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19,101 | An Analytic Formula for Numbers of Restricted Partitions from Conformal Field Theory | We study the correlators of irregular vertex operators in two-dimensional
conformal field theory (CFT) in order to propose an exact analytic formula for
calculating numbers of partitions, that is:
1) for given $N,k$, finding the total number $\lambda(N|k)$ of length $k$
partitions of $N$: $N=n_1+...+n_k;0<n_1\leq{n_2}...\leq{n_k}$.
2) finding the total number $\lambda(N)=\sum_{k=1}^N\lambda(N|k)$ of
partitions of a natural number $N$
We propose an exact analytic expression for $\lambda(N|k)$ by relating
two-point short-distance correlation functions of irregular vertex operators in
$c=1$ conformal field theory ( the form of the operators is established in this
paper): with the first correlator counting the partitions in the upper
half-plane and the second one obtained from the first correlator by conformal
transformations of the form $f(z)=h(z)e^{-{i\over{z}}}$ where $h(z)$ is regular
and non-vanishing at $z=0$. The final formula for $\lambda(N|k)$ is given in
terms of regularized ($\epsilon$-ordered) finite series in the generalized
higher-derivative Schwarzians and incomplete Bell polynomials of the above
conformal transformation at $z=i\epsilon$ ($\epsilon\rightarrow{0}$)
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19,102 | Hyperopic Cops and Robbers | We introduce a new variant of the game of Cops and Robbers played on graphs,
where the robber is invisible unless outside the neighbor set of a cop. The
hyperopic cop number is the corresponding analogue of the cop number, and we
investigate bounds and other properties of this parameter. We characterize the
cop-win graphs for this variant, along with graphs with the largest possible
hyperopic cop number. We analyze the cases of graphs with diameter 2 or at
least 3, focusing on when the hyperopic cop number is at most one greater than
the cop number. We show that for planar graphs, as with the usual cop number,
the hyperopic cop number is at most 3. The hyperopic cop number is considered
for countable graphs, and it is shown that for connected chains of graphs, the
hyperopic cop density can be any real number in $[0,1/2].$
| 1 | 0 | 0 | 0 | 0 | 0 |
19,103 | New pinching estimates for Inverse curvature flows in space forms | We prove new pinching estimate for the inverse curvature flow of strictly
convex hypersurfaces in the space form $N$ of constant sectional curvature
$K_N$ with speed given by $F^{-\alpha}$, where $\alpha\in (0,1]$ for $K_N=0,-1$
and $\alpha=1$ for $K_N=1$, $F$ is a smooth, symmetric homogeneous of degree
one function which is inverse concave and has dual $F_*$ approaching zero on
the boundary of the positive cone $\Gamma_+$. We show that the ratio of the
largest principal curvature to the smallest principal curvature of the flow
hypersurface is controlled by its initial value. This can be used to prove the
smooth convergence of the flow.
| 0 | 0 | 1 | 0 | 0 | 0 |
19,104 | automan: a simple, Python-based, automation framework for numerical computing | We present an easy-to-use, Python-based framework that allows a researcher to
automate their computational simulations. In particular the framework
facilitates assembling several long-running computations and producing various
plots from the data produced by these computations. The framework makes it
possible to reproduce every figure made for a publication with a single
command. It also allows one to distribute the computations across a network of
computers. The framework has been used to write research papers in numerical
computing. This paper discusses the design of the framework, and the benefits
of using it. The ideas presented are general and should help researchers
organize their computations for better reproducibility.
| 1 | 0 | 0 | 0 | 0 | 0 |
19,105 | Extensive characterization of a high Reynolds number decelerating boundary layer using advanced optical metrology | An experiment conducted in the framework of the EUHIT project and designed to
characterize large scale structures in an adverse pressure gradient boundary
layer flow is presented. Up to 16 sCMOS cameras were used in order to perform
large scale turbulent boundary layer PIV measurements with a large field of
view and appropriate spatial resolution. To access the span-wise / wall-normal
signature of the structures as well, stereoscopic PIV measurements in
span-wise/wall-normal planes were performed at specific stream-wise locations.
To complement these large field of view measurements, long-range micro-PIV,
time resolved near wall velocity profiles and film-based measurements were
performed in order to determine the wall-shear stress and its fluctuations at
some specific locations along the model.
| 0 | 1 | 0 | 0 | 0 | 0 |
19,106 | Q-analogues of the Fibo-Stirling numbers | Let $F_n$ denote the $n^{th}$ Fibonacci number relative to the initial
conditions $F_0=0$ and $F_1=1$. Bach, Paudyal, and Remmel introduced Fibonacci
analogues of the Stirling numbers called Fibo-Stirling numbers of the first and
second kind. These numbers serve as the connection coefficients between the
Fibo-falling factorial basis $\{(x)_{\downarrow_{F,n}}:n \geq 0\}$ and the
Fibo-rising factorial basis $\{(x)_{\uparrow_{F,n}}:n \geq 0\}$ which are
defined by $(x)_{\downarrow_{F,0}} = (x)_{\uparrow_{F,0}} = 1$ and for $k \geq
1$, $(x)_{\downarrow_{F,k}} = x(x-F_1) \cdots (x-F_{k-1})$ and
$(x)_{\uparrow_{F,k}} = x(x+F_1) \cdots (x+F_{k-1})$. We gave a general rook
theory model which allowed us to give combinatorial interpretations of the
Fibo-Stirling numbers of the first and second kind.
There are two natural $q$-analogues of the falling and rising Fibo-factorial
basis. That is, let $[x]_q = \frac{q^x-1}{q-1}$. Then we let
$[x]_{\downarrow_{q,F,0}} = \overline{[x]}_{\downarrow_{q,F,0}} =
[x]_{\uparrow_{q,F,0}} = \overline{[x]}_{\uparrow_{q,F,0}}=1$ and, for $k > 0$,
we let $[x]_{\downarrow_{q,F,k}} = [x]_q [x-F_1]_q \cdots [x-F_{k-1}]_q$,
$\overline{[x]}_{\downarrow_{q,F,k}}= [x]_q ([x]_q-[F_1]_q) \cdots
([x]_q-[F_{k-1}]_q)$, $[x]_{\uparrow_{q,F,k}}= [x]_q [x+F_1]_q \cdots
[x+F_{k-1}]_q$, and $\overline{[x]}_{\uparrow_{q,F,k}}= [x]_q ([x]_q+[F_1]_q)
\cdots ([x]_q+[F_{k-1}]_q)$.
In this paper, we show we can modify the rook theory model of Bach, Paudyal,
and Remmel to give combinatorial interpretations for the two different types
$q$-analogues of the Fibo-Stirling numbers which arise as the connection
coefficients between the two different $q$-analogues of the Fibonacci falling
and rising factorial bases. \end{abstract}
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19,107 | Hybrid Dirac Semimetal in CaAgBi Materials Family | Based on their formation mechanisms, Dirac points in three-dimensional
systems can be classified as accidental or essential. The former can be further
distinguished into type-I and type-II, depending on whether the Dirac cone
spectrum is completely tipped over along certain direction. Here, we predict
the coexistence of all three kinds of Dirac points in the low-energy band
structure of CaAgBi-family materials with a stuffed Wurtzite structure. Two
pairs of accidental Dirac points reside on the rotational axis, with one pair
being type-I and the other pair type-II; while another essential Dirac point is
pinned at the high symmetry point on the Brillouin zone boundary. Due to broken
inversion symmetry, the band degeneracy around accidental Dirac points is
completely lifted except along the rotational axis, which may enable the
splitting of chiral carriers at a ballistic p-n junction with a double negative
refraction effect. We clarify their symmetry protections, and find both the
Dirac-cone and Fermi arc topological surface states.
| 0 | 1 | 0 | 0 | 0 | 0 |
19,108 | On the martingale property in the rough Bergomi model | We consider a class of fractional stochastic volatility models (including the
so-called rough Bergomi model), where the volatility is a superlinear function
of a fractional Gaussian process. We show that the stock price is a true
martingale if and only if the correlation $\rho$ between the driving Brownian
motions of the stock and the volatility is nonpositive. We also show that for
each $\rho<0$ and $m> \frac{1}{1-\rho^2}$, the $m$-th moment of the stock
price is infinite at each positive time.
| 0 | 0 | 0 | 0 | 0 | 1 |
19,109 | Weighted Surface Algebras | A finite-dimensional algebra $A$ over an algebraically closed field $K$ is
called periodic if it is periodic under the action of the syzygy operator in
the category of $A-A-$ bimodules. The periodic algebras are self-injective and
occur naturally in the study of tame blocks of group algebras, actions of
finite groups on spheres, hypersurface singularities of finite Cohen-Macaulay
type, and Jacobian algebras of quivers with potentials. Recently, the tame
periodic algebras of polynomial growth have been classified and it is natural
to attempt to classify all tame periodic algebras. We introduce the weighted
surface algebras of triangulated surfaces with arbitrarily oriented triangles
and describe their basic properties. In particular, we prove that all these
algebras, except the singular tetrahedral algebras, are symmetric tame periodic
algebras of period $4$. Moreover, we describe the socle deformations of the
weighted surface algebras and prove that all these algebras are symmetric tame
periodic algebras of period $4$. The main results of the paper form an
important step towards a classification of all periodic symmetric tame algebras
of non-polynomial growth, and lead to a complete description of all algebras of
generalized quaternion type. Further, the orbit closures of the weighted
surface algebras (and their socle deformations) in the affine varieties of
associative $K$-algebra structures contain wide classes of tame symmetric
algebras related to algebras of dihedral and semidihedral types, which occur in
the study of blocks of group algebras with dihedral and semidihedral defect
groups.
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19,110 | A Statistical Learning Approach to Modal Regression | This paper studies the nonparametric modal regression problem systematically
from a statistical learning view. Originally motivated by pursuing a
theoretical understanding of the maximum correntropy criterion based regression
(MCCR), our study reveals that MCCR with a tending-to-zero scale parameter is
essentially modal regression. We show that nonparametric modal regression
problem can be approached via the classical empirical risk minimization. Some
efforts are then made to develop a framework for analyzing and implementing
modal regression. For instance, the modal regression function is described, the
modal regression risk is defined explicitly and its \textit{Bayes} rule is
characterized; for the sake of computational tractability, the surrogate modal
regression risk, which is termed as the generalization risk in our study, is
introduced. On the theoretical side, the excess modal regression risk, the
excess generalization risk, the function estimation error, and the relations
among the above three quantities are studied rigorously. It turns out that
under mild conditions, function estimation consistency and convergence may be
pursued in modal regression as in vanilla regression protocols, such as mean
regression, median regression, and quantile regression. However, it outperforms
these regression models in terms of robustness as shown in our study from a
re-descending M-estimation view. This coincides with and in return explains the
merits of MCCR on robustness. On the practical side, the implementation issues
of modal regression including the computational algorithm and the tuning
parameters selection are discussed. Numerical assessments on modal regression
are also conducted to verify our findings empirically.
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19,111 | Teaching a Machine to Read Maps with Deep Reinforcement Learning | The ability to use a 2D map to navigate a complex 3D environment is quite
remarkable, and even difficult for many humans. Localization and navigation is
also an important problem in domains such as robotics, and has recently become
a focus of the deep reinforcement learning community. In this paper we teach a
reinforcement learning agent to read a map in order to find the shortest way
out of a random maze it has never seen before. Our system combines several
state-of-the-art methods such as A3C and incorporates novel elements such as a
recurrent localization cell. Our agent learns to localize itself based on 3D
first person images and an approximate orientation angle. The agent generalizes
well to bigger mazes, showing that it learned useful localization and
navigation capabilities.
| 1 | 0 | 0 | 1 | 0 | 0 |
19,112 | The fan beam model for the pulse evolution of PSR J0737-3039B | Average radio pulse profile of a pulsar B in a double pulsar system PSR
J0737-3039A/B exhibits an interesting behaviour. During the observation period
between 2003 and 2009, the profile evolves from a single-peaked to a
double-peaked form, following disappearance in 2008 indicating that the
geodetic precession of the pulsar is a possible origin of such behaviour. The
known pulsar beam models can be used to determine the geometry of PSR
J0737-3039B in the context of the precession. We study how the fan-beam
geometry performs in explaining the observed variations of the radio profile
morphology. It is shown that the fan beam can successfully reproduce the
observed evolution of the pulse width, and should be considered as a serious
alternative for the conal-like models.
| 0 | 1 | 0 | 0 | 0 | 0 |
19,113 | Resilience of Core-Periphery Networks in the Case of Rich-Club | Core-periphery networks are structures that present a set of central and
densely connected nodes, namely the core, and a set of non-central and sparsely
connected nodes, namely the periphery. The rich-club refers to a set in which
the highest degree nodes show a high density of connections. Thus, a network
that displays a rich-club can be interpreted as a core-periphery network in
which the core is made up by a number of hubs. In this paper, we test the
resilience of networks showing a progressively denser rich-club and we observe
how this structure is able to affect the network measures in terms of both
cohesion and efficiency in information flow. Additionally, we consider the case
in which, instead of making the core denser, we add links to the periphery.
These two procedures of core and periphery thickening delineate a decision
process in the placement of new links and allow us to conduct a scenario
analysis that can be helpful in the comprehension and supervision of complex
networks under the resilience perspective. The advantages of the two
procedures, as well as their implications, are discussed in relation to both
network effciency and node heterogeneity.
| 1 | 0 | 0 | 0 | 0 | 0 |
19,114 | Reservoir of Diverse Adaptive Learners and Stacking Fast Hoeffding Drift Detection Methods for Evolving Data Streams | The last decade has seen a surge of interest in adaptive learning algorithms
for data stream classification, with applications ranging from predicting ozone
level peaks, learning stock market indicators, to detecting computer security
violations. In addition, a number of methods have been developed to detect
concept drifts in these streams. Consider a scenario where we have a number of
classifiers with diverse learning styles and different drift detectors.
Intuitively, the current 'best' (classifier, detector) pair is application
dependent and may change as a result of the stream evolution. Our research
builds on this observation. We introduce the $\mbox{Tornado}$ framework that
implements a reservoir of diverse classifiers, together with a variety of drift
detection algorithms. In our framework, all (classifier, detector) pairs
proceed, in parallel, to construct models against the evolving data streams. At
any point in time, we select the pair which currently yields the best
performance. We further incorporate two novel stacking-based drift detection
methods, namely the $\mbox{FHDDMS}$ and $\mbox{FHDDMS}_{add}$ approaches. The
experimental evaluation confirms that the current 'best' (classifier, detector)
pair is not only heavily dependent on the characteristics of the stream, but
also that this selection evolves as the stream flows. Further, our
$\mbox{FHDDMS}$ variants detect concept drifts accurately in a timely fashion
while outperforming the state-of-the-art.
| 1 | 0 | 0 | 1 | 0 | 0 |
19,115 | Extremes in Random Graphs Models of Complex Networks | Regarding the analysis of Web communication, social and complex networks the
fast finding of most influential nodes in a network graph constitutes an
important research problem. We use two indices of the influence of those nodes,
namely, PageRank and a Max-linear model. We consider the PageRank %both as
%Galton-Watson branching process and as an autoregressive process with a random
number of random coefficients that depend on ranks of incoming nodes and their
out-degrees and assume that the coefficients are independent and distributed
with regularly varying tail and with the same tail index. Then it is proved
that the tail index and the extremal index are the same for both PageRank and
the Max-linear model and the values of these indices are found. The
achievements are based on the study of random sequences of a random length and
the comparison of the distribution of their maxima and linear combinations.
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19,116 | Estimates of the Reconstruction Error in Partially Redressed Warped Frames Expansions | In recent work, redressed warped frames have been introduced for the analysis
and synthesis of audio signals with non-uniform frequency and time resolutions.
In these frames, the allocation of frequency bands or time intervals of the
elements of the representation can be uniquely described by means of a warping
map. Inverse warping applied after time-frequency sampling provides the key to
reduce or eliminate dispersion of the warped frame elements in the conjugate
variable, making it possible, e.g., to construct frequency warped frames with
synchronous time alignment through frequency. The redressing procedure is
however exact only when the analysis and synthesis windows have compact support
in the domain where warping is applied. This implies that frequency warped
frames cannot have compact support in the time domain. This property is
undesirable when online computation is required. Approximations in which the
time support is finite are however possible, which lead to small reconstruction
errors. In this paper we study the approximation error for compactly supported
frequency warped analysis-synthesis elements, providing a few examples and case
studies.
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19,117 | On the Optimality of Secret Key Agreement via Omniscience | For the multiterminal secret key agreement problem under a private source
model, it is known that the maximum key rate, i.e., the secrecy capacity, can
be achieved through communication for omniscience, but the omniscience strategy
can be strictly suboptimal in terms of minimizing the public discussion rate.
While a single-letter characterization is not known for the minimum discussion
rate needed for achieving the secrecy capacity, we derive single-letter lower
and upper bounds that yield some simple conditions for omniscience to be
discussion-rate optimal. These conditions turn out to be enough to deduce the
optimality of omniscience for a large class of sources including the
hypergraphical sources. Through conjectures and examples, we explore other
source models to which our methods do not easily extend.
| 1 | 0 | 0 | 0 | 0 | 0 |
19,118 | Learning Motion Predictors for Smart Wheelchair using Autoregressive Sparse Gaussian Process | Constructing a smart wheelchair on a commercially available powered
wheelchair (PWC) platform avoids a host of seating, mechanical design and
reliability issues but requires methods of predicting and controlling the
motion of a device never intended for robotics. Analog joystick inputs are
subject to black-box transformations which may produce intuitive and adaptable
motion control for human operators, but complicate robotic control approaches;
furthermore, installation of standard axle mounted odometers on a commercial
PWC is difficult. In this work, we present an integrated hardware and software
system for predicting the motion of a commercial PWC platform that does not
require any physical or electronic modification of the chair beyond plugging
into an industry standard auxiliary input port. This system uses an RGB-D
camera and an Arduino interface board to capture motion data, including visual
odometry and joystick signals, via ROS communication. Future motion is
predicted using an autoregressive sparse Gaussian process model. We evaluate
the proposed system on real-world short-term path prediction experiments.
Experimental results demonstrate the system's efficacy when compared to a
baseline neural network model.
| 1 | 0 | 0 | 0 | 0 | 0 |
19,119 | Kernelized Hashcode Representations for Relation Extraction | Kernel methods have produced state-of-the-art results for a number of NLP
tasks such as relation extraction, but suffer from poor scalability due to the
high cost of computing kernel similarities between natural language structures.
A recently proposed technique, kernelized locality-sensitive hashing (KLSH),
can significantly reduce the computational cost, but is only applicable to
classifiers operating on kNN graphs. Here we propose to use random subspaces of
KLSH codes for efficiently constructing an explicit representation of NLP
structures suitable for general classification methods. Further, we propose an
approach for optimizing the KLSH model for classification problems by
maximizing an approximation of mutual information between the KLSH codes
(feature vectors) and the class labels. We evaluate the proposed approach on
biomedical relation extraction datasets, and observe significant and robust
improvements in accuracy w.r.t. state-of-the-art classifiers, along with
drastic (orders-of-magnitude) speedup compared to conventional kernel methods.
| 1 | 0 | 0 | 1 | 0 | 0 |
19,120 | Can Adversarial Networks Hallucinate Occluded People With a Plausible Aspect? | When you see a person in a crowd, occluded by other persons, you miss visual
information that can be used to recognize, re-identify or simply classify him
or her. You can imagine its appearance given your experience, nothing more.
Similarly, AI solutions can try to hallucinate missing information with
specific deep learning architectures, suitably trained with people with and
without occlusions. The goal of this work is to generate a complete image of a
person, given an occluded version in input, that should be a) without occlusion
b) similar at pixel level to a completely visible people shape c) capable to
conserve similar visual attributes (e.g. male/female) of the original one. For
the purpose, we propose a new approach by integrating the state-of-the-art of
neural network architectures, namely U-nets and GANs, as well as discriminative
attribute classification nets, with an architecture specifically designed to
de-occlude people shapes. The network is trained to optimize a Loss function
which could take into account the aforementioned objectives. As well we propose
two datasets for testing our solution: the first one, occluded RAP, created
automatically by occluding real shapes of the RAP dataset (which collects also
attributes of the people aspect); the second is a large synthetic dataset, AiC,
generated in computer graphics with data extracted from the GTA video game,
that contains 3D data of occluded objects by construction. Results are
impressive and outperform any other previous proposal. This result could be an
initial step to many further researches to recognize people and their behavior
in an open crowded world.
| 1 | 0 | 0 | 0 | 0 | 0 |
19,121 | John, the semi-conductor : a tool for comprovisation | This article presents "John", an open-source software designed to help
collective free improvisation. It provides generated screen-scores running on
distributed, reactive web-browsers. The musicians can then concurrently edit
the scores in their own browser. John is used by ONE, a septet playing
improvised electro-acoustic music with digital musical instruments (DMI). One
of the original features of John is that its design takes care of leaving the
musician's attention as free as possible. Firstly, a quick review of the
context of screen-based scores will help situate this research in the history
of contemporary music notation. Then I will trace back how improvisation
sessions led to John's particular "notational perspective". A brief description
of the software will precede a discussion about the various aspects guiding its
design.
| 1 | 0 | 0 | 0 | 0 | 0 |
19,122 | Eigenvalue and Eigenfunction for the $PT$-symmetric Potential $V = - (ix)^N$ | The real energy spectrum from the $PT$-symmetric Hamiltonian $H = p^2 -
(ix)^N$ with $x\in\mathbb{C}$ was examined within one pair of Stokes wedges in
1998 by Bender and Boettcher. For this Hamiltonian we discuss the following
three questions. First, since their paper used a Runge-Kutta method to
integrate along a path at the center of the Stokes wedges to calculate
eigenvalues $E$ with high accuracy, we wonder if the same eigenvalues can be
obtained if integrate along some other paths in different shapes. Second, what
the corresponding eigenfunctions look like? Should the eigenfunctions be
independent from the shapes of path or not? Third, since for large $N$ the
Hamiltonian contains many pairs of Stokes wedges symmetric with respect to the
imaginary axis of $x$, thus multiple families of real energy spectrum can be
obtained. What do they look like? Any relation among them?
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19,123 | Random walks on activity-driven networks with attractiveness | Virtually all real-world networks are dynamical entities. In social networks,
the propensity of nodes to engage in social interactions (activity) and their
chances to be selected by active nodes (attractiveness) are heterogeneously
distributed. Here, we present a time-varying network model where each node and
the dynamical formation of ties are characterised by these two features. We
study how these properties affect random walk processes unfolding on the
network when the time scales describing the process and the network evolution
are comparable. We derive analytical solutions for the stationary state and the
mean first passage time of the process and we study cases informed by empirical
observations of social networks. Our work shows that previously disregarded
properties of real social systems such heterogeneous distributions of activity
and attractiveness as well as the correlations between them, substantially
affect the dynamical process unfolding on the network.
| 1 | 1 | 0 | 0 | 0 | 0 |
19,124 | Predicting B Cell Receptor Substitution Profiles Using Public Repertoire Data | B cells develop high affinity receptors during the course of affinity
maturation, a cyclic process of mutation and selection. At the end of affinity
maturation, a number of cells sharing the same ancestor (i.e. in the same
"clonal family") are released from the germinal center, their amino acid
frequency profile reflects the allowed and disallowed substitutions at each
position. These clonal-family-specific frequency profiles, called "substitution
profiles", are useful for studying the course of affinity maturation as well as
for antibody engineering purposes. However, most often only a single sequence
is recovered from each clonal family in a sequencing experiment, making it
impossible to construct a clonal-family-specific substitution profile. Given
the public release of many high-quality large B cell receptor datasets, one may
ask whether it is possible to use such data in a prediction model for
clonal-family-specific substitution profiles. In this paper, we present the
method "Substitution Profiles Using Related Families" (SPURF), a penalized
tensor regression framework that integrates information from a rich assemblage
of datasets to predict the clonal-family-specific substitution profile for any
single input sequence. Using this framework, we show that substitution profiles
from similar clonal families can be leveraged together with simulated
substitution profiles and germline gene sequence information to improve
prediction. We fit this model on a large public dataset and validate the
robustness of our approach on an external dataset. Furthermore, we provide a
command-line tool in an open-source software package
(this https URL) implementing these ideas and providing easy
prediction using our pre-fit models.
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19,125 | Energy Efficient Mobile Edge Computing in Dense Cellular Networks | Merging Mobile Edge Computing (MEC), which is an emerging paradigm to meet
the increasing computation demands from mobile devices, with the dense
deployment of Base Stations (BSs), is foreseen as a key step towards the next
generation mobile networks. However, new challenges arise for designing energy
efficient networks since radio access resources and computing resources of BSs
have to be jointly managed, and yet they are complexly coupled with traffic in
both spatial and temporal domains. In this paper, we address the challenge of
incorporating MEC into dense cellular networks, and propose an efficient online
algorithm, called ENGINE (ENErgy constrained offloadINg and slEeping) which
makes joint computation offloading and BS sleeping decisions in order to
maximize the quality of service while keeping the energy consumption low. Our
algorithm leverages Lyapunov optimization technique, works online and achieves
a close-to-optimal performance without using future information. Our simulation
results show that our algorithm can effectively reduce energy consumption
without sacrificing the user quality of service.
| 1 | 0 | 0 | 0 | 0 | 0 |
19,126 | Delone dynamical systems and spectral convergence | In the realm of Delone sets in locally compact, second countable, Hausdorff
groups, we develop a dynamical systems approach in order to study the
continuity behavior of measured quantities arising from point sets. A special
focus is both on the autocorrelation, as well as on the density of states for
random bounded operators. It is shown that for uniquely ergodic limit systems,
the latter measures behave continuously with respect to the Chabauty-Fell
convergence of hulls. In the special situation of Euclidean spaces, our results
complement recent developments in describing spectra as topological limits: we
show that the measured quantities under consideration can be approximated via
periodic analogs.
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19,127 | On biconservative surfaces in Euclidean spaces | In this paper, we study biconservative surfaces with parallel normalized mean
curvature vector in $\mathbb{E}^4$. We obtain complete local classification in
$\mathbb{E}^4$ for a biconservative PNMCV surface. We also give an example to
show the existence of PNMCV biconservative surfaces in $\mathbb{E}^4$.
| 0 | 0 | 1 | 0 | 0 | 0 |
19,128 | Automatic implementation of material laws: Jacobian calculation in a finite element code with TAPENADE | In an effort to increase the versatility of finite element codes, we explore
the possibility of automatically creating the Jacobian matrix necessary for the
gradient-based solution of nonlinear systems of equations. Particularly, we aim
to assess the feasibility of employing the automatic differentiation tool
TAPENADE for this purpose on a large Fortran codebase that is the result of
many years of continuous development. As a starting point we will describe the
special structure of finite element codes and the implications that this code
design carries for an efficient calculation of the Jacobian matrix. We will
also propose a first approach towards improving the efficiency of such a
method. Finally, we will present a functioning method for the automatic
implementation of the Jacobian calculation in a finite element software, but
will also point out important shortcomings that will have to be addressed in
the future.
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19,129 | Asymptotic analysis for Hamilton-Jacobi equations with large drift term | We investigate the asymptotic behavior of solutions of Hamilton-Jacobi
equations with large drift term in an open subset of two-dimensional Euclidean
space. When the drift is given by $\varepsilon^{-1} (H_{x_2}, -H_{x_1})$ of a
Hamiltonian $H$, with $\varepsilon > 0$, we establish the convergence, as
$\varepsilon \to 0+$, of solutions of the Hamilton-Jacobi equations and
identify the limit of the solutions as the solution of systems of ordinary
differential equations on a graph. This result generalizes the previous one
obtained by the author to the case where the Hamiltonian $H$ admits a
degenerate critical point and, as a consequence, the graph may have segments
more than four at a node.
| 0 | 0 | 1 | 0 | 0 | 0 |
19,130 | An Upper Bound of the Minimal Dispersion via Delta Covers | For a point set of $n$ elements in the $d$-dimensional unit cube and a class
of test sets we are interested in the largest volume of a test set which does
not contain any point. For all natural numbers $n$, $d$ and under the
assumption of a $delta$-cover with cardinality $\vert \Gamma_\delta \vert$ we
prove that there is a point set, such that the largest volume of such a test
set without any point is bounded by $\frac{\log \vert \Gamma_\delta \vert}{n} +
\delta$. For axis-parallel boxes on the unit cube this leads to a volume of at
most $\frac{4d}{n}\log(\frac{9n}{d})$ and on the torus to $\frac{4d}{n}\log
(2n)$.
| 1 | 0 | 1 | 0 | 0 | 0 |
19,131 | Three-dimensional band structure of LaSb and CeSb:Absence of band inversion | We have performed angle-resolved photoemission spectroscopy (ARPES) of LaSb
and CeSb, a candidate of topological insulator. Using soft-x-ray photons, we
have accurately determined the three-dimensional bulk band structure and
revealed that the band inversion at the Brillouin-zone corner - a prerequisite
for realizing topological-insulator phase - is absent in both LaSb and CeSb.
Moreover, unlike the ARPES data obtained with soft-x-ray photons, those with
vacuum ultraviolet (VUV) photons were found to suffer significant $k_z$
broadening. These results suggest that LaSb and CeSb are topologically trivial
semimetals, and unusual Dirac-cone-like states observed with VUV photons are
not of the topological origin.
| 0 | 1 | 0 | 0 | 0 | 0 |
19,132 | Stellar-to-halo mass relation of cluster galaxies | In the hierarchical formation model, galaxy clusters grow by accretion of
smaller groups or isolated galaxies. During the infall into the centre of a
cluster, the properties of accreted galaxies change. In particular, both
observations and numerical simulations suggest that its dark matter halo is
stripped by the tidal forces of the host.
We use galaxy-galaxy weak lensing to measure the average mass of dark matter
haloes of satellite galaxies as a function of projected distance to the centre
of the host, for different stellar mass bins. Assuming that the stellar
component of the galaxy is less disrupted by tidal stripping, stellar mass can
be used as a proxy of the infall mass. We study the stellar to halo mass
relation of satellites as a function of the cluster-centric distance to measure
tidal stripping.
We use the shear catalogues of the DES science verification archive, the
CFHTLenS and the CFHT Stripe 82 (CS82) surveys, and we select satellites from
the redMaPPer catalogue of clusters. For galaxies located in the outskirts of
clusters, we find a stellar to halo mass relation in good agreement with the
theoretical expectations from \citet{moster2013} for central galaxies. In the
centre of the cluster, we find that this relation is shifted to smaller halo
mass for a given stellar mass. We interpret this finding as further evidence
for tidal stripping of dark matter haloes in high density environments.
| 0 | 1 | 0 | 0 | 0 | 0 |
19,133 | Undecidability and Finite Automata | Using a novel rewriting problem, we show that several natural decision
problems about finite automata are undecidable (i.e., recursively unsolvable).
In contrast, we also prove three related problems are decidable. We apply one
result to prove the undecidability of a related problem about k-automatic sets
of rational numbers.
| 1 | 0 | 0 | 0 | 0 | 0 |
19,134 | A globally stable attractor that is locally unstable everywhere | We construct two examples of invariant manifolds that despite being locally
unstable at every point in the transverse direction are globally stable. Using
numerical simulations we show that these invariant manifolds temporarily repel
nearby trajectories but act as global attractors. We formulate an explanation
for such global stability in terms of the `rate of rotation' of the stable and
unstable eigenvectors spanning the normal subspace associated with each point
of the invariant manifold. We discuss the role of this rate of rotation on the
transitions between the stable and unstable regimes.
| 0 | 1 | 0 | 0 | 0 | 0 |
19,135 | On Centers and Central Lines of Triangles in the Elliptic Plane | We determine barycentric coordinates of triangle centers in the elliptic
plane. The main focus is put on centers that lie on lines whose euclidean limit
(triangle excess --> 0) is the Euler line or the Brocard line. We also
investigate curves which can serve in elliptic geometry as substitutes for the
euclidean nine-point-circle, the first Lemoine circle or the apollonian
circles.
| 0 | 0 | 1 | 0 | 0 | 0 |
19,136 | Stopping Active Learning based on Predicted Change of F Measure for Text Classification | During active learning, an effective stopping method allows users to limit
the number of annotations, which is cost effective. In this paper, a new
stopping method called Predicted Change of F Measure will be introduced that
attempts to provide the users an estimate of how much performance of the model
is changing at each iteration. This stopping method can be applied with any
base learner. This method is useful for reducing the data annotation bottleneck
encountered when building text classification systems.
| 1 | 0 | 0 | 1 | 0 | 0 |
19,137 | Statistical properties of random clique networks | In this paper, a random clique network model to mimic the large clustering
coefficient and the modular structure that exist in many real complex networks,
such as social networks, artificial networks, and protein interaction networks,
is introduced by combining the random selection rule of the Erdös and Rényi
(ER) model and the concept of cliques. We find that random clique networks
having a small average degree differ from the ER network in that they have a
large clustering coefficient and a power law clustering spectrum, while
networks having a high average degree have similar properties as the ER model.
In addition, we find that the relation between the clustering coefficient and
the average degree shows a non-monotonic behavior and that the degree
distributions can be fit by multiple Poisson curves; we explain the origin of
such novel behaviors and degree distributions.
| 1 | 1 | 0 | 0 | 0 | 0 |
19,138 | Quo Vadis, Action Recognition? A New Model and the Kinetics Dataset | The paucity of videos in current action classification datasets (UCF-101 and
HMDB-51) has made it difficult to identify good video architectures, as most
methods obtain similar performance on existing small-scale benchmarks. This
paper re-evaluates state-of-the-art architectures in light of the new Kinetics
Human Action Video dataset. Kinetics has two orders of magnitude more data,
with 400 human action classes and over 400 clips per class, and is collected
from realistic, challenging YouTube videos. We provide an analysis on how
current architectures fare on the task of action classification on this dataset
and how much performance improves on the smaller benchmark datasets after
pre-training on Kinetics.
We also introduce a new Two-Stream Inflated 3D ConvNet (I3D) that is based on
2D ConvNet inflation: filters and pooling kernels of very deep image
classification ConvNets are expanded into 3D, making it possible to learn
seamless spatio-temporal feature extractors from video while leveraging
successful ImageNet architecture designs and even their parameters. We show
that, after pre-training on Kinetics, I3D models considerably improve upon the
state-of-the-art in action classification, reaching 80.9% on HMDB-51 and 98.0%
on UCF-101.
| 1 | 0 | 0 | 0 | 0 | 0 |
19,139 | Selfish Cops and Active Robber: Multi-Player Pursuit Evasion on Graphs | We introduce and study the game of "Selfish Cops and Active Robber" (SCAR)
which can be seen as an multiplayer variant of the "classic" two-player Cops
and Robbers (CR) game. In classic CR all cops are controlled by a single
player, who has no preference over which cop captures the robber. In SCAR, on
the other hand, each of N-1 cops is controlled by a separate player, and a
single robber is controlled by the N-th player; and the capturing cop player
receives a higher reward than the non-capturing ones. Consequently, SCAR is an
N-player pursuit game on graphs, in which each cop player has an increased
motive to be the one who captures the robber. The focus of our study is the
existence and properties of SCAR Nash Equilibria (NE). In particular, we prove
that SCAR always has one NE in deterministic positional strategies and (for N
greater than two) another in deterministic nonpositional strategies.
Furthermore, we study conditions which, at equilibrium, guarantee either
capture or escape of the robber and show that (because of the antagonism
between the "selfish" cop players) the robber may, in certain SCAR
configurations, be captured later than he would be in classic CR, or even not
captured at all. Finally we define the selfish cop number of a graph and study
its connection to the classic cop number.
| 1 | 0 | 0 | 0 | 0 | 0 |
19,140 | Singly-Thermostated Ergodicity in Gibbs' Canonical Ensemble and the 2016 Ian Snook Prize Award | The 2016 Snook Prize has been awarded to Diego Tapias, Alessandro Bravetti,
and David Sanders for their paper -- Ergodicity of One-Dimensional Systems
Coupled to the Logistic Thermostat. They introduced a relatively stiff
hyperbolic tangent thermostat force and successfully tested its ability to
reproduce Gibbs' canonical distribution for the harmonic oscillator, the
quartic oscillator, and the Mexican Hat potentials. Their work constitutes an
effective response to the 2016 Ian Snook Prize Award goal -- Finding ergodic
algorithms for Gibbs' canonical ensemble using a single thermostat variable. We
confirm their work here and highlight an interesting feature of the Mexican Hat
problem when it is solved with an adaptive integrator.
| 0 | 1 | 0 | 0 | 0 | 0 |
19,141 | Robust Estimation via Robust Gradient Estimation | We provide a new computationally-efficient class of estimators for risk
minimization. We show that these estimators are robust for general statistical
models: in the classical Huber epsilon-contamination model and in heavy-tailed
settings. Our workhorse is a novel robust variant of gradient descent, and we
provide conditions under which our gradient descent variant provides accurate
estimators in a general convex risk minimization problem. We provide specific
consequences of our theory for linear regression, logistic regression and for
estimation of the canonical parameters in an exponential family. These results
provide some of the first computationally tractable and provably robust
estimators for these canonical statistical models. Finally, we study the
empirical performance of our proposed methods on synthetic and real datasets,
and find that our methods convincingly outperform a variety of baselines.
| 0 | 0 | 0 | 1 | 0 | 0 |
19,142 | SMT Solving for Vesicle Traffic Systems in Cells | In biology, there are several questions that translate to combinatorial
search. For example, vesicle traffic systems that move cargo within eukaryotic
cells have been proposed to exhibit several graph properties such as three
connectivity. These properties are consequences of underlying biophysical
constraints. A natural question for biologists is: what are the possible
networks for various combinations of those properties? In this paper, we
present novel SMT based encodings of the properties over vesicle traffic
systems and a tool that searches for the networks that satisfies the properties
using SMT solvers. In our experiments, we show that our tool can search for
networks of sizes that are considered to be relevant by biologists.
| 1 | 0 | 0 | 0 | 0 | 0 |
19,143 | Endemicity and prevalence of multipartite viruses under heterogeneous between-host transmission | Multipartite viruses replicate through a puzzling evolutionary strategy.
Their genome is segmented into two or more parts, and encapsidated in separate
particles that appear to propagate independently. Completing the replication
cycle, however, requires the full genome, so that a persistent infection of a
host requires the concurrent presence of several particles. This represents an
apparent evolutionary drawback of multipartitism, while its advantages remain
unclear. A transition from monopartite to multipartite viral forms has been
described in vitro under conditions of high multiplicity of infection,
suggesting that cooperation between defective mutants is a plausible
evolutionary pathway towards multipartitism. However, it is unknown how the
putative advantages that multipartitism might enjoy affect its epidemiology, or
if an explicit advantage is needed to explain its ecological persistence. To
disentangle which mechanisms might contribute to the rise and fixation of
multipartitism, we here investigate the interaction between viral spreading
dynamics and host population structure. We set up a compartmental model of the
spread of a virus in its different forms and explore its epidemiology using
both analytical and numerical techniques. We uncover that the impact of host
contact structure on spreading dynamics entails a rich phenomenology of
ecological relationships that includes cooperation, competition, and
commensality. Furthermore, we find out that multipartitism might rise to
fixation even in the absence of explicit microscopic advantages. Multipartitism
allows the virus to colonize environments that could not be invaded by the
monopartite form, while homogeneous contacts between hosts facilitate its
spread. We conjecture that there might have been an increase in the diversity
and prevalence of multipartite viral forms concomitantly with the expansion of
agricultural practices.
| 0 | 0 | 0 | 0 | 1 | 0 |
19,144 | Correlating Cell Shape and Cellular Stress in Motile Confluent Tissues | Collective cell migration is a highly regulated process involved in wound
healing, cancer metastasis and morphogenesis. Mechanical interactions among
cells provide an important regulatory mechanism to coordinate such collective
motion. Using a Self-Propelled Voronoi (SPV) model that links cell mechanics to
cell shape and cell motility, we formulate a generalized mechanical inference
method to obtain the spatio-temporal distribution of cellular stresses from
measured traction forces in motile tissues and show that such traction-based
stresses match those calculated from instantaneous cell shapes. We additionally
use stress information to characterize the rheological properties of the
tissue. We identify a motility-induced swim stress that adds to the interaction
stress to determine the global contractility or extensibility of epithelia. We
further show that the temporal correlation of the interaction shear stress
determines an effective viscosity of the tissue that diverges at the
liquid-solid transition, suggesting the possibility of extracting rheological
information directly from traction data.
| 0 | 1 | 0 | 0 | 0 | 0 |
19,145 | Eigenvalue Decay Implies Polynomial-Time Learnability for Neural Networks | We consider the problem of learning function classes computed by neural
networks with various activations (e.g. ReLU or Sigmoid), a task believed to be
computationally intractable in the worst-case. A major open problem is to
understand the minimal assumptions under which these classes admit provably
efficient algorithms. In this work we show that a natural distributional
assumption corresponding to {\em eigenvalue decay} of the Gram matrix yields
polynomial-time algorithms in the non-realizable setting for expressive classes
of networks (e.g. feed-forward networks of ReLUs). We make no assumptions on
the structure of the network or the labels. Given sufficiently-strong
polynomial eigenvalue decay, we obtain {\em fully}-polynomial time algorithms
in {\em all} the relevant parameters with respect to square-loss. Milder decay
assumptions also lead to improved algorithms. This is the first purely
distributional assumption that leads to polynomial-time algorithms for networks
of ReLUs, even with one hidden layer. Further, unlike prior distributional
assumptions (e.g., the marginal distribution is Gaussian), eigenvalue decay has
been observed in practice on common data sets.
| 1 | 0 | 0 | 0 | 0 | 0 |
19,146 | A New Steganographic Technique Matching the Secret Message and Cover image Binary Value | Steganography involves hiding a secret message or image inside another cover
image. Changes are made in the cover image without affecting visual quality of
the image. In contrast to cryptography, Steganography provides complete secrecy
of the communication. Security of very sensitive data can be enhanced by
combining cryptography and steganography. A new technique that uses the concept
of Steganography to obtain the position values from an image is suggested. This
paper proposes a new method where no change is made to the cover image, only
the pixel position LSB (Least Significant Bit) values that match with the
secret message bit values are noted in a separate position file. At the sending
end the position file along with the cover image is sent. At the receiving end
the position file is opened only with a secret key. The bit positions are taken
from the position file and the LSB values from the positions are combined to
get ASCII values and then form characters of the secret message
| 1 | 0 | 0 | 0 | 0 | 0 |
19,147 | On topological fluid mechanics of non-ideal systems and virtual frozen-in dynamics | Euler and Navier-Stokes have variant systems with dynamical invariance of
helicity and thus (weak) topological equivalence, allowing a strong `frozen-in'
(to, or, dually, `Lie-carried' by the \textit{virtual} velocity $V$)
formulation of the vorticity with a flavor of `inverse Helmholtz theorem'. We
remark on the non-ideal (statistical) topological fluid mechanics (TFM) for (1)
the Constantin-Iyer formulation of Navier-Stokes, (2) our own extension of the
Gallavotti-Cohen type dynamical ensembles of modified Navier-Stokes with
energy-helicity constraints and (3) the Galerkin truncated Euler, as the
typical case variants with dynamical time reversibility and helicity
invariance. Ideal TFM is thus bridged with non-ideal flows. An example virtual
(Lie-)carrier of the vorticity in a Galerkin-truncated Euler system is
calculated to demonstrate the issue of determining $V$.
| 0 | 1 | 0 | 0 | 0 | 0 |
19,148 | Topological AdS/CFT | We define a holographic dual to the Donaldson-Witten topological twist of
$\mathcal{N}=2$ gauge theories on a Riemannian four-manifold. This is described
by a class of asymptotically locally hyperbolic solutions to $\mathcal{N}=4$
gauged supergravity in five dimensions, with the four-manifold as conformal
boundary. Under AdS/CFT, minus the logarithm of the partition function of the
gauge theory is identified with the holographically renormalized supergravity
action. We show that the latter is independent of the metric on the boundary
four-manifold, as required for a topological theory. Supersymmetric solutions
in the bulk satisfy first order differential equations for a twisted $Sp(1)$
structure, which extends the quaternionic Kahler structure that exists on any
Riemannian four-manifold boundary. We comment on applications and extensions,
including generalizations to other topological twists.
| 0 | 0 | 1 | 0 | 0 | 0 |
19,149 | Using highly uniform and smooth Selenium colloids as low-loss magnetodielectric building blocks of optical metafluids | We systematically analyzed magnetodielectric resonances of Se colloids for
the first time to exploit the possibility for use as building blocks of
all-dielectric optical metafluids. By taking synergistic advantages of Se
colloids, including (i) high-refractive-index at optical frequencies, (ii)
unprecedented structural uniformity, and (iii) versatile access to copious
quantities, the Kerker-type directional light scattering resulting from
efficient coupling between strong electric and magnetic resonances were
observed directly from Se colloidal suspension. Thus, the use of Se colloid as
a generic magnetodielectric building block highlights an opportunity for the
fluidic low-loss optical antenna, which can be processed via spin-coating and
painting.
| 0 | 1 | 0 | 0 | 0 | 0 |
19,150 | A Vector Field Method for Radiating Black Hole Spacetimes | We develop a commuting vector field method for a general class of radiating
spacetimes. The metrics considered are certain long range perturbations of
Minkowski space including those constructed from global stability problems in
general relativity. Our method provides sharp peeling estimates for solutions
to both linear and nonlinear (null form) scalar fields.
| 0 | 0 | 1 | 0 | 0 | 0 |
19,151 | Experimental Constraint on an Exotic Spin- and Velocity-Dependent Interaction in the Sub-meV Range of Axion Mass with a Spin-Exchange Relaxation-Free Magnetometer | We conducted a search for an exotic spin- and velocity-dependent interaction
for polarized electrons with an experimental approach based on a
high-sensitivity spin-exchange relaxation-free (SERF) magnetometer, which
serves as both a source of polarized electrons and a magnetic-field sensor. The
experiment aims to sensitively detect magnetic-fieldlike effects from the
exotic interaction between the polarized electrons in a SERF vapor cell and
unpolarized nucleons of a closely located solid-state mass. We report
experimental results on the interaction with 82 h of data averaging, which sets
an experimental limit on the coupling strength around $10^{-19}$ for the axion
mass $m_a \lesssim 10^{-3}$ eV, within the important axion window.
| 0 | 1 | 0 | 0 | 0 | 0 |
19,152 | Generalization Error in Deep Learning | Deep learning models have lately shown great performance in various fields
such as computer vision, speech recognition, speech translation, and natural
language processing. However, alongside their state-of-the-art performance, it
is still generally unclear what is the source of their generalization ability.
Thus, an important question is what makes deep neural networks able to
generalize well from the training set to new data. In this article, we provide
an overview of the existing theory and bounds for the characterization of the
generalization error of deep neural networks, combining both classical and more
recent theoretical and empirical results.
| 0 | 0 | 0 | 1 | 0 | 0 |
19,153 | Block Compressive Sensing of Image and Video with Nonlocal Lagrangian Multiplier and Patch-based Sparse Representation | Although block compressive sensing (BCS) makes it tractable to sense
large-sized images and video, its recovery performance has yet to be
significantly improved because its recovered images or video usually suffer
from blurred edges, loss of details, and high-frequency oscillatory artifacts,
especially at a low subrate. This paper addresses these problems by designing a
modified total variation technique that employs multi-block gradient
processing, a denoised Lagrangian multiplier, and patch-based sparse
representation. In the case of video, the proposed recovery method is able to
exploit both spatial and temporal similarities. Simulation results confirm the
improved performance of the proposed method for compressive sensing of images
and video in terms of both objective and subjective qualities.
| 1 | 0 | 0 | 0 | 0 | 0 |
19,154 | A multi-phase-field method for surface tension-induced elasticity | A consistent treatment of the coupling of surface energy and elasticity
within the multi-phase- field framework is presented. The model accurately
reproduces stress distribution in a number of analytically tractable, yet
non-trivial, cases including different types of spherical heterogeneities and a
thin plate suspending in a gas environment. It is then used to study the stress
distribution inside elastic bodies with non-spherical geometries, such as a
solid ellipsoid and a sintered structure. In these latter cases, it is shown
that the interplay between deformation and spatially variable surface curvature
leads to heterogeneous stress distribution across the specimen.
| 0 | 1 | 0 | 0 | 0 | 0 |
19,155 | On the restriction theorem for paraboloid in $\mathbb R^4$ | We prove that recent breaking by Zahl of the $\frac32$ barrier in Wolff's
estimate on the Kakeya maximal operator in $\mathbb R^4$ leads to improving the
$\frac{14}{5}$ threshold for the restriction problem for the paraboloid in
$\mathbb R^4$. One of the ingredients is a new trilinear estimate. The proofs
are deliberately presented in a nontechnical and concise format, so as to make
the arguments more readable and focus attention on the key tools.
| 0 | 0 | 1 | 0 | 0 | 0 |
19,156 | Existence of Stein Kernels under a Spectral Gap, and Discrepancy Bound | We establish existence of Stein kernels for probability measures on
$\mathbb{R}^d$ satisfying a Poincaré inequality, and obtain bounds on the
Stein discrepancy of such measures. Applications to quantitative central limit
theorems are discussed, including a new CLT in Wasserstein distance $W_2$ with
optimal rate and dependence on the dimension. As a byproduct, we obtain a
stability version of an estimate of the Poincaré constant of probability
measures under a second moment constraint. The results extend more generally to
the setting of converse weighted Poincaré inequalities. The proof is based on
simple arguments of calculus of variations.
Further, we establish two general properties enjoyed by the Stein
discrepancy, holding whenever a Stein kernel exists: Stein discrepancy is
strictly decreasing along the CLT, and it controls the skewness of a random
vector.
| 1 | 0 | 1 | 0 | 0 | 0 |
19,157 | High-order asynchrony-tolerant finite difference schemes for partial differential equations | Synchronizations of processing elements (PEs) in massively parallel
simulations, which arise due to communication or load imbalances between PEs,
significantly affect the scalability of scientific applications. We have
recently proposed a method based on finite-difference schemes to solve partial
differential equations in an asynchronous fashion -- synchronization between
PEs is relaxed at a mathematical level. While standard schemes can maintain
their stability in the presence of asynchrony, their accuracy is drastically
affected. In this work, we present a general methodology to derive
asynchrony-tolerant (AT) finite difference schemes of arbitrary order of
accuracy, which can maintain their accuracy when synchronizations are relaxed.
We show that there are several choices available in selecting a stencil to
derive these schemes and discuss their effect on numerical and computational
performance. We provide a simple classification of schemes based on the stencil
and derive schemes that are representative of different classes. Their
numerical error is rigorously analyzed within a statistical framework to obtain
the overall accuracy of the solution. Results from numerical experiments are
used to validate the performance of the schemes.
| 0 | 1 | 0 | 0 | 0 | 0 |
19,158 | Hazard Analysis and Risk Assessment for an Automated Unmanned Protective Vehicle | For future application of automated vehicles in public traffic, ensuring
functional safety is essential. In this context, a hazard analysis and risk
assessment is an important input for designing functionally vehicle automation
systems. In this contribution, we present a detailed hazard analysis and risk
assessment (HARA) according to the ISO 26262 standard for a specific Level 4
application, namely an unmanned protective vehicle operated without human
supervision for motorway hard shoulder roadworks.
| 1 | 0 | 0 | 0 | 0 | 0 |
19,159 | Detailed experimental and numerical analysis of a cylindrical cup deep drawing: pros and cons of using solid-shell elements | The Swift test was originally proposed as a formability test to reproduce the
conditions observed in deep drawing operations. This test consists on forming a
cylindrical cup from a circular blank, using a flat bottom cylindrical punch
and has been extensively studied using both analytical and numerical methods.
This test can also be combined with the Demeri test, which consists in cutting
a ring from the wall of a cylindrical cup, in order to open it afterwards to
measure the springback. This combination allows their use as benchmark test, in
order to improve the knowledge concerning the numerical simulation models,
through the comparison between experimental and numerical results. The focus of
this study is the experimental and numerical analyses of the Swift cup test,
followed by the Demeri test, performed with an AA5754-O alloy at room
temperature. In this context, a detailed analysis of the punch force evolution,
the thickness evolution along the cup wall, the earing profile, the strain
paths and their evolution and the ring opening is performed. The numerical
simulation is performed using the finite element code ABAQUS, with solid and
solid-shell elements, in order to compare the computational efficiency of these
type of elements. The results show that the solid-shell element is more
cost-effective than the solid, presenting global accurate predictions, excepted
for the thinning zones. Both the von Mises and the Hill48 yield criteria
predict the strain distributions in the final cup quite accurately. However,
improved knowledge concerning the stress states is still required, because the
Hill48 criterion showed difficulties in the correct prediction of the
springback, whatever the type of finite element adopted.
| 0 | 1 | 0 | 0 | 0 | 0 |
19,160 | Hubble Frontier Fields: systematic errors in strong lensing models of galaxy clusters - Implications for cosmography | Strong gravitational lensing by galaxy clusters is a fundamental tool to
study dark matter and constrain the geometry of the Universe. Recently, the
Hubble Space Telescope Frontier Fields programme has allowed a significant
improvement of mass and magnification measurements but lensing models still
have a residual root mean square between 0.2 arcsec and few arcsec- onds, not
yet completely understood. Systematic errors have to be better understood and
treated in order to use strong lensing clusters as reliable cosmological
probes. We have analysed two simulated Hubble-Frontier-Fields-like clusters
from the Hubble Frontier Fields Comparison Challenge, Ares and Hera. We use
several estimators (relative bias on magnification, den- sity profiles,
ellipticity and orientation) to quantify the goodness of our reconstructions by
comparing our multiple models, optimized with the parametric software LENSTOOL
, with the input models. We have quantified the impact of systematic errors
arising, first, from the choice of different density profiles and
configurations and, secondly, from the availability of con- straints
(spectroscopic or photometric redshifts, redshift ranges of the background
sources) in the parametric modelling of strong lensing galaxy clusters and
therefore on the retrieval of cosmological parameters. We find that
substructures in the outskirts have a significant im- pact on the position of
the multiple images, yielding tighter cosmological contours. The need for
wide-field imaging around massive clusters is thus reinforced. We show that
competitive cosmological constraints can be obtained also with complex
multimodal clusters and that photometric redshifts improve the constraints on
cosmological parameters when considering a narrow range of (spectroscopic)
redshifts for the sources.
| 0 | 1 | 0 | 0 | 0 | 0 |
19,161 | A Note on the Spectral Transfer Morphisms for Affine Hecke Algebras | E. Opdam introduced the tool of spectral transfer morphism (STM) of affine
Hecke algebras to study the formal degrees of unipotent discrete series
representations. He established a uniqueness property of STM for the affine
Hecke algebras associated of unipotent discrete series representations. Based
on this result, Opdam gave an explanation for Lusztig's arithmetic/geometric
correspondence (in Lusztig's classification of unipotent representations of
$p$-adic adjoint simple groups) in terms of harmonic analysis, and partitioned
the unipotent discrete series representations into $L$-packets based on the
Lusztig-Langlands parameters. The present paper provides some omitted details
for the argument of the uniqueness property of STM. In the last section, we
prove that three finite morphisms of algebraic tori are spectral transfer
morphisms, and hence complete the proof of the uniqueness property.
| 0 | 0 | 1 | 0 | 0 | 0 |
19,162 | Batch-Expansion Training: An Efficient Optimization Framework | We propose Batch-Expansion Training (BET), a framework for running a batch
optimizer on a gradually expanding dataset. As opposed to stochastic
approaches, batches do not need to be resampled i.i.d. at every iteration, thus
making BET more resource efficient in a distributed setting, and when
disk-access is constrained. Moreover, BET can be easily paired with most batch
optimizers, does not require any parameter-tuning, and compares favorably to
existing stochastic and batch methods. We show that when the batch size grows
exponentially with the number of outer iterations, BET achieves optimal
$O(1/\epsilon)$ data-access convergence rate for strongly convex objectives.
Experiments in parallel and distributed settings show that BET performs better
than standard batch and stochastic approaches.
| 1 | 0 | 0 | 0 | 0 | 0 |
19,163 | Coordinate Descent with Bandit Sampling | Coordinate descent methods usually minimize a cost function by updating a
random decision variable (corresponding to one coordinate) at a time. Ideally,
we would update the decision variable that yields the largest decrease in the
cost function. However, finding this coordinate would require checking all of
them, which would effectively negate the improvement in computational
tractability that coordinate descent is intended to afford. To address this, we
propose a new adaptive method for selecting a coordinate. First, we find a
lower bound on the amount the cost function decreases when a coordinate is
updated. We then use a multi-armed bandit algorithm to learn which coordinates
result in the largest lower bound by interleaving this learning with
conventional coordinate descent updates except that the coordinate is selected
proportionately to the expected decrease. We show that our approach improves
the convergence of coordinate descent methods both theoretically and
experimentally.
| 1 | 0 | 0 | 1 | 0 | 0 |
19,164 | Closing the gap for pseudo-polynomial strip packing | The set of 2-dimensional packing problems builds an important class of
optimization problems and Strip Packing together with 2-dimensional Bin Packing
and 2-dimensional Knapsack is one of the most famous of these problems. Given a
set of rectangular axis parallel items and a strip with bounded width and
infinite height the objective is to find a packing of the items into the strip
which minimizes the packing height. We speak of pseudo-polynomial Strip Packing
if we consider algorithms with pseudo-polynomial running time with respect to
the width of the strip.
It is known that there is no pseudo-polynomial algorithm for Strip Packing
with a ratio better than $5/4$ unless $\mathrm{P} = \mathrm{NP}$. The best
algorithm so far has a ratio of $(4/3 + \varepsilon)$. In this paper, we close
this gap between inapproximability result and best known algorithm by
presenting an algorithm with approximation ratio $(5/4 + \varepsilon)$ and thus
categorize the problem accurately. The algorithm uses a structural result which
states that each optimal solution can be transformed such that it has one of a
polynomial number of different forms. The strength of this structural result is
that it applies to other problem settings as well for example to Strip Packing
with rotations (90 degrees) and Contiguous Moldable Task Scheduling. This fact
enabled us to present algorithms with approximation ratio $(5/4 + \varepsilon)$
for these problems as well.
| 1 | 0 | 0 | 0 | 0 | 0 |
19,165 | Notes on the replica symmetric solution of the classical and quantum SK model, including the matrix of second derivatives and the spin glass susceptibility | A review of the replica symmetric solution of the classical and quantum,
infinite-range, Sherrington-Kirkpatrick spin glass is presented.
| 0 | 1 | 0 | 0 | 0 | 0 |
19,166 | Self-supervised Knowledge Distillation Using Singular Value Decomposition | To solve deep neural network (DNN)'s huge training dataset and its high
computation issue, so-called teacher-student (T-S) DNN which transfers the
knowledge of T-DNN to S-DNN has been proposed. However, the existing T-S-DNN
has limited range of use, and the knowledge of T-DNN is insufficiently
transferred to S-DNN. To improve the quality of the transferred knowledge from
T-DNN, we propose a new knowledge distillation using singular value
decomposition (SVD). In addition, we define a knowledge transfer as a
self-supervised task and suggest a way to continuously receive information from
T-DNN. Simulation results show that a S-DNN with a computational cost of 1/5 of
the T-DNN can be up to 1.1\% better than the T-DNN in terms of classification
accuracy. Also assuming the same computational cost, our S-DNN outperforms the
S-DNN driven by the state-of-the-art distillation with a performance advantage
of 1.79\%. code is available on this https URL\_SVD.
| 0 | 0 | 0 | 1 | 0 | 0 |
19,167 | Can justice be fair when it is blind? How social network structures can promote or prevent the evolution of despotism | Hierarchy is an efficient way for a group to organize, but often goes along
with inequality that benefits leaders. To control despotic behaviour, followers
can assess leaders decisions by aggregating their own and their neighbours
experience, and in response challenge despotic leaders. But in hierarchical
social networks, this interactional justice can be limited by (i) the high
influence of a small clique who are treated better, and (ii) the low
connectedness of followers. Here we study how the connectedness of a social
network affects the co-evolution of despotism in leaders and tolerance to
despotism in followers. We simulate the evolution of a population of agents,
where the influence of an agent is its number of social links. Whether a leader
remains in power is controlled by the overall satisfaction of group members, as
determined by their joint assessment of the leaders behaviour. We demonstrate
that centralization of a social network around a highly influential clique
greatly increases the level of despotism. This is because the clique is more
satisfied, and their higher influence spreads their positive opinion of the
leader throughout the network. Finally, our results suggest that increasing the
connectedness of followers limits despotism while maintaining hierarchy.
| 0 | 0 | 0 | 0 | 1 | 0 |
19,168 | GSAE: an autoencoder with embedded gene-set nodes for genomics functional characterization | Bioinformatics tools have been developed to interpret gene expression data at
the gene set level, and these gene set based analyses improve the biologists'
capability to discover functional relevance of their experiment design. While
elucidating gene set individually, inter gene sets association is rarely taken
into consideration. Deep learning, an emerging machine learning technique in
computational biology, can be used to generate an unbiased combination of gene
set, and to determine the biological relevance and analysis consistency of
these combining gene sets by leveraging large genomic data sets. In this study,
we proposed a gene superset autoencoder (GSAE), a multi-layer autoencoder model
with the incorporation of a priori defined gene sets that retain the crucial
biological features in the latent layer. We introduced the concept of the gene
superset, an unbiased combination of gene sets with weights trained by the
autoencoder, where each node in the latent layer is a superset. Trained with
genomic data from TCGA and evaluated with their accompanying clinical
parameters, we showed gene supersets' ability of discriminating tumor subtypes
and their prognostic capability. We further demonstrated the biological
relevance of the top component gene sets in the significant supersets. Using
autoencoder model and gene superset at its latent layer, we demonstrated that
gene supersets retain sufficient biological information with respect to tumor
subtypes and clinical prognostic significance. Superset also provides high
reproducibility on survival analysis and accurate prediction for cancer
subtypes.
| 0 | 0 | 0 | 1 | 1 | 0 |
19,169 | Natasha: Faster Non-Convex Stochastic Optimization Via Strongly Non-Convex Parameter | Given a nonconvex function that is an average of $n$ smooth functions, we
design stochastic first-order methods to find its approximate stationary
points. The convergence of our new methods depends on the smallest (negative)
eigenvalue $-\sigma$ of the Hessian, a parameter that describes how nonconvex
the function is.
Our methods outperform known results for a range of parameter $\sigma$, and
can be used to find approximate local minima. Our result implies an interesting
dichotomy: there exists a threshold $\sigma_0$ so that the currently fastest
methods for $\sigma>\sigma_0$ and for $\sigma<\sigma_0$ have different
behaviors: the former scales with $n^{2/3}$ and the latter scales with
$n^{3/4}$.
| 1 | 0 | 1 | 1 | 0 | 0 |
19,170 | Higher-Order Bounded Model Checking | We present a Bounded Model Checking technique for higher-order programs. The
vehicle of our study is a higher-order calculus with general references. Our
technique is a symbolic state syntactical translation based on SMT solvers,
adapted to a setting where the values passed and stored during computation can
be functions of arbitrary order. We prove that our algorithm is sound, and
devise an optimisation based on points-to analysis to improve scalability. We
moreover provide a prototype implementation of the algorithm with experimental
results showcasing its performance.
| 1 | 0 | 0 | 0 | 0 | 0 |
19,171 | Smoothing for the fractional Schrodinger equation on the torus and the real line | In this paper we study the cubic fractional nonlinear Schrodinger equation
(NLS) on the torus and on the real line. Combining the normal form and the
restricted norm methods we prove that the nonlinear part of the solution is
smoother than the initial data. Our method applies to both focusing and
defocusing nonlinearities. In the case of full dispersion (NLS) and on the
torus, the gain is a full derivative, while on the real line we get a
derivative smoothing with an $\epsilon$ loss. Our result lowers the regularity
requirement of a recent theorem of Kappeler et al. on the periodic defocusing
cubic NLS, and extends it to the focusing case and to the real line. We also
obtain estimates on the higher order Sobolev norms of the global smooth
solutions in the defocusing case.
| 0 | 0 | 1 | 0 | 0 | 0 |
19,172 | Deep Learning Based Cryptographic Primitive Classification | Cryptovirological augmentations present an immediate, incomparable threat.
Over the last decade, the substantial proliferation of crypto-ransomware has
had widespread consequences for consumers and organisations alike. Established
preventive measures perform well, however, the problem has not ceased. Reverse
engineering potentially malicious software is a cumbersome task due to platform
eccentricities and obfuscated transmutation mechanisms, hence requiring
smarter, more efficient detection strategies. The following manuscript presents
a novel approach for the classification of cryptographic primitives in compiled
binary executables using deep learning. The model blueprint, a DCNN, is
fittingly configured to learn from variable-length control flow diagnostics
output from a dynamic trace. To rival the size and variability of contemporary
data compendiums, hence feeding the model cognition, a methodology for the
procedural generation of synthetic cryptographic binaries is defined, utilising
core primitives from OpenSSL with multivariate obfuscation, to draw a vastly
scalable distribution. The library, CryptoKnight, rendered an algorithmic pool
of AES, RC4, Blowfish, MD5 and RSA to synthesis combinable variants which are
automatically fed in its core model. Converging at 91% accuracy, CryptoKnight
is successfully able to classify the sample algorithms with minimal loss.
| 1 | 0 | 0 | 0 | 0 | 0 |
19,173 | The Alexandrov-Fenchel type inequalities, revisited | Various Alexandrov-Fenchel type inequalities have appeared and played
important roles in convex geometry, matrix theory and complex algebraic
geometry. It has been noticed for some time that they share some striking
analogies and have intimate relationships. The purpose of this article is to
shed new light on this by comparatively investigating them in several aspects.
\emph{The principal result} in this article is a complete solution to the
equality characterization problem of various Alexandrov-Fenchel type
inequalities for intersection numbers of nef and big classes on compact
Kähler manifolds, extending earlier results of Boucksom-Favre-Jonsson,
Fu-Xiao and Xiao-Lehmann. Our proof combines a result of Dinh-Nguyên on
Kähler geometry and an idea in convex geometry tracing back to Shephard. In
addition to this central result, we also give a geometric proof of the complex
version of the Alexandrov-Fenchel type inequality for mixed discriminants and a
determinantal type generalization of various Alexandrov-Fenchel type
inequalities.
| 0 | 0 | 1 | 0 | 0 | 0 |
19,174 | Development of non-modal shear induced instabilities in atmospheric tornadoes | In this paper we consider the role of nonmodal instabilities in the dynamics
of atmospheric tornadoes. For this purpose we consider the Euler equation,
continuity equation and the equation of state and linearise them. As an example
we study several different velocity profiles: the so-called Rankine vortex
model; the Burgers-Rott vortex model; Sullivan and modified Sullivan vortex
models. It has been shown that in the two dimensional Rankine vortex model no
instability appears in the inner region of a tornado. On the contrary, outside
this area the physical system undergoes strong exponential instability. We have
found that initially perturbed velocity components lead to amplified sound wave
excitations. The similar results have been shown in Burgers-Rott vortex model
as well. As it was numerically estimated, in this case, the unstable wave
increases its energy by a factor of $400$ only in $\sim 0.5$min. According to
the numerical study, in Sullivan and modified Sullivan models, the instability
does not differ much by the growth. Despite the fact that in the inner area the
exponential instability does not appear in a purely two dimensional case, we
have found that in the modified Sullivan vortex even a small contribution from
vertical velocities can drive unstable nonmodal waves.
| 0 | 1 | 0 | 0 | 0 | 0 |
19,175 | DeepSketch2Face: A Deep Learning Based Sketching System for 3D Face and Caricature Modeling | Face modeling has been paid much attention in the field of visual computing.
There exist many scenarios, including cartoon characters, avatars for social
media, 3D face caricatures as well as face-related art and design, where
low-cost interactive face modeling is a popular approach especially among
amateur users. In this paper, we propose a deep learning based sketching system
for 3D face and caricature modeling. This system has a labor-efficient
sketching interface, that allows the user to draw freehand imprecise yet
expressive 2D lines representing the contours of facial features. A novel CNN
based deep regression network is designed for inferring 3D face models from 2D
sketches. Our network fuses both CNN and shape based features of the input
sketch, and has two independent branches of fully connected layers generating
independent subsets of coefficients for a bilinear face representation. Our
system also supports gesture based interactions for users to further manipulate
initial face models. Both user studies and numerical results indicate that our
sketching system can help users create face models quickly and effectively. A
significantly expanded face database with diverse identities, expressions and
levels of exaggeration is constructed to promote further research and
evaluation of face modeling techniques.
| 1 | 0 | 0 | 0 | 0 | 0 |
19,176 | Time-Inhomogeneous Branching Processes Conditioned on Non-Extinction | In this paper, we consider time-inhomogeneous branching processes and
time-inhomogeneous birth-and-death processes, in which the offspring
distribution and birth and death rates (respectively) vary in time. A classical
result of branching processes states that in the critical regime, a process
conditioned on non-extinction and normalized will converge in distribution to a
standard exponential. In a paper of Jagers, time-inhomogeneous branching
processes are shown to exhibit this convergence as well. In this paper, the
hypotheses of Jagers' result are relaxed, further hypotheses are presented for
convergence in moments, and the result is extended to the continuous-time
analogue of time-inhomogeneous birth-and-death processes. In particular, the
new hypotheses suggest a simple characterization of the critical regime.
| 0 | 0 | 1 | 0 | 0 | 0 |
19,177 | The Dirichlet-to-Neumann operator for quantum graphs | For a compact, connected metric graphs with a boundary that consists of $k$
vertices, we prove that an arbitrary symmetric $k\times k$ matrix with real
entries can be realized as the Dirichlet-to-Neumann operator for the Laplacian
plus a constant.
| 0 | 0 | 1 | 0 | 0 | 0 |
19,178 | A study of the dual problem of the one-dimensional L-infinity optimal transport problem with applications | The Monge-Kantorovich problem for the infinite Wasserstein distance presents
several peculiarities. Among them the lack of convexity and then of a direct
duality. We study in dimension 1 the dual problem introduced by Barron, Bocea
and Jensen. We construct a couple of Kantorovich potentials which is "as less
trivial as possible". More precisely, we build a potential which is non
constant around any point that the plan which is locally optimal moves at
maximal distance. As an application, we show that the set of points which are
displaced to maximal distance by a locally optimal transport plan is minimal.
| 0 | 0 | 1 | 0 | 0 | 0 |
19,179 | Strong coupling Bose polarons in a BEC | We use a non-perturbative renormalization group approach to develop a unified
picture of the Bose polaron problem, where a mobile impurity is strongly
interacting with a surrounding Bose-Einstein condensate (BEC). A detailed
theoretical analysis of the phase diagram is presented and the
polaron-to-molecule transition is discussed. For attractive polarons we argue
that a description in terms of an effective Fröhlich Hamiltonian with
renormalized parameters is possible. Its strong coupling regime is realized
close to a Feshbach resonance, where we predict a sharp increase of the
effective mass. Already for weaker interactions, before the polaron mass
diverges, we predict a transition to a regime where states exist below the
polaron energy and the attractive polaron is no longer the ground state. On the
repulsive side of the Feshbach resonance we recover the repulsive polaron,
which has a finite lifetime because it can decay into low-lying molecular
states. We show for the entire range of couplings that the polaron energy has
logarithmic corrections in comparison with predictions by the mean-field
approach. We demonstrate that they are a consequence of the polaronic mass
renormalization which is due to quantum fluctuations of correlated phonons in
the polaron cloud.
| 0 | 1 | 0 | 0 | 0 | 0 |
19,180 | Triangle packing in (sparse) tournaments: approximation and kernelization | Given a tournament T and a positive integer k, the C_3-Pakcing-T problem asks
if there exists a least k (vertex-)disjoint directed 3-cycles in T. This is the
dual problem in tournaments of the classical minimal feedback vertex set
problem. Surprisingly C_3-Pakcing-T did not receive a lot of attention in the
literature. We show that it does not admit a PTAS unless P=NP, even if we
restrict the considered instances to sparse tournaments, that is tournaments
with a feedback arc set (FAS) being a matching. Focusing on sparse tournaments
we provide a (1+6/(c-1)) approximation algorithm for sparse tournaments having
a linear representation where all the backward arcs have "length" at least c.
Concerning kernelization, we show that C_3-Pakcing-T admits a kernel with O(m)
vertices, where m is the size of a given feedback arc set. In particular, we
derive a O(k) vertices kernel for C_3-Pakcing-T when restricted to sparse
instances. On the negative size, we show that C_3-Pakcing-T does not admit a
kernel of (total bit) size O(k^{2-\epsilon}) unless NP is a subset of coNP /
Poly. The existence of a kernel in O(k) vertices for C_3-Pakcing-T remains an
open question.
| 1 | 0 | 0 | 0 | 0 | 0 |
19,181 | Asymptotics of Chebyshev Polynomials, II. DCT Subsets of $\mathbb{R}$ | We prove Szegő-Widom asymptotics for the Chebyshev polynomials of a
compact subset of $\mathbb{R}$ which is regular for potential theory and obeys
the Parreau-Widom and DCT conditions.
| 0 | 0 | 1 | 0 | 0 | 0 |
19,182 | Tracking Urban Human Activity from Mobile Phone Calling Patterns | Timings of human activities are marked by circadian clocks which in turn are
entrained to different environmental signals. In an urban environment the
presence of artificial lighting and various social cues tend to disrupt the
natural entrainment with the sunlight. However, it is not completely understood
to what extent this is the case. Here we exploit the large-scale data analysis
techniques to study the mobile phone calling activity of people in large cities
to infer the dynamics of urban daily rhythms. From the calling patterns of
about 1,000,000 users spread over different cities but lying inside the same
time-zone, we show that the onset and termination of the calling activity
synchronizes with the east-west progression of the sun. We also find that the
onset and termination of the calling activity of users follows a yearly
dynamics, varying across seasons, and that its timings are entrained to solar
midnight. Furthermore, we show that the average mid-sleep time of people living
in urban areas depends on the age and gender of each cohort as a result of
biological and social factors.
| 0 | 1 | 0 | 0 | 0 | 0 |
19,183 | Efficient conversion from rotating matrix to rotation axis and angle by extending Rodrigues' formula | In computational 3D geometric problems involving rotations, it is often that
people have to convert back and forth between a rotational matrix and a
rotation described by an axis and a corresponding angle. For this purpose,
Rodrigues' rotation formula is a very popular expression to use because of its
simplicity and efficiency. Nevertheless, while converting a rotation matrix to
an axis of rotation and the rotation angle, there exists ambiguity. Further
judgement or even manual interference may be necessary in some situations. An
extension of the Rodrigues' formula helps to find the sine and cosine values of
the rotation angle with respect to a given rotation axis is found and this
simple extension may help to accelerate many applications.
| 1 | 0 | 0 | 0 | 0 | 0 |
19,184 | Statistical methods for characterizing transfusion-related changes in regional oxygenation using Near-infrared spectroscopy (NIRS) in preterm infants | Near infrared spectroscopy (NIRS) is an imaging-based diagnostic tool that
provides non-invasive and continuous evaluation of regional tissue oxygenation
in real-time. In recent years, NIRS has show promise as a useful monitoring
technology to help detect relative tissue ischemia that could lead to
significant morbidity and mortality in preterm infants. However, some issues
inherent in NIRS technology use on neonates, such as wide fluctuation in
signals, signal dropout and low limit of detection of the device, pose
challenges that may obscure reliable interpretation of the NIRS measurements
using current methods of analysis. In this paper, we propose new statistical
methods to analyse mesenteric rSO2 (regional oxygenation) produced by NIRS to
evaluate oxygenation in intestinal tissues and investigate oxygenation response
to red blood cell transfusion (RBC) in preterm infants. We present a mean area
under the curve (MAUC) measure and a slope measure to capture the mean rSO2
level and temporal trajectory of rSO2, respectively. Estimation methods are
developed for these measures and nonparametric testing procedures are proposed
to detect RBC-related changes in mesenteric oxygenation in preterm infants.
Through simulation studies, we show that the proposed methods demonstrate
improved accuracy in characterizing the mean level and changing pattern of
mesenteric rSO2 and also increased statistical power in detecting RBC-related
changes, as compared with standard approaches. We apply our methods to a NIRS
study in preterm infants receiving RBC transfusion from Emory Univerity to
evaluate the pre- and post-transfusion mesenteric oxygenation in preterm
infants.
| 0 | 0 | 0 | 1 | 0 | 0 |
19,185 | To understand deep learning we need to understand kernel learning | Generalization performance of classifiers in deep learning has recently
become a subject of intense study. Deep models, typically over-parametrized,
tend to fit the training data exactly. Despite this "overfitting", they perform
well on test data, a phenomenon not yet fully understood.
The first point of our paper is that strong performance of overfitted
classifiers is not a unique feature of deep learning. Using six real-world and
two synthetic datasets, we establish experimentally that kernel machines
trained to have zero classification or near zero regression error perform very
well on test data, even when the labels are corrupted with a high level of
noise. We proceed to give a lower bound on the norm of zero loss solutions for
smooth kernels, showing that they increase nearly exponentially with data size.
We point out that this is difficult to reconcile with the existing
generalization bounds. Moreover, none of the bounds produce non-trivial results
for interpolating solutions.
Second, we show experimentally that (non-smooth) Laplacian kernels easily fit
random labels, a finding that parallels results for ReLU neural networks. In
contrast, fitting noisy data requires many more epochs for smooth Gaussian
kernels. Similar performance of overfitted Laplacian and Gaussian classifiers
on test, suggests that generalization is tied to the properties of the kernel
function rather than the optimization process.
Certain key phenomena of deep learning are manifested similarly in kernel
methods in the modern "overfitted" regime. The combination of the experimental
and theoretical results presented in this paper indicates a need for new
theoretical ideas for understanding properties of classical kernel methods. We
argue that progress on understanding deep learning will be difficult until more
tractable "shallow" kernel methods are better understood.
| 0 | 0 | 0 | 1 | 0 | 0 |
19,186 | Atomic Data Revisions for Transitions Relevant to Observations of Interstellar, Circumgalactic, and Intergalactic Matter | Measurements of element abundances in galaxies from astrophysical
spectroscopy depend sensitively on the atomic data used. With the goal of
making the latest atomic data accessible to the community, we present a
compilation of selected atomic data for resonant absorption lines at
wavelengths longward of 911.753 {\AA} (the \ion{H}{1} Lyman limit), for key
heavy elements (heavier than atomic number 5) of astrophysical interest. In
particular, we focus on the transitions of those ions that have been observed
in the Milky Way interstellar medium (ISM), the circumgalactic medium (CGM) of
the Milky Way and/or other galaxies, and the intergalactic medium (IGM).
We provide wavelengths, oscillator strengths, associated accuracy grades, and
references to the oscillator strength determinations. We also attempt to
compare and assess the recent oscillator strength determinations. For about
22\% of the lines that have updated oscillator strength values, the differences
between the former values and the updated ones are $\gtrsim$~0.1 dex.
Our compilation will be a useful resource for absorption line studies of the
ISM, as well as studies of the CGM and IGM traced by sight lines to quasars and
gamma-ray bursts. Studies (including those enabled by future generations of
extremely large telescopes) of absorption by galaxies against the light of
background galaxies will also benefit from our compilation.
| 0 | 1 | 0 | 0 | 0 | 0 |
19,187 | Using Nonlinear Normal Modes for Execution of Efficient Cyclic Motions in Soft Robots | With the aim of getting closer to the performance of the animal
muscleskeletal system, elastic elements are purposefully introduced in the
mechanical structure of soft robots. Indeed, previous works have extensively
shown that elasticity can endow robots with the ability of performing tasks
with increased efficiency, peak performances, and mechanical robustness.
However, despite the many achievements, a general theory of efficient motions
in soft robots is still lacking. Most of the literature focuses on specific
examples, or imposes a prescribed behavior through dynamic cancellations, thus
defeating the purpose of introducing elasticity in the first place. This paper
aims at making a step towards establishing such a general framework. To this
end, we leverage on the theory of oscillations in nonlinear dynamical systems,
and we take inspiration from state of the art theories about how the human
central nervous system manages the muscleskeletal system. We propose to
generate regular and efficient motions in soft robots by stabilizing
sub-manifolds of the state space on which the system would naturally evolve. We
select these sub-manifolds as the nonlinear continuation of linear eigenspaces,
called nonlinear normal modes. In such a way, efficient oscillatory behaviors
can be excited. We show the effectiveness of the methods in simulations on an
elastic inverted pendulum, and experimentally on a segmented elastic leg.
| 1 | 0 | 0 | 0 | 0 | 0 |
19,188 | Efficient Deep Learning on Multi-Source Private Data | Machine learning models benefit from large and diverse datasets. Using such
datasets, however, often requires trusting a centralized data aggregator. For
sensitive applications like healthcare and finance this is undesirable as it
could compromise patient privacy or divulge trade secrets. Recent advances in
secure and privacy-preserving computation, including trusted hardware enclaves
and differential privacy, offer a way for mutually distrusting parties to
efficiently train a machine learning model without revealing the training data.
In this work, we introduce Myelin, a deep learning framework which combines
these privacy-preservation primitives, and use it to establish a baseline level
of performance for fully private machine learning.
| 0 | 0 | 0 | 1 | 0 | 0 |
19,189 | Analytical solution of the integral equation for partial wave Coulomb t-matrices at excited-state energy | Starting from the integral representation of the three-dimensional Coulomb
transition matrix elaborated by us formerly with the use of specific symmetry
of the interaction in a four-dimensional Euclidean space introduced by Fock,
the possibility of the analytical solving of the integral equation for the
partial wave transition matrices at the excited bound state energy has been
studied. New analytical expressions for the partial s-, p- and d-wave Coulomb
t-matrices for like-charged particles and the expression for the partial d-wave
t-matrix for unlike-charged particles at the energy of the first excited bound
state have been derived.
| 0 | 1 | 0 | 0 | 0 | 0 |
19,190 | Equilateral $p$-gons in $\mathbb R^d$ and deformed spheres and mod $p$ Fadell-Husseini index | We introduce the concept of $r$-equilateral $m$-gons. We prove the existence
of $r$-equilateral $p$-gons in $\mathbb R^d$ if $r<d$ and the existence of
equilateral $p$-gons in the image of continuous injective maps $f:S^d\to
\mathbb R^{d+1}$. Our ideas are based mainly in the paper of Y. Soibelman
\cite{soibelman}, in which the topological Borsuk number of $\mathbb{R}^2$ is
calculated by means of topological methods and the paper of P. Blagojević and
G. Ziegler \cite{blagojevictetrahedra} where Fadell-Husseini index is used for
solving a problem related to the topological Borsuk problem for $\mathbb{R}^3$.
| 0 | 0 | 1 | 0 | 0 | 0 |
19,191 | Jónsson posets | According to Kearnes and Oman (2013), an ordered set $P$ is \emph{Jónsson}
if it is infinite and the cardinality of every proper initial segment of $P$ is
strictly less than the cardinaliy of $P$. We examine the structure of Jónsson
posets.
| 0 | 0 | 1 | 0 | 0 | 0 |
19,192 | Hypotheses testing on infinite random graphs | Drawing on some recent results that provide the formalism necessary to
definite stationarity for infinite random graphs, this paper initiates the
study of statistical and learning questions pertaining to these objects.
Specifically, a criterion for the existence of a consistent test for complex
hypotheses is presented, generalizing the corresponding results on time series.
As an application, it is shown how one can test that a tree has the Markov
property, or, more generally, to estimate its memory.
| 1 | 0 | 1 | 1 | 0 | 0 |
19,193 | On compact splitting complex submanifolds of quotients of bounded symmetric domains | In the current article our primary objects of study are compact complex
submanifolds of quotient manifolds of irreducible bounded symmetric domains by
torsion free discrete lattices of automorphisms. We are interested in the
characterization of the totally geodesic submanifolds among compact splitting
complex submanifolds, i.e. under the assumption that the tangent sequence
splits holomorphically over the submanifold.
| 0 | 0 | 1 | 0 | 0 | 0 |
19,194 | Octupolar Tensors for Liquid Crystals | A third-order three-dimensional symmetric traceless tensor, called the
\emph{octupolar} tensor, has been introduced to study tetrahedratic nematic
phases in liquid crystals. The octupolar \emph{potential}, a scalar-valued
function generated on the unit sphere by that tensor, should ideally have four
maxima capturing the most probable molecular orientations (on the vertices of a
tetrahedron), but it was recently found to possess an equally generic variant
with \emph{three} maxima instead of four. It was also shown that the
irreducible admissible region for the octupolar tensor in a three-dimensional
parameter space is bounded by a dome-shaped surface, beneath which is a
\emph{separatrix} surface connecting the two generic octupolar states. The
latter surface, which was obtained through numerical continuation, may be
physically interpreted as marking a possible \emph{intra-octupolar} transition.
In this paper, by using the resultant theory of algebraic geometry and the
E-characteristic polynomial of spectral theory of tensors, we give a
closed-form, algebraic expression for both the dome-shaped surface and the
separatrix surface. This turns the envisaged intra-octupolar transition into a
quantitative, possibly observable prediction. Some other properties of
octupolar tensors are also studied.
| 0 | 0 | 1 | 0 | 0 | 0 |
19,195 | Efficient boundary corrected Strang splitting | Strang splitting is a well established tool for the numerical integration of
evolution equations. It allows the application of tailored integrators for
different parts of the vector field. However, it is also prone to order
reduction in the case of non-trivial boundary conditions. This order reduction
can be remedied by correcting the boundary values of the intermediate splitting
step. In this paper, three different approaches for constructing such a
correction in the case of inhomogeneous Dirichlet, Neumann, and mixed boundary
conditions are presented. Numerical examples that illustrate the effectivity
and benefits of these corrections are included.
| 0 | 1 | 0 | 0 | 0 | 0 |
19,196 | SOS-convex Semi-algebraic Programs and its Applications to Robust Optimization: A Tractable Class of Nonsmooth Convex Optimization | In this paper, we introduce a new class of nonsmooth convex functions called
SOS-convex semialgebraic functions extending the recently proposed notion of
SOS-convex polynomials. This class of nonsmooth convex functions covers many
common nonsmooth functions arising in the applications such as the Euclidean
norm, the maximum eigenvalue function and the least squares functions with
$\ell_1$-regularization or elastic net regularization used in statistics and
compressed sensing. We show that, under commonly used strict feasibility
conditions, the optimal value and an optimal solution of SOS-convex
semi-algebraic programs can be found by solving a single semi-definite
programming problem (SDP). We achieve the results by using tools from
semi-algebraic geometry, convex-concave minimax theorem and a recently
established Jensen inequality type result for SOS-convex polynomials. As an
application, we outline how the derived results can be applied to show that
robust SOS-convex optimization problems under restricted spectrahedron data
uncertainty enjoy exact SDP relaxations. This extends the existing exact SDP
relaxation result for restricted ellipsoidal data uncertainty and answers the
open questions left in [Optimization Letters 9, 1-18(2015)] on how to recover a
robust solution from the semi-definite programming relaxation in this broader
setting.
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19,197 | An Uncertainty Principle for Estimates of Floquet Multipliers | We derive a Cramér-Rao lower bound for the variance of Floquet multiplier
estimates that have been constructed from stable limit cycles perturbed by
noise. To do so, we consider perturbed periodic orbits in the plane. We use a
periodic autoregressive process to model the intersections of these orbits with
cross sections, then passing to the limit of a continuum of sections to obtain
a bound that depends on the continuous flow restricted to the (nontrivial)
Floquet mode. We compare our bound against the empirical variance of estimates
constructed using several cross sections. The section-based estimates are close
to being optimal. We posit that the utility of our bound persists in higher
dimensions when computed along Floquet modes for real and distinct multipliers.
Our bound elucidates some of the empirical observations noted in the
literature; e.g., (a) it is the number of cycles (as opposed to the frequency
of observations) that drives the variance of estimates to zero, and (b) the
estimator variance has a positive lower bound as the noise amplitude tends to
zero.
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19,198 | Shielding Google's language toxicity model against adversarial attacks | Lack of moderation in online communities enables participants to incur in
personal aggression, harassment or cyberbullying, issues that have been
accentuated by extremist radicalisation in the contemporary post-truth politics
scenario. This kind of hostility is usually expressed by means of toxic
language, profanity or abusive statements. Recently Google has developed a
machine-learning-based toxicity model in an attempt to assess the hostility of
a comment; unfortunately, it has been suggested that said model can be deceived
by adversarial attacks that manipulate the text sequence of the comment. In
this paper we firstly characterise such adversarial attacks as using
obfuscation and polarity transformations. The former deceives by corrupting
toxic trigger content with typographic edits, whereas the latter deceives by
grammatical negation of the toxic content. Then, we propose a two--stage
approach to counter--attack these anomalies, bulding upon a recently proposed
text deobfuscation method and the toxicity scoring model. Lastly, we conducted
an experiment with approximately 24000 distorted comments, showing how in this
way it is feasible to restore toxicity of the adversarial variants, while
incurring roughly on a twofold increase in processing time. Even though novel
adversary challenges would keep coming up derived from the versatile nature of
written language, we anticipate that techniques combining machine learning and
text pattern recognition methods, each one targeting different layers of
linguistic features, would be needed to achieve robust detection of toxic
language, thus fostering aggression--free digital interaction.
| 1 | 0 | 0 | 0 | 0 | 0 |
19,199 | Diagrammatic Monte-Carlo for weak-coupling expansion of non-Abelian lattice field theories: large-N U(N)xU(N) principal chiral model | We develop numerical tools for Diagrammatic Monte-Carlo simulations of
non-Abelian lattice field theories in the t'Hooft large-N limit based on the
weak-coupling expansion. First we note that the path integral measure of such
theories contributes a bare mass term in the effective action which is
proportional to the bare coupling constant. This mass term renders the
perturbative expansion infrared-finite and allows to study it directly in the
large-N and infinite-volume limits using the Diagrammatic Monte-Carlo approach.
On the exactly solvable example of a large-N O(N) sigma model in D=2 dimensions
we show that this infrared-finite weak-coupling expansion contains, in addition
to powers of bare coupling, also powers of its logarithm, reminiscent of
re-summed perturbation theory in thermal field theory and resurgent
trans-series without exponential terms. We numerically demonstrate the
convergence of these double series to the manifestly non-perturbative dynamical
mass gap. We then develop a Diagrammatic Monte-Carlo algorithm for sampling
planar diagrams in the large-N matrix field theory, and apply it to study this
infrared-finite weak-coupling expansion for large-N U(N)xU(N) nonlinear sigma
model (principal chiral model) in D=2. We sample up to 12 leading orders of the
weak-coupling expansion, which is the practical limit set by the increasingly
strong sign problem at high orders. Comparing Diagrammatic Monte-Carlo with
conventional Monte-Carlo simulations extrapolated to infinite N, we find a good
agreement for the energy density as well as for the critical temperature of the
"deconfinement" transition. Finally, we comment on the applicability of our
approach to planar QCD at zero and finite density.
| 0 | 1 | 0 | 0 | 0 | 0 |
19,200 | Training Shallow and Thin Networks for Acceleration via Knowledge Distillation with Conditional Adversarial Networks | There is an increasing interest on accelerating neural networks for real-time
applications. We study the student-teacher strategy, in which a small and fast
student network is trained with the auxiliary information learned from a large
and accurate teacher network. We propose to use conditional adversarial
networks to learn the loss function to transfer knowledge from teacher to
student. The proposed method is particularly effective for relatively small
student networks. Moreover, experimental results show the effect of network
size when the modern networks are used as student. We empirically study the
trade-off between inference time and classification accuracy, and provide
suggestions on choosing a proper student network.
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