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arxiv_dataset-106001812.02426 | A Diamond-Photonics Platform Based on Silicon-Vacancy Centers in a
Single Crystal Diamond Membrane and a Fiber-Cavity
physics.app-ph physics.optics quant-ph
We realize a potential platform for an efficient spin-photon interface,
namely negatively-charged silicon-vacancy centers in a diamond membrane coupled
to the mode of a fully-tunable, fiber-based, optical resonator. We demonstrate
that introducing the thin ($\sim 200 \, \text{nm}$), single crystal diamond
membrane into the mode of the resonator does not change the cavity properties,
which is one of the crucial points for an efficient spin-photon interface. In
particular, we observe constantly high Finesse values of up to $3000$ and a
linear dispersion in the presence of the membrane. We observe cavity-coupled
fluorescence froman ensemble of SiV$^{-}$ centers with an enhancement factor of
$\sim 1.9$. Furthermore from our investigations we extract the ensemble
absorption and extrapolate an absorption cross section of $(2.9 \, \pm \, 2) \,
\cdot \, 10^{-12} \, \text{cm}^{2}$ for a single SiV$^{-}$ center, much higher
than previously reported.
| arxiv topic:physics.app-ph physics.optics quant-ph |
arxiv_dataset-106011812.02526 | Hilbert scheme of rational curves on a generic quintic threefold
math.AG
Let $X_0$ be a generic quintic threefold in projective space $\mathbf P^4$
over the complex numbers. For a fixed natural number $d$, let $R_d(X_0)$ be the
open sub-scheme of the Hilbert scheme, parameterizing irreducible rational
curves of degree $d$ on $X_0$. In this paper, we show that (1) $R_d(X_0)$ is
smooth and of expected dimension, \par (2) Combining the Calabi-Yau condition
on $X_0$, we further show that it consists of
immersed rational curves.
(3) Parts (1) and (2) imply a statement of Clemens' conjecture: if $C_0\in
R_d(X_0)$ and $c_0:\mathbf P^1\to C_0$ is the normalization, the
\par\hspace{1cc} normal sheaf
is isomorphic to the vector bundle $$N_{c_0/X_0}\simeq \mathcal O_{\mathbf
P^1}(-1)\oplus \mathcal O_{\mathbf P^1}(-1).$$
| arxiv topic:math.AG |
arxiv_dataset-106021812.02626 | Guided Zoom: Questioning Network Evidence for Fine-grained
Classification
cs.CV
We propose Guided Zoom, an approach that utilizes spatial grounding of a
model's decision to make more informed predictions. It does so by making sure
the model has "the right reasons" for a prediction, defined as reasons that are
coherent with those used to make similar correct decisions at training time.
The reason/evidence upon which a deep convolutional neural network makes a
prediction is defined to be the spatial grounding, in the pixel space, for a
specific class conditional probability in the model output. Guided Zoom
examines how reasonable such evidence is for each of the top-k predicted
classes, rather than solely trusting the top-1 prediction. We show that Guided
Zoom improves the classification accuracy of a deep convolutional neural
network model and obtains state-of-the-art results on three fine-grained
classification benchmark datasets.
| arxiv topic:cs.CV |
arxiv_dataset-106031812.02726 | Simulation of Stylized Facts in Agent-Based Computational Economic
Market Models
econ.GN econ.EM q-fin.EC q-fin.TR
We study the qualitative and quantitative appearance of stylized facts in
several agent-based computational economic market (ABCEM) models. We perform
our simulations with the SABCEMM (Simulator for Agent-Based Computational
Economic Market Models) tool recently introduced by the authors (Trimborn et
al. 2019). Furthermore, we present novel ABCEM models created by recombining
existing models and study them with respect to stylized facts as well. This can
be efficiently performed by the SABCEMM tool thanks to its object-oriented
software design. The code is available on GitHub (Trimborn et al. 2018), such
that all results can be reproduced by the reader.
| arxiv topic:econ.GN econ.EM q-fin.EC q-fin.TR |
arxiv_dataset-106041812.02826 | On the Gravitational Instabilities of Protoplanetary Disks
astro-ph.EP
The gravitational instabilities are important to the evolution of the disks
and the planet formation in the disks. We calculate the evolution of the disks
which form from the collapse of the molecular cloud cores. By changing the
properties of the cloud cores and the hydrodynamical viscosity parameters, we
explore their effects on the properties of the gravitational instabilities. We
find that the disk is unstable when the angular velocity of the molecular cloud
core is larger than a critical value. The time duration of the instability
increases as the angular velocity of the core increases. The increase of the
hydrodynamical viscosity parameter hardly affects the stability of the disk,
but decreases the time duration of the critical state of the gravitational
instability in the disk. The instability of the disks can happen at very early
time of evolution of the disk, which is consistent with the observations.
| arxiv topic:astro-ph.EP |
arxiv_dataset-106051812.02926 | Astrometric Interferometry
astro-ph.IM
Astrometry is a powerful technique in astrophysics to measure
three-dimensional positions of stars and other astrophysical objects, including
exoplanets and the gravitational influence they have on each other.
Interferometric astrometry is presented here as just one in a suite of powerful
astrometric techniques, which include space-based, seeing-limited and
wide-angle adaptive optics techniques. Fundamental limits are discussed,
demonstrating that even ground-based techniques have the capability for
astrometry at the single micro-arcsecond level, should sufficiently
sophisticated instrumentation be constructed for both the current generation of
single telescopes and long-baseline optical interferometers.
| arxiv topic:astro-ph.IM |
arxiv_dataset-106061812.03026 | A High-Order Scheme for Image Segmentation via a modified Level-Set
method
math.NA cs.CV cs.NA
In this paper we propose a high-order accurate scheme for image segmentation
based on the level-set method. In this approach, the curve evolution is
described as the 0-level set of a representation function but we modify the
velocity that drives the curve to the boundary of the object in order to obtain
a new velocity with additional properties that are extremely useful to develop
a more stable high-order approximation with a small additional cost. The
approximation scheme proposed here is the first 2D version of an adaptive
"filtered" scheme recently introduced and analyzed by the authors in 1D. This
approach is interesting since the implementation of the filtered scheme is
rather efficient and easy. The scheme combines two building blocks (a monotone
scheme and a high-order scheme) via a filter function and smoothness indicators
that allow to detect the regularity of the approximate solution adapting the
scheme in an automatic way. Some numerical tests on synthetic and real images
confirm the accuracy of the proposed method and the advantages given by the new
velocity.
| arxiv topic:math.NA cs.CV cs.NA |
arxiv_dataset-106071812.03126 | Polarization diversity phase modulator for measuring frequency-bin
entanglement of a biphoton frequency comb in a depolarized channel
quant-ph physics.optics
Phase modulation has emerged as a technique to create and manipulate
high-dimensional frequency-bin entanglement. A necessary step to extending this
technique to depolarized channels, such as those in a quantum networking
environment, is the ability to perform phase modulation independent of photon
polarization. This also necessary to harness hypertanglement in the
polarization and frequency degrees of freedom for operations like Bell state
discrimination. However, practical phase modulators are generally sensitive to
the polarization of light and this makes them unsuited to such applications. We
overcome this limitation by implementing a polarization diversity scheme to
measure frequency-bin entanglement in arbitrarily polarized photon pairs.
| arxiv topic:quant-ph physics.optics |
arxiv_dataset-106081812.03226 | Towards Effective Exploration/Exploitation in Sequential Music
Recommendation
cs.IR
Music streaming companies collectively serve billions of songs per day.
Radio-based music services may intersperse audio advertisements among the songs
as a means to generate revenue, much like traditional FM radio. Regardless of
the monetization approach, the recommender system should decide when to play
content that the listener is known to enjoy (exploit) and content that is novel
to the listener (explore). Recommender systems that rely on this
explore/exploit type framework have been deployed in a wide variety of
applications such as movies, books, music, shopping and more. In this work, we
investigate the impact of different ad/song sequences on listener behavior. In
particular, we focus on the impact of exploring new song content for the
listener given the previous sequence of ads and songs in the listener's
session. Our results show that the prior sequence matters when considering song
exploration and that this prior sequence has an impact on the listener's
tendency to interrupt their current session.
| arxiv topic:cs.IR |
arxiv_dataset-106091812.03326 | Analysis of A Spatially Inhomogeneous Stochastic Partial Differential
Equation Epidemic Model
math.DS
This work proposes and analyzes a family of spatially inhomogeneous epidemic
models. This is our first effort to use stochastic partial differential
equations (SPDEs) to model epidemic dynamics with spatial variations and
environmental noise. After setting up the problem, existence and uniqueness of
solutions of the underlying SPDEs are examined. Then definitions of permanence
and extinction are given. Certain sufficient conditions are provided for the
permanence and extinction. Our hope is that this paper will open up windows for
investigation of epidemic models from a new angle.
| arxiv topic:math.DS |
arxiv_dataset-106101812.03426 | Real-Time Referring Expression Comprehension by Single-Stage Grounding
Network
cs.CV
In this paper, we propose a novel end-to-end model, namely Single-Stage
Grounding network (SSG), to localize the referent given a referring expression
within an image. Different from previous multi-stage models which rely on
object proposals or detected regions, our proposed model aims to comprehend a
referring expression through one single stage without resorting to region
proposals as well as the subsequent region-wise feature extraction.
Specifically, a multimodal interactor is proposed to summarize the local region
features regarding the referring expression attentively. Subsequently, a
grounder is proposed to localize the referring expression within the given
image directly. For further improving the localization accuracy, a guided
attention mechanism is proposed to enforce the grounder to focus on the central
region of the referent. Moreover, by exploiting and predicting visual attribute
information, the grounder can further distinguish the referent objects within
an image and thereby improve the model performance. Experiments on RefCOCO,
RefCOCO+, and RefCOCOg datasets demonstrate that our proposed SSG without
relying on any region proposals can achieve comparable performance with other
advanced models. Furthermore, our SSG outperforms the previous models and
achieves the state-of-art performance on the ReferItGame dataset. More
importantly, our SSG is time efficient and can ground a referring expression in
a 416*416 image from the RefCOCO dataset in 25ms (40 referents per second) on
average with a Nvidia Tesla P40, accomplishing more than 9* speedups over the
existing multi-stage models.
| arxiv topic:cs.CV |
arxiv_dataset-106111812.03526 | Path Dependent Optimal Transport and Model Calibration on Exotic
Derivatives
math.PR math.OC q-fin.MF
In this paper, we introduce and develop the theory of semimartingale optimal
transport in a path dependent setting. Instead of the classical constraints on
marginal distributions, we consider a general framework of path dependent
constraints. Duality results are established, representing the solution in
terms of path dependent partial differential equations (PPDEs). Moreover, we
provide a dimension reduction result based on the new notion of
"semifiltrations", which identifies appropriate Markovian state variables based
on the constraints and the cost function. Our technique is then applied to the
exact calibration of volatility models to the prices of general path dependent
derivatives.
| arxiv topic:math.PR math.OC q-fin.MF |
arxiv_dataset-106121812.03626 | EDF: Ensemble, Distill, and Fuse for Easy Video Labeling
cs.CV
We present a way to rapidly bootstrap object detection on unseen videos using
minimal human annotations. We accomplish this by combining two complementary
sources of knowledge (one generic and the other specific) using bounding box
merging and model distillation. The first (generic) knowledge source is
obtained from ensembling pre-trained object detectors using a novel bounding
box merging and confidence reweighting scheme. We make the observation that
model distillation with data augmentation can train a specialized detector that
outperforms the noisy labels it was trained on, and train a Student Network on
the ensemble detections that obtains higher mAP than the ensemble itself. The
second (specialized) knowledge source comes from training a detector (which we
call the Supervised Labeler) on a labeled subset of the video to generate
detections on the unlabeled portion. We demonstrate on two popular vehicular
datasets that these techniques work to emit bounding boxes for all vehicles in
the frame with higher mean average precision (mAP) than any of the reference
networks used, and that the combination of ensembled and human-labeled data
produces object detections that outperform either alone.
| arxiv topic:cs.CV |
arxiv_dataset-106131812.03726 | Stability preserving approximations of a semilinear hyperbolic gas
transport model
math.NA
We consider the discretization of a semilinear damped wave equation arising,
for instance, in the modeling of gas transport in pipeline networks. For time
invariant boundary data, the solutions of the problem are shown to converge
exponentially fast to steady states. We further prove that this decay behavior
is inherited uniformly by a class of Galerkin approximations, including finite
element, spectral, and structure preserving model reduction methods. These
theoretical findings are illustrated by numerical tests.
| arxiv topic:math.NA |
arxiv_dataset-106141812.03826 | Examples of usage of nearfield acoustic holography methods for far field
estimations: Part 1. CW signals
eess.AS cs.SD physics.app-ph
The paper is devoted to the usage of nearfield acoustic holography methods
for estimating far field of the object. An experiment was carried out in
anechoic chamber. First, acoustic filed was recorded in a plane that was close
to source. This signals records were used to reconstruct the far field by
computation routines. Second, the signal in the far field is measured and the
results are compared. Several methods are tested and research on possible
reduction of the microphone array size is carried out. The most significant
reduction of the measurement facility complexity is usage a linear array in
stead of the planar array that is made possible due to introduced computation
routines
| arxiv topic:eess.AS cs.SD physics.app-ph |
arxiv_dataset-106151812.03926 | Octahedron-Based Projections as Intermediate Representations for
Computer Imaging: TOAST, TEA and More
astro-ph.IM
This paper defines and discusses a set of rectangular all-sky projections
which have no singular points, notably the Tesselated Octahedral Adaptive
Spherical Transformation (or TOAST) developed initially for the WorldWide
Telescope (WWT). These have proven to be useful as intermediate representations
for imaging data where the application transforms dynamically from a
standardized internal format to a specific format (projection, scaling,
orientation, etc.) requested by the user. TOAST is strongly related to the
Hierarchical Triangular Mesh (HTM) pixelization and is particularly well
adapted to the situations where one wishes to traverse a hierarchy of
increasing resolution images. Since it can be recursively computed using a very
simple algorithm it is particularly adaptable to use by graphical processing
units.
| arxiv topic:astro-ph.IM |
arxiv_dataset-106161812.04026 | A scenario for the Galactic cosmic rays between the knee and the
second-knee
astro-ph.HE
We perform a fit to measurements of the cosmic ray spectrum and of the depth
of shower maximum in the energy range between $10^{15}$~eV and $10^{18}$~eV. We
consider a Galactic component that is a mixture of five representative nuclear
species (H, He, N, Si and Fe), for which we adopt rigidity dependent broken
power-law spectra, and we allow for an extragalactic component which becomes
strongly suppressed for decreasing energies. The relative abundances of the
Galactic components at $10^{15}$~eV are taken to be comparable to those
determined by direct measurements at $10^{13}$~eV. The main features of the
spectrum and of the composition are reproduced in these scenarios. The spectral
knee results from the break of the H spectrum at $E_{\rm k}\simeq 3\times
10^{15}$~eV, although it is broaden by the comparable contribution from He
which has a break at about $6\times 10^{15}$~eV. The low-energy ankle at
$E_{\rm la}\simeq 2\times 10^{16}$~eV is associated to the strong suppression
of the H and He Galactic components and the increasing relative contribution of
the heavier ones, but the observed hardening of the spectrum at this energy
turns out to result from the growing contribution of the extragalactic
component. The second-knee at $E_{\rm sk}\simeq 26 E_{\rm k}\simeq 8\times
10^{16}$~eV is associated with the steepening of the Galactic Fe component. The
transition to the regime in which the total cosmic ray flux is dominated by the
extragalactic component takes place at an energy of about $10^{17}$~eV. The
parameters of the fit depend on the hadronic model that is used to interpret
the $X_{\rm max}$ measurements as well as on the specific $X_{\rm max}$ dataset
that is considered in the fit. The impact of the possible existence of a
maximum rigidity cutoff in the Galactic components is also discussed.
| arxiv topic:astro-ph.HE |
arxiv_dataset-106171812.04126 | Governance in Adaptive Normative Multiagent Systems for the Internet of
Smart Things: Challenges and Future Directions
cs.SE
The rapidly changing environments in which companies operate to support the
Internet of Things (IoT) and Autonomous Vehicles is challenging traditional
Multi agent System (MAS) approaches. The requirements of these highly dynamic
environments gave rise to Adaptive Normative MAS approaches. At the same time,
governance is an essential and challenging feature that still needs to be
addressed in adaptive normative MAS. Indeed, governance of individual and
societal agent behavior in Adaptive Normative MASs is still a vague concept
that has not been properly investigated, modeled and implemented. However,
governance is fundamental for solving problems involving MAS coordination,
organizations and institutions. In this paper, we present our ongoing research
towards understanding and improving governance in Adaptive Normative MASs. We
also discuss challenges and future directions that will facilitate the
development of domain specific smart IoT systems with governance features.
| arxiv topic:cs.SE |
arxiv_dataset-106181812.04226 | Coherent Wave Propagation in Multi-Mode systems with Correlated Noise
cond-mat.dis-nn cond-mat.mes-hall physics.optics
Imperfections in multimode systems lead to mode-mixing and interferences
between propagating modes. Such disorder is typically characterized by a finite
correlation time (in quantum evolution) or correlation length (in paraxial
evolution). We show that the long-scale dynamics of an initial excitation that
spread in mode space can be tailored by the coherent dynamics on short-scale.
In particular we unveil a universal crossover from exponential to power-law
ballistic-like decay of the initial mode. Our results have applications to
various wave physics frameworks, ranging from multimode fiber optics to quantum
dots and quantum biology.
| arxiv topic:cond-mat.dis-nn cond-mat.mes-hall physics.optics |
arxiv_dataset-106191812.04326 | Chevalley groups of polynomial rings over Dedekind domains
math.KT math.GR
Let R be a Dedekind domain, and let G be a simply connected
Chevalley-Demazure group scheme of rank =>2. We prove that
G(R[x_1,...,x_n])=G(R)E(R[x_1,...,x_n]) for any n=>1. This extends the
corresponding results of A. Suslin and F. Grunewald, J. Mennicke, and L.
Vaserstein for G=SL_n, Sp_2n. We also deduce some corollaries of the above
result for regular rings R of higher dimension and discrete Hodge algebras over
R.
| arxiv topic:math.KT math.GR |
arxiv_dataset-106201812.04426 | PDE-Net 2.0: Learning PDEs from Data with A Numeric-Symbolic Hybrid Deep
Network
cs.LG cs.NA physics.comp-ph stat.ML
Partial differential equations (PDEs) are commonly derived based on empirical
observations. However, recent advances of technology enable us to collect and
store massive amount of data, which offers new opportunities for data-driven
discovery of PDEs. In this paper, we propose a new deep neural network, called
PDE-Net 2.0, to discover (time-dependent) PDEs from observed dynamic data with
minor prior knowledge on the underlying mechanism that drives the dynamics. The
design of PDE-Net 2.0 is based on our earlier work \cite{Long2018PDE} where the
original version of PDE-Net was proposed. PDE-Net 2.0 is a combination of
numerical approximation of differential operators by convolutions and a
symbolic multi-layer neural network for model recovery. Comparing with existing
approaches, PDE-Net 2.0 has the most flexibility and expressive power by
learning both differential operators and the nonlinear response function of the
underlying PDE model. Numerical experiments show that the PDE-Net 2.0 has the
potential to uncover the hidden PDE of the observed dynamics, and predict the
dynamical behavior for a relatively long time, even in a noisy environment.
| arxiv topic:cs.LG cs.NA physics.comp-ph stat.ML |
arxiv_dataset-106211812.04526 | Magnetically inspired explosive outflows from neutron-star mergers
astro-ph.HE gr-qc
Binary neutron-star mergers have long been associated with short-duration
gamma-ray bursts (GRBs). This connection was confirmed with the first
coincident detection of gravitational waves together with electromagnetic
radiation from GW170817. The basic paradigm for short-duration GRBs includes an
ultra-relativistic jet, but the low-luminosity prompt emission together with
follow-up radio and X-ray observations have hinted that this picture may be
different in the case of GW170817. In particular, it has been proposed that
large amounts of the magnetic energy that is amplified after the merger, can be
released when the remnant collapses to a black hole, giving rise to a
quasi-spherical explosion impacting on the merger ejecta. Through numerical
simulations we investigate this scenario for a range of viewing angles,
injected energies and matter densities at the time of the collapse. Depending
on the magnitude of the energy injection and the remnant density, we find two
types of outflows: one with a narrow relativistic core and one with a
wide-angle, but mildly relativistic outflow. Furthermore, very wide outflows
are possible, but require energy releases in excess of 10^52 erg.
| arxiv topic:astro-ph.HE gr-qc |
arxiv_dataset-106221812.04626 | Optical spectroscopy and demographics of redback millisecond pulsar
binaries
astro-ph.HE astro-ph.SR
We present the first optical spectroscopy of five confirmed (or strong
candidate) redback millisecond pulsar binaries, obtaining complete radial
velocity curves for each companion star. The properties of these millisecond
pulsar binaries with low-mass, hydrogen-rich companions are discussed in the
context of the 14 confirmed and 10 candidate field redbacks. We find that the
neutron stars in redbacks have a median mass of 1.78 +/- 0.09 M_sun with a
dispersion of sigma = 0.21 +/- 0.09. Neutron stars with masses in excess of 2
M_sun are consistent with, but not firmly demanded by, current observations.
Redback companions have median masses of 0.36 +/- 0.04 M_sun with a scatter of
sigma = 0.15 +/- 0.04, and a tail possibly extending up to 0.7-0.9 M_sun.
Candidate redbacks tend to have higher companion masses than confirmed
redbacks, suggesting a possible selection bias against the detection of radio
pulsations in these more massive candidate systems. The distribution of
companion masses between redbacks and the less massive black widows continues
to be strongly bimodal, which is an important constraint on evolutionary models
for these systems. Among redbacks, the median efficiency of converting the
pulsar spindown energy to gamma-ray luminosity is ~10%.
| arxiv topic:astro-ph.HE astro-ph.SR |
arxiv_dataset-106231812.04726 | Polarisabilities from Compton Scattering on 3He
nucl-th hep-ph
This executive summary of recent theory progress in Compton scattering off
3He focuses on determining neutron polarisabilities; see ref. [2] and
references therein for details and a better bibliography. Prepared for the
Proceedings of the 22nd International Conference on Few-Body Problems in
Physics, Caen 9-13 July 2018.
| arxiv topic:nucl-th hep-ph |
arxiv_dataset-106241812.04826 | Spatial-Temporal Digital Image Correlation: A Unified Framework
cs.CV
A comprehensive and systematic framework for easily extending and
implementing the subset-based spatial-temporal digital image correlation (DIC)
algorithm is presented. The framework decouples the three main factors (i.e.
shape function, correlation criterion, and optimization algorithm) involved in
algorithm implementation of DIC and represents different algorithms in a
uniform form. One can freely choose and combine the three factors to meet his
own need, or freely add more parameters to extract analytic results. Subpixel
translation and a simulated image series with different velocity characters are
analyzed using different algorithms based on the proposed framework, confirming
the merit of noise suppression and velocity compatibility. An application of
mitigating air disturbance due to heat haze using spatial-temporal DIC is given
to demonstrate the applicability of the framework.
| arxiv topic:cs.CV |
arxiv_dataset-106251812.04926 | Ancient solutions for Andrews' hypersurface flow
math.DG
We construct the ancient solutions of the hypersurface flows in Euclidean
spaces studied by B. Andrews in 1994. As time $t \rightarrow 0^-$ the solutions
collapse to a round point where $0$ is the singular time. But as
$t\rightarrow-\infty$ the solutions become more and more oval. Near the center
the appropriately-rescaled pointed Cheeger-Gromov limits are round cylinder
solutions $S^J \times \mathbb{R}^{n-J}$, $1 \leq J \leq n-1$. These results are
the analog of the corresponding results in Ricci flow ($J=n-1$) and mean
curvature flow.
| arxiv topic:math.DG |
arxiv_dataset-106261812.05026 | A Fourier-based Picard-iteration approach for a class of McKean-Vlasov
SDEs with L\'evy jumps
math.PR
We consider a class of L\'evy-driven stochastic differential equations (SDEs)
with McKean-Vlasov (MK-V) interaction in the drift coefficient. It is assumed
that the coefficient is bounded, affine in the state variable, and only
measurable in the law of the solution. We study the equivalent functional
fixed-point equation for the unknown time-dependent coefficients of the
associated Markovian SDE. By proving a contraction property for the functional
map in a suitable normed space, we infer existence and uniqueness results for
the MK-V SDE, and derive a discretized Picard iteration scheme that
approximates the law of the solution through its characteristic function.
Numerical illustrations show the effectiveness of our method, which appears to
be appropriate to handle the multi-dimensional setting.
| arxiv topic:math.PR |
arxiv_dataset-106271812.05126 | A combinatorial duality between the weak and strong Bruhat orders
math.CO
In recent work, the authors used an order lowering operator $\nabla$,
introduced by Stanley, to prove the strong Sperner property for the weak Bruhat
order on the symmetric group. Hamaker, Pechenik, Speyer, and Weigandt
interpreted $\nabla$ as a differential operator on Schubert polynomials and
used this to prove a new identity for Schubert polynomials and a determinant
conjecture of Stanley. In this paper we study a raising operator $\Delta$ for
the \emph{strong} Bruhat order, which is in many ways dual to $\nabla$. We
prove a Schubert identity dual to that of Hamaker et al. and derive formulas
for counting weighted paths in the Hasse diagrams of the strong order which
agree with path counting formulas for the weak order. We also show that powers
of $\nabla$ and $\Delta$ have the same Smith normal forms, which we describe
explicitly, answering a question of Stanley.
| arxiv topic:math.CO |
arxiv_dataset-106281812.05226 | Observation of parity-time symmetry breaking in a single spin system
quant-ph
A fundamental axiom of quantum mechanics requires the Hamiltonians to be
Hermitian which guarantees real eigen-energies and probability conservation.
However, a class of non-Hermitian Hamiltonians with Parity-Time
($\mathcal{PT}$) symmetry can still display entirely real spectra. The
Hermiticity requirement may be replaced by $\mathcal{PT}$ symmetry to develop
an alternative formulation of quantum mechanics. A series of experiments have
been carried out with classical systems including optics, electronics,
microwaves, mechanics and acoustics. However, there are few experiments to
investigate $\mathcal{PT}$ symmetric physics in quantum systems.Here we report
the first observation of the $\mathcal{PT}$ symmetry breaking in a single spin
system. We have developed a novel method to dilate a general $\mathcal{PT}$
symmetric Hamiltonian into a Hermitian one, which can be realized in a
practical quantum system.Then the state evolutions under $\mathcal{PT}$
symmetric Hamiltonians, which range from $\mathcal{PT}$ symmetric unbroken to
broken regions, have been experimentally observed with a single
nitrogen-vacancy (NV) center in diamond. Due to the universality of the
dilation method, our result opens a door for further exploiting and
understanding the physical properties of $\mathcal{PT}$ symmetric Hamiltonian
in quantum systems.
| arxiv topic:quant-ph |
arxiv_dataset-106291812.05326 | Efficient quantum cluster algorithms for frustrated transverse field
Ising antiferromagnets and Ising gauge theories
cond-mat.str-el
Working within the Stochastic Series Expansion (SSE) framework, we construct
efficient quantum cluster algorithms for transverse field Ising
antiferromagnets on the pyrochlore lattice and the planar pyrochlore lattice,
for the fully frustrated square lattice Ising model in a transverse field (dual
to the 2+1 dimensional odd Ising gauge theory), and for a transverse field
Ising model with multi-spin interactions on the square lattice, which is dual
to a 2+1 dimensional even Ising gauge theory (and reduces to the two
dimensional quantum loop model in a certain limit). Our cluster algorithms use
a microcanonical update procedure that generalizes and exploits the notion of
"pre-marked motifs" introduced earlier in the context of a quantum cluster
algorithm for triangular lattice transverse field Ising antiferromagnets. We
demonstrate that the resulting algorithms are significantly more efficient than
the standard link percolation based quantum cluster approach. We also introduce
a new canonical update scheme that leads to a further improvement in
measurement of some observables arising from its ability to make
one-dimensional clusters in the "imaginary time" direction. Finally, we
demonstrate that refinements in the choice of premarking strategies can lead to
additional improvements in the efficiency of the microcanonical updates. As a
first example of the physics that can be studied using these algorithmic
developments, we obtain evidence for a power-law ordered
intermediate-temperature phase associated with the two-step melting of
long-range order in the fully frustrated square lattice transverse field Ising
model.
| arxiv topic:cond-mat.str-el |
arxiv_dataset-106301812.05426 | On the Noether Problem for torsion subgroups of tori
math.AG
We consider the Noether Problem for stable and retract rationality for the
sequence of $d$-torsion subgroups $T[d]$ of a torus $T$, $d\geq 1$. We show
that the answer to these questions only depends on $d\pmod{e(T)}$, where $e(T)$
is the period of the generic $T$-torsor. When $T$ is the norm one torus
associated to a finite Galois extension, we find all $d$ such that the Noether
Problem for retract rationality has a positive solution for $d$. We also give
an application to the Grothendieck ring of stacks.
| arxiv topic:math.AG |
arxiv_dataset-106311812.05526 | The spectrum of group-based Latin squares
math.CO
We construct sequencings for many groups that are a semi-direct product of an
odd-order abelian group and a cyclic group of odd prime order. It follows from
these constructions that there is a group-based complete Latin square of order
$n$ if and only if $n \in \{ 1,2,4\}$ or there is a non-abelian group of order
$n$.
| arxiv topic:math.CO |
arxiv_dataset-106321812.05626 | Large Field Ranges from Aligned and Misaligned Winding
hep-th
We search for effective axions with super-Planckian decay constants in type
IIB string models. We argue that such axions can be realised as long winding
trajectories in complex-structure moduli space by an appropriate flux choice.
Our main findings are: The simplest models with aligned winding in a 2-axion
field space fail due to a general no-go theorem. However, equally simple models
with misaligned winding, where the effective axion is not close to any of the
fundamental axions, appear to work to the best of our present understanding.
These models have large decay constants but no large monotonic regions in the
potential, making them unsuitable for large-field inflation. We also show that
our no-go theorem can be avoided by aligning three or more axions. We argue
that, contrary to misaligned models, such models can have both large decay
constants and large monotonic regions in the potential. Our results may be used
to argue against the refined Swampland Distance Conjecture and strong forms of
the axionic Weak Gravity Conjecture. It becomes apparent, however, that
realising inflation is by far harder than just producing a light field with
large periodicity.
| arxiv topic:hep-th |
arxiv_dataset-106331812.05726 | Theoretical Evaluation of Electronic Density-of-states and Transport
Effects on Field Emission from $n$-type Ultrananocrystalline Diamond Films
cond-mat.mtrl-sci
In the nitrogen-incorporated ultrananocrystalline diamond ((N)UNCD) films,
representing an $n$-type highly conductive two-phase material comprised of
$sp^3$ diamond grains and $sp^2$-rich graphitic grain boundaries, the current
is carried by a high concentration of mobile electrons within the large-volume
grain boundary networks. Fabricated in a simple thin-film planar form, (N)UNCD
was found to be an efficient field emitter capable of emitting a significant
amount of charge starting at the applied electric field as low as a few
V/$\mu$m which makes it a promising material for designing electron sources.
Despite the semimetallic conduction, field emission (FE) characteristics of
this material demonstrate a strong deviation from the Fowler-Nordheim law in a
high-current-density regime when (N)UNCD field emitters switch from a
diode-like to resistor-like behavior. Such phenomenon resembles the
current-density saturation effect in conventional semiconductors. In the
present paper, we adapt the formalism developed for conventional semiconductors
to study current-density saturation in (N)UNCD field emitters. We provide a
comprehensive theoretical investigation of ($i$) the influence of partial
penetration of the electric field into the material, ($ii$) transport effects
(such as electric-field-dependent mobility), and ($iii$) features of a complex
density-of-states structure (position and shape of $\pi-\pi^*$ bands,
controlling the concentration of charge carriers) on the FE characteristics of
(N)UNCD. We show that the formation of the current-density saturation plateau
can be explained by the limited supply of electrons within the impurity
$\pi-\pi^*$ bands and decreasing electron mobility in high electric field.
Theoretical calculations are consistent with experiment.
| arxiv topic:cond-mat.mtrl-sci |
arxiv_dataset-106341812.05826 | Stimulated plasmon polariton scattering
cond-mat.mes-hall
The plasmon and phonon polaritons of two-dimensional (2d) and van-der-Waals
materials have recently gained substantial interest. Unfortunately, they are
notoriously hard to observe in linear response because of their strong
confinement, low frequency and longitudinal mode symmetry. Here, we propose a
fundamentally new approach of harnessing nonlinear resonant scattering that we
call stimulated plasmon polariton scattering (SPPS) in analogy to the
opto-acoustic stimulated Brillouin scattering (SBS). We show that SPS allows to
excite, amplify and detect 2d plasmon and phonon polaritons all across the
THz-range while requiring only optical components in the near-IR or visible
range. We present a coupled-mode theory framework for SPS and based on this
find that SPS power gains exceed the very top gains observed in on-chip SBS by
at least an order of magnitude. This opens exciting new possibilities to
fundamental studies of 2d materials and will help closing the THz gap in
spectrocopy and information technology.
| arxiv topic:cond-mat.mes-hall |
arxiv_dataset-106351812.05926 | Addendum to: Kolmogorov complexity of sequences of random numbers
generated in Bell's experiments (series of outcomes)
quant-ph
In the mentioned paper we presented results of the estimation of Kolmogorov
complexity of sequences of random numbers generated in a famous Bell's
experiment, aimed to study the security of QKD. We focused on series of time
differences between successive detections of coincidences, and found that
randomness cannot be taken for granted. It was then criticized that the
theorems that demonstrate the randomness of series produced in Bell's
experiments involve series of measurement outcomes, not of measurement times.
Here we reply to this objection and present data of series of outcomes, showing
that the conclusions in the mentioned paper are valid also in this case.
| arxiv topic:quant-ph |
arxiv_dataset-106361812.06026 | Halo concentrations from extended Press-Schechter merger histories
astro-ph.GA
We apply the model relating halo concentration to formation history proposed
by Ludlow et al. to merger trees generated using an algorithm based on
excursion set theory. We find that while the model correctly predicts the
median relation between halo concentration and mass, it underpredicts the
scatter in concentration at fixed mass. Since the same model applied to N-body
merger trees predicts the correct scatter, we postulate that the missing
scatter is due to the lack of any environmental dependence in merger trees
derived from excursion set theory. We show that a simple modification to the
merger tree construction algorithm, which makes merger rates dependent on
environment, can increase the scatter by the required amount, and
simultaneously provide a qualitatively correct correlation between environment
and formation epoch in the excursion set merger trees.
| arxiv topic:astro-ph.GA |
arxiv_dataset-106371812.06126 | Probing neutron star structure via f-mode oscillations and damping in
dynamical spacetime models
gr-qc astro-ph.HE
Gravitational wave and electromagnetic observations can provide new insights
into the nature of matter at supra-nuclear densities inside neutron stars.
Improvements in electromagnetic and gravitational wave sensing instruments
continue to enhance the accuracy with which they can measure the masses, radii,
and tidal deformability of neutron stars. These better measurements place
tighter constraints on the equation of state of cold matter above nuclear
density. In this article, we discuss a complementary approach to get insights
into the structure of neutron stars by providing a model prediction for
non-linear fundamental eigenmodes (f-modes) and their decay over time, which
are thought to be induced by time-dependent tides in neutron star binaries.
Building on pioneering studies that relate the properties of f-modes to the
structure of neutron stars, we systematically study this link in the
non-perturbative regime using models that utilize numerical relativity. Using a
suite of fully relativistic numerical relativity simulations of oscillating TOV
stars, we establish blueprints for the numerical accuracy needed to accurately
compute the frequency and damping times of f-mode oscillations, which we expect
to be a good guide for the requirements in the binary case. We show that the
resulting f-mode frequencies match established results from linear perturbation
theory, but the damping times within numerical errors depart from linear
predictions. This work lays the foundation for upcoming studies aimed at a
comparison of theoretical models of f-mode signatures in gravitational waves,
and their uncertainties with actual gravitational wave data, searching for
neutron star binaries on highly eccentric orbits, and probing neutron star
structure at high densities.
| arxiv topic:gr-qc astro-ph.HE |
arxiv_dataset-106381812.06226 | A Survey of Privacy Infrastructures and Their Vulnerabilities
cs.CR
Over the last two decades, the scale and complexity of Anonymous networks and
its associated technologies grows exponentially as privacy has become a major
concern of individuals. Also, some cyber attackers make use of privacy
infrastructures including botnets and Tor to do illegal activities like drug,
contraband or DDoS attack. However, anonymous networks are not perfect, there
are some methods could exploit the vulnerabilities and track user information.
In this paper, we analyze few of privacy infrastructures and their
vulnerabilities.
| arxiv topic:cs.CR |
arxiv_dataset-106391812.06326 | Hypercomplex Generalizations of Gaussian-type Measures
math.PR
The article is devoted to a new type of measures which are hypercomplex
generalizations of Gaussian-type measures. The considered such measures are
related with solutions of high order hyperbolic PDEs and related Markov
processes. Their characteristic functionals are investigated. Cylindrical
distributions of these measures are studied.
| arxiv topic:math.PR |
arxiv_dataset-106401812.06426 | Auto-tuning Neural Network Quantization Framework for Collaborative
Inference Between the Cloud and Edge
cs.DC cs.AI cs.CV cs.NE
Recently, deep neural networks (DNNs) have been widely applied in mobile
intelligent applications. The inference for the DNNs is usually performed in
the cloud. However, it leads to a large overhead of transmitting data via
wireless network. In this paper, we demonstrate the advantages of the
cloud-edge collaborative inference with quantization. By analyzing the
characteristics of layers in DNNs, an auto-tuning neural network quantization
framework for collaborative inference is proposed. We study the effectiveness
of mixed-precision collaborative inference of state-of-the-art DNNs by using
ImageNet dataset. The experimental results show that our framework can generate
reasonable network partitions and reduce the storage on mobile devices with
trivial loss of accuracy.
| arxiv topic:cs.DC cs.AI cs.CV cs.NE |
arxiv_dataset-106411812.06526 | Nonlinear Dynamics of Spherical Shells Buckling under Step Pressure
cond-mat.soft nlin.PS
Dynamic buckling is addressed for complete elastic spherical shells subject
to a rapidly applied step in external pressure. Insights from the perspective
of nonlinear dynamics reveal essential mathematical features of the buckling
phenomena. To capture the strong buckling imperfection-sensitivity, initial
geometric imperfections in the form of an axisymmetric dimple at each pole are
introduced. Dynamic buckling under the step pressure is related to the
quasi-static buckling pressure. Both loadings produce catastrophic collapse of
the shell for conditions in which the pressure is prescribed. Damping plays an
important role in dynamic buckling because of the time-dependent nonlinear
interaction among modes, particularly the interaction between the spherically
symmetric 'breathing' mode and the buckling mode. In this paper we argue that
the precise frequency dependence of the damping does not matter as most of the
damping happens at a single frequency (the breathing frequency). In general,
there is not a unique step pressure threshold separating responses associated
with buckling from those that do not buckle. Instead there exists a cascade of
buckling thresholds, dependent on the damping and level of imperfection,
separating pressures for which buckling occurs from those for which it does not
occur. For shells with small and moderately small imperfections the dynamic
step buckling pressure can be substantially below the quasi-static buckling
pressure.
| arxiv topic:cond-mat.soft nlin.PS |
arxiv_dataset-106421812.06626 | Designing Adversarially Resilient Classifiers using Resilient Feature
Engineering
cs.LG cs.CR stat.ML
We provide a methodology, resilient feature engineering, for creating
adversarially resilient classifiers. According to existing work, adversarial
attacks identify weakly correlated or non-predictive features learned by the
classifier during training and design the adversarial noise to utilize these
features. Therefore, highly predictive features should be used first during
classification in order to determine the set of possible output labels. Our
methodology focuses the problem of designing resilient classifiers into a
problem of designing resilient feature extractors for these highly predictive
features. We provide two theorems, which support our methodology. The Serial
Composition Resilience and Parallel Composition Resilience theorems show that
the output of adversarially resilient feature extractors can be combined to
create an equally resilient classifier. Based on our theoretical results, we
outline the design of an adversarially resilient classifier.
| arxiv topic:cs.LG cs.CR stat.ML |
arxiv_dataset-106431812.06726 | Machine Learning as a universal tool for quantitative investigations of
phase transition
cond-mat.stat-mech cond-mat.dis-nn hep-lat physics.comp-ph
The problem of identifying the phase of a given system for a certain value of
the temperature can be reformulated as a classification problem in Machine
Learning. Taking as a prototype the Ising model and using the Support Vector
Machine as a tool to classify Monte Carlo generated configurations, we show
that the critical region of the system can be clearly identified and the
symmetry that drives the transition can be reconstructed from the performance
of the learning process. The role of the discrete symmetry of the system in
obtaining this result is discussed. A finite size analysis of the learned
Support Vector Machine decision function allows us to determine the critical
temperature and critical exponents with a precision that is comparable to that
of the most efficient numerical approaches relying on a known Hamiltonian
description of the system. For the determination of the critical temperature
and of the critical exponent connected with the divergence of the correlation
length, other than the availability of a range of temperatures having
information on both phases, the method we propose does not rest on any physical
input on the system, and in particular is agnostic to its Hamiltonian, its
symmetry properties and its order parameter. Hence, our investigation provides
a first significant step in the direction of devising robust tools for
quantitative analyses of phase transitions in cases in which an order parameter
is not known.
| arxiv topic:cond-mat.stat-mech cond-mat.dis-nn hep-lat physics.comp-ph |
arxiv_dataset-106441812.06826 | Minimax theorems in a fully non-convex setting
math.OC math.FA
In this paper, we establish two minimax theorems for functions $f:X\times
I\to {\bf R}$, where $I$ is a real interval, without assuming that $f(x,\cdot)$
is quasi-concave. Also, some related applications are presented.
| arxiv topic:math.OC math.FA |
arxiv_dataset-106451812.06926 | Imaging the Thermal and Kinematic Sunyaev-Zel'dovich Effect Signals in a
Sample of Ten Massive Galaxy Clusters: Constraints on Internal Velocity
Structures and Bulk Velocities
astro-ph.CO
We have imaged the Sunyaev-Zel'dovich (SZ) effect signals at 140 and 270 GHz
towards ten galaxy clusters with Bolocam and AzTEC/ASTE. We also used Planck
data to constrain the signal at large angular scales, Herschel-SPIRE images to
subtract the brightest galaxies that comprise the cosmic infrared background
(CIB), Chandra imaging to map the electron temperature $T_e$ of the
intra-cluster medium (ICM), and HST imaging to derive models of each galaxy
cluster's mass density. The galaxy clusters gravitationally lens the background
CIB, which produced an on-average reduction in brightness towards the galaxy
clusters' centers after the brightest galaxies were subtracted. We corrected
for this deficit, which was between 5-25% of the 270 GHz SZ effect signal
within $R_{2500}$. Using the SZ effect measurements, along with the X-ray
constraint on $T_e$, we measured each galaxy cluster's average line of sight
(LOS) velocity $v_z$ within $R_{2500}$, with a median per-cluster uncertainty
of +-700 km/s. We found an ensemble-mean <$v_z$> of 430+-210 km/s, and an
intrinsic cluster-to-cluster scatter $\sigma_{int}$ of 470+-340 km/s. We also
obtained maps of $v_z$ over each galaxy cluster's face with an angular
resolution of 70". All four galaxy clusters previously identified as having a
merger oriented along the LOS showed an excess variance in these maps at a
significance of 2-4$\sigma$, indicating an internal $v_z$ rms of $\gtrsim$1000
km/s. None of the six galaxy clusters previously identified as relaxed or plane
of sky mergers showed any such excess variance.
| arxiv topic:astro-ph.CO |
arxiv_dataset-106461812.07026 | State Leakage and Coordination with Causal State Knowledge at the
Encoder
cs.IT math.IT
We revisit the problems of state masking and state amplification through the
lens of empirical coordination. Specifically, we characterize the
rate-equivocation-coordination trade-offs regions of a state-dependent channel
in which the encoder has causal and strictly causal state knowledge. We also
extend this characterization to the cases of two-sided state information and
noisy channel feedback. Our approach is based on the notion of core of the
receiver's knowledge, which we introduce to capture what the decoder can infer
about all the signals involved in the model. Finally, we exploit the
aforementioned results to solve a channel state estimation zero-sum game in
which the encoder prevents the decoder to estimate the channel state
accurately.
| arxiv topic:cs.IT math.IT |
arxiv_dataset-106471812.07126 | BandNet: A Neural Network-based, Multi-Instrument Beatles-Style MIDI
Music Composition Machine
cs.SD cs.MM eess.AS
In this paper, we propose a recurrent neural network (RNN)-based MIDI music
composition machine that is able to learn musical knowledge from existing
Beatles' songs and generate music in the style of the Beatles with little human
intervention. In the learning stage, a sequence of stylistically uniform,
multiple-channel music samples was modeled by a RNN. In the composition stage,
a short clip of randomly-generated music was used as a seed for the RNN to
start music score prediction. To form structured music, segments of generated
music from different seeds were concatenated together. To improve the quality
and structure of the generated music, we integrated music theory knowledge into
the model, such as controlling the spacing of gaps in the vocal melody,
normalizing the timing of chord changes, and requiring notes to be related to
the song's key (C major, for example). This integration improved the quality of
the generated music as verified by a professional composer. We also conducted a
subjective listening test that showed our generated music was close to original
music by the Beatles in terms of style similarity, professional quality, and
interestingness. Generated music samples are at https://goo.gl/uaLXoB.
| arxiv topic:cs.SD cs.MM eess.AS |
arxiv_dataset-106481812.07226 | Formation of Extremely Low-mass White Dwarfs in Double Degenerates
astro-ph.SR
Extremely low-mass white dwarfs (ELM WDs) are helium WDs with a mass less
than $\sim$$0.3\rm\;M_\odot$. Most ELM WDs are found in double degenerates
(DDs) in the ELM Survey led by Brown and Kilic. These systems are supposed to
be significant gravitational-wave sources in the mHz frequency. In this paper,
we firstly analyzed the observational characteristics of ELM WDs and found that
there are two distinct groups in the ELM WD mass and orbital period plane,
indicating two different formation scenarios of such objects, i.e. a stable
Roche lobe overflow channel (RL channel) and common envelope ejection channel
(CE channel). We then systematically investigated the formation of ELM WDs in
DDs by a combination of detailed binary evolution calculation and binary
population synthesis. Our study shows that the majority of ELM WDs with mass
less than $0.22\rm\;M_\odot$ are formed from the RL channel. The most common
progenitor mass in this way is in the range of $1.15-1.45\rm\;M_\odot$ and the
resulting ELM WDs have a peak around $0.18\rm\;M_\odot$ when selection effects
are taken into account, consistent with observations. The ELM WDs with a mass
larger than $0.22\rm\;M_\odot$ are more likely to be from the CE channel and
have a peak of ELM WD mass around $0.25\rm\;M_\odot$ which needs to be
confirmed by future observations. By assuming a constant star formation rate of
2$\rm\;M_\odot yr^{-1}$ for a Milky Way-like galaxy, the birth rate and local
density are $5\times10^{-4}\rm\;yr^{-1}$ and $1500\rm\;kpc^{-3}$, respectively,
for DDs with an ELM WD mass less than $0.25\rm\;M_\odot$.
| arxiv topic:astro-ph.SR |
arxiv_dataset-106491812.07326 | Longtime behavior and weak-strong uniqueness for a nonlocal porous media
equation
math.AP
In this manuscript we consider a non-local porous medium equation with
non-local diffusion effects given by a fractional heat operator
\begin{equation*}
\partial_t u = \mbox{div}(u\nabla p),\qquad
\partial_t p = -(-\Delta)^s p + u^2, \end{equation*} in three space
dimensions for $3/4\le s < 1$ and analyze the long time asymptotics. The proof
is based on energy methods and leads to algebraic decay towards the stationary
solution $u=0$ and $\nabla p=0$ in the $L^2(\mathbb{R}^3)$-norm. The decay rate
depends on the exponent $s$. We also show weak-strong uniqueness of solutions
and continuous dependence from the initial data. As a side product of our
analysis we also show that existence of weak solutions, previously shown in
[Caffarelli, Gualdani, Zamponi 2018] for $3/4\le s \le 1$, holds for $1/2 <
s\le 1$ if we consider our problem in the torus.
| arxiv topic:math.AP |
arxiv_dataset-106501812.07426 | Dark matter imprint on $^8$B neutrino spectrum
hep-ph astro-ph.CO astro-ph.SR
The next generation of solar neutrino detectors will provide a precision
measure of the $^8$B electron-neutrino spectrum in the energy range from 1-15
MeV. Although the neutrino spectrum emitted by $^8$B $\beta$-decay reactions in
the Sun's core is identical to the neutrino spectrum measured in the
laboratory, due to vacuum and matter flavor oscillations, this spectrum will be
very different from that measured on Earth by the different solar neutrino
experiments. We study how the presence of dark matter (DM) in the Sun's core
changes the shape of the $^8$B electron-neutrino spectrum. These modifications
are caused by local variations of the electronic density and the $^8$B neutrino
source, induced by local changes of the temperature, density and chemical
composition. Particularly relevant are the shape changes at low and medium
energy range $(E_\nu\le 10 {\; \rm MeV})$, for which the experimental noise
level is expected to be quite small. If such a distortion in the $^8$B$\nu_e$
spectrum were to be observed, this would strongly hint in favor of the
existence of DM in the Sun's core. The $^8$B electron-neutrino spectrum
provides a complementary method to helioseismology and total neutrino fluxes
for constraining the DM properties. In particular, we study the impact of light
asymmetric DM on solar neutrino spectra. Accurate neutrino spectra measurements
could help to determine whether light asymmetric DM exists in the Sun's core,
since it has been recently advocated that this type of DM might resolve the
solar abundance problem.
| arxiv topic:hep-ph astro-ph.CO astro-ph.SR |
arxiv_dataset-106511812.07526 | Consistent Robust Adversarial Prediction for General Multiclass
Classification
stat.ML cs.LG
We propose a robust adversarial prediction framework for general multiclass
classification. Our method seeks predictive distributions that robustly
optimize non-convex and non-continuous multiclass loss metrics against the
worst-case conditional label distributions (the adversarial distributions) that
(approximately) match the statistics of the training data. Although the
optimized loss metrics are non-convex and non-continuous, the dual formulation
of the framework is a convex optimization problem that can be recast as a risk
minimization model with a prescribed convex surrogate loss we call the
adversarial surrogate loss. We show that the adversarial surrogate losses fill
an existing gap in surrogate loss construction for general multiclass
classification problems, by simultaneously aligning better with the original
multiclass loss, guaranteeing Fisher consistency, enabling a way to incorporate
rich feature spaces via the kernel trick, and providing competitive performance
in practice.
| arxiv topic:stat.ML cs.LG |
arxiv_dataset-106521812.07626 | Universal Successor Features Approximators
cs.LG cs.AI stat.ML
The ability of a reinforcement learning (RL) agent to learn about many reward
functions at the same time has many potential benefits, such as the
decomposition of complex tasks into simpler ones, the exchange of information
between tasks, and the reuse of skills. We focus on one aspect in particular,
namely the ability to generalise to unseen tasks. Parametric generalisation
relies on the interpolation power of a function approximator that is given the
task description as input; one of its most common form are universal value
function approximators (UVFAs). Another way to generalise to new tasks is to
exploit structure in the RL problem itself. Generalised policy improvement
(GPI) combines solutions of previous tasks into a policy for the unseen task;
this relies on instantaneous policy evaluation of old policies under the new
reward function, which is made possible through successor features (SFs). Our
proposed universal successor features approximators (USFAs) combine the
advantages of all of these, namely the scalability of UVFAs, the instant
inference of SFs, and the strong generalisation of GPI. We discuss the
challenges involved in training a USFA, its generalisation properties and
demonstrate its practical benefits and transfer abilities on a large-scale
domain in which the agent has to navigate in a first-person perspective
three-dimensional environment.
| arxiv topic:cs.LG cs.AI stat.ML |
arxiv_dataset-106531812.07726 | An endpoint weak-type estimate for multilinear Calder\'on-Zygmund
operators
math.CA
The purpose of this article is to provide an alternative proof of the
weak-type $\left(1,\ldots,1;\frac{1}{m}\right)$ estimate for $m$-multilinear
Calder\'on-Zygmund operators on $\mathbb{R}^n$ first proved by Grafakos and
Torres. Subsequent proofs in the bilinear setting have been given by Maldonado
and Naibo and also by P\'erez and Torres. The proof given here is motivated by
the proof of the weak-type $(1,1)$ estimate for Calder\'on-Zygmund operators in
the nonhomogeneous setting by Nazarov, Treil, and Volberg.
| arxiv topic:math.CA |
arxiv_dataset-106541812.07826 | Two-stage Combinatorial Optimization Problems under Risk
cs.DS
In this paper a class of combinatorial optimization problems is discussed. It
is assumed that a solution can be constructed in two stages. The current
first-stage costs are precisely known, while the future second-stage costs are
only known to belong to an uncertainty set, which contains a finite number of
scenarios with known probability distribution. A partial solution, chosen in
the first stage, can be completed by performing an optimal recourse action,
after the true second-stage scenario is revealed. A solution minimizing the
Conditional Value at Risk (CVaR) measure is computed. Since expectation and
maximum are boundary cases of CVaR, the model generalizes the traditional
stochastic and robust two-stage approaches, previously discussed in the
existing literature. In this paper some new negative and positive results are
provided for basic combinatorial optimization problems such as the selection or
network problems.
| arxiv topic:cs.DS |
arxiv_dataset-106551812.07926 | Deep laser cooling and efficient magnetic compression of molecules
physics.atom-ph
We introduce a scheme for deep laser cooling of molecules based on robust
dark states at zero velocity. By simulating this scheme, we show it to be a
widely applicable method that can reach the recoil limit or below. We
demonstrate and characterise the method experimentally, reaching a temperature
of 5.4(7) $\mu$K. We solve a general problem of measuring low temperatures for
large clouds by rotating the phase-space distribution and then directly imaging
the complete velocity distribution. Using the same phase-space rotation method,
we rapidly compress the cloud. Applying the cooling method a second time, we
compress both the position and velocity distributions.
| arxiv topic:physics.atom-ph |
arxiv_dataset-106561812.08026 | Near-optimal method for highly smooth convex optimization
math.OC
We propose a near-optimal method for highly smooth convex optimization. More
precisely, in the oracle model where one obtains the $p^{th}$ order Taylor
expansion of a function at the query point, we propose a method with rate of
convergence $\tilde{O}(1/k^{\frac{ 3p +1}{2}})$ after $k$ queries to the oracle
for any convex function whose $p^{th}$ order derivative is Lipschitz.
| arxiv topic:math.OC |
arxiv_dataset-106571812.08126 | Generating Diverse and Meaningful Captions
cs.CV cs.CL cs.LG
Image Captioning is a task that requires models to acquire a multi-modal
understanding of the world and to express this understanding in natural
language text. While the state-of-the-art for this task has rapidly improved in
terms of n-gram metrics, these models tend to output the same generic captions
for similar images. In this work, we address this limitation and train a model
that generates more diverse and specific captions through an unsupervised
training approach that incorporates a learning signal from an Image Retrieval
model. We summarize previous results and improve the state-of-the-art on
caption diversity and novelty. We make our source code publicly available
online.
| arxiv topic:cs.CV cs.CL cs.LG |
arxiv_dataset-106581812.08226 | Towards Plan Transformations for Real-World Pick and Place Tasks
cs.RO
In this paper, we investigate the possibility of applying plan
transformations to general manipulation plans in order to specialize them to
the specific situation at hand. We present a framework for optimizing execution
and achieving higher performance by autonomously transforming robot's behavior
at runtime. We show that plans employed by robotic agents in real-world
environments can be transformed, despite their control structures being very
complex due to the specifics of acting in the real world. The evaluation is
carried out on a plan of a PR2 robot performing pick and place tasks, to which
we apply three example transformations, as well as on a large amount of
experiments in a fast plan projection environment.
| arxiv topic:cs.RO |
arxiv_dataset-106591812.08326 | Direct observation of corner states in second-order topological photonic
crystal slabs
cond-mat.mes-hall physics.class-ph
Recently, higher-order topological phases that do not obey the usual
bulk-edge correspondence principle have been introduced in electronic
insulators and brought into classical systems, featuring with in-gap
corner/hinge states. So far, second-order topological insulators have been
realized in mechanical metamaterials, microwave circuit, topolectrical circuit
and acoustic metamaterials. Here, using near-field scanning measurements, we
show the direct observation of corner states in second-order topological
photonic crystal (PC) slabs consisting of periodic dielectric rods on a perfect
electric conductor (PEC). Based on the generalized two-dimensional (2D)
Su-Schrieffer-Heeger (SSH) model, we show that the emergence of corner states
roots in the nonzero edge dipolar polarization instead of the nonzero bulk
quadrupole polarization. We demonstrate the topological transition of 2D Zak
phases of PC slabs by tuning intra-cell distances between two neighboring rods.
We also directly observe in-gap 1D edge states and 0D corner states in the
microwave regime. Our work presents that the PC slab is a powerful platform to
directly observe topological states, and paves the way to study higher-order
photonic topological insulators.
| arxiv topic:cond-mat.mes-hall physics.class-ph |
arxiv_dataset-106601812.08426 | Monochromatic composite right/left handedness achieved in the quantized
composite right/left handed transmission line
physics.optics
The macro composite right/left handedness (CRLH) accompanies the
positive/negative refraction index in the higher, microwave frequency bands in
the composite right/left handed transmission line (CRLH-TL), respectively. In
this paper, we adjust the refraction index of a quantized CRLH-TL via the
squeezed parameters and the electronic components' parameters in the thermal
squeezed state, and the refraction index shows the positive/negative jumping
around the squeezed angle \(\varphi\)=\(\pi\) when it operates at a single
frequency, and the similar result also arises while the refraction index is
manipulated by the electronic components' parameters. The monochromatic CRLH
achieved here breaks through the original definition in the macro CRLH-TL and
provide a new implementation for the CRLH-TL.
| arxiv topic:physics.optics |
arxiv_dataset-106611812.08526 | Equilibrium properties of the lattice system with SALR interaction
potential on a square lattice: quasi-chemical approximation versus Monte
Carlo simulation
cond-mat.soft
The lattice system with competing interactions that models biological objects
(colloids, ensembles of protein molecules, etc.) is considered. This system is
the lattice fluid on a square lattice with attractive interaction between
nearest neighbours and repulsive interaction between next-next-nearest
neighbours. The geometric order parameter is introduced for describing the
ordered phases in this system. The critical value of the order parameter is
estimated and the phase diagram of the system is constructed. The simple
quasi-chemical approximation (QChA) is proposed for the system under
consideration. The data of Monte Carlo simulation of equilibrium properties of
the model are compared with the results of QChA. It is shown that QChA provides
reasonable semiquantitative results for the systems studied and can be used as
the basis for next order approximations.
| arxiv topic:cond-mat.soft |
arxiv_dataset-106621812.08626 | Optimal Stopping under G-expectation
math.PR
We develop a theory of optimal stopping problems under G-expectation
framework. We first define a new kind of random times, called G-stopping times,
which is suitable for this problem. For the discrete time case with finite
horizon, the value function is defined backwardly and we show that it is the
smallest G-supermartingale dominating the payoff process and the optimal
stopping time exists. Then we extend this result both to the infinite horizon
and to the continuous time case. We also establish the relation between the
value function and solution of reflected BSDE driven by G-Brownian motion.
| arxiv topic:math.PR |
arxiv_dataset-106631812.08726 | Mathematical methods for resource-based type theories
quant-ph
With the wide range of quantum programming languages on offer now, efficient
program verification and type checking for these languages presents a challenge
-- especially when classical debugging techniques may affect the states in a
quantum program. In this work, we make progress towards a program verification
approach using the formalism of operational quantum mechanics and resource
theories. We present a logical framework that captures two mathematical
approaches to resource theory based on monoids (algebraic) and monoidal
categories (categorical). We develop the syntax of this framework as an
intuitionistic sequent calculus, and prove soundness and completeness of an
algebraic and categorical semantics that recover these approaches. We also
provide a cut-elimination theorem, normal form, and analogue of Lambek's
lifting theorem for polynomial systems over the logics. Using these approaches
along with the Curry-Howard-Lambek correspondence for programs, proofs and
categories, this work lays the mathematical groundwork for a type checker for
some resource theory based frameworks, with the possibility of extending it
other quantum programming languages.
| arxiv topic:quant-ph |
arxiv_dataset-106641812.08826 | Chaotic dynamics in a quantum Fermi-Pasta-Ulam problem
cond-mat.dis-nn nlin.CD nlin.SI
We investigate the emergence of chaotic dynamics in a quantum Fermi - Pasta -
Ulam problem for anharmonic vibrations in atomic chains applying
semi-quantitative analysis of resonant interactions complemented by exact
diagonalization numerical studies. The crossover energy separating chaotic high
energy phase and localized (integrable) low energy phase is estimated. It
decreases inversely proportionally to the number of atoms until approaching the
quantum regime where this dependence saturates. The chaotic behavior appears at
lower energies in systems with free or fixed ends boundary conditions compared
to periodic systems. The applications of the theory to realistic molecules are
discussed.
| arxiv topic:cond-mat.dis-nn nlin.CD nlin.SI |
arxiv_dataset-106651812.08926 | A controllable two-membrane-in-the-middle cavity optomechanical system
physics.optics
We report an optomechanical system with two dielectric membranes inside a
Fabry-Perot cavity. The cavity resonant frequencies are measured in such a
two-membrane-in-the-middle system, which show an interesting
band-structure-like diagram. This system exhibits great controllability on the
parameters of the system. The positions and angles of each membrane can be
manipulated on demand by placing two membranes inside the cavity separately.
The eigenfrequencies of the vibrational modes of the membranes can also be
tuned individually with piezoelectricity. This scheme could be
straightforwardly extended to multiple-membrane-in-the-middle systems, where
more than two membranes are involved. Such a well controllable multiple
membrane optomechanical system provides a promising platform for studying
nonlinear and quantum dynamical phenomena in multimode optomechanics with
distinct mechanical oscillators.
| arxiv topic:physics.optics |
arxiv_dataset-106661812.09026 | Deep Reinforcement Learning for Real-Time Optimization in NB-IoT
Networks
cs.NI
NarrowBand-Internet of Things (NB-IoT) is an emerging cellular-based
technology that offers a range of flexible configurations for massive IoT radio
access from groups of devices with heterogeneous requirements. A configuration
specifies the amount of radio resource allocated to each group of devices for
random access and for data transmission. Assuming no knowledge of the traffic
statistics, there exists an important challenge in "how to determine the
configuration that maximizes the long-term average number of served IoT devices
at each Transmission Time Interval (TTI) in an online fashion". Given the
complexity of searching for optimal configuration, we first develop real-time
configuration selection based on the tabular Q-learning (tabular-Q), the Linear
Approximation based Q-learning (LA-Q), and the Deep Neural Network based
Q-learning (DQN) in the single-parameter single-group scenario. Our results
show that the proposed reinforcement learning based approaches considerably
outperform the conventional heuristic approaches based on load estimation
(LE-URC) in terms of the number of served IoT devices. This result also
indicates that LA-Q and DQN can be good alternatives for tabular-Q to achieve
almost the same performance with much less training time. We further advance
LA-Q and DQN via Actions Aggregation (AA-LA-Q and AA-DQN) and via Cooperative
Multi-Agent learning (CMA-DQN) for the multi-parameter multi-group scenario,
thereby solve the problem that Q-learning agents do not converge in
high-dimensional configurations. In this scenario, the superiority of the
proposed Q-learning approaches over the conventional LE-URC approach
significantly improves with the increase of configuration dimensions, and the
CMA-DQN approach outperforms the other approaches in both throughput and
training efficiency.
| arxiv topic:cs.NI |
arxiv_dataset-106671812.09126 | On the geometric and magnetic properties of the monomer, dimer and
trimer of NiFe2O4
cond-mat.mtrl-sci cond-mat.mes-hall
In this work, by employing Density Functional Theory, we compute and discuss
some geometric and magnetic properties of the monomer, dimer and trimer of
NiFe2 O4 . The calculations are performed at the UDFT/ B3LYP level of
calculation, by employing the LANL2DZ effective pseudo potential. The results
of the Mulliken spin densities and the spin polarization will be presented.
Finally the outcome of the system density of states is considered.
| arxiv topic:cond-mat.mtrl-sci cond-mat.mes-hall |
arxiv_dataset-106681812.09226 | Thermoelectric transport in two-dimensional topological insulator state
based on HgTe quantum well
cond-mat.mes-hall
The thermoelectric response of HgTe quantum wells in the state of
two-dimensional topological insulator (2D TI) has been studied experimentally.
Ambipolar thermopower, typical for an electron-hole system, has been observed
across the charge neutrality point, where the carrier type changes from
electrons to holes according to the resistance measurements. The hole-type
thermopower is much stronger than the electron-type one. The thermopower
linearly increases with temperature. We present a theoretical model which
accounts for both the edge and bulk contributions to the electrical
conductivity and thermoelectric effect in a 2D TI, including the effects of
edge to bulk leakage. The model, contrary to previous theoretical studies,
demonstrates that the 2D TI is not expected to show anomalies of thermopower
near the band conductivity threshold, which is consistent with our experimental
results. Based on the experimental data and theoretical analysis, we conclude
that the observed thermopower is mostly of the bulk origin, while the
resistance is determined by both the edge and bulk transport.
| arxiv topic:cond-mat.mes-hall |
arxiv_dataset-106691812.09326 | Proton decay matrix element on the lattice with physical pion mass
hep-lat hep-ph
Proton decay is one of possible signatures of baryon number violation, which
has to exist to explain the baryon asymmetry and the existence of nuclear
matter. Proton decays must be mediated through effective low-energy baryon
number violating operators made of three quarks and a lepton. We calculate
matrix elements of these operators between the proton and various meson final
states using the direct method. We report on preliminary results of matrix
element calculation done with the 2+1 dynamical flavor domain wall fermions at
the physical point for the first time.
| arxiv topic:hep-lat hep-ph |
arxiv_dataset-106701812.09426 | Coherence Temperature in the Diluted Periodic Anderson Model
cond-mat.str-el cond-mat.dis-nn
The Kondo and Periodic Anderson Model (PAM) are known to provide a
microscopic picture of many of the fundamental properties of heavy fermion
materials and, more generally, a variety of strong correlation phenomena in
$4f$ and $5f$ systems. In this paper, we apply the Determinant Quantum Monte
Carlo (DQMC) method to include disorder in the PAM, specifically the removal of
a fraction $x$ of the localized orbitals. We determine the evolution of the
coherence temperature $T^*$, where the local moments and conduction electrons
become entwined in a heavy fermion fluid, with $x$ and with the hybridization
$V$ between localized and conduction orbitals. We recover several of the
principal observed trends in $T^*$ of doped heavy fermions, and also show that,
within this theoretical framework, the calculated Nuclear Magnetic Resonance
(NMR) relaxation rate tracks the experimentally measured behavior in pure and
doped CeCoIn$_5$. Our results contribute to important issues in the
interpretation of local probes of disordered, strongly correlated systems.
| arxiv topic:cond-mat.str-el cond-mat.dis-nn |
arxiv_dataset-106711812.09526 | Functional Aggregate Queries with Additive Inequalities
cs.DB cs.DS cs.IT cs.LG math.IT
Motivated by fundamental applications in databases and relational machine
learning, we formulate and study the problem of answering functional aggregate
queries (FAQ) in which some of the input factors are defined by a collection of
additive inequalities between variables. We refer to these queries as FAQ-AI
for short.
To answer FAQ-AI in the Boolean semiring, we define relaxed tree
decompositions and relaxed submodular and fractional hypertree width
parameters. We show that an extension of the InsideOut algorithm using
Chazelle's geometric data structure for solving the semigroup range search
problem can answer Boolean FAQ-AI in time given by these new width parameters.
This new algorithm achieves lower complexity than known solutions for FAQ-AI.
It also recovers some known results in database query answering.
Our second contribution is a relaxation of the set of polymatroids that gives
rise to the counting version of the submodular width, denoted by #subw. This
new width is sandwiched between the submodular and the fractional hypertree
widths. Any FAQ and FAQ-AI over one semiring can be answered in time
proportional to #subw and respectively to the relaxed version of #subw.
We present three applications of our FAQ-AI framework to relational machine
learning: k-means clustering, training linear support vector machines, and
training models using non-polynomial loss. These optimization problems can be
solved over a database asymptotically faster than computing the join of the
database relations.
| arxiv topic:cs.DB cs.DS cs.IT cs.LG math.IT |
arxiv_dataset-106721812.09626 | Analysis of a SIRI epidemic model with distributed delay and relapse
math.CA math.DS q-bio.PE
We investigate the global behaviour of a SIRI epidemic model with distributed
delay and relapse. From the theory of functional differential equations with
delay, we prove that the solution of the system is unique, bounded, and
positive, for all time. The basic reproduction number $R_{0}$ for the model is
computed. By means of the direct Lyapunov method and LaSalle invariance
principle, we prove that the disease free equilibrium is globally
asymptotically stable when $R_{0} < 1$. Moreover, we show that there is a
unique endemic equilibrium, which is globally asymptotically stable, when
$R_{0} > 1$.
| arxiv topic:math.CA math.DS q-bio.PE |
arxiv_dataset-106731812.09726 | Failure of the trilinear operator space Grothendieck theorem
math.OA math.FA
We give a counterexample to a trilinear version of the operator space
Grothendieck theorem. In particular, we show that for trilinear forms on
$\ell_\infty$, the ratio of the symmetrized completely bounded norm and the
jointly completely bounded norm is in general unbounded, answering a question
of Pisier. The proof is based on a non-commutative version of the generalized
von Neumann inequality from additive combinatorics.
| arxiv topic:math.OA math.FA |
arxiv_dataset-106741812.09826 | Fast configuration-interaction calculations for nobelium and ytterbium
physics.atom-ph
We calculate excitation energies for low states of nobelium, including states
with open $5f$ subshell. An efficient version of the many-electron
configuration-interaction method for treating the atom as a sixteen external
electrons system has been developed and used. The method is tested on
calculations for ytterbium which has external electron structure similar to
nobelium. The results for nobelium are important for prediction of its spectrum
and for interpretation of recent measurements. Ytterbium is mostly used to
study the features of the method.
| arxiv topic:physics.atom-ph |
arxiv_dataset-106751812.09926 | SNAS: Stochastic Neural Architecture Search
cs.LG cs.AI stat.ML
We propose Stochastic Neural Architecture Search (SNAS), an economical
end-to-end solution to Neural Architecture Search (NAS) that trains neural
operation parameters and architecture distribution parameters in same round of
back-propagation, while maintaining the completeness and differentiability of
the NAS pipeline. In this work, NAS is reformulated as an optimization problem
on parameters of a joint distribution for the search space in a cell. To
leverage the gradient information in generic differentiable loss for
architecture search, a novel search gradient is proposed. We prove that this
search gradient optimizes the same objective as reinforcement-learning-based
NAS, but assigns credits to structural decisions more efficiently. This credit
assignment is further augmented with locally decomposable reward to enforce a
resource-efficient constraint. In experiments on CIFAR-10, SNAS takes less
epochs to find a cell architecture with state-of-the-art accuracy than
non-differentiable evolution-based and reinforcement-learning-based NAS, which
is also transferable to ImageNet. It is also shown that child networks of SNAS
can maintain the validation accuracy in searching, with which attention-based
NAS requires parameter retraining to compete, exhibiting potentials to stride
towards efficient NAS on big datasets. We have released our implementation at
https://github.com/SNAS-Series/SNAS-Series.
| arxiv topic:cs.LG cs.AI stat.ML |
arxiv_dataset-106761812.10026 | Induction, Coinduction, and Fixed Points: A Concise Comparative Survey
cs.LO cs.PL math.CT
In this survey article (which hitherto is an ongoing work-in-progress) we
present the formulation of the induction and coinduction principles using the
language and conventions of each of order theory, set theory, programming
languages' type theory, first-order logic, and category theory, for the purpose
of examining some of the similarities and, more significantly, the
dissimilarities between these various mathematical disciplines, and hence shed
some light on the precise relation between these disciplines.
Towards that end, in this article we discuss plenty of related concepts, such
as fixed points, pre-fixed points, post-fixed points, inductive sets and types,
coinductive sets and types, algebras and coalgebras. We conclude the survey by
hinting at the possibility of a more abstract and unified treatment that uses
concepts from category theory such as monads and comonads.
| arxiv topic:cs.LO cs.PL math.CT |
arxiv_dataset-106771812.10126 | Multifaceted nonlinear dynamics in $\mathcal{PT}$-symmetric coupled
Li\'{e}nard oscillators
nlin.CD
We propose a generalized parity-time ($\mathcal{PT}$) -symmetric Li\'enard
oscillator with two different orders of nonlinear position-dependent
dissipation. We study the stability of the stationary states by using the
eigenvalues of Jacobian and evaluate the stability threshold thereafter. In the
first order nonlinear damping model, we discover that the temporal evolution of
both gain and lossy oscillators attains a complete convergence towards the
stable stationary state leading to the emergence of oscillation and amplitude
deaths. Also, the system displays a remarkable manifestation of transient chaos
in the lossy oscillator while the gain counterpart exhibits blow-up dynamics
for certain choice of initial conditions and control parameters. Employing an
external driving force on the loss oscillator, we find that the blow-up
dynamics can be controlled and a pure aperiodic state is achievable. On the
other hand, the second order nonlinear damping model yields a completely
different dynamics on contrary to the first order where the former reveals a
conventional quasi-periodic route to chaos upon decreasing the natural
frequency of both gain and loss oscillators. An electronic circuit scheme for
the experimental realization of the proposed system has also been put forward.
| arxiv topic:nlin.CD |
arxiv_dataset-106781812.10226 | Geometric construction of Heisenberg-Weil representations for finite
unitary groups and Howe correspondences
math.RT math.NT
We give a geometric construction of the Heisenberg-Weil representation of a
finite unitary group by the middle \'{e}tale cohomology of an algebraic variety
over a finite field, whose rational points give a unitary Heisenberg group.
Using also a Frobenius action, we give a geometric realization of the Howe
correspondence for $(\mathit{Sp}_{2n},O_2^-)$ over any finite field including
characteristic two. As an application, we show that unipotency is preserved
under the Howe correspondence.
| arxiv topic:math.RT math.NT |
arxiv_dataset-106791812.10326 | Equivalent Choice Functions and Stable Mechanisms
econ.TH
We study conditions for the existence of stable and group-strategy-proof
mechanisms in a many-to-one matching model with contracts if students'
preferences are monotone in contract terms. We show that "equivalence",
properly defined, to a choice profile under which contracts are substitutes and
the law of aggregate holds is a necessary and sufficient condition for the
existence of a stable and group-strategy-proof mechanism.
Our result can be interpreted as a (weak) embedding result for choice
functions under which contracts are observable substitutes and the observable
law of aggregate demand holds.
| arxiv topic:econ.TH |
arxiv_dataset-106801812.10426 | Stochastic Trust Region Inexact Newton Method for Large-scale Machine
Learning
cs.LG stat.ML
Nowadays stochastic approximation methods are one of the major research
direction to deal with the large-scale machine learning problems. From
stochastic first order methods, now the focus is shifting to stochastic second
order methods due to their faster convergence and availability of computing
resources. In this paper, we have proposed a novel Stochastic Trust RegiOn
Inexact Newton method, called as STRON, to solve large-scale learning problems
which uses conjugate gradient (CG) to inexactly solve trust region subproblem.
The method uses progressive subsampling in the calculation of gradient and
Hessian values to take the advantage of both, stochastic and full-batch
regimes. We have extended STRON using existing variance reduction techniques to
deal with the noisy gradients and using preconditioned conjugate gradient (PCG)
as subproblem solver, and empirically proved that they do not work as expected,
for the large-scale learning problems. Finally, our empirical results prove
efficacy of the proposed method against existing methods with bench marked
datasets.
| arxiv topic:cs.LG stat.ML |
arxiv_dataset-106811812.10526 | Cosmological constant problem: deflation during inflation
gr-qc hep-th
We argue that the discrepancy between the Planck mass scale and the observed
value of the cosmological constant can be largely attenuated if those
quantities are understood as a result of effective, and thus scale-dependent,
couplings. We exemplify this mechanism for the early inflationary epoch of the
universe by solving the corresponding effective gap equations, subject to an
energy condition. Several non-trivial checks and extensions are discussed. A
comparison of our results to the renormalization group flow, obtained within
the asymptotic safety program reveals a stunning agreement.
| arxiv topic:gr-qc hep-th |
arxiv_dataset-106821812.10626 | The Tensor Theory of Connections
math.GM
This paper extends the univariate Theory of Connections, introduced in
(Mortari,2017), to the multivariate case on rectangular domains with detailed
attention to the bivariate case. In particular, it generalizes the bivariate
Coons surface, introduced by (Coons,1984), by providing analytical expressions,
called "constrained expressions," representing all possible surfaces with
assigned boundary constraints in terms of functions and arbitrary-order
derivatives. In two dimensions, these expressions, which contain a freely
chosen function, g(x,y), satisfy all constraints no matter what the g(x,y) is.
The boundary constraints considered in this article are Dirichlet, Neumann, and
any combinations of them. Although the focus of this article is on
two-dimensional spaces, the final section introduces the "Tensor Theory of
Connections," validated by mathematical proof. This represents the multivariate
extension of the Theory of Connections subject to arbitrary-order derivative
constraints in rectangular domains. The main task of this paper is to provide
an analytical procedure to obtain constrained expressions in any space that can
be used to transform constrained problems into unconstrained problems. This
theory is proposed mainly to better solve PDEs and stochastic differential
equations.
| arxiv topic:math.GM |
arxiv_dataset-106831812.10726 | The simplicial volume of mapping tori of 3-manifolds
math.GT math.AT math.GR
We prove that any mapping torus of a closed 3-manifold has zero simplicial
volume. When the fiber is a prime 3-manifold, classification results can be
applied to show vanishing of the simplicial volume, however the case of
reducible fibers is by far more subtle. We thus analyse the possible
self-homeomorphisms of reducible 3-manifolds, and use this analysis to produce
an explicit representative of the fundamental class of the corresponding
mapping tori. To this end, we introduce a new technique for understanding
self-homeomorphisms of connected sums in arbitrary dimensions on the level of
classifying spaces and for computing the simplicial volume. In particular, we
extend our computations to mapping tori of certain connected sums in higher
dimensions. Our main result completes the picture for the vanishing of the
simplicial volume of fiber bundles in dimension four. Moreover, we deduce that
dimension four together with the trivial case of dimension two are the only
dimensions where all mapping tori have vanishing simplicial volume. As a group
theoretic consequence, we derive an alternative proof of the fact that the
fundamental group $G$ of a mapping torus of a 3-manifold $M$ is Gromov
hyperbolic if and only if $M$ is virtually a connected sum $\# S^2\times S^1$
and $G$ does not contain $\mathbb{Z}^2$.
| arxiv topic:math.GT math.AT math.GR |
arxiv_dataset-106841812.10826 | Bohm-Bell type experiments: Classical probability approach to
(no-)signaling and applications to quantum physics and psychology
quant-ph math-ph math.MP math.PR
We consider the problem of representation of quantum states and observables
in the framework of classical probability theory (Kolmogorov's
measure-theoretic axiomatics, 1933). Our aim is to show that, in spite of the
common opinion, correlations of observables $A_1, A_2$ and $B_1,B_2$ involved
in the experiments of the Bohm-Bell type can be expressed as correlations of
classical random variables $a_1, a_2$ and $b_1, b_2.$ The crucial point is that
correlations $\langle A_i, B_j \rangle$ should be treated as conditional on the
selection of the pairs $(i, j).$ The setting selection procedure is based on
two random generators $R_A$ and $R_B.$ They are also considered as observables,
supplementary to the "basic observables" $A_1, A_2$ and $B_1, B_2.$ These
observables are absent in the standard description, e.g., in the scheme for
derivation of the CHSH-inequality. We represent them by classical random
variables $r_a$ and $r_b.$ Following the recent works of Dzhafarov and
collaborators, we apply our conditional correlation approach to characterize
(no-)signaling in the classical probabilistic framework. Consideration the
Bohm-Bell experimental scheme in the presence of signaling is important for
applications outside quantum mechanics, e.g., in psychology and social science.
| arxiv topic:quant-ph math-ph math.MP math.PR |
arxiv_dataset-106851812.10926 | HUOPM: High Utility Occupancy Pattern Mining
cs.DB
Mining useful patterns from varied types of databases is an important
research topic, which has many real-life applications. Most studies have
considered the frequency as sole interestingness measure for identifying high
quality patterns. However, each object is different in nature. The relative
importance of objects is not equal, in terms of criteria such as the utility,
risk, or interest. Besides, another limitation of frequent patterns is that
they generally have a low occupancy, i.e., they often represent small sets of
items in transactions containing many items, and thus may not be truly
representative of these transactions. To extract high quality patterns in real
life applications, this paper extends the occupancy measure to also assess the
utility of patterns in transaction databases. We propose an efficient algorithm
named High Utility Occupancy Pattern Mining (HUOPM). It considers user
preferences in terms of frequency, utility, and occupancy. A novel
Frequency-Utility tree (FU-tree) and two compact data structures, called the
utility-occupancy list and FU-table, are designed to provide global and partial
downward closure properties for pruning the search space. The proposed method
can efficiently discover the complete set of high quality patterns without
candidate generation. Extensive experiments have been conducted on several
datasets to evaluate the effectiveness and efficiency of the proposed
algorithm. Results show that the derived patterns are intelligible, reasonable
and acceptable, and that HUOPM with its pruning strategies outperforms the
state-of-the-art algorithm, in terms of runtime and search space, respectively.
| arxiv topic:cs.DB |
arxiv_dataset-106861812.11026 | Hybrid Wasserstein Distance and Fast Distribution Clustering
stat.ME
We define a modified Wasserstein distance for distribution clustering which
inherits many of the properties of the Wasserstein distance but which can be
estimated easily and computed quickly. The modified distance is the sum of two
terms. The first term --- which has a closed form --- measures the
location-scale differences between the distributions. The second term is an
approximation that measures the remaining distance after accounting for
location-scale differences. We consider several forms of approximation with our
main emphasis being a tangent space approximation that can be estimated using
nonparametric regression. We evaluate the strengths and weaknesses of this
approach on simulated and real examples.
| arxiv topic:stat.ME |
arxiv_dataset-106871812.11126 | Spontaneous localization in self-focusing of ultrashort light pulses
physics.optics
This is a summary directed to PhD students of the research work conducted on
the problem of the production of "light bullets", or multidimensional wave
packets that propagate without distortion in unbounded, homogeneous, nonlinear
media, and on the actual nature of the self-localized light wave packets
spontaneously generated in self-focusing experiments with ultrashort pulses.
| arxiv topic:physics.optics |
arxiv_dataset-106881812.11226 | Fast Training Algorithms for Deep Convolutional Fuzzy Systems with
Application to Stock Index Prediction
q-fin.ST cs.LG
A deep convolutional fuzzy system (DCFS) on a high-dimensional input space is
a multi-layer connection of many low-dimensional fuzzy systems, where the input
variables to the low-dimensional fuzzy systems are selected through a moving
window across the input spaces of the layers. To design the DCFS based on
input-output data pairs, we propose a bottom-up layer-by-layer scheme.
Specifically, by viewing each of the first-layer fuzzy systems as a weak
estimator of the output based only on a very small portion of the input
variables, we design these fuzzy systems using the WM Method. After the
first-layer fuzzy systems are designed, we pass the data through the first
layer to form a new data set and design the second-layer fuzzy systems based on
this new data set in the same way as designing the first-layer fuzzy systems.
Repeating this process layer-by-layer we design the whole DCFS. We also propose
a DCFS with parameter sharing to save memory and computation. We apply the DCFS
models to predict a synthetic chaotic plus random time-series and the real Hang
Seng Index of the Hong Kong stock market.
| arxiv topic:q-fin.ST cs.LG |
arxiv_dataset-106891812.11326 | QoS-aware Full-duplex Concurrent Scheduling for Millimeter Wave Wireless
Backhaul Networks
cs.NI
The development of self-interference (SI) cancelation technology makes
full-duplex (FD) communication possible. Considering the quality of service
(QoS) of flows in small cells densely deployed scenario with limited time slot
(TS) resources, this paper introduces the FD communication into the concurrent
scheduling problem of millimeter-wave (mmWave) wireless backhaul network. We
propose a QoS-aware FD concurrent scheduling algorithm to maximize the number
of flows with their QoS requirements satisfied. Based on the contention graph,
the algorithm makes full use of the FD condition. Both residual
self-interference (RSI) and multi-user interference (MUI) are considered.
Besides, it also fully considers the QoS requirements of flows and ensures the
flows can be transmitted at high rates. Extensive simulations at 60GHz
demonstrate that with high SI cancelation level and appropriate contention
threshold, the proposed FD algorithm can achieve superior performance in terms
of the number of flows with their QoS requirements satisfied and the system
throughput compared with other stateof-of-the-art schemes.
| arxiv topic:cs.NI |
arxiv_dataset-106901812.11426 | Performance and Moli`ere radius measurements using a compact prototype
of LumiCal in an electron test beam
physics.ins-det
A new design of a detector plane of sub-millimetre thickness for an
electromagnetic sampling calorimeter is presented. It is intended to be used in
the luminometers LumiCal and BeamCal in future linear $e^+e^-$ collider
experiments. The detector planes were produced utilising novel connectivity
scheme technologies. They were installed in a compact prototype of the
calorimeter and tested at DESY with an electron beam of energy 1-5 GeV. The
performance of a prototype of a compact LumiCal comprising eight detector
planes was studied. The effective Moli`ere radius at 5 GeV was determined to be
(8.1 +/- 0.1 (stat) +/- 0.3 (syst)) mm, a value well reproduced by the Monte
Carlo (MC) simulation (8.4 +/- 0.1) mm. The dependence of the effective
Moli`ere radius on the electron energy in the range 1-5 GeV was also studied.
Good agreement was obtained between data and MC simulation.
| arxiv topic:physics.ins-det |
arxiv_dataset-106911812.11526 | Improving forecasting accuracy of time series data using a new ARIMA-ANN
hybrid method and empirical mode decomposition
cs.LG stat.ML
Many applications in different domains produce large amount of time series
data. Making accurate forecasting is critical for many decision makers. Various
time series forecasting methods exist which use linear and nonlinear models
separately or combination of both. Studies show that combining of linear and
nonlinear models can be effective to improve forecasting performance. However,
some assumptions that those existing methods make, might restrict their
performance in certain situations. We provide a new Autoregressive Integrated
Moving Average (ARIMA)-Artificial Neural Network(ANN) hybrid method that work
in a more general framework. Experimental results show that strategies for
decomposing the original data and for combining linear and nonlinear models
throughout the hybridization process are key factors in the forecasting
performance of the methods. By using appropriate strategies, our hybrid method
can be an effective way to improve forecasting accuracy obtained by traditional
hybrid methods and also either of the individual methods used separately.
| arxiv topic:cs.LG stat.ML |
arxiv_dataset-106921812.11626 | Unfolding quantum master equation into a system of real-valued
equations: computationally effective expansion over the basis of $SU(N)$
generators
quant-ph
Dynamics of an open $N$-state quantum system is typically modeled with a
Markovian master equation describing the evolution of the system's density
operator. By using generators of $SU(N)$ group as a basis, the density operator
can be transformed into a real-valued 'Bloch vector'. The Lindbladian, a
super-operator which serves a generator of the evolution, %in the master
equation, can be expanded over the same basis and recast in the form of a real
matrix. Together, these expansions result is a non-homogeneous system of
$N^2-1$ real-valued linear differential equations for the Bloch vector. Now one
can, e.g., implement a high-performance parallel simplex algorithm to find a
solution of this system which guarantees exact preservation of the norm and
Hermiticity of the density matrix. However, when performed in a straightforward
way, the expansion turns to be an operation of the time complexity
$\mathcal{O}(N^{10})$. The complexity can be reduced when the number of
dissipative operators is independent of $N$, which is often the case for
physically meaningful models. Here we present an algorithm to transform quantum
master equation into a system of real-valued differential equations and
propagate it forward in time. By using a scalable model, we evaluate
computational efficiency of the algorithm and demonstrate that it is possible
to handle the model system with $N = 10^3$ states on a single node of a
computer cluster.
| arxiv topic:quant-ph |
arxiv_dataset-106931812.11726 | Three-partition Hodge integrals and the topological vertex
math-ph hep-th math.AG math.MP math.QA nlin.SI
A conjecture on the relation between the cubic Hodge integrals and the
topological vertex in topological string theory is resolved. A central role is
played by the notion of generalized shift symmetries in a fermionic realization
of the two-dimensional quantum torus algebra. These algebraic relations of
operators in the fermionic Fock space are used to convert generating functions
of the cubic Hodge integrals and the topological vertex to each other. As a
byproduct, the generating function of the cubic Hodge integrals at special
values of the parameters therein is shown to be a tau function of the
generalized KdV (aka Gelfand-Dickey) hierarchies.
| arxiv topic:math-ph hep-th math.AG math.MP math.QA nlin.SI |
arxiv_dataset-106941812.11826 | UAV Base Station Location Optimization for Next Generation Wireless
Networks: Overview and Future Research Directions
cs.NI
Unmanned aerial vehicles mounted base stations (UAV-BSs) are expected to
become one of the significant components of the Next Generation Wireless
Networks (NGWNs). Rapid deployment, mobility, higher chances of unobstructed
propagation path, and flexibility features of UAV-BSs have attracted
significant attention. Despite, potentially, high gains brought by UAV-BSs in
NGWNs, many challenges are also introduced by them. Optimal location assignment
to UAV-BSs, arguably, is the most widely investigated problem in the literature
on UAV-BSs in NGWNs. This paper presents a comprehensive survey of the
literature on the location optimization of UAV-BSs in NGWNs. A generic
optimization framework through a universal Mixed Integer Non-Linear Programming
(MINLP) formulation is constructed and the specifications of its constituents
are elaborated. The generic problem is classified into a novel taxonomy. Due to
the highly challenging nature of the optimization problem a range of solutions
are adopted in the literature which are also covered under the aforementioned
classification. Furthermore, future research directions on UAV-BS location
optimization in 5G and beyond non-terrestrial aerial communication systems are
discussed.
| arxiv topic:cs.NI |
arxiv_dataset-106951812.11926 | On the maximal function associated to the spherical means on the
Heisenberg group
math.CA
In this paper we deal with lacunary and full versions of the spherical
maximal function on the Heisenberg group $\mathbb{H}^n$, for $n\ge 2$. By
suitable adaptation of an approach developed by M. Lacey in the Euclidean case,
we obtain sparse bounds for these maximal functions, which lead to new
unweighted and weighted estimates. In particular, we deduce the $L^p$
boundedness, for $1<p<\infty$, of the lacunary maximal function associated to
the spherical means on the Heisenberg group. In order to prove the sparse
bounds, we establish $ L^p-L^q $ estimates for local (single scale) variants of
the spherical means.
| arxiv topic:math.CA |
arxiv_dataset-106961901.00053 | Spanning 2-Forests and Resistance Distance in 2-Connected Graphs
math.CO
A spanning 2-forest separating vertices $u$ and $v$ of an undirected
connected graph is a spanning forest with 2 components such that $u$ and $v$
are in distinct components. Aside from their combinatorial significance,
spanning 2-forests have an important application to the calculation of
resistance distance or effective resistance. The resistance distance between
vertices $u$ and $v$ in a graph representing an electrical circuit with unit
resistance on each edge is the number of spanning 2-forests separating $u$ and
$v$ divided by the number of spanning trees in the graph. There are also
well-known matrix theoretic methods for calculating resistance distance, but
the way in which the structure of the underlying graph determines resistance
distance via these methods is not well understood.
For any connected graph $G$ with a 2-separator separating vertices $u$ and
$v$, we show that the number of spanning trees and spanning 2-forests
separating $u$ and $v$ can be expressed in terms of these same quantities for
the smaller separated graphs, which makes computation significantly more
tractable. An important special case is the preservation of the number of
spanning 2-forests if $u$ and $v$ are in the same smaller graph. In this paper
we demonstrate that this method of calculating resistance distance is more
suitable for certain structured families of graphs than the more standard
methods. We apply our results to count the number of spanning 2-forests and
calculate the resistance distance in a family of Sierpinski triangles and in
the family of linear 2-trees with a single bend.
| arxiv topic:math.CO |
arxiv_dataset-106971901.00153 | Occupation time statistics of a gas of interacting diffusing particles
cond-mat.stat-mech
The time which a diffusing particle spends in a certain region of space is
known as the occupation time, or the residence time. Recently the joint
occupation time statistics of an ensemble of non-interacting particles was
addressed using the single-particle statistics. Here we employ the Macroscopic
Fluctuation Theory (MFT) to study the occupation time statistics of many
\emph{interacting} particles. We find that interactions can significantly
change the statistics and, in some models, even cause a singularity of the
large-deviation function describing these statistics. This singularity can be
interpreted as a dynamical phase transition. We also point out to a close
relation between the MFT description of the occupation-time statistics of
non-interacting particles and the level 2 large deviation formalism which
describes the occupation-time statistics of a single particle.
| arxiv topic:cond-mat.stat-mech |
arxiv_dataset-106981901.00253 | Skyrmion Tubes as Magnonic Waveguides
cond-mat.mes-hall cond-mat.mtrl-sci
Various latest experiments have proven the theoretical prediction that domain
walls in planar magnetic structures can channel spin waves as outstanding
magnonic waveguides, establishing a superb platform for building magnonic
devices. Recently, three-dimensional nanomagnetism has been boosted up and
become a significant branch of magnetism, because three-dimensional magnetic
structures expose a lot of emerging physics hidden behind planar ones and will
inevitably provide broader room for device engineering. Skyrmions and
antiSkyrmions, as natural three-dimensional magnetic configurations, are not
considered yet in the context of spin-wave channeling and steering. Here, we
show that skyrmion tubes can act as nonplanar magnonic waveguides if excited
suitably. An isolated skyrmion tube in a magnetic nanoprism induces spatially
separate internal and edge channels of spin waves; the internal channel has a
narrower energy gap, compared to the edge channel, and accordingly can transmit
signals at lower frequencies. Additionally, we verify that those spin-wave
beams along magnetic nanoprism are restricted to the regions of potential
wells. Transmission of spin-wave signals in such waveguides results from the
coherent propagation of locally driven eigenmodes of skyrmions, i.e., the
breathing and rotational modes. Finally, we find that spin waves along the
internal channels are less susceptible to magnetic field than those along the
edge channels. Our work will open a new arena for spin-wave manipulation and
help bridge skyrmionics and magnonics.
| arxiv topic:cond-mat.mes-hall cond-mat.mtrl-sci |
arxiv_dataset-106991901.00353 | Dilution with Digital Microfluidic Biochips: How Unbalanced Splits
Corrupt Target-Concentration
cs.ET
Sample preparation is an indispensable component of almost all biochemical
protocols, and it involves, among others, making dilutions and mixtures of
fluids in certain ratios. Recent microfluidic technologies offer suitable
platforms for automating dilutions on-chip, and typically on a digital
microfluidic biochip (DMFB), a sequence of (1:1) mix-split operations is
performed on fluid droplets to achieve the target concentration factor (CF) of
a sample. An (1:1) mixing model ideally comprises mixing of two unit-volume
droplets followed by a (balanced) splitting into two unit-volume
daughter-droplets. However, a major source of error in fluidic operations is
due to unbalanced splitting, where two unequal-volume droplets are produced
following a split. Such volumetric split-errors occurring in different
mix-split steps of the reaction path often cause a significant drift in the
target-CF of the sample, the precision of which cannot be compromised in
life-critical assays. In order to circumvent this problem, several
error-recovery or error-tolerant techniques have been proposed recently for
DMFBs. Unfortunately, the impact of such fluidic errors on a target-CF and the
dynamics of their behavior have not yet been rigorously analyzed. In this work,
we investigate the effect of multiple volumetric split-errors on various
target-CFs during sample preparation. We also perform a detailed analysis of
the worst-case scenario, i.e., the condition when the error in a target-CF is
maximized. This analysis may lead to the development of new techniques for
error-tolerant sample preparation with DMFBs without using any sensing
operation.
| arxiv topic:cs.ET |
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