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Society needs to prepare for more severe space weather than it has
experienced in the modern technological era. To enable that, we must both
quantify extreme-event characteristics and analyze impacts of lesser events
that are frequent yet severe enough to be informative. Exploratory studies
suggest that economic impacts of a century-level space hurricane and of a
century of lesser space-weather "gales" may turn out to be of the same order of
magnitude. The economic benefits of effective mitigation of the impacts of
space gales may substantially exceed the required investments, even as these
investments provide valuable information to prepare for the worst possible
storms.
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For extracting meaningful topics from texts, their structures should be
considered properly. In this paper, we aim to analyze structured time-series
documents such as a collection of news articles and a series of scientific
papers, wherein topics evolve along time depending on multiple topics in the
past and are also related to each other at each time. To this end, we propose a
dynamic and static topic model, which simultaneously considers the dynamic
structures of the temporal topic evolution and the static structures of the
topic hierarchy at each time. We show the results of experiments on collections
of scientific papers, in which the proposed method outperformed conventional
models. Moreover, we show an example of extracted topic structures, which we
found helpful for analyzing research activities.
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We characterize the response of isolated single- (SWNT) and multi-wall (MWNT)
carbon nanotubes and bundles to static electric fields using first-principles
calculations and density-functional theory. The longitudinal polarizability of
SWNTs scales as the inverse square of the band gap, while in MWNTs and bundles
it is given by the sum of the polarizabilities of the constituent tubes. The
transverse polarizability of SWNTs is insensitive to band gaps and chiralities
and is proportional to the square of the effective radius; in MWNTs the outer
layers dominate the response. The transverse response is intermediate between
metallic and insulating, and a simple electrostatic model based on a
scale-invariance relation captures accurately the first-principles results.
Dielectric response of non-chiral SWNTs in both directions remains linear up to
very high values of applied field.
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Recently, the significant achievements have been made in skeleton-based human
action recognition with the emergence of graph convolutional networks (GCNs).
However, the state-of-the-art (SOTA) models used for this task focus on
constructing more complex higher-order connections between joint nodes to
describe skeleton information, which leads to complex inference processes and
high computational costs. To address the slow inference speed caused by overly
complex model structures, we introduce re-parameterization and
over-parameterization techniques to GCNs and propose two novel high-performance
inference GCNs, namely HPI-GCN-RP and HPI-GCN-OP. After the completion of model
training, model parameters are fixed. HPI-GCN-RP adopts re-parameterization
technique to transform high-performance training model into fast inference
model through linear transformations, which achieves a higher inference speed
with competitive model performance. HPI-GCN-OP further utilizes
over-parameterization technique to achieve higher performance improvement by
introducing additional inference parameters, albeit with slightly decreased
inference speed. The experimental results on the two skeleton-based action
recognition datasets demonstrate the effectiveness of our approach. Our
HPI-GCN-OP achieves performance comparable to the current SOTA models, with
inference speeds five times faster. Specifically, our HPI-GCN-OP achieves an
accuracy of 93\% on the cross-subject split of the NTU-RGB+D 60 dataset, and
90.1\% on the cross-subject benchmark of the NTU-RGB+D 120 dataset. Code is
available at github.com/lizaowo/HPI-GCN.
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In the last decade we have witnessed a rapid growth in data center systems,
requiring new and highly complex networking devices. The need to refresh
networking infrastructure whenever new protocols or functions are introduced,
and the increasing costs that this entails, are of a concern to all data center
providers. New generations of Systems on Chip (SoC), integrating
microprocessors and higher bandwidth interfaces, are an emerging solution to
this problem. These devices permit entirely new systems and architectures that
can obviate the replacement of existing networking devices while enabling
seamless functionality change. In this work, we explore open source, RISC
based, SoC architectures with high performance networking capabilities. The
prototype architectures are implemented on the NetFPGA-SUME platform. Beyond
details of the architecture, we also describe the hardware implementation and
the porting of operating systems to the platform. The platform can be exploited
for the development of practical networking appliances, and we provide use case
examples.
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The primary scientific target of the CMB polarization experiments that are
currently being built and proposed is the detection of primordial tensor
perturbations. As a byproduct, these instruments will significantly improve
constraints on cosmic birefringence, or the rotation of the CMB polarization
plane. If convincingly detected, cosmic birefringence would be a dramatic
manifestation of physics beyond the standard models of particle physics and
cosmology. We forecast the bounds on the cosmic polarization rotation (CPR)
from the upcoming ground-based Simons Observatory (SO) and the space-based
LiteBIRD experiments, as well as a "fourth generation" ground-based CMB
experiment like CMB-S4 and the mid-cost space mission PICO. We examine the
detectability of both a stochastic anisotropic rotation field and an isotropic
rotation by a constant angle. CPR induces new correlations of CMB observables,
including spectra of parity-odd type in the case of isotropic CPR, and
mode-coupling correlations in the anisotropic rotation case. We find that
LiteBIRD and SO will reduce the 1$\sigma$ bound on the isotropic CPR from the
current value of 30 arcmin to 1.5 and 0.6 arcmin, respectively, while
CMB-S4-like and PICO will reduce it to $\sim 0.1$ arcmin. The bounds on the
amplitude of a scale-invariant CPR spectrum will be reduced by 1, 2 and 3
orders of magnitude by LiteBIRD, SO and CMB-S4-like/PICO, respectively. We
discuss implications of the forecasted CPR bounds for pseudoscalar fields,
primordial magnetic fields (PMF), and violations of Lorentz invariance. We find
that CMB-S4-like and PICO can reduce the 1$\sigma$ bound on the amplitude of
the scale-invariant PMF from 1 nG to 0.1 nG, while also probing the magnetic
field of the Milky Way. They will also significantly improve bounds on the
axion-photon coupling, placing stringent constraints on the string theory
axions.
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We present a high-temperature expansion (HTE) of the magnetic susceptibility
and specific heat data of Melzi et al. on Li2VOSiO4 [Phys. Rev. B 64, 024409
(2001)]. The data are very well reproduced by the J1-J2 Heisenberg model on the
square lattice with exchange energies J1=1.25+-0.5 K and J2=5.95+-0.2 K. The
maximum of the specific heat Cv^{max}(T_{max}) is obtained as a function J2/J1
from an improved method based on HTE.
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Heinz Hopf's famous fibrations of the 2n+1-sphere by great circles, the
4n+3-sphere by great 3-spheres, and the 15-sphere by great 7-spheres have a
number of interesting properties. Besides providing the first examples of
homotopically nontrivial maps from one sphere to another sphere of lower
dimension, they all share two striking features:
(1) Their fibers are parallel, in the sense that any two fibers are a
constant distance apart, and
(2) The fibrations are highly symmetric. For example, there is a
fiber-preserving isometry of each total space which takes any given fiber to
any other one.
Hopf fibrations have been characterized up to isometry by the first property
above, initially among all fibrations of spheres by great subspheres, and later
in the stronger sense among all fibrations of spheres by smooth subspheres.
In this paper, we show that the Hopf fibrations are also characterized by
their "fiberwise homogeneity" expressed above in (2), and in the strong sense
among all fibrations of spheres by smooth subspheres.
In the special case of the 3-sphere fibered by great circles, we prove
something stronger. We prove that a fibration of a connected open set by great
circles which is locally fiberwise homogeneous is part of a Hopf fibration.
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We use a one-dimensional optical lattice to modify the dispersion relation of
atomic matter waves. Four-wave mixing in this situation produces atom pairs in
two well defined beams. We show that these beams present a narrow momentum
correlation, that their momenta are precisely tunable, and that this pair
source can be operated both in the regime of low mode occupancy and of high
mode occupancy.
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Penrose et al. investigated the physical incoherence of the spacetime with
negative mass via the bending of light. Precise estimates of time-delay of null
geodesics were needed and played a pivotal role in their proof. In this paper,
we construct an intermediate diagonal metric and make a reduction of this
problem to a causality comparison in the compactified spacetimes regarding
timelike connectedness near the conformal infinities. This different approach
allows us to avoid encountering the difficulties and subtle issues Penrose et
al. met. It provides a new, substantially simple, and physically natural
non-PDE viewpoint to understand the positive mass theorem. This elementary
argument modestly applies to asymptotically flat solutions which are vacuum and
stationary near infinity.
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Through the introduction of auxiliary fermions, or an enlarged spin space,
one can map local fermion Hamiltonians onto local spin Hamiltonians, at the
expense of introducing a set of additional constraints. We present a
variational Monte-Carlo framework to study fermionic systems through
higher-dimensional (>1D) Jordan-Wigner transformations. We provide exact
solutions to the parity and Gauss-law constraints that are encountered in
bosonization procedures. We study the $t$-$V$ model in 2D and demonstrate how
both the ground state and the low-energy excitation spectra can be retrieved in
combination with neural network quantum state ansatze.
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We demonstrate how the separation of the total energy of a self-bound system
into a functional of the internal one-body Fermionic density and a function of
an arbitrary wave vector describing the center-of-mass kinetic energy can be
used to set-up an "internal" Kohn-Sham scheme.
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We experimentally and numerically investigate the exchange interaction of the
yellow excitons in cuprous oxide. By varying the material parameters in the
numerical calculations, we can interpret experimental findings and understand
their origin in the complex band structure and central-cell corrections. In
particular, we experimentally observe the reversal of the ortho- and
paraexciton for the $2S$ yellow exciton, and explain this phenomenon by an
avoided crossing with the green $1S$ orthoexciton in a detailed numerical
analysis. Furthermore, we discuss the exchange splitting as a function of the
principal quantum number $n$ and its deviation from the $n^{-3}$ behavior
expected from a hydrogenlike model. We also explain why the observed exchange
splitting of the green $1S$ exciton is more than twice the splitting of the
yellow $1S$ state.
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Let $\Lambda$ be an Artin algebra. In 2014, T. Adachi, O. Iyama and I. Reiten
proved that the torsion funtorially finite classes in $\mathrm{mod}\,(\Lambda)$
can be described by the $\tau$-tilting theory. The aim of this paper is to
introduce the notion of $F$-torsion class in $\mathrm{mod}\,(\Lambda)$, where
$F$ is an additive subfunctor of $\mathrm{Ext}^1_\Lambda,$ and to characterize
when these clases are preenveloping and $F$-preenveloping. In order to do that,
we introduce the notion of $F$-presilting $\Lambda$-module. The latter is both
a generalization of $\tau$-rigid and $F$-tilting in $\mathrm{mod}(\Lambda).$
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It is challenging for humans to enable visual knowledge discovery in data
with more than 2-3 dimensions with a naked eye. This chapter explores the
efficiency of discovering predictive machine learning models interactively
using new Elliptic Paired coordinates (EPC) visualizations. It is shown that
EPC are capable to visualize multidimensional data and support visual machine
learning with preservation of multidimensional information in 2-D. Relative to
parallel and radial coordinates, EPC visualization requires only a half of the
visual elements for each n-D point. An interactive software system EllipseVis,
which is developed in this work, processes high-dimensional datasets, creates
EPC visualizations, and produces predictive classification models by
discovering dominance rules in EPC. By using interactive and automatic
processes it discovers zones in EPC with a high dominance of a single class.
The EPC methodology has been successful in discovering non-linear predictive
models with high coverage and precision in the computational experiments. This
can benefit multiple domains by producing visually appealing dominance rules.
This chapter presents results of successful testing the EPC non-linear
methodology in experiments using real and simulated data, EPC generalized to
the Dynamic Elliptic Paired Coordinates (DEPC), incorporation of the weights of
coordinates to optimize the visual discovery, introduction of an alternative
EPC design and introduction of the concept of incompact machine learning
methodology based on EPC/DEPC.
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The present paper has two objectives. On one side, we develop and test
numerically divergence free Virtual Elements in three dimensions, for variable
``polynomial'' order. These are the natural extension of the two-dimensional
divergence free VEM elements, with some modification that allows for a better
computational efficiency. We test the element's performance both for the Stokes
and (diffusion dominated) Navier-Stokes equation.
The second, and perhaps main, motivation is to show that our scheme, also in
three dimensions, enjoys an underlying discrete Stokes complex structure. We
build a pair of virtual discrete spaces based on general polytopal partitions,
the first one being scalar and the second one being vector valued, such that
when coupled with our velocity and pressure spaces, yield a discrete Stokes
complex.
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The van der Waals force established between two surfaces plays a central role
in many phenomena, such as adhesion or friction. However, the dependence of
this forces on the distance of separation between plates is very complex. Two
widely different non-retarded and retarded regimes are well known, but these
have been traditionally studied separately. Much less is known about the
important experimentally accesible cross-over regime. In this study, we provide
analytical approximations for the van der Waals forces between two plates that
interpolates exactly between the short distance and long distance behavior, and
provides new insight into the crossover from London to Casimir forces at finite
temperature. At short distance, where the behavior is dominated by non-retarded
interactions, we work out a very accurate simplified approximation for the
Hamaker constant which adopts analytical form for both the Drude and Lorentz
models of dielectric response. We apply our analytical expressions for the
study of forces between metallic plates, and observe very good agreement with
exact results from numerical calculations. Our results show that contributions
of interband transitions remain important in the experimentally accessible
regime of decades nm for several metals, including gold.
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By using a correlated many body method and using the realistic van der Waals
potential we study several statistical measures like the specific heat,
transition temperature and the condensate fraction of the interacting Bose gas
trapped in an anharmonic potential. As the quadratic plus a quartic confinement
makes the trap more tight, the transition temperature increases which makes
more favourable condition to achieve Bose-Einstein condensation (BEC)
experimentally. BEC in 3D isotropic harmonic potential is also critically
studied, the correction to the critical temperature due to finite number of
atoms and also the correction due to inter-atomic interaction are calculated by
the correlated many-body method. Comparison and discussion with the mean-field
results are presented.
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For velocity-jump Markov processes with equivariant internal dynamics, we
remark that population distributions are invariant. This provides a
formalization of the fact that FCD (scale) and other symmetry invariant systems
perform identical spatial searches under input transformations.
|
We report measurements of Rabi oscillations and spectroscopic coherence times
in an Al/AlOx/Al and three Nb/AlOx/Nb dc SQUID phase qubits. One junction of
the SQUID acts as a phase qubit and the other junction acts as a
current-controlled nonlinear isolating inductor, allowing us to change the
coupling to the current bias leads in situ by an order of magnitude. We found
that for the Al qubit a spectroscopic coherence time T2* varied from 3 to 7 ns
and the decay envelope of Rabi oscillations had a time constant T' = 25 ns on
average at 80 mK. The three Nb devices also showed T2* in the range of 4 to 6
ns, but T' was 9 to 15 ns, just about 1/2 the value we found in the Al device.
For all the devices, the time constants were roughly independent of the
isolation from the bias lines, implying that noise and dissipation from the
bias leads were not the principal sources of dephasing and inhomogeneous
broadening.
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We say that a group has property $R_{\infty}$ if any group automorphism has
an infinite number of twisted conjugacy classes. Fel'shtyn and Goncalves prove
that the solvable Baumslag-Solitar groups BS(1,m) have property $R_{\infty}$.
We define a solvable generalization $\Gamma(S)$ of these groups which we show
to have property $R_{\infty}$. We then show that property $R_{\infty}$ is
geometric for these groups, that is, any group quasi-isometric to $\Gamma(S)$
has property $R_{\infty}$ as well.
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Navigating our physical environment requires changing directions and turning.
Despite its ecological importance, we do not have a unified theoretical account
of non-straight-line human movement. Here, we present a unified optimality
criterion that predicts disparate non-straight-line walking phenomena, with
straight-line walking as a special case. We first characterized the metabolic
cost of turning, deriving the cost landscape as a function of turning radius
and rate. We then generalized this cost landscape to arbitrarily complex
trajectories, allowing the velocity direction to deviate from body orientation
(holonomic walking). We used this generalized optimality criterion to
mathematically predict movement patterns in multiple contexts of varying
complexity: walking on prescribed paths, turning in place, navigating an angled
corridor, navigating freely with end-point constraints, walking through doors,
and navigating around obstacles. In these tasks, humans moved at speeds and
paths predicted by our optimality criterion, slowing down to turn and never
using sharp turns. We show that the shortest path between two points is,
counterintuitively, often not energy optimal, and indeed, humans do not use the
shortest path in such cases. Thus, we have obtained a unified theoretical
account that predicts human walking paths and speeds in diverse contexts. Our
model focuses on walking in healthy adults; future work could generalize this
model to other human populations, other animals, and other locomotor tasks.
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The present calculations in perturbative QCD reach the order $\alpha_s^4$ for
several correlators calculated to five loops, and the huge computational
difficulties make unlikely the full six-loop calculation in the near future.
This situation has practical consequences, in particular the treatment of the
higher orders of the perturbation series for the current-current correlator of
light quarks is one of the main sources of errors in the extraction of the
strong coupling from hadronic $\tau$ decays. Several approximate estimates of
the next coefficients of the corresponding Adler function have been proposed,
using various arguments. In the present paper we exploit the analytic structure
of the Adler function in the Borel plane, which allows the definition of an
improved perturbative expansion in powers of a conformal variable which maps
the cut Borel plane onto the unit disk. The new expansions converge in a larger
domain of the Borel plane and, when reexpanded in powers of the strong
coupling, yield definite values for the higher perturbative coefficients. We
apply the method to the Adler function in the $\bar{\rm MS}$ scheme and to a
suitable weighted integral of this function in the complex $s$ plane, chosen
such as to avoid model-dependent assumptions on analyticity. Our results
$c_{5,1}=287 \pm 40$, $c_{6,1}=2948 \pm 208$ and $c_{7,1}=(1.89 \pm 0.75)\times
10^4$, for the six, seven and eigth-loop coefficients, respectively, agree with
a recent determination from Pad\'e approximants applied to the perturbative
expansion of the hadronic $\tau$ decay rate.
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We provide a concrete realization of the cluster algebras associated with
Q-systems as amalgamations of cluster structures on double Bruhat cells in
simple algebraic groups. For nonsimply-laced groups, this provides a
cluster-algebraic formulation of Q-systems of twisted type. It also yields a
uniform proof of the discrete integrability of these Q-systems by identifying
them with the dynamics of factorization mappings on quotients of double Bruhat
cells. On the double Bruhat cell itself, we find these dynamics are closely
related to those of the Fomin-Zelevinsky twist map. This leads to an explicit
formula expressing twisted cluster variables as Laurent monomials in the
untwisted cluster variables obtained from the corresponding mutation sequence.
This holds for Coxeter double Bruhat cells in any symmetrizable Kac-Moody
group, and we show that in affine type the analogous factorization mapping is
also integrable.
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The QCD sector of the system SANC is presented. QCD theoretical predictions
for several processes of high energy interactions of fundamental particles at
the one-loop precision level for up to some 3- and 4-particle processes are
implemented.
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The content of this paper can be roughly organized into a three-level
hierarchy of generality. At the first, most general level, we introduce a new
language which allows us to express various categorical structures in a
systematic and explicit manner in terms of so-called 2-schemes. Although
2-schemes can formalize categorical structures such as symmetric monoidal
categories, they are not limited to this, and can be used to define structures
with no categorical analogue. Most categorical structures come with an
effective graphical calculus such as string diagrams for symmetric monoidal
categories, and the same is true more generally for interesting 2-schemes. In
this work, we focus on one particular non-categorical 2-scheme, whose instances
we refer to as tensor types. At the second level of the hierarchy, we work out
different flavors of this 2-scheme in detail. The effective graphical calculus
of tensor types is that of tensor networks or Penrose diagrams, that is, string
diagrams without a flow of time. As such, tensor types are similar to compact
closed categories, though there are various small but potentially important
differences. Also, the two definitions use completely different mechanisms
despite both being examples of 2-schemes. At the third level of the hierarchy,
we provide a long list of different families of concrete tensor types, in a way
which makes them accessible to concrete computations, motivated by their
potential use in physics. Different tensor types describe different types of
physical models, such as classical or quantum physics, deterministic or
statistical physics, many-body or single-body physics, or matter with or
without symmetries or fermions.
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We give formulae for the Chen-Ruan orbifold cohomology for the orbifolds
given by a Bianchi group acting on complex hyperbolic 3-space. The Bianchi
groups are the arithmetic groups PSL\_2(A), where A is the ring of integers in
an imaginary quadratic number field. The underlying real orbifolds which help
us in our study, given by the action of a Bianchi group on real hyperbolic
3-space (which is a model for its classifying space for proper actions), have
applications in physics.We then prove that, for any such orbifold, its
Chen-Ruan orbifold cohomology ring is isomorphic to the usual cohomology ring
of any crepant resolution of its coarse moduli space.By vanishing of the
quantum corrections, we show that this result fits in with Ruan's Cohomological
Crepant Resolution Conjecture.
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In this work, we leverage advances in sparse coding techniques to reduce the
number of trainable parameters in a fully connected neural network. While most
of the works in literature impose $\ell_1$ regularization, DropOut or
DropConnect techniques to induce sparsity, our scheme considers feature
importance as a criterion to allocate the trainable parameters (resources)
efficiently in the network. Even though sparsity is ensured, $\ell_1$
regularization requires training on all the resources in a deep neural network.
The DropOut/DropConnect techniques reduce the number of trainable parameters in
the training stage by dropping a random collection of neurons/edges in the
hidden layers. However, both these techniques do not pay heed to the underlying
structure in the data when dropping the neurons/edges. Moreover, these
frameworks require a storage space equivalent to the number of parameters in a
fully connected neural network. We address the above issues with a more
structured architecture inspired from spatially-coupled sparse constructions.
The proposed architecture is shown to have a performance akin to a conventional
fully connected neural network with dropouts, and yet achieving a $94\%$
reduction in the training parameters. Extensive simulations are presented and
the performance of the proposed scheme is compared against traditional neural
network architectures.
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Magneto-Raman scattering experiments from the surface of graphite reveal
novel features associated to purely electronic excitations which are observed
in addition to phonon-mediated resonances. Graphene-like and graphite domains
are identified through experiments with $\sim 1\mu m$ spatial resolution
performed in magnetic fields up to 32T. Polarization resolved measurements
emphasize the characteristic selection rules for electronic transitions in
graphene. Graphene on graphite displays the unexpected hybridization between
optical phonon and symmetric across the Dirac point inter Landau level
transitions. The results open new experimental possibilities - to use light
scattering methods in studies of graphene under quantum Hall effect conditions.
|
In a context of constant evolution and proliferation of AI technology,Hybrid
Intelligence is gaining popularity to refer a balanced coexistence between
human and artificial intelligence. The term has been extensively used in the
past two decades to define models of intelligence involving more than one
technology. This paper aims to provide (i) a concise and focused overview of
the adoption of Ontology in the broad context of Hybrid Intelligence regardless
of its definition and (ii) a critical discussion on the possible role of
Ontology to reduce the gap between human and artificial intelligence within
hybrid intelligent systems. Beside the typical benefits provided by an
effective use of ontologies, at a conceptual level, the conducted analysis has
pointed out a significant contribution of Ontology to improve quality and
accuracy, as well as a more specific role to enable extended interoperability,
system engineering and explainable/transparent systems. Additionally, an
application-oriented analysis has shown a significant role in present systems
(70+% of the cases) and, potentially, in future systems. However, despite the
relatively consistent number of papers on the topic, a proper holistic
discussion on the establishment of the next generation of hybrid-intelligent
environments with a balanced co-existence of human and artificial intelligence
is fundamentally missed in literature. Last but not the least, there is
currently a relatively low explicit focus on automatic reasoning and inference
in hybrid intelligent systems.
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Let G be a finite group of automorphisms of a nonsingular complex threefold M
such that the canonical bundle omega_M is locally trivial as a G-sheaf. We
prove that the Hilbert scheme Y=GHilb M parametrising G-clusters in M is a
crepant resolution of X=M/G and that there is a derived equivalence (Fourier-
Mukai transform) between coherent sheaves on Y and coherent G-sheaves on M.
This identifies the K theory of Y with the equivariant K theory of M, and thus
generalises the classical McKay correspondence. Some higher dimensional
extensions are possible.
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In this paper, consensus-based Kalman filtering is extended to deal with the
problem of joint target tracking and sensor self-localization in a distributed
wireless sensor network. The average weighted Kullback-Leibler divergence,
which is a function of the unknown drift parameters, is employed as the cost to
measure the discrepancy between the fused posterior distribution and the local
distribution at each sensor. Further, a reasonable approximation of the cost is
proposed and an online technique is introduced to minimize the approximated
cost function with respect to the drift parameters stored in each node. The
remarkable features of the proposed algorithm are that it needs no additional
data exchanges, slightly increased memory space and computational load
comparable to the standard consensus-based Kalman filter. Finally, the
effectiveness of the proposed algorithm is demonstrated through simulation
experiments on both a tree network and a network with cycles as well as for
both linear and nonlinear sensors.
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We provide new sufficient conditions for the finiteness of the optimal value
and existence of solutions to a general problem of minimizing a proper closed
function over a nonempty closed set. The conditions require an asymptotically
bounded decay of a function, a relaxation of p-supercoercivity, and a certain
relation for the asymptotic cone of the constraint set and the asymptotic
function of the objective function. Our analysis combines these conditions with
a regularization technique. We refine the notion of retractive directions of a
set, extend its definition to functions, and establish some basic relations for
such directions for both sets and functions. Using these tools, we provide
existence of solutions results that generalize many of the results in the
literature for both non-convex and convex problems.
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Unstructured text provides decision-makers with a rich data source in many
domains, ranging from product reviews in retail to nursing notes in healthcare.
To leverage this information, words are typically translated into word
embeddings -- vectors that encode the semantic relationships between words --
through unsupervised learning algorithms such as matrix factorization. However,
learning word embeddings from new domains with limited training data can be
challenging, because the meaning/usage may be different in the new domain,
e.g., the word ``positive'' typically has positive sentiment, but often has
negative sentiment in medical notes since it may imply that a patient tested
positive for a disease. In practice, we expect that only a small number of
domain-specific words may have new meanings. We propose an intuitive two-stage
estimator that exploits this structure via a group-sparse penalty to
efficiently transfer learn domain-specific word embeddings by combining
large-scale text corpora (such as Wikipedia) with limited domain-specific text
data. We bound the generalization error of our transfer learning estimator,
proving that it can achieve high accuracy with substantially less
domain-specific data when only a small number of embeddings are altered between
domains. Furthermore, we prove that all local minima identified by our
nonconvex objective function are statistically indistinguishable from the
global minimum under standard regularization conditions, implying that our
estimator can be computed efficiently. Our results provide the first bounds on
group-sparse matrix factorization, which may be of independent interest. We
empirically evaluate our approach compared to state-of-the-art fine-tuning
heuristics from natural language processing.
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This work focuses on the invariance of important properties between
continuous and discrete models of systems which can be useful in the control
design of large-scale systems and their software implementations. In
particular, this paper discusses the relationships between the QSR
dissipativity of a continuous state dynamical system and of its abstractions
obtained through approximate input-output simulation relations. First,
conditions to guarantee the dissipativity of the continuous system from its
abstractions are provided. The reverse problem of determining the Q, S and R
dissipativity matrices of the abstract system from that of the continuous
system is also considered. Results characterizing the change in the
dissipativity matrices are provided when the system abstraction is obtained.
Since, under certain conditions, QSR dissipative systems are known to be
stable, the results of this paper can be used to construct stable system
abstractions as well. In the second part of this paper, we analyze the
dissipativity of the approximate feedback composition of a continuous dynamical
system and a discrete controller. We present illustrative examples to
demonstrate the results of this paper.
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An unbiased search for debris discs around nearby Sun-like stars is reported.
Thirteen G-dwarfs at 12-15 parsecs distance were searched at 850 $\umu$m
wavelength, and a disc is confirmed around HD 30495. The estimated dust mass is
0.008 M$_{\oplus}$ with a net limit $\la 0.0025$ M$_{\oplus}$ for the average
disc of the other stars. The results suggest there is not a large missed
population of substantial cold discs around Sun-like stars -- HD 30495 is a
bright rather than unusually cool disc, and may belong to a few hundred Myr-old
population of greater dust luminosity. The far-infared and millimetre survey
data for Sun-like stars are well fitted by either steady state or stirred
models, provided that typical comet belts are comparable in size to that in the
Solar System.
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Mean-field games with absorption is a class of games, that have been
introduced in Campi and Fischer (2018) and that can be viewed as natural limits
of symmetric stochastic differential games with a large number of players who,
interacting through a mean-field, leave the game as soon as their private
states hit some given boundary. In this paper, we push the study of such games
further, extending their scope along two main directions. First, we allow the
state dynamics and the costs to have a very general, possibly
infinite-dimensional, dependence on the (non-normalized) empirical
sub-probability measure of the survivors' states. This includes the
particularly relevant case where the mean-field interaction among the players
is done through the empirical measure of the survivors together with the
fraction of absorbed players over time. Second, the boundedness of coefficients
and costs has been considerably relaxed including drift and costs with linear
growth in the state variables, hence allowing for more realistic dynamics for
players' private states. We prove the existence of solutions of the MFG in
strict as well as relaxed feedback form, and we establish uniqueness of the MFG
solutions under monotonicity conditions of Lasry-Lions type. Finally, we show
in a setting with finite-dimensional interaction that such solutions induce
approximate Nash equilibria for the $N$-player game with vanishing error as
$N\rightarrow \infty$.
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With the research into development of quadruped robots picking up pace,
learning based techniques are being explored for developing locomotion
controllers for such robots. A key problem is to generate leg trajectories for
continuously varying target linear and angular velocities, in a stable manner.
In this paper, we propose a two pronged approach to address this problem.
First, multiple simpler policies are trained to generate trajectories for a
discrete set of target velocities and turning radius. These policies are then
augmented using a higher level neural network for handling the transition
between the learned trajectories. Specifically, we develop a neural
network-based filter that takes in target velocity, radius and transforms them
into new commands that enable smooth transitions to the new trajectory. This
transformation is achieved by learning from expert demonstrations. An
application of this is the transformation of a novice user's input into an
expert user's input, thereby ensuring stable manoeuvres regardless of the
user's experience. Training our proposed architecture requires much less expert
demonstrations compared to standard neural network architectures. Finally, we
demonstrate experimentally these results in the in-house quadruped Stoch 2.
|
Convolutional Neural Networks (CNNs) have revolutionized image classification
by extracting spatial features and enabling state-of-the-art accuracy in
vision-based tasks. The squeeze and excitation network proposed module gathers
channelwise representations of the input. Multilayer perceptrons (MLP) learn
global representation from the data and in most image classification models
used to learn extracted features of the image. In this paper, we introduce a
novel aggregated multilayer perceptron, a multi-branch dense layer, within the
Squeeze excitation residual module designed to surpass the performance of
existing architectures. Our approach leverages a combination of squeeze
excitation network module with dense layers. This fusion enhances the network's
ability to capture channel-wise patterns and have global knowledge, leading to
a better feature representation. This proposed model has a negligible increase
in parameters when compared to SENet. We conduct extensive experiments on
benchmark datasets to validate the model and compare them with established
architectures. Experimental results demonstrate a remarkable increase in the
classification accuracy of the proposed model.
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The conditions necessary for a nanotube junction connecting a metallic and
semiconducting nanotube to rectify the current are theoretically investigated.
A tight binding model is used for the analysis, which includes the Hartree-Fock
approximation and the Green's function method.
It is found that the junction has a behavior similar to the backward diode if
the gate electrode is located nearby and the Fermi level of the semiconducting
tube is near the gap.
Such a junction would be advantageous since the required length for the
rectification could be reduced.
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Synthesizing natural head motion to accompany speech for an embodied
conversational agent is necessary for providing a rich interactive experience.
Most prior works assess the quality of generated head motion by comparing them
against a single ground-truth using an objective metric. Yet there are many
plausible head motion sequences to accompany a speech utterance. In this work,
we study the variation in the perceptual quality of head motions sampled from a
generative model. We show that, despite providing more diverse head motions,
the generative model produces motions with varying degrees of perceptual
quality. We finally show that objective metrics commonly used in previous
research do not accurately reflect the perceptual quality of generated head
motions. These results open an interesting avenue for future work to
investigate better objective metrics that correlate with human perception of
quality.
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In this paper, we shall investigate the almost sure limits of the largest and
smallest eigenvalues of a quaternion sample covariance matrix. Suppose that
$\mathbf X_n$ is a $p\times n$ matrix whose elements are independent quaternion
variables with mean zero, variance 1 and uniformly bounded fourth moments.
Denote $\mathbf S_n=\frac{1}{n}\mathbf X_n\mathbf X_n^*$. In this paper, we
shall show that $s_{\max}\left(\mathbf S_n\right)=s_{p}\left(\mathbf
S_n\right)\to\left(1+\sqrt y\right)^2, a.s.$ and $s_{\min}\left(\mathbf
S_n\right)\to\left(1-\sqrt y\right)^2,a.s.$ as $n\to\infty$, where $y=\lim
p/n$,
$s_1\left(\mathbf S_n\right)\le\cdots\le s_{p}\left(\mathbf S_n\right)$ are
the eigenvalues of $\mathbf{S}_n$, $s_{\min}\left(\mathbf
S_n\right)=s_{p-n+1}\left(\mathbf S_n\right)$ when $p>n$ and
$s_{\min}\left(\mathbf S_n\right)=s_1\left(\mathbf S_n\right)$ when $p\le n$.
We also prove that the set of conditions are necessary for
$s_{\max}\left(\mathbf S_n\right)\to\left(1+\sqrt y\right)^2, a.s.$ when the
entries of $\mathbf {X}_n$ are i. i. d.
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We are using archived data from HST of transiting exoplanet L~98-59~b to
place constraints on its potentially hot atmosphere. We analyze the data from
five transit visits and extract the final combined transmission spectrum using
Iraclis. Then we use the inverse atmospheric retrieval code TauREx to analyze
the combined transmission spectrum. There is a weak absorption feature near
1.40~$\mu m$ and 1.55~$\mu m$ in the transmission spectrum, which can be
modeled by a cloudy atmosphere with abundant HCN. However, the unrealistically
high abundance of HCN derived cannot be explained by any equilibrium chemical
model with reasonable assumptions. Thus, the likeliest scenario is that
L~98-59~b has a flat, featureless transmission spectrum in the WFC3/G141
bandpass due to a thin atmosphere with high mean molecular weight, an
atmosphere with an opaque aerosol layer, or no atmosphere, and it is very
unlikely for L~98-59~b to have a clear hydrogen-dominated primary atmosphere.
Due to the narrow wavelength coverage and low spectral resolution of HST/WFC3
G141 grism observation, we cannot tell these different scenarios apart. Our
simulation shows future higher precision measurements over wider wavelengths
from the James Webb Space Telescope (JWST) can be used to better characterize
the planetary atmosphere of L~98-59~b.
|
Herein it is shown that in order to study the statistical properties of DNA
sequences in bacterial chromosomes it suffices to consider only one half of the
chromosome because they are similar to its corresponding complementary sequence
in the other half. This is due to the inverse bilateral symmetry of bacterial
chromosomes. Contrary to the classical result that DNA coding regions of
bacterial genomes are purely uncorrelated random sequences, here it is shown,
via a renormalization group approach, that DNA random fluctuations of single
bases are modulated by log-periodic variations. Distance series of triplets
display long-range correlations in each half of the intact chromosome and in
intronless protein-coding sequences, or both long-range correlations and
log-periodic modulations along the whole chromosome. Hence scaling analyses of
distance series of DNA sequences have to consider the functional units of
bacterial chromosomes.
|
We define a new topological polynomial extending the Bollobas-Riordan one,
which obeys a four-term reduction relation of the deletion/contraction type and
has a natural behavior under partial duality. This allows to write down a
completely explicit combinatorial evaluation of the polynomials, occurring in
the parametric representation of the non-commutative Grosse-Wulkenhaar quantum
field theory. An explicit solution of the parametric representation for
commutative field theories based on the Mehler kernel is also provided.
|
We formulate a self-consistent field theory for polyelectrolyte brushes in
the presence of counterions. We numerically solve the self-consistent field
equations and study the monomer density profile, the distribution of
counterions, and the total charge distribution. We study the scaling relations
for the brush height and compare them to the prediction of other theories. We
find a weak dependence of the brush height on the grafting density.We fit the
counterion distribution outside the brush by the Gouy-Chapman solution for a
virtual charged wall. We calculate the amount of counterions outside the brush
and find that it saturates as the charge of the polyelectrolytes increases.
|
We introduce the concept of an infinite cochain sequence and initiate a
theory of homological algebra for them. We show how these sequences simplify
and improve the construction of infinite coclass families (as introduced by
Eick and Leedham-Green) and how they apply in proving that almost all groups in
such a family have equivalent Quillen categories. We also include some examples
of infinite families of p-groups from different coclass families that have
equivalent Quillen categories.
|
We introduce a notion of connected perimeter for planar sets defined as the
lower semi-continuous envelope of perimeters of approximating sets which are
measure-theoretically connected. A companion notion of simply connected
perimeter is also studied. We prove a representation formula which links the
connected perimeter, the classical perimeter, and the length of suitable
Steiner trees. We also discuss the application of this notion to the existence
of solutions to a nonlocal minimization problem.
|
Background has played an important role in X-ray missions, limiting the
exploitation of science data in several and sometimes unexpected ways. In this
presentation I review past X-ray missions focusing on some important lessons we
can learn from them. I then go on discussing prospects for overcoming
background related limitations in future ones.
|
We report on our findings of the bright, pulsating, helium atmosphere white
dwarf GD 358, based on time-resolved optical spectrophotometry. We identify 5
real pulsation modes and at least 6 combination modes at frequencies consistent
with those found in previous observations. The measured Doppler shifts from our
spectra show variations with amplitudes of up to 5.5 km/s at the frequencies
inferred from the flux variations. We conclude that these are variations in the
line-of-sight velocities associated with the pulsational motion. We use the
observed flux and velocity amplitudes and phases to test theoretical
predictions within the convective driving framework, and compare these with
similar observations of the hydrogen atmosphere white dwarf pulsators (DAVs).
The wavelength dependence of the fractional pulsation amplitudes (chromatic
amplitudes) allows us to conclude that all five real modes share the same
spherical degree, most likely, l=1. This is consistent with previous
identifications based solely on photometry. We find that a high signal-to-noise
mean spectrum on its own is not enough to determine the atmospheric parameters
and that there are small but significant discrepancies between the observations
and model atmospheres. The source of these remains to be identified. While we
infer T_eff=24kK and log g~8.0 from the mean spectrum, the chromatic
amplitudes, which are a measure of the derivative of the flux with respect to
the temperature, unambiguously favour a higher effective temperature, 27kK,
which is more in line with independent determinations from ultra-violet
spectra.
|
Quantile regression and quantile treatment effect methods are powerful
econometric tools for considering economic impacts of events or variables of
interest beyond the mean. The use of quantile methods allows for an examination
of impacts of some independent variable over the entire distribution of
continuous dependent variables. Measurement in many quantative settings in
economic history have as a key input continuous outcome variables of interest.
Among many other cases, human height and demographics, economic growth,
earnings and wages, and crop production are generally recorded as continuous
measures, and are collected and studied by economic historians. In this paper
we describe and discuss the broad utility of quantile regression for use in
research in economic history, review recent quantitive literature in the field,
and provide an illustrative example of the use of these methods based on 20,000
records of human height measured across 50-plus years in the 19th and 20th
centuries. We suggest that there is considerably more room in the literature on
economic history to convincingly and productively apply quantile regression
methods.
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Let $(F_n)$ be the sequence of Fibonacci numbers and, for each positive
integer $k$, let $\mathcal{P}_k$ be the set of primes $p$ such that $\gcd(p -
1, F_{p - 1}) = k$. We prove that the relative density
$\text{r}(\mathcal{P}_k)$ of $\mathcal{P}_k$ exists, and we give a formula for
$\text{r}(\mathcal{P}_k)$ in terms of an absolutely convergent series.
Furthermore, we give an effective criterion to establish if a given $k$
satisfies $\text{r}(\mathcal{P}_k) > 0$, and we provide upper and lower bounds
for the counting function of the set of such $k$'s. As an application of our
results, we give a new proof of a lower bound for the counting function of the
set of integers of the form $\gcd(n, F_n)$, for some positive integer $n$. Our
proof is more elementary than the previous one given by Leonetti and Sanna,
which relies on a result of Cubre and Rouse.
|
In two recent papers, Maroney and Turgut separately and independently show
generalisations of Landauer's erasure principle to indeterministic logical
operations, as well as to logical states with variable energies and entropies.
Here we show that, although Turgut's generalisation seems more powerful, in
that it implies but is not implied by Maroney's and that it does not rely upon
initial probability distributions over logical states, it does not hold for
non-equilibrium states, while Maroney's generalisation holds even in
non-equilibrium. While a generalisation of Turgut's inequality to
non-equilibrium seems possible, it lacks the properties that makes the
equilibrium inequality appealing. The non-equilibrium generalisation also no
longer implies Maroney's inequality, which may still be derived independently.
Furthermore, we show that Turgut's inequality can only give a necessary, but
not sufficient, criteria for thermodynamic reversibility. Maroney's inequality
gives the necessary and sufficient conditions.
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We derive an effective Hamiltonian for the ionic Hubbard model at half
filling, extended to include nearest-neighbor repulsion. Using a spin-particle
transformation, the effective model is mapped onto simple spin-1 models in two
particular cases. Using another spin-particle transformation, a slightly
modified model is mapped into an SU(3) antiferromagnetic Heisenberg model whose
exact ground state is known to be spontaneously dimerized. From the effective
models several properties of the dimerized phase are discussed, like
ferroelectricity and fractional charge excitations. Using bosonization and
recent developments in the theory of macroscopic polarization, we show that the
polarization is proportional to the charge of the elementary excitations.
|
Vertical migrations of zooplankters have been widely described, but their
active movements through shallow, highly dynamic water columns within the inner
shelf may be more complex and difficult to characterize. In this study,
invertebrate larvae, currents, and hydrographic variables were sampled at
different depths during and after the presence of fronts on three different
cruises off the southern coast of South Africa. Internal wave dynamics were
observed in the hydrographic data set but also through satellite imagery,
although strong surface convergent currents were absent and thermal
stratification was weak. During the first two cruises, fronts were more
conspicuous and they preceded strong onshore currents at depth which developed
with the rising tide. Vertical distributions of larvae changed accordingly,
with higher abundances at these deep layers once the front disappeared. The
third cruise was carried out during slack tides, the front was not conspicuous,
deep strong onshore currents did not occur afterward and larval distributions
did not change consistently through time. Overall, the vertical distributions
of many larval taxa matched the vertical profiles of shoreward currents and
multivariate analyses revealed that these flows structured the larval
community, which was neither influenced by temperature nor chlorophyll. Thus,
the ability to regulate active vertical positioning may enhance shoreward
advection and determine nearshore larval distributions.
|
Electroconvective flow between two infinitely long parallel electrodes is
investigated via a multiphysics computational model. The model solves for
spatiotemporal flow properties using two-relaxation-time Lattice Boltzmann
Method for fluid and charge transport coupled to Fast Fourier Transport Poisson
solver for the electric potential. The segregated model agrees with the
previous analytical and numerical results providing a robust approach for
modeling electrohydrodynamic flows.
|
We evaluate the on shell form factors of the electron for arbitrary momentum
transfer and finite electron mass, at two loops in QED, by integrating the
corresponding dispersion relations, which involve the imaginary parts known
since a long time. The infrared divergences are parameterized in terms of a
fictitious small photon mass. The result is expressed in terms of Harmonic
Polylogarithms of maximum weight 4. The expansions for small and large momentum
transfer are also given
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A combination band due to a mechanism whereby a photon excites two or more
vibrational modes ({\it e.g.} a bend and a stretch) of an individual molecule
is commonly seen in laboratory and astronomical spectroscopy. Here, we present
evidence of a much less commonly seen combination band $-$ one where a photon
simultaneously excites two adjacent molecules in an ice. In particular, we
present near-infrared spectra of laboratory CO/N$_2$ ice samples where we
identify a band at 4467.5 cm$^{-1}$ (2.239 $\mu$m) that results from single
photons exciting adjacent pairs of CO and N$_2$ molecules. We also present a
near-infrared spectrum of Neptune's largest satellite Triton taken with the
Gemini-South 8.1 meter telescope and the Immersion Grating Infrared
Spectrograph (IGRINS) that shows this 4467.5 cm$^{-1}$ (2.239 $\mu$m) CO-N$_2$
combination band. The existence of the band in a spectrum of Triton indicates
that CO and N$_2$ molecules are intimately mixed in the ice rather than
existing as separate regions of pure CO and pure N$_2$ deposits. Our finding is
important because CO and N$_2$ are the most volatile species on Triton and so
dominate seasonal volatile transport across its surface. Our result will place
constraints on the interaction between the surface and atmosphere of Triton. 1
|
We propose a new approach based on an all-optical set-up for generating
relativistic polarized electron beams via vortex Laguerre-Gaussian (LG)
laser-driven wakefield acceleration. Using a pre-polarized gas target, we find
that the topology of the vortex wakefield resolves the depolarization issue of
the injected electrons. In full three-dimensional particle-in-cell simulations,
incorporating the spin dynamics via the Thomas-Bargmann Michel Telegdi
equation, the LG laser preserves the electron spin polarization by more than
80% at high beam charge and flux. The method releases the limit on beam flux
for polarized electron acceleration and promises more than an order of
magnitude boost in peak flux, as compared to Gaussian beams. These results
suggest a promising table-top method to produce energetic polarized electron
beams.
|
In design of optical systems based on LED (Light emitting diode) technology,
a crucial task is to handle the unstructured data describing properties of
optical elements in standard formats. This leads to the problem of data fitting
within an appropriate model. Newton's method is used as an upgrade of
previously developed most promising discrete optimization heuristics showing
improvement of both performance and quality of solutions. Experiment also
indicates that a combination of an algorithm that finds promising initial
solutions as a preprocessor to Newton's method may be a winning idea, at least
on some datasets of instances.
|
We discuss possible deviations from QED produced by a virtual excited
spin-3/2 lepton in the reaction $e^+e^- \longrightarrow 2\gamma$. Data recorded
by the OPAL Collaboration at a c.m. energy $\sqrt{s} = 183 GeV$ are used to
establish bounds on the nonstandard-lepton mass and coupling strengths.
|
Financial networks are typically estimated by applying standard time series
analyses to price-based economic variables collected at low-frequency (e.g.,
daily or monthly stock returns or realized volatility). These networks are used
for risk monitoring and for studying information flows in financial markets.
High-frequency intraday trade data sets may provide additional insights into
network linkages by leveraging high-resolution information. However, such data
sets pose significant modeling challenges due to their asynchronous nature,
nonlinear dynamics, and nonstationarity. To tackle these challenges, we
estimate financial networks using random forests. The edges in our network are
determined by using microstructure measures of one firm to forecast the sign of
the change in a market measure (either realized volatility or returns kurtosis)
of another firm. We first investigate the evolution of network connectivity in
the period leading up to the U.S. financial crisis of 2007-09. We find that the
networks have the highest density in 2007, with high degree connectivity
associated with Lehman Brothers in 2006. A second analysis into the nature of
linkages among firms suggests that larger firms tend to offer better predictive
power than smaller firms, a finding qualitatively consistent with prior works
in the market microstructure literature.
|
We introduce two integral representations of monodromy on Lam\'e equation. By
applying them, we obtain results on hyperelliptic-to-elliptic reduction
integral formulae, finite-gap potential and eigenvalues of Lam\'e operator.
|
We derive molecular-gas-phase $^{12}$C/$^{13}$C isotope ratios for the
central few 100 pc of the three nearby starburst galaxies NGC 253, NGC 1068,
and NGC 4945 making use of the $\lambda$ $\sim$ 3 mm $^{12}$CN and $^{13}$CN
$N$ = 1--0 lines in the ALMA Band 3. The $^{12}$C/$^{13}$C isotopic ratios
derived from the ratios of these lines range from 30 to 67 with an average of
41.6 $\pm$ 0.2 in NGC 253, from 24 to 62 with an average of 38.3 $\pm$ 0.4 in
NGC 1068, and from 6 to 44 with an average of 16.9 $\pm$ 0.3 in NGC 4945. The
highest $^{12}$C/$^{13}$C isotopic ratios are determined in some of the
outskirts of the nuclear regions of the three starburst galaxies. The lowest
ratios are associated with the northeastern and southwestern molecular peaks of
NGC 253, the northeastern and southwestern edge of the mapped region in NGC
1068, and the very center of NGC 4945. In case of NGC 1068, the measured ratios
suggest inflow from the outer part of NGC 1068 into the circum-nuclear disk
through both the halo and the bar. Low $^{12}$C/$^{13}$C isotopic ratios in the
central regions of these starburst galaxies indicate the presence of highly
processed material.
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We study the energy distribution and equation of state of the universe
between the end of inflation and the onset of radiation domination (RD),
considering observationally consistent single-field inflationary scenarios,
with a potential 'flattening' at large field values, and a monomial shape
$V(\phi) \propto |\phi|^p$ around the origin. As a proxy for (p)reheating, we
include a quadratic interaction $g^2\phi^2X^2$ between the inflaton $\phi$ and
a light scalar 'daughter' field $X$, with $g^2>0$. We capture the
non-perturbative and non-linear nature of the system dynamics with lattice
simulations, obtaining that: $i)$ the final energy transferred to $X$ depends
only on $p$, not on $g^2$, ; $ii)$ the final transfer of energy is always
negligible for $2 \leq p < 4$, and of order $\sim 50\%$ for $p \geq 4$; $iii)$
the system goes at late times to matter-domination for $p = 2$, and always to
RD for $p > 2$. In the latter case we calculate the number of e-folds until RD,
significantly reducing the uncertainty in the inflationary observables $n_s$
and $r$.
|
We present an orthogonal basis for functions over a slice of the Boolean
hypercube. Our basis is also an orthogonal basis of eigenvectors for the
Johnson and Kneser graphs. As an application of our basis, we streamline
Wimmer's proof of Friedgut's theorem for slices of the Boolean hypercube.
|
We report magnetoresistance oscillations in high magnetic fields, B, up to 45
T and over a wide range of temperature in the Mott-like system Ca3Ru2O7. For B
rotating within the ac-plane, slow and strong Shubnikov-de Haas (SdH)
oscillations periodic in 1/B are observed for T≤1.5 K in the presence of
metamagnetism. These oscillations are highly angular dependent and intimately
correlated with the spin-polarization of the ferromagnetic state. For B||[110],
oscillations are also observed but periodic in B (rather than 1/B) which
persist up to 15 K. While the SdH oscillations are a manifestation of the
presence of small Fermi surface (FS) pockets in the Mott-like system, the
B-periodic oscillations, an exotic quantum phenomenon, may be a result of
anomalous coupling of the magnetic field to the t2g-orbitals that makes the
extremal cross-section of the FS field-dependent.
|
Conventional weak-coupling Rayleigh-Schr\"odinger perturbation theory suffers
from problems that arise from resonant coupling of successive orders in the
perturbation series. Multiple-scale analysis, a powerful and sophisticated
perturbative method that quantitatively analyzes characteristic physical
behaviors occurring on various length or time scales, avoids such problems by
implicitly performing an infinite resummation of the conventional perturbation
series. Multiple-scale perturbation theory provides a good description of the
classical anharmonic oscillator. Here, it is extended to study (1) the
Heisenberg operator equations of motion and (2) the Schr\"odinger equation for
the quantum anharmonic oscillator. In the former case, it leads to a system of
coupled operator differential equations, which is solved exactly. The solution
provides an operator mass renormalization of the theory. In the latter case,
multiple-scale analysis elucidates the connection between weak-coupling
perturbative and semiclassical nonperturbative aspects of the wave function.
|
Recent X-ray observations have proved to be very effective in detecting
previously unknown supernova remnant shells around pulsar wind nebulae (PWNe),
and in these cases the characteristics of the shell provide further clues on
the evolutionary stage of the embedded PWN. However, it is not clear why some
PWNe are still "naked". We carried out an X-ray observational campaign targeted
at the PWN G54.1+0.3, the "close cousin" of the Crab, with the aim to detect
the associated SNR shell. We analyzed an XMM-Newton and Suzaku observations of
G54.1+0.3 and we model out the contribution of dust scattering halo. We
detected an intrinsic faint diffuse X-ray emission surrounding a hard spectrum,
which can be modeled either with a power-law (gamma= 2.9) or with a thermal
plasma model (kT=2.0 keV.). If the shell is thermal, we derive an explosion
energy E=0.5-1.6x10^51 erg, a pre-shock ISM density of 0.2 cm^-3 and an age of
about 2000 yr. Using these results in the MHD model of PWN-SNR evolution, we
obtain an excellent agreement between the predicted and observed location of
the shell and PWN shock.
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Due to stringent thermal budgets in cryogenic technologies such as
superconducting quantum computers and sensors, minimizing the energy
dissipation and power consumption of cryogenic electronic components is pivotal
for large-scale devices. However, electronic building blocks that
simultaneously offer low energy consumption, fast switching, low error rates, a
small footprint and simple fabrication remain elusive. In this work, we
demonstrate a superconducting switch with attojoule switching energy, high
speed (pico-second rise/fall times), and high integration density (on the order
of $10^{-2}$ $\mathrm{\mu m^2}$ per switch). The switch consists of a
superconducting channel and a metal heater separated by an insulating silica
layer, prepared using lift-off techniques. We experimentally demonstrate
digital gate operations utilizing this technology, such as NOT, NAND, NOR, AND,
and OR gates, with a few femtojoule energy consumption and ultralow bit error
rates < $10^{-8}$. In addition, we build volatile memory elements with few
femtojoule energy consumption per operation, a nanosecond operation speed, and
a retention time over $10^5$ s. These superconducting switches open new
possibilities for increasing the size and complexity of modern cryogenic
technologies.
|
Artificial behavioral agents are often evaluated based on their consistent
behaviors and performance to take sequential actions in an environment to
maximize some notion of cumulative reward. However, human decision making in
real life usually involves different strategies and behavioral trajectories
that lead to the same empirical outcome. Motivated by clinical literature of a
wide range of neurological and psychiatric disorders, we propose here a more
general and flexible parametric framework for sequential decision making that
involves a two-stream reward processing mechanism. We demonstrated that this
framework is flexible and unified enough to incorporate a family of problems
spanning multi-armed bandits (MAB), contextual bandits (CB) and reinforcement
learning (RL), which decompose the sequential decision making process in
different levels. Inspired by the known reward processing abnormalities of many
mental disorders, our clinically-inspired agents demonstrated interesting
behavioral trajectories and comparable performance on simulated tasks with
particular reward distributions, a real-world dataset capturing human
decision-making in gambling tasks, and the PacMan game across different reward
stationarities in a lifelong learning setting.
|
Soft-pion theorems are used to show how chiral symmetry constrains the
contributions of low-momentum pions to the quark condensate, the pion decay
constant and hadron masses, all of which have been proposed as signals of
partial restoration of chiral symmetry in matter. These have contributions of
order T^2 for a pion gas or of order m_pi for cold nuclear matter, which have
different coefficients in all three cases, showing that there are no simple
relations between the changes to these quantities in matter. In particular,
such contributions are absent from the masses of vector mesons and nucleons and
so these masses cannot scale as any simple function of the quark condensate.
More generally, pieces of the quark condensate that arise from low-momentum
pions should not be associated with partial restoration of chiral symmetry.
|
Genome assembly using high throughput data with short reads, arguably,
remains an unresolvable task in repetitive genomes, since when the length of a
repeat exceeds the read length, it becomes difficult to unambiguously connect
the flanking regions. The emergence of third generation sequencing (Pacific
Biosciences) with long reads enables the opportunity to resolve complicated
repeats that could not be resolved by the short read data. However, these long
reads have high error rate and it is an uphill task to assemble the genome
without using additional high quality short reads. Recently, Koren et al. 2012
proposed an approach to use high quality short reads data to correct these long
reads and, thus, make the assembly from long reads possible. However, due to
the large size of both dataset (short and long reads), error-correction of
these long reads requires excessively high computational resources, even on
small bacterial genomes. In this work, instead of error correction of long
reads, we first assemble the short reads and later map these long reads on the
assembly graph to resolve repeats.
Contribution: We present a hybrid assembly approach that is both
computationally effective and produces high quality assemblies. Our algorithm
first operates with a simplified version of the assembly graph consisting only
of long contigs and gradually improves the assembly by adding smaller contigs
in each iteration. In contrast to the state-of-the-art long reads error
correction technique, which requires high computational resources and long
running time on a supercomputer even for bacterial genome datasets, our
software can produce comparable assembly using only a standard desktop in a
short running time.
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Let $M$ be a pseudoconvex, oriented, bounded and closed CR submanifold of
$\mathbb{C}^{n}$ of hypersurface type. Our main result says that when a certain
$1$-form on $M$ is exact on the null space of the Levi form, then the complex
Green operator on $M$ satisfies Sobolev estimates. This happens in particular
when $M$ admits a set of plurisubharmonic defining functions or when $M$ is
strictly pseudoconvex except for the points on a simply connected complex
submanifold.
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The very large (100-1000) mass-to-light ratio applicable to the ultra-faint
dwarf galaxies (UFDs) implies a high concentration of dark matter, thus
rendering them ideal theatres for indirect signatures of dark matter. In this
paper, we consider 14 recently discovered UFDs and study the electromagnetic
radiation emanating from them over a wide range, from gamma ray down to radio
frequencies. We analyze the Fermi-LAT data on high energy gamma rays and radio
fluxes at the GMRT and VLA to obtain upper limits on annihilation cross section
$\langle\sigma v\rangle$ in a model independent way. We further discuss the
sensitivity of the Square Kilometer Array radio telescope in probing the
synchrotron radiation from the aforementioned UFDs. We also investigate the
dependences of the said upper limits on the uncertainties in the determination
of various astrophysical parameters.
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We proposed a model of interacting market agents based on the Ising spin
model. The agents can take three actions: "buy," "sell," or "stay inactive." We
defined a price evolution in terms of the system magnetization. The model
reproduces main stylized facts of real markets such as: fat-tailed distribution
of returns and volatility clustering.
|
Homodyne tomography provides a way for measuring generic field-operators.
Here we analyze the determination of the most relevant quantities: intensity,
field, amplitude and phase. We show that tomographic measurements are affected
by additional noise in comparison with the direct detection of each observable
by itself. The case of of coherent states has been analyzed in details and
earlier estimations of tomographic precision are critically discussed.
|
In a recent work, a method for the magnetic resonance (MR) measurement of the
true diffusion propagator was introduced, which was subsequently implemented
and validated for free diffusion on a benchtop MR scanner. Here, we provide a
brief theoretical description of the method and discuss various experimental
regimes.
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We present a consistent total flux catalogue for a $\sim$1 deg$^2$ subset of
the COSMOS region (R.A. $\in [149.55\degr, 150.65\degr]$, DEC $\in [1.80\degr,
2.73\degr]$) with near-complete coverage in 38 bands from the far-ultraviolet
to the far-infrared. We produce aperture matched photometry for 128,304 objects
with i < 24.5 in a manner that is equivalent to the Wright et al. (2016)
catalogue from the low-redshift (z < 0.4) Galaxy and Mass Assembly (GAMA)
survey. This catalogue is based on publicly available imaging from GALEX, CFHT,
Subaru, VISTA, Spitzer and Herschel, contains a robust total flux measurement
or upper limit for every object in every waveband and complements our
re-reduction of publicly available spectra in the same region. We perform a
number of consistency checks, demonstrating that our catalogue is comparable to
existing data sets, including the recent COSMOS2015 catalogue (Laigle et al.
2016). We also release an updated Davies et al. (2015) spectroscopic catalogue
that folds in new spectroscopic and photometric redshift data sets. The
catalogues are available for download at
http://cutout.icrar.org/G10/dataRelease.php. Our analysis is optimised for both
panchromatic analysis over the full wavelength range and for direct comparison
to GAMA, thus permitting measurements of galaxy evolution for 0 < z < 1 while
minimising the systematic error resulting from disparate data reduction
methods.
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Recently, the NANOGrav, PPTA, EPTA, and CPTA collaborations independently
reported their evidence of the Stochastic Gravitational Waves Background
(SGWB). While the inferred gravitational-wave background amplitude and spectrum
are consistent with astrophysical expectations for a signal from the population
of supermassive black-hole binaries (SMBHBs), the search for new physics
remains plausible in this observational window. In this work, we explore the
possibility of explaining such a signal by the scalar-induced gravitational
waves (IGWs) in the very early universe. We use a parameterized broken
power-law function as a general description of the energy spectrum of the SGWB
and fit it to the new results of NANOGrav, PPTA and EPTA. We find that this
approach can put constraints on the parameters of IGW energy spectrum and
further yield restrictions on various inflation models that may produce
primordial black holes (PBHs) in the early universe, which is also expected to
be examined by the forthcoming space-based GW experiments.
|
We investigate transport in a superconducting nanostructure housing a Weyl
point in the spectrum of Andreev bound states. A minimum magnet state is
realized in the vicinity of the point. One or more normal-metal leads are
tunnel-coupled to the nanostructure. We have shown that this minimum magnetic
setup is suitable for realization of all common goals of spintronics: detection
of a magnetic state, conversion of electric currents into spin currents,
potentially reaching the absolute limit of one spin per charge transferred,
detection of spin accumulation in the leads. The peculiarity and possible
advantage of the setup is the ability to switch between magnetic and
non-magnetic states by tiny changes of the control parameters: superconducting
phase differences. We employ this property to demonstrate the feasibility of
less common spintronic effects: spin on demand and alternative spin current.
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This paper describes a benchmark consisting of a set of synthetic
measurements relative to an office environment simulated with the software
IDA-ICE. The simulated environment reproduces a laboratory at the KTH-EES Smart
Building, equipped with a building management system. The data set contains
records collected over a period of several days. The signals to CO$_2$
concentration, mechanical ventilation airflows, air infiltrations and
occupancy. Information on door and window opening is also available. This
benchmark is intended for testing data-based modeling techniques. The ultimate
goal is the development of models to improve the forecast and control of
environmental variables. Among the numerous challenges related to this
framework, we point out the problem of occupancy estimation using information
on CO$_2$ concentration. This can be seen as a blind identification problem.
For benchmarking purposes, we present two different identification approaches:
a baseline overparametrization method and a kernel-based method.
|
We propose a novel algorithm for finding square roots modulo p. Although
there exists a direct formula to calculate square root of an element modulo
prime (3 mod 4), but calculating square root modulo prime (1 mod 4) is non
trivial. Tonelli-Shanks algorithm remains the most widely used and probably the
fastest when averaged over all primes [19]. This paper proposes a new algorithm
for finding square roots modulo all odd primes, which shows improvement over
existing method in practical terms although asymptotically gives the same run
time as Tonelli-Shanks. Apart from practically efficient computation time, the
proposed method does not necessarily require availability of non-residue and
can work with `relative non-residue' also. Such `relative non-residues' are
much easier to find ( probability 2/3) compared to non-residues ( probability
1/2).
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Heavy right handed neutrinos could not only explain the observed neutrino
masses via the seesaw mechanism, but also generate the baryon asymmetry of the
universe via leptogenesis due to their CP-violating interactions in the early
universe. We review recent progress in the theoretical description of this
nonequilibrium process. Improved calculations are particularly important for a
comparison with experimental data in testable scenarios with Majorana masses
below the TeV scale, in which the heavy neutrinos can be found at the LHC, in
the NA62 experiment, at T2K or in future experiments, including SHiP, DUNE and
experiments at the FCC, ILC or CEPC. In addition, the relevant source of
CP-violation may be experimentally accessible, and the heavy neutrinos can give
a sizable contribution to neutrinoless double $\beta$ decay. In these low scale
leptogenesis scenarios, the matter-antimatter asymmetry is generated at
temperatures when the heavy neutrinos are relativistic, and thermal corrections
to the transport equations in the early universe are large.
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We present a statistical analysis of the acoustic emissions induced by
dislocation motion during the creep of ice single crystals. The recorded
acoustic waves provide an indirect measure of the inelastic energy dissipated
during dislocation motion. Compression and torsion creep experiments indicate
that viscoplastic deformation, even in the steady-state (secondary creep), is a
complex and inhomogeneous process characterized by avalanches in the motion of
dislocations. The distribution of avalanche sizes, identified with the acoustic
wave amplitude (or the acoustic wave energy), is found to follow a power law
with a cutoff at large amplitudes which depends on the creep stage (primary,
secondary, tertiary). These results suggest that viscoplastic deformation in
ice and possibly in other materials could be described in the framework of
non-equilibrium critical phenomena.
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Electron tunneling through quantum-dots side coupled to a quantum wire, in
equilibrium and nonequilibrium Kondo regime, is studied. The mean-field
finite-$U$ slave-boson formalism is used to obtain the solution of the problem.
We have found that the transmission spectrum shows a structure with two
anti-resonances localized at the renormalized energies of the quantum dots. The
DOS of the system shows that when the Kondo correlations are dominant there are
two Kondo regimes with its own Kondo temperature. The above behavior of the DOS
can be explained by quantum interference in the transmission through the two
different resonance states of the quantum dots coupled to common leads. This
result is analogous to the Dicke effect in optics. We investigate the many body
Kondo states as a function of the parameters of the system.
|
We consider the two dimensional disordered Bose gas which present a metallic
state at low temperatures. A simple model of an interacting Bose system in a
random field is propose to consider the interaction effect on the transition in
the metallic state.
|
In this paper we investigate a certain category of cotangent sums and more
specifically the sum
$$\sum_{m=1}^{b-1}\cot\left(\frac{\pi m}{b}\right)\sin^{3}\left(2\pi
m\frac{a}{b}\right)\:$$ and associate the distribution of its values to a
generalized totient function $\phi(n,A,B)$, where
$$\phi(n,A,B):=\sum_{\substack{A\leq k \leq B \\ (n,k)=1}}1\:.$$ One of the
methods used consists in the exploitation of relations between trigonometric
sums and the fractional part of a real number.
|
We study the effective potential for composite operators. Introducing a
source coupled to the composite operator, we define the effective potential by
a Legendre transformation. We find that in three or fewer dimensions, one can
use the conventionally defined renormalized operator to couple to the source.
However, in four dimensions, the effective potential for the conventional
renormalized composite operator is divergent. We overcome this difficulty by
adding additional counterterms to the operator and adjusting these order by
order in perturbation theory. These counterterms are found to be
non-polynomial. We find that, because of the extra counterterms, the composite
effective potential is gauge dependent. We display this gauge-dependence
explicitly at two-loop order.
|
We derive the effective action for a domain wall with small thickness in
curved spacetime and show that, apart from the Nambu term, it includes a
contribution proportional to the induced curvature. We then use this action to
study the dynamics of a spherical thick bubble of false vacuum (de Sitter)
surrounded by an infinite region of true vacuum (Schwarzschild).
|
Similar to how standard Young tableaux represent paths in the Young lattice,
Latin rectangles may be use to enumerate paths in the poset of semi-magic
squares with entries zero or one. The symmetries associated to determinant
preserve this poset, and we completely describe the orbits, covering data, and
maximal chains for squares of size 4, 5, and 6. The last item gives the number
of Latin squares in these cases. To calculate efficiently for size 6, we in
turn identify orbits with certain equivalence classes of hypergraphs.
|
The first problem of the 2017 Putnam competition was to characterize a set of
natural numbers closed under both the square-root map $n^2 \mapsto n$ and the
"add 5 and square" map $ n \mapsto (n+5)^2$. We reframe this as a problem on an
infinite directed graph, using this framing both to generalize the problem and
its solution, as well as to determine the first appearance of each number in
this set under a row-wise algorithm that outputs all its elements.
|
Reconstructing the underlying 3D surface of an object from a single image is
a challenging problem that has received extensive attention from the computer
vision community. Many learning-based approaches tackle this problem by
learning a 3D shape prior from either ground truth 3D data or multi-view
observations. To achieve state-of-the-art results, these methods assume that
the objects are specified with respect to a fixed canonical coordinate frame,
where instances of the same category are perfectly aligned. In this work, we
present a new method for joint category-specific 3D reconstruction and object
pose estimation from a single image. We show that one can leverage shape priors
learned on purely synthetic 3D data together with a point cloud pose
canonicalization method to achieve high-quality 3D reconstruction in the wild.
Given a single depth image at test time, we first transform this partial point
cloud into a learned canonical frame. Then, we use a neural deformation field
to reconstruct the 3D surface of the object. Finally, we jointly optimize
object pose and 3D shape to fit the partial depth observation. Our approach
achieves state-of-the-art reconstruction performance across several real-world
datasets, even when trained only on synthetic data. We further show that our
method generalizes to different input modalities, from dense depth images to
sparse and noisy LIDAR scans.
|
We study the gravitational collapse of two thin shells of matter, in
asymptotically flat spacetime or constrained to move within a spherical box. We
show that this simple two-body system has surprisingly rich dynamics, which
includes prompt collapse to a black hole, perpetually oscillating solutions or
black hole formation at arbitrarily large times. Collapse is induced by shell
crossing and the black hole mass depends sensitively on the number of shell
crossings. At certain critical points, the black hole mass exhibits critical
behavior, determined by the change in parity (even or odd) of the number of
crossings, with or without mass-gap during the transition. Some of the features
we observe are reminiscent of confined scalars undergoing "turbulent" dynamics.
|
We present an experimental study of the flow dynamics of a lamellar phase
sheared in the Couette geometry. High-frequency ultrasonic pulses at 36 MHz are
used to measure time-resolved velocity profiles. Oscillations of the viscosity
occur in the vicinity of a shear-induced transition between a high-viscosity
disordered fluid and a low-viscosity ordered fluid. The phase coexistence shows
up as shear bands on the velocity profiles. We show that the dynamics of the
rheological data result from two different processes: (i) fluctuations of slip
velocities at the two walls and (ii) flow dynamics in the bulk of the lamellar
phase. The bulk dynamics are shown to be related to the displacement of the
interface between the two differently sheared regions in the gap of the Couette
cell. Two different dynamical regimes are investigated under applied shear
stress: one of small amplitude oscillations of the viscosity
($\delta\eta/\eta\simeq 3$%) and one of large oscillations
($\delta\eta/\eta\simeq 25$%). A phenomenological model is proposed that may
account for the observed spatio-temporal dynamics
|
An account of the subjective elements of quantum mechanics or of whether, as
Einstein famously asked, the Moon exists when nobody is looking at it.
|
The FE$^2$ method is a very flexible but computationally expensive tool for
multiscale simulations. In conventional implementations, the microscopic
displacements are iteratively solved for within each macroscopic iteration
loop, although the macroscopic strains imposed as boundary conditions at the
micro-scale only represent estimates. In order to reduce the number of
expensive micro-scale iterations, the present contribution presents a
monolithic FE$^2$ scheme, for which the displacements at the micro-scale and at
the macro-scale are solved for in a common Newton-Raphson loop. In this case,
the linear system of equations within each iteration is solved by static
condensation, so that only very limited modifications to the conventional,
staggered scheme are necessary. The proposed monolithic FE$^2$ algorithm is
implemented into the commercial FE code Abaqus. Benchmark examples demonstrate
that the monolithic scheme saves up to ~60% of computational costs.
|
The ability to modulate brain states using targeted stimulation is
increasingly being employed to treat neurological disorders and to enhance
human performance. Despite the growing interest in brain stimulation as a form
of neuromodulation, much remains unknown about the network-level impact of
these focal perturbations. To study the system wide impact of regional
stimulation, we employ a data-driven computational model of nonlinear brain
dynamics to systematically explore the effects of targeted stimulation.
Validating predictions from network control theory, we uncover the relationship
between regional controllability and the focal versus global impact of
stimulation, and we relate these findings to differences in the underlying
network architecture. Finally, by mapping brain regions to cognitive systems,
we observe that the default mode system imparts large global change despite
being highly constrained by structural connectivity. This work forms an
important step towards the development of personalized stimulation protocols
for medical treatment or performance enhancement.
|
The needs for improving observability of medium and low voltage distribution
networks has been significantly increased, in recent year. In this paper, we
focus on practical approaches for placement of affordable Measurement Devices
(MDs), which are providing three phases voltage, current, and power
measurements with certain level of precision. The placement procedure is
composed of a state-estimation algorithm and of a greedy placement scheme. The
proposed state-estimation algorithm is based on the Distflow model, enhanced to
consider the shunt elements (e.g., cable capacitances) of the network, which
are not negligible in low voltage networks with underground cables. The greedy
placement scheme is formulated such that it finds the location of minimum
required number of MDs while certain grid observability limits are satisfied.
These limits are defined as the accuracy of state-estimation results in terms
of voltage magnitudes and line currents over all nodes and lines, respectively.
The effectiveness of the proposed placement procedure has been validated on a
realistic test grid of 10 medium voltage nodes and 75 low voltage nodes, whose
topology and parameters were made available from the Distribution System
Operator (DSO) of the city of Geneva, Switzerland.
|
The link between the electroweak gauge boson masses and the Fermi constant
via the muon lifetime measurement is instrumental for constraining and
eventually pinning down new physics. We consider the simplest extension of the
Standard Model with an additional real scalar SU(2)_L x U(1)_Y singlet and
compute the electroweak precision parameter Delta r, along with the
corresponding theoretical prediction for the W-boson mass. When confronted with
the experimental W-boson mass measurement, our predictions impose limits on the
singlet model parameter space. We identify regions where these correspond to
the most stringent experimental constraints that are currently available.
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Subsets and Splits
Filtered Text Samples
Retrieves 100 samples of text containing the specific phrase "You are a helpful assistant", providing limited insight into the dataset.
Helpful Assistant Text Samples
Returns a limited set of rows containing the phrase 'helpful assistant' in the text, providing basic filtering of relevant entries.