title:
H0LiCOW III. Quantifying the effect of mass along the line of sight to
  the gravitational lens HE 0435-1223 through weighted galaxy counts

abstract:
  Based on spectroscopy and multiband wide-field observations of the
gravitationally lensed quasar HE 0435-1223, we determine the probability
distribution function of the external convergence $\kappa_\mathrm{ext}$ for
this system. We measure the under/overdensity of the line of sight towards the
lens system and compare it to the average line of sight throughout the
universe, determined by using the CFHTLenS as a control field. Aiming to
constrain $\kappa_\mathrm{ext}$ as tightly as possible, we determine
under/overdensities using various combinations of relevant informative weighing
schemes for the galaxy counts, such as projected distance to the lens,
redshift, and stellar mass. We then convert the measured under/overdensities
into a $\kappa_\mathrm{ext}$ distribution, using ray-tracing through the
Millennium Simulation. We explore several limiting magnitudes and apertures,
and account for systematic and statistical uncertainties relevant to the
quality of the observational data, which we further test through simulations.
Our most robust estimate of $\kappa_\mathrm{ext}$ has a median value
$\kappa^\mathrm{med}_\mathrm{ext} = 0.004$ and a standard deviation of
$\sigma_\kappa = 0.025$. The measured $\sigma_\kappa$ corresponds to $2.5\%$
uncertainty on the time delay distance, and hence the Hubble constant $H_0$
inference from this system. The median $\kappa^\mathrm{med}_\mathrm{ext}$ value
is robust to $\sim0.005$ (i.e. $\sim0.5\%$ on $H_0$) regardless of the adopted
aperture radius, limiting magnitude and weighting scheme, as long as the latter
incorporates galaxy number counts, the projected distance to the main lens, and
a prior on the external shear obtained from mass modeling. The availability of
a well-constrained $\kappa_\mathrm{ext}$ makes \hequad\ a valuable system for
measuring cosmological parameters using strong gravitational lens time delays.


title: Capacity of Gaussian Many-Access Channels

abstract:
  Classical multiuser information theory studies the fundamental limits of
models with a fixed (often small) number of users as the coding blocklength
goes to infinity. This work proposes a new paradigm, referred to as {\em
many-user information theory}, where the number of users is allowed to grow
with the blocklength. This paradigm is motivated by emerging systems with a
massive number of users in an area, such as machine-to-machine communication
systems and sensor networks. The focus of the current paper is the {\em
many-access} channel model, which consists of a single receiver and many
transmitters, whose number increases unboundedly with the blocklength.
Moreover, an unknown subset of transmitters may transmit in a given block and
need to be identified. A new notion of capacity is introduced and characterized
for the Gaussian many-access channel with random user activities. The capacity
can be achieved by first detecting the set of active users and then decoding
their messages.


title:
Synchrotron Emission from Dark Matter Annihilation: Predictions for
  Constraints from Non-detections of Galaxy Clusters with New Radio Surveys

abstract:
  The annihilation of dark matter particles is expected to yield a broad
radiation spectrum via the production of Standard Model particles in
astrophysical environments. In particular, electrons and positrons from dark
matter annihilation produce synchrotron radiation in the presence of magnetic
fields. Galaxy clusters are the most massive collapsed structures in the
universe, and are known to host $\sim\mu$G-scale magnetic fields. They are
therefore ideal targets to search for, or to constrain the synchrotron signal
from dark matter annihilation. In this work we use the expected sensitivities
of several planned surveys from the next generation of radio telescopes to
predict the constraints on dark matter annihilation models which will be
achieved in the case of non-detections of diffuse radio emission from galaxy
clusters. Specifically, we consider the Tier 1 survey planned for the Low
Frequency Array (LOFAR) at 120 MHz, the EMU survey planned for the Australian
Square Kilometre Array Pathfinder (ASKAP) at 1.4 GHz, and planned surveys for
APERTIF at 1.4 GHz. We find that, for massive clusters and dark matter masses
$\lesssim 100$ GeV, the predicted limits on the annihilation cross section
would rule out vanilla thermal relic models for even the shallow LOFAR Tier 1,
ASKAP, and APERTIF surveys.


title:
Application of Statistical Relational Learning to Hybrid Recommendation
  Systems

abstract:
  Recommendation systems usually involve exploiting the relations among known
features and content that describe items (content-based filtering) or the
overlap of similar users who interacted with or rated the target item
(collaborative filtering). To combine these two filtering approaches, current
model-based hybrid recommendation systems typically require extensive feature
engineering to construct a user profile. Statistical Relational Learning (SRL)
provides a straightforward way to combine the two approaches. However, due to
the large scale of the data used in real world recommendation systems, little
research exists on applying SRL models to hybrid recommendation systems, and
essentially none of that research has been applied on real big-data-scale
systems. In this paper, we proposed a way to adapt the state-of-the-art in SRL
learning approaches to construct a real hybrid recommendation system.
Furthermore, in order to satisfy a common requirement in recommendation systems
(i.e. that false positives are more undesirable and therefore penalized more
harshly than false negatives), our approach can also allow tuning the trade-off
between the precision and recall of the system in a principled way. Our
experimental results demonstrate the efficiency of our proposed approach as
well as its improved performance on recommendation precision.


title: Electron-cyclotron plasma startup in the GDT experiment

abstract:
  The paper reports on a new plasma startup scenario in the Gas Dynamic Trap
(GDT) magnetic mirror device. The primary 5 MW neutral beam injection (NBI)
plasma heating system fires into a sufficiently dense plasma target ("seed
plasma"), which is commonly supplied by an arc plasma generator. In the
reported experiments, a different approach to seed plasma generation is
explored. One of the channels of the electron cyclotron resonance (ECR) heating
system is used to ionize the neutral gas and build up the density of plasma to
a level suitable for NBI capture. After a short transition (about 1 ms) the
discharge becomes essentially similar to a standard one initiated by the plasma
gun. The paper presents the discharge scenario and experimental data on the
seed plasma evolution during ECR heating, along with the dependencies on
incident microwave power, magnetic configuration and pressure of a neutral gas.
The characteristics of consequent high-power NBI discharge are studied and
differences to the conventional scenario are discussed. A theoretical model
describing the ECR breakdown and the seed plasma accumulation in a large scale
mirror trap is developed on the basis of the GDT experiment.


title: Modular characteristic classes for representations over finite fields

abstract:
  The cohomology of the degree-$n$ general linear group over a finite field of
characteristic $p$, with coefficients also in characteristic $p$, remains
poorly understood. For example, the lowest degree previously known to contain
nontrivial elements is exponential in $n$. In this paper, we introduce a new
system of characteristic classes for representations over finite fields, and
use it to construct a wealth of explicit nontrivial elements in these
cohomology groups. In particular we obtain nontrivial elements in degrees
linear in $n$. We also construct nontrivial elements in the mod $p$ homology
and cohomology of the automorphism groups of free groups, and the general
linear groups over the integers. These elements reside in the unstable range
where the homology and cohomology remain poorly understood.


title: Subgaussian sequences in probability and Fourier analysis

abstract:
  This is a review on subgaussian sequences of random variables, prepared for
the Mediterranean Institute for the Mathematical Sciences (MIMS). We first
describe the main examples of such sequences. Then we focus on examples coming
from the harmonic analysis of Fourier series and we describe the connection of
subgaussian sequences of characters on the unidimensional torus (or any compact
Abelian group) with Sidon sets. We explain the main combinatorial open problem
concerning such subgaussian sequences. We present the answer to the analogous
question for subgaussian bounded mean oscillation (BMO) sequences on the unit
circle. Lastly, we describe several very recent results that provide a
generalization of the preceding ones when the trigonometric system (or its
analogue on a compact Abelian group) is replaced by an arbitrary orthonormal
system bounded in $L_\infty$.


title: The isolation of Luminous Blue Variables: On subdividing the sample

abstract:
  A debate has arisen concerning the fundamental nature of LBVs) and their role
in stellar evolution. While Smith and Tombleson proposed that their isolated
environments indicate that LBVs must be largely the product of binary
evolution, Humphreys et al. have recently expressed the view that the
traditional single-star view still holds if one appropriately selects a
subsample of LBVs. This paper finds the claim of Humphreys et al. to be
quantitatively unjustified. A statistical test of "candidate" as opposed to
"confirmed" LBVs shows no significant difference ($<$1$\sigma$) between their
environments. Even if the sample is further subdivided as proposed, the three
most luminous LBVs are spatially dispersed similar to late O-type dwarfs, which
have much longer lifetimes than expected for classical LBVs. Lower-luminosity
LBVs have a distribution associated with red supergiants (RSGs), but these RSGs
are dominated by stars of 10-15 M$_{\odot}$ initial mass, with much longer
lifetimes than expected for those lower-luminosity LBVs. If one's view is
restricted to the highest-luminosity LBVs, then the appropriate comparison is
with early O-type stars that are their presumed progenitors, when this is done,
it is clear that even the high-luminosity LBVs are more dispersed than
expected. Humphreys et al. also suggest that velocities of LBVs support the
single-star view, being inconsistent with runaways. A quantitative analysis of
the radial velocity distribution of LBVS in M31 and M33 contradicts this,
modest runway speeds expected from mass gainers in binary evolution are
consistent with the observed velocities, although the data lack the precision
to discriminate.


title:
UV spectroscopy of the blue supergiant SBW1: the remarkably weak wind of
  a SN 1987A analog

abstract:
  The Galactic blue supergiant SBW1 with its circumstellar ring nebula
represents the best known analog of the progenitor of SN 1987A. High-resolution
imaging has shown H-alpha and IR structures arising in an ionized flow that
partly fills the ring's interior. To constrain the influence of the stellar
wind on this structure, we obtained an ultraviolet (UV) spectrum of the central
star of SBW1 with the HST Cosmic Origins Spectrograph (COS). The UV spectrum
shows none of the typical wind signatures, indicating a very low mass-loss
rate. Radiative transfer models suggest an extremely low rate below 10$^{-10}$
Msun/yr, although we find that cooling timescales probably become comparable to
or longer than the flow time below 10$^{-8}$ Msun/yr. We therefore adopt this
latter value as a conservative upper limit. For the central star, the model
yields $T_{\rm eff}$=21,000$\pm$1000 K, $L\simeq$5$\times$10$^4$ $L_{\odot}$,
and roughly Solar composition except for enhanced N abundance. SBW1's very low
mass-loss rate may hinder the wind's ability to shape the surrounding nebula.
The very low mass-loss rate also impairs the wind's ability to shed angular
momentum; the spin-down timescale for magnetic breaking is more than 500 times
longer than the age of the ring. This, combined with the star's slow rotation
rate, constrain merger scenarios to form ring nebulae. The mass-loss rate is at
least 10 times lower than expected from mass-loss recipes, without any account
of clumping. The physical explanation for why SBW1's wind is so weak presents
an interesting mystery.


title: Massive stars dying alone: The extremely remote environment of SN 2009ip

abstract:
  We present late-time HST images of the site of supernova (SN) 2009ip taken
almost 3 yr after its bright 2012 luminosity peak. SN 2009ip is now slightly
fainter in broad filters than the progenitor candidate detected by HST in 1999.
The current source continues to be dominated by ongoing late-time CSM
interaction that produces strong H-alpha emission and a weak pseudo-continuum,
as found previously for 1-2 yr after explosion. The intent of these
observations was to search for evidence of recent star formation in the local
(1kpc; 10 arcsec) environment around SN 2009ip, in the remote outskirts of its
host spiral galaxy NGC 7259. We can rule out the presence of any massive
star-forming complexes like 30 Dor or the Carina Nebula at the SN site or
within a few kpc. If the progenitor of SN 2009ip was really a 50-80 Msun star
as archival HST images suggested, then it is strange that there is no sign of
this type of massive star formation anywhere in the vicinity. A possible
explanation is that the progenitor was the product of a merger or binary mass
transfer, rejuvenated after a lifetime that was much longer than 4-5 Myr,
allowing its natal H II region to have faded. A smaller region like the Orion
Nebula would be an unresolved but easily detected point source. This is ruled
out within 1.5 kpc around SN 2009ip, but a small H II region could be hiding in
the glare of SN 2009ip itself. Later images after a few more years have passed
are needed to confirm that the progenitor candidate is truly gone and to test
for the presence of a small H II region or cluster at the SN position.


title: Power of photonic states: from quantum computation to cosmology

abstract:
  This thesis is an exploration of the power of photonic resources, as viewed
from several different but related perspectives. They range from quantum
computation, precision parameter estimation to the thermodynamics of
relativistic quantum systems, as applied to cosmology in particular.
  In chapter 1, we propose a new quantum computational model, called the `power
of one qumode', that relies mainly on a single-mode photonic squeezed state. In
particular, we show the amount of squeezing can quantitatively relate the
resource requirements of factoring to the problem of finding the trace of large
unitary matrices, a result with consequences for understanding how powerful
quantum computation really is. Furthermore, we can connect squeezing to other
known resources like precision, energy, qudit dimensionality and qubit number,
which is a useful stepping stone to finding the resources that enable quantum
computation.
  In chapter 2, we exploit the quantum mechanical properties of photonic states
for use in precision parameter estimation of general linear optical processes,
which is useful for a diverse number of applications, from characterising an
unknown process in a photonic quantum computer to biological imaging. We
introduce a formalism that quantifies this improvement in precision. We also
provide conditions under which one can easily check for photonic states that
are optimal to use in this context, which is a potentially important result for
future experimental efforts.
  In chapter 3, we explore the connection between two-mode squeezed states,
commonly used in quantum optics, and relativistic quantum processes, in
particular in cosmology. Using this connection, we apply recently developed
tools from the thermodynamics of quantum systems perturbed far from equilibrium
to address an old question of entropy production in cosmology from a surprising
new angle.


title: Pl\"ucker relations for quiver Grassmannians

abstract:
  In this text, we exhibit the quiver Pl\"ucker relations for a quiver
Grassmannian and show that they describe the quiver Grassmannian as a closed
subscheme of a product of usual Grassmannians.


title:
Improving Sparse Representation-Based Classification Using Local
  Principal Component Analysis

abstract:
  Sparse representation-based classification (SRC), proposed by Wright et al.,
seeks the sparsest decomposition of a test sample over the dictionary of
training samples, with classification to the most-contributing class. Because
it assumes test samples can be written as linear combinations of their
same-class training samples, the success of SRC depends on the size and
representativeness of the training set. Our proposed classification algorithm
enlarges the training set by using local principal component analysis to
approximate the basis vectors of the tangent hyperplane of the class manifold
at each training sample. The dictionary in SRC is replaced by a local
dictionary that adapts to the test sample and includes training samples and
their corresponding tangent basis vectors. We use a synthetic data set and
three face databases to demonstrate that this method can achieve higher
classification accuracy than SRC in cases of sparse sampling, nonlinear class
manifolds, and stringent dimension reduction.


title: Effects of Spin on High-Energy Radiation from Accreting Black Holes

abstract:
  Observations of jets in X-ray binaries show a correlation between radio power
and black hole spin. This correlation, if confirmed, points towards the idea
that relativistic jets may be powered by the rotational energy of black holes.
In order to examine this further, we perform general-relativistic radiative
transport calculations on magnetically arrested accretion flows, which are
known to produce powerful jets via the Blandford-Znajek (BZ) mechanism. We find
that the X-ray and gamma-ray emission strongly depend on spin and inclination
angle. Surprisingly, the high-energy power does not show the same dependence on
spin as the BZ jet power, but instead can be understood as a redshift effect.
In particular, photons observed perpendicular to the spin axis suffer little
net redshift until originating from close to the horizon. Such observers see
deeper into the hot, dense, highly-magnetized inner disk region. This effect is
largest for rapidly rotating black holes due to a combination of frame dragging
and decreasing horizon radius. While the X-ray emission is dominated by the
near horizon region, the near-infrared radiation originates at larger radii.
Therefore, the ratio of X-ray to near-infrared power is an observational
signature of black hole spin.


title:
Ferromagnetic Quantum Critical Point Avoided by the Appearance of
  Another Magnetic Phase in LaCrGe$_3$ under Pressure

abstract:
  The temperature-pressure phase diagram of the ferromagnet LaCrGe$_3$ is
determined for the first time from a combination of magnetization,
muon-spin-rotation and electrical resistivity measurements. The ferromagnetic
phase is suppressed near $2.1$~GPa, but quantum criticality is avoided by the
appearance of a magnetic phase, likely modulated, AFM$_Q$. Our density
functional theory total energy calculations suggest a near degeneracy of
antiferromagnetic states with small magnetic wave vectors $Q$ allowing for the
potential of an ordering wave vector evolving from $Q=0$ to finite $Q$, as
expected from the most recent theories on ferromagnetic quantum criticality.
Our findings show that LaCrGe$_3$ is a very simple example to study this
scenario of avoided ferromagnetic quantum criticality and will inspire further
study on this material and other itinerant ferromagnets.


title:
A deep X-ray view of the bare AGN Ark 120. I. Revealing the Soft X-ray
  Line Emission

abstract:
  The Seyfert 1 galaxy, Ark 120, is a prototype example of the so-called class
of bare nucleus AGN, whereby there is no known evidence for the presence of
ionized gas along the direct line of sight. Here deep ($>400$ ks exposure),
high resolution X-ray spectroscopy of Ark 120 is presented, from XMM-Newton
observations which were carried out in March 2014, together with simultaneous
Chandra/HETG exposures. The high resolution spectra confirmed the lack of
intrinsic absorbing gas associated with Ark 120, with the only X-ray absorption
present originating from the ISM of our own Galaxy, with a possible slight
enhancement of the Oxygen abundance required with respect to the expected ISM
values in the Solar neighbourhood. However, the presence of several soft X-ray
emission lines are revealed for the first time in the XMM-Newton RGS spectrum,
associated to the AGN and arising from the He and H-like ions of N, O, Ne and
Mg. The He-like line profiles of N, O and Ne appear velocity broadened, with
typical FWHM widths of $\sim5000$ km s$^{-1}$, whereas the H-like profiles are
unresolved. From the clean measurement of the He-like triplets, we deduce that
the broad lines arise from gas of density $n_{\rm e}\sim10^{11}$ cm$^{-3}$,
while the photoionization calculations infer that the emitting gas covers at
least 10 percent of $4\pi$ steradian. Thus the broad soft X-ray profiles appear
coincident with an X-ray component of the optical-UV Broad Line Region on
sub-pc scales, whereas the narrow profiles originate on larger pc scales,
perhaps coincident with the AGN Narrow Line Region. The observations show that
Ark 120 is not intrinsically bare and substantial X-ray emitting gas exists out
of our direct line of sight towards this AGN.


title:
Comparative study of microwave radiation-induced magnetoresistive
  oscillations induced by circularly- and linearly- polarized photo-excitation

abstract:
  A comparative study of the radiation-induced magnetoresistance oscillations
in the high mobility GaAs/AlGaAs heterostructure two dimensional electron
system (2DES) under linearly- and circularlypolarized microwave excitation
indicates a profound difference in the response observed upon rotating the
microwave launcher for the two cases, although circularly polarized microwave
radiation induced magnetoresistance oscillations observed at low magnetic
fields are similar to the oscillations observed with linearly polarized
radiation. For the linearly polarized radiation, the magnetoresistive response
is a strong sinusoidal function of the launcher rotation (or linear
polarization) angle, {\theta}. For circularly polarized radiation, the
oscillatory magnetoresistive response is hardly sensitive to {\theta}.


title:
GfcLLL: A Greedy Selection Based Approach for Fixed-Complexity LLL
  Reduction

abstract:
  The LLL lattice reduction has been widely used to decrease the bit error rate
(BER) of the Babai point, but its running time varies much from matrix to
matrix. To address this problem, some fixed-complexity LLL reductions (FCLLL)
have been proposed. In this paper, we propose two greedy selection based FCLLL
algorithms: GfcLLL(1) and GfcLLL(2). Simulations show that both of them give
Babai points with lower BER in similar or much shorter CPU time than existing
ones.


title: Timing the warm absorber in NGC 4051

abstract:
  We investigated, using spectral-timing analysis, the characterization of
highly ionized outflows in Seyfert galaxies, the so-called warm absorbers.
Here, we present our results on the extensive ~ 600 ks of XMM-Newton archival
observations of the bright and highly variable Seyfert 1 galaxy NGC 4051, whose
spectrum has revealed a complex multicomponent wind. Making use of both RGS and
EPIC-pn data, we performed a detailed analysis through a time-dependent
photoionization code in combination with spectral and Fourier spectral-timing
techniques. The source light curves and the warm absorber parameters obtained
from the data were used to simulate the response of the gas due to variations
in the ionizing flux of the central source. The resulting time variable spectra
were employed to predict the effects of the warm absorber on the time lags and
coherence of the energy dependent light curves. We have found that, in the
absence of any other lag mechanisms, a warm absorber with the characteristics
of the one observed in NGC 4051, is able to produce soft lags, up to 100 s, on
timescales of ~ hours. The time delay is associated with the response of the
gas to changes in the ionizing source, either by photoionization or radiative
recombination, which is dependent on its density. The range of radial distances
that, under our assumptions, yield longer time delays are comparable to the
existing estimates of the location of the warm absorber in NGC 4051. For this
reason, we suggest that it is likely that the observed X-ray time lags may
carry a signature of the warm absorber response time, to changes in the
ionizing continuum. These results highlight the importance of understanding the
contribution of the warm absorber to the AGN X-ray time lags, since it is also
vital information for interpreting the lags associated with propagation and
reverberation effects in the inner emitting regions.


title: Convective dynamo action in a spherical shell: symmetries and modulation

abstract:
  We consider dynamo action driven by three-dimensional rotating anelastic
convection in a spherical shell. Motivated by the behaviour of the solar
dynamo, we examine the interaction of hydromagnetic modes with different
symmetries and demonstrate how complicated interactions between convection,
differential rotation and magnetic fields may lead to modulation of the basic
cycle. For some parameters, Type 1 modulation occurs by the transfer of energy
between modes of different symmetries with little change in the overall
amplitude, for other parameters, the modulation is of Type 2, where the
amplitude is significantly affected (leading to grand minima in activity)
without significant changes in symmetry. Most importantly, we identify the
presence of "supermodulation" in the solutions, where the activity switches
chaotically between Type 1 and Type 2 modulation, this is believed to be an
important process in solar activity.


title: Exact Recovery of Chaotic Systems from Highly Corrupted Data

abstract:
  Learning the governing equations in dynamical systems from time-varying
measurements is of great interest across different scientific fields. This task
becomes prohibitive when such data is moreover highly corrupted, for example,
due to the recording mechanism failing over unknown intervals of time. When the
underlying system exhibits chaotic behavior, such as sensitivity to initial
conditions, it is crucial to recover the governing equations with high
precision. In this work, we consider continuous time dynamical systems $\dot{x}
= f(x)$ where each component of $f: \mathbb{R}^{d} \rightarrow \mathbb{R}^d$ is
a multivariate polynomial of maximal degree $p$; we aim to identify $f$ exactly
from possibly highly corrupted measurements $x(t_1), x(t_2), \dots, x(t_m)$. As
our main theoretical result, we show that if the system is sufficiently ergodic
that this data satisfies a strong central limit theorem (as is known to hold
for chaotic Lorenz systems), then the governing equations $f$ can be exactly
recovered as the solution to an $\ell_1$ minimization problem -- even if a
large percentage of the data is corrupted by outliers. Numerically, we apply
the alternating minimization method to solve the corresponding constrained
optimization problem. Through several examples of 3D chaotic systems and higher
dimensional hyperchaotic systems, we illustrate the power, generality, and
efficiency of the algorithm for recovering governing equations from noisy and
highly corrupted measurement data.


title: Hamiltonian truncation approach to quenches in the Ising field theory

abstract:
  In contrast to lattice systems where powerful numerical techniques such as
matrix product state based methods are available to study the non-equilibrium
dynamics, the non-equilibrium behaviour of continuum systems is much harder to
simulate. We demonstrate here that Hamiltonian truncation methods can be
efficiently applied to this problem, by studying the quantum quench dynamics of
the 1+1 dimensional Ising field theory using a truncated free fermionic space
approach. After benchmarking the method with integrable quenches corresponding
to changing the mass in a free Majorana fermion field theory, we study the
effect of an integrability breaking perturbation by the longitudinal magnetic
field. In both the ferromagnetic and paramagnetic phases of the model we find
persistent oscillations with frequencies set by the low-lying particle
excitations not only for small, but even for moderate size quenches. In the
ferromagnetic phase these particles are the various non-perturbative confined
bound states of the domain wall excitations, while in the paramagnetic phase
the single magnon excitation governs the dynamics, allowing us to capture the
time evolution of the magnetisation using a combination of known results from
perturbation theory and form factor based methods. We point out that the
dominance of low lying excitations allows for the numerical or experimental
determination of the mass spectra through the study of the quench dynamics.


title: Demazure flags, $q$--Fibonacci polynomials and hypergeometric series

abstract:
  We study a family of finite--dimensional representations of the hyperspecial
parabolic subalgebra of the twisted affine Lie algebra of type $\tt A_2^{(2)}$.
We prove that these modules admit a decreasing filtration whose sections are
isomorphic to stable Demazure modules in an integrable highest weight module of
sufficiently large level. In particular, we show that any stable level $m'$
Demazure module admits a filtration by level $m$ Demazure modules for all $m\ge
m'$. We define the graded and weighted generating functions which encode the
multiplicity of a given Demazure module and establish a recursive formulae. In
the case when $m'=1,2$ and $m=2,3$ we determine these generating functions
completely and show that they define hypergeoemetric series and that they are
related to the $q$--Fibonacci polynomials defined by Carlitz.


title: Age-structured population models with Applications

abstract:
  A general model of age-structured population dynamics is developed and the
fundamental properties of its solutions are analyzed. The model is a semilinear
partial differential equation with a nonlinear nonlocal boundary condition.
Existence, uniqueness and regularity of solutions to the model equations are
proved. An intrinsic growth constant is obtained and linked to the existence
and the stability of the trivial and/or the positive equilibrium. Lyapunov
function is constructed to show the global stability of the trivial and/or the
positive equilibrium.
  Key words: Lyapunov function, Partial Differential Equation, Stability,
Mathematical Model, Uniform Persistence, Reproductive Number (or Reproduction
Number)


title:
Lp-Lq estimates of some convolution operators with singular measures on
  the Heisenberg group

abstract:
  We study the boundedness from Lp(Hn) into Lq(Hn) of certain convolution
operators with singular measures on the Heisenberg group.


title: Robust solid $^{129}$Xe longitudinal relaxation times

abstract:
  We find that if solid xenon is formed from liquid xenon, denoted "ice", there
is a 10% increase of $^{129}$Xe longitudinal relaxation $T_1$ time (taken at 77
K and 2 Tesla) over a trickle-freeze formation, denoted "snow". Forming xenon
ice also gives unprecedented reproducibility of $^{129}$Xe $T_1$ measurements
across a range of 77-150 K. This temperature dependence roughly follows the
theory of spin-rotation mediated by Raman scattering of harmonic phonons
(SRRS), though it results in a smaller-than-predicted spin-rotation coupling
strength $c_{K0}/h$. Enriched ice $^{129}$Xe $T_1$ experiments show no isotopic
dependence in bulk relaxation mechanisms at 77 K and at kilogauss fields.


title: Simple fixed-effects inference for complex functional models

abstract:
  We propose simple inferential approaches for the fixed effects in complex
functional mixed effects models. We estimate the fixed effects under the
independence of functional residuals assumption and then bootstrap independent
units (e.g. subjects) to estimate the variability of and conduct inference in
the form of hypothesis testing on the fixed effects parameters. Simulations
show excellent coverage probability of the confidence intervals and size of
tests. Methods are motivated by and applied to the Baltimore Longitudinal Study
of Aging (BLSA), though they are applicable to other studies that collect
correlated functional data.


title: Measuring neutrino mass imprinted on the anisotropic galaxy clustering

abstract:
  The anisotropic galaxy clustering of large scale structure observed by the
Baryon Oscillation Spectroscopic Survey Data Release 11 is analyzed to probe
the sum of neutrino mass in the small $m_\nu < 1eV$ limit in which the early
broadband shape determined before the last scattering surface is immune from
the variation of $m_\nu$. The signature of $m_\nu$ is imprinted on the altered
shape of the power spectrum at later epoch, which provides an opportunity to
access the non--trivial $m_\nu$ through the measured anisotropic correlation
function in redshift space (hereafter RSD instead of Redshift Space
Distortion). The non--linear RSD corrections with massive neutrinos in the
quasi linear regime are approximately estimated using one-loop order terms
computed by tomographic linear solutions. We suggest a new approach to probe
$m_\nu$ simultaneously with all other distance measures and coherent growth
functions, exploiting this deformation of the early broadband shape of the
spectrum at later epoch. If the origin of cosmic acceleration is unknown,
$m_\nu$ is poorly determined after marginalising over all other observables.
However, we find that the measured distances and coherent growth functions are
minimally affected by the presence of mild neutrino mass. Although the standard
model of cosmic acceleration is assumed to be the cosmological constant, the
constraint on $m_\nu$ is little improved. Interestingly, the measured CMB
distance to the last scattering surface sharply slices the degeneracy between
the matter content and $m_\nu$, and the hidden $m_\nu$ is excavated to be
$m_\nu=0.19^{+0.28}_{-0.17} eV$ which is different from massless neutrino more
than 68% confidence.


title: Affect Intensity Estimation Using Multiple Modalities

abstract:
  One of the challenges in affect recognition is accurate estimation of the
emotion intensity level. This research proposes development of an affect
intensity estimation model based on a weighted sum of classification confidence
levels, displacement of feature points and speed of feature point motion. The
parameters of the model were calculated from data captured using multiple
modalities such as face, body posture, hand movement and speech. A preliminary
study was conducted to compare the accuracy of the model with the annotated
intensity levels. An emotion intensity scale ranging from 0 to 1 along the
arousal dimension in the emotion space was used. Results indicated speech and
hand modality significantly contributed in improving accuracy in emotion
intensity estimation using the proposed model.


title:
Aggressive actions and anger detection from multiple modalities using
  Kinect

abstract:
  Prison facilities, mental correctional institutions, sports bars and places
of public protest are prone to sudden violence and conflicts. Surveillance
systems play an important role in mitigation of hostile behavior and
improvement of security by detecting such provocative and aggressive
activities. This research proposed using automatic aggressive behavior and
anger detection to improve the effectiveness of the surveillance systems. An
emotion and aggression aware component will make the surveillance system highly
responsive and capable of alerting the security guards in real time. This
research proposed facial expression, head, hand and body movement and speech
tracking for detecting anger and aggressive actions. Recognition was achieved
using support vector machines and rule based features. The multimodal affect
recognition precision rate for anger improved by 15.2% and recall rate improved
by 11.7% when behavioral rule based features were used in aggressive action
detection.


title: EmoFit: Affect Monitoring System for Sedentary Jobs

abstract:
  Emotional and physical well-being at workplace is important for a positive
work environment and higher productivity. Jobs such as software programming
lead to a sedentary lifestyle and require high interaction with computers.
Working at the same job for years can cause a feeling of intellectual
stagnation and lack of drive. Many employees experience lack of motivation,
mild to extreme depression due to reasons such as aversion towards job
responsibilities and incompatibility with coworkers or boss. This research
proposed an affect monitoring system EmoFit that would play the role of
psychological and physical health trainer. The day to day computer activity and
body language was analyzed to detect the physical and emotional well-being of
the user. Keystrokes, activity interruptions, eye tracking, facial expressions,
body posture and speech were monitored to gauge the users health. The system
also provided activities such as at-desk exercise and stress relief game and
motivational quotes in an attempt to promote users well-being. The experimental
results and positive feedback from test subjects showed that EmoFit would help
improve emotional and physical well-being at jobs that involve significant
computer usage.


title:
Biological dose representation for carbon-ion radiotherapy of
  unconventional fractionation

abstract:
  In carbon-ion radiotherapy, single-beam delivery each day in alternate
directions has been commonly practiced for operational efficiency, taking
advantage of the Bragg peak and the relative biological effectiveness (RBE) for
uniform dose conformation to a tumor. The treatment plans are usually evaluated
with total RBE-weighted dose, which is however deficient in relevance to the
biological effect in the linear-quadratic model due to its quadratic-dose term,
or the dose-fractionation effect. In this study, we reformulate the
extrapolated response dose (ERD), or synonymously BED, which normalizes the
dose-fractionation and cell-repopulation effects as well as the RBE of treating
radiation, based on inactivation of a single model cell system and a typical
treating radiation in carbon-ion RT. The ERD distribution virtually represents
the biological effect of the treatment regardless of radiation modality or
fractionation scheme. We applied the ERD formulation to simplistic model
treatments and to a preclinical survey for hypofractionation based on an actual
prostate-cancer treatment of carbon-ion radiotherapy. The proposed formulation
was demonstrated to be practical and to offer theoretical implications. In the
prostate-cancer case, the ERD distribution was very similar to the
RBE-weighted-dose distribution of the actual treatment in 12 fractions. With
hypofractionation, while the RBE-weighted-dose distribution varied
significantly, the ERD distribution was nearly invariant, implying that the
carbon-ion radiotherapy would be insensitive to fractionation. However,
treatment evaluation with simplistic biological dose is intrinsically limited
and must be complemented in practice somehow by clinical experiences and
biology experiments.


title:
Integrable multi-component generalization of a modified short pulse
  equation

abstract:
  We propose a multi-component generalization of the modified short pulse (SP)
equation which was derived recently as a reduction of Feng's two-component SP
equation. Above all, we address the two-component system in depth. We obtain
the Lax pair, an infinite nember of conservation laws and multisoliton
solutions for the system, demonstrating its integrability. Subsequently, we
show that the two-component system exhibits cusp solitons and breathers for
which the detailed analysis is performed. Specifically, we explore the
interaction process of two cusp solitons and derive the formula for the phase
shift. While cusp solitons are singular solutions, smooth breather solutions
are shown to exist, provided that the parameters characterizing the solutions
satisfy certain condition. Last, we discuss the relation between the proposed
system and existing two-component SP equations.


title:
Algorithm for rigorous integration of Delay Differential Equations and
  the computer-assisted proof of periodic orbits in the Mackey-Glass equation

abstract:
  We present an algorithm for the rigorous integration of Delay Differential
Equations (DDEs) of the form $x'(t)=f(x(t-\tau),x(t))$. As an application, we
give a computer assisted proof of the existence of two attracting periodic
orbits (before and after the first period-doubling bifurcation) in the
Mackey-Glass equation.


title:
Existence of solutions for a fractional semilinear parabolic equation
  with singular initial data

abstract:
  In this paper we obtain necessary conditions and sufficient conditions on the
initial data for the solvability of the Cauchy problem $$ \partial_t
u+(-\Delta)^{\frac{\theta}{2}}u=u^p,\quad x\in{\bf R}^N,\,\,t>0, \qquad
u(0)=\mu\ge 0\quad\mbox{in}\quad{\bf R}^N, $$ where $N\ge 1$, $0<\theta\le 2$,
$p>1$ and $\mu$ is a Radon measure or a measurable function in ${\bf R}^N$. Our
conditions lead optimal estimates of the life span of the solution with $\mu$
behaving like $\lambda |x|^{-A}$ ($A>0$) at the space infinity, as $\lambda \to
+0$.


title:
Elementary Evaluation of Convolution Sums involving the Sum of Divisors
  Function for a Class of positive Integers

abstract:
  We discuss an elementary method for the evaluation of the convolution sums
$\underset{\substack{
  {(l,m)\in\mathbb{N}_{0}^{2}} \\ {\alpha\,l+\beta\,m=n} }
}{\sum}\sigma(l)\sigma(m)$ for those $\alpha,\beta\in\mathbb{N}$ for which
$\gcd{(\alpha,\beta)}=1$ and $\alpha\beta=2^{\nu}\mho$, where
$\nu\in\{0,1,2,3\}$ and $\mho$ is a finite product of distinct odd primes.
Modular forms are used to achieve this result. We also generalize the
extraction of the convolution sum to all natural numbers. Formulae for the
number of representations of a positive integer $n$ by octonary quadratic forms
using convolution sums belonging to this class are then determined when
$\alpha\beta\equiv 0\pmod{4}$ or $\alpha\beta\equiv 0\pmod{3}$. To achieve this
application, we first discuss a method to compute all pairs
$(a,b),(c,d)\in\mathbb{N}^{2}$ necessary for the determination of such formulae
for the number of representations of a positive integer $n$ by octonary
quadratic forms when $\alpha\beta$ has the above form and $\alpha\beta\equiv
0\pmod{4}$ or $\alpha\beta\equiv 0\pmod{3}$. We illustrate our approach by
explicitly evaluating the convolution sum for $\alpha\beta=33=3\cdot 11,\>
\alpha\beta=40=2^{3}\cdot 5$ and $\alpha\beta=56=2^{3}\cdot 7$, and by
revisiting the evaluation of the convolution sums for $\alpha\beta=10$, $11$,
$12$, $15$, $24$. We then apply these convolution sums to determine formulae
for the number of representations of a positive integer $n$ by octonary
quadratic forms. In addition, we determine formulae for the number of
representations of a positive integer $n$ when $(a,b)=(1,1)$, $(1,3)$, $(2,3)$,
$(1,9)$.


title: Generalized Uncertainty Principle and Angular Momentum

abstract:
  Various models of quantum gravity suggest a modification of the Heisenberg's
Uncertainty Principle, to the so-called Generalized Uncertainty Principle,
between position and momentum. In this work we show how this modification
influences the theory of angular momentum in Quantum Mechanics. In particular,
we compute Planck scale corrections to angular momentum eigenvalues, the
Hydrogen atom spectrum, the Stern-Gerlach experiment and the Clebsch-Gordan
coefficients. We also examine effects of the Generalized Uncertainty Principle
on multi-particle systems.


title: Performance Models for Split-execution Computing Systems

abstract:
  Split-execution computing leverages the capabilities of multiple
computational models to solve problems, but splitting program execution across
different computational models incurs costs associated with the translation
between domains. We analyze the performance of a split-execution computing
system developed from conventional and quantum processing units (QPUs) by using
behavioral models that track resource usage. We focus on asymmetric processing
models built using conventional CPUs and a family of special-purpose QPUs that
employ quantum computing principles. Our performance models account for the
translation of a classical optimization problem into the physical
representation required by the quantum processor while also accounting for
hardware limitations and conventional processor speed and memory. We conclude
that the bottleneck in this split-execution computing system lies at the
quantum-classical interface and that the primary time cost is independent of
quantum processor behavior.


title:
User Association with Maximizing Sum Energy Efficiency for Massive MIMO
  Enabled Heterogeneous Cellular Networks

abstract:
  In this paper, we design an association scheme to maximize the sum energy
efficiency for massive multiple-input and multiple-output (MIMO) enabled
heterogeneous cellular networks (HCNs). Considering that the final formulated
problem is in a sum-of-ratio form, we first need to transform it into a
parametric nonfractional form, by which we can achieve its solution through a
two-layer iterative algorithm. The outer layer searches the energy efficiency
parameters and multipliers associated with signal-interference-plus-noise-ratio
(SINR) constraints using Newton-like method, and the inner layer optimizes the
association indices using Lagrange multiplier method. In fact, the inner layer
doesn't need iterative steps when the SINR constraints are not involved in the
original problem, and then the whole algorithm should be a one-layer iterative
one. As for the two-layer iterative algorithm, we also give the corresponding
convergence proof. Numerical results show that the proposed scheme
significantly outperforms the existing one in system throughput and network
energy efficiency. In addition, we also investigate the impacts of the number
of massive antennas and the transmit power of each pico base station on these
association performances.


title: Characterizing Si:P quantum dot qubits with spin resonance techniques

abstract:
  Quantum dots patterned by atomically precise placement of phosphorus donors
in single crystal silicon have long spin lifetimes, advantages in
addressability, large exchange tunability, and are readily available
few-electron systems. To be utilized as quantum bits, it is important to
non-invasively characterise these donor quantum dots post fabrication and
extract the number of bound electron and nuclear spins as well as their
locations. Here, we propose a metrology technique based on electron spin
resonance (ESR) measurements with the on-chip circuitry already needed for
qubit manipulation to obtain atomic scale information about donor quantum dots
and their spin configurations. Using atomistic tight-binding technique and
Hartree self-consistent field approximation, we show that the ESR transition
frequencies are directly related to the number of donors, electrons, and their
locations through the electron-nuclear hyperfine interaction.


title: Smooth quotients of bi-elliptic surfaces

abstract:
  We consider the quotient X of bi-elliptic surface by a finite automorphism
group. If X is smooth, then it is a bi-elliptic surface or ruled surface with
irregularity one. As a corollary any bi-elliptic surface cannot be Galois
covering of projective plane, hence does not have any Galois embedding.


title:
Backward Errors and Small Sample Condition Estimation for
  $\star$-Sylveter Equations

abstract:
  In this paper, we adopt a componentwise perturbation analysis for
$\star$-Sylvester equations. Based on the small condition estimation (SCE), we
devise the algorithms to estimate normwise, mixed and componentwise condition
numbers for $\star$-Sylvester equations. We also define a componentwise
backward error with a sharp and easily computable bound. Numerical examples
illustrate that our algorithm under componentwise perturbations produces
reliable estimates, and the new derived computable bound for the componentwise
backward error is sharp and reliable for well conditioned and moderate
ill-conditioned $\star$-Sylvester equations under large or small perturbations.


title:
Fluctuations of the free energy of the spherical Sherrington-Kirkpatrick
  model with ferromagnetic interaction

abstract:
  We consider a spherical spin system with pure 2-spin spherical
Sherrington-Kirkpatrick Hamiltonian with ferromagnetic Curie-Weiss interaction.
The system shows a two-dimensional phase transition with respect to the
temperature and the coupling constant. We compute the limiting distributions of
the free energy for all parameters away from the critical values. The zero
temperature case corresponds to the well-known phase transition of the largest
eigenvalue of a rank 1 spiked random symmetric matrix. As an intermediate step,
we establish a central limit theorem for the linear statistics of rank 1 spiked
random symmetric matrices.


title:
Parallax of a Mira variable R Ursae Majoris studied with astrometric
  VLBI

abstract:
  We have measured an annual parallax of the Mira variable R~Ursae~Majoris
(R~UMa) with the VLBI exploration for Radio Astronomy (VERA). From the
monitoring VLBI observations spanning about two years, we detected H$_2$O maser
spots in the LSR velocities ranges from 37 to 42 km\,s$^{-1}$. We derived an
annual parallax of 1.97$\pm$0.05\,mas, and it gives a corresponding distance of
508$\pm$13\,pc. The VLBI maps revealed 72 maser spots distributed in $\sim$110
au area around an expected stellar position. Circumstellar kinematics of the
maser spots were also revealed by subtracting a systemic motion in the
Hipparcos catalog from proper motions of each maser spots derived from our VLBI
observations. Infrared photometry is also conducted to measure a $K$ band
apparent magnitude, and we obtained a mean magnitude of $m_K$ =
1.19$\pm$0.02\,mag. Using the trigonometric distance, the $m_K$ is converted to
a $K$ band absolute magnitude of $M_K = -$7.34$\pm$0.06\,mag. This result gives
a much more accurate absolute magnitude of R~UMa than previously provided. We
solved a zero-point of $M_K - \log P$ relation for the Galactic Mira variables
and obtained a relation of $M_K = -$3.52 $\log P$ + (1.09 $\pm$ 0.14). Other
long period variables including red supergiants, whose distances were
determined from astrometric VLBI, were also compiled to explore the different
sequences of $M_K - \log P$ relation.


title: Amplify-and-Forward Full-Duplex Relay with Power Splitting-Based SWIPT

abstract:
  This paper proposes a virtual harvest-transmit model and a
harvest-transmit-store model for amplify-and-forward full-duplex relay (FDR)
networks with power splitting-based simultaneous wireless information and power
transfer. The relay node employs a battery group consisting of two rechargeable
batteries. By switching periodically between two batteries for charging and
discharging in two consecutive time slots of each transmission block, all the
harvested energy in each block has been applied for full duplex transmission in
the virtual harvest-transmit model. By employing energy scheduling, the relay
node switches among the harvesting, relaying, harvesting-relaying, and idle
behaviors at a block level, so that a part of the harvested energy in a block
can be scheduled for future usage in the harvest-transmit-store model. A greedy
switching policy is designed to implement the harvest-transmit-store model,
where the FDR node transmits when its residual energy ensures decoding at the
destination. Numerical results verify the outage performance of the proposed
schemes.


title: Incorporating prior knowledge in medical image segmentation: a survey

abstract:
  Medical image segmentation, the task of partitioning an image into meaningful
parts, is an important step toward automating medical image analysis and is at
the crux of a variety of medical imaging applications, such as computer aided
diagnosis, therapy planning and delivery, and computer aided interventions.
However, the existence of noise, low contrast and objects' complexity in
medical images are critical obstacles that stand in the way of achieving an
ideal segmentation system. Incorporating prior knowledge into image
segmentation algorithms has proven useful for obtaining more accurate and
plausible results. This paper surveys the different types of prior knowledge
that have been utilized in different segmentation frameworks. We focus our
survey on optimization-based methods that incorporate prior information into
their frameworks. We review and compare these methods in terms of the types of
prior employed, the domain of formulation (continuous vs. discrete), and the
optimization techniques (global vs. local). We also created an interactive
online database of existing works and categorized them based on the type of
prior knowledge they use. Our website is interactive so that researchers can
contribute to keep the database up to date. We conclude the survey by
discussing different aspects of designing an energy functional for image
segmentation, open problems, and future perspectives.


title: Unique magnetic structure of YbCo$_2$Si$_2$

abstract:
  We report on the results of powder and single crystal neutron diffraction to
investigate the magnetic order in YbCo$_2$Si$_2$ below the N\'eel temperature
$T_{\rm N} = 1.7~$K in detail. Two different magnetically ordered phases can
clearly be distinguished. At lowest temperatures a commensurate magnetic
structure with a propagation vector ${\bf k}_1 = (0.25~ 0.25~ 1)$ is found,
while the intermediate phase ($T > 0.9~$K) is characterized by an
incommensurate magnetic structure with ${\bf k}_2 = (0.25~ 0.086~ 1)$. The
magnetic structure in YbCo$_2$Si$_2$ is in marked contrast to all other known
RCo$_2$Si$_2$ compounds (R = rare earth element) likely due to some itineracy
of the Yb 4f states being responsible for the magnetism.


title:
How chemical functionalization affects the lattice thermal
  conductivities of antimony films?

abstract:
  Chemical functionalization is an effective means to tune electronic and
crystal structure of two-dimensional material, which may be crucial for moder
microelectronics industry. Based on the first-principle calculation and an
iterative solution of Boltzmann transport equation, we find that antimony films
are potential excellent thermoelectrical materials with rather low thermal
conductivities $k$ ($<$ 2.5 W/mK). The chemical functionalization can induce
the reduction in $k$ to some extent, which is mainly due to the reduction of
phonon lifetimes limited by the anharmonic scattering. More interesting, the
origin of the reduction in $k$ is not the anharmonic interaction but the
harmonic interaction from the depressed phonon spectrum mechanism, and for some
chemical functional atom in halogen, the flat modes appearing in the low
frequency range play also a key factor in the reduction of $k$ by significantly
increasing the three-phonon scattering channels. Our work analyzes the
reduction mechanism in $k$ from the chemical functionalization for antimonene,
and provides a new view to adjust the thermal conductivity which can benefit
thermoelectric material design.


title:
On the generators of the polynomial algebra as a module over the
  Steenrod algebra

abstract:
  Let $P_k:= \mathbb F_2[x_1,x_2,\ldots,x_k]$ be the polynomial algebra over
the prime field of two elements, $\mathbb F_2$, in $k$ variables $x_1, x_2,
\ldots, x_k$, each of degree 1. We are interested in the Peterson hit problem
of finding a minimal set of generators for $P_k$ as a module over the mod-2
Steenrod algebra, $\mathcal{A}$. In this paper, we study the hit problem in
degree $(k-1)(2^d-1)$ with $d$ a positive integer. Our result implies the one
of Mothebe [4,5].


title:
Galaxy And Mass Assembly (GAMA): $\mathcal{M_\star}-R_{\rm e}$ relations
  of $z=0$ bulges, discs and spheroids

abstract:
  We perform automated bulge + disc decomposition on a sample of $\sim$7500
galaxies from the Galaxy And Mass Assembly (GAMA) survey in the redshift range
of 0.002$<$z$<$0.06 using SIGMA, a wrapper around GALFIT3. To achieve robust
profile measurements we use a novel approach of repeatedly fitting the
galaxies, varying the input parameters to sample a large fraction of the input
parameter space. Using this method we reduce the catastrophic failure rate
significantly and verify the confidence in the fit independently of $\chi^2$.
Additionally, using the median of the final fitting values and the 16$^{th}$
and 84$^{th}$ percentile produces more realistic error estimates than those
provided by GALFIT, which are known to be underestimated. We use the results of
our decompositions to analyse the stellar mass - half-light radius relations of
bulges, discs and spheroids. We further investigate the association of
components with a parent disc or elliptical relation to provide definite $z=0$
disc and spheroid $\mathcal{M_\star}-R_{\rm e}$ relations. We conclude by
comparing our local disc and spheroid $\mathcal{M_\star}-R_{\rm e}$ to
simulated data from EAGLE and high redshift data from CANDELS-UDS. We show the
potential of using the mass-size relation to study galaxy evolution in both
cases but caution that for a fair comparison all data sets need to be processed
and analysed in the same manner.


title: AdaNet: Adaptive Structural Learning of Artificial Neural Networks

abstract:
  We present new algorithms for adaptively learning artificial neural networks.
Our algorithms (AdaNet) adaptively learn both the structure of the network and
its weights. They are based on a solid theoretical analysis, including
data-dependent generalization guarantees that we prove and discuss in detail.
We report the results of large-scale experiments with one of our algorithms on
several binary classification tasks extracted from the CIFAR-10 dataset. The
results demonstrate that our algorithm can automatically learn network
structures with very competitive performance accuracies when compared with
those achieved for neural networks found by standard approaches.


title:
On the Fourier Transform of Bessel Functions over Complex Numbers---II:
  the General Case

abstract:
  In this paper, we prove an exponential integral formula for the Fourier
transform of Bessel functions over complex numbers, along with a radial
exponential integral formula. The former will enable us to develop the complex
spectral theory of the relative trace formula for the Shimura-Waldspurger
correspondence and extend the Waldspurger formula from totally real fields to
arbitrary number fields.


title:
Stochastic calculation of the Dirac spectrum on the lattice and a
  determination of chiral condensate in 2+1-flavor QCD

abstract:
  We compute the chiral condensate in 2+1-flavor QCD through the spectrum of
low-lying eigenmodes of Dirac operator. The number of eigenvalues of the Dirac
operator is evaluated using a stochastic method with an eigenvalue filtering
technique on the background gauge configurations generated by lattice QCD
simulations including the effects of dynamical up, down and strange quarks
described by the Mobius domain-wall fermion formulation. The low-lying spectrum
is related to the chiral condensate, which is one of the leading order
low-energy constants in chiral effective theory, as dictated by the
Banks-Casher relation. The spectrum shape and its dependence on the sea quark
masses calculated in numerical simulations are consistent with the expectation
from one-loop chiral perturbation theory. After taking the chiral limit as well
as the continuum limit using the data at three lattice spacings ranging
0.080-0.045 fm, we obtain $\Sigma^{1/3}$(2 GeV) = 270.0(4.9) MeV, with the
error combining those from statistical and from various sources of systematic
errors. Finite volume effect is confirmed to be under control by a direct
comparison of the results from two different volumes at the lightest available
sea quarks corresponding to 230 MeV pions.


title:
Localization, Decomposition, and Dictionary Learning of
  Piecewise-Constant Signals on Graphs

abstract:
  Motivated by the need to extract meaning from large amounts of complex
structured data, we consider three critical problems on graphs: localization,
decomposition, and dictionary learning of piecewise-constant signals. These
graph-based problems are related to many real-world applications, such as
localizing stimulus in brain connectivity networks, and mining traffic events
in city street networks, where the key issue is to find the supports of
localized activated patterns. Counterparts of these problems in classical
signal/image processing, such as impulse detection and foreground detection,
have been studied over the past few decades. We use piecewise-constant graph
signals to model localized patterns, where each piece indicates a localized
pattern that exhibits homogeneous internal behavior and the number of pieces
indicates the number of localized patterns. For such signals, we show that
decomposition and dictionary learning are natural extensions of localization,
the goal of which is not only to efficiently approximate graph signals, but
also to accurately find supports of localized patterns. For each of the three
problems, i.e., localization, decomposition, and dictionary learning, we
propose a specific graph signal model, an optimization problem, and a
computationally efficient solver. The proposed solvers directly find the
supports of arbitrary localized activated patterns without tuning any
thresholds. We then conduct an extensive empirical study to validate the
proposed methods on both simulated and real data including the analysis of a
large volume of spatio-temporal Manhattan urban data. The analysis validates
the effectiveness of the approach and suggests that graph signal processing
tools may aid in urban planning and traffic forecasting.


title:
Near-infrared luminescent phosphors enabled by topotactic reduction of
  bismuth-activated red-emitting crystals

abstract:
  Bismuth-doped luminescent materials have gained significant attention in the
past years owing to their huge potential for the applications in
telecommunications, biomedicine, and displays. However, the controlled
synthesis of these materials, in particular for those luminescing in the
near-infrared (NIR), remains a challenging subject of continuous research
effort. Herein, we show that the low-temperature topotactic reduction by using
Al metal powders as oxygen getters can be adopted as a powerful technique for
the conversion of bismuth-doped red-emitting systems into NIR-emitting cousins
as a result of the creation of unique crystalline networks. Thorough
experimental characterization indicates that the framework oxygen of hosts can
be topotactically extracted, thus producing unique metal-oxygen-metal networks
in the reduced phases while preserving the crystalline structure of the
precursor. We anticipate that this low-temperature topotactic reduction
strategy can be applied to the development of more novel Bi-doped luminescent
materials in various forms that can find a broad range of functional
applications.


title:
A Visualization Method of Four Dimensional Polytopes by Oval Display of
  Parallel Hyperplane Slices

abstract:
  A method to visualize polytopes in a four dimensional euclidian space
$(x,y,z,w)$ is proposed. A polytope is sliced by multiple hyperplanes that are
parallel each other and separated by uniform intervals. Since the hyperplanes
are perpendicular to the $w$ axis, the resulting multiple slices appear in the
three-dimensional $(x,y,z)$ space and they are shown by the standard computer
graphics. The polytope is rotated extrinsically in the four dimensional space
by means of a simple input method based on keyboard typings. The multiple
slices are placed on a parabola curve in the three-dimensional world
coordinates. The slices in a view window form an oval appearance. Both the
simple and the double rotations in the four dimensional space are applied to
the polytope. All slices synchronously change their shapes when a rotation is
applied to the polytope. The compact display in the oval of many slices with
the help of quick rotations facilitate a grasp of the four dimensional
configuration of the polytope.


title: Two new parent compounds for FeSe-based superconducting phases

abstract:
  It is well established that the occurrence of superconductivity in iron
pnictides is closely related to the tetragonal to orthorhombic structural and
antiferromagnetic (AFM) phase transitions. It, however, has not been clear
whether the same scenario is appropriate for iron chalcogenide counterparts due
to the absence of parent compounds for the latter family of superconductors.
Here, we report the synthesis and structure determination of two novel phases
in ethylenediamine intercalated FeSe, one is tetragonal and the other
orthorhombic in room temperature, which can be stabilized with neutral spacer
layers. Both phases can be regarded as the parent compounds for
superconductivity as they are non-superconducting (non-SC) in pristine form and
superconducting (SC) with Tc up to 38K and 46K, respectively after Na doping,
and the switch between SC and no-SC is reversible. Moreover, the two non-SC
parent compounds show no evidence of long-range magnetic ordering down to 2K,
only with dynamic spin fluctuations at low temperatures, suggesting that no
competition between SC and AFM ordering. Our results reveal that undoped iron
selenides are quantum paramagnetic in ground state, implying that they are
distinct from their pnictide counterparts in pairing mechanism.


title:
A study of the Bienstock-Zuckerberg algorithm, Applications in Mining
  and Resource Constrained Project Scheduling

abstract:
  We study a Lagrangian decomposition algorithm recently proposed by Dan
Bienstock and Mark Zuckerberg for solving the LP relaxation of a class of open
pit mine project scheduling problems. In this study we show that the
Bienstock-Zuckerberg (BZ) algorithm can be used to solve LP relaxations
corresponding to a much broader class of scheduling problems, including the
well-known Resource Constrained Project Scheduling Problem (RCPSP), and
multi-modal variants of the RCPSP that consider batch processing of jobs. We
present a new, intuitive proof of correctness for the BZ algorithm that works
by casting the BZ algorithm as a column generation algorithm. This analysis
allows us to draw parallels with the well-known Dantzig-Wolfe (DW) algorithm.
We discuss practical computational techniques for speeding up the performance
of the BZ and DW algorithms on project scheduling problems. Finally, we present
computational experiments independently testing the effectiveness of the BZ and
DW algorithms on different sets of publicly available test instances. Our
computational experiments confirm that the BZ algorithm significantly
outperforms the DW algorithm for the problems considered. Our computational
experiments also show that the proposed speed-up techniques can have a
significant impact on solution time. We provide some insights on what might be
explaining this significant difference in performance.


title:
Using the PPML approach for constructing a low-dissipation,
  operator-splitting scheme for numerical simulations of hydrodynamic flows

abstract:
  An approach for constructing a low-dissipation numerical method is described.
The method is based on a combination of the operator-splitting method, Godunov
method, and piecewise-parabolic method on the local stencil. Numerical method
was tested on a standard suite of hydrodynamic test problems. In addition, the
performance of the method is demonstrated on a global test problem showing the
development of a spiral structure in a gravitationally unstable gaseous
galactic disk.


title: Invariance Preserving Discretization Methods of Dynamical Systems

abstract:
  In this paper, we consider local and uniform invariance preserving steplength
thresholds on a set when a discretization method is applied to a linear or
nonlinear dynamical system. For the forward or backward Euler method, the
existence of local and uniform invariance preserving steplength thresholds is
proved when the invariant sets are polyhedra, ellipsoids, or Lorenz cones.
Further, we also quantify the steplength thresholds of the backward Euler
methods on these sets for linear dynamical systems. Finally, we present our
main results on the existence of uniform invariance preserving steplength
threshold of general discretization methods on general convex sets, compact
sets, and proper cones both for linear and nonlinear dynamical systems.


title: Invariance Conditions for Nonlinear Dynamical Systems

abstract:
  Recently, Horv\'ath, Song, and Terlaky [\emph{A novel unified approach to
invariance condition of dynamical system, submitted to Applied Mathematics and
Computation}] proposed a novel unified approach to study, i.e., invariance
conditions, sufficient and necessary conditions, under which some convex sets
are invariant sets for linear dynamical systems.
  In this paper, by utilizing analogous methodology, we generalize the results
for nonlinear dynamical systems. First, the Theorems of Alternatives, i.e., the
nonlinear Farkas lemma and the \emph{S}-lemma, together with Nagumo's Theorem
are utilized to derive invariance conditions for discrete and continuous
systems. Only standard assumptions are needed to establish invariance of
broadly used convex sets, including polyhedral and ellipsoidal sets. Second, we
establish an optimization framework to computationally verify the derived
invariance conditions. Finally, we derive analogous invariance conditions
without any conditions.


title:
The cohomology of the height four Morava stabilizer group at large
  primes

abstract:
  This is an announcement of some new computational methods in stable homotopy
theory, in particular, methods for using the cohomology of small-height Morava
stabilizer groups to compute the cohomology of large-height Morava stabilizer
groups. As an application, the cohomology of the height four Morava stabilizer
group is computed at large primes (its rank turns out to be $3440$).
Consequently we are able to formulate a plausible conjecture on the rank of the
large-primary cohomology of the Morava stabilizer groups at all heights.


title: Square lattice self-avoiding walks and biased differential approximants

abstract:
  The model of self-avoiding lattice walks and the asymptotic analysis of
power-series have been two of the major research themes of Tony Guttmann. In
this paper we bring the two together and perform a new analysis of the
generating functions for the number of square lattice self-avoiding walks and
some of their metric properties such as the mean-square end-to-end distance.
The critical point $x_c$ for self-avoiding walks is known to a high degree of
accuracy and we utilise this knowledge to undertake a new numerical analysis of
the series using biased differential approximants. The new method is major
advance in asymptotic power-series analysis in that it allows us to bias
differential approximants to have a singularity of order $q$ at $x_c$. When
biasing at $x_c$ with $q\geq 2$ the analysis yields a very accurate estimate
for the critical exponent $\gamma=1.3437500(3)$ thus confirming the conjectured
exact value $\gamma=43/32$ to 8 significant digits and removing a long-standing
minor discrepancy between exact and numerical results. The analysis of the
mean-square end-to-end distance yields $\nu=0.7500002(4)$ thus confirming the
exact value $\nu=3/4$ to 7 significant digits.


title: Utility Indifference Pricing of Insurance Catastrophe Derivatives

abstract:
  We propose a model for an insurance loss index and the claims process of a
single insurance company holding a fraction of the total number of contracts
that captures both ordinary losses and losses due to catastrophes. In this
model we price a catastrophe derivative by the method of utility indifference
pricing. The associated stochastic optimization problem is treated by
techniques for piecewise deterministic Markov processes. A numerical study
illustrates our results.


title:
Predicted thermoelectric properties of olivine-type Fe2GeCh4 (Ch = S, Se
  and Te)

abstract:
  We present here the thermoelectric properties of olivine-type Fe2GeCh4 (Ch =
S, Se and Te) using the linear augmented plane wave method based on first
principles density functional calculations. The calculated transport properties
using the semi-local Boltzmann transport equation reveal very high thermopower
for both S and Se-based compounds compared to their Te counterparts. The main
reason for this high thermopower is the quasi-flat nature of the bands at the
valence and conduction band edges. The calculated thermopower of Fe2GeCh4 is in
good agreement with the experimental reports at room temperature, with the
carrier concentration around 1018-1019cm-3. All the investigated systems show
an anisotropic nature in their electrical conductivity, resulting in a value
less than the order of 102 along the a-axis compared to the b- and c-axes.
Among the studied compounds, Fe2GeS4 and Fe2GeSe4 emerge as promising
candidates with good thermoelectric performance.


title: Effective Control of Cold Collisions with Radio Frequency Fields

abstract:
  We study $^{87}$Rb cold collisions in a static magnetic field and a
single-color radio frequency (RF) field by employing the multi-channel quantum
defect theory in combination with the Floquet method to solve the two-body
time-dependent Schr\"odinger equation. Our results show that RF fields can
modify the two-body scattering length by a large scale through Feshbach
resonances both in low and high static magnetic field regimes. Such RF induced
Feshbach resonances can be applied to quenching experiments or controlling
interactions in spinor condensates. Here, we also show that analogous to
photo-association, RF fields can also associate cold atoms into molecules at a
useful rate.


title:
Global Existence for the Ellipsoidal BGK Model with Initial Large
  Oscillations

abstract:
  The ellipsoidal BGK model was introduced in \cite{Ho} to fit the correct
Prandtl number in the Navier-Stokes approximation of the classical BGK model.
In the paper we establish the global existence of mild solutions to the Cauchy
problem on the model for a class of initial data allowed to have large
oscillations. The proof is motivated by a recent study of the same topic on the
Boltzmann equation in \cite{DHWY}.


title: Superspecial curves of genus $4$ in small characteristic

abstract:
  This paper contains a complete study of superspecial curves of genus $4$ in
characteristic $p\le 7$. We prove that there does not exist a superspecial
curve of genus $4$ in characteristic $7$. This is a negative answer to the
genus $4$ case of the problem proposed by Ekedahl [9] in 1987. This implies the
non-existence of maximal curve of genus $4$ over $\mathbb{F}_{49}$, which
updates the table at {\tt manypoints.org}. We give an algorithm to enumerate
superspecial nonhyperelliptic curves in arbitrary $p \ge 5$, and for $p\le 7$
we excute it with our implementation on a computer algebra system Magma. Our
result in $p=5$ re-proves the uniqueness of maximal curves of genus $4$ over
$\mathbb{F}_{25}$, see [11] for the original theoretical proof. In Appendix, we
present a general method determining Hasse-Witt matrices of curves which are
complete intersections.


title: Click Carving: Segmenting Objects in Video with Point Clicks

abstract:
  We present a novel form of interactive video object segmentation where a few
clicks by the user helps the system produce a full spatio-temporal segmentation
of the object of interest. Whereas conventional interactive pipelines take the
user's initialization as a starting point, we show the value in the system
taking the lead even in initialization. In particular, for a given video frame,
the system precomputes a ranked list of thousands of possible segmentation
hypotheses (also referred to as object region proposals) using image and motion
cues. Then, the user looks at the top ranked proposals, and clicks on the
object boundary to carve away erroneous ones. This process iterates (typically
2-3 times), and each time the system revises the top ranked proposal set, until
the user is satisfied with a resulting segmentation mask. Finally, the mask is
propagated across the video to produce a spatio-temporal object tube. On three
challenging datasets, we provide extensive comparisons with both existing work
and simpler alternative methods. In all, the proposed Click Carving approach
strikes an excellent balance of accuracy and human effort. It outperforms all
similarly fast methods, and is competitive or better than those requiring 2 to
12 times the effort.


title:
Power-Efficient Resource Allocation for MC-NOMA with Statistical Channel
  State Information

abstract:
  In this paper, we study the power-efficient resource allocation for
multicarrier non-orthogonal multiple access (MC-NOMA) systems. The resource
allocation algorithm design is formulated as a non-convex optimization problem
which takes into account the statistical channel state information at
transmitter and quality of service (QoS) constraints. To strike a balance
between system performance and computational complexity, we propose a
suboptimal power allocation and user scheduling with low computational
complexity to minimize the total power consumption. The proposed design
exploits the heterogeneity of QoS requirement to determine the successive
interference cancellation decoding order. Simulation results demonstrate that
the proposed scheme achieves a close-to-optimal performance and significantly
outperforms a conventional orthogonal multiple access (OMA) scheme.


title: Anagram-free Graph Colouring

abstract:
  An anagram is a word of the form $WP$ where $W$ is a non-empty word and $P$
is a permutation of $W$. We study anagram-free graph colouring and give bounds
on the chromatic number. Alon et al. (2002) asked whether anagram-free
chromatic number is bounded by a function of the maximum degree. We answer this
question in the negative by constructing graphs with maximum degree 3 and
unbounded anagram-free chromatic number. We also prove upper and lower bounds
on the anagram-free chromatic number of trees in terms of their radius and
pathwidth. Finally, we explore extensions to edge colouring and
$k$-anagram-free colouring.


title: Brauer groups and Galois cohomology of commutative ring spectra

abstract:
  In this paper we develop methods for classifying Baker-Richter-Szymik's
Azumaya algebras over a commutative ring spectrum, especially in the largely
inaccessible case where the ring is nonconnective. We give
obstruction-theoretic tools, constructing and classifying these algebras and
their automorphisms with Goerss-Hopkins obstruction theory, and give
descent-theoretic tools, applying Lurie's work on $\infty$-categories to show
that a finite Galois extension of rings in the sense of Rognes becomes a
homotopy fixed-point equivalence on Brauer spaces.
  For even-periodic ring spectra $E$, we find that the "algebraic" Azumaya
algebras whose coefficient ring is projective are governed by the Brauer-Wall
group of $\pi_0(E)$, recovering a result of Baker-Richter-Szymik. This allows
us to calculate many examples. For example, we find that the algebraic Azumaya
algebras over Lubin-Tate spectra have either 4 or 2 Morita equivalence classes
depending on whether the prime is odd or even, that all algebraic Azumaya
algebras over the complex K-theory spectrum $KU$ are Morita trivial, and that
the group of the Morita classes of algebraic Azumaya algebras over the
localization $KU[1/2]$ is $\Bbb Z/8 \times \Bbb Z/2$.
  Using our descent results and an obstruction theory spectral sequence, we
also study Azumaya algebras over the real K-theory spectrum $KO$ which become
Morita-trivial $KU$-algebras. We show that there exist exactly two Morita
equivalence classes of these. The nontrivial Morita equivalence class is
realized by an "exotic" $KO$-algebra with the same coefficient ring as
$End_{KO}(KU)$. This requires a careful analysis of what happens in the
homotopy fixed-point spectral sequence for the Picard space of $KU$, previously
studied by Mathew and Stojanoska.


title: On User Association in Multi-Tier Full-Duplex Cellular Networks

abstract:
  We address the user association problem in multi-tier in-band full-duplex
(FD) networks. Specifically, we consider the case of decoupled user association
(DUA) in which users (UEs) are not necessarily served by the same base station
(BS) for uplink (UL) and downlink (DL) transmissions. Instead, UEs can
simultaneously associate to different BSs based on two independent weighted
path-loss user association criteria for UL and DL. We use stochastic geometry
to develop a comprehensive modeling framework for the proposed system model
where BSs and UEs are spatially distributed according to independent point
processes. We derive closed-form expressions for the mean rate utility in FD,
half-duplex (HD) DL, and HD UL networks as well as the mean rate utility of
legacy nodes with only HD capabilities in a multi-tier FD network. We formulate
and solve an optimization problem that aims at maximizing the mean rate utility
of the FD network by optimizing the DL and UL user association criteria. We
investigate the effects of different network parameters including the spatial
density of BSs and power control parameter. We also investigate the effect of
imperfect self-interference cancellation (SIC) and show that it is more severe
at UL, where there exist minimum required SIC capabilities for BSs and UEs for
which FD networks are preferable to HD networks; otherwise, HD networks are
preferable. In addition, we discuss several special cases and provide
guidelines on the possible extensions of the proposed framework. We conclude
that DUA outperforms coupled user association (CUA) in which UEs associate to
the same BS for both UL and DL transmissions.


title: Light curves of light rays passing through a wormhole

abstract:
  Gravitational lensing is a good probe into the topological structure of dark
gravitating celestial objects. In this paper, we investigate the light curve of
a light ray that passes through the throat of an Ellis wormhole, the simplest
example of traversable wormholes. The method developed here is also applicable
to other traversable wormholes. To study whether the light curve of a light ray
that passes through a wormhole throat is distinguishable from that which does
not, we also calculate light curves without the passage of a throat for an
Ellis wormhole, a Schwarzschild black hole, and an ultrastatic wormhole with
the spatial geometry identical to that of the Schwarzschild black hole in the
following two cases: (i) "microlensing," where the source, lens, and observer
are almost aligned in this order and the light ray starts at the source,
refracts in the weak gravitational field of the lens with a small deflection
angle, and reaches the observer, and (ii) "retrolensing," where the source,
observer, and lens are almost aligned in this order, and the light ray starts
at the source, refracts in the vicinity of the light sphere of the lens with a
deflection angle very close to $\pi$, and reaches the observer. We find that
the light curve of the light ray that passes through the throat of the Ellis
wormhole is clearly distinguishable from that by the microlensing but not from
that by the retrolensing. This is because the light curve of a light ray that
passes by a light sphere of a lens with a large deflection angle has common
characters, irrespective of the details of the lens object. This implies that
the light curves of the light rays that pass through the throat of more general
traversable wormholes are qualitatively the same as that of the Ellis wormhole.


title: On Gradient Descent Algorithm for Generalized Phase Retrieval Problem

abstract:
  In this paper, we study the generalized phase retrieval problem: to recover a
signal $\bm{x}\in\mathbb{C}^n$ from the measurements $y_r=\lvert
\langle\bm{a}_r,\bm{x}\rangle\rvert^2$, $r=1,2,\ldots,m$. The problem can be
reformulated as a least-squares minimization problem. Although the cost
function is nonconvex, the global convergence of gradient descent algorithm
from a random initialization is studied, when $m$ is large enough. We improve
the known result of the local convergence from a spectral initialization. When
the signal $\bm{x}$ is real-valued, we prove that the cost function is local
convex near the solution $\{\pm\bm{x}\}$. To accelerate the gradient descent,
we review and apply several efficient line search methods. We also perform a
comparative numerical study of the line search methods and the alternative
projection method. Numerical simulations demonstrate the superior ability of
LBFGS algorithm than other algorithms.


title:
Particle dynamics in a symmetrically driven underdamped inhomogeneous
  periodic potential system

abstract:
  We numerically solve the underdamped Langevin equation to obtain the
trajectories of a particle in a sinusoidal potential driven by a temporally
sinusoidal force in a medium with coefficient of friction periodic in space as
the potential but with a phase difference. With the appropriate choice of
system parameters, like the mean friction coefficient and the period of the
applied field, only two kinds of periodic trajectories are obtained for all
possible initial conditions at low noise strengths: one with a large amplitude
and a large phase lag with respect to the applied field and the other with a
small amplitude and a small phase lag. Thus, the periodic potential system is
effectively mapped dynamically into a bistable system. Though the directional
asymmetry, brought about only by the frictional inhomogeneity, is weak we find
both the phenomena of stochastic resonance, with ready explanation in terms of
the two dynamical states of trajectories, and ratchet effect simultaneously in
the same parameter space. We analyse the results in detail attempting to find
plausible explanations for each.


title:
Clearing out a maze: The hungry random walker and its anomalous
  diffusion

abstract:
  We study chemotaxis in a porous medium using as a model a biased ("hungry")
random walk on a percolating cluster. In close resemblance to the 1980s arcade
game Pac-Man, the hungry random walker consumes food, which is initially
distributed in the maze, and biases its movement towards food-filled sites. We
observe that, on the percolating cluster, the mean-squared displacement of the
pacman process shows anomalous dynamics, which follow a power law with a
dynamical exponent different from both that of a self avoiding random walk as
well as that of an unbiased random walk. The change in dynamics with the
propensity to move towards food is well described by a dynamical exponent that
depends continuously on this propensity, and results in slower differential
growth when compared to the unbiased random walk.


title: Analysis of Double Covers of Factor Graphs

abstract:
  Many quantities of interest in communications, signal processing, artificial
intelligence, and other areas can be expressed as the partition sum of some
factor graph. Although the exact calculation of the partition sum is in many
cases intractable, it can often be approximated rather well by the Bethe
partition sum. In earlier work, we have shown that graph covers are a useful
tool for expressing and analyzing the Bethe approximation. In this paper, we
present a novel technique for analyzing double covers, a technique which
ultimately leads to a deeper understanding of the Bethe approximation.


abstract:
  We investigate various types of Fubini instantons in Dilatonic
Einstein-Gauss-Bonnet theory of gravitation, which describe the decay of the
vacuum state at a hilltop potential through the tunneling without a barrier. It
is shown that the vacuum states are modified by the non-minimally coupled
higher-curvature term. Accordingly, we present the new type of solutions
describing the tunneling from new vacuum states in anti-de Sitter and de Sitter
backgrounds. The decay probabilities of vacuum states are also influenced.
Consequently, we show that the semiclassical exponents can be decreased for
specific parameter ranges, which make the tunneling probabilities enhanced.


title: Approach to Chandrasekhar-Kendall-Woltjer State in a Chiral Plasma

abstract:
  We study the time evolution of the magnetic field in a plasma with a chiral
magnetic current. The Vector Spherical Harmonic functions (VSH) are used to
expand all fields. We define a measure for the Chandrasekhar-Kendall-Woltjer
(CKW) state, which has a simple form in VSH expansion. We propose the
conditions for a general class of initial momentum spectra that will evolve
into the CKW state. For this class of initial conditions, to approach the CKW
state, (i) a non-vanishing chiral magnetic conductivity is necessary, and (ii)
the time integration of the product of the electric resistivity and chiral
magnetic conductivity must grow faster than the time integration of the
resistivity. We give a few examples to test these conditions numerically which
work very well.


title: A Markov chain representation of the Perron-Frobenius eigenvector

abstract:
  We consider the problem of finding the Perron-Frobenius eigenvector of a
primitive matrix. Dividing each of the rows of the matrix by the sum of the
elements in the row, the resulting new matrix is stochastic. We give a formula
for the Perron-Frobenius eigenvector of the original matrix, in terms of a
realization of the Markov chain defined by the associated stochastic matrix.
This formula is a generalization of the classical formula for the invariant
probability measure of a Markov chain.


title:
Einstein-Cartan Gravity with Torsion Field Serving as Origin for
  Cosmological Constant or Dark Energy Density

abstract:
  We analyse the Einstein-Cartan gravity in its standard form cal-R = R +
cal-K^2, where cal-R and R are the Ricci scalar curvatures in the
Einstein-Cartan and Einstein gravity, respectively, and cal-K^2 is the
quadratic contribution of torsion in terms of the contorsion tensor cal-K. We
treat torsion as an external (or a background) field and show that the
contribution of torsion to the Einstein equations can be interpreted in terms
of the torsion energy-momentum tensor, local conservation of which in a curved
spacetime with an arbitrary metric or an arbitrary gravitational field demands
a proportionality of the torsion energy--momentum tensor to a metric tensor, a
covariant derivative of which vanishes because of the metricity condition. This
allows to claim that torsion can serve as origin for vacuum energy density,
given by cosmological constant or dark energy density in the Universe. This is
a model-independent result may explain a small value of cosmological constant,
which is a long--standing problem of cosmology. We show that the obtained
result is valid also in the Poincare' gauge gravitational theory by Kibble (T.
W. B. Kibble, J. Math. Phys. 2, 212 (1961)), where the Einstein-Hilbert action
can be represented in the same form cal-R = R + cal-K^2.


title: The Quantum Field Theory of K-mouflage

abstract:
  We consider K-mouflage models which are K-essence theories coupled to matter.
We analyse their quantum properties and in particular the quantum corrections
to the classical Lagrangian. We setup the renormalisation programme for these
models and show that K-mouflage theories involve a recursive construction
whereby each set of counter-terms introduces new divergent quantum
contributions which in turn must be subtracted by new counter-terms. This tower
of counter-terms can be constructed by recursion and allows one to calculate
the finite renormalised action of the model. In particular, the classical
action is not renormalised and the finite corrections to the renormalised
action contain only higher derivative operators. We establish an operational
criterion for classicality, where the corrections to the classical action are
negligible, and show that this is satisfied in cosmological and astrophysical
situations for (healthy) K-mouflage models which pass the solar system tests.
We also find that these models are quantum stable around astrophysical and
cosmological backgrounds. We then consider the possible embedding of the
K-mouflage models in an Ultra-Violet completion. We find that the healthy
models which pass the solar system tests all violate the positivity constraint
which would follow from the unitarity of the putative UV completion, implying
that these healthy K-mouflage theories have no UV completion. We then analyse
their behaviour at high energy and we find that the classicality criterion is
satisfied in the vicinity of a high energy collision implying that the
classical K-mouflage theory can be applied in this context. Moreover, the
classical description becomes more accurate as the energy increases, in a way
compatible with the classicalisation concept.


title: THz-circuits driven by photo-thermoelectric graphene-junctions

abstract:
  For future on-chip communication schemes, it is essential to integrate
nanoscale materials with an ultrafast optoelectronic functionality into
high-frequency circuits. The atomically thin graphene has been widely
demonstrated to be suitable for photovoltaic and optoelectronic devices because
of its broadband optical absorption and its high electron mobility. Moreover,
the ultrafast relaxation of photogenerated charge carriers has been verified in
graphene. Here, we show that dual-gated graphene junctions can be functional
parts of THz-circuits. As the underlying optoelectronic process, we exploit
ultrafast photo-thermoelectric currents. We describe an immediate
photo-thermoelectric current of the unbiased device following a femtosecond
laser excitation. For a picosecond time-scale after the optical excitation, an
additional photo-thermoelectric contribution shows up, which exhibits the
fingerprint of a spatially inverted temperature profile. The latter can be
understood by the different time-constants and thermal coupling mechanisms of
the electron and phonon baths within graphene to the substrate and the metal
contacts. The interplay of the processes gives rise to ultrafast
electromagnetic transients in high-frequency circuits, and it is equally
important for a fundamental understanding of graphene-based ultrafast
photodetectors and switches.


title:
Transport and selective chaining of bidisperse particles in a travelling
  wave potential

abstract:
  We combine experiments, theory and numerical simulation to investigate the
dynamics of a binary suspension of paramagnetic colloidal particles dispersed
in water and transported above a stripe patterned magnetic garnet film. The
substrate generates a one-dimensional periodic energy landscape above its
surface. The application of an elliptically polarized rotating magnetic field
causes the landscape to translate, inducing direct transport of paramagnetic
particles placed above the film. The ellipticity of the applied field can be
used to control and tune the interparticle interactions, from net repulsive to
net attractive. When considering particles of two distinct sizes, we find that,
depending on their elevation above the surface of the magnetic substrate, the
particles feel effectively different potentials, resulting in different
mobilities. We exploit this feature to induce selective chaining for certain
values of the applied field parameters. In particular, when driving two types
of particles, we force only one type to condense into travelling parallel
chains. These chains confine the movement of the other non-chaining particles
within narrow colloidal channels. This phenomenon is explained by considering
the balance of pairwise magnetic forces between the particles and their
individual coupling with the travelling landscape.


title:
Spin-filtered and Spatially Distinguishable Crossed Andreev Reflection
  in a Silicene-Superconductor Junction

abstract:
  We theoretically investigate the quantum transports in a junction between a
superconductor and a silicene nanoribbon, under the effect of a magnetic
exchange field. We find that for a narrow nanoribbon of silicene, remarkable
crossed Andreev reflection (with a fraction $>50\%$) can be induced in the
energy window of the elastic cotunneling, by destroying some symmetries of the
system. Since the energy responses of electrons to the exchange field are
opposite for opposite spins, these transport channels can be well spin
polarized. Moreover, due to the helicity conservation of the topological edge
states, these three transport channels are spatially separated in three
different locations of the device, making them experimentally distinguishable.
This crossed Andreev reflection is a nonlocal quantum interference between
opposite edges through evanescent modes. If two superconducting leads with
different phases are connected to two edges of the silicene nanoribbon, the
crossed Andreev reflection can present Josephson type oscillations, with a
maximal fraction $\sim 100\%$.


title:
Learning when to trust distant supervision: An application to
  low-resource POS tagging using cross-lingual projection

abstract:
  Cross lingual projection of linguistic annotation suffers from many sources
of bias and noise, leading to unreliable annotations that cannot be used
directly. In this paper, we introduce a novel approach to sequence tagging that
learns to correct the errors from cross-lingual projection using an explicit
debiasing layer. This is framed as joint learning over two corpora, one tagged
with gold standard and the other with projected tags. We evaluated with only
1,000 tokens tagged with gold standard tags, along with more plentiful parallel
data. Our system equals or exceeds the state-of-the-art on eight simulated
low-resource settings, as well as two real low-resource languages, Malagasy and
Kinyarwanda.