title:
Detecting Novel Processes with CANDIES -- An Holistic Novelty Detection
  Technique based on Probabilistic Models

abstract:
  In this article, we propose CANDIES (Combined Approach for Novelty Detection
in Intelligent Embedded Systems), a new approach to novelty detection in
technical systems. We assume that in a technical system several processes
interact. If we observe these processes with sensors, we are able to model the
observations (samples) with a probabilistic model, where, in an ideal case, the
components of the parametric mixture density model we use, correspond to the
processes in the real world. Eventually, at run-time, novel processes emerge in
the technical systems such as in the case of an unpredictable failure. As a
consequence, new kinds of samples are observed that require an adaptation of
the model. CANDIES relies on mixtures of Gaussians which can be used for
classification purposes, too. New processes may emerge in regions of the
models' input spaces where few samples were observed before (low-density
regions) or in regions where already many samples were available (high-density
regions). The latter case is more difficult, but most existing solutions focus
on the former. Novelty detection in low- and high-density regions requires
different detection strategies. With CANDIES, we introduce a new technique to
detect novel processes in high-density regions by means of a fast online
goodness-of-fit test. For detection in low-density regions we combine this
approach with a 2SND (Two-Stage-Novelty-Detector) which we presented in
preliminary work. The properties of CANDIES are evaluated using artificial data
and benchmark data from the field of intrusion detection in computer networks,
where the task is to detect new kinds of attacks.


title: On the Precision to Sort Line-Quadric Intersections

abstract:
  To support exactly tracking a neutron moving along a given line segment
through a CAD model with quadric surfaces, this paper considers the arithmetic
precision required to compute the order of intersection points of two quadrics
along the line segment. When the orders of all but one pair of intersections
are known, we show that a resultant can resolve the order of the remaining pair
using only half the precision that may be required to eliminate radicals by
repeated squaring. We compare the time and accuracy of our technique with
converting to extended precision to calculate roots.


title: $G_\delta$ covers of compact spaces

abstract:
  We solve a long standing question due to Arhangel'skii by constructing a
compact space which has a $G_\delta$ cover with no continuum-sized
($G_\delta$)-dense subcollection. We also prove that in a countably compact
weakly Lindel\"of normal space of countable tightness, every $G_\delta$ cover
has a $\mathfrak{c}$-sized subcollection with a $G_\delta$-dense union and that
in a Lindel\"of space with a base of multiplicity continuum, every $G_\delta$
cover has a continuum sized subcover. We finally apply our results to obtain a
bound on the cardinality of homogeneous spaces which refines De La Vega's
celebrated theorem on the cardinality of homogeneous compacta of countable
tightness.


title: Far from equilibrium: Wealth reallocation in the United States

abstract:
  Studies of wealth inequality often assume that an observed wealth
distribution reflects a system in equilibrium. This constraint is rarely tested
empirically. We introduce a simple model that allows equilibrium but does not
assume it. To geometric Brownian motion (GBM) we add reallocation: all
individuals contribute in proportion to their wealth and receive equal shares
of the amount collected. We fit the reallocation rate parameter required for
the model to reproduce observed wealth inequality in the United States from
1917 to 2012. We find that this rate was positive until the 1980s, after which
it became negative and of increasing magnitude. With negative reallocation, the
system cannot equilibrate. Even with the positive reallocation rates observed,
equilibration is too slow to be practically relevant. Therefore, studies which
assume equilibrium must be treated skeptically. By design they are unable to
detect the dramatic conditions found here when data are analysed without this
constraint.


title: One-loop potential with scale invariance and effective operators

abstract:
  We study quantum corrections to the scalar potential in classically scale
invariant theories, using a manifestly scale invariant regularization. To this
purpose, the subtraction scale $\mu$ of the dimensional regularization is
generated after spontaneous scale symmetry breaking, from a subtraction
function of the fields, $\mu(\phi,\sigma)$. This function is then uniquely
determined from general principles showing that it depends on the dilaton only,
with $\mu(\sigma)\sim \sigma$. The result is a scale invariant one-loop
potential $U$ for a higgs field $\phi$ and dilaton $\sigma$ that contains an
additional {\it finite} quantum correction $\Delta U(\phi,\sigma)$, beyond the
Coleman Weinberg term. $\Delta U$ contains new, non-polynomial effective
operators like $\phi^6/\sigma^2$ whose quantum origin is explained. A flat
direction is maintained at the quantum level, the model has vanishing vacuum
energy and the one-loop correction to the mass of $\phi$ remains small without
tuning (of its self-coupling, etc) beyond the initial, classical tuning (of the
dilaton coupling) that enforces a hierarchy $\langle\sigma\rangle\gg
\langle\phi\rangle$. The approach is useful to models that investigate scale
symmetry at the quantum level.


title: Energy-Recycling Full-Duplex Radios for Next-Generation Networks

abstract:
  In this work, a novel energy-recycling single-antenna full-duplex (FD) radio
is designed, in which a new 3-port element including a power divider and an
energy harvester is added between the circulator and the receiver (RX) chain.
The presence of this new element brings advantages over the state of the art in
terms of both spectral efficiency and energy consumption. In particular, it
provides the means of performing both an arbitrary attenuation of the incoming
signal, which in turn increases the effectiveness of the state-of-the-art
self-interference cancellation strategies subsequently adopted in the RX chain,
and the recycling of a non-negligible portion of the energy leaked through the
non-ideal circulator. The performance of this architecture is analyzed in a
practically relevant 4-node scenario in which 2 nodes operate in FD and 2 nodes
in half-duplex (HD). Analytical approximations are derived for both the
achievable rates of the transmissions performed by the FD and HD radios and the
energy recycled by the FD radios. The accuracy of these derivations is
confirmed by numerical simulations. Quantitatively, achievable rate gains up to
40% over the state-of-the-art alternatives, in the considered scenario, are
highlighted. Furthermore, up to 50% of the leaked energy at the circulator,
i.e., 5% of the energy of the transmitted signal, can be recycled.


title:
Logarithmic Link Invariants of $\overline{U}_q^H(\mathfrak{sl}_2)$ and
  Asymptotic Dimensions of Singlet Vertex Algebras

abstract:
  We study relationships between the restricted unrolled quantum group
$\overline{U}_q^H(\mathfrak{sl}_2)$ at $2r$-th root of unity $q=e^{\pi i/r}, r
\geq 2$, and the singlet vertex operator algebra $\mathcal M(r)$. We use
deformable families of modules to efficiently compute $(1, 1)$-tangle
invariants colored with projective modules of
$\overline{U}_q^H(\mathfrak{sl}_2)$. These relate to the colored Alexander
tangle invariants studied in [ADO, M1]. It follows that the regularized
asymptotic dimensions of characters of $\mathcal M(r)$ coincide with the
corresponding modified traces of open Hopf link invariants. We also discuss
various categorical properties of $\mathcal M(r)$-mod in connection to braided
tensor categories.


title: Anomaly Corrected Heterotic Horizons

abstract:
  We consider supersymmetric near-horizon geometries in heterotic supergravity
up to two loop order in sigma model perturbation theory. We identify the
conditions for the horizons to admit enhancement of supersymmetry. We show that
solutions which undergo supersymmetry enhancement exhibit an sl(2,R) symmetry,
and we describe the geometry of their horizon sections. We also prove a
modified Lichnerowicz type theorem, incorporating $\alpha'$ corrections, which
relates Killing spinors to zero modes of near-horizon Dirac operators.
Furthermore, we demonstrate that there are no AdS2 solutions in heterotic
supergravity up to second order in $\alpha'$ for which the fields are smooth
and the internal space is smooth and compact without boundary. We investigate a
class of nearly supersymmetric horizons, for which the gravitino Killing spinor
equation is satisfied on the spatial cross sections but not the dilatino one,
and present a description of their geometry.


title: Structural evolution of MnTi0.8Ru0.2O3

abstract:
  Here We present the structural studies on MnTi1-xRuxO3(x=0, 0.2) compounds.
The role of Ti ions in the magnetism of MnTiO3 was unclear so here this issue
has been tried to address in this manuscript. The magnetic susceptibility data
shows that the 3-dimensional magnetic character has been improved in the doped
MnTiO3. The x=0 compound goes paramagnetic to antiferromagnetic phase at a
temperature 64K followed by a broad peak at a temperature 100K . But in x=0.2
compound the antiferromagnetic transition temperature has been shifted towards
the lower temperature to 47.5K with a broad peak at temperature 79K. On the
doping of Ru at Ti site a sharp anomaly is observed 47.5K in the case of x=0.2
compound. This sharp anomaly attributes to the improved 3D character of
magnetism in this compound which is weak in x=0 compound.


title:
Dependence of Vortex States in Superconductors on a Chiral Helimagnet
  and an Applied Magnetic Field

abstract:
  We study effects of a chiral helimagnet (CHM) on vortex states in a
superconductor, solving the Ginzburg-Landau equations in a chiral
helimagnet/superconductor bilayer system. We found that vortices form a
periodically modulated triangular lattice, because the magnetic field from the
chiral helimagnet $H_{CHM}$ oscillates spatially. An increase of a critical
current is expected, because vortices are pinned by the $H_{CHM}$.


title:
Chaos in classical string dynamics in $\hat{\gamma}$ deformed $AdS_5
  \times T^{1,1}$

abstract:
  We consider a circular string in $\hat{\gamma}$ deformed $AdS_5 \times
T^{1,1}$ which is localized in the center of $AdS_5$ and winds around the two
circles of deformed $T^{1,1}$. We observe chaos in the phase space of the
circular string implying non-integrability of string dynamics. The chaotic
behaviour in phase space is controlled by energy as well as the deforming
parameter $\hat{\gamma}$. We further show that the point like object exhibits
non-chaotic behaviour. Finally we calculate the Lyapunov exponent for both
extended and point like object in support of our first result.


title:
Simultaneous Wireless Information and Power Transfer Under Different CSI
  Acquisition Schemes

abstract:
  In this work, we consider a multiple-input single-output system in which an
access point (AP) performs a simultaneous wireless information and power
transfer (SWIPT) to serve a user terminal (UT) that is not equipped with
external power supply. In order to assess the efficacy of the SWIPT, we target
a practically relevant scenario characterized by imperfect channel state
information (CSI) at the transmitter, the presence of penalties associated to
the CSI acquisition procedures, and non-zero power consumption for the
operations performed by the UT, such as CSI estimation, uplink signaling and
data decoding. We analyze three different cases for the CSI knowledge at the
AP: no CSI, and imperfect CSI in case of time-division duplexing and
frequency-division duplexing communications. Closed-form representations of the
ergodic downlink rate and both the energy shortage and data outage probability
are derived for the three cases. Additionally, analytic expressions for the
ergodically optimal duration of power transfer and channel estimation/feedback
phases are provided. Our numerical findings verify the correctness of our
derivations, and also show the importance and benefits of CSI knowledge at the
AP in SWIPT systems, albeit imperfect and acquired at the expense of the time
available for the information transfer.


title:
On the Design of Globally Exponentially Stable Hybrid Attitude and
  Gyro-bias Observers

abstract:
  This paper presents hybrid attitude and gyro-bias observers designed directly
on the Special Orthogonal group SO(3). The proposed hybrid observers, enjoying
global exponential stability, rely on a hysteresis-based switching between
different configurations derived from a set of potential functions on SO(3).
Different sets of potential functions have been designed via an appropriate
angular warping transformation applied to some smooth and non-smooth potential
functions on SO(3). We show that the proposed hybrid observers can be expressed
solely in terms of inertial vector measurements and biased angular velocity
readings. Simulation results are given to illustrate the effectiveness of the
proposed attitude estimation approach.


title:
Existence and almost everywhere regularity of isoperimetric clusters for
  fractional perimeters

abstract:
  The existence of minimizers in the fractional isoperimetric problem with
multiple volume constraints is proved, together with a partial regularity
result.


title:
Effect of local and large-scale environments on nuclear activity and
  star formation

abstract:
  Active galactic nuclei (AGN) is one of the main drivers for transition from
star-forming disk to passive spheroidal galaxies. However, the role of
large-scale environment versus one-on-one interactions in triggering different
types of AGN is still uncertain. We present a statistical study of the
prevalence of the nuclear activity in isolated galaxies and physically bound
isolated pairs. For the purpose of this study we considered optically and radio
selected nuclear activity types. We aim to assess the effect of one-on-one
interaction on the fraction of AGN and the role of their large-scale
environment. To study the effect of one-on-one interaction on the fraction of
AGN in isolated galaxy pairs, we compare with a sample of isolated galaxies
homogeneously selected under the same isolation criterion. We examine the
effect of the large-scale environment by comparing with control samples of
single galaxies and galaxy pairs. In general we found no difference in the
prevalence of optical AGN for the considered samples. For massive galaxies, the
fraction of optical AGN in isolated galaxies is slightly higher than that in
control samples. Also the fraction of passives in high mass isolated galaxies
is smaller than in any other sample. Generally, there is no dependence on
optical nuclear activity with local environment. On the other hand, we found
evidence that radio AGN are strongly affected by the local environment. Optical
AGN phenomenon is related to cold gas accretion, while radio AGN is related to
hot gas accretion. In this context, there is more cold gas, fueling the central
optical AGN, in isolated systems. Our results are in agreement with a scenario
where cold gas accretion by secular evolution is the main driver of optical
AGN, while hot gas accretion and one-on-one interactions are the main drivers
of radio AGN activity.


title:
Standing magnetic wave on Ising ferromagnet: Nonequilibrium phase
  transition

abstract:
  The dynamical response of an Ising ferromagnet to a plane polarised standing
magnetic field wave is modelled and studied here by Monte Carlo simulation in
two dimensions. The amplitude of standing magnetic wave is modulated along the
direction x. We have detected two main dynamical phases namely, pinned and
oscillating spin clusters. Depending on the value of field amplitude the system
is found to undergo a phase transition from oscillating spin cluster to pinned
as the system is cooled down. The time averaged magnetisation over a full cycle
of magnetic field oscillations is defined as the dynamic order parameter. The
transition is detected by studying the temperature dependences of the variance
of the dynamic order parameter, the derivative of the dynamic order parameter
and the dynamic specific heat. The dependence of the transition temperature on
the magnetic field amplitude and on the wavelength of the magnetic field wave
is studied at a single frequency. A comprehensive phase boundary is drawn in
the plane described by the temperature and field amplitude for two different
wavelengths of the magnetic wave. The variation of instantaneous line
magnetisation during a period of magnetic field oscillation for standing wave
mode is compared to those for the propagating wave mode. Also the probability
that a spin at any site, flips, is calculated. The above mentioned variations
and the probability of spin flip clearly distinguish between the dynamical
phases formed by propagating magnetic wave and by standing magnetic wave in an
Ising ferromagnet.


title:
From quasiperiodic partial synchronization to collective chaos in
  populations of inhibitory neurons with delay

abstract:
  Collective chaos is shown to emerge, via a period-doubling cascade, from
quasiperiodic partial synchronization in a population of identical inhibitory
neurons with delayed global coupling. This system is thoroughly investigated by
means of an exact model of the macroscopic dynamics, valid in the thermodynamic
limit. The collective chaotic state is reproduced numerically with a finite
population, and persists in the presence of weak heterogeneities. Finally, the
relationship of the model's dynamics with fast neuronal oscillations is
discussed.


title: Semileptonic $B_c$ decays from full lattice QCD

abstract:
  We present first lattice QCD results for semileptonic form factors for the
decays $B_c \to \eta_c l \nu$ and $B_c \to J/\psi l \nu$ over the full $q^2$
range, using both improved non-relativistic QCD (NRQCD) and fully relativistic
(HISQ) formalisms. These can be viewed as prototype calculations for
pseudoscalar to pseudoscalar and pseudoscalar to vector decays involving a $b
\to c$ transition. In particular we can use information from the relativistic
computations to fix the NRQCD current normalisations, which can then be used in
improved computations of decays such as $B \to D l \nu$ and $B \to D^* l \nu$.


title:
Sensitivity of {\Lambda} single-particle energies to the {\Lambda}N
  spin-orbit coupling and to nuclear core structure in p-shell and sd-shell
  hypernuclei

abstract:
  We introduce a mean field model based on realistic 2-body baryon interactions
and calculate spectra of a set of p-shell and sd-shell {\Lambda} hypernuclei -
13{\Lambda}C, 17{\Lambda}O, 21{\Lambda}Ne, 29{\Lambda}Si and 41{\Lambda}Ca. The
hypernuclear spectra are compared with the results of a relativistic mean field
(RMF) model and available experimental data. The sensitivity of {\Lambda}
single-particle energies to the nuclear core structure is explored. Special
attention is paid to the effect of spin-orbit {\Lambda}N interaction on the
energy splitting of the {\Lambda} single particle levels 0p3/2 and 0p1/2. In
particular, we analyze the contribution of the symmetric (SLS) and the
anti-symmetric (ALS) spin-orbit terms to the energy splitting. We give
qualitative predictions for the calculated hypernuclei.


title:
Fault-tolerant Preparation of Stabilizer States for Quantum CSS Codes by
  Classical Error-Correcting Codes

abstract:
  Stabilizer states are extensively studied in quantum information theory for
their structures based on the Pauli group. Calderbank-Shor-Steane (CSS)
stabilizer states are of particular importance in their application to
fault-tolerant quantum computation (FTQC). However, how to fault-tolerantly
prepare arbitrary CSS stabilizer states for general CSS stabilizer codes is
still unknown, and their preparation can be highly costly in computational
resources. In this paper, we show how to prepare a large class of CSS
stabilizer states useful for FTQC. We propose distillation protocols using
syndrome encoding by classical codes or quantum CSS codes. Along the same
lines, we show that classical coding techniques can reduce the ancilla
consumption in Steane syndrome extraction by using additional transversal
controlled-NOT gates and classical computing power. In the scenario of a fixed
ancilla consumption rate, we can increase the frequency of quantum error
correction and effectively lower the error rate.


title: Gushel-Mukai varieties: linear spaces and periods

abstract:
  Beauville and Donagi proved in 1985 that the primitive middle cohomology of a
smooth complex cubic fourfold and the primitive second cohomology of its
variety of lines, a smooth hyperk\"ahler fourfold, are isomorphic as polarized
integral Hodge structures. We prove analogous statements for smooth complex
Gushel-Mukai varieties of dimension 4 (resp. 6), i.e., smooth dimensionally
transverse intersections of the cone over the Grassmannian Gr(2,5), a quadric,
and two hyperplanes (resp. of the cone over Gr(2,5) and a quadric). The
associated hyperk\"ahler fourfold is in both cases a smooth double cover of a
hypersurface in ${\bf P}^5$ called an EPW sextic.


title: Orthogonality of matrices in the Ky Fan $k$-norms

abstract:
  We obtain necessary and sufficient conditions for a matrix $A$ to be
Birkhoff-James orthogonal to another matrix $B$ in the Ky Fan $k$-norms. A
characterization for $A$ to be Birkhoff-James orthogonal to any subspace
$\mathscr W$ of $\mathbb M(n)$ is also obtained.


title:
Light element diffusion in Mg using first principles calculations:
  Anisotropy and elastodiffusion

abstract:
  The light elemental solutes B, C, N, and O can penetrate the surface of Mg
alloys and diffuse during heat treatment or high temperature application,
forming undesirable compounds. We investigate the diffusion of these solutes by
determining their stable interstitial sites and the inter-penetrating network
formed by these sites. We use density functional theory (DFT) to calculate the
site energies, migration barriers, and attempt frequencies for these networks
to inform our analytical model for bulk diffusion. Due to the nature of the
networks, O diffuses isotropically, while B, C, and N diffuse anisotropically.
We compute the elastodiffusion tensor which quantifies changes in diffusivity
due to small strains that perturb the diffusion network geometry and the
migration barriers. The DFT-computed elastic dipole tensor which quantifies the
change in site energies and migration barriers due to small strains is used as
an input to determine the elastodiffusion tensor. We employ the elastodiffusion
tensor to determine the effect of thermal strains on interstitial diffusion and
find that B, C, and N diffusivity increases on crystal expansion, while O
diffusivity decreases. From the elastodiffusion and compliance tensors we
calculate the activation volume of diffusion and find that it is positive and
anisotropic for B, C and N diffusion, whereas it is negative and isotropic for
O diffusion.


title: Effective Field Theory for Rydberg Polaritons

abstract:
  We develop an effective field theory (EFT) to describe the few- and many-body
propagation of one dimensional Rydberg polaritons. We show that the photonic
transmission through the Rydberg medium can be found by mapping the propagation
problem to a non-equilibrium quench, where the role of time and space are
reversed. We include effective range corrections in the EFT and show that they
dominate the dynamics near scattering resonances in the presence of deep bound
states. Finally, we show how the long-range nature of the Rydberg-Rydberg
interactions induces strong effective $N$-body interactions between Rydberg
polaritons. These results pave the way towards studying non-perturbative
effects in quantum field theories using Rydberg polaritons.


title:
Scalable low dimensional manifold model in the reconstruction of noisy
  and incomplete hyperspectral images

abstract:
  We present a scalable low dimensional manifold model for the reconstruction
of noisy and incomplete hyperspectral images. The model is based on the
observation that the spatial-spectral blocks of a hyperspectral image typically
lie close to a collection of low dimensional manifolds. To emphasize this, the
dimension of the manifold is directly used as a regularizer in a variational
functional, which is solved efficiently by alternating direction of
minimization and weighted nonlocal Laplacian. Unlike general 3D images, the
same similarity matrix can be shared across all spectral bands for a
hyperspectral image, therefore the resulting algorithm is much more scalable
than that for general 3D data. Numerical experiments on the reconstruction of
hyperspectral images from sparse and noisy sampling demonstrate the superiority
of our proposed algorithm in terms of both speed and accuracy.


title:
Effective theory and universal relations for Fermi gases near a $d$-wave
  interaction resonance

abstract:
  In this work, we present an effective field theory to describe a
two-component Fermi gas near a $d$-wave interaction resonance. The effective
field theory is renormalizable by matching with the low energy $d$-wave
scattering phase shift. Based on the effective field theory, we derive
universal properties of the Fermi gas by the operator product expansion method.
We find that beyond the contacts defined by adiabatic theorems, the asymptotic
expressions of the momentum distribution and the Raman spectroscopy involve two
extra contacts which provide additional information of correlations of the
system. Our formalism sets the stage for further explorations of many-body
effects in a $d$-wave resonant Fermi gas. Finally we generalise our effective
field theory for interaction resonances of arbitrary higher partial waves.


abstract:
  A model of global magnetic reconnection rate in relativistic collisionless
plasmas is developed and validated by the fully kinetic simulation. Through
considering the force balance at the upstream and downstream of the diffusion
region, we show that the global rate is bounded by a value $\sim 0.3$ even when
the local rate goes up to $\sim O(1)$ and the local inflow speed approaches the
speed of light in strongly magnetized plasmas. The derived model is general and
can be applied to magnetic reconnection under widely different circumstances.


title: Geodesic deviation in a nonlinear gravitational wave spacetime

abstract:
  The tidal effects generated by a nonlinear gravitational wave are
investigated in double-null v - u coordinates, as an exact solution of
Einstein's field equations. The components $\xi^{v}$ and $\xi^{u}$ of the
separation vector behave as in flat space but the transversal components
$\xi^{x}$ and $\xi^{y}$ depend nonlinearly on $v$ through the Bessel and
Neumann functions, far from the null surface $v = 0$. We show that the same
results are obtained by means of the tetrad formalism.


title: Stability of derivations under weak-2-local continuous perturbations

abstract:
  Let $\Omega$ be a compact Hausdorff space and let $A$ be a C$^*$-algebra. We
prove that if every weak-2-local derivation on $A$ is a linear derivation and
every derivation on $C(\Omega,A)$ is inner, then every weak-2-local derivation
$\Delta:C(\Omega,A)\to C(\Omega,A)$ is a {\rm(}linear{\rm)} derivation. As a
consequence we derive that, for every complex Hilbert space $H$, every
weak-2-local derivation $\Delta : C(\Omega,B(H)) \to C(\Omega,B(H))$ is a
(linear) derivation. We actually show that the same conclusion remains true
when $B(H)$ is replaced with an atomic von Neumann algebra. With a modified
technique we prove that, if $B$ denotes a compact C$^*$-algebra (in particular,
when $B=K(H)$), then every weak-2-local derivation on $C(\Omega,B)$ is a
(linear) derivation. Among the consequences, we show that for each von Neumann
algebra $M$ and every compact Hausdorff space $\Omega$, every 2-local
derivation on $C(\Omega,M)$ is a (linear) derivation.


title:
Detection, numerical simulation and approximate inversion of
  optoacoustic signals generated in multi-layered PVA hydrogel based tissue
  phantoms

abstract:
  In this article we characterize optoacoustic signals generated from layered
tissue phantoms via short laser pulses by experimental and numerical means. In
particular, we consider the case where scattering is effectively negligible and
the absorbed energy density follows Beer-Lambert's law, i.e. is characterized
by an exponential decay within the layers and discontinuities at interfaces. We
complement experiments on samples with multiple layers, where the material
properties are known a priori, with numerical calculations for a pointlike
detector, tailored to suit our experimental setup. Experimentally, we
characterize the acoustic signal observed by a piezoelectric detector in the
acoustic far-field in backward mode and we discuss the implication of acoustic
diffraction on our measurements. We further attempt an inversion of an OA
signal in the far-field approximation.


title:
Heteroscedastic stratified two-way EC models of single equations and SUR
  systems

abstract:
  A relevant issue in panel data estimation is heteroscedasticity, which often
occurs when the sample is large and individual units are of varying size.
Furthermore, many of the available panel data sets are unbalanced in nature,
because of attrition or accretion, and micro-econometric models applied to
panel data are frequently multi-equation models. This paper considers the
general least squares estimation of the heteroscedastic stratified two-way
error component (EC) models of both single equations and seemingly unrelated
regressions (SUR) systems (with cross-equations restrictions) on unbalanced
panel data. The derived heteroscedastic estimators of both single equations and
SUR systems improve the estimation efficiency.


title: Cutting sequences on square-tiled surfaces

abstract:
  We characterize cutting sequences of infinite geodesics on square-tiled
surfaces by considering interval exchanges on specially chosen intervals on the
surface. These interval exchanges can be thought of as skew products over a
rotation, and we convert cutting sequences to symbolic trajectories of these
interval exchanges to show that special types of combinatorial lifts of
Sturmian sequences completely describe all cutting sequences on a square-tiled
surface. Our results extend the list of families of surfaces where cutting
sequences are understood to a dense subset of the moduli space of all
translation surfaces.


title: Lepton Flavour Violating Higgs Decays in the (SUSY) Inverse Seesaw

abstract:
  The observation of charged lepton flavour violation would be a smoking gun
for new physics and could help in pinpointing the mechanism at the origin of
neutrino masses and mixing. We present here our recent studies of lepton
flavour violating Higgs decays in the inverse seesaw and its supersymmetric
embedding, two examples of low-scale seesaw mechanisms. We predict branching
ratios as large as $10^{-5}$ for the decays $h\rightarrow \tau \mu$ and $h
\rightarrow \tau e$ in the inverse seesaw, which can be probed in future
colliders. Supersymmetric contributions can enhance the branching ratio of
$h\rightarrow \tau \mu$ up to $1\%$, making it large enough to explain the
small excess observed by ATLAS and CMS.


title:
Spin and Charge Resolved Quantum Gas Microscopy of Antiferromagnetic
  Order in Hubbard Chains

abstract:
  The repulsive Hubbard Hamiltonian is one of the foundational models
describing strongly correlated electrons and is believed to capture essential
aspects of high temperature superconductivity. Ultracold fermions in optical
lattices allow for the simulation of the Hubbard Hamiltonian with a unique
control over kinetic energy, interactions and doping. A great challenge is to
reach the required low entropy and to observe antiferromagnetic spin
correlations beyond nearest neighbors, for which quantum gas microscopes are
ideal. Here we report on the direct, single-site resolved detection of
antiferromagnetic correlations extending up to three sites in spin-$1/2$
Hubbard chains, which requires an entropy well below $s^*=\ln(2)$. Finally, the
simultaneous detection of spin and density opens the route towards the study of
the interplay between magnetic ordering and doping in various dimensions.


title: Impact of post-Born lensing on the CMB

abstract:
  Lensing of the CMB is affected by post-Born lensing, producing corrections to
the convergence power spectrum and introducing field rotation. We show
numerically that the lensing convergence power spectrum is affected at the
$\lesssim 0.2\%$ level on accessible scales, and that this correction and the
field rotation are negligible for observations with arcminute beam and noise
levels $\gtrsim 1 \mu {\text{K}}\,{\text{arcmin}} $. The field rotation
generates $\sim 2.5\%$ of the total lensing B-mode polarization amplitude
($0.2\%$ in power on small scales), but has a blue spectrum on large scales,
making it highly subdominant to the convergence B modes on scales where they
are a source of confusion for the signal from primordial gravitational waves.
Since the post-Born signal is non-linear, it also generates a bispectrum with
the convergence. We show that the post-Born contributions to the bispectrum
substantially change the shape predicted from large-scale structure
non-linearities alone, and hence must be included to estimate the expected
total signal and impact of bispectrum biases on CMB lensing reconstruction
quadratic estimators and other observables. The field-rotation power spectrum
only becomes potentially detectable for noise levels $\ll 1 \mu
{\text{K}}\,{\text{arcmin}}$, but its bispectrum with the convergence may be
observable at $\sim 3\sigma$ with Stage IV observations. Rotation-induced and
convergence-induced B modes are slightly correlated by the bispectrum, and the
bispectrum also produces additional contributions to the lensed BB power
spectrum.


title: Reviewing METI: A Critical Analysis of the Arguments

abstract:
  There is an ongoing debate pertaining to the question of whether Earth should
initiate intentional and powerful radio transmissions to putative
extra-terrestrial (ET) civilizations in the hope of attracting ET's attention.
This practice is known as METI (Messaging to ET Intelligence) or Active SETI.
The debate has recently taken on a sense of urgency, as additional proponents
have announced their intention to commence de novo transmissions as soon as
they become funded and acquire the needed time on a powerful transmitter such
as Arecibo. Arguments in favor of METI are reviewed. It is concluded that METI
is unwise, unscientific, potentially catastrophic, and unethical.


title: Observation of Optomechanical Quantum Correlations at Room Temperature

abstract:
  By shining laser light through a nanomechanical beam, we measure the beam's
thermally driven vibrations and perturb its motion with optical forces at a
level dictated by the Heisenberg measurement-disturbance uncertainty relation.
Such quantum backaction is typically difficult to observe at room temperature
where the motion driven by optical quantum intensity fluctuations is many
orders of magnitude smaller than the thermal motion. We demonstrate a
cross-correlation technique to distinguish optically driven motion from
thermally driven motion, observing this quantum backaction signature up to room
temperature. While it is often difficult to absolutely calibrate optical
detection, we use the scale of the quantum correlations, which is determined by
fundamental constants, to gauge the size of thermal motion, demonstrating a
path towards absolute thermometry with quantum mechanically calibrated ticks.


title:
Effective computation of base points of ideals in two-dimensional local
  rings

abstract:
  In this work we describe a minimal log-resolution of an ideal in a smooth
complex surface from the minimal log-resolution of its generators.


title:
Efficient artificial mineralization route to decontaminate Arsenic(III)
  polluted water -the Tooeleite Way

abstract:
  Increasing exposure to arsenic (As) contaminated ground water is a great
threat to humanity. Suitable technology for As immobilization and removal from
water, especially for As(III) than As(V), is not available yet. However, it is
known that As(III) is more toxic than As(V) and most groundwater aquifers,
particularly the Gangetic basin in India, is alarmingly contaminated with it.
In search of a viable solution here, we took a cue from the natural
mineralization of Tooeleite, a mineral containing Fe(III) and As(III)ions,
grown under acidic condition, in presence of SO42- ions. Complying to this
natural process, we could grow and separate Tooeleite-like templates from
Fe(III) and As(III) containing water at overall circumneutral pH and in absence
of SO42- ions by using highly polar Zn-only ends of wurtzite ZnS nanorods as
insoluble nano-acidic-surfaces. The central idea here is to exploit these
insoluble nano-acidic-surfaces (called as INAS in the manuscript) as nucleation
centres for Tooeleite growth while keeping the overall pH of the aqueous media
neutral. Therefore, we propose a novel method of artificial mineralization of
As(III) by mimicking a natural process at nanoscale.


title: Degree conditions for matchability in $3$-partite hypergraphs

abstract:
  We study conjectures relating degree conditions in $3$-partite hypergraphs to
the matching number of the hypergraph, and use topological methods to prove
special cases. In particular, we prove a strong version of a theorem of Drisko
\cite{drisko} (as generalized by the first two authors \cite{ab}), that every
family of $2n-1$ matchings of size $n$ in a bipartite graph has a partial
rainbow matching of size $n$. We show that milder restrictions on the sizes of
the matchings suffice. Another result that is strengthened is a theorem of
Cameron and Wanless \cite{CamWan}, that every Latin square has a diagonal
(permutation submatrix) in which no symbol appears more than twice. We show
that the same is true under the weaker condition that the square is row-Latin.


title: Muon capture on 3H

abstract:
  The muon capture on 3H leading to muonic neutrino and three neutrons in the
final state is studied under full inclusion of final state interactions.
Predictions for the three-body break-up of 3H are calculated with the AV18
potential, augmented by the Urbana IX three-nucleon force. Our results are
based on the single nucleon weak current operator comprising the dominant
relativistic corrections. This work is a natural extension of our
investigations of the muon capture on 3He leading to 3H or n+d or n+n+p and
muonic neutrino in the final state, presented in Phys. Rev. C90, 024001 (2014).


title:
Strain Control of Fermiology and Many-Body Interactions in
  Two-Dimensional Ruthenates

abstract:
  Here we demonstrate how the Fermi surface topology and quantum many-body
interactions can be manipulated via epitaxial strain in the spin-triplet
superconductor Sr$_2$RuO$_4$ and its isoelectronic counterpart Ba$_2$RuO$_4$
using oxide molecular beam epitaxy (MBE), \emph{in situ} angle-resolved
photoemission spectroscopy (ARPES), and transport measurements. Near the
topological transition of the $\gamma$ Fermi surface sheet, we observe clear
signatures of critical fluctuations, while the quasiparticle mass enhancement
is found to increase rapidly and monotonically with increasing Ru-O bond
distance. Our work demonstrates the possibilities for using epitaxial strain as
a disorder-free means of manipulating emergent properties, many-body
interactions, and potentially the superconductivity in correlated materials.


title:
Forecasts for the WFIRST High Latitude Survey using the BlueTides
  Simulation

abstract:
  We use the BlueTides simulation to predict the properties of the high-$z$
galaxy and active galactic nuclei (AGN) populations for the planned 2200deg$^2$
Wide-Field Infrared Survey Telescope's (WFIRST)-AFTA High Latitude Survey
(HLS). BlueTides is a cosmological hydrodynamic simulation, which incorporates
a variety of baryon physics in a $(400h^{-1} \mathrm{Mpc})^3$ volume evolved to
$z=8$ with 0.7 trillion particles. The galaxy luminosity functions in the
simulation show good agreement with all the current observational constraints
(up to $z=11$) and predicts an enhanced number of UV bright galaxies. At the
proposed depth of the HLS ($m < 26.75$), BlueTides predicts $10^6$ galaxies at
$z=8$ with a few up to $z\sim 15$ due to the enhanced bright end of the galaxy
luminosity function. At $z=8$, galaxies in the mock HLS have specific star
formation rates of $\sim 10 {\rm Gyr}^{-1}$ and ages of $\sim 80 {\rm Myr}$
(both evolving linearly with redshift) and a non-evolving mass-metallicity
relation. BlueTides also predicts $\sim 10^4$ AGN in WFIRST HLS from $z=8$ out
to $z\sim 14$. These AGN host black holes of $M\sim 10^6-10^8 M_\odot$
accreting close to their Eddington luminosity. Galaxies and AGN have host halo
masses of $M_{halo}\sim 10^{11-12} M_\odot$ and a linear bias $b\approx 13-20$.
Given the expected galaxy space densities, their high bias and large volume
probed we speculate that it may be feasible for WFIRST HLS detect the Baryon
Acoustic Oscillation peak in the galaxy power spectrum out to $z=8-9$.


title: Sub-optimality of some continuous shrinkage priors

abstract:
  Two-component mixture priors provide a traditional way to induce sparsity in
high-dimensional Bayes models. However, several aspects of such a prior,
including computational complexities in high-dimensions, interpretation of
exact zeros and non-sparse posterior summaries under standard loss functions,
has motivated an amazing variety of continuous shrinkage priors, which can be
expressed as global-local scale mixtures of Gaussians. Interestingly, we
demonstrate that many commonly used shrinkage priors, including the Bayesian
Lasso, do not have adequate posterior concentration in high-dimensional
settings.


title: Dissipative time evolution of a chiral state after a quantum quench

abstract:
  We investigate the dynamics of fermionic atoms in a high-finesse optical
resonator after a sudden switch on of the coupling between the atoms and the
cavity. The atoms are additionally confined by optical lattices to a ladder
geometry. The tunneling mechanism on a rung of a ladder is induced by a cavity
assisted Raman process. At long times after the quantum quench the arising
steady state can carry a chiral current. In this work we employ exact
diagonalization techniques on small system sizes to study the dissipative
attractor dynamics after the quench towards the steady state and deviations of
the properties of the steady state from predictions obtained by adiabatically
eliminating the cavity mode.


title:
Role of excited states in Shockley-Read-Hall recombination in
  wide-band-gap semiconductors

abstract:
  Defect-assisted recombination is an important limitation on efficiency of
optoelectronic devices. However, since nonradiative capture rates decrease
exponentially with energy of the transition, the mechanisms by which such
recombination can take place in wide-band-gap materials are unclear. Using
electronic structure calculations we uncover the crucial role of electronic
excited states in nonradiative recombination processes. The impact is
elucidated with examples for the group-III nitrides, for which accumulating
experimental evidence indicates that defect-assisted recombination limits
efficiency. Our work provides new insights into the physics of nonradiative
recombination, and the mechanisms are suggested to be ubiquitous in
wide-band-gap semiconductors.


title: Ro-Translational Cavity Cooling of Dielectric Rods and Disks

abstract:
  We study the interaction of dielectric rods and disks with the laser field of
a high finesse cavity. The quantum master equation for the coupled
particle-cavity dynamics, including Rayleigh scattering, is derived for
particle sizes comparable to the laser wavelength. We demonstrate that such
anisotropic nanoparticles can be captured from free flight at velocities higher
than those required to capture dielectric spheres of the same volume, and that
efficient ro-translational cavity cooling into the deep quantum regime is
achievable.


title: Wada property in systems with delay

abstract:
  Delay differential equations take into account the transmission time of the
information. These delayed signals may turn a predictable system into chaotic,
with the usual fractalization of the phase space. In this work, we study the
connection between delay and unpredictability, in particular we focus on the
Wada property in systems with delay. This topological property gives rise to
dramatical changes in the final state for small changes in the history
functions.


title:
Towards information based spatiotemporal patterns as a foundation for
  agent representation in dynamical systems

abstract:
  We present some arguments why existing methods for representing agents fall
short in applications crucial to artificial life. Using a thought experiment
involving a fictitious dynamical systems model of the biosphere we argue that
the metabolism, motility, and the concept of counterfactual variation should be
compatible with any agent representation in dynamical systems. We then propose
an information-theoretic notion of \emph{integrated spatiotemporal patterns}
which we believe can serve as the basic building block of an agent definition.
We argue that these patterns are capable of solving the problems mentioned
before. We also test this in some preliminary experiments.


title: Kelvin's Canonical Circulation Theorem in Hall Magnetohydrodynamics

abstract:
  The purpose of this paper is to show that, thanks to the restoration of the
legitimate connection between the current density and the plasma flow velocity
in Hall magnetohydrodynamics (MHD), Kelvin's Circulation Theorem becomes valid
in Hall MHD. The ion-flow velocity in the usual circulation integral is now
replaced by the canonical ion-flow velocity.


title: Photoelectric effect for twist-deformed space-time

abstract:
  In this article, we investigate the impact of twisted space-time on the
photoelectric effect, i.e., we derive the $\theta$-deformed threshold
frequency. In such a way we indicate that the space-time noncommutativity
strongly enhances the photoelectric process.


title: Integrable deformations of local analytic fibrations with singularities

abstract:
  We study analytic integrable deformations of the germ of a holomorphic
foliation given by $df=0$ at the origin $0 \in \mathbb C^n, n \geq 3$. We
consider the case where $f$ is a germ of an irreducible and reduced holomorphic
function. Our central hypotheses is that, {\em outside of a dimension $\leq
n-3$ analytic subset $Y\subset X$, the analytic hypersurface $X_f : (f=0)$ has
only normal crossings singularities}. We then prove that, as germs, such
deformations also exhibit a holomorphic first integral, depending analytically
on the parameter of the deformation. This applies to the study of integrable
germs writing as $\omega = df + f \eta$ where $f$ is quasi-homogeneous. Under
the same hypotheses for $X_f : (f=0)$ we prove that $\omega$ also admits a
holomorphic first integral. Finally, we conclude that an integrable germ
$\omega = adf + f \eta$ admits a holomorphic first integral provided that: (i)
$X_f: (f=0)$ is irreducible with an isolated singularity at the origin $0 \in
\mathbb C^n, n \geq 3$; \, (ii) the algebraic multiplicities of $\omega$ and
$f$ at the origin satisfy $\nu(\omega) = \nu (df)$. In the case of an isolated
singularity for $(f=0)$ the writing $\omega = adf + f \eta$ is always assured
so that we conclude the existence of a holomorphic first integral. Some
questions related to Relative Cohomology are naturally considered and not all
of them answered.


title:
Forward $J/\psi$ production at high energy: centrality dependence and
  mean transverse momentum

abstract:
  Forward rapidity $J/\psi$ meson production in proton-nucleus collisions can
be an important constraint of descriptions of the small-$x$ nuclear
wavefunction. In an earlier work we studied this process using a dipole cross
section satisfying the Balitsky-Kovchegov equation, fit to HERA inclusive data
and consistently extrapolated to the nuclear case using a standard Woods-Saxon
distribution. In this paper we present further calculations of these cross
sections, studying the mean transverse momentum of the meson and the dependence
on collision centrality. We also extend the calculation to backward rapidities
using nuclear parton distribution functions. We show that the parametrization
is overall rather consistent with the available experimental data. However,
there is a tendency towards a too strong centrality dependence. This can be
traced back to the rather small transverse area occupied by small-$x$ gluons in
the nucleon that is seen in the HERA data, compared to the total inelastic
nucleon-nucleon cross section.


title: Contiguity is limited in free recall

abstract:
  Does the "law of contiguity" apply to free recall? I find that conditional
response probabilities, often used as evidence for contiguity in free recall,
have been displayed insufficiently, limiting the distance from the last item
recalled, and only averaged over all items. When fully expanding the x-axis and
examining the conditional response probabilities separately for the beginning,
middle and end of the presented item list, I show that the law of contiguity
applies only locally, even then only sometimes, and breaks down globally.


title: Large individual differences in free recall

abstract:
  Using single factor ANOVA I show that there are large individual differences
in free recall ({\eta} ranges from 0.09-0.26) including the total recall, the
balance between recency and primacy, and the initial recall (subsequent recalls
show smaller individual differences). All three memory properties are
relatively uncorrelated. The variance in the initial position may be a measure
of executive control and is correlated with total recall (the smaller the
variation, the larger the recall).


title:
Moment bounds for SPDEs with non-Gaussian fields and application to the
  Wong-Zakai problem

abstract:
  Upon its inception the theory of regularity structures allowed for the
treatment for many semilinear perturbations of the stochastic heat equation
driven by space-time white noise. When the driving noise is non-Gaussian the
machinery of theory can still be used but must be combined with an infinite
number of stochastic estimates in order to compensate for the loss of
hypercontractivity. In this paper we obtain a more streamlined and automatic
set of criteria implying these estimates which facilitates the treatment of
some other problems including non-Gaussian noise such as some general phase
coexistence models - as an example we prove here a generalization of the
Wong-Zakai Theorem found by Hairer and Pardoux.


title:
Conditional Response Probabilities Confirm Two Stages of Free Recall,
  Working Memory Very Localized, Second Stage Delocalized, Both with Strong
  Tendencies to Forward Subsequent Recalls

abstract:
  Recently it was shown that free recall consists of two stages: the first few
recalls empty working memory and a second stage concludes the recall (Tarnow,
2015; for a review of the theoretical prediction see Murdock, 1974). Here I
investigate conditional response probabilities in Murdock's 40-1 (1962) free
recall dataset. I find that the conditional response probabilities confirm the
presence of two stages. The first stage is characterized by a large enhancement
of the forward subsequent recall (up to 30 times chance) and a large
suppression of backward recalls (up to 26 times smaller than chance for recalls
between 10 and 40 items away). The second stage forward subsequent recall is
enhanced by a factor of 5 and the probability of backward and forward recalls
are concentrated at small distances. Thus both stages favor forward subsequent
recalls. As in Tarnow (2015), the first stage is much more localized than the
second stage. Working memory capacity is estimated in six ways to be about 4.5
word items for the 40-1 word list.


title:
First direct evidence of two stages in free recall and three
  corresponding estimates of working memory capacity

abstract:
  I find that exactly two stages can be seen directly in sequential free recall
distributions. These distributions show that the first three recalls come from
the emptying of working memory, recalls 6 and above come from a second stage
and the 4th and 5th recalls are mixtures of the two. A discontinuity, a rounded
step function, is shown to exist in the fitted linear slope of the recall
distributions as the recall shifts from the emptying of working memory
(positive slope) to the second stage (negative slope). The discontinuity leads
to a first estimate of the capacity of working memory at 4-4.5 items. Working
memory accounts for the recency effect. The primacy effect comes from the
second stage with a contribution also from working memory for short lists (the
first item). The different slopes of the working memory and secondary stages,
and that the two have different functional forms, accounts for the u-shaped
serial position curve. The total recall is shown to be a linear combination of
the content of working memory and items recalled in the second stage with
3.0-3.9 items coming from working memory, a second estimate of the capacity of
working memory. A third, separate upper limit on the capacity of working memory
is found (3.06 items), corresponding to the requirement that the content of
working memory cannot exceed the total recall, item by item. This third limit
presumably corresponds to the least chunked item. This is the best limit on the
capacity of unchunked working memory.


title:
Free Recall Shows Similar Reactivation Behavior as Recognition & Cued
  Recall

abstract:
  I find that the total retrieval time in word free recall increases linearly
with the total number of items recalled. Measured slopes, the time to retrieve
an additional item, vary from 1.4-4.5 seconds per item depending upon
presentation rate, subject age and whether there is a delay after list
presentation or not. These times to retrieve an additional item obey a second
linear relationship as a function of the recall probability averaged over the
experiment, explicitly independent of subject age, presentation rate and
whether there is a delay after the list presentation or not. This second linear
relationship mimics the relationships in recognition and cued recall (Tarnow,
2008) which suggests that free recall retrieval uses the same reactivation
mechanism as recognition or cued recall. Extrapolation limits the time to
retrieve an additional item to a maximum of 7.2 seconds per item if the
probability of recall is near 0%. Earlier upper limits for recognition and cued
recall varied with the item type between 0.2 and 1.8 seconds per item (Tarnow,
2008). Implications include that there are only two types of short term memory:
working memory and reactivation.


title:
Direct Evidence Delay with A Task Decreases Working Memory Content in
  Free Recall

abstract:
  Recently it was shown that free recall consists of two stages: the first few
recalls empty the working memory and a second stage concludes the recall
(Tarnow, 2015; for a review of the theoretical prediction see Murdock, 1974).
It is commonly believed that a delay with a task before the recall starts
removes the content of working memory (Glanzer & Cunitz, 1966). Here is
presented the first direct evidence that this is indeed the case.


title:
A Precise Measure of Working Memory Reveals Subjects Difficulties
  Managing Limited Capacity

abstract:
  Free recall consists of two separate stages: the emptying of working memory
and reactivation [1]. The Tarnow Unchunkable Test (TUT, [2]) uses double
integer items to separate out only the first stage by making it difficult to
reactivate items due to the lack of intra-item relationships. 193 Russian
college students were tested via the internet version of the TUT. The average
number of items remembered in the 3 item test was 2.54 items. In the 4 item
test, the average number of items decreased to 2.38. This, and a number of
other qualitative distribution differences between the 3 and 4 item tests,
indicates that the average capacity limit of working memory has been reached at
3 items. This provides the first direct measurement of the unchunkable capacity
limit of language based items. That the average number of items remembered
decreased as the number of items increased from 3 to 4 indicates that most
subjects were unable to manage their working memories as the number of items
increased just beyond the average capacity. Further evidence for the difficulty
in managing the capacity limit is that 25% of subjects could not remember any
items correctly at least in one of three 4 item tests and that the Pearson
correlation between the 3 item and 4 item subject recalls was a relatively
small 38%. This failure of managing a basic memory resource should have
important consequences for pedagogy including instruction, text book design and
test design. Because working memory scores are important for academic
achievement, it also suggests that an individual can gain academically by
learning how to manage her or his capacity limit.


title: Nonlocal Schr\"odinger-Kirchhoff equations with external magnetic field

abstract:
  The paper deals with existence and multiplicity of solutions of the
fractional Schr\"{o}dinger--Kirchhoff equation involving an external magnetic
potential. As a consequence, the results can be applied to the special case
\begin{equation*} (a+b[u]_{s,A}^{2\theta-2})(-\Delta)_A^su+V(x)u=f(x,|u|)u\,\,
\quad \text{in $\mathbb{R}^N$}, \end{equation*} where $s\in (0,1)$, $N>2s$,
$a\in \mathbb{R}^+_0$, $b\in \mathbb{R}^+_0$, $\theta\in[1,N/(N-2s))$,
$A:\mathbb{R}^N\rightarrow\mathbb{R}^N$ is a magnetic potential,
$V:\mathbb{R}^N\rightarrow \mathbb{R}^+$ is an electric potential, $(-\Delta
)_A^s$ is the fractional magnetic operator. In the super- and sub-linear cases,
the existence of least energy solutions for the above problem is obtained by
the mountain pass theorem, combined with the Nehari method, and by the direct
methods respectively. In the superlinear-sublinear case, the existence of
infinitely many solutions is investigated by the symmetric mountain pass
theorem.


title: The definition of the thermodynamic entropy in statistical mechanics

abstract:
  A definition of the thermodynamic entropy based on the time-dependent
probability distribution of the macroscopic variables is developed. When a
constraint in a composite system is released, the probability distribution for
the new equilibrium values goes to a narrow peak. Defining the entropy by the
logarithm of the probability distribution automatically makes it a maximum at
the equilibrium values, so it satisfies the Second Law. It is also satisfies
the postulates of thermodynamics. Objections to this definition by Dieks and
Peters are discussed and resolved.


title: Adsorption of polyelectrolytes on silica and gold surfaces

abstract:
  The results of a study that helps understand the mechanisms of adsorption of
polyelectrolytes on particles, using numerical simulation methods, specifically
the one known as dissipative particle dynamics are reported here. The
adsorption of cationic polyelectrolytes of two different polymerization degrees
interacting with two types of surfaces, one made of gold and the other of
silica is predicted and compared. We find that a more negatively charged wall
does not necessarily adsorb more cationic polyelectrolytes because the
electrostatic repulsion between the wall and the polyelectrolytes is stronger.
Additionally, intra chain repulsion plays an important role, because the
largest polyelectrolyte chains have larger excluded volume than the shorter
ones. In regard to the adsorption dependence on the polyelectrolyte
polymerization degree we find that the excluded volume drives the adsorption
throughout the intrachain electrostatic repulsion, because the SiO2 surface is
strongly negative. These results are expected to be useful for several
nanotechnological applications of current interest, such as in gene therapy and
in the improvement of drug delivering mechanisms.


title:
Expected values of parameters associated with the minimum rank of a
  graph

abstract:
  We investigate the expected value of various graph parameters associated with
the minimum rank of a graph, including minimum rank/maximum nullity and related
Colin de Verdi\`ere-type parameters. Let $G(v,p)$ denote the usual
Erd\H{o}s-R\'enyi random graph on $v$ vertices with edge probability $p$. We
obtain bounds for the expected value of the random variables ${\rm
mr}(G(v,p))$, ${\rm M}(G(v,p))$, $\nu(G(v,p))$ and $\xi(G(v,p))$, which yield
bounds on the average values of these parameters over all labeled graphs of
order $v$.


title:
Capacity of the State-Dependent Wiretap Channel: Secure Writing on Dirty
  Paper

abstract:
  In this paper we consider the State-Dependent Wiretap Channel (SD-WC). As the
main idea, we model the SD-WC as a Cognitive Interference Channel (CIC), in
which the primary receiver acts as an eavesdropper for the cognitive
transmitter's message. By this point of view, the Channel State Information
(CSI) in SD-WC plays the role of the primary user's message in CIC which can be
decoded at the eavesdropper. This idea enables us to use the main achievability
approaches of CIC, i.~e., Gel'fand-Pinsker Coding (GPC) and Superposition
Coding (SPC), to find new achievable equivocation-rates for the SD-WC. We show
that these approaches meet the capacity under some constraints on the rate of
the channel state. Similar to the dirty paper channel, extending the results to
the Gaussian case shows that the GPC lead to the capacity of the Gaussian SD-WC
which is equal to the capacity of the wiretap channel without channel state.
Hence, we achieve the capacity of the Gaussian SD-WC using the dirty paper
technique. Moreover, our proposed approaches provide the capacity of the Binary
SD-WC. It is shown that the capacity of the Binary SD-WC is equal to the
capacity of the Binary wiretap channel without channel state.


title: Spontaneous Dimensional Reduction in Quantum Gravity

abstract:
  Hints from a number of different approaches to quantum gravity point to a
phenomenon of "spontaneous dimensional reduction" to two spacetime dimensions
near the Planck scale. I examine the physical meaning of the term "dimension"
in this context, summarize the evidence for dimensional reduction, and discuss
possible physical explanations.


title: Method of calculating densities for isotropic L\'evy Walks

abstract:
  We provide explicit formulas for asymptotic densities of $d$-dimensional
isotropic L\'evy walks, when $d>1$. The densities of multidimensional
undershooting and overshooting L\'evy walks are presented as well.
Interestingly, when the number of dimensions is odd the densities of all these
L\'evy walks are given by elementary functions. When $d$ is even, we can
express the densities as fractional derivatives of hypergeometric functions,
which makes an efficient numerical evaluation possible.


title: Type-II Weyl cone transitions in driven semimetals

abstract:
  Periodically driven systems provide tunable platforms to realize interesting
Floquet topological phases and phase transitions. In electronic systems with
Weyl dispersions, the band crossings are topologically protected even in the
presence of time-periodic perturbations. This robustness permits various routes
to shift and tilt the Weyl spectra in the momentum and energy space using
circularly polarized light of sufficient intensity. We show that type-II Weyl
fermions, in which the Weyl dispersions are tilted with the appearance of
pocket-like Fermi surfaces, can be induced in driven Dirac semimetals and line
node semimetals. Under a circularly polarized drive, both semimemtal systems
immediately generate Weyl node pairs whose types can be further controlled by
the driving amplitude and direction. The resultant phase diagrams demonstrate
experimental feasibilities.


title:
Online Algorithms For Parameter Mean And Variance Estimation In Dynamic
  Regression Models

abstract:
  We study the problem of estimating the parameters of a regression model from
a set of observations, each consisting of a response and a predictor. The
response is assumed to be related to the predictor via a regression model of
unknown parameters. Often, in such models the parameters to be estimated are
assumed to be constant. Here we consider the more general scenario where the
parameters are allowed to evolve over time, a more natural assumption for many
applications. We model these dynamics via a linear update equation with
additive noise that is often used in a wide range of engineering applications,
particularly in the well-known and widely used Kalman filter (where the system
state it seeks to estimate maps to the parameter values here). We derive an
approximate algorithm to estimate both the mean and the variance of the
parameter estimates in an online fashion for a generic regression model. This
algorithm turns out to be equivalent to the extended Kalman filter. We
specialize our algorithm to the multivariate exponential family distribution to
obtain a generalization of the generalized linear model (GLM). Because the
common regression models encountered in practice such as logistic, exponential
and multinomial all have observations modeled through an exponential family
distribution, our results are used to easily obtain algorithms for online mean
and variance parameter estimation for all these regression models in the
context of time-dependent parameters. Lastly, we propose to use these
algorithms in the contextual multi-armed bandit scenario, where so far model
parameters are assumed static and observations univariate and Gaussian or
Bernoulli. Both of these restrictions can be relaxed using the algorithms
described here, which we combine with Thompson sampling to show the resulting
performance on a simulation.


title: The diameter game

abstract:
  A large class of Positional Games are defined on the complete graph on $n$
vertices. The players, Maker and Breaker, take the edges of the graph in turns,
and Maker wins iff his subgraph has a given -- usually monotone -- property.
Here we introduce the $d$-diameter game, which means that Maker wins iff the
diameter of his subgraph is at most $d$. We investigate the biased version of
the game; i.e., when the players may take more than one, and not necessarily
the same number of edges, in a turn. Our main result is that we proved that the
$2$-diameter game has the following surprising property: Breaker wins the game
in which each player chooses one edge per turn, but Maker wins as long as he is
permitted to choose $2$ edges in each turn whereas Breaker can choose as many
as $(1/9)n^{1/8}/(\ln n)^{3/8}$.
  In addition, we investigate $d$-diameter games for $d\ge 3$. The diameter
games are strongly related to the degree games. Thus, we also provide a
generalization of the fair degree game for the biased case.


title:
Convergence of many-body wavefunction expansions using a plane wave
  basis in the thermodynamic limit

abstract:
  Basis set incompleteness error and finite size error can manifest
concurrently in systems for which the two effects are phenomenologically
well-separated in length scale. When this is true, we need not necessarily
remove the two sources of error simultaneously. Instead, the errors can be
found and remedied in different parts of the basis set. This would be of great
benefit to a method such as coupled cluster theory since the combined cost of
$n_{occ}^6 n_{virt}^4$ could be separated into $n_{occ}^6$ and $n_{virt}^4$
costs with smaller prefactors. In this Communication, we present analysis on a
data set due to Baardsen and coworkers, containing coupled cluster doubles
energies for the 2DEG for $r_s=$ 0.5, 1.0 and 2.0 a.u.~at a wide range of basis
set sizes and particle numbers. In obtaining complete basis set limit
thermodynamic limit results, we find that within a small and removable error
the above assertion is correct for this simple system. This approach allows for
the combination of methods which separately address finite size effects and
basis set incompleteness error.


title: Cluster-lensing: A Python Package for Galaxy Clusters & Miscentering

abstract:
  We describe a new open source package for calculating properties of galaxy
clusters, including NFW halo profiles with and without the effects of cluster
miscentering. This pure-Python package, cluster-lensing, provides
well-documented and easy-to-use classes and functions for calculating cluster
scaling relations, including mass-richness and mass-concentration relations
from the literature, as well as the surface mass density $\Sigma(R)$ and
differential surface mass density $\Delta\Sigma(R)$ profiles, probed by weak
lensing magnification and shear. Galaxy cluster miscentering is especially a
concern for stacked weak lensing shear studies of galaxy clusters, where
offsets between the assumed and the true underlying matter distribution can
lead to a significant bias in the mass estimates if not accounted for. This
software has been developed and released in a public GitHub repository, and is
licensed under the permissive MIT license. The cluster-lensing package is
archived on Zenodo (Ford 2016). Full documentation, source code, and
installation instructions are available at
http://jesford.github.io/cluster-lensing/.


title: Magnetic hyperbolic metamaterial of polaritonic nanowires

abstract:
  We show that the axial component of the magnetic permeability tensor is
resonant for a wire medium consisting of high-index epsilon-positive nanowires,
and its real part changes the sign at a certain frequency. At this frequency
the medium experiences the topological transition from the hyperbolic to the
elliptic type of dispersion. We show that the transition regime is
characterized by extremely strong dependence of the permeability on the wave
vector. This implies very high density of electromagnetic states that results
in the filamentary pattern and noticeable Purcell factor for a transversely
oriented magnetic dipole.


title:
Experimental observation of $\beta$-delayed neutrons from $^{9}$Li as a
  way to study short-pulse laser-driven deuteron production

abstract:
  A short-pulse laser-driven deuteron beam is generated in the relativistic
transparency regime and aimed at a beryllium converter to generate neutrons at
the TRIDENT laser facility. These prompt neutrons have been used for active
interrogation to detect nuclear materials, the first such demonstration of a
laser-driven neutron source. During the experiments, delayed neutrons from
$^9$Li decay was observed. It was identified by its characteristic half-life of
178.3 ms. Production is attributed to the nuclear reactions $^9$Be(d,2p)$^9$Li
and $^9$Be(n,p)$^9$Li inside the beryllium converter itself. These reactions
have energy thresholds of 18.42 and 14.26 MeV respectively, and we estimate the
(d,2p) reaction to be the dominant source of $^9$Li production. Therefore, only
the higher-energy portion of the deuteron spectrum contributes to the
production of the delayed neutrons. It was observed that the delayed-neutron
yield decreases with increasing distance between the converter and the deuteron
source. This behavior is consistent with deuteron production with energy
greater than $\sim$20 MeV within a cone with a half-angle greater than
40$^{\circ}$. Prompt-neutron time-of-flight measurements at varying separation
between the converter and the laser target indicate that the fast deuteron
population above threshold is severely depleted on axis out to
$\sim$20$^{\circ}$. These measurements are consistent with emission of the fast
deuterons (i.e., above 10 MeV/nucleon) in a ring-like fashion around the
central axis. Such an inferred ring-like structure is qualitatively consistent
with a documented signature of the breakout afterburner (BOA) laser-plasma ion
acceleration mechanism. The measurement of $\beta$-delayed neutrons from $^9$Li
decay could provide an important new diagnostic tool for the study of the
features of the deuteron production mechanism in a non-intrusive way.


title: No "Evidence for a new phase of dense hydrogen above 325 GPa"

abstract:
  In recent years there has been intense experimental activity to observe solid
metallic hydrogen. Wigner and Huntington predicted that under extreme pressures
insulating molecular hydrogen would dissociate and transition to atomic
metallic hydrogen. Recently Dalladay-Simpson, Howie, and Gregoryanz reported a
phase transition to an insulating phase in molecular hydrogen at a pressure of
325 GPa and 300 K. Because of its scientific importance we have scrutinized
their experimental evidence to determine if their claim is justified. Based on
our analysis, we conclude that they have misinterpreted their data: there is no
evidence for a phase transition at 325 GPa.


title:
Why are flare ribbons associated with the spines of magnetic null points
  generically elongated?

abstract:
  Coronal magnetic null points exist in abundance as demonstrated by
extrapolations of the coronal field, and have been inferred to be important for
a broad range of energetic events. These null points and their associated
separatrix and spine field lines represent discontinuities of the field line
mapping, making them preferential locations for reconnection. This field line
mapping also exhibits strong gradients adjacent to the separatrix (fan) and
spine field lines, that can be analysed using the `squashing factor', $Q$. In
this paper we make a detailed analysis of the distribution of $Q$ in the
presence of magnetic nulls. While $Q$ is formally infinite on both the spine
and fan of the null, the decay of $Q$ away from these structures is shown in
general to depend strongly on the null-point structure. For the generic case of
a non-radially-symmetric null, $Q$ decays most slowly away from the spine/fan
in the direction in which $|{\bf B}|$ increases most slowly. In particular,
this demonstrates that the extended, elliptical high-$Q$ halo around the spine
footpoints observed by Masson et al. (Astrophys. J., 700, 559, 2009) is a
generic feature. This extension of the $Q$ halos around the spine/fan
footpoints is important for diagnosing the regions of the photosphere that are
magnetically connected to any current layer that forms at the null. In light of
this, we discuss how our results can be used to interpret the geometry of
observed flare ribbons in `circular ribbon flares', in which typically a
coronal null is implicated. We conclude that both the physics in the vicinity
of the null and how this is related to the extension of $Q$ away from the
spine/fan can be used in tandem to understand observational signatures of
reconnection at coronal null points.


title: Drinfeld double of $GL_n$ and generalized cluster structures

abstract:
  We construct a generalized cluster structure compatible with the Poisson
bracket on the Drinfeld double of the standard Poisson-Lie group $GL_n$ and
derive from it a generalized cluster structure on $GL_n$ compatible with the
push-forward of the Poisson bracket on the dual Poisson--Lie group.


title: On Avoider-Enforcer games

abstract:
  In the Avoider-Enforcer game on the complete graph $K_n$, the players
(Avoider and Enforcer) each take an edge in turn. Given a graph property
$\mathcal{P}$, Enforcer wins the game if Avoider's graph has the property
$\mathcal{P}$. An important parameter is $\tau_E({\cal P})$, the smallest
integer $t$ such that Enforcer can win the game against any opponent in $t$
rounds.
  In this paper, let $\mathcal{F}$ be an arbitrary family of graphs and
$\mathcal{P}$ be the property that a member of $\mathcal{F}$ is a subgraph or
is an induced subgraph. We determine the asymptotic value of
$\tau_E(\mathcal{P})$ when $\mathcal{F}$ contains no bipartite graph and
establish that $\tau_E(\mathcal{P})=o(n^2)$ if $\mathcal{F}$ contains a
bipartite graph.
  The proof uses the game of JumbleG and the Szemer\'edi Regularity Lemma.


title: Ultrafast Isomerization in Acetylene Dication: To Be or Not To Be

abstract:
  Experimental evidence has pointed toward the existence of ultrafast proton
migration and isomerization as a key process for acetylene and its ions,
however the actual mechanism for ultrafast isomerization of the acetylene
[HCCH]2+ to vinylidene [H2CC]2+ dication remains nebulous. Theoretical studies
show a high potential barrier of over 2eV for the isomerization pathways on the
low lying dicationic states, implying that the corresponding isomerization
should take picoseconds or even longer according to transition state theory.
However a recent experiment at a femtosecond X-ray free electron laser (XFEL)
[Nature Commun. 6, 8199 (2015)] suggests that large amplitude hydrogen
migration proceeds on a sub-100 femtosecond time scale. In order to resolve the
contradiction, we present a complete theoretical study of the dynamics of
acetylene dication produced by Auger decay after X-ray photoionization of the
carbon atom K shell. We find that isomerization does not occur on the sub-100
fs timescale and is not required to explain the time-resolved Coulomb imaging
experiment. This study resolves the seeming contradiction between experiment
and theory concerning the isomerization time scale in acetylene dication. This
work calls for careful interpretation of structural information from the widely
applied Coulomb momentum imaging method but also points out its strengths in
mapping out momentum dispersion dynamics even when structural variation is
minor.


title:
General formulation of coupled radiative and conductive heat transfer
  between compact bodies

abstract:
  We present a general framework for studying strongly coupled radiative and
conductive heat transfer between arbitrarily shaped bodies separated by
sub-wavelength distances. Our formulation is based on a macroscopic approach
that couples our recent fluctuating volume--current (FVC) method of near-field
heat transfer to the more well known Fourier conduction transport equation. We
apply our technique to consider heat exchange between aluminum-zinc oxide
nanorods and show that the presence of bulk plasmon resonances can result in
extremely large radiative heat transfer rates (roughly twenty times larger than
observed in planar geometries), whose interplay with conductive transport leads
to nonlinear temperature profiles along the nanorods.


title: Performing Quantum Computing Experiments in the Cloud

abstract:
  Quantum computing technology has reached a second renaissance in the past
five years. Increased interest from both the private and public sector combined
with extraordinary theoretical and experimental progress has solidified this
technology as a major advancement in the 21st century. As anticipated by many,
the first realisation of quantum computing technology would occur over the
cloud, with users logging onto dedicated hardware over the classical internet.
Recently IBM has released the {\em Quantum Experience} which allows users to
access a five qubit quantum processor. In this paper we take advantage of this
online availability of actual quantum hardware and present four quantum
information experiments that have never been demonstrated before. We utilise
the IBM chip to realise protocols in Quantum Error Correction, Quantum
Arithmetic, Quantum graph theory and Fault-tolerant quantum computation, by
accessing the device remotely through the cloud. While the results are subject
to significant noise, the correct results are returned from the chip. This
demonstrates the power of experimental groups opening up their technology to a
wider audience and will hopefully allow for the next stage development in
quantum information technology.


title:
Active Learning On Weighted Graphs Using Adaptive And Non-adaptive
  Approaches

abstract:
  This paper studies graph-based active learning, where the goal is to
reconstruct a binary signal defined on the nodes of a weighted graph, by
sampling it on a small subset of the nodes. A new sampling algorithm is
proposed, which sequentially selects the graph nodes to be sampled, based on an
aggressive search for the boundary of the signal over the graph. The algorithm
generalizes a recent method for sampling nodes in unweighted graphs. The
generalization improves the sampling performance using the information gained
from the available graph weights. An analysis of the number of samples required
by the proposed algorithm is provided, and the gain over the unweighted method
is further demonstrated in simulations. Additionally, the proposed method is
compared with an alternative state of-the-art method, which is based on the
graph's spectral properties. It is shown that the proposed method significantly
outperforms the spectral sampling method, if the signal needs to be predicted
with high accuracy. On the other hand, if a higher level of inaccuracy is
tolerable, then the spectral method outperforms the proposed aggressive search
method. Consequently, we propose a hybrid method, which is shown to combine the
advantages of both approaches.


title:
The Information-Collecting Vehicle Routing Problem: Stochastic
  Optimization for Emergency Storm Response

abstract:
  Utilities face the challenge of responding to power outages due to storms and
ice damage, but most power grids are not equipped with sensors to pinpoint the
precise location of the faults causing the outage. Instead, utilities have to
depend primarily on phone calls (trouble calls) from customers who have lost
power to guide the dispatching of utility trucks. In this paper, we develop a
policy that routes a utility truck to restore outages in the power grid as
quickly as possible, using phone calls to create beliefs about outages, but
also using utility trucks as a mechanism for collecting additional information.
This means that routing decisions change not only the physical state of the
truck (as it moves from one location to another) and the grid (as the truck
performs repairs), but also our belief about the network, creating the first
stochastic vehicle routing problem that explicitly models information
collection and belief modeling. We address the problem of managing a single
utility truck, which we start by formulating as a sequential stochastic
optimization model which captures our belief about the state of the grid. We
propose a stochastic lookahead policy, and use Monte Carlo tree search (MCTS)
to produce a practical policy that is asymptotically optimal. Simulation
results show that the developed policy restores the power grid much faster
compared to standard industry heuristics.


title: A Framework for FFT-based Homogenization on Anisotropic Lattices

abstract:
  In order to take structural anisotropies of a given composite and different
shapes of its unit cell into account, we generalize the Basic Scheme in
Homogenization by Moulinec and Suquet to arbitrary sampling lattices and
tilings of the d-dimensional Euclidean space. Employing a Fourier transform on
arbitrary lattices, which generate sampling patterns in the unit cell of
interest, we derive a generalization of this scheme. In several cases, this
Fourier transform is of lower dimension than the space itself; for many
lattices it even reduces to a one-dimensional Fourier transform having the same
leading coefficient as the fastest Fourier transform implementation available.
We illustrate the generalized Basic Scheme on an anisotropic laminate and a
generalized ellipsoidal Hashin structure. For both we derive an analytical
solution to the elasticity problem, in two- and three dimensions, respectively.
We then illustrate the possibilities of choosing a pattern. Compared to
classical grids this introduces both a reduction of computation time and a
reduced error of the numerical method. It also allows for anisotropic
subsampling, i.e. choosing a sub lattice of a pixel or voxel grid based on
anisotropy information of the material at hand.


title:
Full characterization of generalized bent functions as (semi)-bent
  spaces, their dual, and the Gray image

abstract:
  In difference to many recent articles that deal with generalized bent (gbent)
functions $f:\mathbb{Z}_2^n \rightarrow \mathbb{Z}_q$ for certain small valued
$q\in \{4,8,16 \}$, we give a complete description of these functions for both
$n$ even and odd and for any $q=2^k$ in terms of both the necessary and
sufficient conditions their component functions need to satisfy. This enables
us to completely characterize gbent functions as algebraic objects, namely as
affine spaces of bent or semi-bent functions with interesting additional
properties, which we in detail describe. We also specify the dual and the Gray
image of gbent functions for $q=2^k$. We discuss the subclass of gbent
functions which corresponds to relative difference sets, which we call
$\mathbb{Z}_q$-bent functions, and point out that they correspond to a class of
vectorial bent functions. The property of being $\mathbb{Z}_q$-bent is much
stronger than the standard concept of a gbent function. We analyse two examples
of this class of functions.


title:
One class of conservative difference schemes for solving molecular
  dynamics equations of motion

abstract:
  Simulation of many-particle system evolution by molecular dynamics takes to
decrease integration step to provide numerical scheme stability on the
sufficiently large time interval. It leads to a significant increase of the
volume of calculations. An approach for constructing symmetric simplectic
numerical schemes with given approximation accuracy in relation to integration
step, for solving molecular dynamics Hamiltonian equations, is proposed in this
paper. Numerical experiments show that obtained under this approach symmetric
simplectic third order scheme is more stable for integration step,
time-reversible and conserves Hamiltonian of the system with more accuracy at a
large integration interval then second order velocity Verlet numerical schemes.


title:
A Generalized Levene's Scale Test for Variance Heterogeneity in the
  Presence of Sample Correlation and Group Uncertainty

abstract:
  We generalize Levene's test for variance (scale) heterogeneity between $k$
groups for more complex data, which includes sample correlation and group
membership uncertainty. Following a two-stage regression framework, we show
that least absolute deviation regression must be used in the stage 1 analysis
to ensure a correct asymptotic $\chi^2_{k-1}/(k-1)$ distribution of the
generalized scale ($gS$) test statistic. We then show that the proposed $gS$
test is independent of the generalized location test, under the joint null
hypothesis of no mean and no variance heterogeneity. Consequently, we
generalize the recently proposed joint location-scale ($gJLS$) test valuable in
settings where there is an interaction effect, but one interacting variable is
not available. We evaluate the proposed method via an extensive simulation
study, and two genetic association application studies.


title: Space-Time Codes Based on Rank-Metric Codes and Their Decoding

abstract:
  We propose a new class of space-time block codes based on finite-field
rank-metric codes in combination with a rank-metric-preserving mapping to the
set of Eisenstein integers. It is shown that these codes achieve maximum
diversity order and improve upon certain existing constructions. Moreover, we
present a new decoding algorithm for these codes which utilizes the algebraic
structure of the underlying finite-field rank-metric codes and employs
lattice-reduction-aided equalization. This decoder does not achieve the same
performance as the classical maximum-likelihood decoding methods, but has
polynomial complexity in the matrix dimension, making it usable for large field
sizes and numbers of antennas.


title: RADON: Repairable Atomic Data Object in Networks

abstract:
  Erasure codes offer an efficient way to decrease storage and communication
costs while implementing atomic memory service in asynchronous distributed
storage systems. In this paper, we provide erasure-code-based algorithms having
the additional ability to perform background repair of crashed nodes. A repair
operation of a node in the crashed state is triggered externally, and is
carried out by the concerned node via message exchanges with other active nodes
in the system. Upon completion of repair, the node re-enters active state, and
resumes participation in ongoing and future read, write, and repair operations.
To guarantee liveness and atomicity simultaneously, existing works assume
either the presence of nodes with stable storage, or presence of nodes that
never crash during the execution. We demand neither of these; instead we
consider a natural, yet practical network stability condition $N1$ that only
restricts the number of nodes in the crashed/repair state during broadcast of
any message.
  We present an erasure-code based algorithm $RADON_C$ that is always live, and
guarantees atomicity as long as condition $N1$ holds. In situations when the
number of concurrent writes is limited, $RADON_C$ has significantly improved
storage and communication cost over a replication-based algorithm $RADON_R$,
which also works under $N1$. We further show how a slightly stronger network
stability condition $N2$ can be used to construct algorithms that never violate
atomicity. The guarantee of atomicity comes at the expense of having an
additional phase during the read and write operations.


title: More Lepton Flavor Violating Observables for LHCb's Run 2

abstract:
  The R_K measurement by LHCb suggests non-standard lepton non-universality
(LNU) to occur in b -> s l+ l- transitions, with effects in muons rather than
electrons. A number of other measurements of b -> s l+ l- transitions by LHCb
and B-factories display disagreement with the SM predictions and, remarkably,
these discrepancies are consistent in magnitude and sign with the R_K effect.
Non-standard LNU suggests non-standard lepton flavor violation (LFV) as well,
for example in B -> K l l' and B_s -> l l'. There are good reasons to expect
that the new effects may be larger for generations closer to the third one. In
this case, the B_s -> mu e decay may be the most difficult to reach
experimentally. We propose and study in detail the radiative counterpart of
this decay, namely B_s -> mu e gamma, whereby the chiral-suppression factor is
replaced by a factor of order alpha/pi. A measurement of this mode would be
sensitive to the same physics as the purely leptonic LFV decay and, depending
on experimental efficiencies, it may be more accessible. A realistic
expectation is a factor of two improvement in statistics for either of the
B_{d,s} modes.


title: Isotropic Schur roots

abstract:
  In this paper, we study the isotropic Schur roots of an acyclic quiver $Q$
with $n$ vertices. We study the perpendicular category $\mathcal{A}(d)$ of a
dimension vector $d$ and give a complete description of it when $d$ is an
isotropic Schur $\delta$. This is done by using exceptional sequences and by
defining a subcategory $\mathcal{R}(Q,\delta)$ attached to the pair
$(Q,\delta)$. The latter category is always equivalent to the category of
representations of a connected acyclic quiver $Q_{\mathcal{R}}$ of tame type,
having a unique isotropic Schur root, say $\delta_{\mathcal{R}}$. The
understanding of the simple objects in $\mathcal{A}(\delta)$ allows us to get a
finite set of generators for the ring of semi-invariants SI$(Q,\delta)$ of $Q$
of dimension vector $\delta$. The relations among these generators come from
the representation theory of the category $\mathcal{R}(Q,\delta)$ and from a
beautiful description of the cone of dimension vectors of
$\mathcal{A}(\delta)$. Indeed, we show that SI$(Q,\delta)$ is isomorphic to the
ring of semi-invariants SI$(Q_{\mathcal{R}},\delta_{\mathcal{R}})$ to which we
adjoin variables. In particular, using a result of Skowro\'nski and Weyman, the
ring SI$(Q,\delta)$ is a polynomial ring or a hypersurface. Finally, we provide
an algorithm for finding all isotropic Schur roots of $Q$. This is done by an
action of the braid group $B_{n-1}$ on some exceptional sequences. This action
admits finitely many orbits, each such orbit corresponding to an isotropic
Schur root of a tame full subquiver of $Q$.


title:
Quantum ergodicity and Benjamini-Schramm convergence of hyperbolic
  surfaces

abstract:
  We present a quantum ergodicity theorem for fixed spectral window and
sequences of compact hyperbolic surfaces converging to the hyperbolic plane in
the sense of Benjamini and Schramm. This addresses a question posed by Colin de
Verdi\`{e}re. Our theorem is inspired by results for eigenfunctions on large
regular graphs by Anantharaman and the first-named author. It applies in
particular to eigenfunctions on compact arithmetic surfaces in the level
aspect, which connects it to a question of Nelson on Maass forms. The proof is
based on a wave propagation approach recently considered by Brooks,
Lindenstrauss and the first-named author on discrete graphs. It does not use
any microlocal analysis, making it quite different from the usual proof of
quantum ergodicity in the large eigenvalue limit. Moreover, we replace the wave
propagator with renormalised averaging operators over discs, which simplifies
the analysis and allows us to make use of a general ergodic theorem of Nevo. As
a consequence of this approach, we require little regularity on the
observables.


title: Linearized GMM Kernels and Normalized Random Fourier Features

abstract:
  The method of "random Fourier features (RFF)" has become a popular tool for
approximating the "radial basis function (RBF)" kernel. The variance of RFF is
actually large. Interestingly, the variance can be substantially reduced by a
simple normalization step as we theoretically demonstrate. We name the improved
scheme as the "normalized RFF (NRFF)".
  We also propose the "generalized min-max (GMM)" kernel as a measure of data
similarity. GMM is positive definite as there is an associated hashing method
named "generalized consistent weighted sampling (GCWS)" which linearizes this
nonlinear kernel. We provide an extensive empirical evaluation of the RBF
kernel and the GMM kernel on more than 50 publicly available datasets. For a
majority of the datasets, the (tuning-free) GMM kernel outperforms the
best-tuned RBF kernel.
  We conduct extensive experiments for comparing the linearized RBF kernel
using NRFF with the linearized GMM kernel using GCWS. We observe that, to reach
a comparable classification accuracy, GCWS typically requires substantially
fewer samples than NRFF, even on datasets where the original RBF kernel
outperforms the original GMM kernel. The empirical success of GCWS (compared to
NRFF) can also be explained from a theoretical perspective. Firstly, the
relative variance (normalized by the squared expectation) of GCWS is
substantially smaller than that of NRFF, except for the very high similarity
region (where the variances of both methods are close to zero). Secondly, if we
make a model assumption on the data, we can show analytically that GCWS
exhibits much smaller variance than NRFF for estimating the same object (e.g.,
the RBF kernel), except for the very high similarity region.


title:
Classification of differential symmetry breaking operators for
  differential forms

abstract:
  We give a complete classification of conformally covariant differential
operators between the spaces of differential $i$-forms on the sphere $S^n$ and
$j$-forms on the totally geodesic hypersphere $S^{n-1}$ by analyzing the
restriction of principal series representations of the Lie group $O(n+1,1)$.
  Further, we provide explicit formul\ae{} for these matrix-valued operators in
the flat coordinates and find factorization identities for them.


title: Accretion mode of the Ultra-Luminous X-ray source M82 X-2

abstract:
  Periodic pulsations have been found in emission from the ultra-luminous X-ray
source (ULX) M82 X-2, strongly suggesting that the emitter is a rotating
neutron star rather than a black hole. However, the radiation mechanisms and
accretion mode involved have not yet been clearly established. In this paper,
we examine the applicability to this object of standard accretion modes for
high mass X-ray binaries (HMXBs). We find that spherical wind accretion, which
drives OB-type HMXBs, cannot apply here but that there is a natural explanation
in terms of an extension of the picture for standard Be-type HMXBs. We show
that a neutron star with a moderately strong magnetic field, accreting from a
disc-shaped wind emitted by a Be-companion, could be compatible with the
observed relation between spin and orbital period. A Roche lobe overflow
picture is also possible under certain conditions.


title: Skew-symmetric operators and reflexivity

abstract:
  In contrast to the subspaces of all $C$-symmetric operators, we show that the
subspaces of all skew-C symmetric operators are reflexive and even
hyperreflexive with the constant $\kappa(\C^s)\leqslant 3$.


title:
Quantitative convergence analysis of iterated expansive, set-valued
  mappings

abstract:
  We develop a framework for quantitative convergence analysis of Picard
iterations of expansive set-valued fixed point mappings. There are two key
components of the analysis. The first is a natural generalization of
single-valued averaged mappings to expansive, set-valued mappings that
characterizes a type of strong calmness of the fixed point mapping. The second
component to this analysis is an extension of the well-established notion of
metric subregularity -- or inverse calmness -- of the mapping at fixed points.
Convergence of expansive fixed point iterations is proved using these two
properties, and quantitative estimates are a natural byproduct of the
framework. To demonstrate the application of the theory, we prove for the first
time a number of results showing local linear convergence of nonconvex cyclic
projections for inconsistent (and consistent) feasibility problems, local
linear convergence of the forward-backward algorithm for structured
optimization without convexity, strong or otherwise, and local linear
convergence of the Douglas--Rachford algorithm for structured nonconvex
minimization. This theory includes earlier approaches for known results, convex
and nonconvex, as special cases.


title:
Stability of ion acoustic nonlinear waves and solitons in magnetized
  plasmas

abstract:
  Early results concerning the shape and stability of ion acoustic waves are
generalized to propagation at an angle to the magnetic field lines. Each wave
has a critical angle for stability. Known soliton results are recovered as
special cases. A historical overview of the problem concludes the paper.