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Title: Derivative Principal Component Analysis for Representing the Time Dynamics of Longitudinal and Functional Data,
Abstract: We propose a nonparametric method to explicitly model and represent the
derivatives of smooth underlying trajectories for longitudinal data. This
representation is based on a direct Karhunen--Loève expansion of the
unobserved derivatives and leads to the notion of derivative principal
component analysis, which complements functional principal component analysis,
one of the most popular tools of functional data analysis. The proposed
derivative principal component scores can be obtained for irregularly spaced
and sparsely observed longitudinal data, as typically encountered in biomedical
studies, as well as for functional data which are densely measured. Novel
consistency results and asymptotic convergence rates for the proposed estimates
of the derivative principal component scores and other components of the model
are derived under a unified scheme for sparse or dense observations and mild
conditions. We compare the proposed representations for derivatives with
alternative approaches in simulation settings and also in a wallaby growth
curve application. It emerges that representations using the proposed
derivative principal component analysis recover the underlying derivatives more
accurately compared to principal component analysis-based approaches especially
in settings where the functional data are represented with only a very small
number of components or are densely sampled. In a second wheat spectra
classification example, derivative principal component scores were found to be
more predictive for the protein content of wheat than the conventional
functional principal component scores. | [
0,
0,
1,
1,
0,
0
] | [
"Statistics",
"Mathematics"
] |
Title: Stokes phenomenon and confluence in non-autonomous Hamiltonian systems,
Abstract: This article studies a confluence of a pair of regular singular points to an
irregular one in a generic family of time-dependent Hamiltonian systems in
dimension 2. This is a general setting for the understanding of the
degeneration of the sixth Painleve equation to the fifth one. The main result
is a theorem of sectoral normalization of the family to an integrable formal
normal form, through which is explained the relation between the local
monodromy operators at the two regular singularities and the non-linear Stokes
phenomenon at the irregular singularity of the limit system. The problem of
analytic classification is also addressed.
Key words: Non-autonomous Hamiltonian systems; irregular singularity;
non-linear Stokes phenomenon; wild monodromy; confluence; local analytic
classification; Painleve equations. | [
0,
0,
1,
0,
0,
0
] | [
"Mathematics",
"Physics"
] |
Title: The independence number of the Birkhoff polytope graph, and applications to maximally recoverable codes,
Abstract: Maximally recoverable codes are codes designed for distributed storage which
combine quick recovery from single node failure and optimal recovery from
catastrophic failure. Gopalan et al [SODA 2017] studied the alphabet size
needed for such codes in grid topologies and gave a combinatorial
characterization for it.
Consider a labeling of the edges of the complete bipartite graph $K_{n,n}$
with labels coming from $F_2^d$ , that satisfies the following condition: for
any simple cycle, the sum of the labels over its edges is nonzero. The minimal
d where this is possible controls the alphabet size needed for maximally
recoverable codes in n x n grid topologies.
Prior to the current work, it was known that d is between $(\log n)^2$ and
$n\log n$. We improve both bounds and show that d is linear in n. The upper
bound is a recursive construction which beats the random construction. The
lower bound follows by first relating the problem to the independence number of
the Birkhoff polytope graph, and then providing tight bounds for it using the
representation theory of the symmetric group. | [
1,
0,
1,
0,
0,
0
] | [
"Computer Science",
"Mathematics"
] |
Title: Spin Angular Momentum of Proton Spin Puzzle in Complex Octonion Spaces,
Abstract: The paper focuses on considering some special precessional motions as the
spin motions, separating the octonion angular momentum of a proton into six
components, elucidating the proton angular momentum in the proton spin puzzle,
especially the proton spin, decomposition, quarks and gluons, and polarization
and so forth. J. C. Maxwell was the first to use the quaternions to study the
electromagnetic fields. Subsequently the complex octonions are utilized to
depict the electromagnetic field, gravitational field, and quantum mechanics
and so forth. In the complex octonion space, the precessional equilibrium
equation infers the angular velocity of precession. The external
electromagnetic strength may induce a new precessional motion, generating a new
term of angular momentum, even if the orbital angular momentum is zero. This
new term of angular momentum can be regarded as the spin angular momentum, and
its angular velocity of precession is different from the angular velocity of
revolution. The study reveals that the angular momentum of the proton must be
separated into more components than ever before. In the proton spin puzzle, the
orbital angular momentum and magnetic dipole moment are independent of each
other, and they should be measured and calculated respectively. | [
0,
1,
0,
0,
0,
0
] | [
"Physics",
"Mathematics"
] |
Title: Physics-Informed Regularization of Deep Neural Networks,
Abstract: This paper presents a novel physics-informed regularization method for
training of deep neural networks (DNNs). In particular, we focus on the DNN
representation for the response of a physical or biological system, for which a
set of governing laws are known. These laws often appear in the form of
differential equations, derived from first principles, empirically-validated
laws, and/or domain expertise. We propose a DNN training approach that utilizes
these known differential equations in addition to the measurement data, by
introducing a penalty term to the training loss function to penalize divergence
form the governing laws. Through three numerical examples, we will show that
the proposed regularization produces surrogates that are physically
interpretable with smaller generalization errors, when compared to other common
regularization methods. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science",
"Physics"
] |
Title: Gradient-based Filter Design for the Dual-tree Wavelet Transform,
Abstract: The wavelet transform has seen success when incorporated into neural network
architectures, such as in wavelet scattering networks. More recently, it has
been shown that the dual-tree complex wavelet transform can provide better
representations than the standard transform. With this in mind, we extend our
previous method for learning filters for the 1D and 2D wavelet transforms into
the dual-tree domain. We show that with few modifications to our original
model, we can learn directional filters that leverage the properties of the
dual-tree wavelet transform. | [
0,
0,
0,
1,
0,
0
] | [
"Computer Science",
"Mathematics"
] |
Title: Steganographic Generative Adversarial Networks,
Abstract: Steganography is collection of methods to hide secret information ("payload")
within non-secret information ("container"). Its counterpart, Steganalysis, is
the practice of determining if a message contains a hidden payload, and
recovering it if possible. Presence of hidden payloads is typically detected by
a binary classifier. In the present study, we propose a new model for
generating image-like containers based on Deep Convolutional Generative
Adversarial Networks (DCGAN). This approach allows to generate more
setganalysis-secure message embedding using standard steganography algorithms.
Experiment results demonstrate that the new model successfully deceives the
steganography analyzer, and for this reason, can be used in steganographic
applications. | [
1,
0,
0,
1,
0,
0
] | [
"Computer Science"
] |
Title: Markov Chain Lifting and Distributed ADMM,
Abstract: The time to converge to the steady state of a finite Markov chain can be
greatly reduced by a lifting operation, which creates a new Markov chain on an
expanded state space. For a class of quadratic objectives, we show an analogous
behavior where a distributed ADMM algorithm can be seen as a lifting of
Gradient Descent algorithm. This provides a deep insight for its faster
convergence rate under optimal parameter tuning. We conjecture that this gain
is always present, as opposed to the lifting of a Markov chain which sometimes
only provides a marginal speedup. | [
1,
0,
1,
1,
0,
0
] | [
"Computer Science",
"Mathematics"
] |
Title: Fast failover of multicast sessions in software-defined networks,
Abstract: With the rapid growth of services that stream to groups of users comes an
increased importance of and demand for reliable multicast. In this paper, we
turn to software-defined networking and develop a novel general-purpose
multi-failure protection algorithm to provide quick failure recovery, via Fast
Failover (FF) groups, for dynamic multicast groups. This extends previous
research, which either could not realize fast failover, worked only for single
link failures, or was only applicable to static multicast groups. However,
while FF is know to be fast, it requires pre-installing back-up rules. These
additional memory requirements, which in a multicast setting are even more
pronounced than for unicast, are often mentioned as a big disadvantage of using
FF.
We develop an OpenFlow application for resilient multicast, with which we
study FF resource usage, in an attempt to better understand the trade-off
between recovery time and resource usage. Our tests on a realistic network
suggest that using FF groups can reduce the recovery time of the network
significantly compared to other methods, especially when the latency between
the controller and the switches is relatively large. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science"
] |
Title: Stacked Structure Learning for Lifted Relational Neural Networks,
Abstract: Lifted Relational Neural Networks (LRNNs) describe relational domains using
weighted first-order rules which act as templates for constructing feed-forward
neural networks. While previous work has shown that using LRNNs can lead to
state-of-the-art results in various ILP tasks, these results depended on
hand-crafted rules. In this paper, we extend the framework of LRNNs with
structure learning, thus enabling a fully automated learning process. Similarly
to many ILP methods, our structure learning algorithm proceeds in an iterative
fashion by top-down searching through the hypothesis space of all possible Horn
clauses, considering the predicates that occur in the training examples as well
as invented soft concepts entailed by the best weighted rules found so far. In
the experiments, we demonstrate the ability to automatically induce useful
hierarchical soft concepts leading to deep LRNNs with a competitive predictive
power. | [
1,
0,
0,
1,
0,
0
] | [
"Computer Science",
"Statistics"
] |
Title: Spec-QP: Speculative Query Planning for Joins over Knowledge Graphs,
Abstract: Organisations store huge amounts of data from multiple heterogeneous sources
in the form of Knowledge Graphs (KGs). One of the ways to query these KGs is to
use SPARQL queries over a database engine. Since SPARQL follows exact match
semantics, the queries may return too few or no results. Recent works have
proposed query relaxation where the query engine judiciously replaces a query
predicate with similar predicates using weighted relaxation rules mined from
the KG. The space of possible relaxations is potentially too large to fully
explore and users are typically interested in only top-k results, so such query
engines use top-k algorithms for query processing. However, they may still
process all the relaxations, many of whose answers do not contribute towards
top-k answers. This leads to computation overheads and delayed response times.
We propose Spec-QP, a query planning framework that speculatively determines
which relaxations will have their results in the top-k answers. Only these
relaxations are processed using the top-k operators. We, therefore, reduce the
computation overheads and achieve faster response times without adversely
affecting the quality of results. We tested Spec-QP over two datasets - XKG and
Twitter, to demonstrate the efficiency of our planning framework at reducing
runtimes with reasonable accuracy for query engines supporting relaxations. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science"
] |
Title: Single Index Latent Variable Models for Network Topology Inference,
Abstract: A semi-parametric, non-linear regression model in the presence of latent
variables is applied towards learning network graph structure. These latent
variables can correspond to unmodeled phenomena or unmeasured agents in a
complex system of interacting entities. This formulation jointly estimates
non-linearities in the underlying data generation, the direct interactions
between measured entities, and the indirect effects of unmeasured processes on
the observed data. The learning is posed as regularized empirical risk
minimization. Details of the algorithm for learning the model are outlined.
Experiments demonstrate the performance of the learned model on real data. | [
0,
0,
0,
1,
0,
0
] | [
"Statistics",
"Computer Science"
] |
Title: Quadratically-Regularized Optimal Transport on Graphs,
Abstract: Optimal transportation provides a means of lifting distances between points
on a geometric domain to distances between signals over the domain, expressed
as probability distributions. On a graph, transportation problems can be used
to express challenging tasks involving matching supply to demand with minimal
shipment expense; in discrete language, these become minimum-cost network flow
problems. Regularization typically is needed to ensure uniqueness for the
linear ground distance case and to improve optimization convergence;
state-of-the-art techniques employ entropic regularization on the
transportation matrix. In this paper, we explore a quadratic alternative to
entropic regularization for transport over a graph. We theoretically analyze
the behavior of quadratically-regularized graph transport, characterizing how
regularization affects the structure of flows in the regime of small but
nonzero regularization. We further exploit elegant second-order structure in
the dual of this problem to derive an easily-implemented Newton-type
optimization algorithm. | [
1,
0,
1,
0,
0,
0
] | [
"Computer Science",
"Mathematics"
] |
Title: Discussion on "Random-projection ensemble classification" by T. Cannings and R. Samworth,
Abstract: Discussion on "Random-projection ensemble classification" by T. Cannings and
R. Samworth. We believe that the proposed approach can find many applications
in economics such as credit scoring (e.g. Altman (1968)) and can be extended to
more general type of classifiers. In this discussion we would like to draw
authors attention to the copula-based discriminant analysis (Han et al. (2013)
and He et al. (2016)). | [
0,
0,
1,
1,
0,
0
] | [
"Statistics",
"Quantitative Finance"
] |
Title: Sub-nanometre resolution of atomic motion during electronic excitation in phase-change materials,
Abstract: Phase-change materials based on Ge-Sb-Te alloys are widely used in industrial
applications such as nonvolatile memories, but reaction pathways for
crystalline-to-amorphous phase-change on picosecond timescales remain unknown.
Femtosecond laser excitation and an ultrashort x-ray probe is used to show the
temporal separation of electronic and thermal effects in a long-lived ($>$100
ps) transient metastable state of Ge$_{2}$Sb$_{2}$Te$_{5}$ with muted
interatomic interaction induced by a weakening of resonant bonding. Due to a
specific electronic state, the lattice undergoes a reversible nondestructive
modification over a nanoscale region, remaining cold for 4 ps. An independent
time-resolved x-ray absorption fine structure experiment confirms the existence
of an intermediate state with disordered bonds. This newly unveiled effect
allows the utilization of non-thermal ultra-fast pathways enabling artificial
manipulation of the switching process, ultimately leading to a redefined speed
limit, and improved energy efficiency and reliability of phase-change memory
technologies. | [
0,
1,
0,
0,
0,
0
] | [
"Physics"
] |
Title: A Density Result for Real Hyperelliptic Curves,
Abstract: Let $\{\infty^+, \infty^-\}$ be the two points above $\infty$ on the real
hyperelliptic curve $H: y^2 = (x^2 - 1) \prod_{i=1}^{2g} (x - a_i)$. We show
that the divisor $([\infty^+] - [\infty^-])$ is torsion in $\operatorname{Jac}
J$ for a dense set of $(a_1, a_2, \ldots, a_{2g}) \in (-1, 1)^{2g}$. In fact,
we prove by degeneration to a nodal $\mathbb{P}^1$ that an associated period
map has derivative generically of full rank. | [
0,
0,
1,
0,
0,
0
] | [
"Mathematics"
] |
Title: On a class of integrable systems of Monge-Ampère type,
Abstract: We investigate a class of multi-dimensional two-component systems of
Monge-Ampère type that can be viewed as generalisations of heavenly-type
equations appearing in self-dual Ricci-flat geometry. Based on the
Jordan-Kronecker theory of skew-symmetric matrix pencils, a classification of
normal forms of such systems is obtained. All two-component systems of
Monge-Ampère type turn out to be integrable, and can be represented as the
commutativity conditions of parameter-dependent vector fields. Geometrically,
systems of Monge-Ampère type are associated with linear sections of the
Grassmannians. This leads to an invariant differential-geometric
characterisation of the Monge-Ampère property. | [
0,
1,
1,
0,
0,
0
] | [
"Mathematics",
"Physics"
] |
Title: Unsupervised Motion Artifact Detection in Wrist-Measured Electrodermal Activity Data,
Abstract: One of the main benefits of a wrist-worn computer is its ability to collect a
variety of physiological data in a minimally intrusive manner. Among these
data, electrodermal activity (EDA) is readily collected and provides a window
into a person's emotional and sympathetic responses. EDA data collected using a
wearable wristband are easily influenced by motion artifacts (MAs) that may
significantly distort the data and degrade the quality of analyses performed on
the data if not identified and removed. Prior work has demonstrated that MAs
can be successfully detected using supervised machine learning algorithms on a
small data set collected in a lab setting. In this paper, we demonstrate that
unsupervised learning algorithms perform competitively with supervised
algorithms for detecting MAs on EDA data collected in both a lab-based setting
and a real-world setting comprising about 23 hours of data. We also find,
somewhat surprisingly, that incorporating accelerometer data as well as EDA
improves detection accuracy only slightly for supervised algorithms and
significantly degrades the accuracy of unsupervised algorithms. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science",
"Statistics",
"Quantitative Biology"
] |
Title: Early Experiences with Crowdsourcing Airway Annotations in Chest CT,
Abstract: Measuring airways in chest computed tomography (CT) images is important for
characterizing diseases such as cystic fibrosis, yet very time-consuming to
perform manually. Machine learning algorithms offer an alternative, but need
large sets of annotated data to perform well. We investigate whether
crowdsourcing can be used to gather airway annotations which can serve directly
for measuring the airways, or as training data for the algorithms. We generate
image slices at known locations of airways and request untrained crowd workers
to outline the airway lumen and airway wall. Our results show that the workers
are able to interpret the images, but that the instructions are too complex,
leading to many unusable annotations. After excluding unusable annotations,
quantitative results show medium to high correlations with expert measurements
of the airways. Based on this positive experience, we describe a number of
further research directions and provide insight into the challenges of
crowdsourcing in medical images from the perspective of first-time users. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science",
"Quantitative Biology"
] |
Title: Convergent Iteration in Sobolev Space for Time Dependent Closed Quantum Systems,
Abstract: Time dependent quantum systems have become indispensable in science and its
applications, particularly at the atomic and molecular levels. Here, we discuss
the approximation of closed time dependent quantum systems on bounded domains,
via iterative methods in Sobolev space based upon evolution operators.
Recently, existence and uniqueness of weak solutions were demonstrated by a
contractive fixed point mapping defined by the evolution operators. Convergent
successive approximation is then guaranteed. This article uses the same mapping
to define quadratically convergent Newton and approximate Newton methods.
Estimates for the constants used in the convergence estimates are provided. The
evolution operators are ideally suited to serve as the framework for this
operator approximation theory, since the Hamiltonian is time dependent. In
addition, the hypotheses required to guarantee quadratic convergence of the
Newton iteration build naturally upon the hypotheses used for the
existence/uniqueness theory. | [
0,
0,
1,
0,
0,
0
] | [
"Physics",
"Mathematics"
] |
Title: Image-based immersed boundary model of the aortic root,
Abstract: Each year, approximately 300,000 heart valve repair or replacement procedures
are performed worldwide, including approximately 70,000 aortic valve
replacement surgeries in the United States alone. This paper describes progress
in constructing anatomically and physiologically realistic immersed boundary
(IB) models of the dynamics of the aortic root and ascending aorta. This work
builds on earlier IB models of fluid-structure interaction (FSI) in the aortic
root, which previously achieved realistic hemodynamics over multiple cardiac
cycles, but which also were limited to simplified aortic geometries and
idealized descriptions of the biomechanics of the aortic valve cusps. By
contrast, the model described herein uses an anatomical geometry reconstructed
from patient-specific computed tomography angiography (CTA) data, and employs a
description of the elasticity of the aortic valve leaflets based on a
fiber-reinforced constitutive model fit to experimental tensile test data.
Numerical tests show that the model is able to resolve the leaflet biomechanics
in diastole and early systole at practical grid spacings. The model is also
used to examine differences in the mechanics and fluid dynamics yielded by
fresh valve leaflets and glutaraldehyde-fixed leaflets similar to those used in
bioprosthetic heart valves. Although there are large differences in the leaflet
deformations during diastole, the differences in the open configurations of the
valve models are relatively small, and nearly identical hemodynamics are
obtained in all cases considered. | [
1,
1,
0,
0,
0,
0
] | [
"Quantitative Biology",
"Physics"
] |
Title: A Data-Driven Analysis of the Influence of Care Coordination on Trauma Outcome,
Abstract: OBJECTIVE: To test the hypothesis that variation in care coordination is
related to LOS. DESIGN We applied a spectral co-clustering methodology to
simultaneously infer groups of patients and care coordination patterns, in the
form of interaction networks of health care professionals, from electronic
medical record (EMR) utilization data. The care coordination pattern for each
patient group was represented by standard social network characteristics and
its relationship with hospital LOS was assessed via a negative binomial
regression with a 95% confidence interval. SETTING AND PATIENTS This study
focuses on 5,588 adult patients hospitalized for trauma at the Vanderbilt
University Medical Center. The EMRs were accessed by healthcare professionals
from 179 operational areas during 158,467 operational actions. MAIN OUTCOME
MEASURES: Hospital LOS for trauma inpatients, as an indicator of care
coordination efficiency. RESULTS: Three general types of care coordination
patterns were discovered, each of which was affiliated with a specific patient
group. The first patient group exhibited the shortest hospital LOS and was
managed by a care coordination pattern that involved the smallest number of
operational areas (102 areas, as opposed to 125 and 138 for the other patient
groups), but exhibited the largest number of collaborations between operational
areas (e.g., an average of 27.1 connections per operational area compared to
22.5 and 23.3 for the other two groups). The hospital LOS for the second and
third patient groups was 14 hours (P = 0.024) and 10 hours (P = 0.042) longer
than the first patient group, respectively. | [
1,
0,
0,
0,
0,
0
] | [
"Statistics",
"Quantitative Biology"
] |
Title: Construction of Non-asymptotic Confidence Sets in 2-Wasserstein Space,
Abstract: In this paper, we consider a probabilistic setting where the probability
measures are considered to be random objects. We propose a procedure of
construction non-asymptotic confidence sets for empirical barycenters in
2-Wasserstein space and develop the idea further to construction of a
non-parametric two-sample test that is then applied to the detection of
structural breaks in data with complex geometry. Both procedures mainly rely on
the idea of multiplier bootstrap (Spokoiny and Zhilova (2015), Chernozhukov et
al. (2014)). The main focus lies on probability measures that have commuting
covariance matrices and belong to the same scatter-location family: we proof
the validity of a bootstrap procedure that allows to compute confidence sets
and critical values for a Wasserstein-based two-sample test. | [
0,
0,
1,
1,
0,
0
] | [
"Mathematics",
"Statistics"
] |
Title: Limits on statistical anisotropy from BOSS DR12 galaxies using bipolar spherical harmonics,
Abstract: We measure statistically anisotropic signatures imprinted in
three-dimensional galaxy clustering using bipolar spherical harmonics (BipoSHs)
in both Fourier space and configuration space. We then constrain a well-known
quadrupolar anisotropy parameter $g_{2M}$ in the primordial power spectrum,
parametrized by $P(\vec{k}) = \bar{P}(k) [ 1 + \sum_{M} g_{2M} Y_{2M}(\hat{k})
]$, with $M$ determining the direction of the anisotropy. Such an anisotropic
signal is easily contaminated by artificial asymmetries due to specific survey
geometry. We precisely estimate the contaminated signal and finally subtract it
from the data. Using the galaxy samples obtained by the Baryon Oscillation
Spectroscopic Survey Data Release 12, we find no evidence for violation of
statistical isotropy, $g_{2M}$ for all $M$ to be of zero within the $2\sigma$
level. The $g_{2M}$-type anisotropy can originate from the primordial curvature
power spectrum involving a directional-dependent modulation $g_* (\hat{k} \cdot
\hat{p})^2$. The bound on $g_{2M}$ is translated into $g_*$ as $-0.09 < g_* <
0.08$ with a $95\%$ confidence level when $\hat{p}$ is marginalized over. | [
0,
1,
0,
0,
0,
0
] | [
"Physics",
"Statistics"
] |
Title: Confidence Intervals for Stochastic Arithmetic,
Abstract: Quantifying errors and losses due to the use of Floating-Point (FP)
calculations in industrial scientific computing codes is an important part of
the Verification, Validation and Uncertainty Quantification (VVUQ) process.
Stochastic Arithmetic is one way to model and estimate FP losses of accuracy,
which scales well to large, industrial codes. It exists in different flavors,
such as CESTAC or MCA, implemented in various tools such as CADNA, Verificarlo
or Verrou. These methodologies and tools are based on the idea that FP losses
of accuracy can be modeled via randomness. Therefore, they share the same need
to perform a statistical analysis of programs results in order to estimate the
significance of the results. In this paper, we propose a framework to perform a
solid statistical analysis of Stochastic Arithmetic. This framework unifies all
existing definitions of the number of significant digits (CESTAC and MCA), and
also proposes a new quantity of interest: the number of digits contributing to
the accuracy of the results. Sound confidence intervals are provided for all
estimators, both in the case of normally distributed results, and in the
general case. The use of this framework is demonstrated by two case studies of
large, industrial codes: Europlexus and code\_aster. | [
1,
0,
0,
1,
0,
0
] | [
"Computer Science",
"Statistics"
] |
Title: Co-segmentation for Space-Time Co-located Collections,
Abstract: We present a co-segmentation technique for space-time co-located image
collections. These prevalent collections capture various dynamic events,
usually by multiple photographers, and may contain multiple co-occurring
objects which are not necessarily part of the intended foreground object,
resulting in ambiguities for traditional co-segmentation techniques. Thus, to
disambiguate what the common foreground object is, we introduce a
weakly-supervised technique, where we assume only a small seed, given in the
form of a single segmented image. We take a distributed approach, where local
belief models are propagated and reinforced with similar images. Our technique
progressively expands the foreground and background belief models across the
entire collection. The technique exploits the power of the entire set of image
without building a global model, and thus successfully overcomes large
variability in appearance of the common foreground object. We demonstrate that
our method outperforms previous co-segmentation techniques on challenging
space-time co-located collections, including dense benchmark datasets which
were adapted for our novel problem setting. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science"
] |
Title: Connecting pairwise spheres by depth: DCOPS,
Abstract: We extend the classical notion of the spherical depth in \mathbb{R}^k, to the
important setup of data on a Riemannian manifold. We show that this notion of
depth satisfies a set of desirable properties. For the empirical version of
this depth function both uniform consistency and the asymptotic distribution
are studied. Consistency is also shown for functional data. The behaviour of
the depth is illustrated through several examples for Riemannian manifold data. | [
0,
0,
1,
1,
0,
0
] | [
"Mathematics",
"Statistics"
] |
Title: TRAMP: Tracking by a Real-time AMbisonic-based Particle filter,
Abstract: This article presents a multiple sound source localization and tracking
system, fed by the Eigenmike array. The First Order Ambisonics (FOA) format is
used to build a pseudointensity-based spherical histogram, from which the
source position estimates are deduced. These instantaneous estimates are
processed by a wellknown tracking system relying on a set of particle filters.
While the novelty within localization and tracking is incremental, the
fully-functional, complete and real-time running system based on these
algorithms is proposed for the first time. As such, it could serve as an
additional baseline method of the LOCATA challenge. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science"
] |
Title: General Bounds for Incremental Maximization,
Abstract: We propose a theoretical framework to capture incremental solutions to
cardinality constrained maximization problems. The defining characteristic of
our framework is that the cardinality/support of the solution is bounded by a
value $k\in\mathbb{N}$ that grows over time, and we allow the solution to be
extended one element at a time. We investigate the best-possible competitive
ratio of such an incremental solution, i.e., the worst ratio over all $k$
between the incremental solution after $k$ steps and an optimum solution of
cardinality $k$. We define a large class of problems that contains many
important cardinality constrained maximization problems like maximum matching,
knapsack, and packing/covering problems. We provide a general
$2.618$-competitive incremental algorithm for this class of problems, and show
that no algorithm can have competitive ratio below $2.18$ in general.
In the second part of the paper, we focus on the inherently incremental
greedy algorithm that increases the objective value as much as possible in each
step. This algorithm is known to be $1.58$-competitive for submodular objective
functions, but it has unbounded competitive ratio for the class of incremental
problems mentioned above. We define a relaxed submodularity condition for the
objective function, capturing problems like maximum (weighted) ($b$-)matching
and a variant of the maximum flow problem. We show that the greedy algorithm
has competitive ratio (exactly) $2.313$ for the class of problems that satisfy
this relaxed submodularity condition.
Note that our upper bounds on the competitive ratios translate to
approximation ratios for the underlying cardinality constrained problems. | [
1,
0,
1,
0,
0,
0
] | [
"Computer Science",
"Mathematics"
] |
Title: Scalable methods for Bayesian selective inference,
Abstract: Modeled along the truncated approach in Panigrahi (2016), selection-adjusted
inference in a Bayesian regime is based on a selective posterior. Such a
posterior is determined together by a generative model imposed on data and the
selection event that enforces a truncation on the assumed law. The effective
difference between the selective posterior and the usual Bayesian framework is
reflected in the use of a truncated likelihood. The normalizer of the truncated
law in the adjusted framework is the probability of the selection event; this
is typically intractable and it leads to the computational bottleneck in
sampling from such a posterior. The current work lays out a primal-dual
approach of solving an approximating optimization problem to provide valid
post-selective Bayesian inference. The selection procedures are posed as
data-queries that solve a randomized version of a convex learning program which
have the advantage of preserving more left-over information for inference. We
propose a randomization scheme under which the optimization has separable
constraints that result in a partially separable objective in lower dimensions
for many commonly used selective queries to approximate the otherwise
intractable selective posterior. We show that the approximating optimization
under a Gaussian randomization gives a valid exponential rate of decay for the
selection probability on a large deviation scale. We offer a primal-dual method
to solve the optimization problem leading to an approximate posterior; this
allows us to exploit the usual merits of a Bayesian machinery in both low and
high dimensional regimes where the underlying signal is effectively sparse. We
show that the adjusted estimates empirically demonstrate better frequentist
properties in comparison to the unadjusted estimates based on the usual
posterior, when applied to a wide range of constrained, convex data queries. | [
0,
0,
0,
1,
0,
0
] | [
"Statistics",
"Mathematics",
"Computer Science"
] |
Title: Modified Recursive Cholesky (Rchol) Algorithm: An Explicit Estimation and Pseudo-inverse of Correlation Matrices,
Abstract: The Cholesky decomposition plays an important role in finding the inverse of
the correlation matrices. As it is a fast and numerically stable for linear
system solving, inversion, and factorization compared to singular valued
decomposition (SVD), QR factorization and LU decomposition. As different
methods exist to find the Cholesky decomposition of a given matrix. This paper
presents the comparative study of a proposed RChol algorithm with the
conventional methods. The RChol algorithm is an explicit way to estimate the
modified Cholesky factors of a dynamic correlation matrix. | [
0,
0,
1,
0,
0,
0
] | [
"Mathematics",
"Statistics",
"Computer Science"
] |
Title: A Utility-Driven Multi-Queue Admission Control Solution for Network Slicing,
Abstract: The combination of recent emerging technologies such as network function
virtualization (NFV) and network programmability (SDN) gave birth to the
Network Slicing revolution. 5G networks consist of multi-tenant infrastructures
capable of offering leased network "slices" to new customers (e.g., vertical
industries) enabling a new telecom business model: Slice-as-aService (SlaaS).
In this paper, we aim i ) to study the slicing admission control problem by
means of a multi-queuing system for heterogeneous tenant requests, ii ) to
derive its statistical behavior model, and iii ) to provide a utility-based
admission control optimization. Our results analyze the capability of the
proposed SlaaS system to be approximately Markovian and evaluate its
performance as compared to legacy solutions. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science",
"Statistics"
] |
Title: Statistical inference for network samples using subgraph counts,
Abstract: We consider that a network is an observation, and a collection of observed
networks forms a sample. In this setting, we provide methods to test whether
all observations in a network sample are drawn from a specified model. We
achieve this by deriving, under the null of the graphon model, the joint
asymptotic properties of average subgraph counts as the number of observed
networks increases but the number of nodes in each network remains finite. In
doing so, we do not require that each observed network contains the same number
of nodes, or is drawn from the same distribution. Our results yield joint
confidence regions for subgraph counts, and therefore methods for testing
whether the observations in a network sample are drawn from: a specified
distribution, a specified model, or from the same model as another network
sample. We present simulation experiments and an illustrative example on a
sample of brain networks where we find that highly creative individuals' brains
present significantly more short cycles. | [
1,
0,
0,
1,
0,
0
] | [
"Statistics",
"Mathematics",
"Quantitative Biology"
] |
Title: Data Race Detection on Compressed Traces,
Abstract: We consider the problem of detecting data races in program traces that have
been compressed using straight line programs (SLP), which are special
context-free grammars that generate exactly one string, namely the trace that
they represent. We consider two classical approaches to race detection ---
using the happens-before relation and the lockset discipline. We present
algorithms for both these methods that run in time that is linear in the size
of the compressed, SLP representation. Typical program executions almost always
exhibit patterns that lead to significant compression. Thus, our algorithms are
expected to result in large speedups when compared with analyzing the
uncompressed trace. Our experimental evaluation of these new algorithms on
standard benchmarks confirms this observation. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science"
] |
Title: Two-Party Function Computation on the Reconciled Data,
Abstract: In this paper, we initiate a study of a new problem termed function
computation on the reconciled data, which generalizes a set reconciliation
problem in the literature. Assume a distributed data storage system with two
users $A$ and $B$. The users possess a collection of binary vectors $S_{A}$ and
$S_{B}$, respectively. They are interested in computing a function $\phi$ of
the reconciled data $S_{A} \cup S_{B}$.
It is shown that any deterministic protocol, which computes a sum and a
product of reconciled sets of binary vectors represented as nonnegative
integers, has to communicate at least $2^n + n - 1$ and $2^n + n - 2$ bits in
the worst-case scenario, respectively, where $n$ is the length of the binary
vectors. Connections to other problems in computer science, such as set
disjointness and finding the intersection, are established, yielding a variety
of additional upper and lower bounds on the communication complexity. A
protocol for computation of a sum function, which is based on use of a family
of hash functions, is presented, and its characteristics are analyzed. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science",
"Mathematics"
] |
Title: Halo assembly bias and the tidal anisotropy of the local halo environment,
Abstract: We study the role of the local tidal environment in determining the assembly
bias of dark matter haloes. Previous results suggest that the anisotropy of a
halo's environment (i.e, whether it lies in a filament or in a more isotropic
region) can play a significant role in determining the eventual mass and age of
the halo. We statistically isolate this effect using correlations between the
large-scale and small-scale environments of simulated haloes at $z=0$ with
masses between $10^{11.6}\lesssim (m/h^{-1}M_{\odot})\lesssim10^{14.9}$. We
probe the large-scale environment using a novel halo-by-halo estimator of
linear bias. For the small-scale environment, we identify a variable $\alpha_R$
that captures the $\textit{tidal anisotropy}$ in a region of radius
$R=4R_{\textrm{200b}}$ around the halo and correlates strongly with halo bias
at fixed mass. Segregating haloes by $\alpha_R$ reveals two distinct
populations. Haloes in highly isotropic local environments
($\alpha_R\lesssim0.2$) behave as expected from the simplest, spherically
averaged analytical models of structure formation, showing a
$\textit{negative}$ correlation between their concentration and large-scale
bias at $\textit{all}$ masses. In contrast, haloes in anisotropic,
filament-like environments ($\alpha_R\gtrsim0.5$) tend to show a
$\textit{positive}$ correlation between bias and concentration at any mass. Our
multi-scale analysis cleanly demonstrates how the overall assembly bias trend
across halo mass emerges as an average over these different halo populations,
and provides valuable insights towards building analytical models that
correctly incorporate assembly bias. We also discuss potential implications for
the nature and detectability of galaxy assembly bias. | [
0,
1,
0,
0,
0,
0
] | [
"Physics"
] |
Title: Towards a general theory for non-linear locally stationary processes,
Abstract: In this paper some general theory is presented for locally stationary
processes based on the stationary approximation and the stationary derivative.
Laws of large numbers, central limit theorems as well as deterministic and
stochastic bias expansions are proved for processes obeying an expansion in
terms of the stationary approximation and derivative. In addition it is shown
that this applies to some general nonlinear non-stationary Markov-models. In
addition the results are applied to derive the asymptotic properties of maximum
likelihood estimates of parameter curves in such models. | [
0,
0,
1,
1,
0,
0
] | [
"Statistics",
"Mathematics"
] |
Title: Single-cell diffraction tomography with optofluidic rotation about a tilted axis,
Abstract: Optical diffraction tomography (ODT) is a tomographic technique that can be
used to measure the three-dimensional (3D) refractive index distribution within
living cells without the requirement of any marker. In principle, ODT can be
regarded as a generalization of optical projection tomography which is
equivalent to computerized tomography (CT). Both optical tomographic techniques
require projection-phase images of cells measured at multiple angles. However,
the reconstruction of the 3D refractive index distribution post-measurement
differs for the two techniques. It is known that ODT yields better results than
projection tomography, because it takes into account diffraction of the imaging
light due to the refractive index structure of the sample. Here, we apply ODT
to biological cells in a microfluidic chip which combines optical trapping and
microfluidic flow to achieve an optofluidic single-cell rotation. In
particular, we address the problem that arises when the trapped cell is not
rotating about an axis perpendicular to the imaging plane, but instead about an
arbitrarily tilted axis. In this paper we show that the 3D reconstruction can
be improved by taking into account such a tilted rotational axis in the
reconstruction process. | [
0,
0,
0,
0,
1,
0
] | [
"Physics",
"Quantitative Biology"
] |
Title: Maps on statistical manifolds exactly reduced from the Perron-Frobenius equations for solvable chaotic maps,
Abstract: Maps on a parameter space for expressing distribution functions are exactly
derived from the Perron-Frobenius equations for a generalized Boole transform
family. Here the generalized Boole transform family is a one-parameter family
of maps where it is defined on a subset of the real line and its probability
distribution function is the Cauchy distribution with some parameters. With
this reduction, some relations between the statistical picture and the orbital
one are shown. From the viewpoint of information geometry, the parameter space
can be identified with a statistical manifold, and then it is shown that the
derived maps can be characterized. Also, with an induced symplectic structure
from a statistical structure, symplectic and information geometric aspects of
the derived maps are discussed. | [
0,
1,
0,
0,
0,
0
] | [
"Mathematics",
"Statistics",
"Physics"
] |
Title: Sparse Matrix Multiplication On An Associative Processor,
Abstract: Sparse matrix multiplication is an important component of linear algebra
computations. Implementing sparse matrix multiplication on an associative
processor (AP) enables high level of parallelism, where a row of one matrix is
multiplied in parallel with the entire second matrix, and where the execution
time of vector dot product does not depend on the vector size. Four sparse
matrix multiplication algorithms are explored in this paper, combining AP and
baseline CPU processing to various levels. They are evaluated by simulation on
a large set of sparse matrices. The computational complexity of sparse matrix
multiplication on AP is shown to be an O(nnz) where nnz is the number of
nonzero elements. The AP is found to be especially efficient in binary sparse
matrix multiplication. AP outperforms conventional solutions in power
efficiency. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science",
"Mathematics"
] |
Title: On the intersection of tame subgroups in groups acting on trees,
Abstract: Let $G$ be a group acting on a tree $T$ with finite edge stabilizers of
bounded order. We provide, in some very interesting cases, upper bounds for the
complexity of the intersection $H\cap K$ of two tame subgroups $H$ and $K$ of
$G$ in terms of the complexities of $H$ and $K$. In particular, we obtain
bounds for the Kurosh rank $Kr(H\cap K)$ of the intersection in terms of Kurosh
ranks $Kr(H)$ and $Kr(K)$, in the case where $H$ and $K$ act freely on the
edges of $T$. | [
0,
0,
1,
0,
0,
0
] | [
"Mathematics"
] |
Title: Digital Advertising Traffic Operation: Flow Management Analysis,
Abstract: In a Web Advertising Traffic Operation the Trafficking Routing Problem (TRP)
consists in scheduling the management of Web Advertising (Adv) campaign between
Trafficking campaigns in the most efficient way to oversee and manage
relationship with partners and internal teams, managing expectations through
integration and post-launch in order to ensure success for every stakeholders
involved. For our own interest we did that independent research projects also
through specific innovative tasks validate towards average working time
declared on "specification required" by the main worldwide industry leading
Advertising Agency. We present a Mixed Integer Linear Programming (MILP)
formulation for end-to-end management of campaign workflow along a
predetermined path and generalize it to include alternative path to oversee and
manage detail-oriented relationship with partners and internal teams to achieve
the goals above mentioned. To meet clients' KPIs, we consider an objective
function that includes the punctuality indicators (the average waiting time and
completion times) but also the main punctuality indicators (the average delay
and the on time performance). Then we investigate their analytical
relationships in the advertising domain through experiments based on real data
from a Traffic Office. We show that the classic punctuality indicators are in
contradiction with the task of reducing waiting times. We propose new
indicators used for a synthesize analysis on projects or process changes for
the wider team that are more sustainable, but also more relevant for
stakeholders. We also show that the flow of a campaign (adv-ways) is the main
bottleneck of a Traffic Office and that alternate paths cannot improve the
performance indicators. | [
1,
0,
1,
0,
0,
0
] | [
"Computer Science",
"Statistics",
"Quantitative Finance"
] |
Title: Addressing Class Imbalance in Classification Problems of Noisy Signals by using Fourier Transform Surrogates,
Abstract: Randomizing the Fourier-transform (FT) phases of temporal-spatial data
generates surrogates that approximate examples from the data-generating
distribution. We propose such FT surrogates as a novel tool to augment and
analyze training of neural networks and explore the approach in the example of
sleep-stage classification. By computing FT surrogates of raw EEG, EOG, and EMG
signals of under-represented sleep stages, we balanced the CAPSLPDB sleep
database. We then trained and tested a convolutional neural network for sleep
stage classification, and found that our surrogate-based augmentation improved
the mean F1-score by 7%. As another application of FT surrogates, we formulated
an approach to compute saliency maps for individual sleep epochs. The
visualization is based on the response of inferred class probabilities under
replacement of short data segments by partial surrogates. To quantify how well
the distributions of the surrogates and the original data match, we evaluated a
trained classifier on surrogates of correctly classified examples, and
summarized these conditional predictions in a confusion matrix. We show how
such conditional confusion matrices can qualitatively explain the performance
of surrogates in class balancing. The FT-surrogate augmentation approach may
improve classification on noisy signals if carefully adapted to the data
distribution under analysis. | [
0,
0,
0,
1,
1,
0
] | [
"Computer Science",
"Statistics"
] |
Title: Simultaneous smoothness and simultaneous stability of a $C^\infty$ strictly convex integrand and its dual,
Abstract: In this paper, we investigate simultaneous properties of a convex integrand
$\gamma$ and its dual $\delta$. The main results are the following three.
(1) For a $C^\infty$ convex integrand $\gamma: S^n\to \mathbb{R}_+$, its dual
convex integrand $\delta: S^n\to \mathbb{R}_+$ is of class $C^\infty$ if and
only if $\gamma$ is a strictly convex integrand.
(2) Let $\gamma: S^n\to \mathbb{R}_+$ be a $C^\infty$ strictly convex
integrand. Then, $\gamma$ is stable if and only if its dual convex integrand
$\delta: S^n\to \mathbb{R}_+$ is stable.
(3) Let $\gamma: S^n\to \mathbb{R}_+$ be a $C^\infty$ strictly convex
integrand. Suppose that $\gamma$ is stable. Then, for any $i$ $(0\le i\le n)$,
a point $\theta_0\in S^n$ is a non-degenerate critical point of $\gamma$ with
Morse index $i$ if and only if its antipodal point $-\theta_0\in S^n$ is a
non-degenerate critical point of the dual convex integrand $\delta$ with Morse
index $(n-i)$. | [
0,
0,
1,
0,
0,
0
] | [
"Mathematics"
] |
Title: Anomalous transport effects on switching currents of graphene-based Josephson junctions,
Abstract: We explore the effect of noise on the ballistic graphene-based small
Josephson junctions in the framework of the resistively and capacitively
shunted model. We use the non-sinusoidal current-phase relation specific for
graphene layers partially covered by superconducting electrodes. The noise
induced escapes from the metastable states, when the external bias current is
ramped, give the switching current distribution, i.e. the probability
distribution of the passages to finite voltage from the superconducting state
as a function of the bias current, that is the information more promptly
available in the experiments. We consider a noise source that is a mixture of
two different types of processes: a Gaussian contribution to simulate an
uncorrelated ordinary thermal bath, and non-Gaussian, $\alpha$-stable (or
Lévy) term, generally associated to non-equilibrium transport phenomena. We
find that the analysis of the switching current distribution makes it possible
to efficiently detect a non-Gaussian noise component in a Gaussian background. | [
0,
1,
0,
0,
0,
0
] | [
"Physics"
] |
Title: PbTe(111) Sub-Thermionic Photocathode: A Route to High-Quality Electron Pulses,
Abstract: The emission properties of PbTe(111) single crystal have been extensively
investigated to demonstrate that PbTe(111) is a promising low root mean square
transverse momentum ({\Delta}p$_T$) and high brightness photocathode. The
density functional theory (DFT) based photoemission analysis successfully
elucidates that the 'hole-like' {\Lambda}$^+_6$ energy band in the $L$ valley
with low effective mass $m^*$ results in low {\Delta}p$_T$. Especially, as a
300K solid planar photocathode, Te-terminated PbTe(111) single crystal is
expected to be a potential 50K electron source. | [
0,
1,
0,
0,
0,
0
] | [
"Physics"
] |
Title: Envy-free Matchings with Lower Quotas,
Abstract: While every instance of the Hospitals/Residents problem admits a stable
matching, the problem with lower quotas (HR-LQ) has instances with no stable
matching. For such an instance, we expect the existence of an envy-free
matching, which is a relaxation of a stable matching preserving a kind of
fairness property. In this paper, we investigate the existence of an envy-free
matching in several settings, in which hospitals have lower quotas and not all
doctor-hospital pairs are acceptable. We first show that, for an HR-LQ
instance, we can efficiently decide the existence of an envy-free matching.
Then, we consider envy-freeness in the Classified Stable Matching model due to
Huang (2010), i.e., each hospital has lower and upper quotas on subsets of
doctors. We show that, for this model, deciding the existence of an envy-free
matching is NP-hard in general, but solvable in polynomial time if quotas are
paramodular. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science",
"Mathematics"
] |
Title: Interacting Multi-particle Classical Szilard Engine,
Abstract: Szilard engine(SZE) is one of the best example of how information can be used
to extract work from a system. Initially, the working substance of SZE was
considered to be a single particle. Later on, researchers has extended the
studies of SZE to multi-particle systems and even to quantum regime. Here we
present a detailed study of classical SZE consisting of $N$ particles with
inter-particle interactions, i.e., the working substance is a low density
non-ideal gas and compare the work extraction with respect to SZE with
non-interacting multi particle system as working substance. We have considered
two cases of interactions namely: (i) hard core interactions and (ii) square
well interaction. Our study reveals that work extraction is less when more
particles are interacting through hard core interactions. More work is
extracted when the particles are interacting via square well interaction.
Another important result for the second case is that as we increase the
particle number the work extraction becomes independent of the initial position
of the partition, as opposed to the first case. Work extraction depends
crucially on the initial position of the partition. More work can be extracted
with larger number of particles when partition is inserted at positions near
the boundary walls. | [
0,
1,
0,
0,
0,
0
] | [
"Physics"
] |
Title: Graph of Virtual Actors (GOVA): a Big Data Analytics Architecture for IoT,
Abstract: With the emergence of cloud computing and sensor technologies, Big Data
analytics for the Internet of Things (IoT) has become the main force behind
many innovative solutions for our society's problems. This paper provides
practical explanations for the question "why is the number of Big Data
applications that succeed and have an effect on our daily life so limited,
compared with all of the solutions proposed and tested in the literature?",
with examples taken from Smart Grids. We argue that "noninvariants" are the
most challenging issues in IoT applications, which can be easily revealed if we
use the term "invariant" to replace the more common terms such as
"information", "knowledge", or "insight" in any Big Data for IoT research. From
our experience with developing Smart Grid applications, we produced a list of
"noninvariants", which we believe to be the main causes of the gaps between Big
Data in a laboratory and in practice in IoT applications. This paper also
proposes Graph of Virtual Actors (GOVA) as a Big Data analytics architecture
for IoT applications, which not only can solve the noninvariants issues, but
can also quickly scale horizontally in terms of computation, data storage,
caching requirements, and programmability of the system. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science"
] |
Title: A Variation of the $q$-Painlevé System with Affine Weyl Group Symmetry of Type $E_7^{(1)}$,
Abstract: Recently a certain $q$-Painlevé type system has been obtained from a
reduction of the $q$-Garnier system. In this paper it is shown that the
$q$-Painlevé type system is associated with another realization of the affine
Weyl group symmetry of type $E_7^{(1)}$ and is different from the well-known
$q$-Painlevé system of type $E_7^{(1)}$ from the point of view of evolution
directions. We also study a connection between the $q$-Painlevé type system
and the $q$-Painlevé system of type $E_7^{(1)}$. Furthermore determinant
formulas of particular solutions for the $q$-Painlevé type system are
constructed in terms of the terminating $q$-hypergeometric function. | [
0,
1,
1,
0,
0,
0
] | [
"Mathematics"
] |
Title: Riemannian geometry in infinite dimensional spaces,
Abstract: We lay foundations of the subject in the title, on which we build in another
paper devoted to isometries in spaces of Kähler metrics. | [
0,
0,
1,
0,
0,
0
] | [
"Mathematics"
] |
Title: Full-angle Negative Reflection with An Ultrathin Acoustic Gradient Metasurface: Floquet-Bloch Modes Perspective and Experimental Verification,
Abstract: Metasurface with gradient phase response offers new alternative for steering
the propagation of waves. Conventional Snell's law has been revised by taking
the contribution of local phase gradient into account. However, the requirement
of momentum matching along the metasurface sets its nontrivial beam
manipulation functionality within a limited-angle incidence. In this work, we
theoretically and experimentally demonstrate that the acoustic gradient
metasurface supports the negative reflection for full-angle incidence. The mode
expansion theory is developed to help understand how the gradient metasurface
tailors the incident beams, and the full-angle negative reflection occurs when
the first negative order Floquet-Bloch mode dominates. The coiling-up space
structures are utilized to build desired acoustic gradient metasurface and the
full-angle negative reflections have been perfectly verified by experimental
measurements. Our work offers the Floquet-Bloch modes perspective for
qualitatively understanding the reflection behaviors of the acoustic gradient
metasurface and enables a new degree of the acoustic wave manipulating. | [
0,
1,
0,
0,
0,
0
] | [
"Physics"
] |
Title: Semigroup C*-algebras and toric varieties,
Abstract: Let S be a finitely generated subsemigroup of Z^2. We derive a general
formula for the K-theory of the left regular C*-algebra for S. | [
0,
0,
1,
0,
0,
0
] | [
"Mathematics"
] |
Title: Error analysis for small-sample, high-variance data: Cautions for bootstrapping and Bayesian bootstrapping,
Abstract: Recent advances in molecular simulations allow the direct evaluation of
kinetic parameters such as rate constants for protein folding or unfolding.
However, these calculations are usually computationally expensive and even
significant computing resources may result in a small number of independent
rate estimates spread over many orders of magnitude. Such small, high-variance
samples are not readily amenable to analysis using the standard uncertainty
("standard error of the mean") because unphysical negative limits of confidence
intervals result. Bootstrapping, a natural alternative guaranteed to yield a
confidence interval within the minimum and maximum values, also exhibits a
striking systematic bias of the lower confidence limit. As we show,
bootstrapping artifactually assigns high probability to improbably low mean
values. A second alternative, the Bayesian bootstrap strategy, does not suffer
from the same deficit and is more logically consistent with the type of
confidence interval desired, but must be used with caution nevertheless.
Neither standard nor Bayesian bootstrapping can overcome the intrinsic
challenge of under-estimating the mean from small, high-variance samples. Our
report is based on extensive re-analysis of multiple estimates for rate
constants obtained from independent atomistic simulations. Although we only
analyze rate constants, similar considerations may apply to other types of
high-variance calculations, such as may occur in highly non-linear averages
like the Jarzynski relation. | [
0,
0,
0,
1,
0,
0
] | [
"Statistics",
"Quantitative Biology"
] |
Title: Computing Influence of a Product through Uncertain Reverse Skyline,
Abstract: Understanding the influence of a product is crucially important for making
informed business decisions. This paper introduces a new type of skyline
queries, called uncertain reverse skyline, for measuring the influence of a
probabilistic product in uncertain data settings. More specifically, given a
dataset of probabilistic products P and a set of customers C, an uncertain
reverse skyline of a probabilistic product q retrieves all customers c in C
which include q as one of their preferred products. We present efficient
pruning ideas and techniques for processing the uncertain reverse skyline query
of a probabilistic product using R-Tree data index. We also present an
efficient parallel approach to compute the uncertain reverse skyline and
influence score of a probabilistic product. Our approach significantly
outperforms the baseline approach derived from the existing literature. The
efficiency of our approach is demonstrated by conducting extensive experiments
with both real and synthetic datasets. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science",
"Statistics"
] |
Title: A branch-and-price approach with MILP formulation to modularity density maximization on graphs,
Abstract: For clustering of an undirected graph, this paper presents an exact algorithm
for the maximization of modularity density, a more complicated criterion to
overcome drawbacks of the well-known modularity. The problem can be interpreted
as the set-partitioning problem, which reminds us of its integer linear
programming (ILP) formulation. We provide a branch-and-price framework for
solving this ILP, or column generation combined with branch-and-bound. Above
all, we formulate the column generation subproblem to be solved repeatedly as a
simpler mixed integer linear programming (MILP) problem. Acceleration
techniques called the set-packing relaxation and the
multiple-cutting-planes-at-a-time combined with the MILP formulation enable us
to optimize the modularity density for famous test instances including ones
with over 100 vertices in around four minutes by a PC. Our solution method is
deterministic and the computation time is not affected by any stochastic
behavior. For one of them, column generation at the root node of the
branch-and-bound tree provides a fractional upper bound solution and our
algorithm finds an integral optimal solution after branching. | [
1,
0,
1,
0,
0,
0
] | [
"Computer Science",
"Mathematics"
] |
Title: Survey of Gravitationally-lensed Objects in HSC Imaging (SuGOHI). I. Automatic search for galaxy-scale strong lenses,
Abstract: The Hyper Suprime-Cam Subaru Strategic Program (HSC SSP) is an excellent
survey for the search for strong lenses, thanks to its area, image quality and
depth. We use three different methods to look for lenses among 43,000 luminous
red galaxies from the Baryon Oscillation Spectroscopic Survey (BOSS) sample
with photometry from the S16A internal data release of the HSC SSP. The first
method is a newly developed algorithm, named YATTALENS, which looks for
arc-like features around massive galaxies and then estimates the likelihood of
an object being a lens by performing a lens model fit. The second method,
CHITAH, is a modeling-based algorithm originally developed to look for lensed
quasars. The third method makes use of spectroscopic data to look for emission
lines from objects at a different redshift from that of the main galaxy. We
find 15 definite lenses, 36 highly probable lenses and 282 possible lenses.
Among the three methods, YATTALENS, which was developed specifically for this
problem, performs best in terms of both completeness and purity. Nevertheless
five highly probable lenses were missed by YATTALENS but found by the other two
methods, indicating that the three methods are highly complementary. Based on
these numbers we expect to find $\sim$300 definite or probable lenses by the
end of the HSC SSP. | [
0,
1,
0,
0,
0,
0
] | [
"Physics",
"Astrophysics"
] |
Title: Learning Sparse Neural Networks through $L_0$ Regularization,
Abstract: We propose a practical method for $L_0$ norm regularization for neural
networks: pruning the network during training by encouraging weights to become
exactly zero. Such regularization is interesting since (1) it can greatly speed
up training and inference, and (2) it can improve generalization. AIC and BIC,
well-known model selection criteria, are special cases of $L_0$ regularization.
However, since the $L_0$ norm of weights is non-differentiable, we cannot
incorporate it directly as a regularization term in the objective function. We
propose a solution through the inclusion of a collection of non-negative
stochastic gates, which collectively determine which weights to set to zero. We
show that, somewhat surprisingly, for certain distributions over the gates, the
expected $L_0$ norm of the resulting gated weights is differentiable with
respect to the distribution parameters. We further propose the \emph{hard
concrete} distribution for the gates, which is obtained by "stretching" a
binary concrete distribution and then transforming its samples with a
hard-sigmoid. The parameters of the distribution over the gates can then be
jointly optimized with the original network parameters. As a result our method
allows for straightforward and efficient learning of model structures with
stochastic gradient descent and allows for conditional computation in a
principled way. We perform various experiments to demonstrate the effectiveness
of the resulting approach and regularizer. | [
1,
0,
0,
1,
0,
0
] | [
"Computer Science",
"Statistics"
] |
Title: Sequential Randomized Matrix Factorization for Gaussian Processes: Efficient Predictions and Hyper-parameter Optimization,
Abstract: This paper presents a sequential randomized lowrank matrix factorization
approach for incrementally predicting values of an unknown function at test
points using the Gaussian Processes framework. It is well-known that in the
Gaussian processes framework, the computational bottlenecks are the inversion
of the (regularized) kernel matrix and the computation of the hyper-parameters
defining the kernel. The main contributions of this paper are two-fold. First,
we formalize an approach to compute the inverse of the kernel matrix using
randomized matrix factorization algorithms in a streaming scenario, i.e., data
is generated incrementally over time. The metrics of accuracy and computational
efficiency of the proposed method are compared against a batch approach based
on use of randomized matrix factorization and an existing streaming approach
based on approximating the Gaussian process by a finite set of basis vectors.
Second, we extend the sequential factorization approach to a class of kernel
functions for which the hyperparameters can be efficiently optimized. All
results are demonstrated on two publicly available datasets. | [
1,
0,
0,
1,
0,
0
] | [
"Computer Science",
"Statistics"
] |
Title: Large-scale dynamos in rapidly rotating plane layer convection,
Abstract: Context: Convectively-driven flows play a crucial role in the dynamo
processes that are responsible for producing magnetic activity in stars and
planets. It is still not fully understood why many astrophysical magnetic
fields have a significant large-scale component. Aims: Our aim is to
investigate the dynamo properties of compressible convection in a rapidly
rotating Cartesian domain, focusing upon a parameter regime in which the
underlying hydrodynamic flow is known to be unstable to a large-scale vortex
instability. Methods: The governing equations of three-dimensional nonlinear
magnetohydrodynamics (MHD) are solved numerically. Different numerical schemes
are compared and we propose a possible benchmark case for other similar codes.
Results: In keeping with previous related studies, we find that convection in
this parameter regime can drive a large-scale dynamo. The components of the
mean horizontal magnetic field oscillate, leading to a continuous overall
rotation of the mean field. Whilst the large-scale vortex instability dominates
the early evolution of the system, it is suppressed by the magnetic field and
makes a negligible contribution to the mean electromotive force that is
responsible for driving the large-scale dynamo. The cycle period of the dynamo
is comparable to the ohmic decay time, with longer cycles for dynamos in
convective systems that are closer to onset. In these particular simulations,
large-scale dynamo action is found only when vertical magnetic field boundary
conditions are adopted at the upper and lower boundaries. Strongly modulated
large-scale dynamos are found at higher Rayleigh numbers, with periods of
reduced activity ("grand minima"-like events) occurring during transient phases
in which the large-scale vortex temporarily re-establishes itself, before being
suppressed again by the magnetic field. | [
0,
1,
0,
0,
0,
0
] | [
"Physics"
] |
Title: Statistical inference for misspecified ergodic Lévy driven stochastic differential equation models,
Abstract: This paper deals with the estimation problem of misspecified ergodic Lévy
driven stochastic differential equation models based on high-frequency samples.
We utilize the widely applicable and tractable Gaussian quasi-likelihood
approach which focuses on (conditional) mean and variance structure. It is
shown that the corresponding Gaussian quasi-likelihood estimators of drift and
scale parameters satisfy tail probability estimates and asymptotic normality at
the same rate as correctly specified case. In this process, extended Poisson
equation for time-homogeneous Feller Markov processes plays an important role
to handle misspecification effect. Our result confirms the practical usefulness
of the Gaussian quasi-likelihood approach for SDE models, more firmly. | [
0,
0,
1,
1,
0,
0
] | [
"Statistics",
"Mathematics"
] |
Title: Automated and Robust Quantification of Colocalization in Dual-Color Fluorescence Microscopy: A Nonparametric Statistical Approach,
Abstract: Colocalization is a powerful tool to study the interactions between
fluorescently labeled molecules in biological fluorescence microscopy. However,
existing techniques for colocalization analysis have not undergone continued
development especially in regards to robust statistical support. In this paper,
we examine two of the most popular quantification techniques for colocalization
and argue that they could be improved upon using ideas from nonparametric
statistics and scan statistics. In particular, we propose a new colocalization
metric that is robust, easily implementable, and optimal in a rigorous
statistical testing framework. Application to several benchmark datasets, as
well as biological examples, further demonstrates the usefulness of the
proposed technique. | [
0,
0,
0,
1,
0,
0
] | [
"Quantitative Biology",
"Statistics"
] |
Title: Subadditivity and additivity of the Yang-Mills action functional in Noncommutative Geometry,
Abstract: We formulate notions of subadditivity and additivity of the Yang-Mills action
functional in noncommutative geometry. We identify a suitable hypothesis on
spectral triples which proves that the Yang-Mills functional is always
subadditive, as per expectation. The additivity property is much stronger in
the sense that it implies the subadditivity property. Under this hypothesis we
obtain a necessary and sufficient condition for the additivity of the
Yang-Mills functional. An instance of additivity is shown for the case of
noncommutative $n$-tori. We also investigate the behaviour of critical points
of the Yang-Mills functional under additivity. At the end we discuss few
examples involving compact spin manifolds, matrix algebras, noncommutative
$n$-torus and the quantum Heisenberg manifolds which validate our hypothesis. | [
0,
0,
1,
0,
0,
0
] | [
"Mathematics",
"Physics"
] |
Title: Specifying a positive threshold function via extremal points,
Abstract: An extremal point of a positive threshold Boolean function $f$ is either a
maximal zero or a minimal one. It is known that if $f$ depends on all its
variables, then the set of its extremal points completely specifies $f$ within
the universe of threshold functions. However, in some cases, $f$ can be
specified by a smaller set. The minimum number of points in such a set is the
specification number of $f$. It was shown in [S.-T. Hu. Threshold Logic, 1965]
that the specification number of a threshold function of $n$ variables is at
least $n+1$. In [M. Anthony, G. Brightwell, and J. Shawe-Taylor. On specifying
Boolean functions by labelled examples. Discrete Applied Mathematics, 1995] it
was proved that this bound is attained for nested functions and conjectured
that for all other threshold functions the specification number is strictly
greater than $n+1$. In the present paper, we resolve this conjecture negatively
by exhibiting threshold Boolean functions of $n$ variables, which are
non-nested and for which the specification number is $n+1$. On the other hand,
we show that the set of extremal points satisfies the statement of the
conjecture, i.e., a positive threshold Boolean function depending on all its
$n$ variables has $n+1$ extremal points if and only if it is nested. To prove
this, we reveal an underlying structure of the set of extremal points. | [
1,
0,
0,
0,
0,
0
] | [
"Mathematics",
"Computer Science"
] |
Title: Using Stock Prices as Ground Truth in Sentiment Analysis to Generate Profitable Trading Signals,
Abstract: The increasing availability of "big" (large volume) social media data has
motivated a great deal of research in applying sentiment analysis to predict
the movement of prices within financial markets. Previous work in this field
investigates how the true sentiment of text (i.e. positive or negative
opinions) can be used for financial predictions, based on the assumption that
sentiments expressed online are representative of the true market sentiment.
Here we consider the converse idea, that using the stock price as the
ground-truth in the system may be a better indication of sentiment. Tweets are
labelled as Buy or Sell dependent on whether the stock price discussed rose or
fell over the following hour, and from this, stock-specific dictionaries are
built for individual companies. A Bayesian classifier is used to generate stock
predictions, which are input to an automated trading algorithm. Placing 468
trades over a 1 month period yields a return rate of 5.18%, which annualises to
approximately 83% per annum. This approach performs significantly better than
random chance and outperforms two baseline sentiment analysis methods tested. | [
0,
0,
0,
0,
0,
1
] | [
"Computer Science",
"Quantitative Finance",
"Statistics"
] |
Title: When does every definable nonempty set have a definable element?,
Abstract: The assertion that every definable set has a definable element is equivalent
over ZF to the principle $V=\text{HOD}$, and indeed, we prove, so is the
assertion merely that every $\Pi_2$-definable set has an ordinal-definable
element. Meanwhile, every model of ZFC has a forcing extension satisfying
$V\neq\text{HOD}$ in which every $\Sigma_2$-definable set has an
ordinal-definable element. Similar results hold for $\text{HOD}(\mathbb{R})$
and $\text{HOD}(\text{Ord}^\omega)$ and other natural instances of
$\text{HOD}(X)$. | [
0,
0,
1,
0,
0,
0
] | [
"Mathematics"
] |
Title: Measurement and Analysis of Quality of Service of Mobile Networks in Afghanistan End User Perspective,
Abstract: Enhanced Quality of Service (QoS) and satisfaction of mobile phone user are
major concerns of a service provider. In order to manage network efficiently
and to provide enhanced end to end Quality of Experience (QoE), operator is
expected to measure and analyze QoS from various perspectives and at different
relevant points of network. The scope of this paper is measurement and
statistically analysis of QoS of mobile networks from end user perspective in
Afghanistan. The study is based on primary data collected on random basis from
1,515 mobile phone users of five cellular operators. The paper furthermore
proposes adequate technical solutions to mobile operators in order to address
existing challenges in the area of QoS and to remain competitive in the market.
Based on the result of processed data, considering geographical locations,
population and telecom regulations of the government, authors recommend
deployment of small cells (SCs), increasing number of regular performance
tests, optimal placement of base stations, increasing number of carriers, and
high order sectorization as proposed technical solutions. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science",
"Statistics"
] |
Title: On the uncertainty of temperature estimation in a rapid compression machine,
Abstract: Rapid compression machines (RCMs) have been widely used in the combustion
literature to study the low-to-intermediate temperature ignition of many fuels.
In a typical RCM, the pressure during and after the compression stroke is
measured. However, measurement of the temperature history in the RCM reaction
chamber is challenging. Thus, the temperature is generally calculated by the
isentropic relations between pressure and temperature, assuming that the
adiabatic core hypothesis holds. To estimate the uncertainty in the calculated
temperature, an uncertainty propagation analysis must be carried out. Our
previous analyses assumed that the uncertainties of the parameters in the
equation to calculate the temperature were normally distributed and
independent, but these assumptions do not hold for typical RCM operating
procedures. In this work, a Monte Carlo method is developed to estimate the
uncertainty in the calculated temperature, while taking into account the
correlation between parameters and the possibility of non-normal probability
distributions. In addition, the Monte Carlo method is compared to an analysis
that assumes normally distributed, independent parameters. Both analysis
methods show that the magnitude of the initial pressure and the uncertainty of
the initial temperature have strong influences on the magnitude of the
uncertainty. Finally, the uncertainty estimation methods studied here provide a
reference value for the uncertainty of the reference temperature in an RCM and
can be generalized to other similar facilities. | [
0,
1,
0,
0,
0,
0
] | [
"Physics",
"Statistics"
] |
Title: Improved Training of Wasserstein GANs,
Abstract: Generative Adversarial Networks (GANs) are powerful generative models, but
suffer from training instability. The recently proposed Wasserstein GAN (WGAN)
makes progress toward stable training of GANs, but sometimes can still generate
only low-quality samples or fail to converge. We find that these problems are
often due to the use of weight clipping in WGAN to enforce a Lipschitz
constraint on the critic, which can lead to undesired behavior. We propose an
alternative to clipping weights: penalize the norm of gradient of the critic
with respect to its input. Our proposed method performs better than standard
WGAN and enables stable training of a wide variety of GAN architectures with
almost no hyperparameter tuning, including 101-layer ResNets and language
models over discrete data. We also achieve high quality generations on CIFAR-10
and LSUN bedrooms. | [
1,
0,
0,
1,
0,
0
] | [
"Computer Science",
"Statistics"
] |
Title: A cancellation theorem for Milnor-Witt correspondences,
Abstract: We show that finite Milnor-Witt correspondences satisfy a cancellation
theorem with respect to the pointed multiplicative group scheme. This has
several notable applications in the theory of Milnor-Witt motives and
Milnor-Witt motivic cohomology. | [
0,
0,
1,
0,
0,
0
] | [
"Mathematics"
] |
Title: Weak Keys and Cryptanalysis of a Cold War Block Cipher,
Abstract: T-310 is a cipher that was used for encryption of governmental communications
in East Germany during the final years of the Cold War. Due to its complexity
and the encryption process,there was no published attack for a period of more
than 40 years until 2018 by Nicolas T. Courtois et al. in [10]. In this thesis
we study the so called 'long term keys' that were used in the cipher, in order
to expose weaknesses which will assist the design of various attacks on T-310. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science"
] |
Title: Spectroscopy of Ultra-diffuse Galaxies in the Coma Cluster,
Abstract: We present spectra of 5 ultra-diffuse galaxies (UDGs) in the vicinity of the
Coma Cluster obtained with the Multi-Object Double Spectrograph on the Large
Binocular Telescope. We confirm 4 of these as members of the cluster,
quintupling the number of spectroscopically confirmed systems. Like the
previously confirmed large (projected half light radius $>$ 4.6 kpc) UDG, DF44,
the systems we targeted all have projected half light radii $> 2.9$ kpc. As
such, we spectroscopically confirm a population of physically large UDGs in the
Coma cluster. The remaining UDG is located in the field, about $45$ Mpc behind
the cluster. We observe Balmer and Ca II H \& K absorption lines in all of our
UDG spectra. By comparing the stacked UDG spectrum against stellar population
synthesis models, we conclude that, on average, these UDGs are composed of
metal-poor stars ([Fe/H] $\lesssim -1.5$). We also discover the first UDG with
[OII] and [OIII] emission lines within a clustered environment, demonstrating
that not all cluster UDGs are devoid of gas and sources of ionizing radiation. | [
0,
1,
0,
0,
0,
0
] | [
"Physics"
] |
Title: On Robust Tie-line Scheduling in Multi-Area Power Systems,
Abstract: The tie-line scheduling problem in a multi-area power system seeks to
optimize tie-line power flows across areas that are independently operated by
different system operators (SOs). In this paper, we leverage the theory of
multi-parametric linear programming to propose algorithms for optimal tie-line
scheduling within a deterministic and a robust optimization framework. Through
a coordinator, the proposed algorithms are proved to converge to the optimal
schedule within a finite number of iterations. A key feature of the proposed
algorithms, besides their finite step convergence, is the privacy of the
information exchanges; the SO in an area does not need to reveal its dispatch
cost structure, network constraints, or the nature of the uncertainty set to
the coordinator. The performance of the algorithms is evaluated using several
power system examples. | [
0,
0,
1,
0,
0,
0
] | [
"Computer Science",
"Mathematics"
] |
Title: Stochastic Input Models in Online Computing,
Abstract: In this paper, we study twelve stochastic input models for online problems
and reveal the relationships among the competitive ratios for the models. The
competitive ratio is defined as the worst ratio between the expected optimal
value and the expected profit of the solution obtained by the online algorithm
where the input distribution is restricted according to the model. To handle a
broad class of online problems, we use a framework called request-answer games
that is introduced by Ben-David et al. The stochastic input models consist of
two types: known distribution and unknown distribution. For each type, we
consider six classes of distributions: dependent distributions, deterministic
input, independent distributions, identical independent distribution, random
order of a deterministic input, and random order of independent distributions.
As an application of the models, we consider two basic online problems, which
are variants of the secretary problem and the prophet inequality problem, under
the twelve stochastic input models. We see the difference of the competitive
ratios through these problems. | [
1,
0,
1,
1,
0,
0
] | [
"Computer Science",
"Mathematics",
"Statistics"
] |
Title: Generating Visual Representations for Zero-Shot Classification,
Abstract: This paper addresses the task of learning an image clas-sifier when some
categories are defined by semantic descriptions only (e.g. visual attributes)
while the others are defined by exemplar images as well. This task is often
referred to as the Zero-Shot classification task (ZSC). Most of the previous
methods rely on learning a common embedding space allowing to compare visual
features of unknown categories with semantic descriptions. This paper argues
that these approaches are limited as i) efficient discrimi-native classifiers
can't be used ii) classification tasks with seen and unseen categories
(Generalized Zero-Shot Classification or GZSC) can't be addressed efficiently.
In contrast , this paper suggests to address ZSC and GZSC by i) learning a
conditional generator using seen classes ii) generate artificial training
examples for the categories without exemplars. ZSC is then turned into a
standard supervised learning problem. Experiments with 4 generative models and
5 datasets experimentally validate the approach, giving state-of-the-art
results on both ZSC and GZSC. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science",
"Statistics"
] |
Title: Mitigating radiation damage of single photon detectors for space applications,
Abstract: Single-photon detectors in space must retain useful performance
characteristics despite being bombarded with sub-atomic particles. Mitigating
the effects of this space radiation is vital to enabling new space applications
which require high-fidelity single-photon detection. To this end, we conducted
proton radiation tests of various models of avalanche photodiodes (APDs) and
one model of photomultiplier tube potentially suitable for satellite-based
quantum communications. The samples were irradiated with 106 MeV protons at
doses approximately equivalent to lifetimes of 0.6 , 6, 12 and 24 months in a
low-Earth polar orbit. Although most detection properties were preserved,
including efficiency, timing jitter and afterpulsing probability, all APD
samples demonstrated significant increases in dark count rate (DCR) due to
radiation-induced damage, many orders of magnitude higher than the 200 counts
per second (cps) required for ground-to-satellite quantum communications. We
then successfully demonstrated the mitigation of this DCR degradation through
the use of deep cooling, to as low as -86 degrees C. This achieved DCR below
the required 200 cps over the 24 months orbit duration. DCR was further reduced
by thermal annealing at temperatures of +50 to +100 degrees C. | [
0,
1,
0,
0,
0,
0
] | [
"Physics"
] |
Title: An exact solution to a Stefan problem with variable thermal conductivity and a Robin boundary condition,
Abstract: In this article it is proved the existence of similarity solutions for a
one-phase Stefan problem with temperature-dependent thermal conductivity and a
Robin condition at the fixed face. The temperature distribution is obtained
through a generalized modified error function which is defined as the solution
to a nonlinear ordinary differential problem of second order. It is proved that
the latter has a unique non-negative bounded analytic solution when the
parameter on which it depends assumes small positive values. Moreover, it is
shown that the generalized modified error function is concave and increasing,
and explicit approximations are proposed for it. Relation between the Stefan
problem considered in this article with those with either constant thermal
conductivity or a temperature boundary condition is also analysed. | [
0,
0,
1,
0,
0,
0
] | [
"Mathematics",
"Physics"
] |
Title: State-of-the-art Speech Recognition With Sequence-to-Sequence Models,
Abstract: Attention-based encoder-decoder architectures such as Listen, Attend, and
Spell (LAS), subsume the acoustic, pronunciation and language model components
of a traditional automatic speech recognition (ASR) system into a single neural
network. In previous work, we have shown that such architectures are comparable
to state-of-theart ASR systems on dictation tasks, but it was not clear if such
architectures would be practical for more challenging tasks such as voice
search. In this work, we explore a variety of structural and optimization
improvements to our LAS model which significantly improve performance. On the
structural side, we show that word piece models can be used instead of
graphemes. We also introduce a multi-head attention architecture, which offers
improvements over the commonly-used single-head attention. On the optimization
side, we explore synchronous training, scheduled sampling, label smoothing, and
minimum word error rate optimization, which are all shown to improve accuracy.
We present results with a unidirectional LSTM encoder for streaming
recognition. On a 12, 500 hour voice search task, we find that the proposed
changes improve the WER from 9.2% to 5.6%, while the best conventional system
achieves 6.7%; on a dictation task our model achieves a WER of 4.1% compared to
5% for the conventional system. | [
1,
0,
0,
1,
0,
0
] | [
"Computer Science"
] |
Title: Bayesian inference for Stable Levy driven Stochastic Differential Equations with high-frequency data,
Abstract: In this article we consider parametric Bayesian inference for stochastic
differential equations (SDE) driven by a pure-jump stable Levy process, which
is observed at high frequency. In most cases of practical interest, the
likelihood function is not available, so we use a quasi-likelihood and place an
associated prior on the unknown parameters. It is shown under regularity
conditions that there is a Bernstein-von Mises theorem associated to the
posterior. We then develop a Markov chain Monte Carlo (MCMC) algorithm for
Bayesian inference and assisted by our theoretical results, we show how to
scale Metropolis-Hastings proposals when the frequency of the data grows, in
order to prevent the acceptance ratio going to zero in the large data limit.
Our algorithm is presented on numerical examples that help to verify our
theoretical findings. | [
0,
0,
1,
1,
0,
0
] | [
"Statistics",
"Mathematics"
] |
Title: The Evolution of Reputation-Based Cooperation in Regular Networks,
Abstract: Despite recent advances in reputation technologies, it is not clear how
reputation systems can affect human cooperation in social networks. Although it
is known that two of the major mechanisms in the evolution of cooperation are
spatial selection and reputation-based reciprocity, theoretical study of the
interplay between both mechanisms remains almost uncharted. Here, we present a
new individual-based model for the evolution of reciprocal cooperation between
reputation and networks. We comparatively analyze four of the leading moral
assessment rules---shunning, image scoring, stern judging, and simple
standing---and base the model on the giving game in regular networks for
Cooperators, Defectors, and Discriminators. Discriminators rely on a proper
moral assessment rule. By using individual-based models, we show that the four
assessment rules are differently characterized in terms of how cooperation
evolves, depending on the benefit-to-cost ratio, the network-node degree, and
the observation and error conditions. Our findings show that the most tolerant
rule---simple standing---is the most robust among the four assessment rules in
promoting cooperation in regular networks. | [
1,
1,
0,
0,
0,
0
] | [
"Quantitative Biology",
"Mathematics"
] |
Title: The ABCD of topological recursion,
Abstract: Kontsevich and Soibelman reformulated and slightly generalised the
topological recursion of math-ph/0702045, seeing it as a quantization of
certain quadratic Lagrangians in $T^*V$ for some vector space $V$. KS
topological recursion is a procedure which takes as initial data a quantum Airy
structure -- a family of at most quadratic differential operators on $V$
satisfying some axioms -- and gives as outcome a formal series of functions in
$V$ (the partition function) simultaneously annihilated by these operators.
Finding and classifying quantum Airy structures modulo gauge group action, is
by itself an interesting problem which we study here. We provide some
elementary, Lie-algebraic tools to address this problem, and give some elements
of classification for ${\rm dim}\,V = 2$. We also describe four more
interesting classes of quantum Airy structures, coming from respectively
Frobenius algebras (here we retrieve the 2d TQFT partition function as a
special case), non-commutative Frobenius algebras, loop spaces of Frobenius
algebras and a $\mathbb{Z}_{2}$-invariant version of the latter. This
$\mathbb{Z}_{2}$-invariant version in the case of a semi-simple Frobenius
algebra corresponds to the topological recursion of math-ph/0702045. | [
0,
0,
1,
0,
0,
0
] | [
"Mathematics",
"Physics"
] |
Title: Evaluating Compositionality in Sentence Embeddings,
Abstract: An important challenge for human-like AI is compositional semantics. Recent
research has attempted to address this by using deep neural networks to learn
vector space embeddings of sentences, which then serve as input to other tasks.
We present a new dataset for one such task, `natural language inference' (NLI),
that cannot be solved using only word-level knowledge and requires some
compositionality. We find that the performance of state of the art sentence
embeddings (InferSent; Conneau et al., 2017) on our new dataset is poor. We
analyze the decision rules learned by InferSent and find that they are
consistent with simple heuristics that are ecologically valid in its training
dataset. Further, we find that augmenting training with our dataset improves
test performance on our dataset without loss of performance on the original
training dataset. This highlights the importance of structured datasets in
better understanding and improving AI systems. | [
0,
0,
0,
1,
0,
0
] | [
"Computer Science",
"Statistics"
] |
Title: Half-range lattice Boltzmann models for the simulation of Couette flow using the Shakhov collision term,
Abstract: The three-dimensional Couette flow between parallel plates is addressed using
mixed lattice Boltzmann models which implement the half-range and the
full-range Gauss-Hermite quadratures on the Cartesian axes perpendicular and
parallel to the walls, respectively. The ability of our models to simulate
rarefied flows are validated through comparison against previously reported
results obtained using the linearized Boltzmann-BGK equation for values of the
Knudsen number (Kn) up to $100$. We find that recovering the non-linear part of
the velocity profile (i.e., its deviation from a linear function) at ${\rm Kn}
\gtrsim 1$ requires high quadrature orders. We then employ the Shakhov model
for the collision term to obtain macroscopic profiles for Maxwell molecules
using the standard $\mu \sim T^\omega$ law, as well as for monatomic Helium and
Argon gases, modeled through ab-initio potentials, where the viscosity is
recovered using the Sutherland model. We validate our implementation by
comparison with DSMC results and find excellent match for all macroscopic
quantities for ${\rm Kn} \lesssim 0.1$. At ${\rm Kn} \gtrsim 0.1$, small
deviations can be seen in the profiles of the diagonal components of the
pressure tensor, the heat flux parallel to the plates, and the velocity
profile, as well as in the values of the velocity gradient at the channel
center. We attribute these deviations to the limited applicability of the
Shakhov collision model for highly out of equilibrium flows. | [
0,
1,
0,
0,
0,
0
] | [
"Physics",
"Mathematics"
] |
Title: Analyzing and improving maximal attainable accuracy in the communication hiding pipelined BiCGStab method,
Abstract: Pipelined Krylov subspace methods avoid communication latency by reducing the
number of global synchronization bottlenecks and by hiding global communication
behind useful computational work. In exact arithmetic pipelined Krylov subspace
algorithms are equivalent to classic Krylov subspace methods and generate
identical series of iterates. However, as a consequence of the reformulation of
the algorithm to improve parallelism, pipelined methods may suffer from
severely reduced attainable accuracy in a practical finite precision setting.
This work presents a numerical stability analysis that describes and quantifies
the impact of local rounding error propagation on the maximal attainable
accuracy of the multi-term recurrences in the preconditioned pipelined BiCGStab
method. Theoretical expressions for the gaps between the true and computed
residual as well as other auxiliary variables used in the algorithm are
derived, and the elementary dependencies between the gaps on the various
recursively computed vector variables are analyzed. The norms of the
corresponding propagation matrices and vectors provide insights in the possible
amplification of local rounding errors throughout the algorithm. Stability of
the pipelined BiCGStab method is compared numerically to that of pipelined CG
on a symmetric benchmark problem. Furthermore, numerical evidence supporting
the effectiveness of employing a residual replacement type strategy to improve
the maximal attainable accuracy for the pipelined BiCGStab method is provided. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science",
"Mathematics"
] |
Title: Trigonometric integrators for quasilinear wave equations,
Abstract: Trigonometric time integrators are introduced as a class of explicit
numerical methods for quasilinear wave equations. Second-order convergence for
the semi-discretization in time with these integrators is shown for a
sufficiently regular exact solution. The time integrators are also combined
with a Fourier spectral method into a fully discrete scheme, for which error
bounds are provided without requiring any CFL-type coupling of the
discretization parameters. The proofs of the error bounds are based on energy
techniques and on the semiclassical G\aa rding inequality. | [
0,
0,
1,
0,
0,
0
] | [
"Mathematics",
"Physics",
"Computer Science"
] |
Title: A Highly Efficient Polarization-Independent Metamaterial-Based RF Energy-Harvesting Rectenna for Low-Power Applications,
Abstract: A highly-efficient multi-resonant RF energy-harvesting rectenna based on a
metamaterial perfect absorber featuring closely-spaced polarization-independent
absorption modes is presented. Its effective area is larger than its physical
area, and so efficiencies of 230% and 130% are measured at power densities of
10 uW/cm2 and 1 uW/cm2 respectively, for a linear absorption mode at 0.75 GHz.
The rectenna exhibits a broad polarization-independent region between 1.4 GHz
and 1.7 GHz with maximum efficiencies of 167% and 36% for those same power
densities. Additionally, by adjustment of the distance between the rectenna and
a reflecting ground plane, the absorption frequency can be adjusted to a
limited extent within the polarization-independent region. Lastly, the rectenna
should be capable of delivering 100 uW of power to a device located within 50 m
of a cell-phone tower under ideal conditions. | [
0,
1,
0,
0,
0,
0
] | [
"Physics"
] |
Title: Mixed Graphical Models for Causal Analysis of Multi-modal Variables,
Abstract: Graphical causal models are an important tool for knowledge discovery because
they can represent both the causal relations between variables and the
multivariate probability distributions over the data. Once learned, causal
graphs can be used for classification, feature selection and hypothesis
generation, while revealing the underlying causal network structure and thus
allowing for arbitrary likelihood queries over the data. However, current
algorithms for learning sparse directed graphs are generally designed to handle
only one type of data (continuous-only or discrete-only), which limits their
applicability to a large class of multi-modal biological datasets that include
mixed type variables. To address this issue, we developed new methods that
modify and combine existing methods for finding undirected graphs with methods
for finding directed graphs. These hybrid methods are not only faster, but also
perform better than the directed graph estimation methods alone for a variety
of parameter settings and data set sizes. Here, we describe a new conditional
independence test for learning directed graphs over mixed data types and we
compare performances of different graph learning strategies on synthetic data. | [
1,
0,
0,
1,
0,
0
] | [
"Computer Science",
"Statistics",
"Quantitative Biology"
] |
Title: Deep Robust Framework for Protein Function Prediction using Variable-Length Protein Sequences,
Abstract: Amino acid sequence portrays most intrinsic form of a protein and expresses
primary structure of protein. The order of amino acids in a sequence enables a
protein to acquire a particular stable conformation that is responsible for the
functions of the protein. This relationship between a sequence and its function
motivates the need to analyse the sequences for predicting protein functions.
Early generation computational methods using BLAST, FASTA, etc. perform
function transfer based on sequence similarity with existing databases and are
computationally slow. Although machine learning based approaches are fast, they
fail to perform well for long protein sequences (i.e., protein sequences with
more than 300 amino acid residues). In this paper, we introduce a novel method
for construction of two separate feature sets for protein sequences based on
analysis of 1) single fixed-sized segments and 2) multi-sized segments, using
bi-directional long short-term memory network. Further, model based on proposed
feature set is combined with the state of the art Multi-lable Linear
Discriminant Analysis (MLDA) features based model to improve the accuracy.
Extensive evaluations using separate datasets for biological processes and
molecular functions demonstrate promising results for both single-sized and
multi-sized segments based feature sets. While former showed an improvement of
+3.37% and +5.48%, the latter produces an improvement of +5.38% and +8.00%
respectively for two datasets over the state of the art MLDA based classifier.
After combining two models, there is a significant improvement of +7.41% and
+9.21% respectively for two datasets compared to MLDA based classifier.
Specifically, the proposed approach performed well for the long protein
sequences and superior overall performance. | [
0,
0,
0,
0,
1,
0
] | [
"Computer Science",
"Quantitative Biology"
] |
Title: Helicity of convective flows from localized heat source in a rotating layer,
Abstract: Experimental and numerical study of the steady-state cyclonic vortex from
isolated heat source in a rotating fluid layer is described. The structure of
laboratory cyclonic vortex is similar to the typical structure of tropical
cyclones from observational data and numerical modelling including secondary
flows in the boundary layer. Differential characteristics of the flow were
studied by numerical simulation using CFD software FlowVision. Helicity
distribution in rotating fluid layer with localized heat source was analysed.
Two mechanisms which play role in helicity generation are found. The first one
is the strong correlation of cyclonic vortex and intensive upward motion in the
central part of the vessel. The second one is due to large gradients of
velocity on the periphery. The integral helicity in the considered case is
substantial and its relative level is high. | [
0,
1,
0,
0,
0,
0
] | [
"Physics"
] |
Title: Fine-Gray competing risks model with high-dimensional covariates: estimation and Inference,
Abstract: The purpose of this paper is to construct confidence intervals for the
regression coefficients in the Fine-Gray model for competing risks data with
random censoring, where the number of covariates can be larger than the sample
size. Despite strong motivation from biostatistics applications,
high-dimensional Fine-Gray model has attracted relatively little attention
among the methodological or theoretical literatures. We fill in this blank by
proposing first a consistent regularized estimator and then the confidence
intervals based on the one-step bias-correcting estimator. We are able to
generalize the partial likelihood approach for the Fine-Gray model under random
censoring despite many technical difficulties. We lay down a methodological and
theoretical framework for the one-step bias-correcting estimator with the
partial likelihood, which does not have independent and identically distributed
entries. We also handle for our theory the approximation error from the inverse
probability weighting (IPW), proposing novel concentration results for time
dependent processes. In addition to the theoretical results and algorithms, we
present extensive numerical experiments and an application to a study of
non-cancer mortality among prostate cancer patients using the linked
Medicare-SEER data. | [
0,
0,
1,
1,
0,
0
] | [
"Statistics",
"Mathematics"
] |
Title: Cartan's Conjecture for Moving Hypersurfaces,
Abstract: Let $f$ be a holomorphic curve in $\mathbb{P}^n({\mathbb{C}})$ and let
$\mathcal{D}=\{D_1,\ldots,D_q\}$ be a family of moving hypersurfaces defined by
a set of homogeneous polynomials $\mathcal{Q}=\{Q_1,\ldots,Q_q\}$. For
$j=1,\ldots,q$, denote by
$Q_j=\sum\limits_{i_0+\cdots+i_n=d_j}a_{j,I}(z)x_0^{i_0}\cdots x_n^{i_n}$,
where $I=(i_0,\ldots,i_n)\in\mathbb{Z}_{\ge 0}^{n+1}$ and $a_{j,I}(z)$ are
entire functions on ${\mathbb{C}}$ without common zeros. Let
$\mathcal{K}_{\mathcal{Q}}$ be the smallest subfield of meromorphic function
field $\mathcal{M}$ which contains ${\mathbb{C}}$ and all
$\frac{a_{j,I'}(z)}{a_{j,I''}(z)}$ with $a_{j,I''}(z)\not\equiv 0$, $1\le j\le
q$. In previous known second main theorems for $f$ and $\mathcal{D}$, $f$ is
usually assumed to be algebraically nondegenerate over
$\mathcal{K}_{\mathcal{Q}}$. In this paper, we prove a second main theorem in
which $f$ is only assumed to be nonconstant. This result can be regarded as a
generalization of Cartan's conjecture for moving hypersurfaces. | [
0,
0,
1,
0,
0,
0
] | [
"Mathematics"
] |
Title: A Fluid-Flow Interpretation of SCED Scheduling,
Abstract: We show that a fluid-flow interpretation of Service Curve Earliest Deadline
First (SCED) scheduling simplifies deadline derivations for this scheduler. By
exploiting the recently reported isomorphism between min-plus and max-plus
network calculus, and expressing deadlines in a max-plus algebra, deadline
computations no longer require pseudo-inverse computations. SCED deadlines are
provided for general convex or concave piecewise linear service curves. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science",
"Mathematics"
] |
Title: Emergence of Topological Nodal Lines and Type II Weyl Nodes in Strong Spin--Orbit Coupling System InNbX2(X=S,Se),
Abstract: Using first--principles density functional calculations, we systematically
investigate electronic structures and topological properties of InNbX2 (X=S,
Se). In the absence of spin--orbit coupling (SOC), both compounds show nodal
lines protected by mirror symmetry. Including SOC, the Dirac rings in InNbS2
split into two Weyl rings. This unique property is distinguished from other
dicovered nodal line materials which normally requires the absence of SOC. On
the other hand, SOC breaks the nodal lines in InNbSe2 and the compound becomes
a type II Weyl semimetal with 12 Weyl points in the Brillouin Zone. Using a
supercell slab calculation we study the dispersion of Fermi arcs surface states
in InNbSe2, we also utilize a coherent potential approximation to probe their
tolernace to the surface disorder effects. The quasi two--dimensionality and
the absence of toxic elements makes these two compounds an ideal experimental
platform for investigating novel properties of topological semimetals. | [
0,
1,
0,
0,
0,
0
] | [
"Physics"
] |
Title: Scheduling with regular performance measures and optional job rejection on a single machine,
Abstract: We address single machine problems with optional jobs - rejection, studied
recently in Zhang et al. [21] and Cao et al. [2]. In these papers, the authors
focus on minimizing regular performance measures, i.e., functions that are
non-decreasing in the jobs completion time, subject to the constraint that the
total rejection cost cannot exceed a predefined upper bound. They also prove
that the considered problems are ordinary NP-hard and provide
pseudo-polynomial-time Dynamic Programming (DP) solutions. In this paper, we
focus on three of these problems: makespan with release-dates; total completion
times; and total weighted completion, and present enhanced DP solutions
demonstrating both theoretical and practical improvements. Moreover, we provide
extensive numerical studies verifying their efficiency. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science",
"Mathematics"
] |
Title: Data-Driven Stochastic Robust Optimization: A General Computational Framework and Algorithm for Optimization under Uncertainty in the Big Data Era,
Abstract: A novel data-driven stochastic robust optimization (DDSRO) framework is
proposed for optimization under uncertainty leveraging labeled multi-class
uncertainty data. Uncertainty data in large datasets are often collected from
various conditions, which are encoded by class labels. Machine learning methods
including Dirichlet process mixture model and maximum likelihood estimation are
employed for uncertainty modeling. A DDSRO framework is further proposed based
on the data-driven uncertainty model through a bi-level optimization structure.
The outer optimization problem follows a two-stage stochastic programming
approach to optimize the expected objective across different data classes;
adaptive robust optimization is nested as the inner problem to ensure the
robustness of the solution while maintaining computational tractability. A
decomposition-based algorithm is further developed to solve the resulting
multi-level optimization problem efficiently. Case studies on process network
design and planning are presented to demonstrate the applicability of the
proposed framework and algorithm. | [
1,
0,
1,
0,
0,
0
] | [
"Computer Science",
"Mathematics",
"Statistics"
] |
Title: Algebraic multiscale method for flow in heterogeneous porous media with embedded discrete fractures (F-AMS),
Abstract: This paper introduces an Algebraic MultiScale method for simulation of flow
in heterogeneous porous media with embedded discrete Fractures (F-AMS). First,
multiscale coarse grids are independently constructed for both porous matrix
and fracture networks. Then, a map between coarse- and fine-scale is obtained
by algebraically computing basis functions with local support. In order to
extend the localization assumption to the fractured media, four types of basis
functions are investigated: (1) Decoupled-AMS, in which the two media are
completely decoupled, (2) Frac-AMS and (3) Rock-AMS, which take into account
only one-way transmissibilities, and (4) Coupled-AMS, in which the matrix and
fracture interpolators are fully coupled. In order to ensure scalability, the
F-AMS framework permits full flexibility in terms of the resolution of the
fracture coarse grids. Numerical results are presented for two- and
three-dimensional heterogeneous test cases. During these experiments, the
performance of F-AMS, paired with ILU(0) as second-stage smoother in a
convergent iterative procedure, is studied by monitoring CPU times and
convergence rates. Finally, in order to investigate the scalability of the
method, an extensive benchmark study is conducted, where a commercial algebraic
multigrid solver is used as reference. The results show that, given an
appropriate coarsening strategy, F-AMS is insensitive to severe fracture and
matrix conductivity contrasts, as well as the length of the fracture networks.
Its unique feature is that a fine-scale mass conservative flux field can be
reconstructed after any iteration, providing efficient approximate solutions in
time-dependent simulations. | [
1,
1,
0,
0,
0,
0
] | [
"Mathematics",
"Physics"
] |
Title: A Bayesian Mixture Model for Clustering on the Stiefel Manifold,
Abstract: Analysis of a Bayesian mixture model for the Matrix Langevin distribution on
the Stiefel manifold is presented. The model exploits a particular
parametrization of the Matrix Langevin distribution, various aspects of which
are elaborated on. A general, and novel, family of conjugate priors, and an
efficient Markov chain Monte Carlo (MCMC) sampling scheme for the corresponding
posteriors is then developed for the mixture model. Theoretical properties of
the prior and posterior distributions, including posterior consistency, are
explored in detail. Extensive simulation experiments are presented to validate
the efficacy of the framework. Real-world examples, including a large scale
neuroimaging dataset, are analyzed to demonstrate the computational
tractability of the approach. | [
0,
0,
0,
1,
0,
0
] | [
"Statistics",
"Mathematics"
] |
Title: Multi-color image compression-encryption algorithm based on chaotic system and fuzzy transform,
Abstract: In this paper an algorithm for multi-color image compression-encryption is
introduced. For compression step fuzzy transform based on exponential b-spline
function is used. In encryption step, a novel combination chaotic system based
on Sine and Tent systems is proposed. Also in the encryption algorithm, 3D
shift based on chaotic system is introduced. The simulation results and
security analysis show that the proposed algorithm is secure and efficient. | [
1,
0,
0,
0,
0,
0
] | [
"Computer Science"
] |
Title: The Dynamical History of Chariklo and its Rings,
Abstract: Chariklo is the only small Solar system body confirmed to have rings. Given
the instability of its orbit, the presence of rings is surprising, and their
origin remains poorly understood. In this work, we study the dynamical history
of the Chariklo system by integrating almost 36,000 Chariklo clones backwards
in time for one Gyr under the influence of the Sun and the four giant planets.
By recording all close encounters between the clones and planets, we
investigate the likelihood that Chariklo's rings could have survived since its
capture to the Centaur population. Our results reveal that Chariklo's orbit
occupies a region of stable chaos, resulting in its orbit being marginally more
stable than those of the other Centaurs. Despite this, we find that it was most
likely captured to the Centaur population within the last 20 Myr, and that its
orbital evolution has been continually punctuated by regular close encounters
with the giant planets. The great majority (> 99%) of those encounters within
one Hill radius of the planet have only a small effect on the rings. We
conclude that close encounters with giant planets have not had a significant
effect on the ring structure. Encounters within the Roche limit of the giant
planets are rare, making ring creation through tidal disruption unlikely. | [
0,
1,
0,
0,
0,
0
] | [
"Physics"
] |
Title: Smooth positon solutions of the focusing modified Korteweg-de Vries equation,
Abstract: The $n$-fold Darboux transformation $T_{n}$ of the focusing real mo\-di\-fied
Kor\-te\-weg-de Vries (mKdV) equation is expressed in terms of the determinant
representation. Using this representation, the $n$-soliton solutions of the
mKdV equation are also expressed by determinants whose elements consist of the
eigenvalues $\lambda_{j}$ and the corresponding eigenfunctions of the
associated Lax equation. The nonsingular $n$-positon solutions of the focusing
mKdV equation are obtained in the special limit
$\lambda_{j}\rightarrow\lambda_{1}$, from the corresponding $n$-soliton
solutions and by using the associated higher-order Taylor expansion.
Furthermore, the decomposition method of the $n$-positon solution into $n$
single-soliton solutions, the trajectories, and the corresponding "phase
shifts" of the multi-positons are also investigated. | [
0,
1,
0,
0,
0,
0
] | [
"Mathematics",
"Physics"
] |
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