations of the epoch of reionization (EOR) power spectrum
provide a rich data set for understanding the transition from the cosmic "dark
ages" to the ionized universe we see today. EOR observations have become an
active area of experimental cosmology, and three first generation
observatories--MWA, PAST, and LOFAR--are currently under development. In this
paper we provide the first quantitative calculation of the three dimensional
power spectrum sensitivity, incorporating the design parameters of a planned
array. This calculation is then used to explore the constraints these first
generation observations can place on the EOR power spectrum. The results
demonstrate the potential of upcoming power spectrum observations to constrain
theories of structure formation and reionization.
|
The aim of the present paper is to obtain some new fractional integral
inequalities for convex functions. Saigo fractional integral operator is used
to establish the results.
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The 'classical interpretation' of the wave function psi(x) reveals an
interesting operational aspect of the Helmholtz spectra. It is shown that the
traditional Sturm-Liouville problem contains the simplest key to predict the
squeezing effect for charged particle states.
|
The connection between a Taylor series and a continued-fraction involves a
nonlinear relation between the Taylor coefficients $\{ a_n \}$ and the
continued-fraction coefficients $\{ b_n \}$. In many instances it turns out
that this nonlinear relation transforms a complicated sequence $\{a_n \}$ into
a very simple one $\{ b_n \}$. We illustrate this simplification in the context
of graph combinatorics.
|
We study a generalized Einstein theory with the following two criteria:{\it
i}) on the solar scale, it must be consistent with the classical tests of
general relativity, {\it ii}) on the galactic scale, the gravitational
potential is a sum of Newtonian and Yukawa potentials so that it may explain
the flat rotation curves of spiral galaxies. Under these criteria, we find that
such a generalized Einstein action must include at least one scalar field and
one vector field as well as the quadratic term of the scalar curvature.
|
Understanding the collective quantum dynamics of nonequilibrium many-body
systems is an outstanding challenge in quantum science. In particular, dynamics
driven by quantum fluctuations are important for the formation of exotic
quantum phases of matter \cite{altman2023quantum}, fundamental high-energy
processes \cite{bauer2023highenergy}, quantum metrology \cite{degen2017sensing,
li2023scrambling}, and quantum algorithms \cite{ebadi2022quantum}. Here, we use
a programmable quantum simulator based on Rydberg atom arrays to experimentally
study collective dynamics across a (2+1)D Ising quantum phase transition. After
crossing the quantum critical point, we observe a gradual growth of
correlations through coarsening of antiferromagnetically ordered
domains~\cite{Samajdar2024}. By deterministically preparing and following the
evolution of ordered domains, we show that the coarsening is driven by the
curvature of domain boundaries, and find that the dynamics accelerate with
proximity to the quantum critical point. We quantitatively explore these
phenomena and further observe long-lived oscillations of the order parameter,
corresponding to an amplitude (Higgs) mode \cite{pekker2015amplitude}. These
observations offer a unique viewpoint into emergent collective dynamics in
strongly correlated quantum systems and nonequilibrium quantum processes.
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Although Large Language Models (LLMs) are becoming increasingly powerful,
they still exhibit significant but subtle weaknesses, such as mistakes in
instruction-following or coding tasks. As these unexpected errors could lead to
severe consequences in practical deployments, it is crucial to investigate the
limitations within LLMs systematically. Traditional benchmarking approaches
cannot thoroughly pinpoint specific model deficiencies, while manual
inspections are costly and not scalable. In this paper, we introduce a unified
framework, AutoDetect, to automatically expose weaknesses in LLMs across
various tasks. Inspired by the educational assessment process that measures
students' learning outcomes, AutoDetect consists of three LLM-powered agents:
Examiner, Questioner, and Assessor. The collaboration among these three agents
is designed to realize comprehensive and in-depth weakness identification. Our
framework demonstrates significant success in uncovering flaws, with an
identification success rate exceeding 30% in prominent models such as ChatGPT
and Claude. More importantly, these identified weaknesses can guide specific
model improvements, proving more effective than untargeted data augmentation
methods like Self-Instruct. Our approach has led to substantial enhancements in
popular LLMs, including the Llama series and Mistral-7b, boosting their
performance by over 10% across several benchmarks. Code and data are publicly
available at https://github.com/thu-coai/AutoDetect.
|
With the progressive advancements in deep graph learning, out-of-distribution
(OOD) detection for graph data has emerged as a critical challenge. While the
efficacy of auxiliary datasets in enhancing OOD detection has been extensively
studied for image and text data, such approaches have not yet been explored for
graph data. Unlike Euclidean data, graph data exhibits greater diversity but
lower robustness to perturbations, complicating the integration of outliers. To
tackle these challenges, we propose the introduction of \textbf{H}ybrid
External and Internal \textbf{G}raph \textbf{O}utlier \textbf{E}xposure (HGOE)
to improve graph OOD detection performance. Our framework involves using
realistic external graph data from various domains and synthesizing internal
outliers within ID subgroups to address the poor robustness and presence of OOD
samples within the ID class. Furthermore, we develop a boundary-aware OE loss
that adaptively assigns weights to outliers, maximizing the use of high-quality
OOD samples while minimizing the impact of low-quality ones. Our proposed HGOE
framework is model-agnostic and designed to enhance the effectiveness of
existing graph OOD detection models. Experimental results demonstrate that our
HGOE framework can significantly improve the performance of existing OOD
detection models across all 8 real datasets.
|
The super-sensitivity attained in quantum phase estimation is known to be
compromised in the presence of decoherence. This is particularly patent at
blind spots -- phase values at which sensitivity is totally lost. One remedy is
to use a precisely known reference phase to shift the operation point of the
sensor to a less vulnerable phase value. We present here an alternative
approach based on combining the probe with an ancillary degree of freedom
containing adjustable parameters to create an entangled quantum state of higher
dimension. We validate this concept by simulating a configuration of a
Mach-Zehnder interferometer with a two-photon probe and a polarization ancilla
of adjustable parameters, entangled at a polarizing beam splitter. At the
interferometer output, the photons are measured after an adjustable unitary
transformation in the polarization subspace. Through calculation of the Fisher
information and simulation of an adaptive estimation procedure, we show that
optimizing the adjustable polarization parameters using an adaptive measurement
process provides globally super-sensitive unbiased phase estimates for a range
of decoherence levels, without prior information or a reference phase.
|
We compute the rational cohomology of the moduli space $\mathcal{M}_{4,1}$ of
non-singular genus $4$ curves with $1$ marked point, using Gorinov-Vassiliev's
method.
|
We analyse the velocity-dependent potentials seen by D0 and D4-brane probes
moving in Type I' background for head-on scattering off the fixed planes. We
find that at short distances (compared to string length) the D0-brane probe has
a nontrivial moduli space metric, in agreement with the prediction of Type I'
matrix model; however, at large distances it is modified by massive open
strings to a flat metric, which is consistent with the spacetime equations of
motion of Type I' theory. We discuss the implication of this result for the
matrix model proposal for M-theory. We also find that the nontrivial metric at
short distances in the moduli space action of the D0-brane probe is reflected
in the coefficient of the higher dimensional v^4 term in the D4-brane probe
action.
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In this paper we consider the class of connected simple Lie groups equipped
with the discrete topology. We show that within this class of groups the
following approximation properties are equivalent: (1) the Haagerup property;
(2) weak amenability; (3) the weak Haagerup property. In order to obtain the
above result we prove that the discrete group GL(2,K) is weakly amenable with
constant 1 for any field K.
|
We present axioms for the real numbers by omitting the field axioms and then
derive the field properties of the real numbers. We prove all our theorems
constructively.
|
The Byzantine agreement problem is considered to be a core problem in
distributed systems. For example, Byzantine agreement is needed to build a
blockchain, a totally ordered log of records. Blockchains are asynchronous
distributed systems, fault-tolerant against Byzantine nodes.
In the literature, the asynchronous byzantine agreement problem is studied in
a fully connected network model where every node can directly send messages to
every other node. This assumption is questionable in many real-world
environments. In the reality, nodes might need to communicate by means of an
incomplete network, and Byzantine nodes might not forward messages.
Furthermore, Byzantine nodes might not behave correctly and, for example,
corrupt messages. Therefore, in order to truly understand Byzantine Agreement,
we need both ingredients: asynchrony and incomplete communication networks.
In this paper, we study the asynchronous Byzantine agreement problem in
incomplete networks. A classic result by Danny Dolev proved that in a
distributed system with n nodes in the presence of f Byzantine nodes, the
vertex connectivity of the system communication graph should be at least
(2f+1). While Dolev's result was for synchronous deterministic systems, we
demonstrate that the same bound also holds for asynchronous randomized systems.
We show that the bound is tight by presenting a randomized algorithm, and a
matching lower bound.
|
We review some of the properties of extensive cosmic ray air showers and
describe a simple model of the radio-frequency radiation generated by shower
electrons and positrons as they bend in the Earth's magnetic field. We perform
simulations by calculating the trajectory and radiation of a few thousand
charged shower particles. The results are then transformed to predict the
strength and polarization of the electromagnetic radiation emitted by the whole
shower.
|
For fibred boundary and fibred cusp metrics, Hausel, Hunsicker, and Mazzeo
identified the space of $L^2$ harmonic forms of fixed degree with the images of
maps between intersection cohomology groups of an associated stratified space
obtained by collapsing the fibres of the fibration at infinity onto its base.
In the present paper, we obtain a generalization of this result to situations
where, rather than a fibration at infinity, there is a Riemannian foliation
with compact leaves admitting a resolution by a fibration. If the associated
stratified space (obtained now by collapsing the leaves of the foliation) is a
Witt space and if the metric considered is a foliated cusp metric, then no such
resolution is required.
|
Molecular Communication (MC) architectures suffer from molecular build-up in
the channel if they do not have appropriate reuptake mechanisms. The molecular
build-up either leads to intersymbol interference (ISI) or reduces the
transmission rate. To measure the molecular build-up, we derive analytic
expressions for the incidence rate and absorption rate for one-dimensional MC
channels where molecular dispersion obeys the Brownian Motion. We verify each
of our key results with Monte Carlo simulations. Our results contribute to the
development of more complicated models and analytic expressions to measure the
molecular build-up and the impact of ISI in MC.
|
We investigate the asymptotic properties of axisymmetric inertial modes
propagating in a spherical shell when viscosity tends to zero. We identify
three kinds of eigenmodes whose eigenvalues follow very different laws as the
Ekman number $E$ becomes very small. First are modes associated with attractors
of characteristics that are made of thin shear layers closely following the
periodic orbit traced by the characteristic attractor. Second are modes made of
shear layers that connect the critical latitude singularities of the two
hemispheres of the inner boundary of the spherical shell. Third are
quasi-regular modes associated with the frequency of neutral periodic orbits of
characteristics. We thoroughly analyse a subset of attractor modes for which
numerical solutions point to an asymptotic law governing the eigenvalues. We
show that three length scales proportional to $E^{1/6}$, $E^{1/4}$ and
$E^{1/3}$ control the shape of the shear layers that are associated with these
modes. These scales point out the key role of the small parameter $E^{1/12}$ in
these oscillatory flows. With a simplified model of the viscous Poincar\'e
equation, we can give an approximate analytical formula that reproduces the
velocity field in such shear layers. Finally, we also present an analysis of
the quasi-regular modes whose frequencies are close to $\sin(\pi/4)$ and
explain why a fluid inside a spherical shell cannot respond to any periodic
forcing at this frequency when viscosity vanishes.
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We construct a reflexive Banach space $X_\mathcal{D}$ with an unconditional
basis such that all spreading models admitted by normalized block sequences in
$X_\mathcal{D}$ are uniformly equivalent to the unit vector basis of $\ell_1$,
yet every infinite-dimensional closed subspace of $X_\mathcal{D}$ fails the
Lebesgue property. This is a new result in a program initiated by Odell in 2002
concerning the strong separation of asymptotic properties in Banach spaces.
|
We study generalizations of a classical link invariant -- the multivariable
Alexander polynomial -- to tangles. The starting point is Archibald's tMVA
invariant for virtual tangles which lives in the setting of circuit algebras,
and whose target space has dimension that is exponential in the number of
strands. Using the Hodge star map and restricting to tangles without closed
components, we define a reduction of the tMVA to an invariant "rMVA" which is
valued in matrices with Laurent polynomial entries, and so has a much more
compact target space. We show the rMVA has the structure of a metamonoid
morphism and is further equivalent to a tangle invariant defined by Bar-Natan.
This invariant also reduces to the Gassner representation on braids and has a
partially defined trace operation for closing open strands of a tangle.
|
An HCMU metric is a conformal metric which has a finite number of
singularities on a compact Riemann surface and satisfies the equation of the
extremal K\"{a}hler metric. In this paper, we give a necessary and sufficient
condition for the existence of a kind of HCMU metrics which has both cusp
singularities and conical singularities.
|
Curating annotations for medical image segmentation is a labor-intensive and
time-consuming task that requires domain expertise, resulting in "narrowly"
focused deep learning (DL) models with limited translational utility. Recently,
foundation models like the Segment Anything Model (SAM) have revolutionized
semantic segmentation with exceptional zero-shot generalizability across
various domains, including medical imaging, and hold a lot of promise for
streamlining the annotation process. However, SAM has yet to be evaluated in a
crowd-sourced setting to curate annotations for training 3D DL segmentation
models. In this work, we explore the potential of SAM for crowd-sourcing
"sparse" annotations from non-experts to generate "dense" segmentation masks
for training 3D nnU-Net models, a state-of-the-art DL segmentation model. Our
results indicate that while SAM-generated annotations exhibit high mean Dice
scores compared to ground-truth annotations, nnU-Net models trained on
SAM-generated annotations perform significantly worse than nnU-Net models
trained on ground-truth annotations ($p<0.001$, all).
|
We present LaMDA: Language Models for Dialog Applications. LaMDA is a family
of Transformer-based neural language models specialized for dialog, which have
up to 137B parameters and are pre-trained on 1.56T words of public dialog data
and web text. While model scaling alone can improve quality, it shows less
improvements on safety and factual grounding. We demonstrate that fine-tuning
with annotated data and enabling the model to consult external knowledge
sources can lead to significant improvements towards the two key challenges of
safety and factual grounding. The first challenge, safety, involves ensuring
that the model's responses are consistent with a set of human values, such as
preventing harmful suggestions and unfair bias. We quantify safety using a
metric based on an illustrative set of human values, and we find that filtering
candidate responses using a LaMDA classifier fine-tuned with a small amount of
crowdworker-annotated data offers a promising approach to improving model
safety. The second challenge, factual grounding, involves enabling the model to
consult external knowledge sources, such as an information retrieval system, a
language translator, and a calculator. We quantify factuality using a
groundedness metric, and we find that our approach enables the model to
generate responses grounded in known sources, rather than responses that merely
sound plausible. Finally, we explore the use of LaMDA in the domains of
education and content recommendations, and analyze their helpfulness and role
consistency.
|
Even Artin groups generalize right-angled Artin groups by allowing the labels
in the defining graph to be even. In this paper a complete characterization of
quasi-projective even Artin groups is given in terms of their defining graphs.
Also, it is shown that quasi-projective even Artin groups are realizable by
K(pi,1) quasi-projective spaces.
|
This paper presents a framework to solve the strategic bidding problem of
participants in an electricity market cleared by employing the full AC Optimal
Power Flow (ACOPF) problem formulation. Traditionally, the independent system
operators (ISOs) leveraged DC Optimal Power Flow (DCOPF) problem formulation to
settle the electricity market. The main quest of this work is to find what
would be the challenges and opportunities if ISOs leverage the full ACOPF as
the market-clearing Problem (MCP)? This paper presents tractable mathematical
programming with equilibrium constraints for the convexified AC market-clearing
problem. Market participants maximize their profit via strategic bidding while
considering the reactive power dispatch of generation units. The equilibrium
constraints are procured by presenting the dual form of the relaxed ACOPF
problem. The strategic bidding problem with ACOPF-based MCP improves the
exactness of the location marginal prices (LMPs) and profit of market
participants compared to the one with DCOPF. It is shown that the strategic
bidding problem with DCOFP-based MCP is unable to model the limitations of
reactive power support. The presented results display cases where the proposed
strategic bidding method renders $52.3\%$ more profit for the Generation
Company (GENCO) than the DCOPF-based MCP model. The proposed strategic bidding
framework also addresses the challenges in coupling real and reactive power
dispatch of generation constraints, ramping constraints, demand response
implications with curtailable and time shiftable loads, and AC line flow
constraints. Therefore, the presented method will help market participants
leverage the more accurate ACOPF model in the strategic bidding problem.
|
We analyze the formation and dynamics of bright unstaggered solitons in the
disk-shaped dipolar Bose-Einstein condensate, which features the interplay of
contact (collisional) and long-range dipole-dipole (DD) interactions between
atoms. The condensate is assumed to be trapped in a strong optical-lattice
potential in the disk's plane, hence it may be approximated by a
two-dimensional (2D) discrete model, which includes the on-site nonlinearity
and cubic long-range (DD) interactions between sites of the lattice. We
consider two such models, that differ by the form of the on-site nonlinearity,
represented by the usual cubic term, or more accurate nonpolynomial one,
derived from the underlying 3D Gross-Pitaevskii equation. Similar results are
obtained for both models. The analysis is focused on effects of the DD
interaction on fundamental localized modes in the lattice (2D discrete
solitons). The repulsive isotropic DD nonlinearity extends the existence and
stability regions of the fundamental solitons. New families of on-site,
inter-site and hybrid solitons, built on top of a finite background, are found
as a result of the interplay of the isotropic repulsive DD interaction and
attractive contact nonlinearity. By themselves, these solutions are unstable,
but they evolve into robust breathers which exist on an oscillating background.
In the presence of the repulsive contact interactions, fundamental localized
modes exist if the DD interaction (attractive isotropic or anisotropic) is
strong enough. They are stable in narrow regions close to the anticontinuum
limit, while unstable solitons evolve into breathers. In the latter case, the
presence of the background is immaterial.
|
We study the behavior of quasi-one-dimensional (quasi-1d) Bose gases by Monte
Carlo techniques, i.e., by the variational Monte Carlo, the diffusion Monte
Carlo, and the fixed-node diffusion Monte Carlo technique. Our calculations
confirm and extend our results of an earlier study [Astrakharchik et al.,
cond-mat/0308585]. We find that a quasi-1d Bose gas i) is well described by a
1d model Hamiltonian with contact interactions and renormalized coupling
constant; ii) reaches the Tonks-Girardeau regime for a critical value of the 3d
scattering length a_3d; iii) enters a unitary regime for |a_3d| -> infinity,
where the properties of the gas are independent of a_3d and are similar to
those of a 1d gas of hard-rods; and iv) becomes unstable against cluster
formation for a critical value of the 1d gas parameter. The accuracy and
implications of our results are discussed in detail.
|
We propose a multi-layer approach to simulate hyperpycnal and hypopycnal
plumes in flows with free surface. The model allows to compute the vertical
profile of the horizontal and the vertical components of the velocity of the
fluid flow. The model can describe as well the vertical profile of the sediment
concentration and the velocity components of each one of the sediment species
that form the turbidity current. To do so, it takes into account the settling
velocity of the particles and their interaction with the fluid. This allows to
better describe the phenomena than a single layer approach. It is in better
agreement with the physics of the problem and gives promising results. The
numerical simulation is carried out by rewriting the multi-layer approach in a
compact formulation, which corresponds to a system with non-conservative
products, and using path-conservative numerical scheme. Numerical results are
presented in order to show the potential of the model.
|
In this work, we derive a system of Boltzmann-type equations to describe the
spread of SARS-CoV-2 virus at the microscopic scale, that is by modeling the
human-to-human mechanisms of transmission. To this end, we consider two
populations, characterized by specific distribution functions, made up of
individuals without symptoms (population $1$) and infected people with symptoms
(population $2$). The Boltzmann operators model the interactions between
individuals within the same population and among different populations with a
probability of transition from one to the other due to contagion or, vice
versa, to recovery. In addition, the influence of innate and adaptive immune
systems is taken into account. Then, starting from the Boltzmann microscopic
description we derive a set of evolution equations for the size and mean state
of each population considered. Mathematical properties of such macroscopic
equations, as equilibria and their stability, are investigated and some
numerical simulations are performed in order to analyze the ability of our
model to reproduce the characteristic features of Covid-19.
|
Robots can rapidly acquire new skills from demonstrations. However, during
generalisation of skills or transitioning across fundamentally different
skills, it is unclear whether the robot has the necessary knowledge to perform
the task. Failing to detect missing information often leads to abrupt movements
or to collisions with the environment. Active learning can quantify the
uncertainty of performing the task and, in general, locate regions of missing
information. We introduce a novel algorithm for active learning and demonstrate
its utility for generating smooth trajectories. Our approach is based on deep
generative models and metric learning in latent spaces. It relies on the
Jacobian of the likelihood to detect non-smooth transitions in the latent
space, i.e., transitions that lead to abrupt changes in the movement of the
robot. When non-smooth transitions are detected, our algorithm asks for an
additional demonstration from that specific region. The newly acquired
knowledge modifies the data manifold and allows for learning a latent
representation for generating smooth movements. We demonstrate the efficacy of
our approach on generalising elementary skills, transitioning across different
skills, and implicitly avoiding collisions with the environment. For our
experiments, we use a simulated pendulum where we observe its motion from
images and a 7-DoF anthropomorphic arm.
|
We develop the theory of spectral invariants in periodic Floer homology (PFH)
of area-preserving surface diffeomorphisms. We use this theory to prove
$C^\infty$ closing lemmas for certain Hamiltonian isotopy classes of
area-preserving surface diffeomorphisms. In particular, we show that for a
$C^\infty$-generic area-preserving diffeomorphism of the torus, the set of
periodic points is dense. Our closing lemmas are quantitative, asserting
roughly speaking that for a given Hamiltonian isotopy, within time $\delta$ a
periodic orbit must appear of period $O(\delta^{-1})$. We also prove a "Weyl
law" describing the asymptotic behavior of PFH spectral invariants.
|
Recently, a new kind of spintronics materials, bipolar magnetic semiconductor
(BMS), has been proposed. The spin polarization of BMS can be conveniently
controlled by a gate voltage, which makes it very attractive in device
engineering. Now, the main challenge is finding more BMS materials. In this
article, we propose that hydrogenated wurtzite SiC nanofilm is a
two-dimensional BMS material. Its BMS character is very robust under the effect
of strain, substrate, or even a strong electric field. The proposed
two-dimensional BMS material paves the way to use this promising new material
in an integrated circuit.
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Extending network lifetime of battery-operated devices is a key design issue
that allows uninterrupted information exchange among distributive nodes in
wireless sensor networks. Collaborative beamforming (CB) and cooperative
transmission (CT) have recently emerged as new communication techniques that
enable and leverage effective resource sharing among collaborative/cooperative
nodes. In this paper, we seek to maximize the lifetime of sensor networks by
using the new idea that closely located nodes can use CB/CT to reduce the load
or even avoid packet forwarding requests to nodes that have critical battery
life. First, we study the effectiveness of CB/CT to improve the signal strength
at a faraway destination using energy in nearby nodes. Then, a 2D disk case is
analyzed to assess the resulting performance improvement. For general networks,
if information-generation rates are fixed, the new routing problem is
formulated as a linear programming problem; otherwise, the cost for routing is
dynamically adjusted according to the amount of energy remaining and the
effectiveness of CB/CT. From the analysis and simulation results, it is seen
that the proposed schemes can improve the lifetime by about 90% in the 2D disk
network and by about 10% in the general networks, compared to existing schemes.
|
A state where spin currents exist in the absence of external fields has
recently been proposed to describe the superconducting state of metals. It is
proposed here that such a state also describes the ground state of aromatic
molecules. It is argued that this point of view provides a more natural
explanation for the large diamagnetic susceptibilities and NMR shifts observed
in these molecules than the conventional viewpoint, and it provides a unified
description of aromatic molecules and superconductors as sought by F. London. A
six-atom ring model is solved by exact diagonalization and parameters in the
model where a ground state spin current exists are found. We suggest that this
physics plays a key role in biological matter.
|
Post-quantum cryptography studies the security of classical, i.e. non-quantum
cryptographic protocols against quantum attacks. Until recently, the considered
adversaries were assumed to use quantum computers and behave like classical
adversaries otherwise. A more conservative approach is to assume that also the
communication between the honest parties and the adversary is (partly) quantum.
We discuss several options to define secure encryption and authentication
against these stronger adversaries who can carry out 'superposition attacks'.
We re-prove a recent result of Boneh and Zhandry, stating that a uniformly
random function (and hence also a quantum-secure pseudorandom function) can
serve as a message-authentication code which is secure, even if the adversary
can evaluate this function in superposition.
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We propose a new correlator in one-dimensional quantum spin chains, the
$s-$Emptiness Formation Probability ($s-$EFP). This is a natural generalization
of the Emptiness Formation Probability (EFP), which is the probability that the
first $n$ spins of the chain are all aligned downwards. In the $s-$EFP we let
the spins in question be separated by $s$ sites. The usual EFP corresponds to
the special case when $s=1$, and taking $s>1$ allows us to quantify non-local
correlations. We express the $s-$EFP for the anisotropic XY model in a
transverse magnetic field, a system with both critical and non-critical
regimes, in terms of a Toeplitz determinant. For the isotropic XY model we find
that the magnetic field induces an interesting length scale.
|
The search for superconducting systems exhibiting nonreciprocal transport
and, specifically, the diode effect, has proliferated in recent years. This
trend encompasses a wide variety of systems, including planar hybrid
structures, asymmetric SQUIDs, and certain noncentrosymmetric superconductors.
A common feature of such systems is a gyrotropic symmetry, realized on
different scales and characterized by a polar vector. Alongside time-reversal
symmetry breaking, the presence of a polar axis allows for magnetoelectric
effects, which, when combined with proximity-induced superconductivity, results
in spontaneous non-dissipative currents that underpin the superconducting diode
effect. This symmetry established, we present a comprehensive theoretical study
of transport in a lateral Josephson junctions composed of a normal metal
supporting the spin Hall effect, and attached to a ferromagnetic insulator. Due
to the presence of the latter, magnetoelectric effects arise without requiring
external magnetic fields. We determine the dependence of the anomalous current
on the spin relaxation length and the transport parameters commonly used in
spintronics to characterize the interface between the metal and the
ferromagnetic insulator. Therefore, our theory naturally unifies nonreciprocal
transport in superconducting systems with classical spintronic effects, such as
the spin Hall effect, spin galvanic effect, and spin Hall magnetoresistance. We
propose an experiment involving measurements of magnetoresistance in the normal
state and nonreciprocal transport in the superconducting state. Such
experiment, on the one hand, allows for determining the parameters of the model
and thus verifying with a greater precision the theories of magnetoelectric
effects in normal systems. On the other hand, it contributes to a deeper
understanding of the underlying microscopic origins that determine these
parameters.
|
By construction, gauge theories require gauge fixing. In conventional
approaches to spontaneously broken gauge theories, the choice of the Unitary
('t Hooft) gauge involves the sacrifice of manifest renormalizability
(unitarity). It is shown that with a suitable modification of the background
field gauge condition, the background field formalism allows manifest unitarity
and renormalizability in a single framework.
|
Longitudinal data tracking under Local Differential Privacy (LDP) is a
challenging task. Baseline solutions that repeatedly invoke a protocol designed
for one-time computation lead to linear decay in the privacy or utility
guarantee with respect to the number of computations. To avoid this, the recent
approach of Erlingsson et al. (2020) exploits the potential sparsity of user
data that changes only infrequently. Their protocol targets the fundamental
problem of frequency estimation protocol for longitudinal binary data, with
$\ell_\infty$ error of $O ( (1 / \epsilon) \cdot (\log d)^{3 / 2} \cdot k \cdot
\sqrt{ n \cdot \log ( d / \beta ) } )$, where $\epsilon$ is the privacy budget,
$d$ is the number of time periods, $k$ is the maximum number of changes of user
data, and $\beta$ is the failure probability. Notably, the error bound scales
polylogarithmically with $d$, but linearly with $k$.
In this paper, we break through the linear dependence on $k$ in the
estimation error. Our new protocol has error $O ( (1 / \epsilon) \cdot (\log d)
\cdot \sqrt{ k \cdot n \cdot \log ( d / \beta ) } )$, matching the lower bound
up to a logarithmic factor. The protocol is an online one, that outputs an
estimate at each time period. The key breakthrough is a new randomizer for
sequential data, FutureRand, with two key features. The first is a composition
strategy that correlates the noise across the non-zero elements of the
sequence. The second is a pre-computation technique which, by exploiting the
symmetry of input space, enables the randomizer to output the results on the
fly, without knowing future inputs. Our protocol closes the error gap between
existing online and offline algorithms.
|
We present an automatic method for joint liver lesion segmentation and
classification using a hierarchical fine-tuning framework. Our dataset is
small, containing 332 2-D CT examinations with lesion annotated into 3 lesion
types: cysts, hemangiomas, and metastases. Using a cascaded U-net that performs
segmentation and classification simultaneously, we trained a strong lesion
segmentation model on the dataset of MICCAI 2017 Liver Tumor Segmentation
(LiTS) Challenge. We used the trained weights to fine-tune a slightly modified
model to obtain improved lesion segmentation and classification, on the smaller
dataset. Since pre-training was done with similar data on a related task, we
were able to learn more representative features (especially higher-level
features in the U-Net's encoder), and improve pixel-wise classification
results. We show an improvement of over 10\% in Dice score and classification
accuracy, compared to a baseline model. We further improve the classification
performance by hierarchically freezing the encoder part of the network and
achieve an improvement of over 15\% in Dice score and classification accuracy.
We compare our results with an existing method and show an improvement of 14\%
in the success rate and 12\% in the classification accuracy.
|
We show that the effects of decoherence on quantum steering ellipsoids can be
controlled by a specific reservoir manipulating, in both Markovian and
non-Markovian realms. Therefore, the so-called maximal steered coherence could
be protected through reservoir engineering implemented by coupling auxiliary
qubits to the reservoir.
|
By extending the classical Peyrard-Bishop model, we are able to obtain a
fully analytical description for the mechanical resistance of DNA under
stretching at variable values of temperature, number of base pairs and
intrachains and interchains bonds stiffness. In order to compare elasticity and
temperature effects, we first analyze the system in the zero temperature
mechanical limit, important to describe several experimental effects including
possible hysteresis. We then analyze temperature effects in the framework of
equilibrium statistical mechanics. In particular, we obtain an analytical
expression for the temperature dependent melting force and unzipping assigned
displacement in the thermodynamical limit, also depending on the relative
stability of intra vs inter molecular bonds. Such results coincide with the
purely mechanical model in the limit of zero temperature and with the
denaturation temperature that we obtain with the classical transfer integral
method. Based on our analytical results, explicit analysis of the phase
diagrams and cooperativity parameters are obtained, where also discreteness
effect can be accounted for. The obtained results are successfully applied in
reproducing the thermomechanical experimental melting of DNA and the response
of DNA hairpins. Due to its generality, the proposed approach can be extended
to other thermomechanically induced molecular melting phenomena.
|
Weak radiative decay B -> X_s gamma is known to be a loop-generated process.
However, it does receive tree-level contributions from CKM-suppressed b -> u
ubar s gamma transitions. In the present paper, we evaluate such contributions
together with similar ones from the QCD penguin operators. For a low value of
the photon energy cutoff E_0 ~ m_b/20 that has often been used in the
literature, they can enhance the inclusive branching ratio by more than 10%.
For E_0 = 1.6 GeV or higher, the effect does not exceed 0.4%, which is due to
phase-space suppression. Our perturbative results contain collinear logarithms
that depend on the light quark masses m_q (q=u,d,s). We have allowed m_b/m_q to
vary from 10 to 50, which corresponds to values of m_q that are typical for the
constituent quark masses. Such a rough method of estimation may be improved in
the future with the help of fragmentation functions once the considered effects
begin to matter in the overall error budget for BR(B -> X_s gamma).
|
We introduce the notion of reflections for selfinjective algebras from the
point of view of torsion theories induced by two-term tilting complexes. As an
application, we determine the transformations of Brauer trees associated with
reflections. In particular, we provide a way to transform every Brauer tree
into a Brauer line.
|
Computing response functions by following the time evolution of
superoperators in Liouville space (whose vectors are ordinary Hilbert space
operators) offers an attractive alternative to the diagrammatic perturbative
expansion of many-body equilibrium and nonequilibrium Green functions. The
bookkeeping of time ordering is naturally maintained in real (physical) time,
allowing the formulation of Wick's theorem for superoperators, giving a
factorization of higher order response functions in terms of two fundamental
Green's functions. Backward propagations and the analytic continuations using
artificial times (Keldysh loops and Matsubara contours) are avoided. A
generating functional for nonlinear response functions unifies quantum field
theory and the classical mode coupling formalism of nonlinear hydrodynamics and
may be used for semiclassical expansions. Classical response functions may be
obtained without the explicit computation of stability matrices.
|
We consider a gas of $N$ identical hard spheres in the whole space, and we
enforce the Boltzmann-Grad scaling. We may suppose that the particles are
essentially independent of each other at some initial time; even so,
correlations will be created by the dynamics. We will prove a structure theorem
for the correlations which develop at positive time. Our result generalizes a
previous result which states that there are phase points where the
three-particle marginal density factorizes into two-particle and one-particle
parts, while further factorization is impossible. The result depends on uniform
bounds which are known to hold on a small time interval, or globally in time
when the mean free path is large.
|
Generating text from structured data is challenging because it requires
bridging the gap between (i) structure and natural language (NL) and (ii)
semantically underspecified input and fully specified NL output. Multilingual
generation brings in an additional challenge: that of generating into languages
with varied word order and morphological properties. In this work, we focus on
Abstract Meaning Representations (AMRs) as structured input, where previous
research has overwhelmingly focused on generating only into English. We
leverage advances in cross-lingual embeddings, pretraining, and multilingual
models to create multilingual AMR-to-text models that generate in twenty one
different languages. For eighteen languages, based on automatic metrics, our
multilingual models surpass baselines that generate into a single language. We
analyse the ability of our multilingual models to accurately capture morphology
and word order using human evaluation, and find that native speakers judge our
generations to be fluent.
|
Generating receding-horizon motion trajectories for autonomous vehicles in
real-time while also providing safety guarantees is challenging. This is
because a future trajectory needs to be planned before the previously computed
trajectory is completely executed. This becomes even more difficult if the
trajectory is required to satisfy continuous-time collision-avoidance
constraints while accounting for a large number of obstacles. To address these
challenges, this paper proposes a novel real-time, receding-horizon motion
planning algorithm named REachability-based trajectory Design via Exact
Formulation of Implicit NEural signed Distance functions (REDEFINED). REDEFINED
first applies offline reachability analysis to compute zonotope-based reachable
sets that overapproximate the motion of the ego vehicle. During online
planning, REDEFINED leverages zonotope arithmetic to construct a neural
implicit representation that computes the exact signed distance between a
parameterized swept volume of the ego vehicle and obstacle vehicles. REDEFINED
then implements a novel, real-time optimization framework that utilizes the
neural network to construct a collision avoidance constraint. REDEFINED is
compared to a variety of state-of-the-art techniques and is demonstrated to
successfully enable the vehicle to safely navigate through complex
environments. Code, data, and video demonstrations can be found at
https://roahmlab.github.io/redefined/.
|
Let $\mathfrak{g}$ be a semisimple Lie algebra. We establish a new relation
between the Goldie rank of a primitive ideal $\mathcal{J}\subset
U(\mathfrak{g})$ and the dimension of the corresponding irreducible
representation $V$ of an appropriate finite W-algebra. Namely, we show that
$\operatorname{Grk}(\mathcal{J}) \leqslant \dim V/d_V$, where $d_V$ is the
index of a suitable equivariant Azumaya algebra on a homogeneous space. We also
compute $d_V$ in representation theoretic terms.
|
We present integral-field spectroscopic observations with the VIMOS-IFU at
the VLT of fast (2000-3000 km/s) Balmer-dominated shocks surrounding the
northwestern rim of the remnant of supernova 1006. The high spatial and
spectral resolution of the instrument enable us to show that the physical
characteristics of the shocks exhibit a strong spatial variation over few
atomic scale lengths across 133 sky locations. Our results point to the
presence of a population of non-thermal protons (10-100 keV) which might well
be the seed particles for generating high-energy cosmic rays. We also present
observations of Tycho's supernova remnant taken with the narrow-band tunable
filter imager OSIRIS at the GTC and the Fabry-Perot interferometer GHaFaS at
the WHT to resolve respectively the broad and narrow H\alpha\ lines across a
large part of the remnant.
|
The control of biofilm formation is a challenging goal that has not been
reached yet in many aspects. One is the role of van der Waals forces and
another the importance of mutual interactions between the adsorbing and the
adsorbed biomolecules ('critical crowding'). Here, a combined exeperimental and
theoretical approach is presented that fundamentally probes both aspects. On
three model proteins, lysozyme, {\alpha}-amylase and bovine serum albumin
(BSA), the adsorption kinetics is studied. Composite substrates are used
enabling a separation of the short- and the long-range forces. Though usually
neglected, experimental evidence is given for the influence of van der Waals
forces on the protein adsorption as revealed by in situ ellipsometry. The three
proteins were chosen for their different conformational stability in order to
investigate the influence of conformational changes on the adsorption kinetics.
Monte Carlo simulations are used to develop a model for these experimental
results by assuming an internal degree of freedom to represent conformational
changes. The simulations also provide data on the distribution of adsorption
sites. By in situ atomic force microscopy we can also test this distribution
experimentally which opens the possibility to e.g. investigate the interactions
between adsorbed proteins.
|
The interaction between electrons and plasmons in trilayer graphene is
investigated within the Overhauser approach resulting in the 'plasmaron'
quasi-particle. This interaction is cast into a field theoretical problem, nd
its effect on the energy spectrum is calculated using improved Wigner-Brillouin
perturbation theory. The plasmaron spectrum is shifted with respect to the bare
electron spectrum by $\Delta E(\mathbf{k})\sim 50\div200\,{\rm meV}$ for ABC
stacked trilayer graphene and for ABA trilayer graphene by $\Delta
E(\mathbf{k})\sim 30\div150\,{\rm meV}$ ($\Delta E(\mathbf{k})\sim 1\div5\,{\rm
meV}$) for the hyperbolic linear) part of the spectrum. The shift in general
increases with the electron concentration $n_{e}$ and electron momentum. The
dispersion of plasmarons is more pronounced in \textit{ABC} stacked than in ABA
tacked trilayer graphene, because of the different energy band structure and
their different plasmon dispersion.
|
We investigate the statistics of gravitational lenses in flat, low-density
cosmological models with different cosmic equations of state w. We compute the
lensing probabilities as a function of image separation \theta using a lens
population described by the mass function of Jenkins et al. and modeled as
singular isothermal spheres on galactic scales and as Navarro, Frenk & White
halos on cluster scales. It is found that COBE-normalized models with w > - 0.4
produce too few arcsecond-scale lenses in comparison with the JVAS/CLASS radio
survey, a result that is consistent with other observational constraints on w.
The wide-separation (\theta > 4'') lensing rate is a particularly sensitive
probe of both w and the halo mass concentration. The absence of these systems
in the current JVAS/CLASS data excludes highly concentrated halos in w < -0.7
models. The constraints can be improved by ongoing and future lensing surveys
of > 10^5 sources.
|
We study ep deep inelastic scattering and the inclusive production of prompt
photon within the framework of the quasi-multi-Regge-kinematic approach,
applying the quark Reggeization hypothesis. We describe structure functions F_2
and F_L supposing that a virtual photon scatters on a Reggeized quark from a
proton, via the effective gamma-Reggeon-quark vertex. It is shown that the main
mechanism of the inclusive prompt photon production in p \bar p collisions is
the fusion of a Reggeized quark and a Reggeized antiquark into a photon, via
the effective Regeon-Reggeon-gamma vertex. We describe the inclusive photon
transverse momentum spectra measured by the CDF and D0 Collaborations within
errors and without free parameters, using the Kimber-Martin-Ryskin unintegrated
quark and gluon distribution functions in a proton.
|
We have investigated a system with two sets of staggered fermions with
charges 1 and -1/2 coupling to a non-compact U(1) gauge field in 4 dimensions.
The model exhibits breaking of chiral symmetries of both fermions at different
values of beta. Chiral condensates, renormalized fermion masses and
renormalized charges have been measured. The renormalized charges show
agreement with one-loop perturbation theory. We examine surfaces of constant
renormalized charges in the space of bare parameters.
|
In this paper, we characterize a class of solutions to the unsteady
2-dimensional flow of a van der Waals fluid involving shock waves, and derive
an asymptotic amplitude equation exhibiting quadratic and cubic nonlinearities
including dissipation and diffraction. We exploit the theory of nonclassical
symmetry reduction to obtain some exact solutions. Because of the
nonlinearities present in the evolution equation, one expects that the wave
profile will eventually encounter distortion and steepening which in the limit
of vanishing dissipation culminates into a shock wave; and once shock is
formed, it will propagate by separating the portions of the continuous region.
Here we have shown how the real gas effects, which manifest themselves through
the van der Waals parameters $\tilde{a}$ and $\tilde{b}$ influence the wave
characteristics, namely the shape, strength, and decay behavior of shocks.
|
Modern electron linear accelerators are often designed to produce smooth
bunch distributions characterized by their macroscopic ensemble-average
moments. However, an increasing number of accelerator applications call for
finer control over the beam distribution, e.g., by requiring specific shapes
for its projection along one coordinate. Ultimately, the control of the beam
distribution at the single-particle level could enable new opportunities in
accelerator science. This review discusses the recent progress toward
controlling electron beam distributions on the "mesoscopic" scale with an
emphasis on shaping the beam or introducing complex correlations required for
some applications. This review emphasizes experimental and theoretical
developments of electron-bunch shaping methods based on bounded external
electromagnetic fields or via interactions with the self-generated velocity and
radiation fields.
|
Software testing is one of the very important Quality Assurance (QA)
components. A lot of researchers deal with the testing process in terms of
tester motivation and how tests should or should not be written. However, it is
not known from the recommendations how the tests are written in real projects.
In this paper, the following was investigated: (i) the denotation of the word
"test" in different natural languages; (ii) whether the number of occurrences
of the word "test" correlates with the number of test cases; and (iii) what
testing frameworks are mostly used. The analysis was performed on 38 GitHub
open source repositories thoroughly selected from the set of 4.3M GitHub
projects. We analyzed 20,340 test cases in 803 classes manually and 170k
classes using an automated approach. The results show that: (i) there exists a
weak correlation (r = 0.655) between the number of occurrences of the word
"test" and the number of test cases in a class; (ii) the proposed algorithm
using static file analysis correctly detected 97% of test cases; (iii) 15% of
the analyzed classes used main() function whose represent regular Java programs
that test the production code without using any third-party framework. The
identification of such tests is very complex due to implementation diversity.
The results may be leveraged to more quickly identify and locate test cases in
a repository, to understand practices in customized testing solutions, and to
mine tests to improve program comprehension in the future.
|
We set forth a method to analyze the orbital angular momentum of a light
field. Instead of using the canonical formalism for the conjugate pair
angle-angular momentum, we model this latter variable by the superposition of
two independent harmonic oscillators along two orthogonal axes. By describing
each oscillator by a standard Wigner function, we derive, via a consistent
change of variables, a comprehensive picture of the orbital angular momentum.
We compare with previous approaches and show how this method works in some
relevant examples.
|
We show the existence of solution for some classes of nonlocal problems. Our
proof combines the presence of sub and supersolution with the pseudomonotone
operators theory.
|
We show that nucleon electromagnetic structure functions of deep inelastic
scattering in Regge-Gribov limit (fixed Q-squared, asymptotically large 1/x and
s) can be well described in the two-component (soft + hard) approach. In the
concrete model elaborated by authors, the soft part of the virtual
photon-nucleon scattering is given by the vector meson dominance, with taking
into account the radial excitations of the rho-meson and nondiagonal
transitions in meson-nucleon interactions. The hard part is calculated by using
the dipole factorization, i.e., the process is considered as the dissociation
of the photon into a q and anti-q - pair (the "color dipole") and the
subsequent interaction of this dipole with the nucleon. The dipole cross
section has a Regge-type s-dependence and vanishes in the limit of large
transverse sizes of the dipole. We give the brief description of the model and
present results of the detailed comparison of model predictions with
experimental data for electromagnetic structure functions of the nucleon.
|
Given a power grid and a transmission (coupling) strength, basin stability is
a measure of synchronization stability for individual nodes. Earlier studies
have focused on the basin stability's dependence of the position of the nodes
in the network for single values of transmission strength. Basin stability
grows from zero to one as transmission strength increases, but often in a
complex, nonmonotonous way. In this study, we investigate the entire functional
form of the basin stability's dependence on transmission strength. To be able
to perform a systematic analysis, we restrict ourselves to small networks. We
scan all isomorphically distinct networks with an equal number of power
producers and consumers of six nodes or less. We find that the shapes of the
basin stability fall into a few, rather well-defined classes, that could be
characterized by the number of edges and the betweenness of the nodes, whereas
other network positional quantities matter less.
|
For two qubits independently coupled to their respective structured
reservoirs (Lorentzian spectrum), quantum beats for entanglement and discord
are found which are the result of quantum interference between correlation
oscillations induced by local non-Markovian environments. We also discuss the
preservation of quantum correlations by the effective suppression of the
spontaneous emission.
|
We present the results of our stellar photometry and spectroscopy for the new
Local Group galaxy VV 124 (UGC 4879) obtained with the 6-m BTA telescope. The
presence of a few bright supergiants in the galaxy indicates that the current
star formation process is weak. The apparent distribution of stars with
different ages in VV 124 does not differ from the analogous distributions of
stars in irregular galaxies, but the ratio of the numbers of young and old
stars indicates that VV 124 belongs to the rare Irr/Sph type of galaxies. The
old stars (red giants) form the most extended structure, a thick disk with an
exponential decrease in the star number density to the edge. Definitely, the
young population unresolvable in images makes a great contribution to the
background emission from the central galactic regions. The presence of young
stars is also confirmed by the [O III] emission line visible in the spectra
that belongs to extensive diffuse galactic regions. The mean radial velocity of
several components (two bright supergiants, the unresolvable stellar
population, and the diffuse gas) is v_h = -70+/-15 km/s and the velocity with
which VV 124 falls into the Local Group is v_LG = -12+/-15 km/s. We confirm the
distance to the galaxy D = 1.1+/-0.1 Mpc and the metallicity of red giants
([Fe/H] = -1.37) found by Kopylov et al. (2008).VV 124 is located on the
periphery of the Local Group approximately at the same distance from M 31 and
our Galaxy and is isolated from other galaxies. The galaxy LeoA nearest to it
is 0.5 Mpc away.
|
Convolutional neural networks (CNNs) are being applied to an increasing
number of problems and fields due to their superior performance in
classification and regression tasks. Since two of the key operations that CNNs
implement are convolution and pooling, this type of networks is implicitly
designed to act on data described by regular structures such as images.
Motivated by the recent interest in processing signals defined in irregular
domains, we advocate a CNN architecture that operates on signals supported on
graphs. The proposed design replaces the classical convolution not with a
node-invariant graph filter (GF), which is the natural generalization of
convolution to graph domains, but with a node-varying GF. This filter extracts
different local features without increasing the output dimension of each layer
and, as a result, bypasses the need for a pooling stage while involving only
local operations. A second contribution is to replace the node-varying GF with
a hybrid node-varying GF, which is a new type of GF introduced in this paper.
While the alternative architecture can still be run locally without requiring a
pooling stage, the number of trainable parameters is smaller and can be
rendered independent of the data dimension. Tests are run on a synthetic source
localization problem and on the 20NEWS dataset.
|
Policy gradient methods are among the most effective methods for large-scale
reinforcement learning, and their empirical success has prompted several works
that develop the foundation of their global convergence theory. However, prior
works have either required exact gradients or state-action visitation measure
based mini-batch stochastic gradients with a diverging batch size, which limit
their applicability in practical scenarios. In this paper, we consider
classical policy gradient methods that compute an approximate gradient with a
single trajectory or a fixed size mini-batch of trajectories under soft-max
parametrization and log-barrier regularization, along with the widely-used
REINFORCE gradient estimation procedure. By controlling the number of "bad"
episodes and resorting to the classical doubling trick, we establish an anytime
sub-linear high probability regret bound as well as almost sure global
convergence of the average regret with an asymptotically sub-linear rate. These
provide the first set of global convergence and sample efficiency results for
the well-known REINFORCE algorithm and contribute to a better understanding of
its performance in practice.
|
The suppression of spurious events in the region of interest for neutrinoless
double beta decay will play a major role in next generation experiments. The
background of detectors based on the technology of cryogenic calorimeters is
expected to be dominated by {\alpha} particles, that could be disentangled from
double beta decay signals by exploiting the difference in the emission of the
scintillation light. CUPID-0, an array of enriched Zn$^{82}$Se scintillating
calorimeters, is the first large mass demonstrator of this technology. The
detector started data-taking in 2017 at the Laboratori Nazionali del Gran Sasso
with the aim of proving that dual read-out of light and heat allows for an
efficient suppression of the {\alpha} background. In this paper we describe the
software tools we developed for the analysis of scintillating calorimeters and
we demonstrate that this technology allows to reach an unprecedented background
for cryogenic calorimeters.
|
The method exploits the contraction of space to systematically obtain compact
solitary solutions. The latter is provided for the incompressible Euler and
Navier-Stokes PDE. The nonlinear response of momentum advection is moved into a
term for contracting space. Then the linear continuity PDE is solved by means
of arbitrarily selected closure functions. The contracting space is then split
into two variables. The compactness of some solutions is enhanced by
numerically integrating the contracting domain while retaining a solution for
the nonlinear PDE. The validation of numerical schemes is demonstrated for the
Euler and Navier-Stokes PDE. As the nonlinear response is isolated in only one
spatial dimension, the method permits to validate arbitrary unstructured meshes
and domain geometries by introducing the spatial dimension n+1.
|
Superlinear scaling in cities, which appears in sociological quantities such
as economic productivity and creative output relative to urban population size,
has been observed but not been given a satisfactory theoretical explanation.
Here we provide a network model for the superlinear relationship between
population size and innovation found in cities, with a reasonable range for the
exponent.
|
Using the framework of quasi-Hamiltonian actions, we compute the obstruction
to prequantization for the moduli space of flat ${\rm PU}(p)$-bundles over a
compact orientable surface with prescribed holonomies around boundary
components, where $p>2$ is prime.
|
From the order-N electronic-structure formulation, a Hamiltonian is derived,
of which lowest eigen state is the generalized or composite-band Wannier state.
This Hamiltonian maps the locality of the Wannier state to that of a virtual
impurity state and to a perturbation from a bonding orbital. These theories are
demonstrated in the diamond-structure solids, where the Wannier states are
constructed by a practical order-N algorithm with the Hamiltonian. The results
give a prototypical picture of the Wannier states in covalent-bonded systems.
|
We consider layered superconductors with a flux lattice perpendicular to the
layers and random columnar defects parallel to the magnetic field B. We show
that the decoupling transition temperature Td, at which the Josephson coupling
vanishes, is enhanced by columnar defects by an amount ~B^2 relative to Td.
Decoupling by increasing field can be followed by a reentrant recoupling
transition for strong disorder. We also consider a commensurate component of
the columnar density and show that its pinning potential is renormalized to
zero above a critical long wavelength disorder. This decommnesuration
transition may account for a recently observed kink in the melting line.
|
Let F* be the field of q elements and let P(n,q) denote the projective space
of dimension n-1 over F*. We construct a family H^{n}_{k,i} of combinatorial
homology modules associated to P(n,q) for a coefficient field F of positive
characteristic co-prime to q. As GL(n,q)-representations these modules are
obtained from the permutation action of GL(n,q) on the set of subspaces of F*.
We prove a branching rule for the H^{n}_{k,i} and use this to determine the
homology representations completely. Results include a duality theorem, the
characterisation of H^{n}_{k,i} through the standard irreducibles of GL(n,q)
over F and applications.
|
We study the radiative corrections to all Kl3 decay modes to leading
non-trivial order in the chiral effective field theory, working with a fully
inclusive prescription on real photon emission. We present new results for Kmu3
modes and update previous results on Ke3 modes. Our analysis provides important
theoretical input for the extraction of the CKM element Vus from Kl3 decays.
|
We show a new duality between the polynomial margin complexity of $f$ and the
discrepancy of the function $f \circ \textsf{XOR}$, called an $\textsf{XOR}$
function. Using this duality, we develop polynomial based techniques for
understanding the bounded error ($\textsf{BPP}$) and the weakly-unbounded error
($\textsf{PP}$) communication complexities of $\textsf{XOR}$ functions. We show
the following.
A weak form of an interesting conjecture of Zhang and Shi (Quantum
Information and Computation, 2009) (The full conjecture has just been reported
to be independently settled by Hatami and Qian (Arxiv, 2017). However, their
techniques are quite different and are not known to yield many of the results
we obtain here). Zhang and Shi assert that for symmetric functions $f : \{0,
1\}^n \rightarrow \{-1, 1\}$, the weakly unbounded-error complexity of $f \circ
\textsf{XOR}$ is essentially characterized by the number of points $i$ in the
set $\{0,1, \dots,n-2\}$ for which $D_f(i) \neq D_f(i+2)$, where $D_f$ is the
predicate corresponding to $f$. The number of such points is called the
odd-even degree of $f$. We show that the $\textsf{PP}$ complexity of $f \circ
\textsf{XOR}$ is $\Omega(k/ \log(n/k))$.
We resolve a conjecture of a different Zhang characterizing the Threshold of
Parity circuit size of symmetric functions in terms of their odd-even degree.
We obtain a new proof of the exponential separation between
$\textsf{PP}^{cc}$ and $\textsf{UPP}^{cc}$ via an $\textsf{XOR}$ function.
We provide a characterization of the approximate spectral norm of symmetric
functions, affirming a conjecture of Ada et al. (APPROX-RANDOM, 2012) which has
several consequences.
Additionally, we prove strong $\textsf{UPP}$ lower bounds for $f \circ
\textsf{XOR}$, when $f$ is symmetric and periodic with period
$O(n^{1/2-\epsilon})$, for any constant $\epsilon > 0$.
|
(Abridged). One of the most metal-deficient blue compact galaxies (BCGs) HS
0822+3542 (Z=1/34 Zsun), is also one of the nearest such objects. A trigger
mechanism for its current SF burst has remained unclear. We report the
discovery of a very blue ((B-V)tot=0.08 and (V-R)tot=0.14) LSB (mu_B^0 > 23.4
arcsec^-2) dwarf irregular (dIrr) galaxy, named SAO 0822+3545. Its small
relative velocity and projected distance of ~11 kpc from the BCG imply their
physical association. For this LSB galaxy, we present spectroscopic results,
total B,V,R magnitudes, the effective radii and surface brightness (SB), and we
describe its morphological properties. We compare the very blue colours of this
dwarf with PEGASE.2 models of the colour evolution of a Z=1/20 Zsun stellar
population, and combine this analysis with the data on the LSBD EW(Ha) values.
The models best describing all available observational data depend on the
relative fraction of massive stars in the IMF used. For a Salpeter IMF with Mup
= 120 Msun, the best model includes a "young" single stellar population (SSP)
with an age of ~10 Myr and an "old" SSP with the age of ~0.2--10 Gyr. The mass
ratio of the old to young components should be in the range of 10 to 30. The
role of interaction in triggering the galaxies major SF episodes during the
last ~100-200 Myr is discussed. For the BCG, based on the spectroscopy with the
6m telescope, we estimate the physical parameters of its SF region and present
the first evidence of an ionized gas supershell. This pair of dwarfs lies deep
within the nearby Lynx-Cancer void, with the nearest bright (L > L*) galaxies
at distances > 3 Mpc. This is probably one of the main factors responsible for
the unevolved state of HS 0822+3542.
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Expressions corresponding to the transmission of a uniaxial optically active
crystal platelet are provided for an optical axis parallel and perpendicular to
the plane of interface. The optical activity is taken into account by a
consistent multipolar expansion of the crystal medium response due to the path
of an electromagnetic wave. Numerical examples of the effect of the optical
activity are given for quartz platelets of chosen thicknesses. The optical
activity's effects on the variations of the transmission of quartz platelets as
a function of the angle of incidence is also investigated.
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The underlying reasons for the difficulty of unitarily implementing the whole
conformal group $SO(4,2)$ in a massless Quantum Field Theory (QFT) are
investigated in this paper. Firstly, we demonstrate that the singular action of
the subgroup of special conformal transformations (SCT), on the standard
Minkowski space $M$, cannot be primarily associated with the vacuum radiation
problems, the reason being more profound and related to the dynamical breakdown
of part of the conformal symmetry (the SCT subgroup, to be more precise) when
representations of null mass are selected inside the representations of the
whole conformal group. Then we show how the vacuum of the massless QFT radiates
under the action of SCT (usually interpreted as transitions to a uniformly
accelerated frame) and we calculate exactly the spectrum of the outgoing
particles, which proves to be a generalization of the Planckian one, this
recovered as a given limit.
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Single particle cryogenic electron microscopy (cryo-EM) is an imaging
technique capable of recovering the high-resolution 3-D structure of biological
macromolecules from many noisy and randomly oriented projection images. One
notable approach to 3-D reconstruction, known as Kam's method, relies on the
moments of the 2-D images. Inspired by Kam's method, we introduce a
rotationally invariant metric between two molecular structures, which does not
require 3-D alignment. Further, we introduce a metric between a stack of
projection images and a molecular structure, which is invariant to rotations
and reflections and does not require performing 3-D reconstruction.
Additionally, the latter metric does not assume a uniform distribution of
viewing angles. We demonstrate uses of the new metrics on synthetic and
experimental datasets, highlighting their ability to measure structural
similarity.
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To maximize future rewards in this ever-changing world, animals must be able
to discover the temporal structure of stimuli and then anticipate or act
correctly at the right time. How the animals perceive, maintain, and use time
intervals ranging from hundreds of milliseconds to multi-seconds in working
memory? How temporal information is processed concurrently with spatial
information and decision making? Why there are strong neuronal temporal signals
in tasks in which temporal information is not required? A systematic
understanding of the underlying neural mechanisms is still lacking. Here, we
addressed these problems using supervised training of recurrent neural network
models. We revealed that neural networks perceive elapsed time through state
evolution along stereotypical trajectory, maintain time intervals in working
memory in the monotonic increase or decrease of the firing rates of
interval-tuned neurons, and compare or produce time intervals by scaling state
evolution speed. Temporal and non-temporal information are coded in subspaces
orthogonal with each other, and the state trajectories with time at different
non-temporal information are quasi-parallel and isomorphic. Such coding
geometry facilitates the decoding generalizability of temporal and non-temporal
information across each other. The network structure exhibits multiple
feedforward sequences that mutually excite or inhibit depending on whether
their preferences of non-temporal information are similar or not. We identified
four factors that facilitate strong temporal signals in non-timing tasks,
including the anticipation of coming events. Our work discloses fundamental
computational principles of temporal processing, and is supported by and gives
predictions to a number of experimental phenomena.
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We investigate the effects of disorder characterising a superconducting thin
film on the proximity-induced superconductivity generated by the film (in,
e.g., a semiconductor) based on the exact numerical analysis of a
three-dimensional microscopic model. To make the problem numerically tractable,
we use a recursive Green's function method in combination with a patching
approach that exploits the short-range nature of the interface Green's function
in the presence of disorder. As a result of the Fermi surface mismatch between
the superconductor (SC) and the semiconductor (SM) in combination with the
confinement-induced quantization of the transverse SC modes, the proximity
effect induced by a clean SC film is typically one to three orders of magnitude
smaller that the corresponding quantity for a bulk SC and exhibits huge
thickness-dependent variations. The presence of disorder has competing effects:
on the one hand it enhances the proximity-induced superconductivity and
suppresses its strong thickness dependence, on the other hand it generates
proximity-induced effective disorder in the SM. The effect of proximity-induced
disorder on the topological superconducting phase and the associated Majorana
modes is studied nonperturbatively.
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This article investigates pathological behavior at the first limit stage in
the sequence of inner mantles, obtained by iterating the definition of the
mantle to get smaller and smaller inner models. I show: (A) it is possible that
the $\omega$-th inner mantle is not a definable class; and (B) it is possible
that the $\omega$-th inner mantle is a definable class but does not satisfy
$\mathsf{AC}$. This answers a pair of questions of Fuchs, Hamkins, and Reitz
[FHR15].
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In this work, we continue to study the formation of particle chains
(clusters) inside the annular sediment during the drying of a colloidal droplet
on a substrate. The average value of the cluster size was determined after
processing experimental data from other authors. We performed a series of
calculations and found the value of the model parameter allowed to get
numerical results agreed with the experiment. Also, a modification of the
previously proposed algorithm is analyzed here.
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Cooperative path-finding in multi-agent systems demands scalable solutions to
navigate agents from their origins to destinations without conflict. Despite
the breadth of research, scalability remains hampered by increased
computational demands in complex environments. This study introduces the
multi-agent RRT* potential field (MA-RRT*PF), an innovative algorithm that
addresses computational efficiency and path-finding efficacy in dense
scenarios. MA-RRT*PF integrates a dynamic potential field with a heuristic
method, advancing obstacle avoidance and optimizing the expansion of random
trees in congested spaces. The empirical evaluations highlight MA-RRT*PF's
significant superiority over conventional multi-agent RRT* (MA-RRT*) in dense
environments, offering enhanced performance and solution quality without
compromising integrity. This work not only contributes a novel approach to the
field of cooperative multi-agent path-finding but also offers a new perspective
for practical applications in densely populated settings where traditional
methods are less effective.
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Consider the discrete 1D Schr\"odinger operator on $\Z$ with an odd $2k$
periodic potential $q$. For small potentials we show that the mapping: $q\to $
heights of vertical slits on the quasi-momentum domain (similar to the
Marchenko-Ostrovski maping for the Hill operator) is a local isomorphism and
the isospectral set consists of $2^k$ distinct potentials. Finally, the
asymptotics of the spectrum are determined as $q\to 0$.
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Kernel techniques are among the most popular and powerful approaches of data
science. Among the key features that make kernels ubiquitous are (i) the number
of domains they have been designed for, (ii) the Hilbert structure of the
function class associated to kernels facilitating their statistical analysis,
and (iii) their ability to represent probability distributions without loss of
information. These properties give rise to the immense success of
Hilbert-Schmidt independence criterion (HSIC) which is able to capture joint
independence of random variables under mild conditions, and permits closed-form
estimators with quadratic computational complexity (w.r.t. the sample size). In
order to alleviate the quadratic computational bottleneck in large-scale
applications, multiple HSIC approximations have been proposed, however these
estimators are restricted to $M=2$ random variables, do not extend naturally to
the $M\ge 2$ case, and lack theoretical guarantees. In this work, we propose an
alternative Nystr\"om-based HSIC estimator which handles the $M\ge 2$ case,
prove its consistency, and demonstrate its applicability in multiple contexts,
including synthetic examples, dependency testing of media annotations, and
causal discovery.
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We compare several ConvNets with different depth and regularization
techniques with multi-unit macaque IT cortex recordings and assess the impact
of the same on representational similarity with the primate visual cortex. We
find that with increasing depth and validation performance, ConvNet features
are closer to cortical IT representations.
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We study a class of noncommutative geometries that give rise to dimensionally
reduced Yang-Mills theories. The emerging geometries describe sets of copies of
an even dimensional manifold. Similarities to the D-branes in string theory are
discussed.
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The bubble structure generated by laser and plasma interactions changes in
size depending on the local plasma density. The self injection electrons
position with respect to wakefield can be controlled by tailoring the
longitudinal plasma density. A regime to enhance the energy of the wakefield
accelerated electrons and improve the beam quality is proposed and achieved
using layered plasmas with increasing densities. Both the wakefield size and
the electron bunch duration are significantly contracted in this regime. The
electrons remain in the strong acceleration phase of the wakefield while their
energy spread decreases because of their tight spatial distribution. An
electron beam of 0.5GeV with less than 0.01 energy spread is obtained through
2.5D PIC simulations.
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SAX J0635.2+0533 is a binary pulsar with a very short pulsation period ($P$ =
33.8 ms) and a high long-term spin down ($\dot P$ $>$ 3.8$\times10^{-13}$ s
s$^{-1}$), which suggests a rotation-powered (instead of an accretion-powered)
nature for this source. While it was discovered at a flux level around
10$^{-11}$ erg cm$^{-2}$ s$^{-1}$, between 2003 and 2004 this source was
detected with XMM-Newton at an average flux of about 10$^{-13}$ erg cm$^{-2}$
s$^{-1}$; moreover, the flux varied of over one order of magnitude on time
scales of a few days, sometimes decreasing below $3\times10^{-14}$ erg
cm$^{-2}$ s$^{-1}$. Since both the rotation-powered and the accretion-powered
scenarios have difficulties to explain these properties, the nature of SAX
J0635.2+0533 is still unclear. Here we report on our recent long-term
monitoring campaign on SAX J0635.2+0533 carried out with Swift and on a
systematic reanalysis of all the RXTE observations performed between 1999 and
2001. We found that during this time interval the source remained almost always
active at a flux level above 10$^{-12}$ erg cm$^{-2}$ s$^{-1}$.
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Ontology can be used for the interpretation of natural language. To construct
an anti-infective drug ontology, one needs to design and deploy a
methodological step to carry out the entity discovery and linking. Medical
synonym resources have been an important part of medical natural language
processing (NLP). However, there are problems such as low precision and low
recall rate. In this study, an NLP approach is adopted to generate candidate
entities. Open ontology is analyzed to extract semantic relations. Six-word
vector features and word-level features are selected to perform the entity
linking. The extraction results of synonyms with a single feature and different
combinations of features are studied. Experiments show that our selected
features have achieved a precision rate of 86.77%, a recall rate of 89.03% and
an F1 score of 87.89%. This paper finally presents the structure of the
proposed ontology and its relevant statistical data.
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We consider the chaotic motion of low-mass bodies in two-body high-order
mean-motion resonances with planets in model planetary systems, and
analytically estimate the Lyapunov and diffusion timescales of the motion in
multiplets of interacting subresonances corresponding to the mean-motion
resonances. We show that the densely distributed (though not overlapping)
high-order mean-motion resonances, when certain conditions on the planetary
system parameters are satisfied, may produce extended planetary chaotic zones
-- "zones of weak chaotization," -- much broader than the well-known planetary
connected chaotic zone, the Wisdom gap. This extended planetary chaotic zone
covers the orbital range between the 2/1 and 1/1 resonances with the planet. On
the other hand, the orbital space inner (closer to the host star) with respect
to the 2/1 resonance location is essentially long-term stable. This difference
arises because the adiabaticity parameter of subresonance multiplets
specifically depends on the particle's orbit size. The revealed effect may
control the structure of planetesimal disks in planetary systems: the orbital
zone between the 2/1 and 1/1 resonances with a planet should be normally free
from low-mass material (only that occasionally captured in the first-order 3/2
or 4/3 resonances may survive); whereas any low-mass population inner to the
2/1 resonance location should be normally long-lived (if not perturbed by
secular resonances, which we do not consider in this study).
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We present the results of work on a hybrid material composed of a tellurite
glass rod doped with nanodiamonds containing nitrogen-vacancy-nitrogen and
paramagnetic nitrogen-vacancy color centers. The reported results include
details on tellurite glass and cane fabrication, confocal and wide-field
imaging of the nanodiamond distribution in their volume, as well as on the
spectroscopic characterization of their fluorescence and Optically Detected
Magnetic Resonance measurements of magnetic fields and temperatures. Magnetic
fields up to 50 G were examined with a sensitivity of 10$^{-5}$ T Hz$^{-1/2}$
whereas temperature measurements were simultaneously performed with a
sensitivity of 74 kHz K$^{-1}$ within the 8 Kelvin range at room temperature.
In that way, we demonstrate the suitability of such systems for fiber magneto-
and thermometry with a reasonable performance already in the form of glass
rods. At the same time, the rods constitute an interesting starting point for
further processing into photonic components such as microstructured fibers or
fiber tapers for the realization of specialized sensing modalities.
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Non-classical correlations arising in complex quantum networks are attracting
growing interest, both from a fundamental perspective and for potential
applications in information processing. In particular, in an entanglement
swapping scenario a new kind of correlations arise, the so-called nonbilocal
correlations that are incompatible with local realism augmented with the
assumption that the sources of states used in the experiment are independent.
In practice, however, bilocality tests impose strict constraints on the
experimental setup and in particular to presence of shared reference frames
between the parties. Here, we experimentally address this point showing that
false positive nonbilocal quantum correlations can be observed even though the
sources of states are independent. To overcome this problem, we propose and
demonstrate a new scheme for the violation of bilocality that does not require
shared reference frames and thus constitute an important building block for
future investigations of quantum correlations in complex networks.
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In perturbative string theory, one is generally interested in asymptotic
observables, such as the S-matrix in flat spacetime, and boundary correlation
functions in anti-de Sitter spacetime. However, there are backgrounds in which
such observables do not exist. We study examples of such backgrounds in 1+1
dimensional string theory. In these examples, the Liouville wall accelerates
and can become spacelike in the past and/or future. When that happens, the
corresponding null infinity, at which the standard scattering states are
defined, is shielded by the Liouville wall. We compute scattering and particle
production amplitudes in these backgrounds in the region in parameter space
where the wall remains timelike, and discuss the continuation of this picture
to the spacelike regime. We also discuss the physics from the point of view of
the dynamics of free fermions in backgrounds with a time-dependent Fermi
surface.
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Masses of fermions in the SO(10) 16-plet are constructed using only the 10,
120 and 126 scalar multiplets. The mass matrices are restricted to be hermitian
and the theory is constructed to have certain assumed quark masses, charged
lepton masses and CKM matrix in accord with data. The remaining free parameters
are found by fitting to light neutrino masses and MSN matrices result as
predictions.
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