title: Large-Scale Multi-Antenna Multi-Sine Wireless Power Transfer

abstract:
  Wireless Power Transfer (WPT) is expected to be a technology reshaping the
landscape of low-power applications such as the Internet of Things, Radio
Frequency identification (RFID) networks, etc. Although there has been some
progress towards multi-antenna multi-sine WPT design, the large-scale design of
WPT, reminiscent of massive MIMO in communications, remains an open challenge.
In this paper, we derive efficient multiuser algorithms based on a
generalizable optimization framework, in order to design transmit sinewaves
that maximize the weighted-sum/minimum rectenna output DC voltage. The study
highlights the significant effect of the nonlinearity introduced by the
rectification process on the design of waveforms in multiuser systems.
Interestingly, in the single-user case, the optimal spatial domain beamforming,
obtained prior to the frequency domain power allocation optimization, turns out
to be Maximum Ratio Transmission (MRT). In contrast, in the general weighted
sum criterion maximization problem, the spatial domain beamforming optimization
and the frequency domain power allocation optimization are coupled. Assuming
channel hardening, low-complexity algorithms are proposed based on asymptotic
analysis, to maximize the two criteria. The structure of the asymptotically
optimal spatial domain precoder can be found prior to the optimization. The
performance of the proposed algorithms is evaluated. Numerical results confirm
the inefficiency of the linear model-based design for the single and multi-user
scenarios. It is also shown that as nonlinear model-based designs, the proposed
algorithms can benefit from an increasing number of sinewaves.


title: Presentations for singular wreath products

abstract:
  For a monoid $M$ and a subsemigroup $S$ of the full transformation semigroup
$T_n$, the wreath product $M\wr S$ is defined to be the semidirect product
$M^n\rtimes S$, with the coordinatewise action of $S$ on $M^n$. The full wreath
product $M\wr T_n$ is isomorphic to the endomorphism monoid of the free $M$-act
on $n$ generators. Here, we are particularly interested in the case that
$S=Sing_n$ is the singular part of $T_n$, consisting of all non-invertible
transformations. Our main results are presentations for $M\wr Sing_n$ in terms
of certain natural generating sets, and we prove these via general results on
semidirect products and wreath products. We re-prove a classical result of
Bulman-Fleming that $M\wr Sing_n$ is idempotent generated if and only if the
set $M/L$ of $L$-classes of $M$ forms a chain under the usual ordering of
$L$-classes, and we give a presentation for $M\wr Sing_n$ in terms of
idempotent generators for such a monoid $M$. Among other results, we also give
estimates for the minimal size of a generating set for $M\wr Sing_n$, as well
as exact values in some cases (including the case that $M$ is finite and $M/L$
is a chain, in which case we also calculate the minimal size of an idempotent
generating set). As an application of our results, we obtain a presentation
(with idempotent generators) for the idempotent generated subsemigroup of the
endomorphism monoid of a uniform partition of a finite set.


title: A note on the size of N-free families

abstract:
  The $\mathcal{N}$ poset consists of four distinct sets $W,X,Y,Z$ such that
$W\subset X$, $Y\subset X$, and $Y\subset Z$ where $W$ is not necessarily a
subset of $Z$. A family $\mathcal{F}$ as a subposet of the $n$-dimensional
Boolean lattice, $\mathcal{B}_n$, is $\mathcal{N}$-free if it does not contain
$\mathcal{N}$ as a subposet. Let $\text{La}(n, \mathcal{N})$ be the size of a
largest $\mathcal{N}$-free family in $\mathcal{B}_n$. Katona and Tarj\'{a}n
proved that $\text{La}(n,\mathcal{N})\geq {n \choose k}+A(n,4,k+1)$, where
$k=\lfloor n/2\rfloor$ and $A(n, 4, k+1)$ is the size of a
single-error-correcting code with constant weight $k+1$. In this note, we prove
for $n$ even and $k=n/2$, $\text{La}(n, \mathcal{N}) \geq {n\choose k}+A(n, 4,
k)$, which improves the bound on $\text{La}(n, \mathcal{N})$ in the second
order term for some values of $n$ and should be an improvement for an infinite
family of values of $n$, depending on the behavior of the function
$A(n,4,\cdot)$.


title:
Proceedings of the 24th International Symposium on Graph Drawing and
  Network Visualization (GD 2016)

abstract:
  This is the arXiv index for the electronic proceedings of the 24th
International Symposium on Graph Drawing and Network Visualization (GD 2016),
which was held in Athens, Greece, September 19-21 2016. It contains the
peer-reviewed and revised accepted papers with an optional appendix.


title:
Existence and non-uniqueness of global weak solutions to inviscid
  primitive and Boussinesq equations

abstract:
  We consider the initial value problem for the inviscid Primitive and
Boussinesq equations in three spatial dimensions. We recast both systems as an
abstract Euler-type system and apply the methods of convex integration of De
Lellis and Sz\'ekelyhidi to show the existence of infinitely many global weak
solutions of the studied equations for general initial data. We also introduce
an appropriate notion of dissipative solutions and show the existence of
suitable initial data which generate infinitely many dissipative solutions.


title: An investgation on the electron's EDM from the electron's MDM

abstract:
  We pursue, in this contribution, an investigation of the contribution of the
electron's magnetic dipole moment (MDM) to the electron's electric dipole
moment (EDM) (or the charged leptons, more generally) in the framework of the
Born-Infeld Electrodynamics and in a gravity background with a non-vanishing
cosmological constant, where CP-symmetry is broken down. Our point of view
consist in associating a non-trivial EDM to a non-symmetry of the charge
distribution of the elementary particle under consideration. The bound on the
electron's EDM published in 2014 is used to constrain the coupling parameter of
the electromagnetic sector to the scalar curvature of the space-time in the
case we consider gravity to be responsible for the asymmetry in the
distribution.


title:
On the Performance Analysis of Underlay Cognitive Radio Systems: A
  Deployment Perspective

abstract:
  We study the performance of cognitive Underlay System (US) that employ power
control mechanism at the Secondary Transmitter (ST) from a deployment
perspective. Existing baseline models considered for performance analysis
either assume the knowledge of involved channels at the ST or retrieve this
information by means of a band manager or a feedback channel, however, such
situations rarely exist in practice. Motivated by this fact, we propose a novel
approach that incorporates estimation of the involved channels at the ST, in
order to characterize the performance of the US in terms of interference power
received at the primary receiver and throughput at the secondary receiver (or
\textit{secondary throughput}). Moreover, we apply an outage constraint that
captures the impact of imperfect channel knowledge, particularly on the
uncertain interference. Besides this, we employ a transmit power constraint at
the ST to classify the operation of the US in terms of an interference-limited
regime and a power-limited regime. In addition, we characterize the expressions
of the uncertain interference and the secondary throughput for the case where
the involved channels encounter Nakagami-$m$ fading. Finally, we investigate a
fundamental tradeoff between the estimation time and the secondary throughput
depicting an optimized performance of the US.


title: Random coalescing geodesics in first-passage percolation

abstract:
  We continue the study of infinite geodesics in planar first-passage
percolation, pioneered by Newman in the mid 1990s. Building on more recent work
of Hoffman, and Damron and Hanson, we develop an ergodic theory for infinite
geodesics via the study of what we shall call `random coalescing geodesics'.
Random coalescing geodesics have a range of nice asymptotic properties, such as
asymptotic directions and linear Busemann functions. We show that random
coalescing geodesics are (in some sense) dense in the space of geodesics. This
allows us to extrapolate properties from random coalescing geodesics to obtain
statements on all infinite geodesics. As an application of this theory we solve
the `midpoint problem' of Benjamini, Kalai and Schramm and address a question
of Furstenberg on the existence of bigeodesics.


title: Parallel Calibration for Sensor Array Radio Interferometers

abstract:
  In order to meet the theoretically achievable imaging performance,
calibration of modern radio interferometers is a mandatory challenge,
especially at low frequencies. In this perspective, we propose a novel parallel
iterative multi-wavelength calibration algorithm. The proposed algorithm
estimates the apparent directions of the calibration sources, the directional
and undirectional complex gains of the array elements and their noise powers,
with a reasonable computational complexity. Furthermore, the algorithm takes
into account the specific variation of the aforementioned parameter values
across wavelength. Realistic numerical simulations reveal that the proposed
scheme outperforms the mono-wavelength calibration scheme and approaches the
derived constrained Cram\'er-Rao bound even with the presence of
non-calibration sources at unknown directions, in a computationally efficient
manner.


title:
Unveiling the nucleon tensor charge at Jefferson Lab: A study of the
  SoLID case

abstract:
  Future experiments at the Jefferson Lab 12 GeV upgrade, in particular, the
Solenoidal Large Intensity Device (SoLID), aim at a very precise data set in
the region where the partonic structure of the nucleon is dominated by the
valence quarks. One of the main goals is to constrain the quark transversity
distributions. We apply recent theoretical advances of the global QCD
extraction of the transversity distributions to study the impact of future
experimental data from the SoLID experiments. Especially, we develop a simple
strategy based on the Hessian matrix analysis that allows one to estimate the
uncertainties of the transversity quark distributions and their tensor charges
extracted from SoLID data simulation. We find that the SoLID measurements with
the proton and the effective neutron targets can improve the precision of the
u- and d-quark transversity distributions up to one order of magnitude in the
range 0.05 < x < 0.6.


title: HashTag Erasure Codes: From Theory to Practice

abstract:
  Minimum-Storage Regenerating (MSR) codes have emerged as a viable alternative
to Reed-Solomon (RS) codes as they minimize the repair bandwidth while they are
still optimal in terms of reliability and storage overhead. Although several
MSR constructions exist, so far they have not been practically implemented
mainly due to the big number of I/O operations. In this paper, we analyze
high-rate MDS codes that are simultaneously optimized in terms of storage,
reliability, I/O operations, and repair-bandwidth for single and multiple
failures of the systematic nodes. The codes were recently introduced in
\cite{7463553} without any specific name. Due to the resemblance between the
hashtag sign \# and the procedure of the code construction, we call them in
this paper \emph{HashTag Erasure Codes (HTECs)}. HTECs provide the lowest
data-read and data-transfer, and thus the lowest repair time for an arbitrary
sub-packetization level $\alpha$, where $\alpha \leq r^{\lceil \sfrac{k}{r}
\rceil}$, among all existing MDS codes for distributed storage including MSR
codes. The repair process is linear and highly parallel. Additionally, we show
that HTECs are the first high-rate MDS codes that reduce the repair bandwidth
for more than one failure. Practical implementations of HTECs in Hadoop release
3.0.0-alpha2 demonstrate their great potentials.


title: A Flexible Recommendation System for Cable TV

abstract:
  Recommendation systems are being explored by Cable TV operators to improve
user satisfaction with services, such as Live TV and Video on Demand (VOD)
services. More recently, Catch-up TV has been introduced, allowing users to
watch recent broadcast content whenever they want to. These services give users
a large set of options from which they can choose from, creating an information
overflow problem. Thus, recommendation systems arise as essential tools to
solve this problem by helping users in their selection, which increases not
only user satisfaction but also user engagement and content consumption. In
this paper we present a learning to rank approach that uses contextual
information and implicit feedback to improve recommendation systems for a Cable
TV operator that provides Live and Catch-up TV services. We compare our
approach with existing state-of-the-art algorithms and show that our approach
is superior in accuracy, while maintaining high scores of diversity and
serendipity.


title: End-to-End Eye Movement Detection Using Convolutional Neural Networks

abstract:
  Common computational methods for automated eye movement detection - i.e. the
task of detecting different types of eye movement in a continuous stream of
gaze data - are limited in that they either involve thresholding on
hand-crafted signal features, require individual detectors each only detecting
a single movement, or require pre-segmented data. We propose a novel approach
for eye movement detection that only involves learning a single detector
end-to-end, i.e. directly from the continuous gaze data stream and
simultaneously for different eye movements without any manual feature crafting
or segmentation. Our method is based on convolutional neural networks (CNN)
that recently demonstrated superior performance in a variety of tasks in
computer vision, signal processing, and machine learning. We further introduce
a novel multi-participant dataset that contains scripted and free-viewing
sequences of ground-truth annotated saccades, fixations, and smooth pursuits.
We show that our CNN-based method outperforms state-of-the-art baselines by a
large margin on this challenging dataset, thereby underlining the significant
potential of this approach for holistic, robust, and accurate eye movement
protocol analysis.


title: A Large-Scale Characterization of User Behaviour in Cable TV

abstract:
  Nowadays, Cable TV operators provide their users multiple ways to watch TV
content, such as Live TV and Video on Demand (VOD) services. In the last years,
Catch-up TV has been introduced, allowing users to watch recent broadcast
content whenever they want to. Understanding how the users interact with such
services is important to develop solutions that may increase user satisfaction
, user engagement and user consumption. In this paper, we characterize, for the
first time, how users interact with a large European Cable TV operator that
provides Live TV, Catch-up TV and VOD services. We analyzed many
characteristics, such as the service usage, user engagement, program type,
program genres and time periods. This characterization will help us to have a
deeper understanding on how users interact with these different services, that
may be used to enhance the recommendation systems of Cable TV providers.


title: NLO cross sections in 4 dimensions without DREG

abstract:
  In this review, we present a new method for computing physical cross sections
at NLO accuracy in QCD without using the standard Dimensional Regularisation.
The algorithm is based on the Loop-Tree Duality theorem, which allow us to
obtain loop integrals as a sum of phase-space integrals; in this way,
transforming loop integrals into phase-space integrals, we propose a method to
merge virtual and real contributions in order to find observables at NLO in
$d=4$ space-time dimensions. In addition, the strategy described is used for
computing the $\gamma^*\to q\bar{q}(g)$ process. A more detailed discussion
related on this topic can be found in Ref [1].


title:
Global extraction of the parton-to-pion fragmentation functions at NLO
  accuracy in QCD

abstract:
  In this review, we discuss the results on the parton-to-pion fragmentation
functions obtained in a combined NLO fit to data of single-inclusive hadron
production in electron-positron annihilation, proton-proton collisions, and
lepton-nucleon deep-inelastic scattering. A more complete discussion can be
found in Ref. [1].


title:
Voltage stabilization in DC microgrids: an approach based on
  line-independent plug-and-play controllers

abstract:
  We consider the problem of stabilizing voltages in DC microGrids (mGs) given
by the interconnection of Distributed Generation Units (DGUs), power lines and
loads. We propose a decentralized control architecture where the primary
controller of each DGU can be designed in a Plug-and-Play (PnP) fashion,
allowing the seamless addition of new DGUs. Differently from several other
approaches to primary control, local design is independent of the parameters of
power lines. Moreover, differently from the PnP control scheme in [1], the
plug-in of a DGU does not require to update controllers of neighboring DGUs.
Local control design is cast into a Linear Matrix Inequality (LMI) problem
that, if unfeasible, allows one to deny plug-in requests that might be
dangerous for mG stability. The proof of closed-loop stability of voltages
exploits structured Lyapunov functions, the LaSalle invariance theorem and
properties of graph Laplacians. Theoretical results are backed up by
simulations in PSCAD.


title: Convergence of Multilevel Stationary Gaussian Quasi-Interpolation

abstract:
  In this paper we present a new multilevel quasi-interpolation algorithm for
smooth periodic functions using scaled Gaussians as basis functions. Recent
research in this area has focussed upon implementations using basis function
with finite smoothness. In this paper we deliver a first error estimates for
the multilevel algorithm using analytic basis functions. The estimate has two
parts, one involving the convergence of a low degree polynomial truncation term
and one involving the control of the remainder of the truncation as the
algorithm proceeds. Thus, numerically one observes a convergent scheme.
Numerical results suggest that the scheme converges much faster than the theory
shows.


title:
Thermal ignition revisited with two-dimensional molecular dynamics: role
  of fluctuations in activated collisions

abstract:
  The problem of thermal ignition in a homogeneous gas is revisited from a
molecular dynamics perspective. A two-dimensional model is adopted, which
assumes reactive disks of type A and B in a fixed area that react to form type
C products if an activation threshold for impact is surpassed. Such a reaction
liberates kinetic energy to the product particles, representative of the heat
release. The results for the ignition delay are compared with those obtained
from the continuum description assuming local thermodynamic equilibrium, in
order to assess the role played by molecular fluctuations. Results show two
regimes of non-equilibrium ignition whereby ignition occurs at different times
as compared to that from the continuum description. The first regime is at low
activation energies, where the ignition time is found to be higher than that
expected from theory for all values of heat release, in agreement with
predictions from Prigogine and Xhrouet who attribute this departure to
non-equilibrium effects. Results suggest the ignition is spatially homogeneous
in this regime. The second regime occurs at high activation energies and
sufficiently large heat release values. In this regime, ignition times are
found to be dependent on domain size, with larger domains yielding shorter
ignition delays than expected. Results for larger systems agree with the
expectations by Prigogine and Mahieu, who predict a non-equilibrium reaction
rate larger than expected for a homogeneous system in equilibrium. Results
yield a large variance for ignition times under these conditions, suggesting a
departure from homogeneous combustion. The results obtained are in qualitative
agreement with experimental observations of auto-ignition at relatively low
temperatures, where hot-spot ignition and associated ignition delays lower than
predicted are generally observed.


title: Non-axisymmetric instabilities in discs with imposed zonal flows

abstract:
  We conduct a linear stability calculation of an ideal Keplerian flow on which
a sinusoidal zonal flow is imposed. The analysis uses the shearing sheet model
and is carried out both in isothermal and adiabatic conditions, with and
without self-gravity (SG). In the non-SG regime a structure in the potential
vorticity (PV) leads to a non-axisymmetric Kelvin-Helmholtz (KH) instability;
in the short-wavelength limit its growth rate agrees with the incompressible
calculation by Lithwick (2007), which only considers perturbations elongated in
the streamwise direction. The instability's strength is analysed as a function
of the structure's properties, and zonal flows are found to be stable if their
wavelength is $\gtrsim 8H$, where $H$ is the disc's scale height, regardless of
the value of the adiabatic index $\gamma$. The non-axisymmetric KH instability
can operate in Rayleigh-stable conditions, and it therefore represents the
limiting factor to the structure's properties. Introducing SG triggers a second
non-axisymmetric instability, which is found to be located around a PV maximum,
while the KH instability is linked to a PV minimum, as expected. In the
adiabatic regime, the same gravitational instability is detected even when the
structure is present only in the entropy (not in the PV) and the instability
spreads to weaker SG conditions as the entropy structure's amplitude is
increased. This eventually yields a non-axisymmetric instability in the non-SG
regime, albeit of weak strength, localised around an entropy maximum.


abstract:
  We introduce a definition for \emph{Families of Optimal Binary Non-MDS
Erasure Codes} for $[n, k]$ codes over $GF(2)$, and propose an algorithm for
finding those families by using hill climbing techniques over Balanced XOR
codes. Due to the hill climbing search, those families of codes have always
better decoding probability than the codes generated in a typical Random Linear
Network Coding scenario, i.e., random linear codes. We also show a surprising
result that for small values of $k$, the decoding probability of our codes in
$GF(2)$ is very close to the decoding probability of the codes obtained by
Random Linear Network Coding but in the higher finite field $GF(4)$.


title: Nationalism, Immigration and the Dynamics of Language Evolution

abstract:
  I study the interplay between language competition and ideology struggle in a
country where there is a native high-status language and a low-status language
spoken by immigrants. Language transition is governed by a three-state model
similar to the Minett-Wang (2008) and the Heinsalu et al. (2014) models. I
introduce the novelty that, among natives, an ideological struggle exists
between a group of nationalists and a group of pro-immigrants, thus a two-state
model as in Abrams-Strogatz (2003). When bilingualism emerges as an
equilibrium, there might be a completely segregated society with monolingual
immigrants and monolingual nationalistic natives, thus an undesired outcome
contrasting with the widespread literature. Removing ideology struggle,
bilingualism is never stable, thus results in Heinsalu et al. (2014) are solely
due to the way conversion rate constants are defined in their model. If
language status is explicitly defined in the model, bilingualism becomes doomed
in the long run.


title:
An Eigenshapes Approach to Compressed Signed Distance Fields and Their
  Utility in Robot Mapping

abstract:
  In order to deal with the scaling problem of volumetric map representations
we propose spatially local methods for high-ratio compression of 3D maps,
represented as truncated signed distance fields. We show that these compressed
maps can be used as meaningful descriptors for selective decompression in
scenarios relevant to robotic applications. As compression methods, we compare
using PCA-derived low-dimensional bases to non-linear auto-encoder networks and
novel mixed architectures that combine both. Selecting two application-oriented
performance metrics, we evaluate the impact of different compression rates on
reconstruction fidelity as well as to the task of map-aided ego-motion
estimation. It is demonstrated that lossily compressed distance fields used as
cost functions for ego-motion estimation, can outperform their uncompressed
counterparts in challenging scenarios from standard RGB-D data-sets.


title: Time-frequency analysis of bivariate signals

abstract:
  Many phenomena are described by bivariate signals or bidimensional vectors in
applications ranging from radar to EEG, optics and oceanography. The
time-frequency analysis of bivariate signals is usually carried out by
analyzing two separate quantities, e.g. rotary components. We show that an
adequate quaternion Fourier transform permits to build relevant time-frequency
representations of bivariate signals that naturally identify geometrical or
polarization properties. First, the quaternion embedding of bivariate signals
is introduced, similar to the usual analytic signal of real signals. Then two
fundamental theorems ensure that a quaternion short term Fourier transform and
a quaternion continuous wavelet transform are well defined and obey desirable
properties such as conservation laws and reconstruction formulas. The resulting
spectrograms and scalograms provide meaningful representations of both the
time-frequency and geometrical/polarization content of the signal. Moreover the
numerical implementation remains simply based on the use of FFT. A toolbox is
available for reproducibility. Synthetic and real-world examples illustrate the
relevance and efficiency of the proposed approach.


title: Presentations of affine Kac-Moody groups

abstract:
  How many generators and relations does ${\mathrm SL}_n({\mathbb F}_q[t,
t^{-1}])$ need? In this paper we exhibit its explicit presentation with $9$
generators and $44$ relations.
  We investigate presentations of affine Kac-Moody groups over finite fields.
Our goal is to derive finite presentations, independent of the field and with
as few generators and relations as we can achieve. It turns out that any simply
connected affine Kac-Moody group over a finite field has a presentation with at
most 11 generators and 70 relations. We describe these presentations explicitly
type by type. As a consequence, we derive explicit presentations of Chevalley
groups $G({\mathbb F}_q[t, t^{-1}])$ and explicit profinite presentations of
profinite Chevalley groups $G({\mathbb F}_q[[t]])$.


title:
Dynamic phase transitions of a driven Ising chain in a dissipative
  cavity

abstract:
  We study the nonequilibrium quantum phase transition of an Ising chain in a
dissipative cavity driven by an external transverse light field. When driving
and dissipation are in balance, the system can reach a nonequilibrium steady
state which undergoes a super-radiant phase transition as the driving strength
increases. Interestingly, the super-radiant field changes the effective bias of
the Ising chain in return and drives its own transition between the
ferromagnetic and paramagnetic phase. We study the rich physics in this system
with sophisticated behavior, and investigate important issues in its dynamics
such as the stability of the system and criticality of the phase transition.


title:
Decomposing transverse momentum balance contributions for quenched jets
  in PbPb collisions at sqrt(s[NN]) = 2.76 TeV

abstract:
  Interactions between jets and the quark-gluon plasma produced in heavy ion
collisions are studied via the angular distributions of summed charged-particle
transverse momenta (pt) with respect to both the leading and subleading jet
axes in high-pt dijet events. The contributions of charged particles in
different momentum ranges to the overall event pt balance are decomposed into
short-range jet peaks and a long-range azimuthal asymmetry in charged-particle
pt. The results for PbPb collisions are compared to those in pp collisions
using data collected in 2011 and 2013, at collision energy sqrt(s[NN]) = 2.76
TeV with integrated luminosities of 166 inverse microbarns and 5.3 inverse
picobarns, respectively, by the CMS experiment at the LHC. Measurements are
presented as functions of PbPb collision centrality, charged-particle pt,
relative azimuth, and radial distance from the jet axis for balanced and
unbalanced dijets.


title: On aether terms in a space-time with a compact extra dimension

abstract:
  In this paper, for the CPT-even and CPT-odd extensions of the QED, we
explicitly obtain the aether-like corrections for the electromagnetic field in
the case when the space-time involves an extra compact spatial dimension
besides of usual four dimensions. Our methodology is based on an explicit
summation over the Kaluza-Klein tower of fields which is no more difficult than
the finite-temperature calculations. The quantum corrections turn out to be
large as the extra dimension is small. We demonstrate that in the CPT-even
case, the extra dimension manifests itself through a new scalar particle.


title: Finite time blow up in the hyperbolic Boussinesq system

abstract:
  In recent work of Luo and Hou, a new scenario for finite time blow up in
solutions of 3D Euler equation has been proposed. The scenario involves a ring
of hyperbolic points of the flow located at the boundary of a cylinder. In this
paper, we propose a two dimensional model that we call "hyperbolic Boussinesq
system". This model is designed to provide insight into the hyperbolic point
blow up scenario. The model features an incompressible velocity vector field, a
simplified Biot-Savart law, and a simplified term modeling buoyancy. We prove
that finite time blow up happens for a natural class of initial data.


title:
Quantifying Radiographic Knee Osteoarthritis Severity using Deep
  Convolutional Neural Networks

abstract:
  This paper proposes a new approach to automatically quantify the severity of
knee osteoarthritis (OA) from radiographs using deep convolutional neural
networks (CNN). Clinically, knee OA severity is assessed using Kellgren \&
Lawrence (KL) grades, a five point scale. Previous work on automatically
predicting KL grades from radiograph images were based on training shallow
classifiers using a variety of hand engineered features. We demonstrate that
classification accuracy can be significantly improved using deep convolutional
neural network models pre-trained on ImageNet and fine-tuned on knee OA images.
Furthermore, we argue that it is more appropriate to assess the accuracy of
automatic knee OA severity predictions using a continuous distance-based
evaluation metric like mean squared error than it is to use classification
accuracy. This leads to the formulation of the prediction of KL grades as a
regression problem and further improves accuracy. Results on a dataset of X-ray
images and KL grades from the Osteoarthritis Initiative (OAI) show a sizable
improvement over the current state-of-the-art.


title: Spacetime quantization effects on 5-dimensional black string evaporation

abstract:
  Spacetime quantization predicts the existence of minimal length and
time-interval. Within 5-dimensional Schwarzschild-like black string background,
the tunneling of scalar particles, fermions and massive bosons are first
studied together in the same generalized uncertainty principle framework. It is
found that, the minimal length and time-interval effect weakens the original
Hawking radiation. To $\mathcal{O}(\frac{1}{M_f^2})$, the corrected
temperatures depend on not only the mass of black string, but also the mass and
angular momentum of emitted particles. The temperature correction for massive
bosons is four times as big as that for scalar particles and fermions. As a
result, the bosons cease to tunnel from the black string before the scalar
particles and fermions do. The evaporation remnant is expected in our analysis,
however it should be verified by full quantum gravity theory.


title:
An invariance principle for the two-dimensional parabolic Anderson model
  with small potential

abstract:
  We prove an invariance principle for the two-dimensional lattice parabolic
Anderson model with small potential. As applications we deduce a Donsker type
convergence result for a discrete random polymer measure, as well as a
universality result for the spectrum of discrete random Schr\"odinger operators
on large boxes with small potentials. Our proof is based on paracontrolled
distributions and some basic results for multiple stochastic integrals of
discrete martingales.


title: A symmetry conserving description of odd-nuclei with the Gogny force

abstract:
  We present an approach for the calculation of odd-nuclei with exact
self-consistent blocking and particle number and angular momentum projection
with the finite range density dependent Gogny force. As an application we
calculate the nucleus $^{31}$Mg at the border of the $N=20$ inversion island.
We evaluate the ground state properties, the excited states and the transition
probabilities. In general we obtain a good description of the measured
observables.


title:
A nonlinear generalization of the Camassa-Holm equation with peakon
  solutions

abstract:
  A nonlinearly generalized Camassa-Holm equation, depending an arbitrary
nonlinearity power $p \neq 0$, is considered. This equation reduces to the
Camassa-Holm equation when $p=1$ and shares one of the Hamiltonian structures
of the Camassa-Holm equation. Two main results are obtained. A classification
of point symmetries is presented and a peakon solution is derived, for all
powers $p \neq 0$.


title:
Thermopower of molecular junctions: Tunneling to hopping crossover in
  DNA

abstract:
  We study the electrical conductance $G$ and the thermopower $S$ of
single-molecule junctions, and reveal signatures of different transport
mechanisms: off-resonant tunneling, on-resonant coherent (ballistic) motion,
and multi-step hopping. These mechanisms are identified by studying the
behavior of $G$ and $S$ while varying molecular length and temperature. Based
on a simple one-dimensional model for molecular junctions, we derive
approximate expressions for the thermopower in these different regimes.
Analytical results are compared to numerical simulations, performed using a
variant of B\"uttiker's probe technique, the so-called voltage-temperature
probe, which allows us to phenomenologically introduce environmentally-induced
elastic and inelastic electron scattering effects, while applying both voltage
and temperature biases across the junction. We further simulate the thermopower
of GC-rich DNA molecules with mediating A:T blocks, and manifest the
tunneling-to-hopping crossover in both the electrical conductance and the
thermopower, in accord with measurements by Y. Li et al., Nature Comm. 7, 11294
(2016).


title:
A Noncompact Weyl-Einstein-Yang-Mills Model: A Semiclassical Quantum
  Gravity

abstract:
  We construct and study perturbative unitarity (i.e., ghost and tachyon
analysis) of a $3+1$-dimensional noncompact Weyl-Einstein-Yang-Mills model. The
model describes a local noncompact Weyl's scale plus $SU(N)$ phase invariant
Higgs-like field, conformally coupled to a generic Weyl-invariant dynamical
background. Here, the Higgs-like sector generates the Weyl's conformal
invariance of system. The action does not admit any dimensionful parameter and
genuine presence of de Sitter vacuum spontaneously breaks the noncompact gauge
symmetry in an analogous manner to the Standard Model Higgs mechanism. As to
flat spacetime, the dimensionful parameter is generated within the dimensional
transmutation in quantum field theories, and thus the symmetry is radiatively
broken through the one-loop Effective Coleman-Weinberg potential. We show that
the mere expectation of reducing to Einstein's gravity in the broken phases
forbids anti-de Sitter space to be its stable vacua. The model is unitary in de
Sitter and flat vacua around which a massless graviton, $N^2-1$ massless scalar
bosons, $N$ massless Dirac fermions, $N^2-1$ Proca-type massive Abelian and
non-Abelian vector bosons are generically propagated.


title:
Monte-Carlo modelling of multi-object adaptive optics performance on the
  European Extremely Large Telescope

abstract:
  The performance of a wide-field adaptive optics system depends on input
design parameters. Here we investigate the performance of a multi-object
adaptive optics system design for the European Extremely Large Telescope, using
an end-to-end Monte-Carlo adaptive optics simulation tool, DASP, with relevance
for proposed instruments such as MOSAIC. We consider parameters such as the
number of laser guide stars, sodium layer depth, wavefront sensor pixel scale,
actuator pitch and natural guide star availability. We provide potential areas
where costs savings can be made, and investigate trade-offs between performance
and cost, and provide solutions that would enable such an instrument to be
built with currently available technology. Our key recommendations include a
trade-off for laser guide star wavefront sensor pixel scale of about 0.7
arcseconds per pixel, and a field of view of at least 7 arcseconds, that EMCCD
technology should be used for natural guide star wavefront sensors even if
reduced frame rate is necessary, and that sky coverage can be improved by a
slight reduction in natural guide star sub-aperture count without significantly
affecting tomographic performance. We find that adaptive optics correction can
be maintained across a wide field of view, up to 7 arcminutes in diameter. We
also recommend the use of at least 4 laser guide stars, and include
ground-layer and multi-object adaptive optics performance estimates.


title:
A detector interferometric calibration experiment for high precision
  astrometry

abstract:
  Context: Exoplanet science has made staggering progress in the last two
decades, due to the relentless exploration of new detection methods and
refinement of existing ones. Yet astrometry offers a unique and untapped
potential of discovery of habitable-zone low-mass planets around all the
solar-like stars of the solar neighborhood. To fulfill this goal, astrometry
must be paired with high precision calibration of the detector.
  Aims: We present a way to calibrate a detector for high accuracy astrometry.
An experimental testbed combining an astrometric simulator and an
interferometric calibration system is used to validate both the hardware needed
for the calibration and the signal processing methods. The objective is an
accuracy of 5e-6 pixel on the location of a Nyquist sampled polychromatic point
spread function.
  Methods: The interferometric calibration system produced modulated Young
fringes on the detector. The Young fringes were parametrized as products of
time and space dependent functions, based on various pixel parameters. The
minimization of func- tion parameters was done iteratively, until convergence
was obtained, revealing the pixel information needed for the calibration of
astrometric measurements.
  Results: The calibration system yielded the pixel positions to an accuracy
estimated at 4e-4 pixel. After including the pixel position information, an
astrometric accuracy of 6e-5 pixel was obtained, for a PSF motion over more
than five pixels. In the static mode (small jitter motion of less than 1e-3
pixel), a photon noise limited precision of 3e-5 pixel was reached.


title:
Phase Separation and Coexistence of Hydrodynamically Interacting
  Microswimmers

abstract:
  A striking feature of the collective behavior of spherical microswimmers is
that for sufficiently strong self-propulsion they phase-separate into a dense
cluster coexisting with a low-density dis- ordered surrounding. Extending our
previous work, we use the squirmer as a model swimmer and the particle-based
simulation method of multi-particle collision dynamics to explore the influence
of hydrodynamics on their phase behavior in a quasi-two-dimensional geometry.
The coarsening dynamics towards the phase-separated state is diffusive in an
intermediate time regime followed by a final ballistic compactification of the
dense cluster. We determine the binodal lines in a phase diagram of P\'eclet
number versus density. Interestingly, the gas binodals are shifted to smaller
densities for increasing mean density or dense-cluster size, which we explain
using a recently introduced pressure balance [S. C. Takatori et al., Phys. Rev.
Lett. 113, 028103 (2014)] extended by a hydrodynamic contribution. Furthermore,
we find that for pushers and pullers the binodal line is shifted to larger
P\'eclet numbers compared to neutral squirmers. Finally, when lowering the
P\'eclet number, the dense phase transforms from a hexagonal "solid" to a
disordered "fluid" state.


title: On the Enumeration of Interval Graphs

abstract:
  We present upper and lower bounds for the number $i_n$ of interval graphs on
$n$ vertices. Answering a question posed by Hanlon, we show that the ordinary
generating function $I(x) = \sum_{n\ge 0} i_n\,x^n$ for the number $i_n$ of
$n$-vertex interval graphs has radius of convergence zero. We also show that
the exponential generating function $J(x) = \sum_{n\ge 0} i_n\,x^n/n!$ has
radius of convergence at least $1/2$.


title:
Age Estimates of Universe: from Globular Clusters to Cosmological Models
  and Probes

abstract:
  We performed the photometric analysis of M2 and M92 globular clusters in g
and r bands of SLOAN photometric system. We transformed these g and r bands
into BV bands of Johnson-Cousins photometric system and built the color
magnitude diagram (CMD). We estimated the age, and metallicity of both the
clusters, by fitting Padova isochrones of different age and metallicities onto
the CMD. We studied Einstein and de Sitter model, bench mark model, the
cosmological parameters by WMAP and Planck surveys. Finally, we compared
estimated age of globular clusters to the ages from the cosmological models and
cosmological parameters values of WMAP and Planck surveys.


title:
MOCCA-SURVEY database I. Accreting white dwarf binary systems in
  globular clusters -- II. Cataclysmic variables -- progenitors and population
  at birth

abstract:
  This is the second in a series of papers associated with cataclysmic
variables (CVs) and related objects, formed in a suite of simulations for
globular cluster evolution performed with the MOCCA Monte Carlo code. We study
the properties of our simulated CV populations throughout the entire cluster
evolution. We find that dynamics extends the range of binary CV progenitor
properties, causing CV formation from binary progenitors that would otherwise
not become CVs. The CV formation rate in our simulations can be separated into
two regimes: an initial burst ($\lesssim$ 1 Gyr) connected with the formation
of the most massive white dwarfs, followed by a nearly constant formation rate.
This result holds for all models regardless of the adopted initial conditions,
even when most CVs form dynamically. Given the cluster age-dependence of CV
properties, we argue that direct comparisons to observed Galactic field CVs
could be misleading, since cluster CVs can be up to 4 times older than their
field counterparts. Our results also illustrate that, due mainly to unstable
mass transfer, some CVs that form in our simulations are destroyed before the
present-day. Finally, some field CVs might have originated from globular
clusters, as found in our simulations, although the fraction of such escapers
should be small relative to the entire Galactic field CV population.


title: Combined Semilocal Exchange Potential with Dynamical Mean-Field Theory

abstract:
  The modern semilocal exchange potential is an accurate and efficient
approximation to the exact exchange potential of density functional theory. We
tried to combine it with the dynamical mean-field theory to derive a new
first-principles many-body approach for studying correlated electronic
materials. As a paradigm, this approach was employed to investigate the
electronic structures and optical properties of strongly correlated ionic
insulator YbS. Compared to the standard density functional theory plus
dynamical mean-field theory which surprisingly failed to give an insulating
solution, the new approach correctly captured all of the important
characteristics of YbS. Not only an energy gap between a fully occupied Yb-4$f$
state and an unoccupied conduction band, but also an absence of Drude peak in
the optical conductivity $\sigma(\omega)$ were successfully reproduced.


title: Quantum exceptional group $G_2$ and its conjugacy classes

abstract:
  We construct quantization of semisimple conjugacy classes of the exceptional
group $G=G_2$ along with and by means of their exact representations in highest
weight modules of the quantum group $U_q(\mathfrak{g})$. With every point $t$
of a fixed maximal torus we associate a highest weight module $M_t$ over
$U_q(\mathfrak{g})$ and realize the quantized polynomial algebra of the class
of $t$ by linear operators on $M_t$. Quantizations corresponding to points of
the same orbit of the Weyl group are isomorphic.


title: The Homflypt polynomial and the oriented Thompson group

abstract:
  We show how to construct unitary representations of the oriented Thompson
group $\vec{F}$ from oriented link invariants. In particular we show that the
suitably normalised HOMFLYPT polynomial defines a positive definite function of
$\vec{F}$.


title:
The ortho-to-para ratio of interstellar NH$_2$: Quasi-classical
  trajectory calculations and new simulations

abstract:
  Based on recent $Herschel$ results, the ortho-to-para ratio (OPR) of NH$_2$
has been measured towards the following high-mass star-forming regions: W31C
(G10.6-0.4), W49N (G43.2-0.1), W51 (G49.5-0.4), and G34.3+0.1. The OPR at
thermal equilibrium ranges from the statistical limit of three at high
temperatures to infinity as the temperature tends toward zero, unlike the case
of H$_{2}$. Depending on the position observed along the lines-of-sight, the
OPR was found to lie either slightly below the high temperature limit of three
(in the range $2.2-2.9$) or above this limit ($\sim3.5$, $\gtrsim 4.2$, and
$\gtrsim 5.0$). In low temperature interstellar gas, where the H$_{2}$ is
para-enriched, our nearly pure gas-phase astrochemical models with nuclear-spin
chemistry can account for anomalously low observed NH$_2$-OPR values. We have
tentatively explained OPR values larger than three by assuming that spin
thermalization of NH$_2$ can proceed at least partially by H-atom exchange
collisions with atomic hydrogen, thus increasing the OPR with decreasing
temperature. In this paper, we present quasi-classical trajectory calculations
of the H-exchange reaction NH$_2$ + H, which show the reaction to proceed
without a barrier, confirming that the H-exchange will be efficient in the
temperature range of interest. With the inclusion of this process, our models
suggest both that OPR values below three arise in regions with temperatures
$\gtrsim20-25$~K, depending on time, and values above three but lower than the
thermal limit arise at still lower temperatures.


title:
Homotopy types of gauge groups over non-simply-connected closed
  4-manifolds

abstract:
  Let $G$ be a simply-connected simple compact Lie group and let $M$ be an
orientable smooth closed 4-manifold. In this paper we calculate the homotopy
type of the suspension of $M$ and the homotopy types of the gauge groups of
principal $G$-bundles over $M$ when $\pi_1(M)$ is: (1)~$\mathbb{Z}^{*m}$,
(2)~$\mathbb{Z}/p^r\mathbb{Z}$, or
(3)~$\mathbb{Z}^{*m}*(*^n_{j=1}\mathbb{Z}/p_j^{r_j}\mathbb{Z})$, where $p$ and
the $p_j$'s are odd primes.


title: Non-Backtracking Spectrum of Degree-Corrected Stochastic Block Models

abstract:
  Motivated by community detection, we characterise the spectrum of the
non-backtracking matrix $B$ in the Degree-Corrected Stochastic Block Model.
  Specifically, we consider a random graph on $n$ vertices partitioned into two
equal-sized clusters. The vertices have i.i.d. weights $\{ \phi_u \}_{u=1}^n$
with second moment $\Phi^{(2)}$. The intra-cluster connection probability for
vertices $u$ and $v$ is $\frac{\phi_u \phi_v}{n}a$ and the inter-cluster
connection probability is $\frac{\phi_u \phi_v}{n}b$.
  We show that with high probability, the following holds: The leading
eigenvalue of the non-backtracking matrix $B$ is asymptotic to $\rho =
\frac{a+b}{2} \Phi^{(2)}$. The second eigenvalue is asymptotic to $\mu_2 =
\frac{a-b}{2} \Phi^{(2)}$ when $\mu_2^2 > \rho$, but asymptotically bounded by
$\sqrt{\rho}$ when $\mu_2^2 \leq \rho$. All the remaining eigenvalues are
asymptotically bounded by $\sqrt{\rho}$. As a result, a clustering
positively-correlated with the true communities can be obtained based on the
second eigenvector of $B$ in the regime where $\mu_2^2 > \rho.$
  In a previous work we obtained that detection is impossible when $\mu_2^2 <
\rho,$ meaning that there occurs a phase-transition in the sparse regime of the
Degree-Corrected Stochastic Block Model.
  As a corollary, we obtain that Degree-Corrected Erd\H{o}s-R\'enyi graphs
asymptotically satisfy the graph Riemann hypothesis, a quasi-Ramanujan
property.
  A by-product of our proof is a weak law of large numbers for
local-functionals on Degree-Corrected Stochastic Block Models, which could be
of independent interest.


title: A cavity and further radial substructures in the disk around HD~97048

abstract:
  Context: Gaps, cavities and rings in circumstellar disks are signposts of
disk evolution and planet-disk interactions. We follow the recent suggestion
that Herbig Ae/Be disks with a flared disk harbour a cavity, and investigate
the disk around HD~97048.
  Aims: We aim to resolve the 34$\pm$ 4 au central cavity predicted by Maaskant
et al. (2013) and to investigate the structure of the disk.
  Methods: We image the disk around HD~97048 using ALMA at 0.85~mm and 2.94~mm,
and ATCA (multiple frequencies) observations. Our observations also include the
12CO J=1-0, 12CO J=3-2 and HCO+ J=4-3 emission lines.
  Results: A central cavity in the disk around HD~97048 is resolved with a
40-46 au radius. Additional radial structure present in the surface brightness
profile can be accounted for either by an opacity gap at ~90 au or by an extra
emitting ring at ~150 au. The continuum emission tracing the dust in the disk
is detected out to 355 au. The 12CO J=3-2 disk is detected 2.4 times farther
out. The 12CO emission can be traced down to $\approx$ 10 au scales.
Non-Keplerian kinematics are detected inside the cavity via the HCO+ J=4-3
velocity map. The mm spectral index measured from ATCA observations suggests
that grain growth has occurred in the HD~97048 disk. Finally, we resolve a
highly inclined disk out to 150 au around the nearby 0.5~$M_{\odot}$ binary
ISO-ChaI 126.
  Conclusions: The data presented here reveal a cavity in the disk of HD 97048,
and prominent radial structure in the surface brightness. The cavity size
varies for different continuum frequencies and gas tracers. The gas inside the
cavity follows non-Keplerian kinematics seen in HCO+ emission. The variable
cavity size along with the kinematical signature suggests the presence of a
substellar companion or massive planet inside the cavity.


title:
Fashion DNA: Merging Content and Sales Data for Recommendation and
  Article Mapping

abstract:
  We present a method to determine Fashion DNA, coordinate vectors locating
fashion items in an abstract space. Our approach is based on a deep neural
network architecture that ingests curated article information such as tags and
images, and is trained to predict sales for a large set of frequent customers.
In the process, a dual space of customer style preferences naturally arises.
Interpretation of the metric of these spaces is straightforward: The product of
Fashion DNA and customer style vectors yields the forecast purchase likelihood
for the customer-item pair, while the angle between Fashion DNA vectors is a
measure of item similarity. Importantly, our models are able to generate
unbiased purchase probabilities for fashion items based solely on article
information, even in absence of sales data, thus circumventing the "cold-start
problem" of collaborative recommendation approaches. Likewise, it generalizes
easily and reliably to customers outside the training set. We experiment with
Fashion DNA models based on visual and/or tag item data, evaluate their
recommendation power, and discuss the resulting article similarities.


title: Information and dimensionality of anisotropic random geometric graphs

abstract:
  This paper deals with the problem of detecting non-isotropic high-dimensional
geometric structure in random graphs. Namely, we study a model of a random
geometric graph in which vertices correspond to points generated randomly and
independently from a non-isotropic $d$-dimensional Gaussian distribution, and
two vertices are connected if the distance between them is smaller than some
pre-specified threshold. We derive new notions of dimensionality which depend
upon the eigenvalues of the covariance of the Gaussian distribution. If
$\alpha$ denotes the vector of eigenvalues, and $n$ is the number of vertices,
then the quantities $\left(\frac{||\alpha||_2}{||\alpha||_3}\right)^6/n^3$ and
$\left(\frac{||\alpha||_2}{||\alpha||_4}\right)^4/n^3$ determine upper and
lower bounds for the possibility of detection. This generalizes a recent result
by Bubeck, Ding, R\'acz and the first named author from [BDER14] which shows
that the quantity $d/n^3$ determines the boundary of detection for isotropic
geometry. Our methods involve Fourier analysis and the theory of characteristic
functions to investigate the underlying probabilities of the model. The proof
of the lower bound uses information theoretic tools, based on the method
presented in [BG15].


title:
The origin of the distinction between microscopic formulas for stress
  and Cauchy stress

abstract:
  Stress is calculated routinely in atomistic simulations. The widely used
microscopic stress formulas derived from classical or quantum mechanics,
however, are distinct from the concept of Cauchy stress, i.e., the true
mechanical tress. This work examines various atomistic stress formulations and
their inconsistencies. Using standard mathematic theorems and the law of
mechanics, we show that Cauchy stress results unambiguously from the definition
of internal force density, thereby removing the long-standing confusion about
the atomistic basis of the fundamental property of Cauchy stress, and leading
to a new atomistic formula for stress that has clear physical meaning and
well-defined values, satisfies conservation law, and is fully consistent with
the concept of Cauchy stress.


title: Quantum optical circulator controlled by a single chirally coupled atom

abstract:
  We demonstrate a fiber-integrated quantum optical circulator that is operated
by a single atom and that relies on the chiral interaction between emitters and
transversally confined light. Like its counterparts in classical optics, our
circulator exhibits an inherent asymmetry between light propagation in the
forward and the backward direction. However, rather than a magnetic field or a
temporal modulation, it is the internal quantum state of the atom that controls
the operation direction of the circulator. This working principle is compatible
with preparing the circulator in a coherent superposition of its operational
states. Such a quantum circulator may thus become a key element for routing and
processing quantum information in scalable integrated optical circuits.
Moreover, it features a strongly nonlinear response at the single-photon level,
thereby enabling, e.g., photon number-dependent routing and novel quantum
simulation protocols.


title:
An Ordered Magnetic Field in the Protoplanetary Disk of AB Aur Revealed
  by Mid-Infrared Polarimetry

abstract:
  Magnetic fields (B-fields) play a key role in the formation and evolution of
protoplanetary disks, but their properties are poorly understood due to the
lack of observational constraints. Using CanariCam at the 10.4-m Gran
Telescopio Canarias, we have mapped out the mid-infrared polarization of the
protoplanetary disk around the Herbig Ae star AB Aur. We detect ~0.44%
polarization at 10.3 micron from AB Aur's inner disk (r < 80 AU), rising to
~1.4% at larger radii. Our simulations imply that the mid-infrared polarization
of the inner disk arises from dichroic emission of elongated particles aligned
in a disk B-field. The field is well ordered on a spatial scale commensurate
with our resolution (~50 AU), and we infer a poloidal shape tilted from the
rotational axis of the disk. The disk of AB Aur is optically thick at 10.3
micron, so polarimetry at this wavelength is probing the B-field near the disk
surface. Our observations therefore confirm that this layer, favored by some
theoretical studies for developing magneto-rotational instability and its
resultant viscosity, is indeed very likely to be magnetized. At radii beyond
~80 AU, the mid-infrared polarization results primarily from scattering by dust
grains with sizes up to ~1 micron, a size indicating both grain growth and,
probably, turbulent lofting of the particles from the disk mid-plane.


title: Painlev\'e IV: roots and zeros

abstract:
  We consider the (real) fourth Painlev\'e equation in which both parameters
vanish, analyzing the square-roots of its solutions and paying special
attention to their zeros.


title:
Sub-wavelength Lithography of Complex 2D and 3D Nanostructures without
  Dyes

abstract:
  One-photon or two photon absorption by dye molecules in photopolymers enable
direct 2D & 3D lithography of micro/nano structures with high spatial
resolution and can be used effectively in fabricating artificially structured
nanomaterials. However, the major bottleneck in unleashing the potential of
this useful technique is the indispensable usage of dyes that are extremely
expensive, highly toxic and usually insoluble in commercially available
photopolymers. Here we report a simple, inexpensive and one-step technique for
direct-writing of micro/nanostructures, with sub-wavelength resolution at
extremely high speeds without using any one photon or two photon absorbing dye.
We incorporated large amount (20 weight %) of inexpensive photoinitiator into
the photopolymer and utilized its two-photon absorbing property for
sub-wavelength patterning. Complex 2D and 3D patterns were fabricated with
sub-micron resolution, in commercially available liquid photopolymer to show
the impact/versatility of this technique.


title:
Localized Polymerization Using Single Photon Photoinitiators in
  Two-photon process for Fabricating Subwavelength Structures

abstract:
  Localized polymerization in subwavelength volumes using two photon dyes has
now become a well-established method for fabrication of subwavelength
structures. Unfortunately, the two photon absorption dyes used in such process
are not only expensive but also proprietary. LTPO-L is an inexpensive, easily
available single photon photoinitiator and has been used extensively for single
photon absorption of UV light for polymerization. These polymerization volumes
however are not localized and extend to micron size resolution having limited
applications. We have exploited high quantum yield of radicals of LTPO-Lfor
absorption of two photons to achieve localized polymerization in subwavelength
volumes, much below the diffraction limit. Critical concentration (10wt%) of
LTPO-Lin acrylate (Sartomer) was found optimal to achieve subwavelength
localized polymerization and has been demonstrated by fabricating 2D/3D complex
nanostructures and functional devices such as variable polymeric gratings with
nanoscaled subwavelength resolution. Systematic studies on influence of LTPO-L
concentration on two photon polymerization of commercially available
photopolymer (Sartomer) show that resolution of the fabricated structures
critically depend on loading of LPTO-L. This is expected to unleash the true
potential of two photon polymerization for fabrication of complex polymeric
nanodevices at a larger scale.


title:
Making Fanaroff-Riley I radio sources. Numerical Hydrodynamic 3D
  Simulations of Low Power Jets

abstract:
  Extragalactic radio sources have been classified into two classes,
Fanaroff-Riley I and II, which differ in morphology and radio power. Strongly
emitting sources belong to the edge-brightened FR II class, and weakly emitting
sources to the edge-darkened FR I class. The origin of this dichotomy is not
yet fully understood. Numerical simulations are successful in generating FR II
morphologies, but they fail to reproduce the diffuse structure of FR Is.
  By means of hydro-dynamical 3D simulations of supersonic jets, we investigate
how the displayed morphologies depend on the jet parameters. Bow shocks and
Mach disks at the jet head, which are probably responsible for the hot spots in
the FR II sources, disappear for a jet kinetic power L_kin < 10^43 erg/s. This
threshold compares favorably with the luminosity at which the FR I/FR II
transition is observed.
  The problem is addressed by numerical means carrying out 3D HD simulations of
supersonic jets that propagate in a non-homogeneous medium with the ambient
temperature that increases with distance from the jet origin, which maintains
constant pressure.
  The jet energy in the lower power sources, instead of being deposited at the
terminal shock, is gradually dissipated by the turbulence. The jets spread out
while propagating, and they smoothly decelerate while mixing with the ambient
medium and produce the plumes characteristic of FR I objects.
  Three-dimensionality is an essential ingredient to explore the FR I evolution
because the properties of turbulence in two and three dimensions are very
different, since there is no energy cascade to small scales in two dimensions,
and two-dimensional simulations with the same parameters lead to FRII-like
behavior.


title:
Measurement of the Muon Production Depths at the Pierre Auger
  Observatory

abstract:
  The muon content of extensive air showers is an observable sensitive to the
primary composition and to the hadronic interaction properties. The Pierre
Auger Observatory uses water-Cherenkov detectors to measure particle densities
at the ground and therefore is sensitive to the muon content of air showers. We
present here a method which allows us to estimate the muon production depths by
exploiting the measurement of the muon arrival times at the ground recorded
with the Surface Detector of the Pierre Auger Observatory. The analysis is
performed in a large range of zenith angles, thanks to the capability of
estimating and subtracting the electromagnetic component, and for energies
between $10^{19.2}$ and $10^{20}$ eV.


title: Noncommutative Dirac quantization condition using the Seiberg-Witten map

abstract:
  We investigate the validity of the Dirac quantization condition (DQC) for
magnetic monopoles in noncommutative space-time. We use an approach based on an
extension of the method introduced by Wu and Yang; the effects of
noncommutativity are analyzed using the Seiberg-Witten map and the
corresponding deformed Maxwell's equations are discussed. By means of a
perturbation expansion in the noncommutativity parameter $\theta$, we show
first that the DQC remains unmodified up to the first and second order. This
result is then generalized to all orders in the expansion parameter for a class
of noncommutative electric currents induced by the Seiberg-Witten map; these
currents reduce to the Dirac delta function in the commutative limit.


title: Reduced Memory Region Based Deep Convolutional Neural Network Detection

abstract:
  Accurate pedestrian detection has a primary role in automotive safety: for
example, by issuing warnings to the driver or acting actively on car's brakes,
it helps decreasing the probability of injuries and human fatalities. In order
to achieve very high accuracy, recent pedestrian detectors have been based on
Convolutional Neural Networks (CNN). Unfortunately, such approaches require
vast amounts of computational power and memory, preventing efficient
implementations on embedded systems. This work proposes a CNN-based detector,
adapting a general-purpose convolutional network to the task at hand. By
thoroughly analyzing and optimizing each step of the detection pipeline, we
develop an architecture that outperforms methods based on traditional image
features and achieves an accuracy close to the state-of-the-art while having
low computational complexity. Furthermore, the model is compressed in order to
fit the tight constrains of low power devices with a limited amount of embedded
memory available. This paper makes two main contributions: (1) it proves that a
region based deep neural network can be finely tuned to achieve adequate
accuracy for pedestrian detection (2) it achieves a very low memory usage
without reducing detection accuracy on the Caltech Pedestrian dataset.


title:
A Computationally Efficient Projection-Based Approach for Spatial
  Generalized Linear Mixed Models

abstract:
  Inference for spatial generalized linear mixed models (SGLMMs) for
high-dimensional non-Gaussian spatial data is computationally intensive. The
computational challenge is due to the high-dimensional random effects and
because Markov chain Monte Carlo (MCMC) algorithms for these models tend to be
slow mixing. Moreover, spatial confounding inflates the variance of fixed
effect (regression coefficient) estimates. Our approach addresses both the
computational and confounding issues by replacing the high-dimensional spatial
random effects with a reduced-dimensional representation based on random
projections. Standard MCMC algorithms mix well and the reduced-dimensional
setting speeds up computations per iteration. We show, via simulated examples,
that Bayesian inference for this reduced-dimensional approach works well both
in terms of inference as well as prediction, our methods also compare favorably
to existing "reduced-rank" approaches. We also apply our methods to two real
world data examples, one on bird count data and the other classifying rock
types.


title:
Coupling sample paths to the partial thermodynamic limit in stochastic
  chemical reaction networks

abstract:
  Many biochemical systems appearing in applications have a multiscale
structure so that they converge to piecewise deterministic Markov processes in
a thermodynamic limit. The statistics of the piecewise deterministic process
can be obtained much more efficiently than those of the exact process. We
explore the possibility of coupling sample paths of the exact model to the
piecewise deterministic process in order to reduce the variance of their
difference. We then apply this coupling to reduce the computational complexity
of a Monte Carlo estimator. In addition to rigorous results concerning the
asymptotic computational complexity of the Monte Carlo estimator, numerical
simulations are performed on some simple biological models confirming that
computational gains are made.


title: An advanced precision analysis of the SM vacuum stability

abstract:
  The talk is devoted to the problem of stability of the Standard Model vacuum.
The effective potential for the Higgs field, which can potentialy exhibit
additional, deeper minimum, is considered as a convenient tool for addressing
the problem. Different methods and approximations used to calculate the
potential are considered. Special attention is paid to the renomalization-group
approach that allows one to carry out three-loop analysis of the problem. By
means of an explicit gauge-independent procedure the absolute stability bounds
on the observed Higgs and top-quark masses are derived. The importance of
high-order corrections is demonstrated. In addition, potential metastablity of
the SM is discussed together with modifications of the analysis due to some New
Physics.


title:
A Derivation of the Vlasov-Stokes System for Aerosol Flows from the
  Kinetic Theory of Binary Gas Mixtures

abstract:
  In this short paper, we formally derive the thin spray equation for a steady
Stokes gas, i.e. the equation consists in a coupling between a kinetic (Vlasov
type) equation for the dispersed phase and a (steady) Stokes equation for the
gas. Our starting point is a system of Boltzmann equations for a binary gas
mixture. The derivation follows the procedure already outlined in
[Bernard-Desvillettes-Golse-Ricci, arXiv:1608.00422 [math.AP]] where the
evolution of the gas is governed by the Navier-Stokes equation.


title: Drag reduction of a car model by linear genetic programming control

abstract:
  We investigate open- and closed-loop active control for aerodynamic drag
reduction of a car model. Turbulent flow around a blunt-edged Ahmed body is
examined at $Re_{H}\approx3\times10^{5}$ based on body height. The actuation is
performed with pulsed jets at all trailing edges combined with a Coanda
deflection surface. The flow is monitored with pressure sensors distributed at
the rear side. We apply a model-free control strategy building on Dracopoulos &
Kent (Neural Comput. & Applic., vol. 6, 1997, pp. 214-228) and Gautier et al.
(J. Fluid Mech., vol. 770, 2015, pp. 442-457). The optimized control laws
comprise periodic forcing, multi-frequency forcing and sensor-based feedback
including also time-history information feedback and combination thereof. Key
enabler is linear genetic programming as simple and efficient framework for
multiple inputs (actuators) and multiple outputs (sensors). The proposed linear
genetic programming control can select the best open- or closed-loop control in
an unsupervised manner. Approximately 33% base pressure recovery associated
with 22% drag reduction is achieved in all considered classes of control laws.
Intriguingly, the feedback actuation emulates periodic high-frequency forcing
by selecting one pressure sensor in the optimal control law. Our control
strategy is, in principle, applicable to all multiple actuators and sensors
experiments.


title: Evolution of an isolated monopole in a spin-1 Bose-Einstein condensate

abstract:
  We simulate the decay dynamics of an isolated monopole defect in the nematic
vector of a spin-1 Bose-Einstein condensate during the polar-to-ferromagnetic
phase transition of the system. Importantly, the decay of the monopole occurs
in the absence of external magnetic fields and is driven principally by the
dynamical instability due to the ferromagnetic spin-exchange interactions. An
initial isolated monopole is observed to relax into a polar-core spin vortex,
thus demonstrating the spontaneous transformation of a point defect of the
polar order parameter manifold to a line defect of the ferromagnetic manifold.
We also investigate the dynamics of an isolated monopole pierced by a quantum
vortex line with winding number k. It is shown to decay into a coreless
Anderson-Toulouse vortex if k = 1 and into a singular vortex with an empty core
if k = 2. In both cases, the resulting vortex is also encircled by a polar-core
vortex ring.


title:
Search for high-mass diphoton resonances in proton-proton collisions at
  13 TeV and combination with 8 TeV search

abstract:
  A search for the resonant production of high-mass photon pairs is presented.
The search focuses on spin-0 and spin-2 resonances with masses between 0.5 and
4.5 TeV, and with a width, relative to the mass, between 1.4E-4 and 5.6E-2. The
data sample corresponds to an integrated luminosity of 12.9 inverse femtobarns
of proton-proton collisions collected with the CMS detector in 2016 at a
center-of-mass energy of 13 TeV. No significant excess is observed relative to
the standard model expectation. The results of the search are combined
statistically with those previously obtained in 2012 and 2015 at sqrt(s) = 8
and 13TeV, respectively, corresponding to integrated luminosities of 19.7 and
3.3 inverse femtobarns, to derive exclusion limits on scalar resonances
produced through gluon-gluon fusion, and on Randall-Sundrum gravitons. The
lower mass limits for Randall-Sundrum gravitons range from 1.95 to 4.45 TeV for
coupling parameters between 0.01 and 0.2. These are the most stringent limits
on Randall-Sundrum graviton production to date.


title: A Model of White Dwarf Pulsar AR Scorpii

abstract:
  A 3.56-hour white dwarf (WD) - M dwarf (MD) close binary system, AR Scorpii,
was recently reported to show pulsating emission in radio, IR, optical, and UV,
with a 1.97-minute period, which suggests the existence of a WD with a rotation
period of 1.95 minutes. We propose a model to explain the temporal and spectral
characteristics of the system. The WD is a nearly perpendicular rotator, with
both open field line beams sweeping the MD stellar wind periodically. A bow
shock propagating into the stellar wind accelerates electrons in the wind.
Synchrotron radiation of these shocked electrons can naturally account for the
broad-band (from radio to X-rays) spectral energy distribution of the system.


title:
Topological constraints on positions of magnetic solitons in
  multiply-connected planar magnetic nano-elements

abstract:
  Here we consider an interplay between the topology of the magnetization
texture (which is a topological soliton, or Skyrmion) in a planar magnetic
nano-element and the topology of the element itself (its connectivity). We
establish the existence of a set of constraints, coupling these topologies,
which are specific for multiply connected elements and are absent in
simply-connected case. As an example, a specific constraint is derived for a
case of planar ring magnet, relating the angular positions of magnetic vortices
and antivortices inside. We analyze the recent experimental data on the vortex
magnetic domain walls in the ring to validate our findings.


title: Gradings on modules over Lie algebras of E types

abstract:
  For any grading by an abelian group $G$ on the exceptional simple Lie algebra
$\mathcal{L}$ of type $E_6$ or $E_7$ over an algebraically closed field of
characteristic zero, we compute the graded Brauer invariants of simple
finite-dimensional modules, thus completing the computation of these invariants
for simple finite-dimensional Lie algebras. This yields the classification of
$G$-graded simple $\mathcal{L}$-modules, as well as necessary and sufficient
conditions for an $\mathcal{L}$-module to admit a $G$-grading compatible with
the given $G$-grading on $\mathcal{L}$.


title:
A Mathematical Theory of Optimal Milestoning (with a Detour via Exact
  Milestoning)

abstract:
  Milestoning is a computational procedure that reduces the dynamics of complex
systems to memoryless jumps between intermediates, or milestones, and only
retains some information about the probability of these jumps and the time lags
between them. Here we analyze a variant of this procedure, termed optimal
milestoning, which relies on a specific choice of milestones to capture exactly
some kinetic features of the original dynamical system. In particular, we prove
that optimal milestoning permits the exact calculation of the mean first
passage times (MFPT) between any two milestones. In so doing, we also analyze
another variant of the method, called exact milestoning, which also permits the
exact calculation of certain MFPTs, but at the price of retaining more
information about the original system's dynamics. Finally, we discuss
importance sampling strategies based on optimal and exact milestoning that can
be used to bypass the simulation of the original system when estimating the
statistical quantities used in these methods.


title: Spectroscopy of singly, doubly, and triply bottom baryons

abstract:
  Recently, some singly bottom baryons have been established experimentally,
but none of doubly or triply bottom baryons has been observed. Under the Regge
phenomenology, the mass of a ground state unobserved doubly or triply bottom
baryon is expressed as a function of masses of the well established light
baryons and singly bottom baryons. Then, the values of Regge slopes and Regge
intercepts for baryons containing one, two, or three bottom quarks are
calculated. After that, masses of the orbitally excited singly, doubly, and
triply bottom baryons are estimated. Our predictions may be useful for the
discovery of these baryons and the $J^P$ assignment of them.


title: Functorial Hierarchical Clustering with Overlaps

abstract:
  This work draws inspiration from three important sources of research on
dissimilarity-based clustering and intertwines those three threads into a
consistent principled functorial theory of clustering. Those three are the
overlapping clustering of Jardine and Sibson, the functorial approach of
Carlsson and M\'{e}moli to partition-based clustering, and the Isbell/Dress
school's study of injective envelopes. Carlsson and M\'{e}moli introduce the
idea of viewing clustering methods as functors from a category of metric spaces
to a category of clusters, with functoriality subsuming many desirable
properties. Our first series of results extends their theory of functorial
clustering schemes to methods that allow overlapping clusters in the spirit of
Jardine and Sibson. This obviates some of the unpleasant effects of chaining
that occur, for example with single-linkage clustering. We prove an equivalence
between these general overlapping clustering functors and projections of weight
spaces to what we term clustering domains, by focusing on the order structure
determined by the morphisms. As a specific application of this machinery, we
are able to prove that there are no functorial projections to cut metrics, or
even to tree metrics. Finally, although we focus less on the construction of
clustering methods (clustering domains) derived from injective envelopes, we
lay out some preliminary results, that hopefully will give a feel for how the
third leg of the stool comes into play.


title: On Volumes of Subregions in Holography and Complexity

abstract:
  The volume of the region inside the bulk Ryu-Takayanagi surface is a
codimension-one object, and a natural generalization of holographic complexity
to the case of subregions in the boundary QFT. We focus on time-independent
geometries, and study the properties of this volume in various circumstances.
We derive a formula for computing the volume for a strip entangling surface and
a general asymptotically AdS bulk geometry. For an AdS black hole geometry, the
volume exhibits non-monotonic behaviour as a function of the size of the
entangling region (unlike the behaviour of the entanglement entropy in this
setup, which is monotonic). For setups in which the holographic entanglement
entropy exhibits transitions in the bulk, such as global AdS black hole,
geometries dual to confining theories and disjoint entangling surfaces, the
corresponding volume exhibits a discontinuous finite jump at the transition
point (and so do the volumes of the corresponding entanglement wedges). We
compute this volume discontinuity in several examples. Lastly, we compute the
codim-zero volume and the bulk action of the entanglement wedge for the case of
a sphere entangling surface and pure AdS geometry.


title: Growth of torsion groups of elliptic curves upon base change

abstract:
  We study how the torsion of elliptic curves over number fields grows upon
base change, and in particular prove various necessary conditions for torsion
growth. For a number field $F$, we show that for a large set of number fields
$L$, whose Galois group of their normal closure over $F$ has certain
properties, it will hold that $E(L)_{tors}=E(F)_{tors}$ for all elliptic curves
$E$ defined over $F$.
  Our methods turn out to be particularly useful in studying the possible
torsion groups $E(K)_{tors}$, where $K$ is a number field and $E$ is a base
change of an elliptic curve defined over $\mathbb Q$. Suppose that $E$ is a
base change of an elliptic curve over $\mathbb Q$ for the remainder of the
abstract. We prove that $E(K)_{tors}=E(\mathbb Q)_{tors}$ for all elliptic
curves $E$ defined over $\mathbb Q$ and all number fields $K$ of degree $d$,
where $d$ is not divisible by a prime $\leq 7$. Using this fact, we determine
all the possible torsion groups $E(K)_{tors}$ over number fields $K$ of prime
degree $p\geq 7$. We determine all the possible degrees of $[\mathbb
Q(P):\mathbb Q]$, where $P$ is a point of prime order $p$ for all $p$ such that
$p\not\equiv 8 \pmod 9$ or $\left( \frac{-D}{p}\right)=1$ for any $D\in
\{1,2,7,11,19,43,67,163\}$; this is true for a set of density
$\frac{1535}{1536}$ of all primes and in particular for all $p<3167$. Using
this result, we determine all the possible prime orders of a point $P\in
E(K)_{tors}$, where $[K:\mathbb Q]=d$, for all $d\leq 3342296$. Finally, we
determine all the possible groups $E(K)_{tors}$, where $K$ is a quartic number
field and $E$ is an elliptic curve defined over $\mathbb Q$ and show that no
quartic sporadic point on a modular curves $X_1(m,n)$ comes from an elliptic
curve defined over $\mathbb Q$.


title:
Principal modes in multimode fibers: exploring the crossover from weak
  to strong mode coupling

abstract:
  We present experimental and numerical studies on principal modes in a
multimode fiber with mode coupling. By applying external stress to the fiber
and gradually adjusting the stress, we have realized a transition from weak to
strong mode coupling, which corresponds to the transition from single
scattering to multiple scattering in mode space. Our experiments show that
principal modes have distinct spatial and spectral characteristic in the weak
and strong mode coupling regimes. We also investigate the bandwidth of the
principal modes, in particular, the dependence of the bandwidth on the delay
time, and the effects of the mode-dependent loss. By analyzing the path-length
distributions, we discover two distinct mechanisms that are responsible for the
bandwidth of principal modes in weak and strong mode coupling regimes. Taking
into account the mode-dependent loss in the fiber, our numerical results are in
good agreement with our experimental observations. Our study paves the way for
exploring potential applications of principal modes in communication, imaging
and spectroscopy.


title:
Interference-Free OFDM: Rethinking OFDM for Interference Networks with
  Inter-Symbol Interference

abstract:
  This paper considers a $K$-user single-input-single-output interference
channel with inter-symbol interference (ISI), in which the channel coefficients
are assumed to be linear time-invariant with finite-length impulse response.
The primary finding of this paper is that, with no channel state information at
a transmitter (CSIT), the sum-spectral efficiency can be made to scale linearly
with $K$, provided that the desired links have longer impulse response than do
the interfering links. This linear gain is achieved by a novel multi-carrier
communication scheme which we call \textit{interference-free orthogonal
frequency division multiplexing (IF-OFDM)}. Furthermore, when a transmitter is
able to learn CSIT from its paired receiver only, a higher sum-spectral
efficiency can be achieved by a two-stage transmission method that concatenates
IF-OFDM and vector coding based on singular value decomposition with
water-filling power allocation. A major implication of the derived results is
that separate encoding across subcarriers per link is sufficient to linearly
increase the sum-spectral efficiency with $K$ in the interference channel with
ISI. Simulation results support this claim.


title:
The nearby interstellar medium towards alpha Leo -- UV observations and
  modeling of a warm cloud within hot gas

abstract:
  We analyze interstellar absorption features in the full UV spectrum of the
nearby (d = 24 pc) B8 IVn star alpha Leo (Regulus) obtained at high resolution
and high S/N by the HST ASTRAL Treasury program. We derive column densities for
many key atomic species and interpret their partial ionizations. The gas in
front of alpha Leo exhibits two absorption components, one of which coincides
in velocity with the local interstellar cloud (LIC) that surrounds the Sun. The
second, smaller, component is shifted by +5.6 km/s relative to the main
component, in agreement with results for other lines of sight in this region of
the sky. The excitation of the C II fine-structure levels and the ratio of Mg I
to Mg II reveal a temperature T = 6500 (+750,-600)K and electron density n(e) =
0.11 (+0.025,-0.03) cm^-3. Our investigation of the ionization balance of all
the available species indicates that about 1/3 of the hydrogen atoms are
ionized and that metals are significantly depleted onto grains. We infer that
N(H I) = 1.9 (+0.9,-0.6) X 10^{18} cm^-2, which indicates that this partly
neutral gas occupies only 2 to 8 pc (about 13%) of the space toward the star,
with the remaining volume presumably being filled with a hot gas that emits
soft X-rays. We do not detect any absorption features from the highly ionized
species that could be produced in an interface between the warm medium and the
surrounding hot gas. Finally, the radial velocity of the LIC agrees with that
of the Local Leo Cold Cloud, indicating that they may be physically related.


title:
Not All Fluctuations are Created Equal: Spontaneous Variations in
  Thermodynamic Function

abstract:
  Almost all processes -- highly correlated, weakly correlated, or correlated
not at all---exhibit statistical fluctuations. Often physical laws, such as the
Second Law of Thermodynamics, address only typical realizations -- as
highlighted by Shannon's asymptotic equipartition property and as entailed by
taking the thermodynamic limit of an infinite number of degrees of freedom.
Indeed, our interpretations of the functioning of macroscopic thermodynamic
cycles are so focused. Using a recently derived Second Law for information
processing, we show that different subsets of fluctuations lead to distinct
thermodynamic functioning in Maxwellian Demons. For example, while typical
realizations may operate as an engine -- converting thermal fluctuations to
useful work -- even "nearby" fluctuations (nontypical, but probable
realizations) behave differently, as Landauer erasers -- converting available
stored energy to dissipate stored information. One concludes that ascribing a
single, unique functional modality to a thermodynamic system, especially one on
the nanoscale, is at best misleading, likely masking an array of simultaneous,
parallel thermodynamic transformations. This alters how we conceive of cellular
processes, engineering design, and evolutionary adaptation.

categories: cond-mat.stat-mech cs.IT math.IT math.ST q-bio.BM q-bio.PE stat.TH


title: Partitioning the Boolean lattice into copies of a poset

abstract:
  Let $P$ be a poset of size $2^k$ that has a greatest and a least element. We
prove that, for sufficiently large $n$, the Boolean lattice $2^{[n]}$ can be
partitioned into copies of $P$. This resolves a conjecture of Lonc.


title:
DiSMEC - Distributed Sparse Machines for Extreme Multi-label
  Classification

abstract:
  Extreme multi-label classification refers to supervised multi-label learning
involving hundreds of thousands or even millions of labels. Datasets in extreme
classification exhibit fit to power-law distribution, i.e. a large fraction of
labels have very few positive instances in the data distribution. Most
state-of-the-art approaches for extreme multi-label classification attempt to
capture correlation among labels by embedding the label matrix to a
low-dimensional linear sub-space. However, in the presence of power-law
distributed extremely large and diverse label spaces, structural assumptions
such as low rank can be easily violated.
  In this work, we present DiSMEC, which is a large-scale distributed framework
for learning one-versus-rest linear classifiers coupled with explicit capacity
control to control model size. Unlike most state-of-the-art methods, DiSMEC
does not make any low rank assumptions on the label matrix. Using double layer
of parallelization, DiSMEC can learn classifiers for datasets consisting
hundreds of thousands labels within few hours. The explicit capacity control
mechanism filters out spurious parameters which keep the model compact in size,
without losing prediction accuracy. We conduct extensive empirical evaluation
on publicly available real-world datasets consisting upto 670,000 labels. We
compare DiSMEC with recent state-of-the-art approaches, including - SLEEC which
is a leading approach for learning sparse local embeddings, and FastXML which
is a tree-based approach optimizing ranking based loss function. On some of the
datasets, DiSMEC can significantly boost prediction accuracies - 10% better
compared to SLECC and 15% better compared to FastXML, in absolute terms.


title:
On the correspondence between classical geometric phase of gyro-motion
  and quantum Berry phase

abstract:
  We show that the geometric phase of the gyro-motion of a classical charged
particle in a uniform time-dependent magnetic field described by Newton's
equation can be derived from a coherent Berry phase for the coherent states of
the Schroedinger equation or the Dirac equation. This correspondence is
established by constructing coherent states for a particle using the energy
eigenstates on the Landau levels and proving that the coherent states can
maintain their status of coherent states during the slow varying of the
magnetic field. It is discovered that orbital Berry phases of the eigenstates
interfere coherently to produce an observable effect (which we termed "coherent
Berry phase"), which is exactly the geometric phase of the classical
gyro-motion. This technique works for particles with and without spin. For
particles with spin, on each of the eigenstates that makes up the coherent
states, the Berry phase consists of two parts that can be identified as those
due to the orbital and the spin motion. It is the orbital Berry phases that
interfere coherently to produce a coherent Berry phase corresponding to the
classical geometric phase of the gyro-motion. The spin Berry phases of the
eigenstates, on the other hand, remain to be quantum phase factors for the
coherent states and have no classical counterpart.


title: On properties of the Casselman-Jacquet functor

abstract:
  In this thesis, we study the Casselman-Jacquet functor. We discuss a new
technical approach which makes the Casselman-Jacquet functor right adjoint to
the Bernstein functor. We give an explanation, using D-modules, of the Bruhat
filtration appearing on the module obtained by applying the Casselman-Jacquet
functor to a principal series representation. We record some conjectures.


title:
Affinoids in the Lubin-Tate perfectoid space and special cases of the
  local Langlands correspondence

abstract:
  Following Weinstein, Boyarchenko-Weinstein and Imai-Tsushima, we construct a
family of affinoids in the Lubin-Tate perfectoid space and formal models such
that the cohomology of the reduction of each formal model realizes the local
Langlands correspondence and the local Jacquet-Langlands correspondence for
certain representations. In the terminology of the essentially tame local
Langlands correspondence, the representations treated here are characterized as
being parametrized by minimal admissible pairs in which the field extensions
are totally ramified.


title: Series Solutions of the Non-Stationary Heun Equation

abstract:
  We consider the non-stationary Heun equation, also known as quantum
Painlev\'e VI, which has appeared in different works on quantum integrable
models and conformal field theory. We use a generalized kernel function
identity to transform the problem to solve this equation into a
differential-difference equation which, as we show, can be solved by efficient
recursive algorithms. We thus obtain series representations of solutions which
provide elliptic generalizations of the Jacobi polynomials. These series
reproduce, in a limiting case, a perturbative solution of the Heun equation due
to Takemura, but our method is different in that we expand in non-conventional
basis functions that allow us to obtain explicit formulas to all orders; in
particular, for special parameter values, our series reduce to a single term.


title: The Number of Fixed Points of AND-OR Networks with Chain Topology

abstract:
  AND-OR networks are Boolean networks where each coordinate function is either
the AND or OR logical operator. We study the number of fixed points of these
Boolean networks in the case that they have a wiring diagram with chain
topology. We find closed formulas for subclasses of these networks and
recursive formulas in the general case. Our results allow for an effective
computation of the number of fixed points in the case that the topology of the
Boolean network is an open chain (finite or infinite) or a closed chain.


title: Heat kernel upper bounds for interacting particle systems

abstract:
  We show a diffusive upper bound on the transition probability of a tagged
particle in the symmetric simple exclusion process. The proof relies on optimal
spectral gap estimates for the dynamics in finite volume, which are of
independent interest. We also show off-diagonal estimates of Carne-Varopoulos
type.


title:
On the p-adic Birch and Swinnerton-Dyer conjecture for elliptic curves
  over number fields

abstract:
  We formulate a multi-variable p-adic Birch and Swinnerton-Dyer conjecture for
p-ordinary elliptic curves A over number fields K. It generalises the
one-variable conjecture of Mazur-Tate-Teitelbaum, who studied the case K=Q and
the phenomenon of exceptional zeros. We discuss old and new theoretical
evidence towards our conjecture and in particular we fully prove it, under mild
conditions, in the following situation: K is imaginary quadratic, A=E_K is the
base-change to K of an elliptic curve over the rationals, and the rank of A is
either 0 or 1.
  The proof is naturally divided into a few cases. Some of them are deduced
from the purely cyclotomic case of elliptic curves over Q, which we obtain from
a refinement of recent work of Venerucci alongside the results of
Greenberg-Stevens, Perrin-Riou, and the author. The only genuinely
multi-variable case (rank 1, two exceptional zeros, three partial derivatives)
is newly established here. Its proof generalises to show that the
`almost-anticyclotomic' case of our conjecture is a consequence of conjectures
of Bertolini-Darmon on families of Heegner points, and of (partly conjectural)
p-adic Gross--Zagier and Waldspurger formulas in families.


title: Pointwise convergence of some multiple ergodic averages

abstract:
  We show that for every ergodic system $(X,\mu,T_1,\ldots,T_d)$ with commuting
transformations, the average \[\frac{1}{N^{d+1}} \sum_{0\leq n_1,\ldots,n_d
\leq N-1} \sum_{0\leq n\leq N-1} f_1(T_1^n \prod_{j=1}^d T_j^{n_j}x)f_2(T_2^n
\prod_{j=1}^d T_j^{n_j}x)\cdots f_d(T_d^n \prod_{j=1}^d T_j^{n_j}x). \]
converges for $\mu$-a.e. $x\in X$ as $N\to\infty$. If $X$ is distal, we prove
that the average \[\frac{1}{N}\sum_{i=0}^{N} f_1(T_1^nx)f_2(T_2^nx)\cdots
f_d(T_d^nx) \] converges for $\mu$-a.e. $x\in X$ as $N\to\infty$. We also
establish the pointwise convergence of averages along cubical configurations
arising from a system commuting transformations. Our methods combine the
existence of sated and magic extensions introduced by Austin and Host
respectively with ideas on topological models by Huang, Shao and Ye.


title:
A critical reassessment of the fundamental properties of GJ 504:
  Chemical composition and age

abstract:
  The recent development of brand new observational techniques and theoretical
models have greatly advanced the exoplanet research field. Despite significant
achievements, which have allowed the detection of thousands extrasolar systems,
a comprehensive understanding of planetary formation and evolution mechanisms
is still desired. One relevant limitation is given by the accuracy in the
measurements of planet-host star ages. The star GJ 504 has been found to host a
substellar companion whose nature is strongly debated. There has been a recent
difference of opinion in the literature owing to the uncertainty on the age of
the system: a young age of $\sim$ 160 Myr would imply a giant planet as a
companion, but a recent revision pointing to a solar age ($\sim$ 4 Gyr) instead
suggests a brown dwarf. With the aim of shedding light on this debated topic,
we have carried out a high-resolution spectroscopic study of GJ 504 to derive
stellar parameters, metallicity, and abundances of both light and heavy
elements, providing a full chemical characterisation. The main objective is to
infer clues on the evolutionary stage (hence the age) of this system. We
performed a strictly differential (line-by-line) analysis of GJ 504 with
respect to two reference stars, that is the planet-host dwarf $\iota$ Hor and
the subgiant HIP 84827. The former is crucial in this context because its
stellar parameters (hence the evolutionary stage) is well constrained from
asteroseismic observations. Regardless of the zero point offsets, our
differential approach allows us to put tight constraints on the age of GJ 504
with respect to $\iota$ Hor, thereby minimising the internal uncertainties. We
found that the surface gravity of GJ 504 is 0.2 $\pm$ 0.07 dex lower than that
of the main-sequence star $\iota$ Hor, suggesting a past turn-off
evolution[...]


title:
Latest Datasets and Technologies Presented in the Workshop on Grasping
  and Manipulation Datasets

abstract:
  This paper reports the activities and outcomes in the Workshop on Grasping
and Manipulation Datasets that was organized under the International Conference
on Robotics and Automation (ICRA) 2016. The half day workshop was packed with
nine invited talks, 12 interactive presentations, and one panel discussion with
ten panelists. This paper summarizes all the talks and presentations and recaps
what has been discussed in the panels session. This summary servers as a review
of recent developments in data collection in grasping and manipulation. Many of
the presentations describe ongoing efforts or explorations that could be
achieved and fully available in a year or two. The panel discussion not only
commented on the current approaches, but also indicates new directions and
focuses. The workshop clearly displayed the importance of quality datasets in
robotics and robotic grasping and manipulation field. Hopefully the workshop
could motivate larger efforts to create big datasets that are comparable with
big datasets in other communities such as computer vision.