title: Clustering on the Edge: Learning Structure in Graphs

abstract:
  With the recent popularity of graphical clustering methods, there has been an
increased focus on the information between samples. We show how learning
cluster structure using edge features naturally and simultaneously determines
the most likely number of clusters and addresses data scale issues. These
results are particularly useful in instances where (a) there are a large number
of clusters and (b) we have some labeled edges. Applications in this domain
include image segmentation, community discovery and entity resolution. Our
model is an extension of the planted partition model and our solution uses
results of correlation clustering, which achieves a partition O(log(n))-close
to the log-likelihood of the true clustering.


title: First results of the new endcap TOF commissioning at BESIII

abstract:
  The upgrade of the current BESIII Endcap TOF (ETOF) is carried out with the
Multi-gap Resistive Plate Chamber (MRPC) technology. The installation of the
new ETOF has been finished in October 2015. The first results of the MRPCs
commissioning at BESIII are reported in this paper.


title:
A Generalization of the Hamilton-Waterloo Problem on Complete
  Equipartite Graphs

abstract:
  The Hamilton-Waterloo problem asks for which $s$ and $r$ the complete graph
$K_n$ can be decomposed into $s$ copies of a given 2-factor $F_1$ and $r$
copies of a given 2-factor $F_2$ (and one copy of a 1-factor if $n$ is even).
In this paper we generalize the problem to complete equipartite graphs
$K_{(n:m)}$ and show that $K_{(xyzw:m)}$ can be decomposed into $s$ copies of a
2-factor consisting of cycles of length $xzm$; and $r$ copies of a 2-factor
consisting of cycles of length $yzm$, whenever $m$ is odd, $s,r\neq 1$,
$\gcd(x,z)=\gcd(y,z)=1$ and $xyz\neq 0 \pmod 4$. We also give some more general
constructions where the cycles in a given two factor may have different
lengths. We use these constructions to find solutions to the Hamilton-Waterloo
problem for complete graphs.


title:
Local existence and uniqueness of strong solutions to the Navier-Stokes
  equations with nonnegative density

abstract:
  In this paper, we consider the initial-boundary value problem to the
nonhomogeneous incompressible Navier-Stokes equations. Local strong solutions
are established, for any initial data $(\rho_0, u_0)\in (W^{1,\gamma} \cap
L^\infty)\times H_{0,\sigma}^1$, with $\gamma>1$, and if $\gamma\geq2$, then
the strong solution is unique. The initial density is allowed to be
nonnegative, and in particular, the initial vacuum is allowed. The assumption
on the initial data is weaker than the previous widely used one that $(\rho_0,
u_0)\in (H^1 \cap L^\infty )\times(H_{0,\sigma}^1 \cap H^2)$, and no
compatibility condition is required.


title:
On the Lagrange and Markov Dynamical Spectra for Anosov Flows in
  dimension 3

abstract:
  We consider the Lagrange and the Markov dynamical spectra associated with a
conservative Anosov flow on a compact manifold of dimension $3$ (including
geodesic flows of negative curvature and suspension flows). We show that for a
large set of real functions and typical conservative Anosov flows, both the
Lagrange and Markov dynamical spectra have a non-empty interior.


title:
Neural mechanisms underlying catastrophic failure in human-machine
  interaction during aerial navigation

abstract:
  Objective. We investigated the neural correlates of workload buildup in a
fine visuomotor task called the boundary avoidance task (BAT). The BAT has been
known to induce naturally occurring failures of human-machine coupling in high
performance aircraft that can potentially lead to a crash; these failures are
termed pilot induced oscillations (PIOs). Approach. We recorded EEG and
pupillometry data from human subjects engaged in a flight BAT simulated within
a virtual 3D environment. Main results. We find that workload buildup in a BAT
can be successfully decoded from oscillatory features in the
electroencephalogram (EEG). Information in delta, theta, alpha, beta, and gamma
spectral bands of the EEG all contribute to successful decoding, however gamma
band activity with a lateralized somatosensory topography has the highest
contribution, while theta band activity with a frontocentral topography has the
most robust contribution in terms of real world usability. We show that the
output of the spectral decoder can be used to predict PIO susceptibility. We
also find that workload buildup in the task induces pupil dilation, the
magnitude of which is significantly correlated with the magnitude of the
decoded EEG signals. These results suggest that PIOs may result from the
dysregulation of cortical networks such as the locus coeruleus (LC) anterior
cingulate cortex (ACC) circuit. Significance. Our findings may generalize to
similar control failures in other cases of tight man machine coupling where
gains and latencies in the control system must be inferred and compensated for
by the human operators. A closed-loop intervention using neurophysiological
decoding of workload buildup that targets the LC ACC circuit may positively
impact operator performance in such situations.


title:
A First Targeted Search for Gravitational-Wave Bursts from Core-Collapse
  Supernovae in Data of First-Generation Laser Interferometer Detectors

abstract:
  We present results from a search for gravitational-wave bursts coincident
with a set of two core-collapse supernovae observed between 2007 and 2011. We
employ data from the Laser Interferometer Gravitational-wave Observatory
(LIGO), the Virgo gravitational-wave observatory, and the GEO 600
gravitational-wave observatory. The targeted core-collapse supernovae were
selected on the basis of (1) proximity (within approximately 15 Mpc), (2)
tightness of observational constraints on the time of core collapse that
defines the gravitational-wave search window, and (3) coincident operation of
at least two interferometers at the time of core collapse. We find no plausible
gravitational-wave candidates. We present the probability of detecting signals
from both astrophysically well-motivated and more speculative
gravitational-wave emission mechanisms as a function of distance from Earth,
and discuss the implications for the detection of gravitational waves from
core-collapse supernovae by the upgraded Advanced LIGO and Virgo detectors.


title: Developing an Action Concept Inventory

abstract:
  We report on progress towards the development of an Action Concept Inventory
(ACI), a test that measures student understanding of action principles in
introductory mechanics and optics. The ACI also covers key concepts of
many-paths quantum mechanics, from which classical action physics arises. We
used a multi-stage iterative development cycle for incorporating expert and
student feedback into successive revisions of the ACI. The student feedback,
including think-aloud interviews, enabled us to identify their misconceptions
about action physics.


title: The Solar Solution: Tracking the Sun with Low Energy Neutrinos

abstract:
  As neutrinos become a significant background for projected dark matter
experiments, the community will become concerned with determining if events
counted in a dark matter experiment are good dark matter candidates or
low-energy neutrinos from astrophysical sources. We investigate the feasibility
of using neutrino-electron scattering in a terrestrial detector medium as a
means to determine the flight direction of the original, low-energy solar
neutrino.Using leading-order weak interactions in the Standard Model and
constrains from energy and momentum conservation, we developed a simple
simulation that suggests that 68% of the time the ejected electron would be
within 0.99 radians of the incident neutrino's direction. This suggests that it
may be fruitful to pursue low-energy neutrino detection capability that can
utilize such ejected electrons.


title: Moduli of Linear Sections of a General Hypersurface

abstract:
  We investigate the global variation of moduli of linear sections of a general
hypersurface. We prove a "generic Torelli" result for a large proportion of
cases, and we obtain a complete picture of the global variation of moduli of
line slices of a general hypersurface.


title: Smart packaging of electronics and integrated MEMS devices using LTCC

abstract:
  Low Temperature Cofired Ceramics (LTCC) has been a popular multi layer
ceramic (MCM) packaging material for many electronic applications. The main
advantage with LTCC would be its ability to embed a major part of the
electronic circuit within itself, apart from its enhanced RF functionality as
against many lossy materials used. The advantages of LTCC in terms of frequency
response, cost, ease of fabrication, etc over many other packaging materials
are presented. The applicability of LTCC as a packaging material, circuit
mounting material, substrate material or a base material for micro devices is
discussed. Switches and filters fabricated on LTCC as a substrate are presented
and their enhanced functionality is shown. Planar switches and RF MEMS switches
on LTCC are discussed with regard to their isolation, insertion losses, return
losses, repeatability, quality factor, parasitic effects and frequency
response. Concern is also shown to parameters like actuation voltages,
actuation times and complexity of fabrication. The parameters studied with
design and fabrication of filters is also discussed, like Q factor, dispersive
effects, limits on frequencies, etc. Discussion is also done with regard to
LTCC as a base material for MEMS sensors and actuators and the performance
variables of the same. Fabrication process parameters are presented. The
important issue of feasibility of integration with microelectronic integrated
circuitry is discussed and its effects are shown.


title: Robust SAR STAP via Kronecker Decomposition

abstract:
  This paper proposes a spatio-temporal decomposition for the detection of
moving targets in multiantenna SAR. As a high resolution radar imaging
modality, SAR detects and localizes non-moving targets accurately, giving it an
advantage over lower resolution GMTI radars. Moving target detection is more
challenging due to target smearing and masking by clutter. Space-time adaptive
processing (STAP) is often used to remove the stationary clutter and enhance
the moving targets. In this work, it is shown that the performance of STAP can
be improved by modeling the clutter covariance as a space vs. time Kronecker
product with low rank factors. Based on this model, a low-rank Kronecker
product covariance estimation algorithm is proposed, and a novel separable
clutter cancelation filter based on the Kronecker covariance estimate is
introduced. The proposed method provides orders of magnitude reduction in the
required number of training samples, as well as improved robustness to
corruption of the training data. Simulation results and experiments using the
Gotcha SAR GMTI challenge dataset are presented that confirm the advantages of
our approach relative to existing techniques.


title:
Functional central limit theorems and $P(phi)_{1}$-processes for the
  classical and relativistic Nelson models

abstract:
  We construct $P(phi)_1$-processes indexed by the full time-line, separately
derived from the functional integral representations of the relativistic and
non-relativistic Nelson models in quantum field theory. These two cases differ
essentially by sample path regularity. Associated with these processes we
define a martingale which, under an appropriate scaling, allows to obtain a
central limit theorem for additive functionals of these processes. We discuss a
number of examples by choosing specific functionals related to particle-field
operators.


title:
Extending Geant4 Parallelism with External Libraries (MPI, TBB) and Its
  Use on HPC Resources

abstract:
  With Geant4 Version 10.0, released in December 2013, one of the most widely
used Monte-Carlo codes has been ported to take full advantage of multi- and
many-core CPUs thanks to the introduction of event-level parallelism via
multithreading. In this paper we review recent developments to allow for a
better integration of parallel Geant4 jobs with external libraries. We have
chosen to develop examples using the popular Intel Threading Building Block
(for short TBB) as an alternative parallelization approach to the native Geant4
POSIX. To simplify the scaling of a Geant4 application across nodes on a
cluster we are improving the support of MPI in Geant4. In particular it is now
possible to run an hybrid MPI/MT application that uses MPI to scale across
nodes and MT to scale across cores. %The recent developments allow users to
easily implement parallel application resources that scale on a very large
number of nodes and cores typical of HPC resources.


title:
Optimal bounds for decay of correlations and {\alpha}-mixing for
  nonuniformly hyperbolic dynamical systems

abstract:
  We investigate the decay rates of correlations for nonuniformly hyperbolic
systems with or without singularities, on piecewise H\"older observables. By
constructing a new scheme of coupling methods using the probability renewal
theory, we obtain the optimal bounds for decay rates of correlations for a
large class of such observables. We also establish the alpha-mixing property
for time series generated by these systems, which leads to a vast ranges of
limiting theorems. Our results apply to rather general hyperbolic systems with
singularities, including Bunimovich flower billiards, semidispersing billiards
on a rectangle and billiards with cusps, and other nonuniformly hyperbolic
maps.


title: A geometric iterated function system on triangles

abstract:
  We construct a converging geometric iterated function system on the moduli
space of ordered triangles, for which the involved functions have geometric
meanings and contain a non-contraction map under the natural metric.


title:
From local to global conjugacy of subgroups of relatively hyperbolic
  groups

abstract:
  Suppose that a finitely generated group $G$ is hyperbolic relative to a
collection of subgroups $\mathbb{P}=\{P_1,\dots,P_m\}$. Let $H_1,H_2$ be
subgroups of $G$ such that $H_1$ is relatively quasiconvex with respect to
$\mathbb{P}$ and $H_2$ is not parabolic. Suppose that $H_2$ is elementwise
conjugate into $H_1$. Then there exists a finite index subgroup of $H_2$ which
is conjugate into $H_1$. The minimal length of the conjugator can be estimated.
In the case where $G$ is a limit group, it is sufficient to assume only that
$H_1$ is a finitely generated and $H_2$ is an arbitrary subgroup of $G$.


title: Analysis of a spatially deconvolved solar pore

abstract:
  Solar pores are active regions with large magnetic field strengths and
apparent simple magnetic configurations. Their properties resemble the ones
found for the sunspot umbra although pores do not show penumbra. Therefore,
solar pores present themselves as an intriguing phenomenon that is not
completely understood. We examine in this work a solar pore observed with
Hinode/SP using two state of the art techniques. The first one is the spatial
deconvolution of the spectropolarimetric data that allows removing the stray
light contamination induced by the spatial point spread function of the
telescope. The second one is the inversion of the Stokes profiles assuming
local thermodynamic equilibrium that let us to infer the atmospheric physical
parameters. After applying these techniques, we found that the spatial
deconvolution method does not introduce artefacts, even at the edges of the
magnetic structure, where large horizontal gradients are detected on the
atmospheric parameters. Moreover, we also describe the physical properties of
the magnetic structure at different heights finding that, in the inner part of
the solar pore, the temperature is lower than outside, the magnetic field
strength is larger than 2 kG and unipolar, and the LOS velocity is almost null.
At neighbouring pixels, we found low magnetic field strengths of same polarity
and strong downward motions that only occur at the low photosphere, below the
continuum optical depth $\log \tau=-1$. Finally, we studied the spatial
relation between different atmospheric parameters at different heights
corroborating the physical properties described before.


title: A decoherence-free subspace in a charge quadrupole qubit

abstract:
  Quantum computing promises significant speed-up for certain types of
computational problems. However, robust implementations of semiconducting
qubits must overcome the effects of charge noise that currently limit coherence
during gate operations. Here we describe a scheme for protecting solid-state
qubits from uniform electric field fluctuations by generalizing the concept of
a decoherence-free subspace for spins, and we propose a specific physical
implementation: a quadrupole charge qubit formed in a triple quantum dot. The
unique design of the quadrupole qubit enables a particularly simple pulse
sequence for suppressing the effects of noise during gate operations.
Simulations yield gate fidelities 10-1,000 times better than traditional charge
qubits, depending on the magnitude of the environmental noise. Our results
suggest that any qubit scheme employing Coulomb interactions (for example,
encoded spin qubits or two-qubit gates) could benefit from such a quadrupolar
design.


title:
Investigation of magnetic phases in parent compounds of
  Iron-chalcogenides via quasiparticle scattering interference

abstract:
  We employ a five-orbital tight-binding model to develop the mean field
solution for various possible spin density wave states in the
iron-chalcogenides. The quasiparticle interference (QPI) technique is applied
to detect signatures of these states due to scatterings arising from
non-magnetic impurities. Apart from the experimentally observed double striped
structure with ordering vector $(\pi/2,\pi/2)$, the QPI method is investigated
for the extended-stripe as well as the orthogonal double stripe phase. We
discuss QPI as a possible tool to detect and classify various magnetic
structures with different electronic structure reconstruction within framework
of the Fe$_{1+y}$Te compound.


title:
Algorithms for Overcoming the Curse of Dimensionality for Certain
  Hamilton-Jacobi Equations Arising in Control Theory and Elsewhere

abstract:
  It is well known that time dependent Hamilton-Jacobi-Isaacs partial
differential equations (HJ PDE), play an important role in analyzing continuous
dynamic games and control theory problems. An important tool for such problems
when they involve geometric motion is the level set method. This was first used
for reachability problems. The cost of these algorithms, and, in fact, all PDE
numerical approximations is exponential in the space dimension and time.
  In this work we propose and test methods for solving a large class of the HJ
PDE relevant to optimal control problems without the use of grids or numerical
approximations. Rather we use the classical Hopf formulas for solving initial
value problems for HJ PDE. We have noticed that if the Hamiltonian is convex
and positively homogeneous of degree one that very fast methods exist to solve
the resulting optimization problem. This is very much related to fast methods
for solving problems in compressive sensing, based on $\ell_1$ optimization. We
seem to obtain methods which are polynomial in the dimension. Our algorithm is
very fast, requires very low memory and is totally parallelizable. We can
evaluate the solution and its gradient in very high dimensions at $10^{-4}$ to
$10^{-8}$ seconds per evaluation on a laptop.
  We carefully explain how to compute numerically the optimal control from the
numerical solution of the associated initial valued HJ-PDE for a class of
optimal control problems. We show that our algorithms compute all the
quantities we need to obtain easily the controller.
  The term curse of dimensionality, was coined by Richard Bellman in 1957 when
considering problems in dynamic optimization.


title:
Pseudopotential MRT lattice Boltzmann model for cavitation bubble
  collapse with high density ratio

abstract:
  The dynamics of the cavitation bubble collapse is a fundamental issue for the
bubble collapse application and prevention. In present work, the modified
forcing scheme for the pseudopotential multi-relaxation-time lattice Boltzmann
model developed by Li Q. et al. is adopted to develop a cavitation bubble
collapse model. In the respects of coexistence curves and Laplace law
verification, the improved pseudopotential multi-relaxation-time lattice
Boltzmann model is investigated. The independence between the kinematic
viscosity and the thermodynamic consistency, surface tension is founded. By
homogeneous and heterogeneous cavitation simulation, the capability of the
present model to describe the cavitation bubble development as well as the
cavitation inception is verified. The bubble collapse between two parallel
walls is simulated. The dynamic process of collapsing bubble is consistent with
the results from experiments and simulations by other numerical method. It is
demonstrated that the present pseudopotential multi-relaxation-time lattice
Boltzmann model is available and efficient, and the lattice Boltzmann method is
an alternative tool for collapsing bubble modeling.


title:
A Sobolev Space theory for stochastic partial differential equations
  with time-fractional derivatives

abstract:
  In this article we present an $L_p$-theory ($p\geq 2$) for the
time-fractional quasi-linear stochastic partial differential equations (SPDEs)
of type $$ \partial^{\alpha}_tu=L(\omega,t,x)u+f(u)+\partial^{\beta}_t
\sum_{k=1}^{\infty}\int^t_0 ( \Lambda^k(\omega,t,x)u+g^k(u))dw^k_t, $$ where
$\alpha\in (0,2)$, $\beta <\alpha+\frac{1}{2}$, and $\partial^{\alpha}_t$ and
$\partial^{\beta}_t$ denote the Caputo derivative of order $\alpha$ and $\beta$
respectively. The processes $w^k_t$, $k\in \mathbb{N}=\{1,2,\cdots\}$, are
independent one-dimensional Wiener processes defined on a probability space
$\Omega$, $L$ is a second order operator of either divergence or non-divergence
type, and $\Lambda^k$ are linear operators of order up to two. The coefficients
of the equations depend on $\omega (\in \Omega), t,x$ and are allowed to be
discontinuous. This class of SPDEs can be used to describe random effects on
transport of particles in medium with thermal memory or particles subject to
sticking and trapping.


title:
Multiple K Means++ Clustering of Satellite Image Using Hadoop MapReduce
  and Spark

abstract:
  Clustering of image is one of the important steps of mining satellite images.
In our experiment we have simultaneously run multiple K-means algorithms with
different initial centroids and values of k in the same iteration of MapReduce
jobs. For initialization of initial centroids we have implemented Scalable
K-Means++ MapReduce (MR) job [1]. We have also run a validation algorithm of
Simplified Silhouette Index [2] for multiple clustering outputs, again in the
same iteration of MR jobs. This paper explored the behavior of above mentioned
clustering algorithms when run on big data platforms like MapReduce and Spark
jobs. Spark has been chosen as it is popular for fast processing particularly
where iterations are involved.


title: Modular invariants and singularity indices of hyperelliptic fibrations

abstract:
  The modular invariants of a family of semistable curves are the degrees of
the corresponding divisors on the image of the moduli map. The singularity
indices were introduced by G. Xiao to classify singular fibers of hyperelliptic
fibrations and to compute global invariants locally. In the semistable case, we
show that the modular invariants corresponding with the boundary classes are
just the singularity indices. As an application, we show that the formula of
Xiao for relative Chern numbers is the same as that of Cornalba-Harris in the
semistable case.


title:
Non-viscous Regularization of the Davey-Stewartson Equations: Analysis
  and Modulation Theory

abstract:
  In the present study we are interested in the Davey-Stewartson equations
(DSE) that model packets of surface and capillary-gravity waves. We focus on
the elliptic-elliptic case, for which it is known that DSE may develop a
finite-time singularity. We propose three systems of non-viscous regularization
to the DSE in variety of parameter regimes under which the finite blow-up of
solutions to the DSE occurs. We establish the global well-posedness of the
regularized systems for all initial data. The regularized systems, which are
inspired by the $\alpha$-models of turbulence and therefore are called the
$\alpha$-regularized DSE, are also viewed as unbounded, singularly perturbed
DSE. Therefore, we also derive reduced systems of ordinary differential
equations for the $\alpha$-regularized DSE by using the modulation theory to
investigate the mechanism with which the proposed non-viscous regularization
prevents the formation of the singularities in the regularized DSE. This is a
follow-up of the work of Cao, Musslimani and Titi on the non-viscous
$\alpha$-regularization of the nonlinear Schr\"odinger equation.


title:
Wave-shape function analysis -- when cepstrum meets time-frequency
  analysis

abstract:
  We propose to combine cepstrum and nonlinear time-frequency (TF) analysis to
study mutiple component oscillatory signals with time-varying frequency and
amplitude and with time-varying non-sinusoidal oscillatory pattern. The concept
of cepstrum is applied to eliminate the wave-shape function influence on the TF
analysis, and we propose a new algorithm, named de-shape synchrosqueezing
transform (de-shape SST). The mathematical model, adaptive non-harmonic model,
is introduced and the de-shape SST algorithm is theoretically analyzed. In
addition to simulated signals, several different physiological, musical and
biological signals are analyzed to illustrate the proposed algorithm.


title:
A series circuit of thermal rectifiers: an effective way to enhance
  rectification ratio

abstract:
  The low rectification ratio limits the application of thermal rectifiers. In
this paper, it is found that a series circuit of thermal rectifiers in
asymmetric graphene/graphene phononic crystal (GPnC) structures can improve
rectification significantly. The simulations by using non-equilibrium molecular
dynamics (NEMD) are performed. Moreover, the size effect on thermal
rectification is also studied and discussed.


title: A computation concerning relative Hilbert-Kunz multiplicities

abstract:
  In preparing the paper "Some extensions of Hilbert-Kunz multiplicity", we had
occasion to perform an intricate set of computations pertaining to a single
illustrative example. In the end, we have decided not to include the
computations in the main paper, but instead to publish them here for later
reference. In particular, the current preprint gives an example where the
converse to one of our main theorems holds, even though it does not fit into
any of the previously known cases where a converse holds.


title:
CV-QKD with Gaussian and non-Gaussian Entangled States over
  Satellite-based Channels

abstract:
  In this work we investigate the effectiveness of continuous-variable (CV)
entangled states, transferred through high-loss atmospheric channels, as a
means of viable quantum key distribution (QKD) between terrestrial stations and
low-Earth orbit (LEO) satellites. In particular, we investigate the role played
by the Gaussian CV states as compared to non-Gaussian states. We find that
beam-wandering induced atmospheric losses lead to QKD performance levels that
are in general quite different from those found in fixed-attenuation channels.
For example, circumstances can be found where no QKD is viable at some fixed
loss in fiber but is viable at the same mean loss in fading channels. We also
find that, in some circumstances, the QKD relative performance of Gaussian and
non-Gaussian states can in atmospheric channels be the reverse of that found in
fixed-attenuation channels. These findings show that the nature of the
atmospheric channel can have a large impact on the QKD performance. Our results
should prove useful for emerging global quantum communications that use LEO
satellites as communication relays.


title: Relative Equilibria in the Spherical, Finite Density 3-Body Problem

abstract:
  The relative equilibria for the spherical, finite density 3 body problem are
identified. Specifically, there are 28 distinct relative equilibria in this
problem which include the classical 5 relative equilibria for the point-mass
3-body problem. None of the identified relative equilibria exist or are stable
over all values of angular momentum. The stability and bifurcation pathways of
these relative equilibria are mapped out as the angular momentum of the system
is increased. This is done under the assumption that they have equal and
constant densities and that the entire system rotates about its maximum moment
of inertia. The transition to finite density greatly increases the number of
relative equilibria in the 3-body problem and ensures that minimum energy
configurations exist for all values of angular momentum.


title: Sch\"utzenberger Products in a Category

abstract:
  The Sch\"utzenberger product of monoids is a key tool for the algebraic
treatment of language concatenation. In this paper we generalize the
Sch\"utzenberger product to the level of monoids in an algebraic category
$\mathscr{D}$, leading to a uniform view of the corresponding constructions for
monoids (Sch\"utzenberger), ordered monoids (Pin), idempotent semirings
(Kl\'ima and Pol\'ak) and algebras over a field (Reutenauer). In addition,
assuming that $\mathscr{D}$ is part of a Stone-type duality, we derive a
characterization of the languages recognized by Sch\"utzenberger products.


title: Darboux Calculus

abstract:
  We introduce a formalism to analyze partially defined functions between
ordered sets. We show that our construction provides a uniform and conceptual
approach to all the main definitions encountered in elementary real analysis
including Dedekind cuts, limits and continuity.


title: Interaction of Two Filament Channels of Different Chiralities

abstract:
  We present observations of interactions between the two filament channels of
different chiralities and associated dynamics that occurred during 2014 April
18 -- 20. While two flux ropes of different helicity with parallel axial
magnetic fields can only undergo a bounce interaction when they are brought
together, the observations at the first glance show that the heated plasma is
moving from one filament channel to the other. The SDO/AIA 171 A observations
and the PFSS magnetic field extrapolation reveal the presence of fan-spine
magnetic configuration over the filament channels with a null point located
above them. Three different events of filament activations, partial eruptions,
and associated filament channel interactions have been observed. The activation
initiated in one filament channel seems to propagate along the neighbour
filament channel. We believe that the activation and partial eruption of the
filaments bring the field lines of flux ropes containing them closer to the
null point and trigger the magnetic reconnection between them and the fan-spine
magnetic configuration. As a result, the hot plasma moves along the outer spine
line toward the remote point. Utilizing the present observations, for the first
time we have discussed how two different-chirality filament channels can
interact and show interrelation.


title:
Estimating Sparse Signals with Smooth Support via Convex Programming and
  Block Sparsity

abstract:
  Conventional algorithms for sparse signal recovery and sparse representation
rely on $l_1$-norm regularized variational methods. However, when applied to
the reconstruction of $\textit{sparse images}$, i.e., images where only a few
pixels are non-zero, simple $l_1$-norm-based methods ignore potential
correlations in the support between adjacent pixels. In a number of
applications, one is interested in images that are not only sparse, but also
have a support with smooth (or contiguous) boundaries. Existing algorithms that
take into account such a support structure mostly rely on non-convex methods
and---as a consequence---do not scale well to high-dimensional problems and/or
do not converge to global optima. In this paper, we explore the use of new
block $l_1$-norm regularizers, which enforce image sparsity while
simultaneously promoting smooth support structure. By exploiting the convexity
of our regularizers, we develop new computationally-efficient recovery
algorithms that guarantee global optimality. We demonstrate the efficacy of our
regularizers on a variety of imaging tasks including compressive image
recovery, image restoration, and robust PCA.


title: Asymmetric R\'enyi Problem and PATRICIA Tries

abstract:
  In 1960, R\'enyi asked for the number of random queries necessary to recover
a hidden bijective labeling of n distinct objects. In each query one selects a
random subset of labels and asks, what is the set of objects that have these
labels? We consider here an asymmetric version of the problem in which in every
query an object is chosen with probability p > 1/2 and we ignore "inconclusive"
queries. We study the number of queries needed to recover the labeling in its
entirety (the height), to recover at least one single element (the fillup
level), and to recover a randomly chosen element (the typical depth). This
problem exhibits several remarkable behaviors: the depth D_n converges in
probability but not almost surely and while it satisfies the central limit
theorem its local limit theorem doesn't hold; the height H_n and the fillup
level F_n exhibit phase transitions with respect to p in the second term. To
obtain these results, we take a unified approach via the analysis of the
external profile, defined at level k as the number of elements recovered by the
kth query. We first establish new precise asymptotic results for the average
and variance, and a central limit law, for the external profile in the regime
where it grows polynomially with n. We then extend the external profile results
to the boundaries of the central region, leading to the solution of our problem
for the height and fillup level. As a bonus, our analysis implies novel results
for analogous parameters of random PATRICIA tries.


title:
Discretization of Fractional Differential Equations by a Piecewise
  Constant Approximation

abstract:
  There has recently been considerable interest in using a nonstandard
piecewise approximation to formulate fractional order differential equations as
difference equations that describe the same dynamical behaviour and are more
amenable to a dynamical systems analysis. Unfortunately, due to mistakes in the
fundamental papers, the difference equations formulated through this process do
not capture the dynamics of the fractional order equations. We show that the
correct application of this nonstandard piecewise approximation leads to a one
parameter family of fractional order differential equations that converges to
the original equation as the parameter tends to zero. A closed formed solution
exists for each member of this family and leads to the formulation of a
difference equation that is of increasing order as time steps are taken. Whilst
this does not lead to a simplified dynamical analysis it does lead to a
numerical method for solving the fractional order differential equation. The
method is shown to be equivalent to a quadrature based method, despite the fact
that it has not been derived from a quadrature. The method can be implemented
with non-uniform time steps. An example is provided showing that the difference
equation can correctly capture the dynamics of the underlying fractional
differential equation.


title:
Sufficient Conditions for Tuza's Conjecture on Packing and Covering
  Triangles

abstract:
  Given a simple graph $G=(V,E)$, a subset of $E$ is called a triangle cover if
it intersects each triangle of $G$. Let $\nu_t(G)$ and $\tau_t(G)$ denote the
maximum number of pairwise edge-disjoint triangles in $G$ and the minimum
cardinality of a triangle cover of $G$, respectively. Tuza conjectured in 1981
that $\tau_t(G)/\nu_t(G)\le2$ holds for every graph $G$. In this paper, using a
hypergraph approach, we design polynomial-time combinatorial algorithms for
finding small triangle covers. These algorithms imply new sufficient conditions
for Tuza's conjecture on covering and packing triangles. More precisely,
suppose that the set $\mathscr T_G$ of triangles covers all edges in $G$. We
show that a triangle cover of $G$ with cardinality at most $2\nu_t(G)$ can be
found in polynomial time if one of the following conditions is satisfied: (i)
$\nu_t(G)/|\mathscr T_G|\ge\frac13$, (ii) $\nu_t(G)/|E|\ge\frac14$, (iii)
$|E|/|\mathscr T_G|\ge2$.
  Keywords: Triangle cover, Triangle packing, Linear 3-uniform hypergraphs,
Combinatorial algorithms


title:
Spurious symmetry-broken phase in a bidirectional two-lane ASEP with
  narrow entrances: A perspective from mean field analysis and current
  minimization principle

abstract:
  As one of the paradigmatic models of non-equilibrium systems, the asymmetric
simple exclusion process (ASEP) has been widely used to study many physical,
chemical, and biological systems. The ASEP shows a range of nontrivial
macroscopic phenomena, among which, the spontaneous symmetry breaking has
gained much attention. Nevertheless, as a basic problem, it has been
controversial that whether there exist one or two symmetry-broken phases in the
ASEP. Based on mean field analysis and current minimization principle, this
paper demonstrates that one of the broken-symmetry phases does not exist in a
bidirectional two-lane ASEP with narrow entrances. Moreover, an exponential
decay feature is observed, which has been used to predict phase boundary in the
thermodynamic limit. Our findings might be generalized to other ASEP models and
thus deepen the understanding of the spontaneous symmetry breaking in
non-equilibrium systems.


title:
Effects of quantum confinement on excited state properties of SrTiO$_3$
  from ab initio many-body perturbation theory

abstract:
  The Ruddlesden-Popper (RP) homologous series Sr$_{n+1}$Ti$_{n}$O$_{3n+1}$
provides a useful template for the study and control of the effects of
dimensionality and quantum confinement on the excited state properties of the
complex oxide SrTiO$_3$. We use ab initio many-body perturbation theory within
the $GW$ approximation and the Bethe-Salpeter equation approach to calculate
quasiparticle energies and absorption spectrum of Sr$_{n+1}$Ti$_{n}$O$_{3n+1}$
for $n=1-5$ and $\infty$. Our computed direct and indirect optical gaps are in
excellent agreement with spectroscopic measurements. The calculated optical
spectra reproduce the main experimental features and reveal excitonic structure
near the gap edge. We find that electron-hole interactions are important across
the series, leading to significant exciton binding energies that increase for
small $n$ and reach a value of 330~meV for $n=1$, a trend attributed to
increased quantum confinement. We find that the lowest-energy singlet exciton
of Sr$_2$TiO$_4$ ($n=1$) localizes in the 2D plane defined by the TiO$_2$
layer, and explain the origin of its localization.


title:
The effects of graphite nanoparticles, phase change material, and film
  cooling on the solar still performance

abstract:
  In this paper, we performed four modifications on the solar still, as (A)
adding the graphite nanoparticles, (B) the graphite nanoparticles together with
the phase change material (PCM), (C) the graphite nanoparticles together with
glass film cooling, and (D) graphite nanoparticles with both PCM and glass film
cooling. The effects of modifications are measured and compared with each
other. The productivities of modified (A), (B), (C), and (D) solar stills are
enhanced by about 50.28%, 65.00%, 56.15% and 73.80%, respectively, as compared
with the conventional solar still. The influences of saline water depths on the
performance of modifications (A) and (B) are also considered. Results revealed
that the best output yield is obtained for 0.5cm water depth for all solar
stills.


title:
On a representation of Humbert's double hypergeometric series $\Phi_3$
  in a series of Gauss's $_2F_1$ function

abstract:
  Very recently a new series representation of Humbert's double hypergeometric
series $\Phi_3$ in series of Gauss's $_2F_1$ function was given by one of us.
The aim of this short research note is to provide an alternative proof of the
result. A few interesting special cases are also given.


title:
ScientoBASE: A Framework and Model for Computing Scholastic Indicators
  of non-local influence of Journals via Native Data Acquisition algorithms

abstract:
  Defining and measuring internationality as a function of influence diffusion
of scientific journals is an open problem. There exists no metric to rank
journals based on the extent or scale of internationality. Measuring
internationality is qualitative, vague, open to interpretation and is limited
by vested interests. With the tremendous increase in the number of journals in
various fields and the unflinching desire of academics across the globe to
publish in "international" journals, it has become an absolute necessity to
evaluate, rank and categorize journals based on internationality. Authors, in
the current work have defined internationality as a measure of influence that
transcends across geographic boundaries. There are concerns raised by the
authors about unethical practices reflected in the process of journal
publication whereby scholarly influence of a select few are artificially
boosted, primarily by resorting to editorial maneuvres. To counter the impact
of such tactics, authors have come up with a new method that defines and
measures internationality by eliminating such local effects when computing the
influence of journals. A new metric, Non-Local Influence Quotient(NLIQ) is
proposed as one such parameter for internationality computation along with
another novel metric, Other-Citation Quotient as the complement of the ratio of
self-citation and total citation. In addition, SNIP and International
Collaboration Ratio are used as two other parameters.


title: Suppressed Density of States in Self-Generated Coulomb Glasses

abstract:
  We investigate the structure of metastable states in self-generated Coulomb
glasses. In dramatic contrast to disordered electron glasses, we find that
these states lack marginal stability. Such absence of marginal stability is
reflected by the suppression of the single-particle density of states into an
exponentially soft gap of the form $g(\epsilon) \sim e^{-V / \xi |\epsilon|}$.
To analytically explain this behavior, we extend the stability criterion of
Efros and Shklovskii to incorporate local charge correlations, in qualitative
agreement with our numerical findings. Our work suggests the existence of a new
class of self-generated glasses dominated by strong geometric frustration.


title: A normality criterion generalizing Gu's result

abstract:
  In this paper we prove a normality criterion for the families of meromorphic
functions involving sharing of functions. Our result generalizes some of the
earlier results on Gu's normality criterion.


title:
Persistent AUV Operations Using a Robust Reactive Mission and Path
  Planning (RRMPP) Architecture

abstract:
  Providing a higher level of decision autonomy and accompanying prompt changes
of an uncertain environment is a true challenge of AUVs autonomous operations.
The proceeding approach introduces a robust reactive structure that
accommodates an AUV's mission planning, task-time management in a top level and
incorporates environmental changes by a synchronic motion planning in a lower
level. The proposed architecture is developed in a hierarchal modular format
and a bunch of evolutionary algorithms are employed by each module to
investigate the efficiency and robustness of the structure in different mission
scenarios while water current data, uncertain static-mobile/motile obstacles,
and vehicles Kino-dynamic constraints are taken into account. The motion
planner is facilitated with online re-planning capability to refine the
vehicle's trajectory based on local variations of the environment. A small
computational load is devoted for re-planning procedure since the upper layer
mission planner renders an efficient overview of the operation area that AUV
should fly thru. Numerical simulations are carried out to investigate
robustness and performance of the architecture in different situations of a
real-world underwater environment. Analysis of the simulation results claims
the remarkable capability of the proposed model in accurate mission
task-time-threat management while guarantying a secure deployment during the
mission.


title:
Robust Optical Flow Estimation of Double-Layer Images under Transparency
  or Reflection

abstract:
  This paper deals with a challenging, frequently encountered, yet not properly
investigated problem in two-frame optical flow estimation. That is, the input
frames are compounds of two imaging layers -- one desired background layer of
the scene, and one distracting, possibly moving layer due to transparency or
reflection. In this situation, the conventional brightness constancy constraint
-- the cornerstone of most existing optical flow methods -- will no longer be
valid. In this paper, we propose a robust solution to this problem. The
proposed method performs both optical flow estimation, and image layer
separation. It exploits a generalized double-layer brightness consistency
constraint connecting these two tasks, and utilizes the priors for both of
them. Experiments on both synthetic data and real images have confirmed the
efficacy of the proposed method. To the best of our knowledge, this is the
first attempt towards handling generic optical flow fields of two-frame images
containing transparency or reflection.


title:
Electrical measurement of magnetic-field-impeded polarity switching of a
  ferromagnetic vortex core

abstract:
  Vortex core polarity switching in NiFe disks has been evidenced using an
all-electrical rectification scheme. Both simulation and experiments yield a
consistent loss of the rectified signal when driving the core at high powers
near its gyrotropic resonant frequency. The frequency range over which the loss
occurs grows and shifts with increasing signal power, consistent with
non-linear core dynamics and periodic switching of the core polarity induced by
the core attaining its critical velocity. We demonstrate that core polarity
switching can be impeded by displacing the core towards the disk's edge where
an increased core stiffness reduces the maximum attainable core velocity.


title: Intrinsic Negative Poisson's Ratio for Single-Layer Graphene

abstract:
  Negative Poisson's ratio (NPR) materials have drawn significant interest
because the enhanced toughness, shear resistance and vibration absorption that
typically are seen in auxetic materials may enable a range of novel
applications. In this work, we report that single-layer graphene exhibits an
intrinsic NPR, which is robust and independent of its size and temperature. The
NPR arises due to the interplay between two intrinsic deformation pathways (one
with positive Poisson's ratio, the other with NPR), which correspond to the
bond stretching and angle bending interactions in graphene. We propose an
energy-based deformation pathway criteria, which predicts that the pathway with
NPR has lower energy and thus becomes the dominant deformation mode when
graphene is stretched by a strain above 6%, resulting in the NPR phenomenon.


title: Two-sided Quantum Amplitude Amplification and Exact-Error Algorithms

abstract:
  Amplitude amplification is a central tool used in Grover's quantum search
algorithm and has been used in various forms in numerous quantum algorithms
since then. It has been shown to completely eliminate one-sided error of
quantum search algorithms where input is accessed in the form of black-box
queries. We generalize amplitude amplification for two-sided error quantum
algorithm for decision problems in the familiar form where input is accessed in
the form of initial states of quantum circuits and where arbitrary projective
measurements may be used to ascertain success or failure. This generalization
allows us to derive interesting applications of amplitude amplification for
distinguishing between two given distributions based on their samples,
detection of faults in quantum circuits and eliminating error of one and
two-sided quantum algorithms with exact errors.


title:
Downlink Transmission of Short Packets: Framing and Control Information
  Revisited

abstract:
  Cellular wireless systems rely on frame-based transmissions. The frame design
is conventionally based on heuristics, consisting of a frame header and a data
part. The frame header contains control information that provides pointers to
the messages within the data part. In this paper, we revisit the principles of
frame design and show the impact of the new design in scenarios that feature
short data packets which are central to various 5G and Internet of Things
applications. We treat framing for downlink transmission in an AWGN broadcast
channel with K users, where the sizes of the messages to the users are random
variables. Using approximations from finite blocklength information theory, we
establish a framework in which a message to a given user is not necessarily
encoded as a single packet, but may be grouped with the messages to other users
and benefit from the improved efficiency of longer codes. This requires changes
in the way control information is sent, and it requires that the users need to
spend power decoding other messages, thereby increasing the average power
consumption. We show that the common heuristic design is only one point on a
curve that represents the trade-off between latency and power consumption.


title:
Exchange-mediated, non-linear, out-of-plane magnetic field dependence of
  the ferromagnetic vortex gyrotropic mode frequency driven by core deformation

abstract:
  We have performed micromagnetic simulations of the vortex gyrotropic mode
resonance in a range of disk geometries subject to spatially uniform
out-of-plane magnetic fields. For disks of small lateral dimensions, we observe
a drop-off in the mode's frequency for field amplitudes approaching the disk
saturation field. This non-linear frequency response is shown to be associated
with an increased vortex core deformation, which results from the demagnetizing
field created when the core is shifted laterally. Such deformation results in
an increase in the average out-of-plane magnetization of the displaced vortex
state, which through an exchange contribution, leads to a sharp decrease in the
vortex stiffness coefficient. It is this decrease in the vortex stiffness
coefficient which leads to the non-linear field dependence of the gyrotropic
mode frequency.


title:
Some stochastic time-fractional diffusion equations with variable
  coefficients and time dependent noise

abstract:
  We prove the existence and uniqueness of mild solution for the stochastic
partial differential equation $$\left(\partial^\alpha - \textit{B} \right)
u(t,x)= u(t,x) \cdot \dot{W}(t,x),$$ where $$\alpha \in (1/2, 1)\cup(1, 2);$$
$\textit{B}$ is an uniform elliptic operator with variable coefficients and
$\dot W$ is a Gaussian noise general in time with space covariance given by
fractional, Riesz and Bessel kernel.


title: Cross-Graph Learning of Multi-Relational Associations

abstract:
  Cross-graph Relational Learning (CGRL) refers to the problem of predicting
the strengths or labels of multi-relational tuples of heterogeneous object
types, through the joint inference over multiple graphs which specify the
internal connections among each type of objects. CGRL is an open challenge in
machine learning due to the daunting number of all possible tuples to deal with
when the numbers of nodes in multiple graphs are large, and because the labeled
training instances are extremely sparse as typical. Existing methods such as
tensor factorization or tensor-kernel machines do not work well because of the
lack of convex formulation for the optimization of CGRL models, the poor
scalability of the algorithms in handling combinatorial numbers of tuples,
and/or the non-transductive nature of the learning methods which limits their
ability to leverage unlabeled data in training. This paper proposes a novel
framework which formulates CGRL as a convex optimization problem, enables
transductive learning using both labeled and unlabeled tuples, and offers a
scalable algorithm that guarantees the optimal solution and enjoys a linear
time complexity with respect to the sizes of input graphs. In our experiments
with a subset of DBLP publication records and an Enzyme multi-source dataset,
the proposed method successfully scaled to the large cross-graph inference
problem, and outperformed other representative approaches significantly.


title:
Observations of an X-shaped Ribbon Flare in the Sun and Its
  Three-dimensional Magnetic Reconnection

abstract:
  We report evolution of an atypical X-shaped flare ribbon which provides novel
observational evidence of three-dimensional (3D) magnetic reconnection at a
separator. The flare occurred on 2014 November 9. High-resolution slit-jaw 1330
A images from the Interface Region Imaging Spectrograph reveal four
chromospheric flare ribbons that converge and form an X-shape. Flare
brightening in the upper chromosphere spreads along the ribbons toward the
center of the "X" (the X-point), and then spreads outward in a direction more
perpendicular to the ribbons. These four ribbons are located in a quadrupolar
magnetic field. Reconstruction of magnetic topology in the active region
suggests the presence of a separator connecting to the X-point outlined by the
ribbons. The inward motion of flare ribbons in the early stage therefore
indicates 3D magnetic reconnection between two sets of non-coplanar loops that
approach laterally, and reconnection proceeds downward along a section of
vertical current sheet. Coronal loops are also observed by the Atmospheric
Imaging Assembly on board the Solar Dynamics Observatory confirming the
reconnection morphology illustrated by ribbon evolution.


title:
Arbitrarily Varying Networks: Capacity-achieving Computationally
  Efficient Codes

abstract:
  We consider the problem of communication over a network containing a hidden
and malicious adversary that can control a subset of network resources, and
aims to disrupt communications. We focus on omniscient node-based adversaries,
i.e., the adversaries can control a subset of nodes, and know the message,
network code and packets on all links. Characterizing information-theoretically
optimal communication rates as a function of network parameters and bounds on
the adversarially controlled network is in general open, even for unicast
(single source, single destination) problems. In this work we characterize the
information-theoretically optimal randomized capacity of such problems, i.e.,
under the assumption that the source node shares (an asymptotically negligible
amount of) independent common randomness with each network node a priori (for
instance, as part of network design). We propose a novel
computationally-efficient communication scheme whose rate matches a natural
information-theoretically "erasure outer bound" on the optimal rate. Our
schemes require no prior knowledge of network topology, and can be implemented
in a distributed manner as an overlay on top of classical distributed linear
network coding.


title: Evolution of science I: Evolution of Mind

abstract:
  The central nervous system and particularly the brain was designed to control
the life cycle of a living being. With increasing size and sophistication, in
mammals, the brain became capable of exercising significant control over life.
In Homo Sapiens the brain became significantly powerful and capable of
comprehension beyond survival needs with visualisation, formal thought and long
term memory. Here we trace the rise of the powers of the brains of the Homo
Sapiens and its capability of three comprehending the three spatial dimensions
as well as time. By tracing the evolution of technology over the last
millennium and particularly the late arrival of astronomy to discuss the
evolution of the formal thinking process in humans. In a follow up paper we
will trace the extensive use of this new faculty by humans to comprehend the
working of the universe.


title: Evolution of science II: Insights into working of Nature

abstract:
  We attempt to provide a comprehensive model of evolution of science across
millennia taking into account the contributions of other intellectual
traditions, cultural value system and increasing in sophistication of humans in
their study of nature. We also briefly discuss the role of technology and its
interplay in the evolution of science. We identify five primary approaches to
the study of nature, namely ad hoc formulations, religious approach, pragmatic
approach, axiomatic approach and the logic based approach. Each of these
approaches have had their prime periods and have contributed significantly to
human understanding of nature and have also overlapped within a society. Each
approach has had a central role over human evolution at some stage. We surmise
that the currently dominant axiomatic method will reach its limits due to
complexity of the system and may never be fully formalised. We suggest that the
future progress of science will more be a logic based approach where
experimentation and simulations rather than axiomatic firmness will be used to
test our understanding of nature.


title:
Construction of a minimal mass blow up solution of the modified
  Benjamin-Ono equation

abstract:
  We construct a minimal mass blow up solution of the modified Benjamin-Ono
equation (mBO) \[ u_{t}+(u^3-D^1 u)_{x}=0, \] which is a standard mass critical
dispersive model. Let $Q\in H^{\frac 12}$, $Q>0$, be the unique ground state
solution of $D^1 Q +Q=Q^3$, constructed using variational arguments by
Weinstein (Comm. PDE, 12 (1987), J. Diff. Eq., 69 (1987)) and Albert, Bona and
Saut (Proc. Royal London Soc., 453 (1997)), and whose uniqueness was recently
proved by Frank and Lenzmann (Acta Math., 210 (2013)).
  We show the existence of a solution $S$ of (mBO) satisfying $\|S
\|_{L^2}=\|Q\|_{L^2}$ and \[ S(t)-\frac1{\lambda^{\frac12}(t)}
Q\left(\frac{\cdot - x(t)}{\lambda(t)}\right)\to 0\quad \mbox{ in }\ H^{\frac
12}(\mathbb R) \mbox{ as }\ t\downarrow 0, \] where \[ \lambda(t)\sim t,\quad
x(t) \sim -|\ln t| \quad \hbox{and}\quad \|S(t)\|_{\dot H^{\frac 12}} \sim
t^{-\frac 12}\|Q\|_{\dot H^{\frac 12}} \quad \hbox{as}\ t\downarrow 0. \] This
existence result is analogous to the one obtained by Martel, Merle and
Rapha\"el (J. Eur. Math. Soc., 17 (2015)) for the mass critical generalized
Korteweg-de Vries equation. However, in contrast with the (gKdV) equation, for
which the blow up problem is now well-understood in a neighborhood of the
ground state, $S$ is the first example of blow up solution for (mBO).
  The proof involves the construction of a blow up profile, energy estimates as
well as refined localization arguments, developed in the context of
Benjamin-Ono type equations by Kenig, Martel and Robbiano (Ann. Inst. H.
Poincar\'e, Anal. Non Lin., 28 (2011)). Due to the lack of information on the
(mBO) flow around the ground state, the energy estimates have to be
considerably sharpened in the present paper.


title:
DeepPicker: a Deep Learning Approach for Fully Automated Particle
  Picking in Cryo-EM

abstract:
  Particle picking is a time-consuming step in single-particle analysis and
often requires significant interventions from users, which has become a
bottleneck for future automated electron cryo-microscopy (cryo-EM). Here we
report a deep learning framework, called DeepPicker, to address this problem
and fill the current gaps toward a fully automated cryo-EM pipeline. DeepPicker
employs a novel cross-molecule training strategy to capture common features of
particles from previously-analyzed micrographs, and thus does not require any
human intervention during particle picking. Tests on the recently-published
cryo-EM data of three complexes have demonstrated that our deep learning based
scheme can successfully accomplish the human-level particle picking process and
identify a sufficient number of particles that are comparable to those manually
by human experts. These results indicate that DeepPicker can provide a
practically useful tool to significantly reduce the time and manual effort
spent in single-particle analysis and thus greatly facilitate high-resolution
cryo-EM structure determination.


title:
Beyond Local Search: Tracking Objects Everywhere with Instance-Specific
  Proposals

abstract:
  Most tracking-by-detection methods employ a local search window around the
predicted object location in the current frame assuming the previous location
is accurate, the trajectory is smooth, and the computational capacity permits a
search radius that can accommodate the maximum speed yet small enough to reduce
mismatches. These, however, may not be valid always, in particular for fast and
irregularly moving objects. Here, we present an object tracker that is not
limited to a local search window and has ability to probe efficiently the
entire frame. Our method generates a small number of "high-quality" proposals
by a novel instance-specific objectness measure and evaluates them against the
object model that can be adopted from an existing tracking-by-detection
approach as a core tracker. During the tracking process, we update the object
model concentrating on hard false-positives supplied by the proposals, which
help suppressing distractors caused by difficult background clutters, and learn
how to re-rank proposals according to the object model. Since we reduce
significantly the number of hypotheses the core tracker evaluates, we can use
richer object descriptors and stronger detector. Our method outperforms most
recent state-of-the-art trackers on popular tracking benchmarks, and provides
improved robustness for fast moving objects as well as for ultra low-frame-rate
videos.


title:
Probing the origin of our universe through primordial gravitational
  waves by Ali CMB project

abstract:
  This is a research highlight invited by SCIENCE CHINA Physics, Mechanics &
Astronomy.


title:
Gluon bound state and asymptotic freedom derived from the
  Bethe--Salpeter equation

abstract:
  In this paper we study the two-body bound states for gluons and ghosts in a
massive Yang-Mills theory which is obtained by generalizing the ordinary
massless Yang-Mills theory in a manifestly Lorentz covariant gauge. First, we
give a systematic derivation of the coupled Bethe-Salpeter equations for gluons
and ghosts by using the Cornwall-Jackiw-Tomboulis effective action of the
composite operators within the framework of the path integral quantization.
Then, we obtain the numerical solutions for the Bethe-Salpeter amplitude
representing the simultaneous bound states of gluons and ghosts by solving the
homogeneous Bethe-Salpeter equation in the ladder approximation. We study how
the inclusion of ghosts affects the two-gluon bound states in the cases of the
standing and running gauge coupling constant. Moreover, we show explicitly that
the approximate solutions obtained for the gluon-gluon amplitude are consistent
with the ultraviolet asymptotic freedom signaled by the negative $\beta$
function.


title: Resonances of third order differential operators

abstract:
  We consider resonances for third order ordinary differential operator with
compactly supported coefficients on the real line. Resonance are defined as
zeros of a Fredholm determinant on a non-physical sheet of three sheeted
Riemann surface. We determine upper bounds of the number of resonances in
complex discs at large radius. We express the trace formula in terms of
resonances only.


title: Perceptually Consistent Color-to-Gray Image Conversion

abstract:
  In this paper, we propose a color to grayscale image conversion algorithm
(C2G) that aims to preserve the perceptual properties of the color image as
much as possible. To this end, we propose measures for two perceptual
properties based on contemporary research in vision science: brightness and
multi-scale contrast. The brightness measurement is based on the idea that the
brightness of a grayscale image will affect the perception of the probability
of color information. The color contrast measurement is based on the idea that
the contrast of a given pixel to its surroundings can be measured as a linear
combination of color contrast at different scales. Based on these measures we
propose a graph based optimization framework to balance the brightness and
contrast measurements. To solve the optimization, an $\ell_1$-norm based method
is provided which converts color discontinuities to brightness discontinuities.
To validate our methods, we evaluate against the existing \cadik and Color250
datasets, and against NeoColor, a new dataset that improves over existing C2G
datasets. NeoColor contains around 300 images from typical C2G scenarios,
including: commercial photograph, printing, books, magazines, masterpiece
artworks and computer designed graphics. We show improvements in metrics of
performance, and further through a user study, we validate the performance of
both the algorithm and the metric.


title: On the origin of the hard X-ray tail in neutron-star X-ray binaries

abstract:
  Neutron star X-ray binaries emit a compact, optically thick, relativistic
radio jet during low-luminosity, usually hard states, as Galactic black-hole
X-ray binaries do. When radio emission is bright, a hard power-law tail without
evidence for an exponential cutoff is observed in most systems. We have
developed a jet model that explains many spectral and timing properties of
black-hole binaries in the states where a jet is present. Our goal is to
investigate whether our jet model can reproduce the hard tail, with the correct
range of photon index and the absence of a high-energy cutoff, in neutron-star
X-ray binaries. We have performed Monte Carlo simulations of the Compton
upscattering of soft, accretion-disk or boundary layer photons, in the jet and
computed the emergent energy spectra, as well as the time lag of hard photons
with respect to softer ones as a function of Fourier frequency. We demonstrate
that our jet model explains the observed power-law distribution with photon
index in the range 1.8-3. With an appropriate choice of the parameters, the
cutoff expected from Comptonization is shifted to energies above ~300 keV,
producing a pure power law without any evidence for a rollover, in agreement
with the observations. Our results reinforce the idea that the link between the
outflow (jet) and inflow (disk) in X-ray binaries does not depend on the nature
of the compact object, but on the process of accretion. Furthermore, we address
the differences of jets in black-hole and neutron-star X-ray binaries and
predict that the break frequency in the spectral energy distribution of
neutron-star X-ray binaries, as a class, will be lower than that of black-hole
binaries.


title:
Detecting Context Dependence in Exercise Item Candidates Selected from
  Corpora

abstract:
  We explore the factors influencing the dependence of single sentences on
their larger textual context in order to automatically identify candidate
sentences for language learning exercises from corpora which are presentable in
isolation. An in-depth investigation of this question has not been previously
carried out. Understanding this aspect can contribute to a more efficient
selection of candidate sentences which, besides reducing the time required for
item writing, can also ensure a higher degree of variability and authenticity.
We present a set of relevant aspects collected based on the qualitative
analysis of a smaller set of context-dependent corpus example sentences.
Furthermore, we implemented a rule-based algorithm using these criteria which
achieved an average precision of 0.76 for the identification of different
issues related to context dependence. The method has also been evaluated
empirically where 80% of the sentences in which our system did not detect
context-dependent elements were also considered context-independent by human
raters.


title: The KB paradigm and its application to interactive configuration

abstract:
  The knowledge base paradigm aims to express domain knowledge in a rich formal
language, and to use this domain knowledge as a knowledge base to solve various
problems and tasks that arise in the domain by applying multiple forms of
inference. As such, the paradigm applies a strict separation of concerns
between information and problem solving. In this paper, we analyze the
principles and feasibility of the knowledge base paradigm in the context of an
important class of applications: interactive configuration problems. In
interactive configuration problems, a configuration of interrelated objects
under constraints is searched, where the system assists the user in reaching an
intended configuration. It is widely recognized in industry that good software
solutions for these problems are very difficult to develop. We investigate such
problems from the perspective of the KB paradigm. We show that multiple
functionalities in this domain can be achieved by applying different forms of
logical inferences on a formal specification of the configuration domain. We
report on a proof of concept of this approach in a real-life application with a
banking company. To appear in Theory and Practice of Logic Programming (TPLP).


title: Ising Superconductivity in Transition Metal Dichalcogenides

abstract:
  In this work, we review the results of several recent works on the
experimental and theoretical studies of monolayer superconducting transition
metal dichalcogenides (TMD) such as superconducting MoS2 and NbSe2. We show how
the strong Ising spin-orbit coupling (SOC), a special type of SOC which pins
electron spins to out-of-plane directions, can affect the superconducting
properties of the materials. Particularly, we discuss how the in-plane upper
critical fields of the materials can be strongly enhanced by Ising SOC and how
TMD materials can be used to engineer topological superconductors and nodal
topological superconductors which support Majorana fermions.


title: On the Performance of Mobile Visible Light Communications

abstract:
  We experimentally characterize the performance of mobile VLC and propose
using OCT precoding to combat mobility-induced performance degradation. Results
show that for approximate 300-Mb/s mobile VLC transmission, OCT precoding
outperforms adaptive-loaded DMT and offers significant packet loss rate
reduction.


title: Classification of p-groups by their Schur multiplier

abstract:
  Let $G$ be a non-abelian $p$-group of order $p^n$ and $M(G)$ be its Schur
multiplier. It is well known result by Green that $|M(G)| \leq
p^{\frac{1}{2}n(n-1)}$. So $|M(G)|= p^{\frac{1}{2}n(n-1)-t(G)}$ for some $t(G)
\geq 0$. The groups has already been classified for $t(G) \leq 5$ by several
authors. For $t(G)=6$ the classification has been done. In this paper we
classify $p$-groups $G$ for $t(G) = 6$ in different method.


title:
Symmetries of Coefficients of Three-Term Relations for the
  Hypergeometric Series

abstract:
  Any three hypergeometric series whose respective parameters, a, b and c,
differ by integers satisfy a linear relation with coefficients that are
rational functions of a, b, c and the variable x. These relations are called
three-term relations. This paper shows that the coefficients of three-term
relations have properties called symmetries, and gives explicit formulas
describing the symmetries.


title:
Asymmetric sequential Landau-Zener dynamics of Bose condensed atoms in a
  cavity

abstract:
  We explore the asymmetric sequential Landau-Zener (LZ) dynamics in an
ensemble of interacting Bose condensed two-level atoms coupled with a cavity
field. Assuming the couplings between all atoms and the cavity field are
identical, the interplay between atom-atom interaction and detuning may lead to
a series of LZ transitions. Unlike the conventional sequential LZ transitions,
which are symmetric to the zero detuning, the LZ transitions of Bose condensed
atoms in a cavity field are asymmetric and sensitively depend on the photon
number distribution of the cavity. In LZ processes involving single excitation
numbers, both the variance of the relative atom number and the step slope of
the sequential population ladder are asymmetric, and the asymmetry become more
significant for smaller excitation numbers. Furthermore, in LZ processes
involving multiple excitation numbers, there may appear asymmetric population
ladders with decreasing step heights. During a dynamical LZ process, due to the
atom-cavity coupling, the cavity field shows dynamical collapse and revivals.
In comparison with the symmetric LZ transitions in a classical field, the
asymmetric LZ transitions in a cavity field originate from the
photon-number-dependent Rabi frequency. The asymmetric sequential LZ dynamics
of Bose condensed atoms in a cavity field may open up a new way to explore the
fundamental many-body physics in coupled atom-photon systems.


title:
Automated detection of extended sources in radio maps: progress from the
  SCORPIO survey

abstract:
  Automated source extraction and parameterization represents a crucial
challenge for the next-generation radio interferometer surveys, such as those
performed with the Square Kilometre Array (SKA) and its precursors. In this
paper we present a new algorithm, dubbed CAESAR (Compact And Extended Source
Automated Recognition), to detect and parametrize extended sources in radio
interferometric maps. It is based on a pre-filtering stage, allowing image
denoising, compact source suppression and enhancement of diffuse emission,
followed by an adaptive superpixel clustering stage for final source
segmentation. A parameterization stage provides source flux information and a
wide range of morphology estimators for post-processing analysis. We developed
CAESAR in a modular software library, including also different methods for
local background estimation and image filtering, along with alternative
algorithms for both compact and diffuse source extraction. The method was
applied to real radio continuum data collected at the Australian Telescope
Compact Array (ATCA) within the SCORPIO project, a pathfinder of the ASKAP-EMU
survey. The source reconstruction capabilities were studied over different test
fields in the presence of compact sources, imaging artefacts and diffuse
emission from the Galactic plane and compared with existing algorithms. When
compared to a human-driven analysis, the designed algorithm was found capable
of detecting known target sources and regions of diffuse emission,
outperforming alternative approaches over the considered fields.


title:
A computational intuition pump to examine group creativity: building on
  the ideas of others

abstract:
  This paper presents a computational approach to modelling group creativity.
It presents an analysis of two studies of group creativity selected from
different research cultures and identifies a common theme ("idea build-up")
that is then used in the formalisation of an agent-based model used to support
reasoning about the complex dynamics of building on the ideas of others.


title: Diamond photonics platform enabled by femtosecond laser writing

abstract:
  We demonstrate the first buried optical waveguides in diamond using focused
femtosecond laser pulses. The properties of nitrogen vacancy centers are
preserved in the waveguides, making them promising for diamond-based
magnetometers or quantum information systems.


title: Resource allocation using metaheuristic search

abstract:
  This research is focused on solving problems in the area of software project
management using metaheuristic search algorithms and as such is research in the
field of search based software engineering. The main aim of this research is to
evaluate the performance of different metaheuristic search techniques in
resource allocation and scheduling problems that would be typical of software
development projects. This paper reports a set of experiments which evaluate
the performance of three algorithms, namely simulated annealing, tabu search
and genetic algorithms. The experimental results indicate that all of the
metaheuristics search techniques can be used to solve problems in resource
allocation and scheduling within a software project. Finally, a comparative
analysis suggests that overall the genetic algorithm had performed better than
simulated annealing and tabu search.


title: Landau gauge Yang-Mills correlation functions

abstract:
  We investigate Landau gauge $SU(3)$ Yang-Mills theory in a systematic vertex
expansion scheme for the effective action with the functional renormalisation
group. Particular focus is put on the dynamical creation of the gluon mass gap
at non-perturbative momenta and the consistent treatment of quadratic
divergences. The non-perturbative ghost and transverse gluon propagators as
well as the momentum-dependent ghost-gluon, three-gluon and four-gluon vertices
are calculated self-consistently with the classical action as only input. The
apparent convergence of the expansion scheme is discussed and within the
errors, our numerical results are in quantitative agreement with available
lattice results.


title: Algorithm on rainbow connection for maximal outerplanar graphs

abstract:
  In this paper, we consider rainbow connection number of maximal outerplanar
graphs(MOPs) on algorithmic aspect. For the (MOP) $G$, we give sufficient
conditions to guarantee that $rc(G) = diam(G).$ Moreover, we produce the graph
with given diameter $d$ and give their rainbow coloring in linear time. X.Deng
et al. $\cite{XD}$ give a polynomial time algorithm to compute the rainbow
connection number of MOPs by the Maximal fan partition method, but only obtain
a compact upper bound. J. Lauri $\cite{JL}$ proved that, for chordal
outerplanar graphs given an edge-coloring, to verify whether it is rainbow
connected is NP-complete under the coloring, it is so for MOPs. Therefore we
construct Central-cut-spine of MOP $G,$ by which we design an algorithm to give
a rainbow edge coloring with at most $2rad(G)+2+c,0\leq c\leq rad(G)-2$ colors
in polynomial time.


title: Scaling solutions for Dilaton Quantum Gravity

abstract:
  Scaling solutions for the effective action in dilaton quantum gravity are
investigated within the functional renormalization group approach. We find
numerical solutions that connect ultraviolet and infrared fixed points as the
ratio between scalar field and renormalization scale $k$ is varied. In the
Einstein frame the quantum effective action corresponding to the scaling
solutions becomes independent of $k$.
  The field equations derived from this effective action can be used directly
for cosmology. Scale symmetry is spontaneously broken by a non-vanishing
cosmological value of the scalar field. For the cosmology corresponding to our
scaling solutions, inflation arises naturally. The effective cosmological
constant becomes dynamical and vanishes asymptotically as time goes to
infinity.


title:
Spectra of linear fractional composition operators on the Hardy and
  weighted Bergman spaces of the half-plane

abstract:
  We compute the spectra and the essential spectra of bounded linear fractional
composition operators acting on the Hardy and weighted Bergman spaces of the
upper half-plane. We are also able to extend the results to weighted Dirichlet
spaces of the upper half-plane.


title: Balanced embedding of degenerating Abelian varieties

abstract:
  For a certain maximal unipotent family of Abelian varieties over the
punctured disc, we show that after a base change, one can complete the family
over a disc such that the whole degeneration can be simultaneously balanced
embedded into a projective space by the theta functions. Then we study the
relationship between the balanced filling-in and the Gromov-Hausdorff limit of
flat K\"{a}hler metrics on the nearby fibers.


title: Incremental and Decremental Secret Key Agreement

abstract:
  We study the rate of change of the multivariate mutual information among a
set of random variables when some common randomness is added to or removed from
a subset. This is formulated more precisely as two new multiterminal secret key
agreement problems which ask how one can increase the secrecy capacity
efficiently by adding common randomness to a small subset of users, and how one
can simplify the source model by removing redundant common randomness that does
not contribute to the secrecy capacity. The combinatorial structure has been
clarified along with some meaningful open problems.


title: Optimal market making

abstract:
  Market makers provide liquidity to other market participants: they propose
prices at which they stand ready to buy and sell a wide variety of assets. They
face a complex optimization problem with both static and dynamic components.
They need indeed to propose bid and offer/ask prices in an optimal way for
making money out of the difference between these two prices (their bid-ask
spread). Since they seldom buy and sell simultaneously, and therefore hold long
and/or short inventories, they also need to mitigate the risk associated with
price changes, and subsequently skew their quotes dynamically. In this paper,
(i) we propose a general modeling framework which generalizes (and reconciles)
the various modeling approaches proposed in the literature since the
publication of the seminal paper "High-frequency trading in a limit order book"
by Avellaneda and Stoikov, (ii) we prove new general results on the existence
and the characterization of optimal market making strategies, (iii) we obtain
new closed-form approximations for the optimal quotes, (iv) we extend the
modeling framework to the case of multi-asset market making and we obtain
general closed-form approximations for the optimal quotes of a multi-asset
market maker, and (v) we show how the model can be used in practice in the
specific (and original) case of two credit indices.


title: Exercising Control When Confronted by a (Brownian) Spider

abstract:
  We consider the Brownian "spider," a construct introduced in \cite{Dubins}
and in \cite{Pitman}. In this note, the author proves the "spider" bounds by
using the dynamic programming strategy of guessing the optimal reward function
and subsequently establishing its optimality by proving its excessiveness.


title: Instabilities, motion and deformation of active fluid droplets

abstract:
  We consider two minimal models of active fluid droplets that exhibit complex
dynamics including steady motion, deformation, rotation and oscillating motion.
First we consider a droplet with a concentration of active contractile matter
adsorbed to its boundary. We analytically predict activity driven instabilities
in the concentration profile, and compare them to the dynamics we find from
simulations. Secondly, we consider a droplet of active polar fluid of constant
concentration. In this system we predict, motion and deformation of the
droplets in certain activity ranges due to instabilities in the polarisation
field. Both these systems show spontaneous transitions to motility and
deformation which resemble dynamics of the cell cytoskeleton in animal cells.


title:
Hybrid Double Quantum Dots: Normal, Superconducting, and Topological
  Regimes

abstract:
  Epitaxial semiconductor-superconductor hybrid materials are an excellent
basis for studying mesoscopic and topological superconductivity, as the
semiconductor inherits a hard superconducting gap while retaining tunable
carrier density. Here, we investigate double-quantum-dot devices made from InAs
nanowires with a patterned epitaxial Al two-facet shell that proximitizes two
gate-defined segments along the nanowire. We follow the evolution of mesoscopic
superconductivity and charging energy in this system as a function of magnetic
field and voltage-tuned barriers. Inter-dot coupling is varied from strong to
weak using side gates, and the ground state is varied between normal,
superconducting, and topological regimes by applying a magnetic field. We
identify the topological transition by tracking the spacing between successive
cotunneling peaks as a function of axial magnetic field and show that the
individual dots host weakly hybridized Majorana modes.


title: Routing with Congestion in Acyclic Digraphs

abstract:
  We study the version of the $k$-disjoint paths problem where $k$ demand pairs
$(s_1,t_1)$, $\dots$, $(s_k,t_k)$ are specified in the input and the paths in
the solution are allowed to intersect, but such that no vertex is on more than
$c$ paths. We show that on directed acyclic graphs the problem is solvable in
time $n^{O(d)}$ if we allow congestion $k-d$ for $k$ paths. Furthermore, we
show that, under a suitable complexity theoretic assumption, the problem cannot
be solved in time $f(k)n^{o(d/\log d)}$ for any computable function $f$.


title: Statistical mechanics analysis of thresholding 1-bit compressed sensing

abstract:
  The one-bit compressed sensing framework aims to reconstruct a sparse signal
by only using the sign information of its linear measurements. To compensate
for the loss of scale information, past studies in the area have proposed
recovering the signal by imposing an additional constraint on the L2-norm of
the signal. Recently, an alternative strategy that captures scale information
by introducing a threshold parameter to the quantization process was advanced.
In this paper, we analyze the typical behavior of the thresholding 1-bit
compressed sensing utilizing the replica method of statistical mechanics, so as
to gain an insight for properly setting the threshold value. Our result shows
that, fixing the threshold at a constant value yields better performance than
varying it randomly when the constant is optimally tuned, statistically.
Unfortunately, the optimal threshold value depends on the statistical
properties of the target signal, which may not be known in advance. In order to
handle this inconvenience, we develop a heuristic that adaptively tunes the
threshold parameter based on the frequency of positive (or negative) values in
the binary outputs. Numerical experiments show that the heuristic exhibits
satisfactory performance while incurring low computational cost.


title: Phantom holomorphic projections arising from Sturm's formula

abstract:
  We show the analytic continuation of certain Siegel Poincar\'e series to
their critical point for weight three in genus two. We proof that this
continuation posesses a nonhomomorphic part and describe it. We show that
Sturm's operator also produces a nonhomorphic share for weight three, we call
it a phantom term. Weight three is the distinguished weight for genus two where
this phenomenon arises.


title: Lower Bound on the Redundancy of PIR Codes

abstract:
  We prove that the redundancy of a $k$-server PIR code of dimension $s$ is
$\Omega(\sqrt{s})$ for all $k \ge 3$. This coincides with a known upper bound
of $O(\sqrt{s})$ on the redundancy of PIR codes. Moreover, for $k=3$ and $k =
4$, we determine the lowest possible redundancy of $k$-server PIR codes
exactly. Similar results were proved independently by Mary Wootters using a
different method.


title:
Thermalization and Bose-Einstein condensation of quantum light in bulk
  nonlinear media

abstract:
  We study the thermalization and the Bose-Einstein condensation of a paraxial,
spectrally narrow beam of quantum light propagating in a lossless bulk Kerr
medium. The spatiotemporal evolution of the quantum optical field is ruled by a
Heisenberg equation analogous to the quantum nonlinear Schr\"odinger equation
of dilute atomic Bose gases. Correspondingly, in the weak-nonlinearity regime,
the phase-space density evolves according to the Boltzmann equation.
Expressions for the thermalization time and for the temperature and the
chemical potential of the eventual Bose-Einstein distribution are found. After
discussing experimental issues, we introduce an optical setup allowing the
evaporative cooling of a guided beam of light towards Bose-Einstein
condensation. This might serve as a novel source of coherent light.


title: Achieving acoustic cloak by using compressible background flow

abstract:
  We propose a scheme of acoustic spherical cloaking by means of background
irrotational flow in compressible fluid. The background flow forms a virtual
curved spacetime and guides the sound waves bypass the cloaked objects. To
satisfy the laws of real fluid, we show that spatially distributed mass source
and momentum source are necessary to supply. The propagation of sound waves in
this system is studied via both geometric acoustics approximation and full wave
approach. The analytic solution of sound fields is obtained for plane wave
incidence. The results reveal the effect of phase retardation (or lead) in
comparison with the ordinary transformation-acoustic cloak. In addition, the
ability of cloaking is also evaluated for unideal background flows by analyzing
the scattering cross section.


title: Sphere-of-influence graphs in normed spaces

abstract:
  We show that any $k$-th closed sphere-of-influence graph in a $d$-dimensional
normed space has a vertex of degree less than~$5^d k$, thus obtaining a common
generalization of results of F\"uredi and Loeb (1994) and Guibas, Pach and
Sharir (1994).


title: Gravitoturbulence in magnetised protostellar discs

abstract:
  Gravitational instability (GI) features in several aspects of protostellar
disk evolution, most notably in angular momentum transport, fragmentation, and
the outbursts exemplified by FU Ori and EX Lupi systems. The outer regions of
protostellar discs may also be coupled to magnetic fields, which could then
modify the development of GI. To understand the basic elements of their
interaction, we perform local 2D ideal and resistive MHD simulations with an
imposed toroidal field. In the regime of moderate plasma beta, we find that the
system supports a hot gravito-turbulent state, characterised by considerable
magnetic energy and stress and a surprisingly large Toomre parameter $Q~10$.
This result has potential implications for disk structure, vertical thickness,
ionisation, etc. Our simulations also reveal the existence of long-lived and
dense `magnetic islands' or plasmoids. Lastly, we find that the presence of a
magnetic field has little impact on the fragmentation criterion of the disk.
Though our focus is on protostellar disks, some of our results may be relevant
for the outer radii of AGN.


title: Observation of the phononic Lamb shift with a synthetic vacuum

abstract:
  The quantum vacuum fundamentally alters the properties of embedded particles.
In contrast to classical empty space, it allows for creation and annihilation
of excitations. For trapped particles this leads to a change in the energy
spectrum, known as Lamb shift. Here, we engineer a synthetic vacuum building on
the unique properties of ultracold atomic gas mixtures. This system makes it
possible to combine high-precision spectroscopy with the ability of switching
between empty space and quantum vacuum. We observe the phononic Lamb shift, an
intruiguing many-body effect orginally conjectured in the context of solid
state physics. Our study therefore opens up new avenues for high-precision
benchmarking of non-trivial theoretical predictions in the realm of the quantum
vacuum.


title:
Analytic aspects of the Tzitz\'eica equation: blow-up analysis and
  existence results

abstract:
  We are concerned with the following class of equations with exponential
nonlinearities: $$
  \Delta u+h_1e^u-h_2e^{-2u}=0 \qquad \mbox{in } B_1\subset\mathbb{R}^2, $$
which is related to the Tzitz\'eica equation. Here $h_1, h_2$ are two smooth
positive functions. The purpose of the paper is to initiate the analytical
study of the above equation and to give a quite complete picture both for what
concerns the blow-up phenomena and the existence issue.
  In the first part of the paper we provide a quantization of local blow-up
masses associated to a blowing-up sequence of solutions. Next we exclude the
presence of blow-up points on the boundary under the Dirichlet boundary
conditions.
  In the second part of the paper we consider the Tzitz\'eica equation on
compact surfaces: we start by proving a sharp Moser-Trudinger inequality
related to this problem. Finally, we give a general existence result.


title: Quantal rotation and its coupling to intrinsic motion in nuclei

abstract:
  Symmetry breaking is an importance concept in nuclear physics and other
fields of physics. Self-consistent coupling between the mean-field potential
and the single-particle motion is a key ingredient in the unified model of Bohr
and Mottelson, which could lead to a deformed nucleus as a consequence of
spontaneous breaking of the rotational symmetry. Some remarks on the
finite-size quantum effects are given. In finite nuclei, the deformation
inevitably introduces the rotation as a symmetry-restoring collective motion
(Anderson-Nambu-Goldstone mode), and the rotation affects the intrinsic motion.
In order to investigate the interplay between the rotational and intrinsic
motions in a variety of collective phenomena, we use the cranking prescription
together with the quasiparticle random phase approximation. At low spin, the
coupling effect can be seen in the generalized intensity relation. A feasible
quantization of the cranking model is presented, which provides a microscopic
approach to the higher-order intensity relation. At high spin, the
semiclassical cranking prescription works well. We discuss properties of
collective vibrational motions under rapid rotation and/or large deformation.
The superdeformed shell structure plays a key role in emergence of a new soft
mode which could lead to instability toward the $K^\pi=1^-$ octupole shape. A
wobbling mode of excitation, which is a clear signature of the triviality, is
discussed in terms of a microscopic point of view. A crucial role played by the
quasiparticle alignment is presented.


title: Local Borcherds Products for Unitary Groups

abstract:
  For a discrete subgroup of an indefinite unitary group $U(1,n+1)$, $n\geq 1$,
consider the attached modular variety. Using local Borcherds products, we study
Heegner divisors in the local Picard group over a boundary component the
compactified variety. We obtain a criterion for local Heegner divisors to be
torsion elements in the local Picard group. As an application, we find that the
obstructions for a local Heegner divisor to be a torsion element can be
described through spaces of vector valued elliptic cusp forms spanned by
certain theta-series.


title:
Design and Analysis of Novel Kernel Measure for Software Fault
  Localization

abstract:
  The problem of software fault localization may be viewed as an approach for
finding hidden faults or bugs in the existing program codes which are
syntactically correct and give fault free output for some input instances but
fail for all other input instances. Some of the reasons include logical errors,
wrong interpretation of specification, coding errors. Finding such faults is
not possible sometimes with the help of compilers. This is where the necessity
and significance of software fault localization stems out. The main
contribution for this work is to first introduce the block hit-miss function
which relates block vectors of execution sequences of software code over sample
runs performed and the decision vector which denotes fault or error free
output. The similarity measure is applied to the block vector and decision
vectors as input and the pair with maximum similarity is considered as faulty
block.


title: Weak solution of Parabolic complex Monge-Amp\'ere equation II

abstract:
  We study the Parabolic complex Monge-Amp\'ere equation in a bounded strictly
pseudoconvex domain in \mathbb{C}^n, with the boundary condition u=\varphi and
the initial condition u=u_0. In this paper, we consider the case where \varphi
is smooth and u_0 is an arbitrary plurisubharmonic function in a neighbourhood
of \Omega satisfying u_0=\varphi(.,0) on the boundary of \Omega.


title: Privacy-Constrained Remote Source Coding

abstract:
  We consider the problem of revealing/sharing data in an efficient and secure
way via a compact representation. The representation should ensure reliable
reconstruction of the desired features/attributes while still preserve privacy
of the secret parts of the data. The problem is formulated as a remote lossy
source coding with a privacy constraint where the remote source consists of
public and secret parts. Inner and outer bounds for the optimal tradeoff region
of compression rate, distortion, and privacy leakage rate are given and shown
to coincide for some special cases. When specializing the distortion measure to
a logarithmic loss function, the resulting rate-distortion-leakage tradeoff for
the case of identical side information forms an optimization problem which
corresponds to the "secure" version of the so-called information bottleneck.


title:
Detecting continuous spontaneous localisation with charged bodies in a
  Paul trap

abstract:
  Continuous spontaneous localisation (CSL) is a model that captures the
effects of a class of extensions to quantum theory which are expected to result
from quantum gravity, and is such that wavefunction collapse is a physical
process. The rate of such a process could be very much lower than the upper
bounds set by searches to date, and yet still modify greatly the interpretation
of quantum mechanics and solve the quantum measurement problem. Consequently
experiments are sought to explore this. We describe an experiment that has the
potential to extend sensitivity to CSL by many orders of magnitude. The method
is to detect heating of the motion of charged macroscopic objects confined in a
Paul trap. We discuss the detection and the chief noise sources. We find that
CSL with standard parameters could be observed using a vibration-isolated ion
trap of size 1 cm at ultra-low pressure, with optical interferometric
detection.