  We study the dynamics of piecewise conformal maps in the Riemann sphere. The
normality and chaotic regions are defined and we state several results and
properties of these sets. We show that the stability of these piecewise maps is
related to the Kleinian group generated by their transformations under certain
hypotheses. The general motivation of the article is to compare the dynamics of
piecewise conformal maps and those of the Kleinian groups and iterations of
rational maps.


  In June 1965, Sister Mary Kenneth Keller, BVM, received the first US PhD in
Computer Science, and this paper outlines her life and accomplishments. As a
scholar, she has the distinction of being an early advocate of
learning-by-example in artificial intelligence. Her main scholarly contribution
was in shaping computer science education in high schools and small colleges.
She was an evangelist for viewing the computer as a symbol manipulator, for
providing computer literacy to everyone, and for the use of computers in
service to humanity. She was far ahead of her time in working to ensure a place
for women in technology and in eliminating barriers preventing their
participation, such as poor access to education and daycare. She was a strong
and spirited woman, a visionary in seeing how computers would revolutionize our
lives. A condensation of this paper appeared as, ``The Legacy of Mary Kenneth
Keller, First U.S. Ph.D. in Computer Science," Jennifer Head and Dianne P.
O'Leary, IEEE Annals of the History of Computing 45(1):55--63, January-March
2023.


  ChatGPT, an implementation and application of large language models, has
gained significant popularity since its initial release. Researchers have been
exploring ways to harness the practical benefits of ChatGPT in real-world
scenarios. Educational researchers have investigated its potential in various
subjects, e.g., programming, mathematics, finance, clinical decision support,
etc. However, there has been limited attention given to its application in data
science education. This paper aims to bridge that gap by utilizing ChatGPT in a
data science course, gathering perspectives from students, and presenting our
experiences and feedback on using ChatGPT for teaching and learning in data
science education. The findings not only distinguish data science education
from other disciplines but also uncover new opportunities and challenges
associated with incorporating ChatGPT into the data science curriculum.


  We present an analysis of the olivine-rich exposures at Bellicia and Arruntia
craters using Dawn Framing Camera (FC) color data. Our results confirm the
existence of olivine-rich materials at these localities as described by
Ammannito et al. (2013a) using Visual Infrared Spectrometer (VIR) data.
Analyzing laboratory spectra of various Howardite-Eucrite-Diogenite meteorites,
high-Ca pyroxenes, olivines and olivine-orthopyroxene mixtures, we derive three
FC spectral band parameters that are indicators of olivine-rich materials.
Combining the three band parameters allows us, for the first time, to reliably
identify sites showing modal olivine contents >40%. The olivine-rich exposures
at Bellicia and Arruntia are mapped using higher spatial resolution FC data.
The exposures are located on the slopes of outer/inner crater walls, on the
floor of Arruntia, in the ejecta, as well as in nearby fresh small impact
craters. The spatial extent of the exposures ranges from a few hundred meters
to few kilometers. The olivine-rich exposures are in accordance with both the
magma ocean and the serial magmatism model (e.g., Righter and Drake 1997;
Yamaguchi et al. 1997). However, it remains unsolved why the olivine-rich
materials are mainly concentrated in the northern hemisphere (~36-42{\deg} N,
46-74{\deg} E) and are almost absent in the Rheasilvia basin.


  Multiple attacks have shown that in-vehicle networks have vulnerabilities
which can be exploited. Securing the Controller Area Network (CAN) for modern
vehicles has become a necessary task for car manufacturers. Some attacks inject
potentially large amount of fake messages into the CAN network; however, such
attacks are relatively easy to detect. In more sophisticated attacks, the
original messages are modified, making the detection a more complex problem. In
this paper, we present a novel machine learning based intrusion detection
method for CAN networks. We focus on detecting message modification attacks,
which do not change the timing patterns of communications. Our proposed
temporal convolutional network-based solution can learn the normal behavior of
CAN signals and differentiate them from malicious ones. The method is evaluated
on multiple CAN-bus message IDs from two public datasets including different
types of attacks. Performance results show that our lightweight approach
compares favorably to the state-of-the-art unsupervised learning approach,
achieving similar or better accuracy for a wide range of scenarios with a
significantly lower false positive rate.


  We present a detailed investigation of the Doppler shift oscillations in a
hot loop during an M7.1 flare on 2014 October 27 observed by the Interface
Region Imaging Spectrograph. The periodic oscillations are observed in the
Doppler shift of Fe XXI 1354.09 A (logT~7.05), and the dominant period is about
3.1 minutes. However, such 3.1-min oscillations are not found in the
line-integrated intensity of Fe XXI 1354.09 A, AIA EUV fluxes, or microwave
emissions. SDO/AIA and Hinode/XRT imaging observations indicate that the
Doppler shift oscillations locate at the hot loop-top region (> 11MK).
Moreover, the differential emission measure (DEM) results show that the
temperature is increasing rapidly when the Doppler shift oscillates, but the
number density does not exhibit the corresponding increases nor oscillations,
implying that the flare loop is likely to oscillate in an incompressible mode.
All these facts suggest that the Doppler shift oscillations at the shorter
period are most likely the standing kink oscillations in a flare loop.
Meanwhile, a longer period of about 10 minutes is identified in the time series
of Doppler shift and line-integrated intensity, GOES SXR fluxes and AIA EUV
light curves, indicating the periodic energy release in this flare, which may
be caused by a slow mode wave.


  The electric (${\alpha}_{\pi}$) and the magnetic (${\beta}_{\pi}$)
polarisabilities are fundamental properties of the pion characterising the
rigidity of its internal structure. They have been precisely measured at the
COMPASS experiment at CERN with a ${\pi}^{-}$ beam of 190~GeV/c assuming
${\alpha}_{\pi}+{\beta}_{\pi}=0$. Muons of the same momentum were used for
controlling of systematic effects. The obtained result
${\alpha}_{\pi}=-{\beta}_{\pi}=(2.0\pm 0.6_{stat.}\pm 0.7_{syst.})\times
10^{-4} fm^3$ is in agreement with the prediction of the Chiral Perturbation
Theory.


  A theory of superconductivity based on the two-body Cooperon propagator is
presented. This theory takes the form of a modified Gorkov equation for the
Green's function and allows one to model the effect of local superconducting
correlations and long range phase fluctuations on the spectral properties of
high temperature superconductors, both above and below Tc. A model is proposed
for the Cooperon propagator, which provides a simple physical picture of the
pseudo-gap phenomenon, as well as new insights into the doping dependence of
the spectral properties. Numerical calculations of the density of states and
spectral functions based on this model are also presented, and compared with
the experimental STM and ARPES data. It is found, in particular, that the
sharpness of the peaks in the density of states is related to the strength and
the range of the superconducting correlations and that the apparent pseudo-gap
in STM and ARPES can be different, although the underlying model is the same.


  Let E/K be an elliptic curve defined over a number field, and let p be a
prime number such that E(K) has full p-torsion. We show that the order of the
p-part of the Shafarevich-Tate group of E/L is unbounded as L varies over
degree p extensions of K. The proof uses O'Neil's period-index obstruction. We
deduce the result from the fact that, under the same hypotheses, there exist
infinitely many elements of the Weil-Chatelet group of E/K of period p and
index p^2.


  We present a measure of the power spectrum on scales from 15 to 800 Mpc/h
using the ROSAT-ESO Flux-Limited X-Ray(REFLEX) galaxy cluster catalogue. The
REFLEX survey provides a sample of the 452 X-ray brightest southern clusters of
galaxies with the nominal flux limit S=3.0 10^{-12}erg/s/cm2 for the ROSAT
energy band (0.1-2.4)keV. Several tests are performed showing no significant
incompletenesses of the REFLEX clusters with X-ray luminosities brighter than
10^{43}erg/s up to scales of about 800 Mpc/h. They also indicate that cosmic
variance might be more important than previous studies suggest. We regard this
as a warning not to draw general cosmological conclusions from cluster samples
with a size smaller than REFLEX. Power spectra, P(k), of comoving cluster
number densities are estimated for flux- and volume-limited subsamples. The
most important result is the detection of a broad maximum within the comoving
wavenumber range 0.022<k<0.030 h/Mpc. The data suggest an increase of the power
spectral amplitude with X-ray luminosity. Compared to optically selected
cluster samples the REFLEX P(k)is flatter for wavenumbers k<0.05 h/Mpc thus
shifting the maximum of P(k) to larger scales. The smooth maximum is not
consistent with the narrow peak detected at k=0.05 h/Mpc using the Abell/ACO
richness $\ge 0$ data. In the range 0.02<k<0.4 h/Mpc general agreement is found
between the slope of the REFLEX P(k) and those obtained with optically selected
galaxies. A semi-analytic description of the biased nonlinear power spectrum in
redshift space gives the best agreement for low-density Cold Dark Matter models
with or without a cosmological constant.


  We study the relaxation modes of an interface between a lyotropic lamellar
phase and a gas or a simple liquid. The response is found to be qualitatively
different from those of both simple liquids and single-component smectic-A
liquid crystals. At low rates it is governed by a non-inertial, diffusive mode
whose decay rate increases quadratically with wavenumber, $|\omega|=Aq^2$. The
coefficient $A$ depends on the restoring forces of surface tension,
compressibility and bending, while the dissipation is dominated by the
so-called slip mechanism, i.e, relative motion of the two components of the
phase parallel to the lamellae. This surface mode has a large penetration depth
which, for sterically stabilised phases, is of order $(dq^2)^{-1}$, where $d$
is the microscopic lamellar spacing.


  In a quantum network that successfully creates links, shared Bell states
between neighboring repeater nodes, with probability $p$ in each time slot, and
performs Bell State Measurements at nodes with success probability $q<1$, the
end to end entanglement generation rate drops exponentially with the distance
between consumers, despite multi-path routing. If repeaters can perform
multi-qubit projective measurements in the GHZ basis that succeed with
probability $q$, the rate does not change with distance in a certain $(p,q)$
region, but decays exponentially outside. This region where the distance
independent rate occurs is the supercritical region of a new percolation
problem. We extend this GHZ protocol to incorporate a time-multiplexing
blocklength $k$, the number of time slots over which a repeater can
mix-and-match successful links to perform fusion on. As $k$ increases, the
supercritical region expands. For a given $(p,q)$, the entanglement rate
initially increases with $k$, and once inside the supercritical region for a
high enough $k$, it decays as $1/k$ GHZ states per time slot. When memory
coherence time exponentially distributed with mean $\mu$ is incorporated, it is
seen that increasing $k$ does not indefinitely increase the supercritical
region; it has a hard $\mu$ dependent limit. Finally, we find that
incorporating space-division multiplexing, i.e., running the above protocol
independently in up to $d$ disconnected network regions, where $d$ is the
network's node degree, one can go beyond the 1 GHZ state per time slot rate
that the above randomized local link-state protocol cannot surpass. As $(p,q)$
increases, one can approach the ultimate min-cut entanglement generation
capacity of $d$ GHZ states per slot.


  The principal aim of this note is to illustrate how factorizations of
singular, even-order partial differential operators yield an elementary
approach to classical inequalities of Hardy-Rellich-type. More precisly,
introducing the two-parameter $n$-dimensional homogeneous scalar differential
expressions $T_{\alpha,\beta} := - \Delta + \alpha |x|^{-2} x \cdot \nabla +
\beta |x|^{-2}$, $\alpha, \beta \in \mathbb{R}$, $x \in \mathbb{R}^n \backslash
\{0\}$, $n \in \mathbb{N}$, $n \geq 2$, and its formal adjoint, denoted by
$T_{\alpha,\beta}^+$, we show that nonnegativity of $T_{\alpha,\beta}^+
T_{\alpha,\beta}$ on $C_0^{\infty}(\mathbb{R}^n \backslash \{0\})$ implies the
fundamental inequality, \begin{align} \int_{\mathbb{R}^n} [(\Delta f)(x)]^2 \,
d^n x &\geq [(n - 4) \alpha - 2 \beta] \int_{\mathbb{R}^n} |x|^{-2} |(\nabla
f)(x)|^2 \, d^n x \notag \\ & \quad - \alpha (\alpha - 4) \int_{\mathbb{R}^n}
|x|^{-4} |x \cdot (\nabla f)(x)|^2 \, d^n x \notag \\ & \quad + \beta [(n - 4)
(\alpha - 2) - \beta] \int_{\mathbb{R}^n} |x|^{-4} |f(x)|^2 \, d^n x, \notag
\end{align} for $f \in C^{\infty}_0(\mathbb{R}^n \backslash \{0\})$. A
particular choice of values for $\alpha$ and $\beta$ yields known
Hardy-Rellich-type inequalities, including the classical Rellich inequality and
an inequality due to Schmincke. By locality, these inequalities extend to the
situation where $\mathbb{R}^n$ is replaced by an arbitrary open set $\Omega
\subseteq \mathbb{R}^n$ for functions $f \in C^{\infty}_0(\Omega \backslash
\{0\})$.
  Perhaps more importantly, we will indicate that our method, in addition to
being elementary, is quite flexible when it comes to a variety of generalized
situations involving the inclusion of remainder terms and higher-order
situations.


  The observation of magnetic diode behavior with ultra-low forward voltage of
5 mV renders new venue for energetically efficient spintronic device research
in the unconventional system of two-dimensional permalloy honeycomb lattice.
Detailed understanding of temperature and magnetic field tuning of diode
behavior is imperative to any practical application. Here, we report a
comprehensive study in this regard by performing electrical measurements on
magnetic diode sample as functions of temperature and magnetic field. Magnetic
diode is found to persist across the broad temperature range. Magnetic field
application unveils a peculiar reentrant characteristic where diode behavior is
suppressed in remnant field but reappears after warming to room temperature.
Analysis of I-V data suggests a modest energy gap, 0.03-0.1 eV, which is
comparable to magnetic Coulomb's interaction energy between emergent magnetic
charges on honeycomb vertices in the reverse biased state. It affirms the role
of magnetic charge correlation in unidirectional conduction in 2D honeycomb
lattice. The experimental results are expected to pave way for the utilization
of magnetic diode in next generation spintronic device applications.


  The pd <--> pi+ t process has been calculated in the energy region around the
Delta-resonance with elementary production/absorption mechanisms involving one
and two nucleons. The isobar degrees of freedom have been explicitly included
in the two-nucleon mechanism via pi-- and rho-exchange diagrams. No free
parameters have been employed in the analysis since all the parameters have
been fixed in previous studies on the simpler pp <--> pi+ d process. The
treatment of the few-nucleon dynamics entailed a Faddeev-based calculation of
the reaction, with continuum calculations for the initial p-d state and
accurate solutions of the three-nucleon bound-state equation. The integral
cross-section was found to be quite sensitive to the NN interaction employed
while the angular dependence showed less sensitivity. Approximately a 4% effect
was found for the one-body mechanism, for the three-nucleon dynamics in the p-d
channel, and for the inclusion of a large, possibly converged, number of
three-body partial states, indicating that these different aspects are of
comparable importance in the calculation of the spin-averaged observables.


  The Internet of Things is anticipated to participate in the execution of a
variety of complex tasks in the near future. IoT objects capable of handling
multiple sensing and actuating functions are the cornerstone of smart
applications such as smart buildings, smart factories, home automation, and
healthcare automation. These smart applications express their demands in terms
of high-level requests. These requests are characterised by the different
requirements of sensing actuating functions, processing and memory needs,
activation zones, latency, etc. In service-oriented architecture-based IoT,
application requests are translated into a business process BP workflow. In
this study, we model such a BP as a virtual network containing a set of virtual
nodes and links connected in a specific topology. These virtual nodes represent
the requested processing and location where sensing or actuation are needed.
The virtual links capture the requested communication requirements between
nodes. In this paper, we introduce a framework, optimised using mixed integer
linear programming MILP, that embeds the BPs from the virtual layer into a
lower-level implementation at the IoT physical layer. The proposed framework
results in a physical plan that optimally allocates the processing needed and
provisions the sensing and actuation at the required locations requirements to
an appropriate set of IoT nodes. The optimisation goal is to minimise the IoT
layer total power consumption and optimise the traffic distribution in a manner
that minimises the traffic latency of each IoT node. Our results show that the
proposed framework enhances the network performance by reducing the power
consumption and latency.


  Predicting on-road abnormalities such as road accidents or traffic violations
is a challenging task in traffic surveillance. If such predictions can be done
in advance, many damages can be controlled. Here in our wok, we tried to
formulate a solution for automated collision prediction in traffic surveillance
videos with computer vision and deep networks. It involves object detection,
tracking, trajectory estimation, and collision prediction. We propose an
end-to-end collision prediction system, named as COLLIDE-PRED, that
intelligently integrates the information of past and future trajectories of
moving objects to predict collisions in videos. It is a pipeline that starts
with object detection, which is used for object tracking, and then trajectory
prediction is performed which concludes by collision detection. The probable
place of collision, and the objects those may cause the collision, both can be
identified correctly with COLLIDE-PRED. The proposed method is experimentally
validated with a number of different videos and proves to be effective in
identifying accident in advance.


  Spectral features in the observed spectra of exoplanets depend on the
composition of their atmospheres. A good knowledge of the main atmospheric
processes that drive the chemical distribution is therefore essential to
interpret exoplanetary spectra. An atmosphere reaches chemical equilibrium if
the rates of the forward and backward chemical reactions converge to the same
value. However, there are atmospheric processes, such as atmospheric transport,
that destabilize this equilibrium. In this work we study the changes in
composition driven by a 3D wind field in WASP-43b using our Global Circulation
Model, THOR. Our model uses validated temperature- and pressure-dependent
chemical timescales that allow us to explore the disequilibrium chemistry of
CO, CO$_2$, H$_2$O and CH$_4$. In WASP-43b the formation of the equatorial jet
has an important impact in the chemical distribution of the different species
across the atmosphere. At low latitudes the chemistry is longitudinally
quenched, except for CO$_2$ at solar abundances. The polar vortexes have a
distinct chemical distribution since these are regions with lower temperature
and atmospheric mixing. Vertical and latitudinal mixing have a secondary impact
in the chemical transport. We determine graphically the effect of
disequilibrium on observed emission spectra. Our results do not show any
significant differences in the emission spectra between the equilibrium and
disequilibrium solutions for C/O = 0.5. However, if C/O is increased to 2.0,
differences in the spectra due to the disequilibrium chemistry of CH$_4$ become
non-negligible. In some spectral ranges the emission spectra can have more than
15$\%$ departures from the equilibrium solution.


  A new theoretical framework is proposed for the description of baryon
light-cone distribution amplitudes, based on the observation that their scale
dependence to leading logarithmic accuracy is described by a completely
integrable model. The physical interpretation is that one is able to find a new
quantum number that distinguishes partonic components in the nucleon with
different scale dependence.


  We present branching fraction and CP asymmetry results for a variety of
charmless B decays based on up to 124 fb^-1 collected by the BABAR experiment
running near the Upsilon(4S) resonance at the PEP-II e+e- B-factory.


  We present a study of the magnetic order and the structural stability of
two-dimensional quantum spin systems in the presence of spin-lattice coupling.
For a square lattice it is shown that the plaquette formation is the most
favourable form of static two-dimensional dimerization. We also demonstrate
that such distortions may coexist with long range magnetic order, in contrast
to the one-dimensional case. Similarly, the coupling to Einstein phonons is
found to reduce, but not to eliminate the staggered magnetic moment. In
addition, we consider the renormalization of the square lattice phonon spectrum
due to spin-phonon coupling in the adiabatic approximation. Towards low
temperatures significant softening mainly of zone boundary phonons is found,
especially around the $(\pi,0)$ point of the Brillouin zone. This result is
compatible with the tendency to plaquette formation in the static limit. We
also point out the importance of a "magnetic pressure" on the lattice due to
spin-phonon coupling. At low temperatures, this results in a tendency towards
shear instabilities of the lattice.


  In a Globular Cluster (GC), the mass loss during the red-giant branch (RGB)
phase and the helium content are fundamental ingredients to constrain the
horizontal branch (HB) morphology. While many papers have been dedicated to the
helium abundance in the different stellar populations, small efforts have been
done to disentangle the effects of mass loss and helium content. We exploit the
nearby GC NGC6121 (M4), which hosts two well-studied main stellar populations,
to infer both helium and RGB mass loss. We combine multi-band Hubble Space
Telescope photometry of RGB and main sequence (MS) stars of M4 with synthetic
spectra to constrain the relative helium content of its stellar populations. We
find that the second generation stars in M4 is enhanced in helium mass fraction
by $\rm \Delta Y = 0.013 \pm 0.002$ with respect to the remaining stars that
have pristine helium content. We then infer the mass of the HB stars by
searching for the best match between the observations and HB populations
modelled assuming the helium abundance of each population estimated from the
MS. By comparing the masses of stars along the HB, we constrain the mass loss
of first- and second-generation stars in M4. We find that the mass lost by the
helium enriched population is $\sim 13$% larger than the mass lost by the first
generation stars ($\rm \Delta \mu = 0.027 \pm 0.006 \ M_\odot$). We discuss the
possibility that this mass loss difference depends on helium abundance, the
different formation environment of the two generations, or a combination of
both.


  We apply round-off to planar rotations, obtaining a one-parameter family of
invertible maps of a two-dimensional lattice. As the angle of rotation
approaches pi/2, the fourth iterate of the map produces piecewise-rectilinear
motion, which develops along the sides of convex polygons.
  We characterise the dynamics ---which resembles outer billiards of
polygons---as the concatenation of so-called strip maps, each providing an
elementary perturbation of an underlying integrable system. Significantly,
there are orbits which are subject to an arbitrarily large number of these
perturbations during a single revolution, resulting in the appearance of a
novel discrete-space version of near-integrable Hamiltonian dynamics.
  We study the asymptotic regime of the limiting integrable system
analytically, and numerically some features of its very rich near-integrable
dynamics. We unveil a dichotomy: there is one regime in which the nonlinearity
tends to zero, and a second where it doesn't. In the latter case, numerical
experiments suggest that the distribution of the periods of orbits is
consistent with that of random dynamics; in the former case the fluctuations
result in an intricate structure of resonances.


  In this paper, I present a simple method of obtaining spin-polarised current
from a QPC with a large Rashba interaction. The origin of this spin
polarisation is the adiabatic evolution of spin "up" of the first QPC sub-band,
into spin "down" of the second QPC sub-band. Unique experimental signatures of
this effect can be obtained using a magnetic focusing setup, with the
characteristic "double" peak of spin-split magnetic focusing only present for
conductances $G>2e^2/h$. These particular magnetic focusing features are
present in recently publish experimental results. Finally, I consider hole
QPCs, where due to the particular kinematic structure of the Rashba
interaction, the required parameters are much less favourable for experimental
realisation.


  Cosmological phase transitions are predicted by Particle Physics models, and
have a variety of important cosmological consequences, which depend strongly on
the dynamics of the transition. In this work we investigate in detail the
general features of the development of a first-order phase transition. We find
thermodynamical constraints on some quantities that determine the dynamics,
namely, the latent heat, the radiation energy density and the false-vacuum
energy density. Using a simple model with a Higgs field, we study numerically
the amount and duration of supercooling and the subsequent reheating and phase
coexistence. We analyze the dependence of the dynamics on the different
parameters of the model, namely, the energy scale, the number of degrees of
freedom and the couplings of the scalar field with bosons and fermions. We also
inspect the implications for the cosmological outcomes of the phase transition.


  We classify the possibilities for the fixed field of the kernel of an
irreducible three-dimensional Artin representation of $\Q$ with solvable image
ramified at one prime by using the classification of the finite irreducible
subgroups of $\PGL_3(\C)$. This allows us to bound the number of such
representations with given Artin conductor.


  We consider a class of left-right symmetric model with enlarged gauge group
$SU(3)_c \times SU(3)_L \times SU(3)_R \times U(1)_X$ without having scalar
bitriplet. In the absence of scalar bitriplet, there is no Dirac mass term for
fermions including usual quarks and leptons. We introduce new isosinglet
vector-like fermions so that all the fermions get their masses through a
universal seesaw mechanism. We extend our discussion to neutrino mass and its
implications in neutrinoless double beta decay ($0\nu\beta\beta$). We show that
for TeV scale $SU(3)_R$ gauge bosons, the heavy-light neutrino mixing
contributes dominantly to $0\nu\beta\beta$ that can be observed at ongoing
experiments. Towards the end we also comment on different possible symmetry
breaking patterns of this enlarged gauge symmetry to that of the standard
model.


  Over the last decades, hand-crafted feature extractors have been used to
encode image visual properties into feature vectors. Recently, data-driven
feature learning approaches have been successfully explored as alternatives for
producing more representative visual features. In this work, we combine both
research venues, focusing on the color quantization problem. We propose two
data-driven approaches to learn image representations through the search for
optimized quantization schemes, which lead to more effective feature extraction
algorithms and compact representations. Our strategy employs Genetic Algorithm,
a soft-computing apparatus successfully utilized in
Information-retrieval-related optimization problems. We hypothesize that
changing the quantization affects the quality of image description approaches,
leading to effective and efficient representations. We evaluate our approaches
in content-based image retrieval tasks, considering eight well-known datasets
with different visual properties. Results indicate that the approach focused on
representation effectiveness outperformed baselines in all tested scenarios.
The other approach, which also considers the size of created representations,
produced competitive results keeping or even reducing the dimensionality of
feature vectors up to 25%.


  Small objects floating on a fluid have a tendency to aggregate due to
capillary forces. This effect has been used, with the help of a magnetic
induction field, to assemble submillimeter metallic spheres into a variety of
structures, whose shape and size can be tuned. Under time-varying fields, these
assemblies can propel themselves due to a breaking of time reversal symmetry in
their adopted shapes. In this article, we study the influence of an in-plane
rotation of the magnetic field on these structures. Various rotational modes
have been observed with different underlying mechanisms. The magnetic
properties of the particles cause them to rotate individually. Dipole-dipole
interactions in the assembly can cause the whole structure to align with the
field. Finally, non-reciprocal deformations can power the rotation of the
assembly. Symmetry plays an important role in the dynamics, as well as the
frequency and amplitude of the applied field. Understanding the interplay of
these effects is essential, both to explain previous observations and to
develop new functions for these assemblies.


  Numerical continuation is used to compute solution branches in a
two-component reaction-diffusion model of Leslie--Gower type. %in the vicinity
of a Turing-Hopf interaction. Two regimes are studied in detail. In the first,
the homogeneous state loses stability to supercritical spatially uniform
oscillations, followed by a subcritical steady state bifurcation of Turing
type. The latter leads to spatially localized states embedded in an oscillating
background that bifurcate from snaking branches of localized steady states.
Using two-parameter continuation we uncover a novel mechanism whereby
disconnected segments of oscillatory states zip up into a continuous snaking
branch of time-periodic localized states, some of which are stable. In the
second, the homogeneous state loses stability to supercritical Turing patterns,
but steady spatially localized states embedded either in the homogeneous state
or in a small amplitude Turing state are nevertheless present. We show that
such behavior is possible when sideband Turing states are strongly subcritical
and explain why this is so in the present model. In both cases the observed
behavior differs significantly from that expected on the basis of a
supercritical primary bifurcation.


  We use Legacy Survey photometric data to probe the stellar halo in multiple
directions of the sky using a probabilistic methodology to identify Blue
Horizontal Branch (BHB) stars. The measured average radial density profile
follows a double power law in the range $ 5 < r_{gc}/{\rm kpc} < 120$, with a
density break at $r_{gc}\approx20$ kpc. This description, however, falls short,
depending on the chosen line-of-sight, with some regions showing no signature
of a break in the profile and a wide range of density slopes, e.g. outer slope
$-5.5 \lesssim \alpha_{out} \lesssim -4$, pointing towards a highly anisotropic
stellar halo. This explains in part the wide range of density profiles reported
in the literature owing to different tracers and sky coverage. Using our
detailed 3-D stellar halo density map, we quantify the shape of the Pisces
overdensity associated with the transient wake response of the Galaxy's (dark)
halo to the Large Magellanic Cloud (LMC). Measured in the LMC's coordinate
system, Pisces stands above the background, is 60 degrees long and 25 degrees
wide and aligned with the LMC's orbit. This would correspond to a wake width of
$\sim 32$ kpc at $\sim 70$ kpc. We do not find a statistically significant
signature of the collective response in density as previously reported in the
literature measured with K giant stars, despite our larger numbers. We release
the catalogue constructed in this study with 95,446 possible BHB stars and
their BHB probability.


  In the field of Autonomous Vehicle (AV) development, having a robust yet
flexible infrastructure enables code to be continuously integrated and
deployed, which in turn accelerates the rapid prototyping process. The
platform-agnostic and scalable container infrastructure, often exploited by
developers in the cloud domain, presents a viable solution addressing this need
in AV development. Developers use tools such as Docker to build containers and
Kubernetes to setup container networks. This paper presents a container
infrastructure strategy for AV development, discusses the scenarios in which
this strategy is useful and performs an analysis on container boundary
overhead, and its impact on a Mix Critical System (MCS). An experiment was
conducted to compare both operation runtime and communication delay of running
a Gaussian Seidel Algorithm with I/O in four different environments: native OS,
new container, existing container, and nested container. The comparison reveals
that running in containers indeed adds a delay to signal response time, but
behaves more deterministically and that nested container does not stack up
delays but makes the process less deterministic. With these concerns in mind,
the developers may be more informed when setting up the container
infrastructure, and take full advantage of the new infrastructure while
avoiding some common pitfalls.


  We provide an experimental study of the existence of Herman rings in a
parametrized family of rational maps preserving antipodal points, and a
discussion of their properties on $\mathbb{RP}^2$. We study analytic maps of
the sphere that project to dianalytic maps on the nonorientable surface,
$\mathbb{RP}^2$. They have a known form and we focus on a subset of degree $3$
dianalytic maps and explore their dynamical properties. In particular, we focus
on maps for which the Fatou set has a Herman ring. We appeal to dynamical
properties of particular maps to justify our assertion that these Fatou
components are Herman rings and analyze the parameter space for this family of
maps.


  In this paper, we investigate a simple class of Horndeski models where the
scalar field plays the role of a k-essence fluid. We present several solutions
for early-time universe, namely inflation and cosmological bounce, by making
use of some reconstruction technique. Moreover, we furnish the formalism to
calculate perturbations in FRW space-time and we compute the spectral index and
the tensor-to-scalar ratio during inflation.


  The quantum phase difference across a superfluid Josephson-like weak link may
exhibit periodic motion describable by a nonlinear equation identical to that
of a rigid pendulum. We have directly observed this mode and find that the
phase oscillation frequency decreases toward zero as the phase amplitude
increases toward $\pi$. We also find that the low amplitude frequency is a
direct measure of the weak link's critical current in quantitative agreement
with theory.


  A light CP-even Higgs boson (h) with a mass of about 10 GeV could explain the
recent BNL measurement of the muon anomalous magnetic moment, in the framework
of a general CP-conserving two-Higgs-doublet extension of the Standard Model
with no tree-level flavor-changing neutral Higgs couplings. However, the
allowed Higgs mass window is quite small and the corresponding model parameters
are very constrained. The Higgs sector can contribute significantly to the
observed BNL result for g-2 without violating known experimental constraints
only if the hZZ coupling (approximately) vanishes and m_h lies between the
Upsilon mass and 2m_B.


  In this paper, we define a q-adic factorial and we demonstrate some
properties of a generalized p-adic gamma function. Also, some numerical
examples have been given


  We consider the Cauchy problem for the one-dimensional periodic cubic
nonlinear fractional Schr\"odinger equation (FNLS) with initial data
distributed via Gibbs measure. We construct global strong solutions with the
flow property to FNLS on the support of the Gibbs measure in the full
dispersive range, thus resolving a question proposed by Sun-Tzvetkov (2021). As
a byproduct, we prove the invariance of the Gibbs measure and almost sure
global well-posedness for FNLS.


  We provide a complete theoretical description of the two-neutrino electron
capture in $^{124}$Xe, improving both the nuclear and the atomic structure
calculations. We improve the general formalism through the use of the Taylor
expansion method, leading to higher order terms in the decay rate of the
process. The nuclear part is treated with pn-QRPA and interacting shell model
(ISM) methods. The nuclear matrix elements (NMEs) are calculated with the
pn-QRPA method with spin restoration by fixing the input parameters so that the
experimental decay rate is reproduced, resulting in values significantly lower
than in previous calculations. The validity of the pn-QRPA NMEs is tested by
showing their values to be comparable with the ones for double-beta decay with
emission of two electrons of $^{128,130}$Te, which have similar pairing
features. Within the ISM, we reproduce the total experimental half-life within
a factor of two and predict the capture fraction to the KK channel of about
74\%. We also predict the capture fractions to other decay channels and show
that for the cumulative decay to the $\rm{KL_{1}}$-$\rm{KO_{1}}$ channels, a
capture fraction of about 24\% could be observed experimentally. On the atomic
side, calculations are improved by accounting for the Pauli blocking of the
decay of innermost nucleon states and by considering all $s$-wave electrons
available for capture, expanding beyond the K and L$_1$ orbitals considered in
previous studies. We also provide improved atomic relaxation energies of the
final atomic states of $^{124}$Te, which may be used as input for background
modeling in liquid Xenon experiments.


  Despite CLIP being the foundation model in numerous vision-language
applications, the CLIP suffers from a severe text spotting bias. Such bias
causes CLIP models to `Parrot' the visual text embedded within images while
disregarding the authentic visual semantics. We uncover that in the most
popular image-text dataset LAION-2B, the captions also densely parrot (spell)
the text embedded in images. Our analysis shows that around 50% of images are
embedded with visual text content, and around 30% of captions words are in
these embedded visual content. Based on such observation, we thoroughly inspect
the different released versions of CLIP models and verify that the visual text
is the dominant factor in measuring the LAION-style image-text similarity for
these models. To examine whether these parrot captions shape the text spotting
bias, we train a series of CLIP models with LAION subsets curated by different
parrot-caption-oriented criteria. We show that training with parrot captions
easily shapes such bias but harms the expected visual-language representation
learning in CLIP models. This suggests that it is urgent to revisit either the
design of CLIP-like models or the existing image-text dataset curation pipeline
built on CLIP score filtering.


  In healthcare, artificial intelligence (AI) has been changing the way doctors
and health experts take care of people. This paper will cover how AI is making
major changes in the health care system, especially with nutrition. Various
machine learning and deep learning algorithms have been developed to extract
valuable information from healthcare data which help doctors, nutritionists,
and health experts to make better decisions and make our lifestyle healthy.
This paper provides an overview of the current state of AI applications in
healthcare with a focus on the utilization of AI-driven recommender systems in
nutrition. It will discuss the positive outcomes and challenges that arise when
AI is used in this field. This paper addresses the challenges to develop AI
recommender systems in healthcare, providing a well-rounded perspective on the
complexities. Real-world examples and research findings are presented to
underscore the tangible and significant impact AI recommender systems have in
the field of healthcare, particularly in nutrition. The ongoing efforts of
applying AI in nutrition lay the groundwork for a future where personalized
recommendations play a pivotal role in guiding individuals toward healthier
lifestyles.


  This paper focuses on the problem of modeling and estimating interaction
effects between covariates and a continuous treatment variable on an outcome,
using a single-index regression approach. The primary motivation is to estimate
an optimal individualized dose rule in an observational study. To model
possibly nonlinear interaction effects between patients' covariates and a
continuous treatment variable, we employ a two-dimensional penalized spline
regression on an index-treatment domain, where the index is defined as a linear
projection of the covariates. The method is illustrated using two applications
as well as simulation experiments. A unique contribution of this work is in the
parsimonious (single-index) parametrization specifically defined for the
interaction effect term.


  Voronoi diagrams are a fundamental geometric data structure for obtaining
proximity relations. We consider collections of axis-aligned orthogonal
polyhedra in two and three-dimensional space under the max-norm, which is a
particularly useful scenario in certain application domains. We construct the
exact Voronoi diagram inside an orthogonal polyhedron with holes defined by
such polyhedra. Our approach avoids creating full-dimensional elements on the
Voronoi diagram and yields a skeletal representation of the input object. We
introduce a complete algorithm in 2D and 3D that follows the subdivision
paradigm relying on a bounding-volume hierarchy; this is an original approach
to the problem. The complexity is adaptive and comparable to that of previous
methods. Under a mild assumption it is $O(n / \Delta + 1 / \Delta^2)$ in 2D or
$O(n\alpha^2 / \Delta^2 +1 / \Delta^3)$ in 3D, where $n$ is the number of
sites, namely edges or facets resp., $\Delta$ is the maximum cell size for the
subdivision to stop, and $\alpha$ bounds vertex cardinality per facet. We also
provide a numerically stable, open-source implementation in Julia, illustrating
the practical nature of our algorithm.


  Accurate image registration is pivotal in biomedical image analysis, where
selecting suitable registration algorithms demands careful consideration. While
numerous algorithms are available, the evaluation metrics to assess their
performance have remained relatively static. This study addresses this
challenge by introducing a novel evaluation metric termed Landmark Hit Rate
(HitR), which focuses on the clinical relevance of image registration accuracy.
Unlike traditional metrics such as Target Registration Error, which emphasize
subresolution differences, HitR considers whether registration algorithms
successfully position landmarks within defined confidence zones. This paradigm
shift acknowledges the inherent annotation noise in medical images, allowing
for more meaningful assessments. To equip HitR with label-noise-awareness, we
propose defining these confidence zones based on an Inter-rater Variance
analysis. Consequently, hit rate curves are computed for varying landmark zone
sizes, enabling performance measurement for a task-specific level of accuracy.
Our approach offers a more realistic and meaningful assessment of image
registration algorithms, reflecting their suitability for clinical and
biomedical applications.


  Time-averaged series of granulation images are analysed using COLIBRI, a
purpose-adapted version of a code originally developed to detect straight or
curvilinear features in aerospace images. The algorithm of image processing
utilises a nonparametric statistical criterion that identifies a straight-line
segment as a linear feature (lineament) if the photospheric brightness at a
certain distance from this line is on both sides stochastically lower or higher
than at the line itself. Curvilinear features can be detected as chains of
lineaments, using a criterion modified in some way. Once the input parameters
used by the algorithm are properly adjusted, the algorithm highlights
``ridges'' and ``trenches'' in the relief of the brightness field, drawing
white and dark lanes. The most remarkable property of the trenching patterns is
a nearly-universally-present parallelism of ridges and trenches. Since the
material upflows are brighter than the downflows, the alternating parallel
light and dark lanes should reflect the presence of roll convection in the
subphotospheric layers. If the numerous images processed by us are
representative, the patterns revealed suggest a widespread occurrence of roll
convection in the outer solar convection zone. In particular, the roll systems
could form the fine structure of larger-scale, supergranular and/or
mesogranular convection flows. Granules appear to be overheated blobs of
material that could develop in convection rolls due to some instabilities of
roll motion.


  We examine Sen's descent relations among (non-)BPS D-branes by using low
energy effective field theories of DpDpbar system. We find that the fluctuation
around the kink solution reproduces the low energy matter content on a non-BPS
D(p-1)-brane. The effective action for these fluctuation modes turns out to be
a generalization of Minahan-Zwiebach model. In addition, it is shown that the
fluctuations around the vortex solution consist of massless fields on a BPS
D(p-2)-brane and they are subject to Dirac-Born-Infeld action. We find the
universality that the above results do not refer to particular forms of the
effective action.


  The status of $N\Delta$ and $\Delta\Delta$ dibaryons introduced by Dyson and
Xuong in 1964 is briefly reviewed with focus on the d*(2380), tentatively
assigned as a $\Delta\Delta$ dibaryon resonance. It is argued that the
apparently small value of width, $\Gamma_{d^\ast}$$\approx$70 MeV, favors
hadronic structure for the d*(2380) dibaryon rather than a six-quark structure.


  We have investigated the poorly-understood origin of nitrogen in the early
Galaxy by determining N abundances in 35 extremely metal-poor halo giants (22
stars have [Fe/H]<-3.0) using the C and O abundances determined in Paper V.
Because any dredge-up of CNO processed material to the surface may complicate
the interpretation of CNO abundances in giants, we have also measured the
surface abundance of lithium. Our sample shows a clear dichotomy between two
groups of stars. The first group shows evidence of C to N conversion through CN
cycling and strong Li dilution, a signature of mixing. The second group shows
no evidence for C to N conversion, and Li is only moderately diluted, and we
conclude that their C and N abundances are very close to those of the gas from
which they formed in the early Galaxy. These "unmixed" stars reflect the
abundances in the early Galaxy: the [C/Fe] ratio is constant (about +0.2 dex)
and the [C/Mg] ratio is close to solar at low metallicity, favouring a high C
production by massive zero-metal supernovae. The [N/Fe] and [N/Mg] ratios
scatter widely. The larger values of these ratios define a flat upper plateau
([N/Mg]= 0.0, [N/Fe]= +0.1), which could reflect higher values within a wide
range of yields of zero-metal Sne II. Alternatively, by analogy with the DLA's,
the lower abundances ([N/Mg]= -1.1, [N/Fe]= -0.7) could reflect generally low
yields from the first Sne II, the other stars being N enhanced by winds of
massive Asymptotic Giant Branch (AGB) stars. At present it cannot be decided
whether primary N is produced primarily in SNe II or in massive AGB stars, or
in both. The stellar N abundances and [N/O] ratios are compatible with those
found in Damped Lyman-alpha (DLA) systems.


  We study the Greek and Roman mythology using the network theory. We construct
a directed network by using a dictionary of Greek and Roman mythology in which
the nodes represent the entries listed in the dictionary and we make
directional links from an entry to other entries that appear in its explanatory
part. We find that this network is clearly not a random network but a directed
scale-free network. Also measuring the various quantities which characterize
the mythology network, we analyze the Greek and Roman mythology and compare it
to other real networks.


  The object of the present paper is to study the locally $\phi $-
semisymmetric Kenmotsu manifolds along with the characterization of such
notion.


  Alternative designs to an electric-LC (ELC) resonator, which is a type of
metamaterial inclusion, are presented in this article. Fitting the resonator
with an interdigital capacitor (IDC) helps to increase the total capacitance of
the structure. In effect, its resonance frequency is shifted downwards. This
implies a decreased overall resonator size with respect to its operating
wavelength. As a result, the metamaterial, composed of an array of IDC-loaded
ELC resonators with their collective electromagnetic response, possesses
improved homogeneity and hence is less influenced by diffraction effects of
individual cells. The impact of incorporating an IDC into ELC resonators in
terms of the electrical size at resonance and other relevant properties are
investigated through both simulation and experiment.


  We present analysis of multiple Chandra and XMM-Newton spectra, separated by
9-19 years, of four of the youngest central compact objects (CCOs) with ages <
2500 yr: CXOU J232327.9+584842 (Cassiopeia A), CXOU J160103.1-513353
(G330.2+1.0), 1WGA J1713.4-3949 (G347.3-0.5), and XMMU J172054.5-372652
(G350.1-0.3). By fitting these spectra with thermal models, we attempt to
constrain each CCO's long-term cooling rate, composition, and magnetic field.
For the CCO in Cassiopeia A, 14 measurements over 19 years indicate a
decreasing temperature at a ten-year rate of 2.2+/-0.2 or 2.8+/-0.3 percent
(1sigma error) for a constant or changing X-ray absorption, respectively. We
obtain cooling rate upper limits of 17 percent for CXOU J160103.1-513353 and 6
percent for XMMU J172054.5-372652. For the oldest CCO, 1WGA J1713.4-3949, its
temperature seems to have increased by 4+/-2 percent over a ten year period.
Assuming each CCO's preferred distance and an emission area that is a large
fraction of the total stellar surface, a non-magnetic carbon atmosphere
spectrum is a good fit to spectra of all four CCOs. If distances are larger and
emission areas are somewhat smaller, then equally good spectral fits are
obtained using a hydrogen atmosphere with B <= 7x10^10 G or B >= 10^12 G for
CXOU J160103.1-513353, B <= 10^10 G or B >= 10^12 G for XMMU J172054.5-372652,
and non-magnetic hydrogen atmosphere for 1WGA J1713.4-3949. In a unified
picture of CCO evolution, our results suggest most CCOs, and hence a sizable
fraction of young neutron stars, have a surface magnetic field that is low
early in their life but builds up over several thousand years.


  We investigate the evolutionary dynamics of an age-structured population
under weak frequency-dependent selection. It turns out that the weak selection
is affected in a non-trivial way by the life-history trait. We can disentangle
the dynamics, based on the appearance of different time scales. These time
scales, which seem to form a universal structure in the interplay of weak
selection and life-history traits, allow us to reduce the infinite dimensional
model to a one-dimensional modified replicator equation. The modified
replicator equation is then used to investigate cooperation (the prisoner's
dilemma) by means of adaptive dynamics. We identify conditions under which age
structure is able to promote cooperation. At the end we discuss the relevance
of our findings.


  We tackle the tasks of automatically identifying comparative sentences and
categorizing the intended preference (e.g., "Python has better NLP libraries
than MATLAB" => (Python, better, MATLAB). To this end, we manually annotate
7,199 sentences for 217 distinct target item pairs from several domains (27% of
the sentences contain an oriented comparison in the sense of "better" or
"worse"). A gradient boosting model based on pre-trained sentence embeddings
reaches an F1 score of 85% in our experimental evaluation. The model can be
used to extract comparative sentences for pro/con argumentation in comparative
/ argument search engines or debating technologies.


  The paper presents the results of a study of the possibility of using the WKB
approach to describe Inhomogeneous Travelling-Wave Accelerating Sections
(ITWAS). This possibility not only simplifies the calculation, but also allows
the use of simpler physical models of transient processes. Using the traveling
wave concept simplifies the understanding of pulsed-excited ITWAS transients
and the development of methods to mitigate their effect on beam parameters.


  Despite the apparent simplicity of meson spectroscopy, light scalar mesons
cannot be accommodated in the usual $q\bar q$ structure. We study the
description of the scalar mesons below 2 GeV in terms of the mixing of a chiral
nonet of tetraquarks with conventional $q\bar q$ states. A strong
diquark-antidiquark component is found for several states. The consideration of
a glueball as dictated by quenched lattice QCD drives a coherent picture of the
isoscalar mesons.


  In addition to deep-water rogue waves which develop from the modulation
instability of an optical CW, wave propagation in optical fibers may also
produce shallow water rogue waves. These extreme wave events are generated in
the modulationally stable normal dispersion regime. A suitable phase or
frequency modulation of a CW laser leads to chirp-free and flat-top pulses or
flaticons which exhibit a stable self-similar evolution. Upon collision,
flaticons at different carrier frequencies, which may also occur in wavelength
division multiplexed transmission systems, merge into a single, high-intensity,
temporally and spatially localized rogue pulse.


  Incorporating both gain and loss into electromagnetic systems provides
possibilities to engineer effects in unprecedented ways. Concerning
electromagnetic effects in isotropic media that have concurrently electric and
magnetic responses, there is in fact a degree of freedom to distribute the gain
and loss in different effective material parameters. In this paper, we
analytically scrutinize wave interactions with those media, and, most
importantly, we contemplate the extreme scenario where such media are
anti-Hermitian. Considering various conditions for excitation, polarization,
and geometry, we uncover important effects and functionalities such as lasing
into both surface waves and propagating waves, conversion of evanescent source
fields to transmitted propagating waves, full absorption, and enhancing
backward to forward scattering ratio. We hope that these findings explicitly
show the potential of anti-Hermiticity to be used in optical physics as well as
microwave engineering for creating and using unconventional wave phenomena.


  Any satisfiability problem in conjunctive normal form can be solved in
polynomial time by reducing it to a 3-sat formulation and transforming this to
a Linear Complementarity problem (LCP) which is then solved as a linear program
(LP). Any instance in this problem class, reduced to a LCP may be solved,
provided certain necessary and sufficient conditions hold. The proof that these
conditions will be satisfied for all problems in this class is the contribution
of this paper and this derivation requires a nonlinear Instrumentalist
methodology rather than a Realistic one and confirms the advantages of a
Variational Inequalities implementation.


  We examine the relation between stellar mass, velocity dispersion, size,
S\'ersic index and $D_n4000$ for ~40,000 quiescent galaxies in the SDSS. At a
fixed stellar mass, galaxies with higher $D_n4000$ have larger velocity
dispersions and smaller sizes. $D_n4000$ is a proxy for stellar population age,
thus these trends suggest that older galaxies typically have larger velocity
dispersions and smaller sizes. We combine velocity dispersion and size into a
dynamical mass estimator, $\sigma^2 R$. At a fixed stellar mass, $\sigma^2 R$
depends on $D_n4000$. The S\'ersic index is also correlated with $D_n4000$. The
dependence of $\sigma^2 R$ and S\'ersic index on $D_n4000$ suggests that
quiescent galaxies are not structurally homologous systems. We derive an
empirical correction for non-homology which is consistent with the analytical
correction derived from the virial theorem. After accounting for non-homologous
galactic structure, we measure $M_\ast \propto M_d^{0.998 \pm 0.004}$ where
$M_\ast$ is the stellar mass and $M_d$ is the dynamical mass derived from the
velocity dispersion and size; stellar mass is directly proportional to
dynamical mass. Quiescent galaxies appear to be in approximate virial
equilibrium and deviations of the fundamental plane parameters from the
expected virial relation may result from mass-to-light ratio variations,
selection effects and the non-homology of quiescent galaxies. We infer the
redshift evolution of velocity dispersion and size for galaxies in our sample
assuming purely passive evolution. The inferred evolution is inconsistent with
direct measurements at higher redshifts. Thus quiescent galaxies do not
passively evolve. Quiescent galaxies have properties consistent with standard
galaxy formation in $\Lambda$CDM. They form at different epochs and evolve
modestly increasing their size, velocity dispersion and S\'ersic index after
they cease star formation.


  We perform a complete "Michel parameter" analysis of all possible helicity
structures which can appear in the process $B \to X_c \ell \bar{\nu}_\ell$. We
take into account the full set of operators parametrizing the effective
Hamiltonian and include the complete one-loop QCD corrections as well as the
non-perturbative contributions. The moments of the leptonic energy as well as
the combined moments of the hadronic energy and hadronic invariant mass are
calculated including the non-standard contributions.


  The Gromov-Wasserstein (GW) distance, rooted in optimal transport (OT)
theory, provides a natural framework for aligning heterogeneous datasets. Alas,
statistical estimation of the GW distance suffers from the curse of
dimensionality and its exact computation is NP hard. To circumvent these
issues, entropic regularization has emerged as a remedy that enables parametric
estimation rates via plug-in and efficient computation using Sinkhorn
iterations. Motivated by further scaling up entropic GW (EGW) alignment methods
to data dimensions and sample sizes that appear in modern machine learning
applications, we propose a novel neural estimation approach. Our estimator
parametrizes a minimax semi-dual representation of the EGW distance by a neural
network, approximates expectations by sample means, and optimizes the resulting
empirical objective over parameter space. We establish non-asymptotic error
bounds on the EGW neural estimator of the alignment cost and optimal plan. Our
bounds characterize the effective error in terms of neural network (NN) size
and the number of samples, revealing optimal scaling laws that guarantee
parametric convergence. The bounds hold for compactly supported distributions,
and imply that the proposed estimator is minimax-rate optimal over that class.
Numerical experiments validating our theory are also provided.


  The stochastic gradient descent (SGD) optimizers are generally used to train
the convolutional neural networks (CNNs). In recent years, several adaptive
momentum based SGD optimizers have been introduced, such as Adam, diffGrad,
Radam and AdaBelief. However, the existing SGD optimizers do not exploit the
gradient norm of past iterations and lead to poor convergence and performance.
In this paper, we propose a novel AdaNorm based SGD optimizers by correcting
the norm of gradient in each iteration based on the adaptive training history
of gradient norm. By doing so, the proposed optimizers are able to maintain
high and representive gradient throughout the training and solves the low and
atypical gradient problems. The proposed concept is generic and can be used
with any existing SGD optimizer. We show the efficacy of the proposed AdaNorm
with four state-of-the-art optimizers, including Adam, diffGrad, Radam and
AdaBelief. We depict the performance improvement due to the proposed optimizers
using three CNN models, including VGG16, ResNet18 and ResNet50, on three
benchmark object recognition datasets, including CIFAR10, CIFAR100 and
TinyImageNet. Code: https://github.com/shivram1987/AdaNorm.


  We demonstrate the distribution of polarization entangled photons of
wavelength 810 nm through standard telecom fibers. This technique allows
quantum communication protocols to be performed over established fiber
infrastructure, and makes use of the smaller and better performing setups
available around 800 nm, as compared to those which use telecom wavelengths
around 1550 nm. We examine the excitation and subsequent quenching of
higher-order spatial modes in telecom fibers up to 6 km in length, and perform
a distribution of high quality entanglement (visibility 95.6%). Finally, we
demonstrate quantum key distribution using entangled 810 nm photons over a 4.4
km long installed telecom fiber link.


  General-purpose multiprocessors (as, in our case, Intel IvyBridge and Intel
Haswell) increasingly add GPU computing power to the former multicore
architectures. When used for embedded applications (for us, Synthetic aperture
radar) with intensive signal processing requirements, they must constantly
compute convolution algorithms, such as the famous Fast Fourier Transform. Due
to its "fractal" nature (the typical butterfly shape, with larger FFTs defined
as combination of smaller ones with auxiliary data array transpose functions),
one can hope to compute analytically the size of the largest FFT that can be
performed locally on an elementary GPU compute block. Then, the full
application must be organized around this given building block size. Now, due
to phenomena involved in the data transfers between various memory levels
across CPUs and GPUs, the optimality of such a scheme is only loosely
predictable (as communications tend to overcome in time the complexity of
computations). Therefore a mix of (theoretical) analytic approach and
(practical) runtime validation is here needed. As we shall illustrate, this
occurs at both stage, first at the level of deciding on a given elementary FFT
block size, then at the full application level.


  In this paper we give an extension of the Birkhoff--Lewis theorem to some
semilinear PDEs. Accordingly we prove existence of infinitely many periodic
orbits with large period accumulating at the origin. Such periodic orbits
bifurcate from resonant finite dimensional invariant tori of the fourth order
normal form of the system. Besides standard nonresonance and nondegeneracy
assumptions, our main result is obtained assuming a regularizing property of
the nonlinearity. We apply our main theorem to a semilinear beam equation and
to a nonlinear Schr\"odinger equation with smoothing nonlinearity.


  In the first half of the present paper, we study higher-level generalizations
of differential modules in positive characteristic. These objects may be
regarded as ring-theoretic counterparts of vector bundles on a curve equipped
with an action of the ring of (logarithmic) differential operators of finite
level introduced by P. Berthelot (and C. Montagnon). The existence assertion
for a cyclic vector of a differential module is generalized to higher level
under mild conditions. In the second half, we introduce (dormant) opers of
level $N > 0$ on a pointed smooth curve whose structure group is either
$\mathrm{GL}_n$ or $\mathrm{PGL}_n$. Some of the results on higher-level
differential modules are applied to prove a duality theorem between dormant
$\mathrm{PGL}_n$-opers of level $N$ and dormant $\mathrm{PGL}_{p^N-n}$-opers of
level $N$. Finally, in the case where the underlying curve is a $3$-pointed
projective line, we establish a bijective correspondence between dormant
$\mathrm{PGL}_2$-opers of level $N$ and certain tamely ramified coverings.


  State space models in which the system state is a finite set--called the
multi-object state--have generated considerable interest in recent years.
Smoothing for state space models provides better estimation performance than
filtering by using the full posterior rather than the filtering density. In
multi-object state estimation, the Bayes multi-object filtering recursion
admits an analytic solution known as the Generalized Labeled Multi-Bernoulli
(GLMB) filter. In this work, we extend the analytic GLMB recursion to propagate
the multi-object posterior. We also propose an implementation of this so-called
multi-scan GLMB posterior recursion using a similar approach to the GLMB filter
implementation.


  Generating realistic talking faces is a complex and widely discussed task
with numerous applications. In this paper, we present DiffTalker, a novel model
designed to generate lifelike talking faces through audio and landmark
co-driving. DiffTalker addresses the challenges associated with directly
applying diffusion models to audio control, which are traditionally trained on
text-image pairs. DiffTalker consists of two agent networks: a
transformer-based landmarks completion network for geometric accuracy and a
diffusion-based face generation network for texture details. Landmarks play a
pivotal role in establishing a seamless connection between the audio and image
domains, facilitating the incorporation of knowledge from pre-trained diffusion
models. This innovative approach efficiently produces articulate-speaking
faces. Experimental results showcase DiffTalker's superior performance in
producing clear and geometrically accurate talking faces, all without the need
for additional alignment between audio and image features.


  Most concurrent blockchain systems rely heavily on the Proof-of-Work (PoW) or
Proof-of-Stake (PoS) mechanisms for decentralized consensus and security
assurance. However, the substantial energy expenditure stemming from
computationally intensive yet meaningless tasks has raised considerable
concerns surrounding traditional PoW approaches, The PoS mechanism, while free
of energy consumption, is subject to security and economic issues. Addressing
these issues, the paradigm of Proof-of-Useful-Work (PoUW) seeks to employ
challenges of practical significance as PoW, thereby imbuing energy consumption
with tangible value. While previous efforts in Proof of Learning (PoL) explored
the utilization of deep learning model training SGD tasks as PoUW challenges,
recent research has revealed its vulnerabilities to adversarial attacks and the
theoretical hardness in crafting a byzantine-secure PoL mechanism. In this
paper, we introduce the concept of incentive-security that incentivizes
rational provers to behave honestly for their best interest, bypassing the
existing hardness to design a PoL mechanism with computational efficiency, a
provable incentive-security guarantee and controllable difficulty.
Particularly, our work is secure against two attacks to the recent work of Jia
et al. [2021], and also improves the computational overhead from $\Theta(1)$ to
$O(\frac{\log E}{E})$. Furthermore, while most recent research assumes trusted
problem providers and verifiers, our design also guarantees frontend
incentive-security even when problem providers are untrusted, and verifier
incentive-security that bypasses the Verifier's Dilemma. By incorporating ML
training into blockchain consensus mechanisms with provable guarantees, our
research not only proposes an eco-friendly solution to blockchain systems, but
also provides a proposal for a completely decentralized computing power market
in the new AI age.


  With the aim of investigating the presence of molecular and dust clumps
linked to two star forming regions identified in the expanding molecular
envelope of the stellar wind bubble RCW78, we analyzed the distribution of the
molecular gas and cold dust. To accomplish this study we performed dust
continuum observations at 870 \mu m and 13CO(2-1) line observations with the
APEX telescope, using LABOCA and SHeFI-1 instruments, respectively, and
analyzed Herschel images at 70, 160, 250, 350, and 500 \mu m. These
observations allowed us to identify cold dust clumps linked to region B (named
the Southern clump) and region C (clumps 1 and 2) and an elongated Filament.
Molecular gas was clearly detected linked to the Southern clump and the
Filament. The velocity of the molecular gas is compatible with the location of
the dense gas in the expanding envelope of RCW78. We estimate dust temperatures
and total masses for the dust condensations from the emissions at different
wavelengths in the far-IR and from the molecular line using LTE and the virial
theorem. Masses obtained through different methods agree within a factor of
2-6. CC-diagrams and SED analysis of young stellar objects confirmed the
presence of intermediate and low mass YSOs in the dust regions, indicating that
moderate star formation is present. In particular, a cluster of IR sources was
identified inside the Southern clump. The IRAC image at 8 \mu m revealed the
existence of an infrared dust bubble of 16 arcsec in radius probably linked to
the O-type star HD117797 located at 4 kpc. The distribution of the near and mid
infrared emission indicate that warm dust is associated with the bubble.


  In considering a class of quasilinear elliptic equations on a Riemannian
manifold with nonnegative Ricci curvature, we give a new proof of Tolksdorf's
result on the construction of separable $p$-harmonic functions in a cone.


  A technique is proposed to generate attosecond pulse trains of radiation from
a Free-Electron Laser amplifier. The optics-free technique synthesises a comb
of longitudinal modes by applying a series of spatio-temporal shifts between
the co-propagating radiation and electron bunch in the FEL. The modes may be
phase-locked by modulating the electron beam energy at the mode spacing
frequency. Three-dimensional simulations demonstrate the generation of a train
of 400as pulses at giga-watt power levels evenly spaced by 2.5fs at a
wavelength of 124 Angstrom. In the X-ray at wavelength 1.5 Angstrom, trains of
23as pulses evenly spaced by 150as and of peak power up to 6GW are predicted.


  Text-driven 3D stylization is a complex and crucial task in the fields of
computer vision (CV) and computer graphics (CG), aimed at transforming a bare
mesh to fit a target text. Prior methods adopt text-independent multilayer
perceptrons (MLPs) to predict the attributes of the target mesh with the
supervision of CLIP loss. However, such text-independent architecture lacks
textual guidance during predicting attributes, thus leading to unsatisfactory
stylization and slow convergence. To address these limitations, we present
X-Mesh, an innovative text-driven 3D stylization framework that incorporates a
novel Text-guided Dynamic Attention Module (TDAM). The TDAM dynamically
integrates the guidance of the target text by utilizing text-relevant spatial
and channel-wise attentions during vertex feature extraction, resulting in more
accurate attribute prediction and faster convergence speed. Furthermore,
existing works lack standard benchmarks and automated metrics for evaluation,
often relying on subjective and non-reproducible user studies to assess the
quality of stylized 3D assets. To overcome this limitation, we introduce a new
standard text-mesh benchmark, namely MIT-30, and two automated metrics, which
will enable future research to achieve fair and objective comparisons. Our
extensive qualitative and quantitative experiments demonstrate that X-Mesh
outperforms previous state-of-the-art methods.


  Kernel based methods provide a way to reconstruct potentially
high-dimensional functions from meshfree samples, i.e., sampling points and
corresponding target values. A crucial ingredient for this to be successful is
the distribution of the sampling points. Since the computation of an optimal
selection of sampling points may be an infeasible task, one promising option is
to use greedy methods.
  Although these methods may be very effective, depending on the specific
greedy criterion the chosen points might quickly lead to instabilities in the
computation. To circumvent this problem, we introduce and investigate a new
class of \textit{stabilized} greedy kernel algorithms, which can be used to
create a scale of new selection strategies.
  We analyze these algorithms, and in particular we prove convergence results
and quantify in a precise way the distribution of the selected points. These
results allow to prove, in the case of certain Sobolev kernels, that the
algorithms have optimal stability and optimal convergence rates, including for
functions outside the native space of the kernel. The results also apply to the
case of the usual $P$-greedy algorithm, significantly improving
state-of-the-art results available in the literature. Illustrative experiments
are presented that support the theoretical findings.


  We analyze the branching ratios of B to D(*) + Ds0*(Ds1) decays using the
factorization hypothesis. The B to D(*) transition form factors are taken from
a model-independent analysis done by Caprini, Lellouch and Neubert based on
heavy quark spin symmetry and dispersive constraints, including short-distance
and power corrections. The leptonic decay constants fDs0* and fDs1 are
calculated assuming a molecular structure for the Ds0* and Ds1 mesons. The
calculated branching ratios of B-meson two-body decays are compared with
experimental data and other theoretical results.


  We introduce a simple and efficient text-controllable high-fidelity music
generation and editing model. It operates on sequences of continuous latent
representations from a low frame rate 48 kHz stereo variational auto encoder
codec that eliminates the information loss drawback of discrete
representations. Based on a diffusion transformer architecture trained on a
flow-matching objective the model can generate and edit diverse high quality
stereo samples of variable duration, with simple text descriptions. We also
explore a new regularized latent inversion method for zero-shot test-time
text-guided editing and demonstrate its superior performance over naive
denoising diffusion implicit model (DDIM) inversion for variety of music
editing prompts. Evaluations are conducted on both objective and subjective
metrics and demonstrate that the proposed model is not only competitive to the
evaluated baselines on a standard text-to-music benchmark - quality and
efficiency-wise - but also outperforms previous state of the art for music
editing when combined with our proposed latent inversion. Samples are available
at https://melodyflow.github.io.


  To improve the global optimization ability of traditional GEP algorithm, a
Multicellular gene expression programming algorithm based on fuzzy control
(Multicellular GEP Algorithm Based On Fuzzy Control, MGEP-FC) is proposed. The
MGEP-FC algorithm describes the size of cross rate, mutation rate and real
number mutation rate by constructing fuzzy membership function. According to
the concentration and dispersion of individual fitness values in population,
the crossover rate, mutation rate and real number set mutation rate of genetic
operation are dynamically adjusted. In order to make the diversity of the
population continue in the iterative process, a new genetic operation scheme is
designed, which combines the new individuals with the parent population to
build a temporary population, and the diversity of the temporary and
subpopulation are optimized. The results of 12 Benchmark optimization
experiments show that the MGEP-FC algorithm has been greatly improved in
stability, global convergence and optimization speed.


  We extend the definition of curvature homogeneity of type (1,3) to include
the possibility that there is a homothety between any two points of a manifold
preserving the first r covariant derivatives of the curvature operator
simultaneously; we call this strong curvature homogeneity of type (1,3) up to
order r. We characterize these properties in terms of model spaces. In
addition, we also present two families of three-dimensional Lorentzian metrics
on Euclidean space to exhibit the behavior of this property. The first example
is curvature homogeneous of type (1,3) of all orders, but is not locally
homogeneous. Within this first family, being strongly curvature homogeneous of
type (1,3) up to order 1 implies local homogeneity. The second example is
strongly curvature homogeneous of type (1,3) up to order one, and is not
locally homogeneous, showing that this new definition is not a trivial one.
Within this family, being strongly curvature homogeneous of type (1,3) up to
order 2 implies local homogeneity.


  We study the relation between Chern numbers and Quantum Phase Transitions
(QPT) in the XY spin-chain model. By coupling the spin chain to a single spin,
it is possible to study topological invariants associated to the coupling
Hamiltonian. These invariants contain global information, in addition to the
usual one (obtained by integrating the Berry connection around a closed loop).
We compute these invariants (Chern numbers) and discuss their relation to QPT.
In particular we show that Chern numbers can be used to label regions
corresponding to different phases.


  In the present paper we find optimal conditions separating the regular case
from the one with Lavrentiev gap for the borderline case of double phase
potencial and related general classes of integrands. We present new results on
density of smooth functions.


  We present a theoretical description of the dynamics of a semi-flexible
polymer being pulled through a nanopore by an external force acting at the
pore. Our theory is based on the tensile blob picture of Pincus in which the
front of the tensile force propagates through the backbone of the polymer, as
suggested by Sakaue and recently applied to study a completely flexible polymer
with self-avoidance, by Dubbledam et al. For a semi-flexible polymer with a
persistence length P , its statistics is self-avoiding for a very long chain.
As the local force increases, the blob size starts to decrease. At the blob
size P/a^2 , where a is the size of a monomer, the statistics becomes that of
an ideal chain. As the blob size further decreases to below the persistence
length P, the statistics is that of a rigid rod. We argue that semi-flexible
polymer in translocation should include the three regions: a self-avoiding
region, an ideal chain region and a rigid rod region, under uneven tension
propagation, instead of a uniform scaling picture as in the case of a
completely flexible polymer. In various regimes under the effect of weak,
intermediate and strong driving forces we derive equations from which we can
calculate the translocation time of the polymer. The translocation exponent is
given by \alpha=1+\mu, where \mu is an effective exponent for the end-to-end
distance of the semi-flexible polymer, having a value between 1/2 and 3/5,
depending on the total contour length of the polymer. Our results are of
relevance for forced translocation of biological polymers such as DNA through a
nanopore.


  An embedded manifold is dual defective if its dual variety is not a
hypersurface. Using the geometry of the variety of lines through a general
point, we characterize scrolls among dual defective manifolds. This leads to an
optimal bound for the dual defect, which improves results due to Ein. Among
other things we also provide a short and easy proof of the famous Landman
Parity Theorem for dual defective manifolds based on our approach to the
subject. We also discuss our conjecture that every dual defective manifold with
cyclic Picard group should be secant defective, of a very special type, namely
a local quadratic entry locus variety.


  In this paper we provide examples of topological dynamical systems having
either finite or countable scrambled sets. In particular we study conditions
for the existence of Li-Yorke, asymptotic and distal pairs in constant--length
substitution dynamical systems. Starting from a circle rotation we also
construct a dynamical system having Li--Yorke pairs, none of which is
recurrent.


  Brain age prediction models have succeeded in predicting clinical outcomes in
neurodegenerative diseases, but can struggle with tasks involving faster
progressing diseases and low quality data. To enhance their performance, we
employ a semi-supervised diffusion model, obtaining a 0.83(p<0.01) correlation
between chronological and predicted age on low quality T1w MR images. This was
competitive with state-of-the-art non-generative methods. Furthermore, the
predictions produced by our model were significantly associated with survival
length (r=0.24, p<0.05) in Amyotrophic Lateral Sclerosis. Thus, our approach
demonstrates the value of diffusion-based architectures for the task of brain
age prediction.


  This note shows the equivalence of two projection operators which both can be
used in cylindrical algebraic decomposition (CAD) . One is known as Brown's
Projection (C. W. Brown (2001)); the other was proposed by Lu Yang in his
earlier work (L.Yang and S.~H. Xia (2000)) that is sketched as follows: given a
polynomial $f$ in $x_1,\,x_2,\,\cdots$, by $f_1$ denote the resultant of $f$
and its partial derivative with respect to $x_1$ (removing the multiple
factors), by $f_2$ denote the resultant of $f_1$ and its partial derivative
with respect to $x_2$, (removing the multiple factors), $\cdots$, repeat this
procedure successively until the last resultant becomes a univariate
polynomial. Making use of an identity, the equivalence of these two projection
operators is evident.


  The ${\cal O}(\alpha_s)$ QCD corrections to the three-body decay width of the
charged Higgs $\Gamma$($H^+\to W^+b\bar{b}$) are discussed in the MSSM model.
Our calculations indicate that the standard QCD corrections to the three-body
decay mode raise the width by about 12% and the supersymmetric QCD
corrections(due to $\tilde{g}, \tilde{t}, \tilde{b}$ exchanges) can be
comparable to or even larger than the standard QCD corrctions in some regions
of the supersymmetric parameter space. This is mainly due to the effect of
large left-right mixing of stop($\tilde{t}$). It could significantly affect the
phenomenology of the $H^+$ search.


  Full-duplex (FD) wireless can significantly enhance spectrum efficiency but
requires effective self-interference (SI) cancellers. RF SI cancellation (SIC)
via frequency-domain equalization (FDE), where bandpass filters channelize the
SI, is suited for integrated circuits (ICs). In this paper, we explore the
limits and higher layer challenges associated with using such cancellers. We
evaluate the performance of a custom FDE-based canceller using two testbeds;
one with mobile FD radios and the other with upgraded, static FD radios in the
PAWR COSMOS testbed. The latter is a lasting artifact for the research
community, alongside a dataset containing baseband waveforms captured on the
COSMOS FD radios, facilitating FD-related experimentation at the higher
networking layers. We evaluate the performance of the FDE-based FD radios in
both testbeds, with experiments showing 95 dB overall achieved SIC (52 dB from
RF SIC) across 20 MHz bandwidth, and an average link-level FD rate gain of
1.87x. We also conduct experiments in (i) uplink-downlink networks with
inter-user interference, and (ii) heterogeneous networks with half-duplex and
FD users. The experimental FD gains in the two types of networks depend on the
users' SNR values and the number of FD users, and are 1.14x-1.25x and
1.25x-1.73x, respectively, confirming previous analytical results.


  We examine the radial asymptotic behavior of spherically symmetric
Lemaitre-Tolman-Bondi dust models by looking at their covariant scalars along
radial rays, which are spacelike geodesics parametrized by proper length
$\ell$, orthogonal to the 4-velocity and to the orbits of SO(3). By introducing
quasi-local scalars defined as integral functions along the rays, we obtain a
complete and covariant representation of the models, leading to an initial
value parametrization in which all scalars can be given by scaling laws
depending on two metric scale factors and two basic initial value functions.
Considering regular "open" LTB models whose space slices allow for a diverging
$\ell$, we provide the conditions on the radial coordinate so that its
asymptotic limit corresponds to the limit as $\ell\to\infty$. The "asymptotic
state" is then defined as this limit, together with asymptotic series expansion
around it, evaluated for all metric functions, covariant scalars (local and
quasi-local) and their fluctuations. By looking at different sets of initial
conditions, we examine and classify the asymptotic states of parabolic,
hyperbolic and open elliptic models admitting a symmetry center. We show that
in the radial direction the models can be asymptotic to any one of the
following spacetimes: FLRW dust cosmologies with zero or negative spatial
curvature, sections of Minkowski flat space (including Milne's space), sections
of the Schwarzschild--Kruskal manifold or self--similar dust solutions.


  The Ramsey number $r_k(s,n)$ is the minimum $N$ such that every red-blue
coloring of the $k$-subsets of $\{1, \ldots, N\}$ contains a red set of size
$s$ or a blue set of size $n$, where a set is red (blue) if all of its
$k$-subsets are red (blue). A $k$-uniform \emph{tight path} of size $s$,
denoted by $P_{s}$, is a set of $s$ vertices $v_1 < \cdots < v_{s}$ in
$\mathbb{Z}$, and all $s-k+1$ edges of the form $\{v_j,v_{j+1},\ldots, v_{j + k
-1}\}$. Let $r_k(P_s, n)$ be the minimum $N$ such that every red-blue coloring
of the $k$-subsets of $\{1, \ldots, N\}$ results in a red $P_{s}$ or a blue set
of size $n$. The problem of estimating both $r_k(s,n)$ and $r_k(P_s, n)$ for
$k=2$ goes back to the seminal work of Erdos and Szekeres from 1935, while the
case $k\ge 3$ was first investigated by Erdos and Rado in 1952.
  In this paper, we deduce a quantitative relationship between multicolor
variants of $r_k(P_s, n)$ and $r_k(n, n)$. This yields several consequences
including the following:
  (1) We determine the correct tower growth rate for both $r_k(s,n)$ and
$r_k(P_s, n)$ for $s \ge k+3$. The question of determining the tower growth
rate of $r_k(s,n)$ for all $s \ge k+1$ was posed by Erdos and Hajnal in 1972.
  (2) We show that determining the tower growth rate of $r_k(P_{k+1}, n)$ is
equivalent to determining the tower growth rate of $r_k(n,n)$, which is a
notorious conjecture of Erdos, Hajnal and Rado from 1965 that remains open.
  Some related off-diagonal hypergraph Ramsey problems are also explored.


  We apply minimal weakly generating sets to study the existence of
Add$(U_R)$-covers for a uniserial module $U_R$. If $U_R$ is a uniserial right
module over a ring $R$, then $S:=$End$ (U_R)$ has at most two maximal (right,
left, two-sided) ideals: one is the set $I$ of all endomorphisms that are not
injective, and the other is the set $K $ of all endomorphisms of $U_R$ that are
not surjective. We prove that if $U_R$ is either finitely generated, or
artinian, or $I \subset K$, then the class Add$(U_R)$ is covering if and only
if it is closed under direct limit. Moreover, we study endomorphism rings of
artinian uniserial modules giving several examples.


  We characterize the weights for which we have the boundedness of standard
weighted integral operators induced by the Bergman-Besov kernels acting between
two general weighted Lebesgue classes on the unit ball of $\mathbb{C}^N$ in
terms of B\'ekoll\'e - Bonami type condition on the weights. To accomplish this
we employ the proof strategy originated by B\'ekoll\'e.


  The effective action for reggeized gluons is based on the gluodynamic
Yang-Mills Lagrangian with external current for longitudinal gluons added, see
[1]. On the base of classical solutions, obtained in [2], the one-loop
corrections to this effective action in light-cone gauge are calculated. The
RFT calculus for reggeized gluons similarly to the RFT introduced in [3] is
proposed and discussed. The correctness of the results is verified by
calculation of the propagator of $A_{+}$ and $A_{-}$ reggeized gluons fields
and application of the obtained results is discussed as well.


  We study integrable models solvable by the nested algebraic Bethe ansatz and
possessing the GL(3)-invariant R-matrix. We consider a composite model where
the total monodromy matrix of the model is presented as a product of two
partial monodromy matrices. Assuming that the last ones can be expanded into
series with respect to the inverse spectral parameter we calculate matrix
elements of the local operators in the basis of the transfer matrix
eigenstates. We obtain determinant representations for these matrix elements.
Thus, we solve the inverse scattering problem in a weak sense.


  We derive an off-shell formulation for the boundary Fayet-Iliopoulos (FI)
terms in locally supersymmetric U(1) gauge theory on 5D $S^1/Z_2$ orbifold.
Some physical consequences of such FI terms, e.g., the supersymmetry breaking
and the generation of 5D kink mass for hypermultiplet are studied within the
full supergravity framework. We especially find that the supersymmetry is
broken by the FI term without charged hypermultiplet for models giving an
AdS$_5$ geometry.


  In military organizations, Cyber Threat Intelligence (CTI) supports
cyberspace operations by providing the commander with essential information
about the adversary, their capabilities and objectives as they operate through
cyberspace. This paper, combines CTI with the MITRE ATT&CK framework in order
to establish an adversary profile. In addition, it identifies the
characteristics of the attack phase by analyzing the WhisperGate operation that
occurred in Ukraine in January 2022, and suggests the minimum essential
measures for defense.


  We consider a linear time-invariant system in discrete time where the state
and input signals satisfy a set of integral quadratic constraints (IQCs).
Analogous to the autonomous linear systems case, we define a new notion of
spectral radius that exactly characterizes stability of this system. In
particular, (i) when the spectral radius is less than one, we show that the
system is asymptotically stable for all trajectories that satisfy the IQCs, and
(ii) when the spectral radius is equal to one, we construct an unstable
trajectory that satisfies the IQCs. Furthermore, we connect our new definition
of the spectral radius to the existing literature on IQCs.


  Arbarello, de Concini, and Kac have constructed a central extension of the
ideles group on a smooth projective algebraic curve. We show a relation of this
central extension with the theta-bundle and the Poincare biextension of the
Jacobian of the curve. As an application we get a new proof of the adelic
formula for the Weil pairing.


  Double perovskite oxides have gained in importance and exhibit negative
magnetoresistance, which is known as colossal magnetoresistance (CMR) effect.
Using a La$_2$CoMnO$_6$ (LCM) thin film we prove that the physical consequences
of the CMR effect do also influence the electron energy loss spectrometry
(EELS) signal. We observe a change of the band gap at low energy losses and are
able to study the magnetisation with chemical sensitivity by employing energy
loss magnetic chiral dichroism (EMCD) below the Curie temperature T$_C$ where
the CMR effect becomes significant.


  We extend to metrizable locally compact groups Rosenthal's theorem describing
those Banach spaces containing no copy of $l_1$. For that purpose, we transfer
to general locally compact groups the notion of interpolation ($I_0$) set,
which was defined by Hartman and Ryll-Nardzewsky [25] for locally compact
abelian groups. Thus we prove that for every sequence $\lbrace g_n
\rbrace_{n<\omega}$ in a locally compact group $G$, then either $\lbrace g_n
\rbrace_{n<\omega}$ has a weak Cauchy subsequence or contains a subsequence
that is an $I_0$ set. This result is subsequently applied to obtain sufficient
conditions for the existence of Sidon sets in a locally compact group $G$, an
old question that remains open since 1974 (see [32] and [20]). Finally, we show
that every locally compact group strongly respects compactness extending
thereby a result by Comfort, Trigos-Arrieta, and Wu [13], who established this
property for abelian locally compact groups.


  In this paper the permanent profile waves governed by a Boussinesq-type wave
equation are analysed. The model involves displacement-type nonlinearities and
dispersion terms. Physically such a model equation describes longitudinal waves
(density change) in biomembranes which have an internal structure composed by
lipid molecules. The possible solutions are constructed and analysed. The phase
plane analysis and numerical simulation reveal a novel phenomenon: the possible
existence of a soliton doublet.


  A review of the main recent results on top quark production from the ATLAS
and CMS experiments is presented. Results on both electroweak single top quark
production and strong top pair production are presented.


  We report on the synthesis and physical properties of the new ternary
intermetallic Ce$_2$Rh$_2$Ga. Its formation and dimorphism have been
investigated by powder and single crystal X-ray diffractometry, as well as by
differential thermal analyses. LT- and HT-Ce$_2$Rh$_2$Ga can be obtained by the
chosen respective thermal treatment. The high-temperature form
(HT-Ce$_2$Rh$_2$Ga), stable above 864(5){\deg}C, is orthorhombic La2Ni3-type
[Cmce, oS20, a=5.851(2) {\AA}, b=9.618 (2) {\AA}, c=7.487 (2) {\AA}, V=421.3(2)
{\AA}3]; the low-temperature form (LT-Ce$_2$Rh$_2$Ga), stable below this
temperature, is monoclinic Pr2Co2Al- (Ca2Ir2Si-) type [C2/c, mS20, a=10.0903(6)
A, b=5.6041(3) A, c=7.8153(4) A, beta=104.995(3) degrees, V=426.88(4) A3]. The
magnetic measurements were conducted on two different samples, namely on the
LT-Ce$_2$Rh$_2$Ga and the other on the HT-Ce$_2$Rh$_2$Ga sample. The
HT-Ce$_2$Rh$_2$Ga compound is found to exhibit a phase transition at 128.5 K.
By virtue of the sharp peak anomaly in the temperature dependence of the
magnetic susceptibility this phase transition is plausibly of antiferromagnetic
origin, but occurs at a remarkably high temperature compared to what is typical
for Ce binary and ternary compounds. LT- Ce$_2$Rh$_2$Gaa has a ground state of
ferromagnetic nature which sets in at a paramagnetic-to-ferromagnetic phase
transition at 5.2 K.


  Segmentation of an object from a video is a challenging task in multimedia
applications. Depending on the application, automatic or interactive methods
are desired; however, regardless of the application type, efficient computation
of video object segmentation is crucial for time-critical applications;
specifically, mobile and interactive applications require near real-time
efficiencies. In this paper, we address the problem of video segmentation from
the perspective of efficiency. We initially redefine the problem of video
object segmentation as the propagation of MRF energies along the temporal
domain. For this purpose, a novel and efficient method is proposed to propagate
MRF energies throughout the frames via bilateral filters without using any
global texture, color or shape model. Recently presented bi-exponential filter
is utilized for efficiency, whereas a novel technique is also developed to
dynamically solve graph-cuts for varying, non-lattice graphs in general linear
filtering scenario. These improvements are experimented for both automatic and
interactive video segmentation scenarios. Moreover, in addition to the
efficiency, segmentation quality is also tested both quantitatively and
qualitatively. Indeed, for some challenging examples, significant time
efficiency is observed without loss of segmentation quality.