  We present analysis of the three-dimensional shape of intracluster gas in
clusters formed in cosmological simulations of the Lambda-CDM cosmology and
compare it to the shape of dark matter distribution and the shape of the
overall isopotential surfaces. We find that in simulations with radiative
cooling, star formation and stellar feedback (CSF), intracluster gas outside
the cluster core is more spherical compared to non-radiative (NR) simulations,
while in the core the gas in the CSF runs is more triaxial and has a distinctly
oblate shape. The latter reflects the ongoing cooling of gas, which settles
into a thick oblate ellipsoid as it loses thermal energy. The shape of the gas
in the inner regions of clusters can therefore be a useful diagnostic of gas
cooling. We find that gas traces the shape of the underlying potential rather
well outside the core, as expected in hydrostatic equilibrium. At smaller
radii, however, the gas and potential shapes differ significantly. In the CSF
runs, the difference reflects the fact that gas is partly rotationally
supported. Interestingly, we find that in NR simulations the difference between
gas and potential shape at small radii is due to random gas motions, which make
the gas distribution more spherical than the equipotential surfaces. Finally,
we use mock Chandra X-ray maps to show that the differences in shapes observed
in three-dimensional distribution of gas are discernible in the ellipticity of
X-ray isophotes. Contrasting the ellipticities measured in simulated clusters
against observations can therefore constrain the amount of cooling of the
intracluster medium and the presence of random gas motions in cluster cores.


  The dependence of the spin reorientation transition in ultra-thin
ferromagnetic films on external magnetic fields is studied. For different
orientations of the applied field with respect to the film, phase diagrams are
calculated within a mean field theory for the classical Heisenberg model. In
particular we find that the spin reorientation transition present in this model
is not suppressed completely by an applied field, as the magnetization
component perpendicular to the field may show spontaneous order in a certain
temperature interval.


  To accurately predict future positions of different agents in traffic
scenarios is crucial for safely deploying intelligent autonomous systems in the
real-world environment. However, it remains a challenge due to the behavior of
a target agent being affected by other agents dynamically and there being more
than one socially possible paths the agent could take. In this paper, we
propose a novel framework, named Dynamic Context Encoder Network (DCENet). In
our framework, first, the spatial context between agents is explored by using
self-attention architectures. Then, the two-stream encoders are trained to
learn temporal context between steps by taking the respective observed
trajectories and the extracted dynamic spatial context as input. The
spatial-temporal context is encoded into a latent space using a Conditional
Variational Auto-Encoder (CVAE) module. Finally, a set of future trajectories
for each agent is predicted conditioned on the learned spatial-temporal context
by sampling from the latent space, repeatedly. DCENet is evaluated on one of
the most popular challenging benchmarks for trajectory forecasting Trajnet and
reports a new state-of-the-art performance. It also demonstrates superior
performance evaluated on the benchmark inD for mixed traffic at intersections.
A series of ablation studies is conducted to validate the effectiveness of each
proposed module. Our code is available at https://github.com/wtliao/DCENet.


  We report here low temperature magnetization isotherms for the single
molecule magnet, $(UO_2-L)_3$. By analyzing the low temperature magnetization
in terms of $M= X_1*B + X_3*B^3$ we extract the linear susceptibility $X_1$ and
the leading order nonlinear susceptibility $X_3$. We find that $X_1$ exhibits a
peak at a temperature of $T_1=10.4 K$ with $Chi_3$ also exhibiting a peak but
at a reduced temperature $T3 = 5 K$. At the lowest temperatures the isotherms
exhibit a critical field $B_c = 11.5 T$ marked by a clear point of inflection.
A minimal Hamiltonian employing S=1 (pseudo) spins with only a single energy
scale (successfully used to model the behavior of bulk f-electron metamagnets)
is shown to provide a good description of the observed linear scaling between
$T_1, T_3$ and $B_c$. We further show that a Heisenberg Hamiltonian previously
employed by Carretta et al. (2013 J. Phys.Cond. Matt. 25 486001) to model this
single molecule magnet gives formulas for the angle averaged susceptibilities
(in the Ising limit) very similar to those of the minimal model.


  In this paper, we propose a self-supervised learning procedure for training a
robust multi-object tracking (MOT) model given only unlabeled video. While
several self-supervisory learning signals have been proposed in prior work on
single-object tracking, such as color propagation and cycle-consistency, these
signals cannot be directly applied for training RNN models, which are needed to
achieve accurate MOT: they yield degenerate models that, for instance, always
match new detections to tracks with the closest initial detections. We propose
a novel self-supervisory signal that we call cross-input consistency: we
construct two distinct inputs for the same sequence of video, by hiding
different information about the sequence in each input. We then compute tracks
in that sequence by applying an RNN model independently on each input, and
train the model to produce consistent tracks across the two inputs. We evaluate
our unsupervised method on MOT17 and KITTI -- remarkably, we find that, despite
training only on unlabeled video, our unsupervised approach outperforms four
supervised methods published in the last 1--2 years, including Tracktor++,
FAMNet, GSM, and mmMOT.


  We show that the validity of the non-commutative Khintchine inequality for
some $q$ with $1<q<2$ implies its validity (with another constant) for all
$1\le p<q$. We prove this for the inequality involving the Rademacher
functions, but also for more general "lacunary" sequences, or even
non-commutative analogues of the Rademacher functions. For instance, we may
apply it to the "Z(2)-sequences" previously considered by Harcharras. The
result appears to be new in that case. It implies that the space $\ell^n_1$
contains (as an operator space) a large subspace uniformly isomorphic (as an
operator space) to $R_k+C_k$ with $k\sim n^{\frac12}$. This naturally raises
several interesting questions concerning the best possible such $k$.
Unfortunately we cannot settle the validity of the non-commutative Khintchine
inequality for $0<p<1$ but we can prove several would be corollaries. For
instance, given an infinite scalar matrix $[x_{ij}]$, we give a necessary and
sufficient condition for $[\pm x_{ij}]$ to be in the Schatten class $S_p$ for
almost all (independent) choices of signs $\pm 1$. We also characterize the
bounded Schur multipliers from $S_2$ to $S_p$. The latter two characterizations
extend to $0<p<1$ results already known for $1\le p\le2$. In addition, we
observe that the hypercontractive inequalities, proved by Carlen and Lieb for
the Fermionic case, remain valid for operator space valued functions, and hence
the Kahane inequalities are valid in this setting.


  Classical anti-commuting spinor fields and their dynamics are derived from
the geometry of the Clifford bundle over spacetime via the BRST formulation. In
conjunction with Kaluza-Klein theory, this results in a geometric description
of all the fields and dynamics of the standard model coupled to gravity and
provides the starting point for a new approach to quantum gravity.


  We examine some of the roots of parity violation for gravitons and uncover a
closely related new effect: correlations between right and left handed
gravitons. Such correlators have spin 4 if they involve gravitons moving along
the same direction, and spin zero for gravitons moving with opposite
directions. In the first case, the most immediate implication would be a degree
of linear polarization for the tensor vacuum fluctuations, which could be seen
by gravity wave detectors sensitive enough to probe the primordial background,
its degree of polarization and anisotropies. Looking at the anisotropy of the
gravity waves linear polarization we identify the parity respecting and
violating components of the effect. The imprint on the CMB temperature and
polarization would be more elusive, since it averages to zero in the two-point
functions, appearing only in their cosmic variance or in fourth order
correlators. In contrast, spin zero correlations would have an effect on the
two point function of the CMB temperature and polarization, enhancing the $BB$
component if they were anti-correlations. Such correlations represent an
amplitude for the production of standing waves, as first envisaged by
Grishchuk, and could also leave an interesting signature for gravity wave
detectors.


  In this pedagogical note I present the operator form of Wick's theorem, i.e.
a procedure to bring a product of 1-particle creation and destruction operators
to normal order, with respect to some reference many-body state. Both the
static and the time-ordered cases are presented. For the latter, in particular,
I provide a simple proof.


  Wikipedia is written in the wikitext markup language. When serving content,
the MediaWiki software that powers Wikipedia parses wikitext to HTML, thereby
inserting additional content by expanding macros (templates and mod-ules).
Hence, researchers who intend to analyze Wikipediaas seen by its readers should
work with HTML, rather than wikitext. Since Wikipedia's revision history is
publicly available exclusively in wikitext format, researchers have had to
produce HTML themselves, typically by using Wikipedia's REST API for ad-hoc
wikitext-to-HTML parsing. This approach, however, (1) does not scale to very
large amounts ofdata and (2) does not correctly expand macros in historical
article revisions. We solve these problems by developing a parallelized
architecture for parsing massive amounts of wikitext using local instances of
MediaWiki, enhanced with the capacity of correct historical macro expansion. By
deploying our system, we produce and release WikiHist.html, English Wikipedia's
full revision history in HTML format. We highlight the advantages of
WikiHist.html over raw wikitext in an empirical analysis of Wikipedia's
hyperlinks, showing that over half of the wiki links present in HTML are
missing from raw wikitext and that the missing links are important for user
navigation.


  Unsupervised learning objectives like language modeling and de-noising
constitute a significant part in producing pre-trained models that perform
various downstream applications from natural language understanding to
conversational tasks. However, despite impressive generative capabilities of
recent large language models, their abilities to capture syntactic or semantic
structure within text lag behind. We hypothesize that the mismatch between
linguistic performance and competence in machines is attributable to
insufficient transfer of linguistic structure knowledge to computational
systems with currently popular pre-training objectives. We show that
punctuation restoration as a learning objective improves in- and
out-of-distribution performance on structure-related tasks like named entity
recognition, open information extraction, chunking, and part-of-speech tagging.
Punctuation restoration is an effective learning objective that can improve
structure understanding and yield a more robust structure-aware representations
of natural language.


  It is known that finite-time blow-up in the 3D Patlak-Keller-Segel system may
occur for arbitrarily small values of the initial mass. It's interesting
whether one can prevent the finite-time blow-up via the stabilizing effect of
the moving fluid. Consider the three-dimensional Patlak-Keller-Segel system
coupled with the linearized Navier-Stokes equations near the Couette flow $(\
Ay, 0, 0 \ )$ in a finite channel $\mathbb{T}\times\mathbb{I}\times\mathbb{T}$
with $ \mathbb{T}=[0,2\pi) $ and $ \mathbb{I}=[-1,1] $, with the non-slip
boundary condition, and we show that if the shear flow is sufficiently strong
(A is large enough), then the solutions to Patlak-Keller-Segel-Navier-Stokes
system are global in time as long as the initial cell mass is sufficiently
small (for example, $M<\frac49$) and $
A\left(\|u_{2,0}(0)\|_{L^{2}}+\|u_{3,0}(0)\|_{L^{2}} \right)\leq C_{0} $, which
seems to be the first result of considering the suppression effect of Couette
flow in the 3D Patlak-Keller-Segel-Navier-Stokes model, and also the first time
considering the non-slip boundary condition.


  In this paper, we discuss distributed adaptive algorithms for synchronization
of complex networks, consensus of multi-agents with or without pinning
controller. The dynamics of individual node is governed by generalized QUAD
condition. We design new algorithms, which can keep the left eigenvector of the
adaptive coupling matrix corresponding to the zero eigenvalue invariant. Based
on this invariance, various distributive adaptive synchronization, consensus,
anti-synchronization models are given.


  In this paper, we investigate the relations between the pitch, the angle of
pitch and drall of parallel ruled surface of a closed spacelike curve with a
spacelike binormal in dual Lorentzian space.


  We report results of a novel high-energy follow-up observation of a potential
Fast Radio Burst. The radio burst was detected by VLA/realfast and followed-up
by the Neil Gehrels Swift Observatory in very low latency utilizing new
operational capabilities of Swift (arXiv:2005.01751), with pointed soft X-ray
and UV observations beginning at T0+32 minutes, and hard X-ray/gamma-ray event
data saved around T0. These observations are $>10$x faster than previous
X-ray/UV follow-up of any radio transient to date. No emission is seen
coincident with the FRB candidate at T0, with a 0.2s fluence $5\sigma$ upper
limit of $1.35\times10^{-8}$ erg cm$^{-2}$ (14-195 keV) for a SGR
1935+2154-like flare, nor at T0+32 minutes down to $3\sigma$ upper limits of
22.18 AB mag in UVOT u band, and $3.33\times10^{-13}$ erg cm$^{-2}$ s$^{-1}$
from 0.3-10 keV for the 2 ks observation. The candidate FRB alone is not
significant enough to be considered astrophysical, so this note serves as a
technical demonstration. These new Swift operational capabilities will allow
future FRB detections to be followed up with Swift at even lower latencies than
demonstrated here: 15-20 minutes should be regularly achievable, and 5-10
minutes occasionally achievable. We encourage FRB detecting facilities to
release alerts in low latency to enable this science.


  Sensor fusion of multiple sources plays an important role in vehicular
systems to achieve refined target position and velocity estimates. In this
article, we address the general registration problem, which is a key module for
a fusion system to accurately correct systematic errors of sensors. A fast
maximum a posteriori (FMAP) algorithm for joint registration-tracking (JRT) is
presented. The algorithm uses a recursive two-step optimization that involves
orthogonal factorization to ensure numerically stability. Statistical
efficiency analysis based on Cram\`{e}r-Rao lower bound theory is presented to
show asymptotical optimality of FMAP. Also, Givens rotation is used to derive a
fast implementation with complexity O(n) with $n$ the number of tracked
targets. Simulations and experiments are presented to demonstrate the promise
and effectiveness of FMAP.


  Feynman's diagrammatic series is a common language for a formally exact
theoretical description of systems of infinitely-many interacting quantum
particles, as well as a foundation for precision computational techniques. Here
we introduce a universal framework for efficient summation of connected or
skeleton Feynman diagrams for generic quantum many-body systems. It is based on
an explicit combinatorial construction of the sum of the integrands by dynamic
programming, at a computational cost that can be made only exponential in the
diagram order on a classical computer and potentially polynomial on a quantum
computer. We illustrate the technique by an unbiased diagrammatic Monte Carlo
calculation of the equation of state of the $2D$ $SU(N)$ Hubbard model in an
experimentally relevant regime, which has remained challenging for
state-of-the-art numerical methods.


  We present a deformed algebra related to the q-exponential and the
q-logarithm functions that emerge from nonextensive statistical mechanics. We
also develop a q-derivative (and consistently a q-integral) for which the
q-exponential is an eigenfunction. The q-derivative and the q-integral have a
dual nature, that is also presented.


  In this paper we consider polytopes given by systems of $n$ inequalities in
$d$ variables, where every inequality has at most two variables with nonzero
coefficient. We denote this family by $LI(2)$. We show that despite of the easy
algebraic structure, polytopes in $LI(2)$ can have high complexity. We
construct a polytope in $LI(2)$, whose number of vertices is almost the number
of vertices of the dual cyclic polytope, the difference is a multiplicative
factor of depending on $d$ and in particular independent of $n$. Moreover we
show that the dual cyclic polytope can not be realized in $LI(2)$.


  The STAR experiment at the Relativistic Heavy-Ion Collider at Brookhaven
National Laboratory is carrying out a spin physics program in high-energy
polarized proton collisions at $\sqrt{s}=200\,$GeV and $\sqrt{s}=500\,$GeV to
gain a deeper insight into the spin structure and dynamics of the proton.
  One of the main objectives of the spin physics program at RHIC is the precise
determination of the polarized gluon distribution function. The STAR detector
is well suited for the reconstruction of various final states involving jets,
$\pi^{0}$, $\pi^{\pm}$, e$^{\pm}$ and $\gamma$, which allows to measure several
different processes. Recent results suggest a gluon spin contribution to the
proton spin at the same level as the quark spin contribution itself.
  The production of $W$ bosons in polarized p+p collisions at
$\sqrt{s}=500\,$GeV opens a new era in the study of the spin-flavor structure
of the proton. $W^{-(+)}$ bosons are produced in $\bar{u}+d\;(\bar{d}+u)$
collisions and can be detected through their leptonic decays,
$e^{-}+\bar{\nu}_{e}\;(e^{+}+\nu_{e})$, where only the respective charged
lepton is measured. Results of $W^{-(+)}$ production suggest a large asymmetry
between the polarization of anti-$u$ and anti-$d$ quarks.


  Ensuring the safe and reliable operation of autonomous vehicles under adverse
weather remains a significant challenge. To address this, we have developed a
comprehensive dataset composed of sensor data acquired in a real test track and
reproduced in the laboratory for the same test scenarios. The provided dataset
includes camera, radar, LiDAR, inertial measurement unit (IMU), and GPS data
recorded under adverse weather conditions (rainy, night-time, and snowy
conditions). We recorded test scenarios using objects of interest such as car,
cyclist, truck and pedestrian -- some of which are inspired by EURONCAP
(European New Car Assessment Programme). The sensor data generated in the
laboratory is acquired by the execution of simulation-based tests in
hardware-in-the-loop environment with the digital twin of each real test
scenario. The dataset contains more than 2 hours of recording, which totals
more than 280GB of data. Therefore, it is a valuable resource for researchers
in the field of autonomous vehicles to test and improve their algorithms in
adverse weather conditions, as well as explore the simulation-to-reality gap.
The dataset is available for download at: https://twicedataset.github.io/site/


  We consider two-way amplify and forward relaying, where multiple full-duplex
user pairs exchange information via a shared full-duplex massive multiple-input
multiple-output (MIMO) relay. Most of the previous massive MIMO relaying works
maximize the spectral efficiency (SE). By contrast, we maximize the non-convex
energy efficiency (EE) metric by approximating it as a pseudo-concave problem,
which is then solved using the classic Dinkelbach approach. We also maximize
the EE of the least energy-efficient user {relying} on the max-min approach.
For solving these optimization problems, we derive closed-form lower bounds for
the ergodic achievable rate both for maximal-ratio combining and zero-forcing
processing at the relay, by using minimum mean squared error channel
estimation. We numerically characterize the accuracy of the lower bounds
derived. We also compare the SE and EE of the proposed design to those of the
existing full-duplex systems and quantify the significant improvement achieved
by the proposed algorithm. We also compare the EE of the proposed full-duplex
system to that of its half-duplex counterparts, and characterize the self-loop
and inter-user interference regimes, for which the proposed full-duplex system
succeeds in outperforming the half-duplex ones.


  We discuss the application of the solitonic techniques to the 5D
Einstein-Maxwell gravity. As an illustration we construct an exact solution
describing two concentric rotating dipole black rings. The properties of the
solution are investigated.


  We discuss a family of integrable systems on the sphere $S^2$ with an
additional integral of third order in momenta. This family contains the
Coryachev-Chaplygin top, the Goryachev system, the system recently discovered
by Dullin and Matveev and two new integrable systems. On the non-physical
sphere with zero radius all these systems are isomorphic to each other.


  Hamiltonian and Schrodinger evolution equations on finite-dimensional
projective space are analyzed in detail. Hartree-Fock (HF) manifold is
introduced as a submanifold of many electron projective space of states.
Evolution equations, exact and linearized, on this manifold are studied.
Comparison of matrices of linearized Schrodinger equations on many electron
projective space and on the corresponding HF manifold reveals the appearance in
the HF case a constraining matrix that involves matrix elements of
many-electron Hamiltonian between HF state and double excited determinants.
Character of dependence of transition energies on the matrix elements of
constraining matrix is established by means of perturbation analysis. It is
demonstrated that success of time-dependent HF theory in calculation of
transition energies is mainly due to the wrong behavior of these energies as
functions of matrix elements of constraining matrix as compared with the exact
transition energies


  We investigate the tail behaviour of the steady state distribution of a
stochastic recursion that generalises Lindley's recursion. This recursion
arises in queuing systems with dependent interarrival and service times, and
includes alternating service systems and carousel storage systems as special
cases. We obtain precise tail asymptotics in three qualitatively different
cases, and compare these with existing results for Lindley's recursion and for
alternating service systems.


  There have been a plethora of investigations carried out in studying
inequalities for the Fourier coefficients of weakly holomorphic modular forms,
for example, on the partition function. Recently, Bringmann, Kane, Rolen, and
Tripp studied asymptotics for the $k$-colored partition function and more
generally, for the fractional partitions arising from the Nekrasov-Okounkov
formula which in turn allowed them to prove generalized multiplicative
inequalities. Motivated by their idea to find interesting inequalities for the
$k$-colored partition functions, denoted by $p_k(n)$, in this paper, we prove a
family of inequalities for the $p_{24}(n)$. The main aim of this paper is to
study the asymptotic expansion with an effective estimate for the error bound
regarding the Fourier coefficients of the modular form $1/\Delta$ (up to a
constant $c$ and a power of $q$), where $\Delta$ is the modular discriminant
function and a well-known combinatorial interpretation for the associated
coefficient sequence is called $24$-colored partitions, denoted by $p_{24}(n)$.
Consequently, we show that $p_{24}(n)$ satisfies $2$-$\log$-concavity,
Tur\'{a}n inequality of order $3$, and Laguerre inequalities of order $m$ with
$2\le m\le 8$ eventually. Our method of estimations for the error term of the
asymptotic expansion for $p_{24}(n)$ can be adapted in a more general paradigm
where the Fourier coefficients of a certain class of Dedekind-eta quotients
which are essentially a modular form of negative weight, admit a Rademacher
type exact formula involving the $I$-Bessel function of positive order.


  Multiple functional ionic and electronic orders are observed in high
temperature superconducting cuprates. The charge density wave order is one of
them and it is spatially localized in spatial regions of the material. It is
also known that the oxygen interstitials introduced by chemical intercalation
self-organize in different oxygen rich regions corresponding with hole rich
regions in the Cu$O_2$ layers left empty by the charge density wave order
domains. However, what happens in between these two order is not known, and
neither there is a method to control this spatial separation. Here we
demonstrate by using scanning nano X-ray diffraction, that dislocations or
grain boundaries in the material can act as boundary between charge density
wave and oxygen rich phases in a optimally doped La$_2$CuO$_4$$_+$$_y$ high
temperature superconductor. Dislocations can be used therefore to control the
anti-correlation of the charge density wave order with the oxygen interstitials
in specific portion of the material.


  Among Heusler compounds, the ones being magnetic semiconductors (also known
as spin-filter materials) are widely studied as they offer novel
functionalities in spintronic/magnetoelectronic devices. The spin-gapless
semiconductors are a special case. They possess a zero or almost-zero energy
gap in one of the two spin channels. We employ the $GW$ approximation, which
allows an elaborate treatment of the electronic correlations, to simulate the
electronic band structure of these materials. Our results suggest that in most
cases the use of $GW$ self energy instead of the usual density functionals is
important to accurately determine the electronic properties of magnetic
semiconductors.


  Researchers increasingly use meta-analysis to synthesize the results of
several studies in order to estimate a common effect. When the outcome variable
is continuous, standard meta-analytic approaches assume that the primary
studies report the sample mean and standard deviation of the outcome. However,
when the outcome is skewed, authors sometimes summarize the data by reporting
the sample median and one or both of (i) the minimum and maximum values and
(ii) the first and third quartiles, but do not report the mean or standard
deviation. To include these studies in meta-analysis, several methods have been
developed to estimate the sample mean and standard deviation from the reported
summary data. A major limitation of these widely used methods is that they
assume that the outcome distribution is normal, which is unlikely to be tenable
for studies reporting medians. We propose two novel approaches to estimate the
sample mean and standard deviation when data are suspected to be non-normal.
Our simulation results and empirical assessments show that the proposed methods
often perform better than the existing methods when applied to non-normal data.


  Optical full vectorial modes have closely attracted much attention because of
their unique optical features and thus may develop the fundamental researches
and new functionalities of light. Beyond the conventional linear polarization
modal coupling, we thoroughly investigate the inherent polarizationdependence
and polarization-isolation features for full vectorial mode coupling in optical
fibers, as well as the coupling crosstalk in view of the modal degeneracy. We
present the general full vectorial coupling mechanism and numerically simulate
the full vectorial mode coupling for both fiber directional and grating
assisted coupling cases. Furthermore, we give the detailed analyses of coupling
crosstalk based on the unified threemode coupling model. Apart from lifting the
modal degeneracy, significantly, the crosstalk can also be reduced by weakening
the coupling coefficient and meanwhile increasing the coupling length. This
extended full vectorial mode coupling mechanismmay provide theoretical guidance
on exploiting new all fiberbased polarization-sensitive passive elements to
control fullvectorial fields and modal polarization states.


  We evaluate the Average Null Energy Condition (ANEC) on momentum eigenstates
generated by the stress tensor in perturbative $\lambda \, \phi^4$ and general
spacetime dimension. We first compute the norm of the stress-tensor state at
second order in $\lambda$; as a by-product of the derivation we obtain the full
expression for the stress tensor 2-point function at this order. We then
compute the ANEC expectation value to first order in $\lambda$, which also
depends on the coupling of the stress-tensor improvement term $\xi$. We study
the bounds on these couplings that follow from the ANEC and unitarity at first
order in perturbation theory. These bounds are stronger than unitarity in some
regions of coupling space.


  In this work, we demonstrate the utility of state representation learning
applied to modeling the time evolution of electron density and temperature
profiles at ASDEX-Upgrade (AUG). The proposed model is a deep neural network
which learns to map the high dimensional profile observations to a lower
dimensional state. The mapped states, alongside the original profile's
corresponding machine parameters are used to learn a forward model to propagate
the state in time. We show that this approach is able to predict AUG discharges
using only a selected set of machine parameters. The state is then further
conditioned to encode information about the confinement regime, which yields a
simple baseline linear classifier, while still retaining the information needed
to predict the evolution of profiles. We then discuss the potential use cases
and limitations of state representation learning algorithms applied to fusion
devices.


  Recently, the diffusion-limited cluster aggregation (DLCA) model was
restudied as a real-world example of showing discontinuous percolation
transitions (PTs). Because a larger cluster is less mobile in Brownian motion,
it comes into contact with other clusters less frequently. Thus, the formation
of a giant cluster is suppressed in the DLCA process. All clusters grow
continuously with respect to time, but the largest cluster grows drastically
with respect to the number of cluster merging events. Here, we study the
discontinuous PT occurring in the DLCA model in more general dimensions such as
two, three, and four dimensions. PTs are also studied for a generalized
velocity, which scales with cluster size $s$ as $v_{s} \propto s^{\eta}$. For
Brownian motion of hard spheres in three dimensions, the mean relative speed
scales as $s^{-1/2}$ and the collision rate $\sigma v_s$ scales as $\sim
s^{1/6}$. We find numerically that the PT type changes from discontinuous to
continuous as $\eta$ crosses over a tricritical point $\eta_{c} \approx 1.2$
(in two dimensions), $\eta_{c} \approx 0.8$ (in three dimensions), and
$\eta_{c} \approx 0.4$ (in four dimensions). We illustrate the root of this
crossover behavior from the perspective of the heterogeneity of cluster-size
distribution. Finally, we study the reaction-limited cluster aggregation (RLCA)
model in the Brownian process, in which cluster merging takes place with finite
probability $r$. We find that the PTs in two and three dimensions are
discontinuous even for small $r$ such as $r=10^{-3}$, but are continuous in
four dimensions.


  In person re-identification (ReID) task, because of its shortage of trainable
dataset, it is common to utilize fine-tuning method using a classification
network pre-trained on a large dataset. However, it is relatively difficult to
sufficiently fine-tune the low-level layers of the network due to the gradient
vanishing problem. In this work, we propose a novel fine-tuning strategy that
allows low-level layers to be sufficiently trained by rolling back the weights
of high-level layers to their initial pre-trained weights. Our strategy
alleviates the problem of gradient vanishing in low-level layers and robustly
trains the low-level layers to fit the ReID dataset, thereby increasing the
performance of ReID tasks. The improved performance of the proposed strategy is
validated via several experiments. Furthermore, without any add-ons such as
pose estimation or segmentation, our strategy exhibits state-of-the-art
performance using only vanilla deep convolutional neural network architecture.


  In this correspondence, we propose hierarchical high-altitude platform
(HAP)-low-altitude platform (LAP) networks with the aim of maximizing the
sum-rate of ground user equipments (UEs). The multiple aerial radio units (RUs)
mounted on HAPs and LAPs are managed by the central unit (CU) via constrained
fronthaul links. The limitation of fronthaul capacity can be addressed through
quantization, employing the cloud radio access network (C-RAN) architecture.
For spectral efficiency, we adopt the rate-splitting multiple access (RSMA),
leveraging the advantages of both space-division multiple access (SDMA) and
non-orthogonal multiple access (NOMA). To achieve this, we jointly optimize
rate splitting, transmit power allocation, quantization noise variance, and UAV
placement using an alternating optimization (AO) approach coupled with
successive convex approximation (SCA) and the weighted minimum mean square
error (WMMSE) method. Numerical results validate the superior performance of
the proposed method compared to benchmark schemes, including partial
optimizations or those without the assistance of LAPs.


  A two-dimensional phononic crystal (PC) can exhibit longitudinal-mode
negative energy refraction on its lowest (acoustical) frequency pass band. The
effective elastodynamic properties of a typical PC are calculated and it is
observed that the components of the effective density tensor can achieve
negative values at certain low frequencies on the acoustical branches for the
longitudinal-mode pass-band, and that negative refraction may be accompanied by
either positive or negative effective density. Furthermore, such a PC has a
high anisotropy ratio at certain low frequencies, offering potential for
application to acoustic cloaking where effective material anisotropy is
essential.


  Using Voiculescu's notion of a matricial microstate we introduce fractal
dimensions and entropies for finite sets of selfadjoint operators in a tracial
von Neumann algebra. We show that they possess properties similar to their
classical predecessors. We relate the new quantities to free entropy and free
entropy dimension and show that a modified version of free Hausdorff dimension
is an algebraic invariant. We compute the free Hausdorff dimension in the cases
where the set generates a finite dimensional algebra or where the set consists
of a single selfadjoint. We show that the free Hausdorff dimension becomes
additive for such sets in the presence of freeness.


  Plasmonic interferometry is a rapidly growing area of research with a huge
potential for applications in terahertz frequency range. In this Letter, we
explore a plasmonic interferometer based on graphene Field Effect Transistor
connected to specially designed antennas. As a key result, we observe helicity-
and phase-sensitive conversion of circularly-polarized radiation into dc
photovoltage caused by the plasmon-interference mechanism: two plasma waves,
excited at the source and drain part of the transistor interfere inside the
channel. The helicity sensitive phase shift between these waves is achieved by
using an asymmetric antenna configuration. The dc signal changes sign with
inversion of the helicity. Suggested plasmonic interferometer is capable for
measuring of phase difference between two arbitrary phase-shifted optical
signals. The observed effect opens a wide avenue for phase-sensisitve probing
of plasma wave excitations in two-dimensional materials.


  We consider some special type extensions of an arbitrary Lie algebra ${\cal
G}$, arising in the theory of Lie-Poisson structures over $({\cal G}^*)^n$,
where ${\cal G}^*$ is the dual of ${\cal G}$. We show that some classes of
these extensions can be constructed in a natural way using some linear bundles
of Lie algebras.


  Maritime transport is a pivotal logistics mode for the long-distance and bulk
transportation of goods. However, the intricate planning involved in this mode
is often hindered by uncertainties, including weather conditions, cargo
diversity, and port dynamics, leading to increased costs. Consequently,
accurately estimating vessel total (stay) time at port and potential delays
becomes imperative for effective planning and scheduling in port operations.
This study aims to develop a port operation solution with competitive
prediction and classification capabilities for estimating vessel Total and
Delay times. This research addresses a significant gap in port analysis models
for vessel Stay and Delay times, offering a valuable contribution to the field
of maritime logistics. The proposed solution is designed to assist
decision-making in port environments and predict service delays. This is
demonstrated through a case study on Brazil ports. Additionally, feature
analysis is used to understand the key factors impacting maritime logistics,
enhancing the overall understanding of the complexities involved in port
operations.


  A precise calculation that translates shifts of X-ray K-absorption edges to
variations of thermodynamic properties allows quantitative characterization of
interior thermodynamic properties of warm dense plasmas by X-ray absorption
techniques, which provides essential information for inertial confinement
fusion and other astrophysical applications. We show that this interpretation
can be achieved through an improved first-principles method. Our calculation
shows that the shift of K-edges exhibits selective sensitivity to thermal
parameters and thus would be a suitable temperature index to warm dense
plasmas. We also show with a simple model that the shift of K-edges can be used
to detect inhomogeneity inside warm dense plasmas when combined with other
experimental tools.


  Our consumption of online information is mediated by filtering, ranking, and
recommendation algorithms that introduce unintentional biases as they attempt
to deliver relevant and engaging content. It has been suggested that our
reliance on online technologies such as search engines and social media may
limit exposure to diverse points of view and make us vulnerable to manipulation
by disinformation. In this paper, we mine a massive dataset of Web traffic to
quantify two kinds of bias: (i) homogeneity bias, which is the tendency to
consume content from a narrow set of information sources, and (ii) popularity
bias, which is the selective exposure to content from top sites. Our analysis
reveals different bias levels across several widely used Web platforms. Search
exposes users to a diverse set of sources, while social media traffic tends to
exhibit high popularity and homogeneity bias. When we focus our analysis on
traffic to news sites, we find higher levels of popularity bias, with smaller
differences across applications. Overall, our results quantify the extent to
which our choices of online systems confine us inside "social bubbles."


  We study the universal logarithmic coefficient of the entanglement entropy
(EE) in a sphere for free fermionic field theories in a $d=4$ Minkowski
spacetime. As a warm-up, we revisit the free massless spin-$1/2$ field case by
employing a dimensional reduction to the $d=2$ half-line and a subsequent
numerical real-time computation on a lattice. Surprisingly, the area
coefficient diverges for a radial discretization but is finite for a geometric
regularization induced by the mutual information. The resultant universal
logarithmic coefficient $-11/90$ is consistent with the literature. For the
free massless spin-$3/2$ field, the Rarita-Schwinger field, we also perform a
dimensional reduction to the half-line. The reduced Hamiltonian coincides with
the spin-$1/2$ one, except for the omission of the lowest total angular
momentum modes. This gives a universal logarithmic coefficient of $-71/90$. We
discuss the physical interpretation of the universal logarithmic coefficient
for free higher spin field theories without a stress-energy tensor.


  Given any nondegenerate k-dimensional minimal submanifold K of codimension
greater than 1, we prove the existence of families of constant mean curvature
submanifolds, with mean curvature varying from one member of the family to
another, which `condense' to K. In particular, our result proves the existence
of constant mean curvature hypersurfaces with nontrivial topology in any
Riemannian manifold.


  Double Bruhat cells in a semisimple group are intersections of cells in two
Bruhat decompositions corresponding to two opposite Borel subgroups. They form
a geometric framework for the study of total positivity in semisimple groups;
they are also closely related to symplectic leaves in the corresponding
Poisson-Lie groups. The term "cells" might be misleading because their topology
can be quite non-trivial. As a first step towards understanding this topology,
we enumerate the connected components of real double Bruhat cells. This result
extends (from the simply-laced case to the general one) and proves the
conjecture made in a joint work with B.Shapiro-M.Shapiro-A.Vainshtein; it also
extends earlier work by B.Shapiro-M.Shapiro-A.Vainshtein and K.Rietsch.


  Although binary classification is a well-studied problem in computer vision,
training reliable classifiers under severe class imbalance remains a
challenging problem. Recent work has proposed techniques that mitigate the
effects of training under imbalance by modifying the loss functions or
optimization methods. While this work has led to significant improvements in
the overall accuracy in the multi-class case, we observe that slight changes in
hyperparameter values of these methods can result in highly variable
performance in terms of Receiver Operating Characteristic (ROC) curves on
binary problems with severe imbalance. To reduce the sensitivity to
hyperparameter choices and train more general models, we propose training over
a family of loss functions, instead of a single loss function. We develop a
method for applying Loss Conditional Training (LCT) to an imbalanced
classification problem. Extensive experiment results, on both CIFAR and Kaggle
competition datasets, show that our method improves model performance and is
more robust to hyperparameter choices. Code is available at
https://github.com/klieberman/roc_lct.


  A generalized complex manifold which satisfies the $\partial
\overline{\partial}$-lemma admits a Hodge decomposition in twisted cohomology.
Using a Courant algebroid theoretic approach we study the behavior of the Hodge
decomposition in smooth and holomorphic families of generalized complex
manifolds. In particular we define period maps, prove a Griffiths
transversality theorem and show that for holomorphic families the period maps
are holomorphic. Further results on the Hodge decomposition for various special
cases including the generalized K\"ahler case are obtained.


  Gauge theories are formulated on the noncommutative two-sphere. These
theories have only finite number of degrees of freedom, nevertheless they
exhibit both the gauge symmetry and the SU(2) "Poincar\'e" symmetry of the
sphere. In particular, the coupling of gauge fields to chiral fermions is
naturally achieved.


  A set of oxide and chalcogenide tetrahedral glasses are investigated using
molecular dynamics simulations. It is shown that unlike stoichiometric
selenides such as GeSe$_2$ and SiSe$_2$, germania and silica display large
standard deviations in the associated bond angle distributions. Within
bond-bending constraints theory, this pattern can be interpreted as a
manifestation of {\it {broken}} (i.e. ineffective) oxygen bond-bending
constraints. The same analysis reveals that the changes in the Ge composition
affects mostly bending around germanium in binary Ge-Se systems, leaving
Se-centred bending almost unchanged. In contrast, the corresponding Se twisting
(quantified by the dihedral angle) depends on the Ge composition and is reduced
when the system becomes rigid. Our results establishes the atomic-scale
foundations of the phenomelogical rigidity theory, thereby profoundly extending
its significance and impact on the structural description of network glasses.


  A strong isoscalar dipole resonance is known to be excited in a variety of
nuclei, including isospin symmetric ones, at approximately 6-7 MeV. A series of
theoretical studies and accumulating experimental evidence support an
interpretation of the above dipole resonance as an elementary surface
vibration. Obviously, such a mode is potentially as interesting as any
collective excitation for a variety of reasons. In addition, though, it is
found to account for the observed isoscalar segment of pygmy dipole strength.
As discussed here, this has important implications for pygmy-strength
interpretations and searches for genuine neutron-skin oscillations.


  We propose a model of dark matter identified with a pseudo-Nambu-Goldstone
boson in the dynamical supersymmetry breaking sector in a gauge mediation
scenario. The dark matter particles annihilate via a below-threshold narrow
resonance into a pair of R-axions each of which subsequently decays into a pair
of light leptons. The Breit-Wigner enhancement explains the excess electron and
positron fluxes reported in the recent cosmic ray experiments PAMELA, ATIC and
PPB-BETS without postulating an overdensity in halo, and the limit on
anti-proton flux from PAMELA is naturally evaded.


  Taking a photo outside, can we predict the immediate future, e.g., how would
the cloud move in the sky? We address this problem by presenting a generative
adversarial network (GAN) based two-stage approach to generating realistic
time-lapse videos of high resolution. Given the first frame, our model learns
to generate long-term future frames. The first stage generates videos of
realistic contents for each frame. The second stage refines the generated video
from the first stage by enforcing it to be closer to real videos with regard to
motion dynamics. To further encourage vivid motion in the final generated
video, Gram matrix is employed to model the motion more precisely. We build a
large scale time-lapse dataset, and test our approach on this new dataset.
Using our model, we are able to generate realistic videos of up to $128\times
128$ resolution for 32 frames. Quantitative and qualitative experiment results
have demonstrated the superiority of our model over the state-of-the-art
models.


  Disorder and doping have profound effects on the intrinsic physical
mechanisms of superconductivity. In this paper, we employed the determinant
quantum Monte Carlo method to investigate the symmetry-allowed superconducting
orders on the two-dimensional honeycomb lattice within the Hubbard model, using
doped graphene as the carrier, focusing their response to bond disorder.
Specifically, we calculated the pairing susceptibility and effective pairing
interactions for the $d+id$ wave and extended $s$-wave pairings for different
electron densities and disorder strengths. Our calculations show that at high
electron densities, increased disorder strength may lead to a transform from
$d+id$ wave dominance to extended $s$ wave dominance. However, at lower
electron densities, neither of the two superconducting pairings appears under
larger disorder strength. Our calculations may contribute to a further
understanding of the superconducting behavior in doped materials affected by
disorder.


  It is proposed that an ultra-light fermionic species, dubbed cosmic magnino
has condensed into a ferromagnetic state in the Universe. The extended
structure of domain walls associated with this ferromagnetism accounts for the
observed Dark Energy. In modification of the situation with an electron gas, it
is proposed that the Stoner criterion is satisfied due to magnetic dipolar
repulsion. The cosmological requirements then yeild a lower bound on the
magnetic moment of the cosmic magnino. The proposed magnetism is supposed to be
associated with a new non-standard electromagnetism. If the magnino is also
electrically charged under this electromagnetism, the corresponding oppositely
charged heavier species would account partially or entirely for the Dark Matter
in the Universe.


  We develop a new formalism to study the dynamics of fluid polytropes in three
dimensions. The stars are modeled as compressible ellipsoids and the
hydrodynamic equations are reduced to a set of ordinary differential equations
for the evolution of the principal axes and other global quantities. Both
viscous dissipation and the gravitational radiation reaction are incorporated.
We establish the validity of our approximations and demonstrate the simplicity
and power of the method by rederiving a number of known results concerning the
stability and dynamical oscillations of rapidly rotating polytropes. In
particular, we present a generalization to compressible fluids of
Chandrasekhar's classical results for the secular and dynamical instabilities
of incompressible Maclaurin spheroids. We also present several applications of
our method to astrophysical problems of great current interest such as the
tidal disruption of a star by a massive black hole, the coalescence of compact
binaries driven by the emission of gravitational waves, and the development of
instabilities in close binary systems.


  In the present communication we consider the one-dimensional (1D)
isotopically disordered lattice with the harmonic potential. Our analytical
method is adequate for any 1D lattice where potential energy can be presented
as the quadratic form $U=\frac12 \sum_{i,j} q(i) U_{ij} q(j)$, where $q(i)$ --
coordinate or velocity of $i$-th particle. There are derived the closed system
of equations for the temporal behavior of the correlation functions. The final
expressions allow to calculate the kinetics and dynamics of the system --
energy, temperature profile, thermal conduction and others. There is developed
the method for the calculation of the evolution of the eigenvalues
(frequencies) and eigenvectors (relaxation times) to their stationary values.
Exact results are obtained for times $\simeq 10^{14}$. The methods are
suggested allowing to extend the range of the relaxation times upto $\simeq
10^{28}$. The spectrum of relaxation times reaches it constant value starting
from the number of particles $N$ in the lattice $N \geq 300$. Thermal
conductance $\kappa$ has the non-monotonic character: for the number of
particles $N < 300$ $ \kappa$ increases as $\kappa \simeq 2.4 \lg N$, reaches
the maximum value equal $\simeq 4.0$ at $N \simeq 300$ and then slowly
decreases upto $N = 700$. The stationary state is unique and satisfies the
Gibbs distribution. An excellent agreement between numerical simulations and
analytical results is obtained where possible.


  Certifying quantum properties with minimal assumptions is a fundamental
problem in quantum information science. Self-testing is a method to infer the
underlying physics of a quantum experiment only from the measured statistics.
While all bipartite pure entangled states can be self-tested, little is known
about how to self-test quantum states of an arbitrary number of systems. Here,
we introduce a framework for network-assisted self-testing and use it to
self-test any pure entangled quantum state of an arbitrary number of systems.
The scheme requires the preparation of a number of singlets that scales
linearly with the number of systems, and the implementation of standard
projective and Bell measurements, all feasible with current technology. When
all the network constraints are exploited, the obtained self-testing
certification is stronger than what is achievable in any Bell-type scenario.
Our work does not only solve an open question in the field, but also shows how
properly designed networks offer new opportunities for the certification of
quantum phenomena.


  We consider a fractional Schr\"{o}dinger-Poisson system with a general
nonlinearity in subcritical and critical case. The Ambrosetti-Rabinowitz
condition is not required. By using a perturbation approach, we prove the
existence of positive solutions. Moreover, we study the asymptotics of
solutions for a vanishing parameter.


  In this note, we study the mean length of the longest increasing subsequence
of a uniformly sampled involution that avoids the pattern $3412$ and another
pattern.


  We describe the properties of a system of red arcs discovered at z=4.04
around the cluster A2390 ($z=0.23$). These arcs are images of a single galaxy,
where the lensing is compounded by an elliptical cluster member lying close to
the critical curve of the cluster. The combined magnification is estimated to
be $\sim 20$, using HST images, depending the gradient of the model potentials,
implying an unlensed magnitude for the source of $I_{AB}=25.5$. Keck
spectroscopy reveals a continuum well fitted by B-stars and attenuated by the
Lyman-series forest with an opacity consistent with z$\sim$4 QSO spectra,
making the arcs relatively red. Damped Ly$\alpha$ absorption is observed at the
source redshift with a relatively high column, n$_{HI}=3\times 10^{21}$.
Curiously, Ly$\alpha$ emission is spatially separated ($\sim 0.5$kpc) from the
bright stellar continuum and lies $\sim$ 300Km/s redward of interstellar
absorption lines at z=4.04. Similar redwardl of young galaxies. Finally, we
briefly comment on the notorious ``straight arc'' in A2390, which is resolved
into two unrelated galaxies at z=0.913 and z=1.033.


  We investigate the electrical control of the exchange coupling (J) between
donor bound electrons in silicon with a detuning gate bias, crucial for the
implementation of the two-qubit gate in a silicon quantum computer. We find the
asymmetric 2P-1P system provides a highly tunable exchange-curve with mitigated
J-oscillation, in which 5 orders of magnitude change in the exchange energy can
be achieved using a modest range of electric field for 15 nm qubit separation.
Compared to the barrier gate control of exchange in the Kane qubit, the
detuning gate design reduces the demanding constraints of precise donor
separation, gate width, density and location, as a range of J spanning over a
few orders of magnitude can be engineered for various donor separations. We
have combined a large-scale full band atomistic tight-binding method with a
full configuration interaction technique to capture the full two-electron
spectrum of gated donors, providing state-of-the-art calculations of exchange
energy in 1P-1P and 2P-1P qubits.


  Persistent Homology (PH) has been successfully used to train networks to
detect curvilinear structures and to improve the topological quality of their
results. However, existing methods are very global and ignore the location of
topological features. In this paper, we remedy this by introducing a new
filtration function that fuses two earlier approaches: thresholding-based
filtration, previously used to train deep networks to segment medical images,
and filtration with height functions, typically used to compare 2D and 3D
shapes. We experimentally demonstrate that deep networks trained using our
PH-based loss function yield reconstructions of road networks and neuronal
processes that reflect ground-truth connectivity better than networks trained
with existing loss functions based on PH. Code is available at
https://github.com/doruk-oner/PH-TopoLoss.


  The amplitude of fluctuation-induced patterns might be expected to be
proportional to the strength of the driving noise, suggesting that such
patterns would be difficult to observe in nature. Here, we show that a large
class of spatially-extended dynamical systems driven by intrinsic noise can
exhibit giant amplification, yielding patterns whose amplitude is comparable to
that of deterministic Turing instabilities. The giant amplification results
from the interplay between noise and non-orthogonal eigenvectors of the linear
stability matrix, yielding transients that grow with time, and which, when
driven by the ever-present intrinsic noise, lead to persistent large amplitude
patterns. This mechanism provides a robust basis for fluctuation-induced
biological pattern formation based on the Turing mechanism, without requiring
fine tuning of diffusion constants.


  We propose that the first stage of membrane fusion need not be the formation
of a single stalk. Instead, we consider a scenario for defect-induced membrane
fusion that proceeds cooperatively via multiple stalk formation. The defects
(stalks or pores) attract each other via membrane-mediated capillary
interactions that result in a condensation transition of the defects. The
resulting dense phase of stalks corresponds to the so-called fusion
intermediate.


  Models of loop quantum gravity based on real connections have a deformed
notion of general covariance, which leads to the phenomenon of signature
change. This result is confirmed here in a general analysis of all
midisuperspace models without local degrees of freedom. As a subclass of
models, 2-dimensional theories of dilaton gravity appear, but a larger set of
examples is possible based only on the condition of anomaly freedom. While the
classical dilaton gravity models are the only such systems without deformed
covariance, they do give rise to signature change when holonomy modifications
are included.


  This paper proposes a classification framework with a rejection option to
mitigate the performance deterioration caused by adversarial examples. While
recent machine learning algorithms achieve high prediction performance, they
are empirically vulnerable to adversarial examples, which are slightly
perturbed data samples that are wrongly classified. In real-world applications,
adversarial attacks using such adversarial examples could cause serious
problems. To this end, various methods are proposed to obtain a classifier that
is robust against adversarial examples. Adversarial training is one of them,
which trains a classifier to minimize the worst-case loss under adversarial
attacks. In this paper, in order to acquire a more reliable classifier against
adversarial attacks, we propose the method of Adversarial Training with a
Rejection Option (ATRO). Applying the adversarial training objective to both a
classifier and a rejection function simultaneously, classifiers trained by ATRO
can choose to abstain from classification when it has insufficient confidence
to classify a test data point. We examine the feasibility of the framework
using the surrogate maximum hinge loss and establish a generalization bound for
linear models. Furthermore, we empirically confirmed the effectiveness of ATRO
using various models and real-world datasets.


  We study the origin of the universe (or pre-inflation) by suggesting that the
primordial space-time in the universe suffered a global topological phase
transition, from a 4D Euclidean manifold to an asymptotic 4D hyperbolic one. We
introduce a complex time, $\tau$, such that its real part becomes dominant
after started the topological phase transition. Before the big bang, $\tau$ is
a space-like coordinate, so that can be considered as a reversal variable.
After the phase transition is converted in a causal variable. The formalism
solves in a natural manner the quantum to classical transition of the
geometrical relativistic quantum fluctuations: $\sigma$, which has a geometric
origin.


  A novel supersolid phase is predicted for an ensemble of Rydberg atoms in the
dipole-blockade regime, interacting via a repulsive dipolar potential
"softened" at short distances. Using exact numerical techniques, we study the
low temperature phase diagram of this system, and observe an intriguing phase
consisting of a crystal of mesoscopic superfluid droplets. At low temperature,
phase coherence throughout the whole system, and the ensuing bulk
superfluidity, are established through tunnelling of identical particles
between neighbouring droplets.


  The fast extraction kicker system is one of the most important accelerator
components, whose inner structure will be the main source of the impedance in
the RCS. It is necessary to understand the kicker impedance before its
installation into the tunnel. The conventional and improved wire methods are
employed for the benchmarking impedance measurement results. The simulation and
measurements confirm that the window-frame ferrite geometry and the end plate
are the important structures causing the coupling impedance. The total
impedance of the eight modules systems is determined by the scaling law from
the measurement and the impedance measurement of the kicker system is
summarized.


  We study domain-walls and bubble nucleation in a non-relativistic vector
field theory with different longitudinal and transverse speeds of sound. We
describe analytical and numerical methods to calculate the orientation
dependent domain-wall tension, $\sigma(\theta)$. We then use this tension to
calculate the critical bubble shape. The longitudinally oriented domain-wall
tends to be the heaviest, and sometime suffers an instability. It can
spontaneously break into zigzag segments. In this case, the critical bubble
develops kinks, and its energy, and therefore the tunneling rate, scales with
the sound speeds very differently than what would be expected for a smooth
bubble.


  This paper presents two first-principles calculations on the lattice- and
electronic- structures of a small-diameter infinite and truncated ZnO nanowire.
The two calculations show excellent agreement with each other. For the small
diameter nanowire, the lattice and electronic properties are determined by the
relaxed surface. We find a similarity between the nanowire surface and the
surface of the bulk material, and discuss the assignment of the rotational
quantum number m to the bands.


  Fluorescent proteins often result in phototoxicity and cytotoxicity, in
particular because some red fluorescent proteins (RFP) produce and release
reactive oxygen species (ROS). The photogeneration of ROS is considered as a
detrimental side effect in cellular imaging or is proactively utilized for
ablating cancerous tissue. As ancient textiles or biomaterials, silk produced
by silkworms can directly be used as fabrics or be processed into materials and
structures to host other functional nanomaterials. We report that transgenic
fusion of far-red fluorescent protein (mKate2) with silk provides a
photosensitizer hybridization platform for photoinducible control of ROS.
Taking advantage of green (visible) light activation, native and regenerated
mKate2 silk can produce and release superoxide and singlet oxygen, in a
comparable manner of visible light-driven plasmonic photocatalysis. Thus, the
genetic expression of mKate2 in silk offers immediately exploitable and
scalable photocatalyst-like biomaterials. We further envision that mKate2 silk
could potentially rule out hazardous concerns associated with foreign
semiconductor photocatalytic nanomaterials.


  We show that an independent four-body momentum scale $\mu_{(4)}$ drives the
tetramer binding energy for fixed trimer energy (or three-body scale
$\mu_{(3)}$) and large scattering length ($a$). The three- and four-body forces
from the one-channel reduction of the atomic interaction near a Feshbach
resonance disentangle $\mu_{(4)}$ and $\mu_{(3)}$. The four-body independent
scale is also manifested through a family of Tjon-lines, with slope given by
$\mu_{(4)}/\mu_{(3)}$ for $a^{-1}=0$. There is the possibility of a new
renormalization group limit cycle due to the new scale.


  Rare decays B_{s,d}-->mu^+ mu^- are evaluated in technicolor model with
scalars. R_b is revisited to constrain the model parameter space. It is found
that restriction on f/f' arising from R_b which was not considered in previous
studies requires f/f' no larger than 1.9 at 95% confidence level, implying no
significantly enhancement for Br(B_{s,d}-->mu^+\mu^-) from neutral scalars in
the model. However, the branching ratio of B_s--> mu^+ mu^- can still be
enhanced by a factor of 5 relative to the standard model prediction. With the
value of f/f' about 1.9, an upgraded Tevatron with an integrated luminosity
20fb^-1 will be sensitive to enhancement of B_s-->mu^+ mu^- in this model
provided that neutral scalar mass m_sigma is below 580 GeV.


  We discuss measures, invariant measures on definable groups, and genericity,
often in an NIP (failure of the independence property) environment. We complete
the proof of the third author's conjectures relating definably compact groups
$G$ in saturated $o$-minimal structures to compact Lie groups. We also prove
some other structural results about such $G$, for example the existence of a
left invariant finitely additive probability measure on definable subsets of
$G$. We finally introduce a new notion "compact domination" (domination of a
definable set by a compact space) and raise some new conjectures in the
$o$-minimal case.


  This paper introduces a micro-lattice based metamaterial for low frequency
wide-band vibration attenuation, that is enabled by engineering the
metamaterial's building blocks to induce local resonance bandgaps for elastic
waves in all directions of propagation. The transmission rate through the
proposed structure is examined and strong wave attenuation is demonstrated for
a remarkably small number of unit cells. Additionally, it is shown that the
bandgaps are tailorable via the geometrical parameters and can be leveraged to
design a hybrid metamaterial with an extremely wide bandgap. Alongside being
thin, lightweight, and capable of attenuating elastic waves in all directions,
the proposed material also possesses the second order functionality of
exhibiting a negative Poisson's ratio and can pave the way for identifying
exotic functional materials.


  Searching for new non-perturbatively renormalizable quantum gravity theories,
functional renormalization group (RG) flows are studied on a theory space of
action functionals depending on the metric and the torsion tensor, the latter
parameterized by three irreducible component fields. A detailed comparison with
Quantum Einstein-Cartan Gravity (QECG), Quantum Einstein Gravity (QEG), and
"tetrad-only" gravity, all based on different theory spaces, is performed. It
is demonstrated that, over a generic theory space, the construction of a
functional RG equation (FRGE) for the effective average action requires the
specification of a metric on the infinite-dimensional field manifold as an
additional input. A modified FRGE is obtained if this metric is
scale-dependent, as it happens in the metric-torsion system considered.


  We report linear polarization measurements of x rays emitted due to
dielectronic recombination into highly charged krypton ions. The ions in the
He-like through O-like charge states were populated in an electron beam ion
trap with the electron beam energy adjusted to recombination resonances in
order to produce $K\alpha$ x rays. The x rays were detected with a newly
developed Compton polarimeter using a beryllium scattering target and 12
silicon x-ray detector diodes sampling the azimuthal distribution of the
scattered x rays. The extracted degrees of linear polarization of several
dielectronic recombination transitions agree with results of relativistic
distorted--wave calculations. We also demonstrate a high sensitivity of the
polarization to the Breit interaction, which is remarkable for a medium-$Z$
element like krypton. The experimental results can be used for polarization
diagnostics of hot astrophysical and laboratory fusion plasmas.


  It was proposed by Ryu and Takayanagi that the entanglement entropy in
conformal field theory (CFT) is related through the AdS/CFT correspondence to
the area of a minimal surface in the bulk. We apply this holographic
geometrical method of calculating the entanglement entropy to study the vacuum
case of a CFT which is holographically dual to empty anti-de Sitter (AdS)
spacetime. We present all possible minimal surfaces spanned on one or two
spherical boundaries at AdS infinity. We give exact analytical expressions for
the regularized areas of these surfaces and identify finite renormalized
quantities. In the case of two disjoint boundaries the existence of two
different phases of the entanglement entropy is confirmed. A trivial phase
corresponds to two disconnected minimal surfaces, while the other one
corresponds to a tube connecting the spherical boundaries. A transition between
these phases is reminiscent of the finite temperature deconfinement transition
in the CFT on the boundary. The exact analytical results are thus consistent
with previous numerical and approximate computations. We also briefly discuss
the character of a spacetime extension of the minimal surface spanned on two
uniformly accelerated boundaries.


  We present an analysis of an 8 arcminute diameter map of the area around the
galaxy cluster Abell 1835 from jiggle map observations at a wavelength of 1.1
mm using the Bolometric Camera (Bolocam) mounted on the Caltech Submillimeter
Observatory (CSO). The data is well described by a model including an extended
Sunyaev-Zel'dovich (SZ) signal from the cluster gas plus emission from two
bright background submm galaxies magnified by the gravitational lensing of the
cluster. The best-fit values for the central Compton value for the cluster and
the fluxes of the two main point sources in the field: SMM J140104+0252, and
SMM J14009+0252 are found to be $y_{0}=(4.34\pm0.52\pm0.69)\times10^{-4}$,
6.5$\pm{2.0}\pm0.7$ mJy and 11.3$\pm{1.9}\pm1.1$ mJy, where the first error
represents the statistical measurement error and the second error represents
the estimated systematic error in the result. This measurement assumes the
presence of dust emission from the cluster's central cD galaxy of $1.8\pm0.5$
mJy, based on higher frequency observations of Abell 1835. The cluster image
represents one of the highest-significance SZ detections of a cluster in the
positive region of the thermal SZ spectrum to date. The inferred central
intensity is compared to other SZ measurements of Abell 1835 and this
collection of results is used to obtain values for $y_{0} =
(3.60\pm0.24)\times10^{-4}$ and the cluster peculiar velocity $v_{z} =
-226\pm275$ km/s.


  Majorana Kramers pairs emerged on surfaces of time-reversal-invariant
topological crystalline superconductors show the Ising anisotropy to an applied
magnetic field. We clarify that crystalline symmetry uniquely determines the
direction of the Majorana Ising spin for given irreducible representations of
pair potential, deriving constraints to topological invariants. Besides,
necessary conditions for nontrivial topological invariants protected by the
n-fold rotational symmetry are shown.


  The paper deals with on-line regression settings with signals belonging to a
Banach lattice. Our algorithms work in a semi-online setting where all the
inputs are known in advance and outcomes are unknown and given step by step. We
apply the Aggregating Algorithm to construct a prediction method whose
cumulative loss over all the input vectors is comparable with the cumulative
loss of any linear functional on the Banach lattice. As a by-product we get an
algorithm that takes signals from an arbitrary domain. Its cumulative loss is
comparable with the cumulative loss of any predictor function from Besov and
Triebel-Lizorkin spaces. We describe several applications of our setting.


  Radar signal deinterleaving is an important part of electronic
reconnaissance. This study proposes a new radar signal deinterleaving method
based on semantic segmentation, which we call "semantic segmentation
deinterleaving" (SSD). We select representative sequence modeling neural
network (NN) architectures and input the difference of time of arrival of the
pulse stream into them. According to semantics contained in different radar
signal types, each pulse in the pulse stream is marked according to the
category of semantics contained, and radar signals are deinterleaved. Compared
to the traditional deinterleaving method, the SSD method can adapt to complex
pulse repetition interval (PRI) modulation environments without searching the
PRI or PRI period. Multiple rounds of search and merging operation are not
required for radar signals with multiple pulses in a period. Compared to other
deinterleaving methods based on NNs, the SSD method does not need to digitize
the data and train a network for each target type. The SSD method also does not
need to iterate input and output data. The proposed method has high robustness
to pulse loss and noise pulses. This research also shows that recurrent NNs
still have more advantages than convolutional NNs in this sequence modeling
task.


  We calculate a temperature dependent part of the one-loop thermodynamic
potential (and the free energy) for charged massive fields in a general class
of irreducible rank 1 symmetric spaces. Both low- and high-temperature
expansions are derived and the role of non-trivial topology influence on
asymptotic properties of the potential is discussed.


  The multi-order Raman scattering is studied up to a fourth order for a
detwinned LaMnO_3 crystal. Based on a comprehensive data analysis of the
polarisation-dependent Raman spectra, we show that the anomalous features in
the multi-order scattering could be the sidebands on the low-energy mode at
about 25 cm-1. We suggest that this low-energy mode stems from the tunneling
transition between the potential energy minima arising near the Jahn-Teller
Mn3+ ion due to the lattice anharmonicity, and the multi-order scattering is
activated by this low-energy electronic motion. The sidebands are dominated by
the oxygen contribution to the phonon density-of-states, however, there is an
admixture of an additional component, which may arise from coupling between the
low-energy electronic motion and the vibrational modes.


  Atoms with different internal states can exhibit different responses to an
artificial magnetic field. An atomic gas mixture of two different components
can therefore be interpreted as a mixture of two atomic gases carrying
different synthetic charges. We consider the superfluid state of such unequally
charged Fermi gases coupled to a magnetic field via the orbital effect and
trapped in a torus geometry. The orbital coupling to the magnetic field favors
an inhomogeneous superfluid state with optimum finite center-of-mass momentum
pairing. The resulting population-balanced orbital Fulde-Ferrell (FF) state is
robust against the magnetic field and does not undergo pair breaking unlike the
conventional BCS and Fulde-Ferrell-Larkin-Ovchinnikov type pairing states under
the Zeeman effect. We contrast the homogeneous and inhomogeneous cases
emphasizing the advantages of the unequally charged systems and present their
momentum distributions. We conclude that an unequally charged atomic Fermi gas
system orbitally coupled to an artificial magnetic field provides an ideal
candidate for experimental realization of the FF state.


  We determine explicitly a boundary triple for the Dirac operator
$H:=-i\alpha\cdot \nabla + m\beta + \mathbb V(x)$ in $\mathbb R^3$, for
$m\in\mathbb R$ and $\mathbb V(x)= |x|^{-1} ( \nu \mathbb{I}_4 +\mu \beta -i
\lambda \alpha\cdot{x}/|x|\,\beta)$, with $\nu,\mu,\lambda \in \mathbb R$.
Consequently we determine all the self-adjoint realizations of $H$ in terms of
the behaviour of the functions of their domain in the origin. When $\sup_{x}
|x||\mathbb V(x)| \leq 1$, we discuss the problem of selecting the
distinguished extension requiring that its domain is included in the domain of
the appropriate quadratic form.


  Weak-lined T Tauri stars (WTTS) represent the important stage of stellar
evolution between the accretion phase and the zero-age main sequence. At this
stage, the star decouples from its accretion disk, and spins up to a higher
rotation rate than in the preceding classical T Tauri phase. Consequently,
dynamo processes can be expected to become even stronger at this stage. High
energy processes can have effects on the remaining circumstellar material,
possibly including protoplanets and planetesimals, and these effects may
account for certain observable properties of asteroids in the current solar
system. Chandra observed for 100 ks the WTTS HDE 283572 which probes the PMS
stage of massive A-type stars. We present first results of the analysis of its
high-resolution X-ray spectrum obtained with the High-Energy Transmission
Grating Spectrometer. A wide range of Fe lines of high ionization states are
observed, indicating a continuous emission measure distribution. No significant
signal is detected longward of the O \textsc{viii} Ly$\alpha$ line because of
the high photoelectric absorption. We also report on the preliminary analysis
of the zeroth order spectra of RY Tau and LkCa21. In particular, we show
evidence of an emission line in RY Tau at 6.4 keV that we identify as
fluorescent emission by neutral Fe caused by a strong X-ray flare which
illuminated some structure in (or surrounding) the CTTS. A comparison of X-ray
spectra of classical T Tau stars, other WTTS, and young main-sequence stars is
made.


  In conventional quantum critical point (QCP) characterized by order parameter
fluctuations, the celebrated Kibble-Zurek mechanism (KZM) and finite-time
scaling (FTS) theory provide universal descriptions of the driven critical
dynamics. However, in strongly correlated fermionic systems where gapless
fermions are usually present in vicinity of QCP, the driven dynamics has rarely
been explored. In this Letter, we investigate the driven critical dynamics in
two-dimensional Dirac systems, which harbor semimetal and Mott insulator phases
separated by the QCP triggered by the interplay between fluctuations of gapless
Dirac fermions and order-parameter bosons. By studying the evolution of
physical quantities for different driving rates through large-scale quantum
Monte Carlo simulation, we confirm that the driven dynamics is described by the
FTS form. Accordingly, our results significantly generalize the KZM theory by
relaxing its requirement for a gapped initial state to the system accommodating
gapless Dirac fermionic excitation. Through successfully extending the KZM and
FTS theory to Dirac QCP, our work not only brings new fundamental perspective
into the nonequilibrium critical dynamics, but also provides a novel
theoretical approach to fathom quantum critical properties in fermionic
systems.


  In materials chiral fermions such as Weyl fermions are characterized by
nonzero chiral charges, which are singular points of Berry curvature in
momentum space. Recently, new types of chiral fermions beyond Weyl fermions
have been discovered in structurally chiral crystals CoSi, RhSi and PtAl. Here,
we have synthesized RhSn single crystals, which have opposite structural
chirality to the CoSi crystals we previously studied. Using angle-resolved
photoemission spectroscopy, we show that the bulk electronic structures of RhSn
are consistent with the band calculations and observe evident surface Fermi
arcs and helical surface bands, confirming the existence of chiral fermions in
RhSn. It is noteworthy that the helical surface bands of the RhSn and CoSi
crystals have opposite handedness, meaning that the chiral fermions are
reversed in the crystals of opposite structural chirality. Our discovery
establishes a direct connection between chiral fermions in momentum space and
chiral lattices in real space.


  News recommendation is different from movie or e-commercial recommendation as
people usually do not grade the news. Therefore, user feedback for news is
always implicit (click behavior, reading time, etc). Inevitably, there are
noises in implicit feedback. On one hand, the user may exit immediately after
clicking the news as he dislikes the news content, leaving the noise in his
positive implicit feedback; on the other hand, the user may be recommended
multiple interesting news at the same time and only click one of them,
producing the noise in his negative implicit feedback. Opposite implicit
feedback could construct more integrated user preferences and help each other
to minimize the noise influence. Previous works on news recommendation only
used positive implicit feedback and suffered from the noise impact. In this
paper, we propose a denoising neural network for news recommendation with
positive and negative implicit feedback, named DRPN. DRPN utilizes both
feedback for recommendation with a module to denoise both positive and negative
implicit feedback to further enhance the performance. Experiments on the
real-world large-scale dataset demonstrate the state-of-the-art performance of
DRPN.


  We propose and numerically demonstrate an efficient cleaning of spatial
structure (spatial filtering) of sound beams by propagating them through at
least twodimensional sonic crystals, i.e. through acoustic structures
periodically modulated in longitudinal and in transversal direction with
respect to the sound propagation direction. We show the spatial filtering in
two configurations: with- and without the angular band-gap. We also show that
besides the spatial filtering the beams can be additionally focalized at a
particular distance behind the sonic crystal in both configurations.


  In this paper, we first review one of difficult parts of the proof of
Witten's conjecture by Kontsevich that had not been emphasized before. In the
derivation of the KdV equations, we review the boson-fermion correspondence
method \cite{K} to show that the trajectory of $\rm GL_\infty$ action on 1 as
an element of the ring $\mathbb{C}[x_1,x_2,...]$ yields the solutions of KP
hierarchies. Then we consider the corresponding theory in which the target
manifold is a K\"{a}hler manifold. We conjecture that this nonlinear sigma
model is equivalent to a "planar graph" theory. Assuming the conjecture holds,
we are able to get the Virasoro constraints in the Virasoro conjecture.


  In this paper we present nonparametric estimators for coefficients in
stochastic differential equation if the data are described by independent,
identically distributed random variables. The problem is formulated as a
nonlinear ill-posed operator equation with a deterministic forward operator
described by the Fokker-Planck equation. We derive convergence rates of the
risk for penalized maximum likelihood estimators with convex penalty terms and
for Newton-type methods. The assumptions of our general convergence results are
verified for estimation of the drift coefficient. The advantages of
log-likelihood compared to quadratic data fidelity terms are demonstrated in
Monte-Carlo simulations.


  This work leverages the U.S. Federal Aviation Administration's Traffic Flow
Management System dataset and DV8, a recently developed tool for highly
interactive visualization of air traffic data, to develop clustering algorithms
for categorizing air traffic by their varying flight paths. Two clustering
methodologies, a spatial-based geographic distance model, and a vector-based
cosine similarity model, are demonstrated and compared for their clustering
effectiveness. Examples of their applications reveal successful, realistic
clustering based on automated clustering result determination and
human-in-the-loop processes, with geographic distance algorithms performing
better for enroute portions of flight paths and cosine similarity algorithms
performing better for near-terminal operations, such as arrival paths. A point
extraction technique is applied to improve computation efficiency.


  Feature selection can facilitate the learning of mixtures of discrete random
variables as they arise, e.g. in crowdsourcing tasks. Intuitively, not all
workers are equally reliable but, if the less reliable ones could be
eliminated, then learning should be more robust. By analogy with Gaussian
mixture models, we seek a low-order statistical approach, and here introduce an
algorithm based on the (pairwise) mutual information. This induces an order
over workers that is well structured for the `one coin' model. More generally,
it is justified by a goodness-of-fit measure and is validated empirically.
Improvement in real data sets can be substantial.


  A time-varying microwave photonic filter (TV-MPF) based on stimulated
Brillouin scattering (SBS) is proposed and utilized to suppress the in-band
noise of broadband arbitrary microwave waveforms, thereby improving the
signal-to-noise ratio (SNR). The filter-controlling signal is designed
according to the signal to be filtered and drives the TV-MPF so that the
passband of the filter is always aligned with the frequencies of the signal to
be filtered. By continuously tracking the signal spectral component, the TV-MPF
only retains the spectral components of the signal and filters out the noise
other than the spectral component of the signal at the current time, so as to
improve the in-band SNR of the signal to be filtered. An experiment is
performed. A variety of signals with different formats and in-band SNRs are
used to test the noise suppression capability of the TV-MPF, and the waveform
mean-square error is calculated to quantify the improvement of the signal,
demonstrating the excellent adaptability of the proposed TV-MPF to different
kinds of signals.


  Photoemission (PES) and inverse-photoemission spectra (IPES) for the
sulphur-passivated InP(001) surface are compared with theoretical predictions
based on density-functional calculations. As a test case for our methods, we
also present a corresponding study of the better known Si(111) surface. The
reported spectra for InP(001)-S agree well with the calculated ones if the
surface is assumed to consist of a mixture of two phases, namely, the fully
S-covered $(2\times2)$-reconstructed structure, which contains four S atoms in
the surface unit-cell, and a $(2\times2)$ structure containing two S and two P
atoms per unit cell. The latter has recently been identified in total-energy
calculations as well as in core-level spectra of S-passivated
Si(111)-$(2\times1)$ is in excellent agreement with the calculations. The
comparison of the experimental-PES with our calculations provides additional
considerations regarding the nature of the sample surface. It is also found
that the commonly-used density-of-states approximation to the photo- and
inverse- photoemission spectra is not valid for these systems.


  Laughlin states have recently been constructed on fractal lattices, and the
charge and braiding statistics of the quasiholes were used to confirm that
these states have Laughlin type topology. Here, we investigate density,
correlation, and entanglement properties of the states on a fractal lattice
derived from a Sierpinski triangle with the purpose of identifying similarities
and differences compared to two-dimensional systems and with the purpose of
investigating whether various probes of topology work for fractal lattices.
Similarly to two-dimensional systems, we find that the connected
particle-particle correlation function decays roughly exponentially with the
distance between the lattice sites measured in the two-dimensional plane, but
the values also depend on the local environment. Contrary to two-dimensional
systems, we find that the entanglement entropy does not follow the area law if
one defines the area to be the number of nearest neighbor bonds that cross the
edge of the selected subsystem. Considering bipartitions with two bonds
crossing the edge, we find a close to logarithmic scaling of the entanglement
entropy with the number of sites in the subsystem. This also means that the
topological entanglement entropy cannot be extracted using the Kitaev-Preskill
or the Levin-Wen methods. Studying the entanglement spectrum for different
bipartitions, we find that the number of states below the entanglement gap is
robust and the same as for Laughlin states on two-dimensional lattices.


  We propose a minimal extension of the Standard Model to accommodate
two-component dark matter (DM) and light neutrino mass. The symmetry of the
Standard Model is enhanced by an unbroken $\mathbb{Z}_2 \times \mathbb{Z}'_2$
such that being odd under each $\mathbb{Z}_2$, there exists one right handed
neutrino and one inert scalar doublet. Therefore, each of the $\mathbb{Z}_2$
sectors contribute to ($i$) light neutrino masses radiatively similar to the
scotogenic models while ($ii$) the two neutral CP even scalars present in two
additional inert doublets play the role of dark matters. Focusing on the
intermediate range of inert scalar doublet DM scenario: $M_W \leq M_{\rm DM}
\lesssim 500 \; {\rm GeV}$, where one scalar doublet DM can not satisfy correct
relic, we show that this entire range becomes allowed within this two-component
scalar doublet DM, thanks to the inter-conversion between the two DM candidates
in presence of neutrino Yukawa couplings with dark sector.


  We calculate the rate for thermal production of axions and saxions via
scattering of quarks, gluons, squarks, and gluinos in the primordial
supersymmetric plasma. Systematic field theoretical methods such as hard
thermal loop resummation are applied to obtain a finite result in a
gauge-invariant way that is consistent to leading order in the strong gauge
coupling. We calculate the thermally produced yield and the decoupling
temperature for both axions and saxions. For the generic case in which saxion
decays into axions are possible, the emitted axions can constitute extra
radiation already prior to big bang nucleosynthesis and well thereafter. We
update associated limits imposed by recent studies of the primordial helium-4
abundance and by precision cosmology of the cosmic microwave background and
large scale structure. We show that the trend towards extra radiation seen in
those studies can be explained by late decays of thermal saxions into axions
and that upcoming Planck results will probe supersymmetric axion models with
unprecedented sensitivity.


  The viscosity parameters plays a fundamental role in applications involving
stochastic primitive equations (SPE), such as accurate weather predictions,
climate modeling, and ocean current simulations. In this paper, we develop
several novel estimators for the anisotropic viscosities in the SPE, using
finite number of Fourier modes of a single sample path observed within a finite
time interval. The focus is on analyzing the consistency and asymptotic
normality of these estimators. We consider a torus domain and treat strong,
pathwise solutions in the presence of additive white noise (in time). Notably,
the analysis for estimating horizontal and vertical viscosities differs due to
the unique structure of the SPE, as well as the fact that both parameters of
interest are next to the highest order derivative. To the best of our
knowledge, this is the first work addressing the estimation of anisotropic
viscosities, with potential applicability of the methodology to other modeling.


  Surface tension of small grains and droplets makes them stable only at a much
lower temperature than in bulk. This makes spontaneous nucleation unfavorable
in many cases. Kinetic approaches are delicate in that one can easily generate
models that do not agree with thermodynamics in the large N limit. Here it is
shown that thermodynamics itself dictates a kind of temperature suppression
inside each small cluster in any gas-cluster mixture. This gives a different
perspective on the "translation-rotation" paradox in that this gives a time
averaged steady state thermal inhomogeneity rather than just temporal
fluctuations in the energy. This not only reduces the barrier to nucleation but
also suggests a change in the thermal radiation spectrum from such a mixture
that is not just a result of the inhibited radiation spectrum from Mie
radiators. Either verification or refutation of this effect will be shown have
important consequences for thermodynamics. An understanding of this effect will
be essential to kinetic approaches to nucleation theory.


  We prove a Wegner estimate for a large class of multiparticle Anderson
Hamiltonians on the lattice. These estimates will allow us to prove Anderson
localization for such systems. A detailed proof of localization will be given
in a subsequent paper.


  Continuously pumped passive nonlinear cavities can be harnessed for the
creation of novel optical frequency combs. While most research has focused on
third-order "Kerr" nonlinear interactions, recent studies have shown that
frequency comb formation can also occur via second-order nonlinear effects.
Here, we report on the formation of quadratic combs in optical parametric
oscillator (OPO) configurations. Specifically, we demonstrate that optical
frequency combs can be generated in the parametric region around half of the
pump frequency in a continuously-driven OPO. We also model the OPO dynamics
through a single time-domain mean-field equation, identifying previously
unknown dynamical regimes, induced by modulation instabilities, which lead to
comb formation. Numerical simulation results are in good agreement with
experimentally observed spectra. Moreover, the analysis of the coherence
properties of the simulated spectra shows the existence of correlated and
phase-locked combs. Our results reveal previously unnoticed dynamics of an
apparently well assessed optical system, and can lead to a new class of
frequency comb sources that may stimulate novel applications by enabling
straightforward access to elusive spectral regions, such as the mid-infrared.


  Quantum walks have been shown to be fruitful tools in analysing the dynamic
properties of quantum systems. This article proposes to use quantum walks as an
approach to Quantum Neural Networks (QNNs). QNNs replace binary McCulloch-Pitts
neurons with a qubit in order to use the advantages of quantum computing in
neural networks. A quantum walk on the firing states of such a QNN is supposed
to simulate central properties of the dynamics of classical neural networks,
such as associative memory. It is shown that a biased discrete Hadamard walk
derived from the updating process of a biological neuron does not lead to a
unitary walk. However, a Stochastic Quantum Walk between the global firing
states of a QNN can be constructed and it is shown that it contains the feature
of associative memory. The quantum contribution to the walk accounts for a
modest speed-up in some regimes.


  We exhibit several families of elliptic curves with torsion group isomorphic
to $ \Z/6\Z$ and generic rank at least $3$. Families of this kind have been
constructed previously by several authors: Lecacheux, Kihara, Eroshkin and Woo.
We mention the details of some of them and we add other examples developed more
recently by Dujella and Peral, and MacLeod.
  Then we apply an algorithm of Gusi\'c and Tadi\'c and we find the exact rank
over $\Q(t)$ to be 3 and we also determine free generators of the Mordell-Weil
group for each family. By suitable specializations, we obtain the known and new
examples of curves over $\Q$ with torsion $ \Z/6\Z$ and rank $8$, which is the
current record.


  The general quintic hypersurface in ${\mathbb P}^4$ is the most famous
example of a Calabi--Yau threefold for which mirror symmetry has been
investigated in detail. There is a description of the mirror as a hypersurface
in a certain weighted projective space. In this note we present a model for the
mirror which is again (the resolution of) a quintic hypersurface in ${\mathbb
P}^4$. We also deal with the special members in the respective families. They
lead to rigid Calabi--Yau threefolds with interesting arithmetical properties.
  In the last section we try to find a similarly nice model for the mirror of
the complete intersection of two cubics in ${\mathbb P}^5$. We also formulate a
general question about mirror models.


  We present a novel, data-driven analysis of Galactic dynamics, using
unsupervised machine learning -- in the form of density estimation with
normalizing flows -- to learn the underlying phase space distribution of 6
million nearby stars from the Gaia DR3 catalog. Solving the collisionless
Boltzmann equation with the assumption of approximate equilibrium, we calculate
-- for the first time ever -- a model-free, unbinned, fully 3D map of the local
acceleration and mass density fields within a 3 kpc sphere around the Sun. As
our approach makes no assumptions about symmetries, we can test for signs of
disequilibrium in our results. We find our results are consistent with
equilibrium at the 10% level, limited by the current precision of the
normalizing flows. After subtracting the known contribution of stars and gas
from the calculated mass density, we find clear evidence for dark matter
throughout the analyzed volume. Assuming spherical symmetry and averaging mass
density measurements, we find a local dark matter density of $0.47\pm
0.05\;\mathrm{GeV/cm}^3$. We fit our results to a generalized NFW, and find a
profile broadly consistent with other recent analyses.


  We develop a mechanism of "isotropy separation for compact objects" that
explicitly describes an invertible $G$-spectrum through its collection of
geometric fixed points and gluing data located in certain variants of the
stable module category. As an application, we carry out a complete analysis of
invertible G-spectra in the case $G=A_5$. A further application is given by
showing that the Picard groups of $\mathrm{Sp}^G$ and a category of derived
Mackey functors agree.


  Understanding the interaction of light with a highly scattering material is
essential for optical microscopy of optically thick and heterogeneous
biological tissues. Ensemble-averaged analytic solutions cannot provide more
than general predictions for relatively simple cases. Yet, biological tissues
contain chiral organic molecules and many of the cells' structures are
birefringent, a property exploited by polarization microscopy for label-free
imaging. Solving Maxwell's equations in such materials is a notoriously hard
problem. Here we present an efficient method to determine the propagation of
electro-magnetic waves in arbitrary anisotropic materials. We demonstrate how
the algorithm enables large scale calculations of the scattered light field in
complex birefringent materials, chiral media, and even materials with a
negative refractive index.