  A conflict between rational and autonomous agents is considered. The paper
addresses a differential game of protecting a target in the 3-D space. This
problem highlights the strong correlation between the highly dynamic scenario,
the uncertainty on the behavior of the adversary, and the online and robust
computation of state-feedback strategies which guarantee the required level of
performance of each player. This work significantly expands previous results
around this problem by providing the players' state-feedback saddle-point
strategies. Additionally, the continuously differentiable Value function of the
multi-agent differential game is obtained and it is shown to be the solution of
the Hamilton-Jacobi-Isaacs equation. Finally, the Barrier surface is explicitly
obtained and illustrative examples highlight the robustness properties and the
guarantees provided by the saddle-point strategies obtained in this paper.


  The structure and morphology of supernova remnants (SNRs) reflect the
properties of the parent supernovae (SNe) and the characteristics of the
inhomogeneous environments through which the remnants expand. Linking the
morphology of SNRs to anisotropies developed in their parent SNe can be
essential to obtain key information on many aspects of the explosion processes
associated with SNe. Nowadays, our capability to study the SN-SNR connection
has been largely improved thanks to multi-dimensional models describing the
long-term evolution from the SN to the SNR as well as to observational data of
growing quality and quantity across the electromagnetic spectrum which allow to
constrain the models. Here we used the numerical resources obtained in the
framework of the "Accordo Quadro INAF-CINECA (2017)" together with a CINECA
ISCRA Award N.HP10BARP6Y to describe the full evolution of a SNR from the
core-collapse to the full-fledged SNR at the age of 2000 years. Our simulations
were compared with observations of SNR Cassiopeia A (Cas A) at the age of $\sim
350$~years. Thanks to these simulations we were able to link the physical,
chemical and morphological properties of a SNR to the physical processes
governing the complex phases of the SN explosion.


  The fluid ball conjecture states that a static perfect fluid space-time is
spherically symmetric. In this paper we construct a Robinson's divergence
formula for the static perfect fluid space-time. Inspired by this conjecture, a
rigidity result for the spatial factor of a static perfect fluid satisfying
some boundary conditions is proved, provided that an equation of state holds.


  Ly$\alpha$ Emitters (LAEs) may represent an important galaxy population in
the low mass regime. We present our deep narrowband imaging surveys in the
COSMOS and ECDF-S fields and study the properties of LAEs at $z=2.23\pm0.03$.
The narrowband surveys conducted at Magellan II telescope allow us to obtain a
sample of 452 LAEs reaching a $5\sigma$ limiting magnitude of $\sim26$ mag. Our
Ly$\alpha$ luminosity functions extend to $10^{41.8}$ erg s$^{-1}$ with steep
faint-end slope. Using multi-wavelength ancillary data, especially the deep
Spitzer/IRAC 3.6$\mu$m and 4.5$\mu$m photometric data, we obtained reliable
stellar mass estimates for 130 IRAC-detected LAEs, spanning a range of $8 <
{\rm log}(M_\star/M_\odot)< 11.5$. For the remaining IRAC-undetected LAEs, the
median-stacked spectral energy distribution yields a stellar mass of ${\rm
log}(M_\star/M_\odot)=7.97^{+0.05}_{-0.07}$ and the rest-frame ultraviolet
emission indicates a median star formation rate of ${\rm log} (SFR/M_\odot$
yr$^{-1})=-0.14\pm0.35$. There are six LAEs detected by the Spitzer/MIPS
24$\mu$m or even Herschel far-infrared observations. Taking into account the
six MIR/FIR detected LAEs, our LAEs cover a wide range in the star formation
rate (${\rm 1<SFR<2000}$ M$_\odot$ yr$^{-1}$). Although LAEs as a population
are diverse in their stellar properties, they are mostly low-mass star-forming
galaxies and follow the star formation main sequence relations or their
extrapolations to the low-mass end, implying a normal star-forming nature of
LAEs. The clustering analysis indicates that our LAEs reside in dark matter
halos with ${\rm <\log(M_{h}/M_{\odot})> =10.8^{+0.56}_{-1.1}}$, suggesting
that they are progenitors of local Large Magellanic Cloud-like galaxies.


  Modular approaches that use a different composition of modules for each
problem are a promising direction in continual learning (CL). However,
searching through the large, discrete space of module compositions is
challenging, especially because evaluating a composition's performance requires
a round of neural network training. We address this challenge through a modular
CL framework, PICLE, that uses a probabilistic model to cheaply compute the
fitness of each composition, allowing PICLE to achieve both perceptual,
few-shot and latent transfer. The model combines prior knowledge about good
module compositions with dataset-specific information. We evaluate PICLE using
two benchmark suites designed to assess different desiderata of CL techniques.
Comparing to a wide range of approaches, we show that PICLE is the first
modular CL algorithm to achieve perceptual, few-shot and latent transfer while
scaling well to large search spaces, outperforming previous state-of-the-art
modular CL approaches on long problem sequences.


  Exploring the concept of the extended Galilei group $\mathcal{G}$, a
representation for the symplectic quantum mechanics in the manifold of
$\mathcal{G}$, written in the light-cone of a five-dimensional De Sitter
space-time, is derived consistently with the method of the Wigner function. A
Hilbert space is constructed endowed with a simplectic structure, studying
unitary operators describing rotations and translations, whose generators
satisfy the Lie algebra of $\mathcal {G}$. This representation gives rise to
the Schr\"{o}dinger (Klein-Gordon-like) equation for the wave functions in
phase-space, such that the dependent variables have the position and linear
momentum contents. Wave functions are associated with the Wigner function
through the Moyal product, such that the wave functions represent a
quasi-amplitude of probability. We construct the Pauli-Schr\"{o}dinger
(Dirac-like) equation in phase-space in its explicitly covariant form. Finally,
we show the equivalence between the five dimensional formalism of phase-space
with the usual formalism, proposing a solution that recover the non-covariant
form of the Pauli-Schr\"{o}dinger equation in phase-space.


  After scattering off nuclei in the Sun, dark matter particles can be
gravitationally captured by the Sun, accumulate in the Sun's core and
annihilate into Standard Model particles. Neutrinos originating from these
annihilations can be detected by the IceCube Neutrino Observatory, located at
the South Pole. Due to the non-observation of these neutrinos, constraints on
the standard spin-dependent and spin-independent dark matter-nucleon scattering
cross sections have been placed. Based on these constraints, we present upper
limits on the coupling constants of the non-relativistic effective theory of
dark matter-nucleon interactions, including velocity and momentum dependent
interactions.


  In over a thousand known cataclysmic variables (CVs), where a white dwarf is
accreting from a hydrogen-rich star, only a dozen have orbital periods below 75
minutes. One way to achieve these short periods requires the donor star to have
undergone substantial nuclear evolution prior to interacting with the white
dwarf, and it is expected that these objects will transition to helium
accretion. These transitional CVs have been proposed as progenitors of helium
CVs. However, no known transitional CV is expected to reach an orbital period
short enough to account for most of the helium CV population, leaving the role
of this evolutionary pathway unclear. Here we report observations of ZTF
J1813+4251, a 51-minute orbital period, fully eclipsing binary system
consisting of a star with a temperature comparable to that of the Sun but a
density 100 times greater due to its helium-rich composition, accreting onto a
white dwarf. Phase-resolved spectra, multi-band light curves and the broadband
spectral energy distribution allow us to obtain precise and robust constraints
on the masses, radii and temperatures of both components. Evolutionary modeling
shows that ZTF J1813+4251 is destined to become a helium CV binary, reaching an
orbital period under 20 minutes, rendering ZTF J1813+4251 a previously missing
link between helium CV binaries and hydrogen-rich CVs.


  Historical economic growth in countries of the former USSR is analysed. It is
shown that Unified Growth Theory is contradicted by the data, which were used,
but not analysed, during the formulation of this theory. Unified Growth Theory
does not explain the mechanism of economic growth. It explains the mechanism of
Malthusian stagnation, which did not exist and it explains the mechanism of the
transition from stagnation to growth that did not happen. Unified Growth Theory
is full of stories but it is hard to decide which of them are reliable because
they are based on unprofessional examination of data. The data show that the
economic growth in the former USSR was never stagnant but hyperbolic.
Industrial Revolution did not boost the economic growth in the former USSR.
Unified Growth Theory needs to be revised or replaced by a reliable theory to
reconcile it with data and to avoid creating the unwarranted sense of security
about the current economic growth.


  The goal of this paper is to give a mathematical model describing the global
be haviour of the nuclear waste disposal process.The physical situation can be
described as an array made of high number of alveoles inside of a low permeable
layer (e.g. clay) included between two layers with slightly higher permeability
(e.g. limestone). Radioactive elements are leaking from their containers over a
period of time ]0,t_m[ . In a porous media (clay) there is a dilution effect
(similar to diffusion) and convection due to some underground water flow. The
real physical situation is simplified by replacing 5 alveoles by one macro
alveole and by considering the convection velocity as a given field. These
simplifications seam to be unimportant for understanding the global effects.
The typical size of such macro alveole is of order : 100 m width, 1000 m
length, 5 m hight. The distance between two alveoles is also of order 100 m.
The size of law permeable layer is of order 150 m hight, and 3000 length. Since
alveoles are small compared to the size of layer and their number is large
direct numerical simulations using the {\em microscopic} model is unrealistic.
On the other hand the ratio between domain length and the length of one alveole
is small, of order 1/30, and allows an asymptotic study with respect to that
small parameter, denoted by \epsilon, using the method of homogenization and
boundary layers.


  The study of the gas kinematic in the central 1.5kpc x 1.5kpc region of M31
has revealed several surprises. The starting point of this investigation was
the detection at the IRAM-30m telescope of molecular gas with very large line
splittings up to 260km/s within the beam (40 pc). In this region, which is
known for its low gas content, we also detect an ionised gas outflow in the
circumnuclear region (within 75pc from the centre) extending to the whole area
in X-ray. Relying on atomic, ionised, and molecular gas, we account for most
observables with a scenario that assumes that a few hundreds Myr ago, M31
underwent a frontal collision with M32, which triggered some star-formation
activity in the centre, and this collision explains the special configuration
of M31 with two rings observed at 0.7kpc and 10kpc. The inner disc (whose
rotation is detected in HI and ionised gas ([NII])) has thus been tilted
(inclination: 43deg, PA: 70deg) with respect to the main disc (inclination:
77deg, PA: 35deg). One of the CO velocity components is compatible with this
inner disc, while the second one comes from a tilted ring-like material with
40deg inclination and PA=-35deg. The relic star formation estimated by previous
works to have occurred more than 100Myr ago could have been triggered by the
collision and could be linked to the outflow detected in the ionised gas. Last,
we demonstrate that the amplitude of the line splittings detected in CO centred
on the systemic velocity with a relatively high spatial resolution (40pc)
cannot be accounted for by a possible weak bar that is roughly aligned along
the minor axis. Although M31 has a triaxial bulge, there are no bar indicators
in the gas component (photometry, no strong skewness of the isovelocities,
etc.).


  In this paper we show a general Strichartz estimate for certain perturbed
wave equation, and here we can drop the nontrapping hypothesis and handle
trapping obstacles with some loss of derivatives for data in the local energy
decay estimates. Then we give the obstacle version of sharp life span for
semilinear wave equations when $n=3,p<p_c$, by using a real interpolation
method, and by getting a corresponding finite time Strichartz estimates(see
section 3). Finally, as an application of the general Strichartz estimates we
have gained, we get the Strauss conjecture for semilinear wave equations with
several convex obstacles when $n=3,4$(see Section 4).


  We trace the origin of the cosmological constant problem to the assumption
that Newton's constant $G$ sets the scale for cosmology. And then we show that
once this assumption is relaxed, the very same cosmic acceleration which has
served to make the cosmological constant problem so very severe instead then
serves to provide us with its potential resolution. We present an alternate
cosmology, one based on conformal gravity, and show that once given only that
the sign of the vacuum energy density $\Lambda$ is explicitly the negative one
associated with spontaneous breakdown of the scale invariance of the conformal
theory (this actually being the choice of sign for $\Lambda$ which precisely
leads to cosmic acceleration in conformal gravity), then that alone, no matter
how big $\Lambda$ might actually be in magnitude, is sufficient to not only
make its measurable contribution to current era cosmology naturally be of order
one today, but to even do so in a way which is completely compatible with the
recent high $z$ supernovae cosmology data. Cosmology can thus live with either
a fundamental $G$ or with the large (and even potentially negative) $\Lambda$
associated with elementary particle physics phase transitions but not with
both. Also, we distinguish between the free energy and the internal energy,
with it being the former which determines cosmological phase transitions and
the latter which is the source of the gravitational field. Then we show that,
even if we make the standard ad hoc assumption that $\Lambda$ actually is
quenched in standard gravity, vacuum energy is nonetheless still found to
dominate standard cosmology at the time of the phase transition which produced
it. However, within conformal gravity no such difficulty is encountered.


  Floating point multiplication is one of the crucial operations in many
application domains such as image processing, signal processing etc. But every
application requires different working features. Some need high precision, some
need low power consumption, low latency etc. But IEEE-754 format is not really
flexible for these specifications and also design is complex. Optimal run-time
reconfigurable hardware implementations may need the use of custom
floating-point formats that do not necessarily follow IEEE specified sizes. In
this paper, we present a run-time-reconfigurable floating point multiplier
implemented on FPGA with custom floating point format for different
applications. This floating point multiplier can have 6 modes of operations
depending on the accuracy or application requirement. With the use of optimal
design with custom IPs (Intellectual Properties), a better implementation is
done by truncating the inputs before multiplication. And a combination of
Karatsuba algorithm and Urdhva-Tiryagbhyam algorithm (Vedic Mathematics) is
used to implement unsigned binary multiplier. This further increases the
efficiency of the multiplier.


  The purpose of this study is to provide means to physicians for automated and
fast recognition of airways diseases. In this work, we mainly focus on measures
that can be easily recorded using a spirometer. The signals used in this
framework are simulated using the linear bi-compartment model of the lungs.
This allows us to simulate ventilation under the hypothesis of ventilation at
rest (tidal breathing). By changing the resistive and elastic parameters, data
samples are realized simulating healthy, fibrosis and asthma breathing. On this
synthetic data, different machine learning models are tested and their
performance is assessed. All but the Naive bias classifier show accuracy of at
least 99%. This represents a proof of concept that Machine Learning can
accurately differentiate diseases based on manufactured spirometry data. This
paves the way for further developments on the topic, notably testing the model
on real data.


  We study the nonlinear propagation of truncated Airyprime pulses in optical
fibers with both anomalous or normal dispersion. Weobservenonlinear
self-accelerating pulses with notable red-shifted spectral notch (double peaks)
or blue-shifted spectral peak depending on whether the dispersion is anomalous
or normal. SuchprocessisinsharpcontrasttothatofAirypulses.The formation of
nonlinear self-accelerating pulses is very sensitive to the truncated
coefficient. The relationship between the characteristics of such accelerated
pulses and the truncated coefficient are disclosed and compared in detail. Our
results not only shed new light on the nonlinear propagation of Airyprime
pulses, but also provide a novel method to generate nonlinear self-accelerating
pulses as well as enable the realization of very efficient wavelength
conversion based on the controlled frequency shift. Based on space-time
duality, self-accelerating spatiotemporal nonlinear light bullets can be
envisaged from the propagation of spatiotemporal Airyprime wave packets in pure
Kerr medium.


  Data exfiltration over the DNS protocol and its detection have been
researched extensively in recent years. Prior studies focused on offline
detection methods, which although capable of detecting attacks, allow a large
amount of data to be exfiltrated before the attack is detected and dealt with.
In this paper, we introduce Information-based Heavy Hitters (ibHH), a real-time
detection method which is based on live estimations of the amount of
information transmitted to registered domains. ibHH uses constant-size memory
and supports constant-time queries, which makes it suitable for deployment on
recursive DNS servers to further reduce detection and response time. In our
evaluation, we compared the performance of the proposed method to that of
leading state-of-the-art DNS exfiltration detection methods on real-world
datasets comprising over 250 billion DNS queries. The evaluation demonstrates
ibHH's ability to successfully detect exfiltration rates as slow as 0.7B/s,
with a false positive alert rate of less than 0.004, with significantly lower
resource consumption compared to other methods.


  Optical fibers are widely used in bioimaging systems as flexible endoscopes
capable of low-invasive penetration inside hollow tissue cavities. Here, we
report on the technique which allows magnetic resonance imaging (MRI) of
hollow-core microstructured fibers (HC-MFs), paving the way for combing MRI and
optical bioimaging. Our approach is based on Layer-by-Layer assembly of
oppositely charged polyelectrolytes and magnetite nanoparticles on the inner
core surface of HC-MFs. Incorporation of magnetite nanoparticles into
polyelectrolyte layers renders HC-MFs visible for MRI and induces the red-shift
in their transmission spectra. Specifically, the transmission shifts up to 60
nm have been revealed for the several-layers composite coating along with the
high-quality contrast of HC-MFs in MRI scans. Our results shed light on
marrying fiber-based endoscopy with MRI that opens novel possibilities for
minimally invasive clinical diagnostics and surgical procedures in vivo.


  We compute spin-dependent matrix elements for decays of S-wave quarkonia in
lattice NRQCD. They appear to be in approximate agreement with the
velocity-scaling rules of NRQCD.


  Large language models (LLMs) have demonstrated their prowess in generating
synthetic text and images; however, their potential for generating tabular data
-- arguably the most common data type in business and scientific applications
-- is largely underexplored. This paper demonstrates that LLMs, used as-is, or
after traditional fine-tuning, are severely inadequate as synthetic table
generators. Due to the autoregressive nature of LLMs, fine-tuning with random
order permutation runs counter to the importance of modeling functional
dependencies, and renders LLMs unable to model conditional mixtures of
distributions (key to capturing real world constraints). We showcase how LLMs
can be made to overcome some of these deficiencies by making them
permutation-aware.


  One of the open questions in modern cosmology is the small scale crisis of
the cold dark matter paradigm. Increasing attention has recently been devoted
to self-interacting dark matter models as a possible answer. However, solving
the so-called "missing satellites" problem requires in addition the presence of
an extra relativistic particle (dubbed dark radiation) scattering with dark
matter in the early universe. Here we investigate the impact of different
theoretical models devising dark matter dark radiation interactions on large
scale cosmological observables. We use cosmic microwave background data to put
constraints on the dark radiation component and its coupling to dark matter. We
find that the values of the coupling allowed by the data imply a cut-off scale
of the halo mass function consistent with the one required to match the
observations of satellites in the Milky Way.


  In this paper, we derive a dynamic surface elasticity model for the
two-dimensional midsurface of a thin, three-dimensional, homogeneous,
isotropic, nonlinear gradient elastic plate of thickness $h$. The resulting
model is parameterized by five, conceivably measurable, physical properties of
the plate, and the stored surface energy reduces to Koiter's plate energy in a
singular limiting case. The model corrects a theoretical issue found in wave
propagation in thin sheets and, when combined with the author's theory of Green
elastic bodies possessing gradient elastic material boundary surfaces, removes
the singularities present in fracture within traditional/classical models. Our
approach diverges from previous research on thin shells and plates, which
primarily concentrated on deriving elasticity theories for material surfaces
from classical three-dimensional Green elasticity. This work is the first in
rigorously developing a surface elasticity model based on a parent nonlinear
gradient elasticity theory.


  Content-based image retrieval (CBIR) with self-supervised learning (SSL)
accelerates clinicians' interpretation of similar images without manual
annotations. We develop a CBIR from the contrastive learning SimCLR and
incorporate a generalized-mean (GeM) pooling followed by L2 normalization to
classify lesion types and retrieve similar images before clinicians' analysis.
Results have shown improved performance. We additionally build an open-source
application for image analysis and retrieval. The application is easy to
integrate, relieving manual efforts and suggesting the potential to support
clinicians' everyday activities.


  We generalize, imposing the field equations only at dominant order, the
Isaacson formula for the gravitational wave (GW) energy-momentum tensor (EMT)
to the class of Horndeski theories in which the tensor modes travel at the
speed of light (reduced Horndeski theories) and scalar waves are present. We
discuss important particular cases such as: theories where scalar waves are
also luminal and theories in which the transverse-traceless gauge can be
achieved in an arbitrary open set. The vanishing of the trace of the
gravitational wave energy-momentum tensor is obtained for theories in which all
wave perturbations propagate at the speed of light. The trace is shown not to
vanish trivially in other cases. We obtain, as a particular case of our general
result, the GW EMTs, in a Brans-Dicke theory, both in the Einstein frame,
recovering previous results in the literature, and in the Jordan frame, thereby
showing the GW EMT is not conformally invariant. We further prove that there
exists a subclass of reduced Horndeski theories where, in contrast to general
relativity, the divergence of the GW EMT does not vanish even after the
imposition of the full equations of motion, assuming an eikonal solution.


  A method called, sigma-consensus, is proposed to eliminate the need for a
user-defined inlier-outlier threshold in RANSAC. Instead of estimating the
noise sigma, it is marginalized over a range of noise scales. The optimized
model is obtained by weighted least-squares fitting where the weights come from
the marginalization over sigma of the point likelihoods of being inliers. A new
quality function is proposed not requiring sigma and, thus, a set of inliers to
determine the model quality. Also, a new termination criterion for RANSAC is
built on the proposed marginalization approach. Applying sigma-consensus,
MAGSAC is proposed with no need for a user-defined sigma and improving the
accuracy of robust estimation significantly. It is superior to the
state-of-the-art in terms of geometric accuracy on publicly available
real-world datasets for epipolar geometry (F and E) and homography estimation.
In addition, applying sigma-consensus only once as a post-processing step to
the RANSAC output always improved the model quality on a wide range of vision
problems without noticeable deterioration in processing time, adding a few
milliseconds. The source code is at https://github.com/danini/magsac.


  The vibrational properties of ferrimagnetic $\mathrm{Mn_3Si_{2}Te_6}$ single
crystals are investigated using Raman spectroscopy and density functional
theory calculations. Eighteen Raman-active modes are identified, fourteen of
which are assigned according to with the trigonal symmetry. Four additional
peaks, obeying the $A_{1g}$ selection rules, are attributed to the overtones.
The unconventional temperature evolution of the $A_{1g}^5$ mode self-energy
suggests a competition between different short-range magnetic correlations that
significantly impact the spin-phonon interaction in $\mathrm{Mn_3Si_{2}Te_6}$.
The research provides a comprehensive insight to the lattice properties,
studies their temperature dependence and shows the arguments for existence of
competing short-range magnetic phases in $\mathrm{Mn_3Si_{2}Te_6}$.


  We prove a general archimedean positivstellensatz for hermitian
operator-valued polynomials and show that it implies the multivariate
Fejer-Riesz Theorem of Dritschel-Rovnyak and positivstellens\"atze of
Ambrozie-Vasilescu and Scherer-Hol. We also obtain several generalizations of
these and related results. The proof of the main result depends on an extension
of the abstract archimedean positivstellensatz for *-algebras that is
interesting in its own right.


  Common nonlinear activation functions used in neural networks can cause
training difficulties due to the saturation behavior of the activation
function, which may hide dependencies that are not visible to vanilla-SGD
(using first order gradients only). Gating mechanisms that use softly
saturating activation functions to emulate the discrete switching of digital
logic circuits are good examples of this. We propose to exploit the injection
of appropriate noise so that the gradients may flow easily, even if the
noiseless application of the activation function would yield zero gradient.
Large noise will dominate the noise-free gradient and allow stochastic gradient
descent toexplore more. By adding noise only to the problematic parts of the
activation function, we allow the optimization procedure to explore the
boundary between the degenerate (saturating) and the well-behaved parts of the
activation function. We also establish connections to simulated annealing, when
the amount of noise is annealed down, making it easier to optimize hard
objective functions. We find experimentally that replacing such saturating
activation functions by noisy variants helps training in many contexts,
yielding state-of-the-art or competitive results on different datasets and
task, especially when training seems to be the most difficult, e.g., when
curriculum learning is necessary to obtain good results.


  3D human pose estimation using monocular images is an important yet
challenging task. Existing 3D pose detection methods exhibit excellent
performance under normal conditions however their performance may degrade due
to occlusion. Recently some occlusion aware methods have also been proposed,
however, the occlusion handling capability of these networks has not yet been
thoroughly investigated. In the current work, we propose an occlusion-guided 3D
human pose estimation framework and quantify its occlusion handling capability
by using different protocols. The proposed method estimates more accurate 3D
human poses using 2D skeletons with missing joints as input. Missing joints are
handled by introducing occlusion guidance that provides extra information about
the absence or presence of a joint. Temporal information has also been
exploited to better estimate the missing joints. A large number of experiments
are performed for the quantification of occlusion handling capability of the
proposed method on three publicly available datasets in various settings
including random missing joints, fixed body parts missing, and complete frames
missing, using mean per joint position error criterion. In addition to that,
the quality of the predicted 3D poses is also evaluated using action
classification performance as a criterion. 3D poses estimated by the proposed
method achieved significantly improved action recognition performance in the
presence of missing joints. Our experiments demonstrate the effectiveness of
the proposed framework for handling the missing joints as well as
quantification of the occlusion handling capability of the deep neural
networks.


  This paper fills the limited statistical understanding of Shapley values as a
variable importance measure from a nonparametric (or smoothing) perspective. We
introduce population-level \textit{Shapley curves} to measure the true variable
importance, determined by the conditional expectation function and the
distribution of covariates. Having defined the estimand, we derive minimax
convergence rates and asymptotic normality under general conditions for the two
leading estimation strategies. For finite sample inference, we propose a novel
version of the wild bootstrap procedure tailored for capturing lower-order
terms in the estimation of Shapley curves. Numerical studies confirm our
theoretical findings, and an empirical application analyzes the determining
factors of vehicle prices.


  Using a new analysis approach, we establish a general convergence theory of
the Shift-Invert Residual Arnoldi (SIRA) method for computing a simple
eigenvalue nearest to a given target $\sigma$ and the associated eigenvector.
In SIRA, a subspace expansion vector at each step is obtained by solving a
certain inner linear system. We prove that the inexact SIRA method mimics the
exact SIRA well, that is, the former uses almost the same outer iterations to
achieve the convergence as the latter does if all the inner linear systems are
iteratively solved with {\em low} or {\em modest} accuracy during outer
iterations. Based on the theory, we design practical stopping criteria for
inner solves. Our analysis is on one step expansion of subspace and the
approach applies to the Jacobi--Davidson (JD) method with the fixed target
$\sigma$ as well, and a similar general convergence theory is obtained for it.
Numerical experiments confirm our theory and demonstrate that the inexact SIRA
and JD are similarly effective and are considerably superior to the inexact
SIA.


  SARAH is a Mathematica package optimized for the fast, efficient and precise
study of supersymmetric models beyond the MSSM: a new model can be defined in a
short form and all vertices are derived. This allows SARAH to create model
files for FeynArts/FormCalc, CalcHep/CompHep and WHIZARD/OMEGA. The newest
version of SARAH now provides the possibility to create model files in the UFO
format which is supported by MadGraph 5, MadAnalysis, GoSam, and soon by
Herwig++. Furthermore, SARAH also calculates the mass matrices, RGEs and
one-loop corrections to the mass spectrum. This information is used to write
source code for SPheno in order to create a precision spectrum generator for
the given model. This spectrum-generator-generator functionality as well as the
output of WHIZARD and CalcHep model files have seen further improvement in this
version. Also models including Dirac Gauginos are supported with the new
version of SARAH, and additional checks for the consistency of model
implementations have been created.


  The spatial expansion of the universe can be described as the emergence of
space with the progress of cosmic time, through a simple equation, $\Delta V =
\Delta t\left(N_{surf}- N_{bulk}\right)$. This law of emergence suggested by
Padmanabhan in the context of general relativity for a flat universe has been
generalized by Sheykhi to Gauss Bonnet and Lovelock gravity for a universe with
any spacial curvature. We investigate whether this generalized holographic
equipartition effectively implies the maximization of horizon entropy. First,
we obtain the constraints imposed by the maximization of horizon entropy in
Einstein, Gauss Bonnet and Lovelock gravities for a universe with any spacial
curvature. We then analyze the consistency of the law of emergence in
\cite{Sheykhi}, with these constraints obtained. Interestingly, both the law of
emergence and the horizon entropy maximization demands an asymptotically de
Sitter universe with $\omega \geq -1$. More specifically, when the degrees of
freedom in the bulk $( N_{bulk})$ becomes equal to the degrees of freedom on
the boundary surface $(N_{surf}),$ the universe attains a state of maximum
horizon entropy. Thus, the law of emergence can be viewed as a tendency for
maximizing the horizon entropy, even in a non flat universe. Our results points
at the deep connection between the law of emergence and horizon thermodynamics,
beyond Einstein gravity irrespective of the spacial curvature.


  We investigate the dispersion relation and damping of plasmon modes in a
bilayer-monolayer graphene heterostructure with carrier densities and at zero
temperature within the random-phase-approximation taking into account the
nonhomogeneity of the dielectric background of the system. We derive analytical
expressions for plasmon frequencies by using long wavelength expansion of
response and bare Coulomb interaction functions. We show that optical plasmon
dispersion curve of the bilayer-monolayer system lies slightly below that of
double-layer graphene (DLG) and the acoustic one lies much lower than that of
DLG. We find that while decay rates of acoustic modes of the system and DLG are
remarkably different, those of optical modes in both double-layer systems are
similar. Except the damping rate of acoustic mode, properties of plasmon
excitations in considered system depend remarkably on the interlayer distance,
inhomogeneity of the background, density ratio and spacer dielectric constant,
especially at large wave-vectors.


  We consider the transport and the noise characteristics for the case of a
T-shape double quantum dot system using the equation of motion method. Our
theoretical results, obtained in an approximation equivalent to the
Hartree-Fock approximation, account for non-zero on-site Coulomb interaction in
both the detector and side dots. The existence of a non-zero Coulomb
interaction implies an additional two resonances in the detector's dot density
of states and thereafter affects the electronic transport properties of the
system. The system's conductance presents two Fano dips as function of the
energy of the localized electronic level in the side dot. The Fano dips in the
system's conductance can be observed both for strong (fast detector) and weak
coupling (slow detector) between the detector dot and the external electrodes.
Due to stronger electronic correlations the noise characteristics in the case
of a slow detector are much higher. This setup may be of interest for the
practical realization of qubit states in quantum dots systems.


  We report on the population properties of 76 compact binary mergers detected
with gravitational waves below a false alarm rate of 1 per year through GWTC-3.
The catalog contains three classes of binary mergers: BBH, BNS, and NSBH
mergers. We infer the BNS merger rate to be between 10 $\rm{Gpc^{-3} yr^{-1}}$
and 1700 $\rm{Gpc^{-3} yr^{-1}}$ and the NSBH merger rate to be between 7.8
$\rm{Gpc^{-3}\, yr^{-1}}$ and 140 $\rm{Gpc^{-3} yr^{-1}}$ , assuming a constant
rate density versus comoving volume and taking the union of 90% credible
intervals for methods used in this work. Accounting for the BBH merger rate to
evolve with redshift, we find the BBH merger rate to be between 17.9
$\rm{Gpc^{-3}\, yr^{-1}}$ and 44 $\rm{Gpc^{-3}\, yr^{-1}}$ at a fiducial
redshift (z=0.2). We obtain a broad neutron star mass distribution extending
from $1.2^{+0.1}_{-0.2} M_\odot$ to $2.0^{+0.3}_{-0.3} M_\odot$. We can
confidently identify a rapid decrease in merger rate versus component mass
between neutron star-like masses and black-hole-like masses, but there is no
evidence that the merger rate increases again before 10 $M_\odot$. We also find
the BBH mass distribution has localized over- and under-densities relative to a
power law distribution. While we continue to find the mass distribution of a
binary's more massive component strongly decreases as a function of primary
mass, we observe no evidence of a strongly suppressed merger rate above $\sim
60 M_\odot$. The rate of BBH mergers is observed to increase with redshift at a
rate proportional to $(1+z)^{\kappa}$ with $\kappa = 2.9^{+1.7}_{-1.8}$ for
$z\lesssim 1$. Observed black hole spins are small, with half of spin
magnitudes below $\chi_i \simeq 0.25$. We observe evidence of negative aligned
spins in the population, and an increase in spin magnitude for systems with
more unequal mass ratio.


  We report a direct lattice calculation of the $K$ to $\pi\pi$ decay matrix
elements for both the $\Delta I=1/2$ and 3/2 amplitudes $A_0$ and $A_2$ on 2+1
flavor, domain wall fermion, $16^3\times32\times16$ lattices. This is a
complete calculation in which all contractions for the required ten, four-quark
operators are evaluated, including the disconnected graphs in which no quark
line connects the initial kaon and final two-pion states. These lattice
operators are non-perturbatively renormalized using the Rome-Southampton method
and the quadratic divergences are studied and removed. This is an important but
notoriously difficult calculation, requiring high statistics on a large volume.
In this paper we take a major step towards the computation of the physical
$K\to\pi\pi$ amplitudes by performing a complete calculation at unphysical
kinematics with pions of mass 422\,MeV at rest in the kaon rest frame. With
this simplification we are able to resolve Re$(A_0)$ from zero for the first
time, with a 25% statistical error and can develop and evaluate methods for
computing the complete, complex amplitude $A_0$, a calculation central to
understanding the $\Delta =1/2$ rule and testing the standard model of CP
violation in the kaon system.


  A semantics is given to possibilistic logic, a logic that handles weighted
classical logic formulae, and where weights are interpreted as lower bounds on
degrees of certainty or possibility, in the sense of Zadeh's possibility
theory. The proposed semantics is based on fuzzy sets of interpretations. It is
tolerant to partial inconsistency. Satisfiability is extended from
interpretations to fuzzy sets of interpretations, each fuzzy set representing a
possibility distribution describing what is known about the state of the world.
A possibilistic knowledge base is then viewed as a set of possibility
distributions that satisfy it. The refutation method of automated deduction in
possibilistic logic, based on previously introduced generalized resolution
principle is proved to be sound and complete with respect to the proposed
semantics, including the case of partial inconsistency.


  Case study-based learning has been successfully integrated into various
courses, including software engineering education. In the context of software
design courses, the use of case studies often entails sharing of real
successful or failed software development. Using examples of real-world case
studies allows educators to reinforce the applicability and usefulness of
fundamental design concepts, relate the importance of evaluating design
trade-offs with respect to stakeholders' requirements, and highlight the
importance of upfront design where students that lack industrial experience
tend to overlook. However, the use of real-world case studies is not
straightforward because 1.) there is a lack of open source repositories for
real software design case studies and 2.) even if case studies are available,
they are often reported without a standardized format, which may hinder the
alignment between the case and the desired learning outcomes. To address the
lack of software design case studies for educational purposes, we propose the
idea of Open Design Case Study, a repository to crowdsource, curate, and
recruit other educators to contribute case studies for teaching software design
courses. The platform will also allow educators and students to share,
brainstorm, and discuss design solutions based on case studies shared publicly
on the repository.


  In the present paper, we study the essential normality of quotient modules
over the polydisc. It is shown that if the zero variety of homogenous ideal $I$
is a distinguished variety, then its quotient module is
$(1,\infty)$-essentially normal. Moreover, we study the boundary representation
of quotient modules.


  We investigate the behavior of the Schr\"odinger equation under the influence
of potentials, focusing on its relationship to quantum revivals and fractality.
Our findings reveal that the solution displays fractal behavior at irrational
times, while exhibiting regularity similar to the initial data at rational
times. These extend the results of Oskolkov \cite{O} and Rodnianski \cite{R2}
on the free Schr\"odinger evolution to the general case regarding potentials.


  We discuss the problem of wormholes from the viewpoint of gluing together two
Reissner--Nordstr\"om-type universes while putting between them a segment of
the Nariai-type world (in both cases there are also present electromagnetic
fields as well as the cosmological constant). Such a toy wormhole represents an
example of one-way topological communication free from causal paradoxes, though
involving a travel to next spacetime sheet since one has to cross at least a
pair of horizons through which the spacetimes' junction occurs. We also
consider the use of thin shells in these constructions. Such a ``material'' for
wormholes we choose taking into account specific properties of the
Nariai--Bertotti--Robinson spacetimes.


  Hybrid 2D-2D materials composed by perpendicularly oriented covalent organic
framework (COFs) and graphene were prepared and tested for energy storage
applications. Diboronic acid molecules covalently attached to graphene oxide
(GO) were used as nucleation sites for directing vertical growth of COF-1
nanosheets (v-COF-GO). The hybrid material shows forest of COF-1 nanosheets
with thickness of ~3 to 15 nm in edge-on orientation relative to GO. The same
reaction performed in absence of molecular pillars resulted in uncontrollable
growth of thick COF-1 platelets parallel to the surface of GO. The v-COF-GO was
converted into conductive carbon material preserving the nanostructure of
precursor with ultrathin porous carbon nanosheets grafted to graphene in
edge-on orientation. It was demonstrated as high-performance electrode material
for supercapacitors. The molecular pillar approach can be used for preparation
of many other 2D-2D materials with control of their relative orientation.


  Ground- and space-based planet searches employing radial velocity techniques
and transit photometry have detected thousands of planet-hosting stars in the
Milky Way. The chemistry of these atmospheres is controlled by the shape and
absolute flux of the stellar spectral energy distribution, however, flux
distributions of relatively inactive low-mass stars are poorly known at
present. To better understand exoplanets orbiting low-mass stars, we have
executed a panchromatic (X-ray to mid-IR) study of the spectral energy
distributions of 11 nearby planet hosting stars, the {\it Measurements of the
Ultraviolet Spectral Characteristics of Low-mass Exoplanetary Systems}
(MUSCLES) Treasury Survey. The MUSCLES program consists of contemporaneous
observations at X-ray, UV, and optical wavelengths. We show that energetic
radiation (X-ray and ultraviolet) is present from magnetically active stellar
atmospheres at all times for stars as late as M5. Emission line luminosities of
\ion{C}{4} and \ion{Mg}{2} are strongly correlated with band-integrated
luminosities. We find that while the slope of the spectral energy distribution,
FUV/NUV, increases by approximately two orders of magnitude form early K to
late M dwarfs ($\approx$~0.01~to~1), the absolute FUV and XUV flux levels at
their corresponding habitable zone distances are constant to within factors of
a few, spanning the range 10~--~70 erg cm$^{-2}$ s$^{-1}$ in the habitable
zone. Despite the lack of strong stellar activity indicators in their optical
spectra, several of the M dwarfs in our sample show spectacular flare emission
in their UV light curves. Finally, we interpret enhanced $L(line)$/$L_{Bol}$
ratios for \ion{C}{4} and \ion{N}{5} as tentative observational evidence for
the interaction of planets with large planetary mass-to-orbital distance ratios
($M_{plan}$/$a_{plan}$) with the transition regions of their host stars.


  For every Tikhonov space $X$ the free abelian topological group $A(X)$ and
the free locally convex vector space $L(X)$ admit a topologically faithful
unitary representation. For compact spaces $X$ this is due to Jorge Galindo.


  A construction is presented that allows to produce subspace codes of long
length using subspace codes of shorter length in combination with a rank metric
code. The subspace distance of the resulting code, called linkage code, is as
good as the minimum subspace distance of the constituent codes. As a special
application, the construction of the best known partial spreads is reproduced.
Finally, for a special case of linkage, a decoding algorithm is presented which
amounts to decoding with respect to the smaller constituent codes and which can
be parallelized.


  We consider measurements, described by a positive-operator-valued measure
(POVM), whose outcome probabilities determine an arbitrary pure state of a
D-dimensional quantum system. We call such a measurement a pure-state
informationally complete (PSI-complete) POVM. We show that a measurement with
2D-1 outcomes cannot be PSI-complete, and then we construct a POVM with 2D
outcomes that suffices, thus showing that a minimal PSI-complete POVM has 2D
outcomes. We also consider PSI-complete POVMs that have only rank-one POVM
elements and construct an example with 3D-2 outcomes, which is a generalization
of the tetrahedral measurement for a qubit. The question of the minimal number
of elements in a rank-one PSI-complete POVM is left open.


  We propose a simple phenomenological model describing vibrational dynamics in
a class of materials (like clathrates), which are crystalline compounds with
closed cavities in their structures. In the spirit of a minimalist approach,
our model includes only the minimum of ingredients necessary to capture the
generic features of this class of compounds as brought to light by experiments.
We consider only two kinds of particles: strongly coupled host atoms, which
form the structural cavities, and guest atoms confined in the cavities. In
spite of the confinement, for relatively small amplitude vibrations of the
guest atoms, their interaction with the host particles is assumed to be weaker
than between the host atoms. We calculate self-consistently the vibrational
mode (phonon) line broadenings for the empty and filled (by the guest atoms)
cavities. We show that the soft phonon dispersion sheet, which appears for
weakly bonded guest atoms, yields to large mode broadening via three waves
anharmonic mode coupling. In turn the Umklapp part of this broadening reduces
drastically the phonon thermoconductivity coefficient. We conclude that for a
system with a soft mode component in the vibrational spectrum phonon broadening
is always larger and thermal conductivity is always appreciably smaller than
for a system without this soft mode (provided all other characteristics are the
same). Although our model is minimal, in the sense of ignoring the complexity
of actual guest-host structures, when properly interpreted, it can yield quite
reasonable values for a variety of measurable quantities.


  The spin Hall effect in a heavy metal thin film allows to probe the magnetic
properties of an adjacent magnetic insulator via magnetotransport measurements.
Here, we investigate the magnetoresistive response of yttrium iron
garnet/platinum heterostructures from room temperature to beyond the Curie
temperature $T_\mathrm{C, YIG} \approx 560\,\mathrm{K}$ of the ferrimagnetic
insulator. We find that the amplitude of the (local) spin Hall
magnetoresistance decreases monotonically from $300\,\mathrm{K}$ towards
$T_\mathrm{C}$, mimicking the evolution of the saturation magnetization of
yttrium iron garnet. Interestingly, the spin Hall magnetoresistance vanishes
around $500\,\mathrm{K}$, well below $T_\mathrm{C}$, which we attribute to the
formation of a parasitic interface layer by interdiffusion. Around room
temperature the non-local magnon-mediated magnetoresistance exhibits a power
law scaling $T^{\alpha}$ with $\alpha = 3/2$, as already reported. The exponent
decreases gradually to $\alpha \sim 1/2$ at around $420\,\mathrm{K}$, before
the non-local magnetoresistance vanishes rapidly at a similar temperature as
the spin Hall magnetoresistance. We attribute the reduced $\alpha$ at high
temperatures to the increasing thermal magnon population which leads to
enhanced scattering of the non-equilibrium magnon population and a reduced
magnon diffusion length. Finally, we find a magnetic field independent offset
voltage in the non-local signal for $T > 470\,\mathrm{K}$ which we associate
with electronic leakage currents through the normally insulating yttrium iron
garnet film. Indeed, this non-local offset voltage is thermally activated with
an energy close to the band gap.


  The SIMPLE experiment is reanalyzed within the context of the WIMP model
independent framework of Tovey et. al.. The results are compared with those of
the UK NAIAD and NaF experiments as recently reported by the Tokyo group,
together with those of the latest UK NAIAD results in 2003, and further
constrain the allowed parameter space.


  Membership inference attacks are designed to determine, using black box
access to trained models, whether a particular example was used in training or
not. Membership inference can be formalized as a hypothesis testing problem.
The most effective existing attacks estimate the distribution of some test
statistic (usually the model's confidence on the true label) on points that
were (and were not) used in training by training many \emph{shadow models} --
i.e. models of the same architecture as the model being attacked, trained on a
random subsample of data. While effective, these attacks are extremely
computationally expensive, especially when the model under attack is large.
  We introduce a new class of attacks based on performing quantile regression
on the distribution of confidence scores induced by the model under attack on
points that are not used in training. We show that our method is competitive
with state-of-the-art shadow model attacks, while requiring substantially less
compute because our attack requires training only a single model. Moreover,
unlike shadow model attacks, our proposed attack does not require any knowledge
of the architecture of the model under attack and is therefore truly
``black-box". We show the efficacy of this approach in an extensive series of
experiments on various datasets and model architectures.


  We study the determination of the symmetry that stabilizes a dark matter (DM)
candidate produced at colliders. Our question is motivated per se, and by
several alternative symmetries that appear in models that provide a DM
particle. To this end, we devise a strategy to determine whether a heavy mother
particle decays into one visible massless particle and one or two DM particles.
The counting of DM particles in these decays is relevant to distinguish the
minimal choice of Z_2, from a Z_3, stabilization symmetry, under which the
heavy particle and the DM are charged and the visible particle is not. Our
method is novel in that it chiefly uses the peak of the energy spectrum of the
visible particle and only secondarily uses the M_T2 endpoint of events in which
the heavy mother particles are pair-produced. We present new theoretical
results concerning the energy distribution of the decay products of a
three-body decay, which are crucial for our method. To demonstrate the
feasibility of our method in investigating the stabilization symmetry, we apply
it in distinguishing the decay of a bottom quark partner into a b quark and one
or two DM particles. The method can be applied generally to distinguish two-
and three-body decays, irrespective of DM.


  Dynamical friction arises from the interaction of a perturber and the
gravitational wake it excites in the ambient medium. This interaction is
usually derived assuming that the perturber has a constant velocity. In
realistic situations, motion is accelerated as for instance by dynamical
friction itself. Here, we study the effect of acceleration on the dynamical
friction force. We characterize the density enhancement associated with a
constantly accelerating perturber with rectilinear motion in an infinite
homogeneous gaseous medium and show that dynamical friction is not a local
force and that its amplitude may depend on the perturber's initial velocity.
The force on an accelerating perturber is maximal between Mach 1 and Mach 2,
where it is smaller than the corresponding uniform motion friction. In the
limit where the perturber's size is much smaller than the distance needed to
change the Mach number by unity through acceleration, a subsonic perturber
feels a force similar to uniform motion friction only if its past history does
not include supersonic episodes. Once an accelerating perturber reaches large
supersonic speeds, accelerated motion friction is marginally stronger than
uniform motion friction. The force on a decelerating supersonic perturber is
weaker than uniform motion friction as the velocity decreases to a few times
the sound speed. Dynamical friction on a decelerating subsonic perturber with
an initial Mach number larger than 2 is much larger than uniform motion
friction and tends to a finite value as the velocity vanishes in contrast to
uniform motion friction.


  Spatiotemporal vortex pulses are wave packets that carry transverse orbital
angular momentum, exhibiting exotic structured wavefronts that can twist
through space and time. Existing methods to generate these pulses require
complex setups like spatial light modulators or computer-optimized structures.
Here, we demonstrate a new approach to generate spatiotemporal vortex pulses
using just a simple diffractive grating. The key is constructing a phase vortex
in frequency-momentum space by leveraging symmetry, resonance, and diffraction.
Our approach is applicable to any wave system. We use a liquid surface wave
platform to directly demonstrate and observe the real-time generation and
evolution of spatiotemporal vortex pulses. This straightforward technique
provides opportunities to explore pulse dynamics and potential applications
across different disciplines.


  The discovery of unconventional ferroelectric behavior in twisted bilayers
has prompted the consideration of moir\'e heterostructures as polar materials.
However, misconceptions about the nature and origin of the observed
ferroelectricity indicate that a better theoretical understanding of the polar
properties of moir\'e heterostructures is needed. In this paper, it is
proposed, and verified with first-principles calculations, that all moir\'e
heterostructures exhibit an out-of-plane moir\'e polar domain (MPD) structure.
In transition metal dichalcogenide bilayers, an interlayer charge transfer
occurs due to the change in stacking arrangements throughout the moir\'e
superlattice, leading to a local out-of-plane dipole moment, with the magnitude
and shape of the MPDs being dominated by the chalcogen atoms. While the MPDs in
all heterostructures are sensitive to the moir\'e period, it is only in the
homo-bilayers that they can be tuned with an out-of-plane electric field. The
misconceptions about ferroelectricity in moir\'e heterostructures are
addressed, and it is proposed that the only scenario in which the MPDs can be
considered ferroelectric domains is via a global van der Waals sliding by one
third of a unit cell in a homo-bilayer. Finally, a general theoretical
discussion of the polar properties of moir\'e heterostructures is provided.


  When sexual violence is a product of organized crime or social imaginary, the
links between sexual violence episodes can be understood as a latent structure.
With this assumption in place, we can use data science to uncover complex
patterns. In this paper we focus on the use of data mining techniques to unveil
complex anomalous spatiotemporal patterns of sexual violence. We illustrate
their use by analyzing all reported rapes in El Salvador over a period of nine
years. Through our analysis, we are able to provide evidence of phenomena that,
to the best of our knowledge, have not been previously reported in literature.
We devote special attention to a pattern we discover in the East, where
underage victims report their boyfriends as perpetrators at anomalously high
rates. Finally, we explain how such analyzes could be conducted in real-time,
enabling early detection of emerging patterns to allow law enforcement agencies
and policy makers to react accordingly.


  Node classification is one of the core tasks on attributed graphs, but
successful graph learning solutions require sufficiently labeled data. To keep
annotation costs low, active graph learning focuses on selecting the most
qualitative subset of nodes that maximizes label efficiency. However, deciding
which heuristic is best suited for an unlabeled graph to increase label
efficiency is a persistent challenge. Existing solutions either neglect
aligning the learned model and the sampling method or focus only on limited
selection aspects. They are thus sometimes worse or only equally good as random
sampling. In this work, we introduce a novel active graph learning approach
called DiffusAL, showing significant robustness in diverse settings. Toward
better transferability between different graph structures, we combine three
independent scoring functions to identify the most informative node samples for
labeling in a parameter-free way: i) Model Uncertainty, ii) Diversity
Component, and iii) Node Importance computed via graph diffusion heuristics.
Most of our calculations for acquisition and training can be pre-processed,
making DiffusAL more efficient compared to approaches combining diverse
selection criteria and similarly fast as simpler heuristics. Our experiments on
various benchmark datasets show that, unlike previous methods, our approach
significantly outperforms random selection in 100% of all datasets and labeling
budgets tested.


  In this paper we study Seidel's mirror map for abelian and Kummer surfaces.
We find that mirror symmetry leads in a very natural way to the classical
parametrization of Kummer surfaces in $\P^3$. Moreover, we describe a family of
embeddings of a given abelian surface into noncommutative projective spaces.


  In this three-part monograph, we prove that steady, incompressible
Navier-Stokes flows posed over the moving boundary, $y = 0$, can be decomposed
into Euler and Prandtl flows in the inviscid limit globally in $[1,\infty)
\times [0,\infty)$, assuming a sufficiently small velocity mismatch. Sharp
decay rates and self-similar asymptotics are extracted for both Prandtl and
Eulerian layers. We then develop a functional framework to capture precise
decay rates of the remainders, and prove the corresponding embedding theorems
by establishing weighted estimates for their higher order tangential
derivatives. These tools are then used in conjunction with a third order energy
analysis, which in particular enables us to control the nonlinearity $vu_y$
globally.


  Estimating and quantifying uncertainty in unknown system parameters from
limited data remains a challenging inverse problem in a variety of real-world
applications. While many approaches focus on estimating constant parameters, a
subset of these problems includes time-varying parameters with unknown
evolution models that often cannot be directly observed. This work develops a
systematic particle filtering approach that reframes the idea behind artificial
parameter evolution to estimate time-varying parameters in nonstationary
inverse problems arising from deterministic dynamical systems. Focusing on
systems modeled by ordinary differential equations, we present two particle
filter algorithms for time-varying parameter estimation: one that relies on a
fixed value for the noise variance of a parameter random walk; another that
employs online estimation of the parameter evolution noise variance along with
the time-varying parameter of interest. Several computed examples demonstrate
the capability of the proposed algorithms in estimating time-varying parameters
with different underlying functional forms and different relationships with the
system states (i.e., additive vs. multiplicative).


  We prove the universality of correlation functions of chiral complex matrix
models in the microscopic limit (N->\infty, z->0, N z=fixed) which magnifies
the crossover region around the origin of the eigenvalue distribution. The
proof exploits the fact that the three-term difference equation for orthogonal
polynomials reduces into a universal second-order differential (Bessel)
equation in the microscopic limit.


  Assuming an instance of the Brodsky-Rinot proxy principle holding at a
regular uncountable cardinal $\kappa$, we construct $2^\kappa$-many pairwise
non-embeddable minimal non-$\sigma$-scattered linear orders of size $\kappa$.
In particular, in G\"odel's constructible universe $L$, these linear orders
exist for any regular uncountable cardinal $\kappa$ that is not weakly compact.
This extends a recent result of Cummings, Eisworth and Moore that takes care of
all the successor cardinals of $L$. At the level of $\aleph_1$, their work
answered an old question of Baumgartner by constructing from $\diamondsuit$ a
minimal Aronszajn line that is not Souslin. Our use of the proxy principle
yields the same conclusion from a weaker assumption which holds for instance in
the generic extension after adding a single Cohen real to a model of $CH$.


  We present accurate measurements of the linear, quadratic, and cubic local
bias of dark matter halos, using curved "separate universe" N-body simulations
which effectively incorporate an infinite-wavelength overdensity. This can be
seen as an exact implementation of the peak-background split argument. We
compare the results with the linear and quadratic bias measured from the
halo-matter power spectrum and bispectrum, and find good agreement. On the
other hand, the standard peak-background split applied to the Sheth & Tormen
(1999) and Tinker et al. (2008) halo mass functions matches the measured linear
bias parameter only at the level of 10%. The prediction from the excursion
set-peaks approach performs much better, which can be attributed to the
stochastic moving barrier employed in the excursion set-peaks prediction. We
also provide convenient fitting formulas for the nonlinear bias parameters
$b_2(b_1)$ and $b_3(b_1)$, which work well over a range of redshifts.


  We present and analyse spectra of the Type IIn supernova 1994W obtained
between 18 and 202 days after explosion. During the first 100 days the line
profiles are composed of three major components: (i) narrow P Cygni lines with
absorption minima at -700 km/s; (ii) broad emission lines with BVZI ~4000 km/s;
(iii) broad wings most apparent in H-alpha. These components are identified
with the expanding circumstellar (CS) envelope (Sollerman, Cumming & Lundqvist
1998), shocked cool gas in the forward postshock region, and multiple Thomson
scattering in the CS envelope, respectively. The absence of broad P Cygni lines
from the supernova (SN) is the result of the formation of an optically thick,
cool, dense shell at the interface of the ejecta and the CS envelope. Models of
the SN deceleration and Thomson scattering wings are used to recover the
Thomson optical depth of the CS envelope and its radial extent, 4E15 cm. The
light curve, which we reproduce by a hydrodynamical model, is powered by a
combination of internal energy leakage after the explosion of an extended
presupernova (~1E15 cm) and luminosity from circumstellar interaction. We
recover the pre-explosion kinematics of the CS envelope and find it to be close
to homologous expansion with outmost velocity ~1100 km/s and a kinematic age of
\~1.5 yr. The high mass and kinetic energy of the CS envelope strongly suggest
that the CS envelope was explosively ejected only a few years before explosion.


  I study the VLA HI survey of HII galaxies by Taylor et al. (1995, ApJS, 99,
427; 1996, ApJS, 102, 189) and the VLA HI survey of low surface brightness
(LSB) dwarf galaxies by Taylor et al. (1996, ApJS, in press) to investigate the
role of galaxy interactions in triggering the bursts of massive star formation
seen in HII galaxies. I find that the companion rate for HII galaxies is more
than twice that of LSB dwarfs (p[HII] = 0.57 p[LSB] = 0.24). I examine the
completeness of the companion samples detected by the two surveys, finding that
because they were observed in identical fashions, there are no relative biases
to cause one sample or the other to have more companions. Thus I conclude that
the difference in the number of HI rich companions is genuine, and signifies a
difference in the local, small scale environments between the two types of
galaxy. I search through published galaxy catalogs to study the large scale
environments of the two samples, finding that at large separations, the two
samples exist in very similar environments on average. The difference in
companion rates between HII galaxies and LSB dwarfs supports the idea that the
bursts of star formation are triggered by galaxy interactions.


  Evidence suggests that brain network dynamics is a key determinant of brain
function and dysfunction. Here we propose a new framework to assess the
dynamics of brain networks based on recurrence analysis. Our framework uses
recurrence plots and recurrence quantification analysis to characterize dynamic
networks. For resting-state magnetoencephalographic dynamic functional networks
(dFNs), we have found that functional networks recur more quickly in people
with epilepsy than healthy controls. This suggests that recurrence of dFNs may
be used as a biomarker of epilepsy. For stereo electroencephalography data, we
have found that dFNs involved in epileptic seizures emerge before seizure
onset, and recurrence analysis allows us to detect seizures. We further observe
distinct dFNs before and after seizures, which may inform neurostimulation
strategies to prevent seizures. Our framework can also be used for
understanding dFNs in healthy brain function and in other neurological
disorders besides epilepsy.


  We show new upper and lower bounds for the complexity of implementation of a
sequence of Boolean matrices proposed by Kaski et al. (arXiv:1208.0554) with
additive circuits.


  We study the competition of quark-antiquark and diquark condensates under the
influence of an external chromomagnetic field modelling the gluon condensate
and in dependence on the chemical potential and temperature. As our results
indicate, an external chromomagnetic field might produce remarkable qualitative
changes in the picture of the color superconducting (CSC) phase formation. This
concerns, in particular, the possibility of a transition to the CSC phase and
diquark condensation at finite temperature.


  Two level quantum system (Qubit) and non-classical states of light such as
single photon and superposition of coherent state are under special attention
in quantum technologies such as quantum computing, quantum communication and
quantum computers. So, behavior of two-level system driven by such inputs is
important. In this paper, the behavior of two-level quantum system driven by
vacuum state, single photon and superposition of coherent state was
investigated by assuming Pauli matrices as system operators in quantum
filtering equations. The purity of conditioned and unconditioned state are also
analyzed when the system is driven by different inputs. The results show that
the stochastic master equation dynamic has more information about the status of
system than master equation dynamic.


  We consider misaligned accretion discs formed after tidal disruption events
occurring when a star encounters a supermassive rotating black hole. We use the
linear theory of warped accretion discs to find the disc shape when the stream
produced by the disrupted star provides a source of mass and angular momentum
that is misaligned with the black hole. The evolution of the surface density
and aspect ratio is found from a one dimensional vertically averaged model.
  We extend previous work which assumed a quasi-stationary disc to allow
unrestricted dynamical propagation of disc tilt and twist through time
dependent backgrounds. We consider a smaller value of the viscosity parameter,
$\alpha =0.01,$ finding the dynamics varies significantly.
  At early times the disc inclination is found to be nearly uniform at small
radii where the aspect ratio is large. However, since torques arise from the
Lense-Thirring effect and the stream there is non uniform precession. We
propose a simple model for this requiring only the background surface density
and aspect ratio.
  At these times the $\alpha \sim 0.01$ disc exhibits a new feature. An
inclined hot inner region joins an outer low inclination cool region via a thin
transition front propagating outwards with a speed exceeding that of bending
waves in the cool region. These waves accumulate where the propagation speeds
match producing an inclination spike separating inner and outer discs. At late
times a sequence of quasi-stationary configurations approximates disc shapes at
small radii. We discuss observational implications of our results.


  Using a refractive index matching method, we investigate the trajectories of
particles in a three dimensional granular packing submitted to cyclic shear
deformation. The particle motion observed during compaction is not diffusive
but exhibits transient cage effect, similar to the one observed in colloidal
glasses. We precisely study the statistics of the step size between two
successive cycles and observe that it is proportional to the shear amplitude.
The link between the microscopic observations and the macroscopic evolution of
the volume fraction during compaction is discussed.


  The very nature of the ground state of the pyrochlore compound
Yb$_2$Ti$_2$O$_7$ is much debated, as experimental results demonstrate evidence
for both a disordered or a long-range ordered ground state. Indeed, the
delicate balance of exchange interactions and anisotropy is believed to lead to
competing states, such as a Quantum Spin Liquid state or a ferromagnetic state
which may originate from an Anderson-Higgs transition. We present a detailed
magnetization study demonstrating a first order ferromagnetic transition at 245
mK and 150 mK in a powder and a single crystal sample respectively. Its
first-order character is preserved up to applied fields of $\sim$ 200 Oe. The
transition stabilizes a ferromagnetic component and involves slow dynamics in
the magnetization. Residual fluctuations are also evidenced, the presence of
which might explain some of the discrepancies between previously published data
for Yb$_2$Ti$_2$O$_7$.


  Deployed real-world machine learning applications are often subject to
uncontrolled and even potentially malicious inputs. Those out-of-domain inputs
can lead to unpredictable outputs and sometimes catastrophic safety issues.
Prior studies on out-of-domain detection require in-domain task labels and are
limited to supervised classification scenarios. Our work tackles the problem of
detecting out-of-domain samples with only unsupervised in-domain data. We
utilize the latent representations of pre-trained transformers and propose a
simple yet effective method to transform features across all layers to
construct out-of-domain detectors efficiently. Two domain-specific fine-tuning
approaches are further proposed to boost detection accuracy. Our empirical
evaluations of related methods on two datasets validate that our method greatly
improves out-of-domain detection ability in a more general scenario.


  Understanding the inner working mechanism of deep neural networks (DNNs) is
essential and important for researchers to design and improve the performance
of DNNs. In this work, the entropy analysis is leveraged to study the neurons
activation behavior of the fully connected layers of DNNs. The entropy of the
activation patterns of each layer can provide a performance metric for the
evaluation of the network model accuracy. The study is conducted based on a
well trained network model. The activation patterns of shallow and deep layers
of the fully connected layers are analyzed by inputting the images of a single
class. It is found that for the well trained deep neural networks model, the
entropy of the neuron activation pattern is monotonically reduced with the
depth of the layers. That is, the neuron activation patterns become more and
more stable with the depth of the fully connected layers. The entropy pattern
of the fully connected layers can also provide guidelines as to how many fully
connected layers are needed to guarantee the accuracy of the model. The study
in this work provides a new perspective on the analysis of DNN, which shows
some interesting results.


  We present our submission to the WMT19 Robustness Task. Our baseline system
is the Charles University (CUNI) Transformer system trained for the WMT18
shared task on News Translation. Quantitative results show that the CUNI
Transformer system is already far more robust to noisy input than the
LSTM-based baseline provided by the task organizers. We further improved the
performance of our model by fine-tuning on the in-domain noisy data without
influencing the translation quality on the news domain.


  This paper studies the long-existing idea of adding a nice smooth function to
"smooth" a non-differentiable objective function in the context of sparse
optimization, in particular, the minimization of
$||x||_1+1/(2\alpha)||x||_2^2$, where $x$ is a vector, as well as the
minimization of $||X||_*+1/(2\alpha)||X||_F^2$, where $X$ is a matrix and
$||X||_*$ and $||X||_F$ are the nuclear and Frobenius norms of $X$,
respectively. We show that they can efficiently recover sparse vectors and
low-rank matrices. In particular, they enjoy exact and stable recovery
guarantees similar to those known for minimizing $||x||_1$ and $||X||_*$ under
the conditions on the sensing operator such as its null-space property,
restricted isometry property, spherical section property, or RIPless property.
To recover a (nearly) sparse vector $x^0$, minimizing
$||x||_1+1/(2\alpha)||x||_2^2$ returns (nearly) the same solution as minimizing
$||x||_1$ almost whenever $\alpha\ge 10||x^0||_\infty$. The same relation also
holds between minimizing $||X||_*+1/(2\alpha)||X||_F^2$ and minimizing
$||X||_*$ for recovering a (nearly) low-rank matrix $X^0$, if $\alpha\ge
10||X^0||_2$. Furthermore, we show that the linearized Bregman algorithm for
minimizing $||x||_1+1/(2\alpha)||x||_2^2$ subject to $Ax=b$ enjoys global
linear convergence as long as a nonzero solution exists, and we give an
explicit rate of convergence. The convergence property does not require a
solution solution or any properties on $A$. To our knowledge, this is the best
known global convergence result for first-order sparse optimization algorithms.


  In this paper, we study a family of general fractional Sobolev spaces
$\MsqpOm$ when $\Om=\Rn$ or $\Om$ is a bounded domain, having a compact,
Lipschitz boundary $\Bdy$, in $\Rn$ for $n\geq2$. Among other results, some
compact embedding results of $\MVsqpRn\hookrightarrow\LqRn$ and
$\MVsqpRn\hookrightarrow\LlRn$ for suitable potential functions $V(x)$ are
described.


  Epitaxial La0.7Sr0.3MnO3 (LSMO) thin films, with different thickness ranging
from 20 nm up to 330 nm, were deposited on (100)-oriented strontium titanate
(STO) substrates by pulsed laser deposition, and their structure and morphology
characterized at room temperature. Magnetic and electric transport properties
of the as-processed thin films reveal an abnormal behavior in the temperature
dependent magnetization M(T) below the antiferrodistortive STO phase transition
(TSTO) and also an anomaly in the magnetoresistance and electrical resistivity
close to the same temperature. Up to 100 nm LSMO thin films, an in-excess
magnetization and pronounced changes in the coercivity are evidenced, achieved
through the interface-mediated magnetoelastic coupling with antiferrodistortive
domain wall movement occurring below TSTO. Contrarily, for thicker LSMO thin
films, above 100 nm, an in-defect magnetization is observed. This reversed
behavior can be understood within the emergence in the upper layer of the film,
observed by high resolution transmission electron microscopy, of a branched
structure needed to relax elastic energy stored in the film which leads to
randomly oriented magnetic domain reconstructions. For enough high-applied
magnetic fields, as thermodynamic equilibrium is reached, a fully suppression
of the anomalous magnetization occurs, wherein the temperature dependence of
the magnetization starts to follow the expected Brillouin behavior.


  The sensitivity of imaging atmospheric Cherenkov telescopes (IACTs) in TeV
gamma-ray observations reachs its maximum at small zenith angles (< 30 degree)
which provide the minimum attainable energy threshold of an instrument.
However, for a specific telescope site a number of gamma-ray sources, or source
candidates, can only be observed at much larger zenith angles (< 60 degree).
Moreover the observations at large zenith angles allow to extend the
observation time window for any object seen at small zenith angles, as well as
to enlarge the dynamic energy range of an instrument towards the highest
observable energies of gamma-rays. Based on Monte Carlo simulations we present
here the results on the sensitivity of a stereoscopic system of 5 IACTs in
observations at large zenith angles. We point out some important parameters of
the telescope design which could substantially improve the efficiency of such
observations with forthcoming IACT arrays like CANGAROO III, HESS and VERITAS.


  We construct a large class of bipartite M x N quantum states which defines a
proper subset of states with positive partial transposes (PPT). Any state from
this class is PPT but the positivity of its partial transposition is recognized
with respect to canonical factorization of the original density operator. We
propose to call elements from this class states with strong positive partial
transposes (SPPT). We conjecture that all SPPT states are separable.


  Herein, we discuss the identification of vanadium trimers in layered LiVO2
and its sulfide analog of LiVS2 with two-dimensional triangular lattices. Our
comprehensive structural studies using synchrotron X-ray diffraction
experiments clarified that vanadium trimers are randomly aligned along the
c-axis direction in LiVO2, while the long-range ordering of vanadium trimers
along the c-axis direction appears in LiVS2. Our results solve the longstanding
issue of cluster patterns in LiVO2 and provide an experimental basis for
identifying the mechanism of trimer formation.


  On the occasion of the $75^{th}$ anniversary of the fission phenomenon, we
present a surprisingly simple result which highlights the important role of
isospin and its conservation in neutron rich fission fragments. We have
analysed the fission fragment mass distribution from two recent heavy-ion
reactions $^{238}$U($^{18}$O,f) and $^{208}$Pb($^{18}$O,f) as well as a thermal
neutron fission reaction $^{245}$Cm(n$^{th}$,f). We find that the conservation
of the total isospin explains the overall trend in the observed relative yields
of fragment masses in each fission pair partition. The isospin values involved
are very large making the effect dramatic. The findings open the way for more
precise calculations of fission fragment distributions in heavy nuclei and may
have far reaching consequences for the drip line nuclei, HI fusion reactions,
and calculation of decay heat in the fission phenomenon.


  Graph Neural Networks (GNNs) have shown remarkable success in molecular
tasks, yet their interpretability remains challenging. Traditional model-level
explanation methods like XGNN and GNNInterpreter often fail to identify valid
substructures like rings, leading to questionable interpretability. This
limitation stems from XGNN's atom-by-atom approach and GNNInterpreter's
reliance on average graph embeddings, which overlook the essential structural
elements crucial for molecules. To address these gaps, we introduce an
innovative \textbf{M}otif-b\textbf{A}sed \textbf{G}NN \textbf{E}xplainer (MAGE)
that uses motifs as fundamental units for generating explanations. Our approach
begins with extracting potential motifs through a motif decomposition
technique. Then, we utilize an attention-based learning method to identify
class-specific motifs. Finally, we employ a motif-based graph generator for
each class to create molecular graph explanations based on these class-specific
motifs. This novel method not only incorporates critical substructures into the
explanations but also guarantees their validity, yielding results that are
human-understandable. Our proposed method's effectiveness is demonstrated
through quantitative and qualitative assessments conducted on six real-world
molecular datasets.


  Recently, evidence for a conducting surface state below 19 K was reported for
the correlated d-electron small gap semiconductor FeSi. In the work reported
herein, the conducting surface state and the bulk phase of FeSi were probed via
electrical resistivity measurements as a function of temperature T, magnetic
field B to 60 T and pressure P to 7.6 GPa, and by means of a magnetic field
modulated microwave spectroscopy (MFMMS) technique. The properties of FeSi were
also compared to those of the Kondo insulator SmB6 to address the question of
whether FeSi is a d-electron analogue of an f-electron Kondo insulator and, in
addition, a topological Kondo insulator. The overall behavior of the
magnetoresistance MR of FeSi at temperatures above and below the onset
temperature (T_S) 19 K of the conducting surface state is similar to that of
SmB6. The two energy gaps, inferred from the resistivity data in the
semiconducting regime, increase with pressure up to about 7 GPa, followed by a
drop which coincides with a sharp suppression of T_S. This behavior is similar
to that reported for SmB6, except that the two energy gaps in SmB6 decrease
with pressure before dropping abruptly at T_S. The MFMMS measurements showed a
sharp feature at T_S (19 K) for FeSi, but no such feature was observed at T_S
4.5 K for SmB6. The absence of a feature at T_S for SmB6 may be due to
experimental issues and will be the subject of a future investigation.


  In this paper we investigate the motion of small compact objects in
non-vacuum spacetimes using methods from effective field theory in curved
spacetime. Although a vacuum formulation is sufficient in many astrophysical
contexts, there are applications such as the role of the self-force in
enforcing cosmic-censorship in the context of the overcharging problem, which
necessitate an extension into the non-vacuum regime. The defining feature of
the self-force problem in non-vacuum spacetimes is the coupling between
gravitational and non-gravitational field perturbations. The formulation of the
self-force problem for non-vacuum spacetimes was recently provided in
simultaneous papers by Zimmerman and Poisson [1] and Linz, Friedmann, Wiseman
[2]. Here we distinguish ourselves by working with the effective action rather
than the field equations. The formalism utilizes the multi-index notation
developed by Zimmerman and Poisson [1] to accommodate the coupling between the
different fields. Using dimensional regularization, we arrive at a finite
expression for the local self-force expressed in terms of multi-index
quantities evaluated in the background spacetime. We then apply the formalism
to compute the coupled gravitational self-force in two explicit cases. First,
we calculate the self-force on a massive particle possessing scalar charge and
moving in an scalarvac spacetime. We then derive an expression for the
self-force on an electrically charged, massive particle moving in an electrovac
spacetime. In both cases, the force is expressed as a sum of local terms
involving tensors defined in the background spacetime and evaluated at the
current position of the particle, as well as tail integrals that depend on the
past history of the particle.


  With the rapid development of geometric deep learning techniques, many
mesh-based convolutional operators have been proposed to bridge irregular mesh
structures and popular backbone networks. In this paper, we show that while
convolutions are helpful, a simple architecture based exclusively on
multi-layer perceptrons (MLPs) is competent enough to deal with mesh
classification and semantic segmentation. Our new network architecture, named
Mesh-MLP, takes mesh vertices equipped with the heat kernel signature (HKS) and
dihedral angles as the input, replaces the convolution module of a ResNet with
Multi-layer Perceptron (MLP), and utilizes layer normalization (LN) to perform
the normalization of the layers. The all-MLP architecture operates in an
end-to-end fashion and does not include a pooling module. Extensive
experimental results on the mesh classification/segmentation tasks validate the
effectiveness of the all-MLP architecture.


  We study conditions on automorphisms of Boolean algebras of the form
$P(\lambda)/I_\kappa$ (where $\lambda$ is an uncountable cardinal and
$I_\kappa$ is the ideal of sets of cardinality less than $\kappa$) which allow
one to conclude that a given automorphism is trivial. We show (among other
things) that every cardinality-preserving automorphism of
$P(2^\kappa)/I_{\kappa^+}$ which is trivial on all sets of cardinality
$\kappa^+$ is trivial, and that $MA_{\aleph_1}$ implies that every automorphism
of $P(\mathbb{R})/Fin$ is trivial on a cocountable set.


  Lane-Keeping Assistance System (LKAS) is convenient and widely available
today, but also extremely security and safety critical. In this work, we design
and implement the first systematic approach to attack real-world DNN-based
LKASes. We identify dirty road patches as a novel and domain-specific threat
model for practicality and stealthiness. We formulate the attack as an
optimization problem, and address the challenge from the inter-dependencies
among attacks on consecutive camera frames. We evaluate our approach on a
state-of-the-art LKAS and our preliminary results show that our attack can
successfully cause it to drive off lane boundaries within as short as 1.3
seconds.


  Noncommutative Chern-Simons gauge theory coupled to nonrelativistic scalars
or spinors is shown to admit the ``exotic'' two-parameter-centrally extended
Galilean symmetry, realized in a unique way consistent with the Seiberg-Witten
map. Nontopological spinor vortices and topological external-field vortices are
constructed by reducing the problem to previously solved self-dual equations.


  Just how many different connected shapes result from slicing a cube along
some of its edges and unfolding it into the plane? In this article we answer
this question by viewing the cube both as a surface and as a graph of vertices
and edges. This dual perspective invites an interplay of geometric, algebraic,
and combinatorial techniques. The initial observation is that a cutting pattern
which unfolds the cubical surface corresponds to a spanning tree of the cube
graph. The Matrix-Tree theorem can be used to calculate the number of spanning
trees in a connected graph, and thus allows us to compute the number of ways to
unfold the cube. Since two or more spanning trees may yield the same unfolding
shape, Burnside's lemma is required to count the number of incongruent
unfoldings. Such a count can be an arduous task. Here we employ a combination
of elementary algebraic and geometric techniques to bring the problem within
the range of simple hand calculations.


  Deep neural networks have played a crucial part in many critical domains,
such as autonomous driving, face recognition, and medical diagnosis. However,
deep neural networks are facing security threats from backdoor attacks and can
be manipulated into attacker-decided behaviors by the backdoor attacker. To
defend the backdoor, prior research has focused on using clean data to remove
backdoor attacks before model deployment. In this paper, we investigate the
possibility of defending against backdoor attacks at test time by utilizing
partially poisoned data to remove the backdoor from the model. To address the
problem, a two-stage method Test-Time Backdoor Defense (TTBD) is proposed. In
the first stage, we propose a backdoor sample detection method DDP to identify
poisoned samples from a batch of mixed, partially poisoned samples. Once the
poisoned samples are detected, we employ Shapley estimation to calculate the
contribution of each neuron's significance in the network, locate the poisoned
neurons, and prune them to remove backdoor in the models. Our experiments
demonstrate that TTBD removes the backdoor successfully with only a batch of
partially poisoned data across different model architectures and datasets
against different types of backdoor attacks.


  The space-time representation of high-dimensional dynamical systems that have
a well defined characteristic time scale has proven to be very useful to deepen
the understanding of such systems and to uncover hidden features in their
output signals. Genuine analogies between one-dimensional (1D) spatially
extended systems (1D SESs) and time delayed systems (TDSs) have been observed,
including similar pattern formation and propagation of localized structures. An
open question is if such analogies are limited to the space-time
representation, or, if it is possible to reconstruct similar attractors, from
the time series of an observed variable. In this work we address this issue by
considering a bistable 1D SES and two TDSs (a bistable system and a model of
two lasers with time delayed coupling). In these three examples we find that we
can reconstruct the underlying attractor in a three-dimensional pseudo-space,
where the evolution is governed by a polynomial potential. We also discuss the
limitations of the analogy between 1D SESs and TDSs.


  Using Kummer theory for a finite extension K of \Qp(\zeta)(where p is a prime
number and \zeta a primitive p-th root of~1), we compute the ramification
filtration and the discriminant of an arbitrary elementary abelian p-extension
of K. We also develop the analogous Artin-Schreier theory for finite extensions
of \Fp((\pi)) and derive similar results for their elementary abelian
p-extensions.


  We prove that the linear matroid that defines generic rigidity of
$d$-dimensional body-rod-bar frameworks (i.e., structures consisting of
disjoint bodies and rods mutually linked by bars) can be obtained from the
union of ${d+1 \choose 2}$ graphic matroids by applying variants of Dilworth
truncation $n_r$ times, where $n_r$ denotes the number of rods. This leads to
an alternative proof of Tay's combinatorial characterizations of generic
rigidity of rod-bar frameworks and that of identified body-hinge frameworks.


  We study lower bound estimates for the number of solutions of systems of
equations over finite fields. Heath-Brown improved the lower bounds given by
the classical \emph{Chevalley-Warning Theorems} by excluding systems of
equations whose solutions form an affine space. We improve each of
Heath-Brown's results and demonstrate sharpness in several cases.


  Wikification of large corpora is beneficial for various NLP applications.
Existing methods focus on quality performance rather than run-time, and are
therefore non-feasible for large data. Here, we introduce RedW, a run-time
oriented Wikification solution, based on Wikipedia redirects, that can Wikify
massive corpora with competitive performance. We further propose an efficient
method for estimating RedW confidence, opening the door for applying more
demanding methods only on top of RedW lower-confidence results. Our
experimental results support the validity of the proposed approach.


  I examine the mean consensus time (i.e., exit time) of the voter model in the
so-called two-clique graph. The two-clique graph is composed of two cliques
interconnected by some links and considered as a toy model of networks with
community structure or multilayer networks. I analytically show that, as the
number of interclique links per node is varied, the mean consensus time
experiences a crossover between a fast consensus regime [i.e., O(N)] and a slow
consensus regime [i.e., O(N^2)], where N is the number of nodes. The fast
regime is consistent with the result for homogeneous well-mixed graphs such as
the complete graph. The slow regime appears only when the entire network has
O(1) interclique links. The present results suggest that the effect of
community structure on the consensus time of the voter model is fairly limited.


  The notion of typical sequences plays a key role in the theory of
information. Central to the idea of typicality is that a sequence $x_1, x_2,
..., x_n$ that is $P_X$-typical should, loosely speaking, have an empirical
distribution that is in some sense close to the distribution $P_X$. The two
most common notions of typicality are that of strong (letter) typicality and
weak (entropy) typicality. While weak typicality allows one to apply many
arguments that can be made with strongly typical arguments, some arguments for
strong typicality cannot be generalized to weak typicality. In this paper, we
consider an alternate definition of typicality, namely one based on the weak*
topology and that is applicable to Polish alphabets (which includes
$\reals^n$). This notion is a generalization of strong typicality in the sense
that it degenerates to strong typicality in the finite alphabet case, and can
also be applied to mixed and continuous distributions. Furthermore, it is
strong enough to prove a Markov lemma, and thus can be used to directly prove a
more general class of results than weak typicality. As an example of this
technique, we directly prove achievability for Gel'fand-Pinsker channels with
input constraints for a large class of alphabets and channels without first
proving a finite alphabet result and then resorting to delicate quantization
arguments. While this large class does not include Gaussian distributions with
power constraints, it is shown to be straightforward to recover this case by
considering a sequence of truncated Gaussian distributions.


  Phase transitions in metastable $\alpha$-, $\kappa(\epsilon)$-, and
$\gamma$-Ga$_2$O$_3$ films to thermodynamically stable $\beta$-Ga$_2$O$_3$
during annealing in air, N$_2$, and vacuum have been systematically
investigated via in-situ high-temperature X-ray diffraction and scanning
electron microscopy. These respective polymorphs exhibited thermal stability to
around 471-525$^\circ$C, 773-825$^\circ$C, and 490-575$^\circ$C before
transforming into $\beta$-Ga$_2$O$_3$, across all tested ambient conditions.
Particular crystallographic orientation relationships were observed before and
after the phase transitions, i.e., (0006) $\alpha$-Ga$_2$O$_3$ $\parallel$
$(\overline{4}02)$ $\beta$-Ga$_2$O$_3$, (004) $\kappa(\epsilon)$-Ga$_2$O$_3$
$\parallel$ (310) and $(\overline{4}02)$ $\beta$-Ga$_2$O$_3$, and (400)
$\gamma$-Ga$_2$O$_3$ $\parallel$ (400) $\beta$-Ga$_2$O$_3$. The phase
transition of $\alpha$-Ga$_2$O$_3$ to $\beta$-Ga$_2$O$_3$ resulted in
catastrophic damage to the film and upheaval of the surface. The respective
primary and possibly secondary causes of this damage are the +8.6% volume
expansion and the dual displacive and reconstructive transformations that occur
during this transition. The $\kappa(\epsilon)$- and $\gamma$-Ga$_2$O$_3$ films
converted to $\beta$-Ga$_2$O$_3$ via singular reconstructive transformations
with small changes in volume and unchanged surface microstructures.


  We generalize the collision term in the one-dimensional Boltzmann-Nordheim
transport equation for quasiparticles that obey the Haldane exclusion
statistics. For the equilibrium situation, this leads to the ``golden rule''
factor for quantum transitions. As an application of this, we calculate the
density response function of a one-dimensional electron gas in a periodic
potential, assuming that the particle-hole excitations are quasiparticles
obeying the new statistics. We also calculate the relaxation time of a nuclear
spin in a metal using the modified golden rule.