title:
DeepSkeleton: Learning Multi-task Scale-associated Deep Side Outputs for
  Object Skeleton Extraction in Natural Images

abstract:
  Object skeletons are useful for object representation and object detection.
They are complementary to the object contour, and provide extra information,
such as how object scale (thickness) varies among object parts. But object
skeleton extraction from natural images is very challenging, because it
requires the extractor to be able to capture both local and non-local image
context in order to determine the scale of each skeleton pixel. In this paper,
we present a novel fully convolutional network with multiple scale-associated
side outputs to address this problem. By observing the relationship between the
receptive field sizes of the different layers in the network and the skeleton
scales they can capture, we introduce two scale-associated side outputs to each
stage of the network. The network is trained by multi-task learning, where one
task is skeleton localization to classify whether a pixel is a skeleton pixel
or not, and the other is skeleton scale prediction to regress the scale of each
skeleton pixel. Supervision is imposed at different stages by guiding the
scale-associated side outputs toward the groundtruth skeletons at the
appropriate scales. The responses of the multiple scale-associated side outputs
are then fused in a scale-specific way to detect skeleton pixels using multiple
scales effectively. Our method achieves promising results on two skeleton
extraction datasets, and significantly outperforms other competitors.
Additionally, the usefulness of the obtained skeletons and scales (thickness)
are verified on two object detection applications: Foreground object
segmentation and object proposal detection.


title: Algebraic independence results for values of Jacobi theta-constants

abstract:
  Let $\theta_3(\tau)=1+2\sum_{\nu=1}^{\infty} q^{\nu^2}$ with $q=e^{i\pi
\tau}$ and $\Im (\tau)>0$ denote the Thetanullwert of the Jacobi theta function
\[\theta(z|\tau) \,=\,\sum_{\nu=-\infty}^{\infty} e^{\pi i\nu^2\tau + 2\pi i\nu
z} \,.\] Moreover, let $\theta_2(\tau)=2\sum_{\nu=0}^{\infty}
q^{{(\nu+1/2)}^2}$ and $\theta_4(\tau)=1+2\sum_{\nu=1}^{\infty}
{(-1)}^{\nu}q^{\nu^2}$. For every even integer $n\geq 6$, which is not a power
of two, we prove constructively the existence of a nontrivial integer
polynomial $Q_n(X,Y)$ such that \[Q_n\Big(
\,\frac{\theta_3^4(n\tau)}{\theta_3^4(\tau)},\frac{\theta_2^4(\tau)}{\theta_3^4(\tau)}\,
\Big) \,=\, 0 \] holds for all complex numbers $\tau$ from the upper half plane
of $\mathbb{C}$. These polynomials are used to prove the algebraic independence
of $\theta_3(n\tau)$ and $\theta_3(\tau)$ for all algebraic numbers $q=e^{i\pi
\tau}$ with $0<|q|<1$. Combining this with former results of the authors, it is
shown that for such algebraic $q$ the numbers $\theta_3(n\tau)$ and
$\theta_3(\tau)$ are algebraically independent over $\mathbb{Q}$ for every
integer $n\geq 2$. A result on the algebraic dependence over $\mathbb{Q}$ of
the three numbers $\theta_3(\ell\tau)$, $\theta_3(m\tau)$, and
$\theta_3(n\tau)$ for integers $\ell,m,n\geq 1$ is also presented.


title: Elements of Torelli topology: II. The extension problem

abstract:
  By Torelli topology the author understands aspects of the topology of
surfaces (potentially) relevant to the study of Torelli groups. The extension
problem in Torelli topology is the problem of determining when a diffeomorphism
of compact connected subsurface of a closed surface can be extended to a
diffeomorphism of the whole surface acting trivially on its homology. The
special case of extensions by the identity diffeomorphism was considered by A.
Putman, whose work was one of the main sources of inspiration for the present
paper.
  It turns out that the answer depends on the position of the subsurface, but
only in a mild and controlled way discovered by A. Putman in the special case
of extensions by the identity. The answer is stated in terms of two homology
groups associated to the subsurface and a homomorphism between them, which we
call the difference map of a diffeomorphism of the subsurface in question.
  The extension problem is motivated by the desire to extend to Torelli groups
some well established tools and results from the theory of Teichm\"uller
modular groups. In particular, in the next paper of this series the analysis of
the extension problem in this paper will be applied to get a description of all
abelian subgroups of Torelli groups. The paper is concluded by some
speculations about what is the Torelli group of a surface with non-empty
boundary.


title:
Permutation Polynomials of the form ${\tt X}^r(a+{\tt X}^{2(q-1)})$ ---
  A Nonexistence Result

abstract:
  Let $f={\tt X}^r(a+{\tt X}^{2(q-1)})\in{\Bbb F}_{q^2}[{\tt X}]$, where
$a\in{\Bbb F}_{q^2}^*$ and $r\ge 1$. The parameters $(q,r,a)$ for which $f$ is
a permutation polynomial (PP) of ${\Bbb F}_{q^2}$ have been determined in the
following cases: (i) $a^{q+1}=1$; (ii) $r=1$; (iii) $r=3$. These parameters
together form three infinite families. For $r>3$ (there is a good reason not to
consider $r=2$) and $a^{q+1}\ne 1$, computer search suggested that $f$ is not a
PP of ${\Bbb F}_{q^2}$ when $q$ is not too small relative to $r$. In the
present paper, we prove that this claim is true. In particular, for each $r>3$,
there are only finitely many $(q,a)$, where $a^{q+1}\ne 1$, for which $f$ is a
PP of ${\Bbb F}_{q^2}$.


title:
An Experimental Study of LSTM Encoder-Decoder Model for Text
  Simplification

abstract:
  Text simplification (TS) aims to reduce the lexical and structural complexity
of a text, while still retaining the semantic meaning. Current automatic TS
techniques are limited to either lexical-level applications or manually
defining a large amount of rules. Since deep neural networks are powerful
models that have achieved excellent performance over many difficult tasks, in
this paper, we propose to use the Long Short-Term Memory (LSTM) Encoder-Decoder
model for sentence level TS, which makes minimal assumptions about word
sequence. We conduct preliminary experiments to find that the model is able to
learn operation rules such as reversing, sorting and replacing from sequence
pairs, which shows that the model may potentially discover and apply rules such
as modifying sentence structure, substituting words, and removing words for TS.


title: Pursuit on a Graph under Partial Information from Sensors

abstract:
  We consider a class of pursuit-evasion problems where an evader enters a
directed acyclic graph and attempts to reach one of the terminal nodes. A
pursuer enters the graph at a later time and attempts to capture the evader
before it reaches a terminal node. The pursuer can only obtain information
about the evader's path via sensors located at each node in the graph; the
sensor measurements are either green or red (indicating whether or not the
evader has passed through that node). We first show that it is NP-hard to
determine whether the pursuer can enter with some nonzero delay and still be
guaranteed to capture the evader, even for the simplest case when the
underlying graph is a tree. This also implies that it is NP-hard to determine
the largest delay at which the pursuer can enter and still have a guaranteed
capture policy. We further show that it is NP-hard to approximate (within any
constant factor) the largest delay at which the pursuer can enter. Finally, we
provide an algorithm to compute the maximum pursuer delay for a class of
node-sweeping policies on tree networks and show that this algorithm runs in
linear-time for bounded-degree trees.


title: Holographic study on the jet quenching parameter in anisotropic systems

abstract:
  We first calculate the jet quenching parameter of an anisotropic plasma with
a U(1) chemical potential via the AdS/CFT duality. The effects of charge,
anisotropy parameter and quark motion direction on the jet quenching parameter
are investigated. We then discuss the situation of anisotropic black brane in
the IR region. We study both the jet quenching parameters along the
longitudinal direction and transverse plane.


title: A Greedy Algorithm to Cluster Specialists

abstract:
  Several recent deep neural networks experiments leverage the
generalist-specialist paradigm for classification. However, no formal study
compared the performance of different clustering algorithms for class
assignment. In this paper we perform such a study, suggest slight modifications
to the clustering procedures, and propose a novel algorithm designed to
optimize the performance of of the specialist-generalist classification system.
Our experiments on the CIFAR-10 and CIFAR-100 datasets allow us to investigate
situations for varying number of classes on similar data. We find that our
\emph{greedy pairs} clustering algorithm consistently outperforms other
alternatives, while the choice of the confusion matrix has little impact on the
final performance.


title: Direct laser cooling Al+ ions optical clocks

abstract:
  Al$^+$ ions optical clock is a very promising optical frequency standard
candidate due to its extremely small blackbody radiation shift. It has been
successfully demonstrated with indirect cooled, quantum-logic-based
spectroscopy technique. Its accuracy is limited by second-order Doppler shift,
and its stability is limited by the number of ions that can be probed in
quantum logic processing. We propose a direct laser cooling scheme of Al$^+$
ions optical clocks where both the stability and accuracy of the clocks are
greatly improved. In the proposed scheme, two Al$^+$ ions traps are utilized.
The first trap is used to trap a large number of Al$^+$ ions to improve the
stability of the clock laser, while the second trap is used to trap a single
Al$^+$ ions to provide the ultimate accuracy. Both traps are cooled with a
continuous wave 167 nm laser. The expected clock laser stability can reach
$9.0\times10^{-17}/\sqrt{\tau}$. For the second trap, in addition to 167 nm
laser Doppler cooling, a second stage pulsed 234 nm two-photon cooling laser is
utilized to further improve the accuracy of the clock laser. The total
systematic uncertainty can be reduced to about $1\times10^{-18}$. The proposed
Al$^+$ ions optical clock has the potential to become the most accurate and
stable optical clock.


title:
Longest Common Subsequence in at Least $k$ Length Order-Isomorphic
  Substrings

abstract:
  We consider the longest common subsequence (LCS) problem with the restriction
that the common subsequence is required to consist of at least $k$ length
substrings. First, we show an $O(mn)$ time algorithm for the problem which
gives a better worst-case running time than existing algorithms, where $m$ and
$n$ are lengths of the input strings. Furthermore, we mainly consider the LCS
in at least $k$ length order-isomorphic substrings problem. We show that the
problem can also be solved in $O(mn)$ worst-case time by an easy-to-implement
algorithm.


title: Linear Stability of Hyperbolic Moment Models for Boltzmann Equation

abstract:
  Grad's moment models for Boltzmann equation were recently regularized to
globally hyperbolic systems, and thus the regularized models attain local
well-posedness for Cauchy data. The hyperbolic regularization is only related
to the convection term in Boltzmann equation. We in this paper studied the
regularized models with the presentation of collision terms. It is proved that
the regularized models are linear stability at the local equilibrium and
satisfy Yong's first stability condition with commonly used approximate
collision terms, and particularly with Boltzmann's binary collision model.


title:
Thermodynamic parameters of single- or multi-band superconductors
  derived from self-field critical currents

abstract:
  Key questions for any superconductor include: what is its maximum
dissipation-free electrical current (its `critical current') and can this be
used to extract fundamental thermodynamic parameters? Present models focus on
depinning of magnetic vortices and implicate materials engineering to maximise
pinning performance. But recently we showed that the self-field critical
current for thin films is a universal property, independent of microstructure,
controlled only by the penetration depth. Here we generalise this observation
to include thin films, wires or nanowires of single- or multi-band s-wave and
d-wave superconductors. Using extended BCS theory we consider dissipation-free
self-field transport currents as Meissner-London currents, avoiding the concept
of pinning altogether. We find quite generally, for type I or type II
superconductors, the current is limited by the relevant critical field divided
by the penetration depth. Our fits to 62 available data sets, from zinc
nanowires to compressed sulphur hydride with critical temperatures of 0.65 to
203 K, respectively, are excellent. Extracted London penetration depths,
superconducting energy gaps and specific heat jumps agree well with reported
bulk values. For multiband or multiphase samples we accurately recover
individual band contributions and phase fractions.


title:
Evolution of clusters in energetic heavy ion bombarded amorphous
  graphite-II: formation and fragmentation phenomena

abstract:
  A study has been conducted into the mechanisms of evolution of clusters and
their subsequent fragmentation under energetic heavy ion bombardment of
amorphous graphite. The evolving clusters and their subsequent fragmentation
under continuing ion bombardment are revealed by detecting various clusters in
the energy spectra of the Direct Recoils emitted as a result of collisions
between ions and surface constituents. The successive Direct Recoil spectra
reveal that the energetics of Carbon Carbon bond formation as well as any
subsequent fragmentation can be related to the processes of energy dissipation
in a cylindrical volume of a few Angstrom surrounding the ion path. The
dependence of cluster with m carbon atoms formation or its subsequent
fragmentation into cluster with m-2 carbon atoms and diatomic carbon C2 is seen
to be a function of the ionic stopping powers in this cylindrical volume.


title: Ramsey Numbers of Odd Cycles Versus Larger Even Wheels

abstract:
  The generalized Ramsey number $R(G_1, G_2)$ is the smallest positive integer
$N$ such that any red-blue coloring of the edges of the complete graph $K_N$
either contains a red copy of $G_1$ or a blue copy of $G_2$. Let $C_m$ denote a
cycle of length $m$ and $W_n$ denote a wheel with $n+1$ vertices. In 2014,
Zhang, Zhang and Chen determined many of the Ramsey numbers $R(C_{2k+1},
W_{n})$ of odd cycles versus larger wheels, leaving open the particular case
where $n = 2j$ is even and $k<j<3k/2$. They conjectured that for these values
of $j$ and $k$, $R(C_{2k+1}, W_{2j})=4j+1$. In 2015, Sanhueza-Matamala
confirmed this conjecture asymptotically, showing that $R(C_{2k+1}, W_{2j}) \le
4j+334$. In this paper, we prove the conjecture of Zhang, Zhang and Chen for
almost all of the remaining cases. In particular, we prove that
$R(C_{2k+1},W_{2j})=4j+1$ if $j-k \ge 251$, $k<j<3k/2$, and $j \ge 212299$.


title:
Alexander polynomial obstruction of bi-orderability for rationally
  homologically fibered knot groups

abstract:
  We show that if the fundamental group of the complement of a rationally
homologically fibered knot in a rational homology 3-sphere is bi-orderable,
then its Alexander polynomial has at least one positive real root. Our argument
can be applied for a finitely generated group which is an HNN extension with
certain properties.


title:
Radial-Velocity Fitting Challenge. II. First results of the analysis of
  the data set

abstract:
  Radial-velocity (RV) signals induce RV variations an order of magnitude
larger than the signal created by the orbit of Earth-twins, thus preventing
their detection. The goal of this paper is to compare the efficiency of the
different methods used to deal with stellar signals to recover extremely
low-mass planets despite. However, because observed RV variations at the m/s
precision level or below is a combination of signals induced by unresolved
orbiting planets, by the star, and by the instrument, performing such a
comparison using real data is extremely challenging. To circumvent this
problem, we generated simulated RV measurements including realistic stellar and
planetary signals. Different teams analyzed blindly those simulated RV
measurements, using their own method to recover planetary signals despite
stellar RV signals. By comparing the results obtained by the different teams
with the planetary and stellar parameters used to generate the simulated RVs,
it is therefore possible to compare the efficiency of these different methods.
The most efficient methods to recover planetary signals {take into account the
different activity indicators,} use red-noise models to account for stellar RV
signals and a Bayesian framework to provide model comparison in a robust
statistical approach. Using the most efficient methodology, planets can be
found down to K/N= K_pl/RV_rms*sqrt{N_obs}=5 with a threshold of K/N=7.5 at the
level of 80-90% recovery rate found for a number of methods. These recovery
rates drop dramatically for K/N smaller than this threshold. In addition, for
the best teams, no false positives with K/N > 7.5 were detected, while a
non-negligible fraction of them appear for smaller K/N. A limit of K/N = 7.5
seems therefore a safe threshold to attest the veracity of planetary signals
for RV measurements with similar properties to those of the different RV
fitting challenge systems.


title:
Deep Coevolutionary Network: Embedding User and Item Features for
  Recommendation

abstract:
  Recommender systems often use latent features to explain the behaviors of
users and capture the properties of items. As users interact with different
items over time, user and item features can influence each other, evolve and
co-evolve over time. The compatibility of user and item's feature further
influence the future interaction between users and items. Recently, point
process based models have been proposed in the literature aiming to capture the
temporally evolving nature of these latent features. However, these models
often make strong parametric assumptions about the evolution process of the
user and item latent features, which may not reflect the reality, and has
limited power in expressing the complex and nonlinear dynamics underlying these
processes. To address these limitations, we propose a novel deep coevolutionary
network model (DeepCoevolve), for learning user and item features based on
their interaction graph. DeepCoevolve use recurrent neural network (RNN) over
evolving networks to define the intensity function in point processes, which
allows the model to capture complex mutual influence between users and items,
and the feature evolution over time. We also develop an efficient procedure for
training the model parameters, and show that the learned models lead to
significant improvements in recommendation and activity prediction compared to
previous state-of-the-arts parametric models.


title: Exploring nonlocal observables in shock wave collisions

abstract:
  We study the time evolution of 2-point functions and entanglement entropy in
strongly anisotropic, inhomogeneous and time-dependent N=4 super Yang-Mills
theory in the large N and large 't Hooft coupling limit using AdS/CFT. On the
gravity side this amounts to calculating the length of geodesics and area of
extremal surfaces in the dynamical background of two colliding gravitational
shockwaves, which we do numerically. We discriminate between three classes of
initial conditions corresponding to wide, intermediate and narrow shocks, and
show that they exhibit different phenomenology with respect to the nonlocal
observables that we determine. Our results permit to use (holographic)
entanglement entropy as an order parameter to distinguish between the two
phases of the cross-over from the transparency to the full-stopping scenario in
dynamical Yang-Mills plasma formation, which is frequently used as a toy model
for heavy ion collisions. The time evolution of entanglement entropy allows to
discern four regimes: highly efficient initial growth of entanglement, linear
growth, (post) collisional drama and late time (polynomial) fall off.
Surprisingly, we found that 2-point functions can be sensitive to the geometry
inside the black hole apparent horizon, while we did not find such cases for
the entanglement entropy.


title: Unsupervised Monocular Depth Estimation with Left-Right Consistency

abstract:
  Learning based methods have shown very promising results for the task of
depth estimation in single images. However, most existing approaches treat
depth prediction as a supervised regression problem and as a result, require
vast quantities of corresponding ground truth depth data for training. Just
recording quality depth data in a range of environments is a challenging
problem. In this paper, we innovate beyond existing approaches, replacing the
use of explicit depth data during training with easier-to-obtain binocular
stereo footage.
  We propose a novel training objective that enables our convolutional neural
network to learn to perform single image depth estimation, despite the absence
of ground truth depth data. Exploiting epipolar geometry constraints, we
generate disparity images by training our network with an image reconstruction
loss. We show that solving for image reconstruction alone results in poor
quality depth images. To overcome this problem, we propose a novel training
loss that enforces consistency between the disparities produced relative to
both the left and right images, leading to improved performance and robustness
compared to existing approaches. Our method produces state of the art results
for monocular depth estimation on the KITTI driving dataset, even outperforming
supervised methods that have been trained with ground truth depth.


title:
Ringel-Hall algebras beyond their quantum groups I: Restriction functor
  and Green's formula

abstract:
  In this paper, we generalize the categorifical construction of a quantum
group and its canonical basis introduced by Lusztig (\cite{Lusztig,Lusztig2})
to the generic form of the whole Ringel-Hall algebra. We clarify the explicit
relation between the Green formula in \cite{Green} and the restriction functor
in \cite{Lusztig2}. By a geometric way to prove the Green formula, we show that
the Hopf structure of a Ringel-Hall algebra can be categorified under Lusztig's
framework.


title: Basis Tensor Gauge Theory

abstract:
  We reformulate gauge theories in analogy with the vierbein formalism of
general relativity. More specifically, we reformulate gauge theories such that
their gauge dynamical degrees of freedom are local fields that transform
linearly under the dual representation of the charged matter field. These local
fields, which naively have the interpretation of non-local operators similar to
Wilson lines, satisfy constraint equations. A set of basis tensor fields are
used to solve these constraint equations, and their field theory is
constructed. A new local symmetry in terms of the basis tensor fields is used
to make this field theory local and maintain a Hamiltonian that is bounded from
below. The field theory of the basis tensor fields is what we call the basis
tensor gauge theory.


title: Functional SAR Model

abstract:
  In this paper, we study a functional SAR model in which explanatory variables
are sampling points of a continuous-time process. We propose a procedure for
the maximum likelihood estimation for the spatial parameter dependence and the
parameter function. Both convergence in probability and almost sure convergence
of this estimator are stated.


title:
Cubic constraints for the resolvents of the ABJM matrix model and its
  cousins

abstract:
  A set of Schwinger-Dyson equations forming constraints for at most three
resolvent functions are considered for a class of Chern-Simons matter matrix
models with two nodes labelled by a non-vanishing number $n$. The two cases
$n=2$ and $n= -2$ label respectively the ABJM matrix model, which is the
hyperbolic lift of the affine $A_1^{(1)}$ quiver matrix model, and the lens
space matrix model. In the planar limit, we derive two cubic loop equations for
the two planar resolvents. One of these reduces to the quadratic one when $n =
\pm 2$.


title:
On asymptotic approximations to the log-Gamma and Riemann-Siegel theta
  functions

abstract:
  We give bounds on the error in the asymptotic approximation of the log-Gamma
function $\ln\Gamma(z)$ for complex $z$ in the right half-plane. These improve
on earlier bounds by Behnke and Sommer (1962), Spira (1971), and Hare (1997).
We show that $|R_{k+1}(z)/T_k(z)| < \sqrt{\pi k}$ for nonzero $z$ in the right
half-plane, where $T_k(z)$ is the $k$-th term in the asymptotic series, and
$R_{k+1}(z)$ is the error incurred in truncating the series after $k$ terms. If
$k \le |z|$, then the stronger bound $|R_{k+1}(z)/T_k(z)| < (k/|z|)^2/(\pi^2-1)
< 0.113$ holds. Similarly for the asymptotic approximation of
$\ln\Gamma(z+\frac{1}{2})$, except that a factor $\eta_k = 1/(1-2^{1-2k})$
multiplies some of the bounds.
  We deduce similar bounds for asymptotic approximation of the Riemann-Siegel
theta function $\vartheta(t)$. We show that the accuracy of a well-known
approximation to $\vartheta(t)$ can be improved by including an exponentially
small term in the approximation. This improves the attainable accuracy for real
$t>0$ from $O(\exp(-\pi t))$ to $O(\exp(-2\pi t))$. We discuss a similar
example due to Olver (1964), and a connection with the Stokes phenomenon.


title:
Making Deep Neural Networks Robust to Label Noise: a Loss Correction
  Approach

abstract:
  We present a theoretically grounded approach to train deep neural networks,
including recurrent networks, subject to class-dependent label noise. We
propose two procedures for loss correction that are agnostic to both
application domain and network architecture. They simply amount to at most a
matrix inversion and multiplication, provided that we know the probability of
each class being corrupted into another. We further show how one can estimate
these probabilities, adapting a recent technique for noise estimation to the
multi-class setting, and thus providing an end-to-end framework. Extensive
experiments on MNIST, IMDB, CIFAR-10, CIFAR-100 and a large scale dataset of
clothing images employing a diversity of architectures --- stacking dense,
convolutional, pooling, dropout, batch normalization, word embedding, LSTM and
residual layers --- demonstrate the noise robustness of our proposals.
Incidentally, we also prove that, when ReLU is the only non-linearity, the loss
curvature is immune to class-dependent label noise.


title:
Mode-locked Yb-doped fiber laser emitting broadband pulses at ultra-low
  repetition rates

abstract:
  We report on an environmentally stable, Yb-doped, all-normal dispersion,
mode-locked fibre laser that is capable of creating broadband pulses with
ultra-low repetition rates. Specifically, through careful positioning of fibre
sections in an all-PM-fibre cavity mode-locked with a nonlinear amplifying loop
mirror, we achieve stable pulse trains with repetition rates as low as 506 kHz.
The pulses have several nanojules of energy and are compressible down to
ultrashort (< 500 fs) durations.


title:
Effects of Herzberg--Teller vibronic coupling on coherent excitation
  energy transfer

abstract:
  In this work, we study the effects of non-Condon vibronic coupling on the
quantum coherence of excitation energy transfer, via the exact
dissipaton-equation-of-motion (DEOM) evaluations on excitonic model systems.
Field-triggered excitation energy transfer dynamics and two dimensional
coherent spectroscopy are simulated for both Condon and non-Condon vibronic
couplings. Our results clearly demonstrate that the non-Condon vibronic
coupling intensifies the dynamical electronic-vibrational energy transfer and
enhances the total system-and-bath quantum coherence. Moreover, the hybrid bath
dynamics for non-Condon effects enriches the theoretical calculation, and
further sheds light on the interpretation of the experimental nonlinear
spectroscopy.


title:
New multivariate tests for assessing covariate balance in matched
  observational studies

abstract:
  We propose new tests for assessing whether covariates in a treatment group
and matched control group are balanced in observational studies. The tests
exhibit high power under a wide range of multivariate alternatives, some of
which existing tests have little power for. The asymptotic permutation null
distributions of the proposed tests are studied and the p-values calculated
through the asymptotic results work well in finite samples, facilitating the
application of the test to large data sets. The tests are illustrated in a
study of the effect of smoking on blood lead levels. The proposed tests are
implemented in an R package BalanceCheck.


title: Parallel self-testing of (tilted) EPR pairs via copies of (tilted) CHSH

abstract:
  Device-independent self-testing allows a verifier to certify that potentially
malicious parties hold on to a specific quantum state, based only on the
observed correlations. Parallel self-testing has recently been explored, aiming
to self-test many copies (i.e. a tensor product) of the target state
concurrently. In this work, we show that $n$ EPR pairs can be self-tested in
parallel through $n$ copies of the well known CHSH game. We generalise this
result further to a parallel self-test of $n$ tilted EPR pairs with arbitrary
angles, and finally we show how our results and calculations can also be
applied to obtain a parallel self-test of $2n$ EPR pairs via $n$ copies of the
Mermin-Peres magic square game.


title: Vector bundles induced from jet schemes

abstract:
  A family of holomorphic vector bundles is constructed on a complex manifold
$X$. The space of the holomorphic sections of these bundles are calculated in
certain cases. As an application, if $X$ is an $N$-dimensional compact K\"ahler
manifold with holonomy group $SU(N)$, the space of holomorphic vector fields on
its jet scheme $J_m(X)$ is calculated. We also prove that the space of the
global sections of the chiral de Rham complex of a K3 surface is the simple
$N=4$ superconformal vertex algebra with central charge $6$.


title:
Accidental permutation symmetries as a test for Grand Unification: the
  supersymmetric $SU(5)$ case

abstract:
  Unification of matter fields implies the existence of accidental permutation
symmetries, which potentially remain immune to large quantum corrections up to
the TeV scale. We investigate the case of a supersymmetric $SU(5)$ grand
unified theory, where such a permutation symmetry is present in the up-type
squark sector. We present a variety of tests allowing to challenge the $SU(5)$
hypothesis based on the observation of squarks at the LHC. These tests appear
as relations among observables involving flavour-violating or
chirality-flipping decays of squarks. Moreover, they rely on top-polarimetry
and charm-tagging. As an example, we discuss the application to the scenario of
Natural Supersymmetry, while more examples can be found in the related journal
publications.


title: Construction of Gray maps for groups of order 16

abstract:
  In this paper we consider Type 1 Gray maps and Type 2 Gray maps for groups of
order 16. First, we confirm that we can construct Type 1 Gray maps for all
groups of order 16, and we actually construct them. Next, we confirm that we
can construct Type 2 Gray maps for several groups of order 16, and we construct
all such maps. Finally we reveal why the other groups do not admit Gray maps.


title:
Deflecting cavity dynamics for time-resolved machine studies of SXFEL
  user facility

abstract:
  Radio frequency deflectors are widely used for time-resolved electron beam
energy, emittance and radiation profile measurements in modern free electron
laser facilities. In this paper, we present the beam dynamics aspects of the
deflecting cavity of SXFEL user facility, which is located at the exit of the
undulator. With a targeted time resolution around 10 fs, it is expected to be
an important tool for time-resolved commissioning and machine studies for SXFEL
user facility.


title:
Sample selection models for discrete and other non-Gaussian response
  variables

abstract:
  Consider observation of a phenomenon of interest subject to selective
sampling due to a censoring mechanism regulated by some other variable. In this
context, an extensive literature exists linked to the so-called Heckman
selection model. A great deal of this work has been developed under Gaussian
assumption of the underlying probability distributions; considerably less work
has dealt with other distributions. We examine a general construction which
encompasses a variety of distributions and allows various options of the
selection mechanism, focusing especially on the case of discrete response.
Inferential methods based on the pertaining likelihood function are developed.


title:
Uniqueness for an inverse problem for a semilinear time-fractional
  diffusion equation

abstract:
  An inverse problem to determine a space-dependent factor in a semilinear
time-fractional diffusion equation is considered. Additional data are given in
the form of an integral with the Borel measure over the time. Uniqueness of the
solution of the inverse problem is studied. The method uses a positivity
principle of the corresponding differential equation that is also proved in the
paper.


title: Kloosterman paths of prime powers moduli

abstract:
  Emmanuel Kowalski and William Sawin proved, using a deep independence result
of Kloosterman sheaves, that the polygonal paths joining the partial sums of
the normalized classical Kloosterman sums S(a,b0;p)/p^{1/2} converge in the
sense of finite distributions to a specific random Fourier series, as a varies
over (Z/pZ)^*, b0 is fixed in (Z/pz)* and p tends to infinity among the odd
prime numbers. This article considers the case of S(a,b0;p^n)/p^{n/2}, as a
varies over (Z/p^nZ)^*, b0 is fixed in (Z/p^nZ)^*, p tends to infinity among
the odd prime numbers and n>=2 is a fixed integer. A convergence in law in the
Banach space of complex-valued continuous function on [0,1] is also
established, as (a,b) varies over (Z/p^nZ)*.(Z/p^nZ)*, p tends to infinity
among the odd prime numbers and n>=2 is a fixed integer. This is the analogue
of the result obtained by Emmanuel Kowalski and William Sawin in the prime
moduli case.


title:
Blending Entropy: A Term for Addressing Information Density in Mediated
  Reality

abstract:
  The virtuality continuum describes the degrees of positive virtuality under
the umbrella term mixed reality. Besides adding virtual information within a
mixed environment, diminished reality aims at reducing real world information.
Mann defined the term mediated reality (MR), which also considered diminished
reality, but without the possibility to describe different degrees of fusion
between a mixed and a diminished reality. That is why this work defines the new
term blending entropy that captures the relations between a mixed and a
diminished reality. The blending entropy is based on the information density of
the mediated reality and the actual area the user has to comprehend, which is
named perceptual frustum. We describe the blending entropy's twodimensional
dependencies and detail important points in the blending entropy's space.


title: Power Allocation and Effective Capacity of AF Successive Relays

abstract:
  In the relay based telecommunications with $K$ relays between the source and
destination, $K+1$ time or frequency slots are required for a single frame
transmission. However, without the relays, only one time or frequency slot is
used for a single frame transmission. Therefore, despite the benefits of
relaying systems, this type of communications is not efficient from the
spectral efficiency viewpoint. One solution to reduce this issue might be the
full-duplex (FD) relays. An old technique which is reconsidered recently to
improve the spectral efficiency of telecommunication systems. However, FD
relays have a certain complexity, so, some similar techniques such as
successive relays with nearly the same performance but less complexity is taken
into account now. In successive relaying systems, two relays between the source
and destination are employed which receive the transmitted frames from the
source and relay it to the destination successively. This structure generally
acts like an FD relays. In this paper, the effective capacity performance of an
amplify and forward (AF) successive relaying systems with power allocation
strategy at the relays are studied perfectly. However, while the inter-rely
interference (IRI) between two successive relays has to be managed well, the
power allocation and the effective capacity is derived under different
assumptions about the IRI. In this way, we assume weak or strong, short or
long-term constraints on the IRI. Then we extract the optimal transmitted power
at the relay to maximize the effective capacity under these constraints.


title:
Measurement of Redshift Space Power Spectrum for BOSS galaxies and the
  Growth Rate at redshift 0.57

abstract:
  We present a measurement of two-dimensional (2D) redshift-space power
spectrum for the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 11
CMASS galaxies in the North Galactic Cap (NGC) based on the method developed by
Jing & Borner (2001). In this method, we first measure the 2D redshift-space
correlation function for the CMASS galaxies, and obtain the 2D power spectrum
based on Fourier Transform of the correlation function. The method is tested
with an N-body mock galaxy catalog, which demonstrates that the method can
yield an accurate and unbiased measurement of the redshift-space power spectrum
given the input 2D correlation function is correct. Compared with previous
measurements in literature that are usually based on direct Fourier Transform
in redshift space, our method has the advantages that the window function and
shot-noise are fully corrected. In fact, our 2D power spectrum, by its
construction, can accurately reproduce the 2D correlation function, and in the
meanwhile can reproduce, for example, the 2D power spectrum of Beutler et al.
(2014) accurately if ours is convolved with the window function they provided.
Thus, our measurement can facilitate a direct comparison with the theoretical
predictions. With this accurate measurement of the 2D power spectrum, we then
develop a method to measure the structure growth rate, by separating the
anisotropic redshift-space power spectrum from the isotropic real-space power
spectrum. We have also carefully corrected for the nonlinearities in the
mapping from real space to redshift space, according to the theoretical model
of Zhang et al. (2013). Finally, we obtain f(zeff)sigma_8(zeff)=0.438\pm0.037
at the effective redshift zeff=0.57, where f(zeff) is the linear growth rate at
redshift zeff. The result is useful for constraining cosmological parameters.
The measurements of 2D power spectrum will be released soon.


title: J/P=1/2+, J/P=3/2+ masses in statistical model

abstract:
  The mass formulae for the baryon octet and decuplet are calculated. These
formulae are function of constituent quark masses and spin spin interaction
terms for the quarks inside the baryons. The coefficients in the mass formulae
is estimated by the statistical model for J/P=1/2+, J/P=3/2+, incorporating the
contributions from \sea" containing uu; dd; ss pairs and gluons . The measured
masses are presented and found to be matching good with some of the
experimental and theoretical data.


title:
An Evaluation of Polarisability Tensors of Arbitrarily Shaped Highly
  Conducting Bodies

abstract:
  A full-wave numerical scheme of polarisability tensors evaluation is
presented. The method accepts highly conducting bodies of arbitrary shape and
explicitly accounts for the radiation as well as ohmic losses. The method is
verified on canonical bodies with known polarisability tensors, such as a
sphere and a cube, as well as on realistic scatterers. The theoretical
developments are followed by a freely available code whose sole user input is
the triangular mesh covering the surface of the body under consideration.


title: Collisions of Small Nuclei in the Thermal Model

abstract:
  An analysis is presented of the expectations of the thermal model for
particle production in collisions of small nuclei. The maxima observed in
particle ratios of strange particles to pions as a function of beam energy in
heavy ion collisions, are reduced when considering smaller nuclei. Of
particular interest is the $\Lambda/\pi^+$ ratio shows the strongest maximum
which survives even in collisions of small nuclei.


title:
Divergence-free Reconstruction Operators for Pressure-Robust Stokes
  Discretizations With Continuous Pressure Finite Elements

abstract:
  Classical inf-sup stable mixed finite elements for the incompressible
(Navier-)Stokes equations are not pressure-robust, i.e., their velocity errors
depend on the continuous pressure. However, a modification only in the right
hand side of a Stokes discretization is able to reestablish
pressure-robustness, as shown recently for several inf-sup stable Stokes
elements with discontinuous discrete pressures. In this contribution, this idea
is extended to low and high order Taylor-Hood and mini elements, which have
continuous discrete pressures. For the modification of the right hand side a
velocity reconstruction operator is constructed that maps discretely
divergence-free test functions to exactly divergence-free ones. The
reconstruction is based on local $H(\mathrm{div})$-conforming flux
equilibration on vertex patches, and fulfills certain orthogonality properties
to provide consistency and optimal a-priori error estimates. Numerical examples
for the incompressible Stokes and Navier-Stokes equations confirm that the new
pressure-robust Taylor-Hood and mini elements converge with optimal order and
outperform significantly the classical versions of those elements when the
continuous pressure is comparably large.


title:
Spin-flop transition accompanied with changing the type of magnetic
  ordering

abstract:
  We discuss theoretically rather rear example of spin-flop transition which is
accompanied with changing the type of magnetic ordering and which seemingly has
not been addressed yet. We demonstrate that changing the type of magnetic
ordering can manifest itself in antiferromagnetic (AF) resonance experiments as
an apparent peculiar switching of the anisotropy at the transition from the
easy-axis type to the easy-plane one. We argue that this kind of spin-flop
transition is observed recently by K.Yu. Povarov et al., Phys. Rev. B 87,
214402 (2013) in Cu(pz)$_2$(ClO$_4$)$_2$ (where pz denotes pyrazine), one of
the best realizations of spin-1/2 Heisenberg AFs on square lattice having a
very small anisotropy. We show that the magnetic ordering changes at the
spin-flop transition in this material in the direction perpendicular to AF
square planes. We examine the microscopic mechanism of such behavior in
Cu(pz)$_2$(ClO$_4$)$_2$ and find that dipolar forces and extremely small
exchange coupling between spins from neighboring planes are responsible for it.


title: Social Learning over Weakly-Connected Graphs

abstract:
  In this paper, we study diffusion social learning over weakly-connected
graphs. We show that the asymmetric flow of information hinders the learning
abilities of certain agents regardless of their local observations. Under some
circumstances that we clarify in this work, a scenario of total influence (or
"mind-control") arises where a set of influential agents ends up shaping the
beliefs of non-influential agents. We derive useful closed-form expressions
that characterize this influence, and which can be used to motivate design
problems to control it. We provide simulation examples to illustrate the
results.


title: Relation between Euler's Elasticae and Sub-Riemannian Geodesics on SE(2)

abstract:
  In this note we describe a relation between Euler's elasticae and
sub-Riemannian geodesics on SE(2). Analyzing the Hamiltonian system of
Pontryagin maximum principle we show that these two curves coincide only in the
case when they are segments of a straight line.


title:
Pure density functional for strong correlations and the thermodynamic
  limit from machine learning

abstract:
  We use density-matrix renormalization group, applied to a one-dimensional
model of continuum Hamiltonians, to accurately solve chains of hydrogen atoms
of various separations and numbers of atoms. We train and test a
machine-learned approximation to $F[n]$, the universal part of the electronic
density functional, to within quantum chemical accuracy. Our calculation (a)
bypasses the standard Kohn-Sham approach, avoiding the need to find orbitals,
(b) includes the strong correlation of highly-stretched bonds without any
specific difficulty (unlike all standard DFT approximations) and (c) is so
accurate that it can be used to find the energy in the thermodynamic limit to
quantum chemical accuracy.


title: Surfaces in $\mathbb{P}^4$ lying on small degree hypersurfaces

abstract:
  Since the work of Ellingsrud and Peskine at the end of 1980s, it has been
known that, with the exception of a finite number of families, smooth compact
complex surfaces in $\mathbb{P}^4$ with prescribed Chern classes must lie on
hypersurfaces of degree $m\leq 5$. The study of surfaces lying on a small
degree hypersurface in $\mathbb{P}^4$---small meaning $\leq5$---seems to be a
way of obtaining empirical data leading to a better conceptual understanding of
surfaces in $\mathbb{P}^4$. From this perspective, two main issues are
considered in the paper:
  - an analogue of the Hartshorne-Lichtenbaum finiteness results for smooth
surfaces of general type contained in a small degree hypersurface in
$\mathbb{P}^4$,
  - a study of the irregularity of smooth surfaces contained in a small degree
hypersurface in $\mathbb{P}^4$.


title:
Efficiency bounds on thermoelectric transport in magnetic fields: The
  role of inelastic processes

abstract:
  We examine the efficiency of an effective two-terminal thermoelectric device
under broken time-reversal symmetry. The setup is derived from a three-terminal
thermoelectric device comprising a thermal terminal and two electronic
contacts, under a magnetic field. We find that breaking time-reversal symmetry
in the presence of the inelastic electron-phonon processes can significantly
enhance the figure of merit for delivering electric power by supplying heat
from a phonon bath, beyond the one for producing the electric power by
investing thermal power from the electronic heat current. The efficiency of
such a device is bounded by the non-negativity of the entropy production of the
original three-terminal junction. The efficiency at maximal power can be quite
close to the Carnot efficiency, but then the electric power vanishes.


title: Vector boson and charmonia measurements in $p$+Pb collisions with ATLAS

abstract:
  The production of electroweak bosons ($Z,\gamma$ and $W$) and charmonia is
sensitive to the initial-state geometry of heavy-ion collisions and to the
parton distribution function with its potential nuclear modification. Since
their leptonic decay products do not interact strongly, their kinematics are
unmodified by the strongly interacting medium, which can be created in a
heavy-ion collision. We report on the latest results of the ATLAS Collaboration
on electroweak boson and charmonia production in $p$+Pb collisions at
$\sqrt{s_{\rm NN}} = 5.02$ TeV. Production yields of $Z$ and $W$ bosons are
presented as a function of (pseudo-)rapidity in different centrality bins. The
forward-backward ratio of J/$\psi$ is shown as a function of transverse
momentum and center-of-mass rapidity.


title:
Large photon drag effect of intrinsic graphene induced by plasmonic
  evanescent field

abstract:
  Large photon drag effect of the massless Dirac Fermions in intrinsic graphene
is predicted for a graphene-on-plasmonic-layer system. The surface plasmons in
the plasmonic layer enlarge the wave number of photon for hundreds of time of
that in vacuum. The evanescent field of the surface plasmons generates
directional motion of carriers in the intrinsic graphene, because of the large
momentum transfer from the surface plasmon to the excited carriers. A model
Hamiltonian is developed on the assumption that the in-plane wavelength of the
surface plasmons is much smaller than the mean free path of the carriers. The
time evolution of density matrix is solved by perturbation method as well as
numerical integration. The non-diagonal density matrix elements with momentum
transfer lead to gauge current that is the optically driven macroscopic direct
current. The dependence of the macroscopic direct current on the incident
direction and intensity of the laser field is studied.


title: Arithmetical rank of binomial ideals

abstract:
  In this paper, we investigate the arithmetical rank of a binomial ideal $J$.
We provide lower bounds for the binomial arithmetical rank and the $J$-complete
arithmetical rank of $J$. Special attention is paid to the case where $J$ is
the binomial edge ideal of a graph. We compute the arithmetical rank of such an
ideal in various cases.


title: Propagation of Acoustic Waves in Troposphere and Stratosphere

abstract:
  Acoustic waves are those waves which travel with the speed of sound through a
medium. H. Lamb has derived a cutoff frequency for stratified and isothermal
medium for the propagation of acoustic waves. In order to find the cutoff
frequency many methods were introduced after Lamb's work. In this paper, we
have chosen the method to determine cutoff frequencies for acoustic waves
propagating in non-isothermal media. This turning point frequency method can be
applied to various atmospheres like solar atmosphere, stellar atmosphere,
earth's atmosphere etc. Here, we have analytically derived the cutoff frequency
and have graphically analyzed and compared with the Lamb's cut-off frequencyfor
earth's troposphere, lower and upper stratosphere.


title:
Quaternion based generalization of Chern-Simons theories in arbitrary
  dimensions

abstract:
  A generalization of Chern-Simons gauge theory is formulated in any dimension
and arbitrary gauge group where gauge fields and gauge parameters are
differential forms of any degree. The quaternion algebra structure of this
formulation is shown to be equivalent to a three Z(2)-gradings structure, thus
clarifying the quaternion role in a previous formulation.


title:
A note on the definition of Bayesian Nash equilibrium of a mechanism
  when strategies of agents are costly actions

abstract:
  In mechanism design theory, a designer would like to implement a desired
social choice function which specifies her favorite outcome for each possible
profile of agents' types. To do so, the designer constructs a mechanism which
describes each agent's feasible strategy set and the outcome function.
Generally speaking, each agent's strategy in a mechanism has two possible
formats: an action, or a message. In this paper, we focus on the former format
and claim that the notion of Bayesian Nash equilibrium of a mechanism should be
based on a profit function instead of the conventional utility function when
strategies of agents are costly actions. Next, we derive the main result: Given
a social choice function which can be implemented by an indirect mechanism in
Bayesian Nash equilibrium, if all strategies of agents are costly actions, then
it cannot be inferred that there exists a direct mechanism that can truthfully
implement the social choice function in Bayesian Nash equilibrium.


title:
Identifying conductivity in electrical impedance tomography with total
  variation regularization

abstract:
  In this paper we investigate the problem of identifying conductivity in
electrical impedance tomography from one boundary measurement. A variational
method with total variation regularization is here proposed to tackle this
problem. We discretize the PDE as well as the conductivity with piecewise
linear, continuous finite elements. We prove the stability and convergence of
this technique. For the numerical solution we propose a projected Armijo
algorithm. Finally, a numerical experiment is presented to illustrate our
theoretical results.


title: Hidden Local Symmetry and Beyond

abstract:
  Gerry Brown was a godfather of our hidden local symmetry (HLS) for the vector
meson from the birth of the theory throughout his life. The HLS is originated
from very nature of the nonlinear realization of the symmetry G based on the
manifold G/H, and thus is universal to any physics based on the nonlinear
realization. Here I focus on the Higgs Lagrangian of the Standard Model (SM),
which is shown to be equivalent to the nonlinear sigma model based on G/H=
SU(2)_L x SU(2)_R/SU(2)_V with additional symmetry, the nonlinearly realized
scale symmetry. Then the SM does have a dynamical gauge boson of the SU(2)_V
HLS, "SM rho meson", in addition to the Higgs as a pseudo dilaton as well as
the NG bosons to be absorbed into the W and Z. Based on the recent work done
with S. Matsuzaki and H. Ohki, I discuss a novel possibility that the SM rho
meson acquires kinetic term by the SM dynamics itself, which then stabilizes
the skyrmion dormant in the SM as a viable candidate for the dark matter, what
we call "Dark SM skyrmion (DSMS)".


title:
Temperature effect on lattice and electronic structures of WTe$_2$ from
  first-principles study

abstract:
  Tungsten ditelluride (WTe$_2$) exhibits extremely large and unsaturated
magnetoresistance (MR). Due to the large spatially extensions of Te-5p and W-5d
orbitals, the electronic properties of WTe$_2$ are sensitive to the lattice
structures, which can probably affect the strongly temperature dependent MR
found in experiment. Based on first-principle calculations, we investigate the
temperature effect on the lattice and electronic structures of WTe$_2$. Our
numerical results show that the thermal expansion coefficients of WTe$_2$ are
highly anisotropic and considerably large. However, the temperature (less than
300 K) has ignorable effect on the Fermi surface of WTe$_2$. Our theoretical
results clarify that the thermal expansion is not the main reason of the
temperature-induced rapid decrease of magnetoresistance.


title:
Dynamic Proximity-aware Resource Allocation in Vehicle-to-Vehicle (V2V)
  Communications

abstract:
  In this paper, a novel proximity and load-aware resource allocation for
vehicle-to-vehicle (V2V) communication is proposed. The proposed approach
exploits the spatio-temporal traffic patterns, in terms of load and vehicles'
physical proximity, to minimize the total network cost which captures the
tradeoffs between load (i.e., service delay) and successful transmissions while
satisfying vehicles's quality-of-service (QoS) requirements. To solve the
optimization problem under slowly varying channel information, it is decoupled
the problem into two interrelated subproblems. First, a dynamic clustering
mechanism is proposed to group vehicles in zones based on their traffic
patterns and proximity information. Second, a matching game is proposed to
allocate resources for each V2V pair within each zone. The problem is cast as
many-to-one matching game in which V2V pairs and resource blocks (RBs) rank one
another in order to minimize their service delay. The proposed game is shown to
belong to the class of matching games with externalities. To solve this game, a
distributed algorithm is proposed using which V2V pairs and RBs interact to
reach a stable matching. Simulation results for a Manhattan model shown that
the proposed scheme yields a higher percentage of V2V pairs satisfying QoS as
well as significant gain in terms of the signal-to-interference-plus-noise
ratio (SINR) as compared to a state-of-art resource allocation baseline.


title:
Gate voltage control of the $AlO_x$/$SrTiO_3$ interface electrical
  properties

abstract:
  Electron-beam deposition of an insulating granular aluminium or of an
off-stoichiometric amorphous alumina layer on a $SrTiO_3$ surface is a simple
way to get a metallic interface from insulating materials. No heating nor
specific preparation of the $SrTiO_3$ surface are needed. In this paper, we
investigate how the electrical properties of this interface can be tuned by the
use of a back gate voltage (electrical field through the $SrTiO_3$ substrate).
We demonstrate that the slow field-effect observed at room temperature can be
used to tune reversibly and in a controlled way the low temperature electrical
properties of the interface. In particular, important parameters of a
transistor such as the amplitude of the resistance response to gate voltage
changes or the existence of an "on" or an "off" state at zero gate voltage and
at low temperature can be adjusted in a single sample. This method should be
applicable to any $SrTiO_3$-based interface in which oxygen vacancies are
involved and might provide a powerful way to study the metal or superconductor
insulator transition observed in such systems.


title: Li-Yorke sensitive and weak mixing dynamical systems

abstract:
  Akin and Kolyada in 2003 [E. Akin, S. Kolyada, Li-Yorke sensitivity,
Nonlinearity 16 (2003) 1421 - 1433] introduced the notion of Li-Yorke
sensitivity. They proved that every weak mixing system $(X, T)$, where $X$ is a
compact metric space and $T$ a continuous map of $X$ is Li-Yorke sensitive. An
example of Li-Yorke sensitive system without weak mixing factors was given in
[M. \v{C}iklov\'a, Li-Yorke sensitive minimal maps, Nonlinearity 19 (2006) 517
- 529] (see also [M. \v{C}iklov\'a-Ml\'{\i}chov\'a, Li-Yorke sensitive minimal
maps II, Nonlinearity 22 (2009) 1569 -1573]). In their paper, Akin and Kolyada
conjectured that every minimal system with a weak mixing factor, is Li-Yorke
sensitive. We provide arguments supporting this conjecture though the proof
seems to be difficult.


title:
Magnetic phases and unusual topological electronic structures of Weyl
  semimetals in strong interaction limit

abstract:
  The interplay of electronic band structures and electron-electron
interactions is known to brew new phases in condensed matter. In this paper, we
investigate thermodynamic phases and corresponding electronic structures of the
Weyl semimetal in the strong onsite Coulomb interaction limit. Based on a
minimum model of the Weyl semimetal with two linear Weyl nodes, it is shown
that generically the Weyl semimetal becomes magnetic in the presence of
interactions. In particular, it is shown that the Dzyaloshinskii-Moriya
exchange interaction is generally induced so that the A-type antiferromagnetic
(A-AFM) phase and the spiral spin density wave (SSDW) states are two generic
phases. Furthermore, we find that Weyl nodes proliferate and it is possible to
doubly enhance the unusual properties of non-interacting Weyl semimetals
through the realization of double-Weyl nodes in strong correlation limit.
Specifically, it is shown that in the SSDW phase, linear Weyl nodes are tuned
into double-Weyl nodes with the corresponding charges being $\pm 2$. As the
spin-orbit coupling increases, a quantum phase transition occurs with the SSDW
phase being turned into an A-AFM phase and at the same time, double-Weyl nodes
are disintegrated into two pairs of linear Weyl nodes. Our results reveal the
unusual interplay between the topology of electronic structures and magnetism
in strongly correlated phases of Weyl semimetals.


title: Shortcuts to adiabaticity in the double well

abstract:
  Shortcuts to adiabaticity are alternative fast processes that reproduce the
same final populations, or even the same final state, as the adiabatic process
in a finite, shorter time. Many of the existing approaches to design shortcuts,
and even new ones have been used throughout this Thesis in the double well
potential. These techniques have allowed us to obtain a great benefit in
processes as varied as matter-wave splitting, multiplexing/ demultiplexing,
beam splitters, cotunneling, population inversion, waveguide optimization,
Tonks-Girardeau gas manipulation and bias inversion.


title: On the local closure of clones on countable sets

abstract:
  We consider clones on countable sets. If such a clone has quasigroup
operations, is locally closed and countable, then there is a function $f :
\mathbb{N} \to \mathbb{N}$ such that the $n$-ary part of $C$ is equal to the
$n$-ary part of $\mathrm{Pol}\,\mathrm{Inv}^{[f(n)]} C$, where
$\mathrm{Inv}^{[f(n)]} C$ denotes the set of $f(n)$-ary invariant relations of
$C$.


title: Evolution of the Magnetic Field Distribution of Active Regions

abstract:
  Aims. Although the temporal evolution of active regions (ARs) is relatively
well understood, the processes involved continue to be the subject of
investigation. We study how the magnetic field of a series of ARs evolves with
time to better characterise how ARs emerge and disperse. Methods. We examine
the temporal variation in the magnetic field distribution of 37 emerging ARs. A
kernel density estimation plot of the field distribution was created on a
log-log scale for each AR at each time step. We found that the central portion
of the distribution is typically linear and its slope was used to characterise
the evolution of the magnetic field. Results. The slopes were seen to evolve
with time, becoming less steep as the fragmented emerging flux coalesces. The
slopes reached a maximum value of ~ -1.5 just before the time of maximum flux
before becoming steeper during the decay phase towards the quiet Sun value of ~
-3. This behaviour differs significantly from a classical diffusion model,
which produces a slope of -1. These results suggest that simple classical
diffusion is not responsible for the observed changes in field distribution,
but that other processes play a significant role in flux dispersion.
Conclusions. We propose that the steep negative slope seen during the late
decay phase is due to magnetic flux reprocessing by (super)granular convective
cells.


title: Cosmic backreaction and Gauss's law

abstract:
  Cosmic backreaction refers to the general question of whether a homogeneous
and isotropic cosmological model is able to predict the correct expansion
dynamics of our inhomogeneous Universe. One aspect of this issue concerns the
validity of the continuous approximation: does a system of point masses expand
the same way as a fluid does? This article shows that it is not exactly the
case in Newtonian gravity, although the associated corrections vanish in an
infinite Universe. It turns out that Gauss's law is a key ingredient for such
corrections to vanish. Backreaction, therefore, generically arises in
alternative theories of gravitation, which threatens the trustworthiness of
their cosmological tests. This phenomenon is illustrated with a toy model of
massive gravity.


title: Search for the decay of nature's rarest isotope $^{\rm {180m}}$Ta

abstract:
  $^{\rm {180m}}$Ta is the rarest naturally occurring quasi-stable isotope and
the longest lived metastable state which is known. Its possible decay via the
$\beta^-$ or the electron capture channel has never been observed. This article
presents a search for the decay of $^{\rm {180m}}$Ta with an ultra low
background Sandwich HPGe gamma spectrometry setup in the HADES underground
laboratory. No signal is observed and improved lower partial half-life limits
are set with a Bayesian analysis to $5.8\cdot10^{16}$ yr for the $\beta^-$
channel and $2.0\cdot10^{17}$ yr for the electron capture channel (90%
credibility). The total half-life of $^{\rm {180m}}$Ta is longer than
$4.5\cdot10^{16}$ yr. This is more than a factor of two improvement compared to
previous searches.


title: Transference and preservation of uniqueness

abstract:
  Motivated by the notion of a set of uniqueness in a locally compact group
$G$, we introduce and study ideals of uniqueness in the Fourier algebra $A(G)$
of $G$, and their accompanying operator version, masa-bimodules of uniqueness.
We establish a transference between the two notions, and use this result to
show that the property of being an ideal of uniqueness is preserved under
natural operations.


title:
Stability of intersections of graphs in the plane and the van Kampen
  obstruction

abstract:
  A map $\varphi:K\to R^2$ of a graph $K$ is approximable by embeddings, if for
each $\varepsilon>0$ there is an $\varepsilon$-close to $\varphi$ embedding
$f:K\to R^2$. Analogous notions were studied in computer science under the
names of cluster planarity and weak simplicity. This short survey is intended
not only for specialists in the area, but also for mathematicians from other
areas. We present criteria for approximability by embeddings (P. Minc, 1997, M.
Skopenkov, 2003) and their algorithmic corollaries. We introduce the van Kampen
(or Hanani-Tutte) obstruction for approximability by embeddings and discuss its
completeness. We discuss analogous problems of moving graphs in the plane apart
(cf. S. Spiez and H. Torunczyk, 1991) and finding closest embeddings (H.
Edelsbrunner). We present higher dimensional van Kampen obstruction, its
completeness result and algorithmic corollary (D. Repovs and A. Skopenkov,
1998).


title: Complex powers for a class of infinite order hypoelliptic operators

abstract:
  We prove the complex powers of a class of infinite order hypoelliptic
pseudodifferential operators can always be represented as hypoelliptic
pseudodifferential operators modulo ultrasmoothing operators. We apply this
result to the study of semigroups generated by square roots of non-negative
hypoelliptic infinite order operators. For this purpose, we derive precise
estimates of the corresponding heat kernel.


title:
Spatial correlations of the spontaneous decay rate as a probe of dense
  and correlated disordered materials

abstract:
  We study theoretically and numerically a new kind of spatial correlation for
waves in disordered media. We define $C_{\Gamma}$ as the correlation function
of the fluorescent decay rate of an emitter at two different positions inside
the medium. We show that the amplitude and the width of $C_{\Gamma}$ provide
decoupled information on the structural correlation of the disordered medium
and on the local environment of the emitter. This result may stimulate the
emergence of new imaging and sensing modalities in complex media.


title:
A hierarchical neural stimulation model for pain relief by variation of
  coil design parameters

abstract:
  Neural stimulation represents a powerful technique for neural disorder
treatment. This paper deals with optimization of coil design parameters to be
used during stimulation for modulation of neuronal firing to achieve pain
relief. Pain mechanism is briefly introduced and a hierarchical stimulation
model from coil stimulation to neuronal firing is proposed. Electromagnetic
field distribution for circular, figure of 8 and Magnetic resonance coupling
figure of 8 coils are analyzed with respect to the variation of stimulation
parameters such as distance between coils, stimulation frequency, number of
turns and radius of coils. MRC figure of 8 coils were responsible for inducing
the maximum Electric field for same amount of driving current in coils.
Variation of membrane potential, ion channel conductance and neuronal firing
frequency in a pyramidal neuronal model due to magnetic and acoustic
stimulation are studied. The frequency of neuronal firing for cortical neurons
is higher during pain state, compared to no pain state. Lowest neuronal firing
frequency 18 Hz was found for MRC figure of 8 coils, compared to 30 Hz for
circular coils. Therefore, MRC figure of 8 coils are most effective for
modulation of neuronal firing, thereby achieving pain relief in comparison to
other coils considered in this study


title:
Crowd Behaviour during High-Stress Evacuations in an Immersive Virtual
  Environment

abstract:
  Understanding the collective dynamics of crowd movements during stressful
emergency situations is central to reducing the risk of deadly crowd disasters.
Yet, their systematic experimental study remains a challenging open problem due
to ethical and methodological constraints. In this paper, we demonstrate the
viability of shared 3D virtual environments as an experimental platform for
conducting crowd experiments with real people. In particular, we show that
crowds of real human subjects moving and interacting in an immersive 3D virtual
environment exhibit typical patterns of real crowds as observed in real-life
crowded situations. These include the manifestation of social conventions and
the emergence of self-organized patterns during egress scenarios. High-stress
evacuation experiments conducted in this virtual environment reveal movements
characterized by mass herding and dangerous overcrowding as they occur in crowd
disasters. We describe the behavioral mechanisms at play under such extreme
conditions and identify critical zones where overcrowding may occur.
Furthermore, we show that herding spontaneously emerges from a density effect
without the need to assume an increase of the individual tendency to imitate
peers. Our experiments reveal the promise of immersive virtual environments as
an ethical, cost-efficient, yet accurate platform for exploring crowd behaviour
in high-risk situations with real human subjects.


title:
Large-scale multiscale particle models in inhomogeneous domains:
  modelling and implementation

abstract:
  In this thesis, we develop multiscale models for particle simulations in
population dynamics. These models are characterised by prescribing particle
motion on two spatial scales: microscopic and macroscopic. At the microscopic
level, each particle has its own mass, position and velocity, while at the
macroscopic level the particles are interpolated to a continuum quantity whose
evolution is governed by a system of transport equations. This way, one can
prescribe various types of interactions on a global scale, whilst still
maintaining high simulation speed for a large number of particles. In addition,
the interplay between particle motion and interaction is well tuned in both
regions of low and high densities.
  We analyse links between models on these two scales and prove that under
certain conditions, a system of interacting particles converges to a nonlinear
coupled system of transport equations. We use this as a motivation to derive a
model defined on both modelling scales and prescribe the intercommunication
between them. Simulation takes place in inhomogeneous domains with arbitrary
conditions at inflow and outflow boundaries. We realise this by modelling
obstacles, sources and sinks. Integrating these aspects into the simulation
requires a route planning algorithm for the particles. Several algorithms are
considered and evaluated on accuracy, robustness and efficiency.
  All aspects mentioned above are combined in a novel open source prototyping
simulation framework called Mercurial. This computational framework allows the
design of geometries and is built for high performance when large numbers of
particles are involved. Mercurial supports various types of inhomogeneities and
global systems of equations.
  We apply our framework to simulate scenarios in crowd dynamics. We compare
our results with test cases from literature to assess the quality of the
simulations.


title: Logarithmic co-Higgs bundles

abstract:
  In this article we introduce a notion of logarithmic co-Higgs sheaves
associated to a simple normal crossing divisor on a projective manifold, and
show their existence with nilpotent co-Higgs fields for fixed ranks and second
Chern classes. Then we deal with various moduli problems with logarithmic
co-Higgs sheaves involved, such as coherent systems and holomorphic triples,
specially over algebraic curves of low genus.


title: Hacking of the AES with Boolean Functions

abstract:
  One of the major issues of cryptography is the cryptanalysis of cipher
algorithms. Cryptanalysis is the study of methods for obtaining the meaning of
encrypted information, without access to the secret information that is
normally required. Some mechanisms for breaking codes include differential
cryptanalysis, advanced statistics and brute-force.
  Recent works also attempt to use algebraic tools to reduce the cryptanalysis
of a block cipher algorithm to the resolution of a system of quadratic
equations describing the ciphering structure.
  In our study, we will also use algebraic tools but in a new way: by using
Boolean functions and their properties. A Boolean function is a function from
$F_2^n\to F_2$ with $n>1$, characterized by its truth table. The arguments of
Boolean functions are binary words of length $n$. Any Boolean function can be
represented, uniquely, by its algebraic normal form which is an equation which
only contains additions modulo 2 - the XOR function - and multiplications
modulo 2 - the AND function.
  Our aim is to describe the AES algorithm as a set of Boolean functions then
calculate their algebraic normal forms by using the M\"obius transforms. After,
we use a specific representation for these equations to facilitate their
analysis and particularly to try a combinatorial analysis. Through this
approach we obtain a new kind of equations system. This equations system is
more easily implementable and could open new ways to cryptanalysis.


title:
Discrete Boltzmann model of shallow water equations with polynomial
  equilibria

abstract:
  A type of discrete Boltzmann model for simulating shallow water flows is
derived by using the Hermite expansion approach. Through analytical analysis,
we study the impact of truncating distribution function and discretizing
particle velocity space. It is found that the convergence behavior of expansion
is nontrivial while the conservation laws are naturally satisfied. Moreover,
the balance of source terms and flux terms for steady solutions is not
sacrificed. Further numerical validations show that the capability of
simulating supercritical flows is enhanced by employing higher order expansion
and quadrature.


title: Non-adiabatic quantum phase transition in a trapped spinor condensate

abstract:
  We study the effect of an external harmonic trapping potential on an outcome
of the non-adiabatic quantum phase transition from an antiferromagnetic to a
phase-separated state in a spin-1 atomic condensate. Previously, we
demonstrated that the dynamics of an untrapped system exhibits double
universality with two different scaling laws appearing due to conservation of
magnetization. We show that in the presence of a trap double universality
persists. However, the corresponding scaling exponents are strongly modified by
transfer of local magnetization across the system. The values of these
exponents cannot be explained by the effect of causality alone, as in the
spinless case. We derive the appropriate scaling laws based on a slow
diffusive-drift relaxation process in the local density approximation.


title:
Small Extended Formulation for Knapsack Cover Inequalities from Monotone
  Circuits

abstract:
  Initially developed for the min-knapsack problem, the knapsack cover
inequalities are used in the current best relaxations for numerous
combinatorial optimization problems of covering type. In spite of their
widespread use, these inequalities yield linear programming (LP) relaxations of
exponential size, over which it is not known how to optimize exactly in
polynomial time. In this paper we address this issue and obtain LP relaxations
of quasi-polynomial size that are at least as strong as that given by the
knapsack cover inequalities.
  For the min-knapsack cover problem, our main result can be stated formally as
follows: for any $\varepsilon >0$, there is a $(1/\varepsilon)^{O(1)}n^{O(\log
n)}$-size LP relaxation with an integrality gap of at most $2+\varepsilon$,
where $n$ is the number of items. Prior to this work, there was no known
relaxation of subexponential size with a constant upper bound on the
integrality gap.
  Our construction is inspired by a connection between extended formulations
and monotone circuit complexity via Karchmer-Wigderson games. In particular,
our LP is based on $O(\log^2 n)$-depth monotone circuits with fan-in~$2$ for
evaluating weighted threshold functions with $n$ inputs, as constructed by
Beimel and Weinreb. We believe that a further understanding of this connection
may lead to more positive results complementing the numerous lower bounds
recently proved for extended formulations.


title:
On mean values of mollifiers and L-functions associated to primitive
  cusp forms

abstract:
  We study the second moment of the L-function associated to a holomorphic
primitive cusp form of even weight perturbed by a new family of mollifiers.
This family is a natural extension of the mollifers considered by Conrey and by
Bui, Conrey and Young. As an application, we improve the current lower bound on
critical zeros of holomorphic primitive cusp forms.


title:
Solutions to overdetermined elliptic problems in nontrivial exterior
  domains

abstract:
  In this paper we construct nontrivial exterior domains $\Omega \subset
\mathbb{R}^N$, for all $N\geq 2$, such that the problem $$\left\{ {ll} -\Delta
u +u -u^p=0,\ u >0 & \mbox{in }\; \Omega, {1mm]
  \ u= 0 & \mbox{on }\; \partial \Omega, [1mm]
  \ \frac{\partial u}{\partial \nu} = \mbox{cte} & \mbox{on }\; \partial
\Omega, \right.$$ admits a positive bounded solution. This result gives a
negative answer to the Berestycki-Caffarelli-Nirenberg conjecture on
overdetermined elliptic problems in dimension 2, the only dimension in which
the conjecture was still open. For higher dimensions, different counterexamples
have been found in the literature; however, our example is the first one in the
form of an exterior domain.


title:
Measurement of ion and electron drift velocity and electronic attachment
  in air for ionization chambers

abstract:
  Air-ionization chambers have been used in radiotherapy and particle therapy
for decades. However, fundamental parameters in action in the detector
responses are sparsely studied. In this work we aimed to measure the electronic
attachment, electrons and ions mobilities of an ionization chamber (IC) in air.
The main idea is to extract these from the actual response of the IC to a
single ionizing particle in order to insure that they were measured in the same
condition they are to be used while neglecting undesired phenomena:
recombination and space charge effect. The non-standard signal shape analysis
performed here were also confronted to a more standard drift chamber
measurements using time-of-flight. It was found that both detectors displayed
compatible results concerning positive and negative ions drift velocities where
literature data is well spread out. In the same time, electron attachment
measurements sit in the middle of known measurements while electron drift
velocities seemed to show an offset compared to the well known and modeled
data.


title:
Analytical $O(\alpha_s)$ corrections to the beam frame double-spin
  density matrix elements of $e^+e^-\to t\bar t$

abstract:
  We provide analytical results for the $O(\alpha_s)$ corrections to the
double-spin density matrix elements in the reaction $e^+e^-\to t\bar t$. These
concern the elements $ll$, $lt$, $ln$, $tt$, $tn$, and $nn$ of the double-spin
density matrix elements where $l,t,n$ stand for longitudinal, transverse and
normal orientations with respect to the beam frame spanned by the electron and
the top quark momentum.


title: Field-effect transistors of high-mobility few-layer SnSe$_{2}$

abstract:
  We report the transport properties of mechanically exfoliated few-layer
SnSe$_{2}$ flakes, whose mobility is found with four probe measurements to be ~
85 cm$^{2}$V$^{-1}$s$^{-1}$ at 300 K, higher than those of the majority of
few-layer transitional metal dichalcogenides (TMDs). The mobility increases
strongly with decreased temperature, indicating a phonon limited transport. The
conductivity of the semiconducting SnSe$_{2}$ shows a metallic behavior, which
is explained by two competing factors involving the different temperature
dependence of mobility and carrier density. The Fermi level is found to be 87
meV below the conduction band minima (CBM) at 300 K and 12 meV below the CBM at
78 K, resulting from a heavy n-type doping. Previous studies have found
SnSe$_{2}$ field-effect transistors (FETs) to be very difficult to turn off. We
find the limiting factor to be the flake thickness compared with the maximum
depletion width. With fully depleted devices, we are able to achieve a current
on-off ratio of ~10$^{5}$. These results demonstrate the great potential of
SnSe2 as a two dimensional (2D) semiconducting material and are helpful for our
understanding of other heavily doped 2D materials.


title:
Dynamical and statistical phenomena of circulation and heat transfer in
  periodically forced rotating turbulent Rayleigh-Benard convection

abstract:
  In this paper, we present results from an experimental study into turbulent
Rayleigh-Benard convection forced externally by periodically modulated
unidirectional rotation rates. We find that the azimuthal rotation velocity
$\dot{\theta}$(t) and thermal amplitude $\delta$(t) of the large-scale
circulation (LSC) are modulated by the forcing, exhibiting a variety of
dynamics including increasing phase delays and a resonant peak in the amplitude
of $\dot{\theta}$(t). We also focus on the influence of modulated rotation
rates on the frequency of occurrence $\eta$ of stochastic
cessation/reorientation events, and on the interplay between such events and
the periodically modulated response of $\dot{\theta}$(t). Here we identify a
mechanism by which $\eta$ can be amplfied by the modulated response and these
normally stochastic events can occur with high regularity. We provide a
modeling framework that explains the observed amplitude and phase responses,
and extend this approach to make predictions for the occurrence of cessation
events and the probability distributions of $\dot{\theta}$(t) and $\delta$(t)
during different phases of a modulation cycle, based on an adiabatic approach
that treats each phase separately. Lastly, we show that such periodic forcing
has consequences beyond influencing LSC dynamics, by investigating how it can
modify the heat transport even under conditions where the Ekman pumping effect
is predominant and strong enhancement of heat transport occurs. We identify
phase and amplitude responses of the heat transport, and show how increased
modulations influence the average Nusselt number.


title:
Methods for Finding Analytic Solutions for Time Dependent Two-Level
  Quantum Systems and Its Generalizations

abstract:
  Two-level systems are one of the most important quantum systems and they form
the basis of quantum computers. We briefly look at the traditional approach to
two-level systems with an external driving field as well as those subjected to
noise. This project is aimed at studying two specific methods for obtaining
analytic solutions for two-level systems. One of the methods enables us to
obtain analytic solutions for driven time-dependent two-level systems while the
other attempts to give exact solution of qubit decoherence using a transfer
matrix method. A thorough study of both papers is done and results are
reproduced. The latter method is generalized for a qutrit system as well as a
two qubit system subjected to noise. A general method is formally derived for
an N-dimensional quantum system and the difficulties in applying the method in
real life systems is discussed.


title:
The Penalty Free Nitsche Method and Nonconforming Finite Elements for
  the Signorini Problem

abstract:
  We design and analyse a Nitsche method for contact problems. Compared to the
seminal work of Chouly and Hild (A Nitsche-based method for unilateral contact
problems: numerical analysis. SIAM J. Numer. Anal. 51 (2013), no. 2) our method
is constructed by expressing the contact conditions in a nonlinear function for
the displacement variable instead of the lateral forces. The contact condition
is then imposed using the nonsymmetric variant of Nitsche's method that does
not require a penalty term for stability. Nonconforming piecewise affine
elements are considered for the bulk discretization. We prove optimal error
estimates in the energy norm.


title: Channelization in Porous Media driven by Erosion and Deposition

abstract:
  We develop and validate a new model to study simultaneous erosion and
deposition in three-dimensional porous media. We study the changes of the
porous structure induced by the deposition and erosion of matter on the solid
surface and find that when both processes are active, channelization in the
porous structure always occurs. The channels can be stable or only temporary
depending mainly on the driving mechanism. Whereas a fluid driven by a constant
pressure drop in general does not form steady channels, imposing a constant
flux always produces stable channels within the porous structure. Furthermore
we investigate how changes of the local deposition and erosion properties
affect the final state of the porous structure, finding that the larger the
range of wall shear stress for which there is neither erosion nor deposition,
the more steady channels are formed in the structure.


title:
Hamilton's equations of motion of a vortex filament in the rotating
  Bose-Einstein condensate and their "soliton" solutions

abstract:
  The equation of motion of a quantized vortex filament in a trapped
Bose-Einstein condensate [A. A. Svidzinsky and A. L. Fetter, Phys. Rev. A {\bf
62}, 063617 (2000)] has been generalized to the case of an arbitrary anharmonic
anisotropic rotating trap and presented in a variational form. For condensate
density profiles of the form $\rho=f(x^2+y^2+\mbox{Re\,}\Psi(x+iy))$ in the
presence of the plane of symmetry $y=0$, the solutions $x(z)$ describing
stationary vortices of U and S types coming to the surface and solitary waves
have been found in quadratures. Analogous three-dimensional configurations of
the vortex filament uniformly moving along the $z$ axis have also been found in
strictly cylindrical geometry. The dependence of solutions on the form of the
function $f(q)$ has been analyzed.


title:
Interaction between the Supernova Remnant HB 3 and the Nearby
  Star-Forming Region W3

abstract:
  We performed millimeter observations in CO lines toward the supernova remnant
(SNR) HB 3. Substantial molecular gas around -45 km s^-1 is detected in the
conjunction region between the SNR HB 3 and the nearby W3 complex. This
molecular gas is distributed along the radio continuum shell of the remnant.
Furthermore, the shocked molecular gas indicated by line wing broadening
features is also distributed along the radio shell and inside it. By both
morphological correspondence and dynamical evidence, we confirm that the SNR HB
3 is interacting with the -45 km s^-1 molecular cloud (MC), in essence, with
the nearby H II region/MC complex W3. The red-shifted line wing broadening
features indicate that the remnant is located at the nearside of the MC. With
this association, we could place the remnant at the same distance as the W3/W4
complex, which is 1.95 +- 0.04 kpc. The spatial distribution of aggregated
young stellar object candidates (YSOc) shows a correlation to the shocked
molecular strip associated with the remnant. We also find a binary clump of CO
at (l = 132.94 deg, b = 1.12 deg) around -51.5 km s^-1 inside the projected
extent of the remnant, and it is associated with significant mid-infrared
(mid-IR) emission. The binary system also has a tail structure resembling the
tidal tails of interacting galaxies. According to the analysis of CO emission
lines, the larger clump in this binary system is about stable, and the smaller
clump is significantly disturbed.


title:
Bi-stability in single impurity Anderson model with strong
  electron-phonon interaction (polaron regime)

abstract:
  We consider a single impurity Anderson model (SIAM) in which the quantum
dot(QD) is strongly coupled to a phonon bath in polaron regime. This coupling
results in an effective e-e attraction. By computing the self energies using a
current conserving approximation which is up to second order in this effective
attraction, we show that if the interaction is strong enough, in non
particle-hole(PH) symmetric case, the system would be bi-stable and we have
hysteresis loop in the I-V characteristic. Moreover, the system shows negative
differential conductance in some bias voltage intervals.


title:
nsroot: Minimalist Process Isolation Tool Implemented With Linux
  Namespaces

abstract:
  Data analyses in the life sciences are moving from tools run on a personal
computer to services run on large computing platforms. This creates a need to
package tools and dependencies for easy installation, configuration and
deployment on distributed platforms. In addition, for secure execution there is
a need for process isolation on a shared platform. Existing virtual machine and
container technologies are often more complex than traditional Unix utilities,
like chroot, and often require root privileges in order to set up or use. This
is especially challenging on HPC systems where users typically do not have root
access. We therefore present nsroot, a lightweight Linux namespaces based
process isolation tool. It allows restricting the runtime environment of data
analysis tools that may not have been designed with security as a top priority,
in order to reduce the risk and consequences of security breaches, without
requiring any special privileges. The codebase of nsroot is small, and it
provides a command line interface similar to chroot. It can be used on all
Linux kernels that implement user namespaces. In addition, we propose combining
nsroot with the AppImage format for secure execution of packaged applications.
nsroot is open sourced and available at: https://github.com/uit-no/nsroot


title:
From the discrete Weyl -- Wigner formalism for symmetric ordering to a
  number -- phase Wigner function

abstract:
  The general Weyl -- Wigner formalism in finite dimensional phase spaces is
investigated. Then this formalism is specified to the case of symmetric
ordering of operators in an odd -- dimensional Hilbert space. A respective
Wigner function on the discrete phase space is found and the limit, when the
dimension of Hilbert space tends to infinity, is considered. It is shown that
this limit gives the number -- phase Wigner function in quantum optics.
Analogous results for the `almost' symmetric ordering in an even -- dimensional
Hilbert space are obtained. Relations between the discrete Wigner functions
introduced in our paper and some other discrete Wigner functions appearing in
literature are studied.


title: Axion Haloscopes with Toroidal Geometry at CAPP/IBS

abstract:
  The present state of the art axion haloscope employs a cylindrical resonant
cavity in a solenoidal field. We, the Center for Axion and Precision Physics
Research (CAPP) of the Institute for Basic Science (IBS) in Korea, are also
pursuing halo axion discovery using this cylindrical geometry. However, the
presence of end caps of cavities increases challenges as we explore higher
frequency regions for the axion at above 2 GHz. To overcome these challenges we
exploit a toroidal design of cavity and magnetic field. A toroidal geometry
offers several advantages, two of which are a larger volume for a given space
and greatly reduced fringe fields which interfere with our preamps, in
particular the planned quantum-based devices. We introduce the concept of
toroidal axion haloscopes and present ongoing research activities and plans at
CAPP/IBS.


title: On the Evolution of High-Redshift Active Galactic Nuclei

abstract:
  We build a simple physical model to study the high-redshift active galactic
Nucleus (AGN) evolution within the co-evolution framework of central black
holes (BHs) and their host galaxies. The correlation between the circular
velocity of a dark halo $V_c$ and the velocity dispersion of a galaxy $\sigma$
is used to link the dark matter halo mass and BH mass. The dark matter halo
mass function is converted to the BH mass function for any given redshift. The
high-redshift optical AGN luminosity functions (LFs) are constructed. At $z\sim
4$, the flattening feature is not shown at the faint end of the optical AGN LF.
This is consistent with observational results. If the optical AGN LF at $z\sim
6$ can be reproduced in the case in which central BHs have the
Eddington-limited accretion, it is possible for the AGN lifetime to have a
small value of $2\times 10^5$ yrs. The X-ray AGN LFs and X-ray AGN number
counts are also calculated at $2.0<z<5.0$ and $z>3$, respectively, using the
same parameters adopted in the calculation for the optical AGN LF at $z\sim 4$.
It is estimated that about 30 AGNs per $\rm{deg}^2$ at $z>6$ can be detected
with a flux limit of $3\times 10^{-17}~\rm{erg~cm^{-2}~s^{-1}}$ in the $0.5-2$
keV band. Additionally, the cosmic reionization is also investigated. The
ultraviolet photons emitted from the high-redshift AGNs mainly contribute to
the cosmic reionization, and the central BHs of the high-redshift AGNs have a
mass range of $10^6-10^8M_\odot$. We also discuss some uncertainties in both
the AGN LFs and AGN number counts originating from the $M_{\rm{BH}}-\sigma$
relation, Eddington ratio, AGN lifetime, and X-ray attenuation in our model.


title: Efficiency of a Stochastic Search with Punctual and Costly Restarts

abstract:
  The mean completion time of a stochastic process may be rendered finite and
minimised by a judiciously chosen restart protocol, which may either be
stochastic or deterministic. Here we study analytically an arbitrary stochastic
search subject to an arbitrary restart protocol, each characterised by a
distribution of waiting times. By a direct enumeration of paths we construct
the joint distribution of completion time and restart number, in a form
amenable to analytical evaluation or quadrature; thereby we optimise the search
over both time and potentially costly restart events. Analysing the effect of a
punctual, i.e. almost deterministic, restart, we demonstrate that the optimal
completion time always increases proportionately with the variance of the
restart distribution; the constant of proportionality depends only on the
search process. We go on to establish simple bounds on the optimal restart
time. Our results are relevant to the analysis and rational design of efficient
and optimal restart protocols.


title: Perfect codes in Cayley graphs

abstract:
  Given a graph $\Gamma$, a subset $C$ of $V(\Gamma)$ is called a perfect code
in $\Gamma$ if every vertex of $\Gamma$ is at distance no more than one to
exactly one vertex in $C$, and a subset $C$ of $V(\Gamma)$ is called a total
perfect code in $\Gamma$ if every vertex of $\Gamma$ is adjacent to exactly one
vertex in $C$. In this paper we study perfect codes and total perfect codes in
Cayley graphs, with a focus on the following themes: when a subgroup of a given
group is a (total) perfect code in a Cayley graph of the group; and how to
construct new (total) perfect codes in a Cayley graph from known ones using
automorphisms of the underlying group. We prove several results around these
questions.


title: Correlations of consumption patterns in social-economic networks

abstract:
  We analyze a coupled anonymized dataset collecting the mobile phone
communication and bank transactions history of a large number of individuals.
After mapping the social structure and introducing indicators of socioeconomic
status, demographic features, and purchasing habits of individuals we show that
typical consumption patterns are strongly correlated with identified
socioeconomic classes leading to patterns of stratification in the social
structure. In addition we measure correlations between merchant categories and
introduce a correlation network, which emerges with a meaningful community
structure. We detect multivariate relations between merchant categories and
show correlations in purchasing habits of individuals. Our work provides novel
and detailed insight into the relations between social and consuming behaviour
with potential applications in recommendation system design.


title:
Lebesgue spectrum of countable multiplicity for conservative flows on
  the torus

abstract:
  We study the spectral measures of conservative mixing flows on the 2-torus
having one degenerate singularity. We show that, for a sufficiently strong
singularity, the spectrum of these flows is typically Lebesgue with infinite
multiplicity. For this, we use two main ingredients: 1) a proof of absolute
continuity of the maximal spectral type for this class of non-uniformly
stretching flows that have an irregular decay of correlations, 2) a geometric
criterion that yields infinite Lebesgue multiplicity of the spectrum and that
is well adapted to rapidly mixing flows.


title:
Statistical analysis of low rank tomography with compressive random
  measurements

abstract:
  We consider the statistical problem of `compressive' estimation of low rank
states with random basis measurements, where the estimation error is expressed
terms of two metrics - the Frobenius norm and quantum infidelity. It is known
that unlike the case of general full state tomography, low rank states can be
identified from a reduced number of observables' expectations. Here we
investigate whether for a fixed sample size $N$, the estimation error
associated to a `compressive' measurement setup is `close' to that of the
setting where a large number of bases are measured. In terms of the Frobenius
norm, we demonstrate that for all states the error attains the optimal rate
$rd/N$ with only $O(r \log{d})$ random basis measurements. We provide an
illustrative example of a single qubit and demonstrate a concentration in the
Frobenius error about its optimal for all qubit states. In terms of the quantum
infidelity, we show that such a concentration does not exist uniformly over all
states. Specifically, we show that for states that are nearly pure and close to
the surface of the Bloch sphere, the mean infidelity scales as $1/\sqrt{N}$ but
the constant converges to zero as the number of settings is increased. This
demonstrates a lack of `compressive' recovery for nearly pure states in this
metric.