title:
Spectrum of the Signless 1-Laplacian and the Dual Cheeger Constant on
  Graphs

abstract:
  Parallel to the signless Laplacian spectral theory, we introduce and develop
the nonlinear spectral theory of signless $1$-Laplacian on graphs. Again, the
first eigenvalue $\mu^+_1$ of the signless 1-Laplacian precisely characterizes
the bipartiteness of a graph and naturally connects to the maxcut problem.
However, the dual Cheeger constant $h^+$, which has only some upper and lower
bounds in the Laplacian spectral theory, is proved to be $1-\mu^+_1$. The
structure of the eigenvectors and the graphic feature of eigenvalues are also
studied. The Courant nodal domain theorem for graphs is extended to the
signless 1-Laplacian. A set-pair version of the Lov\'asz extension, which aims
at the equivalence between discrete combination optimization and continuous
function optimization, is established to recover the relationship
$h^+=1-\mu^+_1$. A local analysis of the associated functional yields an
inverse power method to determine $h^+$ and then produces an efficient
implementation of the recursive spectral cut algorithm for the maxcut problem.


title:
Scalar Solvability of Network Computation Problems and Representable
  Matroids

abstract:
  We consider the following \textit{network computation problem}. In an acyclic
network, there are multiple source nodes, each generating multiple messages,
and there are multiple sink nodes, each demanding a function of the source
messages. The network coding problem corresponds to the case in which every
demand function is equal to some source message, i.e., each sink demands some
source message. Connections between network coding problems and matroids have
been well studied. In this work, we establish a relation between network
computation problems and representable matroids. We show that a network
computation problem in which the sinks demand linear functions of source
messages admits a scalar linear solution if and only if it is matroidal with
respect to a representable matroid whose representation fulfills certain
constraints dictated by the network computation problem. Next, we obtain a
connection between network computation problems and functional dependency
relations (FD-relations) and show that FD-relations can be used to characterize
network computation problem with arbitrary (not necessarily linear) function
demands as well as nonlinear network codes.


title:
First Observational Signature of Rotational Deceleration in a Massive,
  Intermediate-age Star Cluster in the Magellanic Clouds

abstract:
  While the extended main-sequence turn-offs (eMSTOs) found in almost all 1--2
Gyr-old star clusters in the Magellanic Clouds are often explained by
postulating extended star-formation histories, the tight subgiant branches
(SGBs) seen in some clusters challenge this popular scenario. Puzzlingly, the
SGB of the eMSTO cluster NGC 419 is significantly broader at bluer than at
redder colors. We carefully assess and confirm the reality of this
observational trend. If we would assume that the widths of the features in
color--magnitude space were entirely owing to a range in stellar ages, the
star-formation histories of the eMSTO stars and the blue SGB region would be
significantly more prolonged than that of the red part of the SGB. This cannot
be explained by assuming an internal age spread. We show that rotational
deceleration of a population of rapidly rotating stars, a currently hotly
debated alternative scenario, naturally explains the observed trend along the
SGB. Our analysis shows that a `converging' SGB could be produced if the
cluster is mostly composed of rapidly rotating stars that slow down over time
owing to the conservation of angular momentum during their evolutionary
expansion from main-sequence turn-off stars to red giants.


title:
Large Deviations for a Class of Semilinear Stochastic Partial
  Differential Equations

abstract:
  We prove the large deviations principle (LDP) for the law of the solutions to
a class of semilinear stochastic partial differential equations driven by
multiplicative noise. Our proof is based on the weak convergence approach and
significantly improves earlier methods.


title:
Tracer Particles in Two-Dimensional Elastic Networks Diffuse
  Logarithmically Slow

abstract:
  Several experiments on tagged molecules or particles in living systems
suggest that they move anomalously slow - their mean squared displacement (MSD)
increase slower than linearly with time. Leading models aimed at understanding
these experiments predict that the MSD grows as a power law with a growth
exponent that is smaller than unity. However, in some experiments the exponent
is so small $(\sim 0.1-0.2)$ that they hint towards other mechanisms at play.
In this paper, we theoretically demonstrate how in-plane collective modes
excited by thermal fluctuations in a two dimensional membrane lead to
logarithmic time dependence for the mean square displacement of a tracer
particle.


title:
Double-detector for Sparse Signal Detection from One Bit Compressed
  Sensing Measurements

abstract:
  This letter presents the sparse vector signal detection from one bit
compressed sensing measurements, in contrast to the previous works which deal
with scalar signal detection. In this letter, available results are extended to
the vector case and the GLRT detector and the optimal quantizer design are
obtained. Also, a double-detector scheme is introduced in which a sensor level
threshold detector is integrated into network level GLRT to improve the
performance. The detection criteria of oracle and clairvoyant detectors are
also derived. Simulation results show that with careful design of the threshold
detector, the overall detection performance of double-detector scheme would be
better than the sign-GLRT proposed in [1] and close to oracle and clairvoyant
detectors. Also, the proposed detector is applied to spectrum sensing and the
results are near the well known energy detector which uses the real valued data
while the proposed detector only uses the sign of the data.


title: IFU spectroscopy of southern PNe: III

abstract:
  In this paper we describe integral field spectroscopic observations of four
southern Galactic Planetary Nebulae (PNe), M3-4, M3-6, Hen2-29 and Hen2-37
covering the spectral range, 3400-7000 A. We derive the ionisation structure,
the physical conditions, the chemical compositions and the kinematical
characteristics of these PNe and find good agreement with previous studies that
relied upon the long-slit technique in their co-spatial area. From their
chemical compositions as well as their spatial and kinematic characteristics,
we determined that Hen2-29 is of the Peimbert Type I (He and N rich), while the
other three are of Type II. The strength of the nebular He II line reveals that
M3-3, Hen2-29 and Hen2-37 are of mid to high excitation classes while M3-6 is a
low excitation planetary nebula (PN). A series of emission-line maps extracted
from the data cubes were constructed for each PN to describe its overall
structure. These show remarkable morphological diversity. Spatially resolved
spectroscopy of M3-6, shows that the recombination lines of CII, CIII, CIV and
NIII are of nebular origin, rather than arising from the central star as had
been previously proposed. This result increases doubts regarding the weak
emission-line star (WELS) classification raised by Basurah et al. (2016). In
addition, they reinforce the probability that most genuine cases of WELS are
arise from irradiation effects in close binary central stars (Miszalski 2009).


title:
$P-V$ Criticality In the Extended Phase Space of Charged Accelerating
  AdS Black Holes

abstract:
  In this paper, we investigate the $P-V$ criticality and phase transition of
charged accelerating AdS black holes in the extended thermodynamic phase space
in analogy between black hole system and Van der Waals liquid-gas system, where
the cosmological constant $\Lambda$ is treated as a thermodynamical variable
interpreted as dynamic pressure and its conjugate quantity is the thermodynamic
volume of the black holes. When the electric charge vanishes, we find that no
$P-V$ criticality will appear but the Hawking-Page like phase transition will
be present, just as what Schwarzschild-AdS black holes behave like. For the
charged case, the $P-V$ criticality appears and the accelerating black holes
will undergo a small black hole/large phase transition under the condition that
the acceleration parameter $A$ and the horizon radius $r_h$ meet a certain
simple relation $A r_h=a$, where $a$ is a constant in our discussion. To make
$P-V$ criticality appear, there exists an upper bounds for constant $a$. When
$P-V$ criticality appears, we calculate the critical pressure $P_{c}$, critical
temperature $T_{c}$ and critical specific volume $r_{c}$, and we find that
$\frac{P_{c}r_{c}}{T_{c}}$ is an universal number.


title:
Identifying ECUs Using Inimitable Characteristics of Signals in
  Controller Area Networks

abstract:
  In the last several decades, the automotive industry has come to incorporate
the latest Information and Communications (ICT) technology, increasingly
replacing mechanical components of vehicles with electronic components. These
electronic control units (ECUs) communicate with each other in an in-vehicle
network that makes the vehicle both safer and easier to drive. Controller Area
Networks (CANs) are the current standard for such high quality in-vehicle
communication. Unfortunately, however, CANs do not currently offer protection
against security attacks. In particular, they do not allow for message
authentication and hence are open to attacks that replay ECU messages for
malicious purposes. Applying the classic cryptographic method of message
authentication code (MAC) is not feasible since the CAN data frame is not long
enough to include a sufficiently long MAC to provide effective authentication.
In this paper, we propose a novel identification method, which works in the
physical layer of an in-vehicle CAN network. Our method identifies ECUs using
inimitable characteristics of signals enabling detection of a compromised or
alien ECU being used in a replay attack. Unlike previous attempts to address
security issues in the in-vehicle CAN network, our method works by simply
adding a monitoring unit to the existing network, making it deployable in
current systems and compliant with required CAN standards. Our experimental
results show that the bit string and classification algorithm that we utilized
yielded more accurate identification of compromised ECUs than any other method
proposed to date. The false positive rate is more than 2 times lower than the
method proposed by P.-S. Murvay et al. This paper is also the first to identify
potential attack models that systems should be able to detect.


title: ExoMol line lists XV: A new hot line list for hydrogen peroxide

abstract:
  A computed line list for hydrogen peroxide, H$_2{}^{16}$O$_2$, applicable to
temperatures up to $T=1250$~K is presented. A semi-empirical high accuracy
potential energy surface is constructed and used with an {\it ab initio} dipole
moment surface as input TROVE to compute 7.5 million rotational-vibrational
states and around 20 billion transitions with associated Einstein-$A$
coefficients for rotational excitations up to $J=85$. The resulting APTY line
list is complete for wavenumbers below 6~000 cm$^{-1}$ ($\lambda <
1.67$~$\mu$m) and temperatures up to 1250~K. Room-temperature spectra are
compared with laboratory measurements and data currently available in the
HITRAN database and literature. Our rms with line positions from the literature
is 0.152 \cm\ and our absolute intensities agree better than 10\%. The full
line list is available from the CDS databas


title:
ExoMol molecular line lists - XVI: The rotation-vibration spectrum of
  hot H$_2$S

abstract:
  This work presents the AYT2 line list: a comprehensive list of 114 million
$^{1}$H$_2$$^{32}$S vibration-rotation transitions computed using an
empirically-adjusted potential energy surface and an {\it ab initio} dipole
moment surface. The line list gives complete coverage up to 11000 \cm\
(wavelengths longer than 0.91 $\mu$m) for temperatures up to 2000 K. Room
temperature spectra can be simulated up to 20000 \cm\ (0.5 $\mu$m) but the
predictions at visible wavelengths are less reliable. AYT2 is made available in
electronic form as supplementary data to this article and at
\url{www.exomol.com}.


title:
Spatio-Temporal Network Dynamics Framework for Energy-Efficient
  Ultra-Dense Cellular Networks

abstract:
  This article investigates the performance of an ultra-dense network (UDN)
from an energy-efficiency (EE) standpoint leveraging the interplay between
stochastic geometry (SG) and mean-field game (MFG) theory. In this setting,
base stations (BSs) (resp. users) are uniformly distributed over a
two-dimensional plane as two independent homogeneous Poisson point processes
(PPPs), where users associate to their nearest BSs. The goal of every BS is to
maximize its own energy efficiency subject to channel uncertainty, random BS
location, and interference levels. Due to the coupling in interference, the
problem is solved in the mean-field (MF) regime where each BS interacts with
the whole BS population via time-varying MF interference. As a main
contribution, the asymptotic convergence of MF interference to zero is
rigorously proved in a UDN with multiple transmit antennas. It allows us to
derive a closed-form EE representation, yielding a tractable EE optimal power
control policy. This proposed power control achieves more than 1.5 times higher
EE compared to a fixed power baseline.


title:
A Distributed Deep Representation Learning Model for Big Image Data
  Classification

abstract:
  This paper describes an effective and efficient image classification
framework nominated distributed deep representation learning model (DDRL). The
aim is to strike the balance between the computational intensive deep learning
approaches (tuned parameters) which are intended for distributed computing, and
the approaches that focused on the designed parameters but often limited by
sequential computing and cannot scale up. In the evaluation of our approach, it
is shown that DDRL is able to achieve state-of-art classification accuracy
efficiently on both medium and large datasets. The result implies that our
approach is more efficient than the conventional deep learning approaches, and
can be applied to big data that is too complex for parameter designing focused
approaches. More specifically, DDRL contains two main components, i.e., feature
extraction and selection. A hierarchical distributed deep representation
learning algorithm is designed to extract image statistics and a nonlinear
mapping algorithm is used to map the inherent statistics into abstract
features. Both algorithms are carefully designed to avoid millions of
parameters tuning. This leads to a more compact solution for image
classification of big data. We note that the proposed approach is designed to
be friendly with parallel computing. It is generic and easy to be deployed to
different distributed computing resources. In the experiments, the largescale
image datasets are classified with a DDRM implementation on Hadoop MapReduce,
which shows high scalability and resilience.


title: Threshold Decoding for Disjunctive Group Testing

abstract:
  Let $1 \le s < t$, $N \ge 1$ be integers and a complex electronic circuit of
size $t$ is said to be an $s$-active, $\; s \ll t$, and can work as a system
block if not more than $s$ elements of the circuit are defective. Otherwise,
the circuit is said to be an $s$-defective and should be replaced by a similar
$s$-active circuit. Suppose that there exists a possibility to run $N$
non-adaptive group tests to check the $s$-activity of the circuit. As usual, we
say that a (disjunctive) group test yields the positive response if the group
contains at least one defective element. Along with the conventional decoding
algorithm based on disjunctive $s$-codes, we consider a threshold decision rule
with the minimal possible decoding complexity, which is based on the simple
comparison of a fixed threshold $T$, $1 \le T \le N - 1$, with the number of
positive responses $p$, $0 \le p \le N$. For the both of decoding algorithms we
discuss upper bounds on the $\alpha$-level of significance of the statistical
test for the null hypothesis $\left\{ H_0 \,:\, \text{the circuit is
$s$-active} \right\}$ verse the alternative hypothesis $\left\{ H_1 \,:\,
\text{the circuit is $s$-defective} \right\}$.


title: Grassmannians and form factors with $q^2=0$ in N=4 SYM theory

abstract:
  We consider tree level form factors of operators from stress tensor operator
supermultiplet with light-like operator momentum $q^2=0$. We present a
conjecture for the Grassmannian integral representation both for these tree
level form factors as well as for leading singularities of their loop
counterparts. The presented conjecture was successfully checked by reproducing
several known answers in $\mbox{MHV}$ and $\mbox{N}^{k-2}\mbox{MHV}$, $k\geq3$
sectors together with appropriate soft limits. We also discuss the cancellation
of spurious poles and relations between different BCFW representations for such
form factors on simple examples.


title: Soft Lithography using Nectar Droplets

abstract:
  In spite of significant advances in replication technologies, methods to
produce well-defined three dimensional structures are still at its infancy.
Such a limitation would be evident if we were to produce a large array of
simple and, especially, compound convex lenses, also guaranteeing that their
surfaces would be molecularly smooth. Here, we report a novel method to produce
such structures by cloning the 3D shape of nectar drops, found widely in
nature, using conventional soft lithography.The elementary process involves
transfer of a thin patch of the sugar solution coated on a glass slide onto a
hydrophobic substrate on which this patch evolves into a microdroplet. Upon the
absorption of water vapor, such a microdroplet grows linearly with time and its
final size can be controlled by varying its exposure time to water vapor. At
any stage of the evolution of the size of the drop, its shape can be cloned
onto a soft elastomer by following the well-known methods of molding and
crosslinking the same. A unique new science that emerges in our attempt to
understand the transfer of the sugar patch and its evolution to a spherical
drop is the elucidation of the mechanics underlying the contact of a deformable
sphere against a solid support intervening a thin liquid film. A unique aspect
of this work is to demonstrate that higher level structures can also be
generated by transferring even smaller nucleation sites on the surface of the
primary lenses and then allowing them to grow by absorption of water vapor.
What results at the end is either a well-controlled distribution of smooth
hemispherical lenses or compound structures that could have potential
applications in the fundamental studies of contact mechanics, wettability and
even in optics.


title: Modeling of anomalous Wtb interactions using subsidiary fields

abstract:
  A method to simulate anomalous fermion-boson interactions in Wtb vertex is
presented with a minimal set of simulated samples of single top quark events at
the LHC energies. In proposed method additional auxiliary vector fields
corresponding to the Standard Model gauge fields are implemented for each type
of the anomalous vertex structure. The method allows to simulate a
manifestation of anomalous gauge couplings in two approaches used in
experimental analyses either keeping only the linear order contributions in the
anomalous couplings or keeping all contributions in numerators and denominators
as appeared in matrix elements. All the single top quark production mechanisms,
$t$-, $s$- and associative tW-channels are considered. The correctness of the
proposed method is demonstrated.


title:
A nonhomogeneous boundary value problem for the Kuramoto-Sivashinsky
  equation in a quarter plane

abstract:
  We study the initial boundary value problem for one-dimensional
Kuramoto-Sivashinsky equation with nonhomogeneous boundary conditions. Through
the analysis of the boundary integral operator, and applying the known results
on the Cauchy problem, we obtain both the local well-posedness and the global
well-posedness for the nonhomogeneous initial boundary value problem. It is
shown that the Kuramoto-Sivashinsky equation is well-posed in Sobolev space
$C([0,T]; H^s (R^+)) \bigcap L^2(0,T; H^{s+2}(R^+))$ for $s>-2$.


title: Adaptive Learning a Hidden Hypergraph

abstract:
  Learning a hidden hypergraph is a natural generalization of the classical
group testing problem that consists in detecting unknown hypergraph
$H_{un}=H(V,E)$ by carrying out edge-detecting tests. In the given paper we
focus our attention only on a specific family $\mathcal{F}(t,s,\ell)$ of
localized hypergraphs for which the total number of vertices $|V| = t$, the
number of edges $|E|\le s$, $s\ll t$, and the cardinality of any edge
$|e|\le\ell$, $\ell\ll t$. Our goal is to identify all edges of $H_{un}\in
\mathcal{F}(t,s,\ell)$ by using the minimal number of tests. We provide an
adaptive algorithm that matches the information theory bound, i.e., the total
number of tests of the algorithm in the worst case is at most $s\ell\log_2
t(1+o(1))$.


title: Global rigidity of 2-dimensional direction-length frameworks

abstract:
  A 2-dimensional direction-length framework is a collection of points in the
plane which are linked by pairwise constraints that fix the direction or length
of the line segments joining certain pairs of points. We represent it as a pair
$(G,p)$, where $G=(V;D,L)$ is a `mixed' graph and $p:V\to{\mathbb R}^2$ is a
point configuration for $V$. It is globally rigid if every direction-length
framework $(G,q)$ which satisfies the same constraints can be obtained from
$(G,p)$ by a translation or a rotation by $180^\circ$. We show that the problem
of characterising when a generic framework $(G,p)$ is globally rigid can be
reduced to the case when $G$ belongs to a special family of `direction
irreducible' mixed graphs, and prove that {every} generic realisation of a
direction irreducible mixed graph $G$ is globally rigid if and only if $G$ is
2-connected, direction-balanced and redundantly rigid.


title:
Big IoT and social networking data for smart cities: Algorithmic
  improvements on Big Data Analysis in the context of RADICAL city applications

abstract:
  In this paper we present a SOA (Service Oriented Architecture)-based
platform, enabling the retrieval and analysis of big datasets stemming from
social networking (SN) sites and Internet of Things (IoT) devices, collected by
smart city applications and socially-aware data aggregation services. A large
set of city applications in the areas of Participating Urbanism, Augmented
Reality and Sound-Mapping throughout participating cities is being applied,
resulting into produced sets of millions of user-generated events and online SN
reports fed into the RADICAL platform. Moreover, we study the application of
data analytics such as sentiment analysis to the combined IoT and SN data saved
into an SQL database, further investigating algorithmic and configurations to
minimize delays in dataset processing and results retrieval.


title:
Harnessing Self-Interference in Full-Duplex Relaying: An Analog
  Filter-and-Forward Approach

abstract:
  This paper studies a full-duplex filter-and-forward (FD-FF) relay system in
frequency-selective channels. Conventionally, the loop-back signal at the FD
relay is treated as harmful self-interference and needs to be significantly
suppressed via both analog- and digital-domain cancellation. However, the
performance of the conventional self-interference cancellation approach is
fundamentally limited due to the quantization error induced by the
analog-to-digital converter (ADC) with limited dynamic range. In this paper, we
consider an analog filter-and-forward design to help avoid the quantization
error, and surprisingly show that the maximum achievable rate of such an FD-FF
relay system is in fact regardless of the loop-back channel at the FD relay. We
characterize the maximum achievable rate of this channel by jointly optimizing
the transmit power allocation over frequency at the source and the frequency
response of the filter at the relay, subject to their individual power
constraints. Although this problem is non-convex, we obtain its optimal
solution by applying the Lagrange duality method. By simulations it is shown
that the proposed joint source and relay optimization achieves rate gains over
other heuristic designs, and is also advantageous over the conventional
approach by cancelling the relay loop-back signal as self-interference,
especially when the residual self-interference after cancellation is still
significant.


title: On a Hypergraph Approach to Multistage Group Testing Problems

abstract:
  Group testing is a well known search problem that consists in detecting up to
$s$ defective elements of the set $[t]=\{1,\ldots,t\}$ by carrying out tests on
properly chosen subsets of $[t]$. In classical group testing the goal is to
find all defective elements by using the minimal possible number of tests. In
this paper we consider multistage group testing. We propose a general idea how
to use a hypergraph approach to searching defects. For the case $s=2$, we
design an explicit construction, which makes use of $2\log_2t(1+o(1))$ tests in
the worst case and consists of $4$ stages.


title: Inversion of diffraction data for amorphous materials

abstract:
  The general and practical inversion of diffraction data-producing a computer
model correctly representing the material explored - is an important unsolved
problem for disordered materials. Such modeling should proceed by using our
full knowledge base, both from experiment and theory. In this paper, we
describe a robust method to jointly exploit the power of ab initio atomistic
simulation along with the information carried by diffraction data. The method
is applied to two very different systems: amorphous silicon and two
compositions of a solid electrolyte memory material silver-doped GeSe3 . The
technique is easy to implement, is faster and yields results much improved over
conventional simulation methods for the materials explored. By direct
calculation, we show that the method works for both poor and excellent glass
forming materials. It offers a means to add a priori information in first
principles modeling of materials, and represents a significant step toward the
computational design of non-crystalline materials using accurate interatomic
interactions and experimental information.


title: Tip induced unconventional superconductivity on Weyl semimetal TaAs

abstract:
  Weyl fermion is a massless Dirac fermion with definite chirality, which has
been long pursued since 1929. Though it has not been observed as a fundamental
particle in nature, Weyl fermion can be realized as low-energy excitation
around Weyl point in Weyl semimetal, which possesses Weyl fermion cones in the
bulk and nontrivial Fermi arc states on the surface. As a firstly discovered
Weyl semimetal, TaAs crystal possesses 12 pairs of Weyl points in the momentum
space, which are topologically protected against small perturbations. Here, we
report for the first time the tip induced superconductivity on TaAs crystal by
point contact spectroscopy. A conductance plateau and sharp double dips are
observed in the point contact spectra, indicating p-wave like unconventional
superconductivity. Furthermore, the zero bias conductance peak in low
temperature regime is detected, suggesting potentially the existence of
Majorana zero modes. The experimentally observed tunneling spectra can be
interpreted with a novel mirror-symmetry protected topological superconductor
induced in TaAs, which can exhibit zero bias and double finite bias peaks, and
double conductance dips in the measurements. Our work can open a broad avenue
in search for new topological superconducting phases from topological Weyl
materials and trigger intensive investigations for pursuing Majorana fermions.


title: Approximate Joint Matrix Triangularization

abstract:
  We consider the problem of approximate joint triangularization of a set of
noisy jointly diagonalizable real matrices. Approximate joint triangularizers
are commonly used in the estimation of the joint eigenstructure of a set of
matrices, with applications in signal processing, linear algebra, and tensor
decomposition. By assuming the input matrices to be perturbations of
noise-free, simultaneously diagonalizable ground-truth matrices, the
approximate joint triangularizers are expected to be perturbations of the exact
joint triangularizers of the ground-truth matrices. We provide a priori and a
posteriori perturbation bounds on the `distance' between an approximate joint
triangularizer and its exact counterpart. The a priori bounds are theoretical
inequalities that involve functions of the ground-truth matrices and noise
matrices, whereas the a posteriori bounds are given in terms of observable
quantities that can be computed from the input matrices. From a practical
perspective, the problem of finding the best approximate joint triangularizer
of a set of noisy matrices amounts to solving a nonconvex optimization problem.
We show that, under a condition on the noise level of the input matrices, it is
possible to find a good initial triangularizer such that the solution obtained
by any local descent-type algorithm has certain global guarantees. Finally, we
discuss the application of approximate joint matrix triangularization to
canonical tensor decomposition and we derive novel estimation error bounds.


title: The Multiple Quantile Graphical Model

abstract:
  We introduce the Multiple Quantile Graphical Model (MQGM), which extends the
neighborhood selection approach of Meinshausen and Buhlmann for learning sparse
graphical models. The latter is defined by the basic subproblem of modeling the
conditional mean of one variable as a sparse function of all others. Our
approach models a set of conditional quantiles of one variable as a sparse
function of all others, and hence offers a much richer, more expressive class
of conditional distribution estimates. We establish that, under suitable
regularity conditions, the MQGM identifies the exact conditional independencies
with probability tending to one as the problem size grows, even outside of the
usual homoskedastic Gaussian data model. We develop an efficient algorithm for
fitting the MQGM using the alternating direction method of multipliers. We also
describe a strategy for sampling from the joint distribution that underlies the
MQGM estimate. Lastly, we present detailed experiments that demonstrate the
flexibility and effectiveness of the MQGM in modeling hetereoskedastic
non-Gaussian data.


title: Brain network modules of meaningful and meaningless objects

abstract:
  Network modularity is a key feature for efficient information processing in
the human brain. This information processing is however dynamic and networks
can reconfigure at very short time period, few hundreds of millisecond. This
requires neuroimaging techniques with sufficient time resolution. Here we use
the dense electroencephalography, EEG, source connectivity methods to identify
cortical networks with excellent time resolution, in the order of millisecond.
We identify functional networks during picture naming task. Two categories of
visual stimuli were presented, meaningful (tools, animals) and meaningless
(scrambled) objects.
  In this paper, we report the reconfiguration of brain network modularity for
meaningful and meaningless objects. Results showed mainly that networks of
meaningful objects were more modular than those of meaningless objects.
Networks of the ventral visual pathway were activated in both cases. However a
strong occipitotemporal functional connectivity appeared for meaningful object
but not for meaningless object. We believe that this approach will give new
insights into the dynamic behavior of the brain networks during fast
information processing.


title: On $\sigma$-countably tight spaces

abstract:
  Extending a result of R. de la Vega, we prove that an infinite homogeneous
compactum has cardinality $\mathfrak{c}$ if either it is the union of countably
many dense or finitely many arbitrary countably tight subspaces. The question
if every infinite homogeneous and $\sigma$-countably tight compactum has
cardinality $\mathfrak{c}$ remains open.
  We also show that if an arbitrary product is $\sigma$-countably tight then
all but finitely many of its factors must be countably tight.


title: An algebraic proof of K-semistability of the projective plane

abstract:
  We present an algebro-geometric proof of the K-semistability of the
projective plane.


title: Randomized isoperimetric inequalities

abstract:
  We discuss isoperimetric inequalities for convex sets. These include the
classical isoperimetric inequality and that of Brunn-Minkowski,
Blaschke-Santalo, Busemann-Petty and their various extensions. We show that
many such inequalities admit stronger randomized forms in the following sense:
for natural families of associated random convex sets one has stochastic
dominance for various functionals such as volume, surface area, mean width and
others. By laws of large numbers, these randomized versions recover the
classical inequalities. We give an overview of when such stochastic dominance
arises and its applications in convex geometry and probability.


title:
Measurement of complex supercontinuum light pulses using time domain
  ptychography

abstract:
  We demonstrate that time-domain ptychography, a recently introduced ultrafast
pulse reconstruction modality, has properties ideally suited for the temporal
characterization of complex light pulses with large time-bandwidth products as
it achieves temporal resolution on the scale of a single optical cycle using
long probe pulses, low sampling rates, and an extremely fast and robust
algorithm. In comparison to existing techniques, ptychography minimizes the
data to be recorded and processed, and drastically reduces the computational
time of the reconstruction. Experimentally we measure the temporal waveform of
an octave-spanning, 3.5~ps long supercontinuum pulse generated in photonic
crystal fiber, resolving features as short as 5.7~fs with sub-fs resolution and
30~dB dynamic range using 100~fs probe pulses and similarly large delay steps.


title:
Transition Metal and Vacancy Defect Complexes in Phosphorene: A
  Spintronic Perspective

abstract:
  Inducing magnetic moment in otherwise nonmagnetic two-dimensional
semiconducting materials is the key first step to design spintronic materials.
Here, we study the absorption of transition-metals on pristine and defected
single-layer phosphorene, within density functional theory. We predict that
increased transition-metal diffusivity on pristine phosphorene would hinder any
possibility of controlled magnetism, and thus any application. In contrast, the
point-defects will anchor metals, and exponentially reduce the diffusivity.
Similar to other two-dimensional materials, metals bind strongly on both
pristine and defected phosphorene, and we provide a microscopic description of
bonding, which explain the qualitative trend with increasing number of valence
electrons. We further argue that the divacancy complex is imperative in any
practical purpose due to their increased thermodynamic stability over
monovacancy. For most cases, the defect-transition metal complexes retain the
intrinsic semiconduction properties, and also induce a local magnetic moment
with large exchange-splitting and spin-flip energies, which are necessary for
spintronic applications. Specifically, the V/Mn/Fe absorbed at the divacancy
have tremendous promise in this regard. Further, we provide a simple
microscopic model to describe the local moment formation in these transition
metal and defect complexes.


title: Infinite rank Schrodinger-Virasoro type Lie conformal algebras

abstract:
  Motivated by the structure of certain modules over the loop Virasoro Lie
conformal algebra and the Lie structures of Schrodinger-Virasoro algebras, we
construct a class of infinite rank Lie conformal algebras CSV (a, b), where a,
b are complex numbers. The conformal derivations of CSV (a, b) are uniformly
determined. The rank one conformal modules and Z-graded free intermediate
series modules over CSV (a, b) are classified. Corresponding results of the
conformal subalgebra CHV (a, b) of CSV (a, b) are also presented.


title: On the arithmetic of Z_p-extensions

abstract:
  This paper contains three parts.
  In the first part, we give a thorough overview of the theory of
Artin-Schreier-Witt extensions: this theory allows one to understand the
$\mathbf{Z}/p^n\mathbf{Z}$-extensions of any field $K$ of characteristic $p$
via $p$-typical Witt vectors. Let $W_n(K)$ be the ring of $p$-typical Witt
vectors of $K$ of length $n$ and let $\wp = F-\mathrm{id}:
W_n(K)\longrightarrow W_n(K)$, where $F$ is the Frobenius map and $\mathrm{id}$
is the identity map. Artin-Schreier-Witt theory tells us that the abelian group
$W_n(K)/\wp W_n(K)$ represents the set of $\mathbf{Z}/p^n\mathbf{Z}$-extensions
of $K$. Since this theory is hard to find in literature, we have included a
complete treatment in the paper.
  In the second part of the paper, we study $\mathbf{Z}_p$-extensions of a
local field $K=k((T))$ of characteristic $p>0$ where $k$ is a finite field.
Local class field theory and Artin-Schreier-Witt theory give us the Schmid-Witt
symbol $$[\ ,\ ): W(K)/\wp W(K) \times \widehat{K^*} \to
W(\mathbf{F}_p)=\mathbf{Z}_p,$$ which contains the ramification information of
$\mathbf{Z}_p$-extensions of $K$. We present a new simplified formula for $[\
,\ )$. This formula allows one to compute ramification groups, conductors and
discriminants in an easy way.
  In the third part, we study $\mathbf{Z}_p$-extensions of global function
fields over a finite field. First, we give a formula for computing the genus in
such a tower. We show that a previously obtained lower bound for the genus
growth in a $\mathbf{Z}_p$-extension is incorrect and we give a sharp lower
bound. We also study when the genus behaves in a `stable' way. Finally, we find
unique representatives of $\mathbf{Z}_p$-extensions of the rational function
field $k(X)$, and compute the genus in such a tower.


title: EVEREST: Pixel Level Decorrelation of K2 Light curves

abstract:
  We present EVEREST, an open-source pipeline for removing instrumental noise
from K2 light curves. EVEREST employs a variant of pixel level decorrelation
(PLD) to remove systematics introduced by the spacecraft's pointing error and a
Gaussian process (GP) to capture astrophysical variability. We apply EVEREST to
all K2 targets in campaigns 0-7, yielding light curves with precision
comparable to that of the original Kepler mission for stars brighter than $K_p
\approx 13$, and within a factor of two of the Kepler precision for fainter
targets. We perform cross-validation and transit injection and recovery tests
to validate the pipeline, and compare our light curves to the other de-trended
light curves available for download at the MAST High Level Science Products
archive. We find that EVEREST achieves the highest average precision of any of
these pipelines for unsaturated K2 stars. The improved precision of these light
curves will aid in exoplanet detection and characterization, investigations of
stellar variability, asteroseismology, and other photometric studies. The
EVEREST pipeline can also easily be applied to future surveys, such as the TESS
mission, to correct for instrumental systematics and enable the detection of
low signal-to-noise transiting exoplanets. The EVEREST light curves and the
source code used to generate them are freely available online.


title:
Convergence rates of finite difference schemes for the linear advection
  and wave equation with rough coefficient

abstract:
  We prove convergence rates of explicit finite difference schemes for the
linear advection and wave equation in one space dimension with H\"older
continuous coefficient. The obtained convergence rates explicitly depend on the
H\"older regularity of the coefficient and the modulus of continuity of the
initial data. We compare the theoretically established rates with the
experimental rates of a couple of numerical examples.


title: Worldline CPT and massless supermultiplets

abstract:
  The action for a massless particle in 4D Minkowski space has a worldline
time-reversing symmetry corresponding to CPT invariance of the quantum theory.
The analogous symmetry of the N-extended superparticle is shown to be anomalous
when N is odd, in the supertwistor formalism this is because a CPT-violating
worldline-Chern-Simons term is needed to preserve the chiral U(1) gauge
invariance. This accords with the fact that no massless N=1 super-Poincar\'e
irrep is CPT-self-conjugate. There is a CPT self-conjugate supermultiplet when
N is even, but it has $2^{N+1}$ states when N/2 is odd (e.g. the N=2
hypermultiplet) in contrast to just $2^N$ when N/2 is even (e.g. the N=4
Maxwell supermultiplet). This is shown to follow from a Kramers degeneracy of
the superparticle state space when N/2 is odd.


title: Double Bruhat cells and symplectic groupoids

abstract:
  Let $G$ be a connected complex semisimple Lie group, equipped with a standard
multiplicative Poisson structure $\pi_{{\rm st}}$ determined by a pair of
opposite Borel subgroups $(B, B_-)$. We prove that for each $v$ in the Weyl
group $W$ of $G$, the double Bruhat cell $G^{v,v} = BvB \cap B_-vB_-$ in $G$,
together with the Poisson structure $\pi_{{\rm st}}$, is naturally a Poisson
groupoid over the Bruhat cell $BvB/B$ in the flag variety $G/B$.
Correspondingly, every symplectic leaf of $\pi_{{\rm st}}$ in $G^{v,v}$ is a
symplectic groupoid over $BvB/B$. For $u, v \in W$, we show that the double
Bruhat cell $(G^{u,v}, \pi_{{\rm st}})$ has a naturally defined left Poisson
action by the Poisson groupoid $(G^{u, u},\pi_{{\rm st}})$ and a right Poisson
action by the Poisson groupoid $(G^{v,v}, \pi_{{\rm st}})$, and the two actions
commute. Restricting to symplectic leaves of $\pi_{{\rm st}}$, one obtains
commuting left and right Poisson actions on symplectic leaves in $G^{u,v}$ by
symplectic leaves in $G^{u, u}$ and in $G^{v,v}$ as symplectic groupoids.


title:
First-principles approach to thin superconducting slabs and
  heterostructures

abstract:
  We present a fully first-principles method for superconducting thin films.
The layer dependent phonon spectrum is calculated to determine the layer
dependence of the electron-phonon coupling for such systems, which is coupled
to the Kohn-Sham-Bogoliubov-de Gennes equations, and it is solved in a
parameter free way. The theory is then applied to different surface facets of
niobium slabs and to niobium-gold heterostructures. We investigate the
dependence of the transition temperature on the thickness of the slabs and the
inverse proximity effect observed in thin superconducting heterostructures.


title:
Quantum Walks as simulators of neutrino oscillations in vacuum and
  matter

abstract:
  We analyze the simulation of Dirac neutrino oscillations using quantum walks,
both in vacuum and in matter. We show that this simulation, in the continuum
limit, reproduces a set of coupled Dirac equations that describe neutrino
flavor oscillations, and we make use of this to establish a connection with
neutrino phenomenology, thus allowing to fix the parameters of the simulation
for a given neutrino experiment. We also analyze how matter effects for
neutrino propagation can be simulated in the quantum walk. In this way,
important features, such as the MSW effect, can be incorporated. Thus, the
simulation of neutrino oscillations with the help of quantum walks might be
useful to explore these effects in extreme conditions, such as the solar
interior or supernovae, in a complementary way to existing experiments.


title:
A Critical Evaluation of the Role of the Precursor Complex and
  Counterions in Synthesis of Gold Nanoparticles in Micellar Media

abstract:
  We demonstrate here that the gold nanoparticles (AuNPs) obtained in micellar
solutions are susceptible to the precursor complex nature and specific
counterion effects controlling the reaction kinetics, particles size and shape.
The tested approach consisted in reducing the HAuCl4 complex with ascorbic acid
or citric acid in dodecyltrimethylammonium (DTA) solutions, at 318 K, in the
presence of bromide (Br), methanesulfonate (Ms), trifluoroacetate (TFA) or
trifluoromethanesulfonate (Tf) ions. Bromide ions replaced the chloride ions in
the precursor gold complex, and no nanoparticle formation could be observed in
DTA-Br media, in the absence of seeds. In contrast, scanning electron
microscopy images and atomic force microscopy measurements showed that
quasi-spherical AuNPs were formed in DTA-Ms and DTA-TFA solutions, while flat
disk-like or triangular AuNPs were obtained in DTA-Tf solutions, with no need
of adding seeds in all such cases. The results indicated that the reduction of
the precursor gold complex takes place at the micellar interface and that the
specific counterion effects should be taken into account for controlling
nanoparticles formation in micellar media.


title:
Efficient Numerical Optimization For Susceptibility Artifact Correction
  Of EPI-MRI

abstract:
  We present two efficient numerical methods for susceptibility artifact
correction applicable in Echo Planar Imaging (EPI), an ultra fast Magnetic
Resonance Imaging (MRI) technique widely used in clinical applications. Both
methods address a major practical drawback of EPI, the so-called susceptibility
artifacts, which consist of geometrical transformations and intensity
modulations. We consider a tailored variational image registration problem that
is based on a physical distortion model and aims at minimizing the distance of
two oppositely distorted images subject to invertibility constraints. We follow
a discretize-then-optimize approach and present a novel face-staggered
discretization yielding a separable structure in the discretized distance
function and the invertibility constraints. The presence of a smoothness
regularizer renders the overall optimization problem non-separable, but we
present two optimization schemes that exploit the partial separability. First,
we derive a block-Jacobi preconditioner to be used in a Gauss-Newton-PCG
method. Second, we consider a splitting of the separable and non-separable part
and solve the resulting problem using the Alternating Direction Method of
Multipliers (ADMM). We provide a detailed convergence proof for ADMM for this
non-convex optimization problem. Both schemes are of essentially linear
complexity and are suitable for parallel computing. A considerable advantage of
the proposed schemes over established methods is the reduced time-to-solution.
In our numerical experiment using high-resolution 3D imaging data, our parallel
implementation of the ADMM method solves a 3D problem with more than 5 million
degrees of freedom in less than 50 seconds on a standard laptop, which is a
considerable improvement over existing methods.


title: Generalized Heegaard splittings and the disk complex

abstract:
  Let $M$ be an orientable, irreducible $3$-manifold and
$(\mathcal{V},\mathcal{W};F)$ a weakly reducible, unstabilized Heegaard
splitting of $M$ of genus at least three. In this article, we define an
equivalent relation $\sim$ on the set of the generalized Heegaard splittings
obtained by weak reductions and find special subsets of the disk complex
$\mathcal{D}(F)$ named by the "equivalent clusters", where we can find a
canonical function $\Phi$ from the set of equivalent clusters to the set of the
equivalent classes for the relation $\sim$. As an application, we prove that if
$F$ is topologically minimal and the topological index of $F$ is at least
three, then there is a $2$-simplex in $\mathcal{D}(F)$ formed by two weak
reducing pairs such that the equivalent classes of the generalized Heegaard
splittings obtained by weak reductions along the weak reducing pairs for the
relation $\sim$ are different. In the last section, we prove $\Phi$ is a
bijection if the genus of $F$ is three. Using it, we prove there is a canonical
function $\Omega$ from the set of components of $\mathcal{D}_{\mathcal{VW}}(F)$
to the set of the isotopy classes of the generalized Heegaard splittings
obtained by weak reductions and describe what $\Omega$ is.


title: Hypothesis Testing in the High Privacy Limit

abstract:
  Binary hypothesis testing under the Neyman-Pearson formalism is a statistical
inference framework for distinguishing data generated by two different source
distributions. Privacy restrictions may require the curator of the data or the
data respondents themselves to share data with the test only after applying a
randomizing privacy mechanism. Using mutual information as the privacy metric
and the relative entropy between the two distributions of the output
(postrandomization) source classes as the utility metric (motivated by the
Chernoff-Stein Lemma), this work focuses on finding an optimal mechanism that
maximizes the chosen utility function while ensuring that the mutual
information based leakage for both source distributions is bounded. Focusing on
the high privacy regime, an Euclidean information-theoretic (E-IT)
approximation to the tradeoff problem is presented. It is shown that the
solution to the E-IT approximation is independent of the alphabet size and
clarifies that a mutual information based privacy metric preserves the privacy
of the source symbols in inverse proportion to their likelihood.


title:
Text comparison using word vector representations and dimensionality
  reduction

abstract:
  This paper describes a technique to compare large text sources using word
vector representations (word2vec) and dimensionality reduction (t-SNE) and how
it can be implemented using Python. The technique provides a bird's-eye view of
text sources, e.g. text summaries and their source material, and enables users
to explore text sources like a geographical map. Word vector representations
capture many linguistic properties such as gender, tense, plurality and even
semantic concepts like "capital city of". Using dimensionality reduction, a 2D
map can be computed where semantically similar words are close to each other.
The technique uses the word2vec model from the gensim Python library and t-SNE
from scikit-learn.


title: Energy exchanges in reconnection outflows

abstract:
  Reconnection outflows are highly energetic directed flows that interact with
the ambient plasma or with flows from other reconnection regions. Under these
conditions the flow becomes highly unstable and chaotic, as any flow jets
interacting with a medium. We report here massively parallel simulations of the
two cases of interaction between outflow jets and between a single outflow with
an ambient plasma. We find in both case the development of a chaotic magnetic
field, subject to secondary reconnection events that further complicate the
topology of the field lines. The focus of the present analysis is on the energy
balance. We compute each energy channel (electromagnetic, bulk, thermal, for
each species) and find where the most energy is exchanged and in what form. The
main finding is that the largest energy exchange is not at the reconnection
site proper but in the regions where the outflowing jets are destabilized.


title: Dynamics of gravitating hadron matter in Bianchi-IX cosmological model

abstract:
  We perform an analysis of the Einstein-Skyrme cosmological model in
Bianchi-IX background. We analytically describe asymptotic regimes and
semi-analytically -- generic regimes. It appears that depending on the product
of Newtonian constant $\kappa$ with Skyrme coupling $K$, in absence of the
cosmological term there are three regimes possible -- recollapse with $\kK < 2$
and two power-law regimes -- $\propto t^{1/2}$ for $\kK=2$ and $\propto t$ for
$\kK > 2$. In presence of the positive cosmological term, power-law regimes
turn to exponential (de Sitter) ones while recollapse regime turn to
exponential if the value for $\Lambda$-term is sufficiently large, otherwise
the regime remains recollapse. Negative cosmological term leads to the
recollapse regardless of $\kK$. All nonsingular regimes have the squashing
coefficient $a(t) \to 1$ at late times, which is associated with restoring
symmetry dynamics. Also all nonsingular regimes appear to be linearly stable --
exponential solutions always while power-law for an open region of initial
conditions.


title: Badge System Analysis and Design

abstract:
  To incentivize users' participations and steer their online activities,
online social networks start to provide users with various kinds of rewards for
their contributions to the sites. The most frequently distributed rewards
include account levels, reputation scores, different kinds of badges, and even
material awards like small gifts and cash back, etc. Attracted by these
rewards, users will spend more time using the network services. In this paper,
we will mainly focus on "badges reward systems" but the proposed models can be
applied to other reward systems as well. Badges are small icons attached to
users' homepages and profiles denoting their achievements. People like to
accumulate badge for various reasons and different badges can have specific
values for them. Meanwhile, to get badges, they also need to exert efforts to
finish the required tasks, which can lead to certain costs. To understand and
model users' motivations in badge achievement activities, we will study an
existing badge system launched inside a real-world online social network,
Foursquare, in this paper. At the same time, to maximize users' contributions
to online social networks, social network system designers need to determine
the optimal badge system mechanism carefully. Badge system mechanism describes
various detailed aspects of the system and can involve many parameters, e.g.,
categories of existing badges, number of badges available as well as the
minimum contributions required to obtain the badges, which all need to be
designed with meticulous investigations. Based on the model of users' badges
accumulating activities, in this paper, we will also study how to design the
badge system that can incentivize the maximum users' contributions to the
social networks.


title: Reversible Nets of Polyhedra

abstract:
  An example of reversible (or hinge inside-out transformable) figures is the
Dudeney's Haberdasher's puzzle in which an equilateral triangle is dissected
into four pieces, then hinged like a chain, and then is transformed into a
square by rotating the hinged pieces. Furthermore, the entire boundary of each
figure goes into the inside of the other figure and becomes the dissection
lines of the other figure. Many intriguing results on reversibilities of
figures have been found in prior research, but most of them are results on
polygons. This paper generalizes those results to a wider range of general
connected figures. It is shown that two nets obtained by cutting the surface of
an arbitrary convex polyhedron along non-intersecting dissection trees are
reversible. Moreover, a condition for two nets of an isotetrahedron to be both
reversible and tessellative is given.


title:
Robust conversion of singlet spin order in coupled spin-1/2 pairs by
  adiabatically switched RF-fields

abstract:
  We propose a robust and highly efficient NMR technique to create singlet spin
order from longitudinal spin magnetization in coupled spin-1/2 pairs and to
perform backward conversion (singlet order)$\to$magnetization. In this method
we exploit adiabatic switching of an RF-field in order to drive transitions
between the singlet state and the $T_\pm$ triplet states of a spin pair under
study. We demonstrate that the method works perfectly for both strongly and
weakly coupled spin pairs, providing a conversion efficiency between the
singlet spin order and magnetization, which is equal to the theoretical
maximum. We anticipate that the proposed technique is useful for generating
long-lived singlet order, for preserving spin hyperpolarization and for
assessing singlet spin order in nearly equivalent spin pairs in specially
designed molecules and in low-field NMR studies.


title: On resonances and bound states of Smilansky Hamiltonian

abstract:
  We consider the self-adjoint Smilansky Hamiltonian $\mathsf{H}_\varepsilon$
in $L^2(\mathbb{R}^2)$ associated with the formal differential expression
$-\partial_x^2 - \frac12\big(\partial_y^2 + y^2) - \sqrt{2}\varepsilon y
\delta(x)$ in the sub-critical regime, $\varepsilon \in (0,1)$. We demonstrate
the existence of resonances for $\mathsf{H}_\varepsilon$ on a countable
subfamily of sheets of the underlying Riemann surface whose distance from the
physical sheet is finite. On such sheets, we find resonance free regions and
characterise resonances for small $\varepsilon > 0$. In addition, we refine the
previously known results on the bound states of $\mathsf{H}_\varepsilon$ in the
weak coupling regime ($\varepsilon\rightarrow 0+$). In the proofs we use
Birman-Schwinger principle for $\mathsf{H}_\varepsilon$, elements of spectral
theory for Jacobi matrices, and the analytic implicit function theorem.


title: Auxetic Black Phosphorus: A 2D Material with Negative Poisson's Ratio

abstract:
  The Poisson's ratio of a material characterizes its response to uniaxial
strain. Materials normally possess a positive Poisson's ratio - they contract
laterally when stretched, and expand laterally when compressed. A negative
Poisson's ratio is theoretically permissible but has not, with few exceptions
of man-made bulk structures, been experimentally observed in any natural
materials. Here, we show that the negative Poisson's ratio exists in the
low-dimensional natural material black phosphorus, and that our experimental
observations are consistent with first principles simulations. Through
application of uniaxial strain along zigzag and armchair directions, we find
that both interlayer and intralayer negative Poisson's ratios can be obtained
in black phosphorus. The phenomenon originates from the puckered structure of
its in-plane lattice, together with coupled hinge-like bonding configurations.


title: Intertwined Viral Marketing through Online Social Networks

abstract:
  Traditional viral marketing problems aim at selecting a subset of seed users
for one single product to maximize its awareness in social networks. However,
in real scenarios, multiple products can be promoted in social networks at the
same time. At the product level, the relationships among these products can be
quite intertwined, e.g., competing, complementary and independent. In this
paper, we will study the "interTwined Influence Maximization" (i.e., TIM)
problem for one product that we target on in online social networks, where
multiple other competing/complementary/independent products are being promoted
simultaneously. The TIM problem is very challenging to solve due to (1) few
existing models can handle the intertwined diffusion procedure of multiple
products concurrently, and (2) optimal seed user selection for the target
product may depend on other products' marketing strategies a lot. To address
the TIM problem, a unified greedy framework TIER (interTwined Influence
EstimatoR) is proposed in this paper. Extensive experiments conducted on four
different types of real-world social networks demonstrate that TIER can
outperform all the comparison methods with significant advantages in solving
the TIM problem.


title:
Quantization of the dynamics of a particle on a double cone by
  preserving Noether symmetries

abstract:
  The classical quantization of the motion of a free particle and that of an
harmonic oscillator on a double cone are achieved by a quantization scheme
[M.C. Nucci, Theor. Math. Phys. 168 (2011) 994], that preserves the Noether
point symmetries of the underlying Lagrangian in order to construct the
Schroedinger equation. The result is different from that given in [K. Kowalski,
J.Rembielnski, Ann. Phys. 329 (2013) 146]. A comparison of the different
outcomes is provided.


title:
Generation of arbitrary radially polarized array beams by modulating the
  correlation structure

abstract:
  We demonstrate a convenient approach for simultaneously manipulating the
amplitude and polarization of light beams by means of the modulation of the
correlation structure. As an illustration, we constructed a periodic
correlation structure that can generate an arbitrary radially polarized array
(RPA) beam of a radial or rectangular symmetry array in the focal plane from a
radially polarized (RP) beam. The physical realizability conditions for such
source and the far-field beam condition are derived. It is illustrated that the
beamlet shape and the state of polarization (SOP) can be effectively controlled
by the initial correlation structure and the coherence width. Furthermore, by
designing the source correlation structure, a tunable OK-shaped RPA beam and an
optical cage are demonstrated, which can find widespread applications in
non-destructive manipulation of particles and living biological cells. The
arbitrariness in the design of correlation structure prompted us to find more
convenient approaches for controlling the statistics of light beams in terms of
amplitude and polarization.


title: Gauss-Bonnet Gravitational Baryogenesis

abstract:
  In this letter we study some variant forms of gravitational baryogenesis by
using higher order terms containing the partial derivative of the Gauss-Bonnet
scalar coupled to the baryonic current. This scenario extends the well known
theory that uses a similar coupling between the Ricci scalar and the baryonic
current. One appealing feature of the scenario we study is that the predicted
baryon asymmetry during a radiation domination era is non-zero. We calculate
the baryon to entropy ratio for the Gauss-Bonnet term and by using the
observational constraints we investigate which are the allowed forms of the
$R+F(\mathcal{G})$ gravity controlling the evolution. Also we briefly discuss
some alternative higher order terms that can generate a non-zero baryon
asymmetry, even in the conformal invariance limit.


title: Paths of the directed suspension

abstract:
  We prove that the loop space of the directed suspension of a directed space
is homotopy equivalent to the James construction. In particular, it does not
depend on the directed structure of a given directed space.


title: On the Automorphism Group of a Graph

abstract:
  An automorphism of a graph $G$ with $n$ vertices is a bijective map $\phi$
from $V(G)$ to itself such that $\phi(v_i)\phi(v_j)\in E(G)$ $\Leftrightarrow$
$v_i v_j\in E(G)$ for any two vertices $v_i$ and $v_j$ of $G$. Denote by
$\mathfrak{G}$ the group consisting of all automorphisms of $G$. As well-known,
the structure of the action of $\mathfrak{G}$ on $V(G)$ is represented
definitely by its block systems. On the other hand for each permutation
$\sigma$ on $[n]$, there is a natural action on any vector
$\pmb{v}=(v_1,v_2,\ldots,v_n)^t\in \mathbb{R}^n$ such that
$\sigma\pmb{v}=(v_{\sigma^{-1}1},v_{\sigma^{-1}2},\ldots,v_{\sigma^{-1} n})^t$.
Accordingly, we actually have a permutation representation of $\mathfrak{G}$ in
$\mathbb{R}^n$. In this paper, we establish the some connections between block
systems of $\mathfrak{G}$ and its irreducible representations, and by virtue of
that we finally devise an algorithm outputting a generating set and all block
systems of $\mathfrak{G}$ within time $n^{C \log n}$ for some constant $C$.


title: Active Object Localization in Visual Situations

abstract:
  We describe a method for performing active localization of objects in
instances of visual situations. A visual situation is an abstract
concept---e.g., "a boxing match", "a birthday party", "walking the dog",
"waiting for a bus"---whose image instantiations are linked more by their
common spatial and semantic structure than by low-level visual similarity. Our
system combines given and learned knowledge of the structure of a particular
situation, and adapts that knowledge to a new situation instance as it actively
searches for objects. More specifically, the system learns a set of probability
distributions describing spatial and other relationships among relevant
objects. The system uses those distributions to iteratively sample object
proposals on a test image, but also continually uses information from those
object proposals to adaptively modify the distributions based on what the
system has detected. We test our approach's ability to efficiently localize
objects, using a situation-specific image dataset created by our group. We
compare the results with several baselines and variations on our method, and
demonstrate the strong benefit of using situation knowledge and active
context-driven localization. Finally, we contrast our method with several other
approaches that use context as well as active search for object localization in
images.


title: A Subgradient Method for Free Material Design

abstract:
  A small improvement in the structure of the material could save the
manufactory a lot of money. The free material design can be formulated as an
optimization problem. However, due to its large scale, second-order methods
cannot solve the free material design problem in reasonable size. We formulate
the free material optimization (FMO) problem into a saddle-point form in which
the inverse of the stiffness matrix A(E) in the constraint is eliminated. The
size of A(E) is generally large, denoted as N by N. This is the first
formulation of FMO without A(E). We apply the primal-dual subgradient method
[17] to solve the restricted saddle-point formula. This is the first
gradient-type method for FMO. Each iteration of our algorithm takes a total of
$O(N^2)$ foating-point operations and an auxiliary vector storage of size O(N),
compared with formulations having the inverse of A(E) which requires $O(N^3)$
arithmetic operations and an auxiliary vector storage of size $O(N^2)$. To
solve the problem, we developed a closed-form solution to a semidefinite least
squares problem and an efficient parameter update scheme for the gradient
method, which are included in the appendix. We also approximate a solution to
the bounded Lagrangian dual problem. The problem is decomposed into small
problems each only having an unknown of k by k (k = 3 or 6) matrix, and can be
solved in parallel. The iteration bound of our algorithm is optimal for general
subgradient scheme. Finally we present promising numerical results.


title:
Information-Theoretic Lower Bounds on Bayes Risk in Decentralized
  Estimation

abstract:
  We derive lower bounds on the Bayes risk in decentralized estimation, where
the estimator does not have direct access to the random samples generated
conditionally on the random parameter of interest, but only to the data
received from local processors that observe the samples. The received data are
subject to communication constraints, due to quantization and the noise in the
communication channels from the processors to the estimator. We first derive
general lower bounds on the Bayes risk using information-theoretic quantities,
such as mutual information, information density, small ball probability, and
differential entropy. We then apply these lower bounds to the decentralized
case, using strong data processing inequalities to quantify the contraction of
information due to communication constraints. We treat the cases of a single
processor and of multiple processors, where the samples observed by different
processors may be conditionally dependent given the parameter, for
noninteractive and interactive communication protocols. Our results recover and
improve recent lower bounds on the Bayes risk and the minimax risk for certain
decentralized estimation problems, where previously only conditionally
independent sample sets and noiseless channels have been considered. Moreover,
our results provide a general way to quantify the degradation of estimation
performance caused by distributing resources to multiple processors, which is
only discussed for specific examples in existing works.


title:
A field theory approach to the evolution of canonical helicity and
  energy

abstract:
  A redefinition of the Lagrangian of a multi-particle system in fields
reformulates the single-particle, kinetic, and fluid equations governing fluid
and plasma dynamics as a single set of generalized Maxwell's equations and
Ohm's law for canonical force-fields. The Lagrangian includes new terms
representing the coupling between the motion of particle distributions, between
distributions and electromagnetic fields, with relativistic contributions. The
formulation shows that the concepts of self-organization and canonical helicity
transport are applicable across single-particle, kinetic, and fluid regimes, at
classical and relativistic scales. The theory gives the basis for comparing
canonical helicity change to energy change in general systems. For example, in
a fixed, isolated system subject to non-conservative forces, a species'
canonical helicity changes less than total energy only if gradients in density
or distribution function are shallow.

categories: physics.plasm-ph astro-ph.HE astro-ph.SR physics.flu-dyn physics.space-ph


title: On random walk on growing graphs

abstract:
  Random walk on changing graphs is considered. For sequences of finite graphs
increasing monotonically towards a limiting infinite graph, we establish
transition probability upper bounds. It yields sufficient transience criteria
for simple random walk on slowly growing graphs, upon knowing the volume and
Cheeger constant of each graph. For much more specialized cases, we establish
matching lower bounds, and deduce sufficient (weak) recurrence criteria. We
also address recurrence directly in relation to a universality conjecture of
[DHS]. We answer a related question of [SZ, Problem 1.8] about "inhomogeneous
merging" in the negative.


title:
QSR-Dissipativity and Passivity Analysis of Event-Triggered Networked
  Control Cyber-Physical Systems

abstract:
  Input feed-forward output feedback passive (IF-OFP) systems define a great
number of dynamical systems. In this report, we show that dissipativity and
passivity-based control combined with event-triggered networked control systems
(NCS) provide a powerful platform for the design of cyber-physical systems
(CPS). We propose QSR-dissipativity, passivity and L2 stability conditions for
an event-triggered networked control system in three cases where: (i) an
input-output event-triggering sampler condition is located on the plant's
output side, (ii) an input-output event-triggering sampler condition is located
on controller's output side, (iii) input-output event-triggering sampler
conditions are located on the outputs of both the plant and controller. We will
show that this leads to a large decrease in communicational load amongst
sub-units in networked control structures. We show that passivity and stability
conditions depend on passivity levels for the plant and controller. Our results
also illustrate the trade-off among passivity levels, stability, and system's
dependence on the rate of communication between the plant and controller.


title: Completely Reachable Automata

abstract:
  We present a few results and several open problems concerning complete
deterministic finite automata in which every non-empty subset of the state set
occurs as the image of the whole state set under the action of a suitable input
word.


title: Cosmology emerging as the gauge structure of a nonlinear quantum system

abstract:
  Berry phases and gauge structures in parameter spaces of quantum systems are
the foundation of a broad range of quantum effects such as quantum Hall effects
and topological insulators. The gauge structures of interacting many-body
systems, which often present exotic features, are particularly interesting.
While quantum systems are intrinsically linear due to the superposition
principle, nonlinear quantum mechanics can arise as an effective theory for
interacting systems (such as condensates of interacting bosons). Here we show
that gauge structures similar to curved spacetime can arise in nonlinear
quantum systems where the superposition principle breaks down. In the canonical
formalism of the nonlinear quantum mechanics, the geometric phases of quantum
evolutions can be formulated as the classical geometric phases of a harmonic
oscillator that represents the Bogoliubov excitations. We find that the
classical geometric phase can be described by a de Sitter universe. The
fundamental frequency of the harmonic oscillator plays the role of the cosmic
scale factor and the classical geometric phase is an integral of a differential
angle 2-form, which is half of the curvature 2-form of the associated de Sitter
universe. While the gauge structure of a linear quantum system presents
monopole singularity at energy level degeneracy points, nonlinear quantum
systems, corresponding to their quantum critical surfaces in the parameter
spaces, exhibits a conic singularity in their gauge structure, which mimics the
casual singularity at the big bang of the de Sitter universe. This finding
opens up a new approach to studying the gauge and topological structures of
interacting quantum systems and sets up a new stage for quantum simulation of
fundamental physics.


title:
Alzheimer's Disease Diagnostics by a Deeply Supervised Adaptable 3D
  Convolutional Network

abstract:
  Early diagnosis, playing an important role in preventing progress and
treating the Alzheimer's disease (AD), is based on classification of features
extracted from brain images. The features have to accurately capture main
AD-related variations of anatomical brain structures, such as, e.g., ventricles
size, hippocampus shape, cortical thickness, and brain volume. This paper
proposes to predict the AD with a deep 3D convolutional neural network
(3D-CNN), which can learn generic features capturing AD biomarkers and adapt to
different domain datasets. The 3D-CNN is built upon a 3D convolutional
autoencoder, which is pre-trained to capture anatomical shape variations in
structural brain MRI scans. Fully connected upper layers of the 3D-CNN are then
fine-tuned for each task-specific AD classification. Experiments on the
\emph{ADNI} MRI dataset with no skull-stripping preprocessing have shown our
3D-CNN outperforms several conventional classifiers by accuracy and robustness.
Abilities of the 3D-CNN to generalize the features learnt and adapt to other
domains have been validated on the \emph{CADDementia} dataset.


title: The Red Giant Branch in the Tycho-2 Catalogue

abstract:
  Based on multicolor photometry from the 2MASS and Tycho-2 catalogues, we have
produced a sample of 38 368 branch red giants that has less than 1\% of
admixtures and is complete within 500 pc of the Sun. The sample includes 30 671
K giants, 7544 M giants, 49 C giants, and 104 suspected supergiants or S stars.
The photometric distances have been calculated for K, M, and C stars with an
accuracy of 40\%. Tycho-2 proper motions and PCRV radial velocities are used to
analyze the stellar kinematics. The decrease in the stellar distribution
density with distance from the Galactic equator approximated by the barometric
law, contrary to the Besancon model of the Galaxy, and the kinematic parameters
calculated using the Ogorodnikov--Milne model characterize the overwhelming
majority of the selected K and M giants as disk stars with ages of more than 3
Gyr. A small number of K and M giants are extremely young or, conversely,
thick-disk ones. The latter show a nonuniform distribution in the phase space
of coordinates and velocities, arguing against isothermality and full
relaxation of the disk and for the theory of dynamical streams or
superclusters. The spatial distribution and kinematics of the selected C stars
force us to consider them as asymptotic branch giants with masses of more than
2 $M_{\odot}$ and ages of less than 2 Gyr probably associated with the Gould
Belt. The offset of the Sun above the Galactic equator has been found from the
distribution of stars to be $13\pm2$ pc, which coincides with the previously
obtained value for the clump red giants.


title: Electroabsorption in MoS$_2$

abstract:
  To translate electrical into optical signals one uses the modulation of
either the refractive index or the absorbance of a material by an electric
field. Contemporary electroabsorption modulators (EAMs) employ the quantum
confined Stark effect (QCSE), the field-induced red-shift and broadening of the
strong excitonic absorption resonances characteristic of low-dimensional
semiconductor structures. Here we show an unprecedentedly strong transverse
electroabsorption (EA) signal in a monolayer of the two-dimensional
semiconductor MoS2. The EA spectrum is dominated by an apparent linewidth
broadening of around 15% at a modulated voltage of only Vpp = 0.5 V. Contrary
to the conventional QCSE, the signal increases linearly with the applied field
strength and arises from a linear variation of the distance between the
strongly overlapping exciton and trion resonances. The achievable modulation
depths exceeding 0.1 dBnm-1 bear the scope for extremely compact, ultrafast,
energy-efficient EAMs for integrated photonics, including on-chip optical
communication.


title: Sub-sampled Newton Methods with Non-uniform Sampling

abstract:
  We consider the problem of finding the minimizer of a convex function $F:
\mathbb R^d \rightarrow \mathbb R$ of the form $F(w) := \sum_{i=1}^n f_i(w) +
R(w)$ where a low-rank factorization of $\nabla^2 f_i(w)$ is readily available.
We consider the regime where $n \gg d$. As second-order methods prove to be
effective in finding the minimizer to a high-precision, in this work, we
propose randomized Newton-type algorithms that exploit \textit{non-uniform}
sub-sampling of $\{\nabla^2 f_i(w)\}_{i=1}^{n}$, as well as inexact updates, as
means to reduce the computational complexity. Two non-uniform sampling
distributions based on {\it block norm squares} and {\it block partial leverage
scores} are considered in order to capture important terms among $\{\nabla^2
f_i(w)\}_{i=1}^{n}$. We show that at each iteration non-uniformly sampling at
most $\mathcal O(d \log d)$ terms from $\{\nabla^2 f_i(w)\}_{i=1}^{n}$ is
sufficient to achieve a linear-quadratic convergence rate in $w$ when a
suitable initial point is provided. In addition, we show that our algorithms
achieve a lower computational complexity and exhibit more robustness and better
dependence on problem specific quantities, such as the condition number,
compared to similar existing methods, especially the ones based on uniform
sampling. Finally, we empirically demonstrate that our methods are at least
twice as fast as Newton's methods with ridge logistic regression on several
real datasets.


title:
Symmetry and Natural Quantum Structures for Three-Particles in
  One-Dimension

abstract:
  How do symmetries induce natural and useful quantum structures? This question
is investigated in the context of models of three interacting particles in
one-dimension. Such models display a wide spectrum of possibilities for
dynamical systems, from integrability to hard chaos. This article demonstrates
that the related but distinct notions of integrability, separability, and
solvability identify meaningful collective observables for Hamiltonians with
sufficient symmetry. In turn, these observables induce tensor product
structures on the Hilbert space that are especially useful for storing and
processing quantum information and provide guidance to interpretation and
phenomenology of quantum few-body physics.


title: Selfish Pups: Weaning Conflict and Milk Theft in Free-Ranging Dogs

abstract:
  Parent-offspring conflict theory predicts the emergence of weaning conflict
between a mother and her offspring arising from skewed relatedness benefits.
Empirical observations of weaning conflict has not been carried out in canids.
In a field-based study on free-ranging dogs we observed that suckling bout
durations reduce, proportion of mother-initiated suckling bouts reduce and
mother-initiated suckling terminations increase, with pup age. We identified
the 7th - 13th week period of pup age as the zone of conflict between the
mother and her pups, beyond which suckling solicitations cease, and before
which suckling refusals are few. We also report for the first time milk theft
by pups who take advantage of the presence of multiple lactating females, due
to the promiscuous mating system of the dogs. This behaviour, though apparently
disadvantageous for the mothers, is perhaps adaptive for the dogs in the face
of high mortality and competition for resources.


title:
Integrated Task and Motion Planning for Multiple Robots under Path and
  Communication Uncertainties

abstract:
  We consider a problem called task ordering with path uncertainty (TOP-U)
where multiple robots are provided with a set of task locations to visit in a
bounded environment, but the length of the path between a pair of task
locations is initially known only coarsely by the robots. The objective of the
robots is to find the order of tasks that reduces the path length (or, energy
expended) to visit the task locations in such a scenario. To solve this
problem, we propose an abstraction called a task reachability graph (TRG) that
integrates the task ordering with the path planning by the robots. The TRG is
updated dynamically based on inter-task path costs calculated using a
sampling-based motion planner, and, a Hidden Markov Model (HMM)-based technique
that calculates the belief in the current path costs based on the environment
perceived by the robot's sensors and task completion information received from
other robots. We then describe a Markov Decision Process (MDP)-based algorithm
that can select the paths that reduce the overall path length to visit the task
locations and a coordination algorithm that resolves path conflicts between
robots. We have shown analytically that our task selection algorithm finds the
lowest cost path returned by the motion planner, and, that our proposed
coordination algorithm is deadlock free. We have also evaluated our algorithm
on simulated Corobot robots within different environments while varying the
number of task locations, obstacle geometries and number of robots, as well as
on physical Corobot robots. Our results show that the TRG-based approach can
perform considerably better in planning and locomotion times, and number of
re-plans, while traveling almost-similar distances as compared to a closest
first, no uncertainty (CFNU) task selection algorithm.


title: On the additive bases problem in finite fields

abstract:
  We prove that if $G$ is an Abelian group and $A_1,\ldots,A_k \subseteq G$
satisfy $m A_i=G$ (the $m$-fold sumset), then $A_1+\ldots+A_k=G$ provided that
$k \ge c_m \log n$. This generalizes a result of Alon, Linial, and Meshulam
[Additive bases of vector spaces over prime fields. J. Combin. Theory Ser. A,
57(2):203--210, 1991] regarding the so called additive bases.


title: Polyhedral Horofunction Compactification as Polyhedral Ball

abstract:
  In this paper we answer positively a question raised by Kapovich and Leeb in
a recent paper titled "Finsler bordifications of symmetric and certain locally
symmetric spaces". Specifically, we show that for a finite-dimensional vector
space with polyhedral norm, its horofunction compactification is homeomorphic
to the dual unit ball of the norm by an explicit map. To prove this we
establish a criterion for converging sequences in the horofunction
compactification, and generalize the basic notion of the moment map in the
theory of toric varieties.


title: Uniform measures on braid monoids and dual braid monoids

abstract:
  We aim at studying the asymptotic properties of typical positive braids,
respectively positive dual braids. Denoting by $\mu_k$ the uniform distribution
on positive (dual) braids of length $k$, we prove that the sequence $(\mu_k)_k$
converges to a unique probability measure $\mu_{\infty}$ on infinite positive
(dual) braids. The key point is that the limiting measure $\mu_{\infty}$ has a
Markovian structure which can be described explicitly using the combinatorial
properties of braids encapsulated in the M\"obius polynomial. As a by-product,
we settle a conjecture by Gebhardt and Tawn (J. Algebra, 2014) on the shape of
the Garside normal form of large uniform braids.


title:
Fourier solution of two-dimensional Navier Stokes equation with periodic
  boundary conditions and incompressible flow

abstract:
  An approximate solution to the two dimensional Navier Stokes equation with
periodic boundary conditions is obtained by representing the x any y components
of fluid velocity with complex Fourier basis vectors. The chosen space of basis
vectors is finite to allow for numerical calculations, but of variable size.
Comparisons of the resulting approximate solutions as they vary with the size
of the chosen vector space allow for extrapolation to an infinite basis vector
space. Results suggest that such a solution, with the full basis vector space
and which would give the exact solution, would fail for certain initial
velocity configurations when initial velocity and time t exceed certain limits.


title:
Rademacher Complexity Bounds for a Penalized Multiclass Semi-Supervised
  Algorithm

abstract:
  We propose Rademacher complexity bounds for multiclass classifiers trained
with a two-step semi-supervised model. In the first step, the algorithm
partitions the partially labeled data and then identifies dense clusters
containing $\kappa$ predominant classes using the labeled training examples
such that the proportion of their non-predominant classes is below a fixed
threshold. In the second step, a classifier is trained by minimizing a margin
empirical loss over the labeled training set and a penalization term measuring
the disability of the learner to predict the $\kappa$ predominant classes of
the identified clusters. The resulting data-dependent generalization error
bound involves the margin distribution of the classifier, the stability of the
clustering technique used in the first step and Rademacher complexity terms
corresponding to partially labeled training data. Our theoretical result
exhibit convergence rates extending those proposed in the literature for the
binary case, and experimental results on different multiclass classification
problems show empirical evidence that supports the theory.


title:
Interacting composite fermions: Nature of the 4/5, 5/7, 6/7, and 6/17
  fractional quantum Hall states

abstract:
  Numerical studies by W\'ojs, Yi and Quinn have suggested that an
unconventional fractional quantum Hall effect is plausible at filling factors
$\nu=$ 1/3 and 1/5, provided the interparticle interaction has an unusual form
for which the energy of two fermions in the relative angular momentum three
channel dominates. The interaction between composite fermions in the second
$\Lambda$ level (composite fermion analog of the electronic Landau level)
satisfies this property, and recent studies have supported unconventional
fractional quantum Hall effect of composite fermions at $\nu^*=$ 4/3 and 5/3,
which manifests as fractional quantum Hall effect of electrons at $\nu=$ 4/11,
4/13, 5/13, and 5/17. I investigate in this article the nature of the
fractional quantum Hall states at $\nu=$ 4/5, 5/7, 6/17, and 6/7, which
correspond to composite fermions at $\nu^*=$ 4/3, 5/3 and 6/5, and find that
all these fractional quantum Hall states are conventional. The underlying
reason is that the interaction between composite fermions depends substantially
on both the number and the direction of the vortices attached to the electrons.
I also study in detail the states with different spin polarizations at 6/17 and
6/7 and predict the critical Zeeman energies for the spin phase transitions
between them. I calculate the excitation gaps at 4/5, 5/7, 6/7, and 6/17 and
compare them against recent experiments.


title:
A Dual EnKF for Estimating Water Level, Bottom Roughness, and Bathymetry
  in a 1-D Hydrodynamic Model

abstract:
  Data assimilation has been applied to coastal hydrodynamic models to better
estimate system states or parameters by incorporating observed data into the
model. Kalman Filter (KF) is one of the most studied data assimilation methods
whose application is limited to linear systems. For nonlinear systems such as
hydrodynamic models a variation of the KF called Ensemble Kalman Filter (EnKF)
is applied to update the system state in the context of Monte Carlo simulation.
In this research, a dual EnKF approach is used to simultaneously estimate state
(water surface elevation) and parameters (bottom roughness and bathymetry) of
the shallow water models. The sensitivity of the filter to 1) the quantity and
precision of the observations, and 2) the initial estimation of parameters is
investigated in a 1-D shallow water problem located in the Gulf of Mexico.
Results show that starting from an initial estimate of bottom roughness and
bathymetry within a logical range and utilizing observations available at a
limited number of gages the dual EnKF is able to improve the bottom roughness
and bathymetry fields. The performance of the filter is sensitive to the
precision of measured data, especially in the case of estimating Mannings n and
bathymetry simultaneously.


title:
Representation learning for very short texts using weighted word
  embedding aggregation

abstract:
  Short text messages such as tweets are very noisy and sparse in their use of
vocabulary. Traditional textual representations, such as tf-idf, have
difficulty grasping the semantic meaning of such texts, which is important in
applications such as event detection, opinion mining, news recommendation, etc.
We constructed a method based on semantic word embeddings and frequency
information to arrive at low-dimensional representations for short texts
designed to capture semantic similarity. For this purpose we designed a
weight-based model and a learning procedure based on a novel median-based loss
function. This paper discusses the details of our model and the optimization
methods, together with the experimental results on both Wikipedia and Twitter
data. We find that our method outperforms the baseline approaches in the
experiments, and that it generalizes well on different word embeddings without
retraining. Our method is therefore capable of retaining most of the semantic
information in the text, and is applicable out-of-the-box.


title: Trimmed Serendipity Finite Element Differential Forms

abstract:
  We introduce the family of trimmed serendipity finite element differential
form spaces, defined on cubical meshes in any number of dimensions, for any
polynomial degree, and for any form order. The relation between the trimmed
serendipity family and the (non-trimmed) serendipity family developed by Arnold
and Awanou [Math. Comp. 83(288) 2014] is analogous to the relation between the
trimmed and (non-trimmed) polynomial finite element differential form families
on simplicial meshes from finite element exterior calculus. We provide degrees
of freedom in the general setting and prove that they are unisolvent for the
trimmed serendipity spaces. The sequence of trimmed serendipity spaces with a
fixed polynomial order r provides an explicit example of a system described by
Christiansen and Gillette [ESAIM:M2AN 50(3) 2016], namely, a minimal compatible
finite element system on squares or cubes containing order r-1 polynomial
differential forms.


title:
Lattice stability and high pressure melting mechanism of dense hydrogen
  up to 1.5 TPa

abstract:
  Lattice stability and metastability, as well as melting, are important
features of the physics and chemistry of dense hydrogen. Using ab initio
molecular dynamics (AIMD), the classical superheating limit and melting line of
metallic hydrogen are investigated up to 1.5 TPa. The computations show that
the classical superheating degree is about 100 K, and the classical melting
curve becomes flat at a level of 350 K when beyond 500 GPa. This information
allows us to estimate the well depth and the potential barriers that must be
overcome when the crystal melts. Inclusion of nuclear quantum effects (NQE)
using path integral molecular dynamics (PIMD) predicts that both superheating
limit and melting temperature are lowered to below room temperature, but the
latter never reach absolute zero. Detailed analysis indicates that the melting
is thermally activated, rather than driven by pure zero-point motion (ZPM).
This argument was further supported by extensive PIMD simulations,
demonstrating the stability of Fddd structure against liquefaction at low
temperatures.

categories: cond-mat.mtrl-sci cond-mat.stat-mech physics.chem-ph physics.comp-ph


title:
Deriving the trajectory equations of gyrocenter with a multi-parameter
  Lie transform method

abstract:
  It's pointed out that the values of the generators derived by the modern
gyrokinetic theory are inappropriately amplified by the pullback transform with
the existence of electromagnetic perturbation, and the trajectory equations of
the gyrocenter include terms containing the perturbative magnetic vector
potential not in the form of its curl. These terms are not physical ones, as
the perturbative magnetic vector potential could include an arbitrary gauge
term. In this paper, instead of the single-parameter Lie transform method
utilized by the modern gyrokinetic theory, a multi-parameter Lie transform
method is utilized. All characteristic scales of the system can be taken into
account. With the assistance of a kind of linear cancellation rule, the new
method can decouple the gyroangle $\theta$ from the remaining degrees of
freedom up to the second order of the parameter as the ratio between the Larmor
radius and the transverse length scale of the equilibrium magnetic field. With
this new method, those nonphysical terms don't appear anymore in the trajectory
equations.


title:
Quantum state and circuit distinguishability with single-qubit
  measurements

abstract:
  We show that the Quantum State Distinguishability (QSD), which is a
QSZK-complete problem, and the Quantum Circuit Distinguishability (QCD), which
is a QIP-complete problem, can be solved by the verifier who can perform only
single-qubit measurements. To show these results, we use measurement-based
quantum computing: the honest prover sends a graph state to the verifier, and
the verifier can perform universal quantum computing on it with only
single-qubit measurements. If the prover is malicious, he does not necessarily
generate the correct graph state, but the verifier can verify the correctness
of the graph state by measuring the stabilizer operators.


title:
Networked MIMO with Fractional Joint Transmission in Energy Harvesting
  Systems

abstract:
  This paper considers two base stations (BSs) powered by renewable energy
serving two users cooperatively. With different BS energy arrival rates, a
fractional joint transmission (JT) strategy is proposed, which divides each
transmission frame into two subframes. In the first subframe, one BS keeps
silent to store energy while the other transmits data, and then they perform
zero-forcing JT (ZF-JT) in the second subframe. We consider the average
sum-rate maximization problem by optimizing the energy allocation and the time
fraction of ZF-JT in two steps. Firstly, the sum-rate maximization for given
energy budget in each frame is analyzed. We prove that the optimal transmit
power can be derived in closed-form, and the optimal time fraction can be found
via bi-section search. Secondly, approximate dynamic programming (DP) algorithm
is introduced to determine the energy allocation among frames. We adopt a
linear approximation with the features associated with system states, and
determine the weights of features by simulation. We also operate the
approximation several times with random initial policy, named as policy
exploration, to broaden the policy search range. Numerical results show that
the proposed fractional JT greatly improves the performance. Also, appropriate
policy exploration is shown to perform close to the optimal.


title: Diophantine approximation in angular domains

abstract:
  Let $\alpha$ and $\beta$ be real numbers such that $1$, $\alpha$ and $\beta$
are linearly independent over $\mathbb{Q}$. A classical result of Dirichlet
asserts that there are infinitely many triples of integers $(x_0,x_1,x_2)$ such
that $|x_0+\alpha x_1+\beta x_2| < \max\{|x_1|,|x_2|\}^{-2}$. In 1976, W. M.
Schmidt asked what can be said under the restriction that $x_1$ and $x_2$ be
positive. Upon denoting by $\gamma\cong 1.618$ the golden ratio, he proved that
there are triples $(x_0,x_1,x_2) \in \mathbb{Z}^3$ with $x_1,x_2>0$ for which
the product $|x_0 + \alpha x_1 + \beta x_2| \max\{|x_1|,|x_2|\}^\gamma$ is
arbitrarily small. Although Schmidt later conjectured that $\gamma$ can be
replaced by any number smaller than $2$, N. Moshchevitin proved very recently
that it cannot be replaced by a number larger than $1.947$. In this paper, we
present a construction showing that the result of Schmidt is in fact optimal.


title: A Hierarchical Distributed Processing Framework for Big Image Data

abstract:
  This paper introduces an effective processing framework nominated ICP (Image
Cloud Processing) to powerfully cope with the data explosion in image
processing field. While most previous researches focus on optimizing the image
processing algorithms to gain higher efficiency, our work dedicates to
providing a general framework for those image processing algorithms, which can
be implemented in parallel so as to achieve a boost in time efficiency without
compromising the results performance along with the increasing image scale. The
proposed ICP framework consists of two mechanisms, i.e. SICP (Static ICP) and
DICP (Dynamic ICP). Specifically, SICP is aimed at processing the big image
data pre-stored in the distributed system, while DICP is proposed for dynamic
input. To accomplish SICP, two novel data representations named P-Image and
Big-Image are designed to cooperate with MapReduce to achieve more optimized
configuration and higher efficiency. DICP is implemented through a parallel
processing procedure working with the traditional processing mechanism of the
distributed system. Representative results of comprehensive experiments on the
challenging ImageNet dataset are selected to validate the capacity of our
proposed ICP framework over the traditional state-of-the-art methods, both in
time efficiency and quality of results.