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Title: The heat trace for the drifting Laplacian and Schrödinger operators on manifolds,
Abstract: We study the heat trace for both the drifting Laplacian as well as
Schrödinger operators on compact Riemannian manifolds. In the case of a
finite regularity potential or weight function, we prove the existence of a
partial (six term) asymptotic expansion of the heat trace for small times as
well as a suitable remainder estimate. We also demonstrate that the more
precise asymptotic behavior of the remainder is determined by and conversely
distinguishes higher (Sobolev) regularity on the potential or weight function.
In the case of a smooth weight function, we determine the full asymptotic
expansion of the heat trace for the drifting Laplacian for small times. We then
use the heat trace to study the asymptotics of the eigenvalue counting
function. In both cases the Weyl law coincides with the Weyl law for the
Riemannian manifold with the standard Laplace-Beltrami operator. We conclude by
demonstrating isospectrality results for the drifting Laplacian on compact
manifolds. | [
0,
0,
1,
0,
0,
0
] | [
"Mathematics",
"Physics"
] |
Title: Generative Adversarial Networks for Black-Box API Attacks with Limited Training Data,
Abstract: As online systems based on machine learning are offered to public or paid
subscribers via application programming interfaces (APIs), they become
vulnerable to frequent exploits and attacks. This paper studies adversarial
machine learning in the practical case when there are rate limitations on API
calls. The adversary launches an exploratory (inference) attack by querying the
API of an online machine learning system (in particular, a classifier) with
input data samples, collecting returned labels to build up the training data,
and training an adversarial classifier that is functionally equivalent and
statistically close to the target classifier. The exploratory attack with
limited training data is shown to fail to reliably infer the target classifier
of a real text classifier API that is available online to the public. In
return, a generative adversarial network (GAN) based on deep learning is built
to generate synthetic training data from a limited number of real training data
samples, thereby extending the training data and improving the performance of
the inferred classifier. The exploratory attack provides the basis to launch
the causative attack (that aims to poison the training process) and evasion
attack (that aims to fool the classifier into making wrong decisions) by
selecting training and test data samples, respectively, based on the confidence
scores obtained from the inferred classifier. These stealth attacks with small
footprint (using a small number of API calls) make adversarial machine learning
practical under the realistic case with limited training data available to the
adversary. | [
1,
0,
0,
1,
0,
0
] | [
"Computer Science",
"Statistics"
] |
Title: Coloring ($P_6$, diamond, $K_4$)-free graphs,
Abstract: We show that every ($P_6$, diamond, $K_4$)-free graph is $6$-colorable.
Moreover, we give an example of a ($P_6$, diamond, $K_4$)-free graph $G$ with
$\chi(G) = 6$. This generalizes some known results in the literature. | [
1,
0,
0,
0,
0,
0
] | [
"Mathematics"
] |
Title: Origin of meteoritic stardust unveiled by a revised proton-capture rate of $^{17}$O,
Abstract: Stardust grains recovered from meteorites provide high-precision snapshots of
the isotopic composition of the stellar environment in which they formed.
Attributing their origin to specific types of stars, however, often proves
difficult. Intermediate-mass stars of 4-8 solar masses are expected to
contribute a large fraction of meteoritic stardust. However, no grains have
been found with characteristic isotopic compositions expected from such stars.
This is a long-standing puzzle, which points to serious gaps in our
understanding of the lifecycle of stars and dust in our Galaxy. Here we show
that the increased proton-capture rate of $^{17}$O reported by a recent
underground experiment leads to $^{17}$O/$^{16}$O isotopic ratios that match
those observed in a population of stardust grains, for proton-burning
temperatures of 60-80 million K. These temperatures are indeed achieved at the
base of the convective envelope during the late evolution of intermediate-mass
stars of 4-8 solar masses, which reveals them as the most likely site of origin
of the grains. This result provides the first direct evidence that these stars
contributed to the dust inventory from which the Solar System formed. | [
0,
1,
0,
0,
0,
0
] | [
"Physics"
] |
Title: Some Connections Between Cycles and Permutations that Fix a Set and Touchard Polynomials and Covers of Multisets,
Abstract: We present a new proof of a fundamental result concerning cycles of random
permutations which gives some intuition for the connection between Touchard
polynomials and the Poisson distribution. We also introduce a rather novel
permutation statistic and study its distribution. This quantity, indexed by
$m$, is the number of sets of size $m$ fixed by the permutation. This leads to
a new and simpler derivation of the exponential generating function for the
number of covers of certain multisets. | [
0,
0,
1,
0,
0,
0
] | [
"Mathematics"
] |
Title: Strong Functional Representation Lemma and Applications to Coding Theorems,
Abstract: This paper shows that for any random variables $X$ and $Y$, it is possible to
represent $Y$ as a function of $(X,Z)$ such that $Z$ is independent of $X$ and
$I(X;Z|Y)\le\log(I(X;Y)+1)+4$ bits. We use this strong functional
representation lemma (SFRL) to establish a bound on the rate needed for
one-shot exact channel simulation for general (discrete or continuous) random
variables, strengthening the results by Harsha et al. and Braverman and Garg,
and to establish new and simple achievability results for one-shot
variable-length lossy source coding, multiple description coding and Gray-Wyner
system. We also show that the SFRL can be used to reduce the channel with state
noncausally known at the encoder to a point-to-point channel, which provides a
simple achievability proof of the Gelfand-Pinsker theorem. | [
1,
0,
1,
0,
0,
0
] | [
"Computer Science",
"Mathematics"
] |
Title: On Abrikosov Lattice Solutions of the Ginzburg-Landau Equations,
Abstract: We prove existence of Abrikosov vortex lattice solutions of the
Ginzburg-Landau equations of superconductivity, with multiple magnetic flux
quanta per a fundamental cell. We also revisit the existence proof for the
Abrikosov vortex lattices, streamlining some arguments and providing some
essential details missing in earlier proofs for a single magnetic flux quantum
per a fundamental cell. | [
0,
0,
1,
0,
0,
0
] | [
"Physics",
"Mathematics"
] |
Title: A Survey on the Adoption of Cloud Computing in Education Sector,
Abstract: Education is a key factor in ensuring economic growth, especially for
countries with growing economies. Today, students have become more
technologically savvy as teaching and learning uses more advance technology day
in, day out. Due to virtualize resources through the Internet, as well as
dynamic scalability, cloud computing has continued to be adopted by more
organizations. Despite the looming financial crisis, there has been increasing
pressure for educational institutions to deliver better services using minimal
resources. Leaning institutions, both public and private can utilize the
potential advantage of cloud computing to ensure high quality service
regardless of the minimal resources available. Cloud computing is taking a
center stage in academia because of its various benefits. Various learning
institutions use different cloud-based applications provided by the service
providers to ensure that their students and other users can perform both
academic as well as business-related tasks. Thus, this research will seek to
establish the benefits associated with the use of cloud computing in learning
institutions. The solutions provided by the cloud technology ensure that the
research and development, as well as the teaching is more sustainable and
efficient, thus positively influencing the quality of learning and teaching
within educational institutions. This has led to various learning institutions
adopting cloud technology as a solution to various technological challenges
they face on a daily routine. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science"
] |
Title: Deep Neural Networks as Gaussian Processes,
Abstract: It has long been known that a single-layer fully-connected neural network
with an i.i.d. prior over its parameters is equivalent to a Gaussian process
(GP), in the limit of infinite network width. This correspondence enables exact
Bayesian inference for infinite width neural networks on regression tasks by
means of evaluating the corresponding GP. Recently, kernel functions which
mimic multi-layer random neural networks have been developed, but only outside
of a Bayesian framework. As such, previous work has not identified that these
kernels can be used as covariance functions for GPs and allow fully Bayesian
prediction with a deep neural network.
In this work, we derive the exact equivalence between infinitely wide deep
networks and GPs. We further develop a computationally efficient pipeline to
compute the covariance function for these GPs. We then use the resulting GPs to
perform Bayesian inference for wide deep neural networks on MNIST and CIFAR-10.
We observe that trained neural network accuracy approaches that of the
corresponding GP with increasing layer width, and that the GP uncertainty is
strongly correlated with trained network prediction error. We further find that
test performance increases as finite-width trained networks are made wider and
more similar to a GP, and thus that GP predictions typically outperform those
of finite-width networks. Finally we connect the performance of these GPs to
the recent theory of signal propagation in random neural networks. | [
1,
0,
0,
1,
0,
0
] | [
"Computer Science",
"Statistics",
"Mathematics"
] |
Title: The Brown-Peterson spectrum is not $E_{2(p^2+2)}$ at odd primes,
Abstract: Recently, Lawson has shown that the 2-primary Brown-Peterson spectrum does
not admit the structure of an $E_{12}$ ring spectrum, thus answering a question
of May in the negative. We extend Lawson's result to odd primes by proving that
the p-primary Brown-Peterson spectrum does not admit the structure of an
$E_{2(p^2+2)}$ ring spectrum. We also show that there can be no map $MU \to BP$
of $E_{2p+3}$ ring spectra at any prime. | [
0,
0,
1,
0,
0,
0
] | [
"Mathematics"
] |
Title: A depth-based method for functional time series forecasting,
Abstract: An approach is presented for making predictions about functional time series.
The method is applied to data coming from periodically correlated processes and
electricity demand, obtaining accurate point forecasts and narrow prediction
bands that cover high proportions of the forecasted functional datum, for a
given confidence level. The method is computationally efficient and
substantially different to other functional time series methods, offering a new
insight for the analysis of these data structures. | [
0,
0,
0,
1,
0,
0
] | [
"Statistics",
"Mathematics"
] |
Title: Sterile Neutrinos and B-L Symmetry,
Abstract: We revisit the relation between the neutrino masses and the spontaneous
breaking of the B-L gauge symmetry. We discuss the main scenarios for Dirac and
Majorana neutrinos and point out two simple mechanisms for neutrino masses. In
this context the neutrino masses can be generated either at tree level or at
quantum level and one predicts the existence of very light sterile neutrinos
with masses below the eV scale. The predictions for lepton number violating
processes such as mu to e and mu to e gamma are discussed in detail. The impact
from the cosmological constraints on the effective number of relativistic
degree of freedom is investigated. | [
0,
1,
0,
0,
0,
0
] | [
"Physics"
] |
Title: A computer-based recursion algorithm for automatic charge of power device of electric vehicles carrying electromagnet,
Abstract: This paper proposes a computer-based recursion algorithm for automatic charge
of power device of electric vehicles carrying electromagnet. The charging
system includes charging cable with one end connecting gang socket,
electromagnetic gear driving the connecting socket and a charging pile breaking
or closing, and detecting part for detecting electric vehicle static call or
start state. The gang socket mentioned above is linked to electromagnetic gear,
and the detecting part is connected with charging management system containing
the intelligent charging power module which controls the electromagnetic drive
action to close socket with a charging pile at static state and to break at
start state. Our work holds an electric automobile with convenience, safety low
maintenance cost. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science"
] |
Title: A Divergence Bound for Hybrids of MCMC and Variational Inference and an Application to Langevin Dynamics and SGVI,
Abstract: Two popular classes of methods for approximate inference are Markov chain
Monte Carlo (MCMC) and variational inference. MCMC tends to be accurate if run
for a long enough time, while variational inference tends to give better
approximations at shorter time horizons. However, the amount of time needed for
MCMC to exceed the performance of variational methods can be quite high,
motivating more fine-grained tradeoffs. This paper derives a distribution over
variational parameters, designed to minimize a bound on the divergence between
the resulting marginal distribution and the target, and gives an example of how
to sample from this distribution in a way that interpolates between the
behavior of existing methods based on Langevin dynamics and stochastic gradient
variational inference (SGVI). | [
1,
0,
0,
1,
0,
0
] | [
"Statistics",
"Mathematics",
"Computer Science"
] |
Title: On Some properties of dyadic operators,
Abstract: In this paper, the objects of our investigation are some dyadic operators,
including dyadic shifts, multilinear paraproducts and multilinear Haar
multipliers. We mainly focus on the continuity and compactness of these
operators. First, we consider the continuity properties of these operators.
Then, by the Fréchet-Kolmogorov-Riesz-Tsuji theorem, the non-compactness
properties of these dyadic operators will be studied. Moreover, we show that
their commutators are compact with \textit{CMO} functions, which is quite
different from the non-compaceness properties of these dyadic operators. These
results are similar to those for Calderón-Zygmund singular integral
operators. | [
0,
0,
1,
0,
0,
0
] | [
"Mathematics"
] |
Title: Nonlocal Nonlinear Schrödinger Equations and Their Soliton Solutions,
Abstract: We study standard and nonlocal nonlinear Schrödinger (NLS) equations
obtained from the coupled NLS system of equations (Ablowitz-Kaup-Newell-Segur
(AKNS) equations) by using standard and nonlocal reductions respectively. By
using the Hirota bilinear method we first find soliton solutions of the coupled
NLS system of equations then using the reduction formulas we find the soliton
solutions of the standard and nonlocal NLS equations. We give examples for
particular values of the parameters and plot the function $|q(t,x)|^2$ for the
standard and nonlocal NLS equations. | [
0,
1,
0,
0,
0,
0
] | [
"Physics",
"Mathematics"
] |
Title: Tracking network dynamics: a survey of distances and similarity metrics,
Abstract: From longitudinal biomedical studies to social networks, graphs have emerged
as a powerful framework for describing evolving interactions between agents in
complex systems. In such studies, after pre-processing, the data can be
represented by a set of graphs, each representing a system's state at different
points in time. The analysis of the system's dynamics depends on the selection
of the appropriate analytical tools. After characterizing similarities between
states, a critical step lies in the choice of a distance between graphs capable
of reflecting such similarities. While the literature offers a number of
distances that one could a priori choose from, their properties have been
little investigated and no guidelines regarding the choice of such a distance
have yet been provided. In particular, most graph distances consider that the
nodes are exchangeable and do not take into account node identities. Accounting
for the alignment of the graphs enables us to enhance these distances'
sensitivity to perturbations in the network and detect important changes in
graph dynamics. Thus the selection of an adequate metric is a decisive --yet
delicate--practical matter.
In the spirit of Goldenberg, Zheng and Fienberg's seminal 2009 review, the
purpose of this article is to provide an overview of commonly-used graph
distances and an explicit characterization of the structural changes that they
are best able to capture. We use as a guiding thread to our discussion the
application of these distances to the analysis of both a longitudinal
microbiome dataset and a brain fMRI study. We show examples of using
permutation tests to detect the effect of covariates on the graphs'
variability. Synthetic examples provide intuition as to the qualities and
drawbacks of the different distances. Above all, we provide some guidance for
choosing one distance over another in certain types of applications. | [
1,
0,
0,
1,
0,
0
] | [
"Computer Science",
"Statistics"
] |
Title: Machine learning for classification and quantification of monoclonal antibody preparations for cancer therapy,
Abstract: Monoclonal antibodies constitute one of the most important strategies to
treat patients suffering from cancers such as hematological malignancies and
solid tumors. In order to guarantee the quality of those preparations prepared
at hospital, quality control has to be developed. The aim of this study was to
explore a noninvasive, nondestructive, and rapid analytical method to ensure
the quality of the final preparation without causing any delay in the process.
We analyzed four mAbs (Inlfiximab, Bevacizumab, Ramucirumab and Rituximab)
diluted at therapeutic concentration in chloride sodium 0.9% using Raman
spectroscopy. To reduce the prediction errors obtained with traditional
chemometric data analysis, we explored a data-driven approach using statistical
machine learning methods where preprocessing and predictive models are jointly
optimized. We prepared a data analytics workflow and submitted the problem to a
collaborative data challenge platform called Rapid Analytics and Model
Prototyping (RAMP). This allowed to use solutions from about 300 data
scientists during five days of collaborative work. The prediction of the four
mAbs samples was considerably improved with a misclassification rate and the
mean error rate of 0.8% and 4%, respectively. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science",
"Statistics",
"Quantitative Biology"
] |
Title: Observation of Skyrmions at Room Temperature in Co2FeAl Heusler Alloy Ultrathin Films,
Abstract: Magnetic skyrmions are topological spin structures having immense potential
for energy efficient spintronic devices. However, observations of skyrmions at
room temperature are limited to patterned nanostructures. Here, we report the
observation of stable skyrmions in unpatterned Ta/Co2FeAl(CFA)/MgO thin film
heterostructures at room temperature and in zero external magnetic field
employing magnetic force microscopy. The skyrmions are observed in a trilayer
structure comprised of heavy metal (HM)/ferromagnet (FM)/Oxide interfaces which
result in strong interfacial Dzyaloshinskii-Moriya interaction (i-DMI) as
evidenced by Brillouin light scattering measurements, in agreement with the
results of micromagnetic simulations. We also emphasize on room temperature
observation of multiple skyrmions which can be stabilized for suitable choices
of CFA layer thickness, perpendicular magnetic anisotropy, and i-DMI. These
results open up a new paradigm for designing room temperature spintronic
devices based on skyrmions in FM continuous thin films. | [
0,
1,
0,
0,
0,
0
] | [
"Physics"
] |
Title: Bayesian Nonparametric Spectral Estimation,
Abstract: Spectral estimation (SE) aims to identify how the energy of a signal (e.g., a
time series) is distributed across different frequencies. This can become
particularly challenging when only partial and noisy observations of the signal
are available, where current methods fail to handle uncertainty appropriately.
In this context, we propose a joint probabilistic model for signals,
observations and spectra, where SE is addressed as an exact inference problem.
Assuming a Gaussian process prior over the signal, we apply Bayes' rule to find
the analytic posterior distribution of the spectrum given a set of
observations. Besides its expressiveness and natural account of spectral
uncertainty, the proposed model also provides a functional-form representation
of the power spectral density, which can be optimised efficiently. Comparison
with previous approaches, in particular against Lomb-Scargle, is addressed
theoretically and also experimentally in three different scenarios. Code and
demo available at this https URL. | [
0,
0,
0,
1,
0,
0
] | [
"Statistics",
"Mathematics",
"Computer Science"
] |
Title: Imprecise dynamic walking with time-projection control,
Abstract: We present a new walking foot-placement controller based on 3LP, a 3D model
of bipedal walking that is composed of three pendulums to simulate falling,
swing and torso dynamics. Taking advantage of linear equations and closed-form
solutions of the 3LP model, our proposed controller projects intermediate
states of the biped back to the beginning of the phase for which a discrete LQR
controller is designed. After the projection, a proper control policy is
generated by this LQR controller and used at the intermediate time. This
control paradigm reacts to disturbances immediately and includes rules to
account for swing dynamics and leg-retraction. We apply it to a simulated Atlas
robot in position-control, always commanded to perform in-place walking. The
stance hip joint in our robot keeps the torso upright to let the robot
naturally fall, and the swing hip joint tracks the desired footstep location.
Combined with simple Center of Pressure (CoP) damping rules in the low-level
controller, our foot-placement enables the robot to recover from strong pushes
and produce periodic walking gaits when subject to persistent sources of
disturbance, externally or internally. These gaits are imprecise, i.e.,
emergent from asymmetry sources rather than precisely imposing a desired
velocity to the robot. Also in extreme conditions, restricting linearity
assumptions of the 3LP model are often violated, but the system remains robust
in our simulations. An extensive analysis of closed-loop eigenvalues, viable
regions and sensitivity to push timings further demonstrate the strengths of
our simple controller. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science",
"Mathematics"
] |
Title: A Hand Combining Two Simple Grippers to Pick up and Arrange Objects for Assembly,
Abstract: This paper proposes a novel robotic hand design for assembly tasks. The idea
is to combine two simple grippers -- an inner gripper which is used for precise
alignment, and an outer gripper which is used for stable holding. Conventional
robotic hands require complicated compliant mechanisms or complicated control
strategy and force sensing to conduct assemble tasks, which makes them costly
and difficult to pick and arrange small objects like screws or washers.
Compared to the conventional hands, the proposed design provides a low-cost
solution for aligning, picking up, and arranging various objects by taking
advantages of the geometric constraints of the positioning fingers and gravity.
It is able to deal with small screws and washers, and eliminate the position
errors of cylindrical objects or objects with cylindrical holes. In the
experiments, both real-world tasks and quantitative analysis are performed to
validate the aligning, picking, and arrangements abilities of the design. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science"
] |
Title: Second sound in systems of one-dimensional fermions,
Abstract: We study sound in Galilean invariant systems of one-dimensional fermions. At
low temperatures, we find a broad range of frequencies in which in addition to
the waves of density there is a second sound corresponding to ballistic
propagation of heat in the system. The damping of the second sound mode is
weak, provided the frequency is large compared to a relaxation rate that is
exponentially small at low temperatures. At lower frequencies the second sound
mode is damped, and the propagation of heat is diffusive. | [
0,
1,
0,
0,
0,
0
] | [
"Physics"
] |
Title: The equational theory of the natural join and inner union is decidable,
Abstract: The natural join and the inner union operations combine relations of a
database. Tropashko and Spight [24] realized that these two operations are the
meet and join operations in a class of lattices, known by now as the relational
lattices. They proposed then lattice theory as an algebraic approach to the
theory of databases, alternative to the relational algebra. Previous works [17,
22] proved that the quasiequational theory of these lattices-that is, the set
of definite Horn sentences valid in all the relational lattices-is undecidable,
even when the signature is restricted to the pure lattice signature. We prove
here that the equational theory of relational lattices is decidable. That, is
we provide an algorithm to decide if two lattice theoretic terms t, s are made
equal under all intepretations in some relational lattice. We achieve this goal
by showing that if an inclusion t $\le$ s fails in any of these lattices, then
it fails in a relational lattice whose size is bound by a triple exponential
function of the sizes of t and s. | [
1,
0,
1,
0,
0,
0
] | [
"Computer Science",
"Mathematics"
] |
Title: A robotic vision system to measure tree traits,
Abstract: The autonomous measurement of tree traits, such as branching structure,
branch diameters, branch lengths, and branch angles, is required for tasks such
as robotic pruning of trees as well as structural phenotyping. We propose a
robotic vision system called the Robotic System for Tree Shape Estimation
(RoTSE) to determine tree traits in field settings. The process is composed of
the following stages: image acquisition with a mobile robot unit, segmentation,
reconstruction, curve skeletonization, conversion to a graph representation,
and then computation of traits. Quantitative and qualitative results on apple
trees are shown in terms of accuracy, computation time, and robustness.
Compared to ground truth measurements, the RoTSE produced the following
estimates: branch diameter (mean-squared error $0.99$ mm), branch length
(mean-squared error $45.64$ mm), and branch angle (mean-squared error $10.36$
degrees). The average run time was 8.47 minutes when the voxel resolution was
$3$ mm$^3$. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science",
"Quantitative Biology"
] |
Title: Toward Unsupervised Text Content Manipulation,
Abstract: Controlled generation of text is of high practical use. Recent efforts have
made impressive progress in generating or editing sentences with given textual
attributes (e.g., sentiment). This work studies a new practical setting of text
content manipulation. Given a structured record, such as `(PLAYER: Lebron,
POINTS: 20, ASSISTS: 10)', and a reference sentence, such as `Kobe easily
dropped 30 points', we aim to generate a sentence that accurately describes the
full content in the record, with the same writing style (e.g., wording,
transitions) of the reference. The problem is unsupervised due to lack of
parallel data in practice, and is challenging to minimally yet effectively
manipulate the text (by rewriting/adding/deleting text portions) to ensure
fidelity to the structured content. We derive a dataset from a basketball game
report corpus as our testbed, and develop a neural method with unsupervised
competing objectives and explicit content coverage constraints. Automatic and
human evaluations show superiority of our approach over competitive methods
including a strong rule-based baseline and prior approaches designed for style
transfer. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science",
"Statistics"
] |
Title: Unsupervised learning of object landmarks by factorized spatial embeddings,
Abstract: Learning automatically the structure of object categories remains an
important open problem in computer vision. In this paper, we propose a novel
unsupervised approach that can discover and learn landmarks in object
categories, thus characterizing their structure. Our approach is based on
factorizing image deformations, as induced by a viewpoint change or an object
deformation, by learning a deep neural network that detects landmarks
consistently with such visual effects. Furthermore, we show that the learned
landmarks establish meaningful correspondences between different object
instances in a category without having to impose this requirement explicitly.
We assess the method qualitatively on a variety of object types, natural and
man-made. We also show that our unsupervised landmarks are highly predictive of
manually-annotated landmarks in face benchmark datasets, and can be used to
regress these with a high degree of accuracy. | [
1,
0,
0,
1,
0,
0
] | [
"Computer Science"
] |
Title: A Capillary Surface with No Radial Limits,
Abstract: In 1996, Kirk Lancaster and David Siegel investigated the existence and
behavior of radial limits at a corner of the boundary of the domain of
solutions of capillary and other prescribed mean curvature problems with
contact angle boundary data. In Theorem 3, they provide an example of a
capillary surface in a unit disk $D$ which has no radial limits at
$(0,0)\in\partial D.$ In their example, the contact angle ($\gamma$) cannot be
bounded away from zero and $\pi.$
Here we consider a domain $\Omega$ with a convex corner at $(0,0)$ and find a
capillary surface $z=f(x,y)$ in $\Omega\times\mathbb{R}$ which has no radial
limits at $(0,0)\in\partial\Omega$ such that $\gamma$ is bounded away from $0$
and $\pi.$ | [
0,
0,
1,
0,
0,
0
] | [
"Mathematics",
"Physics"
] |
Title: Multi-agent Gaussian Process Motion Planning via Probabilistic Inference,
Abstract: This paper deals with motion planning for multiple agents by representing the
problem as a simultaneous optimization of every agent's trajectory. Each
trajectory is considered as a sample from a one-dimensional continuous-time
Gaussian process (GP) generated by a linear time-varying stochastic
differential equation driven by white noise. By formulating the planning
problem as probabilistic inference on a factor graph, the structure of the
pertaining GP can be exploited to find the solution efficiently using numerical
optimization. In contrast to planning each agent's trajectory individually,
where only the current poses of other agents are taken into account, we propose
simultaneous planning of multiple trajectories that works in a predictive
manner. It takes into account the information about each agent's whereabouts at
every future time instant, since full trajectories of each agent are found
jointly during a single optimization procedure. We compare the proposed method
to an individual trajectory planning approach, demonstrating significant
improvement in both success rate and computational efficiency. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science",
"Mathematics"
] |
Title: Sharpening Jensen's Inequality,
Abstract: This paper proposes a new sharpened version of the Jensen's inequality. The
proposed new bound is simple and insightful, is broadly applicable by imposing
minimum assumptions, and provides fairly accurate result in spite of its simple
form. Applications to the moment generating function, power mean inequalities,
and Rao-Blackwell estimation are presented. This presentation can be
incorporated in any calculus-based statistical course. | [
0,
0,
1,
1,
0,
0
] | [
"Mathematics",
"Statistics"
] |
Title: On the intersection graph of ideals of $\mathbb{Z}_m$,
Abstract: Let $m>1$ be an integer, and let $I(\mathbb{Z}_m)^*$ be the set of all
non-zero proper ideals of $\mathbb{Z}_m$. The intersection graph of ideals of
$\mathbb{Z}_m$, denoted by $G(\mathbb{Z}_m)$, is a graph with vertices
$I(\mathbb{Z}_m)^*$ and two distinct vertices $I,J\in I(\mathbb{Z}_m)^*$ are
adjacent if and only if $I\cap J\neq 0$. Let $n>1$ be an integer and
$\mathbb{Z}_n$ be a $\mathbb{Z}_m$-module. In this paper, we introduce and
study a kind of graph structure of $\mathbb{Z}_m$, denoted by
$G_n(\mathbb{Z}_m)$. It is the undirected graph with the vertex set
$I(\mathbb{Z}_m)^*$, and two distinct vertices $I$ and $J$ are adjacent if and
only if $I\mathbb{Z}_n\cap J\mathbb{Z}_n\neq 0$. Clearly,
$G_m(\mathbb{Z}_m)=G(\mathbb{Z}_m)$. We obtain some graph theoretical
properties of $G_n(\mathbb{Z}_m)$ and we compute some of its numerical
invariants, namely girth, independence number, domination number, maximum
degree and chromatic index. We also determine all integer numbers $n$ and $m$
for which $G_n(\mathbb{Z}_m)$ is Eulerian. | [
0,
0,
1,
0,
0,
0
] | [
"Mathematics"
] |
Title: Optimization of Executable Formal Interpreters developed in Higher-order Theorem Proving Systems,
Abstract: In recent publications, we presented a novel formal symbolic process virtual
machine (FSPVM) framework that combined higher-order theorem proving and
symbolic execution for verifying the reliability and security of smart
contracts developed in the Ethereum blockchain system without suffering the
standard issues surrounding reusability, consistency, and automation. A
specific FSPVM, denoted as FSPVM-E, was developed in Coq based on a general,
extensible, and reusable formal memory (GERM) framework, an extensible and
universal formal intermediate programming language, denoted as Lolisa, which is
a large subset of the Solidity programming language that uses generalized
algebraic datatypes, and a corresponding formally verified interpreter for
Lolisa, denoted as FEther, which serves as a crucial component of FSPVM-E.
However, our past work has demonstrated that the execution efficiency of the
standard development of FEther is extremely low. As a result, FSPVM-E fails to
achieve its expected verification effect. The present work addresses this issue
by first identifying three root causes of the low execution efficiency of
formal interpreters. We then build abstract models of these causes, and present
respective optimization schemes for rectifying the identified conditions.
Finally, we apply these optimization schemes to FEther, and demonstrate that
its execution efficiency has been improved significantly. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science",
"Mathematics"
] |
Title: Personalized Thread Recommendation for MOOC Discussion Forums,
Abstract: Social learning, i.e., students learning from each other through social
interactions, has the potential to significantly scale up instruction in online
education. In many cases, such as in massive open online courses (MOOCs),
social learning is facilitated through discussion forums hosted by course
providers. In this paper, we propose a probabilistic model for the process of
learners posting on such forums, using point processes. Different from existing
works, our method integrates topic modeling of the post text, timescale
modeling of the decay in post activity over time, and learner topic interest
modeling into a single model, and infers this information from user data. Our
method also varies the excitation levels induced by posts according to the
thread structure, to reflect typical notification settings in discussion
forums. We experimentally validate the proposed model on three real-world MOOC
datasets, with the largest one containing up to 6,000 learners making 40,000
posts in 5,000 threads. Results show that our model excels at thread
recommendation, achieving significant improvement over a number of baselines,
thus showing promise of being able to direct learners to threads that they are
interested in more efficiently. Moreover, we demonstrate analytics that our
model parameters can provide, such as the timescales of different topic
categories in a course. | [
1,
0,
0,
1,
0,
0
] | [
"Computer Science",
"Statistics"
] |
Title: CREATE: Cohort Retrieval Enhanced by Analysis of Text from Electronic Health Records using OMOP Common Data Model,
Abstract: Background: Widespread adoption of electronic health records (EHRs) has
enabled secondary use of EHR data for clinical research and healthcare
delivery. Natural language processing (NLP) techniques have shown promise in
their capability to extract the embedded information in unstructured clinical
data, and information retrieval (IR) techniques provide flexible and scalable
solutions that can augment the NLP systems for retrieving and ranking relevant
records. Methods: In this paper, we present the implementation of Cohort
Retrieval Enhanced by Analysis of Text from EHRs (CREATE), a cohort retrieval
system that can execute textual cohort selection queries on both structured and
unstructured EHR data. CREATE is a proof-of-concept system that leverages a
combination of structured queries and IR techniques on NLP results to improve
cohort retrieval performance while adopting the Observational Medical Outcomes
Partnership (OMOP) Common Data Model (CDM) to enhance model portability. The
NLP component empowered by cTAKES is used to extract CDM concepts from textual
queries. We design a hierarchical index in Elasticsearch to support CDM concept
search utilizing IR techniques and frameworks. Results: Our case study on 5
cohort identification queries evaluated using the IR metric, P@5 (Precision at
5) at both the patient-level and document-level, demonstrates that CREATE
achieves an average P@5 of 0.90, which outperforms systems using only
structured data or only unstructured data with average P@5s of 0.54 and 0.74,
respectively. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science",
"Quantitative Biology"
] |
Title: Charge transfer and metallicity in LaNiO$_3$/LaMnO$_3$ superlattices,
Abstract: Motivated by recent experiments, we use the $+U$ extension of the generalized
gradient approximation to density functional theory to study superlattices
composed of alternating layers of LaNiO$_3$ and LaMnO$_3$. For comparison we
also study a rocksalt ((111) double perovskite) structure and bulk LaNiO$_3$
and LaMnO$_3$. A Wannier function analysis indicates that band parameters are
transferable from bulk to superlattice situations with the exception of the
transition metal d-level energy, which has a contribution from the change in
d-shell occupancy. The charge transfer from Mn to Ni is found to be moderate in
the superlattice, indicating metallic behavior, in contrast to the insulating
behavior found in recent experiments, while the rocksalt structure is found to
be insulating with a large Mn-Ni charge transfer. We suggest a high density of
cation antisite defects may account for the insulating behavior experimentally
observed in short-period superlattices. | [
0,
1,
0,
0,
0,
0
] | [
"Physics"
] |
Title: Report: Performance comparison between C2075 and P100 GPU cards using cosmological correlation functions,
Abstract: In this report, some cosmological correlation functions are used to evaluate
the differential performance between C2075 and P100 GPU cards. In the past, the
correlation functions used in this work have been widely studied and exploited
on some previous GPU architectures. The analysis of the performance indicates
that a speedup in the range from 13 to 15 is achieved without any additional
optimization process for the P100 card. | [
1,
1,
0,
0,
0,
0
] | [
"Physics",
"Computer Science"
] |
Title: On the Analysis of Bacterial Cooperation with a Characterization of 2D Signal Propagation,
Abstract: The exchange of small molecular signals within microbial populations is
generally referred to as quorum sensing (QS). QS is ubiquitous in nature and
enables microorganisms to respond to fluctuations of living environments by
working together. In this work, a QS-based communication system within a
microbial population in a two-dimensional (2D) environment is analytically
modeled. Notably, the diffusion and degradation of signaling molecules within
the population is characterized. Microorganisms are randomly distributed on a
2D circle where each one releases molecules at random times. The number of
molecules observed at each randomly-distributed bacterium is analyzed. Using
this analysis and some approximation, the expected density of cooperating
bacteria is derived. The analytical results are validated via a particle-based
simulation method. The model can be used to predict and control behavioral
dynamics of microscopic populations that have imperfect signal propagation. | [
0,
0,
0,
0,
1,
0
] | [
"Quantitative Biology",
"Mathematics"
] |
Title: Training of Deep Neural Networks based on Distance Measures using RMSProp,
Abstract: The vanishing gradient problem was a major obstacle for the success of deep
learning. In recent years it was gradually alleviated through multiple
different techniques. However the problem was not really overcome in a
fundamental way, since it is inherent to neural networks with activation
functions based on dot products. In a series of papers, we are going to analyze
alternative neural network structures which are not based on dot products. In
this first paper, we revisit neural networks built up of layers based on
distance measures and Gaussian activation functions. These kinds of networks
were only sparsely used in the past since they are hard to train when using
plain stochastic gradient descent methods. We show that by using Root Mean
Square Propagation (RMSProp) it is possible to efficiently learn multi-layer
neural networks. Furthermore we show that when appropriately initialized these
kinds of neural networks suffer much less from the vanishing and exploding
gradient problem than traditional neural networks even for deep networks. | [
1,
0,
0,
1,
0,
0
] | [
"Computer Science",
"Statistics"
] |
Title: Wild Bootstrapping Rank-Based Procedures: Multiple Testing in Nonparametric Split-Plot Designs,
Abstract: Split-plot or repeated measures designs are frequently used for planning
experiments in the life or social sciences. Typical examples include the
comparison of different treatments over time, where both factors may possess an
additional factorial structure. For such designs, the statistical analysis
usually consists of several steps. If the global null is rejected, multiple
comparisons are usually performed. Usually, general factorial repeated measures
designs are inferred by classical linear mixed models. Common underlying
assumptions, such as normality or variance homogeneity are often not met in
real data. Furthermore, to deal even with, e.g., ordinal or ordered categorical
data, adequate effect sizes should be used. Here, multiple contrast tests and
simultaneous confidence intervals for general factorial split-plot designs are
developed and equipped with a novel asymptotically correct wild bootstrap
approach.
Because the regulatory authorities typically require the calculation of
confidence intervals, this work also provides simultaneous confidence intervals
for single contrasts and for the ratio of different contrasts in meaningful
effects. Extensive simulations are conducted to foster the theoretical
findings. Finally, two different datasets exemplify the applicability of the
novel procedure. | [
0,
0,
1,
1,
0,
0
] | [
"Statistics",
"Mathematics"
] |
Title: Graphical Sequent Calculi for Modal Logics,
Abstract: The syntax of modal graphs is defined in terms of the continuous cut and
broken cut following Charles Peirce's notation in the gamma part of his
graphical logic of existential graphs. Graphical calculi for normal modal
logics are developed based on a reformulation of the graphical calculus for
classical propositional logic. These graphical calculi are of the nature of
deep inference. The relationship between graphical calculi and sequent calculi
for modal logics is shown by translations between graphs and modal formulas. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science",
"Mathematics"
] |
Title: On the tensor semigroup of affine kac-moody lie algebras,
Abstract: In this paper, we are interested in the decomposition of the tensor product
of two representations of a symmetrizable Kac-Moody Lie algebra $\mathfrak g$.
Let $P\_+$ be the set of dominant integral weights. For $\lambda\in P\_+$ ,
$L(\lambda)$ denotes the irreducible, integrable, highest weight representation
of g with highest weight $\lambda$. Let $P\_{+,\mathbb Q}$ be the rational
convex cone generated by $P\_+$. Consider the tensor cone $\Gamma(\mathfrak g)
:= \{(\lambda\_1 ,\lambda\_2, \mu) $\in$ P\_{+,\mathbb Q}^3\,| \exists N
\textgreater{} 1 L(N\mu) \subset L(N \lambda\_1)\otimes L(N \lambda\_2)\}$. If
$\mathfrak g$ is finite dimensional, $\Gamma(\mathfrak g)$ is a polyhedral
convex cone described in 2006 by Belkale-Kumar by an explicit finite list of
inequalities. In general, $\Gamma(\mathfrak g)$ is nor polyhedral, nor closed.
In this article we describe the closure of $\Gamma(\mathfrak g)$ by an explicit
countable family of linear inequalities, when $\mathfrak g$ is untwisted
affine. This solves a Brown-Kumar's conjecture in this case. We also obtain
explicit saturation factors for the semigroup of triples $(\lambda\_1,
\lambda\_2 , \mu) $\in$ P\_+^3$ such that $L(\mu) $\subset$ L(\lambda\_1)
\otimes L(\lambda\_2)$. Note that even the existence of such saturation factors
is not obvious since the semigroup is not finitely generated. For example, in
type $A , we prove that any integer $d\geq 2$ is a saturation factor,
generalizing the case ${\tilde A}\_1$ shown by Brown-Kumar. | [
0,
0,
1,
0,
0,
0
] | [
"Mathematics",
"Physics"
] |
Title: On the Power of Truncated SVD for General High-rank Matrix Estimation Problems,
Abstract: We show that given an estimate $\widehat{A}$ that is close to a general
high-rank positive semi-definite (PSD) matrix $A$ in spectral norm (i.e.,
$\|\widehat{A}-A\|_2 \leq \delta$), the simple truncated SVD of $\widehat{A}$
produces a multiplicative approximation of $A$ in Frobenius norm. This
observation leads to many interesting results on general high-rank matrix
estimation problems, which we briefly summarize below ($A$ is an $n\times n$
high-rank PSD matrix and $A_k$ is the best rank-$k$ approximation of $A$):
(1) High-rank matrix completion: By observing
$\Omega(\frac{n\max\{\epsilon^{-4},k^2\}\mu_0^2\|A\|_F^2\log
n}{\sigma_{k+1}(A)^2})$ elements of $A$ where $\sigma_{k+1}\left(A\right)$ is
the $\left(k+1\right)$-th singular value of $A$ and $\mu_0$ is the incoherence,
the truncated SVD on a zero-filled matrix satisfies $\|\widehat{A}_k-A\|_F \leq
(1+O(\epsilon))\|A-A_k\|_F$ with high probability.
(2)High-rank matrix de-noising: Let $\widehat{A}=A+E$ where $E$ is a Gaussian
random noise matrix with zero mean and $\nu^2/n$ variance on each entry. Then
the truncated SVD of $\widehat{A}$ satisfies $\|\widehat{A}_k-A\|_F \leq
(1+O(\sqrt{\nu/\sigma_{k+1}(A)}))\|A-A_k\|_F + O(\sqrt{k}\nu)$.
(3) Low-rank Estimation of high-dimensional covariance: Given $N$
i.i.d.~samples $X_1,\cdots,X_N\sim\mathcal N_n(0,A)$, can we estimate $A$ with
a relative-error Frobenius norm bound? We show that if $N =
\Omega\left(n\max\{\epsilon^{-4},k^2\}\gamma_k(A)^2\log N\right)$ for
$\gamma_k(A)=\sigma_1(A)/\sigma_{k+1}(A)$, then $\|\widehat{A}_k-A\|_F \leq
(1+O(\epsilon))\|A-A_k\|_F$ with high probability, where
$\widehat{A}=\frac{1}{N}\sum_{i=1}^N{X_iX_i^\top}$ is the sample covariance. | [
0,
0,
1,
1,
0,
0
] | [
"Computer Science",
"Mathematics",
"Statistics"
] |
Title: Don't Look Back: Robustifying Place Categorization for Viewpoint- and Condition-Invariant Place Recognition,
Abstract: When a human drives a car along a road for the first time, they later
recognize where they are on the return journey typically without needing to
look in their rear-view mirror or turn around to look back, despite significant
viewpoint and appearance change. Such navigation capabilities are typically
attributed to our semantic visual understanding of the environment [1] beyond
geometry to recognizing the types of places we are passing through such as
"passing a shop on the left" or "moving through a forested area". Humans are in
effect using place categorization [2] to perform specific place recognition
even when the viewpoint is 180 degrees reversed. Recent advances in deep neural
networks have enabled high-performance semantic understanding of visual places
and scenes, opening up the possibility of emulating what humans do. In this
work, we develop a novel methodology for using the semantics-aware higher-order
layers of deep neural networks for recognizing specific places from within a
reference database. To further improve the robustness to appearance change, we
develop a descriptor normalization scheme that builds on the success of
normalization schemes for pure appearance-based techniques such as SeqSLAM [3].
Using two different datasets - one road-based, one pedestrian-based, we
evaluate the performance of the system in performing place recognition on
reverse traversals of a route with a limited field of view camera and no
turn-back-and-look behaviours, and compare to existing state-of-the-art
techniques and vanilla off-the-shelf features. The results demonstrate
significant improvements over the existing state of the art, especially for
extreme perceptual challenges that involve both great viewpoint change and
environmental appearance change. We also provide experimental analyses of the
contributions of the various system components. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science"
] |
Title: Linear Additive Markov Processes,
Abstract: We introduce LAMP: the Linear Additive Markov Process. Transitions in LAMP
may be influenced by states visited in the distant history of the process, but
unlike higher-order Markov processes, LAMP retains an efficient
parametrization. LAMP also allows the specific dependence on history to be
learned efficiently from data. We characterize some theoretical properties of
LAMP, including its steady-state and mixing time. We then give an algorithm
based on alternating minimization to learn LAMP models from data. Finally, we
perform a series of real-world experiments to show that LAMP is more powerful
than first-order Markov processes, and even holds its own against deep
sequential models (LSTMs) with a negligible increase in parameter complexity. | [
1,
0,
0,
1,
0,
0
] | [
"Computer Science",
"Statistics"
] |
Title: Radial and circular synchronization clusters in extended starlike network of van der Pol oscillators,
Abstract: We consider extended starlike networks where the hub node is coupled with
several chains of nodes representing star rays. Assuming that nodes of the
network are occupied by nonidentical self-oscillators we study various forms of
their cluster synchronization. Radial cluster emerges when the nodes are
synchronized along a ray, while circular cluster is formed by nodes without
immediate connections but located on identical distances to the hub. By its
nature the circular synchronization is a new manifestation of so called remote
synchronization [Phys. Rev. E 85 (2012), 026208]. We report its long-range form
when the synchronized nodes interact through at least three intermediate nodes.
Forms of long-range remote synchronization are elements of scenario of
transition to the total synchronization of the network. We observe that the far
ends of rays synchronize first. Then more circular clusters appear involving
closer to hub nodes. Subsequently the clusters merge and, finally, all network
become synchronous. Behavior of the extended starlike networks is found to be
strongly determined by the ray length, while varying the number of rays
basically affects fine details of a dynamical picture. Symmetry of the star
also extensively influences the dynamics. In an asymmetric star circular
cluster mainly vanish in favor of radial ones, however, long-range remote
synchronization survives. | [
1,
1,
0,
0,
0,
0
] | [
"Physics",
"Mathematics"
] |
Title: TherML: Thermodynamics of Machine Learning,
Abstract: In this work we offer a framework for reasoning about a wide class of
existing objectives in machine learning. We develop a formal correspondence
between this work and thermodynamics and discuss its implications. | [
0,
0,
0,
1,
0,
0
] | [
"Computer Science",
"Physics"
] |
Title: Forecasting Across Time Series Databases using Recurrent Neural Networks on Groups of Similar Series: A Clustering Approach,
Abstract: With the advent of Big Data, nowadays in many applications databases
containing large quantities of similar time series are available. Forecasting
time series in these domains with traditional univariate forecasting procedures
leaves great potentials for producing accurate forecasts untapped. Recurrent
neural networks (RNNs), and in particular Long Short-Term Memory (LSTM)
networks, have proven recently that they are able to outperform
state-of-the-art univariate time series forecasting methods in this context
when trained across all available time series. However, if the time series
database is heterogeneous, accuracy may degenerate, so that on the way towards
fully automatic forecasting methods in this space, a notion of similarity
between the time series needs to be built into the methods. To this end, we
present a prediction model that can be used with different types of RNN models
on subgroups of similar time series, which are identified by time series
clustering techniques. We assess our proposed methodology using LSTM networks,
a widely popular RNN variant. Our method achieves competitive results on
benchmarking datasets under competition evaluation procedures. In particular,
in terms of mean sMAPE accuracy, it consistently outperforms the baseline LSTM
model and outperforms all other methods on the CIF2016 forecasting competition
dataset. | [
1,
0,
0,
1,
0,
0
] | [
"Computer Science",
"Statistics"
] |
Title: Probing magnetism in the vortex phase of PuCoGa$_5$ by X-ray magnetic circular dichroism,
Abstract: We have measured X-ray magnetic circular dichroism (XMCD) spectra at the Pu
$M_{4,5}$ absorption edges from a newly-prepared high-quality single crystal of
the heavy fermion superconductor $^{242}$PuCoGa$_{5}$, exhibiting a critical
temperature $T_{c} = 18.7~{\rm K}$. The experiment probes the vortex phase
below $T_{c}$ and shows that an external magnetic field induces a Pu 5$f$
magnetic moment at 2 K equal to the temperature-independent moment measured in
the normal phase up to 300 K by a SQUID device. This observation is in
agreement with theoretical models claiming that the Pu atoms in PuCoGa$_{5}$
have a nonmagnetic singlet ground state resulting from the hybridization of the
conduction electrons with the intermediate-valence 5$f$ electronic shell.
Unexpectedly, XMCD spectra show that the orbital component of the $5f$ magnetic
moment increases significantly between 30 and 2 K; the antiparallel spin
component increases as well, leaving the total moment practically constant. We
suggest that this indicates a low-temperature breakdown of the complete
Kondo-like screening of the local 5$f$ moment. | [
0,
1,
0,
0,
0,
0
] | [
"Physics"
] |
Title: Joint secrecy over the K-Transmitter Multiple Access Channel,
Abstract: This paper studies the problem of secure communication over a K-transmitter
multiple access channel in the presence of an external eavesdropper, subject to
a joint secrecy constraint (i.e., information leakage rate from the collection
of K messages to an eavesdropper is made vanishing). As a result, we establish
the joint secrecy achievable rate region. To this end, our results build upon
two techniques in addition to the standard information-theoretic methods. The
first is a generalization of Chia-El Gamal's lemma on entropy bound for a set
of codewords given partial information. The second is to utilize a compact
representation of a list of sets that, together with properties of mutual
information, leads to an efficient Fourier-Motzkin elimination. These two
approaches could also be of independent interests in other contexts. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science",
"Mathematics"
] |
Title: Well-posedness of nonlinear transport equation by stochastic perturbation,
Abstract: We are concerned with multidimensional nonlinear stochastic transport
equation driven by Brownian motions. For irregular fluxes, by using stochastic
BGK approximations and commutator estimates, we gain the existence and
uniqueness of stochastic entropy solutions. Besides, for $BV$ initial data, the
$BV$ and Hölder regularities are also derived for the unique stochastic
entropy solution. Particularly, for the transport equation, we gain a
regularization result, i.e. while the existence fails for the transport
equation, we prove that a multiplicative stochastic perturbation of Brownian
type is enough to render the equation well-posed. This seems to be another
explicit example (the first example is given in [22]) of a PDE of fluid
dynamics that becomes well-posed under the influence of a multiplicative
Brownian type noise. | [
0,
0,
1,
0,
0,
0
] | [
"Mathematics",
"Physics"
] |
Title: DropIn: Making Reservoir Computing Neural Networks Robust to Missing Inputs by Dropout,
Abstract: The paper presents a novel, principled approach to train recurrent neural
networks from the Reservoir Computing family that are robust to missing part of
the input features at prediction time. By building on the ensembling properties
of Dropout regularization, we propose a methodology, named DropIn, which
efficiently trains a neural model as a committee machine of subnetworks, each
capable of predicting with a subset of the original input features. We discuss
the application of the DropIn methodology in the context of Reservoir Computing
models and targeting applications characterized by input sources that are
unreliable or prone to be disconnected, such as in pervasive wireless sensor
networks and ambient intelligence. We provide an experimental assessment using
real-world data from such application domains, showing how the Dropin
methodology allows to maintain predictive performances comparable to those of a
model without missing features, even when 20\%-50\% of the inputs are not
available. | [
1,
0,
0,
1,
0,
0
] | [
"Computer Science",
"Statistics"
] |
Title: A Single-Channel Architecture for Algebraic Integer Based 8$\times$8 2-D DCT Computation,
Abstract: An area efficient row-parallel architecture is proposed for the real-time
implementation of bivariate algebraic integer (AI) encoded 2-D discrete cosine
transform (DCT) for image and video processing. The proposed architecture
computes 8$\times$8 2-D DCT transform based on the Arai DCT algorithm. An
improved fast algorithm for AI based 1-D DCT computation is proposed along with
a single channel 2-D DCT architecture. The design improves on the 4-channel AI
DCT architecture that was published recently by reducing the number of integer
channels to one and the number of 8-point 1-D DCT cores from 5 down to 2. The
architecture offers exact computation of 8$\times$8 blocks of the 2-D DCT
coefficients up to the FRS, which converts the coefficients from the AI
representation to fixed-point format using the method of expansion factors.
Prototype circuits corresponding to FRS blocks based on two expansion factors
are realized, tested, and verified on FPGA-chip, using a Xilinx Virtex-6
XC6VLX240T device. Post place-and-route results show a 20% reduction in terms
of area compared to the 2-D DCT architecture requiring five 1-D AI cores. The
area-time and area-time${}^2$ complexity metrics are also reduced by 23% and
22% respectively for designs with 8-bit input word length. The digital
realizations are simulated up to place and route for ASICs using 45 nm CMOS
standard cells. The maximum estimated clock rate is 951 MHz for the CMOS
realizations indicating 7.608$\cdot$10$^9$ pixels/seconds and a 8$\times$8
block rate of 118.875 MHz. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science",
"Mathematics"
] |
Title: How proper are Bayesian models in the astronomical literature?,
Abstract: The well-known Bayes theorem assumes that a posterior distribution is a
probability distribution. However, the posterior distribution may no longer be
a probability distribution if an improper prior distribution (non-probability
measure) such as an unbounded uniform prior is used. Improper priors are often
used in the astronomical literature to reflect a lack of prior knowledge, but
checking whether the resulting posterior is a probability distribution is
sometimes neglected. It turns out that 23 articles out of 75 articles (30.7%)
published online in two renowned astronomy journals (ApJ and MNRAS) between Jan
1, 2017 and Oct 15, 2017 make use of Bayesian analyses without rigorously
establishing posterior propriety. A disturbing aspect is that a Gibbs-type
Markov chain Monte Carlo (MCMC) method can produce a seemingly reasonable
posterior sample even when the posterior is not a probability distribution
(Hobert and Casella, 1996). In such cases, researchers may erroneously make
probabilistic inferences without noticing that the MCMC sample is from a
non-existing probability distribution. We review why checking posterior
propriety is fundamental in Bayesian analyses, and discuss how to set up
scientifically motivated proper priors. | [
0,
1,
0,
0,
0,
0
] | [
"Statistics",
"Physics"
] |
Title: Von Neumann dimension, Hodge index theorem and geometric applications,
Abstract: This note contains a reformulation of the Hodge index theorem within the
framework of Atiyah's $L^2$-index theory. More precisely, given a compact
Kähler manifold $(M,h)$ of even complex dimension $2m$, we prove that
$$\sigma(M)=\sum_{p,q=0}^{2m}(-1)^ph_{(2),\Gamma}^{p,q}(M)$$ where $\sigma(M)$
is the signature of $M$ and $h_{(2),\Gamma}^{p,q}(M)$ are the $L^2$-Hodge
numbers of $M$ with respect to a Galois covering having $\Gamma$ as group of
Deck transformations. Likewise we also prove an $L^2$-version of the
Frölicher index theorem. Afterwards we give some applications of these two
theorems and finally we conclude this paper by collecting other properties of
the $L^2$-Hodge numbers. | [
0,
0,
1,
0,
0,
0
] | [
"Mathematics"
] |
Title: Hybrid CTC-Attention based End-to-End Speech Recognition using Subword Units,
Abstract: In this paper, we present an end-to-end automatic speech recognition system,
which successfully employs subword units in a hybrid CTC-Attention based
system. The subword units are obtained by the byte-pair encoding (BPE)
compression algorithm. Compared to using words as modeling units, using
characters or subword units does not suffer from the out-of-vocabulary (OOV)
problem. Furthermore, using subword units further offers a capability in
modeling longer context than using characters. We evaluate different systems
over the LibriSpeech 1000h dataset. The subword-based hybrid CTC-Attention
system obtains 6.8% word error rate (WER) on the test_clean subset without any
dictionary or external language model. This represents a significant
improvement (a 12.8% WER relative reduction) over the character-based hybrid
CTC-Attention system. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science"
] |
Title: Weak lensing power spectrum reconstruction by counting galaxies.-- I: the ABS method,
Abstract: We propose an Analytical method of Blind Separation (ABS) of cosmic
magnification from the intrinsic fluctuations of galaxy number density in the
observed galaxy number density distribution. The ABS method utilizes the
different dependences of the signal (cosmic magnification) and contamination
(galaxy intrinsic clustering) on galaxy flux, to separate the two. It works
directly on the measured cross galaxy angular power spectra between different
flux bins. It determines/reconstructs the lensing power spectrum analytically,
without assumptions of galaxy intrinsic clustering and cosmology. It is
unbiased in the limit of infinite number of galaxies. In reality the lensing
reconstruction accuracy depends on survey configurations, galaxy biases, and
other complexities, due to finite number of galaxies and the resulting shot
noise fluctuations in the cross galaxy power spectra. We estimate its
performance (systematic and statistical errors) in various cases. We find that,
stage IV dark energy surveys such as SKA and LSST are capable of reconstructing
the lensing power spectrum at $z\simeq 1$ and $\ell\la 5000$ accurately. This
lensing reconstruction only requires counting galaxies, and is therefore highly
complementary to the cosmic shear measurement by the same surveys. | [
0,
1,
0,
0,
0,
0
] | [
"Physics",
"Astrophysics",
"Statistics"
] |
Title: Optimal Output Consensus of High-Order Multi-Agent Systems with Embedded Technique,
Abstract: In this paper, we study an optimal output consensus problem for a multi-agent
network with agents in the form of multi-input multi-output minimum-phase
dynamics. Optimal output consensus can be taken as an extended version of the
existing output consensus problem for higher-order agents with an optimization
requirement, where the output variables of agents are driven to achieve a
consensus on the optimal solution of a global cost function. To solve this
problem, we first construct an optimal signal generator, and then propose an
embedded control scheme by embedding the generator in the feedback loop. We
give two kinds of algorithms based on different available information along
with both state feedback and output feedback, and prove that these algorithms
with the embedded technique can guarantee the solvability of the problem for
high-order multi-agent systems under standard assumptions. | [
1,
0,
1,
0,
0,
0
] | [
"Computer Science",
"Mathematics"
] |
Title: Predicting Parkinson's Disease using Latent Information extracted from Deep Neural Networks,
Abstract: This paper presents a new method for medical diagnosis of neurodegenerative
diseases, such as Parkinson's, by extracting and using latent information from
trained Deep convolutional, or convolutional-recurrent Neural Networks (DNNs).
In particular, our approach adopts a combination of transfer learning, k-means
clustering and k-Nearest Neighbour classification of deep neural network
learned representations to provide enriched prediction of the disease based on
MRI and/or DaT Scan data. A new loss function is introduced and used in the
training of the DNNs, so as to perform adaptation of the generated learned
representations between data from different medical environments. Results are
presented using a recently published database of Parkinson's related
information, which was generated and evaluated in a hospital environment. | [
1,
0,
0,
1,
0,
0
] | [
"Computer Science",
"Quantitative Biology"
] |
Title: Representation Theorems for Solvable Sesquilinear Forms,
Abstract: New results are added to the paper [4] about q-closed and solvable
sesquilinear forms. The structure of the Banach space
$\mathcal{D}[||\cdot||_\Omega]$ defined on the domain $\mathcal{D}$ of a
q-closed sesquilinear form $\Omega$ is unique up to isomorphism, and the
adjoint of a sesquilinear form has the same property of q-closure or of
solvability. The operator associated to a solvable sesquilinear form is the
greatest which represents the form and it is self-adjoint if, and only if, the
form is symmetric. We give more criteria of solvability for q-closed
sesquilinear forms. Some of these criteria are related to the numerical range,
and we analyse in particular the forms which are solvable with respect to inner
products. The theory of solvable sesquilinear forms generalises those of many
known sesquilinear forms in literature. | [
0,
0,
1,
0,
0,
0
] | [
"Mathematics"
] |
Title: Spectral Efficient and Energy Aware Clustering in Cellular Networks,
Abstract: The current and envisaged increase of cellular traffic poses new challenges
to Mobile Network Operators (MNO), who must densify their Radio Access Networks
(RAN) while maintaining low Capital Expenditure and Operational Expenditure to
ensure long-term sustainability. In this context, this paper analyses optimal
clustering solutions based on Device-to-Device (D2D) communications to mitigate
partially or completely the need for MNOs to carry out extremely dense RAN
deployments. Specifically, a low complexity algorithm that enables the creation
of spectral efficient clusters among users from different cells, denoted as
enhanced Clustering Optimization for Resources' Efficiency (eCORE) is
presented. Due to the imbalance between uplink and downlink traffic, a
complementary algorithm, known as Clustering algorithm for Load Balancing
(CaLB), is also proposed to create non-spectral efficient clusters when they
result in a capacity increase. Finally, in order to alleviate the energy
overconsumption suffered by cluster heads, the Clustering Energy Efficient
algorithm (CEEa) is also designed to manage the trade-off between the capacity
enhancement and the early battery drain of some users. Results show that the
proposed algorithms increase the network capacity and outperform existing
solutions, while, at the same time, CEEa is able to handle the cluster heads
energy overconsumption. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science"
] |
Title: A Brain-Inspired Trust Management Model to Assure Security in a Cloud based IoT Framework for Neuroscience Applications,
Abstract: Rapid popularity of Internet of Things (IoT) and cloud computing permits
neuroscientists to collect multilevel and multichannel brain data to better
understand brain functions, diagnose diseases, and devise treatments. To ensure
secure and reliable data communication between end-to-end (E2E) devices
supported by current IoT and cloud infrastructure, trust management is needed
at the IoT and user ends. This paper introduces a Neuro-Fuzzy based
Brain-inspired trust management model (TMM) to secure IoT devices and relay
nodes, and to ensure data reliability. The proposed TMM utilizes node
behavioral trust and data trust estimated using Adaptive Neuro-Fuzzy Inference
System and weighted-additive methods respectively to assess the nodes
trustworthiness. In contrast to the existing fuzzy based TMMs, the NS2
simulation results confirm the robustness and accuracy of the proposed TMM in
identifying malicious nodes in the communication network. With the growing
usage of cloud based IoT frameworks in Neuroscience research, integrating the
proposed TMM into the existing infrastructure will assure secure and reliable
data communication among the E2E devices. | [
0,
0,
0,
0,
1,
0
] | [
"Computer Science",
"Quantitative Biology"
] |
Title: A Neural Network Approach for Mixing Language Models,
Abstract: The performance of Neural Network (NN)-based language models is steadily
improving due to the emergence of new architectures, which are able to learn
different natural language characteristics. This paper presents a novel
framework, which shows that a significant improvement can be achieved by
combining different existing heterogeneous models in a single architecture.
This is done through 1) a feature layer, which separately learns different
NN-based models and 2) a mixture layer, which merges the resulting model
features. In doing so, this architecture benefits from the learning
capabilities of each model with no noticeable increase in the number of model
parameters or the training time. Extensive experiments conducted on the Penn
Treebank (PTB) and the Large Text Compression Benchmark (LTCB) corpus showed a
significant reduction of the perplexity when compared to state-of-the-art
feedforward as well as recurrent neural network architectures. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science"
] |
Title: DCFNet: Deep Neural Network with Decomposed Convolutional Filters,
Abstract: Filters in a Convolutional Neural Network (CNN) contain model parameters
learned from enormous amounts of data. In this paper, we suggest to decompose
convolutional filters in CNN as a truncated expansion with pre-fixed bases,
namely the Decomposed Convolutional Filters network (DCFNet), where the
expansion coefficients remain learned from data. Such a structure not only
reduces the number of trainable parameters and computation, but also imposes
filter regularity by bases truncation. Through extensive experiments, we
consistently observe that DCFNet maintains accuracy for image classification
tasks with a significant reduction of model parameters, particularly with
Fourier-Bessel (FB) bases, and even with random bases. Theoretically, we
analyze the representation stability of DCFNet with respect to input
variations, and prove representation stability under generic assumptions on the
expansion coefficients. The analysis is consistent with the empirical
observations. | [
0,
0,
0,
1,
0,
0
] | [
"Computer Science",
"Statistics"
] |
Title: Symmetries, Invariants and Generating Functions: Higher-order Statistics of Biased Tracers,
Abstract: Gravitationally collapsed objects are known to be biased tracers of an
underlying density contrast. Using symmetry arguments, generalised biasing
schemes have recently been developed to relate the halo density contrast
$\delta_h$ with the underlying density contrast $\delta$, divergence of
velocity $\theta$ and their higher-order derivatives. This is done by
constructing invariants such as $s, t, \psi,\eta$. We show how the generating
function formalism in Eulerian standard perturbation theory (SPT) can be used
to show that many of the additional terms based on extended Galilean and
Lifshitz symmetry actually do not make any contribution to the higher-order
statistics of biased tracers. Other terms can also be drastically simplified
allowing us to write the vertices associated with $\delta_h$ in terms of the
vertices of $\delta$ and $\theta$, the higher-order derivatives and the bias
coefficients. We also compute the cumulant correlators (CCs) for two different
tracer populations. These perturbative results are valid for tree-level
contributions but at an arbitrary order. We also take into account the
stochastic nature bias in our analysis. Extending previous results of a local
polynomial model of bias, we express the one-point cumulants ${\cal S}_N$ and
their two-point counterparts, the CCs i.e. ${\cal C}_{pq}$, of biased tracers
in terms of that of their underlying density contrast counterparts. As a
by-product of our calculation we also discuss the results using approximations
based on Lagrangian perturbation theory (LPT). | [
0,
1,
0,
0,
0,
0
] | [
"Physics",
"Mathematics"
] |
Title: Nonparametric Variational Auto-encoders for Hierarchical Representation Learning,
Abstract: The recently developed variational autoencoders (VAEs) have proved to be an
effective confluence of the rich representational power of neural networks with
Bayesian methods. However, most work on VAEs use a rather simple prior over the
latent variables such as standard normal distribution, thereby restricting its
applications to relatively simple phenomena. In this work, we propose
hierarchical nonparametric variational autoencoders, which combines
tree-structured Bayesian nonparametric priors with VAEs, to enable infinite
flexibility of the latent representation space. Both the neural parameters and
Bayesian priors are learned jointly using tailored variational inference. The
resulting model induces a hierarchical structure of latent semantic concepts
underlying the data corpus, and infers accurate representations of data
instances. We apply our model in video representation learning. Our method is
able to discover highly interpretable activity hierarchies, and obtain improved
clustering accuracy and generalization capacity based on the learned rich
representations. | [
1,
0,
0,
1,
0,
0
] | [
"Computer Science",
"Statistics"
] |
Title: Corpus-compressed Streaming and the Spotify Problem,
Abstract: In this work, we describe a problem which we refer to as the \textbf{Spotify
problem} and explore a potential solution in the form of what we call
corpus-compressed streaming schemes.
Inspired by the problem of constrained bandwidth during use of the popular
Spotify application on mobile networks, the Spotify problem applies in any
number of practical domains where devices may be periodically expected to
experience degraded communication or storage capacity. One obvious solution
candidate which comes to mind immediately is standard compression. Though
obviously applicable, standard compression does not in any way exploit all
characteristics of the problem; in particular, standard compression is
oblivious to the fact that a decoder has a period of virtually unrestrained
communication. Towards applying compression in a manner which attempts to
stretch the benefit of periods of higher communication capacity into periods of
restricted capacity, we introduce as a solution the idea of a corpus-compressed
streaming scheme.
This report begins with a formal definition of a corpus-compressed streaming
scheme. Following a discussion of how such schemes apply to the Spotify
problem, we then give a survey of specific corpus-compressed scheming schemes
guided by an exploration of different measures of description complexity within
the Chomsky hierarchy of languages. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science"
] |
Title: An intrinsic parallel transport in Wasserstein space,
Abstract: If M is a smooth compact connected Riemannian manifold, let P(M) denote the
Wasserstein space of probability measures on M. We describe a geometric
construction of parallel transport of some tangent cones along geodesics in
P(M). We show that when everything is smooth, the geometric parallel transport
agrees with earlier formal calculations. | [
0,
0,
1,
0,
0,
0
] | [
"Mathematics"
] |
Title: Factor Analysis for Spectral Estimation,
Abstract: Power spectrum estimation is an important tool in many applications, such as
the whitening of noise. The popular multitaper method enjoys significant
success, but fails for short signals with few samples. We propose a statistical
model where a signal is given by a random linear combination of fixed, yet
unknown, stochastic sources. Given multiple such signals, we estimate the
subspace spanned by the power spectra of these fixed sources. Projecting
individual power spectrum estimates onto this subspace increases estimation
accuracy. We provide accuracy guarantees for this method and demonstrate it on
simulated and experimental data from cryo-electron microscopy. | [
0,
0,
1,
1,
0,
0
] | [
"Statistics",
"Mathematics"
] |
Title: GoT-WAVE: Temporal network alignment using graphlet-orbit transitions,
Abstract: Global pairwise network alignment (GPNA) aims to find a one-to-one node
mapping between two networks that identifies conserved network regions. GPNA
algorithms optimize node conservation (NC) and edge conservation (EC). NC
quantifies topological similarity between nodes. Graphlet-based degree vectors
(GDVs) are a state-of-the-art topological NC measure. Dynamic GDVs (DGDVs) were
used as a dynamic NC measure within the first-ever algorithms for GPNA of
temporal networks: DynaMAGNA++ and DynaWAVE. The latter is superior for larger
networks. We recently developed a different graphlet-based measure of temporal
node similarity, graphlet-orbit transitions (GoTs). Here, we use GoTs instead
of DGDVs as a new dynamic NC measure within DynaWAVE, resulting in a new
approach, GoT-WAVE.
On synthetic networks, GoT-WAVE improves DynaWAVE's accuracy by 25% and speed
by 64%. On real networks, when optimizing only dynamic NC, each method is
superior ~50% of the time. While DynaWAVE benefits more from also optimizing
dynamic EC, only GoT-WAVE can support directed edges. Hence, GoT-WAVE is a
promising new temporal GPNA algorithm, which efficiently optimizes dynamic NC.
Future work on better incorporating dynamic EC may yield further improvements. | [
1,
0,
0,
1,
0,
0
] | [
"Computer Science",
"Mathematics"
] |
Title: Symmetric structure for the endomorphism algebra of projective-injective module in parabolic category,
Abstract: We show that for any singular dominant integral weight $\lambda$ of a complex
semisimple Lie algebra $\mathfrak{g}$, the endomorphism algebra $B$ of any
projective-injective module of the parabolic BGG category
$\mathcal{O}_\lambda^{\mathfrak{p}}$ is a symmetric algebra (as conjectured by
Khovanov) extending the results of Mazorchuk and Stroppel for the regular
dominant integral weight. Moreover, the endomorphism algebra $B$ is equipped
with a homogeneous (non-degenerate) symmetrizing form. In the appendix, there
is a short proof due to K. Coulembier and V. Mazorchuk showing that the
endomorphism algebra $B_\lambda^{\mathfrak{p}}$ of the basic
projective-injective module of $\mathcal{O}_\lambda^{\mathfrak{p}}$ is a
symmetric algebra. | [
0,
0,
1,
0,
0,
0
] | [
"Mathematics"
] |
Title: Kähler metrics via Lorentzian Geometry in dimension four,
Abstract: Given a semi-Riemannian $4$-manifold $(M,g)$ with two distinguished vector
fields satisfying properties determined by their shear, twist and various Lie
bracket relations, a family of Kähler metrics $g_K$ is constructed, defined
on an open set in $M$, which coincides with $M$ in many typical examples. Under
certain conditions $g$ and $g_K$ share various properties, such as a Killing
vector field or a vector field with a geodesic flow. In some cases the Kähler
metrics are complete. The Ricci and scalar curvatures of $g_K$ are computed
under certain assumptions in terms of data associated to $g$. Many examples are
described, including classical spacetimes in warped products, for instance de
Sitter spacetime, as well as gravitational plane waves, metrics of Petrov type
$D$ such as Kerr and NUT metrics, and metrics for which $g_K$ is an SKR metric.
For the latter an inverse ansatz is described, constructing $g$ from the SKR
metric. | [
0,
0,
1,
0,
0,
0
] | [
"Mathematics",
"Physics"
] |
Title: Sleep Stage Classification Based on Multi-level Feature Learning and Recurrent Neural Networks via Wearable Device,
Abstract: This paper proposes a practical approach for automatic sleep stage
classification based on a multi-level feature learning framework and Recurrent
Neural Network (RNN) classifier using heart rate and wrist actigraphy derived
from a wearable device. The feature learning framework is designed to extract
low- and mid-level features. Low-level features capture temporal and frequency
domain properties and mid-level features learn compositions and structural
information of signals. Since sleep staging is a sequential problem with
long-term dependencies, we take advantage of RNNs with Bidirectional Long
Short-Term Memory (BLSTM) architectures for sequence data learning. To simulate
the actual situation of daily sleep, experiments are conducted with a resting
group in which sleep is recorded in resting state, and a comprehensive group in
which both resting sleep and non-resting sleep are included.We evaluate the
algorithm based on an eight-fold cross validation to classify five sleep stages
(W, N1, N2, N3, and REM). The proposed algorithm achieves weighted precision,
recall and F1 score of 58.0%, 60.3%, and 58.2% in the resting group and 58.5%,
61.1%, and 58.5% in the comprehensive group, respectively. Various comparison
experiments demonstrate the effectiveness of feature learning and BLSTM. We
further explore the influence of depth and width of RNNs on performance. Our
method is specially proposed for wearable devices and is expected to be
applicable for long-term sleep monitoring at home. Without using too much prior
domain knowledge, our method has the potential to generalize sleep disorder
detection. | [
1,
0,
0,
1,
0,
0
] | [
"Computer Science",
"Quantitative Biology"
] |
Title: Martin David Kruskal: a biographical memoir,
Abstract: Martin David Kruskal was one of the most versatile theoretical physicists of
his generation and is distinguished for his enduring work in several different
areas, most notably plasma physics, a memorable detour into relativity, and his
pioneering work in nonlinear waves. In the latter, together with Norman
Zabusky, he invented the concept of the soliton and, with others, developed its
application to classes of partial differential equations of physical
significance. | [
0,
1,
0,
0,
0,
0
] | [
"Physics",
"Mathematics"
] |
Title: Unified theory for finite Markov chains,
Abstract: We provide a unified framework to compute the stationary distribution of any
finite irreducible Markov chain or equivalently of any irreducible random walk
on a finite semigroup $S$. Our methods use geometric finite semigroup theory
via the Karnofsky-Rhodes and the McCammond expansions of finite semigroups with
specified generators; this does not involve any linear algebra. The original
Tsetlin library is obtained by applying the expansions to $P(n)$, the set of
all subsets of an $n$ element set. Our set-up generalizes previous
groundbreaking work involving left-regular bands (or $\mathscr{R}$-trivial
bands) by Brown and Diaconis, extensions to $\mathscr{R}$-trivial semigroups by
Ayyer, Steinberg, Thiéry and the second author, and important recent work by
Chung and Graham. The Karnofsky-Rhodes expansion of the right Cayley graph of
$S$ in terms of generators yields again a right Cayley graph. The McCammond
expansion provides normal forms for elements in the expanded $S$. Using our
previous results with Silva based on work by Berstel, Perrin, Reutenauer, we
construct (infinite) semaphore codes on which we can define Markov chains.
These semaphore codes can be lumped using geometric semigroup theory. Using
normal forms and associated Kleene expressions, they yield formulas for the
stationary distribution of the finite Markov chain of the expanded $S$ and the
original $S$. Analyzing the normal forms also provides an estimate on the
mixing time. | [
0,
0,
1,
0,
0,
0
] | [
"Mathematics",
"Computer Science"
] |
Title: Crowd ideation of supervised learning problems,
Abstract: Crowdsourcing is an important avenue for collecting machine learning data,
but crowdsourcing can go beyond simple data collection by employing the
creativity and wisdom of crowd workers. Yet crowd participants are unlikely to
be experts in statistics or predictive modeling, and it is not clear how well
non-experts can contribute creatively to the process of machine learning. Here
we study an end-to-end crowdsourcing algorithm where groups of non-expert
workers propose supervised learning problems, rank and categorize those
problems, and then provide data to train predictive models on those problems.
Problem proposal includes and extends feature engineering because workers
propose the entire problem, not only the input features but also the target
variable. We show that workers without machine learning experience can
collectively construct useful datasets and that predictive models can be
learned on these datasets. In our experiments, the problems proposed by workers
covered a broad range of topics, from politics and current events to problems
capturing health behavior, demographics, and more. Workers also favored
questions showing positively correlated relationships, which has interesting
implications given many supervised learning methods perform as well with strong
negative correlations. Proper instructions are crucial for non-experts, so we
also conducted a randomized trial to understand how different instructions may
influence the types of problems proposed by workers. In general, shifting the
focus of machine learning tasks from designing and training individual
predictive models to problem proposal allows crowdsourcers to design
requirements for problems of interest and then guide workers towards
contributing to the most suitable problems. | [
0,
0,
0,
1,
0,
0
] | [
"Computer Science",
"Statistics"
] |
Title: Joins in the strong Weihrauch degrees,
Abstract: The Weihrauch degrees and strong Weihrauch degrees are partially ordered
structures representing degrees of unsolvability of various mathematical
problems. Their study has been widely applied in computable analysis,
complexity theory, and more recently, also in computable combinatorics. We
answer an open question about the algebraic structure of the strong Weihrauch
degrees, by exhibiting a join operation that turns these degrees into a
lattice. Previously, the strong Weihrauch degrees were only known to form a
lower semi-lattice. We then show that unlike the Weihrauch degrees, which are
known to form a distributive lattice, the lattice of strong Weihrauch degrees
is not distributive. Therefore, the two structures are not isomorphic. | [
1,
0,
1,
0,
0,
0
] | [
"Mathematics",
"Computer Science"
] |
Title: A combinatorial model for the free loop fibration,
Abstract: We introduce the abstract notion of a closed necklical set in order to
describe a functorial combinatorial model of the free loop fibration $\Omega
Y\rightarrow \Lambda Y\rightarrow Y$ over the geometric realization $Y=|X|$ of
a path connected simplicial set $X.$ In particular, to any path connected
simplicial set $X$ we associate a closed necklical set
$\widehat{\mathbf{\Lambda}}X$ such that its geometric realization
$|\widehat{\mathbf{\Lambda}}X|$, a space built out of gluing "freehedrical" and
"cubical" cells, is homotopy equivalent to the free loop space $\Lambda Y$ and
the differential graded module of chains $C_*(\widehat{\mathbf{\Lambda}}X)$
generalizes the coHochschild chain complex of the chain coalgebra $C_\ast(X).$ | [
0,
0,
1,
0,
0,
0
] | [
"Mathematics"
] |
Title: Detailed proof of Nazarov's inequality,
Abstract: The purpose of this note is to provide a detailed proof of Nazarov's
inequality stated in Lemma A.1 in Chernozhukov, Chetverikov, and Kato (2017,
Annals of Probability). | [
0,
0,
1,
1,
0,
0
] | [
"Mathematics"
] |
Title: TRPL+K: Thick-Restart Preconditioned Lanczos+K Method for Large Symmetric Eigenvalue Problems,
Abstract: The Lanczos method is one of the standard approaches for computing a few
eigenpairs of a large, sparse, symmetric matrix. It is typically used with
restarting to avoid unbounded growth of memory and computational requirements.
Thick-restart Lanczos is a popular restarted variant because of its simplicity
and numerically robustness. However, convergence can be slow for highly
clustered eigenvalues so more effective restarting techniques and the use of
preconditioning is needed. In this paper, we present a thick-restart
preconditioned Lanczos method, TRPL+K, that combines the power of locally
optimal restarting (+K) and preconditioning techniques with the efficiency of
the thick-restart Lanczos method. TRPL+K employs an inner-outer scheme where
the inner loop applies Lanczos on a preconditioned operator while the outer
loop augments the resulting Lanczos subspace with certain vectors from the
previous restart cycle to obtain eigenvector approximations with which it thick
restarts the outer subspace. We first identify the differences from various
relevant methods in the literature. Then, based on an optimization perspective,
we show an asymptotic global quasi-optimality of a simplified TRPL+K method
compared to an unrestarted global optimal method. Finally, we present extensive
experiments showing that TRPL+K either outperforms or matches other
state-of-the-art eigenmethods in both matrix-vector multiplications and
computational time. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science",
"Mathematics"
] |
Title: e-Fair: Aggregation in e-Commerce for Exploiting Economies of Scale,
Abstract: In recent years, many new and interesting models of successful online
business have been developed, including competitive models such as auctions,
where the product price tends to rise, and group-buying, where users cooperate
obtaining a dynamic price that tends to go down. We propose the e-fair as a
business model for social commerce, where both sellers and buyers are grouped
to maximize benefits. e-Fairs extend the group-buying model aggregating demand
and supply for price optimization as well as consolidating shipments and
optimize withdrawals for guaranteeing additional savings. e-Fairs work upon
multiple dimensions: time to aggregate buyers, their geographical distribution,
price/quantity curves provided by sellers, and location of withdrawal points.
We provide an analytical model for time and spatial optimization and simulate
realistic scenarios using both real purchase data from an Italian marketplace
and simulated ones. Experimental results demonstrate the potentials offered by
e-fairs and show benefits for all the involved actors. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science",
"Quantitative Finance"
] |
Title: Stable spike clusters for the precursor Gierer-Meinhardt system in R2,
Abstract: We consider the Gierer-Meinhardt system with small inhibitor diffusivity,
very small activator diffusivity and a precursor inhomogeneity.
For any given positive integer k we construct a spike cluster consisting of
$k$ spikes which all approach the same nondegenerate local minimum point of the
precursor inhomogeneity. We show that this spike cluster can be linearly
stable. In particular, we show the existence of spike clusters for spikes
located at the vertices of a polygon with or without centre. Further, the
cluster without centre is stable for up to three spikes, whereas the cluster
with centre is stable for up to six spikes.
The main idea underpinning these stable spike clusters is the following: due
to the small inhibitor diffusivity the interaction between spikes is repulsive,
and the spikes are attracted towards the local minimum point of the precursor
inhomogeneity. Combining these two effects can lead to an equilibrium of spike
positions within the cluster such that the cluster is linearly stable. | [
0,
0,
1,
0,
0,
0
] | [
"Mathematics"
] |
Title: Scaling Limits for Super--replication with Transient Price Impact,
Abstract: We prove limit theorems for the super-replication cost of European options in
a Binomial model with transient price impact. We show that if the time step
goes to zero and the effective resilience between consecutive trading times
remains constant then the limit of the super--replication prices coincide with
the scaling limit for temporary price impact with a modified market depth. | [
0,
0,
0,
0,
0,
1
] | [
"Quantitative Finance",
"Mathematics"
] |
Title: Kernel-based Inference of Functions over Graphs,
Abstract: The study of networks has witnessed an explosive growth over the past decades
with several ground-breaking methods introduced. A particularly interesting --
and prevalent in several fields of study -- problem is that of inferring a
function defined over the nodes of a network. This work presents a versatile
kernel-based framework for tackling this inference problem that naturally
subsumes and generalizes the reconstruction approaches put forth recently by
the signal processing on graphs community. Both the static and the dynamic
settings are considered along with effective modeling approaches for addressing
real-world problems. The herein analytical discussion is complemented by a set
of numerical examples, which showcase the effectiveness of the presented
techniques, as well as their merits related to state-of-the-art methods. | [
1,
0,
0,
1,
0,
0
] | [
"Computer Science",
"Mathematics"
] |
Title: Noncommutative products of Euclidean spaces,
Abstract: We present natural families of coordinate algebras of noncommutative products
of Euclidean spaces. These coordinate algebras are quadratic ones associated
with an R-matrix which is involutive and satisfies the Yang-Baxter equations.
As a consequence they enjoy a list of nice properties, being regular of finite
global dimension. Notably, we have eight-dimensional noncommutative euclidean
spaces which are particularly well behaved and are deformations parametrised by
a two-dimensional sphere. Quotients include noncommutative seven-spheres as
well as noncommutative "quaternionic tori". There is invariance for an action
of $SU(2) \times SU(2)$ in parallel with the action of $U(1) \times U(1)$ on a
"complex" noncommutative torus which allows one to construct quaternionic toric
noncommutative manifolds. Additional classes of solutions are disjoint from the
classical case. | [
0,
0,
1,
0,
0,
0
] | [
"Mathematics",
"Physics"
] |
Title: Reservoir Computing for Detection of Steady State in Performance Tests of Compressors,
Abstract: Fabrication of devices in industrial plants often includes undergoing quality
assurance tests or tests that seek to determine some attributes or capacities
of the device. For instance, in testing refrigeration compressors, we want to
find the true refrigeration capacity of the compressor being tested. Such test
(also called an episode) may take up to four hours, being an actual hindrance
to applying it to the total number of compressors produced. This work seeks to
reduce the time spent on such industrial trials by employing Recurrent Neural
Networks (RNNs) as dynamical models for detecting when a test is entering the
so-called steady-state region. Specifically, we use Reservoir Computing (RC)
networks which simplify the learning of RNNs by speeding up training time and
showing convergence to a global optimum. Also, this work proposes a
self-organized subspace projection method for RC networks which uses
information from the beginning of the episode to define a cluster to which the
episode belongs to. This assigned cluster defines a particular binary input
that shifts the operating point of the reservoir to a subspace of trajectories
for the duration of the episode. This new method is shown to turn the RC model
robust in performance with respect to varying combination of reservoir
parameters, such as spectral radius and leak rate, when compared to a standard
RC network. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science",
"Statistics"
] |
Title: Temporal-related Convolutional-Restricted-Boltzmann-Machine capable of learning relational order via reinforcement learning procedure?,
Abstract: In this article, we extend the conventional framework of
convolutional-Restricted-Boltzmann-Machine to learn highly abstract features
among abitrary number of time related input maps by constructing a layer of
multiplicative units, which capture the relations among inputs. In many cases,
more than two maps are strongly related, so it is wise to make multiplicative
unit learn relations among more input maps, in other words, to find the optimal
relational-order of each unit. In order to enable our machine to learn
relational order, we developed a reinforcement-learning method whose optimality
is proven to train the network. | [
1,
0,
0,
1,
0,
0
] | [
"Computer Science",
"Statistics"
] |
Title: Predicting how and when hidden neurons skew measured synaptic interactions,
Abstract: A major obstacle to understanding neural coding and computation is the fact
that experimental recordings typically sample only a small fraction of the
neurons in a circuit. Measured neural properties are skewed by interactions
between recorded neurons and the "hidden" portion of the network. To properly
interpret neural data and determine how biological structure gives rise to
neural circuit function, we thus need a better understanding of the
relationships between measured effective neural properties and the true
underlying physiological properties. Here, we focus on how the effective
spatiotemporal dynamics of the synaptic interactions between neurons are
reshaped by coupling to unobserved neurons. We find that the effective
interactions from a pre-synaptic neuron $r'$ to a post-synaptic neuron $r$ can
be decomposed into a sum of the true interaction from $r'$ to $r$ plus
corrections from every directed path from $r'$ to $r$ through unobserved
neurons. Importantly, the resulting formula reveals when the hidden units
have---or do not have---major effects on reshaping the interactions among
observed neurons. As a particular example of interest, we derive a formula for
the impact of hidden units in random networks with "strong"
coupling---connection weights that scale with $1/\sqrt{N}$, where $N$ is the
network size, precisely the scaling observed in recent experiments. With this
quantitative relationship between measured and true interactions, we can study
how network properties shape effective interactions, which properties are
relevant for neural computations, and how to manipulate effective interactions. | [
0,
1,
0,
0,
0,
0
] | [
"Quantitative Biology",
"Statistics"
] |
Title: Stateless Puzzles for Real Time Online Fraud Preemption,
Abstract: The profitability of fraud in online systems such as app markets and social
networks marks the failure of existing defense mechanisms. In this paper, we
propose FraudSys, a real-time fraud preemption approach that imposes
Bitcoin-inspired computational puzzles on the devices that post online system
activities, such as reviews and likes. We introduce and leverage several novel
concepts that include (i) stateless, verifiable computational puzzles, that
impose minimal performance overhead, but enable the efficient verification of
their authenticity, (ii) a real-time, graph-based solution to assign fraud
scores to user activities, and (iii) mechanisms to dynamically adjust puzzle
difficulty levels based on fraud scores and the computational capabilities of
devices. FraudSys does not alter the experience of users in online systems, but
delays fraudulent actions and consumes significant computational resources of
the fraudsters. Using real datasets from Google Play and Facebook, we
demonstrate the feasibility of FraudSys by showing that the devices of honest
users are minimally impacted, while fraudster controlled devices receive daily
computational penalties of up to 3,079 hours. In addition, we show that with
FraudSys, fraud does not pay off, as a user equipped with mining hardware
(e.g., AntMiner S7) will earn less than half through fraud than from honest
Bitcoin mining. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science",
"Quantitative Finance"
] |
Title: Pore cross-talk in colloidal filtration,
Abstract: Blockage of pores by particles is found in many processes, including
filtration and oil extraction. We present filtration experiments through a
linear array of ten channels with one dimension which is sub-micron, through
which a dilute dispersion of Brownian polystyrene spheres flows under the
action of a fixed pressure drop. The growth rate of a clog formed by particles
at a pore entrance systematically increases with the number of already
saturated (entirely clogged) pores, indicating that there is an interaction or
"cross-talk" between the pores. This observation is interpreted based on a
phenomenological model, stating that a diffusive redistribution of particles
occurs along the membrane, from clogged to free pores. This one-dimensional
model could be extended to two-dimensional membranes. | [
0,
1,
0,
0,
0,
0
] | [
"Physics"
] |
Title: Explicit minimisation of a convex quadratic under a general quadratic constraint: a global, analytic approach,
Abstract: A novel approach is introduced to a very widely occurring problem, providing
a complete, explicit resolution of it: minimisation of a convex quadratic under
a general quadratic, equality or inequality, constraint. Completeness comes via
identification of a set of mutually exclusive and exhaustive special cases.
Explicitness, via algebraic expressions for each solution set. Throughout,
underlying geometry illuminates and informs algebraic development. In
particular, centrally to this new approach, affine equivalence is exploited to
re-express the same problem in simpler coordinate systems. Overall, the
analysis presented provides insight into the diverse forms taken both by the
problem itself and its solution set, showing how each may be intrinsically
unstable. Comparisons of this global, analytic approach with the, intrinsically
complementary, local, computational approach of (generalised) trust region
methods point to potential synergies between them. Points of contact with
simultaneous diagonalisation results are noted. | [
0,
0,
1,
1,
0,
0
] | [
"Mathematics"
] |
Title: Morphisms of open games,
Abstract: We define a notion of morphisms between open games, exploiting a surprising
connection between lenses in computer science and compositional game theory.
This extends the more intuitively obvious definition of globular morphisms as
mappings between strategy profiles that preserve best responses, and hence in
particular preserve Nash equilibria. We construct a symmetric monoidal double
category in which the horizontal 1-cells are open games, vertical 1-morphisms
are lenses, and 2-cells are morphisms of open games. States (morphisms out of
the monoidal unit) in the vertical category give a flexible solution concept
that includes both Nash and subgame perfect equilibria. Products in the
vertical category give an external choice operator that is reminiscent of
products in game semantics, and is useful in practical examples. We illustrate
the above two features with a simple worked example from microeconomics, the
market entry game. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science",
"Mathematics"
] |
Title: U(1)$\times$SU(2) Gauge Invariance Made Simple for Density Functional Approximations,
Abstract: A semi-relativistic density-functional theory that includes spin-orbit
couplings and Zeeman fields on equal footing with the electromagnetic
potentials, is an appealing framework to develop a unified first-principles
computational approach for non-collinear magnetism, spintronics, orbitronics,
and topological states. The basic variables of this theory include the
paramagnetic current and the spin-current density, besides the particle and the
spin density, and the corresponding exchange-correlation (xc) energy functional
is invariant under local U(1)$\times$SU(2) gauge transformations. The xc-energy
functional must be approximated to enable practical applications, but, contrary
to the case of the standard density functional theory, finding simple
approximations suited to deal with realistic atomistic inhomogeneities has been
a long-standing challenge. Here, we propose a way out of this impasse by
showing that approximate gauge-invariant functionals can be easily generated
from existing approximate functionals of ordinary density-functional theory by
applying a simple {\it minimal substitution} on the kinetic energy density,
which controls the short-range behavior of the exchange hole. Our proposal
opens the way to the construction of approximate, yet non-empirical
functionals, which do not assume weak inhomogeneity and should therefore have a
wide range of applicability in atomic, molecular and condensed matter physics. | [
0,
1,
0,
0,
0,
0
] | [
"Physics",
"Mathematics"
] |
Title: L^2-Betti numbers of rigid C*-tensor categories and discrete quantum groups,
Abstract: We compute the $L^2$-Betti numbers of the free $C^*$-tensor categories, which
are the representation categories of the universal unitary quantum groups
$A_u(F)$. We show that the $L^2$-Betti numbers of the dual of a compact quantum
group $G$ are equal to the $L^2$-Betti numbers of the representation category
$Rep(G)$ and thus, in particular, invariant under monoidal equivalence. As an
application, we obtain several new computations of $L^2$-Betti numbers for
discrete quantum groups, including the quantum permutation groups and the free
wreath product groups. Finally, we obtain upper bounds for the first
$L^2$-Betti number in terms of a generating set of a $C^*$-tensor category. | [
0,
0,
1,
0,
0,
0
] | [
"Mathematics",
"Physics"
] |
Title: Hierarchical internal representation of spectral features in deep convolutional networks trained for EEG decoding,
Abstract: Recently, there is increasing interest and research on the interpretability
of machine learning models, for example how they transform and internally
represent EEG signals in Brain-Computer Interface (BCI) applications. This can
help to understand the limits of the model and how it may be improved, in
addition to possibly provide insight about the data itself. Schirrmeister et
al. (2017) have recently reported promising results for EEG decoding with deep
convolutional neural networks (ConvNets) trained in an end-to-end manner and,
with a causal visualization approach, showed that they learn to use spectral
amplitude changes in the input. In this study, we investigate how ConvNets
represent spectral features through the sequence of intermediate stages of the
network. We show higher sensitivity to EEG phase features at earlier stages and
higher sensitivity to EEG amplitude features at later stages. Intriguingly, we
observed a specialization of individual stages of the network to the classical
EEG frequency bands alpha, beta, and high gamma. Furthermore, we find first
evidence that particularly in the last convolutional layer, the network learns
to detect more complex oscillatory patterns beyond spectral phase and
amplitude, reminiscent of the representation of complex visual features in
later layers of ConvNets in computer vision tasks. Our findings thus provide
insights into how ConvNets hierarchically represent spectral EEG features in
their intermediate layers and suggest that ConvNets can exploit and might help
to better understand the compositional structure of EEG time series. | [
1,
0,
0,
1,
0,
0
] | [
"Computer Science",
"Quantitative Biology"
] |
Title: Large-scale validation of an automatic EEG arousal detection algorithm using different heterogeneous databases,
Abstract: $\textbf{Objective}$: To assess the validity of an automatic EEG arousal
detection algorithm using large patient samples and different heterogeneous
databases
$\textbf{Methods}$: Automatic scorings were confronted with results from
human expert scorers on a total of 2768 full-night PSG recordings obtained from
two different databases. Of them, 472 recordings were obtained during clinical
routine at our sleep center and were subdivided into two subgroups of 220
(HMC-S) and 252 (HMC-M) recordings each, attending to the procedure followed by
the clinical expert during the visual review (semi-automatic or purely manual,
respectively). In addition, 2296 recordings from the public SHHS-2 database
were evaluated against the respective manual expert scorings.
$\textbf{Results}$: Event-by-event epoch-based validation resulted in an
overall Cohen kappa agreement K = 0.600 (HMC-S), 0.559 (HMC-M), and 0.573
(SHHS-2). Estimated inter-scorer variability on the datasets was, respectively,
K = 0.594, 0.561 and 0.543. Analyses of the corresponding Arousal Index scores
showed associated automatic-human repeatability indices ranging in 0.693-0.771
(HMC-S), 0.646-0.791 (HMC-M), and 0.759-0.791 (SHHS-2).
$\textbf{Conclusions}$: Large-scale validation of our automatic EEG arousal
detector on different databases has shown robust performance and good
generalization results comparable to the expected levels of human agreement.
Special emphasis has been put on allowing reproducibility of the results and
implementation of our method has been made accessible online as open source
code | [
0,
0,
0,
0,
1,
0
] | [
"Computer Science",
"Quantitative Biology"
] |
Title: Mechanisms of near-surface structural evolution in nanocrystalline materials during sliding contact,
Abstract: The wear-driven structural evolution of nanocrystalline Cu was simulated with
molecular dynamics under constant normal loads, followed by a quantitative
analysis. While the microstructure far away from the sliding contact remains
unchanged, grain growth accompanied by partial dislocations and twin formation
was observed near the contact surface, with more rapid coarsening promoted by
higher applied normal loads. The structural evolution continues with increasing
number of sliding cycles and eventually saturates to a stable distinct layer of
coarsened grains, separated from the finer matrix by a steep gradient in grain
size. The coarsening process is balanced by the rate of material removal when
the normal load is high enough. The observed structural evolution leads to an
increase in hardness and decrease in friction coefficient, which also saturate
after a number of sliding cycles. This work provides important mechanistic
understanding of nanocrystalline wear, while also introducing a methodology for
atomistic simulations of cyclic wear damage under constant applied normal
loads. | [
0,
1,
0,
0,
0,
0
] | [
"Physics"
] |
Title: Generalized Hölder's inequality on Morrey spaces,
Abstract: The aim of this paper is to present necessary and sufficient conditions for
generalized Hölder's inequality on generalized Morrey spaces. We also
obtain similar results on weak Morrey spaces and on generalized weak Morrey
spaces. The necessary and sufficient conditions for the generalized
Hölder's inequality on these spaces are obtained through estimates for
characteristic functions of balls in $\mathbb{R}^d$. | [
0,
0,
1,
0,
0,
0
] | [
"Mathematics"
] |
Title: Ranks of rational points of the Jacobian varieties of hyperelliptic curves,
Abstract: In this paper, we obtain bounds for the Mordell-Weil ranks over cyclotomic
extensions of a wide range of abelian varieties defined over a number field $F$
whose primes above $p$ are totally ramified over $F/\mathbb{Q}$. We assume that
the abelian varieties may have good non-ordinary reduction at those primes. Our
work is a generalization of \cite{Kim}, in which the second author generalized
Perrin-Riou's Iwasawa theory for elliptic curves over $\mathbb{Q}$ with
supersingular reduction (\cite{Perrin-Riou}) to elliptic curves defined over
the above-mentioned number field $F$. On top of non-ordinary reduction and the
ramification of the field $F$, we deal with the additional difficulty that the
dimensions of the abelian varieties can be any number bigger than 1 which
causes a variety of issues. As a result, we obtain bounds for the ranks over
cyclotomic extensions $\mathbb{Q}(\mu_{p^{\max(M,N)+n}})$ of the Jacobian
varieties of {\it ramified} hyperelliptic curves $y^{2p^M}=x^{3p^N}+ax^{p^N}+b$
among others. | [
0,
0,
1,
0,
0,
0
] | [
"Mathematics"
] |
Title: Occlusion-Aware Risk Assessment for Autonomous Driving in Urban Environments,
Abstract: Navigating safely in urban environments remains a challenging problem for
autonomous vehicles. Occlusion and limited sensor range can pose significant
challenges to safely navigate among pedestrians and other vehicles in the
environment. Enabling vehicles to quantify the risk posed by unseen regions
allows them to anticipate future possibilities, resulting in increased safety
and ride comfort. This paper proposes an algorithm that takes advantage of the
known road layouts to forecast, quantify, and aggregate risk associated with
occlusions and limited sensor range. This allows us to make predictions of risk
induced by unobserved vehicles even in heavily occluded urban environments. The
risk can then be used either by a low-level planning algorithm to generate
better trajectories, or by a high-level one to plan a better route. The
proposed algorithm is evaluated on intersection layouts from real-world map
data with up to five other vehicles in the scene, and verified to reduce
collision rates by 4.8x comparing to a baseline method while improving driving
comfort. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science"
] |
Title: Quantum oscillations and Dirac-Landau levels in Weyl superconductors,
Abstract: When magnetic field is applied to metals and semimetals quantum oscillations
appear as individual Landau levels cross the Fermi level. Quantum oscillations
generally do not occur in superconductors (SC) because magnetic field is either
expelled from the sample interior or, if strong enough, drives the material
into the normal state. In addition, elementary excitations of a superconductor
-- Bogoliubov quasiparticles -- do not carry a well defined electric charge and
therefore do not couple in a simple way to the applied magnetic field. We
predict here that in Weyl superconductors certain types of elastic strain have
the ability to induce chiral pseudo-magnetic field which can reorganize the
electronic states into Dirac-Landau levels with linear band crossings at low
energy. The resulting quantum oscillations in the quasiparticle density of
states and thermal conductivity can be experimentally observed under a bending
deformation of a thin film Weyl SC and provide new insights into this
fascinating family of materials. | [
0,
1,
0,
0,
0,
0
] | [
"Physics"
] |
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