  We calculate the production of prompt and thermal photons from Pb+Pb
collisions at 5.02A TeV at the Large Hadron Collider (LHC) and at 39A TeV at
the proposed Future Circular Collider (FCC) facility. The photon spectra and
anisotropic flow at these energies are compared with the results obtained from
2.76A TeV Pb+Pb collisions at the LHC for three different centrality bins. The
prompt photons originating from initial hard scatterings are found to increase
by a factor of 1.5 to 2 at 5.02A TeV in the $p_T$ region 2 to 15 GeV and the
enhancement is found to be about 5 to 15 times at FCC energy compared to 2.76A
TeV in the same $p_T$ region. The evolution of the Quark-Gluon Plasma (QGP)
formed in Pb+Pb collisions at LHC and FCC energies are studied using a
hydrodynamical model and the $p_T$ spectra and elliptic flow of thermal photons
are calculated using state-of-the-art photon rates. The relative enhancement in
the production of thermal photons is found to be more compared to prompt
photons at FCC than at the LHC energies. Although the production of direct
(prompt+thermal) photons is found to enhance significantly with increase in
beam energy, the photon elliptic flow increases only marginally and does not
show strong sensitivity to the collision energy.


  Let $r(k)$ denote the maximum number of edges in a $k$-uniform intersecting
family with covering number $k$. Erd\H{o}s and Lov\'asz proved that $ \lfloor
k! (e-1) \rfloor \leq r(k) \leq k^k.$ Frankl, Ota, and Tokushige improved the
lower bound to $r(k) \geq \left( k/2 \right)^{k-1}$, and Tuza improved the
upper bound to $r(k) \leq (1-e^{-1}+o(1))k^k$. We establish that $ r(k) \leq (1
+ o(1)) k^{k-1}$.


  Breakthroughs in physics and astrophysics are often driven by technological
advances, with the recent detection of gravitational waves being one such
example. This white paper focuses upon how improved astrometric and
spectroscopic measurements from a new generation of precise, accurate, and
stable astronomical instrumentation can address two of the fundamental
mysteries of our time -- dark energy and dark matter -- and probe the nature of
spacetime. Instrumentation is now on the cusp of enabling new cosmological
measurements based on redshifts (cosmic redshift drift) and extremely precise
time-series measurements of accelerations, astrophysical source positions
(astrometry), and angles (cosmic parallax). These allow tests of the
fundamental framework of the universe (the Friedmann equations of general
relativity and whether cosmic expansion is physically accelerating) and its
contents (dark energy evolution and dark matter behavior), while also anchoring
the cosmic distance scale ($H_0$).


  In this paper we initiate the study of SSB in 3+1 dimensional rotating,
charged, asymptotically AdS black holes. The theory living on their boundary, R
x S^2, has the interpretation of a 2+1 dimensional rotating holographic
superconductor. We study the appearance of a marginal mode of the condensate as
the temperature is decreased. We find that the transition temperature depends
on the rotation. At temperatures just below T_c, the transition temperature at
zero rotation, there exists a critical value of the rotation, which destroys
the superconducting order. This behaviour is analogous to the emergence of a
critical applied magnetic field and we show that the superconductor in fact
produces the expected London field in the planar limit.


  For any smooth projective moduli space $M$ of Gieseker stable sheaves on a
complex projective K3 surface (or an abelian surface) S, we prove that the Chow
motive $\mathfrak{h}(M)$ becomes a direct summand of a motive $\bigoplus
\mathfrak{h}(S^{k_i})(n_i)$ with $k_i\leq \dim(M)$. The result implies that
finite dimensionality of $\mathfrak{h}(M)$ follows from finite dimensionality
of $\mathfrak{h}(S)$. The technique also applies to moduli spaces of twisted
sheaves and to moduli spaces of stable objects in ${\rm D}^{\rm b}(S,\alpha)$
for a Brauer class $\alpha\in{\rm Br}(S)$. In a similar vein, we investigate
the relation between the Chow motives of a K3 surface $S$ and a cubic fourfold
$X$ when there exists an isometry $\widetilde H(S,\alpha,\mathbb{Z}) \simeq
\widetilde H({\cal A}_X,\mathbb{Z})$. In this case, we prove that there is an
isomorphism of transcendental Chow motives $\mathfrak{t}(S)(1) \simeq
\mathfrak{t}(X)$.


  Buchdahl, by imposing a few physical assumptions on the matter, i.e., its
density is a nonincreasing function of the radius and the fluid is a perfect
fluid, and on the configuration, such as the exterior is the Schwarzschild
solution, found that the radius $r_0$ to mass $m$ ratio of a star would obey
the Buchdahl bound $r_0/m\geq9/4$. He noted that the bound was saturated by the
Schwarzschild interior solution, the solution with $\rho_{\rm m}(r)= {\rm
constant}$, where $\rho_{\rm m}(r)$ is the energy density of the matter at $r$,
when the central central pressure blows to infinity. Generalizations of this
bound have been studied. One generalization was given by Andr\'easson by
including electrically charged matter and imposing that $p+2p_T \leq\rho_{\rm
m}$, where $p$ is the radial pressure and $p_T$ the tangential pressure. His
bound is given by $r_0/m\geq9/\left(1+\sqrt{1+3\,q^2/r_0^2}\right)^{2}$, the
Buchdahl-Andr\'easson bound, with $q$ being the star's total electric charge.
Following Andr\'easson's proof, the configuration that saturates the Buchdahl
bound is an uncharged shell, rather than the Schwarzschild interior solution.
By extension, the configurations that saturate the Buchdahl-Andr\'easson bound
are charged shells. One expects then, in turn, that there should exist an
electrically charged equivalent to the interior Schwarzschild limit. We find
here that this equivalent is provided by the equation $\rho_{\rm m}(r) +
{Q^2(r)}/ {\left(8\pi\,r^4\right)}= {\rm constant}$, where $Q(r)$ is the
electric charge at $r$. This equation was put forward by Cooperstock and de la
Cruz, and Florides, and realized in Guilfoyle's stars. When the central
pressure goes to infinity Guilfoyle's stars are configurations that saturate
the Buchdahl-Andr\'easson bound. It remains to find a proof in Buchdahl's
manner such that these configurations are the limiting configurations of the
bound.


  Technical debt (TD) is a metaphor to describe the trade-off between
short-term workarounds and long-term goals in software development. Despite
being widely used to explain technical issues in business terms, industry and
academia still lack a proper way to manage technical debt while explicitly
considering business priorities. In this paper, we report on a multiple-case
study of how two big software development companies handle technical debt
items, and we show how taking the business perspective into account can improve
the decision making for the prioritization of technical debt. We also propose a
first step toward an approach that uses business process management (BPM) to
manage technical debt. We interviewed a set of IT business stakeholders, and we
collected and analyzed different sets of technical debt items, comparing how
these items would be prioritized using a purely technical versus a
business-oriented approach. We found that the use of business process
management to support technical debt management makes the technical debt
prioritization decision process more aligned with business expectations. We
also found evidence that the business process management approach can help
technical debt management achieve business objectives.


  Many tasks can be easily solved using machine learning techniques. However,
some tasks cannot readily be solved using statistical models, requiring a
symbolic approach instead. Program induction is one of the ways that such tasks
can be solved by means of capturing an interpretable and generalizable
algorithm through training. However, contemporary approaches to program
induction are not sophisticated enough to readily be applied to various types
of tasks as they tend to be formulated as a single, all-encompassing model,
usually parameterized by neural networks. In an attempt to make program
induction a viable solution for many scenarios, we propose a framework for
learning parameterized programs via search gradients using evolution
strategies. This formulation departs from traditional program induction as it
allows for the programmer to impart task-specific code to the program 'sketch',
while also enjoying the benefits of accelerated learning through end-to-end
gradient-based optimization.


  We prove quantitative estimates for averages of the von Mangoldt and M\"obius
functions along polynomial progressions $n+P_1(m),\ldots, n+P_k(m)$ for a large
class of polynomials $P_i$. The error terms obtained save an arbitrary power of
logarithm, matching the classical Siegel--Walfisz error term. These results
give the first quantitative bounds for the Tao--Ziegler polynomial patterns in
the primes result, and in the M\"obius case they are new even qualitatively for
some collections of polynomials.
  The proofs are based on a quantitative generalised von Neumann theorem of
Peluse, a recent result of Leng on strong bounds for the Gowers uniformity of
the primes, and analysis of a ``Siegel model'' for the von Mangoldt function
along polynomial progressions.


  The goal of this work is to construct integral Chern classes and higher cycle
classes for a smooth variety over a perfect field of characteristic p>0 that
are compatible with the rigid Chern classes defined by Petrequin. The Chern
classes we define have coefficients in the overconvergent de Rham-Witt complex
of Davis, Langer and Zink and the construction is based on the theory of cycle
modules discussed by Rost. We prove a comparison theorem in the case of a
quasi-projective variety.


  Molecular dynamics simulations of folding in an off-lattice protein model
reveal a nucleation scenario, in which a few well-defined contacts are formed
with high probability in the transition state ensemble of conformations. Their
appearance determines folding cooperativity and drives the model protein into
its folded conformation.


  In this work we propose a subtle change in Axelrod's model for the
dissemination of culture. The mechanism consists of excluding non-interacting
neighbours from the set of neighbours out of which an agent is drawn for
potential cultural interactions. Although the alteration proposed does not
alter topologically the configuration space, it yields significant qualitative
changes, specifically the emergence of surface tension, driving the system in
some cases to metastable states. The transient behaviour is considerably
richer, and cultural regions have become stable leading to the formation of
different spatio-temporal structures. A new metastable "glassy" phase emerges
between the globalised phase and the polarised, multicultural phase.


  We present a comprehensive analysis of the rest-frame UV to near-IR spectral
energy distributions and rest-frame optical spectra of four of the brightest
gravitationally lensed galaxies in the literature: RCSGA 032727-132609 at
z=1.70, MS1512-cB58 at z=2.73, SGAS J152745.1+065219 at z=2.76 and SGAS
J122651.3+215220 at z=2.92. This includes new Spitzer imaging for RCSGA0327 as
well as new spectra, near-IR imaging and Spitzer imaging for SGAS1527 and
SGAS1226. Lensing magnifications of 3-4 magnitudes allow a detailed study of
the stellar populations and physical conditions. We compare star formation
rates as measured from the SED fit, the H-alpha and [OII] emission lines, and
the UV+IR bolometric luminosity where 24 micron photometry is available. The
SFR estimate from the SED fit is consistently higher than the other indicators,
which suggests that the Calzetti dust extinction law used in the SED fitting is
too flat for young star-forming galaxies at z~2. Our analysis finds similar
stellar population parameters for all four lensed galaxies: stellar masses
3-7*10^9 M_sun, young ages ~ 100 Myr, little dust content E(B-V)=0.10-0.25, and
star formation rates around 20-100 M_sun/yr. Compared to typical values for the
galaxy population at z~2, this suggests we are looking at newly formed,
starbursting systems that have only recently started the build-up of stellar
mass. These results constitute the first detailed, uniform analysis of a sample
of the growing number of strongly lensed galaxies known at z~2.


  We examine the top squark (stop) and gluino reach of the proposed 33 TeV
energy upgrade of the Large Hadron Collider (LHC33) in the Minimal
Supersymmetric Standard Model (MSSM) with light higgsinos and relatively heavy
electroweak gauginos. In our analysis, we assume that stops decay to higgsinos
via ${\tilde t}_1 \to t {\tilde{Z}}_1$, $\tilde{t}_1 \to t\tilde{Z}_2$ and
$\tilde{t}$$_1 \to b\tilde{W}_1$ with branching fractions in the ratio 1:1:2
(expected if the decay occurs dominantly via the superpotential Yukawa
coupling) while gluinos decay via $\tilde{g}\to t\tilde{t}_1$ or via three-body
decays to third generation quarks plus higgsinos. These decay patterns are
motivated by models of natural supersymmetry where higgsinos are expected to be
close in mass to $m_Z$, but gluinos may be as heavy as $5 - 6$ TeV and stops
may have masses up to $\sim 3 $ TeV. We devise cuts to optimize the signals
from stop and gluino pair production at LHC33. We find that experiments at
LHC33 should be able to discover stops with $> 5\sigma$ significance if
$m_{\tilde{t}_1} < 2.3 \ (2.8) \ [3.2]$ TeV for an integrated luminosity of 0.3
(1)[3] ab$^{-1}$. The corresponding reach for gluinos extends to 5 (5.5) [6]
TeV. These results imply that experiments at LHC33 should be able to discover
at least one of the stop or gluino pair signals even with an integrated
luminosity of 0.3 ab$^{-1}$ for natural SUSY models with no worse than 3%
electroweak fine-tuning, and quite likely both gluinos and stops for an
integrated luminosity of 3 ab$^{-1}$.


  For two families of Weierstrass elliptic functions - based on triangular or
square lattices - we prove that the set of Misiurewicz parameters has the
Lebesgue measure zero in C.


  The Einstein Telescope (ET), the European project for a third-generation
gravitational-wave detector, has a reference configuration based on a
triangular shape consisting of three nested detectors with 10 km arms, where in
each arm there is a `xylophone' configuration made of an interferometer tuned
toward high frequencies, and an interferometer tuned toward low frequencies and
working at cryogenic temperature. Here, we examine the scientific perspectives
under possible variations of this reference design. We perform a detailed
evaluation of the science case for a single triangular geometry observatory,
and we compare it with the results obtained for a network of two L-shaped
detectors (either parallel or misaligned) located in Europe, considering
different choices of arm-length for both the triangle and the 2L geometries. We
also study how the science output changes in the absence of the low-frequency
instrument, both for the triangle and the 2L configurations. We examine a broad
class of simple `metrics' that quantify the science output, related to compact
binary coalescences, multi-messenger astronomy and stochastic backgrounds, and
we then examine the impact of different detector designs on a more specific set
of scientific objectives.


  In this paper we prove that if $X $ is a Banach space, then for every lower
semi-continuous bounded below function $f, $ there exists a $\left(\varphi_1,
\varphi_2\right)-$convex function $g, $ with arbitrarily small norm, such that
$f + g $ attains its strong minimum on $X. $ This result extends some of the
well-known varitional principles as that of Ekeland [18], that of
Borwein-Preiss [6] and that of Deville-Godefroy-Zizler [14, 15].


  Using the numerical renormalization group (NRG) method we study a magnetic
impurity coupled to a quantum wire with Rashba and Dresselhaus spin-orbit
coupling (SOC) in an external magnetic field. We consider the low-filling
regime with the Fermi energy close to the bottom of the band and report the
results for local static and dynamic properties in the Kondo regime. In the
absence of the field, local impurity properties remain isotropic in spin space
despite the SOC-induced magnetic anisotropy of the conduction band. In the
presence of the field, clear fingerprints of anisotropy are revealed through
the strong field-direction dependence of the impurity spin polarization and
spectra, in particular of the Kondo peak height. The detailed behavior depends
on the relative magnitudes of the impurity and band $g$-factors. For the case
of impurity $g$-factor somewhat lower than the band $g$-factor, the maximal
Kondo peak suppression is found for field oriented along the effective SOC
field axis, while for a field perpendicular to this direction we observe a
compensation effect (``revival of the Kondo peak''): the SOC counteracts the
Kondo peak splitting effects of the local Zeeman field. We demonstrate that the
SOC-induced anisotropy, measurable by tunneling spectroscopy techniques, can
help to determine the ratio of Rashba and Dresselhaus SOC strengths in the
wire.


  We propose the extension of Fr\'{e}chet-Hoeffding copula bounds for circular
data. The copula is a powerful tool for describing the dependency of random
variables. In two dimensions, the Fr\'{e}chet-Hoeffding upper (lower) bound
indicates the perfect positive (negative) dependence between two random
variables. However, for circular random variables, the usual concept of
dependency is not accepted because of their periodicity. In this work, we
redefine Fr\'{e}chet-Hoeffding bounds and consider modified Fr\'{e}chet and
Mardia families of copulas for modelling the dependency of two circular random
variables. Simulation studies are also given to demonstrate the behavior of the
model.


  Submodular maximization is one of the central topics in combinatorial
optimization. It has found numerous applications in the real world. In the past
decades, a series of algorithms have been proposed for this problem. However,
most of the state-of-the-art algorithms are randomized. There remain
non-negligible gaps with respect to approximation ratios between deterministic
and randomized algorithms in submodular maximization.
  In this paper, we propose deterministic algorithms with improved
approximation ratios for non-monotone submodular maximization. Specifically,
for the matroid constraint, we provide a deterministic $0.283-o(1)$
approximation algorithm, while the previous best deterministic algorithm only
achieves a $1/4$ approximation ratio. For the knapsack constraint, we provide a
deterministic $1/4$ approximation algorithm, while the previous best
deterministic algorithm only achieves a $1/6$ approximation ratio. For the
linear packing constraints with large widths, we provide a deterministic
$1/6-\epsilon$ approximation algorithm. To the best of our knowledge, there is
currently no deterministic approximation algorithm for the constraints.


  We demonstrate that the differential magnetic susceptibility of a fractional
quantum Hall disk, representing a Coulomb island in a Fabry--Perot
interferometer, is exactly proportional to the island's conductance and its
paramagnetic peaks are the equilibrium counterparts of the Coulomb blockade
conductance peaks. Using as a thermodynamic potential the partition functions
of the edge states' effective conformal field theory we find the positions of
the Coulomb blockade peaks, when the area of the island is varied, the
modulations of the distance between them as well as the thermal decay and
broadening of the peaks when temperature is increased. The finite-temperature
estimates of the peak's heights and widths could give important information
about the experimental observability of the Coulomb blockade. In addition, the
predicted peak asymmetry and displacement at finite temperature due to neutral
multiplicities could serve to distinguish different fractional quantum Hall
states with similar zero-temperature Coulomb blockade patterns.


  Most works on pyrochlore magnets deal with the interacting spin-1/2 local
moments. We here study the spin-one local moments on the pyrochlore lattice,
and propose a generic interacting spin model on a pyrochlore lattice. Our spin
model includes the antiferromagnetic Heisenberg interaction, the
Dzyaloshinskii-Moriya interaction and the single-ion spin anisotropy. We
develop a flavor wave theory and combine with a mean-field approach to study
the global phase diagram of this model and establish the relation between
different phases in the phase diagram. We find the regime of the quantum
paramagnetic phase where a degenerate line of the magnetic excitations emerges
in the momentum space. We further predict the critical properties of the
transition out of the quantum paramagnet to the proximate orders. The presence
of quantum order by disorder in the parts of the ordered phases is then
suggested. We point out the existence of degenerate and topological excitations
in various phases. We discuss the relevance with fluoride pyrochlore material
NaCaNi$_2$F$_7$ and explain the role of the spin-orbit coupling and the
magnetic structures of the Ru-based pyrochlore A$_2$Ru$_2$O$_7$ and the
Mo-based pyrochlore A$_2$Mo$_2$O$_7$.


  We present an approach to reduce the performance disparity between geographic
regions without degrading performance on the overall user population for ASR. A
popular approach is to fine-tune the model with data from regions where the ASR
model has a higher word error rate (WER). However, when the ASR model is
adapted to get better performance on these high-WER regions, its parameters
wander from the previous optimal values, which can lead to worse performance in
other regions. In our proposed method, we utilize the elastic weight
consolidation (EWC) regularization loss to identify directions in parameters
space along which the ASR weights can vary to improve for high-error regions,
while still maintaining performance on the speaker population overall. Our
results demonstrate that EWC can reduce the word error rate (WER) in the region
with highest WER by 3.2% relative while reducing the overall WER by 1.3%
relative. We also evaluate the role of language and acoustic models in ASR
fairness and propose a clustering algorithm to identify WER disparities based
on geographic region.


  Object detection with on-board sensors (e.g., lidar, radar, and camera) play
a crucial role in autonomous driving (AD), and these sensors complement each
other in modalities. While crowdsensing may potentially exploit these sensors
(of huge quantity) to derive more comprehensive knowledge, \textit{federated
learning} (FL) appears to be the necessary tool to reach this potential: it
enables autonomous vehicles (AVs) to train machine learning models without
explicitly sharing raw sensory data. However, the multimodal sensors introduce
various data heterogeneity across distributed AVs (e.g., label quantity skews
and varied modalities), posing critical challenges to effective FL. To this
end, we present AutoFed as a heterogeneity-aware FL framework to fully exploit
multimodal sensory data on AVs and thus enable robust AD. Specifically, we
first propose a novel model leveraging pseudo-labeling to avoid mistakenly
treating unlabeled objects as the background. We also propose an
autoencoder-based data imputation method to fill missing data modality (of
certain AVs) with the available ones. To further reconcile the heterogeneity,
we finally present a client selection mechanism exploiting the similarities
among client models to improve both training stability and convergence rate.
Our experiments on benchmark dataset confirm that AutoFed substantially
improves over status quo approaches in both precision and recall, while
demonstrating strong robustness to adverse weather conditions.


  Active particles contain internal degrees of freedom with the ability to take
in and dissipate energy and, in the process, execute systematic movement.
Examples include all living organisms and their motile constituents such as
molecular motors. This article reviews recent progress in applying the
principles of nonequilibrium statistical mechanics and hydrodynamics to form a
systematic theory of the behaviour of collections of active particles -- active
matter -- with only minimal regard to microscopic details. A unified view of
the many kinds of active matter is presented, encompassing not only living
systems but inanimate analogues. Theory and experiment are discussed side by
side.


  By looking at the relationship between the recurrence properties of a
countable group action with a quasi-invariant measure and the structure of its
ergodic components we establish a simple general description of the Hopf
decomposition of the action into the conservative and the dissipative parts in
terms of the Radon--Nikodym derivatives of the action. As an application we
prove that the conservative part of the boundary action of a discrete group of
isometries of a Gromov hyperbolic space with respect to any invariant
quasi-conformal stream coincides (mod 0) with the big horospheric limit set of
the group.


  We summarise the properties of the Sloan Digital Sky Survey (SDSS) project,
discuss our software infrastructure, and outline the architecture of the SDSS
image processing pipelines.
  We then discuss two of the algorithms used in the SDSS image processing; the
KL-transform based modelling of the spatial variation of the PSF, and the use
of galaxy models in star/galaxy separation.
  We conclude with the first author's personal opinions on the challenges that
the astronomical community faces with major software projects.


  An analytical investigation of beamstrahlung-induced blow-up in Gaussian
beams with arbitrary dimensions is presented, using various approximations for
the strength of the hourglass effect and crab waist scheme. The results,
applied to the FCC-ee resonances, are compared with simulations and previous
calculations, and relative luminosity values are also calculated. The stability
of resultant conformations are analysed to rule out the existence of a
flip-flop phenomenon in the longitudinal plane analogous to the well-known
transverse counterpart. Implications for the top-up injection procedures are
discussed, and a phenomenological model is proposed to study the
transverse-longitudinal coupling in the blowup dynamics.


  We report on the theoretical analysis as well as the numerical simulations
about the nonlinear dynamics of cavity solitons in a passive Kerr resonator
operating in the multistable regime under the condition of a sufficiently
strong pump. In this regime, the adjacent tilted cavity resonances might
overlap, thus leading to the co-existence of combinatory states of temporal
cavity solitons and the extended modulation instability patterns. Very
interestingly, the cavity in the regime of multistablity may sustain distinct
families of cavity solitons, vividly termed as super cavity solitons with much
higher intensity and broader spectra if compared with those in the conventional
bi-stable regime. The description of such complex cavity dynamics in the
multstable regime requires either the infinite-dimensional Ikeda map, or the
derived mean-field coupled Lugiato-Lefever equations by involving the
contributing cavity resonances. With the latter model, for the first time, we
revealed the existence of different orders of super cavity solitons, whose
stationary solutions were obtained by using the Newton-Raphson algorithm. Along
this line, with the continuation calculation, we have plotted the Hopf /
saddle-node bifurcation curves, thus identifying the existing map of the stable
and breathing (super) cavity solitons. With this defined parameter space, we
have proposed an efficient method to excite and switch the super cavity
solitons by adding an appropriate intensity (or phase) perturbation on the
pump. Such deterministic cavity soliton manipulation technique is demonstrated
to underpin the multi-level coding, which may enable the large capacity
all-optical buffering based on the passive fiber ring cavities.


  We present a self-improving, Neural Tree Expansion (NTE) method for
multi-robot online planning in non-cooperative environments, where each robot
attempts to maximize its cumulative reward while interacting with other
self-interested robots. Our algorithm adapts the centralized, perfect
information, discrete-action space method from AlphaZero to a decentralized,
partial information, continuous action space setting for multi-robot
applications. Our method has three interacting components: (i) a centralized,
perfect-information "expert" Monte Carlo Tree Search (MCTS) with large
computation resources that provides expert demonstrations, (ii) a
decentralized, partial-information "learner" MCTS with small computation
resources that runs in real-time and provides self-play examples, and (iii)
policy & value neural networks that are trained with the expert demonstrations
and bias both the expert and the learner tree growth. Our numerical experiments
demonstrate Neural Tree Expansion's computational advantage by finding better
solutions than a MCTS with 20 times more resources. The resulting policies are
dynamically sophisticated, demonstrate coordination between robots, and play
the Reach-Target-Avoid differential game significantly better than the
state-of-the-art control-theoretic baseline for multi-robot, double-integrator
systems. Our hardware experiments on an aerial swarm demonstrate the
computational advantage of Neural Tree Expansion, enabling online planning at
20Hz with effective policies in complex scenarios.


  Motivated by the geometric structures of supersymmetric holographic RG-flows,
we scan for N=2 AdS_4 solutions in M-theory. One particularly well understood
holographic RG flow in M-theory is dual to a mass deformation of the N=8
Chern-Simons theory. We utilize an Ansatz which is a natural generalization of
this background in our scan. We find a single new solution with non-trivial
internal flux and the topology of S^7. Interestingly, despite our Ansatz being
quite general, within our system we rule out solutions with internal flux on
more general Sasaki-Einstein seven manifolds.


  By employing a mapping to classical anharmonic oscillators, we explore a
class of solutions to the Nonlinear Schrodinger Equation (NLSE) in 1+1
dimensions and, by extension, asymptotically in general dimensions. We discuss
a possible way for creating approximate rogue wave like solutions to the NLSE
by truncating exact solutions at their nodes and stitching them with other
solutions to the NLSE. The resulting waves are similar to compactons with the
notable difference that they are not localized but rather extend over all of
space. We discuss rogue waves in a \phi^4 field theory in the context of a
discretized Lagrangian and rogue wave behavior is shown to evolve into a steady
state. Due to time-reversal invariance of this theory, the steady state found
could alternatively evolve into a rogue wave giving rise to a large wave which
seems to appear from nothing.


  Facing the dramatic increase of real-time applications and time-sensitive
services, large-scale ultra-low delay requirements are put forward for the
sixth generation (6G) wireless networks. To support massive ultra-reliable and
low-latency communications (mURLLC), in this paper we propose an adaptive
finite blocklength framework to reduce the over-the-air delay for short packet
transmissions with multiple-access and delay-bounded demands. In particular, we
first give the specified over-the-air delay model. Then, we reveal the tradeoff
relationship among queuing delay, transmission delay, and the number of
retransmissions along with the change of finite blocklength, as well as
formulate the adaptive blocklength framework. Based on the adaptive blocklength
framework and associated with grant-free (GF) access protocol, we formulate the
average over-the-air delay minimization problem, where the blocklength can be
adaptively changed in terms of transmission time interval (TTI) design and
bandwidth allocation to achieve the optimal tradeoff and obtain its minimum
over-the-air delay. We develop the cooperative multi-agent deep Q-network
(M-DQN) scheme with a grouping mechanism to efficiently solve the average
over-the-air delay minimization problem. Numerical results validate our
proposed adaptive blocklength scheme outperforms corresponding schemes in
long-term evolution (LTE) and the fifth generation (5G) new radio (NR).


  The classical Einstein's gravity can be reformulated from the constrained
U(2,2) gauge theory on the ordinary (commutative) four-dimensional spacetime.
Here we consider a noncommutative manifold with a symplectic structure and
construct a U(2,2) gauge theory on such a manifold by using the covariant
coordinate method. Then we use the Seiberg-Witten map to express noncommutative
quantities in terms of their commutative counterparts up to the first-order in
noncommutative parameters. After imposing constraints we obtain a
noncommutative gravity theory described by the Lagrangian with up to
nonvanishing first order corrections in noncommutative parameters. This result
coincides with our previous one obtained for the noncommutative SL(2,C)
gravity.


  We characterize the stellar populations in the nuclear region of the barred
spiral galaxy NGC 4900 using the integral field spectrometer OASIS and the
synthesis code LavalSB and the code from Moll\'{a} & Garc\'{\i}a-Vargas (2000)
for the young ($< 10$ Myr) and the old stellar populations, respectively. The
high spatial resolution of the instrument allows us to find an old population
uniformely distributed and younger regions located at the end of the galaxy bar
and on each side of a nuclear bar.


  We generalize the decomposition theorem of Hochschild, Kostant and Rosenberg
for Hochschild (co-)homology to arbitrary morphisms between complex spaces or
schemes over a field of characteristic zero. To be precise, we show that for
each such morphism, the Hochschild complex, as introduced in math.AG/0606593,
decomposes naturally in the derived category into the direct sum of the derived
symmetric powers of the shifted cotangent complex, a result due to Quillen in
the affine case.
  Even in the affine case, our proof is new and provides further information.
It shows that the decomposition is given explicitly and naturally by the
universal Atiyah-Chern character, the exponential of the universal Atiyah
class.
  We further use the decomposition theorem to show that the semiregularity map
for perfect complexes factors through Hochschild homology and, in turn, factors
the Atiyah-Hochschild character through the characteristic homomorphism from
Hochschild cohomology to the graded centre of the derived category.


  We demonstrate that the decay eta -> 3 pi represents a sensitive probe for
the breaking of chiral symmetry by the quark masses. The transition amplitude
is proportional to the mass ratio (m_d^2-m_u^2)/(m_s^2-m^2). The factor of
proportionality is calculated by means of dispersion relations, using chiral
perturbation theory to determine the subtraction constants. The theoretical
uncertainties in the result are shown to be remarkably small, so that eta-decay
may be used to accurately measure this ratio of quark masses.


  Very recently we proposed a predictive 2 Higgs Doublet Model with $S_{3}$
flavour symmetry that successfully accounts for fermion masses and mixings. In
this letter, motivated by the $750$ GeV Higgs diphoton resonance recently
reported by the ATLAS and CMS collaborations, we modify this model by adding
exotic top partners with electric charge $\frac{5}{3}$ and a electrically
charged scalar singlet. These exotic top partners decay into a charged scalar
singlet and the SM up type quarks, whereas the charged scalar singlet will
mainly decay into SM up and down type quarks. This simple modification enables
our model to successfully account for the Higgs diphoton excess at
$750\,\text{GeV}$ provided that the exotic quark masses are in the range
$[1,2]$ TeV, for $O(1)$ exotic quark Yukawa couplings.


  Ultracold plasmas (UCP) provide a well-controlled system for studying
multiple aspects in plasma physics that include collisions and strong coupling
effects. By applying a short electric field pulse to a UCP, a plasma electron
center-of-mass (CM) oscillation can be initiated. In accessible parameter
ranges, the damping rate of this oscillation is determined by the electron-ion
collision rate. We performed measurements of the oscillation damping rate with
such parameters and compared the measured rates to both a molecular dynamic
(MD) simulation that includes strong coupling effects and to Monte-Carlo
collisional operator simulation designed to predict the damping rate including
only weak coupling considerations. We found agreement between experimentally
measured damping rate and the MD result. This agreement did require including
the influence of a previously unreported UCP heating mechanism whereby the
presence of a DC electric field during ionization increased the electron
temperature, but estimations and simulations indicate that such a heating
mechanism should be present for our parameters. The measured damping rate at
our coldest electron temperature conditions was much faster than the weak
coupling prediction obtained from the Monte-Carlo operator simulation, which
indicates the presence of significant strong coupling influence. The density
averaged electron strong coupling parameter $\Gamma$ measured at our coldest
electron temperature conditions was 0.35.


  We generalize the projection-based quantum measurement-driven $k$-SAT
algorithm of Benjamin, Zhao, and Fitzsimons (BZF, arxiv:1711.02687) to
arbitrary strength quantum measurements, including the limit of continuous
monitoring. In doing so, we clarify that this algorithm is a particular case of
the measurement-driven quantum control strategy elsewhere referred to as "Zeno
dragging". We argue that the algorithm is most efficient with finite time and
measurement resources in the continuum limit, where measurements have an
infinitesimal strength and duration. Moreover, for solvable $k$-SAT problems,
the dynamics generated by the algorithm converge deterministically towards
target dynamics in the long-time (Zeno) limit, implying that the algorithm can
successfully operate autonomously via Lindblad dissipation, without detection.
We subsequently study both the conditional and unconditional dynamics of the
algorithm implemented via generalized measurements, quantifying the advantages
of detection for heralding errors. These strategies are investigated first in a
computationally-trivial $2$-qubit $2$-SAT problem to build intuition, and then
we consider the scaling of the algorithm on $3$-SAT problems encoded with $4 -
10$ qubits. The average number of shots needed to obtain a solution scales with
qubit number as $\lambda^n$. For vanishing dragging time (with final readout
only), we find $\lambda = 2$ (corresponding to a brute-force search over
possible solutions). However, the deterministic (autonomous) property of the
algorithm in the adiabatic (Zeno) limit implies that we can drive $\lambda$
arbitrarily close to $1$, at the cost of a growing pre-factor. We numerically
investigate the tradeoffs in these scalings with respect to algorithmic runtime
and assess their implications for using this analog measurement-driven approach
to quantum computing in practice.


  Our aim in this paper is to determine the tautological algebra generated by
the cohomology classes of the Brill Noether loci in the rational cohomology of
the moduli stack $\mathcal{U}_C(n,d)$ of semistable bundles of rank $n$ and
degree $d$. When $C$ is a general smooth projective curve of genus $g\geq 2$,
$n=2$, $d=2g-2$, the tautological algebra of $ \mathcal{U}_C(2,2g-2)$ (resp.
$\mathcal{SU}_C(2,L)$, $deg(L)=2g-2)$) is generated by the divisor classes
(resp. the Theta divisor $\Theta$).


  The two BL Lac objects, 1ES 1215+303 and 1ES 1218+304, separated by 0.8
degree, were observed with the MAGIC Cherenkov telescopes in 2010-2011. The
January 2011 observations resulted in the first detection above 100 GeV of 1ES
1215+303 (known also as ON-325) which has been flagged as a promising Very High
Energy (VHE, E > 100 GeV) gamma-ray source candidate by the Fermi-LAT
Collaboration in October 2010. The January 2011 observations were triggered by
the high optical state of the source, as reported by the Tuorla blazar
monitoring program. A comparison with the 2010 data suggests that 1ES 1215+303
was also flaring in VHE gamma-rays. In addition, the Swift Target of
Opportunity (ToO) observations in X-rays showed that the flux was almost
doubled with respect to previous observations (December 2009). Instead, 1ES
1218+304 is a well known VHE gamma-ray emitter located in the same field of
view, which was then simultaneously observed with MAGIC. In this contribution
we present preliminary results of the MAGIC observations of these two VHE
gamma-ray emitting AGNs.


  We present an all solid-state narrow line-width laser source emitting
$670\,\mathrm{mW}$ output power at $671\,\mathrm{nm}$ delivered in a
diffraction-limited beam. The \linebreak source is based on a
fre-quency-doubled diode-end-linebreak pumped ring laser operating on the
${^4F}_{3/2} \rightarrow {^4I}_{13/2}$ transition in Nd:YVO$_4$. By using
periodically-poled po-tassium titanyl phosphate (ppKTP) in an external build-up
cavity, doubling efficiencies of up to 86% are obtained. Tunability of the
source over $100\,\rm GHz$ is accomplished. We demonstrate the suitability of
this robust frequency-stabilized light source for laser cooling of lithium
atoms. Finally a simplified design based on intra-cavity doubling is described
and first results are presented.


  An efficient method for finding a better maximizer of computationally
extensive probability distributions is proposed on the basis of a Bayesian
optimization technique. A key idea of the proposed method is to use extreme
values of acquisition functions by Gaussian processes for the next training
phase, which should be located near a local maximum or a global maximum of the
probability distribution. Our Bayesian optimization technique is applied to the
posterior distribution in the effective physical model estimation, which is a
computationally extensive probability distribution. Even when the number of
sampling points on the posterior distributions is fixed to be small, the
Bayesian optimization provides a better maximizer of the posterior
distributions in comparison to those by the random search method, the steepest
descent method, or the Monte Carlo method. Furthermore, the Bayesian
optimization improves the results efficiently by combining the steepest descent
method and thus it is a powerful tool to search for a better maximizer of
computationally extensive probability distributions.


  We present high-resolution observations of several molecular lines in
OH231.8+4.2 taken with the IRAM interferometer. All molecules are distributed
in a narrow region along the symmetry axis, and flow outwards following a
velocity gradient similar to that found in CO. The HCO+ emission is found to be
very clumpy and strongly enhanced in the shock-accelerated lobes, indicating
that the formation of this molecule is probably dominated by shock induced
reactions. SO is present in the axial outflow as well as in an expanding
equatorial disk. The SiO maser emission seems to arise from the innermost parts
of such a disk. We also report the first detection of NS in circumstellar
envelopes.


  Efficient analysis and simulation of multiscale stochastic systems of
chemical kinetics is an ongoing area for research, and is the source of many
theoretical and computational challenges. In this paper, we present a
significant improvement to the constrained approach, which is a method for
computing effective dynamics of slowly changing quantities in these systems,
but which does not rely on the quasi-steady-state assumption (QSSA). The QSSA
can cause errors in the estimation of effective dynamics for systems where the
difference in timescales between the "fast" and "slow" variables is not so
pronounced.
  This new application of the constrained approach allows us to compute the
effective generator of the slow variables, without the need for expensive
stochastic simulations. This is achieved by finding the null space of the
generator of the constrained system. For complex systems where this is not
possible, or where the constrained subsystem is itself multiscale, the
constrained approach can then be applied iteratively. This results in breaking
the problem down into finding the solutions to many small eigenvalue problems,
which can be efficiently solved using standard methods.
  Since this methodology does not rely on the quasi steady-state assumption,
the effective dynamics that are approximated are highly accurate, and in the
case of systems with only monomolecular reactions, are exact. We will
demonstrate this with some numerics, and also use the effective generators to
sample paths of the slow variables which are conditioned on their endpoints, a
task which would be computationally intractable for the generator of the full
system.


  The proliferation of video content demands efficient and flexible neural
network based approaches for generating new video content. In this paper, we
propose a novel approach that combines zero-shot text-to-video generation with
ControlNet to improve the output of these models. Our method takes multiple
sketched frames as input and generates video output that matches the flow of
these frames, building upon the Text-to-Video Zero architecture and
incorporating ControlNet to enable additional input conditions. By first
interpolating frames between the inputted sketches and then running
Text-to-Video Zero using the new interpolated frames video as the control
technique, we leverage the benefits of both zero-shot text-to-video generation
and the robust control provided by ControlNet. Experiments demonstrate that our
method excels at producing high-quality and remarkably consistent video content
that more accurately aligns with the user's intended motion for the subject
within the video. We provide a comprehensive resource package, including a demo
video, project website, open-source GitHub repository, and a Colab playground
to foster further research and application of our proposed method.


  We construct the model incorporating both an arbitrary shift of cosmological
constant and Goldstone boson corresponding to the spontaneous breaking down the
global shift symmetry in the matter action. The gravity breaks down the
symmetry explicitly and transforms the Goldstone boson to the inflaton field.


  Although, poly(dimethylsiloxane) (PDMS) is a widely used material in numerous
applications, such as micro- or nanofabrication, the method of its selective
etching has not been known up to now. In this work authors present two methods
of etching the pure, additive-free and cured PDMS as a positive resist
material.
  To achieve the chemical modification of the polymer necessary for selective
etching, energetic ions were used. We created 7 um and 45 um thick PDMS layers
and patterned them by a focused proton microbeam with various, relatively large
fluences. In this paper authors demonstrate that 30 wt% Potassium Hydroxide
(KOH) or 30 wt% sodium hydroxide (NaOH) at 70 oC temperature etch proton
irradiated PDMS selectively, and remove the chemically sufficiently modified
areas. In case of KOH development, the maximum etching rate was approximately
3.5 um/minute and it occurs at about 7.5*10^15 ion*cm-2. In case of NaOH
etching the maximum etching rate is slightly lower, 1.75 um/minute and can be
found at the slightly higher fluence of 8.75*10^15 ion*cm-2.
  These results are of high importance since up to this time it has not been
known how to develop the additive-free, cross-linked poly(dimethylsiloxane) in
lithography as a positive tone resist material.


  We use three IR cutoffs, including the future event horizon, the Hubble and
Granda-Oliveros (GO) cutoffs, to construct three holographic models of dark
energy. Additionally, we consider a Friedmann-Robertson-Walker (FRW) universe
filled by a dark matter (DM) and a dark energy that interact with each other
through a mutual sign-changeable interaction. Thereinafter, we address the
evolution of the some cosmological parameters, such as the equation of state
and dimensionless density parameters of dark energy as well as the deceleration
parameter, during the cosmic evolution from the matter dominated era until the
late time acceleration. We observe that a holographic dark energy (HDE) model
with Hubble cutoff interacting with DM may be in line with the current
universe. Our study shows that models with the future event horizon as the IR
cutoff or the GO cutoff are in good agreement with the observational data. In
fact, we find out that these obtained models can predict the universe
transition from a deceleration phase to the acceleration one in a compatible
way with observations. The three obtained models may also allow the equation of
state parameter to cross the phantom line, a result which depends on the values
of the system's constants such as the value of the interaction coupling
constant.


  In this article, we investigate the interactions of a Yang-Mills (YM) wave
fluctuation of a classical isotropic, homogeneous YM condensate, which models
gluon plasma, with a Gravitational Wave (GW). We re-analyse the study of
fluctuations of the gluon plasma using vector decomposition of the gauge field
into scalar, longitudinal, and transverse modes. We find that there is an
energy transfer between isotropic gluon condensate and plasmon modes, but the
effect is delayed, and dependent on the initial conditions. We also studied
quarks in the background of YM condensate and GW. We find that the quarks break
the isotropy of the condensate and the GW couples quarks of different flavours
of the SU(2) group. The GW induces flavour fluctuations, and this has
interesting implications for experimental observations and quark-gluon plasma
physics.


  A general adaptive refinement strategy for solving linear elliptic partial
differential equation with random data is proposed and analysed herein. The
adaptive strategy extends the a posteriori error estimation framework
introduced by Guignard and Nobile in 2018 (SIAM J. Numer. Anal., 56,
3121--3143) to cover problems with a nonaffine parametric coefficient
dependence. A suboptimal, but nonetheless reliable and convenient
implementation of the strategy involves approximation of the decoupled PDE
problems with a common finite element approximation space. Computational
results obtained using such a single-level strategy are presented in this paper
(part I). Results obtained using a potentially more efficient multilevel
approximation strategy, where meshes are individually tailored, will be
discussed in part II of this work. The codes used to generate the numerical
results are available on GitHub


  The travel time required for one civilisation to explore the Milky Way using
probes is a crucial component of Fermi's Paradox. Previous attempts to estimate
this travel time have assumed that the probe's motion is simple, moving at a
constant maximum velocity, with powered flight producing the necessary change
in velocity required at each star to complete its chosen trajectory. This
approach ignores lessons learned from interplanetary exploration, where orbital
slingshot maneouvres can provide significant velocity boosts at little to no
fuel cost. It is plausible that any attempt to explore the Galaxy would utilise
such economising techniques, despite there being an upper limit to these
velocity boosts, related to the escape velocity of the object being used to
provide the slingshot.
  In order to investigate the effects of these techniques, we present multiple
realisations of single probes exploring a small patch of the Milky Way. We
investigate 3 separate scenarios, studying the slingshot effect on trajectories
defined by simple heuristics. These scenarios are: i) standard powered flight
to the nearest unvisited star without using slingshot techniques; ii) flight to
the nearest unvisited star using slingshot techniques, and iii) flight to the
next unvisited star which provides the maximal velocity boost under a slingshot
trajectory.
  We find that adding slingshot velocity boosts can decrease the travel time by
up to two orders of magnitude over simple powered flight. In the third case,
selecting a route which maximises velocity boosts also reduces the travel time
relative to powered flight, but by a much reduced factor. From these
simulations, we suggest that adding realistic probe trajectories tends to
strengthen Fermi's Paradox.


  Let T be a compact torus and (M,\omega) a
  Hamiltonian T-space. In a previous paper, the authors showed that the
T-equivariant K-theory of the manifold M surjects onto the ordinary integral
K-theory of the symplectic quotient M \mod T of M by T, under certain technical
conditions on the moment map. In this paper, we use equivariant Morse theory to
give a method for computing the K-theory of the symplectic quotient by
obtaining an explicit description of the kernel of the surjection \kappa:
K^*_T(M) \onto K^*(M \mod T). Our results are K-theoretic analogues of the work
of Tolman and Weitsman for Borel equivariant cohomology. Further, we prove that
under suitable technical conditions on the T-orbit stratification of M, there
is an explicit Goresky-Kottwitz-MacPherson (``GKM'') type combinatorial
description of the K-theory of a Hamiltonian T-space in terms of fixed point
data. Finally, we illustrate our methods by computing the ordinary K-theory of
compact symplectic toric manifolds, which arise as symplectic quotients of an
affine space \C^N by a linear torus action.


  Invisible psi and Upsilon decays into light neutralinos, within the MSSM or
N(n)MSSM, are smaller than for nu nubar production, even if light spin-0
particles are coupled to quarks and neutralinos. In a more general way, light
dark matter particles are normally forbidden, unless they can annihilate
sufficiently through a new interaction stronger than weak interactions (at
lower energies), as induced by a light spin-1 U boson, or heavy-fermion
exchanges in the case of scalar dark matter. We discuss the possible
contributions of U-boson, heavy-fermion, or spin-0 exchanges to invisible psi
and Upsilon decays.
  U-exchanges could lead, but not necessarily, to significant branching
fractions for invisible decays into light dark matter. We show how one can get
the correct relic density together with sufficiently small invisible branching
fractions, and the resulting constraints on the U couplings to ordinary
particles and dark matter, in particular |c_chi.f_bV| < 5 10^-3 from Upsilon
decays, for 2 m_chi smaller than a few GeV. We also explain why there is no
model-independent way to predict psi and Upsilon branching fractions into light
dark matter, from dark matter annihilation cross sections at freeze-out time.


  One of the most popular and studied recursive series is the Fibonacci
sequence. It is challenging to see how Fibonacci numbers can be used to
generate other recursive sequences. In our article, we describe some families
of integer recurrence sequences as rational polynomial linear combinations of
Fibonacci numbers.


  Recurrent Neural Networks (RNNs) are powerful sequence modeling tools.
However, when dealing with high dimensional inputs, the training of RNNs
becomes computational expensive due to the large number of model parameters.
This hinders RNNs from solving many important computer vision tasks, such as
Action Recognition in Videos and Image Captioning. To overcome this problem, we
propose a compact and flexible structure, namely Block-Term tensor
decomposition, which greatly reduces the parameters of RNNs and improves their
training efficiency. Compared with alternative low-rank approximations, such as
tensor-train RNN (TT-RNN), our method, Block-Term RNN (BT-RNN), is not only
more concise (when using the same rank), but also able to attain a better
approximation to the original RNNs with much fewer parameters. On three
challenging tasks, including Action Recognition in Videos, Image Captioning and
Image Generation, BT-RNN outperforms TT-RNN and the standard RNN in terms of
both prediction accuracy and convergence rate. Specifically, BT-LSTM utilizes
17,388 times fewer parameters than the standard LSTM to achieve an accuracy
improvement over 15.6\% in the Action Recognition task on the UCF11 dataset.


  We show that the defining relations needed to describe a generalized q-Schur
algebra as a quotient of a quantized enveloping algebra are determined
completely by the defining ideal of a certain finite affine variety, the points
of which correspond bijectively to the set of weights. This explains, unifies,
and extends previous results.


  This paper describes the Bayesian Technique for Multi-image Analysis
(BaTMAn), a novel image-segmentation technique based on Bayesian statistics
that characterizes any astronomical dataset containing spatial information and
performs a tessellation based on the measurements and errors provided as input.
The algorithm iteratively merges spatial elements as long as they are
statistically consistent with carrying the same information (i.e. identical
signal within the errors). We illustrate its operation and performance with a
set of test cases including both synthetic and real Integral-Field
Spectroscopic data. The output segmentations adapt to the underlying spatial
structure, regardless of its morphology and/or the statistical properties of
the noise. The quality of the recovered signal represents an improvement with
respect to the input, especially in regions with low signal-to-noise ratio.
However, the algorithm may be sensitive to small-scale random fluctuations, and
its performance in presence of spatial gradients is limited. Due to these
effects, errors may be underestimated by as much as a factor of two. Our
analysis reveals that the algorithm prioritizes conservation of all the
statistically-significant information over noise reduction, and that the
precise choice of the input data has a crucial impact on the results. Hence,
the philosophy of BaTMAn is not to be used as a `black box' to improve the
signal-to-noise ratio, but as a new approach to characterize spatially-resolved
data prior to its analysis. The source code is publicly available at
http://astro.ft.uam.es/SELGIFS/BaTMAn .


  In this article, we introduce a new method for solving general quadratic
functional equations in $\mathbb{C}^n$. By utilizing Nevanlinna theory in
$\mathbb{C}^n$, we explore the existence and form of solutions for the several
systems of general quadratic difference or partial differential-difference
equations of the form $af^2 + 2\alpha fg + bg^2 + 2\beta f + 2\gamma g + C=0$,
where $f$ and $g$ are non-constant meromorphic functions in $\mathbb{C}^n$. The
results in this paper are some improvements and generalizations of several
existing results on the existence and forms of solutions for these systems.
Specifically, the existing results were related to Circular-type $ f^2+g^2=1 $
and quadratic trinomial functional equations $ f^2+2\alpha fg+g^2=1 $. We
provide examples to illustrate the validity of our conclusions regarding the
existence and forms of solutions for such system of equations.


  In this paper we first study the structure of the scalar and vector-valued
nearly invariant subspaces with a finite defect. We then subsequently produce
some fruitful applications of our new results. We produce a decomposition
theorem for the vector-valued nearly invariant subspaces with a finite defect.
More specifically, we show every vector-valued nearly invariant subspace with a
finite defect can be written as the isometric image of a backwards shift
invariant subspace. We also show that there is a link between the vector-valued
nearly invariant subspaces and the scalar-valued nearly invariant subspaces
with a finite defect. This is a powerful result which allows us to gain insight
in to the structure of scalar subspaces of the Hardy space using vector-valued
Hardy space techniques. These results have far reaching applications, in
particular they allow us to develop an all encompassing approach to the study
of the kernels of: the Toeplitz operator, the truncated Toeplitz operator, the
truncated Toeplitz operator on the multiband space and the dual truncated
Toeplitz operator.


  Retrieving resources in a distributed environment is more difficult than
finding data in centralised databases. In the last decade P2P system arise as
new and effective distributed architectures for resource sharing, but searching
in such environments could be difficult and time-consuming. In this paper we
discuss efficiency of resource discovery in PROSA, a self-organising P2P system
heavily inspired by social networks. All routing choices in PROSA are made
locally, looking only at the relevance of the next peer to each query. We show
that PROSA is able to effectively answer queries for rare documents, forwarding
them through the most convenient path to nodes that much probably share
matching resources. This result is heavily related to the small-world structure
that naturally emerges in PROSA.


  We present the results of a monitoring campaign aimed at deriving rotation
periods for a representative sample of stars in the young (30 Myr) open cluster
IC 2602. Rotation periods were derived for 29 of 33 stars monitored. The
periods derived range from 0.2d (one of the shortest known rotation periods of
any single open cluster star) to about 10d (which is almost twice as long as
the longest period previously known for a cluster of this age). We are able to
confirm 8 previously known periods and derive 21 new ones, delineating the long
period end of the distribution. Despite our sensitivity to longer periods, we
do not detect any variables with periods longer than about 10d. The combination
of these data with those for IC 2391, an almost identical cluster, leads to the
following conclusions:
  1) The fast rotators in a 30 Myr cluster are distributed across the entire
0.5 < B-V < 1.6 color range.
  2) 6 stars in our sample are slow rotators, with periods longer than 6d.
  3) The amplitude of variability depends on both the color and the period. The
dependence on the latter might be important in understanding the selection
effects in the currently available rotation period database and in planning
future observations.
  4) The interpretation of these data in terms of theoretical models of
rotating stars suggests both that disk-interaction is the norm rather than the
exception in young stars and that disk-locking times range from zero to a few
Myr.


  Multiparty quantum communication is an important branch of quantum networks.
It enables private information transmission with information-theoretic security
among legitimate parties. We propose a sender-controlled
measurement-device-independent multiparty quantum communication protocol. The
sender Alice divides a private message into several parts and delivers them to
different receivers for secret sharing with imperfect measurement devices and
untrusted ancillary nodes. Furthermore, Alice acts as an active controller and
checks the security of quantum channels and the reliability of each receiver
before she encodes her private message for secret sharing, which makes the
protocol convenient for multiparity quantum communication.


  We present evidence for the detection of primordial non-Gaussianity of the
local type (fNL), using the temperature information of the Cosmic Microwave
Background (CMB) from the WMAP 3-year data. We employ the bispectrum estimator
of non-Gaussianity described in (Yadav et al. 2007) which allows us to analyze
the entirety of the WMAP data without an arbitrary cut-off in angular scale.
Using the combined information from WMAP's two main science channels up to
lmax=750 and the conservative Kp0 foreground mask we find 27 < fNL < 147 at 95%
C.L., with a central value of fNL=87. This corresponds to a rejection of fNL=0
at more than 99.5% significance. We find that this detection is robust to
variations in lmax, frequency and masks, and that no known foreground,
instrument systematic, or secondary anisotropy explains our signal while
passing our suite of tests. We explore the impact of several analysis choices
on the stated significance and find 2.5 sigma for the most conservative view.
We conclude that the WMAP 3-year data disfavors canonical single field
slow-roll inflation.


  We study the classical geodesic motions of nonzero rest mass test particles
and photons in five-dimensional warped product spaces. We show that it is
possible to obtain a general picture of these motions, using the natural
decoupling that occurs in such spaces between the motions in the fifth
dimension and the motion in the hypersurfaces. This splitting allows the use of
phase space analysis in order to investigate the possible confinement of
particles and photons to hypersurfaces in five-dimensional warped product
spaces. Using such analysis, we find a novel form of quasi-confinement which is
oscillatory and neutrally stable. We also find that this class of warped
product spaces locally satisfy the Z2 symmetry by default. The importance of
such a confinement is that it is purely due to the classical gravitational
effects, without requiring the presence of brane-type confinement mechanisms.


  In Hermitian topological systems, the bulk-boundary correspondence strictly
constraints boundary transport to values determined by the topological
properties of the bulk. We demonstrate that this constraint can be lifted in
non-Hermitian Floquet insulators. Provided that the insulator supports an
anomalous topological phase, non-Hermiticity allows us to modify the boundary
states independently of the bulk, without sacrificing their topological nature.
We explore the ensuing possibilities for a Floquet topological insulator with
non-Hermitian time-reversal symmetry, where the helical transport via
counterpropagating boundary states can be tailored in ways that overcome the
constraints imposed by Hermiticity. Non-Hermitian boundary state engineering
specifically enables the enhancement of boundary transport relative to bulk
motion, helical transport with a preferred direction, and chiral transport in
the same direction on opposite boundaries. We explain the experimental
relevance of our findings for the example of photonic waveguide lattices.


  This paper introduces a novel application of Kolmogorov-Arnold Networks
(KANs) to time series forecasting, leveraging their adaptive activation
functions for enhanced predictive modeling. Inspired by the Kolmogorov-Arnold
representation theorem, KANs replace traditional linear weights with
spline-parametrized univariate functions, allowing them to learn activation
patterns dynamically. We demonstrate that KANs outperforms conventional
Multi-Layer Perceptrons (MLPs) in a real-world satellite traffic forecasting
task, providing more accurate results with considerably fewer number of
learnable parameters. We also provide an ablation study of KAN-specific
parameters impact on performance. The proposed approach opens new avenues for
adaptive forecasting models, emphasizing the potential of KANs as a powerful
tool in predictive analytics.


  Quasi-N-body simulations, such as FastPM, provide a fast way to simulate
cosmological structure formation, but have yet to adequately include the
effects of massive neutrinos. We present a method to include neutrino particles
in FastPM, enabling computation of the CDM and total matter power spectra to
percent-level accuracy in the non-linear regime. The CDM-neutrino cross-power
can also be computed at a sufficient accuracy to constrain cosmological
observables. To avoid the shot noise that typically plagues neutrino particle
simulations, we employ a quasi-random algorithm to sample the relevant
Fermi-Dirac distribution when setting the initial neutrino thermal velocities.
We additionally develop an effective distribution function to describe a set of
non-degenerate neutrinos as a single particle to speed up non-degenerate
simulations. The simulation is accurate for the full range of physical
interest, $M_\nu \lesssim 0.6$eV, and applicable to redshifts $z\lesssim2$.
Such accuracy can be achieved by initializing particles with the two-fluid
approximation transfer functions (using the REPS package). Convergence can be
reached in $\sim 25$ steps, with a starting redshift of $z=99$. Probing
progressively smaller scales only requires an increase in the number of CDM
particles being simulated, while the number of neutrino particles can remain
fixed at a value less than or similar to the number of CDM particles. In turn,
the percentage increase in runtime-per-step due to neutrino particles is
between $\sim 5-20\%$ for runs with $1024^3$ CDM particles, and decreases as
the number of CDM particles is increased. The code has been made publicly
available, providing an invaluable resource to produce fast predictions for
cosmological surveys and studying reconstruction.


  We study traversable Lorentzian wormholes in the three-dimensional low energy
string theory by adding some matter source involving a dilaton field. It will
be shown that there are two-different types of wormhole solutions such as BTZ
and black string wormholes depending on the dilaton backgrounds, respectively.
We finally obtain the desirable solutions which confine exotic matter near the
throat of wormhole by adjusting NS charge.


  The paper proves existence of renormalized solutions for a class of
velocity-discrete coplanar stationary Boltzmann equations with given indata.
The proof is based on the construction of a sequence of approximations with L1
compactness for an integrated collision frequency and gain term. The
compactness is obtained using the Kolmogorov Riesz theorem.


  Despite the huge effort to contain the infection, the novel SARS-CoV-2
coronavirus has rapidly become pandemics, mainly due to its extremely high
human-to-human transmission capability, and a surprisingly high viral charge of
symptom-less people. While the seek of a vaccine is still ongoing, promising
results have been obtained with antiviral compounds. In particular, lactoferrin
is found to have beneficial effects both in preventing and soothing the
infection. Here, we explore the possible molecular mechanisms with which
lactoferrin interferes with SARS-CoV-2 cell invasion, preventing attachment
and/or entry of the virus. To this aim, we search for possible interactions
lactoferrin may have with virus structural proteins and host receptors.
Representing the molecular iso-electron surface of proteins in terms of
2D-Zernike descriptors, we (i) identified putative regions on the lactoferrin
surface able to bind sialic acid receptors on the host cell membrane,
sheltering the cell from the virus attachment; (ii) showed that no significant
shape complementarity is present between lactoferrin and the ACE2 receptor,
while (iii) two high complementarity regions are found on the N- and C-terminal
domains of the SARS-CoV-2 spike protein, hinting at a possible competition
between lactoferrin and ACE2 for the binding to the spike protein.


  Neural sequence-to-sequence text-to-speech synthesis (TTS) can produce
high-quality speech directly from text or simple linguistic features such as
phonemes. Unlike traditional pipeline TTS, the neural sequence-to-sequence TTS
does not require manually annotated and complicated linguistic features such as
part-of-speech tags and syntactic structures for system training. However, it
must be carefully designed and well optimized so that it can implicitly extract
useful linguistic features from the input features. In this paper we
investigate under what conditions the neural sequence-to-sequence TTS can work
well in Japanese and English along with comparisons with deep neural network
(DNN) based pipeline TTS systems. Unlike past comparative studies, the pipeline
systems also use autoregressive probabilistic modeling and a neural vocoder. We
investigated systems from three aspects: a) model architecture, b) model
parameter size, and c) language. For the model architecture aspect, we adopt
modified Tacotron systems that we previously proposed and their variants using
an encoder from Tacotron or Tacotron2. For the model parameter size aspect, we
investigate two model parameter sizes. For the language aspect, we conduct
listening tests in both Japanese and English to see if our findings can be
generalized across languages. Our experiments suggest that a) a neural
sequence-to-sequence TTS system should have a sufficient number of model
parameters to produce high quality speech, b) it should also use a powerful
encoder when it takes characters as inputs, and c) the encoder still has a room
for improvement and needs to have an improved architecture to learn
supra-segmental features more appropriately.


  We propose a scheme of the interaction-free all-optical switching in a
multi-atom cavity QED system consisting of three-level atoms confined in a
cavity and coupled by a free-space control laser. A signal laser field is
coupled into the cavity and its transmission through and reflection from the
cavity form two output channels. We show that the free-space control laser
induces destructive quantum interference in the excitation of the intra-cavity
normal mode, which can be used to switch on or off of the output signal light
of the reflection and the transmission channels. When the control light is
coupled to the atoms, the input signal light is nearly totally reflected and
this means that there is no direct coupling of the control light and the signal
light through the cavity-confined atoms. We present analytical and numerical
calculations that show this type of the interaction-free all-optical switching
in the coupled cavity-atom system can be realized with high switching
efficiencies and at low light intensities.


  The purpose was to investigate the spatial heterogeneity of prostate-specific
membrane antigen (PSMA) positron emission tomography (PET) uptake within
parotid glands. We aim to quantify patterns in well-defined regions to
facilitate further investigations. Furthermore, we investigate whether uptake
is correlated with computed tomography (CT) texture features. Parotid glands
from [18F]DCFPyL PSMA PET/CT images of 30 prostate cancer patients were
analyzed. Thresholding was used to define high-uptake regions, and uptake
statistics were computed within various divisions. Spearman's rank correlation
coefficient was calculated between PSMA PET uptake and the Grey Level Run
Length Matrix (GLRLM) using a long and short run length emphasis (GLRLML and
GLRLMS) in subregions of parotid glands. PSMA PET uptake was significantly
higher (p < 0.001) in lateral/posterior regions of the glands than
anterior/medial regions. Maximum uptake was found in the lateral half of
parotid glands in 50 out of 60 glands. The difference in SUV between parotid
halves is greatest when parotids are divided by a plane separating the
anterior/medial and posterior/lateral halves symmetrically. PSMA PET uptake was
significantly correlated with CT GLRLML (p < 0.001), and anti-correlated with
CT GLRLMS (p < 0.001). Uptake of PSMA PET is heterogeneous within parotid
glands, with uptake biased towards lateral and posterior regions. Uptake
patterns within parotid glands were found to be strongly correlated with CT
texture features, suggesting the possible future use of CT texture features as
a proxy for inferring PSMA PET uptake in salivary glands.


  We study electromagnetic streaming instabilities in thermal viscous regions
of rotating astrophysical objects, such as, protostellar and protoplanetary
magnetized accretion disks, molecular clouds, their cores, and elephant trunks.
The obtained results can also be applied to any regions of interstellar medium,
where different equilibrium velocities between charged species can arise. We
consider a weakly and highly ionized three-component plasma consisting of
neutrals and magnetized electrons and ions. The vertical perturbations along
the background magnetic field are investigated. The effect of perturbation of
collisional frequencies due to density perturbations of species is taken into
account. The growth rates of perturbations are found in a wide region of wave
number spectrum for media, where the thermal pressure is larger than the
magnetic pressure. It is shown that in cases of strong collisional coupling of
neutrals with ions the contribution of the viscosity is negligible.


  The determination of the speed of Coronal Mass Ejections (CMEs) is usually
done by tracking brighter features (such as the CME front and core) in visible
light coronagraphic images and by deriving unidimensional profiles of the CME
speed as a function of altitude or time. Nevertheless, CMEs are usually
characterized by the presence of significant density inhomogeneities
propagating outward with different radial and latitudinal projected speeds,
resulting in a complex evolution eventually forming the Interplanetary CME. In
this work, we demonstrate for the first time how coronagraphic image sequences
can be analyzed with cross-correlation technique to derive 2D maps of the
almost instantaneous plasma speed distribution within the body of CMEs. The
technique is first tested with the analysis of synthetic data, and then applied
to real observations. Results from this work allow to characterize the
distribution and time evolution of kinetic energy inside CMEs, as well as the
mechanical energy (combined with the kinetic and potential energy) partition
between the core and front of the CME. In the future, CMEs will be observed by
two channels (VL and UV Ly-$\alpha$) coronagraphs, such as Metis on-board ESA
Solar Orbiter mission as well as Ly-$\alpha$ Solar Telescope (LST) on-board
Chinese Advanced Space-based Solar Observatory (ASO-S) mission. Our results
will help the analysis of these future observations, helping in particular to
take into account the 2D distribution of Ly-$\alpha$ Doppler dimming effect.


  Finding quantitative aspects of quantum phenomena which cannot be explained
by any classical model has foundational importance for understanding the
boundary between classical and quantum theory. It also has practical
significance for identifying information processing tasks for which those
phenomena provide a quantum advantage. Using the framework of generalized
noncontextuality as our notion of classicality, we find one such nonclassical
feature within the phenomenology of quantum minimum error state discrimination.
Namely, we identify quantitative limits on the success probability for minimum
error state discrimination in any experiment described by a noncontextual
ontological model. These constraints constitute noncontextuality inequalities
that are violated by quantum theory, and this violation implies a quantum
advantage for state discrimination relative to noncontextual models.
Furthermore, our noncontextuality inequalities are robust to noise and are
operationally formulated, so that any experimental violation of the
inequalities is a witness of contextuality, independently of the validity of
quantum theory. Along the way, we introduce new methods for analyzing
noncontextuality scenarios, and demonstrate a tight connection between our
minimum error state discrimination scenario and a Bell scenario.


  We deal with nonlinear elliptic and parabolic systems that are the Bellman
like systems associated to stochastic differential games with mean field
dependent dynamics. The key novelty of the paper is that we allow heavily mean
field dependent dynamics. This in particular leads to a system of PDE's with
critical growth, for which it is rare to have an existence and/or regularity
result. In the paper, we introduce a structural assumptions that cover many
cases in stochastic differential games with mean filed dependent dynamics for
which we are able to establish the existence of a weak solution. In addition,
we present here a completely new method for obtaining the maximum/minimum
principles for systems with critical growths, which is a starting point for
further existence and also qualitative analysis.


  The issue of seamless identification of users previously tracked using
existing real-time optical position tracking system such as the OptiTrack
system and maintaining continuous tracking state (history) of each of those
users is a hard problem. In this article, we present a theoretical framework to
integrate existing tracking systems with features such as user identification
and history of up to `n' person activity. In our approach, we assume no direct
communication with the tracking system, but access to all data it collects.
Also, there are no guarantees that 1) the order of each tracked
retro-reflective sphere reported is the same, and 2) that there will be any
particular number of spheres in the room at any given time. We describe how the
data is fused with existing tracking data to provide a seamless transition
between other forms of position tracking.


  We prove the global well-posedness of three dimensional compressible
Navier-Stokes equations for some classes of large initial data, which is of
large oscillation for the density and large energy for the velocity. The
structure of the system (especially, the effective viscous flux) is fully
exploited.


  In this paper we explore the emergence of explosive synchronization (ES) in a
star network by considering the dynamics of coupled phase oscillators in the
presence of noise. While ES has been the subject of many recent studies, in
most cases deterministic dynamics was considered to explore the first-order
phase transition. This raises the issue of how robust ES is in situations where
fluctuations cannot be suppressed. Thus, to address this issue, we consider a
situation where the natural frequency is considered to be correlated with their
degrees. We observe that noise plays a crucial role when it is present in the
hub. By considering the model examples of Kuramoto and Stuart Landau
oscillators on each node, we examine the effect of noise strength in the hub.


  Explainable machine learning offers the potential to provide stakeholders
with insights into model behavior by using various methods such as feature
importance scores, counterfactual explanations, or influential training data.
Yet there is little understanding of how organizations use these methods in
practice. This study explores how organizations view and use explainability for
stakeholder consumption. We find that, currently, the majority of deployments
are not for end users affected by the model but rather for machine learning
engineers, who use explainability to debug the model itself. There is thus a
gap between explainability in practice and the goal of transparency, since
explanations primarily serve internal stakeholders rather than external ones.
Our study synthesizes the limitations of current explainability techniques that
hamper their use for end users. To facilitate end user interaction, we develop
a framework for establishing clear goals for explainability. We end by
discussing concerns raised regarding explainability.


  We show that the supertube configurations exist in all supersymmetric type
IIA backgrounds which are purely geometrical and which have, at least, one flat
direction. In other words, they exist in any spacetime of the form R^{1,1} x
M_8, with M_8 any of the usual reduced holonomy manifolds. These generalised
supertubes preserve 1/4 of the supersymmetries preserved by the choice of the
manifold M_8. We also support this picture with the construction of their
corresponding family of IIA supergravity backgrounds preserving from 1/4 to
1/32 of the total supercharges.


  Relations among integrals of logarithms, polylogarithms and Euler sums are
presented. A unifying element being the introduction of Nielsen's generalized
polylogarithms.


  Transport phenomena are ubiquitous in physics, and it is generally understood
that the environmental disorder and noise deteriorates the transfer of
excitations. There are however cases in which transport can be enhanced by
fluctuations. In the present work we show, by means of micromagnetics
simulations, that transport efficiency in a chain of classical macrospins can
be greatly increased by an optimal level of dephasing noise. We demonstrate
also the same effect in a simplified model, the dissipative Discrete Nonlinear
Schr\"odinger equation subject to phase noise. Our results point towards the
realisation of a large class of magnonics and spintronics devices, where
disorder and noise can be used to enhance spin-dependent transport efficiency.


  Attribute weighting and differential weighting, two major mechanisms for
computing context-dependent similarity or dissimilarity measures are studied
and compared. A dissimilarity measure based on subset size in the context is
proposed and its metrization and application are given. It is also shown that
while all attribute weighting dissimilarity measures are metrics differential
weighting dissimilarity measures are usually non-metric.


  The theory of mesoscopic fluctuations is applied to inhomogeneous solids
consisting of chaotically distributed regions with different crystalline
structure. This approach makes it possible to describe statistical properties
of such mixture by constructing a renormalized Hamiltonian. The relative
volumes occupied by each of the coexisting structures define the corresponding
geometric probabilities. In the case of a frozen heterophase system these
probabilities should be given a priori. And in the case of a thermal
heterophase mixture the structural probabilities are to be defined
self-consistently by minimizing a thermodynamical potential. This permits to
find the temperature behavior of the probabilities which is especially
important near the points of structural phase transitions. The presense of
these structural fluctuations yields a softening of a crystal and a decrease of
the effective Debye temperature. These effects can be directly seen by nuclear
gamma resonance since the occurrence of structural fluctuations is accompanied
by a noticeable sagging of the M\"ossbauer factor at the point of structural
phase transition. The structural fluctuations also lead to the attenuation of
sound and increase of isothermic compressibility.


  The breakup of inertial, solid aggregates in an incompressible, homogeneous
and isotropic three-dimensional turbulent flow is studied by means of a direct
numerical simulation, and by a Lagrangian tracking of the aggregates at varying
Stokes number and fluid-to-particle density ratio. Within the point-particle
approximation of the Maxey-Riley-Gatignol equations of motion, we analyse the
statistics of the time series of shear and drag stresses, which are here both
deemed as responsible for particle breakup. We observe that, regardless of the
Stokes number, the shear stresses produced by the turbulent velocity gradients
similarly impact the breakup statistics of inertial and neutrally buoyant
aggregates, and dictate the breakup rate of loose aggregates. When the density
ratio is different from unity, drag stresses become dominant and are seen to be
able to cause to breakup of also the most resistant aggregates. The present
work paves the way for including the role of inertia in population balance
models addressing particle breakup in turbulent flows.


  From an effective field theory of electromagnetism in vacuum including all
lowest-order nonlinear terms consistent with Lorentz invariance and locality of
photon/photon interactions, we derive an effective medium description of strong
background fields as regards their influence on a weak probe. We mainly
consider as background a pump beam with well-defined wave vector and
polarization. This leads us to define a nonlinear index of vacuum which, in the
Euler-Heisenberg model derived from QED, has an optimal value of $1.555 \times
10^{-33} \, {\rm cm}^{2}/{\rm W}$ for a linearly polarized pump as seen by a
counter-propagating, orthogonally polarized probe. We further generalize the
model to include coupling to an axion field. In the limit where the axion mass
is much smaller than the typical photon energy, this yields dispersive
corrections, and the axionic signature is found to be greatly enhanced for a
circularly polarized pump as compared to a linearly polarized one. The
formalism here presented points to a simplification of the DeLLight experiment
[X. Sarazin et al., Eur. Phys. J. D 70, 13 (2016)] aiming to measure the
deflection of a probe by a tightly focused laser pulse.


  Remote sensing images are used for a variety of analyses, from agricultural
monitoring, to disaster relief, to resource planning, among others. The images
can be corrupted due to a number of reasons, including instrument errors and
natural obstacles such as clouds. We present here a novel approach for
reconstruction of missing information in such cases using only the corrupted
image as the input. The Deep Image Prior methodology eliminates the need for a
pre-trained network or an image database. It is shown that the approach easily
beats the performance of traditional single-image methods.


  This paper considers a cloud-RAN architecture with cache-enabled
multi-antenna Edge Nodes (ENs) that deliver content to cache-enabled end-users.
The ENs are connected to a central server via limited-capacity fronthaul links,
and, based on the information received from the central server and the cached
contents, they transmit on the shared wireless medium to satisfy users'
requests. By leveraging cooperative transmission as enabled by ENs' caches and
fronthaul links, as well as multicasting opportunities provided by users'
caches, a close-to-optimal caching and delivery scheme is proposed. As a
result, the minimum Normalized Delivery Time (NDT), a high-SNR measure of
delivery latency, is characterized to within a multiplicative constant gap of
$3/2$ under the assumption of uncoded caching and fronthaul transmission, and
of one-shot linear precoding. This result demonstrates the interplay among
fronthaul links capacity, ENs' caches, and end-users' caches in minimizing the
content delivery time.


  The experimental data on atmospheric and solar neutrinos suggest that there
is near-maximal mixing between \nu_\mu and \nu_\tau but that their masses are
hierarchically separated. In models of Abelian horizontal symmetries, mixing of
O(1) generically implies that the corresponding masses are of the same order of
magnitude. We describe two new mechanisms by which a large hierarchy between
strongly mixed neutrinos can be achieved in this framework. First, a discrete
Abelian symmetry can give the desired result in three ways: mass enhancement,
mixing enhancement and mass suppression. Second, holomorphic zeros can give
mass suppression.


  Airports are constantly facing a variety of hazards and threats from natural
disasters to cybersecurity attacks and airport stakeholders are confronted with
making operational decisions under irregular conditions. We introduce the
concept of the foundational twin, which can serve as a resilient data platform,
incorporating multiple data sources and enabling the interaction between an
umbrella of twins. We then focus on providing data sources and metrics for each
foundational twin, with an emphasis on the environmental airport twin for major
US airports.


  The constraints imposed by nano- and microscale confinement on the
conformational degrees of freedom of thermally fluctuating biopolymers are
utilized in contemporary nano-devices to specifically elongate and manipulate
single chains. A thorough theoretical understanding and quantification of the
statistical conformations of confined polymer chains is thus a central concern
in polymer physics. We present an analytical calculation of the radial
distribution function of harmonically confined semiflexible polymers in the
weakly bending limit. Special emphasis has been put on a proper treatment of
global modes, i.e. the possibility of the chain to perform global movements
within the channel. We show that the effect of these global modes significantly
impacts the chain statistics in cases of weak and intermediate confinement.
Comparing our analytical model to numerical data from Monte Carlo simulations
we find excellent agreement over a broad range of parameters.


  Semi-implicit methods are powerful and efficient tools for the
three-dimensional modeling of coastal and oceanic processes. A semi-implicit
finite difference method for 3D hydrostatic primitive equations is presented in
this paper. The governing equations are time-discretized with an implicit
treatment of barotropic pressure gradient and vertical viscosity. The
discretized momentum equations along a water column are coupled with the
depth-integrated continuity equation of the column to construct a linear system
for free-surface elevations. The novelty of this work lies in formulating an
efficient method with the order of complexity O(N) for coupling the momentum
and the continuity equations. In this method, the horizontal velocity
components are expressed in terms of neighbor free-surface elevations by some
simple recursive formulas and then are substituted in the integrated continuity
equation.


  We investigate a canonical way of defining bisimilarity of systems when their
semantics is given by a coreflection, typically in a category of transition
systems. We use the fact, from Joyal et al., that coreflections preserve open
morphisms situations in the sense that a coreflection induces a path
subcategory in the category of systems in such a way that open bisimilarity
with respect to the induced path category coincides with usual bisimilarity of
their semantics. We prove that this method is particularly well-suited for
systems with quantitative information: we canonically recover the path category
of probabilistic systems from Cheng et al., and of timed systems from Nielsen
et al., and, finally, we propose a new canonical path category for hybrid
systems.


  The field of laser-matter interaction traditionally deals with the response
of atoms, molecules and plasmas to an external light wave. However, the recent
sustained technological progress is opening up the possibility of employing
intense laser radiation to trigger or substantially influence physical
processes beyond atomic-physics energy scales. Available optical laser
intensities exceeding $10^{22}\;\text{W/cm$^2$}$ can push the fundamental
light-electron interaction to the extreme limit where radiation-reaction
effects dominate the electron dynamics, can shed light on the structure of the
quantum vacuum, and can trigger the creation of particles like electrons, muons
and pions and their corresponding antiparticles. Also, novel sources of intense
coherent high-energy photons and laser-based particle colliders can pave the
way to nuclear quantum optics and may even allow for potential discovery of new
particles beyond the Standard Model. These are the main topics of the present
article, which is devoted to a review of recent investigations on high-energy
processes within the realm of relativistic quantum dynamics, quantum
electrodynamics, nuclear and particle physics, occurring in extremely intense
laser fields.


  Heusler alloy Co2FeAl was employed as ferromagnetic layers in
Co2FeAl/Ru/Co2FeAl synthetic antiferromagnet structures. The experimental
results show that the structure with a Ru thickness of 0.45 nm takes on
strongly antiferromagnetic coupling, which maintains up to 150 oC annealing for
1 hour. The structure has a very low saturation magnetization Ms of 425 emu/cc,
a low switching field Hsw of 4.3 Oe and a high saturation field Hs of 5257 Oe
at room temperature, which are favorable for application in ultrahigh density
magnetic read heads or other magnetic memory devices. XRD study testifies that
the as-deposited Co2FeAl film is in B2 phase. Therefore Heusler alloys can be
used to fabricate SyAF and it is possible to make "all-Heusler" spin-valves or
magnetic tunneling junctions with better magnetic switching properties and high
magnetoresistance.


  We establish the existence and the uniqueness for the Boussinesq system in
the whole 3D space in the critical space of continuous in time with values in
the power 3 integrable in space functions for the velocity and square
integrable in time with values in the power 3/2 integrable in space.


  We present MedSim, a novel semantic SIMilarity method based on public
well-established bio-MEDical knowledge graphs (KGs) and large-scale corpus, to
study the therapeutic substitution of antibiotics. Besides hierarchy and corpus
of KGs, MedSim further interprets medicine characteristics by constructing
multi-dimensional medicine-specific feature vectors. Dataset of 528 antibiotic
pairs scored by doctors is applied for evaluation and MedSim has produced
statistically significant improvement over other semantic similarity methods.
Furthermore, some promising applications of MedSim in drug substitution and
drug abuse prevention are presented in case study.


  This paper addresses the tradeoff between standard accuracy on clean examples
and robustness against adversarial examples in deep neural networks (DNNs).
Although adversarial training (AT) improves robustness, it degrades the
standard accuracy, thus yielding the tradeoff. To mitigate this tradeoff, we
propose a novel AT method called ARREST, which comprises three components: (i)
adversarial finetuning (AFT), (ii) representation-guided knowledge distillation
(RGKD), and (iii) noisy replay (NR). AFT trains a DNN on adversarial examples
by initializing its parameters with a DNN that is standardly pretrained on
clean examples. RGKD and NR respectively entail a regularization term and an
algorithm to preserve latent representations of clean examples during AFT. RGKD
penalizes the distance between the representations of the standardly pretrained
and AFT DNNs. NR switches input adversarial examples to nonadversarial ones
when the representation changes significantly during AFT. By combining these
components, ARREST achieves both high standard accuracy and robustness.
Experimental results demonstrate that ARREST mitigates the tradeoff more
effectively than previous AT-based methods do.


  The boson-pair coherent state developed in Part (I) is generalized to the
case in which the state is a mixture of even-boson and odd-boson number states.
A general framework is shown and its three concrete examples are discussed.
Main idea is in the application of the deformed boson scheme presented by the
present authors.