  A quantum algorithm for combinatorial search is presented that provides a
simple framework for utilizing search heuristics. The algorithm is evaluated in
a new case that is an unstructured version of the graph coloring problem. It
performs significantly better than the direct use of quantum parallelism, on
average, in cases corresponding to previously identified phase transitions in
search difficulty. The conditions underlying this improvement are described.
Much of the algorithm is independent of particular problem instances, making it
suitable for implementation as a special purpose device.


  The growing demand for key healthcare resources such as clinical expertise
and facilities has motivated the emergence of artificial intelligence (AI)
based decision support systems. We address the problem of predicting clinical
workups for specialty referrals. As an alternative for manually-created
clinical checklists, we propose a data-driven model that recommends the
necessary set of diagnostic procedures based on the patients' most recent
clinical record extracted from the Electronic Health Record (EHR). This has the
potential to enable health systems expand timely access to initial medical
specialty diagnostic workups for patients. The proposed approach is based on an
ensemble of feed-forward neural networks and achieves significantly higher
accuracy compared to the conventional clinical checklists.


  Stochastic PDEs are ubiquitous in mathematical modeling. Yet, many such
equations are too singular to admit classical treatment. In this article we
review some recent progress in defining, approximating and studying the
properties of a few examples of such equations. We focus mainly on the
dynamical Phi4 equation, KPZ equation and Parabolic Anderson Model, as well as
touch on a few other equations which arise mainly in physics.


  Neural networks have shown great promises in planning, control, and general
decision making for learning-enabled cyber-physical systems (LE-CPSs),
especially in improving performance under complex scenarios. However, it is
very challenging to formally analyze the behavior of neural network based
planners for ensuring system safety, which significantly impedes their
applications in safety-critical domains such as autonomous driving. In this
work, we propose a hierarchical neural network based planner that analyzes the
underlying physical scenarios of the system and learns a system-level behavior
planning scheme with multiple scenario-specific motion-planning strategies. We
then develop an efficient verification method that incorporates
overapproximation of the system state reachable set and novel partition and
union techniques for formally ensuring system safety under our physics-aware
planner. With theoretical analysis, we show that considering the different
physical scenarios and building a hierarchical planner based on such analysis
may improve system safety and verifiability. We also empirically demonstrate
the effectiveness of our approach and its advantage over other baselines in
practical case studies of unprotected left turn and highway merging, two common
challenging safety-critical tasks in autonomous driving.


  The important consequences of the recent results of the numerical evaluations
of eighth and tenth order QED contributions to the anomalous magnetic moment of
electron are commented. The correctness of the results of the numerical
evaluation of new eighth order QED corrections to the electron anomaly are
supported by the demonstration of their consistency with the new analytical
expressions for the QED contributions to $a_e$ from the diagrams with
fourth-order light-by-light scattering muon and tau-lepton loops. The
consistency of the similar results are demonstrated in the case of eighth order
massive dependent contribution to the muon anomalous magnetic moment.


  An open source two-dimensional (2D) thermal finite element (FE) model of the
Directed Energy Deposition (DED) process is developed using the Python-based
FEniCS framework. The model incrementally deposits material ahead of the laser
focus point according to the geometry of the part. The laser heat energy is
supplied by a Gaussian-distributed heat source while the phase change is
represented by increased heat capacity around the solidus-liquidus temperature
range. Experimental validation of the numerical model is performed by matching
with the melt pool temperature measurements taken by a dual wavelength
pyrometer during the build process of a box-shaped Ti--6Al--4V part with large
geometrical voids. Effects of large geometrical voids on the melt pool shape
and maximum melt pool temperature are examined. Both the numerical and
experimental data show an increase in the melt pool size and temperature during
deposition above large voids. The trailing edge of the melt pool's temperature
profile obtained using the developed numerical model closely matches pyrometer
measurements.


  The measurement of the Lamb shift in muonic hydrogen and the subsequent
emergence of the proton-radius puzzle have motivated an experimental campaign
devoted to measuring the Lamb shift in other light muonic atoms, such as muonic
deuterium and helium. For these systems it has been shown that two-photon
exchange nuclear structure corrections are the largest source of uncertainty
and consequently the bottleneck for exploiting the experimental precision to
extract the nuclear charge radius. Utilizing techniques and methods developed
to study electromagnetic reactions in light nuclei, recent calculations of
nuclear structure corrections to the muonic Lamb shift have reached
unprecedented precision, reducing the uncertainty with respect to previous
estimates by a factor of 5 in certain cases. These results will be useful for
shedding light on the nature of the proton-radius puzzle and other open
questions pertaining to it. Here, we review and update calculations for muonic
deuterium and tritium atoms, and for muonic helium-3 and helium-4 ions. We
present a thorough derivation of the formalism and discuss the results in
relation to other approaches where available. We also describe how to assess
theoretical uncertainties, for which the language of chiral effective field
theory furnishes a systematic approach that could be further exploited in the
future.


  We investigated the detailed radio structure of the jet of 1H 0323+342 using
high-resolution multi-frequency Very Long Baseline Array observations. This
source is known as the nearest $\gamma$-ray emitting radio-loud narrow-line
Seyfert 1 (NLS1) galaxy. We discovered that the morphology of the inner jet is
well characterized by a parabolic shape, indicating the jet being continuously
collimated near the jet base. On the other hand, we found that the jet expands
more rapidly at larger scales, resulting in a conical-like shape. The location
of the "collimation break" is coincident with a bright quasi-stationary feature
at 7 mas from core (corresponding to a deprojected distance of the order of
$\sim$100pc), where the jet width locally contracts together with highly
polarized signals, suggesting a recollimation shock. We found that the
collimation region is coincident with the region where the jet speed gradually
accelerates, suggesting the coexistence of the jet acceleration and collimation
zone, ending up with the recollimation shock, which could be a potential site
of high-energy $\gamma$-ray flares detected by the Fermi-LAT. Remarkably, these
observational features of the 1H 0323+342 jet are overall very similar to those
of the nearby radio galaxy M87 and HST-1 as well as some blazars, suggesting
that a common jet formation mechanism might be at work. Based on the similarity
of the jet profile between the two sources, we also briefly discuss the mass of
the central black hole of 1H 0323+342, which is also still highly controversial
on this source and NLS1s in general.


  Using depth of coherent sheaves on noetherian algebraic stacks, we construct
non-Azumaya maximal orders in unramified central simple algebras over schemes
of dimension at least $3$.


  Splitting due to tunnelling via the potential energy barrier has played a
significant role in the study of molecular spectra since the early days of
spectroscopy. The observation of the ammonia doublet led to attempts to find a
phosphine analogous, but these have so far failed due to its considerably
higher barrier. Full dimensional, variational nuclear motion calculations are
used to predict splittings as a function of excitation energy. Simulated
spectra suggest that such splittings should be observable in the near infrared
via overtones of the $\nu_2$ bending mode starting with $4\nu_2$.


  This paper initiates the study of a class of schemes that we call
correspondence scrolls, which includes the rational normal scrolls and linearly
embedded projective bundle of decomposable bundles, as well as degenerate K3
surfaces, Calabi-Yau 3-folds, and many other examples.


  In learning with noisy labels, for every instance, its label can randomly
walk to other classes following a transition distribution which is named a
noise model. Well-studied noise models are all instance-independent, namely,
the transition depends only on the original label but not the instance itself,
and thus they are less practical in the wild. Fortunately, methods based on
instance-dependent noise have been studied, but most of them have to rely on
strong assumptions on the noise models. To alleviate this issue, we introduce
confidence-scored instance-dependent noise (CSIDN), where each instance-label
pair is equipped with a confidence score. We find with the help of confidence
scores, the transition distribution of each instance can be approximately
estimated. Similarly to the powerful forward correction for
instance-independent noise, we propose a novel instance-level forward
correction for CSIDN. We demonstrate the utility and effectiveness of our
method through multiple experiments under synthetic label noise and real-world
unknown noise.


  Maximum likelihood estimation (MLE) of latent variable models is often recast
as the minimization of a free energy functional over an extended space of
parameters and probability distributions. This perspective was recently
combined with insights from optimal transport to obtain novel particle-based
algorithms for fitting latent variable models to data. Drawing inspiration from
prior works which interpret `momentum-enriched' optimization algorithms as
discretizations of ordinary differential equations, we propose an analogous
dynamical-systems-inspired approach to minimizing the free energy functional.
The result is a dynamical system that blends elements of Nesterov's Accelerated
Gradient method, the underdamped Langevin diffusion, and particle methods.
Under suitable assumptions, we prove that the continuous-time system minimizes
the functional. By discretizing the system, we obtain a practical algorithm for
MLE in latent variable models. The algorithm outperforms existing particle
methods in numerical experiments and compares favourably with other MLE
algorithms.


  The physics of the "dark energy" that drives the current cosmological
acceleration remains mysterious, and the dark sector may involve new light
dynamical fields. If these light scalars couple to matter, a screening
mechanism must prevent them from mediating an unacceptably strong fifth force
locally. Here we consider a concrete example: the chameleon mechanism. We show
that the same coupling between the chameleon field and matter employed by the
screening mechanism also has catastrophic consequences for the chameleon during
the Universe's first minutes. The chameleon couples to the trace of the
stress-energy tensor, which is temporarily non-zero in a radiation-dominated
universe whenever a particle species becomes non-relativistic. These "kicks"
impart a significant velocity to the chameleon field, causing its effective
mass to vary non-adiabatically and resulting in the copious production of
quantum fluctuations. Dissipative effects strongly modify the background
evolution of the chameleon field, invalidating all previous classical
treatments of chameleon cosmology. Moreover, the resulting fluctuations have
extremely high characteristic energies, which casts serious doubt on the
validity of the effective theory. Our results demonstrate that quantum particle
production can profoundly affect scalar-tensor gravity, a possibility not
previously considered. Working in this new context, we also develop the theory
and numerics of particle production in the regime of strong dissipation.


  We present an end-to-end differentiable neural network architecture to
perform anomaly detection in multivariate time series by incorporating a
Sequential Probability Ratio Test on the prediction residual. The architecture
is a cascade of dynamical systems designed to separate linearly predictable
components of the signal such as trends and seasonality, from the non-linear
ones. The former are modeled by local Linear Dynamic Layers, and their residual
is fed to a generic Temporal Convolutional Network that also aggregates global
statistics from different time series as context for the local predictions of
each one. The last layer implements the anomaly detector, which exploits the
temporal structure of the prediction residuals to detect both isolated point
anomalies and set-point changes. It is based on a novel application of the
classic CUMSUM algorithm, adapted through the use of a variational
approximation of f-divergences. The model automatically adapts to the time
scales of the observed signals. It approximates a SARIMA model at the get-go,
and auto-tunes to the statistics of the signal and its covariates, without the
need for supervision, as more data is observed. The resulting system, which we
call STRIC, outperforms both state-of-the-art robust statistical methods and
deep neural network architectures on multiple anomaly detection benchmarks.


  In this paper we develop a manifestly geometric framework for equivariant
manifold neural ordinary differential equations (NODEs), and use it to analyse
their modelling capabilities for symmetric data. First, we consider the action
of a Lie group $G$ on a smooth manifold $M$ and establish the equivalence
between equivariance of vector fields, symmetries of the corresponding Cauchy
problems, and equivariance of the associated NODEs. We also propose a novel
formulation of the equivariant NODEs in terms of the differential invariants of
the action of $G$ on $M$, based on Lie theory for symmetries of differential
equations, which provides an efficient parameterisation of the space of
equivariant vector fields in a way that is agnostic to both the manifold $M$
and the symmetry group $G$. Second, we construct augmented manifold NODEs,
through embeddings into equivariant flows, and show that they are universal
approximators of equivariant diffeomorphisms on any path-connected $M$.
Furthermore, we show that the augmented NODEs can be incorporated in the
geometric framework and parameterised using higher order differential
invariants. Finally, we consider the induced action of $G$ on different fields
on $M$ and show how it can be used to generalise previous work, on, e.g.,
continuous normalizing flows, to equivariant models in any geometry.


  We study the Muskat problem describing the vertical motion of two immiscible
fluids in a two-dimensional homogeneous porous medium in an $L_p$-setting with
$p\in(1,\infty)$. The Sobolev space $W^s_p(\mathbb{R})$ with $s=1+1/p$ is a
critical space for this problem. We prove, for $s\in (1+1/p,2),$ that the
Rayleigh-Taylor condition identifies an open subset of $W^s_p(\mathbb{R})$
within which the Muskat problem is of parabolic type. This enables us to
establish the local well-posedness of the problem in all these subcritical
spaces together with a parabolic smoothing property.


  We address the phenomenon of drag reduction by dilute polymeric additive to
turbulent flows, using Direct Numerical Simulations (DNS) of the FENE-P model
of viscoelastic flows. It had been amply demonstrated that these model
equations reproduce the phenomenon, but the results of DNS were not analyzed so
far with the goal of interpreting the phenomenon. In order to construct a
useful framework for the understanding of drag reduction we initiate in this
paper an investigation of the most important modes that are sustained in the
viscoelastic and Newtonian turbulent flows respectively. The modes are obtained
empirically using the Karhunen-Loeve decomposition, allowing us to compare the
most energetic modes in the viscoelastic and Newtonian flows. The main finding
of the present study is that the spatial profile of the most energetic modes is
hardly changed between the two flows. What changes is the energy associated
with these modes, and their relative ordering in the decreasing order from the
most energetic to the least. Modes that are highly excited in one flow can be
strongly suppressed in the other, and vice versa. This dramatic energy
redistribution is an important clue to the mechanism of drag reduction as is
proposed in this paper. In particular there is an enhancement of the energy
containing modes in the viscoelastic flow compared to the Newtonian one; drag
reduction is seen in the energy containing modes rather than the dissipative
modes as proposed in some previous theories.


  Purpose: Iterative projection reconstruction algorithms are currently the
preferred reconstruction method in proton computed tomography (pCT). However,
due to inconsistencies in the measured data arising from proton energy
straggling and multiple Coulomb scattering, noise in the reconstructed image
increases with successive iterations. In the current work, we investigated the
use of total variation superiorization (TVS) schemes that can be applied as an
algorithmic add-on to perturbation-resilient iterative projection algorithms
for pCT image reconstruction. Methods: The block-iterative diagonally relaxed
orthogonal projections (DROP) algorithm was used for reconstructing Geant4
Monte Carlo simulated pCT data sets. Two TVS schemes added on to DROP were
investigated; the first carried out the superiorization steps once per cycle
and the second once per block. Simplifications of these schemes, involving the
elimination of the computationally expensive feasibility proximity checking
step of the TVS framework, were also investigated. The modulation transfer
function and contrast discrimination function were used to quantify spatial and
density resolution, respectively. Results: With both TVS schemes, superior
spatial and density resolution was achieved compared to the standard DROP
algorithm. Eliminating the feasibility proximity check improved the image
quality, in particular image noise, in the once-per-block superiorization,
while also halving image reconstruction time. Overall, the greatest image
quality was observed when carrying out the superiorization once-per-block and
eliminating the feasibility proximity check. Conclusions: The low contrast
imaging made possible with TVS holds a promise for its incorporation into our
future pCT studies.


  We propose an abstract conceptual framework for analysing complex security
systems using a new notion of modes and mode transitions. A mode is an
independent component of a system with its own objectives, monitoring data,
algorithms, and scope and limits. The behaviour of a mode, including its
transitions to other modes, is determined by interpretations of the mode's
monitoring data in the light of its objectives and capabilities -- these
interpretations we call beliefs. We formalise the conceptual framework
mathematically and, by quantifying and visualising beliefs in
higher-dimensional geometric spaces, we argue our models may help both design,
analyse and explain systems. The mathematical models are based on simplicial
complexes.


  A simple Standard Model Extension based on $T_7$ flavor symmetry which
accommodates lepton mass and mixing with non-zero $\theta_{13}$ and CP
violation phase is proposed. At the tree- level, the realistic lepton mass and
mixing pattern is derived through the spontaneous symmetry breaking by just one
vacuum expectation value ($v$) which is the same as in the Standard Model.
Neutrinos get small masses from one $SU(2)_L$ doublet and two $SU(2)_L$
singlets in which one being in $\underline{1}$ and the two others in
$\underline{3}$ and $\underline{3}^*$ under $T_7$ , respectively. The model
also gives a remarkable prediction of Dirac CP violation
$\delta_{CP}=172.598^\circ$ in both normal and inverted hierarchies which is
still missing in the neutrino mixing matrix.


  This article is provides an introduction to the quantum theory of optics in
nonlinear dielectric media. We begin with a short summary of the classical
theory of nonlinear optics, that is nonlinear optics done with classical
fields. We then discuss the canonical formalism for fields and its
quantization. This is applied to quantizing the electromagnetic field in free
space. The definition of a nonclassical state of the electromagnetic field is
presented, and several examples are examined. This is followed by a brief
introduction to entanglement in the context of field modes. The next task is
the quantization of the electromagnetic field in an inhomogeneous, linear
dielectric medium. Before going on to field quantization in nonlinear media, we
discuss a number of commonly employed phenomenological models for quantum
nonlinear optical processes. We then quantize the field in both nondispersive
and dispersive nonlinear media. Flaws in the most commonly used methods of
accomplishing this task are pointed out and discussed. Once the quantization
has been completed, it is used to study a multimode theory of parametric down
conversion and the propagation of quantum solitons.


  We construct a long-range Baxter equation encoding anomalous dimensions of
composite operators in the SL(2|1) sector of N = 4 supersymmetric Yang-Mills
theory. The formalism is based on the analytical Bethe Ansatz. We compare
predictions of the Baxter equations for short operators with available
multiloop perturbative calculations.


  We present optical characterization, calibration, and performance tests of
the Mesospheric Airglow/Aerosol Tomography Spectroscopy (MATS) satellite, which
for the first time for a satellite applies a linear-astigmatism-free confocal
off-axis reflective optical design. Mechanical tolerances of the telescope were
investigated using Monte-Carlo methods and single-element perturbations. The
sensitivity analysis results indicate that tilt errors of the tertiary mirror
and a surface RMS error of the secondary mirror mainly degrade optical
performance. From the Monte-Carlo simulation, the tolerance limits were
calculated to $\pm$0.5 mm, $\pm$1 mm, and $\pm$0.15$^\circ$ for decenter,
despace, and tilt, respectively. We performed characterization measurements and
optical tests with the flight model of the satellite. Multi-channel relative
pointing, total optical system throughput, and distortion of each channel were
characterized for end-users. Optical performance was evaluated by measuring
modulation transfer function (MTF) and point spread function (PSF). The final
MTF performance is 0.25 MTF at 20 lp/mm for the ultraviolet channel (304.5 nm),
and 0.25 - 0.54 MTF at 10 lp/mm for infrared channels. The salient fact of the
PSF measurement of this system is that there is no noticeable linear
astigmatism detected over wide field of view (5.67$^\circ$ $\times$
0.91$^\circ$). All things considered, the design method showed great advantages
in wide field of view observations with satellite-level optical performance.


  Let X be a Gorenstein orbifold and let Y be a crepant resolution of X. We
state a conjecture relating the genus-zero Gromov--Witten invariants of X to
those of Y, which differs in general from the Crepant Resolution Conjectures of
Ruan and Bryan--Graber, and prove our conjecture when X = P(1,1,2) and X =
P(1,1,1,3). As a consequence, we see that the original form of the
Bryan--Graber Conjecture holds for P(1,1,2) but is probably false for
P(1,1,1,3). Our methods are based on mirror symmetry for toric orbifolds.


  We produce arbitrarily large equivalence classes of matings with the
aeroplane polynomial. These are obtained by a slight generalisation of the
technique of proof of a similar result for Wittner captures.


  Whereas air shower simulations are very valuable tools for interpreting
cosmic ray data, there is a long standing problem: is seems to be impossible to
accommodate at the same time the longitudinal development of air showers and
the number of muons measured at ground. Using a new hadronic interaction model
(EPOS) in air shower simulations produces considerably more muons, in agreement
with results from the HiRes-MIA experiment. We find that this is mainly due to
a better description of baryon-antibaryon production in hadronic interactions.
This is a new aspect of air shower physics which has never been considered so
far.


  We compute hadronic transitions between heavy quarkonium states with two, or
one, pion/eta particles in the final state. We use the multipole expansion but
not the twist expansion. The latter cannot be justified for the energy release
of hadronic transitions between heavy quarkonium states with different
principal quantum numbers. Instead, we use a counting based on the dimension of
the interpolating field of the hybrid. This alternative counting allows us to
still use chiral low-energy theorems to compute the pion production by local
gluonic operators. We explore the phenomenological impact of this counting.
Remarkably enough, for the two-pion transitions, we obtain the same predictions
for the normalized differential decay rate as those obtained assuming the twist
expansion. We implement this computational scheme using the hadronic
representation of the effective theory potential NRQCD. We assume that the
inverse Bohr radius of the heavy quarkonium is much larger than $\Lambda_{\rm
QCD}$ but do not impose any constraint on the relative size of $\Lambda_{\rm
QCD}$ and the typical kinetic energy of the bound state.


  Many recent news headlines have labeled face recognition technology as biased
or racist. We report on a methodical investigation into differences in face
recognition accuracy between African-American and Caucasian image cohorts of
the MORPH dataset. We find that, for all four matchers considered, the impostor
and the genuine distributions are statistically significantly different between
cohorts. For a fixed decision threshold, the African-American image cohort has
a higher false match rate and a lower false non-match rate. ROC curves compare
verification rates at the same false match rate, but the different cohorts
achieve the same false match rate at different thresholds. This means that ROC
comparisons are not relevant to operational scenarios that use a fixed decision
threshold. We show that, for the ResNet matcher, the two cohorts have
approximately equal separation of impostor and genuine distributions. Using
ICAO compliance as a standard of image quality, we find that the initial image
cohorts have unequal rates of good quality images. The ICAO-compliant subsets
of the original image cohorts show improved accuracy, with the main effect
being to reducing the low-similarity tail of the genuine distributions.


  A simple model for the reaction-driven propulsion of a small device is
proposed as a model for (part of) a molecular machine in aqueous media. Motion
of the device is driven by an asymmetric distribution of reaction products. The
propulsive velocity of the device is calculated as well as the scale of the
velocity fluctuations. The effects of hydrodynamic flow as well as a number of
different scenarios for the kinetics of the reaction are addressed.


  Let $\Omega\subseteq\mathbb R^n$ be a non-empty open set for which the
Sobolev embedding $H_0^2(\Omega)\longrightarrow L^2(\Omega)$ is compact, and
let $V\in L^\infty(\Omega)$ be a potential taking only positive real values and
satisfying the asymptotics
$V(\cdot)\asymp\left\langle\cdot\right\rangle^{-\alpha}$ for some
$\alpha\in\left]3,\infty\right[$. We establish the discreteness of the set of
real transmission eigenvalues for both Schr\"odinger and Helmholtz scattering
with these potentials.


  With the increasing application of deep learning (DL) algorithms in wireless
communications, the physical layer faces new challenges caused by adversarial
attack. Such attack has significantly affected the neural network in computer
vision. We chose DL-based analog channel state information (CSI) to show the
effect of adversarial attack on DL-based communication system. We present a
practical method to craft white-box adversarial attack on DL-based CSI feedback
process. Our simulation results showed the destructive effect adversarial
attack caused on DL-based CSI feedback by analyzing the performance of
normalized mean square error. We also launched a jamming attack for comparison
and found that the jamming attack could be prevented with certain precautions.
As DL algorithm becomes the trend in developing wireless communication, this
work raises concerns regarding the security in the use of DL-based algorithms.


  For sensitive optical interferometry, it is crucial to control the evolution
of the optical path difference (OPD) of the wavefront between the individual
telescopes of the array. The OPD between a pair of telescopes is induced by
differential optical properties such as atmospheric refraction, telescope
alignment, etc. This has classically been measured using a fringe tracker that
provides corrections to a piston actuator to account for this difference. An
auxiliary method, known as the Piston Reconstruction Experiment (P-REx) has
been developed to measure the OPD, or differential 'piston' of the wavefront,
induced by the atmosphere at each telescope. Previously, this method was
outlined and results obtained from LBT adaptive optics (AO) data for a single
telescope aperture were presented. P-REx has now been applied off-line to
previously acquired VLT's GRAVITY CIAO wavefront sensing data to estimate the
atmospheric OPD for the six VLTI baselines. Comparisons with the OPD obtained
from the VLTI GRAVITY fringe tracker were made. The results indicate that the
telescope and instrumental noise of the combined VLTI and GRAVITY systems
dominate over the atmospheric turbulence contributions. However, good agreement
between simulated and on-sky P-REx data indicates that if the telescope and
instrumental noise were reduced to atmospheric piston noise levels, P-REx has
the potential to reduce the OPD root mean square of piston turbulence by up to
a factor of 10 for frequencies down to 1 Hz. In such conditions, P-REx will
assist in pushing the sensitivity limits of optical fringe tracking with long
baseline interferometers.


  Nucleon isovector form factors calculated on a 2+1-flavor
domain-wall-fermions ensemble with strange and degenerate up and down quarks at
physical mass and lattice cut off, $a^{-1}$, of about 1.730(4) GeV, are
reported. The ensemble was generated jointly by RBC and UKQCD collaborations
with a spatial extent of $48a$ or about 5.5 fm. The form factors are calculated
in collaboration with LHP collaboration as well. The resulting shape parameters
of the form factors, such as vector-charge mean squared radius, $\langle
r_1^2\rangle$, or anomalous magnetic moment, $F_2(0)$ appear less dependent on
possible excited-state contaminations than the corresponding charges.
Preliminary estimates are $\langle r_1^2\rangle \sim 0.142(13)\, \mbox{fm}^2$
and $F_2(0) \sim 3.22(8)$.


  Genes/Proteins do not work alone within our body, rather as a group they
perform certain activities indicated as pathways. Signalling transduction
pathways (STPs) are some of the important pathways that transmit biological
signals from protein-to-protein controlling several cellular activities.
However, many diseases such as cancer target some of these signalling pathways
for their growth and malignance, but demystifying their underlying mechanisms
are a very complicated tasks. In this study, we use a fully Bayesian approach
to develop methodologies in discovering novel driver bio-markers in aberrant
STPs given two-conditional high-throughput gene expression data. This project,
namely PathTurbEr (Pathway Perturbation Driver), is applied on a global gene
expression dataset derived from the lapatinib (an EGFR/HER dual inhibitor)
sensitive and resistant samples from breast cancer cell lines (SKBR3).
Differential expression analysis revealed 512 differentially expressed genes
(DEGs) and their signalling pathway enrichment analysis revealed 22 singalling
pathways as aberrated including PI3K-AKT, Hippo, Chemokine, and TGF-beta
singalling pathway as highly dysregulated in lapatinib resistance. Next, we
model the aberrant activities in TGF-beta STP as a causal Bayesian network (BN)
from given observational datasets using three Markov Chain Monte Carlo (MCMC)
sampling methods, i.e. Neighbourhood sampler (NS) and Hit-and-Run (HAR)
sampler, which has already proven to have more robust inference with lower
chances of getting stuck at local optima and faster convergence compared to
other state-of-art methods. Next, we examined the structural features of the
optimal BN as a statistical process that generates the global structure using,
$p_1$-model, a special class of Exponential Random Graph Models (ERGMs) and
MCMC methods for their hyper-parameter sampling....


  A trending astronomical phenomenon to study is the variation in brightness of
asteroids, caused by its rotation on its own axis, non-spherical shapes,
changes of albedo along its surface and its position relative to the sun. The
latter behaviour can be visualized on a "Phase Curve" (phase angle vs. reduced
magnitude). To enable the comparison between several models proposed for this
curve we present a Python package called Pyedra. Pyedra implements three
phase-curve-models, and also providing capabilities for visualization as well
as integration with external datasets. The package is fully documented and
tested following a strict quality-assurance workflow, with a user-friendly
programmatic interface. In future versions, we will include more models, and
additional estimation of quantities derived from parameters like diameter, and
types of albedo; as well as enabling correlation of information of physical and
orbital parameters.


  We prove \emph{global} uniqueness for an inverse problem for the fractional
conductivity equation on domains that are bounded in one direction. The
conductivities are assumed to be isotropic and nontrivial in the exterior of
the domain, while the data is given in the form of partial Dirichlet-to-Neumann
(DN) maps measured in nondisjoint open subsets of the exterior. This can be
seen as the fractional counterpart of the classical inverse conductivity
problem. The proof is based on a unique continuation property (UCP) for the DN
maps and an exterior determination method from the partial exterior DN maps.
This is analogous to the classical boundary determination method by Kohn and
Vogelius. The most important technical novelty is the construction of sequences
of special solutions to the fractional conductivity equation whose Dirichlet
energies in the limit can be concentrated at any given point in the exterior.
This is achieved independently of the UCP and despite the nonlocality of the
equation. Due to the recent counterexamples by the last two authors, our
results almost completely characterize uniqueness for the inverse fractional
conductivity problem with partial data for isotropic global conductivities.


  In the era of Internet of Things (IoT), network-wide anomaly detection is a
crucial part of monitoring IoT networks due to the inherent security
vulnerabilities of most IoT devices. Principal Components Analysis (PCA) has
been proposed to separate network traffics into two disjoint subspaces
corresponding to normal and malicious behaviors for anomaly detection. However,
the privacy concerns and limitations of devices' computing resources compromise
the practical effectiveness of PCA. We propose a federated PCA-based
Grassmannian optimization framework that coordinates IoT devices to aggregate a
joint profile of normal network behaviors for anomaly detection. First, we
introduce a privacy-preserving federated PCA framework to simultaneously
capture the profile of various IoT devices' traffic. Then, we investigate the
alternating direction method of multipliers gradient-based learning on the
Grassmann manifold to guarantee fast training and the absence of detecting
latency using limited computational resources. Empirical results on the NSL-KDD
dataset demonstrate that our method outperforms baseline approaches. Finally,
we show that the Grassmann manifold algorithm is highly adapted for IoT anomaly
detection, which permits drastically reducing the analysis time of the system.
To the best of our knowledge, this is the first federated PCA algorithm for
anomaly detection meeting the requirements of IoT networks.


  Using the renormalisation group framework we classify different extensions of
the standard model according to their degree of naturality. A new relevant
class of perturbative models involving elementary scalars is the one in which
the theory simultaneously satisfies the Veltman conditions and is conformal at
the classical level. We term these extensions perturbative natural conformal
(PNC) theories. We show that PNC models are very constrained and thus highly
predictive. Among the several PNC examples that we exhibit, we discover a
remarkably simple PNC extension of the standard model in which the Higgs is
predicted to have the experimental value of the mass equal to 126 GeV. This
model also predicts the existence of one more standard model singlet scalar
boson with a mass of 541 GeV and the Higgs self-coupling to emerge radiatively.
We study several other PNC examples that generally predict a somewhat smaller
mass of the Higgs to the perturbative order we have investigated them. Our
results can be a useful guide when building extensions of the standard model
featuring fundamental scalars.


  This paper intends to give some new estimates for Tsallis relative operator
entropy ${{T}_{v}}\left( A|B \right)=\frac{A{{\natural}_{v}}B-A}{v}$. Let $A$
and $B$ be two positive invertible operators with the spectra contained in the
interval $J \subset (0,\infty)$. We prove for any $v\in \left[ -1,0 \right)\cup
\left( 0,1 \right]$, $$ (\ln_v t)A+\left(
A{{\natural}_{v}}B+tA{{\natural}_{v-1}}B \right)\le {{T}_{v}}\left( A|B \right)
\le (\ln_v s)A+{{s}^{v-1}}\left( B-sA \right) $$ where $s,t\in J$. Especially,
the upper bound for Tsallis relative operator entropy is a non-trivial new
result. Meanwhile, some related and new results are also established. In
particular, the monotonicity for Tsallis relative operator entropy is improved.
  Furthermore, we introduce the exponential type relative operator entropies
which are special cases of the perspective and we give inequalities among them
and usual relative operator entropies.


  It is known that the normalized algorithmic information distance $N$ is not
computable and not semicomputable. We show that for all $\epsilon < 1/2$, there
exist no semicomputable functions that differ from $N$ by at most~$\epsilon$.
Moreover, for any computable function $f$ such that $|\lim_t f(x,y,t) - N(x,y)|
\le \epsilon$ and for all $n$, there exist strings $x,y$ of length $n$ such
that $\sum_t |f(x,y,t+1) - f(x,y,t)| \ge \Omega(\log n)$. This is optimal up to
constant factors. We also show that the maximal number of oscillations of a
limit approximation of $N$ is $\Omega(n/\log n)$. This strengthens the
$\omega(1)$ lower bound from [K. Ambos-Spies, W. Merkle, and S.A. Terwijn,
2019, Normalized information distance and the oscillation hierarchy], see
arXiv:1708.03583 .


  A detailed study of the lowest states $1s_0, 2p_{-1}, 2p_0$ of the hydrogen
atom placed in a magnetic field $B\in(0-4.414\times 10^{13} {\rm G})$ and their
electromagnetic transitions ($1s_{0} \leftrightarrow 2p_{-1}$ and $ 1s_{0}
\leftrightarrow 2p_{0}$) is carried out in the Born Oppenheimer approximation.
The variational method is used with a physically motivated recipe to design
simple trial functions applicable to the whole domain of magnetic fields. We
show that the proposed functions yield very accurate results for the ionization
(binding) energies. Dipole and oscillator strengths are in good agreement with
results by Ruder {\em et al.} \cite{Ruderbook} although we observe deviations
up to $\sim 30%$ for the oscillator strength of the (linearly polarized)
electromagnetic transition $1s_{0} \leftrightarrow 2p_{0}$ at strong magnetic
fields $B\gtrsim 1000$ a.u.


  Recent experiments found that a hot solid sphere that is able to sustain a
stable Leidenfrost vapour layer in a liquid exhibits significant drag reduction
during free fall. The variation of the drag coefficient with Reynolds number
shows substantial deviation from the characteristic drag crisis behavior at
high Reynolds numbers. Results obtained with liqiuds of different viscosities
show that onset of the drag crisis depends on the viscosity ratio of the vapor
to the liquid. The key feature of the vapour layer in facilitating tangential
flow and in altering the behaviour of the boundary layer can be captured by the
Navier slip model that is defined by a slip length. Here, direct numerical and
large eddy simulations of flow past a sphere at moderate to high Reynolds
numbers ($10^2 \leq \mbox{Re} \leq 4 \times 10^4$) are employed to quantify
comparisons with experimental results in terms of variations of the drag
coefficient with Reynolds number and the form of the downstream wake on the
sphere. This provides a simple one parameter characterization of the drag
reduction phenomenon.


  A potential source of dominant backgrounds for many rare-event searches or
screening detectors is from radon daughters, specifically $^{210}$Pb, deposited
on detector surfaces, often during detector fabrication. Performing a
late-stage etch is challenging because it may damage the detector. This paper
describes a late-stage etching technique that reduces surface $^{210}$Pb and
$^{210}$Po by $>99\times$ at 90% C.L.


  In reservoir simulation, solution of the coupled systems of nonlinear
algebraic equations that are associated with fully-implicit (backward Euler)
discretization is challenging. Having a robust and efficient nonlinear solver
is necessary in order for reservoir simulation to serve as the primary tool for
managing the recovery processes of large-scale reservoirs. Here, we develop a
continuation method based on the use of a dissipation operator. We focus on
nonlinear two-phase flow and transport in heterogeneous formations in the
presence of viscous, gravitational, and capillary forces. The homotopy is
constructed by adding numerical dissipation to the coupled discrete
conservation equations. A continuation parameter is introduced to control the
amount of dissipation. Numerical evidence of multi-dimensional models and
detailed analysis of single-cell problems are used to explain how the
dissipation operator improves the nonlinear convergence of the coupled system
of equations. An adaptive strategy to determine the dissipation coefficient is
proposed. The dissipation level is computed locally for each cell interface. We
demonstrate the efficiency of the dissipation-based continuation (DBC)
nonlinear solver using several examples, including 1D scalar transport and 2D
heterogeneous problems with fully-coupled flow and transport. The DBC solver
has better convergence properties compared with the standard damped-Newton
solvers used in reservoir simulation.


  Let $X$ and $Y$ be any two graphs of order $n$. The friends-and-strangers
graph $\mathsf{FS}(X,Y)$ of $X$ and $Y$ is a graph with vertex set consisting
of all bijections $\sigma :V(X) \mapsto V(Y)$, in which two bijections
$\sigma$, $\sigma'$ are adjacent if and only if they differ precisely on two
adjacent vertices of $X$, and the corresponding mappings are adjacent in $Y$.
The most fundamental question that one can ask about these
friends-and-strangers graphs is whether or not they are connected. Let
$\mathsf{Lollipop}_{n-k,k}$ be a lollipop graph of order $n$ obtained by
identifying one end of a path of order $n-k+1$ with a vertex of a complete
graph of order $k$. Defant and Kravitz started to study the connectedness of
$\mathsf{FS}(\mathsf{Lollipop}_{n-k,k},Y)$. In this paper, we give a sufficient
and necessary condition for $\mathsf{FS}(\mathsf{Lollipop}_{n-k,k},Y)$ to be
connected for all $2\leq k\leq n$.


  CO$_2$-forced surface warming in general circulation models (GCMs) is
initially polar-amplified in the Arctic but not Antarctic -- a largely
hemispherically antisymmetric signal. Nevertheless, we show in CESM1 and eleven
LongRunMIP GCMs that the hemispherically symmetric component of
global-mean-normalized, zonal-mean warming ($T^*_\mathrm{sym}$) under
4\(\times\)CO$_2$ changes weakly or becomes moderately more polar-amplified
from the first decade to near-equilibrium. Conversely, the antisymmetric
warming component ($T^*_\mathrm{asym}$) weakens with time in all models,
moderately in some including FAMOUS but effectively vanishing in others
including CESM1. We explore mechanisms underlying the robust $T^*_\mathrm{sym}$
behavior with a diffusive moist energy balance model (MEBM), which given
radiative feedback parameter ($\lambda$) and ocean heat uptake ($\mathcal{O}$)
fields diagnosed from CESM1 adequately reproduces the CESM1 $T^*_\mathrm{sym}$
and $T^*_\mathrm{asym}$ fields. In further MEBM simulations perturbing
$\lambda$ and $\mathcal{O}$, $T^*_\mathrm{sym}$ is sensitive to their symmetric
components only, and more to that of $\lambda$. A three-box, two-timescale
model fitted to FAMOUS and CESM1 reveals a curiously short Antarctic
fast-response timescale in FAMOUS. In additional CESM1 simulations spanning a
broader range of forcings, $T^*_\mathrm{sym}$ changes modestly across
2-16\(\times\)CO$_2$, and $T^*_\mathrm{sym}$ in a Pliocene-like simulation is
more polar-amplified but likewise approximately time-invariant. Determining the
real-world relevance of these behaviors -- which imply that a surprising amount
of information about near-equilibrium polar amplification emerges within
decades -- merits further study.


  The first part of this paper describes in detail the action of small gauge
transformations in heterotic supergravity. We show a convenient gauge fixing is
`holomorphic gauge' together with a condition on the holomorphic top form. This
gauge fixing, combined with supersymmetry and the Bianchi identity, allows us
to determine a set of non-linear PDEs for the terms in the Hodge decomposition.
Although solving these in general is highly non-trivial, we give a prescription
for their solution perturbatively in alpha' and apply this to the moduli space
metric. The second part of this paper relates small gauge transformations to a
choice of connection on the moduli space. We show holomorphic gauge is related
to a~choice of holomorphic structure and Lee form on a `universal bundle'.
Connections on the moduli space have field strengths that appear in the second
order deformation theory and we point out it is generically the case that
higher order deformations do not commute.


  We study non-linear $\sigma$-models defined on noncommutative torus as a two
dimensional string world-sheet. We consider a quantum group as a noncommutative
space-time as well as two points, a circle, and a noncommutative torus. Using
the establised results we show that the trivial harmonic unitaries of the
noncommutative chiral model, which are known as local minima, are not global
minima by comparing those with the symmetric unitaries coming from instanton
solutions of noncommutative Ising model, which corresponds to the two points
target space. In addition,we introduce a $\mathbb{Z}^2$-action on field maps to
noncommutative torus and show how it acts on solutions of various
Euler-Lagrange equations.


  Confounders in deep learning are in general detrimental to model's
generalization where they infiltrate feature representations. Therefore,
learning causal features that are free of interference from confounders is
important. Most previous causal learning based approaches employ back-door
criterion to mitigate the adverse effect of certain specific confounder, which
require the explicit identification of confounder. However, in real scenarios,
confounders are typically diverse and difficult to be identified. In this
paper, we propose a novel Confounder Identification-free Causal Visual Feature
Learning (CICF) method, which obviates the need for identifying confounders.
CICF models the interventions among different samples based on front-door
criterion, and then approximates the global-scope intervening effect upon the
instance-level interventions from the perspective of optimization. In this way,
we aim to find a reliable optimization direction, which avoids the intervening
effects of confounders, to learn causal features. Furthermore, we uncover the
relation between CICF and the popular meta-learning strategy MAML, and provide
an interpretation of why MAML works from the theoretical perspective of causal
learning for the first time. Thanks to the effective learning of causal
features, our CICF enables models to have superior generalization capability.
Extensive experiments on domain generalization benchmark datasets demonstrate
the effectiveness of our CICF, which achieves the state-of-the-art performance.


  Methods of *-representations in Hilbert space are applied to study of systems
of $n$ subspaces in a linear space. It is proved that the problem of
description of $n$-transitive subspaces in a finite-dimensional linear space is
*-wild for $n \geq 5$.


  Large language models (LLMs) are useful tools with the capacity for
performing specific types of knowledge work at an effective scale. However, LLM
deployments in high-risk and safety-critical domains pose unique challenges,
notably the issue of ``hallucination,'' where LLMs can generate fabricated
information. This is particularly concerning in settings such as drug safety,
where inaccuracies could lead to patient harm. To mitigate these risks, we have
developed and demonstrated a proof of concept suite of guardrails specifically
designed to mitigate certain types of hallucinations and errors for drug
safety, and potentially applicable to other medical safety-critical contexts.
These guardrails include mechanisms to detect anomalous documents to prevent
the ingestion of inappropriate data, identify incorrect drug names or adverse
event terms, and convey uncertainty in generated content. We integrated these
guardrails with an LLM fine-tuned for a text-to-text task, which involves
converting both structured and unstructured data within adverse event reports
into natural language. This method was applied to translate individual case
safety reports, demonstrating effective application in a pharmacovigilance
processing task. Our guardrail framework offers a set of tools with broad
applicability across various domains, ensuring LLMs can be safely used in
high-risk situations by eliminating the occurrence of key errors, including the
generation of incorrect pharmacovigilance-related terms, thus adhering to
stringent regulatory and quality standards in medical safety-critical
environments.


  Let $g$ be an affine Lie algebra with index set $I = \{0, 1, 2, \cdots , n\}$
and $g^L$ be its Langlands dual. It is conjectured that for each Dynkin node $i
\in I \setminus \{0\}$ the affine Lie algebra $g$ has a positive geometric
crystal whose ultra-discretization is isomorphic to the limit of certain
coherent family of perfect crystals for $g^L$. In this paper we construct a
positive geometric crystal $V(D_5^{(1)})$ in the level zero fundamental spin
$D_5^{(1)}$- module $W(\varpi_5)$. Then we define explicit $0$-action on the
level $l$ known $D_5^{(1)}$- perfect crystal $B^{5, l}$ and show that $\{B^{5,
l}\}_{l \geq 1}$ is a coherent family of perfect crystals with limit $B^{5,
\infty}$. Finally we show that the ultra-discretization of $V(D_5^{(1)})$ is
isomorphic to $B^{5, \infty}$ as crystals which proves the conjecture in this
case.


  Using a spin-charge separation of the gluon field in the Landau gauge we show
that the SU(2) Yang-Mills theory in the low-temperature phase can be considered
as a nematic liquid crystal. The ground state of the nematic crystal is
characterized by the A^2 condensate of the gluon field. The liquid crystal
possesses various topological defects (instantons, monopoles and vortices)
which are suggested to play a role in non-perturbative features of the theory.


  We demonstrate a new approach to the computation of ratios of elliptic
integrals. It turns out that almost closed polygons interscribed between two
conics retain some of the properties of such closed polygons. We apply these
retained properties to compute ratios of an incomplete elliptic integral over
the complete one. This computation is based on an iterative procedure to
determine the sequence of vertices of a polygon interscribed between two
conics. Surprisingly, some iteration numbers are the denominators of the
convergent fractions for thye ratio of some elliptic integrals. The algorithm
ensures high precision, is numerically stable and as fast as the
arithmetic-geometric mean method, though not faster. Nonetheless, there are
reasons to consider the proposed algorithm as it is quite differentfrom other
integration methods and may be applicable to other problems.


  We characterize complete RNP-differentiability spaces as those spaces which
are rectifiable in terms of doubling metric measure spaces satisfying some
local $(1, p)$-Poincar\'e inequalities. This gives a full characterization of
spaces admitting a strong form of a differentiability structure in the sense of
Cheeger, and provides a partial converse to his theorem. The proof is based on
a new `thickening' construction, which can be used to enlarge subsets into
spaces admitting Poincar\'e inequalities. We also introduce a new notion of
quantitative connectivity which characterizes spaces satisfying local
Poincar\'e inequalities. This characterization is of independent interest, and
has several applications separate from differentiability spaces. We resolve a
question of Tapio Rajala on the existence of Poincar\'e inequalities for the
class of $MCP(K, n)$-spaces which satisfy a weak Ricci-bound. We show that
deforming a geodesic metric measure space by Muckenhoupt weights preserves the
property of possessing a Poincar\'e inequality. Finally, the new condition
allows us to show that many classes of weak, Orlicz and non-homogeneous
Poincar\'e inequalities `self-improve' to classical $(1, q)$-Poincar\'e
inequalities for some $q \in [1,\infty)$, which is related to Keith's and
Zhong's theorem on self-improvement of Poincar\'e inequalities.


  We investigate questions related to the minimal degree of invariants of
finitely generated diagonalizable groups. These questions were raised in
connection to security of a public key cryptosystem based on invariants of
diagonalizable groups. We derive results for minimal degrees of invariants of
finite groups, abelian groups and algebraic groups. For algebraic groups we
relate the minimal degree of the group to the minimal degrees of its tori.
Finally, we investigate invariants of certain supergroups that are superanalogs
of tori. It is interesting to note that a basis of these invariants is not
given by monomials.


  We study scattering of quasi one-dimensional matter-waves at an interface of
two spatial domains, one with repulsive and one with attractive interatomic
interactions. It is shown that the incidence of a Gaussian wavepacket from the
repulsive to the attractive region gives rise to generation of a soliton train.
More specifically, the number of emergent solitons can be controlled e.g. by
the variation of the amplitude or the width of the incoming wavepacket.
Furthermore, we study the reflectivity of a soliton incident from the
attractive region to the repulsive one. We find the reflection coefficient
numerically and employ analytical methods, that treat the soliton as a particle
(for moderate and large amplitudes) or a quasi-linear wavepacket (for small
amplitudes), to determine the critical soliton momentum - as function of the
soliton amplitude - for which total reflection is observed.


  The problem of photon adding and subtracting is studied, using conditional
output measurement on a beam splitter. It is shown that for various classes of
states the corresponding photon-added and -subtracted states can be prepared.
Analytical results are presented, with special emphasis on photon-added and
-subtracted squeezed vacuum states, which are found to represent two different
types of Schroedinger-cat-like states. Effects of realistic photocounting and
Fock-state preparation are discussed.


  Nicolas Monod introduced the class of groups with the fixed-point property
for cones, characterized by always admitting a non-zero fixed point whenever
acting (suitably) on proper weakly complete cones. He proved that his class of
groups contains the class of groups with subexponential growth and is contained
in the class of supramenable groups. In this paper we investigate what Monod's
results say about the existence of invariant traces on (typically non-unital)
C*-algebras equipped with an action of a group with the fixed-point property
for cones. As an application of these results we provide results on the
existence (and non-existence) of traces on the (non-uniform) Roe algebra.


  We study status updating under two-way delay in a system consisting of a
sampler, a sink, and a controller residing at the sink. The controller controls
the sampling process by sending request packets to the sampler. Upon receiving
a request, the sampler generates a sample and transmits the status update
packet to the sink. Transmissions of both request and status update packets
encounter random delays. We develop optimal control policies to minimize the
average age of information (AoI) using the tools of Markov decision processes
in two scenarios. We begin with the system having at most one active request,
i.e., a generated request for which the sink has not yet received a status
update packet. Then, as the main distinctive feature of this paper, we initiate
pipelining-type status updating by studying a system having at most two active
requests. Furthermore, we conduct AoI analysis by deriving the average AoI
expressions for the Zero-Wait-1, Zero-Wait-2, and Wait-1 policies. According to
the Zero-Wait-1 policy, whenever a status update packet is delivered to the
sink, a new request packet is inserted into the system. The Zero-Wait-2 policy
operates similarly, except that the system holds two active requests. According
to the Wait-1 policy, whenever a status update packet is delivered to the sink,
a new request is sent after a waiting time which is a function of the current
AoI. Numerical results illustrate the performance of each status updating
policy under different system parameter values.


  Weight sharing has become a de facto standard in neural architecture search
because it enables the search to be done on commodity hardware. However, recent
works have empirically shown a ranking disorder between the performance of
stand-alone architectures and that of the corresponding shared-weight networks.
This violates the main assumption of weight-sharing NAS algorithms, thus
limiting their effectiveness. We tackle this issue by proposing a
regularization term that aims to maximize the correlation between the
performance rankings of the shared-weight network and that of the standalone
architectures using a small set of landmark architectures. We incorporate our
regularization term into three different NAS algorithms and show that it
consistently improves performance across algorithms, search-spaces, and tasks.


  In the present lectures the following topics are considered: general
properties of neutrinos, neutrino mass phenomenology (Dirac and Majorana
masses), neutrino masses in the simplest extensions of the standard model
(including the seesaw mechanism), neutrino oscillations in vacuum, neutrino
oscillations in matter (the MSW effect) in 2- and 3-flavour schemes,
implications of CP, T and CPT symmetries for neutrino oscillations, double beta
decay, solar neutrino oscillations and the solar neutrino problem, and
atmospheric neutrinos. We also give a short overview of the results of the
accelerator and reactor neutrino experiments and of future projects. Finally,
we discuss how the available experimental data on neutrino masses and lepton
mixing can be summarized in the phenomenologically allowed forms of the
neutrino mass matrix.


  The relation of generalized (skewed) quark distributions to nucleon wave
functions is discussed in the context of light-cone quantization.


  We search for infrared zeros of the beta function and evaluate the anomalous
dimension of the mass at the associated fixed point for asymptotically free
vector-like fermionic gauge theories with gauge group SU(N). The fixed points
of the beta function are studied at the two, three and four loop level in two
different explicit schemes. These are the modified regularization invariant,
RI', scheme and the minimal momentum subtraction, mMOM, scheme. The search is
performed in Landau gauge where the beta function of the gauge parameter
vanishes. We then compare our findings to earlier identical investigations
performed in the modified minimal subtraction, $\bar{\text{MS}}$, scheme.
  It is found that the value of the anomalous dimension of the mass is smaller
at three and four loops than at two loops. This seems to be a generic pattern
that is observed in all three different schemes. We then estimate the value of
the anomalous dimension to be $\gamma \sim 0.225-0.375$ for twelve fundamental
flavors and three colors, $\gamma \sim 0.500 - 0.593$ for two adjoint flavors
and two colors and finally $\gamma \sim 1.12-1.70$ for two two-indexed flavors
and three colors with the lower and upper bound set by the minimum and maximum
value respectively over all three schemes and at three and four loops. Our
analysis suggests that the former two theories lie in the conformal window
while the latter belongs to the chirally broken phase.


  In contrast to earlier reports, where the spectrum of the {\sl energy
density} of photonic black-body radiation modified by SU(2) effects was
discussed, we discuss the low-frequency spectrum of the {\sl radiance} at
temperatures ranging between 5 and 20 Kelvin. We conclude that compared to the
conventional theory the only observable effect is associated with the spectral
gap (total screening). We also discuss how a low-temperature black body cavity
under the influence of a sufficiently strong static electric field is forced to
emit according to Planck's radiation law (pure U(1) theory) even at low
frequencies and how this effect can be utilized to measure SU(2) induced
deviations.


  Understanding the fundamental mechanism behind the success of transformer
networks is still an open problem in the deep learning literature. Although
their remarkable performance has been mostly attributed to the self-attention
mechanism, the literature still lacks a solid analysis of these networks and
interpretation of the functions learned by them. To this end, we study the
training problem of attention/transformer networks and introduce a novel convex
analytic approach to improve the understanding and optimization of these
networks. Particularly, we first introduce a convex alternative to the
self-attention mechanism and reformulate the regularized training problem of
transformer networks with our alternative convex attention. Then, we cast the
reformulation as a convex optimization problem that is interpretable and easier
to optimize. Moreover, as a byproduct of our convex analysis, we reveal an
implicit regularization mechanism, which promotes sparsity across tokens.
Therefore, we not only improve the optimization of attention/transformer
networks but also provide a solid theoretical understanding of the functions
learned by them. We also demonstrate the effectiveness of our theory through
several numerical experiments.


  The feasibility of existing data stream algorithms is often hindered by the
weakly supervised condition of data streams. A self-evolving deep neural
network, namely Parsimonious Network (ParsNet), is proposed as a solution to
various weakly-supervised data stream problems. A self-labelling strategy with
hedge (SLASH) is proposed in which its auto-correction mechanism copes with
\textit{the accumulation of mistakes} significantly affecting the model's
generalization. ParsNet is developed from a closed-loop configuration of the
self-evolving generative and discriminative training processes exploiting
shared parameters in which its structure flexibly grows and shrinks to overcome
the issue of concept drift with/without labels. The numerical evaluation has
been performed under two challenging problems, namely sporadic access to ground
truth and infinitely delayed access to the ground truth. Our numerical study
shows the advantage of ParsNet with a substantial margin from its counterparts
in the high-dimensional data streams and infinite delay simulation protocol. To
support the reproducible research initiative, the source code of ParsNet along
with supplementary materials are made available at https://bit.ly/2qNW7p4.


  Recent experimental and theoretical results show that weakly interacting
atomic Bose-Bose mixtures with attractive interspecies interaction are
stabilized by beyond-mean-field effects. Here we consider the peculiar
properties of these systems in a strictly one-dimensional configuration, taking
also into account the nontrivial role of spin-orbit and Rabi couplings. We show
that when the value of inter- and intraspecies interaction strengths are such
that mean-field contributions to the energy cancel, a self-bound bright soliton
fully governed by quantum fluctuations exists. We derive the phase diagram of
the phase transition between a single-peak soliton and a multipeak (striped)
soliton, produced by the interplay between spin-orbit, Rabi couplings and
beyond-mean-field effects, which also affect the breathing mode frequency of
the atomic cloud. Finally, we prove that a phase imprinting of the single-peak
soliton leads to a self-confined propagating solitary wave even in the presence
of spin-orbit coupling.


  I compare several network-level measures of centrality to common measures of
author reputation and influence (e.g. hindex, i10index), all taken over the
data set of papers published in 2017 at major computer systems conferences and
some controls. I hypothesize that centrality measures will correlate strongly
with the reputation and influence measures. My results confirm several expected
correlations and exhibit a few surprising absences of correlation. In
particular, there was an absence of statistically significant correlation
between degree centrality and hindex,


  In this paper, we describe features of two new robot prototypes that are
actuated by an actively controlled gyro (flywheel, symmetric rotor) inside a
hollow sphere that is located in the middle of the robots. No external
actuators are used. The outside structure of the robots and the gyro are
connected by a gimbal, which is similar in structure to a control moment
gyroscope in spacecrafts. The joints of the gimbal can be actuated. In this
way, the orientation of axis for the gyro in relation to the egg can be
changed. Since the inertia of the fast rotating gyro is large in relation to
the outside structure, a relative rotation of the axis against the outside
structure results in a motion of the egg by inertia principle. In this way, we
can use this principle for controlling the robot to move forward and turn
around. The robots are shaped as spheroidal ellipsoids so they resemble eggs.
So far, we have built and tested two robot prototypes.


  Background: Data fitting approaches to modeling allow for parametric formulae
that may not reveal the physical quantities involved and their influence on the
function being studied. In this paper the author models the approach to
equilibrium function by a method that allows the physical quantities to be
defined beforehand, allows their influence to be studied, and can be used to
predict how each physical quantity affects approach to equilibrium. Methods: An
ordinary differential equation (ODE) is used to model the approach to
equilibrium function for the case where collimation is changed at fixed
detector size. A parallel model is used to study the approach to equilibrium as
a function of detector size for fixed collimation. Both models are validated by
experimental measurements in a 60cm body phantom. Influence of detector size is
simulated by using leaded sleeves of varying sizes wrapped around a 100mm
pencil chamber. This creates sleeve gaps of 10 - 60mm around the chamber. A
100mm detector size is the pencil chamber without a leaded sleeve. Results:
Model accurately describes the experimental data for the cases studied. Except
for the smallest collimation of 5mm, linear regression analysis shows good
correlation between data and model according to the R^2 values at all
collimations. Further analysis of the model reveals minimum detector size that
will integrate 98% of the signal for a given collimation is, d=4.95L.
Additional analysis shows the minimum collimation at which a given detector
will collect 98% of the signal is, L=5.49d. Conclusion: Modeling by
differential equations is an accurate method for the approach to equilibrium
function, and has advantages over curve fitting methods.


  To describe possible effects of medium, besides the hamiltonian introduced by
Mikheev, Smirnov and Wolfenstein (MSW), in principle, there may exist new terms
in the evolution equation for the neutrino oscillation due to the environment.
Considering a two-energy-level quantum system: $\nu_1-\nu_2$, two-species
neutrino system which is embedded in a matter environment, we solve the
neutrino evolution equation precisely with the possible extra terms,
especially, those cause alternations between pure and mixed states of the
neutrino quantum system. We obtain some remarkable features for the neutrino
oscillations, which are different from that of MSW and accessible to be
observed in solar neutrino observation and/or in the planned long-baseline
neutrino experiments.


  In this paper, we report experimental results in collectting and processing
5G NR I/Q samples in the 3.7~GHz C-band by using software-defined radio
(SDR)-mounted helikite. We use MATLAB's 5G toolbox to post-process the
collected data, to obtain the synchronization signal block (SSB) from the I/Q
samples and then go through the cell search, synchronization procedures, and
reference signal received power (RSRP) and reference signal received quality
(RSRQ) calculation. We plot these performance metrics for various physical cell
identities as a function of the helikite's altitude. Furthermore, building on
our experience with the collected and post-processed data, we discuss potential
vulnerabilities of 5G NR systems to surveillance, jamming attacks, and post
quantum era attacks.


  Emojis, as a new way of conveying nonverbal cues, are widely adopted in
computer-mediated communications. In this paper, first from a message sender
perspective, we focus on people's motives in using four types of emojis --
positive, neutral, negative, and non-facial. We compare the willingness levels
of using these emoji types for seven typical intentions that people usually
apply nonverbal cues for in communication. The results of extensive statistical
hypothesis tests not only report the popularities of the intentions, but also
uncover the subtle differences between emoji types in terms of intended uses.
Second, from a perspective of message recipients, we further study the
sentiment effects of emojis, as well as their duplications, on verbal messages.
Different from previous studies in emoji sentiment, we study the sentiments of
emojis and their contexts as a whole. The experiment results indicate that the
powers of conveying sentiment are different between four emoji types, and the
sentiment effects of emojis vary in the contexts of different valences.


  In an earlier paper (physics/0006012) we had developed a method for computing
the effective energy transfer between any two Fourier modes in fluid or
magnetohydrodynamic (MHD) flows. This method is applied to a pseudo-spectral,
direct numerical simulation (DNS) study of energy transfer in the quasi-steady
state of 2-D MHD turbulence with large scale kinetic forcing. Two aspects of
energy transfer are studied: the energy fluxes, and the energy transfer between
different wavenumber regions ({\it shells}). The picture of energy fluxes that
emerges is quite complex - there is a forward cascade of magnetic energy, an
inverse cascade of kinetic energy, a flux of energy from the kinetic to the
magnetic field, and a reverse flux which transfers the energy back to the
kinetic from the magnetic. The energy transfer between different wave number
shells is also complex - local and nonlocal transfers often possess opposing
features, i.e., energy transfer between some wave number shells occurs from
kinetic to magnetic, and between other wave number shells this transfer is
reversed. The net transfer of energy is from kinetic to magnetic. The results
obtained from the flux studies and the shell-to-shell energy transfer studies
are consistent with each other.


  Hardware accelerators (HAs) are essential building blocks for fast and
energy-efficient computing systems. Accelerator Quick Error Detection (A-QED)
is a recent formal technique which uses Bounded Model Checking for pre-silicon
verification of HAs. A-QED checks an HA for self-consistency, i.e., whether
identical inputs within a sequence of operations always produce the same
output. Under modest assumptions, A-QED is both sound and complete. However, as
is well-known, large design sizes significantly limit the scalability of formal
verification, including A-QED. We overcome this scalability challenge through a
new decomposition technique for A-QED, called A-QED with Decomposition
(A-QED$^2$). A-QED$^2$ systematically decomposes an HA into smaller, functional
sub-modules, called sub-accelerators, which are then verified independently
using A-QED. We prove completeness of A-QED$^2$; in particular, if the full HA
under verification contains a bug, then A-QED$^2$ ensures detection of that bug
during A-QED verification of the corresponding sub-accelerators. Results on
over 100 (buggy) versions of a wide variety of HAs with millions of logic gates
demonstrate the effectiveness and practicality of A-QED$^2$.


  In this article we present a method for automatic integration of parametric
integrals over the unit hypercube using a neural network. The method fits a
neural network to the primitive of the integrand using a loss function designed
to minimize the difference between multiple derivatives of the network and the
function to be integrated. We apply this method to two example integrals
resulting from the sector decomposition of a one-loop and two-loop scalar
integrals. Our method can achieve per-mil and percent accuracy for these
integrals over a range of invariant values. Once the neural network is fitted,
the evaluation of the integral is between 40 and 125 times faster than the
usual numerical integration method for our examples, and we expect the speed
gain to increase with the complexity of the integrand.


  We present a 90 per cent flux-complete sample of the 201 X-ray brightest
clusters of galaxies in the northern hemisphere (dec > 0 deg), at high Galactic
latitudes (|b| > 20 deg), with measured redshifts z < 0.3 and fluxes higher
than 4.4 x 10^(-12) erg cm^(-2) s^{-1) in the 0.1-2.4 keV band. The sample,
called the ROSAT Brightest Cluster Sample (BCS), is selected from ROSAT All-Sky
Survey data and is the largest X-ray selected cluster sample compiled to date.
In addition to Abell clusters, which form the bulk of the sample, the BCS also
contains the X-ray brightest Zwicky clusters and other clusters selected from
their X-ray properties alone. Effort has been made to ensure the highest
possible completeness of the sample and the smallest possible contamination by
non-cluster X-ray sources. X-ray fluxes are computed using an algorithm
tailored for the detection and characterization of X-ray emission from galaxy
clusters. These fluxes are accurate to better than 15 per cent (mean 1 sigma
error).
  We find the cumulative log N-log S distribution of clusters to follow a power
law k S^(-alpha) with alpha=1.31 (+0.06)(-0.03) (errors are the 10th and 90th
percentiles) down to fluxes of 2 x 10^(-12) erg cm^(-2) s^(-1), i.e.
considerably below the BCS flux limit. Although our best-fitting slope
disagrees formally with the canonical value of -1.5 for a Euclidean
distribution, the BCS log N-log S distribution is consistent with a
non-evolving cluster population if cosmological effects are taken into account.


  The Magnetic Tower of Hanoi puzzle - a modified "base 3" version of the
classical Tower of Hanoi puzzle as described in earlier papers, is actually a
small set of independent sister-puzzles, depending on the "pre-coloring"
combination of the tower's posts. Starting with Red facing up on a Source post,
working through an Intermediate - colored or Neutral post, and ending Blue
facing up on a Destination post, we identify the different pre-coloring
combinations in (S,I,D) order. The Tower's pre-coloring combinations are
{[(R,B,B) / (R,R,B)] ; [(R,B,N) / (N,R,B)] ; [(N,B,N) / (N,R,N)] ; [R,N,B] ;
[(R,N,N) / (N,N,B)] ; [N,N,N]}. In this paper we investigate these
sister-puzzles, identify the algorithm that optimally solves each pre-colored
puzzle, and prove its Optimality. As it turns out, five of the six algorithms,
challenging on their own, are part of the algorithm solving the "natural", Free
Magnetic Tower of Hanoi puzzle [N,N,N]. We start by showing that the N-disk
Colored Tower [(R,B,B) / (R,R,B)] is solved by (3^N - 1)/2 moves. Defining
"Algorithm Duration" as the ratio of number of algorithm-moves solving the
puzzle to the number of algorithm-moves solving the Colored Tower, we find the
Duration-Limits for all sister-puzzles. In the order of the list above they are
{[1] ; [10/11] ; [10/11] ; [8/11] ; [7/11] ; [20/33]}. Thus, the Duration-Limit
of the Optimal Algorithm solving the Free Magnetic Tower of Hanoi puzzle is
20/33 or 606 0/00. On the road to optimally solve this colorful Magnetic
puzzle, we hit other "forward-moving" puzzle-solving algorithms. Overall we
looked at 10 pairs of integer sequences. Of the twenty integer sequences, five
are listed in the On-line Encyclopedia of Integer Sequences, the other fifteen
- not yet. The large set of different solutions is a clear indication to the
freedom-of-wondering that makes this Magnetic Tower of Hanoi puzzle so
colorful.


  Given an oligomorphic group $G$ and a measure $\mu$ for $G$ (in a sense that
we introduce), we define a rigid tensor category $\underline{\mathrm{Perm}}(G;
\mu)$ of "permutation modules," and, in certain cases, an abelian envelope
$\underline{\mathrm{Rep}}(G; \mu)$ of this category. When $G$ is the infinite
symmetric group, this recovers Deligne's interpolation category. Other choices
for $G$ lead to fundamentally new tensor categories. For example, we construct
the first known semi-simple pre-Tannakian categories in positive characteristic
with super-exponential growth. One interesting aspect of our construction is
that, unlike previous work in this direction, our categories are concrete: the
objects are modules over a ring, and the tensor product receives a universal
bi-linear map. Central to our constructions is a novel theory of integration on
oligomorphic groups, which could be of more general interest. Classifying the
measures on an oligomorphic group appears to be a difficult problem, which we
solve in only a few cases.


  In this article, we review basic facts about disordered systems, especially
the existence of many metastable states and and the resulting failure of
dimensional reduction. Besides techniques based on the Gaussian variational
method and replica-symmetry breaking (RSB), the functional renormalization
group (FRG) is the only general method capable of attacking strongly disordered
systems. We explain the basic ideas of the latter method and why it is
difficult to implement. We finally review current progress for elastic
manifolds in disorder.


  It is shown that multiple volume reflections from different planes of one
bent crystal becomes possible when particles move at a small angle with respect
to a crystal axis. Such a Multiple Volume Reflection makes it possible to
increase the particle deflection angle inside one crystal by more than four
times and can be used to increase the efficiency of beam extraction and
collimation at the LHC and many other accelerators.


  The overwhelmingly increasing amount of stored data has spurred researchers
seeking different methods in order to optimally take advantage of it which
mostly have faced a response time problem as a result of this enormous size of
data. Most of solutions have suggested materialization as a favourite solution.
However, such a solution cannot attain Real- Time answers anyhow. In this paper
we propose a framework illustrating the barriers and suggested solutions in the
way of achieving Real-Time OLAP answers that are significantly used in decision
support systems and data warehouses.


  We generalize the coupled-cluster (CC) approach with singles, doubles, and
the non-iterative treatment of triples termed $\Lambda$CCSD(T) to Hamiltonians
containing three-body interactions. The resulting method and the underlying CC
approach with singles and doubles only (CCSD) are applied to the medium-mass
closed-shell nuclei O16, O24, and Ca40. By comparing the results of CCSD and
$\Lambda$CCSD(T) calculations with explicit treatment of three-nucleon
interactions to those obtained using an approximate treatment in which they are
included effectively via the zero-, one-, and two-body components of the
Hamiltonian in normal-ordered form, we quantify the contributions of the
residual three-body interactions neglected in the approximate treatment. We
find these residual normal-ordered three-body contributions negligible for the
$\Lambda$CCSD(T) method, although they can become significant in the
lower-level CCSD approach, particularly when the nucleon-nucleon interactions
are soft.


  We study the dipole signal in the spectral index (x) of the differential
number counts using quasars in the CatWISE2020 catalog of infrared sources. The
index is extracted by using the log-likelihood method. We obtain the value
$x=1.579 \pm 0.001$ for a quasar sample of 1355352 sources. We extract the
dipole signal in this parameter by employing $\chi^{2}$ minimization, assuming
a sky model of x up to the quadrupole term. We find that the dipole amplitude
|D| is 0.005 \pm 0.002 and dipole direction (l, b) in Galactic coordinate
system equal to $(201.50^{\circ} \pm 27.87^{\circ}, -29.37^{\circ} \pm
19.86^{\circ})$. The direction of dipole anisotropy is found to be very close
to the hemispherical power asymmetry $(l,b)=(221^\circ,-27^{\circ})$ in the
Cosmic Microwave Background (CMB). We also obtain a signal of quadrupole
anisotropy which is correlated with the ecliptic poles and can be attributed to
ecliptic bias.}


  The geometry of the intermediate state (IS) flux structures of type-I
superconductors, observed during early stages of magnetic flux penetration
induced by an externally applied perpendicular magnetic field, is approached in
terms of minimal surfaces. This approach follows from the assumption that a
local free energy minimization constraint, for each individual flux structure,
dominates for sufficiently spatially separated magnetic flux regions, i.e. when
over global free energy minimization predicts very low periodicity of sample
intermediate state.


  This paper contains a review of available methods for establishing improved
interpolation inequalities on the sphere for subcritical exponents. Pushing
further these techniques we also establish some new results, clarify the range
of applicability of the various existing methods and state several explicit
estimates.


  We calculate the helicity and chirality effects experienced by a spin-1/2
particle subjected to classical electromagnetic and gravitational fields. The
helicity evolution is then determined in the non-relativistic, relativistic,
and ultra-relativistic regimes. We find that inertia-gravitation can
distinguish between helicity and chirality. Helicity is not conserved, in
general, even when the particles are massless. In this case, however, the
inertial fields can hardly be applied to the fermions.


  Raman measurements are performed on defect-free wurzite GaP nanowires.
Resonance Raman measurements are carried out over the excitation energy range
between 2.19 and 2.71 eV. Resonances at 2.38 eV and 2.67 eV of the E1(LO) mode
and at 2.67 eV of the A1(LO) are observed. The presence of these intensity
resonances clearly demonstrates the existence of energy states with Gamma_9hh
and Gamma_7V (Gamma_7C) symmetries of the valence (conduction) band and allows
to measure WZ phase GaP band energies at the Gamma point. In addition, we have
investigated temperature dependent resonant Raman measurements, which allowed
us to extrapolate the zero temperature values of Gamma point energies, along
with the crystal field and spin-orbit splitting energies. Above results provide
a feedback for refining available theoretical calculations to derive the
correct wurtzite III-V semiconductor band structure.


  Computational modeling of human multimodal language is an emerging research
area in natural language processing spanning the language, visual and acoustic
modalities. Comprehending multimodal language requires modeling not only the
interactions within each modality (intra-modal interactions) but more
importantly the interactions between modalities (cross-modal interactions). In
this paper, we propose the Recurrent Multistage Fusion Network (RMFN) which
decomposes the fusion problem into multiple stages, each of them focused on a
subset of multimodal signals for specialized, effective fusion. Cross-modal
interactions are modeled using this multistage fusion approach which builds
upon intermediate representations of previous stages. Temporal and intra-modal
interactions are modeled by integrating our proposed fusion approach with a
system of recurrent neural networks. The RMFN displays state-of-the-art
performance in modeling human multimodal language across three public datasets
relating to multimodal sentiment analysis, emotion recognition, and speaker
traits recognition. We provide visualizations to show that each stage of fusion
focuses on a different subset of multimodal signals, learning increasingly
discriminative multimodal representations.


  We review some recent work on the enhancement and application of both r- and
h- adaptation techniques, benefitting of the functionalities of the remeshing
platform Mmg: www.mmgtools.org. Several contributions revolve around the
level-set adaptation capabilities of the platform. These have been used to
identify complex surfaces and then to either produce conformal 3D meshes, or to
define a metric allowing to perform h-adaptation and control geometrical errors
in the context of immersed boundary flow simulations. The performance of the
recent distributed memory parallel implementation ParMmg is also discussed. In
a similar spirit, we propose some improvements of $r-$adaptation methods to
handle embedded fronts.


  The design of a security scheme for beamforming prediction is critical for
next-generation wireless networks (5G, 6G, and beyond). However, there is no
consensus about protecting the beamforming prediction using deep learning
algorithms in these networks. This paper presents the security vulnerabilities
in deep learning for beamforming prediction using deep neural networks (DNNs)
in 6G wireless networks, which treats the beamforming prediction as a
multi-output regression problem. It is indicated that the initial DNN model is
vulnerable against adversarial attacks, such as Fast Gradient Sign Method
(FGSM), Basic Iterative Method (BIM), Projected Gradient Descent (PGD), and
Momentum Iterative Method (MIM), because the initial DNN model is sensitive to
the perturbations of the adversarial samples of the training data. This study
also offers two mitigation methods, such as adversarial training and defensive
distillation, for adversarial attacks against artificial intelligence
(AI)-based models used in the millimeter-wave (mmWave) beamforming prediction.
Furthermore, the proposed scheme can be used in situations where the data are
corrupted due to the adversarial examples in the training data. Experimental
results show that the proposed methods effectively defend the DNN models
against adversarial attacks in next-generation wireless networks.


  Modelling interactions is critical in learning complex dynamical systems,
namely systems of interacting objects with highly non-linear and time-dependent
behaviour. A large class of such systems can be formalized as
$\textit{geometric graphs}$, $\textit{i.e.}$, graphs with nodes positioned in
the Euclidean space given an $\textit{arbitrarily}$ chosen global coordinate
system, for instance vehicles in a traffic scene. Notwithstanding the arbitrary
global coordinate system, the governing dynamics of the respective dynamical
systems are invariant to rotations and translations, also known as
$\textit{Galilean invariance}$. As ignoring these invariances leads to worse
generalization, in this work we propose local coordinate frames per node-object
to induce roto-translation invariance to the geometric graph of the interacting
dynamical system. Further, the local coordinate frames allow for a natural
definition of anisotropic filtering in graph neural networks. Experiments in
traffic scenes, 3D motion capture, and colliding particles demonstrate that the
proposed approach comfortably outperforms the recent state-of-the-art.


  Concrete calculations have pointed out that amplitudes in perturbative
gravity exhibit unanticipated cancellations taming their ultraviolet behaviour
independently of supersymmetry. Similar ultraviolet behaviour of N=4
super-Yang-Mills and N=8 maximal supergravity has explicitly been observed
until three loops. These cancellations can be connected to two manifest
features of gravitational theories: firstly gauge invariance from
diffeomorphism symmetries and secondly that amplitudes are colourless and
exhibits crossing symmetry. We will give a simple physical explanation of the
cancellations exhibited in gravity amplitudes. We will discuss these two
properties in turn as well as the role of supersymmetry and string theory
dualities in the structure of multiloop amplitudes in supergravity.


  In this note we study the geometry of the component of the origin in the
Uniform Spanning Forest of $\mathbb{Z}^d$, as well as in the Uniform Spanning
Tree of wired subgraphs of $\mathbb{Z}^d$, when $d \ge 5$. In particular, we
study connectivity properties with respect to the Euclidean and the intrinsic
distance. We intend to supplement these with further estimates in the future.
We are making this preliminary note available, as one of our estimates is used
in work of Bhupatiraju, Hanson and J\'arai on sandpiles.


  The sensitivity of proton-induced $J/\psi$ and $\Upsilon$ production to the
possible $\bar u/\bar d$ asymmetry in the nucleon is studied. The ratio of the
quarkonium production cross sections at large $x_F$ on hydrogen over deuterium
targets, $\sigma (p+p) / \sigma (p+d)$, is shown to be sensitive to this
asymmetry. Predictions of various theoretical models for this ratio are
presented.


  We show that the conductivity of a two-dimensional electron gas can be
intrinsically anisotropic despite isotropic Fermi surface, energy dispersion,
and disorder configuration. In the model we study, the anisotropy stems from
the interplay between Dirac and Schr\"odinger features combined in a special
two-band Hamiltonian describing the quasiparticles similar to the low-energy
excitations in phosphorene. As a result, even scalar isotropic disorder
scattering alters the nature of the carriers and results in anisotropic
transport. Solving the Boltzmann equation exactly for such carriers with
point-like random impurities we find a hidden knob to control the anisotropy
just by tuning either the Fermi energy or temperature. Our results are expected
to be generally applicable beyond the model studied here, and should stimulate
further search for the alternative ways to control electron transport in
advanced materials.


  In this paper, we derive a dispersion relation for sound waves in viscous and
heat conducting fluids. In particular this dispersion (i.e. variation of speed
of sound with frequency) is shown to be of second order of magnitude, w.r.t.
Knudsen numbers, as in the Stokes [2] case, corresponding to non-conductive
fluid (Prandtl number P r = $\infty$). This formula completes the classical
attenuation relation called Stokes-Kirchhoff. We represent in a simplified
manner the Kirchhoff approach to derive this attenuation [1], starting from the
3D compressible Navier-stokes system. The classical Stokes-Kirchhoff formula
has been questioned recently in [3] and a different (and incorrect) formula was
proposed. We point out the non-trivial assumptions that are violated in the new
derivation in [3] to reestablish the classical Stokes-Kirchhoff formula.
Finally, we give an explanation to differences in dispersion and attenuation
formulae that one may find in the literature through analysing the form of the
considered attenuated solutions.


  We determine Furstenberg entropy spectra of ergodic stationary actions of
$SL(d,\mathbb{R})$ and its lattices. The constraints on entropy spectra are
derived from a refinement of the Nevo-Zimmer projective factor theorem. The
realisation part is achieved by means of building Poisson bundles over
stationary random subgroups.


  A common goal in comparative effectiveness research is to estimate treatment
effects on pre-specified subpopulations of patients. Though widely used in
medical research, causal inference methods for such subgroup analysis remain
underdeveloped, particularly in observational studies. In this article, we
develop a suite of analytical methods and visualization tools for causal
subgroup analysis. First, we introduce the estimand of subgroup weighted
average treatment effect and provide the corresponding propensity score
weighting estimator. We show that balancing covariates within a subgroup bounds
the bias of the estimator of subgroup causal effects. Second, we design a new
diagnostic graph -- the Connect-S plot -- for visualizing the subgroup
covariate balance. Finally, we propose to use the overlap weighting method to
achieve exact balance within subgroups. We further propose a method that
combines overlap weighting and LASSO, to balance the bias-variance tradeoff in
subgroup analysis. Extensive simulation studies are presented to compare the
proposed method with several existing methods. We apply the proposed methods to
the Patient-centered Results for Uterine Fibroids (COMPARE-UF) registry data to
evaluate alternative management options for uterine fibroids for relief of
symptoms and quality of life.


  \textit{Ab-initio} calculation of intrinsic spin Hall conductivity (SHC)
generally requires a strict convergence criterion and a dense k-point mesh to
sample the Brillouin zone, making its convergence challenging and
time-consuming. Here we present a scheme for efficiently and accurately
calculating SHC based on maximally localized Wannier function (MLWF). The
quantities needed by the Kubo formula of SHC are derived in the space of MLWF
and it is shown that only the Hamiltonian, the overlap and the spin operator
matrices are required from the initial \textit{ab-initio} calculation. The
computation of these matrices and the interpolation of Kubo formula on a dense
k-point mesh can be easily achieved. We validate our results by prototypical
calculations on fcc Pt and GaAs, which demonstrate that the Wannier
interpolation approach is of high accuracy and efficiency. Calculations of
$\alpha$-Ta and $\beta$-Ta show that SHC of $\beta$-Ta is 2.7 times of
$\alpha$-Ta, while both have the opposite sign relative to fcc Pt and are an
order of magnitude smaller than Pt. The calculated spin Hall angle of $-0.156$,
is quite consistent with previous experiment on $\beta$-Ta, further suggesting
intrinsic contribution may dominate in $\beta$-Ta. Our approach could
facilitate large-scale SHC calculations, and may benefit the discovery of
materials with high intrinsic SHC.


  Pre-trained Large Language Models (LLMs) have significantly advanced natural
language processing capabilities but are susceptible to biases present in their
training data, leading to unfair outcomes in various applications. While
numerous strategies have been proposed to mitigate bias, they often require
extensive computational resources and may compromise model performance. In this
work, we introduce AXOLOTL, a novel post-processing framework, which operates
agnostically across tasks and models, leveraging public APIs to interact with
LLMs without direct access to internal parameters. Through a three-step process
resembling zero-shot learning, AXOLOTL identifies biases, proposes resolutions,
and guides the model to self-debias its outputs. This approach minimizes
computational costs and preserves model performance, making AXOLOTL a promising
tool for debiasing LLM outputs with broad applicability and ease of use.