  This paper aimed at extending a model developed by Ladeveze to capture
thermal expansion and coupled thermo-mechanical phenomena, as such as those
encountered at elevated and extreme temperatures. In the new model a linear
thermal expansion coefficient is added to equation of state to account for the
thermal to mechanical coupling effects. The mechanical to thermal effects are
introduced by assuming an internal heat generation due to residual strain
effects. The constitutive relations of the coupled thermo-mechanical behaviors
of ceramic matrix composite material model were incorporated into Abaqus finite
element code as user defined material software. An extension of the methodology
presented by Letombes to calibrate the ceramic matrix composite damage model
parameters based on a woven silicon-carbide silicon-carbide material developed
by Safran Group. Feasibility tests (tension-compression, tension-tension
cyclic, simple tension tests) based on a dog bone and open hole specimen tests
demonstrated a good capturing of nonlinear as well as coupled
thermos-mechanical behaviors in the silicon-carbide silicon-carbide material.


  Decoherence of a center spin or qubit in a spin bath is essentially
determined by the many-body bath evolution. We develop a cluster-correlation
expansion (CCE) theory for the spin bath dynamics relevant to the qubit
decoherence problem. A cluster correlation term is recursively defined as the
evolution of a group of bath spins divided by the cluster correlations of all
the subgroups. The so-defined correlation accounts for the authentic collective
excitations within a given group. The bath propagator is the product of all
possible cluster correlation terms. For a finite-time evolution as in the qubit
decoherence problem, a convergent result can be obtained by truncating the
expansion up to a certain cluster size. The two-spin cluster truncation of the
CCE corresponds to the pair-correlation approximation [PRB 74,195301(2006)]. In
terms of the standard linked cluster expansion, a cluster correlation term is
the infinite summation of all the connected diagrams with all and only the
spins in the group flip-flopped, and thus the expansion is exact whenever
converges. When the individual contribution of each higher-order correlation
term to the decoherence is small, as the usual case for relatively large baths
where the decoherence could complete well within the bath spin flip-flop time,
the CCE coincides with the cluster expansion [PRB 74,035322(2006)]. For small
baths, however, the qubit decoherence may not complete within the bath spin
flip-flop timescale and thus individual higher-order cluster correlations could
grow significant. In such cases, only the CCE converges to the exact coherent
dynamics of multi-spin clusters. We check the accuracy of the CCE in an exactly
solvable spin-chain model.


  Applying stochastic differential equations, we study the squeezing and
statistical properties of the cavity and output modes of a degenerate
three-level laser whose cavity contains a parametric amplifier and coupled to a
squeezed vacuum reservoir. We consider the case in which the top and bottom
levels of the three-level cascade atoms injected into the cavity are coupled by
the pump mode emerging from the parametric amplifier. It turns out that the
presence of the squeezed vacuum reservoir and the parametric amplifier
contribute considerably to the mean photon number and the degree of squeezing
of the cavity and output modes. It appears that almost perfect squeezing can be
achieved at steady state and at threshold for a suitable choice of parameters.


  In this article, we first propose the modified Hannan-Rissanen Method for
estimating the parameters of the autoregressive moving average (ARMA) process
with symmetric stable noise and symmetric stable generalized autoregressive
conditional heteroskedastic (GARCH) noise. Next, we propose the modified
empirical characteristic function method for the estimation of GARCH parameters
with symmetric stable noise. Further, we show the efficiency, accuracy, and
simplicity of our methods through Monte-Carlo simulation. Finally, we apply our
proposed methods to model financial data.


  The half-lives of newly observed $\alpha$-emitters $^{105}$Te and $^{109}$Xe
[Seweryniak \textit{et al.}, Phys. Rev. C \textbf{73}, 061301(R) (2006);
Liddick \textit{et al.}, Phys. Rev. Lett. \textbf{97}, 082501 (2006)] are
investigated by the density-dependent cluster model. The half-lives of
$\alpha$-emitters close to the N=Z line are also studied in a unified framework
where the influence of the nuclear deformation is properly taken into account.
Good agreement between model and data is obtained and some possible
$\alpha$-emitters are suggested for future experiments.


  We investigate the effect of surface disorder on the chiral surface states of
a three-dimensional quantum Hall system. Utilizing a transfer-matrix method, we
find that the localization length of the surface state along the magnetic field
decreases with the surface disorder strength in the weak disorder regime, but
increases anomalously in the strong disorder regime. In the strong disorder
regime, the surface states mainly locate at the first inward layer to avoid the
strong disorder in the outmost layer. The anomalous increase of the
localization length can be explained by an effective model, which maps the
strong disorder on the surface layer to the weak disorder on the first inward
layer. Our work demonstrates that surface disorder can be an effective way to
control the transport behavior of the surface states along the magnetic field.
We also investigate the effect of surface disorder on the full distribution of
conductances P(g) of the surface states in the quasi-one-dimensional (1D)
regime for various surface disorder strengths. In particular, we find that P(g)
is Gaussian in the quasi-1D metal regime and log-normal in the quasi-1D
insulator regime. In the crossover regime, P(g) exhibits highly nontrivial
forms, whose shapes coincide with the results obtained from the
Dorokhov-Mello-Pereyra-Kumar equation of a weakly disordered quasi-1D wire in
the absence of time-reversal symmetry. Our results suggest that P(g) is fully
determined by the average conductance, independent of the details of the
system, in agreement with the single-parameter scaling hypothesis.


  We present a tomographic method for the reconstruction of the full entangled
quantum state for the cyclotron and spin degrees of freedom of an electron in a
Penning trap. Numerical simulations of the reconstruction of several
significant quantum states show that the method turns out to be quite accurate.


  This manuscript provides a review of methods for increasing the frame per
second of single-board computers. The main emphasis is on the Jetson family of
single-board computers from Nvidia Company, due to the possibility of using a
graphical interface for calculations. But taking into account the popular
low-cost segment of single-board computers as RaspberryPI family, BananaPI,
OrangePI, etc., we also provided an overview of methods for increasing the
frame per second without using a Graphics Processing Unit. We considered
frameworks, software development kit, and various libraries that can be used in
the process of increasing the frame per second in single-board computers.
Finally, we tested the presented methods for the YOLOv4-tiny model with a
custom dataset on the Jetson nano and presented the results in the table.


  We extend the formalism of entanglement renormalization to the study of
boundary critical phenomena. The multi-scale entanglement renormalization
ansatz (MERA), in its scale invariant version, offers a very compact
approximation to quantum critical ground states. Here we show that, by adding a
boundary to the scale invariant MERA, an accurate approximation to the critical
ground state of an infinite chain with a boundary is obtained, from which one
can extract boundary scaling operators and their scaling dimensions. Our
construction, valid for arbitrary critical systems, produces an effective chain
with explicit separation of energy scales that relates to Wilson's RG
formulation of the Kondo problem. We test the approach by studying the quantum
critical Ising model with free and fixed boundary conditions.


  Recent advances in the technology of transmission electron microscopy have
allowed for a more precise visualization of materials and physical processes,
such as metal oxidation. Nevertheless, the quality of information is limited by
the damage caused by an electron beam, movement of the specimen or other
environmental factors. A novel registration method has been proposed to remove
those limitations by acquiring a series of low dose microscopy frames and
performing a computational registration on them to understand and visualize the
sample. This process can be represented as a prefix sum with a complex and
computationally intensive binary operator and a parallelization is necessary to
enable processing long series of microscopy images. With our parallelization
scheme, the time of registration of results from ten seconds of microscopy
acquisition has been decreased from almost thirteen hours to less than seven
minutes on 512 Intel IvyBridge cores.


  Fermi-LAT reveals two huge gamma-ray bubbles existing in the Galactic Center,
called 'Fermi Bubbles'. The existence of two microwave bubbles at the same
region are also reported by the observation by WMAP, dubbed 'WMAP haze'. In
order to explain these components, It has been argued that the gamma-rays arise
from Inverse-Compton scattering of relativistic electrons accelerated by plasma
turbulence, and the microwaves are radiated by synchrotron radiation. But no
previous research reproduces both the Fermi Bubbles and WMAP haze under typical
magnetic fields in the galaxy. We assume that shocks present in the bubbles and
the efficiency of the acceleration by plasma turbulence, 'stochastic
acceleration', changes with the distance from the shock front. The distance
from the shock front increases with time, accordingly the efficiency of the
acceleration changes with time. We also consider the time development of the
electrons escape from the turbulence by diffusive loss. Our model succeed to
reproduce both the observed characteristics of the Fermi Bubbles and WMAP haze
under typical magnetic fields.


  CONTEXT: The study of pulsation in Pre--Main--Sequence intermediate-mass
stars represents an important tool for deriving information on fundamental
stellar parameters and internal structure, as well as for testing current
theoretical models. Interest in this class of variable stars has significantly
increased during the last decade and about 30 members are presently known in
the literature. AIMS: We have constructed the frequency spectrum of the
oscillations in V346 Ori. We apply asteroseismic tools to these data to
estimate the intrinsic parameters (mass, luminosity, effective temperature) of
V346 Ori and to obtain information on its internal structure. METHODS: CCD time
series photometry in the Johnson V filter has been obtained for a total of
145.7 h of observations distributed over 36 nights. The resulting light curves
have been subjected to a detailed frequency analysis using updated numerical
techniques. Photometric and spectroscopic data have also been acquired to
determine reliable estimates of the stellar properties. RESULTS: We have
identified 13 oscillation frequencies, 6 of which with higher significance.
These have been compared with the predictions of non-radial adiabatic models.
The resulting best fit model has a mass of 2.1$\pm$0.2 $M_{\odot}$, luminosity
$\log{L/L_{\odot}}=1.37^{+0.11}_{-0.13}$, and effective temperature
7300$\pm$200 K. These values are marginally consistent with the association of
V346 Ori to Orion OB1a. Alternatively, V346 Ori could be placed at a slightly
larger distance than previously estimated.


  We generalize reduction theorems for classical connections to operators with
values in $k$-th order natural bundles. Using the first reduction theorem in
order two we classify all (0,2)-tensor fields on the cotangent bundle of a
manifold with a linear (non-symmetric) connection.


  The CLEF eRisk Laboratory explores solutions to different tasks related to
risk detection on the Internet. In the 2023 edition, Task 1 consisted of
searching for symptoms of depression, the objective of which was to extract
user writings according to their relevance to the BDI Questionnaire symptoms.
Task 2 was related to the problem of early detection of pathological gambling
risks, where the participants had to detect users at risk as quickly as
possible. Finally, Task 3 consisted of estimating the severity levels of signs
of eating disorders. Our research group participated in the first two tasks,
proposing solutions based on Transformers. For Task 1, we applied different
approaches that can be interesting in information retrieval tasks. Two
proposals were based on the similarity of contextualized embedding vectors, and
the other one was based on prompting, an attractive current technique of
machine learning. For Task 2, we proposed three fine-tuned models followed by
decision policy according to criteria defined by an early detection framework.
One model presented extended vocabulary with important words to the addressed
domain. In the last task, we obtained good performances considering the
decision-based metrics, ranking-based metrics, and runtime. In this work, we
explore different ways to deploy the predictive potential of Transformers in
eRisk tasks.


  The ground states of all even-even nuclei have angular momentum, $I$, equal
to zero, I=0, and positive parity, $\pi=+$. This feature was believed to be a
consequence of the attractive short-range interaction between nucleons.
However, in the presence of two-body random interactions, the predominance of
$I^{\pi}=0^+$ ground states (0 g.s.) was found to be robust both for bosons and
for an even number of fermions. For simple systems, such as $d$ bosons, $sp$
bosons, $sd$ bosons, and a few fermions in single-$j$ shells for small $j$,
there are a few approaches to predict and/or explain spin $I$ ground state ($I$
g.s.) probabilities. An empirical approach to predict $I$ g.s. probabilities is
available for general cases, such as fermions in a single-$j$ ($j>7/2$) or
many-$j$ shells and various boson systems, but a more fundamental understanding
of the robustness of 0 g.s. dominance is still out of reach. Further
interesting results are also reviewed concerning other robust phenomena of
many-body systems in the presence of random two-body interactions, such as the
odd-even staggering of binding energies, generic collectivity, the behavior of
average energies, correlations, and regularities of many-body systems
interacting by a displaced two-body random ensemble.


  We theoretically study graphene nanoribbons in the presence of spatially
varying magnetic fields produced e.g. by nanomagnets. We show both analytically
and numerically that an exceptionally large Rashba spin orbit interaction (SOI)
of the order of 10 meV can be produced by the non-uniform magnetic field. As a
consequence, helical modes exist in armchair nanoribbons that exhibit nearly
perfect spin polarization and are robust against boundary defects. This paves
the way to realizing spin filter devices in graphene nanoribbons in the
temperature regime of a few Kelvins. If a nanoribbon in the helical regime is
in proximity contact to an s-wave superconductor, the nanoribbon can be tuned
into a topological phase sustaining Majorana fermions.


  This paper establishes the Gleason result for finitely generated ideals in
the context of Frechet algebras, and, in particular, provides an affirmative
answer to a question about the Gleason result in commutative Frechet algebras
(Carpenter posed this question for uniform Frechet algebras in 1970). As a
welcome bonus of our method, locally Stein algebras are completely
characterized, and, as an application of this characterization, an affirmative
answer to the Gleason problem (1964) for such algebras is provided recapturing
all the classical results on the Gleason problem in the theory of several
complex variables.


  In this paper, we study the distribution function of the time of explosion of
a stochastic differential equation modeling the length of the dominant crack
due to fatigue. The main novelty is that initial condition is regarded as an
anticipating random variable and the stochastic integral is in the forward
sense. Under suitable conditions, we use the substitution formula from Russo
and Vallois to find the local solution of this equation. Then, we find the law
of blow up time by proving some results on barrier crossing probabilities of
Brownian bridge.


  Interpretation of precision measurements of the cosmic microwave background
(CMB) will require a detailed understanding of the recombination era, which
determines such quantities as the acoustic oscillation scale and the Silk
damping scale. This paper is the second in a series devoted to the subject of
helium recombination, with a focus on two-photon processes in He I. The
standard treatment of these processes includes only the spontaneous two-photon
decay from the 2^1S level. We extend this treatment by including five
additional effects, some of which have been suggested in recent papers but
whose impact on He I recombination has not been fully quantified. These are:
(i) stimulated two-photon decays; (ii) two-photon absorption of redshifted HeI
line radiation; (iii) two-photon decays from highly excited levels in HeI (n^1S
and n^1D, with n>=3); (iv) Raman scattering; and (v) the finite width of the
2^1P^o resonance. We find that effect (iii) is highly suppressed when one takes
into account destructive interference between different intermediate states
contributing to the two-photon decay amplitude. Overall, these effects are
found to be insignificant: they modify the recombination history at the level
of several parts in 10^4.


  Every second order system of autonomous differential equations can be
described by an autonomous holonomic dynamical system with a Lagrangian part,
an effective potential and a set of generalized forces. The kinematic part of
the Lagrangian defines the kinetic metric which subsequently defines a
Riemannian geometry in the configuration space. We consider the generic
function $I=K_{ab}(t,q^{c})\dot{q}^{a}\dot{q}^{b}+K_{a}(t,q^{c})\dot{q}%
^{a}+K(t,q^{c})$ and require the quadratic first integral condition $dI/dt=0$
without involving any type of symmetry Lie or Noether. Condition $dI/dt=0$
leads to a system of equations involving the coefficients $K_{ab}%
(t,q^{c}),K_{a}(t,q^{c}),K(t,q^{c})$ whose solution will produce all possible
quadratic first integrals of the original system of autonomous differential
equations. We show that the new system of equations relates the quadratic first
integrals of the holonomic system with the geometric collineations of the
kinetic metric and in particular with the Killing tensors of order two. We
consider briefly various results concerning the Killing tensors of second-order
and prove a general formula which gives in the case of a flat kinetic metric
the generic Killing tensor in terms of the vectors of the special projective
algebra of the kinetic metric. This establishes the connection between the
geometry defined by the kinetic metric and the quadratic first integrals of the
original system of differential equations.


  The Metallic Ratio is fascinating topic that continually generated news
ideas. A Riemannian manifold endowed with a Metallic structure will be called a
Metallic Riemannian manifold. The main purpose of the present paper is to study
the geometry of transversal lightlike submanifolds and radical transversal
lightlike submanifolds and of Metallic Semi-Riemannian manifolds. We
investigate the geometry of distributions and obtain necessary and sufficient
conditions for the induced connection on these manifolds to be metric
connection. We also obtain characterization of transversal lightlike
submanifolds of Metallic semi-Riemannian manifolds. Finally, we give an
example.


  The equilibrium three dimensional shape of relatively short loops of DNA is
studied using an elastic model that takes into account anisotropy in bending
rigidities. Using a reasonable estimate for the anisotropy, it is found that
cyclized DNA with lengths that are not integer multiples of the pitch take on
nontrivial shapes that involve bending out of planes and formation of kinks.
The effect of sequence inhomogeneity on the shape of DNA is addressed, and
shown to enhance the geometrical features. These findings could shed some light
on the role of DNA conformation in protein--DNA interactions.


  We describe new functionality in the GYRE stellar oscillation code for
modeling tides in binary systems. Using a multipolar expansion in space and a
Fourier-series expansion in time, we decompose the tidal potential into a
superposition of partial tidal potentials. The equations governing the
small-amplitude response of a spherical star to an individual partial potential
are the linear, non-radial, non-adiabatic oscillation equations with an extra
inhomogeneous forcing term. We introduce a new executable, gyre_tides, that
directly solves these equations within the GYRE numerical framework. Applying
this to selected problems, we find general agreement with results in the
published literature but also uncover some differences between our direct
solution methodology and the modal decomposition approach adopted by many
authors.
  In its present form gyre_tides can model equilibrium and dynamical tides of
aligned binaries in which radiative diffusion dominates the tidal dissipation
(typically, intermediate and high-mass stars on the main sequence). Milestones
for future development include incorporation of other dissipation processes,
spin-orbit misalignment, and the Coriolis force arising from rotation.


  A model-independent reconstruction of mechanical profiles (density, pressure)
of the solar interior is outlined using the adiabatic sound speed and bouyancy
frequency profiles. These can be inferred from helioseismology if both p- and
g-mode frequencies are measured. A simulated reconstruction is presented using
a solar model bouyancy frequency and available sound speed data.


  This paper presents a type theory with a form of equality reflection:
provable equalities can be used to coerce the type of a term. Coercions and
other annotations, including implicit arguments, are dropped during reduction
of terms. We develop the metatheory for an undecidable version of the system
with unannotated terms. We then devise a decidable system with annotated terms,
justified in terms of the unannotated system. Finally, we show how the approach
can be extended to account for large eliminations, using what we call
quasi-implicit products.


  Using molecular dynamics (MD) simulations, we find the formation of heaps in
a system of granular particles contained in a box with oscillating bottom and
fixed sidewalls. The simulation includes the effect of static friction, which
is found to be crucial in maintaining a stable heap. We also find another
mechanism for heap formation in systems under constant vertical shear. In both
systems, heaps are formed due to a net downward shear by the sidewalls. We
discuss the origin of net downward shear for the vibration induced heap.


  We simplify the construction of projection complexes due to
Bestvina-Bromberg-Fujiwara. To do so, we introduce a sharper version of the
Behrstock inequality, and show that it can always be enforced. Furthermore, we
use the new setup to prove acylindricity results for the action on the
projection complexes. We also treat quasi-trees of metric spaces associated to
projection complexes, and prove an acylindricity criterion in that context as
well.


  Hills (1988) predicted that runaway stars could be accelerated to velocities
larger than 1000 km/s by dynamical encounters with the supermassive black hole
(SMBH) in the Galactic center. The recently discovered hypervelocity star SDSS
J090745.0+024507 (hereafter HVS) is escaping the Galaxy at high speed and could
be the first object in this class. With the measured radial velocity and the
estimated distance to the HVS, we trace back its trajectory in the Galactic
potential. Assuming it was ejected from the center, we find that a $\sim$ 2
mas/yr proper motion is necessary for the star to have come within a few
parsecs of the SMBH. We perform three-body scattering experiments to constrain
the progenitor encounter which accelerated the HVS. As proposed by Yu &
Tremaine (2003), we consider the tidal disruption of binary systems by the SMBH
and the encounter between a star and a binary black hole, as well as an
alternative scenario involving intermediate mass black holes. We find that the
tidal disruption of a stellar binary ejects stars with a larger velocity
compared to the encounter between a single star and a binary black hole, but
has a somewhat smaller ejection rate due to the greater availability of single
stars.


  Text-to-Image (T2I) diffusion models have recently gained traction for their
versatility and user-friendliness in 2D content generation and editing.
However, training a diffusion model specifically for 3D scene editing is
challenging due to the scarcity of large-scale datasets. Currently, editing 3D
scenes necessitates either retraining the model to accommodate various 3D edits
or developing specific methods tailored to each unique editing type. Moreover,
state-of-the-art (SOTA) techniques require multiple synchronized edited images
from the same scene to enable effective scene editing. Given the current
limitations of T2I models, achieving consistent editing effects across multiple
images remains difficult, leading to multi-view inconsistency in editing. This
inconsistency undermines the performance of 3D scene editing when these images
are utilized. In this study, we introduce a novel, training-free 3D scene
editing technique called \textsc{Free-Editor}, which enables users to edit 3D
scenes without the need for model retraining during the testing phase. Our
method effectively addresses the issue of multi-view style inconsistency found
in state-of-the-art (SOTA) methods through the implementation of a single-view
editing scheme. Specifically, we demonstrate that editing a particular 3D scene
can be achieved by modifying only a single view. To facilitate this, we present
an Edit Transformer that ensures intra-view consistency and inter-view style
transfer using self-view and cross-view attention mechanisms, respectively. By
eliminating the need for model retraining and multi-view editing, our approach
significantly reduces editing time and memory resource requirements, achieving
runtimes approximately 20 times faster than SOTA methods. We have performed
extensive experiments on various benchmark datasets, showcasing the diverse
editing capabilities of our proposed technique.


  Applying the higher order holonomy corrections to the perturbation theory of
cosmology, the lattice power law of Loop Quantum Cosmology, $\tilde{\mu}\propto
p^{\beta}$, is analysed and the range of $\beta$ is decided to be [-1,0] which
is different from the conventional range $-0.1319>\beta\geq-5/2$ \cite{lqct}.
At the same time, we find that there is a anomaly free condition in this
theory, and we obtain this condition in the vector and tensor mode. We also
find that the nonzero mass of gravitational wave essentially results from the
quantum nature of Riemannian geometry of loop quantum gravity.


  In this work, we explore the integration of discontinuous Orientation
Selection into steering interfaces intending to preserve the seamless sensation
of real-world movement, while mitigating the risk of inducing cybersickness.
Our implementation encounters conflicts in standard input mappings, prompting
us to adopt bimanual interaction as a solution. Recognizing the complexity that
may arise from this step, we also develop unimanual alternatives, e.g.,
utilizing a Human-Joystick, commonly referred to as Leaning interface. The
outcomes of an empirical study centered around a primed search task yield
unexpected findings. We observed a sample of users spanning multiple levels of
gaming experience and a balanced gender distribution exhibit no significant
difficulties with the bimanual, asymmetric interfaces. Remarkably, the
performance of Orientation Selection is, as in prior work, at least on par with
Snap Rotation. Moreover, through a subsequent exploratory analysis, we uncover
indications that Pointing-Directed Steering outperforms embodied interfaces in
usability and task load in the given setting.


  In large-$N_c$ conformal field theories with classical holographic duals,
inverse coupling constant corrections are obtained by considering
higher-derivative terms in the corresponding gravity theory. In this work, we
use type IIB supergravity and bottom-up Gauss-Bonnet gravity to study the
dynamics of boost-invariant Bjorken hydrodynamics at finite coupling. We
analyze the time-dependent decay properties of non-local observables (scalar
two-point functions and Wilson loops) probing the different models of Bjorken
flow and show that they can be expressed generically in terms of a few field
theory parameters. In addition, our computations provide an analytically
quantifiable probe of the coupling-dependent validity of hydrodynamics at early
times in a simple model of heavy-ion collisions, which is an observable closely
analogous to the hydrodynamization time of a quark-gluon plasma. We find that
to third order in the hydrodynamic expansion, the convergence of hydrodynamics
is improved and that generically, as expected from field theory considerations
and recent holographic results, the applicability of hydrodynamics is delayed
as the field theory coupling decreases.


  Black box models only provide results for deep learning tasks, and lack
informative details about how these results were obtained. Knowing how input
variables are related to outputs, in addition to why they are related, can be
critical to translating predictions into laboratory experiments, or defending a
model prediction under scrutiny. In this paper, we propose a general theory
that defines a variance tolerance factor (VTF) inspired by influence function,
to interpret features in the context of black box neural networks by ranking
the importance of features, and construct a novel architecture consisting of a
base model and feature model to explore the feature importance in a Rashomon
set that contains all well-performing neural networks. Two feature importance
ranking methods in the Rashomon set and a feature selection method based on the
VTF are created and explored. A thorough evaluation on synthetic and benchmark
datasets is provided, and the method is applied to two real world examples
predicting the formation of noncrystalline gold nanoparticles and the chemical
toxicity 1793 aromatic compounds exposed to a protozoan ciliate for 40 hours.


  Accurate prediction of the water properties from a low-cost ab-initio method
still a foremost problem for chemists and physicist. Though density functional
approaches starting from semilocal to hybrid functionals are tested, those are
not efficiently performed for all the properties together, especially,
considering energies, conformal ranking, structural and dynamics of water.
Also, the inclusion of the long-range van der Waals (vdW) interaction does not
improve the ordering stability of isomer. However, relying on the simple
revision of the Tao-Mo (revTM) semilocal meta-generalized gradient
approximations, we demonstrate that all properties of the water can be
accurately predicted. A consistent improvement over several popular ab-initio
methods is achieved, indicating the accuracy of this method for describing
hydrogen bonding of water.


  We develop a model of bailout stigma where accepting a bailout signals a
firm's balance-sheet weakness and worsens its funding prospect. To avoid
stigma, high-quality firms either withdraw from subsequent financing after
receiving bailouts or refuse bailouts altogether to send a favorable signal.
The former leads to a short-lived stimulation with a subsequent market freeze
even worse than if there were no bailouts. The latter revives the funding
market, albeit with delay, to the level achievable without any stigma, and
implements a constrained optimal outcome. A menu of multiple bailout programs
also compounds bailout stigma and worsens market freeze.


  Recommender systems have become indispensable in music streaming services,
enhancing user experiences by personalizing playlists and facilitating the
serendipitous discovery of new music. However, the existing recommender systems
overlook the unique challenges inherent in the music domain, specifically
shuffle play, which provides subsequent tracks in a random sequence. Based on
our observation that the shuffle play sessions hinder the overall training
process of music recommender systems mainly due to the high unique transition
rates of shuffle play sessions, we propose a Music Recommender System with
Shuffle Play Recommendation Enhancement (MUSE). MUSE employs the
self-supervised learning framework that maximizes the agreement between the
original session and the augmented session, which is augmented by our novel
session augmentation method, called transition-based augmentation. To further
facilitate the alignment of the representations between the two views, we
devise two fine-grained matching strategies, i.e., item- and similarity-based
matching strategies. Through rigorous experiments conducted across diverse
environments, we demonstrate MUSE's efficacy over 12 baseline models on a
large-scale Music Streaming Sessions Dataset (MSSD) from Spotify. The source
code of MUSE is available at \url{https://github.com/yunhak0/MUSE}.


  Scintillation characteristics of a thallium doped sodium iodide (NaI(Tl))
crystal with a dimension of 0.6 x 0.6 x 2 cm3 are studied by attaching a
silicon photomultiplier (SiPM) direct to the crystal over a temperature range
from 93 to 300 K. The scintillation light output and decay time are measured by
irradiating 59.54 keV gamma-rays from a 241Am source. We observed approximately
20% increase in light yield at 230K compared to that at the room temperature.
At this condition, the NaI(Tl) crystal coupled with the SiPM can be a good
candidate for future dark matter search detector.


  The purpose of this paper is to study the limiting distribution of special
{\it additive functionals} on random planar maps, namely the number of
occurrences of a given {\it pattern}. The main result is a central limit
theorem for these pattern counts in the case of pattern with a simple boundary.
The proof relies on a combination of analytic and combinatorial methods
together with a moment method due to Gao and Wormald~\cite{GaoWormald}. It is
an important issue to handle the overlap structure of two pattern which is the
main difficulty in the proof.


  We present Bill2d, a modern and efficient C++ package for classical
simulations of two-dimensional Hamiltonian systems. Bill2d can be used for
various billiard and diffusion problems with one or more charged particles with
interactions, different external potentials, an external magnetic field,
periodic and open boundaries, etc. The software package can also calculate many
key quantities in complex systems such as Poincar\'e sections, survival
probabilities, and diffusion coefficients. While aiming at a large class of
applicable systems, the code also strives for ease-of-use, efficiency, and
modularity for the implementation of additional features. The package comes
along with a user guide, a developer's manual, and a documentation of the
application program interface (API).


  A predictive, point-cloud tracer is presented that determines with a
quantified uncertainty the Lagrangian motion of a group of point-particles
within a finite region. The tracer assumes a random forcing within confidence
intervals to account for the empiricism of data-driven force models and
stochasticity related to the chaotic nature of the subcloud scale dynamics. It
builds on the closed Subgrid Particle-Averaged Reynolds Stress-Equivalent
(SPARSE) formulation presented in Dom\'inguez-V\'azquez~\textit{et al.}
[\textit{Int. J. Multiph. Flow.} 161, 104375] that assumes a deterministic
forcing. SPARSE describes the first two moments of particle clouds with moment
equations in closed-form, with a theoretical third-order convergence rate with
respect to the standard deviations of the cloud variables. The cloud model
alleviates computational cost and enhances the convergence rate as compared to
Monte Carlo (MC) based point-particle methods. The randomness in the forcing
model leads to virtual stresses that correlate random forcing and field
fluctuations. These stresses strain and rotate the random cloud as compared to
a deterministically forced cloud and thus determine to what extent the random
forcing propagates into the confidence intervals of the dispersed solution. In
symmetric flows the magnitude of the virtual stress is zero. Tests in
analytical carrier-fields and in a decaying homogeneous isotropic turbulence
flow computed with a discontinuous Galerkin (DG) compressible DNS solver are
performed to verify and validate the SPARSE method for randomly forced
particles.


  A classical result states that the determinant of an alternating link is
equal to the number of spanning trees in a checkerboard graph of an alternating
connected projection of the link.
  We generalize this result to show that the determinant is the alternating sum
of the number of quasi-trees of genus j of the dessin of a non-alternating
link.
  Furthermore, we obtain formulas for other link invariants by counting
quantities on dessins. In particular we will show that the $j$-th coefficient
of the Jones polynomial is given by sub-dessins of genus less or equal to $j$.


  Symmetric couplings among aggregates of $n$ chromophores increase the
transfer rate of excitons by a factor $n^2$, a quantum mechanical phenomenon
called "supertransfer." In this work we demonstrate how supertransfer effects
induced by geometrical symmetries can enhance the exciton diffusion length by a
factor $n$ along cylindrically symmetric structures, consisting of arrays of
rings of chromophores, and along spiral arrays. We analyse both closed system
dynamics and open quantum dynamics, modelled by combining a random bosonic bath
with static disorder. In the closed system case, we use the symmetries of the
system within a short-time approximation to obtain a closed analytical
expression for the diffusion length that explicitly reveals the supertransfer
contribution. When subject to disorder, we show that supertransfer can enhance
excitonic diffusion lengths for small disorders and characterize the crossover
from coherent to incoherent motion. Owing to the quasi-1D nature of the model,
disorder ultimately localizes the excitons, diminishing but not destroying the
effects of supertransfer. When dephasing effects are included, we study the
scaling of diffusion with both time and number of chromophores and observe that
the transition from a coherent, ballistic regime to an incoherent, random-walk
regime occurs at the same point as the change from supertransfer to classical
scaling.


  Face clustering is a useful tool for applications like automatic face
annotation and retrieval. The main challenge is that it is difficult to cluster
images from the same identity with different face poses, occlusions, and image
quality. Traditional clustering methods usually ignore the relationship between
individual images and their neighbors which may contain useful context
information. In this paper, we repurpose the well-known Transformer and
introduce a Face Transformer for supervised face clustering. In Face
Transformer, we decompose the face clustering into two steps: relation encoding
and linkage predicting. Specifically, given a face image, a \textbf{relation
encoder} module aggregates local context information from its neighbors and a
\textbf{linkage predictor} module judges whether a pair of images belong to the
same cluster or not. In the local linkage graph view, Face Transformer can
generate more robust node and edge representations compared to existing
methods. Experiments on both MS-Celeb-1M and DeepFashion show that our method
achieves state-of-the-art performance, e.g., 91.12\% in pairwise F-score on
MS-Celeb-1M.


  The system of our interest is a dilute binary mixture, in which we consider
that the species have different temperatures as an initial condition. To study
their time evolution, we use the full version of the Boltzmann equation, under
the hypothesis of partial local equilibrium for both species. Neither a
diffusion force nor mass diffusion appears in the system. We also estimate the
time in which the temperatures of the components reach the full local
equilibrium. In solving the Boltzmann equation, we imposed no assumptions on
the collision term. We work out its solution by using the well known
Chapman-Enskog method to first order in the gradients. The time in which the
temperatures relax is obtained following Landau's original idea. The result is
that the relaxation time for the temperatures is much smaller than the
characteristic hydrodynamical times but greater than a collisional time. The
main conclusion is that there is no need to study binary mixtures with
different temperatures when hydrodynamical properties are sought.


  Many problems that appear in biomedical decision making, such as diagnosing
disease and predicting response to treatment, can be expressed as binary
classification problems. The costs of false positives and false negatives vary
across application domains and receiver operating characteristic (ROC) curves
provide a visual representation of this trade-off. Nonparametric estimators for
the ROC curve, such as a weighted support vector machine (SVM), are desirable
because they are robust to model misspecification. While weighted SVMs have
great potential for estimating ROC curves, their theoretical properties were
heretofore underdeveloped. We propose a method for constructing confidence
bands for the SVM ROC curve and provide the theoretical justification for the
SVM ROC curve by showing that the risk function of the estimated decision rule
is uniformly consistent across the weight parameter. We demonstrate the
proposed confidence band method and the superior sensitivity and specificity of
the weighted SVM compared to commonly used methods in diagnostic medicine using
simulation studies. We present two illustrative examples: diagnosis of
hepatitis C and a predictive model for treatment response in breast cancer.


  We used the 10.4m Gran Telescopio Canarias to search for the optical
counterparts to four isolated $\gamma$-ray pulsars, all detected in the X-rays
by either \xmm\ or \chan\ but not yet in the optical. Three of them are
middle-aged pulsars -- PSR\, J1846+0919 (0.36 Myr), PSR\, J2055+2539 (1.2 Myr),
PSR\, J2043+2740 (1.2 Myr) -- and one, PSR\, J1907+0602, is a young pulsar
(19.5 kyr). For both PSR\, J1907+0602 and PSR\, J2055+2539 we found one object
close to the pulsar position. However, in both cases such an object cannot be a
viable candidate counterpart to the pulsar. For PSR\, J1907+0602, because it
would imply an anomalously red spectrum for the pulsar and for PSR\, J2055+2539
because the pulsar would be unrealistically bright ($r'=20.34\pm0.04$) for the
assumed distance and interstellar extinction. For PSR\, J1846+0919, we found no
object sufficiently close to the expected position to claim a possible
association, whereas for PSR\, J2043+2740 we confirm our previous findings that
the object nearest to the pulsar position is an unrelated field star. We used
our brightness limits ($g' \approx 27$), the first obtained with a
large-aperture telescope for both PSR\, J1846+0919 and PSR\, J2055+2539, to
constrain the optical emission properties of these pulsars and investigate the
presence of spectral turnovers at low energies in their multi-wavelength
spectra.


  In his discussion of Davies and Gather [Ann. Statist. 33 (2005) 977--1035]
[math.ST/0508497] Tyler pointed out that the theory developed there could not
be applied to the case of directional data. He related the breakdown of
directional functionals to the problem of definability. In this addendum we
provide a concept of breakdown defined in terms of definability and not in
terms of bias. If a group of finite order $k$ acts on the sample space we show
that the breakdown point can be bounded above by $(k-1)/k$. In the case of
directional data there is a group of order $k=2$ giving an upper bound of 1/2.


  We examine a recently proposed class of integrable deformations to
two-dimensional conformal field theories. These {\lambda}-deformations
interpolate between a WZW model and the non-Abelian T-dual of a Principal
Chiral Model on a group G or, between a G/H gauged WZW model and the
non-Abelian T-dual of the geometric coset G/H.
  {\lambda}-deformations have been conjectured to represent quantum group
q-deformations for the case where the deformation parameter is a root of unity.
In this work we show how such deformations can be given an embedding as full
string backgrounds whose target spaces satisfy the equations of type-II
supergravity. One illustrative example is a deformation of the Sl(2,R)/U(1)
black-hole CFT. A further example interpolates between the $\frac{SU(2)\times
SU(2)}{SU(2)}\times\frac{SL(2,R)\times SL(2,R)}{SL(2,R)} \times U(1)^4$ gauged
WZW model and the non-Abelian T-dual of $AdS_3\times S^3\times T^4$ supported
with Ramond flux.


  New star cluster candidates projected toward the Large and Small Magellanic
Clouds (L/SMC) have been recently discovered from relatively deep imaging
surveys. We here conduct a sound analysis of 24 star cluster candidates located
in the outer regions of the L/SMC using PSF photometry produced by the Survey
of the Magellanic Stellar History. With only one exception, the studied objects
resulted to be genuine stellar aggregates. We conclude on their physical
reality once their observed color-magnitude diagrams (CMDs) were statistically
decontaminated by the presence of field stars, and the resulting cleaned CMDs
for stars with assigned membership probabilities higher than 50\% were compared
with synthetic CMDs generated for thousand combinations of ages, distances,
metallicities, star cluster mass and binary fractions. The parameter of the
best-matched synthetic CMDs obtained from a likelihood approach were adopted as
the star cluster astrophysical properties. The present star cluster sample
spans a wide range of distances, from those star clusters located in front of
the LMC, to those along the onset of the Magellanic Bridge, up to those behind
the SMC. Their ages reveal different formation episodes that took place along
the galaxy formation and others as a consequence of the galaxy interactions.
From their estimated metallicities and ages, we speculate with the possibility
that relatively metal-deficient gaseous flows have existed between these
galaxies during nearly the last one Gyr (log(age /yr) $\approx$ 9.0), that made
possible the formation of young star clusters in the galaxy peripheries.
Despide the L/SMC interactions, the studied star clusters are similar or more
massive than their counterparts in the Milky Way, which suggests that tidal
effects are relatively more important in our Galaxy.


  We experimentally compare two types of interface structures with magnetic and
non-magnetic Weyl semimetals. They are the junctions between a gold normal
layer and magnetic Weyl semimetal Ti$_2$MnAl, and a ferromagnetic nickel layer
and non-magnetic Weyl semimetal WTe$_2$, respectively. Due to the ferromagnetic
side of the junction, we investigate spin-polarized transport through the Weyl
semimetal surface. For both structures, we demonstrate similar current-voltage
characteristics, with hysteresis at low currents and sharp peaks in
differential resistance at high ones. Despite this behavior resembles the known
current-induced magnetization dynamics in ferromagnetic structures, evolution
of the resistance peaks with magnetic field is unusual. We connect the observed
effects with current-induced spin dynamics in Weyl topological surface states.


  Motivated by the prospects of increased measurement bandwidth, improved
signal to noise ratio and access to the full complex magnetic susceptibility we
develop a technique to extract microwave voltages from our high resistance (10
k{\Omega}) (Ga,Mn)As microbars. We drive magnetization precession with
microwave frequency current, using a mechanism that relies on the spin orbit
interaction. A capacitively coupled lambda/2 microstrip resonator is employed
as an impedance matching network, enabling us to measure the microwave voltage
generated during magnetisation precession.


  This article introduces a new instrumental variable approach for estimating
unknown population parameters with data having nonrandom missing values. With
coarse and discrete instruments, Shao and Wang (2016) proposed a semiparametric
method that uses the added information to identify the tilting parameter from
the missing data propensity model. A naive application of this idea to
continuous instruments through arbitrary discretizations is apt to be
inefficient, and maybe questionable in some settings. We propose a
nonparametric method not requiring arbitrary discretizations but involves
scanning over continuous dichotomizations of the instrument; and combining scan
statistics to estimate the unknown parameters via weighted integration.
  We establish the asymptotic normality of the proposed integrated estimator
and that of the underlying scan processes uniformly across the instrument
sample space. Simulation studies and the analysis of a real data set
demonstrate the gains of the methodology over procedures that rely either on
arbitrary discretizations or moments of the instrument.


  We propose a sampling method to include the negative contribution to
probability density distribution in a sampling procedure. This sampling method
is a universal solution for all negative probability problem and shows
extraordinarily power in negative cross section problem. A Monte Carlo
simulation including negative cross section contribution is developed and
successfully preformed to simulate reflection electron energy loss spectroscopy
(REELS) spectra for Ag and Au as examples. Excellent agreement is found between
simulated spectra and experimental measurements. Notably improved fits to
experimental REELS spectra in low energy loss range illustrate the method's
strength as well as the necessity of negative cross section contribution.


  Recent inelastic neutron scattering (INS) experiments of the triangular
antiferromagnet Ba$_3$CoSb$_2$O$_9$ revealed strong deviations from
semiclassical theories. We demonstrate that key features of the INS data are
well reproduced by a parton Schwinger boson theory beyond the saddle-point
approximation. The measured magnon dispersion is well reproduced by the
dispersion of two-spinon bound states (poles of the emergent gauge fields
propagator), while the low-energy continuum scattering is reproduced by a
quasifree two-spinon continuum, suggesting that a free-spinon gas is a good
initial framework to study magnetically ordered states near a quantum melting
point.


  The eigenfunctions of the Laplacian are a central object from the realms of
analytic number theory to geometric analysis. We prove that H\"ormander
$L^2$-$L^{\infty}$ estimates are equivalent to restriction estimates to small
geodesic spheres for a certain class of manifolds.


  In earlier work it was pointed out that for warped product spacetimes the
conformal (geometrical moduli) excitations of the internal compactified factor
spaces should be observable as massive scalar fields in the external spacetime.
Here we show that these scalar fields (gravitational excitons) describe weakly
interacting particles and can be considered as dark matter component. Masses of
the gravexcitons are defined by the form of the effective potential of the
theory and the stabilization scales of the internal space. This implies that
different stabilization scales result in different types of DM. An essential
role is played by the effective potential. On the one hand, its minima fix
possible stabilization scales of the internal spaces; on the other hand, they
provide possible values for the effective cosmological constant.


  We reconsider trans-Planckian corrections to inflationary spectra by taking
into account a physical effect which has been overlooked and which could have
important consequences. We assume that the short length scale characterizing
the new physics is endowed with a finite width, the origin of which could be
found in quantum gravity. As a result, the leading corrections responsible for
superimposed osillations in the CMB temperature anisotropies are generically
damped by the blurring of the UV scale. To determine the observational
ramifications of this damping, we compare it to that which effectively occurs
when computing the angular power spectrum of temperature anisotropies. The
former gives an overall change of the oscillation amplitudes whereas the latter
depends on the angular scale. Therefore, in principle they could be
distinguished. In any case, the observation of superimposed oscillations would
place tight constraint on the variance of the UV cutoff.


  We demonstrate the existence of sudden, finite-time, singularities, with
constant scale factor, expansion rate and density, in expanding Bianchi type IX
universes with free anisotropic pressures. A new type of non-simultaneous
anisotropic sudden singularity arises because of the divergences of the
pressures, which may be of barrel or pancake type. The effect of one or more
directions of expansion hitting a sudden singularity is tantamount to
dimensional reductions as the non-singular directions continue expanding and
can see the sudden singularity in their past.


  We examine the globular cluster systems (GCS) of a sample of 34 S0 galaxies
from a WFPC2 snapshot survey in the V and I-bands. Of these 34 galaxies, 29
have measurable globular cluster systems. The mean color of the GCSs of
individual galaxies vary from V-I=0.85 mag to V-I=1.17 mag. The average color
of GCSs in all 29 S0 galaxies, V-I=1.00 +/- 0.07 mag, is similar to the value
of V-I=1.04 +/- 0.04 derived for ellipticals in a companion paper. The mean
metallicity of a cluster system is correlated to the luminosity (or mass) of
the host galaxy, but is not dependent on the Hubble type. Our measurements of
the local specific frequency, on the other hand, confirm that the cluster
formation efficiency is a function of Hubble type. The mean local specific
frequency of our sample within the WFPC2 field-of-view is 1.0 +/- 0.6, lower
than S_(N Local)=2.4 +/- 1.8 derived for ellipticals in a similar analysis.
Although we are able to confirm a bimodal color distribution in only one galaxy
from the shallow 'snapshot' images analyzed in this paper statistical tests
suggest that 10-20% of S0s are bimodal it at the present level of photometric
accuracy. There are no significant trends in GCS properties with membership or
location of the S0 host in a galaxy cluster. We have measured the turnover
luminosity of the globular cluster luminosity function (GCLF) for the richest
few GCSs and find the GCLF distances to be in agreement with other estimates.
The globular clusters in S0 galaxies have average half-light radii of ~2.6 pc
which is similar to that of other galaxies, including our own.


  We present a pedagogical introduction to Bose-Einstein condensation in traps
with spherical symmetry, namely the spherical box and the thick shell,
sometimes called bubble trap. In order to obtain the critical temperature for
Bose-Einstein condensation, we describe how to calculate the cumulative state
number and density of states in these geometries, using numerical and
analytical (semi-classical) approaches. The differences in the results of both
methods are a manifestation of Weyl's theorem, i.e., they reveal how the
geometry of the trap (boundary condition) affects the number of the eigenstates
counted. Using the same calculation procedure, we analyzed the impact of going
from three-dimensions to two-dimensions, as we move from a thick shell to a
two-dimensional shell. The temperature range we obtained, for most commonly
used atomic species and reasonable confinement volumes, is compatible with
current cold atom experiments, which demonstrates that these trapping
potentials may be employed in experiments.


  Let $G$ be a graph and c a proper k-coloring of G, i.e. any two adjacent
vertices u and v have different colors c(u) and c(v). A proper k-coloring is a
b-coloring if there exists a vertex in every color class that contains all the
colors in its closed neighborhood. The maximum number of colors k admitting
b-coloring of G is the b-chromatic number. We present two separate approaches
to the conjecture posed by Blidia et. al that the b-chromatic number equals to
d+1 for every d-regular graph of girth at least five except the Petersen graph.


  In the context of smart grids and load balancing, daily peak load forecasting
has become a critical activity for stakeholders of the energy industry. An
understanding of peak magnitude and timing is paramount for the implementation
of smart grid strategies such as peak shaving. The modelling approach proposed
in this paper leverages high-resolution and low-resolution information to
forecast daily peak demand size and timing. The resulting multi-resolution
modelling framework can be adapted to different model classes. The key
contributions of this paper are a) a general and formal introduction to the
multi-resolution modelling approach, b) a discussion on modelling approaches at
different resolutions implemented via Generalised Additive Models and Neural
Networks and c) experimental results on real data from the UK electricity
market. The results confirm that the predictive performance of the proposed
modelling approach is competitive with that of low- and high-resolution
alternatives.


  Despite the value of VR (Virtual Reality) for educational purposes, the
instructional power of VR in Biology Laboratory education remains
under-explored. Laboratory lectures can be challenging due to students' low
motivation to learn abstract scientific concepts and low retention rate.
Therefore, we designed a VR-based lecture on fermentation and compared its
effectiveness with lectures using PowerPoint slides and a desktop application.
Grounded in the theory of distributed cognition and motivational theories, our
study examined how learning happens in each condition from students' learning
outcomes, behaviors, and perceptions. Our result indicates that VR facilitates
students' long-term retention to learn by cultivating their longer visual
attention and fostering a higher sense of immersion, though students'
short-term retention remains the same across all conditions. This study extends
current research on VR studies by identifying the characteristics of each
teaching artifact and providing design implications for integrating VR
technology into higher education.


  The isomorphism problem for graphs (GI) and the isomorphism problem for
groups (GrISO) have been studied extensively by researchers. The current best
algorithms for both these problems run in quasipolynomial time. In this paper,
we study the isomorphism problem of graphs that are defined in terms of groups,
namely power graphs, directed power graphs, and enhanced power graphs. It is
not enough to check the isomorphism of the underlying groups to solve the
isomorphism problem of such graphs as the power graphs (or the directed power
graphs or the enhanced power graphs) of two nonisomorphic groups can be
isomorphic. Nevertheless, it is interesting to ask if the underlying group
structure can be exploited to design better isomorphism algorithms for these
graphs. We design polynomial time algorithms for the isomorphism problems for
the power graphs, the directed power graphs and the enhanced power graphs
arising from finite nilpotent groups. In contrast, no polynomial time algorithm
is known for the group isomorphism problem, even for nilpotent groups of class
2.
  We note that our algorithm does not require the underlying groups of the
input graphs to be given. The isomorphism problems of power graphs and enhanced
power graphs are solved by first computing the directed power graphs from the
input graphs. The problem of efficiently computing the directed power graph
from the power graph or the enhanced power graph is due to Cameron [IJGT'22].
Therefore, we give a solution to Cameron's question.


  Consider the iteration of an invertible matrix on the projective space: are
the Morse components normally hyperbolic? As far as we know, this was only
stablished when the matrix is diagonalizable over the complex numbers. In this
article we prove that this is true in the far more general context of an
arbitrary element of a semisimple Lie group acting on its generalized flag
manifolds: the so called translations on flag manifolds. This context
encompasses the iteration of an invertible non-diagonazible matrix on the real
or complex projective space, the classical flag manifolds of real or complex
nested subspaces and also symplectic grassmanians. Without these tools from Lie
theory we do not know how to solve this problem even for the projective space.


  Absorption imaging is a commonly adopted method to acquire, with high
temporal resolution, spatial information on a partially transparent object. It
relies on the interference between a probe beam and the coherent response of
the object. In the low saturation regime, it is well described by a Beer
Lambert attenuation. In this paper we theoretically derive the absorption of a
$\sigma$ polarized laser probe by an ensemble of two-level systems in any
saturation regime. We experimentally demonstrate that the absorption cross
section in dense $^{87}$Rb cold atom ensembles is reduced, with respect to the
single particle response, by a factor proportional to the optical density b of
the medium. To explain this reduction, we developed a model that incorporates,
in the single particle response, the incoherent electromagnetic background
emitted by the surrounding ensemble. We show that it qualitatively reproduces
the experimental results. Our calibration factor that has a universal
dependence on optical density $b$ for $\sigma$ polarized light : $\alpha$ =
1.17(9) + 0.255(2)b allows to obtain quantitative and absolute, in situ, images
of dense quantum systems.


  Trends in hardware, the prevalence of the cloud, and the rise of highly
demanding applications have ushered an era of specialization that quickly
changes how data is processed at scale. These changes are likely to continue
and accelerate in the next years as new technologies are adopted and deployed:
smart NICs, smart storage, smart memory, disaggregated storage, disaggregated
memory, specialized accelerators (GPUS, TPUs, FPGAs), and a wealth of ASICs
specifically created to deal with computationally expensive tasks (e.g.,
cryptography or compression). In this tutorial, we focus on data processing on
FPGAs, a technology that has received less attention than, e.g., TPUs or GPUs
but that is, however, increasingly being deployed in the cloud for data
processing tasks due to the architectural flexibility of FPGAs, along with
their ability to process data at line rate, something not possible with other
types of processors or accelerators.
  In the tutorial, we will cover what FPGAs are, their characteristics, their
advantages and disadvantages, as well as examples from deployments in the
industry and how they are used in various data processing tasks. We will
introduce FPGA programming with high-level languages and describe hardware and
software resources available to researchers. The tutorial includes case studies
borrowed from research done in collaboration with companies that illustrate the
potential of FPGAs in data processing and how software and hardware are
evolving to take advantage of the possibilities offered by FPGAs. The use cases
include: (1) approximated nearest neighbor search, which is relevant to
databases and machine learning, (2) remote disaggregated memory, showing how
the cloud architecture is evolving and demonstrating the potential for operator
offloading and line rate data processing, and (3) recommendation system as an
application with tight latency constraints.


  For appropriate orthonormal wavelet basis $\{\psi_{j\,k}^e
\}_{j\in\mathbb{Z}\,k\in\mathbb{Z}^d\,e\in\{0,1\}^d}$, constants $p$ and
$\gamma$, if $\mathcal{I}_{\gamma}$ denotes the Riesz fractional integral
operator of order $\gamma$ and $(\eta_{j\,k\,e})_{j\in\mathbb{Z}
k\in\mathbb{Z}^d \,e\in\{0,1\}^d}$ a sequence of independent identically
distributed symmetric $p$-stable random variables, we investigate the
convergence of the series $\sum\limits_{j\,k\,e} \eta_{j\,k\,e}
\mathcal{I}_{\gamma} \psi_{j\,k\,}^e$. Similar results are also studied for
modified fractional integral operators. Finally, some geometric properties
related to self similarity are studied.


  Electric discharges were detected directly in the cloudy atmospheres of
Earth, Jupiter and Saturn, are debatable for Venus, and indirectly inferred for
Neptune and Uranus in our solar system. Sprites (and other types of transient
luminous events) have been detected only on Earth, and are theoretically
predicted for Jupiter, Saturn and Venus. Cloud formation is a common phenomenon
in ultra-cool atmospheres such as in Brown Dwarf and extrasolar planetary
atmospheres. Cloud particles can be expected to carry considerable charges
which may trigger discharge events via small-scale processes between individual
cloud particles (intra-cloud discharges) or large-scale processes between
clouds (inter-cloud discharges). We investigate electrostatic breakdown
characteristics, like critical field strengths and critical charge densities
per surface, to demonstrate under which conditions mineral clouds undergo
electric discharge events which may trigger or be responsible for sporadic
X-ray emission. We apply results from our kinetic dust cloud formation model
that is part of the Drift-Phoenix model atmosphere simulations. We present a
first investigation of the dependence of the breakdown conditions in Brown
Dwarf and giant gas exoplanets on the local gas-phase chemistry, the effective
temperature and primordial gas-phase metallicity. Our results suggest that
different intra-cloud discharge processes dominate at different heights inside
mineral clouds: local coronal (point discharges) and small-scale sparks at the
bottom region of the cloud where the gas density is high, and flow discharges
and large-scale sparks near, and maybe above, the cloud top. The comparison of
the thermal degree of ionisation and the number density of cloud particles
allows us to suggest the efficiency with which discharges will occur in
planetary atmospheres.


  Can a computer which runs for time $\omega^2$ compute more than one which
runs for time $\omega$? No. Not, at least, for the infinite computer we
describe. Our computer gets more powerful when the set of its steps gets
larger. We prove that they theory of second order arithmetic cannot be decided
by computers running to countable time.


  In this paper, we present various schemes of cloaking an arbitrary objects
via anomalous localized resonance and provide their analysis in two and three
dimensions. This is a way to cloak an object using negative index materials in
which the cloaking device is independent of the object. As a result, we show
that in two dimensional quasistatic regime an annular plasmonic structure $-I$
cloaks small but finite size objects near by. We also discuss its connections
with superlensing and cloaking using complementary media. In particular, we
confirm the possibility that a lens can act like a cloak and conversely. This
possibility was raised about a decade ago in the literature.


  The dynamical map represents a fundamental concept in quantum field theory,
providing a solution of the field equations in the Fock space of asymptotic
fields. In this paper, we show how to express the dynamical map of a scalar
field in the language of quantum effective action. This grants us new insights
into the study of topological defects in quantum field theory, showing a
connection between the usual least-action principle and Umezawa's boson
transformation method.


  We study a new class of estimands in causal inference, which are the
solutions to a stochastic nonlinear optimization problem that in general cannot
be obtained in closed form. The optimization problem describes the
counterfactual state of a system after an intervention, and the solutions
represent the optimal decisions in that counterfactual state. In particular, we
develop a counterfactual mean-variance optimization approach, which can be used
for optimal allocation of resources after an intervention. We propose a
doubly-robust nonparametric estimator for the optimal solution of the
counterfactual mean-variance program. We go on to analyze rates of convergence
and provide a closed-form expression for the asymptotic distribution of our
estimator. Our analysis shows that the proposed estimator is robust against
nuisance model misspecification, and can attain fast $\sqrt{n}$ rates with
tractable inference even when using nonparametric methods. This result is
applicable to general nonlinear optimization problems subject to linear
constraints whose coefficients are unknown and must be estimated. In this way,
our findings contribute to the literature in optimization as well as causal
inference. We further discuss the problem of calibrating our counterfactual
covariance estimator to improve the finite-sample properties of our proposed
optimal solution estimators. Finally, we evaluate our methods via simulation,
and apply them to problems in healthcare policy and portfolio construction.


  Let $F$ be a $p$--adic field, i.e., a finite extension of $\mathbb Q_p$ for
some prime $p$. The local Langlands correspondence attaches to each continuous
$n$--dimensional $\Phi$-semisimple representation $\rho$ of $W'_F$, the
Weil--Deligne group for $\bar F/F$, an irreducible admissible representation
$\pi(\rho)$ of $GL_n(F)$ such that, among other things, the local $L$- and
$\varepsilon$-factors of pairs are preserved. This correspondence should be
robust and preserve various parallel operations on the arithmetic and analytic
sides, such as taking the exterior square or symmetric square. In this paper,
we show that this is the case for the local arithmetic and analytic symmetric
square and exterior square $\varepsilon$--factors, that is, that
$\varepsilon(s,\Lambda^2\rho,\psi)=\varepsilon(s,\pi(\rho),\Lambda^2,\psi)$ and
$\varepsilon(s,Sym^2\rho,\psi)=\varepsilon(s,\pi(\rho),Sym^2,\psi)$. The
agreement of the $L$-functions also follows by our methods, but this was
already known by Henniart. The proof is a robust deformation argument, combined
with local/global techniques, which reduces the problem to the stability of the
analytic $\gamma$-factor $\gamma(s,\pi,\Lambda^2,\psi)$ under highly ramified
twists when $\pi$ is supercuspidal. This last step is achieved by relating the
$\gamma$-factor to a Mellin transform of a partial Bessel function attached to
the representation and then analyzing the asymptotics of the partial Bessel
function, inspired in part by the theory of Shalika germs for Bessel integrals.
The stability for every irreducible admissible representation $\pi$ then
follows from those of the corresponding arithmetic $\gamma$--factors as a
corollary.


  Object detection in three-dimensional (3D) space attracts much interest from
academia and industry since it is an essential task in AI-driven applications
such as robotics, autonomous driving, and augmented reality. As the basic
format of 3D data, the point cloud can provide detailed geometric information
about the objects in the original 3D space. However, due to 3D data's sparsity
and unorderedness, specially designed networks and modules are needed to
process this type of data. Attention mechanism has achieved impressive
performance in diverse computer vision tasks; however, it is unclear how
attention modules would affect the performance of 3D point cloud object
detection and what sort of attention modules could fit with the inherent
properties of 3D data. This work investigates the role of the attention
mechanism in 3D point cloud object detection and provides insights into the
potential of different attention modules. To achieve that, we comprehensively
investigate classical 2D attentions, novel 3D attentions, including the latest
point cloud transformers on SUN RGB-D and ScanNetV2 datasets. Based on the
detailed experiments and analysis, we conclude the effects of different
attention modules. This paper is expected to serve as a reference source for
benefiting attention-embedded 3D point cloud object detection. The code and
trained models are available at:
https://github.com/ShiQiu0419/attentions_in_3D_detection.


  The perfect physical and geometrical parameters of the main-sequence close
visual binary system (CVBS), HIP\,105947, are explicitly presented. These
parameters have been constructed conclusively using Al-Wardat's complex method
for analyzing CVBSs, which is a method for constructing a synthetic spectral
energy distribution (SED) for the entire binary system using individual SED for
each component star. Which in its turn built using Kurucz
({\fontfamily{cmtt}\selectfont ATLAS9}) line-blanketed plane-parallel models.
At the same time, the orbital parameters for the system are calculated using
Tokovinin's dynamical method for constructing the best orbits of the
interferometric binary system. Henceforth, the mass-sum of the components, the
$\triangle\theta $ and $\triangle\rho $ residuals for the system are
introduced. The combination of Al-Wardat's and Tokovinin's methods yields the
estimation of the physical and geometrical parameters to their best values. The
positions of the components of the system on the evolutionary tracks and
isochrones are plotted, and their formation and evolution are discussed.


  Low energy states of self-gravitating systems with finite angular momentum
are considered. A constraint is introduced to confine cores and other condensed
objects within the system boundaries by gravity alone. This excludes previously
observed astrophysically irrelevant asymmetric configurations with a single
core. We show that for an intermediate range of a short-distance cutoff and
small angular momentum, the equilibrium configuration is an asymmetric binary.
For larger angular momentum or for a smaller range of the short distance
cutoff, the equilibrium configuration consists of a central core and an
equatorial ring. The mass of the ring varies between zero for vanishing
rotation and the full system mass for the maximum angular momentum $L_{max}$ a
localized gravitationally bound system can have. The value of $L_{max}$ scales
as $\sqrt{\ln(1/x_0)}$, where $x_0$ is a ratio of a short-distance cutoff range
to the system size. An example of the soft gravitational potential is
considered; the conclusions are shown to be valid for other forms of
short-distance regularization.


  A simple, intuitive approach to the assessment of probabilistic inferences is
introduced. The Shannon information metrics are translated to the probability
domain. The translation shows that the negative logarithmic score and the
geometric mean are equivalent measures of the accuracy of a probabilistic
inference. Thus there is both a quantitative reduction in perplexity, which is
the inverse of the geometric mean of the probabilities, as good inference
algorithms reduce the uncertainty and a qualitative reduction due to the
increased clarity between the original set of probabilistic forecasts and their
central tendency, the geometric mean. Further insight is provided by showing
that the R\'enyi and Tsallis entropy functions translated to the probability
domain are both the weighted generalized mean of the distribution. The
generalized mean of probabilistic forecasts forms a spectrum of performance
metrics referred to as a Risk Profile. The arithmetic mean is used to measure
the decisiveness, while the -2/3 mean is used to measure the robustness.


  We introduce several-dozen experimentally-found invariants of Poncelet
N-periodics in the confocal ellipse pair (Elliptic Billiard). Recall this
family is fully defined by two integrals of motion (linear and angular
momentum), so any "new" invariants are dependent upon them. Nevertheless,
proving them may require sophisticated methods. We reference some two-dozen
proofs already contributed. We hope this article will motivate contributions
for those still lacking proof.


  Relativistic shocks are usually thought to occur in violent astrophysical
explosions. These collisionless shocks are mediated by a plasma kinetic
streaming instability, often loosely referred to as the Weibel instability,
which generates strong magnetic fields "from scratch" very efficiently. In this
review paper we discuss the shock micro-physics and present a recent model of
"pre-conditioning" of an initially unmagnetized upstream region via the
cosmic-ray-driven Weibel-type instability.


  Microwave heating of a high-temperature plasma confined in a large-scale open
magnetic trap, including all important wave effects like diffraction,
absorption, dispersion and wave beam aberrations, is described for the first
time within the first-principle technique based on consistent Maxwell's
equations. With this purpose, the quasi-optical approach is generalized over
weakly inhomogeneous gyrotrotropic media with resonant absorption and spatial
dispersion, and a new form of the integral quasi-optical equation is proposed.
An effective numerical technique for this equation's solution is developed and
realized in a new code QOOT, which is verified with the simulations of
realistic electron cyclotron heating scenarios at the Gas Dynamic Trap at the
Budker Institute of Nuclear Physics (Novosibirsk, Russia).


  In relation to the superspace modifications of 11D supergeometry required to
describe the M-theory low-energy effective action, we present an analysis of
infinitesimal supergravity fluctuations about the flat superspace limit. Our
investigation confirms Howe's interpretation of our previous Bianchi identity
analysis. However, the analysis also shows that should 11D supergravity obey
the rules of other off-shell supergravity theories, the complete M-theory
corrections will necessarily excite our previously anticipated spin-1/2
engineering dimension-1/2 spinor auxiliary multiplet superfield. The analysis
of fluctuations yields more evidence that Howe's 1997 theorem is specious when
applied to Poincar\' e supergravity or 11D supergravity/M-theory. We end by
commenting upon recent advances in this area.


  Learning-based visual data compression and analysis have attracted great
interest from both academia and industry recently. More training as well as
testing datasets, especially good quality video datasets are highly desirable
for related research and standardization activities. Tencent Video Dataset
(TVD) is established to serve various purposes such as training neural
network-based coding tools and testing machine vision tasks including object
detection and tracking. TVD contains 86 video sequences with a variety of
content coverage. Each video sequence consists of 65 frames at 4K (3840x2160)
spatial resolution. In this paper, the details of this dataset, as well as its
performance when compressed by VVC and HEVC video codecs, are introduced.


  We study the $\epsilon$-level sets of the signed distance function to a
planar Jordan curve $\Gamma$, and ask what properties of $\Gamma$ ensure that
the $\epsilon$-level sets are Jordan curves, or uniform quasicircles, or
uniform chord-arc curves for all sufficiently small $\epsilon$. Sufficient
conditions are given in term of a scaled invariant parameter for measuring the
local deviation of subarcs from their chords. The chordal conditions given are
sharp.


  Using magnetic tweezers to investigate the mechanical response of single
chromatin fibers, we show that fibers submitted to large positive torsion
transiently trap positive turns, at a rate of one turn per nucleosome. A
comparison with the response of fibers of tetrasomes (the (H3-H4)2 tetramer
bound with ~50 bp of DNA) obtained by depletion of H2A-H2B dimers, suggests
that the trapping reflects a nucleosome chiral transition to a metastable form
built on the previously documented righthanded tetrasome. In view of its low
energy, <8 kT, we propose this transition is physiologically relevant and
serves to break the docking of the dimers on the tetramer which in the absence
of other factors exerts a strong block against elongation of transcription by
the main RNA polymerase.


  Let G be a reductive p-adic group. We study how a local Langlands
correspondence for irreducible tempered G-representations can be extended to a
local Langlands correspondence for all irreducible smooth representations of G.
We prove that, under a natural condition involving compatibility with
unramified twists, this is possible in a canonical way.
  To this end we introduce analytic R-groups associated to non-tempered
essentially square-integrable representations of Levi subgroups of G. We
establish the basic properties of these new R-groups, which generalize
Knapp--Stein R-groups.


  Homomorphic encryption is a method used in cryptopgraphy to create programs
that can interact with encrypted data without ever leaving the data in the
clear. This has many potential applications in cybersecurity. This paper uses
automorphisms of affine space to create a form of homomorphic encryption for
straight line programs. The encryption method used for the data is known as
multivariate encryption. This gives a potentially powerful new method in cyber
security based on techniques from algebraic geometry.


  The nature of atomic vapors, their natural alignment with interatomic
transitions, and their ease of use make them highly suited for spectrally
narrow-banded optical filters. Atomic filters come in two flavors: a filter
based on the absorption of light by the Doppler broadened atomic vapor, i.e., a
notch filter, and a bandpass filter based on the transmission of resonant light
caused by the Faraday effect. The notch filter uses the absorption of resonant
photons to filter out a small spectral band around the atomic transition. The
off-resonant part of the spectrum is fully transmitted. Atomic vapors based on
the Faraday effect allow for suppression of the detuned spectral fraction.
Transmission of light originates from the magnetically induced rotation of
linear polarized light close to an atomic resonance. This filter constellation
allows selective acceptance of specific light frequencies. In this manuscript,
we discuss these two types of filters and elucidate the specialties of atomic
line filters. We also present a practical guide on building such filter setups
from scratch and discuss an approach to achieve an almost perfect atomic
spectrum backed by theoretical calculations.


  The main goal of this paper is to elaborate the model-framework
parametrization of effective coupling constants of the extended chiral
lagrangian which is suitable for the description of the low-energy matrix
elements of vector, axial-vector, scalar and pseudoscalar currents as well as
of the matrix elements of the pseudoscalar gluon density. We establish the
connection between the structural coupling constants of the phenomenological
chiral lagrangian and the coefficients of effective lagrangians obtained in the
QCD-bosonization models by means of the derivative expansion. The large-N_c
relations for corresponding structural constants are elaborated. On this way we
find the new set of OZI rules. In particular, one of them predicts the
branching ratio of the decays $\psi' \rightarrow J/\psi + \pi$ or $\eta$.


  We use the Taylor resolution of a monomial ideal to compute the Tor algebra
of the Stanley-Reisner ring of a simplicial complement of a simplicial complex.


  Ehresmann's introduction of differentiable groupoids in the 1950s may be seen
as a starting point for two diverging lines of research, many-object Lie theory
(the study of Lie algebroids and Lie groupoids) and sketch theory. This thesis
uses tangent categories to build a bridge between these two lines of research,
providing a structural account of Lie algebroids and the Lie functor.
  To accomplish this, we develop the theory of involution algebroids, which are
a tangent-categorical sketch of Lie algebroids. We show that the category of
Lie algebroids is precisely the category of involution algebroids in smooth
manifolds, and that the category of Weil algebras is precisely the classifying
category of an involution algebroid. This exhibits the category of Lie
algebroids as a tangent-categorical functor category, and the Lie functor via
precomposition with a functor $\partial: \mathsf{Weil}_1 \to
\mathcal{T}_{\mathsf{Gpd}},$ bringing Lie algebroids and the Lie functor into
the realm of functorial semantics.


  Soft robots have a myriad of potentials because of their intrinsically
compliant bodies, enabling safe interactions with humans and adaptability to
unpredictable environments. However, most of them have limited actuation
speeds, require complex control systems, and lack sensing capabilities. To
address these challenges, here we geometrically design a class of metacaps
whose rich nonlinear mechanical behaviors can be harnessed to create soft
robots with unprecedented functionalities. Specifically, we demonstrate a
sensor-less metacap gripper that can grasp objects in 3.75 ms upon physical
contact and a pneumatically actuated gripper with tunable actuation behaviors
that have little dependence on the rate of input. Both grippers can be readily
integrated into a robotic platform for practical applications. Furthermore, we
demonstrate that the metacap enables propelling of a swimming robot, exhibiting
amplified swimming speed as well as untethered, electronics-free swimming with
tunable speeds. Our metacaps provide new strategies to design the
next-generation soft robots that require high transient output energy and are
capable of autonomous and electronics-free maneuvering.


  Multiple applications running on Edge computers can be orchestrated to
achieve the desired goal. Orchestration of applications is prominent when
working with Internet of Things based applications, Autonomous driving and
Autonomous Aerial vehicles. As the applications receive modified
classifiers/code, there will be multiple applications that need to be updated.
If all the classifiers are synchronously updated there would be increased
throughput and bandwidth degradation. On the other hand, delaying updates of
applications which need immediate update hinders performance and delays
progress towards end goal. The updates of applications should be prioritized
and updates should happen according to this priority. This paper explores the
setup and benchmarks to understand the impact of updates when multiple
applications working to achieve same objective are orchestrated with
prioritized updates. We discuss methods to build a distributed, reliable and
scalable system called "DSOC"(Docker Swarm Orchestration Component).


  Magnetic van der Waals materials provide an ideal playground for exploring
the fundamentals of low-dimensional magnetism and open new opportunities for
ultrathin spin processing devices. The Mermin-Wagner theorem dictates that as
in reduced dimensions isotropic spin interactions cannot retain long-range
correlations; the order is stabilized by magnetic anisotropy. Here, using
ultrashort pulses of light, we demonstrate all-optical control of magnetic
anisotropy in the two-dimensional van der Waals antiferromagnet NiPS$_3$.
Tuning the photon energy in resonance with an orbital transition between
crystal-field split levels of the nickel ions, we demonstrate the selective
activation of a sub-THz two-dimensional magnon mode. The pump polarization
control of the magnon amplitude confirms that the activation is governed by the
instantaneous magnetic anisotropy axis emergent in response to photoexcitation
of orbital states with a lowered symmetry. Our results establish pumping of
orbital resonances as a universal route for manipulating magnetic order in
low-dimensional (anti)ferromagnets.


  Bayesian transfer learning (BTL) is defined in this paper as the task of
conditioning a target probability distribution on a transferred source
distribution. The target globally models the interaction between the source and
target, and conditions on a probabilistic data predictor made available by an
independent local source modeller. Fully probabilistic design is adopted to
solve this optimal decision-making problem in the target. By successfully
transferring higher moments of the source, the target can reject unreliable
source knowledge (i.e. it achieves robust transfer). This dual-modeller
framework means that the source's local processing of raw data into a
transferred predictive distribution -- with compressive possibilities -- is
enriched by (the possible expertise of) the local source model. In addition,
the introduction of the global target modeller allows correlation between the
source and target tasks -- if known to the target -- to be accounted for.
Important consequences emerge. Firstly, the new scheme attains the performance
of fully modelled (i.e. conventional) multitask learning schemes in (those
rare) cases where target model misspecification is avoided. Secondly, and more
importantly, the new dual-modeller framework is robust to the model
misspecification that undermines conventional multitask learning. We thoroughly
explore these issues in the key context of interacting Gaussian process
regression tasks. Experimental evidence from both synthetic and real data
settings validates our technical findings: that the proposed BTL framework
enjoys robustness in transfer while also being robust to model
misspecification.


  We study array imaging of a sparse scene of point-like sources or scatterers
in a homogeneous medium. For source imaging the sensors in the array are
receivers that collect measurements of the wave field. For imaging scatterers
the array probes the medium with waves and records the echoes. In either case
the image formation is stated as a sparsity promoting $\ell_1$ optimization
problem, and the goal of the paper is to quantify the resolution. We consider
both narrow-band and broad-band imaging, and a geometric setup with a small
array. We take first the case of the unknowns lying on the imaging grid, and
derive resolution limits that depend on the sparsity of the scene. Then we
consider the general case with the unknowns at arbitrary locations. The
analysis is based on estimates of the cumulative mutual coherence and a related
concept, which we call interaction coefficient. It complements recent results
in compressed sensing by deriving deterministic resolution limits that account
for worse case scenarios in terms of locations of the unknowns in the imaging
region, and also by interpreting the results in some cases where uniqueness of
the solution does not hold. We demonstrate the theoretical predictions with
numerical simulations.


  Wireless random access protocols are attracting a revived research interest
as a simple yet effective solution for machine-type communications. In the
quest to improve reliability and spectral efficiency of such schemes, the use
of multiple receivers has recently emerged as a promising option. We study the
potential of this approach considering a population of users that transmit data
packets following a simple slotted ALOHA policy to a set of non-cooperative
receivers or relays (uplink phase). These, in turn, independently forward -
part of - what decoded towards a collecting sink (downlink phase). For an
on-off fading channel model, we provide exact expressions for uplink throughput
and packet loss rate for an arbitrary number of relays, characterising the
benefits of multi-receiver schemes. Moreover, a lower bound on the minimum
amount of downlink resources needed to deliver all information collected on the
uplink is provided. The bound is proven to be achievable via random linear
coding when no constraints in terms of latency are set. We complement our study
discussing a family of simple forwarding policies that require no packet-level
coding, and optimising their performance based on the amount of available
downlink resources. The behaviour of both random linear coding and simplified
policies is also characterised when receivers are equipped with finite buffers,
revealing non-trivial tradeoffs.


  We report on the preliminary results of a three-year monitoring campaign of
Galactic and Magellanic LBVs with both moderate and high resolution
spectroscopy. We have collected more than 500 moderate-resolution spectra of 20
stars in the red portion of the optical spectrum, which includes the
wind-sensitive transitions of H$\alpha$ and He I 5876 and 6678 Angstroms. We
summarize our detailed study of 15 years of high resolution H$\alpha$
spectroscopy of the prototypical luminous blue variable, P Cygni. We report on
the discovery of discrete absorption components in P Cygni's H$\alpha$ profile,
and we discuss their relationship to structure in the wind. These results are
compared to our recent high resolution interferometric imaging of the $H$-band
emitting region surrounding the star. We discuss recent observations of $\eta$
Car, highlighting its unusual recovery from the previous periastron passage.
Our results on HDE 326823 indicate that the star has a short period binary
orbit, with Roche Lobe overflow onto an unseen massive companion.


  We investigate the aggregation kinetics of a simulated telechelic polymer
gel. In the hybrid Molecular Dynamics (MD) / Monte Carlo (MC) algorithm,
aggregates of associating end groups form and break according to MC rules,
while the position of the polymers in space is dictated by MD. As a result, the
aggregate sizes change every time step. In order to describe this aggregation
process, we employ master equations. They define changes in the number of
aggregates of a certain size in terms of reaction rates. These reaction rates
indicate the likelihood that two aggregates combine to form a large one, or
that a large aggregate splits into two smaller parts. The reaction rates are
obtained from the simulations for a range of temperatures.
  Our results indicate that the rates are not only temperature dependent, but
also a function of the sizes of the aggregates involved in the reaction. Using
the measured rates, solutions to the master equations are shown to be stable
and in agreement with the aggregate size distribution, as obtained directly
from simulation data. Furthermore, we show how temperature induced variations
in these rates give rise to the observed changes in the aggregate distribution
that characterizes the sol-gel transition.


  To accelerate sampling, diffusion models (DMs) are often distilled into
generators that directly map noise to data in a single step. In this approach,
the resolution of the generator is fundamentally limited by that of the teacher
DM. To overcome this limitation, we propose Progressive Growing of Diffusion
Autoencoder (PaGoDA), a technique to progressively grow the resolution of the
generator beyond that of the original teacher DM. Our key insight is that a
pre-trained, low-resolution DM can be used to deterministically encode
high-resolution data to a structured latent space by solving the PF-ODE forward
in time (data-to-noise), starting from an appropriately down-sampled image.
Using this frozen encoder in an auto-encoder framework, we train a decoder by
progressively growing its resolution. From the nature of progressively growing
decoder, PaGoDA avoids re-training teacher/student models when we upsample the
student model, making the whole training pipeline much cheaper. In experiments,
we used our progressively growing decoder to upsample from the pre-trained
model's 64x64 resolution to generate 512x512 samples, achieving 2x faster
inference compared to single-step distilled Stable Diffusion like LCM. PaGoDA
also achieved state-of-the-art FIDs on ImageNet across all resolutions from
64x64 to 512x512. Additionally, we demonstrated PaGoDA's effectiveness in
solving inverse problems and enabling controllable generation.


  A common thread of open-domain question answering (QA) models employs a
retriever-reader pipeline that first retrieves a handful of relevant passages
from Wikipedia and then peruses the passages to produce an answer. However,
even state-of-the-art readers fail to capture the complex relationships between
entities appearing in questions and retrieved passages, leading to answers that
contradict the facts. In light of this, we propose a novel knowledge Graph
enhanced passage reader, namely Grape, to improve the reader performance for
open-domain QA. Specifically, for each pair of question and retrieved passage,
we first construct a localized bipartite graph, attributed to entity embeddings
extracted from the intermediate layer of the reader model. Then, a graph neural
network learns relational knowledge while fusing graph and contextual
representations into the hidden states of the reader model. Experiments on
three open-domain QA benchmarks show Grape can improve the state-of-the-art
performance by up to 2.2 exact match score with a negligible overhead increase,
with the same retriever and retrieved passages. Our code is publicly available
at https://github.com/jumxglhf/GRAPE.


  Let $X$ be a terminal weak $\bQ$-Fano threefold. We prove that $P_{-6}(X)>0$
and $P_{-8}(X)>1$. We also prove that the anti-canonical volume has a universal
lower bound $-K_X^3 \geq 1/330$. This lower bound is optimal.


  We constructed canonical non-highest weight unitary irreducible
representation of $\hat{so}(1,n)$ current algebra as well as canonical
non-highest weight non-unitary representations, We constructed certain
Laplacian operators as elements of the universal enveloping algebra, acting in
representation space. We speculated about a possible relation of those
Laplacians with the loop operator for the Yang-Mills.