  We introduce a restriction of the classical 2-party deterministic
communication protocol where Alice and Bob are restricted to using only
comparison functions. We show that the complexity of a function in the model
is, up to a constant factor, determined by a complexity measure analogous to
Yao's tiling number, which we call the geometric tiling number which can be
computed in polynomial time. As a warm-up, we consider an analogous restricted
decision tree model and observe a 1-dimensional analog of the above results.


  A computational algorithm based on recursive equations is developed in order
to estimate multigluon production processes at high energy hadron colliders.
The partonic reactions gg->(n-2)g with n up to n=9 are studied and comparisons
with known approximations are presented.


  Fermion compositness, and other new physics which can be described by an
exchange of very massive particles ($Z^\prime$ boson, leptoquarks, sparticles
with R-parity violating couplings), can be manifest itself as the presence of a
strong four-fermion contact interaction. For the processes $e^+e^-\to
\mu^+\mu^-$, $\tau^+\tau^-$, $\bar{b}b$ and $\bar{c}c$ at a future $e^+e^-$
linear collider (LC) with $\sqrt{s}=0.5$ TeV, we examine the sensitivity of the
helicity cross sections to four-fermion contact interactions. If longitudinal
polarization of the electron beam were available, two polarized integrated
cross sections would offer the opportunity to separate the helicity cross
sections and, in this way, to derive model-independent bounds on the relevant
parameters. The measurement of these polarized cross sections with optimal
kinematical cuts could significantly increase the sensitivity of helicity cross
sections to contact interaction parameters and could give crucial information
on the chiral structure of such new interactions. In addition, we consider the
application of the proposed approach to the search for manifestations of a
$Z^\prime$ for typical extended model examples.


  Finite type nilpotent spaces are weakly equivalent if and only if their
singular cochains are quasi-isomorphic as E-infinity algebras. The cochain
functor from the homotopy category of finite type nilpotent spaces to the
homotopy category of E-infinity algebras is faithful but not full.


  Demonstrations are a powerful way of increasing the transparency of AI
policies. Though informative demonstrations may be selected a priori through
the machine teaching paradigm, student learning may deviate from the
preselected curriculum in situ. This paper thus explores augmenting a
curriculum with a closed-loop teaching framework inspired by principles from
the education literature, such as the zone of proximal development and the
testing effect. We utilize tests accordingly to close to the loop and maintain
a novel particle filter model of human beliefs throughout the learning process,
allowing us to provide demonstrations that are targeted to the human's current
understanding in real time. A user study finds that our proposed closed-loop
teaching framework reduces the regret in human test responses by 43% over a
baseline.


  Under the assumption that the dijet excess seen by the CDF Collaboration near
150 Gev in Wjj production is due to the lightest technipion of the low-scale
technicolor process $\rho_T \rightarrow W \pi_T$, we study its observability in
LHC detectors for 8 TeV collisions and 20 inverse femtobarns of integrated
luminosity. We describe interesting new kinematic tests that can provide
independent confirmation of this LSTC hypothesis. We show that cuts similar to
those employed by CDF, and recently by ATLAS, cannot confirm the dijet signal.
We propose cuts tailored to the LSTC hypothesis and its backgrounds at the LHC
that may reveal $\rho_T \rightarrow \ell\nu jj$. Observation of the
isospin-related channel $\rho^{\pm}_T \rightarrow Z \pi^{\pm}_T \rightarrow
\ell^+\ell^- jj$ and of $\rho^{\pm}_T \rightarrow WZ$ in the
$\ell^+\ell^-\ell^{pm}\nu_\ell$ and $\ell^+\ell^- jj$ modes will be important
confirmations of the LSTC interpretation of the CDF signal. The $Z\pi_T$
channel is experimentally cleaner than $W\pi_T$ and its rate is known from
$W\pi_T$ by phase space. It can be discovered or excluded with the collider
data expected by the end of 2012. The $WZ \rightarrow 3\ell\nu$ channel is
cleanest of all and its rate is determined from $W\pi_T$ and the LSTC parameter
$\sin\chi$. This channel and $WZ \to \ell^+\ell^- jj$ are discussed as a
function of $\sin\chi$.


  Large Eddy Simulation (LES) with dynamic Smagorinsky model has been applied
to numerically investigate the complicated flow structures that evolve in the
near wake of a cylindrical after body aligned with a uniform Mach 2.46 flow.
Mean flow field properties obtained from numerical simulations, such as axial
velocity, pressure on base surface, have been compared with the experimental
measurements as well as with other published results. It has been found that
standard k-epsilon model fails to predict the flow properties in the
recirculation region where better agreement has been observed between the data
obtained from LES and experimental measurements. Flow Statistics like turbulent
kinetic energy and primary Reynolds stress have also been calculated and
compared with the results obtained from experiments in order to quantitatively
assess the ability of LES technique to predict the turbulence properties of
flow field in the highly compressible shear layer region. The data obtained
from LES has been further analyzed to understand the evolution of coherent
structures in the flow field. Proper Orthogonal Decomposition (POD) of the data
obtained from central plane in the wake region has been performed in order to
reveal the most energetic structures present in the flow field.


  In two dimensions, we propose and analyze an a posteriori error estimator for
the acoustic spectral problem based on the virtual element method in
$\H(\div;\Omega)$. Introducing an auxiliary unknown, we use the fact that the
primal formulation of the acoustic problem is equivalent to a mixed
formulation, in order to prove a superconvergence result, necessary to despise
high order terms. Under the virtual element approach, we prove that our local
indicator is reliable and globally efficient in the $\L^2$-norm. We provide
numerical results to assess the performance of the proposed error estimator.


  We expose in detail the principle that the relative geometric invariant
theory of equivariant morphisms is related to the GIT for linearizations near
the boundary of the $G$-effective ample cone. We then apply this principle to
construct and reconstruct various universal moduli spaces. In particular, we
constructed the universal moduli space over $\overline{M_g}$ of Simpson's
$p$-semistable coherent sheaves and a canonical dominating morphism from the
universal Hilbert scheme over $\overline{M_g}$ to a compactified universal
Picard.


  Salicylidenaniline (SA) is an archetypal system for excited-state
intramolecular proton transfer (ESIPT) in non-planar systems. Multiple channels
for relaxation involving both the keto and enol forms have been proposed after
excitation to S$_1$ with near-UV light. Here we present transient absorption
measurements of hot gas-phase SA, jet-cooled SA, and SA in Ar clusters using
cavity-enhanced transient absorption spectroscopy (CE-TAS). Assignment of the
spectra is aided by simulated TAS spectra, computed by applying time-dependent
complete active space configuration interaction (TD-CASCI) to structures drawn
from nonadiabatic molecular dynamics simulations. We find prompt ESIPT in all
conditions followed by the rapid parallel generation of the trans-keto
metastable photochrome state and fluorescent keto state in parallel. Increasing
the internal energy increases the photochrome yield and decreases the
fluorescent yield and fluorescent state lifetime observed in TAS. In Ar
clusters, internal conversion of SA is severely hindered but the photochrome
yield is unchanged. Taken together, these results are consistent with the
photochrome being produced via the vibrationally excited keto population after
ESIPT.


  We develop Bayesian nonparametric models for spatially indexed data of mixed
type. Our work is motivated by challenges that occur in environmental
epidemiology, where the usual presence of several confounding variables that
exhibit complex interactions and high correlations makes it difficult to
estimate and understand the effects of risk factors on health outcomes of
interest. The modeling approach we adopt assumes that responses and confounding
variables are manifestations of continuous latent variables, and uses
multivariate Gaussians to jointly model these. Responses and confounding
variables are not treated equally as relevant parameters of the distributions
of the responses only are modeled in terms of explanatory variables or risk
factors. Spatial dependence is introduced by allowing the weights of the
nonparametric process priors to be location specific, obtained as probit
transformations of Gaussian Markov random fields. Confounding variables and
spatial configuration have a similar role in the model, in that they only
influence, along with the responses, the allocation probabilities of the areas
into the mixture components, thereby allowing for flexible adjustment of the
effects of observed confounders, while allowing for the possibility of residual
spatial structure, possibly occurring due to unmeasured or undiscovered
spatially varying factors. Aspects of the model are illustrated in simulation
studies and an application to a real data set.


  Stochastic MPECs have found increasing relevance for modeling a broad range
of settings in engineering and statistics. Yet, there seem to be no efficient
first/zeroth-order schemes equipped with non-asymptotic rate guarantees for
resolving even deterministic variants of such problems. We consider SMPECs
where the parametrized lower-level equilibrium problem is given by a
deterministic/stochastic VI problem whose mapping is strongly monotone. We
develop a zeroth-order implicit algorithmic framework by leveraging a locally
randomized spherical smoothing scheme. We present schemes for single-stage and
two-stage stochastic MPECs when the upper-level problem is either convex or
nonconvex. (I). Single-stage SMPECs: In convex regimes, our proposed inexact
schemes are characterized by a complexity in upper-level projections,
upper-level samples, and lower-level projections of
$\mathcal{O}(\tfrac{1}{\epsilon^2})$, $\mathcal{O}(\tfrac{1}{\epsilon^2})$, and
$\mathcal{O}(\tfrac{1}{\epsilon^2}\ln(\tfrac{1}{\epsilon}))$ , respectively.
Analogous bounds for the nonconvex regime are
$\mathcal{O}(\tfrac{1}{\epsilon})$, $\mathcal{O}(\tfrac{1}{\epsilon^2})$, and
$\mathcal{O}(\tfrac{1}{\epsilon^3})$, respectively . (II). Two-stage SMPECs: In
convex regimes, our proposed inexact schemes have a complexity in upper-level
projections, upper-level samples, and lower-level projections of
$\mathcal{O}(\tfrac{1}{\epsilon^2}),\mathcal{O}(\tfrac{1}{\epsilon^2})$, and
$\mathcal{O}(\tfrac{1}{\epsilon^2}\ln(\tfrac{1}{\epsilon}))$ while the
corresponding bounds in the nonconvex regime are
$\mathcal{O}(\tfrac{1}{\epsilon})$, $\mathcal{O}(\tfrac{1}{\epsilon^2})$, and
$\mathcal{O}(\tfrac{1}{\epsilon^2}\ln(\tfrac{1}{\epsilon}))$ , respectively .
In addition, we derive statements for exact as well as accelerated
counterparts. We also provide a comprehensive set of numerical results for
validating the theoretical findings.


  We study the emission rates of scalar, spinor and vector particles from a 5
dimensional black hole for arbitrary partial waves. The solution is lifted to 6
dimensions, and the near horizon $ BTZ \times S^3$ geometry of the black hole
solution is probed to determine the greybody factors. We show that the exact
decay rates can be reproduced from a $(1+1)$-dimensional conformal field theory
which lies on the boundary of the near horizon geometry. The AdS/CFT
correspondence is used to determine the dimension of the CFT operators
corresponding to the bulk fields. These operators couple to plane waves
incident on the CFT from infinity to produce emission in the bulk.


  We report on an extensive study of the viscosity of liquid water at
near-ambient conditions, performed within the Green-Kubo theory of linear
response and equilibrium ab initio molecular dynamics (AIMD), based on
density-functional theory (DFT). In order to cope with the long simulation
times necessary to achieve an acceptable statistical accuracy, our ab initio
approach is enhanced with deep-neural-network potentials (NNP). This approach
is first validated against AIMD results, obtained by using the
Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional and paying careful
attention to crucial, yet often overlooked, aspects of the statistical data
analysis. Then, we train a second NNP to a dataset generated from the Strongly
Constrained and Appropriately Normed (SCAN) functional. Once the error
resulting from the imperfect prediction of the melting line is offset by
referring the simulated temperature to the theoretical melting one, our SCAN
predictions of the shear viscosity of water are in very good agreement with
experiments.


  We study the hyperboloidal initial value problem for the one-dimensional wave
equation perturbed by a smooth potential. We show that the evolution decomposes
into a finite-dimensional spectral part and an infinite-dimensional radiation
part. For the radiation part we prove a set of Strichartz estimates. As an
application we study the long-time asymptotics of Yang-Mills fields on a
wormhole spacetime.


  In numerical experiments involving nonlinear solitary waves propagating
through nonhomogeneous media one observes "breathing" in the sense of the
amplitude of the wave going up and down on a much faster scale than the motion
of the wave. In this paper we investigate this phenomenon in the simplest case
of stationary waves in which the evolution corresponds to relaxation to a
nonlinear ground state. The particular model is the popular $ \delta_0 $
impurity in the cubic nonlinear Schroedinger equation on the line. We give
asymptotics of the amplitude on a finite but relevant time interval and show
their remarkable agreement with numerical experiments. We stress the nonlinear
origin of the "breathing patterns" caused by the selection of the ground state
depending on the initial data, and by the non-normality of the linearized
operator.


  Many machine learning adversarial attacks find adversarial samples of a
victim model ${\mathcal M}$ by following the gradient of some attack objective
functions, either explicitly or implicitly. To confuse and detect such attacks,
we take the proactive approach that modifies those functions with the goal of
misleading the attacks to some local minimals, or to some designated regions
that can be easily picked up by an analyzer. To achieve this goal, we propose
adding a large number of artifacts, which we called $attractors$, onto the
otherwise smooth function. An attractor is a point in the input space, where
samples in its neighborhood have gradient pointing toward it. We observe that
decoders of watermarking schemes exhibit properties of attractors and give a
generic method that injects attractors from a watermark decoder into the victim
model ${\mathcal M}$. This principled approach allows us to leverage on known
watermarking schemes for scalability and robustness and provides explainability
of the outcomes. Experimental studies show that our method has competitive
performance. For instance, for un-targeted attacks on CIFAR-10 dataset, we can
reduce the overall attack success rate of DeepFool to 1.9%, whereas known
defense LID, FS and MagNet can reduce the rate to 90.8%, 98.5% and 78.5%
respectively.


  Implications are explored of promoting non-conformal scale-invariant theories
to conformal theories by nonlinearly realizing the missing symmetry. Properties
of the associated Nambu-Goldstone mode imply that conformal invariance cannot
be spontaneously broken to scale invariance in unitary theories and that, as
well known, scale invariant unitary theories in two dimensions are also
conformal. The promoted theories have only conformal primaries and no
descendants. The (non-)decoupling of the Nambu-Goldstone mode is explicitly
shown in examples of scale invariant theories that are actually (not)
conformal.


  Autoencoders provide a powerful framework for learning compressed
representations by encoding all of the information needed to reconstruct a data
point in a latent code. In some cases, autoencoders can "interpolate": By
decoding the convex combination of the latent codes for two datapoints, the
autoencoder can produce an output which semantically mixes characteristics from
the datapoints. In this paper, we propose a regularization procedure which
encourages interpolated outputs to appear more realistic by fooling a critic
network which has been trained to recover the mixing coefficient from
interpolated data. We then develop a simple benchmark task where we can
quantitatively measure the extent to which various autoencoders can interpolate
and show that our regularizer dramatically improves interpolation in this
setting. We also demonstrate empirically that our regularizer produces latent
codes which are more effective on downstream tasks, suggesting a possible link
between interpolation abilities and learning useful representations.


  We report on a concept inventory for special relativity: the development
process, data analysis methods, and results from an introductory relativity
class. The Relativity Concept Inventory tests understanding of kinematic
relativistic concepts. An unusual feature is confidence testing for each
question. This can provide additional information; for example high confidence
correlated with incorrect answers suggests a misconception. A novel aspect of
our data analysis is the use of Monte Carlo simulations to determine the
significance of correlations. This approach is particularly useful for small
sample sizes, such as ours. Our results include a gender bias that was not
present in other assessment, similar to that reported for the Force Concept
Inventory.


  The reference links to the modern classical umbral calculus before that known
as blissardian symbolic method are numerous. Rota founded and then extended
finite operator calculus has links to references which are plenty numerous. The
references via links to the difference q calculus umbra way treaded or without
even referring to umbra are giant numerous. These reference links now result in
counting in thousands the relevant papers .
  The purpose of the present attempt is to offer one of the keys to enter the
world of those thousands of references.


  This is an extension of quantum spinor construction in \cite{DF2}. We define
quantum affine Clifford algebras based on the tensor category and the solutions
of q-KZ equations, construct quantum spinor representations of $U_q(\hat{\frak
gl}(n))$ and explain classical and quantum boson-fermion correspondence.


  The mergers of black hole-neutron star binaries are calcuated using a
pseudo-general relativistic potential that incorporates ${\mathcal
O}(v^2/c^2)^3$ post-Newtonian corrections. Both normal matter neutron stars and
self-bound strange quark matter stars are considered as black hole partners. As
long as the neutron stars are not too massive relative to the black hole mass,
orbital decay terminates in stable mass transfer rather than an actual merger.
For a normal neutron star, mass transfer results in a widening of the orbit but
the stable transfer ends before the minimum neutron star mass is reached. For a
strange star, mass transfer does not result in an appreciable enlargement of
the orbital separation, and the stable transfer continues until the strange
star essentially disappears. These differences might be observable through
their respective gravitational wave signatures.


  We propose a Bayesian nonparametric method for low-pass filtering that can
naturally handle unevenly-sampled and noise-corrupted observations. The
proposed model is constructed as a latent-factor model for time series, where
the latent factors are Gaussian processes with non-overlapping spectra. With
this construction, the low-pass version of the time series can be identified as
the low-frequency latent component, and therefore it can be found by means of
Bayesian inference. We show that the model admits exact training and can be
implemented with minimal numerical approximations. Finally, the proposed model
is validated against standard linear filters on synthetic and real-world time
series.


  Generative models operate at fixed resolution, even though natural images
come in a variety of sizes. As high-resolution details are downsampled away and
low-resolution images are discarded altogether, precious supervision is lost.
We argue that every pixel matters and create datasets with variable-size
images, collected at their native resolutions. To take advantage of varied-size
data, we introduce continuous-scale training, a process that samples patches at
random scales to train a new generator with variable output resolutions. First,
conditioning the generator on a target scale allows us to generate higher
resolution images than previously possible, without adding layers to the model.
Second, by conditioning on continuous coordinates, we can sample patches that
still obey a consistent global layout, which also allows for scalable training
at higher resolutions. Controlled FFHQ experiments show that our method can
take advantage of multi-resolution training data better than discrete
multi-scale approaches, achieving better FID scores and cleaner high-frequency
details. We also train on other natural image domains including churches,
mountains, and birds, and demonstrate arbitrary scale synthesis with both
coherent global layouts and realistic local details, going beyond 2K resolution
in our experiments. Our project page is available at:
https://chail.github.io/anyres-gan/.


  We set up a correspondence between solutions of the Yang-Mills equations on
${\mathbb R}\times S^3$ and in Minkowski spacetime via de Sitter space. Some
known Abelian and non-Abelian exact solutions are rederived. For the Maxwell
case we present a straightforward algorithm to generate an infinite number of
explicit solutions, with fields and potentials in Minkowski coordinates given
by rational functions of increasing complexity. We illustrate our method with a
nontrivial example.


  As learning-based methods make their way from perception systems to
planning/control stacks, robot control systems have started to enjoy the
benefits that data-driven methods provide. Because control systems directly
affect the motion of the robot, data-driven methods, especially black box
approaches, need to be used with caution considering aspects such as stability
and interpretability. In this paper, we describe a differentiable and
hierarchical control architecture. The proposed representation, called
\textit{multi-abstractive neural controller}, uses the input image to control
the transitions within a novel discrete behavior planner (referred to as the
visual automaton generative network, or \textit{vAGN}). The output of a vAGN
controls the parameters of a set of dynamic movement primitives which provides
the system controls. We train this neural controller with real-world driving
data via behavior cloning and show improved explainability, sample efficiency,
and similarity to human driving.


  We consider the problem of fusing measurements from multiple sensors, where
the sensing regions overlap and data are non-negative---possibly resulting from
a count of indistinguishable discrete entities. Because of overlaps, it is, in
general, impossible to fuse this information to arrive at an accurate estimate
of the overall amount or count of material present in the union of the sensing
regions. Here we study the range of overall values consistent with the data.
Posed as a linear programming problem, this leads to interesting questions
associated with the geometry of the sensor regions, specifically, the
arrangement of their non-empty intersections. We define a computational tool
called the fusion polytope and derive a condition for this to be in the
positive orthant thus simplifying calculations. We show that, in two
dimensions, inflated tiling schemes based on rectangular regions fail to
satisfy this condition, whereas inflated tiling schemes based on hexagons do.


  We theoretically and numerically investigate the generation of
fractional-charge vortex dipoles in spinor condensates with non-zero
magnetization. We find that in the antiferromagnetic phase of spin-1 and spin-2
and the cyclic phase of spin-2 condensate with non-zero magnetization coupling
of the density (phonon) and a spin-excitation mode results in two critical
speeds for vortex-antivortex pair creation in the condensate. As a result, a
Gaussian obstacle potential moving across the antiferromagnetic spin-1 or
spin-2 and cyclic spin-2 spinor condensates with non-zero magnetization can
lead to the creation of fractional-charge vortex dipoles. On the other hand,
for zero magnetization, the two modes get decoupled, which is illustrated by a
single critical speed for vortex-antivortex pair creation in the condensate due
to the phonon excitation mode.


  With power consumption becoming a critical processor design issue,
specialized architectures for low power processing are becoming popular.
Several studies have shown that neural networks can be used for signal
processing and pattern recognition applications. This study examines the design
of memristor based multicore neural processors that would be used primarily to
process data directly from sensors. Additionally, we have examined the design
of SRAM based neural processors for the same task. Full system evaluation of
the multicore processors based on these specialized cores were performed taking
I/O and routing circuits into consideration. The area and power benefits were
compared with traditional multicore RISC processors. Our results show that the
memristor based architectures can provide an energy efficiency between three
and five orders of magnitude greater than that of RISC processors for the
benchmarks examined.


  As part of an ongoing investigation of student learning in upper-division
quantum mechanics, we needed a high-quality conceptual assessment instrument
for comparing outcomes of different curricular approaches. The 14 item
open-ended Quantum Mechanics Assessment Tool (QMAT) was previously developed
for this purpose. However, open-ended tests require complex scoring rubrics,
are difficult to score consistently, and demand substantial investment of
faculty time to grade. Here, we present the process of converting open-ended
questions to multiple-choice (MC) format. We highlight the construction of
effective distractors and the use of student interviews to revise and validate
questions and distractors. We examine other elements of the process, including
results of a preliminary implementation of the MC assessment given at Cal Poly
Pomona and CU Boulder.


  Based on extensive statistical-equilibrium calculations, we performed a
non-LTE analysis of the K {\sc i} 7699 equivalent-width data of metal-deficient
stars for the purpose of clarifying the behavior of the photospheric potassium
abundance in disk/halo stars. While the resulting non-LTE abundance corrections
turned out to be considerably large, amounting to 0.2--0.7 dex, their effect on
the [K/Fe] vs. [Fe/H] relation is not very important, since these corrections
do not show any significant metallicity dependence. Hence, we again confirmed
the results of previous LTE studies, that [K/Fe] shows a gradual systematic
increase toward a lowered metallicity up to [K/Fe] $\sim$ 0.3--0.5 at [Fe/H]
$\sim$ -1 to -2, such as in the case of $\alpha$ elements.


  We study semigroup algebras arising from lattice polytopes, compute their
volume polynomials (particularizing work of Hochster), and establish strong
Lefschetz properties (generalizing work of the first three authors). This
resolves several conjectures concerning unimodality properties of the
$h^\ast$-polynomial of lattice polytopes arising within Ehrhart theory.


  We review new and published results to examine how well the bolometric flux
of starbursts can be recovered from ultraviolet (UV) and optical observations.
We show that the effective absorption of starbursts can be substantial, up to
\~10 mag in the far UV, and ~5 mag in H-alpha, but apparently not as high as
some claims in the literature (several tens to a thousand mag). The bolometric
fluxes of an IUE sample of starbursts can be recovered to 0.14 dex accuracy
using the UV flux and spectral slope. However, this relationship breaks down
for Ultra Luminous Infrared Galaxies (ULIGs). The H-alpha flux combined with
the Balmer decrement can be used to predict the bolometric flux to 0.5 dex
accuracy for starbursts including most ULIGs. These results imply a foreground
screen component to the dust distribution.


  To investigate the origin of elevated globular cluster abundances observed
around Ultra-Diffuse Galaxies (UDGs), we simulate globular cluster populations
hosted by UDGs formed through tidal heating. Specifically, globular cluster
(GC) formation is modeled as occurring in regions of dense star formation.
Because star-formation-rate-densities are higher at high redshift, dwarf
galaxies in massive galaxy clusters, which formed most of their stars at high
redshift, form a large fraction of their stars in globular clusters. Given that
UDGs formed through environmental processes are more likely to be accreted at
high redshift, these systems have more GCs than non-UDGs. In particular, our
model predicts that massive UDGs have twice the GC mass of non-UDGs of similar
stellar mass, in rough agreement with observations. Although this effect is
somewhat diminished by GC disruption, we find that the relationship between GC
mass fraction and cluster-centric distance, and the relationship between GC
mass fraction and galaxy half-light radius are remarkably similar to
observations. Among our model objects, both UDGs and non-UDGs present a
correlation between halo mass and GC mass, although UDGs have lower dynamical
masses at a given GC mass. Furthermore, because of the effectiveness of GC
disruption, we predict that GCs around UDGs should have a more top heavy mass
function than GCs around non-UDGs. This analysis suggests that dwarfs with
older stellar populations, such as UDGs, should have higher globular cluster
mass fractions than objects with young stellar populations, such as isolated
dwarfs.


  The dynamic capacity theorem characterizes the reliable communication rates
of a quantum channel when combined with the noiseless resources of classical
communication, quantum communication, and entanglement. In prior work, we
proved the converse part of this theorem by making contact with many previous
results in the quantum Shannon theory literature. In this work, we prove the
theorem with an "ab initio" approach, using only the most basic tools in the
quantum information theorist's toolkit: the Alicki-Fannes' inequality, the
chain rule for quantum mutual information, elementary properties of quantum
entropy, and the quantum data processing inequality. The result is a simplified
proof of the theorem that should be more accessible to those unfamiliar with
the quantum Shannon theory literature. We also demonstrate that the "quantum
dynamic capacity formula" characterizes the Pareto optimal trade-off surface
for the full dynamic capacity region. Additivity of this formula simplifies the
computation of the trade-off surface, and we prove that its additivity holds
for the quantum Hadamard channels and the quantum erasure channel. We then
determine exact expressions for and plot the dynamic capacity region of the
quantum dephasing channel, an example from the Hadamard class, and the quantum
erasure channel.


  Accurately predicting road networks from satellite images requires a global
understanding of the network topology. We propose to capture such high-level
information by introducing a graph-based framework that simulates the addition
of sequences of graph edges using a reinforcement learning (RL) approach. In
particular, given a partially generated graph associated with a satellite
image, an RL agent nominates modifications that maximize a cumulative reward.
As opposed to standard supervised techniques that tend to be more restricted to
commonly used surrogate losses, these rewards can be based on various complex,
potentially non-continuous, metrics of interest. This yields more power and
flexibility to encode problem-dependent knowledge. Empirical results on several
benchmark datasets demonstrate enhanced performance and increased high-level
reasoning about the graph topology when using a tree-based search. We further
highlight the superiority of our approach under substantial occlusions by
introducing a new synthetic benchmark dataset for this task.


  Stochastic Loewner evolution (SLE) is a differential equation driven by a
one-dimensional Brownian motion (BM), whose solution gives a stochastic process
of conformal transformation on the upper half complex-plane $\H$. As an
evolutionary boundary of image of the transformation, a random curve (the SLE
curve) is generated, which is starting from the origin and running in $\H$
toward the infinity as time is going. The SLE curves provides a variety of
statistical ensembles of important fractal curves, if we change the diffusion
constant of the driving BM. In the present paper, we consider the
Schwarz-Christoffel transformation (SCT), which is a conformal map from $\H$ to
the region $\H$ with a slit starting from the origin. We prepare a binomial
system of SCTs, one of which generates a slit in $\H$ with an angle $\alpha
\pi$ from the positive direction of the real axis, and the other of which with
an angle $(1-\alpha) \pi$. One parameter $\kappa >0$ is introduced to control
the value of $\alpha$ and the length of slit. Driven by a one-dimensional
random walk, which is a binomial stochastic process, a random iteration of SCTs
is performed. By interpolating tips of slits by straight lines, we have a
random path in $\H$, which we call an Iterative SCT (ISCT) path. It is
well-known that, as the number of steps $N$ of random walk goes infinity, each
path of random walk divided by $\sqrt{N}$ converges to a Brownian curve. Then
we expect that the ISCT paths divided by $\sqrt{N}$ (the rescaled ISCT paths)
converge to the SLE curves in $N \to \infty$. Our numerical study implies that,
for sufficiently large $N$, the rescaled ISCT paths will have the same
statistical properties as the SLE curves have, supporting our expectation.


  We study the potential of an e+- e- Linear Collider for charged lepton
flavour violation studies in a supersymmetric framework where neutrino masses
and mixings are explained by a type-I seesaw. Focusing on e-mu flavour
transitions, we evaluate the background from standard model and supersymmetric
charged currents to the e mu + missing E_T signal. We study the energy
dependence of both signal and background, and the effect of beam polarisation
in increasing the signal over background significance. Finally, we consider the
mu- mu- + missing E_T final state in e- e- collisions that, despite being
signal suppressed by requiring two e-mu flavour transitions, is found to be a
clear signature of charged lepton flavour violation due to a very reduced
standard model background.


  We explored the possibility of realizing quantum anomalous Hall effect by
placing heavy-element atomic layer on top of monolayer CrI$_{3}$ with a natural
cleavage surface and broken time-reversal symmetry. We showed that CrI$_{3}$/X
(X = Bi, Sb, or As) systems can open up a sizable bulk gap to harbour quantum
anomalous Hall effect, e.g., CrI$_{3}$/Bi is a natural magnetic insulator with
a bulk gap of 30~meV, which can be further enlarged via strain engineering or
adjusting spin orientations. We also found that the ferromagnetic properties
(magnetic anisotropic energy and Curie temperature) of pristine CrI$_{3}$ can
be further improved due to the presence of heavy atomic layers, and the spin
orientation can be utilized as a useful knob to tune the band structure and
Fermi level of CrI$_{3}$/Bi system. The topological nature, together with the
enhanced ferromagnetism, can unlock new potential applications for
CrI$_{3}$-based materials in spintronics and electronics.


  In this paper, we investigate the three dimensional stationary compressible
Navier-Stokes equations, and obtain Liouville type theorems if a smooth
solution $(\rho, \mathbf{u})$ satisfies some suitable conditions. In
particular, our results improve and generalize the corresponding result of Li
and Yu (2014) [8].


  We consider a system of nonlinear equations that extends the Maxwell theory.
It was pointed out in a previous paper that symmetric solutions of these
equations display properties characteristic of magnetic oscillations. In this
paper I study a discrete model of the equations in two dimensions. This leads
to the discovery of a new mechanism of vortex lattice formation. Namely, when a
parameter corresponding to a magnetic field normal to the surface increases
above a certain critical level, the trivial uniform-magnetic-field solution
becomes, in a certain sense, unstable and a periodic vortex lattice solution
emerges. The discrete vortex solutions are proven to exist, and can also be
found numerically with high accuracy. Description of magnetic vortices given by
the equations is optical in spirit, and may be particularly attractive in the
context of high-$T_c$ superconductivity and the quantum Hall effects. Moreover,
analysis of parameters involved in the discrete theory suggests existence of
continuous domain solutions---a conjecture that seems unobvious on grounds of
the current topological and variational methods.


  The Maxwell equations have a fairly simple form. However, finding solutions
of Maxwell's equations is an extremely difficult task. Therefore, various
simplifying approaches are often used in optics. One such simplifying approach
is to use the approximation of geometric optics. The approximation of geometric
optics is constructed with the assumption that the wavelengths are small
(short-wavelength approximation). The basis of geometric optics is the eikonal
equation. The eikonal equation can be obtained from the wave equation
(Helmholtz equation). Thus, the eikonal equation relates the wave and geometric
optics. In fact, the eikonal equation is a quasi-classical approximation (the
Wentzel-Kramers-Brillouin method) of wave optics. This paper shows the
application of geometric methods of electrodynamics to the calculation of
optical devices, such as Maxwell and Luneburg lenses. The eikonal equation,
which was transformed to the ODE system by the method of characteristics, is
considered. The resulting system is written for the case of Maxwell and
Luneburg lenses.


  High-resolution time- and angle-resolved photoemission measurements were
conducted on the topological insulator ZrTe5. With strong femtosecond
photoexcitation, a possible ultrafast phase transition from a weak to a strong
topological insulating phase was experimentally realized by recovering the
energy gap inversion in a time scale that was shorter than 0.15 ps. This
photoinduced transient strong topological phase can last longer than 2 ps at
the highest excitation fluence studied, and it cannot be attributed to the
photoinduced heating of electrons or modification of the conduction band
filling. Additionally, the measured unoccupied electronic states are consistent
with the first-principles calculation based on experimental crystal lattice
constants, which favor a strong topological insulating phase. These findings
provide new insights into the longstanding controversy about the strong and
weak topological properties in ZrTe5, and they suggest that many-body effects
including electron-electron interactions must be taken into account to
understand the equilibrium weak topological insulating phase in ZrTe5.


  There has been an increasing interest in testing the equality of large
Pearson's correlation matrices. However, in many applications it is more
important to test the equality of large rank-based correlation matrices since
they are more robust to outliers and nonlinearity. Unlike the Pearson's case,
testing the equality of large rank-based statistics has not been well explored
and requires us to develop new methods and theory. In this paper, we provide a
framework for testing the equality of two large U-statistic based correlation
matrices, which include the rank-based correlation matrices as special cases.
Our approach exploits extreme value statistics and the Jackknife estimator for
uncertainty assessment and is valid under a fully nonparametric model.
Theoretically, we develop a theory for testing the equality of U-statistic
based correlation matrices. We then apply this theory to study the problem of
testing large Kendall's tau correlation matrices and demonstrate its
optimality. For proving this optimality, a novel construction of least
favourable distributions is developed for the correlation matrix comparison.


  In this paper, we investigate discounted economic model predictive control
(E-MPC) schemes without terminal conditions in scenarios where the optimal
operating behavior is a periodic orbit. For such a setting, it is known that a
linearly discounted stage cost guarantees asymptotic stability of any
arbitrarily small neighborhood of the optimal orbit if the prediction horizon
is sufficiently long. However, in some examples very long prediction horizons
are needed to achieve the desired performance. In this work, we extend these
results by providing the same qualitative stability guarantees for a large
class of discount functions. Numerical examples illustrate the influence of the
discount function and show that with suitable discounting we can achieve
significantly better performance than the linearly discounted E-MPC, even for
short prediction horizons.


  Low-energy instabilities in the hole doped cuprates include, besides short
range antiferromagnetic fluctuations and superconductivity, also ubiquitous
translational and rotational symmetry breakings. The overwhelming majority of
interpretations of these possibly related properties rely on mappings onto
three bands spanned by the three atomic orbitals Cu3d(x2-y2)(sigma),
O2px(sigma), and O2py(sigma), these three local orbitals spanning the
Zhang-Rice band (ZRB), the lower Hubbard bands (LHB) and the upper Hubbard
bands (UHB), respectively. Here we demonstrate by means of supercell Density
Functional Theory (DFT) (a) how oxygen intercalation affects the structures of
the buffer layers, and (b) how the attenuated crystal field pulls two
additional oxygen bands in the CuO2 plane to the Fermi level. The
self-consistent changes in electronic structure reflected in the corresponding
changes in external potential comprise formal properties of the Hohenberg-Kohn
theorems. Validation of present days' approximate exchange-correlation
potentials to capture these qualitative effects by means of supercell DFT is
made by comparing computed doping dependent structural shifts to corresponding
experimentally observed correlations. The simplest generalization of
Bardeen-Cooper-Schrieffer (BCS) theory is offered to articulate high critical
temperature superconductivity (HTS) from a normal state where crystal field
causes states related to two non-hybridizing bands to coalesce at EF.


  It has been widely accepted that Long Short-Term Memory (LSTM) network,
coupled with attention mechanism and memory module, is useful for aspect-level
sentiment classification. However, existing approaches largely rely on the
modelling of semantic relatedness of an aspect with its context words, while to
some extent ignore their syntactic dependencies within sentences. Consequently,
this may lead to an undesirable result that the aspect attends on contextual
words that are descriptive of other aspects. In this paper, we propose a
proximity-weighted convolution network to offer an aspect-specific syntax-aware
representation of contexts. In particular, two ways of determining proximity
weight are explored, namely position proximity and dependency proximity. The
representation is primarily abstracted by a bidirectional LSTM architecture and
further enhanced by a proximity-weighted convolution. Experiments conducted on
the SemEval 2014 benchmark demonstrate the effectiveness of our proposed
approach compared with a range of state-of-the-art models.


  The magnetoresistance oscillations in GaAs/Al$_x$Ga$_{1-x}$As
heterostructures induced by millimeterwave radiation recently observed by Zudov
et al. [Phys. Rev. B {\bf 64}, 201311 (2001)] is theoretically reproduced by
introducing a model based on the finite temperature Fermi liquid theory of dc
conductivity and the electron reservoir hypothesis. The obtained oscillation
patterns show excellent agreement with the experimental result by Zudov et al.
and are independent of the polarization of the radiation field in accordance
with the experimental observation by Smet et al. [Phys. Rev. Lett. {\bf 95},
116804 (2005)].


  We demonstrate the existence of ferromagnetism in the Periodic Anderson Model
(PAM) at conduction-band filling near a quarter. We show that this
ferromagnetism is not supported by Ruderman-Kittel-Kasuya-Yosida (RKKY)
interactions but is instead driven by the precursors of charge density wave
(CDW) formation in the conduction electron band. To study the effect of spatial
correlations, we compare Dynamical Mean field Approximation (DMFA) and
Dynamical Cluster Approximation (DCA) results. We find that both RKKY and CDW
driven ferromagnetism persist as short-range correlations are incorporated into
the theory. Both DMFA and DCA show the precursors of CDW formation through the
strong enhancement of the d-electron CDW susceptibility as the temperature
decreases, up to the ferromagnetic transition temperature. In addition, the DCA
captures the signal of a band gap opening due to Peierls instability.


  By analyzing 2.93 fb$^{-1}$ of $e^+e^-$ collision data taken at the
center-of-mass energy of 3.773 GeV with the BESIII detector, the branching
fractions of the inclusive decays $D^+\to K^0_S X$ and $D^0\to K^0_S X$ are
measured to be $(32.78\pm 0.13\pm 0.27)\%$ and $(20.54\pm 0.12\pm 0.18)\%$,
respectively, where the first uncertainties are statistical and the second are
systematic. These results are consistent with the world averages of previous
measurements, but with improved precision.


  We present a method to measure the integral vertical intensity and angular
distribution of atmospheric muons using a stationary thick plastic scintillator
bar detector with PMTs at both of its ends over exposures of a few hours in a
laboratory setting. The total flux is obtained from the event rate and the
angular distribution is inferred from the distribution of the recorded pulse
charges, which are correlated with the track length inside the plastic
scintillator. A muon generator algorithm was developed and used together with a
simple simulation including the effects of the detector resolution, nonlinear
saturation of the PMTs, and laboratory building coverage. As a proof of
principle we made a measurement assuming a standard $\cos^n\theta$
omnienergetic angular distribution with azimuthal isotropy and different models
for the energy spectrum of the source. Using measurements at 5 different
azimuthal orientations, we measure an average exponent $n=(1.90\pm 0.06({\rm
stat})\pm 0.10({\rm syst}))$, and an average vertical intensity of
$I_0=(101.2\pm 1.8({\rm stat})\pm 5.5({\rm syst}))$ $~{\rm m}^{-2}{\rm
s}^{-1}{\rm sr}^{-1}$ at the location with geographic coordinates
19.33$^\circ$N~99.19$^\circ$W, altitude 2,268 m above sea level, and
geomagnetic cut-off of 8.2 GV.


  We begin with an overview of the experimental results for the temperature and
doping dependences of the optical-conductivity spectral weight in cuprate
superconductors across the whole phase diagram. Then we discuss recent attempts
to explain the observed behavior of the spectral weight using reduced and full
models with unconventional $d_{x^2-y^2}$ charge-density waves.


  The possibility to induce predetermined coherent quantum dynamics by
controlling only the dissipative environmental parameters (such as temperature
and pressure) is studied using the combined optimal control and environment
engineering frameworks. As an example, we consider the problem of transforming
an optically excited donor state into free charge carriers via intermediate
higher-lying bridge state(s), with a view to solar energy conversion. In this
context, vibrational bath engineering allows to promote fast, directional
charge transfer and to suppress recombinative losses.


  Uncertainties in the theoretical prediction for the inclusive $B\to
X_s\gamma$ decay rate are discussed. We emphasize that there is no operator
product expansion for this process. Nonetheless, some nonperturbative effects
involving a virtual $c\bar c$ loop are calculable using the operator product
expansion. They give a contribution to the decay rate that involves the B meson
matrix element of an infinite tower of operators. The higher dimension
operators give effects that are only suppressed by powers of
$m_b\Lambda_{QCD}/m_c^2 \sim 0.6$, but come with small coefficients.


  The article considers systems of interacting particles on networks with
adaptively coupled dynamics. Such processes appear frequently in natural
processes and applications. Relying on the notion of graph convergence, we
prove that for large systems the dynamics can be approximated by the
corresponding continuum limit. Well-posedness of the latter is also
established.


  In this paper, a ratio-dependent Holling-Tanner system with nonlocal
diffusion is taken into account, where the prey is subject to a strong Allee
effect. To be special, by applying Schauder's fixed point theorem and iterative
technique, we provide a general theory on the existence of traveling waves for
such system. Then appropriate upper and lower solutions and a novel sequence,
similar to squeeze method, are constructed to demonstrate the existence of
traveling waves for c>c*. Moreover, the existence of traveling wave for c=c* is
also established by spreading speed theory and comparison principle. Finally,
the nonexistence of traveling waves for c<c* is investigated, and the minimal
wave speed then is determined.


  With the wide adoption of machine learning techniques, requirements have
evolved beyond sheer high performance, often requiring models to be
trustworthy. A common approach to increase the trustworthiness of such systems
is to allow them to refrain from predicting. Such a framework is known as
selective prediction. While selective prediction for classification tasks has
been widely analyzed, the problem of selective regression is understudied. This
paper presents a novel approach to selective regression that utilizes
model-agnostic non-parametric uncertainty estimation. Our proposed framework
showcases superior performance compared to state-of-the-art selective
regressors, as demonstrated through comprehensive benchmarking on 69 datasets.
Finally, we use explainable AI techniques to gain an understanding of the
drivers behind selective regression. We implement our selective regression
method in the open-source Python package doubt and release the code used to
reproduce our experiments.


  Ever since the formulation of quantum mechanics, there is very little
understanding of the process of the collapse of a wavefunction. We have
proposed a dynamical model to emulate the measurement postulates of quantum
mechanics. We postulate that a non-Hermitian Hamiltonian operates during the
process of measurement, which evolves any state to an attracting equilibrium
state, thus, mimicking a "collapse". We demonstrate this using a 2-level system
and then extend it to an N-level system. For a 2-level system, we also
demonstrate that the dynamics generated by the Lindblad master equation can be
replicated as an incoherent sum of the evolution by two separate non-Hermitian
Hamiltonians.


  Heat flow between a large ``bath'' and a smaller system brings them
progressively closer to thermal equilibrium while increasing their entropy.
Deviations from this trend are fluctuations involving a small fraction of a
statistical ensemble of systems interacting with the bath: in this respect,
quantum and classical thermodynamics are in agreement. Can there be drastic
differences between them? Here we address a distinctly quantum mechanical
setting that displays such differences: disturbances of thermal equilibrium
between two-level systems (TLS) and a bath by frequent and brief quantum
(non-demolishing) measurements of the TLS energy-states. If the measurements
are frequent enough to induce either the Zeno or the anti-Zeno regime, namely,
the slowdown or speedup of the TLS relaxation, then the resulting entropy and
temperature of both the system and the bath are found to be completely
unrelated to what is expected by standard thermodynamical rules that hold for
memoryless baths. The practical advantage of these anomalies is the possibility
of very fast control of heat and entropy, allowing cooling and
state-purification of quantum systems much sooner than their thermal
equilibration time.


  Simulation-based digital twins must provide accurate, robust and reliable
digital representations of their physical counterparts. Quantifying the
uncertainty in their predictions plays, therefore, a key role in making
better-informed decisions that impact the actual system. The update of the
simulation model based on data must be then carefully implemented. When applied
to complex standing structures such as bridges, discrepancies between the
computational model and the real system appear as model bias, which hinders the
trustworthiness of the digital twin and increases its uncertainty. Classical
Bayesian updating approaches aiming to infer the model parameters often fail at
compensating for such model bias, leading to overconfident and unreliable
predictions. In this paper, two alternative model bias identification
approaches are evaluated in the context of their applicability to digital twins
of bridges. A modularized version of Kennedy and O'Hagan's approach and another
one based on Orthogonal Gaussian Processes are compared with the classical
Bayesian inference framework in a set of representative benchmarks.
Additionally, two novel extensions are proposed for such models: the inclusion
of noise-aware kernels and the introduction of additional variables not present
in the computational model through the bias term. The integration of such
approaches in the digital twin corrects the predictions, quantifies their
uncertainty, estimates noise from unknown physical sources of error and
provides further insight into the system by including additional pre-existing
information without modifying the computational model.


  Metallic layers are known to be used for the suppression of wave transmission
when their thickness is sufficiently higher than the skin depth of metal. If in
addition to blocking the transmission, metallic layers have the feature of
blocking the reflection, too, they would make perfect absorbers. In this work,
we propose an experimental approach of using a single thin layer of Manganese
(Mn) as both the transmission suppresser and the reflection suppresser. This
approach leads to obtaining lithography-free ultra-broadband perfect absorption
in an ultra-wide spectrum ranging from Ultraviolet (UV) to Far Infrared (FIR).
The measured average absorption is approximately 99%. Such a promising result
can be achieved by only coating a single Mn layer on high-roughness substrates
that include random nano-pyramids on it. In other words, we do not need a stack
of different materials and combinations of geometrical features. The high
roughness is realized on a commercial Silicon wafer substrate by inductively
coupled plasma (ICP) etching. The key to this ultra-wideband absorption is
electromagnetic field tapering which exists due to the graded-index feature of
the structure (known as moth-eye effect), along with the ideal optical
properties of Mn which makes it an excellent metal for broadband absorption
applications. A full experimental characterization of the fabricated samples is
presented along with the physical analysis of the phenomena. The findings of
this paper can be used for the realization of lithography-free, cost-effective
and high-throughput mass production of broadband absorbers.


  In this paper, we establish a higher rank extension of rigidity theorems of
Sullivan, Tukia, Yue, and Kim-Oh for representations of rank one discrete
subgroups of divergence type, in terms of the push-forwards of conformal
measures via boundary maps. We consider a certain class of higher rank discrete
subgroups, which we call hypertransverse subgroups. It includes all rank one
discrete subgroups, Anosov subgroups, relatively Anosov subgroups, and their
subgroups.
  Our proof of the rigidity theorem generalizes the idea of Kim-Oh to
self-joinings of higher rank hypertransverse subgroups, overcoming the lack of
CAT(-1) geometry on symmetric spaces. In contrast to the work of Sullivan,
Tukia, and Yue, our argument is closely related to the study of horospherical
foliations. We also show the ergodicity of horospherical foliations with
respect to Burger-Roblin measures. This generalizes the classical work of
Hedlund, Burger, and Roblin in rank one and of Lee-Oh for Borel Ansov subgroups
in higher rank.


  We present direct evidence that magnetic clouds (MCs) have highly flattened
and curved cross section resulting from their interaction with the ambient
solar wind. Lower limits on the transverse size are obtained for three MCs
observed by ACE and Ulysses from the latitudinal separation between the two
spacecraft, ranging from 40$^{\circ}$ to 70$^{\circ}$. The cross-section aspect
ratio of the MCs is estimated to be no smaller than $6:1$. We offer a simple
model to extract the radius of curvature of the cross section, based on the
elevation angle of the MC normal distributed over latitude. Application of the
model to Wind observations from 1995 - 1997 (close to solar minimum) shows that
the cross section is bent concavely outward by a structured solar wind with a
radius of curvature of $\sim$ 0.3 AU. Near solar maximum, MCs tend to be convex
outward in the solar wind with a uniform speed; the radius of curvature is
proportional to the heliographic distance of MCs, as demonstrated by Ulysses
observations between 1999 and 2003. These results improve our knowledge of the
global morphology of MCs in the pre-Stereo era, which is crucial for space
weather prediction and heliosphere studies.


  Understanding the rich physics of magnetization dynamics in perpendicular
synthetic antiferromagnets (p-SAFs) is crucial for developing next-generation
spintronic devices. In this work, we systematically investigate the
magnetization dynamics in p-SAFs combining time-resolved magneto-optical Kerr
effect (TR-MOKE) measurements with theoretical modeling. These model analyses,
based on a Landau-Lifshitz-Gilbert approach incorporating exchange coupling,
provide details about the magnetization dynamic characteristics including the
amplitudes, directions, and phases of the precession of p-SAFs under varying
magnetic fields. These model-predicted characteristics are in excellent
quantitative agreement with TR-MOKE measurements on an asymmetric p-SAF. We
further reveal the damping mechanisms of two procession modes co-existing in
the p-SAF and successfully identify individual contributions from different
sources, including Gilbert damping of each ferromagnetic layer, spin pumping,
and inhomogeneous broadening. Such a comprehensive understanding of
magnetization dynamics in p-SAFs, obtained by integrating high-fidelity TR-MOKE
measurements and theoretical modeling, can guide the design of p-SAF-based
architectures for spintronic applications.


  We derive optimality conditions for the optimum sample allocation problem in
stratified sampling, formulated as the determination of the fixed strata sample
sizes that minimize the total cost of the survey, under the assumed level of
variance of the stratified $\pi$ estimator of the population total (or mean)
and one-sided upper bounds imposed on sample sizes in strata. In this context,
we presume that the variance function is of some generic form that, in
particular, covers the case of the simple random sampling without replacement
design in strata. The optimality conditions mentioned above will be derived
from the Karush-Kuhn-Tucker conditions. Based on the established optimality
conditions, we provide a formal proof of the optimality of the existing
procedure, termed here as LRNA, which solves the allocation problem considered.
We formulate the LRNA in such a way that it also provides the solution to the
classical optimum allocation problem (i.e. minimization of the estimator's
variance under a fixed total cost) under one-sided lower bounds imposed on
sample sizes in strata. In this context, the LRNA can be considered as a
counterparty to the popular recursive Neyman allocation procedure that is used
to solve the classical problem of an optimum sample allocation with added
one-sided upper bounds. Ready-to-use R-implementation of the LRNA is available
through our stratallo package, which is published on the Comprehensive R
Archive Network (CRAN) package repository.


  Local inertial frame invariance is taken as the fundamental principle of
physical geometry, where a local inertial frame is represented by a verbein.
Invariance of the vierbein with respect to local Lorentz transformations then
expresses local inertial frame invariance. The dynamics of physical geometry
develops as a gauge theory of the verbein that is closely analogous to the
Yang-Mills field provided the verbein connection and curvature correspond to
the geometric potential and field respectively. The resulting theory is shown
to be equivalent to Einstein's tensor form of relativistic gravitation.


  In a material prone to a nematic instability, anisotropic strain in principle
provides a preferred symmetry-breaking direction for the electronic nematic
state to follow. This is consistent with experimental observations, where
electronic nematicity and structural anisotropy typically appear hand-in-hand.
In this work, we discover that electronic nematicity can be locally decoupled
from the underlying structural anisotropy in strain-engineered iron-selenide
(FeSe) thin films. We use heteroepitaxial molecular beam epitaxy to grow FeSe
with a nanoscale network of modulations that give rise to spatially varying
strain. We map local anisotropic strain by analyzing scanning tunneling
microscopy topographs, and visualize electronic nematic domains from
concomitant spectroscopic maps. While the domains form so that the energy of
nemato-elastic coupling is minimized, we observe distinct regions where
electronic nematic ordering fails to flip direction, even though the underlying
structural anisotropy is locally reversed. The findings point towards a
nanometer-scale stiffness of the nematic order parameter.


  The advancements in computer vision and image processing techniques have led
to emergence of new application in the domain of visual surveillance, targeted
advertisement, content-based searching, and human-computer interaction etc. Out
of the various techniques in computer vision, face analysis, in particular, has
gained much attention. Several previous studies have tried to explore different
applications of facial feature processing for a variety of tasks, including age
and gender classification. However, despite several previous studies having
explored the problem, the age and gender classification of in-wild human faces
is still far from the achieving the desired levels of accuracy required for
real-world applications. This paper, therefore, attempts to bridge this gap by
proposing a hybrid model that combines self-attention and BiLSTM approaches for
age and gender classification problems. The proposed models performance is
compared with several state-of-the-art model proposed so far. An improvement of
approximately 10percent and 6percent over the state-of-the-art implementations
for age and gender classification, respectively, are noted for the proposed
model. The proposed model is thus found to achieve superior performance and is
found to provide a more generalized learning. The model can, therefore, be
applied as a core classification component in various image processing and
computer vision problems.


  The quantum Rabi-Stark model, where the linear dipole coupling and the
nonlinear Stark-like coupling are present on an equal footing, are studied
within the Bogoliubov operators approach. Transcendental functions responsible
for the exact solutions are derived in a compact way, much simpler than
previous ones obtained in the Bargmann representation. The zeros of
transcendental functions reproduce completely the regular spectra. In terms of
the explicit pole structure of these functions, two kinds of exceptional
eigenvalues are obtained and distinguished in a transparent manner. Very
interestingly, a first-order quantum phase transition indicated by level
crossing of the ground state and the first excited state is induced by the
positive nonlinear Stark-like coupling, which is however absent in any previous
isotropic quantum Rabi models. When the absolute value of the nonlinear
coupling strength is equal to twice the cavity frequency, this model can be
reduced to an effective quantum harmonic oscillator, and solutions are then
obtained analytically. The spectra collapse phenomenon is observed at a
critical coupling, while below this critical coupling, infinite discrete
spectra accumulate into a finite energy from below.


  We revisit the minimal supersymmetric SU(5) grand unified theory with three
right-handed neutrinos in which universality conditions for soft-supersymmetry
breaking parameters are imposed at an input scale above the unification scale.
If the Majorana masses for the neutrinos are around $10^{15}$ GeV, large mixing
angles and phases in the neutrino sector lead to flavor-violation and
CP-violation in the right-handed down squark and left-handed slepton sectors.
Since the observed Higgs boson mass and the proton decay constraints indicate
sfermions have masses larger than a few TeV, flavor and CP constraints are less
restrictive. We explore the constraints on models with a universal
soft-supersymmetry breaking input parameters coming from proton stability,
electric dipole moments, $\mu\to e\gamma$ decays, and the Higgs mass observed
at the LHC. Regions compatible with all constraints can be found if non-zero
A-terms are taken.


  We define an associative algebra AS_h(S) generated by framed arcs and links
over a punctured surface S which is a quantization of the Poisson algebra C(S)
of arcs and curves on S. We then construct a Poisson algebra homomorphism from
C(S) to the space of smooth functions on the decorated Teichmuller space
endowed with the Weil-Petersson Poisson structure. The construction relies on a
collection of geodesic lengths identities in hyperbolic geometry which
generalize Penner's Ptolemy relation, the trace identities and Wolpert's cosine
formula. As a consequence, we derive an explicit formula for the geodesic
lengths functions in terms of the edge lengths of an ideally triangulated
decorated hyperbolic surface.


  In this note we prove the following fact: if finite many elements
$p_1,p_2,...,p_n$ of a unique factorization domain are given such that the
greatest common divisor of each pair $(p_i,p_j)$ can be expressed as a linear
combination of $p_i$ and $p_j$ then the greatest common divisor of all $p_i$s
also can be expressed as a linear combination of $p_1,...,p_n$. We prove am
analogous statement in commutative rings.


  In materials without inversion symmetry, Berry curvature dipole (BCD) arises
from the uneven distribution of Berry curvature in momentum space. This leads
to nonlinear anomalous Hall effects even in systems with preserved
time-reversal symmetry. A key goal is to engineer systems with prominent BCD
near the Fermi level. Notably, TaAs, a type-I Weyl semimetal, exhibits
substantial Berry curvature but a small BCD around the Fermi level. In this
study, we employed first-principles methods to comprehensively investigate the
BCD in TaAs. Our findings reveal significant cancellation effects not only
within individual Weyl points but crucially, among distinct Weyl point pairs in
bulk TaAs. We propose a strategic approach to enhance the BCD in TaAs by
employing a layer-stacking technique. This greatly amplifies the BCD compared
to the bulk material. By tuning the number of slab layers, we can selectively
target specific Weyl point pairs near the Fermi level, while quantum
confinement effects suppress contributions from other pairs, mitigating
cancellation effects. Especially, the BCD of an 8-layer TaAs slab surpasses the
bulk value near the Fermi level by orders of magnitude.


  The effect of binary alloy disorder on the ferromagnetic phases of f-electron
materials is studied within the periodic Anderson model. We find that disorder
in the conduction band can drastically enhance the Curie temperature due to an
increase of the local f-moment. The effect may be explained qualitatively and
even quantitatively by a simple theoretical ansatz. The emergence of an alloy
Kondo insulator at non-integer filling is also pointed out.


  The goal of this article is to find a correct approximated solution using a
polynomial of sixth degree for the free boundary problem corresponding to the
diffusion of oxygen in a spherical medium with simultaneous absorption at a
constant rate, and to show some mistakes in previously published solutions.


  Unmanned Aerial Vehicle (UAV) technology is becoming more prevalent and more
diverse in its application. 5G and beyond networks must enable UAV
connectivity. This will require the network operator to consider this new type
of user in the planning and operation of the network. This work presents the
challenges an operator will encounter and should consider in the future as UAVs
become users of the network. We analyse the 3GPP specifications, the existing
research literature, and a publicly available UAV connectivity dataset, to
describe the challenges. We classify these challenges into network planning and
network optimisation categories. We discuss the challenge of planning network
coverage when considering coverage for flying users and the PCI collision and
confusion issues that can be aggravated by these users. In discussing network
optimisation challenges, we introduce Automatic Neighbouring Relation (ANR) and
handover challenges, specifically the number of neighbours in the Neighbour
Relation Table (NRT), and their potential deletion and block-listing, the
frequent number of handovers and the possibility that the UAV disconnects
because of handover issues. We discuss possible approaches to address the
presented challenges and use a real-world dataset to support our findings about
these challenges and their importance.


  Most differentially private (DP) algorithms assume a central model in which a
reliable third party inserts noise to queries made on datasets, or a local
model where the users locally perturb their data. However, the central model is
vulnerable via a single point of failure, and in the local model, the utility
of the data deteriorates significantly. The recently proposed shuffle model is
an intermediate framework between the central and the local paradigms where the
users send their locally privatized data to a server where messages are
shuffled, effacing the link between a privatized message and the corresponding
user, giving a better trade-off between privacy and utility than the local
model, as its privacy gets amplified without adding more noise. In this paper,
we theoretically derive the strictest known bound for DP guarantee for the
shuffle models with $k$-Randomized Response local randomizers. There on, we
focus on the utility of the shuffle model for histogram queries. Leveraging on
the matrix inversion method, which is used to approximate the original
distribution from the empirical one produced by the $k$-RR mechanism, we
de-noise the histogram produced by the shuffle model to evaluate the total
variation distance of the resulting histogram from the true one, which we
regard as the measure of utility of the privacy mechanism. We perform
experiments on both synthetic and real data to compare the privacy-utility
trade-off of the shuffle model with that of the central one privatized by
adding the state-of-the-art Gaussian noise to each bin. Although the
experimental results stay consistent with the literature that favour the
central model, we see that, the difference in statistical utilities between the
central and the shuffle models is very small, showing that they are almost
comparable under the same level of DP.


  In this work we present a theoretical framework within Einstein's classical
general relativity which models stellar compact objects such as PSR J1614-2230
and SAX J1808.4-3658. The Einstein field equations are solved by assuming that
the interior of the compact object is described by a class I spacetime. The
so-called Karmarkar condition arising from this requirement is integrated to
reduce the gravitational behaviour to a single generating function. By
appealing to physics we adopt a form for the gravitational potential which is
sufficiently robust to accurately describe compact objects. Our model satisfies
all the requirements for physically realistic stellar structures.


  Strong gravitational lensing by galaxies in MOdified Newtonian Dynamics
(MOND) has until now been restricted to spherically symmetric models. These
models were able to account for the size of the Einstein ring of observed
lenses, but were unable to account for double-imaged systems with collinear
images, as well as four-image lenses. Non-spherical models are generally
cumbersome to compute numerically in MOND, but we present here a class of
analytic non-spherical models that can be applied to fit double-imaged and
quadruple-imaged systems. We use them to obtain a reasonable MOND fit to ten
double-imaged systems, as well as to the quadruple-imaged system Q2237+030
which is an isolated bulge-disc lens producing an Einstein cross. However, we
also find five double-imaged systems and three quadruple-imaged systems for
which no reasonable MOND fit can be obtained with our models. We argue that
this is mostly due to the intrinsic limitation of the analytic models, even
though the presence of small amounts of additional dark mass on galaxy scales
in MOND is also plausible.


  Since core-collapse supernova simulations still struggle to produce robust
neutrino-driven explosions in 3D, it has been proposed that asphericities
caused by convection in the progenitor might facilitate shock revival by
boosting the activity of non-radial hydrodynamic instabilities in the
post-shock region. We investigate this scenario in depth using 42 relativistic
2D simulations with multi-group neutrino transport to examine the effects of
velocity and density perturbations in the progenitor for different perturbation
geometries that obey fundamental physical constraints (like the anelastic
condition). As a framework for analysing our results, we introduce
semi-empirical scaling laws relating neutrino heating, average turbulent
velocities in the gain region, and the shock deformation in the saturation
limit of non-radial instabilities. The squared turbulent Mach number, <Ma^2>,
reflects the violence of aspherical motions in the gain layer, and explosive
runaway occurs for <Ma^2>~0.3, corresponding to a reduction of the critical
neutrino luminosity by ~25% compared to 1D. In the light of this theory,
progenitor asphericities aid shock revival mainly by creating anisotropic mass
flux onto the shock: Differential infall efficiently converts velocity
perturbations in the progenitor into density perturbations (Delta rho/rho) at
the shock of the order of the initial convective Mach number Ma. The
anisotropic mass flux and ram pressure deform the shock and thereby amplify
post-shock turbulence. Large-scale (l=2,l=1) modes prove most conducive to
shock revival, whereas small-scale perturbations require unrealistically high
convective Mach numbers. Initial density perturbations in the progenitor are
only of order Ma^2 and therefore play a subdominant role.


  Producing original and arranging existing musical outcomes is an art that
takes years of learning and practice to master. Yet, despite the constant
advances in the field of AI-powered musical creativity, production of quality
musical outcomes remains a prerogative of the humans. Here we demonstrate that
a single bubble in water can be used to produce creative musical outcomes, when
it nonlinearly oscillates under an acoustic pressure signal that encodes a
piece of classical music. The audio signal of the response of the bubble
resembles an electric guitar version of the original composition. We suggest,
and provide plausible theoretical supporting arguments, that this property of
the bubble can be used to create physics-inspired AI systems capable of
simulating human creativity in arrangement and composition of music.


  We use Schwinger's formula, introduced by himself in the early fifties to
compute effective actions for QED, and recently applied to the Casimir effect,
to obtain the partition functions for both the bosonic and fermionic harmonic
oscillator.


  We propose a $q$-analog of classical plethystic conjectures due to Foulkes.
In our conjectures, a divided difference of plethysms of Hall-Littlewood
polynomials $H_n(\mathbf{x};q)$ replaces the analogous difference of plethysms
of complete homogeneous symmetric functions $h_n(\mathbf{x})$ in Foulkes
conjecture. At $q=0$, we get back the original statement of Foulkes, and we
show that our version holds at $q=1$. We discuss further supporting evidence,
as well as various generalizations.


  Coloured probability tree models are statistical models coding conditional
independence between events depicted in a tree graph. They are more general
than the very important class of context-specific Bayesian networks. In this
paper, we study the algebraic properties of their ideal of model invariants.
The generators of this ideal can be easily read from the tree graph and have a
straightforward interpretation in terms of the underlying model: they are
differences of odds ratios coming from conditional probabilities. One of the
key findings in this analysis is that the tree is a convenient tool for
understanding the exact algebraic way in which the sum-to-1 conditions on the
parameter space translate into the sum-to-one conditions on the joint
probabilities of the statistical model. This enables us to identify necessary
and sufficient graphical conditions for a staged tree model to be a toric
variety intersected with a probability simplex.


  We systematically assess several limiting cases of modified gravity, where
particular theoretical or observational conditions hold. This framework
includes the well known scalar-tensor gravity and No Slip Gravity and No Run
Gravity, and we extend it to three new limits: Only Run, Only Light, and Only
Growth Gravities. These limits give simplifications that allow deeper
understanding of modified gravity, including demonstration that gravitational
effects on light and matter can have opposite signs in their deviation from
general relativity. We also show observational predictions for the different
cosmic structure growth rates $f\sigma_8$ and the ratio of gravitational wave
standard siren luminosity to photon standard candle luminosity distance
relations, defining a new statistic $D_G$ that emphasizes their complementarity
and ability to distinguish models.


  We show that if A is a finite subset of an abelian group with additive energy
at least c|A|^3 then there is a subset L of A with |L|=O(c^{-1}\log |A|) such
that |A \cap Span(L)| >> c^{1/3}|A|.


  We discuss how the conditions at high redshift differ from those at low
redshift, and what the impact is on the galaxy population. We focus in
particular on the role of gaseous dissipation and its impact on sustaining high
star formation rates as well as on driving star-bursts in mergers. Gas
accretion onto galaxies at high redshifts occurs on a halo dynamical time
allowing for very efficiently sustained star formation. In addition cold
accretion flows are able to drive turbulence in high redshift disks at the
level observed if at least 20% of the accretion energy is converted into random
motion in the gaseous disk. In general we find that the fraction of gas
involved in galaxy mergers is a strong function of time and increases with
redshift. A model combining the role of dissipation during mergers and
continued infall of satellite galaxies allows to reproduce the observed
size-evolution of early-type galaxies with redshift. Furthermore we investigate
how the evolution of the faint-end of the luminosity function can be explained
in terms of the evolution of the underlying dark matter evolution.


  Scaling and lossy coding are widely used in video transmission and storage.
Previous methods for enhancing the resolution of such videos often ignore the
inherent interference between resolution loss and compression artifacts, which
compromises perceptual video quality. To address this problem, we present a
mixed-resolution coding framework, which cooperates with a reference-based
DCNN. In this novel coding chain, the reference-based DCNN learns the direct
mapping from low-resolution (LR) compressed video to their high-resolution (HR)
clean version at the decoder side. We further improve reconstruction quality by
devising an efficient deformable alignment module with receptive field block to
handle various motion distances and introducing a disentangled loss that helps
networks distinguish the artifact patterns from texture. Extensive experiments
demonstrate the effectiveness of proposed innovations by comparing with
state-of-the-art single image, video and reference-based restoration methods.


  The MicroBooNE experiment searched for an excess of electron-neutrinos in the
Booster Neutrino Beam (BNB), providing direct constraints on
$\nu_e$-interpretations of the MiniBooNE low-energy excess (LEE). In this
article, we show that if the MiniBooNE LEE is caused instead by an excess of
$\overline{\nu}_e$, then liquid argon detectors, such as MicroBooNE, SBND and
ICARUS, would have poor sensitivity to it. This is due to a strong suppression
of $\overline{\nu}_e -{}^{40}$Ar cross sections in the low-energy region of the
excess. The MicroBooNE results are consistent at the $2\sigma$~C.L with a
scenario in which the MiniBooNE excess is sourced entirely by
$\overline{\nu}_e$ interactions. The opportune location of ANNIE, a Gd-loaded
water Cherenkov detector, allows for a direct search for a $\overline{\nu}_e$
flux excess in the BNB using inverse-beta-decay events.


  In a 2008 paper, the first author and Van Tuyl proved that the regularity of
the edge ideal of a graph G is at most one greater than the matching number of
G. In this note, we provide a generalization of this result to any square-free
monomial ideal. We define a 2-collage in a simple hypergraph to be a collection
of edges with the property that for any edge E of the hypergraph, there exists
an edge F in the collage such that |E \ F| < 2. The Castelnuovo-Mumford
regularity of the edge ideal of a simple hypergraph is bounded above by a
multiple of the minimum size of a 2-collage. We also give a recursive formula
to compute the regularity of a vertex-decomposable hypergraph. Finally, we show
that regularity in the graph case is bounded by a certain statistic based on
maximal packings of nondegenerate star subgraphs.


  The active region magnetic field surrounding the filament plays an important
role in filament formation, their evolution and disruption. We investigated a
filament eruption that occurred in southern hemisphere of the Sun on July 08,
2011 using AIA and HMI data. The filament was located in a region close to the
active region NOAA 11247 with its West-most footpoint anchored in the negative
polarity plage region and the East-most in the positive polarity plage region.
During observations, the magnetic flux was emerging in the active region and
also in the plage regions. The flux emergence was stopped in West-most
footpoint of the plage region about an hour before the filament eruption. A
converging motion was also observed for many hours in the Western footpoint of
the filament. The filament had left-handed twist and the net injected magnetic
helicity was positive in both footpoints. Both sign of magnetic helicity were
observed in the Western footpoint of the filament where the eruption has
initiated. Further, an anti-clockwise rotational motion was observed in both
the footpoints just after the onset of filament eruption which lasted for 6 min
during the eruption process. The emerging flux, converging motion and injection
of opposite magnetic helicity could be responsible for destabilizing of the
Western footpoint of the filament leading to eruption. The torque imbalance
between the expanded portion of the flux tube and the photosphere may have
caused the rotation in the footpoint region which changed the trend in the
injected magnetic helicity after the filament eruption.


  Our objective is to formally verify the correctness of the hundreds of
expression optimization rules used within the GraalVM compiler. When defining
the semantics of a programming language, expressions naturally form abstract
syntax trees, or, terms. However, in order to facilitate sharing of common
subexpressions, modern compilers represent expressions as term graphs. Defining
the semantics of term graphs is more complicated than defining the semantics of
their equivalent term representations. More significantly, defining
optimizations directly on term graphs and proving semantics preservation is
considerably more complicated than on the equivalent term representations. On
terms, optimizations can be expressed as conditional term rewriting rules, and
proofs that the rewrites are semantics preserving are relatively
straightforward. In this paper, we explore an approach to using term rewrites
to verify term graph transformations of optimizations within the GraalVM
compiler. This approach significantly reduces the overall verification effort
and allows for simpler encoding of optimization rules.


  We have proposed an analytical approach for exact solution of multi-channel
scattering problems, in presence of Dirac Delta function couplings. Our
solution is quite general and is valid for any set of potentials, if the
Green's functions of the uncoupled potentials are known at the crossing point.
Using our model, it is possible to express N-channel problem by N independent
`single' channel problems and hence one can have a realistic solution of
multi-channel scattering problem. In this paper we have shown that transition
probability from first diabatic potential to any other potential can be easily
evaluated using a very simple analytical formula - which only require value of
eigenfunction of first uncoupled potential and value of Green's function of
other uncoupled potential, at the crossing.


  We study asymptotic behaviour of the correlation functions of bipartite
sparse random $N\times N$ matrices. We assume that the graphs have $N$
vertices, the ratio of parts is $\displaystyle\frac{\alpha}{1-\alpha}$ and the
average number of edges attached to one vertex is $\alpha\cdot p$ or
$(1-\alpha)\cdot p$. To each edge of the graph $e_{ij}$ we assign a weight
given by a random variable $a_{ij}$ with all moments finite. It is shown that
the main term of the correlation function of $k$-th and $m$-th moments of the
integrated density of states is $N^{-1}n_{k,m}$. The closed system of recurrent
relations for coefficients $\{n_{k,m}\}_{k,m=1}^\infty$ was obtained.


  The dynamics group of an asynchronous cellular automaton (ACA) relates
properties of its long term dynamics to the structure of Coxeter groups. The
key mathematical feature connecting these diverse fields is involutions.
Group-theoretic results in the latter domain may lead to insight about the
dynamics in the former, and vice-versa. In this article, we highlight some
central themes and common structures, and discuss novel approaches to some open
and open-ended problems. We introduce the state automaton of an ACA, and show
how the root automaton of a Coxeter group is essentially part of the state
automaton of a related ACA.


  This brief note corrects some errors in the paper quoted in the title,
highlights a combinatorial result which may have been overlooked, and points to
further improvements in recent literature.


  Light dark matter (DM) with a large DM-nucleon spin-independent cross section
and furthermore proper isospin violation (ISV) $f_n/f_p\approx-0.7$ may provide
a way to understand the confusing DM direct detection results. Combing with the
stringent astrophysical and collider constraints, we systematically investigate
the origin of ISV first via general operator analyses and further via
specifying three kinds of (single) mediators: A light $Z'$ from chiral
$U(1)_X$, an approximate spectator Higgs doublet (It can explain the $W+jj$
anomaly simultaneously) and color triplets. In addition, although $Z'$ from an
exotic $U(1)_X$ mixing with $U(1)_Y$ generating $f_n=0$, we can combine it with
the conventional Higgs to achieve proper ISV. As a concrete example, we propose
the $U(1)_X$ model where the $U(1)_X$ charged light sneutrino is the inelastic
DM, which dominantly annihilates to light dark states such as $Z'$ with sub-GeV
mass. This model can address the recent GoGeNT annual modulation consistent
with other DM direct detection results and free of exclusions.


  Initial results of a project to detect the radio-frequency pulse associated
with extensive air showers of cosmic rays are described briefly. This work is
being performed at the CASA/MIA array in Utah, with the intention of designing
equipment that can be used in conjunction with the Auger Giant Array proposal.


  Datasets with non-trivial large scale topology can be hard to embed in
low-dimensional Euclidean space with existing dimensionality reduction
algorithms. We propose to model topologically complex datasets using vector
bundles, in such a way that the base space accounts for the large scale
topology, while the fibers account for the local geometry. This allows one to
reduce the dimensionality of the fibers, while preserving the large scale
topology. We formalize this point of view, and, as an application, we describe
an algorithm which takes as input a dataset together with an initial
representation of it in Euclidean space, assumed to recover part of its large
scale topology, and outputs a new representation that integrates local
representations, obtained through local linear dimensionality reduction, along
the initial global representation. We demonstrate this algorithm on examples
coming from dynamical systems and chemistry. In these examples, our algorithm
is able to learn topologically faithful embeddings of the data in lower target
dimension than various well known metric-based dimensionality reduction
algorithms.


  Diffuse synchrotron radio emission from cosmic-ray electrons is observed at
the center of a number of galaxy clusters. These sources can be classified
either as giant radio halos, which occur in merging clusters, or as mini halos,
which are found only in cool-core clusters. In this paper, we present the first
discovery of a cool-core cluster with an associated mini halo that also shows
ultra-steep-spectrum emission extending well beyond the core that resembles
radio halo emission. The large-scale component is discovered thanks to LOFAR
observations at 144 MHz. We also analyse GMRT observations at 610 MHz to
characterise the spectrum of the radio emission. An X-ray analysis reveals that
the cluster is slightly disturbed, and we suggest that the steep-spectrum radio
emission outside the core could be produced by a minor merger that powers
electron re-acceleration without disrupting the cool core. This discovery
suggests that, under particular circumstances, both a mini and giant halo could
co-exist in a single cluster, opening new perspectives for particle
acceleration mechanisms in galaxy clusters.


  We have observed the prompt emission of GRB100418A, from its beginning by the
MAXI/SSC (0.7-7 keV) on board the International Space Station followed by the
Swift/XRT (0.3-10 keV) observation. The light curve can be fitted by a
combination of a power law component and an exponential component (decay
constant is $31.6\pm 1.6$ sec). The X-ray spectrum is well expressed by the
Band function with $E_{\rm p}\leq$8.3 keV. This is the brightest GRB showing a
very low value of $E_{\rm p}$. It satisfies the Yonetoku-relation ($E_{\rm
p}$-$L_{\rm p}$). It is also consistent with the Amati relation ($E_{\rm
p}$-$E_{\rm iso}$) in 2.5$\sigma$ level.


  This paper introduces a new member of the family of Variational Autoencoders
(VAE) that constrains the rate of information transferred by the latent layer.
The latent layer is interpreted as a communication channel, the information
rate of which is bound by imposing a pre-set signal-to-noise ratio. The new
constraint subsumes the mutual information between the input and latent
variables, combining naturally with the likelihood objective of the observed
data as used in a conventional VAE. The resulting Bounded-Information-Rate
Variational Autoencoder (BIR-VAE) provides a meaningful latent representation
with an information resolution that can be specified directly in bits by the
system designer. The rate constraint can be used to prevent overtraining, and
the method naturally facilitates quantisation of the latent variables at the
set rate. Our experiments confirm that the BIR-VAE has a meaningful latent
representation and that its performance is at least as good as state-of-the-art
competing algorithms, but with lower computational complexity.


  We analyze the light-flavor particle mass spectra and show that in the region
up to ~1.8GeV the Hagedorn temperature for baryons is about 30% smaller than
for mesons, reflecting the fact that the number of baryon states grows more
rapidly with the mass. We also show that the spectra are well reproduced in a
model where hadrons are compound objects of quanta, whose available number
increases with mass. The rapid growth of number of hadronic states is a
combinatorial effect. We also point out that an upper limit on the excitation
energy of these quanta results in a maximum number of hadron states that can be
formed. According to this combinatorial saturation, no more light-flavor hadron
resonances exist above a certain mass.


  This work relates the framework of model-based clustering for spatial
functional data where the data are surfaces. We first introduce a Bayesian
spatial spline regression model with mixed-effects (BSSR) for modeling spatial
function data. The BSSR model is based on Nodal basis functions for spatial
regression and accommodates both common mean behavior for the data through a
fixed-effects part, and variability inter-individuals thanks to a
random-effects part. Then, in order to model populations of spatial functional
data issued from heterogeneous groups, we integrate the BSSR model into a
mixture framework. The resulting model is a Bayesian mixture of spatial spline
regressions with mixed-effects (BMSSR) used for density estimation and
model-based surface clustering. The models, through their Bayesian formulation,
allow to integrate possible prior knowledge on the data structure and
constitute a good alternative to recent mixture of spatial spline regressions
model estimated in a maximum likelihood framework via the
expectation-maximization (EM) algorithm. The Bayesian model inference is
performed by Markov Chain Monte Carlo (MCMC) sampling. We derive two Gibbs
sampler to infer the BSSR and the BMSSR models and apply them on simulated
surfaces and a real problem of handwritten digit recognition using the MNIST
data set. The obtained results highlight the potential benefit of the proposed
Bayesian approaches for modeling surfaces possibly dispersed in particular in
clusters.


  Low-energy quasiparticle excitations in the superconducting (SC) state of
UBe$_{13}$ were studied by means of specific-heat ($C$) measurements in a
rotating field. Quite unexpectedly, the magnetic-field dependence of $C(H)$ is
linear in $H$ with no angular dependence at low fields in the SC state,
implying that the gap is fully open over the Fermi surfaces, in stark contrast
to the previous expectation. In addition, a characteristic cubic anisotropy of
$C(H)$ was observed above 2~T with a maximum (minimum) for $H$ $||$ $[001]$
($[111]$) within the $(1\bar{1}0)$ plane, both in the normal as well as in the
SC states. This oscillation possibly originates from the anisotropic response
of the heavy quasiparticle bands, and might be a key to understand the unusual
properties of UBe$_{13}$.


  Heavy resonances are an integral part of many extensions of the Standard
Model. The discovery of such heavy resonances are a primary goal at the LHC and
future hadron colliders. When a particle with TeV-scale mass decays into
electroweak-scale objects, these objects are highly boosted and their decay
products are then strongly collimated, possibly to an extent that they cannot
be resolved in the calorimeters of the detectors any more. We develop taggers
for electroweak-scale resonances by combining the good energy resolution of the
hadronic calorimeter with the superior spatial resolution of the tracking
detector. Using track-based techniques we reconstruct heavy $W'$ and $Z'$
bosons and constrain the branching ratio of the rare Higgs boson decay $H \to Z
A \to l^+l^-$ jets. The taggers show a good momentum-independent performance up
to very large boosts. Using the proposed techniques will allow experiments at
the LHC and a future hadron collider to significantly extend its reach in
searches for heavy resonances.