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Existing optimization-based methods for non-rigid registration typically
minimize an alignment error metric based on the point-to-point or
point-to-plane distance between corresponding point pairs on the source surface
and target surface. However, these metrics can result in slow convergence or a
loss of detail. In this paper, we propose SPARE, a novel formulation that
utilizes a symmetrized point-to-plane distance for robust non-rigid
registration. The symmetrized point-to-plane distance relies on both the
positions and normals of the corresponding points, resulting in a more accurate
approximation of the underlying geometry and can achieve higher accuracy than
existing methods. To solve this optimization problem efficiently, we propose an
alternating minimization solver using a majorization-minimization strategy.
Moreover, for effective initialization of the solver, we incorporate a
deformation graph-based coarse alignment that improves registration quality and
efficiency. Extensive experiments show that the proposed method greatly
improves the accuracy of non-rigid registration problems and maintains
relatively high solution efficiency. The code is publicly available at
https://github.com/yaoyx689/spare.
|
The observed power spectrum in redshift space appears distorted due to the
peculiar motion of galaxies, known as redshift-space distortions (RSD). While
all the effects in RSD are accounted for by the simple mapping formula from
real to redshift spaces, accurately modeling redshift-space power spectrum is
rather difficult due to the non-perturbative properties of the mapping. Still,
however, a perturbative treatment may be applied to the power spectrum at
large-scales, and on top of a careful modeling of the Finger-of-God effect
caused by the small-scale random motion, the redshift-space power spectrum can
be expressed as a series of expansion which contains the higher-order
correlations of density and velocity fields. In our previous work [JCAP 8
(Aug., 2016) 050], we provide a perturbation-theory inspired model for power
spectrum in which the higher-order correlations are evaluated directly from the
cosmological $N$-body simulations. Adopting a simple Gaussian ansatz for
Finger-of-God effect, the model is shown to quantitatively describe the
simulation results. Here, we further push this approach, and present an
accurate power spectrum template which can be used to estimate the growth of
structure as a key to probe gravity on cosmological scales. Based on the
simulations, we first calibrate the uncertainties and systematics in the
pertrubation theory calculation in a fiducial cosmological model. Then, using
the scaling relations, the calibrated power spectrum template is applied to a
different cosmological model. We demonstrate that with our new template, the
best-fitted growth functions are shown to reproduce the fiducial values in a
good accuracy of 1 \% at $k<0.18 \hompc$ for cosmologies with different Hubble
parameters.
|
We investigate the decomposition of the total entropy production in
continuous stochastic dynamics when there are odd-parity variables that change
their signs under time reversal. The first component of the entropy production,
which satisfies the fluctuation theorem, is associated with the usual excess
heat that appears during transitions between stationary states. The remaining
housekeeping part of the entropy production can be further split into two
parts. We show that this decomposition can be achieved in infinitely many ways
characterized by a single parameter {\sigma}. For an arbitrary value of
{\sigma}, one of the two parts contributing to the housekeeping entropy
production satisfies the fluctuation theorem. We show that for a range of
{\sigma} values this part can be associated with the breakage of the detailed
balance in the steady state, and can be regarded as a continuous version of the
corresponding entropy production that has been obtained previously for discrete
state variables. The other part of the housekeeping entropy does not satisfy
the fluctuation theorem and is related to the parity asymmetry of the
stationary state distribution. We discuss our results in connection with the
difference between continuous and discrete variable cases especially in the
conditions for the detailed balance and the parity symmetry of the stationary
state distribution.
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We investigate the collective behavior of a system of chaotic Rossler
oscillators indirectly coupled through a common environment that possesses its
own dynamics and which in turn is modulated by the interaction with the
oscillators. By varying the parameter representing the coupling strength
between the oscillators and the environment, we find two collective states
previously not reported in systems with environmental coupling: (i) nontrivial
collective behavior, characterized by a periodic evolution of macroscopic
variables coexisting with the local chaotic dynamics; and (ii) dynamical
clustering, consisting of the formation of differentiated subsets of
synchronized elements within the system. These states are relevant for many
physical and biological systems where interactions with a dynamical environment
are frequent.
|
Solute segregation plays an important role in formation of long-period
stacking ordered (LPSO) structure in Mg-M-RE (M: Zn, Ni etc., RE: Y, Gd, etc.)
alloy systems. In this work, the planar segregation in Mg-Al-Gd alloy is
characterized by high angle annular dark field (HAADF) scanning transmission
electron microscopy (STEM) and three-dimensional atom probe (3DAP). It is found
there is no planar fault accompanying the segregation, and the spatial
distribution of segregation may resemble the periodicity of LPSO structure. The
segregation is further quantified by 3DAP, and it mainly enriches with Gd
atoms. The segregation behaviour is rationalized by First-Principles
calculation.
|
Is there a mathematical theory underlying intelligence? Control theory
addresses the output side, motor control, but the work of the last 30 years has
made clear that perception is a matter of Bayesian statistical inference, based
on stochastic models of the signals delivered by our senses and the structures
in the world producing them. We will start by sketching the simplest such
model, the hidden Markov model for speech, and then go on illustrate the
complications, mathematical issues and challenges that this has led to.
|
We prove that for bounded, divergence-free vector fields in
$L^1_{loc}((0,+\infty);BV_{loc}(R^d;R^d))$, regularisation by convolution of
the vector field selects a single solution of the transport equation for any
integrable initial datum. We recall the vector field constructed by Depauw in
[10], which lies in the above class of vector fields. We show that the
transport equation along this vector field has at least two bounded weak
solutions for any bounded initial datum.
|
Recent theoretical developments in the studies of two-photon exchange effects
in elastic electron-proton scattering are reviewed. Two-photon exchange
mechanism is considered a likely source of discrepancy between polarized and
unpolarized experimental measurements of the proton electric form factor at
momentum transfers of several GeV$^2$. This mechanism predicts measurable
effects that are currently studied experimentally.
|
Learning matching costs has been shown to be critical to the success of the
state-of-the-art deep stereo matching methods, in which 3D convolutions are
applied on a 4D feature volume to learn a 3D cost volume. However, this
mechanism has never been employed for the optical flow task. This is mainly due
to the significantly increased search dimension in the case of optical flow
computation, ie, a straightforward extension would require dense 4D
convolutions in order to process a 5D feature volume, which is computationally
prohibitive. This paper proposes a novel solution that is able to bypass the
requirement of building a 5D feature volume while still allowing the network to
learn suitable matching costs from data. Our key innovation is to decouple the
connection between 2D displacements and learn the matching costs at each 2D
displacement hypothesis independently, ie, displacement-invariant cost
learning. Specifically, we apply the same 2D convolution-based matching net
independently on each 2D displacement hypothesis to learn a 4D cost volume.
Moreover, we propose a displacement-aware projection layer to scale the learned
cost volume, which reconsiders the correlation between different displacement
candidates and mitigates the multi-modal problem in the learned cost volume.
The cost volume is then projected to optical flow estimation through a 2D
soft-argmin layer. Extensive experiments show that our approach achieves
state-of-the-art accuracy on various datasets, and outperforms all published
optical flow methods on the Sintel benchmark.
|
Interacting individuals in complex systems often give rise to coherent motion
exhibiting coordinated global structures. Such phenomena are ubiquitously
observed in nature, from cell migration, bacterial swarms, animal and insect
groups, and even human societies. Primary mechanisms responsible for the
emergence of collective behavior have been extensively identified, including
local alignments based on average or relative velocity, non-local pairwise
repulsive-attractive interactions such as distance-based potentials, interplay
between local and non-local interactions, and cognitive-based inhomogeneous
interactions. However, discovering how to adapt these mechanisms to modulate
emergent behaviours remains elusive. Here, we demonstrate that it is possible
to generate coordinated structures in collective behavior at desired moments
with intended global patterns by fine-tuning an inter-agent interaction rule.
Our strategy employs deep neural networks, obeying the laws of dynamics, to
find interaction rules that command desired collective structures. The
decomposition of interaction rules into distancing and aligning forces,
expressed by polynomial series, facilitates the training of neural networks to
propose desired interaction models. Presented examples include altering the
mean radius and size of clusters in vortical swarms, timing of transitions from
random to ordered states, and continuously shifting between typical modes of
collective motions. This strategy can even be leveraged to superimpose
collective modes, resulting in hitherto unexplored but highly practical hybrid
collective patterns, such as protective security formations. Our findings
reveal innovative strategies for creating and controlling collective motion,
paving the way for new applications in robotic swarm operations, active matter
organisation, and for the uncovering of obscure interaction rules in biological
systems.
|
Sentiment analysis is a widely studied NLP task where the goal is to
determine opinions, emotions, and evaluations of users towards a product, an
entity or a service that they are reviewing. One of the biggest challenges for
sentiment analysis is that it is highly language dependent. Word embeddings,
sentiment lexicons, and even annotated data are language specific. Further,
optimizing models for each language is very time consuming and labor intensive
especially for recurrent neural network models. From a resource perspective, it
is very challenging to collect data for different languages.
In this paper, we look for an answer to the following research question: can
a sentiment analysis model trained on a language be reused for sentiment
analysis in other languages, Russian, Spanish, Turkish, and Dutch, where the
data is more limited? Our goal is to build a single model in the language with
the largest dataset available for the task, and reuse it for languages that
have limited resources. For this purpose, we train a sentiment analysis model
using recurrent neural networks with reviews in English. We then translate
reviews in other languages and reuse this model to evaluate the sentiments.
Experimental results show that our robust approach of single model trained on
English reviews statistically significantly outperforms the baselines in
several different languages.
|
In this paper we deal with a large class of dynamical systems having a
version of the spectral gap property. Our primary class of systems comes from
random dynamics, but we also deal with the deterministic case. We show that if
a random dynamical system has a fiberwise spectral gap property as well as an
exponential decay of correlations in the base, then, developing on
Gou\"{e}zel's approach, the system satisfies the almost sure invariance
principle. The result is then applied to uniformly expanding random systems
like those studied by Denker and Gordin and Mayer, Skorulski, and Urba\'nski.
|
Unsupervised and self-supervised objectives, such as next token prediction,
have enabled pre-training generalist models from large amounts of unlabeled
data. In reinforcement learning (RL), however, finding a truly general and
scalable unsupervised pre-training objective for generalist policies from
offline data remains a major open question. While a number of methods have been
proposed to enable generic self-supervised RL, based on principles such as
goal-conditioned RL, behavioral cloning, and unsupervised skill learning, such
methods remain limited in terms of either the diversity of the discovered
behaviors, the need for high-quality demonstration data, or the lack of a clear
adaptation mechanism for downstream tasks. In this work, we propose a novel
unsupervised framework to pre-train generalist policies that capture diverse,
optimal, long-horizon behaviors from unlabeled offline data such that they can
be quickly adapted to any arbitrary new tasks in a zero-shot manner. Our key
insight is to learn a structured representation that preserves the temporal
structure of the underlying environment, and then to span this learned latent
space with directional movements, which enables various zero-shot policy
"prompting" schemes for downstream tasks. Through our experiments on simulated
robotic locomotion and manipulation benchmarks, we show that our unsupervised
policies can solve goal-conditioned and general RL tasks in a zero-shot
fashion, even often outperforming prior methods designed specifically for each
setting. Our code and videos are available at
https://seohong.me/projects/hilp/.
|
A crucial result in quantum chaos, which has been established for a long
time, is that the spectral properties of classically integrable systems
generically are described by Poisson statistics whereas those of time-reversal
symmetric, classically chaotic systems coincide with those of random matrices
from the Gaussian orthogonal ensemble (GOE). Does this result hold for
two-dimensional Dirac material systems? To address this fundamen- tal question,
we investigate the spectral properties in a representative class of graphene
billiards with shapes of classically integrable circular-sector billiards.
Naively one may expect to observe Poisson statistics, which is indeed true for
energies close to the band edges where the quasiparticle obeys the
Schr\"odinger equation. However, for energies near the Dirac point, where the
quasiparticles behave like massless Dirac fermions, Pois- son statistics is
extremely rare in the sense that it emerges only under quite strict symmetry
constraints on the straight boundary parts of the sector. An arbitrarily small
amount of imperfection of the boundary results in GOE statistics. This implies
that, for circular sector confinements with arbitrary angle, the spectral
properties will generically be GOE. These results are corroborated by extensive
numerical computation. Furthermore, we provide a physical understanding for our
results.
|
Image-based vibration mode identification gained increased attentions in
civil and construction communities. A recent video-based motion magnification
method was developed to measure and visualize small structure motions. This new
approach presents a potential for low-cost vibration measurement and mode shape
identification. Pilot studies using this approach on simple rigid body
structures was reported. Its validity on complex outdoor structures have not
been investigated. The objective is to investigate the capacity of video-based
motion magnification approach in measuring the modal frequency and visualizing
the mode shapes of complex steel bridges. A novel method that increases the
performance of the current motion magnification for efficient structure modal
analysis is introduced. This method was tested in both indoor and outdoor
environments for validation. The results of the investigation show that motion
magnification can be an efficient tool for modal analysis on complex bridge
structures. With the developed method, mode frequencies of multiple structures
are simultaneously measured and mode shapes of each structure are automatically
visualized.
|
It has been proposed that the Poincare and some other symmetries of
noncommutative field theories should be twisted. Here we extend this idea to
gauge transformations and find that twisted gauge symmetries close for
arbitrary gauge group. We also analyse twisted-invariant actions in
noncommutative theories.
|
The reliable operation of micro and nanomechanical devices necessitates a
thorough knowledge of the water film thickness present on the surfaces of these
devices with an accuracy in the nm range. In this work, the thickness of an
ultra-thin water layer was measured by distance tunnelling spectroscopy and
distance dynamic force spectroscopy during desorption in an ultra-high vacuum
system, from about 2.5 nm up to complete desorption at 1E-8 mbar. The
tunnelling current as well as the amplitude of vibration and the normal force
were detected as a function of the probe-sample distance. In these experiments,
a direct conversion of the results of both methods is possible. From the
standpoint of surface science, taking the state-of-the-art concerning
adsorbates on surfaces into consideration, dynamic force spectroscopy provides
the most accurate values. The previously reported tunnelling spectroscopy,
requiring the application of significantly high voltages, generally leads to
values that are 25 times higher than values determined by dynamic force
spectroscopy.
|
In this work, we perform Bayesian inference tasks for the chemical master
equation in the tensor-train format. The tensor-train approximation has been
proven to be very efficient in representing high dimensional data arising from
the explicit representation of the chemical master equation solution. An
additional advantage of representing the probability mass function in the
tensor train format is that parametric dependency can be easily incorporated by
introducing a tensor product basis expansion in the parameter space. Time is
treated as an additional dimension of the tensor and a linear system is derived
to solve the chemical master equation in time. We exemplify the tensor-train
method by performing inference tasks such as smoothing and parameter inference
using the tensor-train framework. A very high compression ratio is observed for
storing the probability mass function of the solution. Since all linear algebra
operations are performed in the tensor-train format, a significant reduction of
the computational time is observed as well.
|
We demonstrate for the first time the magnetic field distribution of the pure
vortex state in lightly doped Mg$_{1-x}$Al$_x$B$_2$ ($x\leq 0.025$) powder
samples, by using $^{11}$B NMR in magnetic fields of 23.5 and 47 kOe. The
magnetic field distribution at T=5 K is Al-doping dependent, revealing a
considerable decrease of anisotropy in respect to pure MgB$_2$. This result
correlates nicely with magnetization measurements and is consistent with
$\sigma$-band hole driven superconductivity for MgB$_2$.
|
This paper explores an old problem, {\em Byzantine fault-tolerant Broadcast}
(BB), under a new model, {\em selective broadcast model}. The new model
"interpolates" between the two traditional models in the literature. In
particular, it allows fault-free nodes to exploit the benefits of a broadcast
channel (a feature from reliable broadcast model) and allows faulty nodes to
send mismatching messages to different neighbors (a feature from point-to-point
model) simultaneously. The {\em selective broadcast} model is motivated by the
potential for {\em directional} transmissions on a wireless channel.
We provide a collection of results for a single-hop wireless network under
the new model. First, we present an algorithm for {\em Multi-Valued} BB that is
order-optimal in bit complexity. Then, we provide an algorithm that is designed
to achieve BB efficiently in terms of message complexity. Third, we determine
some lower bounds on both bit and message complexities of BB problems in the
{\em selective broadcast model}. Finally, we present a conjecture on an "exact"
lower bound on the bit complexity of BB under the {\em selective broadcast}
model.
|
SmB6 is a mixed valence Kondo insulator that exhibits a sharp increase in
resistance following an activated behavior that levels off and saturates below
4K. This behavior can be explained by the proposal of SmB6 representing a new
state of matter, a Topological Kondo insulator, in which a Kondo gap is
developed and topologically protected surface conduction dominates
low-temperature transport. Exploiting its non-linear dynamics, a tunable SmB6
oscillator device was recently demonstrated, where a small DC current generates
large oscillating voltages at frequencies from a few Hz to hundreds of MHz.
This behavior was explained by a theoretical model describing the thermal and
electronic dynamics of coupled surface and bulk states. However, a crucial
aspect of this model, the predicted temperature oscillation in the surface
state, hasn't been experimentally observed to date. This is largely due to the
technical difficulty of detecting an oscillating temperature of the very thin
surface state. Here we report direct measurements of the time-dependent surface
state temperature in SmB6 with a RuO micro-thermometer. Our results agree
quantitatively with the theoretically simulated temperature waveform, and hence
support the validity of the oscillator model, which will provide accurate
theoretical guidance for developing future SmB6oscillators at higher
frequencies.
|
One of the long-standing problems in the field of high-energy heavy-ion
collisions is that the dynamical models based on viscous hydrodynamics fail to
describe the experimental elliptic flow $v_2$ and the triangular flow $v_3$
simultaneously in ultra-central collisions. The problem, known as the
"ultra-central flow puzzle", is specifically that hydrodynamics-based models
predict the flow ratio of the two-particle cumulant method $v_2\{2\}/v_3\{2\} >
1$ while $v_2\{2\}/v_3\{2\} \sim 1$ in the experimental data. In this Letter,
we focus on the effects of hydrodynamic fluctuations during the space-time
evolution of the QGP fluid on the flow observables in the ultra-central
collisions. Using the (3+1)-dimensional integrated dynamical model which
includes relativistic fluctuating hydrodynamics, we analyze the anisotropic
flow coefficients $v_n\{2\}$ in 0-0.2% central Pb+Pb collisions at
$\sqrt{s_\text{NN}}=2.76~\text{TeV}$. We find that the hydrodynamic
fluctuations decrease the model overestimate of $v_2\{2\}/v_3\{2\}$ from the
experimental data by about 19% within the present setup of $\eta/s = 1/2\pi$.
This means that the hydrodynamic fluctuations qualitatively have an effect to
improve the situation for the puzzle, but the effect of the hydrodynamic
fluctuations alone is quantitatively insufficient to resolve the puzzle. The
decrease of the ratio largely depends on the shear viscosity $\eta/s$, which
calls for future comprehensive analyses with, for example, a realistic
temperature-dependent viscosity.
|
We study transcendental meromorphic functions having two prepole asymptotic
values and no critical values. We prove that these functions acting on their
Julia sets are non-ergodic, which illustrates the antithesis of the Keen-Kotus
result in [KK2] on the ergodicity of another subfamily of functions with two
asymptotic values and no critical values.
|
We define and develop the infrastructure of homotopical inverse diagrams in
categories with attributes.
Specifically, given a category with attributes $C$ and an ordered homotopical
inverse category $I$, we construct the category with attributes $C^I$ of
homotopical diagrams of shape $I$ in $C$ and Reedy types over these; and we
show how various logical structure ($\Pi$-types, identity types, and so on)
lifts from $C$ to $C^I$. This may be seen as providing a general class of
diagram models of type theory.
In a companion paper "The homotopy theory of type theories"
(arXiv:1610.00037), we apply the present results to construct semi-model
structures on categories of contextual categories.
|
Mammals have a high metabolism that produces heat proportionally to the power
3/4 of their mass at rest. Any excess of heat has to be dissipated in the
surrounding environment to prevent overheating. Most of that dissipation occurs
through the skin, but the efficiency of that mechanism decreases with the
animal's mass. The role of the other mechanisms for dissipating heat is then
raised, more particularly the one linked to the lung that forms a much larger
surface area than the skin. The dissipation occurring in the lung is however
often neglected, even though there exists no real knowledge of its dynamics,
hidden by the complexity of the organ's geometry and of the physics of the
exchanges. Here we show, based on an original and analytical model of the
exchanges in the lung, that all mammals, independently of their mass, dissipate
through their lung the same proportion of the heat they produced, about 6-7 %.
We found that the heat dissipation in mammals' lung is driven by a number,
universal among mammals, that arises from the dynamics of the temperature of
the bronchial mucosa. We propose a scenario to explain how evolution might have
tuned the lung for heat exchanges. Furthermore, our analysis allows to define
the pulmonary heat and water diffusive capacities. We show in the human case
that these capacities follow closely the oxygen consumption. Our work lays the
foundations for more detailed analysis of the heat exchanges occurring in the
lung. Future studies should focus on refining our understanding of the
universal number identified. In an ecological framework, our analysis paves the
way to a better understanding of the mammals' strategies for thermoregulation
and of the effect of warming environments on mammals' metabolism.
|
The ac Stark shift of hyperfine levels of neutral atoms can be calculated
using the third order perturbation theory(TOPT), where the third order
corrections are quadratic in the atom-photon interaction and linear in the
hyperfine interaction. In this paper, we use Green's function to derive the
$E^{[2+\epsilon]}$ method which can give close values to those of TOPT for the
differential light shift between two hyperfine levels. It comes with a simple
form and easy incorporation of theoretical and experimental atomic structure
data. Furthermore, we analyze the order of approximation and give the condition
under which $E^{[2+\epsilon]}$ method is valid.
|
The current modus operandi in adapting pre-trained models involves updating
all the backbone parameters, ie, full fine-tuning. This paper introduces Visual
Prompt Tuning (VPT) as an efficient and effective alternative to full
fine-tuning for large-scale Transformer models in vision. Taking inspiration
from recent advances in efficiently tuning large language models, VPT
introduces only a small amount (less than 1% of model parameters) of trainable
parameters in the input space while keeping the model backbone frozen. Via
extensive experiments on a wide variety of downstream recognition tasks, we
show that VPT achieves significant performance gains compared to other
parameter efficient tuning protocols. Most importantly, VPT even outperforms
full fine-tuning in many cases across model capacities and training data
scales, while reducing per-task storage cost.
|
In this paper, we address several Erd\H os--Ko--Rado type questions for
families of partitions. Two partitions of $[n]$ are {\it $t$-intersecting} if
they share at least $t$ parts, and are {\it partially $t$-intersecting} if some
of their parts intersect in at least $t$ elements. The question of what is the
largest family of pairwise $t$-intersecting partitions was studied for several
classes of partitions: Peter Erd\H os and Sz\'ekely studied partitions of $[n]$
into $\ell$ parts of unrestricted size; Ku and Renshaw studied unrestricted
partitions of $[n]$; Meagher and Moura, and then Godsil and Meagher studied
partitions into $\ell$ parts of equal size. We improve and generalize the
results proved by these authors. Meagher and Moura, following the work of Erd\H
os and Sz\'ekely, introduced the notion of partially $t$-intersecting
partitions, and conjectured, what should be the largest partially
$t$-intersecting family of partitions into $\ell$ parts of equal size $k$. The
main result of this paper is the proof of their conjecture for all $t, k$,
provided $\ell$ is sufficiently large. All our results are applications of the
spread approximation technique, introduced by Zakharov and the author. In order
to use it, we need to refine some of the theorems from the original paper. As a
byproduct, this makes the present paper a self-contained presentation of the
spread approximation technique for $t$-intersecting problems.
|
Self-supervised monocular depth estimation methods have been increasingly
given much attention due to the benefit of not requiring large, labelled
datasets. Such self-supervised methods require high-quality salient features
and consequently suffer from severe performance drop for indoor scenes, where
low-textured regions dominant in the scenes are almost indiscriminative. To
address the issue, we propose a self-supervised indoor monocular depth
estimation framework called $\mathrm{F^2Depth}$. A self-supervised optical flow
estimation network is introduced to supervise depth learning. To improve
optical flow estimation performance in low-textured areas, only some patches of
points with more discriminative features are adopted for finetuning based on
our well-designed patch-based photometric loss. The finetuned optical flow
estimation network generates high-accuracy optical flow as a supervisory signal
for depth estimation. Correspondingly, an optical flow consistency loss is
designed. Multi-scale feature maps produced by finetuned optical flow
estimation network perform warping to compute feature map synthesis loss as
another supervisory signal for depth learning. Experimental results on the NYU
Depth V2 dataset demonstrate the effectiveness of the framework and our
proposed losses. To evaluate the generalization ability of our
$\mathrm{F^2Depth}$, we collect a Campus Indoor depth dataset composed of
approximately 1500 points selected from 99 images in 18 scenes. Zero-shot
generalization experiments on 7-Scenes dataset and Campus Indoor achieve
$\delta_1$ accuracy of 75.8% and 76.0% respectively. The accuracy results show
that our model can generalize well to monocular images captured in unknown
indoor scenes.
|
We look at the odd nilpotent orbits of osp(2n+1,2n), giving a combinatorial
interpretation which enables us, via the square map, to explain the link with
even nilpotent orbits. We then study the closure ordering of the odd nilpotent
orbits. Finally, we give a desingularization of the odd nilpotent cone.
|
Based on 58 million BESII J/psi events, the bar{K}^*(892)^0K^+pi^- channel in
K^+K^-pi^+pi^- is studied. A clear low mass enhancement in the invariant mass
spectrum of K^+pi^- is observed. The low mass enhancement does not come from
background of other J/psi decay channels, nor from phase space. Two independent
partial wave analyses have been performed. Both analyses favor that the low
mass enhancement is the kappa, an isospinor scalar resonant state. The average
mass and width of the kappa in the two analyses are 878 +- 23^{+64}_{-55}
MeV/c^2 and 499 +- 52^{+55}_{-87} MeV/c^2, respectively, corresponding to a
pole at (841 +- 30^{+81}_{-73}) - i(309 +- 45^{+48}_{-72}) MeV/c^2.
|
Within the framework of the Projective Unified Field Theory the distribution
of a dark matter gas around a central body is calculated. As a result the
well-known formulas of the Newtonian gravitational interaction are altered.
This dark matter effect leads to an additional radial force (towards the
center) in the equation of motion of a test body, being used for the
explanation of the so-called ``Pioneer effect'', measured in the solar system,
but without a convincing theoretical basis up to now. Further the relationship
of the occurring new force to the so-called ``fifth force'' is discussed.
|
We study interacting bosons on a lattice in a magnetic field. When the number
of flux quanta per plaquette is close to a rational fraction, the low energy
physics is mapped to a multi-species continuum model: bosons in the lowest
Landau level where each boson is given an internal degree of freedom, or
pseudospin. We find that the interaction potential between the bosons involves
terms that do not conserve pseudospin, corresponding to umklapp processes,
which in some cases can also be seen as BCS-type pairing terms. We argue that
in experimentally realistic regimes for bosonic atoms in optical lattices with
synthetic magnetic fields, these terms are crucial for determining the nature
of allowed ground states. In particular, we show numerically that certain
paired wavefunctions related to the Moore-Read Pfaffian state are stabilized by
these terms, whereas certain other wavefunctions can be destabilized when
umklapp processes become strong.
|
Coronal loops form the basic building blocks of the magnetically closed solar
corona yet much is still to be determined concerning their possible fine-scale
structuring and the rate of heat deposition within them. Using an improved
multi-stranded loop model to better approximate the numerically challenging
transition region, this paper examines synthetic NASA Solar Dynamics
Observatory's (SDO) Atmospheric Imaging Assembly (AIA) emission simulated in
response to a series of prescribed spatially and temporally random, impulsive
and localised heating events across numerous sub-loop elements with a strong
weighting towards the base of the structure; the nanoflare heating scenario.
The total number of strands and nanoflare repetition times are varied
systematically in such a way that the total energy content remains
approximately constant across all the cases analysed. Repeated time lag
detection during an emission time series provides a good approximation for the
nanoflare repetition time for low-frequency heating. Furthermore, using a
combination of AIA 171/193 and 193/211 channel ratios in combination with
spectroscopic determination of the standard deviation of the loop apex
temperature over several hours alongside simulations from the outlined
multi-stranded loop model, it is demonstrated that both the imposed heating
rate and number of strands can be realised.
|
In our recent paper [Phys. Rev. E 90, 032132 (2014)] we have studied the
dynamics of a mobile impurity particle weakly interacting with the
Tonks-Girardeau gas and pulled by a small external force, $F$. Working in the
regime when the thermodynamic limit is taken prior to the small force limit, we
have found that the Bloch oscillations of the impurity velocity are absent in
the case of a light impurity. Further, we have argued that for a light impurity
the steady state drift velocity, $V_D$, remains finite in the limit
$F\rightarrow 0$. These results are in contradiction with earlier works by
Gangardt, Kamenev and Schecter [Phys. Rev. Lett. 102, 070402 (2009), Annals of
Physics 327, 639 (2012)]. One of us (OL) has conjectured [Phys. Rev. A 91,
040101 (2015)] that the central assumption of these works - the adiabaticity of
the dynamics - can break down in the thermodynamic limit. In the preceding
Comment [Phys. Rev. E 92, 016101 (2015)] Schecter, Gangardt and Kamenev have
argued against this conjecture and in support of the existence of Bloch
oscillations and linearity of $V_D(F)$. They have suggested that the ground
state of the impurity-fluid system is a quasi-bound state and that this is
sufficient to ensure adiabaticity in the thermodynamic limit. Their analytical
argument is based on a certain truncation of the Hilbert space of the system.
We argue that extending the results and intuition based on their truncated
model on the original many-body problem lacks justification.
|
The Sagdeev potential technique has been used to investigate the existence
and the polarity of dust ion acoustic solitary structures in an unmagnetized
collisionless nonthermal dusty plasma consisting of negatively charged static
dust grains, adiabatic warm ions and nonthermal electrons when the velocity of
the wave frame is equal to the linearized velocity of the dust ion acoustic
wave for long wave length plane wave perturbation, i.e., when the velocity of
the solitary structure is equal to the acoustic speed. A compositional
parameter space has been drawn which shows the nature of existence and the
polarity of dust ion acoustic solitary structures at the acoustic speed. This
compositional parameter space clearly indicates the regions for the existence
of positive and negative potential dust ion acoustic solitary structures.
Again, this compositional parameter space shows that the present system
supports the negative potential double layer at the acoustic speed along a
particular curve in the parametric plane. However, the negative potential
double layer is unable to restrict the occurrence of all negative potential
solitary waves. As a result, in a particular region of the parameter space,
there exist negative potential solitary waves after the formation of negative
potential double layer. But the amplitudes of these supersolitons are bounded.
A finite jump between amplitudes of negative potential solitons separated by
the negative potential double layer has been observed, and consequently, the
present system supports the supersolitons at the acoustic speed in a
neighbourhood of the curve along which negative potential double layer exist.
The effects of the parameters on the amplitude of the solitary structures at
the acoustic speed have been discussed.
|
Jamison and Sprague defined a graph $G$ to be a $k$-threshold graph with
thresholds $\theta_1 , \ldots, \theta_k$ (strictly increasing) if one can
assign real numbers $(r_v)_{v \in V(G)}$, called ranks, such that for every
pair of vertices $v,w$, we have $vw \in E(G)$ if and only if the inequality
$\theta_i \leq r_v + r_w$ holds for an odd number of indices $i$. When $k=1$ or
$k=2$, the precise choice of thresholds $\theta_1, \ldots, \theta_k$ does not
matter, as a suitable transformation of the ranks transforms a representation
with one choice of thresholds into a representation with any other choice of
thresholds. Jamison asked whether this remained true for $k \geq 3$ or whether
different thresholds define different classes of graphs for such $k$, offering
\$50 for a solution of the problem. Letting $C_t$ for $t > 1$ denote the class
of $3$-threshold graphs with thresholds $-1, 1, t$, we prove that there are
infinitely many distinct classes $C_t$, answering Jamison's question. We also
consider some other problems on multithreshold graphs, some of which remain
open.
|
We estimate the evolution of the galaxy-galaxy merger fraction for
$M_\star>10^{10.5}M_\odot$ galaxies over $0.25<z<1$ in the $\sim$18.6 deg$^2$
deep CLAUDS+HSC-SSP surveys. We do this by training a Random Forest Classifier
to identify merger candidates from a host of parametric morphological features,
and then visually follow-up likely merger candidates to reach a high-purity,
high-completeness merger sample. Correcting for redshift-dependent detection
bias, we find that the merger fraction at $z=0$ is 1.0$\pm$0.2%, that the
merger fraction evolves as $(1+z)^{2.3 \pm 0.4}$, and that a typical massive
galaxy has undergone $\sim$0.3 major mergers since $z=1$. This pilot study
illustrates the power of very deep ground-based imaging surveys combined with
machine learning to detect and study mergers through the presence of faint, low
surface brightness merger features out to at least $z\sim1$.
|
We present a new approach to determine numerically the statistical behavior
of small-scale structures in hydrodynamic turbulence. Starting from the
functional integral representation of the random-force-driven Burgers equation
we show that Monte Carlo simulations allow us to determine the anomalous
scaling of high-order moments of velocity differences. Given the general
applicability of Monte Carlo methods, this opens up the possibility to address
also other systems relevant to turbulence within this framework.
|
This paper summarizes the outcomes of the 5th International Workshop on
Femtocells held at King's College London, UK, on the 13th and 14th of February,
2012.The workshop hosted cutting-edge presentations about the latest advances
and research challenges in small cell roll-outs and heterogeneous cellular
networks. This paper provides some cutting edge information on the developments
of Self-Organizing Networks (SON) for small cell deployments, as well as
related standardization supports on issues such as carrier aggregation (CA),
Multiple-Input-Multiple-Output (MIMO) techniques, and enhanced Inter-Cell
Interference Coordination (eICIC), etc. Furthermore, some recent efforts on
issues such as energy-saving as well as Machine Learning (ML) techniques on
resource allocation and multi-cell cooperation are described. Finally, current
developments on simulation tools and small cell deployment scenarios are
presented. These topics collectively represent the current trends in small cell
deployments.
|
The authors have recently proposed a ``microcanonical functional integral"
representation of the density of quantum states of the gravitational field. The
phase of this real--time functional integral is determined by a
``microcanonical" or Jacobi action, the extrema of which are classical
solutions at fixed total energy, not at fixed total time interval as in
Hamilton's action. This approach is fully general but is especially well suited
to gravitating systems because for them the total energy can be fixed simply as
a boundary condition on the gravitational field. In this paper we describe how
to obtain Jacobi's action for general relativity. We evaluate it for a certain
complex metric associated with a rotating black hole and discuss the relation
of the result to the density of states and to the entropy of the black hole.
(Dedicated to Yvonne Choquet-Bruhat in honor of her retirement.)
|
Species distribution models (SDM) are a key tool in ecology, conservation and
management of natural resources. Two key components of the state-of-the-art
SDMs are the description for species distribution response along environmental
covariates and the spatial random effect. Joint species distribution models
(JSDMs) additionally include interspecific correlations which have been shown
to improve their descriptive and predictive performance compared to single
species models. Current JSDMs are restricted to hierarchical generalized linear
modeling framework. These parametric models have trouble in explaining changes
in abundance due, e.g., highly non-linear physical tolerance limits which is
particularly important when predicting species distribution in new areas or
under scenarios of environmental change. On the other hand, semi-parametric
response functions have been shown to improve the predictive performance of
SDMs in these tasks in single species models. Here, we propose JSDMs where the
responses to environmental covariates are modeled with additive multivariate
Gaussian processes coded as linear models of coregionalization. These allow
inference for wide range of functional forms and interspecific correlations
between the responses. We propose also an efficient approach for inference with
Laplace approximation and parameterization of the interspecific covariance
matrices on the euclidean space. We demonstrate the benefits of our model with
two small scale examples and one real world case study. We use cross-validation
to compare the proposed model to analogous semi-parametric single species
models and parametric single and joint species models in interpolation and
extrapolation tasks. The proposed model outperforms the alternative models in
all cases. We also show that the proposed model can be seen as an extension of
the current state-of-the-art JSDMs to semi-parametric models.
|
An exciting recent development is the uptake of deep neural networks in many
scientific fields, where the main objective is outcome prediction with the
black-box nature. Significance testing is promising to address the black-box
issue and explore novel scientific insights and interpretation of the
decision-making process based on a deep learning model. However, testing for a
neural network poses a challenge because of its black-box nature and unknown
limiting distributions of parameter estimates while existing methods require
strong assumptions or excessive computation. In this article, we derive
one-split and two-split tests relaxing the assumptions and computational
complexity of existing black-box tests and extending to examine the
significance of a collection of features of interest in a dataset of possibly a
complex type such as an image. The one-split test estimates and evaluates a
black-box model based on estimation and inference subsets through sample
splitting and data perturbation. The two-split test further splits the
inference subset into two but require no perturbation. Also, we develop their
combined versions by aggregating the p-values based on repeated sample
splitting. By deflating the bias-sd-ratio, we establish asymptotic null
distributions of the test statistics and the consistency in terms of Type II
error. Numerically, we demonstrate the utility of the proposed tests on seven
simulated examples and six real datasets. Accompanying this paper is our Python
library dnn-inference (https://dnn-inference.readthedocs.io/en/latest/) that
implements the proposed tests.
|
(abridged) In this paper we describe in detail the reduction, preparation and
reliability of the photometric catalogues which comprise the 1.2 deg^2
CFH12K-VIRMOS deep field. The survey reaches a limiting magnitude of BAB~26.5,
VAB~26.2, RAB~25.9 IAB~25.0 and contains 90,729 extended sources in the
magnitude range 18.0<IAB<24.0. We demonstrate our catalogues are free from
systematic biases and are complete and reliable down these limits. We estimate
that the upper limit on bin-to-bin systematic photometric errors for the I-
limited sample is ~10% in this magnitude range. We estimate that 68% of the
catalogues sources have absolute per co-ordinate astrometric uncertainties less
than ~0.38" and ~0.32" (alpha,delta). Our internal (filter-to-filter) per
co-ordinate astrometric uncertainties are 0.08" and 0.08" (alpha,delta). We
quantify the completeness of our survey in the joint space defined by object
total magnitude and peak surface brightness. Finally, we present numerous
comparisons between our catalogues and published literature data: galaxy and
star counts, galaxy and stellar colours, and the clustering of both point-like
and extended populations. In all cases our measurements are in excellent
agreement with literature data to IAB<24.0. This combination of depth and areal
coverage makes this multi-colour catalogue a solid foundation to select
galaxies for follow-up spectroscopy with VIMOS on the ESO-VLT and a unique
database to study the formation and evolution of the faint galaxy population to
z~1 and beyond.
|
A heliopause spectrum at 122 AU from the Sun is presented for galactic
electrons over an energy range from 1 MeV to 50 GeV that can be considered the
lowest possible local interstellar spectrum (LIS). The focus is on the spectral
shape of the LIS below 1.0 GeV. The study is done by using a comprehensive
numerical model for solar modulation in comparison with Voyager 1 observations
at 110 AU from the Sun and PAMELA data at Earth. Below 1.0 GeV, this LIS
exhibits a power law,E to the power -(1.55+-0.05), where E is the kinetic
energy. However, reproducing the PAMELA electron spectrum averaged for 2009,
requires a LIS with a different power law of the form E to the power
-(3.15+-0.05) above about 5 GeV. Combining the two power laws with a smooth
transition from low to high energies yields a LIS over the full energy range
that is relevant and applicable to the modulation of cosmic ray electrons in
the heliosphere. The break occurs between 800 MeV and 2 GeV as a characteristic
feature of this LIS.
|
The constrained Hamiltonian systems admitting no gauge conditions are
considered. The methods to deal with such systems are discussed and developed.
As a concrete application, the relationship between the Dirac and reduced phase
space quantizations is investigated for spin models belonging to the class of
systems under consideration. It is traced out that the two quantization methods
may give similar, or essentially different physical results, and, moreover, a
class of constrained systems, which can be quantized only by the Dirac method,
is discussed. A possible interpretation of the gauge degrees of freedom is
given.
|
Wave-particle interaction is a key process in particle diffusion in
collisionless plasmas. We look into the interaction of single plasma waves with
individual particles and discuss under which circumstances this is a chaotic
process, leading to diffusion. We derive the equations of motion for a particle
in the fields of a magnetostatic, circularly polarized, monochromatic wave and
show that no chaotic particle motion can arise under such circumstances. A
novel and exact analytic solution for the equations is presented. Additional
plasma waves lead to a breakdown of the analytic solution and chaotic particle
trajectories become possible. We demonstrate this effect by considering a
linearly polarized, monochromatic wave, which can be seen as the superposition
of two circularly polarized waves. Test particle simulations are provided to
illustrate and expand our analytical considerations.
|
In this paper, we compute the cyclic homology of the Taft algebras and of
their Auslander algebras. Given a Hopf algebra $\Lambda,$ the Grothendieck
groups of projective $\Lambda -$modules and of all $\Lambda -$modules are
endowed with a ring structure, which in the case of the Taft algebras is
commutative (\cite{C2}, \cite{G}). We also describe the first Chern character
for these algebras.
|
Numerous video frame sampling methodologies detailed in the literature
present a significant challenge in determining the optimal video frame method
for Video RAG pattern without a comparative side-by-side analysis. In this
work, we investigate the trade-offs in frame sampling methods for Video & Frame
Retrieval using natural language questions. We explore the balance between the
quantity of sampled frames and the retrieval recall score, aiming to identify
efficient video frame sampling strategies that maintain high retrieval efficacy
with reduced storage and processing demands. Our study focuses on the storage
and retrieval of image data (video frames) within a vector database required by
Video RAG pattern, comparing the effectiveness of various frame sampling
techniques. Our investigation indicates that the recall@k metric for both
text-to-video and text-to-frame retrieval tasks using various methods covered
as part of this work is comparable to or exceeds that of storing each frame
from the video. Our findings are intended to inform the selection of frame
sampling methods for practical Video RAG implementations, serving as a
springboard for innovative research in this domain.
|
Bi$_2$Te$_3$ is a topological insulator whose unique properties result from
topological surface states in the band gap. The neutralization of scattered low
energy Na$^+$, which is sensitive to dipoles that induce inhomogeneities in the
local surface potential, is larger when scattered from Te than from Bi,
indicating an upwards dipole at the Te sites and a downwards dipole above Bi.
These dipoles are caused by the spatial distribution of the conductive
electrons in the topological surface states. This result demonstrates how this
alkali ion scattering method can be applied to provide direct experimental
evidence of the spatial distribution of electrons in filled surface states.
|
Gas is the transaction-fee metering system of the Ethereum network. Users of
the network are required to select a gas price for submission with their
transaction, creating a risk of overpaying or delayed/unprocessed transactions
in this selection. In this work, we investigate data in the aftermath of the
London Hard Fork and shed insight into the transaction dynamics of the net-work
after this major fork. As such, this paper provides an update on work previous
to 2019 on the link between EthUSD BitUSD and gas price. For forecasting, we
compare a novel combination of machine learning methods such as Direct
Recursive Hybrid LSTM, CNNLSTM, and Attention LSTM. These are combined with
wavelet threshold denoising and matrix profile data processing toward the
forecasting of block minimum gas price, on a 5-min timescale, over multiple
lookaheads. As the first application of the matrix profile being applied to gas
price data and forecasting we are aware of, this study demonstrates that matrix
profile data can enhance attention-based models however, given the hardware
constraints, hybrid models outperformed attention and CNNLSTM models. The
wavelet coherence of inputs demonstrates correlation in multiple variables on a
1 day timescale, which is a deviation of base free from gas price. A
Direct-Recursive Hybrid LSTM strategy outperforms other models. Hybrid models
have favourable performance up to a 20 min lookahead with performance being
comparable to attention models when forecasting 25/50-min ahead. Forecasts over
a range of lookaheads allow users to make an informed decision on gas price
selection and the optimal window to submit their transaction in without fear of
their transaction being rejected. This, in turn, gives more detailed insight
into gas price dynamics than existing recommenders, oracles and forecasting
approaches, which provide simple heuristics or limited lookahead horizons.
|
Chemically peculiar Ap and Bp stars host strong large-scale magnetic fields
in the range of $200$~G up to $30$~kG, which are often considered to be the
origin of fossil magnetic fields. We assess the evolution of such fossil fields
during the star formation process and the pre-main sequence evolution of
intermediate stars, considering fully convective models, models including a
transition to a radiative protostar and models with a radiative core. We also
examine the implications of the interaction between the fossil field and the
core dynamo. We employ analytic and semi-analytic calculations combined with
current observational constraints. For fully convective models, we show that
magnetic field decay via convection can be expected to be very efficient for
realistic parameters of turbulent resistivities. Based on the observed magnetic
field strength - density relation, as well as the expected amount of flux loss
due to ambipolar diffusion, it appears unlikely that convection could be
suppressed via strong enough magnetic fields. On the other hand, a transition
from a convective to a radiative core could very naturally explain the survival
of a significant amount of flux, along with the presence of a critical mass. We
show that in some cases, the interaction of a fossil field with a core dynamo
may further lead to changes in the surface magnetic field structure. In the
future, it will be important to understand in more detail how the accretion
rate evolves as a function of time during the formation of intermediate-mass
protostars, including its impact on the protostellar structure. The latter may
even allow to derive quantitative predictions concerning the expected
population of large scale magnetic fields in radiative stars.
|
In this paper, we formulate an evolutionary multiple access channel game with
continuous-variable actions and coupled rate constraints. We characterize Nash
equilibria of the game and show that the pure Nash equilibria are Pareto
optimal and also resilient to deviations by coalitions of any size, i.e., they
are strong equilibria. We use the concepts of price of anarchy and strong price
of anarchy to study the performance of the system. The paper also addresses how
to select one specifc equilibrium solution using the concepts of normalized
equilibrium and evolutionary stable strategies. We examine the long-run
behavior of these strategies under several classes of evolutionary game
dynamics such as Brown-von Neumann-Nash dynamics, and replicator dynamics.
|
Proxy means testing (PMT) and community-based targeting (CBT) are two of the
leading methods for targeting social assistance in developing countries. In
this paper, we present a hybrid targeting method that incorporates CBT's
emphasis on local information and preferences with PMT's reliance on verifiable
indicators. Specifically, we outline a Bayesian framework for targeting that
resembles PMT in that beneficiary selection is based on a weighted sum of
sociodemographic characteristics. We nevertheless propose calibrating the
weights to preference rankings from community targeting exercises, implying
that the weights used by our method reflect how potential beneficiaries
themselves substitute sociodemographic features when making targeting
decisions. We discuss several practical extensions to the model, including a
generalization to multiple rankings per community, an adjustment for elite
capture, a method for incorporating auxiliary information on potential
beneficiaries, and a dynamic updating procedure. We further provide an
empirical illustration using data from Burkina Faso and Indonesia.
|
We show that there exists a universal quantum Turing machine (UQTM) that can
simulate every other QTM until the other QTM has halted and then halt itself
with probability one. This extends work by Bernstein and Vazirani who have
shown that there is a UQTM that can simulate every other QTM for an arbitrary,
but preassigned number of time steps. As a corollary to this result, we give a
rigorous proof that quantum Kolmogorov complexity as defined by Berthiaume et
al. is invariant, i.e. depends on the choice of the UQTM only up to an additive
constant. Our proof is based on a new mathematical framework for QTMs,
including a thorough analysis of their halting behaviour. We introduce the
notion of mutually orthogonal halting spaces and show that the information
encoded in an input qubit string can always be effectively decomposed into a
classical and a quantum part.
|
We present results of convective turbulent dynamo simulations including a
coronal layer in a spherical wedge. We find an equatorward migration of the
radial and azimuthal fields similar to the behavior of sunspots during the
solar cycle. The migration of the field coexist with a spoke-like differential
rotation and anti-solar (clockwise) meridional circulation. Even though the
migration extends over the whole convection zone, the mechanism causing this is
not yet fully understood.
|
The success of various applications including robotics, digital content
creation, and visualization demand a structured and abstract representation of
the 3D world from limited sensor data. Inspired by the nature of human
perception of 3D shapes as a collection of simple parts, we explore such an
abstract shape representation based on primitives. Given a single depth image
of an object, we present 3D-PRNN, a generative recurrent neural network that
synthesizes multiple plausible shapes composed of a set of primitives. Our
generative model encodes symmetry characteristics of common man-made objects,
preserves long-range structural coherence, and describes objects of varying
complexity with a compact representation. We also propose a method based on
Gaussian Fields to generate a large scale dataset of primitive-based shape
representations to train our network. We evaluate our approach on a wide range
of examples and show that it outperforms nearest-neighbor based shape retrieval
methods and is on-par with voxel-based generative models while using a
significantly reduced parameter space.
|
Small cells deployed in licensed spectrum and unlicensed access via WiFi
provide different ways of expanding wireless services to low mobility users.
That reduces the demand for conventional macro-cellular networks, which are
better suited for wide-area mobile coverage. The mix of these technologies seen
in practice depends in part on the decisions made by wireless service providers
that seek to maximize revenue, and allocations of licensed and unlicensed
spectrum by regulators. To understand these interactions we present a model in
which a service provider allocates available licensed spectrum across two
separate bands, one for macro- and one for small-cells, in order to serve two
types of users: mobile and fixed. We assume a service model in which the
providers can charge a (different) price per unit rate for each type of service
(macro- or small-cell); unlicensed access is free. With this setup we study how
the addition of unlicensed spectrum affects prices and the optimal allocation
of bandwidth across macro-/small-cells. We also characterize the optimal
fraction of unlicensed spectrum when new bandwidth becomes available.
|
The full architecture of an electrostatic kinetic energy harvester (KEH)
based on the concept of near-limits KEH is reported. This concept refers to the
conversion of kinetic energy to electric energy, from environmental vibrations
of arbitrary forms, and at rates that target the physical limits set by the
device's size and the input excitation characteristics. This is achieved thanks
to the synthesis of particular KEH's mass dynamics, that maximize the harvested
energy. Synthesizing these dynamics requires little hypotheses on the exact
form of the input vibrations. In the proposed architecture, these dynamics are
implemented by an adequate mechanical control which is synthesized by the
electrostatic transducer. An interface circuit is proposed to carry out the
necessary energy transfers between the transducer and the system's energy tank.
A computation and finite-state automaton unit controls the interface circuit,
based on the external input and on the system's mechanical state. The operation
of the reported near-limits KEH is illustrated in simulations that demonstrate
proof of concept of the proposed architecture. A figure of $68\%$ of the
absolute limit of the KEH's input energy for the considered excitation is
attained. This can be further improved by complete system optimization that
takes into account the application constraints, the control law, the mechanical
design of the transducer, the electrical interface design, and the sensing and
computation blocks.
|
For at least 40 years, there has been debate and disagreement as to the role
of mathematics in the computer science curriculum. This paper presents the
results of an analysis of the math requirements of 199 Computer Science BS/BA
degrees from 158 U.S. universities, looking not only at which math courses are
required, but how they are used as prerequisites (and corequisites) for
computer science (CS) courses. Our analysis shows that while there is consensus
that discrete math is critical for a CS degree, and further that calculus is
almost always required for the BS in CS, there is little consensus as to when a
student should have mastered these subjects. Based on our analysis of how math
requirements impact access, retention and on-time degree completion for the BS
and the BA in CS, we provide several recommendations for CS departments to
consider.
|
We study the optimal control of district heating networks using a reduced
order model based on a system theoretic description close to the underlying
Euler equations. In the presented scenarios, the central task is to limit the
maximal feed-in power occurring as a product of control and state variables.
The underlying dynamics of heating networks acting as optimization constraints
pose the central computational complexity, prohibiting the determination of an
optimal control online. The advection of the injected energy density on the
network results in an index-1, quadratic in state differential algebraic
equation, challenging to reduce. The suggested reduced model decreases the
computation time of the optimization significantly. The effectiveness of the
presented approach is demonstrated for an existing, large-scale heating network
including changes of flux directions.
|
Spontaneous emergence of periodic oscillations due to self-organization is
ubiquitous in turbulent flows. The emergence of such oscillatory instabilities
in turbulent fluid mechanical systems is often studied in different
system-specific frameworks. We uncover the existence of a universal scaling
behaviour during self-organization in turbulent flows leading to oscillatory
instability. Our experiments show that the spectral amplitude of the dominant
mode of oscillations scales inversely with the Hurst exponent of a fluctuating
state variable following an inverse power law relation. Interestingly, we
observe the same power law behaviour with a constant exponent near -2 across
various turbulent systems such as aeroacoustic, thermoacoustic and aeroelastic
systems.
|
How to obtain an unbiased ranking model by learning to rank with biased user
feedback is an important research question for IR. Existing work on unbiased
learning to rank (ULTR) can be broadly categorized into two groups -- the
studies on unbiased learning algorithms with logged data, namely the
\textit{offline} unbiased learning, and the studies on unbiased parameters
estimation with real-time user interactions, namely the \textit{online}
learning to rank. While their definitions of \textit{unbiasness} are different,
these two types of ULTR algorithms share the same goal -- to find the best
models that rank documents based on their intrinsic relevance or utility.
However, most studies on offline and online unbiased learning to rank are
carried in parallel without detailed comparisons on their background theories
and empirical performance. In this paper, we formalize the task of unbiased
learning to rank and show that existing algorithms for offline unbiased
learning and online learning to rank are just the two sides of the same coin.
We evaluate six state-of-the-art ULTR algorithms and find that most of them can
be used in both offline settings and online environments with or without minor
modifications. Further, we analyze how different offline and online learning
paradigms would affect the theoretical foundation and empirical effectiveness
of each algorithm on both synthetic and real search data. Our findings could
provide important insights and guideline for choosing and deploying ULTR
algorithms in practice.
|
We measure the clustering of dark matter halos in a large set of
collisionless cosmological simulations of the flat LCDM cosmology. Halos are
identified using the spherical overdensity algorithm, which finds the mass
around isolated peaks in the density field such that the mean density is Delta
times the background. We calibrate fitting functions for the large scale bias
that are adaptable to any value of Delta we examine. We find a ~6% scatter
about our best fit bias relation. Our fitting functions couple to the halo mass
functions of Tinker et. al. (2008) such that bias of all dark matter is
normalized to unity. We demonstrate that the bias of massive, rare halos is
higher than that predicted in the modified ellipsoidal collapse model of Sheth,
Mo, & Tormen (2001), and approaches the predictions of the spherical collapse
model for the rarest halos. Halo bias results based on friends-of-friends halos
identified with linking length 0.2 are systematically lower than for halos with
the canonical Delta=200 overdensity by ~10%. In contrast to our previous
results on the mass function, we find that the universal bias function evolves
very weakly with redshift, if at all. We use our numerical results, both for
the mass function and the bias relation, to test the peak-background split
model for halo bias. We find that the peak-background split achieves a
reasonable agreement with the numerical results, but ~20% residuals remain,
both at high and low masses.
|
We present calculations for the temperature-dependent electronic structure
and magnetic properties of thin ferromagnetic EuO films. The treatment is based
on a combination of a multiband-Kondo lattice model with first-principles
TB-LMTO band structure calculations. The method avoids the problem of
double-counting of relevant interactions and takes into account the correct
symmetry of the atomic orbitals. We discuss the temperature-dependent
electronic structures of EuO(100) films in terms of quasiparticle densities of
states and quasiparticle band structures. The Curie temperature T_C of the EuO
films turns out to be strongly thickness-dependent, starting from a very low
value = 15K for the monolayer and reaching the bulk value at about 25 layers.
|
Gaussian boson sampling constitutes a prime candidate for an experimental
demonstration of quantum advantage within reach with current technological
capabilities. The original proposal employs photon-number-resolving detectors,
however the latter are not widely available. On the other hand, inexpensive
threshold detectors can be combined into a single click-counting detector to
achieve approximate photon number resolution. We investigate the problem of
sampling from a general multi-mode Gaussian state using click-counting
detectors and show that the probability of obtaining a given outcome is related
to a new matrix function which is dubbed as the Kensingtonian. We show how the
latter relates to the Torontonian and the Hafnian, thus bridging the gap
between known Gaussian boson sampling variants. We then prove that, under
standard complexity-theoretical conjectures, the model can not be simulated
efficiently.
|
We present Iris, the VAO (Virtual Astronomical Observatory) application for
analyzing SEDs (spectral energy distributions). Iris is the result of one of
the major science initiatives of the VAO, and the first version was released in
September 2011. Iris combines key features of several existing software
applications to streamline and enhance SED analysis. With Iris, users may read
and display SEDs, select data ranges for analysis, fit models to SEDs, and
calculate confidence limits on best-fit parameters. SED data may be uploaded
into the application from IVOA-compliant VOTable and FITS format files, or
retrieved directly from NED. Data written in unsupported formats may be
converted using SedImporter, a new application provided with Iris. The
components of Iris have been contributed by members of the VAO. Specview,
contributed by STScI, provides a GUI for reading, editing, and displaying SEDs,
as well as defining models and parameter values. Sherpa, contributed by the
Chandra project at SAO, provides a library of models, fit statistics, and
optimization methods; the underlying I/O library, SEDLib, is a VAO product
written by SAO to current IVOA (International Virtual Observatory Alliance)
data model standards. NED is a service provided by IPAC for easy location of
data for a given extragalactic source, including SEDs. SedImporter is a new
tool for converting non-standard SED data files into a format supported by
Iris. We demonstrate the use of SedImporter to retrieve SEDs from a variety of
sources--from the NED SED service, from the user's own data, and from other VO
applications using SAMP (Simple Application Messaging Protocol). We also
demonstrate the use of Iris to read, display, select ranges from, and fit
models to SEDs. Finally, we discuss the architecture of Iris, and the use of
IVOA standards so that Specview, Sherpa, SEDLib and SedImporter work together
seamlessly.
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This paper introduces Camera-free Diffusion (CamFreeDiff) model for
360-degree image outpainting from a single camera-free image and text
description. This method distinguishes itself from existing strategies, such as
MVDiffusion, by eliminating the requirement for predefined camera poses.
Instead, our model incorporates a mechanism for predicting homography directly
within the multi-view diffusion framework. The core of our approach is to
formulate camera estimation by predicting the homography transformation from
the input view to a predefined canonical view. The homography provides
point-level correspondences between the input image and targeting panoramic
images, allowing connections enforced by correspondence-aware attention in a
fully differentiable manner. Qualitative and quantitative experimental results
demonstrate our model's strong robustness and generalization ability for
360-degree image outpainting in the challenging context of camera-free inputs.
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This paper studies a statistical network model generated by a large number of
randomly sized overlapping communities, where any pair of nodes sharing a
community is linked with probability $q$ via the community. In the special case
with $q=1$ the model reduces to a random intersection graph which is known to
generate high levels of transitivity also in the sparse context. The parameter
$q$ adds a degree of freedom and leads to a parsimonious and analytically
tractable network model with tunable density, transitivity, and degree
fluctuations. We prove that the parameters of this model can be consistently
estimated in the large and sparse limiting regime using moment estimators based
on partially observed densities of links, 2-stars, and triangles.
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When elastic solids are sheared, a nonlinear effect named after Poynting
gives rise to normal stresses or changes in volume. We provide a novel relation
between the Poynting effect and the microscopic Gr\"uneisen parameter, which
quantifies how stretching shifts vibrational modes. By applying this relation
to random spring networks, a minimal model for, e.g., biopolymer gels and solid
foams, we find that networks contract or develop tension because they vibrate
faster when stretched. The amplitude of the Poynting effect is sensitive to the
network's linear elastic moduli, which can be tuned via its preparation
protocol and connectivity. Finally, we show that the Poynting effect can be
used to predict the finite strain scale where the material stiffens under
shear.
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We describe stationary and axisymmetric gas configurations surrounding black
holes. They consist of a collisionless relativistic kinetic gas of identical
massive particles following bound orbits in a Schwarzschild exterior spacetime
and are modeled by a one-particle distribution function which is the product of
a function of the energy and a function of the orbital inclination associated
with the particle's trajectory. The morphology of the resulting configuration
is analyzed.
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By an exact analytical approach we study the magnetothermal transport in the
spin-1/2 easy-axis Heisenberg model, in particular the thermal conductivity and
spin Seebeck effect as a function of anisotropy, magnetic field and
temperature. We stress a distinction between the commnon spin Seebeck effect
with fixed boundary conditions and the one (intrinsic) with open boundary
conditions. In the open boundary spin Seebeck effect we find exceptional
features at the critical fields between the low field antiferromagnetic phase,
the gapless one and the ferromagnetic at high fields. We further study the
development of these features as a function of easy-axis anisotropy and
temperature. We point out the potential of these results to experimental
studies in spin chain compounds, candidates for spin current generation in the
field of spintronics.
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We examine the renormalized free energy of the free Dirac fermion and the
free scalar on a (2+1)-dimensional geometry $\mathbb{R} \times \Sigma$, with
$\Sigma$ having spherical topology and prescribed area. Using heat kernel
methods, we perturbatively compute this energy when $\Sigma$ is a small
deformation of the round sphere, finding that at any temperature the round
sphere is a local maximum. At low temperature the free energy difference is due
to the Casimir effect. We then numerically compute this free energy for a class
of large axisymmetric deformations, providing evidence that the round sphere
globally maximizes it, and we show that the free energy difference relative to
the round sphere is unbounded below as the geometry on $\Sigma$ becomes
singular. Both our perturbative and numerical results in fact stem from the
stronger finding that the difference between the heat kernels of the round
sphere and a deformed sphere always appears to have definite sign. We
investigate the relevance of our results to physical systems like monolayer
graphene consisting of a membrane supporting relativistic QFT degrees of
freedom.
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We provide a complete thermodynamic solution of a 1D hopping model in the
presence of a random potential by obtaining the density of states. Since the
partition function is related to the density of states by a Laplace transform,
the density of states determines completely the thermodynamic behavior of the
system. We have also shown that the transfer matrix technique, or the so-called
dynamic programming, used to obtain the density of states in the 1D hopping
model may be generalized to tackle a long-standing problem in statistical
significance assessment for one of the most important proteomic tasks - peptide
sequencing using tandem mass spectrometry data.
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We have analyzed in a systematic way about nine years of INTEGRAL data
(17-100 keV) focusing on Supergiant Fast X-ray Transients (SFXTs) and three
classical High Mass X-ray Binaries (HMXBs). Our approach has been twofold:
image based analysis, sampled over a ~ks time frame to investigate the
long-term properties of the sources, and lightcurve based analysis, sampled
over a 100s time frame to seize the fast variability of each source during its
~ks activity. We find that while the prototypical SFXTs (IGR J17544-2619, XTE
J1739-302 and SAX J1818.6-1703) are among the sources with the lowest ~ks based
duty cycle ($<$1% activity over nine years of data), when studied at the 100s
level, they are the ones with the highest detection percentage, meaning that,
when active, they tend to have many bright short-term flares with respect to
the other SFXTs. To investigate in a coherent and self consistent way all the
available results within a physical scenario, we have extracted cumulative
luminosity distributions for all the sources of the sample. The
characterization of such distributions in hard X-rays, presented for the first
time in this work for the SFXTs, shows that a power-law model is a plausible
representation for SFXTs, while it can only reproduce the very high luminosity
tail of the classical HMXBs, and even then, with a significantly steeper
power-law slope with respect to SFXTs. The physical implications of these
results within the frame of accretion in wind-fed systems are discussed.
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We introduce 4D Motion Scaffolds (MoSca), a neural information processing
system designed to reconstruct and synthesize novel views of dynamic scenes
from monocular videos captured casually in the wild. To address such a
challenging and ill-posed inverse problem, we leverage prior knowledge from
foundational vision models, lift the video data to a novel Motion Scaffold
(MoSca) representation, which compactly and smoothly encodes the underlying
motions / deformations. The scene geometry and appearance are then disentangled
from the deformation field, and are encoded by globally fusing the Gaussians
anchored onto the MoSca and optimized via Gaussian Splatting. Additionally,
camera poses can be seamlessly initialized and refined during the dynamic
rendering process, without the need for other pose estimation tools.
Experiments demonstrate state-of-the-art performance on dynamic rendering
benchmarks.
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In this paper we prove a class of second order Caffarelli-Kohn-Nirenberg
inequalities which contains the sharp second order uncertainty principle
recently established by Cazacu, Flynn and Lam \cite{CFL2020} as a special case.
We also show the sharpness of our inequalities for several classes of
parameters. Finally, we prove two stability versions of the sharp second order
uncertainty principle of Cazacu, Flynn and Lam by showing that the difference
of both sides of the inequality controls the distance to the set of extremal
functions in $L^2$ norm of gradient of functions.
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The orthogonal polynomials with recurrence relation \[(\la\_n+\mu\_n-z)
F\_n(z)=\mu\_{n+1} F\_{n+1}(z)+\la\_{n-1} F\_{n-1}(z)\] with two kinds of cubic
transition rates $\la\_n$ and $\mu\_n,$ corresponding to indeterminate
Stieltjes moment problems, are analyzed. We derive generating functions for
these two classes of polynomials, which enable us to compute their Nevanlinna
matrices. We discuss the asymptotics of the Nevanlinna matrices in the complex
plane.
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Supernova remnants are expected to contain braided (or stochastic) magnetic
fields, which are in some regions directed mainly perpendicular to the shock
normal. For particle acceleration due to repeated shock crossings, the
transport in the direction of the shock normal is crucial. The mean squared
deviation along the shock normal is then proportional to the square root of the
time. This kind of anomalous transport is called sub-diffusion. We use a
Monte-Carlo method to examine this non-Markovian transport and the
acceleration. As a result of this simulation we are able to examine the
propagator, density and pitch-angle distribution of accelerated particles, and
especially the spectral properties. These are in broad agreement with analytic
predictions for both the sub-diffusive and the diffusive regimes, but the
steepening of the spectrum predicted when changing from diffusive to
sub-diffusive transport is found to be even more pronounced than predicted.
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This paper is primarily intended as an introduction for the mathematically
inclined to some of the rich algebraic combinatorics arising in for instance
CFT. It is essentially self-contained, apart from some of the background
motivation and examples which are included to give the reader a sense of the
context. The theory is still a work-in-progress, and emphasis is given here to
several open questions and problems.
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Studying algorithms admitting nontrivial symmetries is a prospective way of
constructing new short algorithms of matrix multiplication. The main result of
the article is that if there exists an algorithm of multiplicative length
$l\leq22$ for multuplication of $3\times3$ matrices then its automorphism group
is isomorphic to a subgroup of $S_l\times S_3$.
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Graph representation learning (GRL) is critical for extracting insights from
complex network structures, but it also raises security concerns due to
potential privacy vulnerabilities in these representations. This paper
investigates the structural vulnerabilities in graph neural models where
sensitive topological information can be inferred through edge reconstruction
attacks. Our research primarily addresses the theoretical underpinnings of
similarity-based edge reconstruction attacks (SERA), furnishing a
non-asymptotic analysis of their reconstruction capacities. Moreover, we
present empirical corroboration indicating that such attacks can perfectly
reconstruct sparse graphs as graph size increases. Conversely, we establish
that sparsity is a critical factor for SERA's effectiveness, as demonstrated
through analysis and experiments on (dense) stochastic block models. Finally,
we explore the resilience of private graph representations produced via noisy
aggregation (NAG) mechanism against SERA. Through theoretical analysis and
empirical assessments, we affirm the mitigation of SERA using NAG . In
parallel, we also empirically delineate instances wherein SERA demonstrates
both efficacy and deficiency in its capacity to function as an instrument for
elucidating the trade-off between privacy and utility.
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Rigidity of an ordered phase in condensed matter results in collective
excitation modes spatially extending in macroscopic dimensions. Magnon is a
quantum of an elementary excitation in the ordered spin system, such as
ferromagnet. Being low dissipative, dynamics of magnons in ferromagnetic
insulators has been extensively studied and widely applied for decades in the
contexts of ferromagnetic resonance, and more recently of Bose-Einstein
condensation as well as spintronics. Moreover, towards hybrid systems for
quantum memories and transducers, coupling of magnons and microwave photons in
a resonator have been investigated. However, quantum-state manipulation at the
single-magnon level has remained elusive because of the lack of anharmonic
element in the system. Here we demonstrate coherent coupling between a magnon
excitation in a millimetre-sized ferromagnetic sphere and a superconducting
qubit, where the interaction is mediated by the virtual photon excitation in a
microwave cavity. We obtain the coupling strength far exceeding the damping
rates, thus bringing the hybrid system into the strong coupling regime.
Furthermore, we find a tunable magnon-qubit coupling scheme utilising a
parametric drive with a microwave. Our approach provides a versatile tool for
quantum control and measurement of the magnon excitations and thus opens a new
discipline of quantum magnonics.
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Vision-language models can assess visual context in an image and generate
descriptive text. While the generated text may be accurate and syntactically
correct, it is often overly general. To address this, recent work has used
optical character recognition to supplement visual information with text
extracted from an image. In this work, we contend that vision-language models
can benefit from additional information that can be extracted from an image,
but are not used by current models. We modify previous multimodal frameworks to
accept relevant information from any number of auxiliary classifiers. In
particular, we focus on person names as an additional set of tokens and create
a novel image-caption dataset to facilitate captioning with person names. The
dataset, Politicians and Athletes in Captions (PAC), consists of captioned
images of well-known people in context. By fine-tuning pretrained models with
this dataset, we demonstrate a model that can naturally integrate facial
recognition tokens into generated text by training on limited data. For the PAC
dataset, we provide a discussion on collection and baseline benchmark scores.
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We present the first detailed computations of wave optics effects in the
gravitational lensing of binary systems. The field is conceptually rich,
combining the caustic singularities produced in classical gravitational lensing
with quantum (wave) interference effects. New techniques have enabled us to
overcome previous barriers to computation. Recent developments in radio
astronomy present observational opportunities which, while still futuristic,
appear promising.
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The product of two empirical constants, the dimensionless fine structure
constant and the von Klitzing constant (an electrical resistance), turns out to
be an exact dimensionless number. Then the accuracy and cosmological time
variation (if any) of these two constants are tied. Also this product defines a
natural unit of electrical resistance, the inverse of a quantum of conductance.
When the speed of light c is taken away from the fine structure constant, as
has been shown elsewhere, its constancy implies the constancy of the ratio e2/h
(the inverse of the von Klitzing constant), e the charge of the electron and h
Planck constant. This forces the charge of the electron e to be constant as
long as the action h (an angular momentum) is a true constant too. From the
constancy of the Rydberg constant the Compton wavelength, h/mc, is then a true
constant and consequently there is no expansion at the quantum mechanical
level. The momentum mc is also a true constant and then general relativity
predicts that the universe is not expanding, as shown elsewhere. The time
variation of the speed of light explains the observed Hubble red shift. And
there is a mass-boom effect. From this a coherent cosmological system of
constant units can be defined.
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We show that K3 surfaces with non-symplectic automorphisms of prime order can
be used to construct new compact irreducible G2-manifolds. This technique was
carried out in detail by Kovalev and Lee for non-symplectic involutions. We use
Chen-Ruan orbifold cohomology to determine the Hodge diamonds of certain
complex threefolds, which are the building blocks for this approach.
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A present prevailing open problem planetary nebulae research, and
photoionized gaseous nebulae research at large, is the systematic discrepancies
in ionic abundances derived from recombination and collisionally excited lines
in many H II regions and planetary nebulae. Peimbert (1967) proposed that these
discrepancies were due to 'temperature fluctuations' in the plasma, but the
amplitude of such fluctuations remain unexplained by standard phtoionization
modeling. In this letter we show that large amplitude temperature oscillations
are expected to form in gaseous nebulae photoionized by short-period binary
stars. Such stars yield periodically varying ionizing radiation fields, which
induce periodic oscilla- tions in the heating-minus-cooling function across the
nebula. For flux oscillation periods of a few days any temperature
perturbations in the gas with frequencies similar to those of the ionizing
source will undergo resonant amplification. In this case, the rate of growth of
the perturbations increases with the amplitude of the variations of the
ionizing flux and with decreasing nebular equilibrium temperature. We also
present a line ratios diagnostic plot that combines [O III] collisional lines
and O II recombination lines for diagnosing equilibrium and fluctuation am-
plitude temperatures in gaseous nebulae. When applying this diagnostic to the
planetary nebula M 1-42 we find an equilibrium temperature of ~6000 K and a
resonant temperature fluctuation amplitude (Trtf ) of ~4000 K. This equilibrium
temperature is significantly lower than the temperature estimated when
temperature perturbations are ignored.
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We describe what cosmology looks like in the context of the geometric theory
of gravity (GSG) based on a single scalar field. There are two distinct classes
of cosmological solutions. An interesting feature is the possibility of having
a bounce without invoking exotic equations of state for the cosmic fluid. We
also discuss cosmological perturbation and present the basis of structure
formation by gravitational instability in the framework of the geometric scalar
gravity.
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The purpose of this paper is two-fold: we systematically introduce the notion
of Cheeger deformations on fiber bundles with compact structure groups, and
recover in a very simple and unified fashion several results that either
already appear in the literature or are known by experts, though are not
explicitly written elsewhere. We re-prove: Schwachh\"ofer--Tuschmann Theorem on
bi-quotients, many results due to Fukaya and Yamaguchi, as well as, naturally
extend the work of Searle--Sol\'orzano--Wilhelm on regularization properties of
Cheeger deformations, among others. In this sense, this paper should be
understood as a survey intended to demonstrate the power of Cheeger
deformations. Even though some of the results here appearing may not be known
as stated in the presented form, they were already expected, being our
contribution to the standardization and spread of the technique via a unique
language.
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We use the coupled cluster method to study the zero-temperature properties of
an extended two-dimensional Heisenberg antiferromagnet formed from spin-1/2
moments on an infinite spatially anisotropic kagome lattice of corner-sharing
isosceles triangles, with nearest-neighbor bonds only. The bonds have exchange
constants $J_{1}>0$ along two of the three lattice directions and $J_{2} \equiv
\kappa J_{1} > 0$ along the third. In the classical limit the ground-state (GS)
phase for $\kappa < 1/2$ has collinear ferrimagnetic (N\'{e}el$'$) order where
the $J_2$-coupled chain spins are ferromagnetically ordered in one direction
with the remaining spins aligned in the opposite direction, while for $\kappa >
1/2$ there exists an infinite GS family of canted ferrimagnetic spin states,
which are energetically degenerate. For the spin-1/2 case we find that quantum
analogs of both these classical states continue to exist as stable GS phases in
some regions of the anisotropy parameter $\kappa$, namely for
$0<\kappa<\kappa_{c_1}$ for the N\'{e}el$'$ state and for (at least part of)
the region $\kappa>\kappa_{c_2}$ for the canted phase. However, they are now
separated by a paramagnetic phase without either sort of magnetic order in the
region $\kappa_{c_1} < \kappa < \kappa_{c_2}$, which includes the isotropic
kagome point $\kappa = 1$ where the stable GS phase is now believed to be a
topological ($\mathbb{Z}_2$) spin liquid. Our best numerical estimates are
$\kappa_{c_1} = 0.515 \pm 0.015$ and $\kappa_{c_2} = 1.82 \pm 0.03$.
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This dissertation focuses on a theoretical study of interacting electrons in
one dimension. The research elucidates the ground state (zero temperature)
electronic phase diagram of an aluminum arsenide quantum wire which is an
example of an interacting one dimensional electron liquid. Using one
dimensional field theoretic methods involving abelian bosonization and the
renormalization group we show the existence of a spin gapped quantum wire with
electronic ground states such as charge density wave and singlet
superconductivity. The superconducting state arises due to the unique umklapp
interaction present in the aluminum arsenide quantum wire bandstructure
discussed in this dissertation. It is characterized by Cooper pairs carrying a
finite pairing momentum. This is a realization of the Fulde-Ferrell-Larkin-
Ovchinnikov state which is known to lead to inhomogeneous superconductivity.
The dissertation also presents a theoretical analysis of the finite temperature
single hole spectral function of the one dimensional electron liquid with
gapless spin and charge modes (Luttinger liquid). The hole spectral function is
measured in angle resolved photoemission spectroscopy experiments. The results
predict a kink in the effective electronic dispersion of the Luttinger liquid.
A systematic study of the temperature and interaction dependence of the kink
provides an alternative way to detect spincharge separation in one dimensional
systems where the peak due to the spin part of the spectral function is
suppressed.
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Stochastic bilevel optimization finds widespread applications in machine
learning, including meta-learning, hyperparameter optimization, and neural
architecture search. To extend stochastic bilevel optimization to distributed
data, several decentralized stochastic bilevel optimization algorithms have
been developed. However, existing methods often suffer from slow convergence
rates and high communication costs in heterogeneous settings, limiting their
applicability to real-world tasks. To address these issues, we propose two
novel decentralized stochastic bilevel gradient descent algorithms based on
simultaneous and alternating update strategies. Our algorithms can achieve
faster convergence rates and lower communication costs than existing methods.
Importantly, our convergence analyses do not rely on strong assumptions
regarding heterogeneity. More importantly, our theoretical analysis clearly
discloses how the additional communication required for estimating
hypergradient under the heterogeneous setting affects the convergence rate. To
the best of our knowledge, this is the first time such favorable theoretical
results have been achieved with mild assumptions in the heterogeneous setting.
Furthermore, we demonstrate how to establish the convergence rate for the
alternating update strategy when combined with the variance-reduced gradient.
Finally, experimental results confirm the efficacy of our algorithms.
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The Ensemble Kalman filter assumes the observations to be Gaussian random
variables with a pre-specified mean and variance. In practice, observations may
also have detection limits, for instance when a gauge has a minimum or maximum
value. In such cases most data assimilation schemes discard out-of-range
values, treating them as "not a number", at a loss of possibly useful
qualitative information.
The current work focuses on the development of a data assimilation scheme
that tackles observations with a detection limit. We present the Ensemble
Kalman Filter Semi-Qualitative (EnKF-SQ) and test its performance against the
Partial Deterministic Ensemble Kalman Filter (PDEnKF) of Borup et al. (2015).
Both are designed to explicitly assimilate the out-of-range observations: the
out-of-range values are qualitative by nature (inequalities), but one can
postulate a probability distribution for them and then update the ensemble
members accordingly. The EnKF-SQ is tested within the framework of twin
experiments, using both linear and non-linear toy models. Different sensitivity
experiments are conducted to assess the influence of the ensemble size,
observation detection limit and a number of observations on the performance of
the filter. Our numerical results show that assimilating qualitative
observations using the proposed scheme improves the overall forecast mean,
making it viable for testing on more realistic applications such as sea-ice
models.
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In this work, we propose a linear machine learning force matching approach
that can directly extract pair atomic interactions from ab initio calculations
in amorphous structures. The local feature representation is specifically
chosen to make the linear weights a force field as a force/potential function
of the atom pair distance. Consequently, this set of functions is the closest
representation of the ab initio forces given the two-body approximation and
finite scanning in the configurational space. We validate this approach in
amorphous silica. Potentials in the new force field (consisting of tabulated
Si-Si, Si-O, and O-O potentials) are significantly softer than existing
potentials that are commonly used for silica, even though all of them produce
the tetrahedral network structure and roughly similar glass properties. This
suggests that those commonly used classical force fields do not offer
fundamentally accurate representations of the atomic interaction in silica. The
new force field furthermore produces a lower glass transition temperature
($T_g\sim$1800 K) and a positive liquid thermal expansion coefficient,
suggesting the extraordinarily high $T_g$ and negative liquid thermal expansion
of simulated silica could be artifacts of previously developed classical
potentials. Overall, the proposed approach provides a fundamental yet intuitive
way to evaluate two-body potentials against ab initio calculations, thereby
offering an efficient way to guide the development of classical force fields.
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We study the equations of Wheeler-Feynman electrodynamics which is an
action-at-a-distance theory about world-lines of charges that interact through
their corresponding advanced and retarded Li\'enard-Wiechert field terms. The
equations are non-linear, neutral, and involve time-like advanced as well as
retarded arguments of unbounded delay. Using a reformulation in terms of
Maxwell-Lorentz electrodynamics without self-interaction, which we have
introduced in a preceding work, we are able to establish the existence of
conditional solutions. These are solutions that solve the Wheeler-Feynman
equations on any finite time interval with prescribed continuations outside of
this interval. As a byproduct we also prove existence and uniqueness of
solutions to the Synge equations on the time half-line for a given history of
charge trajectories.
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We consider the open set constructed by M. Shub in [42] of partially
hyperbolic skew products on the space $\mathbb{T}^2\times \mathbb{T}^2$ whose
non-wandering set is not stable. We show that there exists an open set
$\mathcal{U}$ of such diffeomorphisms such that if $F_S\in \mathcal{U}$ then
its measure of maximal entropy is unique, hyperbolic and, generically,
describes the distribution of periodic points. Moreover, the non-wandering set
of such an $F_S\in \mathcal{U}$ contains closed invariant subsets carrying
entropy arbitrarily close to the topological entropy of $F_S$ and within which
the dynamics is conjugate to a subshift of finite type. Under an additional
assumption on the base dynamics, we verify that $F_S$ preserves a unique SRB
measure, which is physical, whose basin has full Lebesgue measure and coincides
with the measure of maximal entropy. We also prove that there exists a residual
subset $\mathcal{R}$ of $\mathcal{U}$ such that if $F_S\in \mathcal{R}$ then
the topological and periodic entropies of $F_S$ are equal, $F_S$ is asymptotic
per-expansive, has a sub-exponential growth rate of the periodic orbits and
admits a principal strongly faithful symbolic extension with embedding.
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We present the charged-particle pseudorapidity density in Pb-Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=5.02\,\mathrm{Te\kern-.25exV}$ in centrality classes
measured by ALICE. The measurement covers a wide pseudorapidity range from
$-3.5$ to $5$, which is sufficient for reliable estimates of the total number
of charged particles produced in the collisions. For the most central (0-5%)
collisions we find $21\,400\pm 1\,300$ while for the most peripheral (80-90%)
we find $230\pm 38$. This corresponds to an increase of $(27\pm4)\%$ over the
results at $\sqrt{s_{\mathrm{NN}}}=2.76\,\mathrm{Te\kern-.25exV}$ previously
reported by ALICE. The energy dependence of the total number of charged
particles produced in heavy-ion collisions is found to obey a modified
power-law like behaviour. The charged-particle pseudorapidity density of the
most central collisions is compared to model calculations --- none of which
fully describes the measured distribution. We also present an estimate of the
rapidity density of charged particles. The width of that distribution is found
to exhibit a remarkable proportionality to the beam rapidity, independent of
the collision energy from the top SPS to LHC energies.
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A second order extrapolation method is presented for shell model
calculations, where shell model energies of truncated spaces are well described
as a function of energy variance by quadratic curves and exact shell model
energies can be obtained by the extrapolation. This new extrapolation can give
more precise energy than those of first order extrapolation method. It is also
clarified that first order extrapolation gives a lower limit of shell model
energy. In addition to the energy, we derive the second order extrapolation
formula for expectation values of other observables.
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Quantum collision models are receiving increasing attention as they describe
many nontrivial phenomena in dynamics of open quantum systems. In a general
scenario of both fundamental and practical interest, a quantum system
repeatedly interacts with individual particles or modes forming a correlated
and structured reservoir; however, classical and quantum environment
correlations greatly complicate the calculation and interpretation of the
system dynamics. Here we propose an exact solution to this problem based on the
tensor network formalism. We find a natural Markovian embedding for the system
dynamics, where the role of an auxiliary system is played by virtual indices of
the network. The constructed embedding is amenable to analytical treatment for
a number of timely problems like the system interaction with two-photon
wavepackets, structured photonic states, and one-dimensional spin chains. We
also derive a time-convolution master equation and relate its memory kernel
with the environment correlation function, thus revealing a clear physical
picture of memory effects in the dynamics. The results advance tensor-network
methods in the fields of quantum optics and quantum transport.
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Subsets and Splits