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Title: Automated Vulnerability Detection in Source Code Using Deep Representation Learning,
Abstract: Increasing numbers of software vulnerabilities are discovered every year
whether they are reported publicly or discovered internally in proprietary
code. These vulnerabilities can pose serious risk of exploit and result in
system compromise, information leaks, or denial of service. We leveraged the
wealth of C and C++ open-source code available to develop a large-scale
function-level vulnerability detection system using machine learning. To
supplement existing labeled vulnerability datasets, we compiled a vast dataset
of millions of open-source functions and labeled it with carefully-selected
findings from three different static analyzers that indicate potential
exploits. The labeled dataset is available at: this https URL. Using
these datasets, we developed a fast and scalable vulnerability detection tool
based on deep feature representation learning that directly interprets lexed
source code. We evaluated our tool on code from both real software packages and
the NIST SATE IV benchmark dataset. Our results demonstrate that deep feature
representation learning on source code is a promising approach for automated
software vulnerability detection. | [
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] |
Title: Phase locking the spin precession in a storage ring,
Abstract: This letter reports the successful use of feedback from a spin polarization
measurement to the revolution frequency of a 0.97 GeV/$c$ bunched and polarized
deuteron beam in the Cooler Synchrotron (COSY) storage ring in order to control
both the precession rate ($\approx 121$ kHz) and the phase of the horizontal
polarization component. Real time synchronization with a radio frequency (rf)
solenoid made possible the rotation of the polarization out of the horizontal
plane, yielding a demonstration of the feedback method to manipulate the
polarization. In particular, the rotation rate shows a sinusoidal function of
the horizontal polarization phase (relative to the rf solenoid), which was
controlled to within a one standard deviation range of $\sigma = 0.21$ rad. The
minimum possible adjustment was 3.7 mHz out of a revolution frequency of 753
kHz, which changes the precession rate by 26 mrad/s. Such a capability meets a
requirement for the use of storage rings to look for an intrinsic electric
dipole moment of charged particles. | [
0,
1,
0,
0,
0,
0
] |
Title: Learning Vertex Representations for Bipartite Networks,
Abstract: Recent years have witnessed a widespread increase of interest in network
representation learning (NRL). By far most research efforts have focused on NRL
for homogeneous networks like social networks where vertices are of the same
type, or heterogeneous networks like knowledge graphs where vertices (and/or
edges) are of different types. There has been relatively little research
dedicated to NRL for bipartite networks. Arguably, generic network embedding
methods like node2vec and LINE can also be applied to learn vertex embeddings
for bipartite networks by ignoring the vertex type information. However, these
methods are suboptimal in doing so, since real-world bipartite networks concern
the relationship between two types of entities, which usually exhibit different
properties and patterns from other types of network data. For example,
E-Commerce recommender systems need to capture the collaborative filtering
patterns between customers and products, and search engines need to consider
the matching signals between queries and webpages. This work addresses the
research gap of learning vertex representations for bipartite networks. We
present a new solution BiNE, short for Bipartite Network Embedding}, which
accounts for two special properties of bipartite networks: long-tail
distribution of vertex degrees and implicit connectivity relations between
vertices of the same type. Technically speaking, we make three contributions:
(1) We design a biased random walk generator to generate vertex sequences that
preserve the long-tail distribution of vertices; (2) We propose a new
optimization framework by simultaneously modeling the explicit relations (i.e.,
observed links) and implicit relations (i.e., unobserved but transitive links);
(3) We explore the theoretical foundations of BiNE to shed light on how it
works, proving that BiNE can be interpreted as factorizing multiple matrices. | [
1,
0,
0,
1,
0,
0
] |
Title: Liouville integrability of conservative peakons for a modified CH equation,
Abstract: The modified Camassa-Holm equation (also called FORQ) is one of numerous
$cousins$ of the Camassa-Holm equation possessing non-smoth solitons
($peakons$) as special solutions. The peakon sector of solutions is not
uniquely defined: in one peakon sector (dissapative) the Sobolev $H^1$ norm is
not preserved, in the other sector (conservative), introduced in [2], the time
evolution of peakons leaves the $H^1$ norm invariant. In this Letter, it is
shown that the conservative peakon equations of the modified Camassa-Holm can
be given an appropriate Poisson structure relative to which the equations are
Hamiltonian and, in fact, Liouville integrable. The latter is proved directly
by exploiting the inverse spectral techniques, especially asymptotic analysis
of solutions, developed elsewhere (in [3]). | [
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0
] |
Title: State Representation Learning for Control: An Overview,
Abstract: Representation learning algorithms are designed to learn abstract features
that characterize data. State representation learning (SRL) focuses on a
particular kind of representation learning where learned features are in low
dimension, evolve through time, and are influenced by actions of an agent. The
representation is learned to capture the variation in the environment generated
by the agent's actions; this kind of representation is particularly suitable
for robotics and control scenarios. In particular, the low dimension
characteristic of the representation helps to overcome the curse of
dimensionality, provides easier interpretation and utilization by humans and
can help improve performance and speed in policy learning algorithms such as
reinforcement learning.
This survey aims at covering the state-of-the-art on state representation
learning in the most recent years. It reviews different SRL methods that
involve interaction with the environment, their implementations and their
applications in robotics control tasks (simulated or real). In particular, it
highlights how generic learning objectives are differently exploited in the
reviewed algorithms. Finally, it discusses evaluation methods to assess the
representation learned and summarizes current and future lines of research. | [
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0
] |
Title: Tracking Emerges by Colorizing Videos,
Abstract: We use large amounts of unlabeled video to learn models for visual tracking
without manual human supervision. We leverage the natural temporal coherency of
color to create a model that learns to colorize gray-scale videos by copying
colors from a reference frame. Quantitative and qualitative experiments suggest
that this task causes the model to automatically learn to track visual regions.
Although the model is trained without any ground-truth labels, our method
learns to track well enough to outperform the latest methods based on optical
flow. Moreover, our results suggest that failures to track are correlated with
failures to colorize, indicating that advancing video colorization may further
improve self-supervised visual tracking. | [
1,
0,
0,
0,
0,
0
] |
Title: Equilibrium distributions and discrete Schur-constant models,
Abstract: This paper introduces Schur-constant equilibrium distribution models of
dimension n for arithmetic non-negative random variables. Such a model is
defined through the (several orders) equilibrium distributions of a univariate
survival function. First, the bivariate case is considered and analyzed in
depth, stressing the main characteristics of the Poisson case. The analysis is
then extended to the multivariate case. Several properties are derived,
including the implicit correlation and the distribution of the sum. | [
0,
0,
0,
1,
0,
0
] |
Title: Tempered homogeneous spaces,
Abstract: Let $G$ be a semisimple real Lie group with finite center and $H$ a connected
closed subgroup.
We establish a geometric criterion which detects whether the representation
of $G$ in $L^2(G/H)$ is tempered. | [
0,
0,
1,
0,
0,
0
] |
Title: Consistency of Dirichlet Partitions,
Abstract: A Dirichlet $k$-partition of a domain $U \subseteq \mathbb{R}^d$ is a
collection of $k$ pairwise disjoint open subsets such that the sum of their
first Laplace-Dirichlet eigenvalues is minimal. A discrete version of Dirichlet
partitions has been posed on graphs with applications in data analysis. Both
versions admit variational formulations: solutions are characterized by
minimizers of the Dirichlet energy of mappings from $U$ into a singular space
$\Sigma_k \subseteq \mathbb{R}^k$. In this paper, we extend results of N.\
García Trillos and D.\ Slepčev to show that there exist solutions of the
continuum problem arising as limits to solutions of a sequence of discrete
problems. Specifically, a sequence of points $\{x_i\}_{i \in \mathbb{N}}$ from
$U$ is sampled i.i.d.\ with respect to a given probability measure $\nu$ on $U$
and for all $n \in \mathbb{N}$, a geometric graph $G_n$ is constructed from the
first $n$ points $x_1, x_2, \ldots, x_n$ and the pairwise distances between the
points. With probability one with respect to the choice of points $\{x_i\}_{i
\in \mathbb{N}}$, we show that as $n \to \infty$ the discrete Dirichlet
energies for functions $G_n \to \Sigma_k$ $\Gamma$-converge to (a scalar
multiple of) the continuum Dirichlet energy for functions $U \to \Sigma_k$ with
respect to a metric coming from the theory of optimal transport. This, along
with a compactness property for the aforementioned energies that we prove,
implies the convergence of minimizers. When $\nu$ is the uniform distribution,
our results also imply the statistical consistency statement that Dirichlet
partitions of geometric graphs converge to partitions of the sampled space in
the Hausdorff sense. | [
0,
0,
1,
1,
0,
0
] |
Title: Experimental investigation of the wake behind a rotating sphere,
Abstract: The wake behind a sphere, rotating about an axis aligned with the streamwise
direction, has been experimentally investigated in a low-velocity water tunnel
using LIF visualizations and PIV measurements. The measurements focused on the
evolution of the flow regimes that appear depending on two control parameters,
namely the Reynolds number $Re$ and the dimensionless rotation or swirl rate
$\Omega$, which is the ratio of the maximum azimuthal velocity of the body to
the free stream velocity. In the present investigation, we cover the range of
$Re$ smaller than 400 and $\Omega$ from 0 and 4. Different wakes regimes such
as an axisymmetric flow, a low helical state and a high helical mode are
represented in the ($Re$, $\Omega$) parameter plane. | [
0,
1,
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0
] |
Title: Extended superalgebras from twistor and Killing spinors,
Abstract: The basic first-order differential operators of spin geometry that are Dirac
operator and twistor operator are considered. Special types of spinors defined
from these operators such as twistor spinors and Killing spinors are discussed.
Symmetry operators of massless and massive Dirac equations are introduced and
relevant symmetry operators of twistor spinors and Killing spinors are
constructed from Killing-Yano (KY) and conformal Killing-Yano (CKY) forms in
constant curvature and Einstein manifolds. The squaring map of spinors gives KY
and CKY forms for Killing and twistor spinors respectively. They constitute a
graded Lie algebra structure in some special cases. By using the graded Lie
algebra structure of KY and CKY forms, extended Killing and conformal
superalgebras are constructed in constant curvature and Einstein manifolds. | [
0,
0,
1,
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0,
0
] |
Title: Joint Computation and Communication Cooperation for Mobile Edge Computing,
Abstract: This paper proposes a novel joint computation and communication cooperation
approach in mobile edge computing (MEC) systems, which enables user cooperation
in both computation and communication for improving the MEC performance. In
particular, we consider a basic three-node MEC system that consists of a user
node, a helper node, and an access point (AP) node attached with an MEC server.
We focus on the user's latency-constrained computation over a finite block, and
develop a four-slot protocol for implementing the joint computation and
communication cooperation. Under this setup, we jointly optimize the
computation and communication resource allocation at both the user and the
helper, so as to minimize their total energy consumption subject to the user's
computation latency constraint. We provide the optimal solution to this
problem. Numerical results show that the proposed joint cooperation approach
significantly improves the computation capacity and the energy efficiency at
the user and helper nodes, as compared to other benchmark schemes without such
a joint design. | [
1,
0,
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0,
0,
0
] |
Title: Propagating wave correlations in complex systems,
Abstract: We describe a novel approach for computing wave correlation functions inside
finite spatial domains driven by complex and statistical sources. By exploiting
semiclassical approximations, we provide explicit algorithms to calculate the
local mean of these correlation functions in terms of the underlying classical
dynamics. By defining appropriate ensemble averages, we show that fluctuations
about the mean can be characterised in terms of classical correlations. We give
in particular an explicit expression relating fluctuations of diagonal
contributions to those of the full wave correlation function. The methods have
a wide range of applications both in quantum mechanics and for classical wave
problems such as in vibro-acoustics and electromagnetism. We apply the methods
here to simple quantum systems, so-called quantum maps, which model the
behaviour of generic problems on Poincaré sections. Although low-dimensional,
these models exhibit a chaotic classical limit and share common characteristics
with wave propagation in complex structures. | [
0,
1,
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] |
Title: On the Dynamics of Supermassive Black Holes in Gas-Rich, Star-Forming Galaxies: the Case for Nuclear Star Cluster Coevolution,
Abstract: We introduce a new model for the formation and evolution of supermassive
black holes (SMBHs) in the RAMSES code using sink particles, improving over
previous work the treatment of gas accretion and dynamical evolution. This new
model is tested against a suite of high-resolution simulations of an isolated,
gas-rich, cooling halo. We study the effect of various feedback models on the
SMBH growth and its dynamics within the galaxy.
In runs without any feedback, the SMBH is trapped within a massive bulge and
is therefore able to grow quickly, but only if the seed mass is chosen larger
than the minimum Jeans mass resolved by the simulation. We demonstrate that, in
the absence of supernovae (SN) feedback, the maximum SMBH mass is reached when
Active Galactic Nucleus (AGN) heating balances gas cooling in the nuclear
region.
When our efficient SN feedback is included, it completely prevents bulge
formation, so that massive gas clumps can perturb the SMBH orbit, and reduce
the accretion rate significantly. To overcome this issue, we propose an
observationally motivated model for the joint evolution of the SMBH and a
parent nuclear star cluster (NSC), which allows the SMBH to remain in the
nuclear region, grow fast and resist external perturbations. In this scenario,
however, SN feedback controls the gas supply and the maximum SMBH mass now
depends on the balance between AGN heating and gravity. We conclude that
SMBH/NSC co-evolution is crucial for the growth of SMBH in high-z galaxies, the
progenitors of massive elliptical today. | [
0,
1,
0,
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] |
Title: A Concave Optimization Algorithm for Matching Partially Overlapping Point Sets,
Abstract: Point matching refers to the process of finding spatial transformation and
correspondences between two sets of points. In this paper, we focus on the case
that there is only partial overlap between two point sets. Following the
approach of the robust point matching method, we model point matching as a
mixed linear assignment-least square problem and show that after eliminating
the transformation variable, the resulting problem of minimization with respect
to point correspondence is a concave optimization problem. Furthermore, this
problem has the property that the objective function can be converted into a
form with few nonlinear terms via a linear transformation. Based on these
properties, we employ the branch-and-bound (BnB) algorithm to optimize the
resulting problem where the dimension of the search space is small. To further
improve efficiency of the BnB algorithm where computation of the lower bound is
the bottleneck, we propose a new lower bounding scheme which has a
k-cardinality linear assignment formulation and can be efficiently solved.
Experimental results show that the proposed algorithm outperforms
state-of-the-art methods in terms of robustness to disturbances and point
matching accuracy. | [
1,
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] |
Title: GdRh$_2$Si$_2$: An exemplary tetragonal system for antiferromagnetic order with weak in-plane anisotropy,
Abstract: The anisotropy of magnetic properties commonly is introduced in textbooks
using the case of an antiferromagnetic system with Ising type anisotropy. This
model presents huge anisotropic magnetization and a pronounced metamagnetic
transition and is well-known and well-documented both, in experiments and
theory. In contrast, the case of an antiferromagnetic $X$-$Y$ system with weak
in-plane anisotropy is only poorly documented. We studied the anisotropic
magnetization of the compound GdRh$_2$Si$_2$ and found that it is a perfect
model system for such a weak-anisotropy setting because the Gd$^{3+}$ ions in
GdRh$_2$Si$_2$ have a pure spin moment of S=7/2 which orders in a simple AFM
structure with ${\bf Q} = (001)$. We observed experimentally in $M(B)$ a
continuous spin-flop transition and domain effects for field applied along the
$[100]$- and the $[110]$-direction, respectively. We applied a mean field model
for the free energy to describe our data and combine it with an Ising chain
model to account for domain effects. Our calculations reproduce the
experimental data very well. In addition, we performed magnetic X-ray
scattering and X-ray magnetic circular dichroism measurements, which confirm
the AFM propagation vector to be ${\bf Q} = (001)$ and indicate the absence of
polarization on the rhodium atoms. | [
0,
1,
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] |
Title: A Kullback-Leibler Divergence-based Distributionally Robust Optimization Model for Heat Pump Day-ahead Operational Schedule in Distribution Networks,
Abstract: For its high coefficient of performance and zero local emissions, the heat
pump (HP) has recently become popular in North Europe and China. However, the
integration of HPs may aggravate the daily peak-valley gap in distribution
networks significantly. | [
1,
0,
0,
0,
0,
0
] |
Title: Metropolis-Hastings Algorithms for Estimating Betweenness Centrality in Large Networks,
Abstract: Betweenness centrality is an important index widely used in different domains
such as social networks, traffic networks and the world wide web. However, even
for mid-size networks that have only a few hundreds thousands vertices, it is
computationally expensive to compute exact betweenness scores. Therefore in
recent years, several approximate algorithms have been developed. In this
paper, first given a network $G$ and a vertex $r \in V(G)$, we propose a
Metropolis-Hastings MCMC algorithm that samples from the space $V(G)$ and
estimates betweenness score of $r$. The stationary distribution of our MCMC
sampler is the optimal sampling proposed for betweenness centrality estimation.
We show that our MCMC sampler provides an $(\epsilon,\delta)$-approximation,
where the number of required samples depends on the position of $r$ in $G$ and
in many cases, it is a constant. Then, given a network $G$ and a set $R \subset
V(G)$, we present a Metropolis-Hastings MCMC sampler that samples from the
joint space $R$ and $V(G)$ and estimates relative betweenness scores of the
vertices in $R$. We show that for any pair $r_i, r_j \in R$, the ratio of the
expected values of the estimated relative betweenness scores of $r_i$ and $r_j$
respect to each other is equal to the ratio of their betweenness scores. We
also show that our joint-space MCMC sampler provides an
$(\epsilon,\delta)$-approximation of the relative betweenness score of $r_i$
respect to $r_j$, where the number of required samples depends on the position
of $r_j$ in $G$ and in many cases, it is a constant. | [
1,
0,
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0,
0,
0
] |
Title: Learning Flexible and Reusable Locomotion Primitives for a Microrobot,
Abstract: The design of gaits for robot locomotion can be a daunting process which
requires significant expert knowledge and engineering. This process is even
more challenging for robots that do not have an accurate physical model, such
as compliant or micro-scale robots. Data-driven gait optimization provides an
automated alternative to analytical gait design. In this paper, we propose a
novel approach to efficiently learn a wide range of locomotion tasks with
walking robots. This approach formalizes locomotion as a contextual policy
search task to collect data, and subsequently uses that data to learn
multi-objective locomotion primitives that can be used for planning. As a
proof-of-concept we consider a simulated hexapod modeled after a recently
developed microrobot, and we thoroughly evaluate the performance of this
microrobot on different tasks and gaits. Our results validate the proposed
controller and learning scheme on single and multi-objective locomotion tasks.
Moreover, the experimental simulations show that without any prior knowledge
about the robot used (e.g., dynamics model), our approach is capable of
learning locomotion primitives within 250 trials and subsequently using them to
successfully navigate through a maze. | [
1,
0,
0,
1,
0,
0
] |
Title: Statistical comparison of (brain) networks,
Abstract: The study of random networks in a neuroscientific context has developed
extensively over the last couple of decades. By contrast, techniques for the
statistical analysis of these networks are less developed. In this paper, we
focus on the statistical comparison of brain networks in a nonparametric
framework and discuss the associated detection and identification problems. We
tested network differences between groups with an analysis of variance (ANOVA)
test we developed specifically for networks. We also propose and analyse the
behaviour of a new statistical procedure designed to identify different
subnetworks. As an example, we show the application of this tool in
resting-state fMRI data obtained from the Human Connectome Project. Finally, we
discuss the potential bias in neuroimaging findings that is generated by some
behavioural and brain structure variables. Our method can also be applied to
other kind of networks such as protein interaction networks, gene networks or
social networks. | [
0,
1,
0,
1,
0,
0
] |
Title: Sensitivity analysis using perturbed-law based indices for quantiles and application to an industrial case,
Abstract: In this paper, we present perturbed law-based sensitivity indices and how to
adapt them for quantile-oriented sensitivity analysis. We exhibit a simple way
to compute these indices in practice using an importance sampling estimator for
quantiles. Some useful asymptotic results about this estimator are also
provided. Finally, we apply this method to the study of a numerical model which
simulates the behaviour of a component in a hydraulic system in case of severe
transient solicitations. The sensitivity analysis is used to assess the impact
of epistemic uncertainties about some physical parameters on the output of the
model. | [
0,
0,
1,
1,
0,
0
] |
Title: Giant Planets Can Act As Stabilizing Agents on Debris Disks,
Abstract: We have explored the evolution of a cold debris disk under the gravitational
influence of dwarf planet sized objects (DPs), both in the presence and absence
of an interior giant planet. Through detailed long-term numerical simulations,
we demonstrate that, when the giant planet is not present, DPs can stir the
eccentricities and inclinations of disk particles, in linear proportion to the
total mass of the DPs; on the other hand, when the giant planet is included in
the simulations, the stirring is approximately proportional to the mass
squared. This creates two regimes: below a disk mass threshold (defined by the
total mass of DPs), the giant planet acts as a stabilizing agent of the orbits
of cometary nucleii, diminishing the effect of the scatterers; above the
threshold, the giant contributes to the dispersion of the particles. | [
0,
1,
0,
0,
0,
0
] |
Title: Definition of geometric space around analytic fractal trees using derivative coordinate funtions,
Abstract: The concept of derivative coordinate functions proved useful in the
formulation of analytic fractal functions to represent smooth symmetric binary
fractal trees [1]. In this paper we introduce a new geometry that defines the
fractal space around these fractal trees. We present the canonical and
degenerate form of this fractal space and extend the fractal geometrical space
to R3 specifically and Rn by a recurrence relation. We also discuss the usage
of such fractal geometry. | [
1,
0,
0,
0,
0,
0
] |
Title: Self-Organizing Maps as a Storage and Transfer Mechanism in Reinforcement Learning,
Abstract: The idea of reusing information from previously learned tasks (source tasks)
for the learning of new tasks (target tasks) has the potential to significantly
improve the sample efficiency reinforcement learning agents. In this work, we
describe an approach to concisely store and represent learned task knowledge,
and reuse it by allowing it to guide the exploration of an agent while it
learns new tasks. In order to do so, we use a measure of similarity that is
defined directly in the space of parameterized representations of the value
functions. This similarity measure is also used as a basis for a variant of the
growing self-organizing map algorithm, which is simultaneously used to enable
the storage of previously acquired task knowledge in an adaptive and scalable
manner.We empirically validate our approach in a simulated navigation
environment and discuss possible extensions to this approach along with
potential applications where it could be particularly useful. | [
0,
0,
0,
1,
0,
0
] |
Title: Distributed model predictive control for continuous-time nonlinear systems based on suboptimal ADMM,
Abstract: The paper presents a distributed model predictive control (DMPC) scheme for
continuous-time nonlinear systems based on the alternating direction method of
multipliers (ADMM). A stopping criterion in the ADMM algorithm limits the
iterations and therefore the required communication effort during the
distributed MPC solution at the expense of a suboptimal solution. Stability
results are presented for the suboptimal DMPC scheme under two different ADMM
convergence assumptions. In particular, it is shown that the required
iterations in each ADMM step are bounded, which is also confirmed in simulation
studies. | [
0,
0,
1,
0,
0,
0
] |
Title: Implementing focal-plane phase masks optimized for real telescope apertures with SLM-based digital adaptive coronagraphy,
Abstract: Direct imaging of exoplanets or circumstellar disk material requires extreme
contrast at the 10-6 to 10-12 levels at < 100 mas angular separation from the
star. Focal-plane mask (FPM) coronagraphic imaging has played a key role in
this field, taking advantage of progress in Adaptive Optics on ground-based 8+m
class telescopes. However, large telescope entrance pupils usually consist of
complex, sometimes segmented, non-ideal apertures, which include a central
obstruction for the secondary mirror and its support structure. In practice,
this negatively impacts wavefront quality and coronagraphic performance, in
terms of achievable contrast and inner working angle. Recent theoretical works
on structured darkness have shown that solutions for FPM phase profiles,
optimized for non-ideal apertures, can be numerically derived. Here we present
and discuss a first experimental validation of this concept, using reflective
liquid crystal spatial light modulators as adaptive FPM coronagraphs. | [
0,
1,
0,
0,
0,
0
] |
Title: Verifying Asynchronous Interactions via Communicating Session Automata,
Abstract: The relationship between communicating automata and session types is the
cornerstone of many diverse theories and tools, including type checking, code
generation, and runtime verification. A serious limitation of session types is
that, while endpoint programs interact asynchronously, the underlying property
which guarantees safety of session types is too synchronous: it requires a
one-to-one synchronisation between send and receive actions. This paper
proposes a sound procedure to verify properties of communicating session
automata (CSA), i.e., communicating automata that correspond to multiparty
session types. We introduce a new asynchronous compatibility property for CSA,
called k-multiparty compatibility (k-MC), which is a strict superset of the
synchronous multiparty compatibility proposed in the literature. It is
decomposed into two bounded properties: (i) a condition called k-safety which
guarantees that, within the bound, all sent messages can be received and each
automaton can make a move; and (ii) a condition called k-exhaustivity which
guarantees that all k-reachable send actions can be fired within the bound. We
show that k-exhaustive systems soundly and completely characterise systems
where each automaton behaves uniformly for any bound greater or equal to k. We
show that checking k-MC is PSPACE-complete, but can be done efficiently over
large systems by using partial order reduction techniques. We demonstrate that
several examples from the literature are k-MC, but not synchronous compatible. | [
1,
0,
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0
] |
Title: Additional cases of positive twisted torus knots,
Abstract: A twisted torus knot is a knot obtained from a torus knot by twisting
adjacent strands by full twists. The twisted torus knots lie in $F$, the genus
2 Heegaard surface for $S^3$. Primitive/primitive and primitive/Seifert knots
lie in $F$ in a particular way. Dean gives sufficient conditions for the
parameters of the twisted torus knots to ensure they are primitive/primitive or
primitive/Seifert. Using Dean's conditions, Doleshal shows that there are
infinitely many twisted torus knots that are fibered and that there are twisted
torus knots with distinct primitive/Seifert representatives with the same slope
in $F$. In this paper, we extend Doleshal's results to show there is a four
parameter family of positive twisted torus knots. Additionally, we provide new
examples of twisted torus knots with distinct representatives with the same
surface slope in $F$. | [
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0
] |
Title: Action-conditional Sequence Modeling for Recommendation,
Abstract: In many online applications interactions between a user and a web-service are
organized in a sequential way, e.g., user browsing an e-commerce website. In
this setting, recommendation system acts throughout user navigation by showing
items. Previous works have addressed this recommendation setup through the task
of predicting the next item user will interact with. In particular, Recurrent
Neural Networks (RNNs) has been shown to achieve substantial improvements over
collaborative filtering baselines. In this paper, we consider interactions
triggered by the recommendations of deployed recommender system in addition to
browsing behavior. Indeed, it is reported that in online services interactions
with recommendations represent up to 30\% of total interactions. Moreover, in
practice, recommender system can greatly influence user behavior by promoting
specific items. In this paper, we extend the RNN modeling framework by taking
into account user interaction with recommended items. We propose and evaluate
RNN architectures that consist of the recommendation action module and the
state-action fusion module. Using real-world large-scale datasets we
demonstrate improved performance on the next item prediction task compared to
the baselines. | [
0,
0,
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1,
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] |
Title: Limits of End-to-End Learning,
Abstract: End-to-end learning refers to training a possibly complex learning system by
applying gradient-based learning to the system as a whole. End-to-end learning
system is specifically designed so that all modules are differentiable. In
effect, not only a central learning machine, but also all "peripheral" modules
like representation learning and memory formation are covered by a holistic
learning process. The power of end-to-end learning has been demonstrated on
many tasks, like playing a whole array of Atari video games with a single
architecture. While pushing for solutions to more challenging tasks, network
architectures keep growing more and more complex.
In this paper we ask the question whether and to what extent end-to-end
learning is a future-proof technique in the sense of scaling to complex and
diverse data processing architectures. We point out potential inefficiencies,
and we argue in particular that end-to-end learning does not make optimal use
of the modular design of present neural networks. Our surprisingly simple
experiments demonstrate these inefficiencies, up to the complete breakdown of
learning. | [
1,
0,
0,
1,
0,
0
] |
Title: Quantum Graphs: $ \mathcal{PT}$-symmetry and reflection symmetry of the spectrum,
Abstract: Not necessarily self-adjoint quantum graphs -- differential operators on
metric graphs -- are considered. Assume in addition that the underlying metric
graph possesses an automorphism (symmetry) $ \mathcal P $. If the differential
operator is $ \mathcal P \mathcal T$-symmetric, then its spectrum has
reflection symmetry with respect to the real line. Our goal is to understand
whether the opposite statement holds, namely whether the reflection symmetry of
the spectrum of a quantum graph implies that the underlying metric graph
possesses a non-trivial automorphism and the differential operator is $
\mathcal P \mathcal T$-symmetric. We give partial answer to this question by
considering equilateral star-graphs. The corresponding Laplace operator with
Robin vertex conditions possesses reflection-symmetric spectrum if and only if
the operator is $ \mathcal P \mathcal T$-symmetric with $ \mathcal P $ being an
automorphism of the metric graph. | [
0,
0,
1,
0,
0,
0
] |
Title: On Diophantine equations involving sums of Fibonacci numbers and powers of $2$,
Abstract: In this paper, we completely solve the Diophantine equations $F_{n_1} +
F_{n_2} = 2^{a_1} + 2^{a_2} + 2^{a_3}$ and $ F_{m_1} + F_{m_2} + F_{m_3}
=2^{t_1} + 2^{t_2} $, where $F_k$ denotes the $k$-th Fibonacci number. In
particular, we prove that $\max \{n_1, n_2, a_1, a_2, a_3 \}\leq 18$ and $\max
\{ m_1, m_2, m_3, t_1, t_2 \}\leq 16$. | [
0,
0,
1,
0,
0,
0
] |
Title: T-duality in rational homotopy theory via $L_\infty$-algebras,
Abstract: We combine Sullivan models from rational homotopy theory with Stasheff's
$L_\infty$-algebras to describe a duality in string theory. Namely, what in
string theory is known as topological T-duality between $K^0$-cocycles in type
IIA string theory and $K^1$-cocycles in type IIB string theory, or as Hori's
formula, can be recognized as a Fourier-Mukai transform between twisted
cohomologies when looked through the lenses of rational homotopy theory. We
show this as an example of topological T-duality in rational homotopy theory,
which in turn can be completely formulated in terms of morphisms of
$L_\infty$-algebras. | [
0,
0,
1,
0,
0,
0
] |
Title: RankDCG: Rank-Ordering Evaluation Measure,
Abstract: Ranking is used for a wide array of problems, most notably information
retrieval (search). There are a number of popular approaches to the evaluation
of ranking such as Kendall's $\tau$, Average Precision, and nDCG. When dealing
with problems such as user ranking or recommendation systems, all these
measures suffer from various problems, including an inability to deal with
elements of the same rank, inconsistent and ambiguous lower bound scores, and
an inappropriate cost function. We propose a new measure, rankDCG, that
addresses these problems. This is a modification of the popular nDCG algorithm.
We provide a number of criteria for any effective ranking algorithm and show
that only rankDCG satisfies all of them. Results are presented on constructed
and real data sets. We release a publicly available rankDCG evaluation package. | [
1,
0,
0,
0,
0,
0
] |
Title: FUV Spectral Signatures of Molecules and the Evolution of the Gaseous Coma of Comet 67P/Churyumov-Gerasimenko,
Abstract: The Alice far-ultraviolet imaging spectrograph onboard Rosetta observed
emissions from atomic and molecular species from within the coma of comet
67P/Churyumov-Gerasimenko during the entire escort phase of the mission from
2014 August to 2016 September. The initial observations showed that emissions
of atomic hydrogen and oxygen close to the surface were produced by energetic
electron impact dissociation of H2O. Following delivery of the lander, Philae,
on 2014 November 12, the trajectory of Rosetta shifted to near-terminator
orbits that allowed for these emissions to be observed against the shadowed
nucleus that, together with the compositional heterogeneity, enabled us to
identify unique spectral signatures of dissociative electron impact excitation
of H2O, CO2, and O2. CO emissions were found to be due to both electron and
photoexcitation processes. Thus we are able, from far-ultraviolet spectroscopy,
to qualitatively study the evolution of the primary molecular constituents of
the gaseous coma from start to finish of the escort phase. Our results show
asymmetric outgassing of H2O and CO2 about perihelion, H2O dominant before and
CO2 dominant after, consistent with the results from both the in situ and other
remote sensing instruments on Rosetta. | [
0,
1,
0,
0,
0,
0
] |
Title: Conduction Channels of an InAs-Al nanowire Josephson weak link,
Abstract: We present a quantitative characterization of an electrically tunable
Josephson junction defined in an InAs nanowire proximitized by an
epitax-ially-grown superconducting Al shell. The gate-dependence of the number
of conduction channels and of the set of transmission coefficients are
extracted from the highly nonlinear current-voltage characteristics. Although
the transmissions evolve non-monotonically, the number of independent channels
can be tuned, and configurations with a single quasi-ballistic channel
achieved. | [
0,
1,
0,
0,
0,
0
] |
Title: Using the Tsetlin Machine to Learn Human-Interpretable Rules for High-Accuracy Text Categorization with Medical Applications,
Abstract: Medical applications challenge today's text categorization techniques by
demanding both high accuracy and ease-of-interpretation. Although deep learning
has provided a leap ahead in accuracy, this leap comes at the sacrifice of
interpretability. To address this accuracy-interpretability challenge, we here
introduce, for the first time, a text categorization approach that leverages
the recently introduced Tsetlin Machine. In all brevity, we represent the terms
of a text as propositional variables. From these, we capture categories using
simple propositional formulae, such as: if "rash" and "reaction" and
"penicillin" then Allergy. The Tsetlin Machine learns these formulae from a
labelled text, utilizing conjunctive clauses to represent the particular facets
of each category. Indeed, even the absence of terms (negated features) can be
used for categorization purposes. Our empirical comparison with Naïve Bayes,
decision trees, linear support vector machines (SVMs), random forest, long
short-term memory (LSTM) neural networks, and other techniques, is quite
conclusive. The Tsetlin Machine either performs on par with or outperforms all
of the evaluated methods on both the 20 Newsgroups and IMDb datasets, as well
as on a non-public clinical dataset. On average, the Tsetlin Machine delivers
the best recall and precision scores across the datasets. Finally, our GPU
implementation of the Tsetlin Machine executes 5 to 15 times faster than the
CPU implementation, depending on the dataset. We thus believe that our novel
approach can have a significant impact on a wide range of text analysis
applications, forming a promising starting point for deeper natural language
understanding with the Tsetlin Machine. | [
0,
0,
0,
1,
0,
0
] |
Title: Deep Learning with Experience Ranking Convolutional Neural Network for Robot Manipulator,
Abstract: Supervised learning, more specifically Convolutional Neural Networks (CNN),
has surpassed human ability in some visual recognition tasks such as detection
of traffic signs, faces and handwritten numbers. On the other hand, even
state-of-the-art reinforcement learning (RL) methods have difficulties in
environments with sparse and binary rewards. They requires manually shaping
reward functions, which might be challenging to come up with. These tasks,
however, are trivial to human. One of the reasons that human are better
learners in these tasks is that we are embedded with much prior knowledge of
the world. These knowledge might be either embedded in our genes or learned
from imitation - a type of supervised learning. For that reason, the best way
to narrow the gap between machine and human learning ability should be to mimic
how we learn so well in various tasks by a combination of RL and supervised
learning. Our method, which integrates Deep Deterministic Policy Gradients and
Hindsight Experience Replay (RL method specifically dealing with sparse
rewards) with an experience ranking CNN, provides a significant speedup over
the learning curve on simulated robotics tasks. Experience ranking allows
high-reward transitions to be replayed more frequently, and therefore help
learn more efficiently. Our proposed approach can also speed up learning in any
other tasks that provide additional information for experience ranking. | [
1,
0,
0,
0,
0,
0
] |
Title: Isotope Shifts in the 7s$\rightarrow$8s Transition of Francium: Measurements and Comparison to \textit{ab initio} Theory,
Abstract: We observe the electric-dipole forbidden $7s\rightarrow8s$ transition in the
francium isotopes $^{208-211}$Fr and $^{213}$Fr using a two-photon excitation
scheme. We collect the atoms online from an accelerator and confine them in a
magneto optical trap for the measurements. In combination with previous
measurements of the $7s\rightarrow7p_{1/2}$ transition we perform a King Plot
analysis. We compare the thus determined ratio of the field shift constants
(1.230 $\pm$ 0.019) to results obtained from new ab initio calculations (1.234
$\pm$ 0.010) and find excellent agreement. | [
0,
1,
0,
0,
0,
0
] |
Title: Mechanisms for bacterial gliding motility on soft substrates,
Abstract: The motility mechanism of certain rod-shaped bacteria has long been a
mystery, since no external appendages are involved in their motion which is
known as gliding. However, the physical principles behind gliding motility
still remain poorly understood. Using myxobacteria as a canonical example of
such organisms, we identify here the physical principles behind gliding
motility, and develop a theoretical model that predicts a two-regime behavior
of the gliding speed as a function of the substrate stiffness. Our theory
describes the elastic, viscous, and capillary interactions between the
bacterial membrane carrying a traveling wave, the secreted slime acting as a
lubricating film, and the substrate which we model as a soft solid. Defining
the myxobacterial gliding as the horizontal motion on the substrate under zero
net force, we find the two-regime behavior is due to two different mechanisms
of motility thrust. On stiff substrates, the thrust arises from the bacterial
shape deformations creating a flow of slime that exerts a pressure along the
bacterial length. This pressure in conjunction with the bacterial shape
provides the necessary thrust for propulsion. However, we show that such a
mechanism cannot lead to gliding on very soft substrates. Instead, we show that
capillary effects lead to the formation of a ridge at the slime-substrate-air
interface, which creates a thrust in the form of a localized pressure gradient
at the tip of the bacteria. To test our theory, we perform experiments with
isolated cells on agar substrates of varying stiffness and find the measured
gliding speeds to be in good agreement with the predictions from our
elasto-capillary-hydrodynamic model. The physical mechanisms reported here
serve as an important step towards an accurate theory of friction and
substrate-mediated interaction between bacteria in a swarm of cells
proliferating in soft media. | [
0,
0,
0,
0,
1,
0
] |
Title: Random Walk in a N-cube Without Hamiltonian Cycle to Chaotic Pseudorandom Number Generation: Theoretical and Practical Considerations,
Abstract: Designing a pseudorandom number generator (PRNG) is a difficult and complex
task. Many recent works have considered chaotic functions as the basis of built
PRNGs: the quality of the output would indeed be an obvious consequence of some
chaos properties. However, there is no direct reasoning that goes from chaotic
functions to uniform distribution of the output. Moreover, embedding such kind
of functions into a PRNG does not necessarily allow to get a chaotic output,
which could be required for simulating some chaotic behaviors.
In a previous work, some of the authors have proposed the idea of walking
into a $\mathsf{N}$-cube where a balanced Hamiltonian cycle has been removed as
the basis of a chaotic PRNG. In this article, all the difficult issues observed
in the previous work have been tackled. The chaotic behavior of the whole PRNG
is proven. The construction of the balanced Hamiltonian cycle is theoretically
and practically solved. An upper bound of the expected length of the walk to
obtain a uniform distribution is calculated. Finally practical experiments show
that the generators successfully pass the classical statistical tests. | [
1,
1,
0,
0,
0,
0
] |
Title: A Hardware Platform for Efficient Multi-Modal Sensing with Adaptive Approximation,
Abstract: We present Warp, a hardware platform to support research in approximate
computing, sensor energy optimization, and energy-scavenged systems. Warp
incorporates 11 state-of-the-art sensor integrated circuits, computation, and
an energy-scavenged power supply, all within a miniature system that is just
3.6 cm x 3.3 cm x 0.5 cm. Warp's sensor integrated circuits together contain a
total of 21 sensors with a range of precisions and accuracies for measuring
eight sensing modalities of acceleration, angular rate, magnetic flux density
(compass heading), humidity, atmospheric pressure (elevation), infrared
radiation, ambient temperature, and color. Warp uses a combination of analog
circuits and digital control to facilitate further tradeoffs between sensor and
communication accuracy, energy efficiency, and performance. This article
presents the design of Warp and presents an evaluation of our hardware
implementation. The results show how Warp's design enables performance and
energy efficiency versus ac- curacy tradeoffs. | [
1,
0,
0,
0,
0,
0
] |
Title: Accelerating Permutation Testing in Voxel-wise Analysis through Subspace Tracking: A new plugin for SnPM,
Abstract: Permutation testing is a non-parametric method for obtaining the max null
distribution used to compute corrected $p$-values that provide strong control
of false positives. In neuroimaging, however, the computational burden of
running such an algorithm can be significant. We find that by viewing the
permutation testing procedure as the construction of a very large permutation
testing matrix, $T$, one can exploit structural properties derived from the
data and the test statistics to reduce the runtime under certain conditions. In
particular, we see that $T$ is low-rank plus a low-variance residual. This
makes $T$ a good candidate for low-rank matrix completion, where only a very
small number of entries of $T$ ($\sim0.35\%$ of all entries in our experiments)
have to be computed to obtain a good estimate. Based on this observation, we
present RapidPT, an algorithm that efficiently recovers the max null
distribution commonly obtained through regular permutation testing in
voxel-wise analysis. We present an extensive validation on a synthetic dataset
and four varying sized datasets against two baselines: Statistical
NonParametric Mapping (SnPM13) and a standard permutation testing
implementation (referred as NaivePT). We find that RapidPT achieves its best
runtime performance on medium sized datasets ($50 \leq n \leq 200$), with
speedups of 1.5x - 38x (vs. SnPM13) and 20x-1000x (vs. NaivePT). For larger
datasets ($n \geq 200$) RapidPT outperforms NaivePT (6x - 200x) on all
datasets, and provides large speedups over SnPM13 when more than 10000
permutations (2x - 15x) are needed. The implementation is a standalone toolbox
and also integrated within SnPM13, able to leverage multi-core architectures
when available. | [
1,
0,
0,
1,
0,
0
] |
Title: Image restoration of solar spectra,
Abstract: When recording spectra from the ground, atmospheric turbulence causes
degradation of the spatial resolution. We present a data reduction method that
restores the spatial resolution of the spectra to their undegraded state. By
assuming that the point spread function (PSF) estimated from a strictly
synchronized, broadband slit-jaw camera is the same as the PSF that spatially
degraded the spectra, we can quantify what linear combination of undegraded
spectra is present in each degraded data point. The set of equations obtained
in this way is found to be generally well-conditioned and sufficiently diagonal
to be solved using an iterative linear solver. The resulting solution has
regained a spatial resolution comparable to that of the restored slit-jaw
images. | [
0,
1,
0,
0,
0,
0
] |
Title: Automated Tiling of Unstructured Mesh Computations with Application to Seismological Modelling,
Abstract: Sparse tiling is a technique to fuse loops that access common data, thus
increasing data locality. Unlike traditional loop fusion or blocking, the loops
may have different iteration spaces and access shared datasets through indirect
memory accesses, such as A[map[i]] -- hence the name "sparse". One notable
example of such loops arises in discontinuous-Galerkin finite element methods,
because of the computation of numerical integrals over different domains (e.g.,
cells, facets). The major challenge with sparse tiling is implementation -- not
only is it cumbersome to understand and synthesize, but it is also onerous to
maintain and generalize, as it requires a complete rewrite of the bulk of the
numerical computation. In this article, we propose an approach to extend the
applicability of sparse tiling based on raising the level of abstraction.
Through a sequence of compiler passes, the mathematical specification of a
problem is progressively lowered, and eventually sparse-tiled C for-loops are
generated. Besides automation, we advance the state-of-the-art by introducing:
a revisited, more efficient sparse tiling algorithm; support for
distributed-memory parallelism; a range of fine-grained optimizations for
increased run-time performance; implementation in a publicly-available library,
SLOPE; and an in-depth study of the performance impact in Seigen, a real-world
elastic wave equation solver for seismological problems, which shows speed-ups
up to 1.28x on a platform consisting of 896 Intel Broadwell cores. | [
1,
1,
0,
0,
0,
0
] |
Title: A copula approach for dependence modeling in multivariate nonparametric time series,
Abstract: This paper is concerned with modeling the dependence structure of two (or
more) time-series in the presence of a (possible multivariate) covariate which
may include past values of the time series. We assume that the covariate
influences only the conditional mean and the conditional variance of each of
the time series but the distribution of the standardized innovations is not
influenced by the covariate and is stable in time. The joint distribution of
the time series is then determined by the conditional means, the conditional
variances and the marginal distributions of the innovations, which we estimate
nonparametrically, and the copula of the innovations, which represents the
dependency structure. We consider a nonparametric as well as a semiparametric
estimator based on the estimated residuals. We show that under suitable
assumptions these copula estimators are asymptotically equivalent to estimators
that would be based on the unobserved innovations. The theoretical results are
illustrated by simulations and a real data example. | [
0,
0,
1,
1,
0,
0
] |
Title: A geometric second-order-rectifiable stratification for closed subsets of Euclidean space,
Abstract: Defining the $m$-th stratum of a closed subset of an $n$ dimensional
Euclidean space to consist of those points, where it can be touched by a ball
from at least $n-m$ linearly independent directions, we establish that the
$m$-th stratum is second-order rectifiable of dimension $m$ and a Borel set.
This was known for convex sets, but is new even for sets of positive reach. The
result is based on a new criterion for second-order rectifiability. | [
0,
0,
1,
0,
0,
0
] |
Title: Probabilistic Formulations of Regression with Mixed Guidance,
Abstract: Regression problems assume every instance is annotated (labeled) with a real
value, a form of annotation we call \emph{strong guidance}. In order for these
annotations to be accurate, they must be the result of a precise experiment or
measurement. However, in some cases additional \emph{weak guidance} might be
given by imprecise measurements, a domain expert or even crowd sourcing.
Current formulations of regression are unable to use both types of guidance. We
propose a regression framework that can also incorporate weak guidance based on
relative orderings, bounds, neighboring and similarity relations. Consider
learning to predict ages from portrait images, these new types of guidance
allow weaker forms of guidance such as stating a person is in their 20s or two
people are similar in age. These types of annotations can be easier to generate
than strong guidance. We introduce a probabilistic formulation for these forms
of weak guidance and show that the resulting optimization problems are convex.
Our experimental results show the benefits of these formulations on several
data sets. | [
0,
0,
0,
1,
0,
0
] |
Title: DCN+: Mixed Objective and Deep Residual Coattention for Question Answering,
Abstract: Traditional models for question answering optimize using cross entropy loss,
which encourages exact answers at the cost of penalizing nearby or overlapping
answers that are sometimes equally accurate. We propose a mixed objective that
combines cross entropy loss with self-critical policy learning. The objective
uses rewards derived from word overlap to solve the misalignment between
evaluation metric and optimization objective. In addition to the mixed
objective, we improve dynamic coattention networks (DCN) with a deep residual
coattention encoder that is inspired by recent work in deep self-attention and
residual networks. Our proposals improve model performance across question
types and input lengths, especially for long questions that requires the
ability to capture long-term dependencies. On the Stanford Question Answering
Dataset, our model achieves state-of-the-art results with 75.1% exact match
accuracy and 83.1% F1, while the ensemble obtains 78.9% exact match accuracy
and 86.0% F1. | [
1,
0,
0,
0,
0,
0
] |
Title: An optimal unrestricted learning procedure,
Abstract: We study learning problems involving arbitrary classes of functions $F$,
distributions $X$ and targets $Y$. Because proper learning procedures, i.e.,
procedures that are only allowed to select functions in $F$, tend to perform
poorly unless the problem satisfies some additional structural property (e.g.,
that $F$ is convex), we consider unrestricted learning procedures that are free
to choose functions outside the given class.
We present a new unrestricted procedure that is optimal in a very strong
sense: the required sample complexity is essentially the best one can hope for,
and the estimate holds for (almost) any problem, including heavy-tailed
situations. Moreover, the sample complexity coincides with the what one would
expect if $F$ were convex, even when $F$ is not. And if $F$ is convex, the
procedure turns out to be proper. Thus, the unrestricted procedure is actually
optimal in both realms, for convex classes as a proper procedure and for
arbitrary classes as an unrestricted procedure. | [
0,
0,
0,
1,
0,
0
] |
Title: Means of infinite sets I,
Abstract: We open a new field on how one can define means on infinite sets. We
investigate many different ways on how such means can be constructed. One
method is based on sequences of ideals, other deals with accumulation points,
one uses isolated points, other deals with average using integral, other with
limit of average on surroundings and one deals with evenly distributed samples.
We study various properties of such means and their relations to each other. | [
0,
0,
1,
0,
0,
0
] |
Title: On tamed almost complex four manifolds,
Abstract: This paper proves that on any tamed closed almost complex four-manifold
$(M,J)$ whose dimension of $J$-anti-invariant cohomology is equal to self-dual
second Betti number minus one, there exists a new symplectic form compatible
with the given almost complex structure $J$. In particular, if the self-dual
second Betti number is one, we give an affirmative answer to Donaldson question
for tamed closed almost complex four-manifolds that is a conjecture in joint
paper of Tosatti, Weinkove and Yau. Our approach is along the lines used by
Buchdahl to give a unified proof of the Kodaira conjecture. Thus, our main
result gives an affirmative answer to the Kodaira conjecture in symplectic
version. | [
0,
0,
1,
0,
0,
0
] |
Title: Evaluation and Prediction of Polygon Approximations of Planar Contours for Shape Analysis,
Abstract: Contours may be viewed as the 2D outline of the image of an object. This type
of data arises in medical imaging as well as in computer vision and can be
modeled as data on a manifold and can be studied using statistical shape
analysis. Practically speaking, each observed contour, while theoretically
infinite dimensional, must be discretized for computations. As such, the
coordinates for each contour as obtained at k sampling times, resulting in the
contour being represented as a k-dimensional complex vector. While choosing
large values of k will result in closer approximations to the original contour,
this will also result in higher computational costs in the subsequent analysis.
The goal of this study is to determine reasonable values for k so as to keep
the computational cost low while maintaining accuracy. To do this, we consider
two methods for selecting sample points and determine lower bounds for k for
obtaining a desired level of approximation error using two different criteria.
Because this process is computationally inefficient to perform on a large
scale, we then develop models for predicting the lower bounds for k based on
simple characteristics of the contours. | [
0,
0,
0,
1,
0,
0
] |
Title: Perturbative Expansion of Irreversible Work in Fokker-Planck Equation a la Quantum Mechanics,
Abstract: We discuss the systematic expansion of the solution of the Fokker-Planck
equation with the help of the eigenfunctions of the time-dependent
Fokker-Planck operator. The expansion parameter is the time derivative of the
external parameter which controls the form of an external potential. Our
expansion corresponds to the perturbative calculation of the adiabatic motion
in quantum mechanics. With this method, we derive a new formula to calculate
the irreversible work order by order, which is expressed as the expectation
value with a pseudo density matrix. Applying this method to the case of the
harmonic potential, we show that the first order term of the expansion gives
the exact result. Because we do not need to solve the coupled differential
equations of moments, our method simplifies the calculations of various
functions such as the fluctuation of the irreversible work per unit time. We
further investigate the exact optimized protocol to minimize the irreversible
work by calculating its variation with respect to the control parameter itself. | [
0,
1,
1,
0,
0,
0
] |
Title: Water-based and Biocompatible 2D Crystal Inks: from Ink Formulation to All- Inkjet Printed Heterostructures,
Abstract: Fully exploiting the properties of 2D crystals requires a mass production
method able to produce heterostructures of arbitrary complexity on any
substrate, including plastic. Solution processing of graphene allows simple and
low-cost techniques such as inkjet printing to be used for device fabrication.
However, available inkjet printable formulations are still far from ideal as
they are either based on toxic solvents, have low concentration, or require
time-consuming and expensive formulation processing. In addition, none of those
formulations are suitable for thin-film heterostructure fabrication due to the
re-mixing of different 2D crystals, giving rise to uncontrolled interfaces,
which results in poor device performance and lack of reproducibility. In this
work we show a general formulation engineering approach to achieve highly
concentrated, and inkjet printable water-based 2D crystal formulations, which
also provides optimal film formation for multi-stack fabrication. We show
examples of all-inkjet printed heterostructures, such as large area arrays of
photosensors on plastic and paper and programmable logic memory devices, fully
exploiting the design flexibility of inkjet printing. Finally, dose-escalation
cytotoxicity assays in vitro also confirm the inks biocompatible character,
revealing the possibility of extending use of such 2D crystal formulations to
drug delivery and biomedical applications. | [
0,
1,
0,
0,
0,
0
] |
Title: Clustering to Reduce Spatial Data Set Size,
Abstract: Traditionally it had been a problem that researchers did not have access to
enough spatial data to answer pressing research questions or build compelling
visualizations. Today, however, the problem is often that we have too much
data. Spatially redundant or approximately redundant points may refer to a
single feature (plus noise) rather than many distinct spatial features. We use
a machine learning approach with density-based clustering to compress such
spatial data into a set of representative features. | [
0,
0,
0,
1,
0,
0
] |
Title: The Quest for Scalability and Accuracy in the Simulation of the Internet of Things: an Approach based on Multi-Level Simulation,
Abstract: This paper presents a methodology for simulating the Internet of Things (IoT)
using multi-level simulation models. With respect to conventional simulators,
this approach allows us to tune the level of detail of different parts of the
model without compromising the scalability of the simulation. As a use case, we
have developed a two-level simulator to study the deployment of smart services
over rural territories. The higher level is base on a coarse grained,
agent-based adaptive parallel and distributed simulator. When needed, this
simulator spawns OMNeT++ model instances to evaluate in more detail the issues
concerned with wireless communications in restricted areas of the simulated
world. The performance evaluation confirms the viability of multi-level
simulations for IoT environments. | [
1,
0,
0,
0,
0,
0
] |
Title: Harmonic spinors from twistors and potential forms,
Abstract: Symmetry operators of twistor spinors and harmonic spinors can be constructed
from conformal Killing-Yano forms. Transformation operators relating twistors
to harmonic spinors are found in terms of potential forms. These constructions
are generalized to gauged twistor spinors and gauged harmonic spinors. The
operators that transform gauged twistor spinors to gauged harmonic spinors are
found. Symmetry operators of gauged harmonic spinors in terms of conformal
Killing-Yano forms are obtained. Algebraic conditions to obtain solutions of
the Seiberg-Witten equations are discussed. | [
0,
0,
1,
0,
0,
0
] |
Title: Goodness-of-fit tests for the functional linear model based on randomly projected empirical processes,
Abstract: We consider marked empirical processes indexed by a randomly projected
functional covariate to construct goodness-of-fit tests for the functional
linear model with scalar response. The test statistics are built from
continuous functionals over the projected process, resulting in computationally
efficient tests that exhibit root-n convergence rates and circumvent the curse
of dimensionality. The weak convergence of the empirical process is obtained
conditionally on a random direction, whilst the almost surely equivalence
between the testing for significance expressed on the original and on the
projected functional covariate is proved. The computation of the test in
practice involves calibration by wild bootstrap resampling and the combination
of several p-values, arising from different projections, by means of the false
discovery rate method. The finite sample properties of the tests are
illustrated in a simulation study for a variety of linear models, underlying
processes, and alternatives. The software provided implements the tests and
allows the replication of simulations and data applications. | [
0,
0,
0,
1,
0,
0
] |
Title: Efficient method for estimating the number of communities in a network,
Abstract: While there exist a wide range of effective methods for community detection
in networks, most of them require one to know in advance how many communities
one is looking for. Here we present a method for estimating the number of
communities in a network using a combination of Bayesian inference with a novel
prior and an efficient Monte Carlo sampling scheme. We test the method
extensively on both real and computer-generated networks, showing that it
performs accurately and consistently, even in cases where groups are widely
varying in size or structure. | [
1,
1,
0,
0,
0,
0
] |
Title: The Pluto System After New Horizons,
Abstract: The discovery of Pluto in 1930 presaged the discoveries of both the Kuiper
Belt and ice dwarf planets, which are the third class of planets in our solar
system. From the 1970s to the 19990s numerous fascinating attributes of the
Pluto system were discovered, including multiple surface volatile species,
Pluto's large satellite Charon, and its atmosphere. These attributes, and the
1990s discovery of the Kuiper Belt and Pluto's cohort of small Kuiper Belt
planets, motivated the exploration of Pluto. That mission, called New Horizons
(NH), revolutionized knowledge of Pluto and its system of satellites in 2015.
Beyond providing rich geological, compositional, and atmospheric data sets, New
Horizons demonstrated that Pluto itself has been surprisingly geologically
active throughout the past 4 billion years, and that the planet exhibits a
surprisingly complex range of atmospheric phenomenology and geologic expression
that rival Mars in their richness. | [
0,
1,
0,
0,
0,
0
] |
Title: Global-in-time Strichartz estimates and cubic Schrodinger equation on metric cone,
Abstract: We study the Strichartz estimates for Schrödinger equation on a metric cone
$X$, where the metric cone $X=C(Y)=(0,\infty)_r\times Y$ and the cross section
$Y$ is a $(n-1)$-dimensional closed Riemannian manifold $(Y,h)$. The equipped
metric on $X$ is given by $g=dr^2+r^2h$, and let $\Delta_g$ be the Friedrich
extension positive Laplacian on $X$ and $V=V_0 r^{-2}$ where
$V_0\in\CC^\infty(Y)$ is a real function such that the operator
$\Delta_h+V_0+(n-2)^2/4$ is a strictly positive operator on $L^2(Y)$. We
establish the full range of the global-in-time Strichartz estimate without loss
for the Schödinger equation associated with the operator $\LL_V=\Delta_g+V_0
r^{-2}$ including the endpoint estimate both in homogeneous and inhomogeneous
cases. As an application, we study the well-posed theory and scattering theory
for the Schödinger equation with cubic nonlinearity on this setting. | [
0,
0,
1,
0,
0,
0
] |
Title: Compressive Embedding and Visualization using Graphs,
Abstract: Visualizing high-dimensional data has been a focus in data analysis
communities for decades, which has led to the design of many algorithms, some
of which are now considered references (such as t-SNE for example). In our era
of overwhelming data volumes, the scalability of such methods have become more
and more important. In this work, we present a method which allows to apply any
visualization or embedding algorithm on very large datasets by considering only
a fraction of the data as input and then extending the information to all data
points using a graph encoding its global similarity. We show that in most
cases, using only $\mathcal{O}(\log(N))$ samples is sufficient to diffuse the
information to all $N$ data points. In addition, we propose quantitative
methods to measure the quality of embeddings and demonstrate the validity of
our technique on both synthetic and real-world datasets. | [
1,
0,
0,
1,
0,
0
] |
Title: An Expectation-Maximization Algorithm for the Fractal Inverse Problem,
Abstract: We present an Expectation-Maximization algorithm for the fractal inverse
problem: the problem of fitting a fractal model to data. In our setting the
fractals are Iterated Function Systems (IFS), with similitudes as the family of
transformations. The data is a point cloud in ${\mathbb R}^H$ with arbitrary
dimension $H$. Each IFS defines a probability distribution on ${\mathbb R}^H$,
so that the fractal inverse problem can be cast as a problem of parameter
estimation. We show that the algorithm reconstructs well-known fractals from
data, with the model converging to high precision parameters. We also show the
utility of the model as an approximation for datasources outside the IFS model
class. | [
1,
0,
0,
1,
0,
0
] |
Title: Generation of controllable plasma wakefield noise in particle-in-cell simulations,
Abstract: Numerical simulations of beam-plasma instabilities may produce quantitatively
incorrect results because of unrealistically high initial noise from which the
instabilities develop. Of particular importance is the wakefield noise, the
potential perturbations that have a phase velocity which is equal to the beam
velocity. Controlling the noise level in simulations may offer the possibility
of extrapolating simulation results to the more realistic low-noise case. We
propose a novel method for generating wakefield noise with a controllable
amplitude by randomly located charged rods propagating ahead of the beam. We
also illustrate the method with particle-in-cell simulations. The generation of
this noise is not accompanied by parasitic Cherenkov radiation waves. | [
0,
1,
0,
0,
0,
0
] |
Title: Variable Exponent Fock Spaces,
Abstract: In this article we introduce Variable exponent Fock spaces and study some of
their basic properties such as the boundedness of evaluation functionals,
density of polynomials, boundedness of a Bergman-type projection and duality. | [
0,
0,
1,
0,
0,
0
] |
Title: Pattern representation and recognition with accelerated analog neuromorphic systems,
Abstract: Despite being originally inspired by the central nervous system, artificial
neural networks have diverged from their biological archetypes as they have
been remodeled to fit particular tasks. In this paper, we review several
possibilites to reverse map these architectures to biologically more realistic
spiking networks with the aim of emulating them on fast, low-power neuromorphic
hardware. Since many of these devices employ analog components, which cannot be
perfectly controlled, finding ways to compensate for the resulting effects
represents a key challenge. Here, we discuss three different strategies to
address this problem: the addition of auxiliary network components for
stabilizing activity, the utilization of inherently robust architectures and a
training method for hardware-emulated networks that functions without perfect
knowledge of the system's dynamics and parameters. For all three scenarios, we
corroborate our theoretical considerations with experimental results on
accelerated analog neuromorphic platforms. | [
1,
0,
0,
1,
0,
0
] |
Title: Dynamic Policies for Cooperative Networked Systems,
Abstract: A set of economic entities embedded in a network graph collaborate by
opportunistically exchanging their resources to satisfy their dynamically
generated needs. Under what conditions their collaboration leads to a
sustainable economy? Which online policy can ensure a feasible resource
exchange point will be attained, and what information is needed to implement
it? Furthermore, assuming there are different resources and the entities have
diverse production capabilities, which production policy each entity should
employ in order to maximize the economy's sustainability? Importantly, can we
design such policies that are also incentive compatible even when there is no a
priori information about the entities' needs? We introduce a dynamic production
scheduling and resource exchange model to capture this fundamental problem and
provide answers to the above questions. Applications range from infrastructure
sharing, trade and organisation management, to social networks and sharing
economy services. | [
1,
0,
0,
0,
0,
0
] |
Title: On certain families of planar patterns and fractals,
Abstract: This survey article is dedicated to some families of fractals that were
introduced and studied during the last decade, more precisely, families of
Sierpiński carpets: limit net sets, generalised Sierpiński carpets and
labyrinth fractals. We give a unifying approach of these fractals and several
of their topological and geometrical properties, by using the framework of
planar patterns. | [
0,
0,
1,
0,
0,
0
] |
Title: PMU-Based Estimation of Dynamic State Jacobian Matrix,
Abstract: In this paper, a hybrid measurement- and model-based method is proposed which
can estimate the dynamic state Jacobian matrix in near real-time. The proposed
method is computationally efficient and robust to the variation of network
topology. A numerical example is given to show that the proposed method is able
to provide good estimation for the dynamic state Jacobian matrix and is
superior to the model-based method under undetectable network topology change.
The proposed method may also help identify big discrepancy in the assumed
network model. | [
1,
0,
0,
0,
0,
0
] |
Title: DeepDownscale: a Deep Learning Strategy for High-Resolution Weather Forecast,
Abstract: Running high-resolution physical models is computationally expensive and
essential for many disciplines. Agriculture, transportation, and energy are
sectors that depend on high-resolution weather models, which typically consume
many hours of large High Performance Computing (HPC) systems to deliver timely
results. Many users cannot afford to run the desired resolution and are forced
to use low resolution output. One simple solution is to interpolate results for
visualization. It is also possible to combine an ensemble of low resolution
models to obtain a better prediction. However, these approaches fail to capture
the redundant information and patterns in the low-resolution input that could
help improve the quality of prediction. In this paper, we propose and evaluate
a strategy based on a deep neural network to learn a high-resolution
representation from low-resolution predictions using weather forecast as a
practical use case. We take a supervised learning approach, since obtaining
labeled data can be done automatically. Our results show significant
improvement when compared with standard practices and the strategy is still
lightweight enough to run on modest computer systems. | [
0,
0,
0,
1,
0,
0
] |
Title: Open quantum random walks on the half-line: the Karlin-McGregor formula, path counting and Foster's Theorem,
Abstract: In this work we consider open quantum random walks on the non-negative
integers. By considering orthogonal matrix polynomials we are able to describe
transition probability expressions for classes of walks via a matrix version of
the Karlin-McGregor formula. We focus on absorbing boundary conditions and, for
simpler classes of examples, we consider path counting and the corresponding
combinatorial tools. A non-commutative version of the gambler's ruin is studied
by obtaining the probability of reaching a certain fortune and the mean time to
reach a fortune or ruin in terms of generating functions. In the case of the
Hadamard coin, a counting technique for boundary restricted paths in a lattice
is also presented. We discuss an open quantum version of Foster's Theorem for
the expected return time together with applications. | [
0,
0,
1,
0,
0,
0
] |
Title: Nevanlinna classes associated to a closed set on $\partial$D,
Abstract: We introduce Nevanlinna classes of holomorphic functions associated to a
closed set on the boundary of the unit disc in the complex plane and we get
Blaschke type theorems relative to these classes by use of several complex
variables methods. This gives alternative proofs of some results of Favorov \&
Golinskii, useful, in particular, for the study of eigenvalues of non self
adjoint Schr{ö}dinger operators. | [
0,
0,
1,
0,
0,
0
] |
Title: Exploring the nuances in the relationship "culture-strategy" for the business world,
Abstract: The current article explores interesting, significant and recently identified
nuances in the relationship "culture-strategy". The shared views of leading
scholars at the University of National and World Economy in relation with the
essence, direction, structure, role and hierarchy of "culture-strategy"
relation are defined as a starting point of the analysis. The research emphasis
is directed on recent developments in interpreting the observed realizations of
the aforementioned link among the community of international scholars and
consultants, publishing in selected electronic scientific databases. In this
way a contemporary notion of the nature of "culture-strategy" relationship for
the entities from the world of business is outlined. | [
0,
0,
0,
0,
0,
1
] |
Title: Audio style transfer,
Abstract: 'Style transfer' among images has recently emerged as a very active research
topic, fuelled by the power of convolution neural networks (CNNs), and has
become fast a very popular technology in social media. This paper investigates
the analogous problem in the audio domain: How to transfer the style of a
reference audio signal to a target audio content? We propose a flexible
framework for the task, which uses a sound texture model to extract statistics
characterizing the reference audio style, followed by an optimization-based
audio texture synthesis to modify the target content. In contrast to mainstream
optimization-based visual transfer method, the proposed process is initialized
by the target content instead of random noise and the optimized loss is only
about texture, not structure. These differences proved key for audio style
transfer in our experiments. In order to extract features of interest, we
investigate different architectures, whether pre-trained on other tasks, as
done in image style transfer, or engineered based on the human auditory system.
Experimental results on different types of audio signal confirm the potential
of the proposed approach. | [
1,
1,
0,
0,
0,
0
] |
Title: Hyperbolic pseudoinverses for kinematics in the Euclidean group,
Abstract: The kinematics of a robot manipulator are described in terms of the mapping
connecting its joint space and the 6-dimensional Euclidean group of motions
$SE(3)$. The associated Jacobian matrices map into its Lie algebra
$\mathfrak{se}(3)$, the space of twists describing infinitesimal motion of a
rigid body. Control methods generally require knowledge of an inverse for the
Jacobian. However for an arm with fewer or greater than six actuated joints or
at singularities of the kinematic mapping this breaks down. The Moore-Penrose
pseudoinverse has frequently been used as a surrogate but is not invariant
under change of coordinates. Since the Euclidean Lie algebra carries a pencil
of invariant bilinear forms that are indefinite, a family of alternative
hyperbolic pseudoinverses is available. Generalised Gram matrices and the
classification of screw systems are used to determine conditions for their
existence. The existence or otherwise of these pseudoinverses also relates to a
classical problem addressed by Sylvester concerning the conditions for a system
of lines to be in involution or, equivalently, the corresponding system of
generalised forces to be in equilibrium. | [
0,
0,
1,
0,
0,
0
] |
Title: Acute sets,
Abstract: A set of points in $\mathbb{R}^d$ is acute, if any three points from this set
form an acute triangle. In this note we construct an acute set in
$\mathbb{R}^d$ of size at least $1.618^d$. Also, we present a simple example of
an acute set of size at least $2^{\frac{d}{2}}$. | [
0,
0,
1,
0,
0,
0
] |
Title: Session Analysis using Plan Recognition,
Abstract: This paper presents preliminary results of our work with a major financial
company, where we try to use methods of plan recognition in order to
investigate the interactions of a costumer with the company's online interface.
In this paper, we present the first steps of integrating a plan recognition
algorithm in a real-world application for detecting and analyzing the
interactions of a costumer. It uses a novel approach for plan recognition from
bare-bone UI data, which reasons about the plan library at the lowest
recognition level in order to define the relevancy of actions in our domain,
and then uses it to perform plan recognition.
We present preliminary results of inference on three different use-cases
modeled by domain experts from the company, and show that this approach manages
to decrease the overload of information required from an analyst to evaluate a
costumer's session - whether this is a malicious or benign session, whether the
intended tasks were completed, and if not - what actions are expected next. | [
1,
0,
0,
0,
0,
0
] |
Title: Budgeted Experiment Design for Causal Structure Learning,
Abstract: We study the problem of causal structure learning when the experimenter is
limited to perform at most $k$ non-adaptive experiments of size $1$. We
formulate the problem of finding the best intervention target set as an
optimization problem, which aims to maximize the average number of edges whose
directions are resolved. We prove that the corresponding objective function is
submodular and a greedy algorithm suffices to achieve
$(1-\frac{1}{e})$-approximation of the optimal value. We further present an
accelerated variant of the greedy algorithm, which can lead to orders of
magnitude performance speedup. We validate our proposed approach on synthetic
and real graphs. The results show that compared to the purely observational
setting, our algorithm orients the majority of the edges through a considerably
small number of interventions. | [
1,
0,
0,
1,
0,
0
] |
Title: Feeble fish in time-dependent waters and homogenization of the G-equation,
Abstract: We study the following control problem. A fish with bounded aquatic
locomotion speed swims in fast waters. Can this fish, under reasonable
assumptions, get to a desired destination? It can, even if the flow is
time-dependent. Moreover, given a prescribed sufficiently large time $t$, it
can be there at exactly the time $t$. The major difference from our previous
work is the time-dependence of the flow. We also give an application to
homogenization of the G-equation. | [
0,
0,
1,
0,
0,
0
] |
Title: Betti tables for indecomposable matrix factorizations of $XY(X-Y)(X-λY)$,
Abstract: We classify the Betti tables of indecomposable graded matrix factorizations
over the simple elliptic singularity $f_\lambda = XY(X-Y)(X-\lambda Y)$ by
making use of an associated weighted projective line of genus one. | [
0,
0,
1,
0,
0,
0
] |
Title: Discrete Integrable Systems, Supersymmetric Quantum Mechanics, and Framed BPS States - I,
Abstract: It is possible to understand whether a given BPS spectrum is generated by a
relevant deformation of a 4D N=2 SCFT or of an asymptotically free theory from
the periodicity properties of the corresponding quantum monodromy. With the aim
of giving a better understanding of the above conjecture, in this paper we
revisit the description of framed BPS states of four-dimensional relativistic
quantum field theories with eight conserved supercharges in terms of
supersymmetric quantum mechanics. We unveil aspects of the deep
interrelationship in between the Seiberg-dualities of the latter, the discrete
symmetries of the theory in the bulk, and quantum discrete integrable systems. | [
0,
1,
1,
0,
0,
0
] |
Title: Generalized Robust Bayesian Committee Machine for Large-scale Gaussian Process Regression,
Abstract: In order to scale standard Gaussian process (GP) regression to large-scale
datasets, aggregation models employ factorized training process and then
combine predictions from distributed experts. The state-of-the-art aggregation
models, however, either provide inconsistent predictions or require
time-consuming aggregation process. We first prove the inconsistency of typical
aggregations using disjoint or random data partition, and then present a
consistent yet efficient aggregation model for large-scale GP. The proposed
model inherits the advantages of aggregations, e.g., closed-form inference and
aggregation, parallelization and distributed computing. Furthermore,
theoretical and empirical analyses reveal that the new aggregation model
performs better due to the consistent predictions that converge to the true
underlying function when the training size approaches infinity. | [
0,
0,
0,
1,
0,
0
] |
Title: Network Inference from a Link-Traced Sample using Approximate Bayesian Computation,
Abstract: We present a new inference method based on approximate Bayesian computation
for estimating parameters governing an entire network based on link-traced
samples of that network. To do this, we first take summary statistics from an
observed link-traced network sample, such as a recruitment network of subjects
in a hard-to-reach population. Then we assume prior distributions, such as
multivariate uniform, for the distribution of some parameters governing the
structure of the network and behaviour of its nodes. Then, we draw many
independent and identically distributed values for these parameters. For each
set of values, we simulate a population network, take a link-traced sample from
that network, and find the summary statistics for that sample. The statistics
from the sample, and the parameters that eventually led to that sample, are
collectively treated as a single point. We take a Kernel Density estimate of
the points from many simulations, and observe the density across the hyperplane
coinciding with the statistic values of the originally observed sample. This
density function is treat as a posterior estimate of the paramaters of the
network that provided the observed sample.
We also apply this method to a network of precedence citations between legal
documents, centered around cases overseen by the Supreme Court of Canada, is
observed. The features of certain cases that lead to their frequent citation
are inferred, and their effects estimated by ABC. Future work and extensions
are also briefly discussed. | [
1,
1,
0,
1,
0,
0
] |
Title: Variational Dropout Sparsifies Deep Neural Networks,
Abstract: We explore a recently proposed Variational Dropout technique that provided an
elegant Bayesian interpretation to Gaussian Dropout. We extend Variational
Dropout to the case when dropout rates are unbounded, propose a way to reduce
the variance of the gradient estimator and report first experimental results
with individual dropout rates per weight. Interestingly, it leads to extremely
sparse solutions both in fully-connected and convolutional layers. This effect
is similar to automatic relevance determination effect in empirical Bayes but
has a number of advantages. We reduce the number of parameters up to 280 times
on LeNet architectures and up to 68 times on VGG-like networks with a
negligible decrease of accuracy. | [
1,
0,
0,
1,
0,
0
] |
Title: A note on clustered cells,
Abstract: This note contains additions to the paper 'Clustered cell decomposition in
P-minimal structures' (arXiv:1612.02683). We discuss a question which was
raised in that paper, on the order of clustered cells. We also consider a
notion of cells of minimal order, which is a slight optimalisation of the
theorem from the original paper. | [
0,
0,
1,
0,
0,
0
] |
Title: Record statistics of a strongly correlated time series: random walks and Lévy flights,
Abstract: We review recent advances on the record statistics of strongly correlated
time series, whose entries denote the positions of a random walk or a Lévy
flight on a line. After a brief survey of the theory of records for independent
and identically distributed random variables, we focus on random walks. During
the last few years, it was indeed realized that random walks are a very useful
"laboratory" to test the effects of correlations on the record statistics. We
start with the simple one-dimensional random walk with symmetric jumps (both
continuous and discrete) and discuss in detail the statistics of the number of
records, as well as of the ages of the records, i.e., the lapses of time
between two successive record breaking events. Then we review the results that
were obtained for a wide variety of random walk models, including random walks
with a linear drift, continuous time random walks, constrained random walks
(like the random walk bridge) and the case of multiple independent random
walkers. Finally, we discuss further observables related to records, like the
record increments, as well as some questions raised by physical applications of
record statistics, like the effects of measurement error and noise. | [
0,
1,
1,
0,
0,
0
] |
Title: On nonlinear instability of Prandtl's boundary layers: the case of Rayleigh's stable shear flows,
Abstract: In this paper, we study Prandtl's boundary layer asymptotic expansion for
incompressible fluids on the half-space in the inviscid limit. In \cite{Gr1},
E. Grenier proved that Prandtl's Ansatz is false for data with Sobolev
regularity near Rayleigh's unstable shear flows. In this paper, we show that
this Ansatz is also false for Rayleigh's stable shear flows. Namely we
construct unstable solutions near arbitrary stable monotonic boundary layer
profiles. Such shear flows are stable for Euler equations, but not for
Navier-Stokes equations: adding a small viscosity destabilizes the flow. | [
0,
0,
1,
0,
0,
0
] |
Title: Subspace Clustering with Missing and Corrupted Data,
Abstract: Given full or partial information about a collection of points that lie close
to a union of several subspaces, subspace clustering refers to the process of
clustering the points according to their subspace and identifying the
subspaces. One popular approach, sparse subspace clustering (SSC), represents
each sample as a weighted combination of the other samples, with weights of
minimal $\ell_1$ norm, and then uses those learned weights to cluster the
samples. SSC is stable in settings where each sample is contaminated by a
relatively small amount of noise. However, when there is a significant amount
of additive noise, or a considerable number of entries are missing, theoretical
guarantees are scarce. In this paper, we study a robust variant of SSC and
establish clustering guarantees in the presence of corrupted or missing data.
We give explicit bounds on amount of noise and missing data that the algorithm
can tolerate, both in deterministic settings and in a random generative model.
Notably, our approach provides guarantees for higher tolerance to noise and
missing data than existing analyses for this method. By design, the results
hold even when we do not know the locations of the missing data; e.g., as in
presence-only data. | [
0,
0,
0,
1,
0,
0
] |
Title: Monte Carlo Tensor Network Renormalization,
Abstract: Techniques for approximately contracting tensor networks are limited in how
efficiently they can make use of parallel computing resources. In this work we
demonstrate and characterize a Monte Carlo approach to the tensor network
renormalization group method which can be used straightforwardly on modern
computing architectures. We demonstrate the efficiency of the technique and
show that Monte Carlo tensor network renormalization provides an attractive
path to improving the accuracy of a wide class of challenging computations
while also providing useful estimates of uncertainty and a statistical
guarantee of unbiased results. | [
0,
1,
0,
0,
0,
0
] |
Title: SSGP topologies on abelian groups of positive finite divisible rank,
Abstract: Let G be an abelian group. For a subset A of G, Cyc(A) denotes the set of all
elements x of G such that the cyclic subgroup generated by x is contained in A,
and G is said to have the small subgroup generating property (abbreviated to
SSGP) if the smallest subgroup of G generated by Cyc(U) is dense in G for every
neighbourhood U of zero of G. SSGP groups form a proper subclass of the class
of minimally almost periodic groups. Comfort and Gould asked for a
characterization of abelian groups G which admit an SSGP group topology, and
they solved this problem for bounded torsion groups (which have divisible rank
zero). Dikranjan and the first author proved that an abelian group of infinite
divisible rank admits an SSGP group topology. In the remaining case of positive
finite divisible rank, the same authors found a necessary condition on G in
order to admit an SSGP group topology and asked if this condition is also
sufficient. We answer this question positively, thereby completing the
characterization of abelian groups which admit an SSGP group topology. | [
0,
0,
1,
0,
0,
0
] |
Title: Intelligent Pothole Detection and Road Condition Assessment,
Abstract: Poor road conditions are a public nuisance, causing passenger discomfort,
damage to vehicles, and accidents. In the U.S., road-related conditions are a
factor in 22,000 of the 42,000 traffic fatalities each year. Although we often
complain about bad roads, we have no way to detect or report them at scale. To
address this issue, we developed a system to detect potholes and assess road
conditions in real-time. Our solution is a mobile application that captures
data on a car's movement from gyroscope and accelerometer sensors in the phone.
To assess roads using this sensor data, we trained SVM models to classify road
conditions with 93% accuracy and potholes with 92% accuracy, beating the base
rate for both problems. As the user drives, the models use the sensor data to
classify whether the road is good or bad, and whether it contains potholes.
Then, the classification results are used to create data-rich maps that
illustrate road conditions across the city. Our system will empower civic
officials to identify and repair damaged roads which inconvenience passengers
and cause accidents. This paper details our data science process for collecting
training data on real roads, transforming noisy sensor data into useful
signals, training and evaluating machine learning models, and deploying those
models to production through a real-time classification app. It also highlights
how cities can use our system to crowdsource data and deliver road repair
resources to areas in need. | [
1,
0,
0,
0,
0,
0
] |
Title: Concrete Autoencoders for Differentiable Feature Selection and Reconstruction,
Abstract: We introduce the concrete autoencoder, an end-to-end differentiable method
for global feature selection, which efficiently identifies a subset of the most
informative features and simultaneously learns a neural network to reconstruct
the input data from the selected features. Our method is unsupervised, and is
based on using a concrete selector layer as the encoder and using a standard
neural network as the decoder. During the training phase, the temperature of
the concrete selector layer is gradually decreased, which encourages a
user-specified number of discrete features to be learned. During test time, the
selected features can be used with the decoder network to reconstruct the
remaining input features. We evaluate concrete autoencoders on a variety of
datasets, where they significantly outperform state-of-the-art methods for
feature selection and data reconstruction. In particular, on a large-scale gene
expression dataset, the concrete autoencoder selects a small subset of genes
whose expression levels can be use to impute the expression levels of the
remaining genes. In doing so, it improves on the current widely-used
expert-curated L1000 landmark genes, potentially reducing measurement costs by
20%. The concrete autoencoder can be implemented by adding just a few lines of
code to a standard autoencoder. | [
1,
0,
0,
1,
0,
0
] |
Title: Emergence and complexity in theoretical models of self-organized criticality,
Abstract: In this thesis we present few theoretical studies of the models of
self-organized criticality. Following a brief introduction of self-organized
criticality, we discuss three main problems. The first problem is about growing
patterns formed in the abelian sandpile model (ASM). The patterns exhibit
proportionate growth where different parts of the pattern grow in same rate,
keeping the overall shape unchanged. This non-trivial property, often found in
biological growth, has received increasing attention in recent years. In this
thesis, we present a mathematical characterization of a large class of such
patterns in terms of discrete holomorphic functions. In the second problem, we
discuss a well known model of self-organized criticality introduced by Zhang in
1989. We present an exact analysis of the model and quantitatively explain an
intriguing property known as the emergence of quasi-units. In the third
problem, we introduce an operator algebra to determine the steady state of a
class of stochastic sandpile models. | [
0,
1,
1,
0,
0,
0
] |
Title: An Extension of Averaged-Operator-Based Algorithms,
Abstract: Many of the algorithms used to solve minimization problems with
sparsity-inducing regularizers are generic in the sense that they do not take
into account the sparsity of the solution in any particular way. However,
algorithms known as semismooth Newton are able to take advantage of this
sparsity to accelerate their convergence. We show how to extend these
algorithms in different directions, and study the convergence of the resulting
algorithms by showing that they are a particular case of an extension of the
well-known Krasnosel'ski\u{\i}--Mann scheme. | [
0,
0,
0,
1,
0,
0
] |
Title: Along the sun-drenched roadside: On the interplay between urban street orientation entropy and the buildings' solar potential,
Abstract: We explore the relation between urban road network characteristics
particularly circuitry, street orientation entropy and the city's topography on
the one hand and the building's orientation entropy on the other in order to
quantify their effect on the city's solar potential. These statistical measures
of the road network reveal the interplay between the built environment's design
and its sustainability. | [
0,
1,
0,
0,
0,
0
] |
Title: $HD(M\setminus L)>0.353$,
Abstract: The complement $M\setminus L$ of the Lagrange spectrum $L$ in the Markov
spectrum $M$ was studied by many authors (including Freiman, Berstein, Cusick
and Flahive). After their works, we disposed of a countable collection of
points in $M\setminus L$.
In this article, we describe the structure of $M\setminus L$ near a
non-isolated point $\alpha_{\infty}$ found by Freiman in 1973, and we use this
description to exhibit a concrete Cantor set $X$ whose Hausdorff dimension
coincides with the Hausdorff dimension of $M\setminus L$ near
$\alpha_{\infty}$.
A consequence of our results is the lower bound $HD(M\setminus L)>0.353$ on
the Hausdorff dimension $HD(M\setminus L)$ of $M\setminus L$. Another
by-product of our analysis is the explicit construction of new elements of
$M\setminus L$, including its largest known member $c\in M\setminus L$
(surpassing the former largest known number $\alpha_4\in M\setminus L$ obtained
by Cusick and Flahive in 1989). | [
0,
0,
1,
0,
0,
0
] |
Title: Good Clusterings Have Large Volume,
Abstract: The clustering of a data set is one of the core tasks in data analytics. Many
clustering algorithms exhibit a strong contrast between a favorable performance
in practice and bad theoretical worst-cases. Prime examples are least-squares
assignments and the popular $k$-means algorithm. We are interested in this
contrast and study it through polyhedral theory. Several popular clustering
algorithms can be connected to finding a vertex of the so-called bounded-shape
partition polytopes. The vertices correspond to clusterings with extraordinary
separation properties, in particular allowing the construction of a separating
power diagram, defined by its so-called sites, such that each cluster has its
own cell.
First, we quantitatively measure the space of all sites that allow
construction of a separating power diagram for a clustering by the volume of
the normal cone at the corresponding vertex. This gives rise to a new quality
criterion for clusterings, and explains why good clusterings are also the most
likely to be found by some classical algorithms. Second, we characterize the
edges of the bounded-shape partition polytopes. Through this, we obtain an
explicit description of the normal cones. This allows us to compute measures
with respect to the new quality criterion, and even compute "most stable"
sites, and thereby "most stable" power diagrams, for the separation of
clusters. The hardness of these computations depends on the number of edges
incident to a vertex, which may be exponential. However, the computational
effort is rewarded with a wealth of information that can be gained from the
results, which we highlight through some proof-of-concept computations. | [
0,
0,
1,
0,
0,
0
] |
Title: Regularity of Lie Groups,
Abstract: We solve the regularity problem for Milnor's infinite dimensional Lie groups
in the $C^0$-topological context, and provide necessary and sufficient
regularity conditions for the standard setting ($C^k$-topology). We prove that
the evolution map is $C^0$-continuous on its domain $\textit{iff}\hspace{1pt}$
the Lie group $G$ is locally $\mu$-convex. We furthermore show that if the
evolution map is defined on all smooth curves, then $G$ is Mackey complete -
This is a completeness condition formulated in terms of the Lie group
operations that generalizes Mackey completeness as defined for locally convex
vector spaces. Then, under the presumption that $G$ is locally $\mu$-convex, we
show that each $C^k$-curve, for $k\in \mathbb{N}_{\geq
1}\sqcup\{\mathrm{lip},\infty\}$, is integrable (contained in the domain of the
evolution map) $\textit{iff}\hspace{1pt}$ $G$ is Mackey complete and
$\mathrm{k}$-confined. The latter condition states that each $C^k$-curve in the
Lie algebra $\mathfrak{g}$ of $G$ can be uniformly approximated by a special
type of sequence consisting of piecewise integrable curves - A similar result
is proven for the case $k\equiv 0$; and we provide several mild conditions that
ensure that $G$ is $\mathrm{k}$-confined for each $k\in
\mathbb{N}\sqcup\{\mathrm{lip},\infty\}$. We finally discuss the
differentiation of parameter-dependent integrals in the standard topological
context. In particular, we show that if the evolution map is well defined and
continuous on $C^k([0,1],\mathfrak{g})$ for $k\in \mathbb{N}\sqcup\{\infty\}$,
then it is smooth thereon $\textit{iff}\hspace{1pt}$ $\mathfrak{g}$ is
$\hspace{0.2pt}$ Mackey complete for $k\in \mathbb{N}_{\geq 1}\sqcup\{\infty\}$
$\hspace{1pt}/\hspace{1pt}$ integral complete for $k\equiv 0$. This result is
obtained by calculating the directional derivatives explicitly - recovering the
standard formulas that hold in the Banach case. | [
0,
0,
1,
0,
0,
0
] |
Title: Convergence rates for nonequilibrium Langevin dynamics,
Abstract: We study the exponential convergence to the stationary state for
nonequilibrium Langevin dynamics, by a perturbative approach based on
hypocoercive techniques developed for equilibrium Langevin dynamics. The
Hamiltonian and overdamped limits (corresponding respectively to frictions
going to zero or infinity) are carefully investigated. In particular, the
maximal magnitude of admissible perturbations are quantified as a function of
the friction. Numerical results based on a Galerkin discretization of the
generator of the dynamics confirm the theoretical lower bounds on the spectral
gap. | [
0,
1,
1,
0,
0,
0
] |
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