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18,601 | A Consistent Bayesian Formulation for Stochastic Inverse Problems Based on Push-forward Measures | We formulate, and present a numerical method for solving, an inverse problem
for inferring parameters of a deterministic model from stochastic observational
data (quantities of interest). The solution, given as a probability measure, is
derived using a Bayesian updating approach for measurable maps that finds a
posterior probability measure, that when propagated through the deterministic
model produces a push-forward measure that exactly matches the observed
probability measure on the data. Our approach for finding such posterior
measures, which we call consistent Bayesian inference, is simple and only
requires the computation of the push-forward probability measure induced by the
combination of a prior probability measure and the deterministic model. We
establish existence and uniqueness of observation-consistent posteriors and
present stability and error analysis. We also discuss the relationships between
consistent Bayesian inference, classical/statistical Bayesian inference, and a
recently developed measure-theoretic approach for inference. Finally,
analytical and numerical results are presented to highlight certain properties
of the consistent Bayesian approach and the differences between this approach
and the two aforementioned alternatives for inference.
| 0 | 0 | 1 | 1 | 0 | 0 |
18,602 | Coherent State Mapping Ring-Polymer Molecular Dynamics for Non-Adiabatic quantum propagations | We introduce the coherent state mapping ring-polymer molecular dynamics
(CS-RPMD), a new method that accurately describes electronic non-adiabatic
dynamics with explicit nuclear quantization. This new approach is derived by
using coherent state mapping representation for the electronic degrees of
freedom (DOF) and the ring-polymer path-integral representation for the nuclear
DOF. CS-RPMD Hamiltonian does not contain any inter-bead coupling term in the
state-dependent potential, which is a key feature that ensures correct
electronic Rabi oscillations. Hamilton's equation of motion is used to sample
initial configurations and propagate the trajectories, preserving the
distribution with classical symplectic evolution. In the special one-bead limit
for mapping variables, CS-RPMD preserves the detailed balance. Numerical tests
of this method with a two-state model system show a very good agreement with
exact quantum results over a broad range of electronic couplings.
| 0 | 1 | 0 | 0 | 0 | 0 |
18,603 | Stochastic Gradient Descent in Continuous Time: A Central Limit Theorem | Stochastic gradient descent in continuous time (SGDCT) provides a
computationally efficient method for the statistical learning of
continuous-time models, which are widely used in science, engineering, and
finance. The SGDCT algorithm follows a (noisy) descent direction along a
continuous stream of data. The parameter updates occur in continuous time and
satisfy a stochastic differential equation. This paper analyzes the asymptotic
convergence rate of the SGDCT algorithm by proving a central limit theorem
(CLT) for strongly convex objective functions and, under slightly stronger
conditions, for non-convex objective functions as well. An L$^p$ convergence
rate is also proven for the algorithm in the strongly convex case. The
mathematical analysis lies at the intersection of stochastic analysis and
statistical learning.
| 0 | 0 | 1 | 1 | 0 | 0 |
18,604 | KMS states on $C^*$-algebras associated to a family of $*$-commuting local homeomorphisms | We consider a family of $*$-commuting local homeomorphisms on a compact
space, and build a compactly aligned product system of Hilbert bimodules (in
the sense of Fowler). This product system has a Nica-Toeplitz algebra and a
Cuntz-Pimsner algebra. Both algebras carry a gauge action of a
higher-dimensional torus, and there are many possible dynamics obtained by
composing with different embeddings of the real line in this torus. We study
the KMS states of these dynamics. For large inverse temperatures, we describe
the simplex of KMS states on the Nica-Toeplitz algebra. To study KMS states for
smaller inverse temperature, we consider a preferred dynamics for which there
is a single critical inverse temperature. We find a KMS state on the
Nica-Toeplitz algebra at this critical inverse temperature which factors
through the Cuntz-Pimsner algebra. We then illustrate our results by
considering backward shifts on the infinite-path spaces of a class of
$k$-graphs.
| 0 | 0 | 1 | 0 | 0 | 0 |
18,605 | Multi-Labelled Value Networks for Computer Go | This paper proposes a new approach to a novel value network architecture for
the game Go, called a multi-labelled (ML) value network. In the ML value
network, different values (win rates) are trained simultaneously for different
settings of komi, a compensation given to balance the initiative of playing
first. The ML value network has three advantages, (a) it outputs values for
different komi, (b) it supports dynamic komi, and (c) it lowers the mean
squared error (MSE). This paper also proposes a new dynamic komi method to
improve game-playing strength. This paper also performs experiments to
demonstrate the merits of the architecture. First, the MSE of the ML value
network is generally lower than the value network alone. Second, the program
based on the ML value network wins by a rate of 67.6% against the program based
on the value network alone. Third, the program with the proposed dynamic komi
method significantly improves the playing strength over the baseline that does
not use dynamic komi, especially for handicap games. To our knowledge, up to
date, no handicap games have been played openly by programs using value
networks. This paper provides these programs with a useful approach to playing
handicap games.
| 1 | 0 | 0 | 0 | 0 | 0 |
18,606 | Lifting high-dimensional nonlinear models with Gaussian regressors | We study the problem of recovering a structured signal $\mathbf{x}_0$ from
high-dimensional data $\mathbf{y}_i=f(\mathbf{a}_i^T\mathbf{x}_0)$ for some
nonlinear (and potentially unknown) link function $f$, when the regressors
$\mathbf{a}_i$ are iid Gaussian. Brillinger (1982) showed that ordinary
least-squares estimates $\mathbf{x}_0$ up to a constant of proportionality
$\mu_\ell$, which depends on $f$. Recently, Plan & Vershynin (2015) extended
this result to the high-dimensional setting deriving sharp error bounds for the
generalized Lasso. Unfortunately, both least-squares and the Lasso fail to
recover $\mathbf{x}_0$ when $\mu_\ell=0$. For example, this includes all even
link functions. We resolve this issue by proposing and analyzing an alternative
convex recovery method. In a nutshell, our method treats such link functions as
if they were linear in a lifted space of higher-dimension. Interestingly, our
error analysis captures the effect of both the nonlinearity and the problem's
geometry in a few simple summary parameters.
| 0 | 0 | 0 | 1 | 0 | 0 |
18,607 | Functional Conceptual Substratum as a New Cognitive Mechanism for Mathematical Creation | We describe a new cognitive ability, i.e., functional conceptual substratum,
used implicitly in the generation of several mathematical proofs and
definitions. Furthermore, we present an initial (first-order) formalization of
this mechanism together with its relation to classic notions like primitive
positive definability and Diophantiveness. Additionally, we analyze the
semantic variability of functional conceptual substratum when small syntactic
modifications are done. Finally, we describe mathematically natural inference
rules for definitions inspired by functional conceptual substratum and show
that they are sound and complete w.r.t. standard calculi.
| 0 | 0 | 1 | 0 | 0 | 0 |
18,608 | Applying Gromov's Amenable Localization to Geodesic Flows | Let $M$ be a compact connected smooth Riemannian $n$-manifold with boundary.
We combine Gromov's amenable localization technique with the Poincaré
duality to study the traversally generic geodesic flows on $SM$, the space of
the spherical tangent bundle. Such flows generate stratifications of $SM$,
governed by rich universal combinatorics. The stratification reflects the ways
in which the geodesic flow trajectories interact with the boundary $\d(SM)$.
Specifically, we get lower estimates of the numbers of connected components of
these flow-generated strata of any given codimension $k$. These universal
bounds are expressed in terms of the normed homology $H_k(M; \R)$ and $H_k(DM;
\R)$, where $DM = M\cup_{\d M} M$ denotes the double of $M$. The norms here are
the Gromov simplicial semi-norms in homology. The more complex the metric on
$M$ is, the more numerous the strata of $SM$ and $S(DM)$ are. So one may regard
our estimates as analogues of the Morse inequalities for the geodesics on
manifolds with boundary.
It turns out that some close relatives of the normed homology spaces form
obstructions to the existence of globally $k$-convex traversally generic
metrics on $M$.
| 0 | 0 | 1 | 0 | 0 | 0 |
18,609 | Modeling the Ellsberg Paradox by Argument Strength | We present a formal measure of argument strength, which combines the ideas
that conclusions of strong arguments are (i) highly probable and (ii) their
uncertainty is relatively precise. Likewise, arguments are weak when their
conclusion probability is low or when it is highly imprecise. We show how the
proposed measure provides a new model of the Ellsberg paradox. Moreover, we
further substantiate the psychological plausibility of our approach by an
experiment (N = 60). The data show that the proposed measure predicts human
inferences in the original Ellsberg task and in corresponding argument strength
tasks. Finally, we report qualitative data taken from structured interviews on
folk psychological conceptions on what argument strength means.
| 1 | 0 | 1 | 0 | 0 | 0 |
18,610 | Correction to the paper "Some remarks on Davie's uniqueness theorem" | The property 4 in Proposition 2.3 from the paper "Some remarks on Davie's
uniqueness theorem" is replaced with a weaker assertion which is sufficient for
the proof of the main results. Technical details and improvements are given.
| 0 | 0 | 1 | 0 | 0 | 0 |
18,611 | An Estimation and Analysis Framework for the Rasch Model | The Rasch model is widely used for item response analysis in applications
ranging from recommender systems to psychology, education, and finance. While a
number of estimators have been proposed for the Rasch model over the last
decades, the available analytical performance guarantees are mostly asymptotic.
This paper provides a framework that relies on a novel linear minimum
mean-squared error (L-MMSE) estimator which enables an exact, nonasymptotic,
and closed-form analysis of the parameter estimation error under the Rasch
model. The proposed framework provides guidelines on the number of items and
responses required to attain low estimation errors in tests or surveys. We
furthermore demonstrate its efficacy on a number of real-world collaborative
filtering datasets, which reveals that the proposed L-MMSE estimator performs
on par with state-of-the-art nonlinear estimators in terms of predictive
performance.
| 0 | 0 | 0 | 1 | 0 | 0 |
18,612 | Do planets remember how they formed? | One of the most directly observable features of a transiting multi-planet
system is their size-ordering when ranked in orbital separation. Kepler has
revealed a rich diversity of outcomes, from perfectly ordered systems, like
Kepler-80, to ostensibly disordered systems, like Kepler-20. Under the
hypothesis that systems are born via preferred formation pathways, one might
reasonably expect non-random size-orderings reflecting these processes.
However, subsequent dynamical evolution, often chaotic and turbulent in nature,
may erode this information and so here we ask - do systems remember how they
formed? To address this, we devise a model to define the entropy of a planetary
system's size-ordering, by first comparing differences between neighboring
planets and then extending to accommodate differences across the chain. We
derive closed-form solutions for many of the micro state occupancies and
provide public code with look-up tables to compute entropy for up to ten-planet
systems. All three proposed entropy definitions exhibit the expected property
that their credible interval increases with respect to a proxy for time. We
find that the observed Kepler multis display a highly significant deficit in
entropy compared to a randomly generated population. Incorporating a filter for
systems deemed likely to be dynamically packed, we show that this result is
robust against the possibility of missing planets too. Put together, our work
establishes that Kepler systems do indeed remember something of their younger
years and highlights the value of information theory for exoplanetary science.
| 0 | 1 | 0 | 0 | 0 | 0 |
18,613 | Demarcating circulation regimes of synchronously rotating terrestrial planets within the habitable zone | We investigate the atmospheric dynamics of terrestrial planets in synchronous
rotation within the habitable zone of low-mass stars using the Community
Atmosphere Model (CAM). The surface temperature contrast between day and night
hemispheres decreases with an increase in incident stellar flux, which is
opposite the trend seen on gas giants. We define three dynamical regimes in
terms of the equatorial Rossby deformation radius and the Rhines length. The
slow rotation regime has a mean zonal circulation that spans from day to night
side, with both the Rossby deformation radius and the Rhines length exceeding
planetary radius, which occurs for planets around stars with effective
temperatures of 3300 K to 4500 K (rotation period > 20 days). Rapid rotators
have a mean zonal circulation that partially spans a hemisphere and with banded
cloud formation beneath the substellar point, with the Rossby deformation
radius is less than planetary radius, which occurs for planets orbiting stars
with effective temperatures of less than 3000 K (rotation period < 5 days). In
between is the Rhines rotation regime, which retains a thermally-direct
circulation from day to night side but also features midlatitude
turbulence-driven zonal jets. Rhines rotators occur for planets around stars in
the range of 3000 K to 3300 K (rotation period ~ 5 to 20 days), where the
Rhines length is greater than planetary radius but the Rossby deformation
radius is less than planetary radius. The dynamical state can be
observationally inferred from comparing the morphology of the thermal emission
phase curves of synchronously rotating planets.
| 0 | 1 | 0 | 0 | 0 | 0 |
18,614 | Versatile Large-Area Custom-Feature van der Waals Epitaxy of Topological Insulators | As the focus of applied research in topological insulators (TI) evolves, the
need to synthesize large-area TI films for practical device applications takes
center stage. However, constructing scalable and adaptable processes for
high-quality TI compounds remains a challenge. To this end, a versatile van der
Waals epitaxy (vdWE) process for custom-feature Bismuth Telluro-Sulfide TI
growth and fabrication is presented, achieved through selective-area
fluorination and modification of surface free-energy on mica. The TI features
grow epitaxially in large single-crystal trigonal domains, exhibiting armchair
or zigzag crystalline edges highly oriented with the underlying mica lattice
and only two preferred domain orientations mirrored at $180^\circ$. As-grown
feature thickness dependence on lateral dimensions and denuded zones at
boundaries are observed, as explained by a semi-empirical two-species surface
migration model with robust estimates of growth parameters and elucidating the
role of selective-area surface modification. Topological surface states
contribute up to 60% of device conductance at room-temperature, indicating
excellent electronic quality. High-yield microfabrication and the adaptable
vdWE growth mechanism with readily alterable precursor and substrate
combinations, lend the process versatility to realize crystalline TI synthesis
in arbitrary shapes and arrays suitable for facile integration with processes
ranging from rapid prototyping to scalable manufacturing.
| 0 | 1 | 0 | 0 | 0 | 0 |
18,615 | Sharp off-diagonal weighted norm estimates for the Bergman projection | We prove that for $1<p\le q<\infty$, $qp\geq {p'}^2$ or $p'q'\geq q^2$,
$\frac{1}{p}+\frac{1}{p'}=\frac{1}{q}+\frac{1}{q'}=1$, $$\|\omega
P_\alpha(f)\|_{L^p(\mathcal{H},y^{\alpha+(2+\alpha)(\frac{q}{p}-1)}dxdy)}\le
C_{p,q,\alpha}[\omega]_{B_{p,q,\alpha}}^{(\frac{1}{p'}+\frac{1}{q})\max\{1,\frac{p'}{q}\}}\|\omega
f\|_{L^p(\mathcal{H},y^{\alpha}dxdy)}$$ where $P_\alpha$ is the weighted
Bergman projection of the upper-half plane $\mathcal{H}$, and
$$[\omega]_{B_{p,q,\alpha}}:=\sup_{I\subset
\mathbb{R}}\left(\frac{1}{|I|^{2+\alpha}}\int_{Q_I}\omega^{q}dV_\alpha\right)\left(\frac{1}{|I|^{2+\alpha}}\int_{Q_I}\omega^{-p'}dV_\alpha\right)^{\frac{q}{p'}},$$
with $Q_I=\{z=x+iy\in \mathbb{C}: x\in I, 0<y<|I|\}$.
| 0 | 0 | 1 | 0 | 0 | 0 |
18,616 | An Automated Scalable Framework for Distributing Radio Astronomy Processing Across Clusters and Clouds | The Low Frequency Array (LOFAR) radio telescope is an international aperture
synthesis radio telescope used to study the Universe at low frequencies. One of
the goals of the LOFAR telescope is to conduct deep wide-field surveys. Here we
will discuss a framework for the processing of the LOFAR Two Meter Sky Survey
(LoTSS). This survey will produce close to 50 PB of data within five years.
These data rates require processing at locations with high-speed access to the
archived data. To complete the LoTSS project, the processing software needs to
be made portable and moved to clusters with a high bandwidth connection to the
data archive. This work presents a framework that makes the LOFAR software
portable, and is used to scale out LOFAR data reduction. Previous work was
successful in preprocessing LOFAR data on a cluster of isolated nodes. This
framework builds upon it and and is currently operational. It is designed to be
portable, scalable, automated and general. This paper describes its design and
high level operation and the initial results processing LoTSS data.
| 0 | 1 | 0 | 0 | 0 | 0 |
18,617 | Learning multiple visual domains with residual adapters | There is a growing interest in learning data representations that work well
for many different types of problems and data. In this paper, we look in
particular at the task of learning a single visual representation that can be
successfully utilized in the analysis of very different types of images, from
dog breeds to stop signs and digits. Inspired by recent work on learning
networks that predict the parameters of another, we develop a tunable deep
network architecture that, by means of adapter residual modules, can be steered
on the fly to diverse visual domains. Our method achieves a high degree of
parameter sharing while maintaining or even improving the accuracy of
domain-specific representations. We also introduce the Visual Decathlon
Challenge, a benchmark that evaluates the ability of representations to capture
simultaneously ten very different visual domains and measures their ability to
recognize well uniformly.
| 1 | 0 | 0 | 1 | 0 | 0 |
18,618 | Cosmic quantum optical probing of quantum gravity through a gravitational lensLens | We consider the nonunitary quantum dynamics of neutral massless scalar
particles used to model photons around a massive gravitational lens. The
gravitational interaction between the lensing mass and asymptotically free
particles is described by their second-quantized scattering wavefunctions.
Remarkably, the zero-point spacetime fluctuations can induce significant
decoherence of the scattered states with spontaneous emission of gravitons,
thereby reducing the particles' coherence as well as energy. This new effect
suggests that, when photon polarizations are negligible, such quantum gravity
phenomena could lead to measurable anomalous redshift of recently studied
astrophysical lasers through a gravitational lens in the range of black holes
and galaxy clusters.
| 0 | 1 | 0 | 0 | 0 | 0 |
18,619 | Combinatorial Miller-Hagberg Algorithm for Randomization of Dense Networks | We propose a slightly revised Miller-Hagberg (MH) algorithm that efficiently
generates a random network from a given expected degree sequence. The revision
was to replace the approximated edge probability between a pair of nodes with a
combinatorically calculated edge probability that better captures the
likelihood of edge presence especially where edges are dense. The computational
complexity of this combinatorial MH algorithm is still in the same order as the
original one. We evaluated the proposed algorithm through several numerical
experiments. The results demonstrated that the proposed algorithm was
particularly good at accurately representing high-degree nodes in dense,
heterogeneous networks. This algorithm may be a useful alternative of other
more established network randomization methods, given that the data are
increasingly becoming larger and denser in today's network science research.
| 1 | 0 | 0 | 0 | 0 | 0 |
18,620 | Topological Insulators in Random Lattices | Our understanding of topological insulators is based on an underlying
crystalline lattice where the local electronic degrees of freedom at different
sites hybridize with each other in ways that produce nontrivial band topology,
and the search for material systems to realize such phases have been strongly
influenced by this. Here we theoretically demonstrate topological insulators in
systems with a random distribution of sites in space, i. e., a random lattice.
This is achieved by constructing hopping models on random lattices whose ground
states possess nontrivial topological nature (characterized e. g., by Bott
indices) that manifests as quantized conductances in systems with a boundary.
By tuning parameters such as the density of sites (for a given range of fermion
hopping), we can achieve transitions from trivial to topological phases. We
discuss interesting features of these transitions. In two spatial dimensions,
we show this for all five symmetry classes (A, AII, D, DIII and C) that are
known to host nontrivial topology in crystalline systems. We expect similar
physics to be realizable in any dimension and provide an explicit example of a
$Z_2$ topological insulator on a random lattice in three spatial dimensions.
Our study not only provides a deeper understanding of the topological phases of
non-interacting fermions, but also suggests new directions in the pursuit of
the laboratory realization of topological quantum matter.
| 0 | 1 | 0 | 0 | 0 | 0 |
18,621 | DiGrad: Multi-Task Reinforcement Learning with Shared Actions | Most reinforcement learning algorithms are inefficient for learning multiple
tasks in complex robotic systems, where different tasks share a set of actions.
In such environments a compound policy may be learnt with shared neural network
parameters, which performs multiple tasks concurrently. However such compound
policy may get biased towards a task or the gradients from different tasks
negate each other, making the learning unstable and sometimes less data
efficient. In this paper, we propose a new approach for simultaneous training
of multiple tasks sharing a set of common actions in continuous action spaces,
which we call as DiGrad (Differential Policy Gradient). The proposed framework
is based on differential policy gradients and can accommodate multi-task
learning in a single actor-critic network. We also propose a simple heuristic
in the differential policy gradient update to further improve the learning. The
proposed architecture was tested on 8 link planar manipulator and 27 degrees of
freedom(DoF) Humanoid for learning multi-goal reachability tasks for 3 and 2
end effectors respectively. We show that our approach supports efficient
multi-task learning in complex robotic systems, outperforming related methods
in continuous action spaces.
| 1 | 0 | 0 | 1 | 0 | 0 |
18,622 | Narratives of Quantum Theory in the Age of Quantum Technologies | Quantum technologies can be presented to the public with or without
introducing a strange trait of quantum theory responsible for their
non-classical efficiency. Traditionally the message was centered on the
superposition principle, while entanglement and properties such as
contextuality have been gaining ground recently. A less theoretical approach is
focused on simple protocols that enable technological applications. It results
in a pragmatic narrative built with the help of the resource paradigm and
principle-based reconstructions. I discuss the advantages and weaknesses of
these methods. To illustrate the importance of new metaphors beyond the
Schrödinger cat, I briefly describe a non-mathematical narrative about
entanglement that conveys an idea of some of its unusual properties. If quantum
technologists are to succeed in building trust in their work, they ought to
provoke an aesthetic perception in the public commensurable with the
mathematical beauty of quantum theory experienced by the physicist. The power
of the narrative method lies in its capacity to do so.
| 0 | 1 | 0 | 0 | 0 | 0 |
18,623 | Is Information in the Brain Represented in Continuous or Discrete Form? | The question of continuous-versus-discrete information representation in the
brain is a fundamental yet unresolved physiological question. Historically,
most analyses assume a continuous representation without considering the
alternative possibility of a discrete representation. Our work explores the
plausibility of both representations, and answers the question from a
communications engineering perspective. Drawing on the well-established
Shannon's communications theory, we posit that information in the brain is
represented in a discrete form. Using a computer simulation, we show that
information cannot be communicated reliably between neurons using a continuous
representation, due to the presence of noise; neural information has to be in a
discrete form. In addition, we designed 3 (human) behavioral experiments on
probability estimation and analyzed the data using a novel discrete (quantized)
model of probability. Under a discrete model of probability, two distinct
probabilities (say, 0.57 and 0.58) are treated indifferently. We found that
data from all participants were better fit to discrete models than continuous
ones. Furthermore, we re-analyzed the data from a published (human) behavioral
study on intertemporal choice using a novel discrete (quantized) model of
intertemporal choice. Under such a model, two distinct time delays (say, 16
days and 17 days) are treated indifferently. We found corroborating results,
showing that data from all participants were better fit to discrete models than
continuous ones. In summary, all results reported here support our discrete
hypothesis of information representation in the brain, which signifies a major
demarcation from the current understanding of the brain's physiology.
| 0 | 0 | 0 | 0 | 1 | 0 |
18,624 | Real-Time Background Subtraction Using Adaptive Sampling and Cascade of Gaussians | Background-Foreground classification is a fundamental well-studied problem in
computer vision. Due to the pixel-wise nature of modeling and processing in the
algorithm, it is usually difficult to satisfy real-time constraints. There is a
trade-off between the speed (because of model complexity) and accuracy.
Inspired by the rejection cascade of Viola-Jones classifier, we decompose the
Gaussian Mixture Model (GMM) into an adaptive cascade of classifiers. This way
we achieve a good improvement in speed without compensating for accuracy. In
the training phase, we learn multiple KDEs for different durations to be used
as strong prior distribution and detect probable oscillating pixels which
usually results in misclassifications. We propose a confidence measure for the
classifier based on temporal consistency and the prior distribution. The
confidence measure thus derived is used to adapt the learning rate and the
thresholds of the model, to improve accuracy. The confidence measure is also
employed to perform temporal and spatial sampling in a principled way. We
demonstrate a speed-up factor of 5x to 10x and 17 percent average improvement
in accuracy over several standard videos.
| 1 | 0 | 0 | 1 | 0 | 0 |
18,625 | Multilevel nested simulation for efficient risk estimation | We investigate the problem of computing a nested expectation of the form
$\mathbb{P}[\mathbb{E}[X|Y]
\!\geq\!0]\!=\!\mathbb{E}[\textrm{H}(\mathbb{E}[X|Y])]$ where $\textrm{H}$ is
the Heaviside function. This nested expectation appears, for example, when
estimating the probability of a large loss from a financial portfolio. We
present a method that combines the idea of using Multilevel Monte Carlo (MLMC)
for nested expectations with the idea of adaptively selecting the number of
samples in the approximation of the inner expectation, as proposed by (Broadie
et al., 2011). We propose and analyse an algorithm that adaptively selects the
number of inner samples on each MLMC level and prove that the resulting MLMC
method with adaptive sampling has an $\mathcal{O}\left(
\varepsilon^{-2}|\log\varepsilon|^2 \right)$ complexity to achieve a root
mean-squared error $\varepsilon$. The theoretical analysis is verified by
numerical experiments on a simple model problem. We also present a stochastic
root-finding algorithm that, combined with our adaptive methods, can be used to
compute other risk measures such as Value-at-Risk (VaR) and Conditional
Value-at-Risk (CVaR), with the latter being achieved with
$\mathcal{O}\left(\varepsilon^{-2}\right)$ complexity.
| 0 | 0 | 0 | 0 | 0 | 1 |
18,626 | Construction of a relativistic Ornstein-Uhlenbeck process | Based on a version of Dudley's Wiener process on the mass shell in the
momentum Minkowski space of a massive point particle, a model of a relativistic
Ornstein--Uhlenbeck process is constructed by addition of a specific drift
term. The invariant distribution of this momentum process as well as other
associated processes are computed.
| 0 | 0 | 1 | 0 | 0 | 0 |
18,627 | Safe Trajectory Synthesis for Autonomous Driving in Unforeseen Environments | Path planning for autonomous vehicles in arbitrary environments requires a
guarantee of safety, but this can be impractical to ensure in real-time when
the vehicle is described with a high-fidelity model. To address this problem,
this paper develops a method to perform trajectory design by considering a
low-fidelity model that accounts for model mismatch. The presented method
begins by computing a conservative Forward Reachable Set (FRS) of a
high-fidelity model's trajectories produced when tracking trajectories of a
low-fidelity model over a finite time horizon. At runtime, the vehicle
intersects this FRS with obstacles in the environment to eliminate trajectories
that can lead to a collision, then selects an optimal plan from the remaining
safe set. By bounding the time for this set intersection and subsequent path
selection, this paper proves a lower bound for the FRS time horizon and sensing
horizon to guarantee safety. This method is demonstrated in simulation using a
kinematic Dubin's car as the low-fidelity model and a dynamic unicycle as the
high-fidelity model.
| 1 | 0 | 0 | 0 | 0 | 0 |
18,628 | A Data and Model-Parallel, Distributed and Scalable Framework for Training of Deep Networks in Apache Spark | Training deep networks is expensive and time-consuming with the training
period increasing with data size and growth in model parameters. In this paper,
we provide a framework for distributed training of deep networks over a cluster
of CPUs in Apache Spark. The framework implements both Data Parallelism and
Model Parallelism making it suitable to use for deep networks which require
huge training data and model parameters which are too big to fit into the
memory of a single machine. It can be scaled easily over a cluster of cheap
commodity hardware to attain significant speedup and obtain better results
making it quite economical as compared to farm of GPUs and supercomputers. We
have proposed a new algorithm for training of deep networks for the case when
the network is partitioned across the machines (Model Parallelism) along with
detailed cost analysis and proof of convergence of the same. We have developed
implementations for Fully-Connected Feedforward Networks, Convolutional Neural
Networks, Recurrent Neural Networks and Long Short-Term Memory architectures.
We present the results of extensive simulations demonstrating the speedup and
accuracy obtained by our framework for different sizes of the data and model
parameters with variation in the number of worker cores/partitions; thereby
showing that our proposed framework can achieve significant speedup (upto 11X
for CNN) and is also quite scalable.
| 1 | 0 | 0 | 1 | 0 | 0 |
18,629 | ICLabel: An automated electroencephalographic independent component classifier, dataset, and website | The electroencephalogram (EEG) provides a non-invasive, minimally
restrictive, and relatively low cost measure of mesoscale brain dynamics with
high temporal resolution. Although signals recorded in parallel by multiple,
near-adjacent EEG scalp electrode channels are highly-correlated and combine
signals from many different sources, biological and non-biological, independent
component analysis (ICA) has been shown to isolate the various source generator
processes underlying those recordings. Independent components (IC) found by ICA
decomposition can be manually inspected, selected, and interpreted, but doing
so requires both time and practice as ICs have no particular order or intrinsic
interpretations and therefore require further study of their properties.
Alternatively, sufficiently-accurate automated IC classifiers can be used to
classify ICs into broad source categories, speeding the analysis of EEG studies
with many subjects and enabling the use of ICA decomposition in near-real-time
applications. While many such classifiers have been proposed recently, this
work presents the ICLabel project comprised of (1) an IC dataset containing
spatiotemporal measures for over 200,000 ICs from more than 6,000 EEG
recordings, (2) a website for collecting crowdsourced IC labels and educating
EEG researchers and practitioners about IC interpretation, and (3) the
automated ICLabel classifier. The classifier improves upon existing methods in
two ways: by improving the accuracy of the computed label estimates and by
enhancing its computational efficiency. The ICLabel classifier outperforms or
performs comparably to the previous best publicly available method for all
measured IC categories while computing those labels ten times faster than that
classifier as shown in a rigorous comparison against all other publicly
available EEG IC classifiers.
| 1 | 0 | 0 | 1 | 0 | 0 |
18,630 | Inference on a New Class of Sample Average Treatment Effects | We derive new variance formulas for inference on a general class of estimands
of causal average treatment effects in a Randomized Control Trial (RCT). We
generalize Robins (1988) and show that when the estimand of interest is the
Sample Average Treatment Effect of the Treated (SATT or SATC for controls), a
consistent variance estimator exists. Although these estimands are equal to the
Sample Average Treatment Effect (SATE) in expectation, potentially large
differences in both accuracy and coverage can occur by the change of estimand,
even asymptotically. Inference on the SATE, even using a conservative
confidence interval, provides incorrect coverage of the SATT or SATC. We derive
the variance and limiting distribution of a new and general class of
estimands---any mixing between SATT and SATC---for which the SATE is a specific
case. We demonstrate the applicability of the new theoretical results using
Monte-Carlo simulations and an empirical application with hundreds of online
experiments with an average sample size of approximately one hundred million
observations per experiment. An R package, estCI, that implements all the
proposed estimation procedures is available.
| 0 | 0 | 1 | 1 | 0 | 0 |
18,631 | A split step Fourier/discontinuous Galerkin scheme for the Kadomtsev--Petviashvili equation | In this paper we propose a method to solve the Kadomtsev--Petviashvili
equation based on splitting the linear part of the equation from the nonlinear
part. The linear part is treated using FFTs, while the nonlinear part is
approximated using a semi-Lagrangian discontinuous Galerkin approach of
arbitrary order.
We demonstrate the efficiency and accuracy of the numerical method by
providing a range of numerical simulations. In particular, we find that our
approach can outperform the numerical methods considered in the literature by
up to a factor of five. Although we focus on the Kadomtsev--Petviashvili
equation in this paper, the proposed numerical scheme can be extended to a
range of related models as well.
| 0 | 1 | 1 | 0 | 0 | 0 |
18,632 | Dense Transformer Networks | The key idea of current deep learning methods for dense prediction is to
apply a model on a regular patch centered on each pixel to make pixel-wise
predictions. These methods are limited in the sense that the patches are
determined by network architecture instead of learned from data. In this work,
we propose the dense transformer networks, which can learn the shapes and sizes
of patches from data. The dense transformer networks employ an encoder-decoder
architecture, and a pair of dense transformer modules are inserted into each of
the encoder and decoder paths. The novelty of this work is that we provide
technical solutions for learning the shapes and sizes of patches from data and
efficiently restoring the spatial correspondence required for dense prediction.
The proposed dense transformer modules are differentiable, thus the entire
network can be trained. We apply the proposed networks on natural and
biological image segmentation tasks and show superior performance is achieved
in comparison to baseline methods.
| 1 | 0 | 0 | 1 | 0 | 0 |
18,633 | Tetragonal CH3NH3PbI3 Is Ferroelectric | Halide perovskite (HaP) semiconductors are revolutionizing photovoltaic (PV)
solar energy conversion by showing remarkable performance of solar cells made
with esp. tetragonal methylammonium lead tri-iodide (MAPbI3). In particular,
the low voltage loss of these cells implies a remarkably low recombination rate
of photogenerated carriers. It was suggested that low recombination can be due
to spatial separation of electrons and holes, a possibility if MAPbI3 is a
semiconducting ferroelectric, which, however, requires clear experimental
evidence. As a first step we show that, in operando, MAPbI3 (unlike MAPbBr3) is
pyroelectric, which implies it can be ferroelectric. The next step, proving it
is (not) ferroelectric, is challenging, because of the material s relatively
high electrical conductance (a consequence of an optical band gap suitable for
PV conversion!) and low stability under high applied bias voltage. This
excludes normal measurements of a ferroelectric hysteresis loop to prove
ferroelctricity s hallmark for switchable polarization. By adopting an approach
suitable for electrically leaky materials as MAPbI3, we show here ferroelectric
hysteresis from well-characterized single crystals at low temperature (still
within the tetragonal phase, which is the room temperature stable phase). Using
chemical etching, we also image polar domains, the structural fingerprint for
ferroelectricity, periodically stacked along the polar axis of the crystal,
which, as predicted by theory, scale with the overall crystal size. We also
succeeded in detecting clear second-harmonic generation, direct evidence for
the material s non-centrosymmetry. We note that the material s ferroelectric
nature, can, but not obviously need to be important in a PV cell, operating
around room temperature.
| 0 | 1 | 0 | 0 | 0 | 0 |
18,634 | A Simple and Efficient MapReduce Algorithm for Data Cube Materialization | Data cube materialization is a classical database operator introduced in Gray
et al.~(Data Mining and Knowledge Discovery, Vol.~1), which is critical for
many analysis tasks. Nandi et al.~(Transactions on Knowledge and Data
Engineering, Vol.~6) first studied cube materialization for large scale
datasets using the MapReduce framework, and proposed a sophisticated
modification of a simple broadcast algorithm to handle a dataset with a 216GB
cube size within 25 minutes with 2k machines in 2012. We take a different
approach, and propose a simple MapReduce algorithm which (1) minimizes the
total number of copy-add operations, (2) leverages locality of computation, and
(3) balances work evenly across machines. As a result, the algorithm shows
excellent performance, and materialized a real dataset with a cube size of
35.0G tuples and 1.75T bytes in 54 minutes, with 0.4k machines in 2014.
| 1 | 0 | 0 | 0 | 0 | 0 |
18,635 | Group Invariance, Stability to Deformations, and Complexity of Deep Convolutional Representations | The success of deep convolutional architectures is often attributed in part
to their ability to learn multiscale and invariant representations of natural
signals. However, a precise study of these properties and how they affect
learning guarantees is still missing. In this paper, we consider deep
convolutional representations of signals; we study their invariance to
translations and to more general groups of transformations, their stability to
the action of diffeomorphisms, and their ability to preserve signal
information. This analysis is carried by introducing a multilayer kernel based
on convolutional kernel networks and by studying the geometry induced by the
kernel mapping. We then characterize the corresponding reproducing kernel
Hilbert space (RKHS), showing that it contains a large class of convolutional
neural networks with homogeneous activation functions. This analysis allows us
to separate data representation from learning, and to provide a canonical
measure of model complexity, the RKHS norm, which controls both stability and
generalization of any learned model. In addition to models in the constructed
RKHS, our stability analysis also applies to convolutional networks with
generic activations such as rectified linear units, and we discuss its
relationship with recent generalization bounds based on spectral norms.
| 1 | 0 | 0 | 1 | 0 | 0 |
18,636 | Completion of High Order Tensor Data with Missing Entries via Tensor-train Decomposition | In this paper, we aim at the completion problem of high order tensor data
with missing entries. The existing tensor factorization and completion methods
suffer from the curse of dimensionality when the order of tensor N>>3. To
overcome this problem, we propose an efficient algorithm called TT-WOPT
(Tensor-train Weighted OPTimization) to find the latent core tensors of tensor
data and recover the missing entries. Tensor-train decomposition, which has the
powerful representation ability with linear scalability to tensor order, is
employed in our algorithm. The experimental results on synthetic data and
natural image completion demonstrate that our method significantly outperforms
the other related methods. Especially when the missing rate of data is very
high, e.g., 85% to 99%, our algorithm can achieve much better performance than
other state-of-the-art algorithms.
| 1 | 0 | 0 | 0 | 0 | 0 |
18,637 | On the inner products of some Deligne--Lusztig type representations | In this paper we introduce a family of Deligne--Lusztig type varieties
attached to connected reductive groups over quotients of discrete valuation
rings, naturally generalising the higher Deligne--Lusztig varieties and some
constructions related to the algebraisation problem raised by Lusztig. We
establish the inner product formula between the representations associated to
these varieties and the higher Deligne--Lusztig representations.
| 0 | 0 | 1 | 0 | 0 | 0 |
18,638 | An invariant for embedded Fano manifolds covered by linear spaces | For an embedded Fano manifold $X$, we introduce a new invariant $S_X$ related
to the dimension of covering linear spaces. The aim of this paper is to
classify Fano manifolds $X$ which have large $S_X$.
| 0 | 0 | 1 | 0 | 0 | 0 |
18,639 | Delivery Latency Trade-Offs of Heterogeneous Contents in Fog Radio Access Networks | A Fog Radio Access Network (F-RAN) is a cellular wireless system that enables
content delivery via the caching of popular content at edge nodes (ENs) and
cloud processing. The existing information-theoretic analyses of F-RAN systems,
and special cases thereof, make the assumption that all requests should be
guaranteed the same delivery latency, which results in identical latency for
all files in the content library. In practice, however, contents may have
heterogeneous timeliness requirements depending on the applications that
operate on them. Given per-EN cache capacity constraint, there exists a
fundamental trade-off among the delivery latencies of different users'
requests, since contents that are allocated more cache space generally enjoy
lower delivery latencies. For the case with two ENs and two users, the optimal
latency trade-off is characterized in the high-SNR regime in terms of the
Normalized Delivery Time (NDT) metric. The main results are illustrated by
numerical examples.
| 1 | 0 | 0 | 0 | 0 | 0 |
18,640 | Leaking Uninitialized Secure Enclave Memory via Structure Padding (Extended Abstract) | Intel software guard extensions (SGX) aims to provide an isolated execution
environment, known as an enclave, for a user-level process to maximize its
confidentiality and integrity. In this paper, we study how uninitialized data
inside a secure enclave can be leaked via structure padding. We found that,
during ECALL and OCALL, proxy functions that are automatically generated by the
Intel SGX Software Development Kit (SDK) fully copy structure variables from an
enclave to the normal memory to return the result of an ECALL function and to
pass input parameters to an OCALL function. If the structure variables contain
padding bytes, uninitialized enclave memory, which might contain confidential
data like a private key, can be copied to the normal memory through the padding
bytes. We also consider potential countermeasures against these security
threats.
| 1 | 0 | 0 | 0 | 0 | 0 |
18,641 | Asymptotic and numerical analysis of a stochastic PDE model of volume transmission | Volume transmission is an important neural communication pathway in which
neurons in one brain region influence the neurotransmitter concentration in the
extracellular space of a distant brain region. In this paper, we apply
asymptotic analysis to a stochastic partial differential equation model of
volume transmission to calculate the neurotransmitter concentration in the
extracellular space. Our model involves the diffusion equation in a
three-dimensional domain with interior holes that randomly switch between being
either sources or sinks. These holes model nerve varicosities that alternate
between releasing and absorbing neurotransmitter, according to when they fire
action potentials. In the case that the holes are small, we compute
analytically the first two nonzero terms in an asymptotic expansion of the
average neurotransmitter concentration. The first term shows that the
concentration is spatially constant to leading order and that this constant is
independent of many details in the problem. Specifically, this constant first
term is independent of the number and location of nerve varicosities, neural
firing correlations, and the size and geometry of the extracellular space. The
second term shows how these factors affect the concentration at second order.
Interestingly, the second term is also spatially constant under some mild
assumptions. We verify our asymptotic results by high-order numerical
simulation using radial basis function-generated finite differences.
| 0 | 0 | 0 | 0 | 1 | 0 |
18,642 | Mixtures of Hidden Truncation Hyperbolic Factor Analyzers | The mixture of factor analyzers model was first introduced over 20 years ago
and, in the meantime, has been extended to several non-Gaussian analogues. In
general, these analogues account for situations with heavy tailed and/or skewed
clusters. An approach is introduced that unifies many of these approaches into
one very general model: the mixture of hidden truncation hyperbolic factor
analyzers (MHTHFA) model. In the process of doing this, a hidden truncation
hyperbolic factor analysis model is also introduced. The MHTHFA model is
illustrated for clustering as well as semi-supervised classification using two
real datasets.
| 0 | 0 | 0 | 1 | 0 | 0 |
18,643 | Representations on Partially Holomorphic Cohomology Spaces, Revisited | This is a semi--expository update and rewrite of my 1974 AMS AMS Memoir
describing Plancherel formulae and partial Dolbeault cohomology realizations
for standard tempered representations for general real reductive Lie groups.
Even after so many years, much of that Memoir is up to date, but of course
there have been a number of refinements, advances and new developments, most of
which have applied to smaller classes of real reductive Lie groups. Here we
rewrite that AMS Memoir in in view of these advances and indicate the ties with
some of the more recent (or at least less classical) approaches to geometric
realization of unitary representations.
| 0 | 0 | 1 | 0 | 0 | 0 |
18,644 | Underground tests of quantum mechanics. Whispers in the cosmic silence? | By performing X-rays measurements in the "cosmic silence" of the underground
laboratory of Gran Sasso, LNGS-INFN, we test a basic principle of quantum
mechanics: the Pauli Exclusion Principle (PEP), for electrons. We present the
achieved results of the VIP experiment and the ongoing VIP2 measurement aiming
to gain two orders of magnitude improvement in testing PEP. We also use a
similar experimental technique to search for radiation (X and gamma) predicted
by continuous spontaneous localization models, which aim to solve the
"measurement problem".
| 0 | 1 | 0 | 0 | 0 | 0 |
18,645 | Implications for Post-Processing Nucleosynthesis of Core-Collapse Supernova Models with Lagrangian Particles | We investigate core-collapse supernova (CCSN) nucleosynthesis with
self-consistent, axisymmetric (2D) simulations performed using the
radiation-hydrodynamics code Chimera. Computational costs have traditionally
constrained the evolution of the nuclear composition within multidimensional
CCSN models to, at best, a 14-species $\alpha$-network capable of tracking only
$(\alpha,\gamma)$ reactions from $^{4}$He to $^{60}$Zn. Such a simplified
network limits the ability to accurately evolve detailed composition and
neutronization or calculate the nuclear energy generation rate. Lagrangian
tracer particles are commonly used to extend the nuclear network evolution by
incorporating more realistic networks in post-processing nucleosynthesis
calculations. However, limitations such as poor spatial resolution of the
tracer particles, inconsistent thermodynamic evolution, including misestimation
of expansion timescales, and uncertain determination of the multidimensional
mass-cut at the end of the simulation impose uncertainties inherent to this
approach. We present a detailed analysis of the impact of such uncertainties
for four self-consistent axisymmetric CCSN models initiated from stellar
metallicity, non-rotating progenitors of 12 $M_\odot$, 15 $M_\odot$, 20
$M_\odot$, and 25 $M_\odot$ and evolved with the smaller $\alpha$-network to
more than 1 s after the launch of an explosion.
| 0 | 1 | 0 | 0 | 0 | 0 |
18,646 | High Performance Parallel Image Reconstruction for New Vacuum Solar Telescope | Many technologies have been developed to help improve spatial resolution of
observational images for ground-based solar telescopes, such as adaptive optics
(AO) systems and post-processing reconstruction. As any AO system correction is
only partial, it is indispensable to use post-processing reconstruction
techniques. In the New Vacuum Solar Telescope (NVST), speckle masking method is
used to achieve the diffraction limited resolution of the telescope. Although
the method is very promising, the computation is quite intensive, and the
amount of data is tremendous, requiring several months to reconstruct
observational data of one day on a high-end computer. To accelerate image
reconstruction, we parallelize the program package on a high performance
cluster. We describe parallel implementation details for several reconstruction
procedures. The code is written in C language using Message Passing Interface
(MPI) and optimized for parallel processing in a multi-processor environment.
We show the excellent performance of parallel implementation, and the whole
data processing speed is about 71 times faster than before. Finally, we analyze
the scalability of the code to find possible bottlenecks, and propose several
ways to further improve the parallel performance. We conclude that the
presented program is capable of executing in real-time reconstruction
applications at NVST.
| 0 | 1 | 0 | 0 | 0 | 0 |
18,647 | Approximation of Bandwidth for the Interactive Operation in Video on Demand System | An interactive session of video-on-demand (VOD) streaming procedure deserves
smooth data transportation for the viewer, irrespective of their geographic
location. To access the required video, bandwidth management during the video
objects transportation at any interactive session is a mandatory prerequisite.
It has been observed in the domain likes movie on demand, electronic
encyclopedia, interactive games, and educational resources. The required data
is imported from the distributed storage servers through the high speed
backbone network. This paper presents the viewer driven session based
multi-user model with respect to the overlay mesh network. In virtue of
reality, the direct implication of this work elaborately shows the required
bandwidth is a causal part in the video on demand system. The analytic model of
session based single viewer bandwidth requirement model presents the bandwidth
requirement for any interactive session like, pause, move slow, rewind, skip
some number of frames, or move fast with some constant number of frames. This
work presents the bandwidth requirement model for any interactive session that
brings the trade-off in data-transportation and storage costs for different
system resources and also for the various system configurations.
| 1 | 0 | 0 | 0 | 0 | 0 |
18,648 | Twisted Recurrence via Polynomial Walks | In this paper we show how polynomial walks can be used to establish a twisted
recurrence for sets of positive density in $\mathbb{Z}^d$. In particular, we
prove that if $\Gamma \leq \operatorname{GL}_d(\mathbb{Z})$ is finitely
generated by unipotents and acts irreducibly on $\mathbb{R}^d$, then for any
set $B \subset \mathbb{Z}^d$ of positive density, there exists $k \geq 1$ such
that for any $v \in k \mathbb{Z}^d$ one can find $\gamma \in \Gamma$ with
$\gamma v \in B - B$. Our method does not require the linearity of the action,
and we prove a twisted recurrence for semigroups of maps from $\mathbb{Z}^d$ to
$\mathbb{Z}^d$ satisfying some irreducibility and polynomial assumptions. As
one of the consequences, we prove a non-linear analog of Bogolubov's theorem --
for any set $B \subset \mathbb{Z}^2$ of positive density, and $p(n) \in
\mathbb{Z}[n]$, with $p(0) = 0$ and $\operatorname{deg}(p) \geq 2$, there
exists $k \geq 1$ such that $k \mathbb{Z} \subset \{ x - p(y) \, | \, (x,y) \in
B-B \}$. Unlike the previous works on twisted recurrence that used recent
results of Benoist-Quint and Bourgain-Furman-Lindenstrauss-Mozes on
equidistribution of random walks on automorphism groups of tori, our method
relies on the classical Weyl equidistribution for polynomial orbits on tori.
| 0 | 0 | 1 | 0 | 0 | 0 |
18,649 | Well-posedness and scattering for the Boltzmann equations: Soft potential with cut-off | We prove the global existence of the unique mild solution for the Cauchy
problem of the cut-off Boltzmann equation for soft potential model $\gamma=2-N$
with initial data small in $L^N_{x,v}$ where $N=2,3$ is the dimension. The
proof relies on the existing inhomogeneous Strichartz estimates for the kinetic
equation by Ovcharov and convolution-like estimates for the gain term of the
Boltzmann collision operator by Alonso, Carneiro and Gamba. The global dynamics
of the solution is also characterized by showing that the small global solution
scatters with respect to the kinetic transport operator in $L^N_{x,v}$. Also
the connection between function spaces and cut-off soft potential model
$-N<\gamma<2-N$ is characterized in the local well-posedness result for the
Cauchy problem with large initial data.
| 0 | 0 | 1 | 0 | 0 | 0 |
18,650 | Wikipedia in academia as a teaching tool: from averse to proactive faculty profiles | This study concerned the active use of Wikipedia as a teaching tool in the
classroom in higher education, trying to identify different usage profiles and
their characterization. A questionnaire survey was administrated to all
full-time and part-time teachers at the Universitat Oberta de Catalunya and the
Universitat Pompeu Fabra, both in Barcelona, Spain. The questionnaire was
designed using the Technology Acceptance Model as a reference, including items
about teachers web 2.0 profile, Wikipedia usage, expertise, perceived
usefulness, easiness of use, visibility and quality, as well as Wikipedia
status among colleagues and incentives to use it more actively. Clustering and
statistical analysis were carried out using the k-medoids algorithm and
differences between clusters were assessed by means of contingency tables and
generalized linear models (logit). The respondents were classified in four
clusters, from less to more likely to adopt and use Wikipedia in the classroom,
namely averse (25.4%), reluctant (17.9%), open (29.5%) and proactive (27.2%).
Proactive faculty are mostly men teaching part-time in STEM fields, mainly
engineering, while averse faculty are mostly women teaching full-time in
non-STEM fields. Nevertheless, questionnaire items related to visibility,
quality, image, usefulness and expertise determine the main differences between
clusters, rather than age, gender or domain. Clusters involving a positive view
of Wikipedia and at least some frequency of use clearly outnumber those with a
strictly negative stance. This goes against the common view that faculty
members are mostly sceptical about Wikipedia. Environmental factors such as
academic culture and colleagues opinion are more important than faculty
personal characteristics, especially with respect to what they think about
Wikipedia quality.
| 1 | 0 | 0 | 0 | 0 | 0 |
18,651 | A trans-disciplinary review of deep learning research for water resources scientists | Deep learning (DL), a new-generation of artificial neural network research,
has transformed industries, daily lives and various scientific disciplines in
recent years. DL represents significant progress in the ability of neural
networks to automatically engineer problem-relevant features and capture highly
complex data distributions. I argue that DL can help address several major new
and old challenges facing research in water sciences such as
inter-disciplinarity, data discoverability, hydrologic scaling, equifinality,
and needs for parameter regionalization. This review paper is intended to
provide water resources scientists and hydrologists in particular with a simple
technical overview, trans-disciplinary progress update, and a source of
inspiration about the relevance of DL to water. The review reveals that various
physical and geoscientific disciplines have utilized DL to address data
challenges, improve efficiency, and gain scientific insights. DL is especially
suited for information extraction from image-like data and sequential data.
Techniques and experiences presented in other disciplines are of high relevance
to water research. Meanwhile, less noticed is that DL may also serve as a
scientific exploratory tool. A new area termed 'AI neuroscience,' where
scientists interpret the decision process of deep networks and derive insights,
has been born. This budding sub-discipline has demonstrated methods including
correlation-based analysis, inversion of network-extracted features,
reduced-order approximations by interpretable models, and attribution of
network decisions to inputs. Moreover, DL can also use data to condition
neurons that mimic problem-specific fundamental organizing units, thus
revealing emergent behaviors of these units. Vast opportunities exist for DL to
propel advances in water sciences.
| 1 | 0 | 0 | 1 | 0 | 0 |
18,652 | A new NS3 Implementation of CCNx 1.0 Protocol | The ccns3Sim project is an open source implementation of the CCNx 1.0
protocols for the NS3 simulator. We describe the implementation and several
important features including modularity and process delay simulation. The
ccns3Sim implementation is a fresh NS3-specific implementation. Like NS3
itself, it uses C++98 standard, NS3 code style, NS3 smart pointers, NS3 xUnit,
and integrates with the NS3 documentation and manual. A user or developer does
not need to learn two systems. If one knows NS3, one should be able to get
started with the CCNx code right away. A developer can easily use their own
implementation of the layer 3 protocol, layer 4 protocol, forwarder, routing
protocol, Pending Interest Table (PIT) or Forwarding Information Base (FIB) or
Content Store (CS). A user may configure or specify a new implementation for
any of these features at runtime in the simulation script. In this paper, we
describe the software architecture and give examples of using the simulator. We
evaluate the implementation with several example experiments on ICN caching.
| 1 | 0 | 0 | 0 | 0 | 0 |
18,653 | MultiRefactor: Automated Refactoring To Improve Software Quality | In this paper, a new approach is proposed for automated software maintenance.
The tool is able to perform 26 different refactorings. It also contains a large
selection of metrics to measure the impact of the refactorings on the software
and six different search based optimization algorithms to improve the software.
This tool contains both mono-objective and multi-objective search techniques
for software improvement and is fully automated. The paper describes the
various capabilities of the tool, the unique aspects of it, and also presents
some research results from experimentation. The individual metrics are tested
across five different codebases to deduce the most effective metrics for
general quality improvement. It is found that the metrics that relate to more
specific elements of the code are more useful for driving change in the search.
The mono-objective genetic algorithm is also tested against the multi-objective
algorithm to see how comparable the results gained are with three separate
objectives. When comparing the best solutions of each individual objective the
multi-objective approach generates suitable improvements in quality in less
time, allowing for rapid maintenance cycles.
| 1 | 0 | 0 | 0 | 0 | 0 |
18,654 | Learning Postural Synergies for Categorical Grasping through Shape Space Registration | Every time a person encounters an object with a given degree of familiarity,
he/she immediately knows how to grasp it. Adaptation of the movement of the
hand according to the object geometry happens effortlessly because of the
accumulated knowledge of previous experiences grasping similar objects. In this
paper, we present a novel method for inferring grasp configurations based on
the object shape. Grasping knowledge is gathered in a synergy space of the
robotic hand built by following a human grasping taxonomy. The synergy space is
constructed through human demonstrations employing a exoskeleton that provides
force feedback, which provides the advantage of evaluating the quality of the
grasp. The shape descriptor is obtained by means of a categorical non-rigid
registration that encodes typical intra-class variations. This approach is
especially suitable for on-line scenarios where only a portion of the object's
surface is observable. This method is demonstrated through simulation and real
robot experiments by grasping objects never seen before by the robot.
| 1 | 0 | 0 | 0 | 0 | 0 |
18,655 | Perturbations of self-adjoint operators in semifinite von Neumann algebras: Kato-Rosenblum theorem | In the paper, we prove an analogue of the Kato-Rosenblum theorem in a
semifinite von Neumann algebra. Let $\mathcal{M}$ be a countably decomposable,
properly infinite, semifinite von Neumann algebra acting on a Hilbert space
$\mathcal{H}$ and let $\tau$ be a faithful normal semifinite tracial weight of
$\mathcal M$. Suppose that $H$ and $H_1$ are self-adjoint operators affiliated
with $\mathcal{M}$. We show that if $H-H_1$ is in $\mathcal{M}\cap
L^{1}\left(\mathcal{M},\tau\right)$, then the ${norm}$ absolutely continuous
parts of $H$ and $H_1$ are unitarily equivalent. This implies that the real
part of a non-normal hyponormal operator in $\mathcal M$ is not a perturbation
by $\mathcal{M}\cap L^{1}\left(\mathcal{M},\tau\right)$ of a diagonal operator.
Meanwhile, for $n\ge 2$ and $1\leq p<n$, by modifying Voiculescu's invariant we
give examples of commuting $n$-tuples of self-adjoint operators in
$\mathcal{M}$ that are not arbitrarily small perturbations of commuting
diagonal operators modulo $\mathcal{M}\cap L^{p}\left(\mathcal{M},\tau\right)$.
| 0 | 0 | 1 | 0 | 0 | 0 |
18,656 | Dust radiative transfer modelling of the infrared ring around the magnetar SGR 1900$+$14 | A peculiar infrared ring-like structure was discovered by {\em Spitzer}
around the strongly magnetised neutron star SGR 1900$+$14. This infrared
structure was suggested to be due to a dust-free cavity, produced by the SGR
Giant Flare occurred in 1998, and kept illuminated by surrounding stars. Using
a 3D dust radiative transfer code, we aimed at reproducing the emission
morphology and the integrated emission flux of this structure assuming
different spatial distributions and densities for the dust, and different
positions for the illuminating stars. We found that a dust-free ellipsoidal
cavity can reproduce the shape, flux, and spectrum of the ring-like infrared
emission, provided that the illuminating stars are inside the cavity and that
the interstellar medium has high gas density ($n_H\sim$1000 cm$^{-3}$). We
further constrain the emitting region to have a sharp inner boundary and to be
significantly extended in the radial direction, possibly even just a cavity in
a smooth molecular cloud. We discuss possible scenarios for the formation of
the dustless cavity and the particular geometry that allows it to be IR-bright.
| 0 | 1 | 0 | 0 | 0 | 0 |
18,657 | Application of transfer matrix and transfer function analysis to grating-type dielectric laser accelerators: ponderomotive focusing of electrons | The question of suitability of transfer matrix description of electrons
traversing grating-type dielectric laser acceleration (DLA) structures is
addressed. It is shown that although matrix considerations lead to interesting
insights, the basic transfer properties of DLA cells cannot be described by a
matrix. A more general notion of a transfer function is shown to be a simple
and useful tool for formulating problems of particle dynamics in DLA. As an
example, a focusing structure is proposed which works simultaneously for all
electron phases.
| 0 | 1 | 0 | 0 | 0 | 0 |
18,658 | Discretization-free Knowledge Gradient Methods for Bayesian Optimization | This paper studies Bayesian ranking and selection (R&S) problems with
correlated prior beliefs and continuous domains, i.e. Bayesian optimization
(BO). Knowledge gradient methods [Frazier et al., 2008, 2009] have been widely
studied for discrete R&S problems, which sample the one-step Bayes-optimal
point. When used over continuous domains, previous work on the knowledge
gradient [Scott et al., 2011, Wu and Frazier, 2016, Wu et al., 2017] often rely
on a discretized finite approximation. However, the discretization introduces
error and scales poorly as the dimension of domain grows. In this paper, we
develop a fast discretization-free knowledge gradient method for Bayesian
optimization. Our method is not restricted to the fully sequential setting, but
useful in all settings where knowledge gradient can be used over continuous
domains. We show how our method can be generalized to handle (i) batch of
points suggestion (parallel knowledge gradient); (ii) the setting where
derivative information is available in the optimization process
(derivative-enabled knowledge gradient). In numerical experiments, we
demonstrate that the discretization-free knowledge gradient method finds global
optima significantly faster than previous Bayesian optimization algorithms on
both synthetic test functions and real-world applications, especially when
function evaluations are noisy; and derivative-enabled knowledge gradient can
further improve the performances, even outperforming the gradient-based
optimizer such as BFGS when derivative information is available.
| 1 | 0 | 1 | 1 | 0 | 0 |
18,659 | Measuring the Robustness of Graph Properties | In this paper, we propose a perturbation framework to measure the robustness
of graph properties. Although there are already perturbation methods proposed
to tackle this problem, they are limited by the fact that the strength of the
perturbation cannot be well controlled. We firstly provide a perturbation
framework on graphs by introducing weights on the nodes, of which the magnitude
of perturbation can be easily controlled through the variance of the weights.
Meanwhile, the topology of the graphs are also preserved to avoid
uncontrollable strength in the perturbation. We then extend the measure of
robustness in the robust statistics literature to the graph properties.
| 1 | 0 | 0 | 1 | 0 | 0 |
18,660 | Better Software Analytics via "DUO": Data Mining Algorithms Using/Used-by Optimizers | This paper claims that a new field of empirical software engineering research
and practice is emerging: data mining using/used-by optimizers for empirical
studies, or DUO. For example, data miners can generate the models that are
explored by optimizers.Also, optimizers can advise how to best adjust the
control parameters of a data miner. This combined approach acts like an agent
leaning over the shoulder of an analyst that advises "ask this question next"
or "ignore that problem, it is not relevant to your goals". Further, those
agents can help us build "better" predictive models, where "better" can be
either greater predictive accuracy, or faster modeling time (which, in turn,
enables the exploration of a wider range of options). We also caution that the
era of papers that just use data miners is coming to an end. Results obtained
from an unoptimized data miner can be quickly refuted, just by applying an
optimizer to produce a different (and better performing) model. Our conclusion,
hence, is that for software analytics it is possible, useful and necessary to
combine data mining and optimization using DUO.
| 1 | 0 | 0 | 0 | 0 | 0 |
18,661 | Lesion detection and Grading of Diabetic Retinopathy via Two-stages Deep Convolutional Neural Networks | We propose an automatic diabetic retinopathy (DR) analysis algorithm based on
two-stages deep convolutional neural networks (DCNN). Compared to existing
DCNN-based DR detection methods, the proposed algorithm have the following
advantages: (1) Our method can point out the location and type of lesions in
the fundus images, as well as giving the severity grades of DR. Moreover, since
retina lesions and DR severity appear with different scales in fundus images,
the integration of both local and global networks learn more complete and
specific features for DR analysis. (2) By introducing imbalanced weighting map,
more attentions will be given to lesion patches for DR grading, which
significantly improve the performance of the proposed algorithm. In this study,
we label 12,206 lesion patches and re-annotate the DR grades of 23,595 fundus
images from Kaggle competition dataset. Under the guidance of clinical
ophthalmologists, the experimental results show that our local lesion detection
net achieve comparable performance with trained human observers, and the
proposed imbalanced weighted scheme also be proved to significantly improve the
capability of our DCNN-based DR grading algorithm.
| 1 | 0 | 0 | 0 | 0 | 0 |
18,662 | DRYVR:Data-driven verification and compositional reasoning for automotive systems | We present the DRYVR framework for verifying hybrid control systems that are
described by a combination of a black-box simulator for trajectories and a
white-box transition graph specifying mode switches. The framework includes (a)
a probabilistic algorithm for learning sensitivity of the continuous
trajectories from simulation data, (b) a bounded reachability analysis
algorithm that uses the learned sensitivity, and (c) reasoning techniques based
on simulation relations and sequential composition, that enable verification of
complex systems under long switching sequences, from the reachability analysis
of a simpler system under shorter sequences. We demonstrate the utility of the
framework by verifying a suite of automotive benchmarks that include powertrain
control, automatic transmission, and several autonomous and ADAS features like
automatic emergency braking, lane-merge, and auto-passing controllers.
| 1 | 0 | 0 | 0 | 0 | 0 |
18,663 | Deep Reinforcement Learning for Programming Language Correction | Novice programmers often struggle with the formal syntax of programming
languages. To assist them, we design a novel programming language correction
framework amenable to reinforcement learning. The framework allows an agent to
mimic human actions for text navigation and editing. We demonstrate that the
agent can be trained through self-exploration directly from the raw input, that
is, program text itself, without any knowledge of the formal syntax of the
programming language. We leverage expert demonstrations for one tenth of the
training data to accelerate training. The proposed technique is evaluated on
6975 erroneous C programs with typographic errors, written by students during
an introductory programming course. Our technique fixes 14% more programs and
29% more compiler error messages relative to those fixed by a state-of-the-art
tool, DeepFix, which uses a fully supervised neural machine translation
approach.
| 1 | 0 | 0 | 0 | 0 | 0 |
18,664 | Dispersionless and multicomponent BKP hierarchies with quantum torus symmetries | In this article, we will construct the additional perturbative quantum torus
symmetry of the dispersionless BKP hierarchy basing on the $W_{\infty}$
infinite dimensional Lie symmetry. These results show that the complete quantum
torus symmetry is broken from the BKP hierarchy to its dispersionless
hierarchy. Further a series of additional flows of the multicomponent BKP
hierarchy will be defined and these flows constitute an $N$-folds direct
product of the positive half of the quantum torus symmetries.
| 0 | 1 | 1 | 0 | 0 | 0 |
18,665 | A Sampling Framework for Solving Physics-driven Inverse Source Problems | Partial differential equations are central to describing many physical
phenomena. In many applications these phenomena are observed through a sensor
network, with the aim of inferring their underlying properties. Leveraging from
certain results in sampling and approximation theory, we present a new
framework for solving a class of inverse source problems for physical fields
governed by linear partial differential equations. Specifically, we demonstrate
that the unknown field sources can be recovered from a sequence of, so called,
generalised measurements by using multidimensional frequency estimation
techniques. Next we show that---for physics-driven fields---this sequence of
generalised measurements can be estimated by computing a linear weighted-sum of
the sensor measurements; whereby the exact weights (of the sums) correspond to
those that reproduce multidimensional exponentials, when used to linearly
combine translates of a particular prototype function related to the Green's
function of our underlying field. Explicit formulae are then derived for the
sequence of weights, that map sensor samples to the exact sequence of
generalised measurements when the Green's function satisfies the generalised
Strang-Fix condition. Otherwise, the same mapping yields a close approximation
of the generalised measurements. Based on this new framework we develop
practical, noise robust, sensor network strategies for solving the inverse
source problem, and then present numerical simulation results to verify their
performance.
| 1 | 0 | 1 | 0 | 0 | 0 |
18,666 | An Application of $h$-principle to Manifold Calculus | Manifold calculus is a form of functor calculus that analyzes contravariant
functors from some categories of manifolds to topological spaces by providing
analytic approximations to them. In this paper we apply the theory of
h-principle to construct several examples of analytic functors in this sense.
We prove that the analytic approximation of the Lagrangian embeddings functor
$\mathrm{emb}_{\mathrm{Lag}}(-,N)$ is the totally real embeddings functor
$\mathrm{emb}_{\mathrm{TR}}(-,N)$. Under certain conditions we provide a
geometric construction for the homotopy fiber of $ \mathrm{emb}(M,N)
\rightarrow \mathrm{imm}(M,N)$. This construction also provides an example of a
functor which is itself empty when evaluated on most manifolds but it's
analytic approximation is almost always non-empty.
| 0 | 0 | 1 | 0 | 0 | 0 |
18,667 | Grasping Unknown Objects in Clutter by Superquadric Representation | In this paper, a quick and efficient method is presented for grasping unknown
objects in clutter. The grasping method relies on real-time superquadric (SQ)
representation of partial view objects and incomplete object modelling, well
suited for unknown symmetric objects in cluttered scenarios which is followed
by optimized antipodal grasping. The incomplete object models are processed
through a mirroring algorithm that assumes symmetry to first create an
approximate complete model and then fit for SQ representation. The grasping
algorithm is designed for maximum force balance and stability, taking advantage
of the quick retrieval of dimension and surface curvature information from the
SQ parameters. The pose of the SQs with respect to the direction of gravity is
calculated and used together with the parameters of the SQs and specification
of the gripper, to select the best direction of approach and contact points.
The SQ fitting method has been tested on custom datasets containing objects in
isolation as well as in clutter. The grasping algorithm is evaluated on a PR2
and real time results are presented. Initial results indicate that though the
method is based on simplistic shape information, it outperforms other learning
based grasping algorithms that also work in clutter in terms of time-efficiency
and accuracy.
| 1 | 0 | 0 | 0 | 0 | 0 |
18,668 | Learning to Play with Intrinsically-Motivated Self-Aware Agents | Infants are experts at playing, with an amazing ability to generate novel
structured behaviors in unstructured environments that lack clear extrinsic
reward signals. We seek to mathematically formalize these abilities using a
neural network that implements curiosity-driven intrinsic motivation. Using a
simple but ecologically naturalistic simulated environment in which an agent
can move and interact with objects it sees, we propose a "world-model" network
that learns to predict the dynamic consequences of the agent's actions.
Simultaneously, we train a separate explicit "self-model" that allows the agent
to track the error map of its own world-model, and then uses the self-model to
adversarially challenge the developing world-model. We demonstrate that this
policy causes the agent to explore novel and informative interactions with its
environment, leading to the generation of a spectrum of complex behaviors,
including ego-motion prediction, object attention, and object gathering.
Moreover, the world-model that the agent learns supports improved performance
on object dynamics prediction, detection, localization and recognition tasks.
Taken together, our results are initial steps toward creating flexible
autonomous agents that self-supervise in complex novel physical environments.
| 0 | 0 | 0 | 1 | 0 | 0 |
18,669 | $\ell_1$-minimization method for link flow correction | A computational method, based on $\ell_1$-minimization, is proposed for the
problem of link flow correction, when the available traffic flow data on many
links in a road network are inconsistent with respect to the flow conservation
law. Without extra information, the problem is generally ill-posed when a large
portion of the link sensors are unhealthy. It is possible, however, to correct
the corrupted link flows \textit{accurately} with the proposed method under a
recoverability condition if there are only a few bad sensors which are located
at certain links. We analytically identify the links that are robust to
miscounts and relate them to the geometric structure of the traffic network by
introducing the recoverability concept and an algorithm for computing it. The
recoverability condition for corrupted links is simply the associated
recoverability being greater than 1. In a more realistic setting, besides the
unhealthy link sensors, small measurement noises may be present at the other
sensors. Under the same recoverability condition, our method guarantees to give
an estimated traffic flow fairly close to the ground-truth data and leads to a
bound for the correction error. Both synthetic and real-world examples are
provided to demonstrate the effectiveness of the proposed method.
| 1 | 1 | 0 | 0 | 0 | 0 |
18,670 | Current Flow Group Closeness Centrality for Complex Networks | Current flow closeness centrality (CFCC) has a better discriminating ability
than the ordinary closeness centrality based on shortest paths. In this paper,
we extend this notion to a group of vertices in a weighted graph, and then
study the problem of finding a subset $S$ of $k$ vertices to maximize its CFCC
$C(S)$, both theoretically and experimentally. We show that the problem is
NP-hard, but propose two greedy algorithms for minimizing the reciprocal of
$C(S)$ with provable guarantees using the monotoncity and supermodularity. The
first is a deterministic algorithm with an approximation factor
$(1-\frac{k}{k-1}\cdot\frac{1}{e})$ and cubic running time; while the second is
a randomized algorithm with a
$(1-\frac{k}{k-1}\cdot\frac{1}{e}-\epsilon)$-approximation and nearly-linear
running time for any $\epsilon > 0$. Extensive experiments on model and real
networks demonstrate that our algorithms are effective and efficient, with the
second algorithm being scalable to massive networks with more than a million
vertices.
| 1 | 0 | 0 | 0 | 0 | 0 |
18,671 | Visualization of Constraint Handling Rules: Semantics and Applications | The work in the paper presents an animation extension ($CHR^{vis}$) to
Constraint Handling Rules (CHR). Visualizations have always helped programmers
understand data and debug programs. A picture is worth a thousand words. It can
help identify where a problem is or show how something works. It can even
illustrate a relation that was not clear otherwise. $CHR^{vis}$ aims at
embedding animation and visualization features into CHR programs. It thus
enables users, while executing programs, to have such executions animated. The
paper aims at providing the operational semantics for $CHR^{vis}$. The
correctness of $CHR^{vis}$ programs is also discussed. Some applications of the
new extension are also introduced.
| 1 | 0 | 0 | 0 | 0 | 0 |
18,672 | Simplified Energy Landscape for Modularity Using Total Variation | Networks capture pairwise interactions between entities and are frequently
used in applications such as social networks, food networks, and protein
interaction networks, to name a few. Communities, cohesive groups of nodes,
often form in these applications, and identifying them gives insight into the
overall organization of the network. One common quality function used to
identify community structure is modularity. In Hu et al. [SIAM J. App. Math.,
73(6), 2013], it was shown that modularity optimization is equivalent to
minimizing a particular nonconvex total variation (TV) based functional over a
discrete domain. They solve this problem, assuming the number of communities is
known, using a Merriman, Bence, Osher (MBO) scheme.
We show that modularity optimization is equivalent to minimizing a convex
TV-based functional over a discrete domain, again, assuming the number of
communities is known. Furthermore, we show that modularity has no convex
relaxation satisfying certain natural conditions. We therefore, find a
manageable non-convex approximation using a Ginzburg Landau functional, which
provably converges to the correct energy in the limit of a certain parameter.
We then derive an MBO algorithm with fewer hand-tuned parameters than in Hu et
al. and which is 7 times faster at solving the associated diffusion equation
due to the fact that the underlying discretization is unconditionally stable.
Our numerical tests include a hyperspectral video whose associated graph has
2.9x10^7 edges, which is roughly 37 times larger than was handled in the paper
of Hu et al.
| 0 | 0 | 1 | 1 | 0 | 0 |
18,673 | A Hard Look at the Neutron Stars and Accretion Disks in 4U 1636-53, GX 17+2, and 4U 1705-44 with $\emph{NuSTAR}$ | We present $\emph{NuSTAR}$ observations of neutron star (NS) low-mass X-ray
binaries: 4U 1636-53, GX 17+2, and 4U 1705-44. We observed 4U 1636-53 in the
hard state, with an Eddington fraction, $F_{\mathrm{Edd}}$, of 0.01; GX 17+2
and 4U 1705-44 were in the soft state with fractions of 0.57 and 0.10,
respectively. Each spectrum shows evidence for a relativistically broadened Fe
K$_{\alpha}$ line. Through accretion disk reflection modeling, we constrain the
radius of the inner disk in 4U 1636-53 to be $R_{in}=1.03\pm0.03$ ISCO
(innermost stable circular orbit) assuming a dimensionless spin parameter
$a_{*}=cJ/GM^{2}=0.0$, and $R_{in}=1.08\pm0.06$ ISCO for $a_{*}=0.3$ (errors
quoted at 1 $\sigma$). This value proves to be model independent. For
$a_{*}=0.3$ and $M=1.4\ M_{\odot}$, for example, $1.08\pm0.06$ ISCO translates
to a physical radius of $R=10.8\pm0.6$ km, and the neutron star would have to
be smaller than this radius (other outcomes are possible for allowed spin
parameters and masses). For GX 17+2, $R_{in}=1.00-1.04$ ISCO for $a_{*}=0.0$
and $R_{in}=1.03-1.30$ ISCO for $a_{*}=0.3$. For $a_{*}=0.3$ and $M=1.4\
M_{\odot}$, $R_{in}=1.03-1.30$ ISCO translates to $R=10.3-13.0$ km. The inner
accretion disk in 4U 1705-44 may be truncated just above the stellar surface,
perhaps by a boundary layer or magnetosphere; reflection models give a radius
of 1.46-1.64 ISCO for $a_{*}=0.0$ and 1.69-1.93 ISCO for $a_{*}=0.3$. We
discuss the implications that our results may have on the equation of state of
ultradense, cold matter and our understanding of the innermost accretion flow
onto neutron stars with low surface magnetic fields, and systematic errors
related to the reflection models and spacetime metric around less idealized
neutron stars.
| 0 | 1 | 0 | 0 | 0 | 0 |
18,674 | Approximating Weighted Duo-Preservation in Comparative Genomics | Motivated by comparative genomics, Chen et al. [9] introduced the Maximum
Duo-preservation String Mapping (MDSM) problem in which we are given two
strings $s_1$ and $s_2$ from the same alphabet and the goal is to find a
mapping $\pi$ between them so as to maximize the number of duos preserved. A
duo is any two consecutive characters in a string and it is preserved in the
mapping if its two consecutive characters in $s_1$ are mapped to same two
consecutive characters in $s_2$. The MDSM problem is known to be NP-hard and
there are approximation algorithms for this problem [3, 5, 13], but all of them
consider only the "unweighted" version of the problem in the sense that a duo
from $s_1$ is preserved by mapping to any same duo in $s_2$ regardless of their
positions in the respective strings. However, it is well-desired in comparative
genomics to find mappings that consider preserving duos that are "closer" to
each other under some distance measure [19]. In this paper, we introduce a
generalized version of the problem, called the Maximum-Weight Duo-preservation
String Mapping (MWDSM) problem that captures both duos-preservation and
duos-distance measures in the sense that mapping a duo from $s_1$ to each
preserved duo in $s_2$ has a weight, indicating the "closeness" of the two
duos. The objective of the MWDSM problem is to find a mapping so as to maximize
the total weight of preserved duos. In this paper, we give a polynomial-time
6-approximation algorithm for this problem.
| 1 | 0 | 0 | 0 | 0 | 0 |
18,675 | On the virtual singular braid monoid | We study the algebraic structures of the virtual singular braid monoid,
$VSB_n$, and the virtual singular pure braid monoid, $VSP_n$. The monoid
$VSB_n$ is the splittable extension of $VSP_n$ by the symmetric group $S_n$. We
also construct a representation of $VSB_n$.
| 0 | 0 | 1 | 0 | 0 | 0 |
18,676 | Discrete Games in Endogenous Networks: Equilibria and Policy | In games of friendship links and behaviors, I propose $k$-player Nash
stability---a family of equilibria, indexed by a measure of robustness given by
the number of permitted link changes, which is (ordinally and cardinally)
ranked in a probabilistic sense. Application of the proposed framework to
adolescents' tobacco smoking and friendship decisions suggests that: (a.)
friendship networks respond to increases of tobacco prices and this response
amplifies the intended policy effect on smoking, (b.) racially desegregating
high-schools, via stimulating the social interactions of students with
different intrinsic propensity to smoke, decreases the overall smoking
prevalence, (c.) adolescents are averse to sharing friends so that there is a
rivalry for friendships, (d.) when data on individuals' friendship network is
not available, the importance of price centered policy tools is underestimated.
| 1 | 1 | 0 | 0 | 0 | 0 |
18,677 | Evaluating regulatory reform of network industries: a survey of empirical models based on categorical proxies | Proxies for regulatory reforms based on categorical variables are
increasingly used in empirical evaluation models. We surveyed 63 studies that
rely on such indices to analyze the effects of entry liberalization,
privatization, unbundling, and independent regulation of the electricity,
natural gas, and telecommunications sectors. We highlight methodological issues
related to the use of these proxies. Next, taking stock of the literature, we
provide practical advice for the design of the empirical strategy and discuss
the selection of control and instrumental variables to attenuate endogeneity
problems undermining identification of the effects of regulatory reforms.
| 0 | 0 | 0 | 0 | 0 | 1 |
18,678 | Theory of ground states for classical Heisenberg spin systems II | We apply the theory of ground states for classical, finite, Heisenberg spin
systems previously published to a couple of spin systems that can be considered
as finite models $K_{12},\,K_{15}$ and $K_{18}$ of the AF Kagome lattice. The
model $K_{12}$ is isomorphic to the cuboctahedron. In particular, we find
three-dimensional ground states that cannot be viewed as resulting from the
well-known independent rotation of subsets of spin vectors. For a couple of
ground states with translational symmetry we calculate the corresponding wave
numbers. Finally we study the model $K_{12w}$ without boundary conditions which
exhibits new phenomena as, e.~g., two-dimensional families of three-dimensional
ground states.
| 0 | 1 | 0 | 0 | 0 | 0 |
18,679 | Relative Property (T) for Nilpotent Subgroups | We show that relative Property (T) for the abelianization of a nilpotent
normal subgroup implies relative Property (T) for the subgroup itself. This and
other results are a consequence of a theorem of independent interest, which
states that if $H$ is a closed subgroup of a locally compact group $G$, and $A$
is a closed subgroup of the center of $H$, such that $A$ is normal in $G$, and
$(G/A, H/A)$ has relative Property (T), then $(G, H^{(1)})$ has relative
Property (T), where $H^{(1)}$ is the closure of the commutator subgroup of $H$.
In fact, the assumption that $A$ is in the center of $H$ can be replaced with
the weaker assumption that $A$ is abelian and every $H$-invariant finite
measure on the unitary dual of $A$ is supported on the set of fixed points.
| 0 | 0 | 1 | 0 | 0 | 0 |
18,680 | Discriminant analysis in small and large dimensions | We study the distributional properties of the linear discriminant function
under the assumption of normality by comparing two groups with the same
covariance matrix but different mean vectors. A stochastic representation for
the discriminant function coefficients is derived which is then used to obtain
their asymptotic distribution under the high-dimensional asymptotic regime. We
investigate the performance of the classification analysis based on the
discriminant function in both small and large dimensions. A stochastic
representation is established which allows to compute the error rate in an
efficient way. We further compare the calculated error rate with the optimal
one obtained under the assumption that the covariance matrix and the two mean
vectors are known. Finally, we present an analytical expression of the error
rate calculated in the high-dimensional asymptotic regime. The finite-sample
properties of the derived theoretical results are assessed via an extensive
Monte Carlo study.
| 0 | 0 | 1 | 1 | 0 | 0 |
18,681 | Sparse Bayesian Inference for Dense Semantic Mapping | Despite impressive advances in simultaneous localization and mapping, dense
robotic mapping remains challenging due to its inherent nature of being a
high-dimensional inference problem. In this paper, we propose a dense semantic
robotic mapping technique that exploits sparse Bayesian models, in particular,
the relevance vector machine, for high-dimensional sequential inference. The
technique is based on the principle of automatic relevance determination and
produces sparse models that use a small subset of the original dense training
set as the dominant basis. The resulting map posterior is continuous, and
queries can be made efficiently at any resolution. Moreover, the technique has
probabilistic outputs per semantic class through Bayesian inference. We
evaluate the proposed relevance vector semantic map using publicly available
benchmark datasets, NYU Depth V2 and KITTI; and the results show promising
improvements over the state-of-the-art techniques.
| 1 | 0 | 0 | 0 | 0 | 0 |
18,682 | Singularities and Semistable Degenerations for Symplectic Topology | We overview our recent work defining and studying normal crossings varieties
and subvarieties in symplectic topology. This work answers a question of Gromov
on the feasibility of introducing singular (sub)varieties into symplectic
topology in the case of normal crossings singularities. It also provides a
necessary and sufficient condition for smoothing normal crossings symplectic
varieties. In addition, we explain some connections with other areas of
mathematics and discuss a few directions for further research.
| 0 | 0 | 1 | 0 | 0 | 0 |
18,683 | One-step Local M-estimator for Integrated Jump-Diffusion Models | In this paper, robust nonparametric estimators, instead of local linear
estimators, are adapted for infinitesimal coefficients associated with
integrated jump-diffusion models to avoid the impact of outliers on accuracy.
Furthermore, consider the complexity of iteration of the solution for local
M-estimator, we propose the one-step local M-estimators to release the
computation burden. Under appropriate regularity conditions, we prove that
one-step local M-estimators and the fully iterative M-estimators have the same
performance in consistency and asymptotic normality. Through simulation, our
method present advantages in bias reduction, robustness and reducing
computation cost. In addition, the estimators are illustrated empirically
through stock index under different sampling frequency.
| 0 | 0 | 1 | 1 | 0 | 0 |
18,684 | Python Open Source Waveform Extractor (POWER): An open source, Python package to monitor and post-process numerical relativity simulations | Numerical simulations of Einstein's field equations provide unique insights
into the physics of compact objects moving at relativistic speeds, and which
are driven by strong gravitational interactions. Numerical relativity has
played a key role to firmly establish gravitational wave astrophysics as a new
field of research, and it is now paving the way to establish whether
gravitational wave radiation emitted from compact binary mergers is accompanied
by electromagnetic and astro-particle counterparts. As numerical relativity
continues to blend in with routine gravitational wave data analyses to validate
the discovery of gravitational wave events, it is essential to develop open
source tools to streamline these studies. Motivated by our own experience as
users and developers of the open source, community software, the Einstein
Toolkit, we present an open source, Python package that is ideally suited to
monitor and post-process the data products of numerical relativity simulations,
and compute the gravitational wave strain at future null infinity in high
performance environments. We showcase the application of this new package to
post-process a large numerical relativity catalog and extract higher-order
waveform modes from numerical relativity simulations of eccentric binary black
hole mergers and neutron star mergers. This new software fills a critical void
in the arsenal of tools provided by the Einstein Toolkit Consortium to the
numerical relativity community.
| 1 | 1 | 0 | 0 | 0 | 0 |
18,685 | Uniform confidence bands for nonparametric errors-in-variables regression | This paper develops a method to construct uniform confidence bands for a
nonparametric regression function where a predictor variable is subject to a
measurement error. We allow for the distribution of the measurement error to be
unknown, but assume that there is an independent sample from the measurement
error distribution. The sample from the measurement error distribution need not
be independent from the sample on response and predictor variables. The
availability of a sample from the measurement error distribution is satisfied
if, for example, either 1) validation data or 2) repeated measurements (panel
data) on the latent predictor variable with measurement errors, one of which is
symmetrically distributed, are available. The proposed confidence band builds
on the deconvolution kernel estimation and a novel application of the
multiplier (or wild) bootstrap method. We establish asymptotic validity of the
proposed confidence band under ordinary smooth measurement error densities,
showing that the proposed confidence band contains the true regression function
with probability approaching the nominal coverage probability. To the best of
our knowledge, this is the first paper to derive asymptotically valid uniform
confidence bands for nonparametric errors-in-variables regression. We also
propose a novel data-driven method to choose a bandwidth, and conduct
simulation studies to verify the finite sample performance of the proposed
confidence band. Applying our method to a combination of two empirical data
sets, we draw confidence bands for nonparametric regressions of medical costs
on the body mass index (BMI), accounting for measurement errors in BMI.
Finally, we discuss extensions of our results to specification testing, cases
with additional error-free regressors, and confidence bands for conditional
distribution functions.
| 0 | 0 | 1 | 1 | 0 | 0 |
18,686 | Unconventional superconductivity in the BiS$_2$-based layered superconductor NdO$_{0.71}$F$_{0.29}$BiS$_2$ | We investigate the superconducting-gap anisotropy in one of the recently
discovered BiS$_2$-based superconductors, NdO$_{0.71}$F$_{0.29}$BiS$_2$ ($T_c$
$\sim$ 5 K), using laser-based angle-resolved photoemission spectroscopy.
Whereas the previously discovered high-$T_c$ superconductors such as copper
oxides and iron-based superconductors, which are believed to have
unconventional superconducting mechanisms, have $3d$ electrons in their
conduction bands, the conduction band of BiS$_2$-based superconductors mainly
consists of Bi 6$p$ electrons, and hence the conventional superconducting
mechanism might be expected. Contrary to this expectation, we observe a
strongly anisotropic superconducting gap. This result strongly suggests that
the pairing mechanism for NdO$_{0.71}$F$_{0.29}$BiS$_2$ is unconventional one
and we attribute the observed anisotropy to competitive or cooperative multiple
paring interactions.
| 0 | 1 | 0 | 0 | 0 | 0 |
18,687 | Low noise sensitivity analysis of Lq-minimization in oversampled systems | The class of Lq-regularized least squares (LQLS) are considered for
estimating a p-dimensional vector \b{eta} from its n noisy linear observations
y = X\b{eta}+w. The performance of these schemes are studied under the
high-dimensional asymptotic setting in which p grows linearly with n. In this
asymptotic setting, phase transition diagrams (PT) are often used for comparing
the performance of different estimators. Although phase transition analysis is
shown to provide useful information for compressed sensing, the fact that it
ignores the measurement noise not only limits its applicability in many
application areas, but also may lead to misunderstandings. For instance,
consider a linear regression problem in which n > p and the signal is not
exactly sparse. If the measurement noise is ignored in such systems,
regularization techniques, such as LQLS, seem to be irrelevant since even the
ordinary least squares (OLS) returns the exact solution. However, it is
well-known that if n is not much larger than p then the regularization
techniques improve the performance of OLS. In response to this limitation of PT
analysis, we consider the low-noise sensitivity analysis. We show that this
analysis framework (i) reveals the advantage of LQLS over OLS, (ii) captures
the difference between different LQLS estimators even when n > p, and (iii)
provides a fair comparison among different estimators in high signal-to-noise
ratios. As an application of this framework, we will show that under mild
conditions LASSO outperforms other LQLS even when the signal is dense. Finally,
by a simple transformation we connect our low-noise sensitivity framework to
the classical asymptotic regime in which n/p goes to infinity and characterize
how and when regularization techniques offer improvements over ordinary least
squares, and which regularizer gives the most improvement when the sample size
is large.
| 0 | 0 | 1 | 1 | 0 | 0 |
18,688 | Robust Transceiver Design Based on Interference Alignment for Multi-User Multi-Cell MIMO Networks with Channel Uncertainty | In this paper, we firstly exploit the inter-user interference (IUI) and
inter-cell interference (ICI) as useful references to develop a robust
transceiver design based on interference alignment for a downlink multi-user
multi-cell multiple-input multiple-output (MIMO) interference network under
channel estimation error. At transmitters, we propose a two-tier transmit
beamforming strategy, we first achieve the inner beamforming direction and
allocated power by minimizing the interference leakage as well as maximizing
the system energy efficiency, respectively. Then, for the outer beamformer
design, we develop an efficient conjugate gradient Grassmann manifold subspace
tracking algorithm to minimize the distances between the subspace spanned by
interference and the interference subspace in the time varying channel. At
receivers, we propose a practical interference alignment based on fast and
robust fast data projection method (FDPM) subspace tracking algorithm, to
achieve the receive beamformer under channel uncertainty. Numerical results
show that our proposed robust transceiver design achieves better performance
compared with some existing methods in terms of the sum rate and the energy
efficiency.
| 1 | 0 | 0 | 0 | 0 | 0 |
18,689 | Machine learning quantum mechanics: solving quantum mechanics problems using radial basis function networks | Inspired by the recent work of Carleo and Troyer[1], we apply machine
learning methods to quantum mechanics in this article. The radial basis
function network in a discrete basis is used as the variational wavefunction
for the ground state of a quantum system. Variational Monte Carlo(VMC)
calculations are carried out for some simple Hamiltonians. The results are in
good agreements with theoretical values. The smallest eigenvalue of a Hermitian
matrix can also be acquired using VMC calculations. Our results demonstrate
that machine learning techniques are capable of solving quantum mechanical
problems.
| 0 | 1 | 0 | 0 | 0 | 0 |
18,690 | Scale-free networks are rare | A central claim in modern network science is that real-world networks are
typically "scale free," meaning that the fraction of nodes with degree $k$
follows a power law, decaying like $k^{-\alpha}$, often with $2 < \alpha < 3$.
However, empirical evidence for this belief derives from a relatively small
number of real-world networks. We test the universality of scale-free structure
by applying state-of-the-art statistical tools to a large corpus of nearly 1000
network data sets drawn from social, biological, technological, and
informational sources. We fit the power-law model to each degree distribution,
test its statistical plausibility, and compare it via a likelihood ratio test
to alternative, non-scale-free models, e.g., the log-normal. Across domains, we
find that scale-free networks are rare, with only 4% exhibiting the
strongest-possible evidence of scale-free structure and 52% exhibiting the
weakest-possible evidence. Furthermore, evidence of scale-free structure is not
uniformly distributed across sources: social networks are at best weakly scale
free, while a handful of technological and biological networks can be called
strongly scale free. These results undermine the universality of scale-free
networks and reveal that real-world networks exhibit a rich structural
diversity that will likely require new ideas and mechanisms to explain.
| 1 | 0 | 0 | 1 | 1 | 0 |
18,691 | Enlargeability, foliations, and positive scalar curvature | We extend the deep and important results of Lichnerowicz, Connes, and
Gromov-Lawson which relate geometry and characteristic numbers to the existence
and non-existence of metrics of positive scalar curvature (PSC). In particular,
we show: that a spin foliation with Hausdorff homotopy groupoid of an
enlargeable manifold admits no PSC metric; that any metric of PSC on such a
foliation is bounded by a multiple of the reciprocal of the foliation K-area of
the ambient manifold; and that Connes' vanishing theorem for characteristic
numbers of PSC foliations extends to a vanishing theorem for Haefliger
cohomology classes.
| 0 | 0 | 1 | 0 | 0 | 0 |
18,692 | A simple mathematical model for unemployment: a case study in Portugal with optimal control | We propose a simple mathematical model for unemployment. Despite its
simpleness, we claim that the model is more realistic and useful than recent
models available in the literature. A case study with real data from Portugal
supports our claim. An optimal control problem is formulated and solved, which
provides some non-trivial and interesting conclusions.
| 0 | 0 | 0 | 0 | 0 | 1 |
18,693 | Interpreting Deep Neural Networks Through Variable Importance | While the success of deep neural networks (DNNs) is well-established across a
variety of domains, our ability to explain and interpret these methods is
limited. Unlike previously proposed local methods which try to explain
particular classification decisions, we focus on global interpretability and
ask a universally applicable question: given a trained model, which features
are the most important? In the context of neural networks, a feature is rarely
important on its own, so our strategy is specifically designed to leverage
partial covariance structures and incorporate variable dependence into feature
ranking. Our methodological contributions in this paper are two-fold. First, we
propose an effect size analogue for DNNs that is appropriate for applications
with highly collinear predictors (ubiquitous in computer vision). Second, we
extend the recently proposed "RelATive cEntrality" (RATE) measure (Crawford et
al., 2019) to the Bayesian deep learning setting. RATE applies an information
theoretic criterion to the posterior distribution of effect sizes to assess
feature significance. We apply our framework to three broad application areas:
computer vision, natural language processing, and social science.
| 1 | 0 | 0 | 1 | 0 | 0 |
18,694 | Conformality of $1/N$ corrections in SYK-like models | The Sachdev-Ye--Kitaev is a quantum mechanical model of $N$ Majorana fermions
which displays a number of appealing features -- solvability in the strong
coupling regime, near-conformal invariance and maximal chaos -- which make it a
suitable model for black holes in the context of the AdS/CFT holography. In
this paper we show for the colored SYK model and several of its tensor model
cousins that the next-to-leading order in the $N$ expansion preserves the
conformal invariance of the $2$-point function in the strong coupling regime,
up to the contribution of the Goldstone bosons leading to the spontaneous
breaking of the symmetry and which are already seen in the leading order
$4$-point function. We also comment on the composite field approach for
computing correlation functions in colored tensor models.
| 0 | 1 | 0 | 0 | 0 | 0 |
18,695 | Segal-type models of higher categories | Higher category theory is an exceedingly active area of research, whose rapid
growth has been driven by its penetration into a diverse range of scientific
fields. Its influence extends through key mathematical disciplines, notably
homotopy theory, algebraic geometry and algebra, mathematical physics, to
encompass important applications in logic, computer science and beyond. Higher
categories provide a unifying language whose greatest strength lies in its
ability to bridge between diverse areas and uncover novel applications.
In this foundational work we introduce a new approach to higher categories.
It builds upon the theory of iterated internal categories, one of the simplest
possible higher categorical structures available, by adopting a novel and
remarkably simple "weak globularity" postulate and demonstrating that the
resulting model provides a fully general theory of weak n-categories. The
latter are among the most complex of the higher structures, and are crucial for
applications. We show that this new model of "weakly globular n-fold
categories" is suitably equivalent to the well studied model of weak
n-categories due to Tamsamani and Simpson.
| 0 | 0 | 1 | 0 | 0 | 0 |
18,696 | Low-Mass Dark Matter Search with CDMSlite | The SuperCDMS experiment is designed to directly detect weakly interacting
massive particles (WIMPs) that may constitute the dark matter in our Galaxy.
During its operation at the Soudan Underground Laboratory, germanium detectors
were run in the CDMSlite mode to gather data sets with sensitivity specifically
for WIMPs with masses ${<}$10 GeV/$c^2$. In this mode, a higher detector-bias
voltage is applied to amplify the phonon signals produced by drifting charges.
This paper presents studies of the experimental noise and its effect on the
achievable energy threshold, which is demonstrated to be as low as 56
eV$_{\text{ee}}$ (electron equivalent energy). The detector-biasing
configuration is described in detail, with analysis corrections for voltage
variations to the level of a few percent. Detailed studies of the
electric-field geometry, and the resulting successful development of a fiducial
parameter, eliminate poorly measured events, yielding an energy resolution
ranging from ${\sim}$9 eV$_{\text{ee}}$ at 0 keV to 101 eV$_{\text{ee}}$ at
${\sim}$10 eV$_{\text{ee}}$. New results are derived for astrophysical
uncertainties relevant to the WIMP-search limits, specifically examining how
they are affected by variations in the most probable WIMP velocity and the
Galactic escape velocity. These variations become more important for WIMP
masses below 10 GeV/$c^2$. Finally, new limits on spin-dependent low-mass
WIMP-nucleon interactions are derived, with new parameter space excluded for
WIMP masses $\lesssim$3 GeV/$c^2$
| 0 | 1 | 0 | 0 | 0 | 0 |
18,697 | Gravity with free initial conditions: a solution to the cosmological constant problem testable by CMB B-mode polarization | In standard general relativity the universe cannot be started with arbitrary
initial conditions, because four of the ten components of the Einstein's field
equations (EFE) are constraints on initial conditions. In the previous work it
was proposed to extend the gravity theory to allow free initial conditions,
with a motivation to solve the cosmological constant problem. This was done by
setting four constraints on metric variations in the action principle, which is
reasonable because the gravity's physical degrees of freedom are at most six.
However, there are two problems about this theory; the three constraints in
addition to the unimodular condition were introduced without clear physical
meanings, and the flat Minkowski spacetime is unstable against perturbations.
Here a new set of gravitational field equations is derived by replacing the
three constraints with new ones requiring that geodesic paths remain geodesic
against metric variations. The instability problem is then naturally solved.
Implications for the cosmological constant $\Lambda$ are unchanged; the theory
converges into EFE with nonzero $\Lambda$ by inflation, but $\Lambda$ varies on
scales much larger than the present Hubble horizon. Then galaxies are formed
only in small $\Lambda$ regions, and the cosmological constant problem is
solved by the anthropic argument. Because of the increased degrees of freedom
in metric dynamics, the theory predicts new non-oscillatory modes of metric
anisotropy generated by quantum fluctuation during inflation, and CMB B-mode
polarization would be observed differently from the standard predictions by
general relativity.
| 0 | 1 | 0 | 0 | 0 | 0 |
18,698 | Gradual Learning of Recurrent Neural Networks | Recurrent Neural Networks (RNNs) achieve state-of-the-art results in many
sequence-to-sequence modeling tasks. However, RNNs are difficult to train and
tend to suffer from overfitting. Motivated by the Data Processing Inequality
(DPI), we formulate the multi-layered network as a Markov chain, introducing a
training method that comprises training the network gradually and using
layer-wise gradient clipping. We found that applying our methods, combined with
previously introduced regularization and optimization methods, resulted in
improvements in state-of-the-art architectures operating in language modeling
tasks.
| 1 | 0 | 0 | 1 | 0 | 0 |
18,699 | Borel subsets of the real line and continuous reducibility | We study classes of Borel subsets of the real line $\mathbb{R}$ such as
levels of the Borel hierarchy and the class of sets that are reducible to the
set $\mathbb{Q}$ of rationals, endowed with the Wadge quasi-order of
reducibility with respect to continuous functions on $\mathbb{R}$. Notably, we
explore several structural properties of Borel subsets of $\mathbb{R}$ that
diverge from those of Polish spaces with dimension zero. Our first main result
is on the existence of embeddings of several posets into the restriction of
this quasi-order to any Borel class that is strictly above the classes of open
and closed sets, for instance the linear order $\omega_1$, its reverse
$\omega_1^\star$ and the poset $\mathcal{P}(\omega)/\mathsf{fin}$ of inclusion
modulo finite error. As a consequence of its proof, it is shown that there are
no complete sets for these classes. We further extend the previous theorem to
targets that are reducible to $\mathbb{Q}$. These non-structure results
motivate the study of further restrictions of the Wadge quasi-order. In our
second main theorem, we introduce a combinatorial property that is shown to
characterize those $F_\sigma$ sets that are reducible to $\mathbb{Q}$. This is
applied to construct a minimal set below $\mathbb{Q}$ and prove its uniqueness
up to Wadge equivalence. We finally prove several results concerning gaps and
cardinal characteristics of the Wadge quasi-order and thereby answer questions
of Brendle and Geschke.
| 0 | 0 | 1 | 0 | 0 | 0 |
18,700 | Pairing from dynamically screened Coulomb repulsion in bismuth | Recently, Prakash et. al. have discovered bulk superconductivity in single
crystals of bismuth, which is a semi metal with extremely low carrier density.
At such low density, we argue that conventional electron-phonon coupling is too
weak to be responsible for the binding of electrons into Cooper pairs. We study
a dynamically screened Coulomb interaction with effective attraction generated
on the scale of the collective plasma modes. We model the electronic states in
bismuth to include three Dirac pockets with high velocity and one hole pocket
with a significantly smaller velocity. We find a weak coupling instability,
which is greatly enhanced by the presence of the hole pocket. Therefore, we
argue that bismuth is the first material to exhibit superconductivity driven by
retardation effects of Coulomb repulsion alone. By using realistic parameters
for bismuth we find that the acoustic plasma mode does not play the central
role in pairing. We also discuss a matrix element effect, resulting from the
Dirac nature of the conduction band, which may affect $T_c$ in the $s$-wave
channel without breaking time-reversal symmetry.
| 0 | 1 | 0 | 0 | 0 | 0 |
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