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High order surface radiation conditions for time-harmonic waves in exterior domains | We formulate a new family of high order on-surface radiation conditions to
approximate the outgoing solution to the Helmholtz equation in exterior
domains. Motivated by the pseudo-differential expansion of the
Dirichlet-to-Neumann operator developed by Antoine et al. (J. Math. Anal. Appl.
229:184-211, 1999), we design a systematic procedure to apply
pseudo-differential symbols of arbitrarily high order. Numerical results are
presented to illustrate the performance of the proposed method for solving both
the Dirichlet and the Neumann boundary value problems. Possible improvements
and extensions are also discussed.
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Probabilistic PARAFAC2 | The PARAFAC2 is a multimodal factor analysis model suitable for analyzing
multi-way data when one of the modes has incomparable observation units, for
example because of differences in signal sampling or batch sizes. A fully
probabilistic treatment of the PARAFAC2 is desirable in order to improve
robustness to noise and provide a well founded principle for determining the
number of factors, but challenging because the factor loadings are constrained
to be orthogonal. We develop two probabilistic formulations of the PARAFAC2
along with variational procedures for inference: In the one approach, the mean
values of the factor loadings are orthogonal leading to closed form variational
updates, and in the other, the factor loadings themselves are orthogonal using
a matrix Von Mises-Fisher distribution. We contrast our probabilistic
formulation to the conventional direct fitting algorithm based on maximum
likelihood. On simulated data and real fluorescence spectroscopy and gas
chromatography-mass spectrometry data, we compare our approach to the
conventional PARAFAC2 model estimation and find that the probabilistic
formulation is more robust to noise and model order misspecification. The
probabilistic PARAFAC2 thus forms a promising framework for modeling multi-way
data accounting for uncertainty.
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Quantizing Euclidean motions via double-coset decomposition | Concepts from mathematical crystallography and group theory are used here to
quantize the group of rigid-body motions, resulting in a "motion alphabet" with
which to express robot motion primitives. From these primitives it is possible
to develop a dictionary of physical actions. Equipped with an alphabet of the
sort developed here, intelligent actions of robots in the world can be
approximated with finite sequences of characters, thereby forming the
foundation of a language in which to articulate robot motion. In particular, we
use the discrete handedness-preserving symmetries of macromolecular crystals
(known in mathematical crystallography as Sohncke space groups) to form a
coarse discretization of the space $\rm{SE}(3)$ of rigid-body motions. This
discretization is made finer by subdividing using the concept of double-coset
decomposition. More specifically, a very efficient, equivolumetric quantization
of spatial motion can be defined using the group-theoretic concept of a
double-coset decomposition of the form $\Gamma \backslash \rm{SE}(3) / \Delta$,
where $\Gamma$ is a Sohncke space group and $\Delta$ is a finite group of
rotational symmetries such as those of the icosahedron. The resulting discrete
alphabet is based on a very uniform sampling of $\rm{SE}(3)$ and is a tool for
describing the continuous trajectories of robots and humans. The general
"signals to symbols" problem in artificial intelligence is cast in this
framework for robots moving continuously in the world, and we present a
coarse-to-fine search scheme here to efficiently solve this decoding problem in
practice.
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Evolutionary Stability of Reputation Management System in Peer to Peer Networks | Each participant in peer-to-peer network prefers to free-ride on the
contribution of other participants. Reputation based resource sharing is a way
to control the free riding. Instead of classical game theory we use
evolutionary game theory to analyse the reputation based resource sharing in
peer to peer system. Classical game-theoretical approach requires global
information of the population. However, the evolutionary games only assumes
light cognitive capabilities of users, that is, each user imitates the behavior
of other user with better payoff. We find that without any extra benefit
reputation strategy is not stable in the system. We also find the fraction of
users who calculate the reputation for controlling the free riding in
equilibrium. In this work first we made a game theoretical model for the
reputation system and then we calculate the threshold of the fraction of users
with which the reputation strategy is sustainable in the system. We found that
in simplistic conditions reputation calculation is not evolutionarily stable
strategy but if we impose some initial payment to all users and then distribute
that payment among the users who are calculating reputation then reputation is
evolutionary stable strategy.
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A Study of FOSS'2013 Survey Data Using Clustering Techniques | FOSS is an acronym for Free and Open Source Software. The FOSS 2013 survey
primarily targets FOSS contributors and relevant anonymized dataset is publicly
available under CC by SA license. In this study, the dataset is analyzed from a
critical perspective using statistical and clustering techniques (especially
multiple correspondence analysis) with a strong focus on women contributors
towards discovering hidden trends and facts. Important inferences are drawn
about development practices and other facets of the free software and OSS
worlds.
| 1 | 0 | 0 | 1 | 0 | 0 |
Intermetallic Nanocrystals: Syntheses and Catalytic Applications | At the forefront of nanochemistry, there exists a research endeavor centered
around intermetallic nanocrystals, which are unique in terms of long-range
atomic ordering, well-defined stoichiometry, and controlled crystal structure.
In contrast to alloy nanocrystals with no atomic ordering, it has been
challenging to synthesize intermetallic nanocrystals with a tight control over
their size and shape. This review article highlights recent progress in the
synthesis of intermetallic nanocrystals with controllable sizes and
well-defined shapes. We begin with a simple analysis and some insights key to
the selection of experimental conditions for generating intermetallic
nanocrystals. We then present examples to highlight the viable use of
intermetallic nanocrystals as electrocatalysts or catalysts for various
reactions, with a focus on the enhanced performance relative to their alloy
counterparts that lack atomic ordering. We conclude with perspectives on future
developments in the context of synthetic control, structure-property
relationship, and application.
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Linear-scaling electronic structure theory: Electronic temperature in the Kernel Polynomial Method | Linear-scaling electronic structure methods based on the calculation of
moments of the underlying electronic Hamiltonian offer a computationally
efficient and numerically robust scheme to drive large-scale atomistic
simulations, in which the quantum-mechanical nature of the electrons is
explicitly taken into account. We compare the kernel polynomial method to the
Fermi operator expansion method and establish a formal connection between the
two approaches. We show that the convolution of the kernel polynomial method
may be understood as an effective electron temperature. The results of a number
of possible kernels are formally examined, and then applied to a representative
tight-binding model.
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Characterizing the 2016 Russian IRA Influence Campaign | Until recently, social media were seen to promote democratic discourse on
social and political issues. However, this powerful communication ecosystem has
come under scrutiny for allowing hostile actors to exploit online discussions
in an attempt to manipulate public opinion. A case in point is the ongoing U.S.
Congress investigation of Russian interference in the 2016 U.S. election
campaign, with Russia accused of, among other things, using trolls (malicious
accounts created for the purpose of manipulation) and bots (automated accounts)
to spread propaganda and politically biased information. In this study, we
explore the effects of this manipulation campaign, taking a closer look at
users who re-shared the posts produced on Twitter by the Russian troll accounts
publicly disclosed by U.S. Congress investigation. We collected a dataset of 13
million election-related posts shared on Twitter in the year of 2016 by over a
million distinct users. This dataset includes accounts associated with the
identified Russian trolls as well as users sharing posts in the same time
period on a variety of topics around the 2016 elections. We use label
propagation to infer the users' ideology based on the news sources they share.
We are able to classify a large number of users as liberal or conservative with
precision and recall above 84%. Conservative users who retweet Russian trolls
produced significantly more tweets than liberal ones, about 8 times as many in
terms of tweets. Additionally, trolls' position in the retweet network is
stable over time, unlike users who retweet them who form the core of the
election-related retweet network by the end of 2016. Using state-of-the-art bot
detection techniques, we estimate that about 5% and 11% of liberal and
conservative users are bots, respectively.
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Nonlinear Mapping Convergence and Application to Social Networks | This paper discusses discrete-time maps of the form $x(k + 1) = F(x(k))$,
focussing on equilibrium points of such maps. Under some circumstances,
Lefschetz fixed-point theory can be used to establish the existence of a single
locally attractive equilibrium (which is sometimes globally attractive) when a
general property of local attractivity is known for any equilibrium. Problems
in social networks often involve such discrete-time systems, and we make an
application to one such problem.
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Correlating Cellular Features with Gene Expression using CCA | To understand the biology of cancer, joint analysis of multiple data
modalities, including imaging and genomics, is crucial. The involved nature of
gene-microenvironment interactions necessitates the use of algorithms which
treat both data types equally. We propose the use of canonical correlation
analysis (CCA) and a sparse variant as a preliminary discovery tool for
identifying connections across modalities, specifically between gene expression
and features describing cell and nucleus shape, texture, and stain intensity in
histopathological images. Applied to 615 breast cancer samples from The Cancer
Genome Atlas, CCA revealed significant correlation of several image features
with expression of PAM50 genes, known to be linked to outcome, while Sparse CCA
revealed associations with enrichment of pathways implicated in cancer without
leveraging prior biological understanding. These findings affirm the utility of
CCA for joint phenotype-genotype analysis of cancer.
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Links with nontrivial Alexander polynomial which are topologically concordant to the Hopf link | We give infinitely many $2$-component links with unknotted components which
are topologically concordant to the Hopf link, but not smoothly concordant to
any $2$-component link with trivial Alexander polynomial. Our examples are
pairwise non-concordant.
| 0 | 0 | 1 | 0 | 0 | 0 |
Shape optimization in laminar flow with a label-guided variational autoencoder | Computational design optimization in fluid dynamics usually requires to solve
non-linear partial differential equations numerically. In this work, we explore
a Bayesian optimization approach to minimize an object's drag coefficient in
laminar flow based on predicting drag directly from the object shape. Jointly
training an architecture combining a variational autoencoder mapping shapes to
latent representations and Gaussian process regression allows us to generate
improved shapes in the two dimensional case we consider.
| 1 | 0 | 0 | 0 | 0 | 0 |
An Empirical Analysis of Vulnerabilities in Python Packages for Web Applications | This paper examines software vulnerabilities in common Python packages used
particularly for web development. The empirical dataset is based on the PyPI
package repository and the so-called Safety DB used to track vulnerabilities in
selected packages within the repository. The methodological approach builds on
a release-based time series analysis of the conditional probabilities for the
releases of the packages to be vulnerable. According to the results, many of
the Python vulnerabilities observed seem to be only modestly severe; input
validation and cross-site scripting have been the most typical vulnerabilities.
In terms of the time series analysis based on the release histories, only the
recent past is observed to be relevant for statistical predictions; the
classical Markov property holds.
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A combination chaotic system and application in color image encryption | In this paper, by using Logistic, Sine and Tent systems we define a
combination chaotic system. Some properties of the chaotic system are studied
by using figures and numerical results. A color image encryption algorithm is
introduced based on new chaotic system. Also this encryption algorithm can be
used for gray scale or binary images.
The experimental results of the encryption algorithm show that the encryption
algorithm is secure and practical.
| 1 | 0 | 0 | 0 | 0 | 0 |
A Hybrid MILP and IPM for Dynamic Economic Dispatch with Valve Point Effect | Dynamic economic dispatch with valve-point effect (DED-VPE) is a non-convex
and non-differentiable optimization problem which is difficult to solve
efficiently. In this paper, a hybrid mixed integer linear programming (MILP)
and interior point method (IPM), denoted by MILP-IPM, is proposed to solve such
a DED-VPE problem, where the complicated transmission loss is also included.
Due to the non-differentiable characteristic of DED-VPE, the classical
derivative-based optimization methods can not be used any more. With the help
of model reformulation, a differentiable non-linear programming (NLP)
formulation which can be directly solved by IPM is derived. However, if the
DED-VPE is solved by IPM in a single step, the optimization will easily trap in
a poor local optima due to its non-convex and multiple local minima
characteristics. To exploit a better solution, an MILP method is required to
solve the DED-VPE without transmission loss, yielding a good initial point for
IPM to improve the quality of the solution. Simulation results demonstrate the
validity and effectiveness of the proposed MILP-IPM in solving DED-VPE.
| 0 | 0 | 1 | 0 | 0 | 0 |
Using Big Data Technologies for HEP Analysis | The HEP community is approaching an era were the excellent performances of
the particle accelerators in delivering collision at high rate will force the
experiments to record a large amount of information. The growing size of the
datasets could potentially become a limiting factor in the capability to
produce scientific results timely and efficiently. Recently, new technologies
and new approaches have been developed in industry to answer to the necessity
to retrieve information as quickly as possible to analyze PB and EB datasets.
Providing the scientists with these modern computing tools will lead to
rethinking the principles of data analysis in HEP, making the overall
scientific process faster and smoother.
In this paper, we are presenting the latest developments and the most recent
results on the usage of Apache Spark for HEP analysis. The study aims at
evaluating the efficiency of the application of the new tools both
quantitatively, by measuring the performances, and qualitatively, focusing on
the user experience. The first goal is achieved by developing a data reduction
facility: working together with CERN Openlab and Intel, CMS replicates a real
physics search using Spark-based technologies, with the ambition of reducing 1
PB of public data in 5 hours, collected by the CMS experiment, to 1 TB of data
in a format suitable for physics analysis.
The second goal is achieved by implementing multiple physics use-cases in
Apache Spark using as input preprocessed datasets derived from official CMS
data and simulation. By performing different end-analyses up to the publication
plots on different hardware, feasibility, usability and portability are
compared to the ones of a traditional ROOT-based workflow.
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Predicting non-linear dynamics by stable local learning in a recurrent spiking neural network | Brains need to predict how the body reacts to motor commands. It is an open
question how networks of spiking neurons can learn to reproduce the non-linear
body dynamics caused by motor commands, using local, online and stable learning
rules. Here, we present a supervised learning scheme for the feedforward and
recurrent connections in a network of heterogeneous spiking neurons. The error
in the output is fed back through fixed random connections with a negative
gain, causing the network to follow the desired dynamics, while an online and
local rule changes the weights. The rule for Feedback-based Online Local
Learning Of Weights (FOLLOW) is local in the sense that weight changes depend
on the presynaptic activity and the error signal projected onto the
postsynaptic neuron. We provide examples of learning linear, non-linear and
chaotic dynamics, as well as the dynamics of a two-link arm. Using the Lyapunov
method, and under reasonable assumptions and approximations, we show that
FOLLOW learning is stable uniformly, with the error going to zero
asymptotically.
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Adaptive Exploration-Exploitation Tradeoff for Opportunistic Bandits | In this paper, we propose and study opportunistic bandits - a new variant of
bandits where the regret of pulling a suboptimal arm varies under different
environmental conditions, such as network load or produce price. When the
load/price is low, so is the cost/regret of pulling a suboptimal arm (e.g.,
trying a suboptimal network configuration). Therefore, intuitively, we could
explore more when the load/price is low and exploit more when the load/price is
high. Inspired by this intuition, we propose an Adaptive Upper-Confidence-Bound
(AdaUCB) algorithm to adaptively balance the exploration-exploitation tradeoff
for opportunistic bandits. We prove that AdaUCB achieves $O(\log T)$ regret
with a smaller coefficient than the traditional UCB algorithm. Furthermore,
AdaUCB achieves $O(1)$ regret with respect to $T$ if the exploration cost is
zero when the load level is below a certain threshold. Last, based on both
synthetic data and real-world traces, experimental results show that AdaUCB
significantly outperforms other bandit algorithms, such as UCB and TS (Thompson
Sampling), under large load/price fluctuations.
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A Quantile Estimate Based on Local Curve Fitting | Quantile estimation is a problem presented in fields such as quality control,
hydrology, and economics. There are different techniques to estimate such
quantiles. Nevertheless, these techniques use an overall fit of the sample when
the quantiles of interest are usually located in the tails of the distribution.
Regression Approach for Quantile Estimation (RAQE) is a method based on
regression techniques and the properties of the empirical distribution to
address this problem. The method was first presented for the problem of
capability analysis. In this paper, a generalization of the method is
presented, extended to the multiple sample scenario, and data from real
examples is used to illustrate the proposed approaches. In addition,
theoretical framework is presented to support the extension for multiple
homogeneous samples and the use of the uncertainty of the estimated
probabilities as a weighting factor in the analysis.
| 0 | 0 | 0 | 1 | 0 | 0 |
Diagnosing added value of convection-permitting regional models using precipitation event identification and tracking | Dynamical downscaling with high-resolution regional climate models may offer
the possibility of realistically reproducing precipitation and weather events
in climate simulations. As resolutions fall to order kilometers, the use of
explicit rather than parametrized convection may offer even greater fidelity.
However, these increased model resolutions both allow and require increasingly
complex diagnostics for evaluating model fidelity. In this study we use a suite
of dynamically downscaled simulations of the summertime U.S. (WRF driven by
NCEP) with systematic variations in parameters and treatment of convection as a
test case for evaluation of model precipitation. In particular, we use a novel
rainstorm identification and tracking algorithm that allocates essentially all
rainfall to individual precipitation events (Chang et al. 2016). This approach
allows multiple insights, including that, at least in these runs, model wet
bias is driven by excessive areal extent of precipitating events. Biases are
time-dependent, producing excessive diurnal cycle amplitude. We show that this
effect is produced not by new production of events but by excessive enlargement
of long-lived precipitation events during daytime, and that in the domain
average, precipitation biases appear best represented as additive offsets. Of
all model configurations evaluated, convection-permitting simulations most
consistently reduced biases in precipitation event characteristics.
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An integral formula for Riemannian $G$-structures with applications to almost hermitian and almost contact structures | For a Riemannian $G$-structure, we compute the divergence of the vector field
induced by the intrinsic torsion. Applying the Stokes theorem, we obtain the
integral formula on a closed oriented Riemannian manifold, which we interpret
in certain cases. We focus on almost harmitian and almost contact metric
structures.
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Putin's peaks: Russian election data revisited | We study the anomalous prevalence of integer percentages in the last
parliamentary (2016) and presidential (2018) Russian elections. We show how
this anomaly in Russian federal elections has evolved since 2000.
| 0 | 0 | 0 | 1 | 0 | 0 |
On rate of convergence in non-central limit theorems | The main result of this paper is the rate of convergence to Hermite-type
distributions in non-central limit theorems. To the best of our knowledge, this
is the first result in the literature on rates of convergence of functionals of
random fields to Hermite-type distributions with ranks greater than 2. The
results were obtained under rather general assumptions on the spectral
densities of random fields. These assumptions are even weaker than in the known
convergence results for the case of Rosenblatt distributions. Additionally,
Lévy concentration functions for Hermite-type distributions were
investigated.
| 0 | 0 | 1 | 0 | 0 | 0 |
Optimal Output Regulation for Square, Over-Actuated and Under-Actuated Linear Systems | This paper considers two different problems in trajectory tracking control
for linear systems. First, if the control is not unique which is most input
energy efficient. Second, if exact tracking is infeasible which control
performs most accurately. These are typical challenges for over-actuated
systems and for under-actuated systems, respectively. We formulate both goals
as optimal output regulation problems. Then we contribute two new sets of
regulator equations to output regulation theory that provide the desired
solutions. A thorough study indicates solvability and uniqueness under weak
assumptions. E.g., we can always determine the solution of the classical
regulator equations that is most input energy efficient. This is of great value
if there are infinitely many solutions. We derive our results by a linear
quadratic tracking approach and establish a useful link to output regulation
theory.
| 1 | 0 | 0 | 0 | 0 | 0 |
Pattern recognition techniques for Boson Sampling validation | The difficulty of validating large-scale quantum devices, such as Boson
Samplers, poses a major challenge for any research program that aims to show
quantum advantages over classical hardware. To address this problem, we propose
a novel data-driven approach wherein models are trained to identify common
pathologies using unsupervised machine learning methods. We illustrate this
idea by training a classifier that exploits K-means clustering to distinguish
between Boson Samplers that use indistinguishable photons from those that do
not. We train the model on numerical simulations of small-scale Boson Samplers
and then validate the pattern recognition technique on larger numerical
simulations as well as on photonic chips in both traditional Boson Sampling and
scattershot experiments. The effectiveness of such method relies on
particle-type-dependent internal correlations present in the output
distributions. This approach performs substantially better on the test data
than previous methods and underscores the ability to further generalize its
operation beyond the scope of the examples that it was trained on.
| 1 | 0 | 0 | 0 | 0 | 0 |
Conformal k-NN Anomaly Detector for Univariate Data Streams | Anomalies in time-series data give essential and often actionable information
in many applications. In this paper we consider a model-free anomaly detection
method for univariate time-series which adapts to non-stationarity in the data
stream and provides probabilistic abnormality scores based on the conformal
prediction paradigm. Despite its simplicity the method performs on par with
complex prediction-based models on the Numenta Anomaly Detection benchmark and
the Yahoo! S5 dataset.
| 1 | 0 | 0 | 1 | 0 | 0 |
Applications of Trajectory Data from the Perspective of a Road Transportation Agency: Literature Review and Maryland Case Study | Transportation agencies have an opportunity to leverage
increasingly-available trajectory datasets to improve their analyses and
decision-making processes. However, this data is typically purchased from
vendors, which means agencies must understand its potential benefits beforehand
in order to properly assess its value relative to the cost of acquisition.
While the literature concerned with trajectory data is rich, it is naturally
fragmented and focused on technical contributions in niche areas, which makes
it difficult for government agencies to assess its value across different
transportation domains. To overcome this issue, the current paper explores
trajectory data from the perspective of a road transportation agency interested
in acquiring trajectories to enhance its analyses. The paper provides a
literature review illustrating applications of trajectory data in six areas of
road transportation systems analysis: demand estimation, modeling human
behavior, designing public transit, traffic performance measurement and
prediction, environment and safety. In addition, it visually explores 20
million GPS traces in Maryland, illustrating existing and suggesting new
applications of trajectory data.
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Towards the dual motivic Steenrod algebra in positive characteristic | The dual motivic Steenrod algebra with mod $\ell$ coefficients was computed
by Voevodsky over a base field of characteristic zero, and by Hoyois, Kelly,
and {\O}stv{\ae}r over a base field of characteristic $p \neq \ell$. In the
case $p = \ell$, we show that the conjectured answer is a retract of the actual
answer. We also describe the slices of the algebraic cobordism spectrum $MGL$:
we show that the conjectured form of $s_n MGL$ is a retract of the actual
answer.
| 0 | 0 | 1 | 0 | 0 | 0 |
Toeplitz Quantization and Convexity | Let $T^m_f $ be the Toeplitz quantization of a real $ C^{\infty}$ function
defined on the sphere $ \mathbb{CP}(1)$. $T^m_f $ is therefore a Hermitian
matrix with spectrum $\lambda^m= (\lambda_0^m,\ldots,\lambda_m^m)$. Schur's
theorem says that the diagonal of a Hermitian matrix $A$ that has the same
spectrum of $ T^m_f $ lies inside a finite dimensional convex set whose extreme
points are $\{( \lambda_{\sigma(0)}^m,\ldots,\lambda_{\sigma(m)}^m)\}$, where
$\sigma$ is any permutation of $(m+1)$ elements. In this paper, we prove that
these convex sets "converge" to a huge convex set in $L^2([0,1])$ whose extreme
points are $ f^*\circ \phi$, where $ f^*$ is the decreasing rearrangement of $
f$ and $ \phi $ ranges over the set of measure preserving transformations of
the unit interval $ [0,1]$.
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The Paulsen Problem, Continuous Operator Scaling, and Smoothed Analysis | The Paulsen problem is a basic open problem in operator theory: Given vectors
$u_1, \ldots, u_n \in \mathbb R^d$ that are $\epsilon$-nearly satisfying the
Parseval's condition and the equal norm condition, is it close to a set of
vectors $v_1, \ldots, v_n \in \mathbb R^d$ that exactly satisfy the Parseval's
condition and the equal norm condition? Given $u_1, \ldots, u_n$, the squared
distance (to the set of exact solutions) is defined as $\inf_{v} \sum_{i=1}^n
\| u_i - v_i \|_2^2$ where the infimum is over the set of exact solutions.
Previous results show that the squared distance of any $\epsilon$-nearly
solution is at most $O({\rm{poly}}(d,n,\epsilon))$ and there are
$\epsilon$-nearly solutions with squared distance at least $\Omega(d\epsilon)$.
The fundamental open question is whether the squared distance can be
independent of the number of vectors $n$.
We answer this question affirmatively by proving that the squared distance of
any $\epsilon$-nearly solution is $O(d^{13/2} \epsilon)$. Our approach is based
on a continuous version of the operator scaling algorithm and consists of two
parts. First, we define a dynamical system based on operator scaling and use it
to prove that the squared distance of any $\epsilon$-nearly solution is $O(d^2
n \epsilon)$. Then, we show that by randomly perturbing the input vectors, the
dynamical system will converge faster and the squared distance of an
$\epsilon$-nearly solution is $O(d^{5/2} \epsilon)$ when $n$ is large enough
and $\epsilon$ is small enough. To analyze the convergence of the dynamical
system, we develop some new techniques in lower bounding the operator capacity,
a concept introduced by Gurvits to analyze the operator scaling algorithm.
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On architectural choices in deep learning: From network structure to gradient convergence and parameter estimation | We study mechanisms to characterize how the asymptotic convergence of
backpropagation in deep architectures, in general, is related to the network
structure, and how it may be influenced by other design choices including
activation type, denoising and dropout rate. We seek to analyze whether network
architecture and input data statistics may guide the choices of learning
parameters and vice versa. Given the broad applicability of deep architectures,
this issue is interesting both from theoretical and a practical standpoint.
Using properties of general nonconvex objectives (with first-order
information), we first build the association between structural, distributional
and learnability aspects of the network vis-à-vis their interaction with
parameter convergence rates. We identify a nice relationship between feature
denoising and dropout, and construct families of networks that achieve the same
level of convergence. We then derive a workflow that provides systematic
guidance regarding the choice of network sizes and learning parameters often
mediated4 by input statistics. Our technical results are corroborated by an
extensive set of evaluations, presented in this paper as well as independent
empirical observations reported by other groups. We also perform experiments
showing the practical implications of our framework for choosing the best
fully-connected design for a given problem.
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Iron Snow in the Martian Core? | The decline of Mars' global magnetic field some 3.8-4.1 billion years ago is
thought to reflect the demise of the dynamo that operated in its liquid core.
The dynamo was probably powered by planetary cooling and so its termination is
intimately tied to the thermochemical evolution and present-day physical state
of the Martian core. Bottom-up growth of a solid inner core, the
crystallization regime for Earth's core, has been found to produce a long-lived
dynamo leading to the suggestion that the Martian core remains entirely liquid
to this day. Motivated by the experimentally-determined increase in the Fe-S
liquidus temperature with decreasing pressure at Martian core conditions, we
investigate whether Mars' core could crystallize from the top down. We focus on
the "iron snow" regime, where newly-formed solid consists of pure Fe and is
therefore heavier than the liquid. We derive global energy and entropy
equations that describe the long-timescale thermal and magnetic history of the
core from a general theory for two-phase, two-component liquid mixtures,
assuming that the snow zone is in phase equilibrium and that all solid falls
out of the layer and remelts at each timestep. Formation of snow zones occurs
for a wide range of interior and thermal properties and depends critically on
the initial sulfur concentration, x0. Release of gravitational energy and
latent heat during growth of the snow zone do not generate sufficient entropy
to restart the dynamo unless the snow zone occupies at least 400 km of the
core. Snow zones can be 1.5-2 Gyrs old, though thermal stratification of the
uppermost core, not included in our model, likely delays onset. Models that
match the available magnetic and geodetic constraints have x0~10% and snow
zones that occupy approximately the top 100 km of the present-day Martian core.
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Motion Segmentation via Global and Local Sparse Subspace Optimization | In this paper, we propose a new framework for segmenting feature-based moving
objects under affine subspace model. Since the feature trajectories in practice
are high-dimensional and contain a lot of noise, we firstly apply the sparse
PCA to represent the original trajectories with a low-dimensional global
subspace, which consists of the orthogonal sparse principal vectors.
Subsequently, the local subspace separation will be achieved via automatically
searching the sparse representation of the nearest neighbors for each projected
data. In order to refine the local subspace estimation result and deal with the
missing data problem, we propose an error estimation to encourage the projected
data that span a same local subspace to be clustered together. In the end, the
segmentation of different motions is achieved through the spectral clustering
on an affinity matrix, which is constructed with both the error estimation and
sparse neighbors optimization. We test our method extensively and compare it
with state-of-the-art methods on the Hopkins 155 dataset and Freiburg-Berkeley
Motion Segmentation dataset. The results show that our method is comparable
with the other motion segmentation methods, and in many cases exceed them in
terms of precision and computation time.
| 1 | 0 | 0 | 0 | 0 | 0 |
Topological strings linking with quasi-particle exchange in superconducting Dirac semimetals | We demonstrate a topological classification of vortices in three dimensional
time-reversal invariant topological superconductors based on superconducting
Dirac semimetals with an s-wave superconducting order parameter by means of a
pair of numbers $(N_\Phi,N)$, accounting how many units $N_\Phi$ of magnetic
fluxes $hc/4e$ and how many $N$ chiral Majorana modes the vortex carries. From
these quantities, we introduce a topological invariant which further classifies
the properties of such vortices under linking processes. While such processes
are known to be related to instanton processes in a field theoretic
description, we demonstrate here that they are, in fact, also equivalent to the
fractional Josephson effect on junctions based at the edges of quantum spin
Hall systems. This allows one to consider microscopically the effects of
interactions in the linking problem. We therefore demonstrate that associated
to links between vortices, one has the exchange of quasi-particles, either
Majorana zero-modes or $e/2$ quasi-particles, which allows for a topological
classification of vortices in these systems, seen to be $\mathbb{Z}_8$
classified. While $N_\Phi$ and $N$ are shown to be both even or odd in the
weakly-interacting limit, in the strongly interacting scenario one loosens this
constraint. In this case, one may have further fractionalization possibilities
for the vortices, whose excitations are described by $SO(3)_3$-like conformal
field theories with quasi-particle exchanges of more exotic types.
| 0 | 1 | 0 | 0 | 0 | 0 |
Self-Imitation Learning | This paper proposes Self-Imitation Learning (SIL), a simple off-policy
actor-critic algorithm that learns to reproduce the agent's past good
decisions. This algorithm is designed to verify our hypothesis that exploiting
past good experiences can indirectly drive deep exploration. Our empirical
results show that SIL significantly improves advantage actor-critic (A2C) on
several hard exploration Atari games and is competitive to the state-of-the-art
count-based exploration methods. We also show that SIL improves proximal policy
optimization (PPO) on MuJoCo tasks.
| 0 | 0 | 0 | 1 | 0 | 0 |
Controllability to Equilibria of the 1-D Fokker-Planck Equation with Zero-Flux Boundary Condition | We consider the problem of controlling the spatiotemporal probability
distribution of a robotic swarm that evolves according to a reflected diffusion
process, using the space- and time-dependent drift vector field parameter as
the control variable. In contrast to previous work on control of the
Fokker-Planck equation, a zero-flux boundary condition is imposed on the
partial differential equation that governs the swarm probability distribution,
and only bounded vector fields are considered to be admissible as control
parameters. Under these constraints, we show that any initial probability
distribution can be transported to a target probability distribution under
certain assumptions on the regularity of the target distribution. In
particular, we show that if the target distribution is (essentially) bounded,
has bounded first-order and second-order partial derivatives, and is bounded
from below by a strictly positive constant, then this distribution can be
reached exactly using a drift vector field that is bounded in space and time.
Our proof is constructive and based on classical linear semigroup theoretic
concepts.
| 1 | 0 | 1 | 0 | 0 | 0 |
Buy your coffee with bitcoin: Real-world deployment of a bitcoin point of sale terminal | In this paper we discuss existing approaches for Bitcoin payments, as
suitable for a small business for small-value transactions. We develop an
evaluation framework utilizing security, usability, deployability criteria,,
examine several existing systems, tools. Following a requirements engineering
approach, we designed, implemented a new Point of Sale (PoS) system that
satisfies an optimal set of criteria within our evaluation framework. Our open
source system, Aunja PoS, has been deployed in a real world cafe since October
2014.
| 1 | 0 | 0 | 0 | 0 | 0 |
Tackling non-linearities with the effective field theory of dark energy and modified gravity | We present the extension of the effective field theory framework to the
mildly non-linear scales. The effective field theory approach has been
successfully applied to the late time cosmic acceleration phenomenon and it has
been shown to be a powerful method to obtain predictions about cosmological
observables on linear scales. However, mildly non-linear scales need to be
consistently considered when testing gravity theories because a large part of
the data comes from those scales. Thus, non-linear corrections to predictions
on observables coming from the linear analysis can help in discriminating among
different gravity theories. We proceed firstly by identifying the necessary
operators which need to be included in the effective field theory Lagrangian in
order to go beyond the linear order in perturbations and then we construct the
corresponding non-linear action. Moreover, we present the complete recipe to
map any single field dark energy and modified gravity models into the
non-linear effective field theory framework by considering a general action in
the Arnowitt-Deser-Misner formalism. In order to illustrate this recipe we
proceed to map the beyond-Horndeski theory and low-energy Horava gravity into
the effective field theory formalism. As a final step we derived the 4th order
action in term of the curvature perturbation. This allowed us to identify the
non-linear contributions coming from the linear order perturbations which at
the next order act like source terms. Moreover, we confirm that the stability
requirements, ensuring the positivity of the kinetic term and the speed of
propagation for scalar mode, are automatically satisfied once the viability of
the theory is demanded at linear level. The approach we present here will allow
to construct, in a model independent way, all the relevant predictions on
observables at mildly non-linear scales.
| 0 | 1 | 0 | 0 | 0 | 0 |
A recommender system to restore images with impulse noise | We build a collaborative filtering recommender system to restore images with
impulse noise for which the noisy pixels have been previously identified. We
define this recommender system in terms of a new color image representation
using three matrices that depend on the noise-free pixels of the image to
restore, and two parameters: $k$, the number of features; and $\lambda$, the
regularization factor. We perform experiments on a well known image database to
test our algorithm and we provide image quality statistics for the results
obtained. We discuss the roles of bias and variance in the performance of our
algorithm as determined by the values of $k$ and $\lambda$, and provide
guidance on how to choose the values of these parameters. Finally, we discuss
the possibility of using our collaborative filtering recommender system to
perform image inpainting and super-resolution.
| 1 | 0 | 0 | 1 | 0 | 0 |
A Parallel Simulator for Massive Reservoir Models Utilizing Distributed-Memory Parallel Systems | This paper presents our work on developing parallel computational methods for
two-phase flow on modern parallel computers, where techniques for linear
solvers and nonlinear methods are studied and the standard and inexact Newton
methods are investigated. A multi-stage preconditioner for two-phase flow is
applied and advanced matrix processing strategies are studied. A local
reordering method is developed to speed the solution of linear systems.
Numerical experiments show that these computational methods are effective and
scalable, and are capable of computing large-scale reservoir simulation
problems using thousands of CPU cores on parallel computers. The nonlinear
techniques, preconditioner and matrix processing strategies can also be applied
to three-phase black oil, compositional and thermal models.
| 1 | 0 | 0 | 0 | 0 | 0 |
Bifurcation structure of cavity soliton dynamics in a VCSEL with saturable absorber and time-delayed feedback | We consider a wide-aperture surface-emitting laser with a saturable absorber
section subjected to time-delayed feedback. We adopt the mean-field approach
assuming a single longitudinal mode operation of the solitary VCSEL. We
investigate cavity soliton dynamics under the effect of time- delayed feedback
in a self-imaging configuration where diffraction in the external cavity is
negligible. Using bifurcation analysis, direct numerical simulations and
numerical path continuation methods, we identify the possible bifurcations and
map them in a plane of feedback parameters. We show that for both the
homogeneous and localized stationary lasing solutions in one spatial dimension
the time-delayed feedback induces complex spatiotemporal dynamics, in
particular a period doubling route to chaos, quasiperiodic oscillations and
multistability of the stationary solutions.
| 0 | 1 | 0 | 0 | 0 | 0 |
Early warning signal for interior crises in excitable systems | The ability to reliably predict critical transitions in dynamical systems is
a long-standing goal of diverse scientific communities. Previous work focused
on early warning signals related to local bifurcations (critical slowing down)
and non-bifurcation type transitions. We extend this toolbox and report on a
characteristic scaling behavior (critical attractor growth) which is indicative
of an impending global bifurcation, an interior crisis in excitable systems. We
demonstrate our early warning signal in a conceptual climate model as well as
in a model of coupled neurons known to exhibit extreme events. We observed
critical attractor growth prior to interior crises of chaotic as well as
strange-nonchaotic attractors. These observations promise to extend the classes
of transitions that can be predicted via early warning signals.
| 0 | 1 | 0 | 0 | 0 | 0 |
Harmonic Mean Iteratively Reweighted Least Squares for Low-Rank Matrix Recovery | We propose a new iteratively reweighted least squares (IRLS) algorithm for
the recovery of a matrix $X \in \mathbb{C}^{d_1\times d_2}$ of rank $r
\ll\min(d_1,d_2)$ from incomplete linear observations, solving a sequence of
low complexity linear problems. The easily implementable algorithm, which we
call harmonic mean iteratively reweighted least squares (HM-IRLS), optimizes a
non-convex Schatten-$p$ quasi-norm penalization to promote low-rankness and
carries three major strengths, in particular for the matrix completion setting.
First, we observe a remarkable global convergence behavior of the algorithm's
iterates to the low-rank matrix for relevant, interesting cases, for which any
other state-of-the-art optimization approach fails the recovery. Secondly,
HM-IRLS exhibits an empirical recovery probability close to $1$ even for a
number of measurements very close to the theoretical lower bound $r (d_1 +d_2
-r)$, i.e., already for significantly fewer linear observations than any other
tractable approach in the literature. Thirdly, HM-IRLS exhibits a locally
superlinear rate of convergence (of order $2-p$) if the linear observations
fulfill a suitable null space property. While for the first two properties we
have so far only strong empirical evidence, we prove the third property as our
main theoretical result.
| 1 | 0 | 1 | 0 | 0 | 0 |
The Italian Pension Gap: a Stochastic Optimal Control Approach | We study the gap between the state pension provided by the Italian pension
system pre-Dini reform and post-Dini reform. The goal is to fill the gap
between the old and the new pension by joining a defined contribution pension
scheme and adopting an optimal investment strategy that is target-based. We
find that it is possible to cover, at least partially, this gap with the
additional income of the pension scheme, especially in the presence of late
retirement and in the presence of stagnant career. Workers with dynamic career
and workers who retire early are those who are most penalised by the reform.
Results are intuitive and in line with previous studies on the subject.
| 0 | 0 | 0 | 0 | 0 | 1 |
Immigration-induced phase transition in a regulated multispecies birth-death process | Power-law-distributed species counts or clone counts arise in many biological
settings such as multispecies cell populations, population genetics, and
ecology. This empirical observation that the number of species $c_{k}$
represented by $k$ individuals scales as negative powers of $k$ is also
supported by a series of theoretical birth-death-immigration (BDI) models that
consistently predict many low-population species, a few intermediate-population
species, and very high-population species. However, we show how a simple global
population-dependent regulation in a neutral BDI model destroys the power law
distributions. Simulation of the regulated BDI model shows a high probability
of observing a high-population species that dominates the total population.
Further analysis reveals that the origin of this breakdown is associated with
the failure of a mean-field approximation for the expected species abundance
distribution. We find an accurate estimate for the expected distribution
$\langle c_k \rangle$ by mapping the problem to a lower-dimensional Moran
process, allowing us to also straightforwardly calculate the covariances
$\langle c_k c_\ell \rangle$. Finally, we exploit the concepts associated with
energy landscapes to explain the failure of the mean-field assumption by
identifying a phase transition in the quasi-steady-state species counts
triggered by a decreasing immigration rate.
| 0 | 0 | 0 | 0 | 1 | 0 |
Nanoscale assembly of superconducting vortices with scanning tunnelling microscope tip | Vortices play a crucial role in determining the properties of superconductors
as well as their applications. Therefore, characterization and manipulation of
vortices, especially at the single vortex level, is of great importance. Among
many techniques to study single vortices, scanning tunneling microscopy (STM)
stands out as a powerful tool, due to its ability to detect the local
electronic states and high spatial resolution. However, local control of
superconductivity as well as the manipulation of individual vortices with the
STM tip is still lacking. Here we report a new function of the STM, namely to
control the local pinning in a superconductor through the heating effect. Such
effect allows us to quench the superconducting state at nanoscale, and leads to
the growth of vortex-clusters whose size can be controlled by the bias voltage.
We also demonstrate the use of an STM tip to assemble single quantum vortices
into desired nanoscale configurations.
| 0 | 1 | 0 | 0 | 0 | 0 |
STACCATO: A Novel Solution to Supernova Photometric Classification with Biased Training Sets | We present a new solution to the problem of classifying Type Ia supernovae
from their light curves alone given a spectroscopically confirmed but biased
training set, circumventing the need to obtain an observationally expensive
unbiased training set. We use Gaussian processes (GPs) to model the
supernovae's (SN) light curves, and demonstrate that the choice of covariance
function has only a small influence on the GPs ability to accurately classify
SNe. We extend and improve the approach of Richards et al (2012} -- a diffusion
map combined with a random forest classifier -- to deal specifically with the
case of biassed training sets. We propose a novel method, called STACCATO
(SynThetically Augmented Light Curve ClassificATiOn') that synthetically
augments a biased training set by generating additional training data from the
fitted GPs. Key to the success of the method is the partitioning of the
observations into subgroups based on their propensity score of being included
in the training set. Using simulated light curve data, we show that STACCATO
increases performance, as measured by the area under the Receiver Operating
Characteristic curve (AUC), from 0.93 to 0.96, close to the AUC of 0.977
obtained using the 'gold standard' of an unbiased training set and
significantly improving on the previous best result of 0.88. STACCATO also
increases the true positive rate for SNIa classification by up to a factor of
50 for high-redshift/low brightness SNe.
| 0 | 1 | 0 | 0 | 0 | 0 |
Coupling of multiscale and multi-continuum approaches | Simulating complex processes in fractured media requires some type of model
reduction. Well-known approaches include multi-continuum techniques, which have
been commonly used in approximating subgrid effects for flow and transport in
fractured media. Our goal in this paper is to (1) show a relation between
multi-continuum approaches and Generalized Multiscale Finite Element Method
(GMsFEM) and (2) to discuss coupling these approaches for solving problems in
complex multiscale fractured media. The GMsFEM, a systematic approach,
constructs multiscale basis functions via local spectral decomposition in
pre-computed snapshot spaces. We show that GMsFEM can automatically identify
separate fracture networks via local spectral problems. We discuss the relation
between these basis functions and continuums in multi-continuum methods. The
GMsFEM can automatically detect each continuum and represent the interaction
between the continuum and its surrounding (matrix). For problems with
simplified fracture networks, we propose a simplified basis construction with
the GMsFEM. This simplified approach is effective when the fracture networks
are known and have simplified geometries. We show that this approach can
achieve a similar result compared to the results using the GMsFEM with spectral
basis functions. Further, we discuss the coupling between the GMsFEM and
multi-continuum approaches. In this case, many fractures are resolved while for
unresolved fractures, we use a multi-continuum approach with local
Representative Volume Element (RVE) information. As a result, the method deals
with a system of equations on a coarse grid, where each equation represents one
of the continua on the fine grid. We present various basis construction
mechanisms and numerical results.
| 0 | 0 | 1 | 0 | 0 | 0 |
Spaces which invert weak homotopy equivalences | It is well known that if $X$ is a CW-complex, then for every weak homotopy
equivalence $f:A\to B$, the map $f_*:[X,A]\to [X,B]$ induced in homotopy
classes is a bijection. For which spaces $X$ is $f^*:[B,X]\to [A,X]$ a
bijection for every weak equivalence $f$? This question was considered by J.
Strom and T. Goodwillie. In this note we prove that a non-empty space inverts
weak equivalences if and only if it is contractible.
| 0 | 0 | 1 | 0 | 0 | 0 |
Minimal surfaces in the 3-sphere by desingularizing intersecting Clifford tori | For each integer $k \geq 2$, we apply gluing methods to construct sequences
of minimal surfaces embedded in the round $3$-sphere. We produce two types of
sequences, all desingularizing collections of intersecting Clifford tori.
Sequences of the first type converge to a collection of $k$ Clifford tori
intersecting with maximal symmetry along these two circles. Near each of the
circles, after rescaling, the sequences converge smoothly on compact subsets to
a Karcher-Scherk tower of order $k$. Sequences of the second type desingularize
a collection of the same $k$ Clifford tori supplemented by an additional
Clifford torus equidistant from the original two circles of intersection, so
that the latter torus orthogonally intersects each of the former $k$ tori along
a pair of disjoint orthogonal circles, near which the corresponding rescaled
sequences converge to a singly periodic Scherk surface. The simpler examples of
the first type resemble surfaces constructed by Choe and Soret \cite{CS} by
different methods where the number of handles desingularizing each circle is
the same. There is a plethora of new examples which are more complicated and on
which the number of handles for the two circles differs. Examples of the second
type are new as well.
| 0 | 0 | 1 | 0 | 0 | 0 |
Results from EDGES High-Band: I. Constraints on Phenomenological Models for the Global $21$ cm Signal | We report constraints on the global $21$ cm signal due to neutral hydrogen at
redshifts $14.8 \geq z \geq 6.5$. We derive our constraints from low foreground
observations of the average sky brightness spectrum conducted with the EDGES
High-Band instrument between September $7$ and October $26$, $2015$.
Observations were calibrated by accounting for the effects of antenna beam
chromaticity, antenna and ground losses, signal reflections, and receiver
parameters. We evaluate the consistency between the spectrum and
phenomenological models for the global $21$ cm signal. For tanh-based
representations of the ionization history during the epoch of reionization, we
rule out, at $\geq2\sigma$ significance, models with duration of up to $\Delta
z = 1$ at $z\approx8.5$ and higher than $\Delta z = 0.4$ across most of the
observed redshift range under the usual assumption that the $21$ cm spin
temperature is much larger than the temperature of the cosmic microwave
background (CMB) during reionization. We also investigate a `cold' IGM scenario
that assumes perfect Ly$\alpha$ coupling of the $21$ cm spin temperature to the
temperature of the intergalactic medium (IGM), but that the IGM is not heated
by early stars or stellar remants. Under this assumption, we reject tanh-based
reionization models of duration $\Delta z \lesssim 2$ over most of the observed
redshift range. Finally, we explore and reject a broad range of Gaussian models
for the $21$ cm absorption feature expected in the First Light era. As an
example, we reject $100$ mK Gaussians with duration (full width at half
maximum) $\Delta z \leq 4$ over the range $14.2\geq z\geq 6.5$ at $\geq2\sigma$
significance.
| 0 | 1 | 0 | 0 | 0 | 0 |
Novel paradigms for advanced distribution grid energy management | The electricity distribution grid was not designed to cope with load dynamics
imposed by high penetration of electric vehicles, neither to deal with the
increasing deployment of distributed Renewable Energy Sources. Distribution
System Operators (DSO) will increasingly rely on flexible Distributed Energy
Resources (flexible loads, controllable generation and storage) to keep the
grid stable and to ensure quality of supply. In order to properly integrate
demand-side flexibility, DSOs need new energy management architectures, capable
of fostering collaboration with wholesale market actors and pro-sumers. We
propose the creation of Virtual Distribution Grids (VDG) over a common physical
infrastructure , to cope with heterogeneity of resources and actors, and with
the increasing complexity of distribution grid management and related resources
allocation problems. Focusing on residential VDG, we propose an agent-based
hierarchical architecture for providing Demand-Side Management services through
a market-based approach, where households transact their surplus/lack of energy
and their flexibility with neighbours, aggregators, utilities and DSOs. For
implementing the overall solution, we consider fine-grained control of smart
homes based on Inter-net of Things technology. Homes seamlessly transact
self-enforcing smart contracts over a blockchain-based generic platform.
Finally, we extend the architecture to solve existing problems on smart home
control, beyond energy management.
| 1 | 0 | 0 | 0 | 0 | 0 |
Uniformly Bounded Sets in Quasiperiodically Forced Dynamical Systems | This paper addresses structures of state space in quasiperiodically forced
dynamical systems. We develop a theory of ergodic partition of state space in a
class of measure-preserving and dissipative flows, which is a natural extension
of the existing theory for measure-preserving maps. The ergodic partition
result is based on eigenspace at eigenvalue 0 of the associated Koopman
operator, which is realized via time-averages of observables, and provides a
constructive way to visualize a low-dimensional slice through a
high-dimensional invariant set. We apply the result to the systems with a
finite number of attractors and show that the time-average of a continuous
observable is well-defined and reveals the invariant sets, namely, a finite
number of basins of attraction. We provide a characterization of invariant sets
in the quasiperiodically forced systems. A theorem on uniform boundedness of
the invariant sets is proved. The series of analytical results enables
numerical analysis of invariant sets in the quasiperiodically forced systems
based on the ergodic partition and time-averages. Using this, we analyze a
nonlinear model of complex power grids that represents the short-term swing
instability, named the coherent swing instability. We show that our analytical
results can be used to understand stability regions in such complex systems.
| 1 | 0 | 0 | 0 | 0 | 0 |
Understand Functionality and Dimensionality of Vector Embeddings: the Distributional Hypothesis, the Pairwise Inner Product Loss and Its Bias-Variance Trade-off | Vector embedding is a foundational building block of many deep learning
models, especially in natural language processing. In this paper, we present a
theoretical framework for understanding the effect of dimensionality on vector
embeddings. We observe that the distributional hypothesis, a governing
principle of statistical semantics, requires a natural unitary-invariance for
vector embeddings. Motivated by the unitary-invariance observation, we propose
the Pairwise Inner Product (PIP) loss, a unitary-invariant metric on the
similarity between two embeddings. We demonstrate that the PIP loss captures
the difference in functionality between embeddings, and that the PIP loss is
tightly connect with two basic properties of vector embeddings, namely
similarity and compositionality. By formulating the embedding training process
as matrix factorization with noise, we reveal a fundamental bias-variance
trade-off between the signal spectrum and noise power in the dimensionality
selection process. This bias-variance trade-off sheds light on many empirical
observations which have not been thoroughly explained, for example the
existence of an optimal dimensionality. Moreover, we discover two new results
about vector embeddings, namely their robustness against over-parametrization
and their forward stability. The bias-variance trade-off of the PIP loss
explicitly answers the fundamental open problem of dimensionality selection for
vector embeddings.
| 0 | 0 | 0 | 1 | 0 | 0 |
Strongly correlated one-dimensional Bose-Fermi quantum mixtures: symmetry and correlations | We consider multi-component quantum mixtures (bosonic, fermionic, or mixed)
with strongly repulsive contact interactions in a one-dimensional harmonic
trap. In the limit of infinitely strong repulsion and zero temperature, using
the class-sum method, we study the symmetries of the spatial wave function of
the mixture. We find that the ground state of the system has the most symmetric
spatial wave function allowed by the type of mixture. This provides an example
of the generalized Lieb-Mattis theorem. Furthermore, we show that the symmetry
properties of the mixture are embedded in the large-momentum tails of the
momentum distribution, which we evaluate both at infinite repulsion by an exact
solution and at finite interactions using a numerical DMRG approach. This
implies that an experimental measurement of the Tan's contact would allow to
unambiguously determine the symmetry of any kind of multi-component mixture.
| 0 | 1 | 0 | 0 | 0 | 0 |
Joint Pose and Principal Curvature Refinement Using Quadrics | In this paper we present a novel joint approach for optimising surface
curvature and pose alignment. We present two implementations of this joint
optimisation strategy, including a fast implementation that uses two frames and
an offline multi-frame approach. We demonstrate an order of magnitude
improvement in simulation over state of the art dense relative point-to-plane
Iterative Closest Point (ICP) pose alignment using our dense joint
frame-to-frame approach and show comparable pose drift to dense point-to-plane
ICP bundle adjustment using low-cost depth sensors. Additionally our improved
joint quadric based approach can be used to more accurately estimate surface
curvature on noisy point clouds than previous approaches.
| 1 | 0 | 0 | 0 | 0 | 0 |
Stable basic sets for finite special linear and unitary group | In this paper we show, using Deligne-Lusztig theory and Kawanaka's theory of
generalised Gelfand-Graev representations, that the decomposition matrix of the
special linear and unitary group in non defining characteristic can be made
unitriangular with respect to a basic set that is stable under the action of
automorphisms.
| 0 | 0 | 1 | 0 | 0 | 0 |
Correspondences without a Core | We study the formal properties of correspondences of curves without a core,
focusing on the case of étale correspondences. The motivating examples come
from Hecke correspondences of Shimura curves. Given a correspondence without a
core, we construct an infinite graph $\mathcal{G}_{gen}$ together with a large
group of "algebraic" automorphisms $A$. The graph $\mathcal{G}_{gen}$ measures
the "generic dynamics" of the correspondence. We construct specialization maps
$\mathcal{G}_{gen}\rightarrow\mathcal{G}_{phys}$ to the "physical dynamics" of
the correspondence. We also prove results on the number of bounded étale
orbits, in particular generalizing a recent theorem of Hallouin and Perret. We
use a variety of techniques: Galois theory, the theory of groups acting on
infinite graphs, and finite group schemes.
| 0 | 0 | 1 | 0 | 0 | 0 |
Oxidative species-induced excitonic transport in tubulin aromatic networks: Potential implications for neurodegenerative disease | Oxidative stress is a pathological hallmark of neurodegenerative tauopathic
disorders such as Alzheimer's disease and Parkinson's disease-related dementia,
which are characterized by altered forms of the microtubule-associated protein
(MAP) tau. MAP tau is a key protein in stabilizing the microtubule architecture
that regulates neuron morphology and synaptic strength. The precise role of
reactive oxygen species (ROS) in the tauopathic disease process, however, is
poorly understood. It is known that the production of ROS by mitochondria can
result in ultraweak photon emission (UPE) within cells. One likely absorber of
these photons is the microtubule cytoskeleton, as it forms a vast network
spanning neurons, is highly co-localized with mitochondria, and shows a high
density of aromatic amino acids. Functional microtubule networks may traffic
this ROS-generated endogenous photon energy for cellular signaling, or they may
serve as dissipaters/conduits of such energy. Experimentally, after in vitro
exposure to exogenous photons, microtubules have been shown to reorient and
reorganize in a dose-dependent manner with the greatest effect being observed
around 280 nm, in the tryptophan and tyrosine absorption range. In this paper,
recent modeling efforts based on ambient temperature experiment are presented,
showing that tubulin polymers can feasibly absorb and channel these
photoexcitations via resonance energy transfer, on the order of dendritic
length scales. Since microtubule networks are compromised in tauopathic
diseases, patients with these illnesses would be unable to support effective
channeling of these photons for signaling or dissipation. Consequent emission
surplus due to increased UPE production or decreased ability to absorb and
transfer may lead to increased cellular oxidative damage, thus hastening the
neurodegenerative process.
| 0 | 1 | 0 | 0 | 0 | 0 |
On radial Schroedinger operators with a Coulomb potential | This paper presents a thorough analysis of 1-dimensional Schroedinger
operators whose potential is a linear combination of the Coulomb term 1/r and
the centrifugal term 1/r^2. We allow both coupling constants to be complex.
Using natural boundary conditions at 0, a two parameter holomorphic family of
closed operators is introduced. We call them the Whittaker operators, since in
the mathematical literature their eigenvalue equation is called the Whittaker
equation. Spectral and scattering theory for Whittaker operators is studied.
Whittaker operators appear in quantum mechanics as the radial part of the
Schroedinger operator with a Coulomb potential.
| 0 | 0 | 1 | 0 | 0 | 0 |
Extrema-weighted feature extraction for functional data | Motivation: Although there is a rich literature on methods for assessing the
impact of functional predictors, the focus has been on approaches for dimension
reduction that can fail dramatically in certain applications. Examples of
standard approaches include functional linear models, functional principal
components regression, and cluster-based approaches, such as latent trajectory
analysis. This article is motivated by applications in which the dynamics in a
predictor, across times when the value is relatively extreme, are particularly
informative about the response. For example, physicians are interested in
relating the dynamics of blood pressure changes during surgery to post-surgery
adverse outcomes, and it is thought that the dynamics are more important when
blood pressure is significantly elevated or lowered.
Methods: We propose a novel class of extrema-weighted feature (XWF)
extraction models. Key components in defining XWFs include the marginal density
of the predictor, a function up-weighting values at high quantiles of this
marginal, and functionals characterizing local dynamics. Algorithms are
proposed for fitting of XWF-based regression and classification models, and are
compared with current methods for functional predictors in simulations and a
blood pressure during surgery application.
Results: XWFs find features of intraoperative blood pressure trajectories
that are predictive of postoperative mortality. By their nature, most of these
features cannot be found by previous methods.
| 0 | 0 | 0 | 1 | 0 | 0 |
A representation theorem for stochastic processes with separable covariance functions, and its implications for emulation | Many applications require stochastic processes specified on two- or
higher-dimensional domains; spatial or spatial-temporal modelling, for example.
In these applications it is attractive, for conceptual simplicity and
computational tractability, to propose a covariance function that is separable;
e.g., the product of a covariance function in space and one in time. This paper
presents a representation theorem for such a proposal, and shows that all
processes with continuous separable covariance functions are second-order
identical to the product of second-order uncorrelated processes. It discusses
the implications of separable or nearly separable prior covariances for the
statistical emulation of complicated functions such as computer codes, and
critically reexamines the conventional wisdom concerning emulator structure,
and size of design.
| 0 | 0 | 1 | 1 | 0 | 0 |
Facial Recognition Enabled Smart Door Using Microsoft Face API | Privacy and Security are two universal rights and, to ensure that in our
daily life we are secure, a lot of research is going on in the field of home
security, and IoT is the turning point for the industry, where we connect
everyday objects to share data for our betterment. Facial recognition is a
well-established process in which the face is detected and identified out of
the image. We aim to create a smart door, which secures the gateway on the
basis of who we are. In our proof of concept of a smart door we have used a
live HD camera on the front side of setup attached to a display monitor
connected to the camera to show who is standing in front of the door, also the
whole system will be able to give voice outputs by processing text them on the
Raspberry Pi ARM processor used and show the answers as output on the screen.
We are using a set of electromagnets controlled by the microcontroller, which
will act as a lock. So a person can open the smart door with the help of facial
recognition and at the same time also be able to interact with it. The facial
recognition is done by Microsoft face API but our state of the art desktop
application operating over Microsoft Visual Studio IDE reduces the
computational time by detecting the face out of the photo and giving that as
the output to Microsoft Face API, which is hosted over Microsoft Azure cloud
support.
| 1 | 0 | 0 | 0 | 0 | 0 |
Veamy: an extensible object-oriented C++ library for the virtual element method | This paper summarizes the development of Veamy, an object-oriented C++
library for the virtual element method (VEM) on general polygonal meshes, whose
modular design is focused on its extensibility. The linear elastostatic and
Poisson problems in two dimensions have been chosen as the starting stage for
the development of this library. The theory of the VEM, upon which Veamy is
built, is presented using a notation and a terminology that resemble the
language of the finite element method (FEM) in engineering analysis. Several
examples are provided to demonstrate the usage of Veamy, and in particular, one
of them features the interaction between Veamy and the polygonal mesh generator
PolyMesher. A computational performance comparison between VEM and FEM is also
conducted. Veamy is free and open source software.
| 1 | 0 | 0 | 0 | 0 | 0 |
Composition by Conversation | Most musical programming languages are developed purely for coding virtual
instruments or algorithmic compositions. Although there has been some work in
the domain of musical query languages for music information retrieval, there
has been little attempt to unify the principles of musical programming and
query languages with cognitive and natural language processing models that
would facilitate the activity of composition by conversation. We present a
prototype framework, called MusECI, that merges these domains, permitting
score-level algorithmic composition in a text editor while also supporting
connectivity to existing natural language processing frameworks.
| 1 | 0 | 0 | 0 | 0 | 0 |
Electrostatic and induction effects in the solubility of water in alkanes | Experiments show that at 298~K and 1 atm pressure the transfer free energy,
$\mu^{\rm ex}$, of water from its vapor to liquid normal alkanes $C_nH_{2n+2}$
($n=5\ldots12$) is negative. Earlier it was found that with the united-atom
TraPPe model for alkanes and the SPC/E model for water, one had to artificially
enhance the attractive alkane-water cross interaction to capture this behavior.
Here we revisit the calculation of $\mu^{\rm ex}$ using the polarizable AMOEBA
and the non-polarizable Charmm General (CGenFF) forcefields. We test both the
AMOEBA03 and AMOEBA14 water models; the former has been validated with the
AMOEBA alkane model while the latter is a revision of AMOEBA03 to better
describe liquid water. We calculate $\mu^{\rm ex}$ using the test particle
method. With CGenFF, $\mu^{\rm ex}$ is positive and the error relative to
experiments is about 1.5 $k_{\rm B}T$. With AMOEBA, $\mu^{\rm ex}$ is negative
and deviations relative to experiments are between 0.25 $k_{\rm B}T$ (AMOEBA14)
and 0.5 $k_{\rm B}T$ (AMOEBA03). Quantum chemical calculations in a continuum
solvent suggest that zero point effects may account for some of the deviation.
Forcefield limitations notwithstanding, electrostatic and induction effects,
commonly ignored in considerations of water-alkane interactions, appear to be
decisive in the solubility of water in alkanes.
| 0 | 1 | 0 | 0 | 0 | 0 |
Impact of theoretical priors in cosmological analyses: the case of single field quintessence | We investigate the impact of general conditions of theoretical stability and
cosmological viability on dynamical dark energy models. As a powerful example,
we study whether minimally coupled, single field Quintessence models that are
safe from ghost instabilities, can source the CPL expansion history recently
shown to be mildly favored by a combination of CMB (Planck) and Weak Lensing
(KiDS) data. We find that in their most conservative form, the theoretical
conditions impact the analysis in such a way that smooth single field
Quintessence becomes significantly disfavored with respect to the standard LCDM
cosmological model. This is due to the fact that these conditions cut a
significant portion of the (w0;wa) parameter space for CPL, in particular
eliminating the region that would be favored by weak lensing data. Within the
scenario of a smooth dynamical dark energy parametrized with CPL, weak lensing
data favors a region that would require multiple fields to ensure gravitational
stability.
| 0 | 1 | 0 | 0 | 0 | 0 |
Spin tracking of polarized protons in the Main Injector at Fermilab | The Main Injector (MI) at Fermilab currently produces high-intensity beams of
protons at energies of 120 GeV for a variety of physics experiments.
Acceleration of polarized protons in the MI would provide opportunities for a
rich spin physics program at Fermilab. To achieve polarized proton beams in the
Fermilab accelerator complex, detailed spin tracking simulations with realistic
parameters based on the existing facility are required. This report presents
studies at the MI using a single 4-twist Siberian snake to determine the
depolarizing spin resonances for the relevant synchrotrons. Results will be
presented first for a perfect MI lattice, followed by a lattice that includes
the real MI imperfections, such as the measured magnet field errors and
quadrupole misalignments. The tolerances of each of these factors in
maintaining polarization in the Main Injector will be discussed.
| 0 | 1 | 0 | 0 | 0 | 0 |
Wormholes and masses for Goldstone bosons | There exist non-trivial stationary points of the Euclidean action for an
axion particle minimally coupled to Einstein gravity, dubbed wormholes. They
explicitly break the continuos global shift symmetry of the axion in a
non-perturbative way, and generate an effective potential that may compete with
QCD depending on the value of the axion decay constant. In this paper, we
explore both theoretical and phenomenological aspects of this issue. On the
theory side, we address the problem of stability of the wormhole solutions, and
we show that the spectrum of the quadratic action features only positive
eigenvalues. On the phenomenological side, we discuss, beside the obvious
application to the QCD axion, relevant consequences for models with ultralight
dark matter, black hole superradiance, and the relaxation of the electroweak
scale. We conclude discussing wormhole solutions for a generic coset and the
potential they generate.
| 0 | 1 | 0 | 0 | 0 | 0 |
A class of states supporting diffusive spin dynamics in the isotropic Heisenberg model | The spin transport in isotropic Heisenberg model in the sector with zero
magnetization is generically super-diffusive. Despite that, we here demonstrate
that for a specific set of domain-wall-like initial product states it can
instead be diffusive. We theoretically explain the time evolution of such
states by showing that in the limiting regime of weak spatial modulation they
are approximately product states for very long times, and demonstrate that even
in the case of larger spatial modulation the bipartite entanglement entropy
grows only logarithmically in time. In the limiting regime we derive a simple
closed equation governing the dynamics, which in the continuum limit and for
the initial step magnetization profile results in a solution expressed in terms
of Fresnel integrals.
| 0 | 1 | 0 | 0 | 0 | 0 |
Learning to Invert: Signal Recovery via Deep Convolutional Networks | The promise of compressive sensing (CS) has been offset by two significant
challenges. First, real-world data is not exactly sparse in a fixed basis.
Second, current high-performance recovery algorithms are slow to converge,
which limits CS to either non-real-time applications or scenarios where massive
back-end computing is available. In this paper, we attack both of these
challenges head-on by developing a new signal recovery framework we call {\em
DeepInverse} that learns the inverse transformation from measurement vectors to
signals using a {\em deep convolutional network}. When trained on a set of
representative images, the network learns both a representation for the signals
(addressing challenge one) and an inverse map approximating a greedy or convex
recovery algorithm (addressing challenge two). Our experiments indicate that
the DeepInverse network closely approximates the solution produced by
state-of-the-art CS recovery algorithms yet is hundreds of times faster in run
time. The tradeoff for the ultrafast run time is a computationally intensive,
off-line training procedure typical to deep networks. However, the training
needs to be completed only once, which makes the approach attractive for a host
of sparse recovery problems.
| 1 | 0 | 0 | 1 | 0 | 0 |
Multi-message Authentication over Noisy Channel with Secure Channel Codes | In this paper, we investigate multi-message authentication to combat
adversaries with infinite computational capacity. An authentication framework
over a wiretap channel $(W_1,W_2)$ is proposed to achieve information-theoretic
security with the same key. The proposed framework bridges the two research
areas in physical (PHY) layer security: secure transmission and message
authentication. Specifically, the sender Alice first transmits message $M$ to
the receiver Bob over $(W_1,W_2)$ with an error correction code; then Alice
employs a hash function (i.e., $\varepsilon$-AWU$_2$ hash functions) to
generate a message tag $S$ of message $M$ using key $K$, and encodes $S$ to a
codeword $X^n$ by leveraging an existing strongly secure channel coding with
exponentially small (in code length $n$) average probability of error; finally,
Alice sends $X^n$ over $(W_1,W_2)$ to Bob who authenticates the received
messages. We develop a theorem regarding the requirements/conditions for the
authentication framework to be information-theoretic secure for authenticating
a polynomial number of messages in terms of $n$. Based on this theorem, we
propose an authentication protocol that can guarantee the security
requirements, and prove its authentication rate can approach infinity when $n$
goes to infinity. Furthermore, we design and implement an efficient and
feasible authentication protocol over binary symmetric wiretap channel (BSWC)
by using \emph{Linear Feedback Shifting Register} based (LFSR-based) hash
functions and strong secure polar code. Through extensive experiments, it is
demonstrated that the proposed protocol can achieve low time cost, high
authentication rate, and low authentication error rate.
| 1 | 0 | 0 | 0 | 0 | 0 |
The Garden of Eden theorem: old and new | We review topics in the theory of cellular automata and dynamical systems
that are related to the Moore-Myhill Garden of Eden theorem.
| 0 | 1 | 1 | 0 | 0 | 0 |
Bosonization in Non-Relativistic CFTs | We demonstrate explicitly the correspondence between all protected operators
in a 2+1 dimensional non-supersymmetric bosonization duality in the
non-relativistic limit. Roughly speaking we consider $SU(N)$ Chern-Simons field
theory at level $k$ with $N_f$ flavours of fundamental boson, and match its
chiral sector to that of a $SU(k)$ theory at level $N$ with $N_f$ fundamental
fermions. We present the matching at the level of indices and individual
operators, seeing the mechanism of failure for $N_f > N$, and point out that
the non-relativistic setting is a particularly friendly setting for studying
interesting questions about such dualities.
| 0 | 1 | 0 | 0 | 0 | 0 |
Learning latent representations for style control and transfer in end-to-end speech synthesis | In this paper, we introduce the Variational Autoencoder (VAE) to an
end-to-end speech synthesis model, to learn the latent representation of
speaking styles in an unsupervised manner. The style representation learned
through VAE shows good properties such as disentangling, scaling, and
combination, which makes it easy for style control. Style transfer can be
achieved in this framework by first inferring style representation through the
recognition network of VAE, then feeding it into TTS network to guide the style
in synthesizing speech. To avoid Kullback-Leibler (KL) divergence collapse in
training, several techniques are adopted. Finally, the proposed model shows
good performance of style control and outperforms Global Style Token (GST)
model in ABX preference tests on style transfer.
| 1 | 0 | 0 | 0 | 0 | 0 |
Directed negative-weight percolation | We consider a directed variant of the negative-weight percolation model in a
two-dimensional, periodic, square lattice. The problem exhibits edge weights
which are taken from a distribution that allows for both positive and negative
values. Additionally, in this model variant all edges are directed. For a given
realization of the disorder, a minimally weighted loop/path configuration is
determined by performing a non-trivial transformation of the original lattice
into a minimum weight perfect matching problem. For this problem, fast
polynomial-time algorithms are available, thus we could study large systems
with high accuracy. Depending on the fraction of negatively and positively
weighted edges in the lattice, a continuous phase transition can be identified,
whose characterizing critical exponents we have estimated by a finite-size
scaling analyses of the numerically obtained data. We observe a strong change
of the universality class with respect to standard directed percolation, as
well as with respect to undirected negative-weight percolation. Furthermore,
the relation to directed polymers in random media is illustrated.
| 0 | 1 | 0 | 0 | 0 | 0 |
Integrating Lipschitzian Dynamical Systems using Piecewise Algorithmic Differentiation | In this article we analyze a generalized trapezoidal rule for initial value
problems with piecewise smooth right hand side \(F:\R^n\to\R^n\). When applied
to such a problem the classical trapezoidal rule suffers from a loss of
accuracy if the solution trajectory intersects a nondifferentiability of \(F\).
The advantage of the proposed generalized trapezoidal rule is threefold:
Firstly we can achieve a higher convergence order than with the classical
method. Moreover, the method is energy preserving for piecewise linear
Hamiltonian systems. Finally, in analogy to the classical case we derive a
third order interpolation polynomial for the numerical trajectory. In the
smooth case the generalized rule reduces to the classical one. Hence, it is a
proper extension of the classical theory. An error estimator is given and
numerical results are presented.
| 0 | 0 | 1 | 0 | 0 | 0 |
Effects of Planetesimal Accretion on the Thermal and Structural Evolution of Sub-Neptunes | A remarkable discovery of NASA's Kepler mission is the wide diversity in the
average densities of planets of similar mass. After gas disk dissipation, fully
formed planets could interact with nearby planetesimals from a remnant
planetesimal disk. These interactions would often lead to planetesimal
accretion due to the relatively high ratio between the planet size and the hill
radius for typical planets. We present calculations using the open-source
stellar evolution toolkit MESA (Modules for Experiments in Stellar
Astrophysics) modified to include the deposition of planetesimals into the H/He
envelopes of sub-Neptunes (~1-20 MEarth). We show that planetesimal accretion
can alter the mass-radius isochrones for these planets. The same initial planet
as a result of the same total accreted planetesimal mass can have up to ~5%
difference in mean densities several Gyr after the last accretion due to
inherent stochasticity of the accretion process. During the phase of rapid
accretion these differences are more dramatic. The additional energy deposition
from the accreted planetesimals increase the ratio between the planet's radius
to that of the core during rapid accretion, which in turn leads to enhanced
loss of atmospheric mass. As a result, the same initial planet can end up with
very different envelope mass fractions. These differences manifest as
differences in mean densities long after accretion stops. These effects are
particularly important for planets initially less massive than ~10 MEarth and
with envelope mass fraction less than ~10%, thought to be the most common type
of planets discovered by Kepler.
| 0 | 1 | 0 | 0 | 0 | 0 |
Estimation bounds and sharp oracle inequalities of regularized procedures with Lipschitz loss functions | We obtain estimation error rates and sharp oracle inequalities for
regularization procedures of the form \begin{equation*}
\hat f \in argmin_{f\in
F}\left(\frac{1}{N}\sum_{i=1}^N\ell(f(X_i), Y_i)+\lambda \|f\|\right)
\end{equation*} when $\|\cdot\|$ is any norm, $F$ is a convex class of
functions and $\ell$ is a Lipschitz loss function satisfying a Bernstein
condition over $F$. We explore both the bounded and subgaussian stochastic
frameworks for the distribution of the $f(X_i)$'s, with no assumption on the
distribution of the $Y_i$'s. The general results rely on two main objects: a
complexity function, and a sparsity equation, that depend on the specific
setting in hand (loss $\ell$ and norm $\|\cdot\|$).
As a proof of concept, we obtain minimax rates of convergence in the
following problems: 1) matrix completion with any Lipschitz loss function,
including the hinge and logistic loss for the so-called 1-bit matrix completion
instance of the problem, and quantile losses for the general case, which
enables to estimate any quantile on the entries of the matrix; 2) logistic
LASSO and variants such as the logistic SLOPE; 3) kernel methods, where the
loss is the hinge loss, and the regularization function is the RKHS norm.
| 0 | 0 | 1 | 1 | 0 | 0 |
On closed Lie ideals of certain tensor products of $C^*$-algebras | For a simple $C^*$-algebra $A$ and any other $C^*$-algebra $B$, it is proved
that every closed ideal of $A \otimes^{\min} B$ is a product ideal if either
$A$ is exact or $B$ is nuclear. Closed commutator of a closed ideal in a Banach
algebra whose every closed ideal possesses a quasi-central approximate identity
is described in terms of the commutator of the Banach algebra. If $\alpha$ is
either the Haagerup norm, the operator space projective norm or the
$C^*$-minimal norm, then this allows us to identify all closed Lie ideals of $A
\otimes^{\alpha} B$, where $A$ and $B$ are simple, unital $C^*$-algebras with
one of them admitting no tracial functionals, and to deduce that every
non-central closed Lie ideal of $B(H) \otimes^{\alpha} B(H)$ contains the
product ideal $K(H) \otimes^{\alpha} K(H)$. Closed Lie ideals of $A
\otimes^{\min} C(X)$ are also determined, $A$ being any simple unital
$C^*$-algebra with at most one tracial state and $X$ any compact Hausdorff
space. And, it is shown that closed Lie ideals of $A \otimes^{\alpha} K(H)$ are
precisely the product ideals, where $A$ is any unital $C^*$-algebra and
$\alpha$ any completely positive uniform tensor norm.
| 0 | 0 | 1 | 0 | 0 | 0 |
On the Chemistry of the Young Massive Protostellar core NGC 2264 CMM3 | We present the first gas-grain astrochemical model of the NGC 2264 CMM3
protostellar core. The chemical evolution of the core is affected by changing
its physical parameters such as the total density and the amount of
gas-depletion onto grain surfaces as well as the cosmic ray ionisation rate,
$\zeta$. We estimated $\zeta_{\text {CMM3}}$ = 1.6 $\times$ 10$^{-17}$
s$^{-1}$. This value is 1.3 times higher than the standard CR ionisation rate,
$\zeta_{\text {ISM}}$ = 1.3 $\times$ 10$^{-17}$ s$^{-1}$. Species response
differently to changes into the core physical conditions, but they are more
sensitive to changes in the depletion percentage and CR ionisation rate than to
variations in the core density. Gas-phase models highlighted the importance of
surface reactions as factories of large molecules and showed that for sulphur
bearing species depletion is important to reproduce observations.
Comparing the results of the reference model with the most recent millimeter
observations of the NGC 2264 CMM3 core showed that our model is capable of
reproducing the observed abundances of most of the species during early stages
($\le$ 3$\times$10$^4$ yrs) of their chemical evolution. Models with variations
in the core density between 1 - 20 $\times$ 10$^6$ cm$^{-3}$ are also in good
agreement with observations during the early time interval 1 $\times$ 10$^4 <$
t (yr) $<$ 5 $\times$ 10$^4$. In addition, models with higher CR ionisation
rates (5 - 10) $\times \zeta_{\text {ISM}}$ are often overestimating the
fractional abundances of the species. However, models with $\zeta_{\text
{CMM3}}$ = 5 $\zeta_{\text {ISM}}$ may best fit observations at times $\sim$ 2
$\times$ 10$^4$ yrs. Our results suggest that CMM3 is (1 - 5) $\times$ 10$^4$
yrs old. Therefore, the core is chemically young and it may host a Class 0
object as suggested by previous studies.
| 0 | 1 | 0 | 0 | 0 | 0 |
Uniform Consistency in Stochastic Block Model with Continuous Community Label | \cite{bickel2009nonparametric} developed a general framework to establish
consistency of community detection in stochastic block model (SBM). In most
applications of this framework, the community label is discrete. For example,
in \citep{bickel2009nonparametric,zhao2012consistency} the degree corrected SBM
is assumed to have a discrete degree parameter. In this paper, we generalize
the method of \cite{bickel2009nonparametric} to give consistency analysis of
maximum likelihood estimator (MLE) in SBM with continuous community label. We
show that there is a standard procedure to transform the $||\cdot||_2$ error
bound to the uniform error bound. We demonstrate the application of our general
results by proving the uniform consistency (strong consistency) of the MLE in
the exponential network model with interaction effect. Unfortunately, in the
continuous parameter case, the condition ensuring uniform consistency we
obtained is much stronger than that in the discrete parameter case, namely
$n\mu_n^5/(\log n)^{8}\rightarrow\infty$ versus $n\mu_n/\log
n\rightarrow\infty$. Where $n\mu_n$ represents the average degree of the
network. But continuous is the limit of discrete. So it is not surprising as we
show that by discretizing the community label space into sufficiently small
(but not too small) pieces and applying the MLE on the discretized community
label space, uniform consistency holds under almost the same condition as in
discrete community label space. Such a phenomenon is surprising since the
discretization does not depend on the data or the model. This reminds us of the
thresholding method.
| 0 | 0 | 0 | 1 | 0 | 0 |
Fine-scale population structure analysis in Armadillidium vulgare (Isopoda: Oniscidea) reveals strong female philopatry | In the last decades, dispersal studies have benefitted from the use of
molecular markers for detecting patterns differing between categories of
individuals, and have highlighted sex-biased dispersal in several species. To
explain this phenomenon, sex-related handicaps such as parental care have been
recently proposed as a hypothesis. Herein we tested this hypothesis in
Armadillidium vulgare, a terrestrial isopod in which females bear the totality
of the high parental care costs. We performed a fine-scale analysis of
sex-specific dispersal patterns, using males and females originating from five
sampling points located within 70 meters of each other. Based on microsatellite
markers and both F-statistics and spatial autocorrelation analyses, our results
revealed that while males did not present a significant structure at this
geographic scale, females were significantly more similar to each other when
they were collected in the same sampling point. These results support the
sex-handicap hypothesis, and we suggest that widening dispersal studies to
other isopods or crustaceans, displaying varying levels of parental care but
differing in their ecology or mating system, might shed light on the processes
underlying the evolution of sex-biased dispersal.
| 0 | 0 | 0 | 0 | 1 | 0 |
Fast transforms over finite fields of characteristic two | An additive fast Fourier transform over a finite field of characteristic two
efficiently evaluates polynomials at every element of an $\mathbb{F}_2$-linear
subspace of the field. We view these transforms as performing a change of basis
from the monomial basis to the associated Lagrange basis, and consider the
problem of performing the various conversions between these two bases, the
associated Newton basis, and the '' novel '' basis of Lin, Chung and Han (FOCS
2014). Existing algorithms are divided between two families, those designed for
arbitrary subspaces and more efficient algorithms designed for specially
constructed subspaces of fields with degree equal to a power of two. We
generalise techniques from both families to provide new conversion algorithms
that may be applied to arbitrary subspaces, but which benefit equally from the
specially constructed subspaces. We then construct subspaces of fields with
smooth degree for which our algorithms provide better performance than existing
algorithms.
| 1 | 0 | 0 | 0 | 0 | 0 |
Universality of group embeddability | Working in the framework of Borel reducibility, we study various notions of
embeddability between groups. We prove that the embeddability between countable
groups, the topological embeddability between (discrete) Polish groups, and the
isometric embeddability between separable groups with a bounded bi-invariant
complete metric are all invariantly universal analytic quasi-orders. This
strengthens some results from [Wil14] and [FLR09].
| 0 | 0 | 1 | 0 | 0 | 0 |
Plenoptic Monte Carlo Object Localization for Robot Grasping under Layered Translucency | In order to fully function in human environments, robot perception will need
to account for the uncertainty caused by translucent materials. Translucency
poses several open challenges in the form of transparent objects (e.g.,
drinking glasses), refractive media (e.g., water), and diffuse partial
occlusions (e.g., objects behind stained glass panels). This paper presents
Plenoptic Monte Carlo Localization (PMCL) as a method for localizing object
poses in the presence of translucency using plenoptic (light-field)
observations. We propose a new depth descriptor, the Depth Likelihood Volume
(DLV), and its use within a Monte Carlo object localization algorithm. We
present results of localizing and manipulating objects with translucent
materials and objects occluded by layers of translucency. Our PMCL
implementation uses observations from a Lytro first generation light field
camera to allow a Michigan Progress Fetch robot to perform grasping.
| 1 | 0 | 0 | 0 | 0 | 0 |
CUR Decompositions, Similarity Matrices, and Subspace Clustering | A general framework for solving the subspace clustering problem using the CUR
decomposition is presented. The CUR decomposition provides a natural way to
construct similarity matrices for data that come from a union of unknown
subspaces $\mathscr{U}=\underset{i=1}{\overset{M}\bigcup}S_i$. The similarity
matrices thus constructed give the exact clustering in the noise-free case.
Additionally, this decomposition gives rise to many distinct similarity
matrices from a given set of data, which allow enough flexibility to perform
accurate clustering of noisy data. We also show that two known methods for
subspace clustering can be derived from the CUR decomposition. An algorithm
based on the theoretical construction of similarity matrices is presented, and
experiments on synthetic and real data are presented to test the method.
Additionally, an adaptation of our CUR based similarity matrices is utilized
to provide a heuristic algorithm for subspace clustering; this algorithm yields
the best overall performance to date for clustering the Hopkins155 motion
segmentation dataset.
| 1 | 0 | 0 | 1 | 0 | 0 |
Approximating Geometric Knapsack via L-packings | We study the two-dimensional geometric knapsack problem (2DK) in which we are
given a set of n axis-aligned rectangular items, each one with an associated
profit, and an axis-aligned square knapsack. The goal is to find a
(non-overlapping) packing of a maximum profit subset of items inside the
knapsack (without rotating items). The best-known polynomial-time approximation
factor for this problem (even just in the cardinality case) is (2 + \epsilon)
[Jansen and Zhang, SODA 2004].
In this paper, we break the 2 approximation barrier, achieving a
polynomial-time (17/9 + \epsilon) < 1.89 approximation, which improves to
(558/325 + \epsilon) < 1.72 in the cardinality case. Essentially all prior work
on 2DK approximation packs items inside a constant number of rectangular
containers, where items inside each container are packed using a simple greedy
strategy. We deviate for the first time from this setting: we show that there
exists a large profit solution where items are packed inside a constant number
of containers plus one L-shaped region at the boundary of the knapsack which
contains items that are high and narrow and items that are wide and thin. As a
second major and the main algorithmic contribution of this paper, we present a
PTAS for this case. We believe that this will turn out to be useful in future
work in geometric packing problems.
We also consider the variant of the problem with rotations (2DKR), where
items can be rotated by 90 degrees. Also, in this case, the best-known
polynomial-time approximation factor (even for the cardinality case) is (2 +
\epsilon) [Jansen and Zhang, SODA 2004]. Exploiting part of the machinery
developed for 2DK plus a few additional ideas, we obtain a polynomial-time (3/2
+ \epsilon)-approximation for 2DKR, which improves to (4/3 + \epsilon) in the
cardinality case.
| 1 | 0 | 0 | 0 | 0 | 0 |
Impact and mitigation strategy for future solar flares | It is widely established that extreme space weather events associated with
solar flares are capable of causing widespread technological damage. We develop
a simple mathematical model to assess the economic losses arising from these
phenomena over time. We demonstrate that the economic damage is characterized
by an initial period of power-law growth, followed by exponential amplification
and eventual saturation. We outline a mitigation strategy to protect our planet
by setting up a magnetic shield to deflect charged particles at the Lagrange
point L$_1$, and demonstrate that this approach appears to be realizable in
terms of its basic physical parameters. We conclude our analysis by arguing
that shielding strategies adopted by advanced civilizations will lead to
technosignatures that are detectable by upcoming missions.
| 0 | 1 | 0 | 0 | 0 | 0 |
Empirical Bayes Matrix Completion | We develop an empirical Bayes (EB) algorithm for the matrix completion
problems. The EB algorithm is motivated from the singular value shrinkage
estimator for matrix means by Efron and Morris (1972). Since the EB algorithm
is essentially the EM algorithm applied to a simple model, it does not require
heuristic parameter tuning other than tolerance. Numerical results demonstrated
that the EB algorithm achieves a good trade-off between accuracy and efficiency
compared to existing algorithms and that it works particularly well when the
difference between the number of rows and columns is large. Application to real
data also shows the practical utility of the EB algorithm.
| 0 | 0 | 1 | 1 | 0 | 0 |
Excitonic Instability and Pseudogap Formation in Nodal Line Semimetal ZrSiS | Electron correlation effects are studied in ZrSiS using a combination of
first-principles and model approaches. We show that basic electronic properties
of ZrSiS can be described within a two-dimensional lattice model of two nested
square lattices. High degree of electron-hole symmetry characteristic for ZrSiS
is one of the key features of this model. Having determined model parameters
from first-principles calculations, we then explicitly take electron-electron
interactions into account and show that at moderately low temperatures ZrSiS
exhibits excitonic instability, leading to the formation of a pseudogap in the
electronic spectrum. The results can be understood in terms of
Coulomb-interaction-assisted pairing of electrons and holes reminiscent to that
of an excitonic insulator. Our finding allows us to provide a physical
interpretation to the unusual mass enhancement of charge carriers in ZrSiS
recently observed experimentally.
| 0 | 1 | 0 | 0 | 0 | 0 |
The Riemannian Geometry of Deep Generative Models | Deep generative models learn a mapping from a low dimensional latent space to
a high-dimensional data space. Under certain regularity conditions, these
models parameterize nonlinear manifolds in the data space. In this paper, we
investigate the Riemannian geometry of these generated manifolds. First, we
develop efficient algorithms for computing geodesic curves, which provide an
intrinsic notion of distance between points on the manifold. Second, we develop
an algorithm for parallel translation of a tangent vector along a path on the
manifold. We show how parallel translation can be used to generate analogies,
i.e., to transport a change in one data point into a semantically similar
change of another data point. Our experiments on real image data show that the
manifolds learned by deep generative models, while nonlinear, are surprisingly
close to zero curvature. The practical implication is that linear paths in the
latent space closely approximate geodesics on the generated manifold. However,
further investigation into this phenomenon is warranted, to identify if there
are other architectures or datasets where curvature plays a more prominent
role. We believe that exploring the Riemannian geometry of deep generative
models, using the tools developed in this paper, will be an important step in
understanding the high-dimensional, nonlinear spaces these models learn.
| 1 | 0 | 0 | 1 | 0 | 0 |
Portable, high-performance containers for HPC | Building and deploying software on high-end computing systems is a
challenging task. High performance applications have to reliably run across
multiple platforms and environments, and make use of site-specific resources
while resolving complicated software-stack dependencies. Containers are a type
of lightweight virtualization technology that attempt to solve this problem by
packaging applications and their environments into standard units of software
that are: portable, easy to build and deploy, have a small footprint, and low
runtime overhead. In this work we present an extension to the container runtime
of Shifter that provides containerized applications with a mechanism to access
GPU accelerators and specialized networking from the host system, effectively
enabling performance portability of containers across HPC resources. The
presented extension makes possible to rapidly deploy high-performance software
on supercomputers from containerized applications that have been developed,
built, and tested in non-HPC commodity hardware, e.g. the laptop or workstation
of a researcher.
| 1 | 0 | 0 | 0 | 0 | 0 |
Learning a Deep Convolution Network with Turing Test Adversaries for Microscopy Image Super Resolution | Adversarially trained deep neural networks have significantly improved
performance of single image super resolution, by hallucinating photorealistic
local textures, thereby greatly reducing the perception difference between a
real high resolution image and its super resolved (SR) counterpart. However,
application to medical imaging requires preservation of diagnostically relevant
features while refraining from introducing any diagnostically confusing
artifacts. We propose using a deep convolutional super resolution network
(SRNet) trained for (i) minimising reconstruction loss between the real and SR
images, and (ii) maximally confusing learned relativistic visual Turing test
(rVTT) networks to discriminate between (a) pair of real and SR images (T1) and
(b) pair of patches in real and SR selected from region of interest (T2). The
adversarial loss of T1 and T2 while backpropagated through SRNet helps it learn
to reconstruct pathorealism in the regions of interest such as white blood
cells (WBC) in peripheral blood smears or epithelial cells in histopathology of
cancerous biopsy tissues, which are experimentally demonstrated here.
Experiments performed for measuring signal distortion loss using peak signal to
noise ratio (pSNR) and structural similarity (SSIM) with variation of SR scale
factors, impact of rVTT adversarial losses, and impact on reporting using SR on
a commercially available artificial intelligence (AI) digital pathology system
substantiate our claims.
| 1 | 0 | 0 | 0 | 0 | 0 |
Quantum dynamics of a hydrogen-like atom in a time-dependent box: non-adiabatic regime | We consider a hydrogen atom confined in time-dependent trap created by a
spherical impenetrable box with time-dependent radius. For such model we study
the behavior of atomic electron under the (non-adiabatic) dynamical confinement
caused by the rapidly moving wall of the box. The expectation values of the
total and kinetic energy, average force, pressure and coordinate are analyzed
as a function of time for linearly expanding, contracting and harmonically
breathing boxes. It is shown that linearly extending box leads to de-excitation
of the atom, while the rapidly contracting box causes the creation of very high
pressure on the atom and transition of the atomic electron into the unbound
state. In harmonically breathing box diffusive excitation of atomic electron
may occur in analogy with that for atom in a microwave field.
| 0 | 1 | 0 | 0 | 0 | 0 |
Richardson's solutions in the real- and complex-energy spectrum | The constant pairing Hamiltonian holds exact solutions worked out by
Richardson in the early Sixties. This exact solution of the pairing Hamiltonian
regained interest at the end of the Nineties. The discret complex-energy states
had been included in the Richardson's solutions by Hasegawa et al. [1]. In this
contribution we reformulate the problem of determining the exact eigenenergies
of the pairing Hamiltonian when the continuum is included through the single
particle level density. The solutions with discret complex-energy states is
recovered by analytic continuation of the equations to the complex energy
plane. This formulation may be applied to loosely bound system where the
correlations with the continuum-spectrum of energy is really important. Some
details are given to show how the many-body eigenenergy emerges as sum of the
pair-energies.
| 0 | 1 | 0 | 0 | 0 | 0 |
Complexity Results for MCMC derived from Quantitative Bounds | This paper considers how to obtain MCMC quantitative convergence bounds which
can be translated into tight complexity bounds in high-dimensional setting. We
propose a modified drift-and-minorization approach, which establishes a
generalized drift condition defined in a subset of the state space. The subset
is called the "large set", and is chosen to rule out some "bad" states which
have poor drift property when the dimension gets large. Using the "large set"
together with a "centered" drift function, a quantitative bound can be obtained
which can be translated into a tight complexity bound. As a demonstration, we
analyze a certain realistic Gibbs sampler algorithm and obtain a complexity
upper bound for the mixing time, which shows that the number of iterations
required for the Gibbs sampler to converge is constant. It is our hope that
this modified drift-and-minorization approach can be employed in many other
specific examples to obtain complexity bounds for high-dimensional Markov
chains.
| 0 | 0 | 0 | 1 | 0 | 0 |
Symmetries and regularity for holomorphic maps between balls | Let $f:{\mathbb B}^n \to {\mathbb B}^N$ be a holomorphic map. We study
subgroups $\Gamma_f \subseteq {\rm Aut}({\mathbb B}^n)$ and $T_f \subseteq {\rm
Aut}({\mathbb B}^N)$. When $f$ is proper, we show both these groups are Lie
subgroups. When $\Gamma_f$ contains the center of ${\bf U}(n)$, we show that
$f$ is spherically equivalent to a polynomial. When $f$ is minimal we show that
there is a homomorphism $\Phi:\Gamma_f \to T_f$ such that $f$ is equivariant
with respect to $\Phi$. To do so, we characterize minimality via the triviality
of a third group $H_f$. We relate properties of ${\rm Ker}(\Phi)$ to older
results on invariant proper maps between balls. When $f$ is proper but
completely non-rational, we show that either both $\Gamma_f$ and $T_f$ are
finite or both are noncompact.
| 0 | 0 | 1 | 0 | 0 | 0 |
On the treatment of $\ell$-changing proton-hydrogen Rydberg atom collisions | Energy-conserving, angular momentum-changing collisions between protons and
highly excited Rydberg hydrogen atoms are important for precise understanding
of atomic recombination at the photon decoupling era, and the elemental
abundance after primordial nucleosynthesis. Early approaches to $\ell$-changing
collisions used perturbation theory for only dipole-allowed ($\Delta \ell=\pm
1$) transitions. An exact non-perturbative quantum mechanical treatment is
possible, but it comes at computational cost for highly excited Rydberg states.
In this note we show how to obtain a semi-classical limit that is accurate and
simple, and develop further physical insights afforded by the non-perturbative
quantum mechanical treatment.
| 0 | 1 | 0 | 0 | 0 | 0 |
Complex Economic Activities Concentrate in Large Cities | Why do some economic activities agglomerate more than others? And, why does
the agglomeration of some economic activities continue to increase despite
recent developments in communication and transportation technologies? In this
paper, we present evidence that complex economic activities concentrate more in
large cities. We find this to be true for technologies, scientific
publications, industries, and occupations. Using historical patent data, we
show that the urban concentration of complex economic activities has been
continuously increasing since 1850. These findings suggest that the increasing
urban concentration of jobs and innovation might be a consequence of the
growing complexity of the economy.
| 1 | 0 | 0 | 0 | 0 | 0 |
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