  The lock-in frequency and lock-in range concepts were introduced in 1966 by
Floyd Gardner to describe the frequency differences of phase-locked loop based
circuit for which the loop can acquire lock within one beat, i.e. without cycle
slipping. These concepts became popular among engineering community and were
given in various engineering publications. However rigorous mathematical
explanations these concepts turned out to be a challenging task, thus, in the
2nd edition of Gardner's well-known work, Phaselock Techniques, he wrote that
"despite its vague reality, lock-in range is a useful concept" and posed the
problem "to define exactly any unique lock-in frequency". In this paper an
effective solution for Gardner's problem on the unique definition of the
lock-in frequency and lock-in range is discussed. The lock-in range and lock-in
frequency computation is explained on the example of classical second-order PLL
with lead-lag and active proportional-integral filters. The obtained results
can also be used for the lock-in range computation of such PLL-based circuits
as two-phase PLL, two-phase Costas loop, BPSK Costas loop, and optical Costas
loop, used in intersatellite communication.


  Oscillation frequency of spin torque oscillator with a perpendicularly
magnetized free layer and an in-plane magnetized pinned layer is theoretically
investigated by taking into account the field-like torque. It is shown that the
field-like torque plays an important role in finding the balance between the
energy supplied by the spin torque and the dissipation due to the damping,
which results in a steady precession. The validity of the developed theory is
confirmed by performing numerical simulations based on the
Landau-Lifshitz-Gilbert equation.


  The non-Abelian braiding of Majorana fermions is one of the most promising
operations providing a key building block for the realization of topological
quantum computation. Recently, the chiral Majorana fermions were observed in a
hybrid junction btween a quantum anomalous Hall insulator and an s-wave
superconductor. Here we show that if a quantum dot or Majorana zero mode
couples to the chiral Majorana fermions, the resulting resonant exchange of
chiral Majorana fermions can lead to the non-Abelian braiding. Remarkably, any
operation in the braid group can be achieved by this scheme. We further propose
electrical transport experiments to observe the braiding of four chiral
Majorana fermions and demonstrate the non-Abelian braiding statistics in
four-terminal devices of the hybrid junctions. Both a conductance peak due to
the braiding and the braiding-order dependent conductance are predicted. These
findings pave a way to perform any braiding operation of chiral Majorana
fermions by electrically controllable quantum dots.


  A mixed finite element method for the Navier-Stokes equations is introduced
in which the stress is a primary variable. The variational formulation retains
the mathematical structure of the Navier-Stokes equations and the classical
theory extends naturally to this setting. Finite element spaces satisfying the
associated inf-sup conditions are developed.


  Photonic crystals doped with resonant atoms allow for uniquely advantageous
nonlinear modes of optical propagation: (a) Self-induced transparency (SIT)
solitons and multi-dimensional localized "bullets" propagating at photonic band
gap frequencies. These modes can exist even at ultraweak intensities (few
photons) and therefore differ substantially either from solitons in
Kerr-nonlinear photonic crystals or from SIT solitons in uniform media. (b)
Cross-coupling between pulses exhibiting electromagnetically induced
transparency (EIT) and SIT gap solitons. We show that extremely strong
correlations (giant cross-phase modulation) can be formed between the two
pulses. These features may find applications in high-fidelity classical and
quantum optical communications.


  Floating particles that are initially distributed uniformly on the surface of
a turbulent fluid, subsequently coagulate, until finally a steady state is
reached. This being so, they manifestly form a compressible system. In this
experiment, the information dimension D_1, and the Lyapunov exponents of the
coagulated floaters, are measured. The trajectories and the velocity fields of
the particles are captured in a sequence of rapidly acquired images. Then the
velocity sequence is randomly shuffled in time to generate new trajectories.
This analysis mimics the Kraichnan ensemble and yields properties of a velocity
correlation function that is delta-correlated in time (but not in space). The
measurements are compared with theoretical expectations and with simulations of
Boffetta et al., that closely mimic the laboratory experiment reported here.


  We have investigated the combined effects of a multiplicative noise and
nonlinear conductivity on the charge density wave (CDW) dynamics of the
quasi-one dimensional conductor Rb0.30MoO3. When the amplitude of a bipolar
rectangular voltage pulse excitation is modulated by a multiplicative Gaussian
white noise perturbation, the average pulse amplitude is smaller than the
unperturbed one and shows a non monotonous behaviour when the pulse amplitude
is increased. We analyze the transient response in terms of an increase of
phase coherence of the charge-density-wave.


  We prove some new $L^p$ estimates for maximal Bochner-Riesz operator in the
plane.


  In a decentralized household energy system comprised of various devices such
as home appliances, electric vehicles, and solar panels, end-users are able to
dig deeper into the system's details and further achieve energy sustainability
if they are presented with data on the electric energy consumption and
production at the granularity of the device. However, many databases in this
field are siloed from other domains, including solely information pertaining to
energy. This may result in the loss of information (e.g. weather) on each
device's energy use. Meanwhile, a large number of these datasets have been
extensively used in computational modeling techniques such as machine learning
models. While such computational approaches achieve great accuracy and
performance by concentrating only on a local view of datasets, model
reliability cannot be guaranteed since such models are very vulnerable to data
input fluctuations when information omission is taken into account. This
article tackles the data isolation issue in the field of smart energy systems
by examining Semantic Web methods on top of a household energy system. We offer
an ontology-based approach for managing decentralized data at the device-level
resolution in a system. As a consequence, the scope of the data associated with
each device may easily be expanded in an interoperable manner throughout the
Web, and additional information, such as weather, can be obtained from the Web,
provided that the data is organized according to W3C standards.


  The autoignition delays of iso-butanol, oxygen, and nitrogen mixtures have
been measured in a heated rapid compression machine (RCM). At compressed
pressures of 15 and 30 bar, over the temperature range 800-950 K, and for
equivalence ratio of $\phi$ = 0.5 in air, no evidence of an NTC region of
overall ignition delay is found. By comparing the data from this study taken at
$\phi$ = 0.5 to previous data collected at $\phi$ = 1.0 (Weber et al. 2013), it
was found that the $\phi$ = 0.5 mixture was less reactive (as measured by the
inverse of the ignition delay) than the $\phi$ = 1.0 mixture for the same
compressed pressure. Furthermore, a recent chemical kinetic model of
iso-butanol combustion was updated using the automated software Reaction
Mechanism Generator (RMG) to include low- temperature chain branching pathways.
Comparison of the ignition delays with the updated model showed reasonable
agreement for most of the experimental conditions. Nevertheless, further work
is needed to fully understand the low temperature pathways that control
iso-butanol autoignition in the RCM.


  We report an investigation on the properties of 0.33 ML of Sn on Ge(111) at
temperatures down to 5 K. Low-energy electron diffraction and scanning
tunneling microscopy show that the (3x3) phase formed at 200 K, reverts to a
new (root-3xroot-3)R30 phase below 30 K. The vertical distortion characteristic
of the (3x3) phase is lost across the phase transition. Angle-resolved
photoemission experiments show that concomitantly with the structural phase
transition, a metal-insulator phase transition takes place. In agreement with
theoretical predictions, the (root-3xroot-3)R30 ground state is interpreted as
the experimental realization of a Mott insulator for a narrow half-filled band
in a two-dimensional triangular lattice.


  We introduce and analyze a fast iterative method based on sequential Bregman
projections for nonlinear inverse problems in Banach spaces. The key idea, in
contrast to the standard Landweber method, is to use multiple search directions
per iteration in combination with a regulation of the step width in order to
reduce the total number of iterations. This method is suitable for both exact
and noisy data. In the latter case, we obtain a regularization method. An
algorithm with two search directions is used for the numerical identification
of a parameter in an elliptic boundary value problem.


  We discuss 94 Extended Green Objects (EGOs) in the northern Galactic plane
cataloged by Cyganowski et al, based on near-infrared narrowband H2 (2.122
{\mu}m and continuum observations from the United Kingdom Infrared Telescope.
This data set is three times larger than our previous study, and is unbiased by
preselection. As discussed in the previous paper, the morphologies of the 4.5
{\mu}m emission generally resemble those of the near-infrared continuum, but
are different from those of the H2 emission. Of our sample, only 28% of EGOs
with H2 emission show similar morphologies between 4.5 {\mu}m and H2 emission.
These results suggest that the 4.5 {\mu}m emission mainly comes from scattered
continuum from the embedded young stellar object (YSO), and partially from H2
emission. About half of EGOs are associated with H2 outflows, if the H2 outflow
incompleteness is considered. The H2 outflow detection rate for EGOs with
K-band detections (61%) is significantly higher than for those without K-band
detections (36%). This difference may be due to the fact that both H2 and
K-band emissions are associated with outflows, i.e., H2 emission and K-band
continuum are associated with shocks and outflow cavities, respectively. We
also compared the correlation between the H2 outflows and Class I 44 GHz
methanol masers from literature. The methanol masers can be located upstream or
downstream of the H2 outflows and some bright H2 spots or outflows are not
associated with methanol masers, suggesting that methanol masers and H2
emission trace different excitation conditions.


  In this paper, we propose a convolutional layer inspired by optical flow
algorithms to learn motion representations. Our representation flow layer is a
fully-differentiable layer designed to capture the `flow' of any representation
channel within a convolutional neural network for action recognition. Its
parameters for iterative flow optimization are learned in an end-to-end fashion
together with the other CNN model parameters, maximizing the action recognition
performance. Furthermore, we newly introduce the concept of learning `flow of
flow' representations by stacking multiple representation flow layers. We
conducted extensive experimental evaluations, confirming its advantages over
previous recognition models using traditional optical flows in both
computational speed and performance. Code/models available here:
https://piergiaj.github.io/rep-flow-site/


  We prove the existence of regular dissipative solutions and global attractors
for the 3D Brinkmann-Forchheimer equations with the nonlinearity of an
arbitrary polynomial growth rate. In order to obtain this result, we prove the
maximal regularity estimate for the corresponding semi-linear stationary Stokes
problem using some modification of the nonlinear localization technique. The
applications of our results to the Brinkmann-Forchheimer equation with the
Navier-Stokes inertial term are also considered.


  We theoretically show that the carrier transport in monolayer Fe3GeTe2
experiences a transition between anomalous Hall effect and spin Hall effect
when the spin polarization of disorders switches between out-of-plane and
in-plane. These Hall effects are allowed when the magnetization is polarized
in-plane, breaking the C3 rotation symmetry. The transition originates from the
selection rule of spin scattering, the strong spin-orbit coupling, and the van
Hove singularities near the Fermi surface. The scattering selection rule
tolerates the sign change of the disorder spin, which provides a convenient
method to detect the switching of antiferromagnetic insulators regardless of
the interfacial roughness in a heterostructure. This provides a convenient
platform for the study of 2D spintronics through various van-der-Waals
heterostructures.


  Modern learning models are characterized by large hyperparameter spaces and
long training times. These properties, coupled with the rise of parallel
computing and the growing demand to productionize machine learning workloads,
motivate the need to develop mature hyperparameter optimization functionality
in distributed computing settings. We address this challenge by first
introducing a simple and robust hyperparameter optimization algorithm called
ASHA, which exploits parallelism and aggressive early-stopping to tackle
large-scale hyperparameter optimization problems. Our extensive empirical
results show that ASHA outperforms existing state-of-the-art hyperparameter
optimization methods; scales linearly with the number of workers in distributed
settings; and is suitable for massive parallelism, as demonstrated on a task
with 500 workers. We then describe several design decisions we encountered,
along with our associated solutions, when integrating ASHA in Determined AI's
end-to-end production-quality machine learning system that offers
hyperparameter tuning as a service.


  Fully frustrated one-dimensional diamond Josephson chains have been shown [B.
Dou\c{c}ot and J. Vidal, Phys. Rev. Lett. {\bf 88}, 227005 (2002)] to posses a
remarkable property: The superfluid phase occurs through the condensation of
pairs of Cooper pairs. By means of Monte Carlo simulations we analyze
quantitatively the Insulator to $4e$-Superfluid transition. We determine the
location of the critical point and discuss the behaviour of the phase-phase
correlators. For comparison we also present the case of a diamond chain at zero
and 1/3 frustration where the standard $2e$-condensation is observed.


  In this paper, we investigate the kinetically coupled early dark energy (EDE)
and scalar field dark matter to address cosmological tensions. The EDE model
presents an intriguing theoretical approach to resolving the Hubble tension,
but it exacerbates the large-scale structure tension. We consider the
interaction between dark matter and EDE, such that the drag of dark energy on
dark matter suppresses structure growth, which can alleviate large-scale
structure tension. We replace cold dark matter with scalar field dark matter,
which has the property of suppressing structure growth on small scales. We
employed the Markov Chain Monte Carlo method to constrain the model parameters,
our new model reveals a non-zero coupling constant of $0.030 \pm 0.026$ at a
68% confidence level. The coupled model yields the Hubble constant value of
$72.38^{+0.71}_{-0.82}$ km/s/Mpc, which resolves the Hubble tension. However,
similar to the EDE model, it also obtains a larger $S_8$ value compared to the
$\Lambda$CDM model, further exacerbating the large-scale structure tension. The
EDE model and the new model yield the best-fit values of $0.8316$ and $0.8146$
for $S_8$, respectively, indicating that the new model partially alleviates the
negative effect of the EDE model. However, this signature disappears when
comparing marginalised posterior probabilities, and both models produce similar
results. The values obtained from the EDE model and the new model are
$0.822^{+0.011}_{-0.0093}$ and $0.819^{+0.013}_{-0.0092}$, respectively, at a
68% confidence level.


  Following the well-established terminology in commutative algebra, any (not
necessarily commutative) finite-dimensional local algebra $A$ with radical $J$
will be said to be short provided $J^3 = 0$. As in the commutative case, we
show: if a short local algebra $A$ has an indecomposable non-projective
Gorenstein-projective module $M$, then either $A$ is self-injective (so that
all modules are Gorenstein-projective) and then $|J^2| \le 1$, or else $|J^2| =
|J/J^2| - 1$ and $|JM| = |J^2||M/JM|$. More generally, we focus the attention
to semi-Gorenstein-projective and $\infty$-torsionfree modules, even to
$\mho$-paths of length 2, 3 and 4. In particular, we show that the existence of
a non-projective reflexive module implies that $|J^2| < |J/J^2|$ and further
restrictions. In addition, we consider exact complexes of projective modules
with a non-projective image. Again, as in the commutative case, we see that if
such a complex exists, then $A$ is self-injective or satisfies the condition
$|J^2| = |J/J^2| - 1.$ Also, we show that any non-projective
semi-Gorenstein-projective module $M$ satisfies $Ext^1(M,M) \neq 0$. In this
way, we prove the Auslander-Reiten conjecture (one of the classical homological
conjectures) for arbitrary short local algebras.
  Many arguments used in the commutative case actually work in general, but
there are interesting differences and some of our results may be new also in
the commutative case.


  In this paper, we report an experiment, which demonstrates computation of
topological charges of two optical vortices via non-degenerate four-wave-mixing
process. We show that the output signal beam carries orbital angular momentum
which equals to the subtraction of the orbital angular momenta of the probe
light and the backward pump light. The ⁸⁵Rb atoms are used as the
nonlinear medium, which transfer the orbital angular momenta of lights.


  The d-dimensional Lambda-Fleming-Viot generator acting on functions g(x),
with x being a vector of d allele frequencies, can be written as a
Wright-Fisher generator acting on functions g with a modified random linear
argument of x induced by partitioning occurring in the Lambda-Fleming-Viot
process. The eigenvalues and right polynomial eigenvectors are easy to see from
this representation. The two-dimensional process, which has a one-dimensional
generator, is considered in detail. A non-linear equation is found for the
Green's function. In a model with genic selection a proof is given that there
is a critical selection value such that if the selection coefficient is greater
or equal to the critical value then fixation, when the boundary 1 is hit, has
probability 1 beginning from any non-zero frequency. This is an analytic proof
different from proofs by Der, Epstein and Plotkin (2011) and Foucart (2013).
When fixation is not certain the fixation probability can be computed from an
algorithm in the paper. An application in the infinitely-many-alleles
Lambda-Fleming-Viot process is finding an interesting identity for the
frequency spectrum of alleles that is based on size-biassing. The moment dual
process in the Fleming-Viot process is the usual Lambda-coalescent tree back in
time. The Wright-Fisher representation using a different set of polynomials
g_n(x) as test functions produces a dual death process which has a similarity
to the Kingman coalescent and decreases by units of one. The eigenvalues of the
process are analogous to the Jacobi polynomials when expressed in terms of
g_n(x), playing the role of x^n. E[g_n(X)] under the stationary distribution
when there is mutation is analogous to the n th moment in a Beta distribution.
There is a version g_n(X), when X and n are d-dimensional, and even an
intriguing Ewens' sampling formula analogy when d tends to infinity.


  In this paper we present an efficient computer aided mass classification
method in digitized mammograms using Artificial Neural Network (ANN), which
performs benign-malignant classification on region of interest (ROI) that
contains mass. One of the major mammographic characteristics for mass
classification is texture. ANN exploits this important factor to classify the
mass into benign or malignant. The statistical textural features used in
characterizing the masses are mean, standard deviation, entropy, skewness,
kurtosis and uniformity. The main aim of the method is to increase the
effectiveness and efficiency of the classification process in an objective
manner to reduce the numbers of false-positive of malignancies. Three layers
artificial neural network (ANN) with seven features was proposed for
classifying the marked regions into benign and malignant and 90.91% sensitivity
and 83.87% specificity is achieved that is very much promising compare to the
radiologist's sensitivity 75%.


  Let X be a projective variety, $\sigma$ an automorphism of X, L a
$\sigma$-ample invertible sheaf on X, and Z a closed subscheme of X. Inside the
twisted homogeneous coordinate ring $B = B(X, L, \sigma)$, let I be the right
ideal of sections vanishing at Z. We study the subring R = k + I of B. Under
mild conditions on Z and $\sigma$, R is the idealizer of I in B: the maximal
subring of B in which I is a two-sided ideal.
  We give geometric conditions on Z and $\sigma$ that determine the algebraic
properties of R, and show that if Z and $\sigma$ are sufficiently general, in a
sense we make precise, then R is left and right noetherian, has finite left and
right cohomological dimension, is strongly right noetherian but not strongly
left noetherian, and satisfies right $\chi_d$ (where d = \codim Z) but fails
left $\chi_1$. We also give an example of a right noetherian ring with infinite
right cohomological dimension, partially answering a question of Stafford and
Van den Bergh. This generalizes results of Rogalski in the case that Z is a
point in $\mathbb{P}^d$.


  Passenger request prediction is essential for operations planning, control,
and management in ride-sharing platforms. While the demand prediction problem
has been studied extensively, the Origin-Destination (OD) flow prediction of
passengers has received less attention from the research community. This paper
develops a Graph Neural Network framework along with the Attention Mechanism to
predict the OD flow of passengers. The proposed framework exploits various
linear and non-linear dependencies that arise among requests originating from
different locations and captures the repetition pattern and the contextual data
of that place. Moreover, the optimal size of the grid cell that covers the road
network and preserves the complexity and accuracy of the model is determined.
Extensive simulations are conducted to examine the characteristics of our
proposed approach and its various components. The results show the superior
performance of our proposed model compared to the existing baselines.


  To make precision measurements with a CsI(Tl) calorimeter in a high
luminosity environment requires that the crystals are well calibrated and
continually monitored for radiation damage. This should not effect the total
integrated luminosity which is particularly important for the \babar
calorimeter to enable it to make CP violation measurements in the $B$ meson
system. To achieve this goal a fibre-optic light pulser system was designed
using xenon flash lamps as the light source. A novel light distribution method
was developed using an array of graded index microlenses. Some initial results
from performance studies are presented.


  We demonstrate control by applied electric field of the charge states in
single self-assembled InP quantum dots placed in GaInP Schottky structures
grown by metalorganic vapor phase epitaxy. This has been enabled by growth
optimization leading to suppression of formation of large dots uncontrollably
accumulating charge. Using bias- and polarization-dependent
micro-photoluminescence, we identify the exciton multi-particle states and
carry out a systematic study of the neutral exciton state dipole moment and
polarizability. This analysis allows for the characterization of the exciton
wavefunction properties at the single dot level for this type of quantum dots.
Photocurrent measurements allow further characterization of exciton properties
by electrical means, opening new possibilities for resonant excitation studies
for such system.


  We investigate the impact of different properties of the nuclear equation of
state in core-collapse supernovae, with a focus on the proto-neutron-star
contraction and its impact on the shock evolution. To this end, we introduce a
range of equations of state that vary the nucleon effective mass,
incompressibility, symmetry energy, and nuclear saturation point. This allows
us to point to the different effects in changing these properties from the
Lattimer and Swesty to the Shen et al. equations of state, the two most
commonly used equations of state in simulations. In particular, we trace the
contraction behavior to the effective mass, which determines the thermal
nucleonic contributions to the equation of state. Larger effective masses lead
to lower pressures at nuclear densities and a lower thermal index. This results
in a more rapid contraction of the proto-neutron star and consequently higher
neutrino energies, which aids the shock evolution to a faster explosion.


  The coexistence of superconductivity and ferromagnetism is a long-standing
issue in superconductivity due to the antagonistic nature of these two ordered
states. Experimentally identifying and characterizing novel heterointerface
superconductors that coexist with magnetism presents significant challenges.
Here, we report the experimental observation of two-dimensional long-range
ferromagnetic order in the KTaO$_3$ heterointerface superconductor, showing the
coexistence of superconductivity and ferromagnetism. Remarkably, our direct
current superconducting quantum interference device measurements reveal an
in-plane magnetization hysteresis loop persisting above room temperature.
Moreover, the first-principles calculations and X-ray magnetic circular
dichroism measurements provide decisive insights into the origin of the
observed robust ferromagnetism, attributing it to oxygen vacancies that
localize electrons in nearby Ta 5$d$ states. Our findings not only suggest
KTaO$_3$ heterointerfaces as time-reversal symmetry breaking superconductors,
but also inject fresh momentum into the exploration of the intricate interplay
between superconductivity and magnetism, enhanced by the strong spin-orbit
coupling inherent to the heavy Ta in 5$d$ orbitals of KTaO$_3$
heterointerfaces.


  This paper introduces the School Bus Routing Problem with Open Offer Policy
(SBRP-OOP) that seeks to improve capacity usage and minimize the bus fleet by
openly offering a monetary incentive to students willing to opt out of using a
bus. We propose a mathematical formulation to determine a pricing strategy that
balances the trade-off between incentive payments for students who choose not
to use the bus with the expected savings obtained from operating fewer buses.
To evaluate the effectiveness of the approach, we conducted simulations using
both synthetic and real instances from a real operational context in the
Williamsville Central School District (WCSD) of New York.


  We show that for any irreducible representation of $Sp_{4n}(F_{q})$, the
subspace of all its $Sp_{2n}(F_{q^{2}})$-invariants is at most one-dimensional.
In terms of Lusztig symbols, we give a complete list of irreducible unipotent
representations of $Sp_{4n}(F_{q})$ which have a nonzero
$Sp_{2n}(F_{q^{2}})$-invariant and, in particular, we prove that every
irreducible unipotent cuspidal representation has a one-dimensional subspace of
$Sp_{2n}(F_{q^{2}})$-invariants. As an application, we give an elementary proof
of the fact that the unipotent cuspidal representation is defined over $Q$,
which was proved by Lusztig.


  We demonstrate the reversible in situ photoreduction of molecular junctions
of phosphomolybdate [PMo12O40]3- monolayer self-assembled on flat gold
electrodes, connected by the tip of a conductive atomic force microscope. The
conductance of the one electron reduced [PMo12O40]4- molecular junction is
increased by ca. 10, this open-shell state is stable in the junction in air at
room temperature. The analysis of a large current-voltage dataset by
unsupervised machine learning and clustering algorithms reveals that the
electron transport in the pristine phosphomolybdate junctions leads to
symmetric current-voltage curves, controlled by the lowest unoccupied molecular
orbital (LUMO) at 0.6 - 0.7 eV above the Fermi energy with ca. 25% of the
junctions having a better electronic coupling to the electrodes than the main
part of the dataset. This analysis also shows that a small fraction (ca. 18% of
the dataset) of the molecules is already reduced. The UV light in situ
photoreduced phosphomolybdate junctions are systematically featuring slightly
asymmetric current - voltage behaviors, which is ascribed to electron transport
mediated by the single occupied molecular orbital (SOMO) nearly at resonance
with the Fermi energy of the electrode and by a closely located single
unoccupied molecular orbital (SUMO) at ca. 0.3 eV above the SOMO with a weak
electronic coupling to the electrodes (ca. 50% of the dataset) or at ca. 0.4 eV
but with a better electrode coupling (ca. 50% of the dataset). These results
shed lights to the electronic properties of reversible switchable redox
polyoxometalates, a key point for potential applications in nanoelectronic
devices.


  One way in which the human immunodeficiency virus (HIV-1) replicates within a
host is by infecting activated CD4+ T-cells, which then produce additional
copies of the virus. Even with the introduction of antiretroviral drug therapy,
which has been very successful over the past decade, a large obstacle to the
complete eradication of the virus is the presence of viral reservoirs in the
form of latently infected CD4+ T-cells. We consider a model of HIV infection
that describes T-cell and viral interactions, as well as, the production and
activation of latently infected T-cells. Upon determining equilibrium states of
the latent cell model, the local and global asymptotic behavior of solutions is
examined, and the basic reproduction number of the system is computed to be
strictly less than that of the corresponding three-component model, which omits
the effects of latent infection. In particular, this implies that a wider
variety of parameter values will lead to viral eradication as $t \to \infty$
due to the appearance of latent CD4+ T-cells. With this realization we discuss
possible alternative notions for eradication and persistence of infection other
than traditional tools. These results are further illustrated by a number of
numerical simulations.


  Recently, the development of open-source large language models (LLMs) has
advanced rapidly. Nevertheless, due to data constraints, the capabilities of
most open-source LLMs are primarily focused on English. To address this issue,
we introduce the concept of $\textit{chat vector}$ to equip pre-trained
language models with instruction following and human value alignment via simple
model arithmetic. The chat vector is derived by subtracting the weights of a
pre-trained base model (e.g. LLaMA2) from those of its corresponding chat model
(e.g. LLaMA2-chat). By simply adding the chat vector to a continual pre-trained
model's weights, we can endow the model with chat capabilities in new languages
without the need for further training. Our empirical studies demonstrate the
superior efficacy of the chat vector from three different aspects: instruction
following, toxicity mitigation, and multi-turn dialogue. Moreover, to showcase
the adaptability of our approach, we extend our experiments to encompass
various languages, base models, and chat vectors. The results underscore the
chat vector's simplicity, effectiveness, and wide applicability, making it a
compelling solution for efficiently enabling conversational capabilities in
pre-trained language models. Our code is available at
https://github.com/aqweteddy/ChatVector.


  The tidal disruption event (TDE) PS1-10jh lacked strong Balmer lines but
showed strong, broad, He II emission both before maximum light and for at least
8 months thereafter. Gezari et al. interpreted this as evidence for the
disruption of a rare hydrogen-deficient star. However, Guillochon et al. have
argued instead that the disrupted star was a normal main-sequence star and that
the strength of the He II emission compared with the Balmer lines is a result
the emission being similar to the broad-line region (BLR) of an AGN, but
lacking the outer, lower-ionization BLR gas. We show that the profile of He II
4686 in PS1-10jh is similar to the blueshifted profiles of high-ionization
lines in AGNs. We find an He II 4686/Halpha ratio for PS1-10jh of ~ 3.7. We
show that both the high-velocity gas of the inner BLR of normal AGNs and the
spectra of type II-P supernovae right after shock break out also produce very
high He II 4686/Halpha ratios. A high He II 4686/Halpha ratio can thus be
produced with a solar H/He abundance ratio. We demonstrate from photoionization
modelling that the estimated He II 4686/Halpha ratio can be produced with a BLR
truncated before the He++ Stroemgren length if the density is ~ 10^{11}
cm^{-3}. The similarity of the He II 4686 emission in PS1-10jh to the emission
from the inner BLRs of AGNs supports the idea that the emission after a TDE
event is similar to that of normal AGNs.


  Managing inputs that are novel, unknown, or out-of-distribution is critical
as an agent moves from the lab to the open world. Novelty-related problems
include being tolerant to novel perturbations of the normal input, detecting
when the input includes novel items, and adapting to novel inputs. While
significant research has been undertaken in these areas, a noticeable gap
exists in the lack of a formalized definition of novelty that transcends
problem domains. As a team of researchers spanning multiple research groups and
different domains, we have seen, first hand, the difficulties that arise from
ill-specified novelty problems, as well as inconsistent definitions and
terminology. Therefore, we present the first unified framework for formal
theories of novelty and use the framework to formally define a family of
novelty types. Our framework can be applied across a wide range of domains,
from symbolic AI to reinforcement learning, and beyond to open world image
recognition. Thus, it can be used to help kick-start new research efforts and
accelerate ongoing work on these important novelty-related problems. This
extended version of our AAAI 2021 paper included more details and examples in
multiple domains.


  In this paper, we study second-order and fourth-order elliptic problems which
include not only a Poisson equation in the bulk but also an inhomogeneous
Laplace--Beltrami equation on the boundary of the domain. The bulk and the
surface PDE are coupled by a boundary condition that is either of Dirichlet or
Robin type. We point out that both the Dirichlet and the Robin type boundary
condition can be handled simultaneously through our formalism without having to
change the framework. Moreover, we investigate the eigenvalue problems
associated with these second-order and fourth-order elliptic systems. We
further discuss the relation between these elliptic problems and certain
parabolic problems, especially the Allen--Cahn equation and the Cahn--Hilliard
equation with dynamic boundary conditions.


  Recently, Optimal Transport has been proposed as a probabilistic framework in
Machine Learning for comparing and manipulating probability distributions. This
is rooted in its rich history and theory, and has offered new solutions to
different problems in machine learning, such as generative modeling and
transfer learning. In this survey we explore contributions of Optimal Transport
for Machine Learning over the period 2012 -- 2022, focusing on four sub-fields
of Machine Learning: supervised, unsupervised, transfer and reinforcement
learning. We further highlight the recent development in computational Optimal
Transport, and its interplay with Machine Learning practice.


  Generation-recombination interband transitions via acoustic phonons are
allowed in a disordered graphene because of violation of the energy-momentum
conservation requirements. The generation-recombination processes are analyzed
for the case of scattering by a short-range disorder and the deformation
interaction of carriers with in-plane acoustic modes. The
generation-recombination rates were calculated for the cases of intrinsic and
heavily-doped graphene at room temperature. The transient evolution of
nonequilibrium carriers is described by the exponential fit dependent on doping
conditions and disorder level. The characteristic relaxation times are
estimated to be about 150 - 400 ns for sample with the maximal sheet resistance
~5 kOhm. This rate is comparable with the generation-recombination processes
induced by the thermal radiation.


  We show a new physical phenomenon expected for the ratio R_{pA} of the
unintegrated gluon distribution of a nucleus over the unintegrated gluon
distribution of a proton scaled up by the atomic factor A^{1/3} in the
fluctuation-dominated (diffusive scaling) region at high energy. We calculate
the dependence of R_{pA} on the atomic number A, the rapidity Y and the
transverse gluon momentum k_{\perp}. We find that R_{pA} exhibits an increasing
gluon shadowing with growing rapidity, approaching 1/A^{1/3} at asymptotic
rapidities which means total gluon shadowing, due to the effect of gluon number
fluctuations or Pomeron loops. The increase of R_{pA} with rising gluon
momentum decreases as the rapidity grows. In contrast, in the geometric scaling
region where the effect of fluctuations is negligible, the ratio R_{pA} shows
only partial gluon shadowing in the fixed-coupling case, basically independent
on the rapidity and the gluon momentum.


  The late eighteenth and early nineteenth centuries have long been considered
as a formative period for modern Irish political traditions such as
nationalism, republicanism and unionism. For Europe it was the time of a turn
over in science moving from observation to experiment and from speculation to
fact. Richard Kirwan was a well known natural philosopher in Europe and a
respected man of science in his time. Throughout all the wars, he was connected
with his colleagues in a network reaching across Europe and even to America.
Using a few examples, this article is intended to provide an insight how the
network worked in a time that was marked by political conflicts and
revolutionary events in both science and social life.


  Relying on the obtained results in Rev.[1](physics/0505035), we derive the
formula relating the red-shift of light signals coming from distant galaxies to
the distance of these galaxies from us and the time of detecting of these light
signals. The red-shift coefficient, instead of the Hubble parameter, is
introduced. It varies with time and positive at all times. Its nowadays value
equals the Hubble parameter. It increases forever as time is running from the
past to the future. The derived formula enables us to estimate the nowadays
increasing rate of the red-shift coefficient, which is nothing but the nowadays
value of the "acceleration of the expansion of the Universe".


  The Global-Local non-invasive coupling is an improvement of the submodeling
technique, which permits to locally enhance structure computations by
introducing patches with refined models and to take into accounts all the
interactions. In order to circumvent its inherently limited computational
performance, we propose and implement an asynchronous version of the method.
The asynchronous coupling reduces the dependency on communications, failures,
and load imbalance. We present the theory and the implementation of the method
in the linear case and illustrate its performance on academic cases inspired by
actual industrial problems.


  We present an \textit{exactly solvable} model of a monomer-monomer $A + B \to
\emptyset$ reaction on a 2D inhomogeneous, catalytic substrate and study the
equilibrium properties of the two-species adsorbate. The substrate contains
randomly placed catalytic bonds of mean density $q$ which connect neighboring
adsorption sites. The interacting $A$ and $B$ (monomer) species undergo
continuous exchanges with corresponding adjacent gaseous reservoirs. A reaction
$A + B \to \emptyset$ takes place instantaneously if $A$ and $B$ particles
occupy adsorption sites connected by a catalytic bond. We find that for the
case of \textit{annealed} disorder in the placement of the catalytic bonds the
reaction model under study can be mapped onto the general spin $S = 1$ (GS1)
model. Here we concentrate on a particular case in which the model reduces to
an exactly solvable Blume-Emery-Griffiths (BEG) model (T. Horiguchi, Phys.
Lett. A {\bf 113}, 425 (1986); F.Y. Wu, Phys. Lett. A, {\bf 116}, 245 (1986))
and derive an exact expression for the disorder-averaged equilibrium pressure
of the two-species adsorbate. We show that at equal partial vapor pressures of
the $A$ and $B$ species this system exhibits a second-order phase transition
which reflects a spontaneous symmetry breaking with large fluctuations and
progressive coverage of the entire substrate by either one of the species.


  Reynolds & Begelman (1997) have recently proposed a model in which the broad
and extremely redshifted iron line seen during a deep minimum of the light
curve of the Seyfert 1 galaxy MCG-6-30-15 originates from matter spiralling
into a Schwarzschild black hole, contrary to previous claims that the black
hole may be spinning rapidly (Iwasawa et al 1996; Dabrowski et al 1997). Here
we calculate in detail the X-ray spectrum produced by their model using the
full reflected continuum emission, including absorption features. This
calculation takes into account the doppler and relativistic effects. For the
range of parameters we consider, we find that the spectrum should show a large
photoelectric absorption edge of iron, which is not seen in the data. The
absorption edge is a consequence of the line emitting matter within the
innermost stable orbit being highly ionized, and is largely independent of the
parameters chosen for their model. If we restrict our attention to the 3-10 keV
band we may effectively remove this absorption edge by fitting a steeper power
law, but this results in a significant underprediction of the 0.4-0.5 keV flux.
We conclude that the data on MCG-6-30-15 are more consistent with the Kerr than
the Schwarzschild model.


  In this paper, we investigate the Dual-source Transformer architecture on the
WikiReading information extraction and machine reading comprehension dataset.
The proposed model outperforms the current state-of-the-art by a large margin.
Next, we introduce WikiReading Recycled - a newly developed public dataset,
supporting the task of multiple property extraction. It keeps the spirit of the
original WikiReading but does not inherit the identified disadvantages of its
predecessor.


  Semiclassical path integral expression for a quantum system coupled to a
harmonic bath is derived based on the stationary phase condition. It is
discovered that the system path is non-Markovian. Most strikingly, the system
path not only couples to its past (as in the Langevin equation), but also to
its future, i.e. the equation of motion for the system is an
integro-differential equation that involves all times. Numerical tests are
performed to confirm that the future-involved term is indeed necessary. Because
of the future-non-Markovian nature of the equation, the numerical solution
cannot be obtained by iterative methods. Instead, root search algorithms must
be employed.


  Motivated by some cutting edge circular data such as from Smart Home
technologies and roulette spins from online and casino, we construct some new
rich classes of discrete distributions on the circle. We give four new general
methods of construction, namely (i) maximum entropy, (ii) centered wrapping,
(iii) marginalized and (iv) conditionalized methods. We motivate these methods
on the line and then work on the circular case and provide some properties to
gain insight into these constructions. We mainly focus on the last two methods
(iii) and (iv) in the context of circular location families, as they are
amenable to general methodology. We show that the marginalized and
conditionalized discrete circular location families inherit important
properties from their parent continuous families. In particular, for the von
Mises and wrapped Cauchy as the parent distribution, we examine their
properties including the maximum likelihood estimators, the hypothesis test for
uniformity and give a test of serial independence. Using our discrete circular
distributions, we demonstrate how to determine changepoint when the data arise
in a sequence and how to fit mixtures of this distribution. Illustrative
examples are given which triggered the work. For example, for roulette data, we
test for uniformity (unbiasedness) , test for serial correlation, detect
changepoint in streaming roulette-spins data, and fit mixtures. We analyse a
smart home data using our mixtures. We examine the effect of ignoring
discreteness of the underlying population, and discuss marginalized versus
conditionalized approaches. We give various extensions of the families with
skewness and kurtosis, to those supported on an irregular lattice, and discuss
potential extension to general manifolds by showing a construction on the torus


  In this paper, we analyzed inflation from k-essence in the framework of
Horndeski gravity. In the specific, we considered models of canonical scalar
field and k-essence with quadratic kinetic term. Viable inflationary models can
be reconstructed by starting from the cosmological data. Several possibilities
are explored in order to correctly reproduce the spectral index and the
tensor-to-scalar ratio of primordial cosmological perturbations.


  A marked metric measure space (mmm-space) is a triple (X,r,mu), where (X,r)
is a complete and separable metric space and mu is a probability measure on XxI
for some Polish space I of possible marks. We study the space of all
(equivalence classes of) marked metric measure spaces for some fixed I. It
arises as state space in the construction of Markov processes which take values
in random graphs, e.g. tree-valued dynamics describing randomly evolving
genealogical structures in population models. We derive here the topological
properties of the space of mmm-spaces needed to study convergence in
distribution of random mmm-spaces. Extending the notion of the Gromov-weak
topology introduced in (Greven, Pfaffelhuber and Winter, 2009), we define the
marked Gromov-weak topology, which turns the set of mmm-spaces into a Polish
space. We give a characterization of tightness for families of distributions of
random mmm- spaces and identify a convergence determining algebra of functions,
called polynomials.


  Millimetre-wave communication (licensed or unlicensed) is envisaged to be an
important part of the fifth generation (5G) multi-RAT ecosystem. In this paper,
we consider the spectrum bands shared by 5G cellular base stations and some
existing networks, such as WiGig. Sharing the same band among such multiple
radio access technologies (RATs) is very challenging due to the lack of
centralized coordination and demands novel and efficient interference
mitigation and coexistence mechanisms to reduce the mutual interference. To
address this important challenge, we propose in this paper a novel multi-RAT
coexistence mechanism where neighbouring 5G and WiGig base stations, each
serving their own associated UEs, schedule their beam configurations in a
distributed manner such that their own utility function, e.g. spectral
efficiency, is maximized. We formulate the problem as a combinatorial
optimization problem and show via simulations that our proposed distributed
algorithms yield a comparable spectral efficiency for the entire networks as
that using an exhaustive search, which requires global coordination among
coexisting RATs and also has a much higher algorithmic complexity.


  We present a pilot study on the origin and assembly history of the ICL for
four galaxy clusters at 0.44<z<0.57 observed with the Hubble Space Telescope
from the Cluster Lensing and Supernova Survey with Hubble (CLASH) sample. Using
this sample of clusters we set an empirical limit on the amount of scatter in
ICL surface brightness profiles of such clusters at z=0.5 and constrain the
progenitor population and formation mechanism of the ICL by measuring the ICL
surface brightness profile, the ICL color and color gradient, and the total ICL
luminosity within 10<r<110 kpc. The observed scatter is physical, which we
associate with differences in ICL assembly process, formation epoch, and/or ICL
content. Using stellar population synthesis models we transform the observed
colors to metallicity. For three of the four clusters we find clear negative
gradients that, on average, decrease from super solar in the central regions of
the BCG to sub-solar in the ICL. Such negative color/metallicity gradients can
arise from tidal stripping of L* galaxies and/or the disruption of dwarf
galaxies, but not major mergers with the BCG. We also find that the ICL at 110
kpc has a color comparable to m*+2 red sequence galaxies and a total luminosity
between 10<r<110 kpc of 4-8 L*. This suggests that the ICL is dominated by
stars liberated from galaxies with L>0.2 L* and that neither dwarf disruption
nor major mergers with the BCG alone can explain the observed level of
luminosity and remain consistent with either the observed evolution in the
faint end slope of the luminosity function or predictions for the number of BCG
major mergers since z=1. Taken together, the results of this pilot study are
suggestive of a formation history for these clusters in which the ICL is
built-up by the stripping of >0.2 L* galaxies, and disfavor significant
contribution to the ICL by dwarf disruption or major mergers with the BCG.


  We present a self-organized stochastic model for the dynamics of a single
flux line in random media. The dynamics for the flux line in the longitudinal
and the transversal direction to an averaged moving direction are coupled to
each other. The roughness exponents of the flux line are measured for each
direction, which are close to $\alpha_{\parallel}\approx 0.63$ for the
longitudinal and $\alpha_{\perp}\approx 0.5$ for the transversal direction,
respectively. The dynamic exponents are obtained as $z\approx 1$ for both
directions. We discuss the classification of universality for the stochastic
model.


  We present an analysis of the s-process elements Zr, Ba, and La and the
r-process element Eu in a sample of 50 stars in 19 open clusters. Stellar
abundances of each element are based on measures of a minimum of two lines per
species via both equivalent width and spectrum synthesis techniques. We
investigate cluster mean neutron-capture abundance trends as a function of
cluster age and location in the Milky Way disk and compare them to results
found in other studies in the literature. We find a statistically significant
trend of increasing cluster [Ba/Fe] as a function of decreasing cluster age, in
agreement with recent findings for other open cluster samples, supporting the
increased importance of low-mass asymptotic giant branch stars to the
generation of s-process elements. However, the other s-process elements,
[La/Fe] and [Zr/Fe], do not show similar dependences, in contrast to
theoretical expectations and the limited observational data from other studies.
Conversely, cluster [Eu/Fe] ratios show a slight increase with increasing
cluster age, although with marginal statistical significance. Ratios of
[s/r]-process abundances, [Ba/Eu] and [La/Eu], however, show more clearly the
increasing efficiency of s-process relative to r-process enrichment in open
cluster chemical evolution, with significant increases among younger clusters.
Last, cluster neutron-capture element abundances appear to be independent of
Galactocentric distance. We conclude that a homogeneous analysis of a larger
sample of open clusters is needed to resolve the apparent discrepant
conclusions between different studies regarding s-process element abundance
trends with age to better inform models of galactic chemical evolution.


  For $C$ a complete algebraically closed extension of $\mathbb{Q}_p$, we show
that a one-dimensional $p$-divisible group $G/ \mathcal{O}_C$ can be defined
over a complete discretely valued subfield $L \subset C$ with Hodge-Tate period
ratios contained in $L$ if and only if $G$ has CM, if and only if the period
ratios generate an extension of $\mathbb{Q}_p$ of degree equal to the height of
the connected part of $G$. This is a $p$-adic analog of a classical
transcendence result of Schneider which states that for $\tau$ in the complex
upper half plane, $\tau$ and $j(\tau)$ are simultaneously algebraic over
$\mathbb{Q}$ if and only if $\tau$ is contained in a quadratic extension of
$\mathbb{Q}$. We also briefly discuss a conjectural generalization to shtukas
with one paw.


  In this paper, we study the optimistic online convex optimization problem in
dynamic environments. Existing works have shown that Ader enjoys an
$O\left(\sqrt{\left(1+P_T\right)T}\right)$ dynamic regret upper bound, where
$T$ is the number of rounds, and $P_T$ is the path length of the reference
strategy sequence. However, Ader is not environment-adaptive. Based on the fact
that optimism provides a framework for implementing environment-adaptive, we
replace Greedy Projection (GP) and Normalized Exponentiated Subgradient (NES)
in Ader with Optimistic-GP and Optimistic-NES respectively, and name the
corresponding algorithm ONES-OGP. We also extend the doubling trick to the
adaptive trick, and introduce three characteristic terms naturally arise from
optimism, namely $M_T$, $\widetilde{M}_T$ and $V_T+1_{L^2\rho\left(\rho+2
P_T\right)\leqslant\varrho^2 V_T}D_T$, to replace the dependence of the dynamic
regret upper bound on $T$. We elaborate ONES-OGP with adaptive trick and its
subgradient variation version, all of which are environment-adaptive.


  In this paper for either the sharp front Surface Quasi-Geostrophic equation
or the Muskat problem we rule out the "splash singularity" blow-up scenario; in
other words we prove that the contours evolving from either of these systems
can not intersect at a single point while the free boundary remains smooth.
Splash singularities have been shown to hold for the free boundary
incompressible Euler equation in the form of the water waves contour evolution
problem \cite{ADCPJ}. Our result confirms the numerical simulations in
\cite{CFMR} where it is shown that the curvature blows up due to the contours
collapsing at a point. Here we prove that maintaining control of the curvature
will remove the possibility of pointwise interphase collapse. Another
conclusion that we provide is a better understanding of the work \cite{DP3} in
which squirt singularities are ruled out; here a positive volume of fluid
between the contours can not be ejected in finite time.


  Sports game data is becoming increasingly complex, often consisting of
multivariate data such as player performance stats, historical team records,
and athletes' positional tracking information. While numerous visual analytics
systems have been developed for sports analysts to derive insights, few tools
target fans to improve their understanding and engagement of sports data during
live games. By presenting extra data in the actual game views, embedded
visualization has the potential to enhance fans' game-viewing experience.
However, little is known about how to design such kinds of visualizations
embedded into live games. In this work, we present a user-centered design study
of developing interactive embedded visualizations for basketball fans to
improve their live game-watching experiences. We first conducted a formative
study to characterize basketball fans' in-game analysis behaviors and tasks.
Based on our findings, we propose a design framework to inform the design of
embedded visualizations based on specific data-seeking contexts. Following the
design framework, we present five novel embedded visualization designs
targeting five representative contexts identified by the fans, including
shooting, offense, defense, player evaluation, and team comparison. We then
developed Omnioculars, an interactive basketball game-viewing prototype that
features the proposed embedded visualizations for fans' in-game data analysis.
We evaluated Omnioculars in a simulated basketball game with basketball fans.
The study results suggest that our design supports personalized in-game data
analysis and enhances game understanding and engagement.


  Autonomous driving is an active research topic in both academia and industry.
However, most of the existing solutions focus on improving the accuracy by
training learnable models with centralized large-scale data. Therefore, these
methods do not take into account the user's privacy. In this paper, we present
a new approach to learn autonomous driving policy while respecting privacy
concerns. We propose a peer-to-peer Deep Federated Learning (DFL) approach to
train deep architectures in a fully decentralized manner and remove the need
for central orchestration. We design a new Federated Autonomous Driving network
(FADNet) that can improve the model stability, ensure convergence, and handle
imbalanced data distribution problems while is being trained with federated
learning methods. Intensively experimental results on three datasets show that
our approach with FADNet and DFL achieves superior accuracy compared with other
recent methods. Furthermore, our approach can maintain privacy by not
collecting user data to a central server.


  Chiral fermions can be embedded into Souriau's massless spinning particle
model by "enslaving" the spin, viewed as a gauge constraint. The latter is not
invariant under Lorentz boosts; spin enslavement can be restored, however, by a
subsequent Wigner-Souriau (WS) translation, analogous to a compensating gauge
transformation. The combined transformation is precisely the recently uncovered
twisted boost, which we now extend to finite transformations. WS-translations
are identified with the stability group of a motion acting on the right on the
Poincare group, whereas the natural Poincare action corresponds to action on
the left. The relation to non-commutative mechanics is explained.


  Water splitting reactions through photocatalysis is an efficient and
sustainable technique for the generation of green energy. The photocatalyst's
ability to effect simultaneous generation of hydrogen and oxygen, along with
efficiency in utilisation of charged carriers, conversion of solar energy to
hydrogen, fast migration, and low recombination rates of carriers, are the
parameters to decide its suitability in water splitting. In literature,
comprehensive calculation and analysis of all these performance parameters for
a potential photocatalyst are rare. In this work, we have performed
first-principles-based computations to find new efficient photocatalysts from
the family of Janus MXenes and assessed their performance parameters. Strain
engineering has been invoked in search of new materials. Out of 14 studied
materials, we find 5 materials: Sc$_{2}$COS, Zr$_{2}$COS, Hf$_{2}$COS, and
ZrHfCO$_{2}$ under zero or finite tensile strain and Hf$_{2}$COSe at 6\%
tensile strain meeting the requirements of simultaneous reactions to split
water. The computations of various efficiency-related parameters demonstrate
that Zr$_{2}$COS, Hf$_{2}$COS, and Hf$_{2}$COSe have excellent efficiencies,
significantly better than the well-known photocatalysts. The origin of such
performances lies in their electronic and optical properties, which are
analysed systematically.


  We construct the first aperiodic tiles for two amenable 3-dimensional Lie
groups: Sol and the Heisenberg group. Our construction relies on the use of
higher-dimensional uniformly finite homology. In particular, we settle
completely the existence of aperiodic tiles for all of the non-compact
geometries of 3-manifolds appearing in the geometrization conjecture.


  It is well known that ensemble methods often provide enhanced performance in
reinforcement learning. In this paper, we explore this concept further by using
group-aided training within the distributional reinforcement learning paradigm.
Specifically, we propose an extension to categorical reinforcement learning,
where distributional learning targets are implicitly based on the total
information gathered by an ensemble. We empirically show that this may lead to
much more robust initial learning, a stronger individual performance level, and
good efficiency on a per-sample basis.


  The kinematics of Compton-effect with violated invariance of the velocity of
light has been considered. It has been shown that in this case
faster-than-light motion of the Compton electron is possible. The motion (if it
exists really) begins with the energy of the incident gamma-quantum above 360
keV.


  We say that a $2$-dimensional CW complex is a multibranched surface if we
remove all points whose open neighborhoods are homeomorphic to the
$2$-dimensional Euclidean space, then we obtain a $1$-dimensional complex which
is homeomorphic to a disjoint union of some $S^1$'s. We define the genus of a
multibranched surface $X$ as the minimum number of genera of $3$-dimensional
manifold into which $X$ can be embedded. We prove some inequalities which give
upper bounds for the genus of a multibranched surface. A multibranched surface
is a generalization of graphs. Therefore, we can define "minors" of
multibranched surfaces analogously. We study various properties of the minors
of multibranched surfaces.


  There are over 100 Be stars that are known to have neutron star companions
but only one such system with a black hole. Previous theoretical work suggests
this is not due to their formation but due to differences in X-ray luminosity.
It has also been proposed that the truncation of the Be star's circumstellar
disc is dependent on the mass of the compact object. Hence, Be star discs in
black hole binaries are smaller. Since accretion onto the compact object from
the Be star's disc is what powers the X-ray luminosity, a smaller disc in black
hole systems leads to a lower luminosity. In this paper, simulations are
performed with a range of eccentricities and compact object mass. The disc's
size and density are shown to be dependent on both quantities. Mass capture
and, in turn, X-ray luminosity are heavily dependent on the size and density of
the disc. Be/black hole binaries are expected to be up to ~10 times fainter
than Be/neutron star binaries when both systems have the same eccentricity and
can be 100 times fainter when comparing systems with different eccentricity.


  We analyze a microscopic origin of the Kondo effect-assisted orbital order in
heavy-fermion materials. By studying the periodic two-orbital Anderson model
with two local electrons, we show that frustration of Hund's rule coupling due
to the Kondo effect leads to an incommensurate spiral orbital and magnetic
order, which exists only inside the Kondo screened (heavy-electron) phase. This
spiral state can be observed in neutron and resonant X-ray scattering
measurements in ${\rm U}$- and ${\rm Pr}$-based heavy-fermion compounds, and
realized in cold atomic gases, e.g. fermionic ${}^{173}{\rm Yb}$.


  Background: Clustering phenomena in $N \neq Z$ nuclei provide an opportunity
to understand the interplay between cluster and nucleon degrees of freedom.
  Purpose:To study resonances in the $^{18}$O spectrum, populated in
$^{14}$C+$\alpha$ elastic scattering.
  Method: The Thick Target Inverse Kinematics (TTIK) technique was used to
measure the excitation function for the $^{14}$C+$\alpha$ elastic scattering. A
42 MeV $^{14}$C beam was used to populate states of excitation energy up to
14.9 MeV in $^{18}$O. The analysis was performed using a multi-level,
multi-channel R-Matrix approach.
  Results: Detailed spectroscopic information, including spin-parities, partial
$\alpha$- and neutron- decay widths and dimensionless reduced widths, was
obtained for excited states in $^{18}$O between 8 and 14.9 MeV in excitation
energy. Cluster-Nucleon Configuration Interaction Model calculations of the
same quantities are performed and compared to the experimental results.
  Conclusions: Strong fragmentation of large $\alpha$-cluster strengths is
observed in the spectrum of $^{18}$O making the $\alpha$-cluster structure of
$^{18}$O quite different from the pattern of known quasi-rotational bands of
alternating parity that are characteristic of $N=Z$, even-even nuclei like
$^{16}$O and $^{20}$Ne.


  Compactness in deep learning can be critical to a model's viability in
low-resource applications, and a common approach to extreme model compression
is quantization. We consider Iterative Product Quantization (iPQ) with
Quant-Noise to be state-of-the-art in this area, but this quantization
framework suffers from preventable inference quality degradation due to
prevalent empty clusters. In this paper, we propose several novel enhancements
aiming to improve the accuracy of iPQ with Quant-Noise by focusing on resolving
empty clusters. Our contribution, which we call Partitioning-Guided k-means (PG
k-means), is a heavily augmented k-means implementation composed of three main
components. First, we propose a partitioning-based pre-assignment strategy that
ensures no initial empty clusters and encourages an even weight-to-cluster
distribution. Second, we propose an empirically superior empty cluster
resolution heuristic executed via cautious partitioning of large clusters.
Finally, we construct an optional optimization step that consolidates
intuitively dense clusters of weights to ensure shared representation. The
proposed approach consistently reduces the number of empty clusters in iPQ with
Quant-Noise by 100x on average, uses 8x fewer iterations during empty cluster
resolution, and improves overall model accuracy by up to 12%, when applied to
RoBERTa on a variety of tasks in the GLUE benchmark.


  The analysis of small recurrent substructures, so called network motifs, has
become a standard tool of complex network science to unveil the design
principles underlying the structure of empirical networks. In many natural
systems network nodes are associated with an intrinsic property according to
which they can be ordered and compared against each other. Here, we expand
standard motif analysis to be able to capture the hierarchical structure in
such ordered networks. Our new approach is based on the identification of all
ordered 3-node substructures and the visualization of their significance
profile. We present a technique to calculate the fine grained motif spectrum by
resolving the individual members of isomorphism classes (sets of substructures
formed by permuting node-order). We apply this technique to computer generated
ensembles of ordered networks and to empirical food web data, demonstrating the
importance of considering node order for food-web analysis. Our approach may
not only be helpful to identify hierarchical patterns in empirical food webs
and other natural networks, it may also provide the base for extending motif
analysis to other types of multi-layered networks.


  In recent years, crowdsourcing, aka human aided computation has emerged as an
effective platform for solving problems that are considered complex for
machines alone. Using human is time-consuming and costly due to monetary
compensations. Therefore, a crowd based algorithm must judiciously use any
information computed through an automated process, and ask minimum number of
questions to the crowd adaptively.
  One such problem which has received significant attention is {\em entity
resolution}. Formally, we are given a graph $G=(V,E)$ with unknown edge set $E$
where $G$ is a union of $k$ (again unknown, but typically large $O(n^\alpha)$,
for $\alpha>0$) disjoint cliques $G_i(V_i, E_i)$, $i =1, \dots, k$. The goal is
to retrieve the sets $V_i$s by making minimum number of pair-wise queries $V
\times V\to\{\pm1\}$ to an oracle (the crowd). When the answer to each query is
correct, e.g. via resampling, then this reduces to finding connected components
in a graph. On the other hand, when crowd answers may be incorrect, it
corresponds to clustering over minimum number of noisy inputs. Even, with
perfect answers, a simple lower and upper bound of $\Theta(nk)$ on query
complexity can be shown. A major contribution of this paper is to reduce the
query complexity to linear or even sublinear in $n$ when mild side information
is provided by a machine, and even in presence of crowd errors which are not
correctable via resampling. We develop new information theoretic lower bounds
on the query complexity of clustering with side information and errors, and our
upper bounds closely match with them. Our algorithms are naturally
parallelizable, and also give near-optimal bounds on the number of adaptive
rounds required to match the query complexity.


  Randomized linear system solvers have become popular as they have the
potential to reduce floating point complexity while still achieving desirable
convergence rates. One particularly promising class of methods, random
sketching solvers, has achieved the best known computational complexity bounds
in theory, but is blunted by two practical considerations: there is no clear
way of choosing the size of the sketching matrix apriori; and there is a
nontrivial storage cost of the sketched system. In this work, we make progress
towards addressing these issues by implicitly generating the sketched system
and solving it simultaneously through an iterative procedure. As a result, we
replace the question of the size of the sketching matrix with determining
appropriate stopping criteria; we also avoid the costs of explicitly
representing the sketched linear system; and our implicit representation also
solves the system at the same time, which controls the per-iteration
computational costs.
  Additionally, our approach allows us to generate a connection between random
sketching methods and randomized iterative solvers (e.g., randomized Kaczmarz
method, randomized Gauss-Seidel). As a consequence, we exploit this connection
to (1) produce a stronger, more precise convergence theory for such randomized
iterative solvers under arbitrary sampling schemes (i.i.d., adaptive,
permutation, dependent, etc.), and (2) improve the rates of convergence of
randomized iterative solvers at the expense of a user-determined increases in
per-iteration computational and storage costs. We demonstrate these concepts on
numerical examples on forty-nine distinct linear systems.


  Ackermann's function can be expressed using an iterative algorithm, which
essentially takes the form of a term rewriting system. Although the termination
of this algorithm is far from obvious, its equivalence to the traditional
recursive formulation--and therefore its totality--has a simple proof in
Isabelle/HOL. This is a small example of formalising mathematics using a proof
assistant, with a focus on the treatment of difficult recursions.


  The bandgap and band bowing parameter of semiconductor alloys are calculated
with a fast and realistic approach. The method is a dielectric scaling
approximation that is based on a scissor approximation. It adds an energy shift
to the bandgap provided by the local density approximation (LDA) of the density
functional theory (DFT). The energy shift consists of a material-independent
constant weighted by the inverse of the high-frequency dielectric constant. The
salient feature of the approach is the fast calculation of the dielectric
constant of alloys via the Green function (GF) of the TB-LMTO (tight-binding
linear muffin-tin orbitals) in the atomic sphere approximation (ASA). When it
is applied to highly mismatched semiconductor alloys (HMAs) like Zn Te$_x$
Se$_{1-x}$, this method provides a band bowing parameter that is different from
the band bowing parameter calculated with the LDA due to the bowing exhibited
also by the high-frequency dielectric constant.


  Hyperelastic transformation theory has proven shear-wave manipulation devices
with various functions can be designed by utilizing neo-Hookean material with
appropriate pre-deformation. However, it is still elusive that how can such
devices match with the background medium in which they embedded. In this work,
we present a systematic formulation of the transmission and reflection of
elastic waves at the interface between un-deformed and pre-deformed
hyperelastic materials. With the combination of theoretical analyses and
numerical simulations, we specifically investigate the shear-wave propagation
from an un-deformed neo-Hookean material to the one subject to different
homogeneous deformations. Among three typical deformation modes, we found
"constrained" uniaxial tension and simple shear guarantee total transmission,
whereas "ordinary" uniaxial tension and hydrostatic compression cause wave
reflection. On this basis, three embedded shear-wave manipulation devices,
including a unidirectional cloak, a splicable beam bend, and a concave lens,
are proposed and verified through numerical simulations. This work may pave the
way for the design and realization of soft-matter-based wave control devices.
Potential applications can be anticipated in nondestructive testing, structure
impact protection, biomedical imaging, and soft robotics.


  In this paper, we investigate the effectiveness of two-stage classification
strategies in detecting north Atlantic right whale upcalls. Time-frequency
measurements of data from passive acoustic monitoring devices are evaluated as
images. Vocalization spectrograms are preprocessed for noise reduction and tone
removal. First stage of the algorithm eliminates non-upcalls by an energy
detection algorithm. In the second stage, two sets of features are extracted
from the remaining signals using contour-based and texture based methods. The
former is based on extraction of time-frequency features from upcall contours,
and the latter employs a Local Binary Pattern operator to extract
distinguishing texture features of the upcalls. Subsequently evaluation phase
is carried out by using several classifiers to assess the effectiveness of both
the contour-based and texture-based features for upcall detection. Experimental
results with the data set provided by the Cornell University Bioacoustics
Research Program reveal that classifiers show accuracy improvements of 3% to 4%
when using LBP features over time-frequency features. Classifiers such as the
Linear Discriminant Analysis, Support Vector Machine, and TreeBagger achieve
high upcall detection rates with LBP features.


  We consider a lattice gas with quenched impurities or `quenched-annealed
binary mixture' on the Bethe lattice. The quenched part represents a porous
matrix in which the (annealed) lattice gas resides. This model features the 3
main factors of fluids in random porous media: wetting, randomness and
confinement. The recursive character of the Bethe lattice enables an exact
treatment, whose key ingredient is an integral equation yielding the
one-particle effective field distribution. Our analysis shows that this
distribution consists of two essentially different parts. The first one is a
continuous spectrum and corresponds to the macroscopic volume accessible to the
fluid, the second is discrete and comes from finite closed cavities in the
porous medium. Those closed cavities are in equilibrium with the bulk fluid
within the grand canonical ensemble we use, but are inaccessible in real
experimental situations. Fortunately, we are able to isolate their
contributions. Separation of the discrete spectrum facilitates also the
numerical solution of the main equation. The numerical calculations show that
the continuous spectrum becomes more and more rough as the temperature
decreases, and this limits the accuracy of the solution at low temperatures.


  This paper considers networked sensing in cellular network, where multiple
base stations (BSs) first compress their received echo signals from multiple
targets and then forward the quantized signals to the cloud via
limited-capacity backhaul links, such that the cloud can leverage all useful
echo signals to perform high-resolution localization. Under this setup, we
manage to characterize the posterior Cramer-Rao Bound (PCRB) for localizing all
the targets as a function of the transmit covariance matrix and the compression
noise covariance matrix of each BS. Then, a PCRB minimization problem subject
to the transmit power constraints and the backhaul capacity constraints is
formulated to jointly design the BSs' transmission and compression strategies.
We propose an efficient algorithm to solve this problem based on the
alternating optimization technique. Specifically, it is shown that when either
the transmit covariance matrices or the compression noise covariance matrices
are fixed, the successive convex approximation technique can be leveraged to
optimize the other type of covariance matrices locally. Numerical results are
provided to verify the effectiveness of our proposed algorithm.


  Numerous research studies on dust and molecular filaments have been conducted
in star-forming sites, but only a limited number of studies have focused on
ionized filaments. To observationally study this aspect, we present an analysis
of multi-wavelength data of an area of $\sim$74.6 arcmin $\times$ 55 arcmin
around l = 345.5 degree. Using the 843 MHz continuum map, two distinct ionized
filaments (i.e., IF-A (extent $\sim$8.5 arcmin) and IF-B (extent $\sim$22.65
arcmin)) hosting ionized clumps powered by massive OB stars are identified.
Using the $^{13}$CO(2-1) and C$^{18}$O(2-1) line data, the parent molecular
clouds of IF-A and IF-B are studied in a velocity range of [$-$21, $-$10] km
s$^{-1}$, and have filamentary appearances. At least two cloud components
around $-$18 and $-$15 km s$^{-1}$ toward the parent clouds of IF-A and IF-B
are investigated, and are connected in velocity space. These filamentary clouds
also spatially overlap with each other along the major axis, backing the
filamentary twisting/coupling nature. Noticeable Class I protostars and massive
stars appear to be observed toward the common zones of the cloud components.
These findings support the collision of two filamentary clouds around 1.2 Myr
ago. The existence of the ionized filaments seems to be explained by the
combined feedback of massive stars. The molecular filaments associated with
IF-A and IF-B favour the outcomes of the most recent model concerning the
escape and the trap of the ionizing radiation from an O star formed in a
filament.


  We study the robustness of learned image compression models against
adversarial attacks and present a training-free defense technique based on
simple image transform functions. Recent learned image compression models are
vulnerable to adversarial attacks that result in poor compression rate, low
reconstruction quality, or weird artifacts. To address the limitations, we
propose a simple but effective two-way compression algorithm with random input
transforms, which is conveniently applicable to existing image compression
models. Unlike the na\"ive approaches, our approach preserves the original
rate-distortion performance of the models on clean images. Moreover, the
proposed algorithm requires no additional training or modification of existing
models, making it more practical. We demonstrate the effectiveness of the
proposed techniques through extensive experiments under multiple compression
models, evaluation metrics, and attack scenarios.


  The $K\to\pi\pi$ decay amplitudes are studied within the framework of
generalized factorization in which the effective Wilson coefficients are
gauge-invariant, renormalization-scale and -scheme independent while
factorization is applied to the tree-level hadronic matrix elements.
Nonfactorized contributions to the hadronic matrix elements of (V-A)(V-A)
four-quark operators, which are needed to account for the suppression of the
$\Delta I=3/2 K\to\pi\pi$ amplitude $A_2$ and the enhancement of the $\Delta
I=1/2 A_0$ amplitude, are phenomenologically extracted from the measured
$K^+\to\pi^+\pi^0$ decay and found to be large. The $A_0/A_2$ ratio is
predicted to lie in the range 15-17 for $m_s(1 GeV)=(127-150)$ MeV. Vertex and
penguin-type radiative corrections to the matrix elements of four-quark
operators and nonfactorized effects due to soft-gluon exchange account for the
bulk of the $\Delta I=1/2$ rule. Comparison of the present analysis with the
chiral-loop approach is given.


  We introduce a method to segment the visual field into independently moving
regions, trained with no ground truth or supervision. It consists of an
adversarial conditional encoder-decoder architecture based on Slot Attention,
modified to use the image as context to decode optical flow without attempting
to reconstruct the image itself. In the resulting multi-modal representation,
one modality (flow) feeds the encoder to produce separate latent codes (slots),
whereas the other modality (image) conditions the decoder to generate the first
(flow) from the slots. This design frees the representation from having to
encode complex nuisance variability in the image due to, for instance,
illumination and reflectance properties of the scene. Since customary
autoencoding based on minimizing the reconstruction error does not preclude the
entire flow from being encoded into a single slot, we modify the loss to an
adversarial criterion based on Contextual Information Separation. The resulting
min-max optimization fosters the separation of objects and their assignment to
different attention slots, leading to Divided Attention, or DivA. DivA
outperforms recent unsupervised multi-object motion segmentation methods while
tripling run-time speed up to 104FPS and reducing the performance gap from
supervised methods to 12% or less. DivA can handle different numbers of objects
and different image sizes at training and test time, is invariant to
permutation of object labels, and does not require explicit regularization.


  Hyperbolic structures are obtained by tiling a hyperbolic surface with
negative Gaussian curvature. These structures generally exhibit two percolation
transitions: a system-wide connection can be established at a certain
occupation probability $p=p_{c1}$ and there emerges a unique giant cluster at
$p_{c2} > p_{c1}$. There have been debates about locating the upper transition
point of a prototypical hyperbolic structure called the enhanced binary tree
(EBT), which is constructed by adding loops to a binary tree. This work
presents its lower bound as $p_{c2} \gtrsim 0.55$ by using phenomenological
renormalization-group methods and discusses some solvable models related to the
EBT.


  Cavity quantum electrodynamics (QED), the study of the interaction between
quantized emitters and photons confined in an optical cavity, is an important
tool for quantum science in computing, networking, and synthetic matter. In
atomic cavity QED, this approach typically relies upon an ultra-high vacuum
chamber that hosts a cold trapped atomic ensemble and an optical cavity.
Upgrading the cavity necessitates a months-long laborious process of removing
external optics, venting, replacing the resonator, baking, and replacing
optics, constituting a substantial bottleneck to innovation in resonator
design. In this work, we demonstrate that the flexibility of optical cavities,
and the quick turnaround time in switching between them, can be restored with
the vacuum loadlock technique--reducing the cycle time to install a cavity,
bake it, and transport it into the science chamber to days, achieving
3x10^(-10) Torr pressure in the science chamber. By reducing vacuum
limitations, this approach is particularly powerful for labs interested in
quickly exploring novel optic cavities, or any other atomic physics relying on
in-vacuum optics.


  We address dynamical supersymmetry breaking within a N=1 supersymmetric
Standard-like Model based on a Z_2 x Z_2 Type IIA orientifold with intersecting
D6-branes. The model possesses an additional, confining gauge sector with the
USp(2)_A x USp(2)_B x USp(4) gauge group, where the gaugino condensation
mechanism allows for the breaking of supersymmetry and stabilizes moduli. We
derive the leading contribution to the non-perturbative effective
superpotential and determine numerically the minima of the supergravity
potential. These minima break supersymmetry and fix two undetermined moduli,
which in turn completely specify the gauge couplings at the string scale. For
this specific construction the minima have a negative cosmological constant. We
expect that for other supersymmetric Standard-like models with intersecting
D6-branes, which also possess confining gauge sectors, the supersymmetry
breaking mechanism would have qualitatively similar features.


  Multiple recent studies have identified the metallic antiferromagnet Mn$_2$Au
to be a candidate for spintronic applications due to apparent in-plane
anisotropy, preserved magnetic properties above room temperature, and
current-induced N\'eel vector switching. Crystal growth is complicated by the
fact that Mn$_2$Au melts incongruently. We present a bismuth flux method to
grow millimeter-scale bulk single crystals of Mn$_2$Au in order to examine the
intrinsic anisotropic electrical and magnetic properties. Flux quenching
experiments reveal that the Mn$_2$Au crystals precipitate below 550{\deg}C,
about 100{\deg}C below the decomposition temperature of Mn$_2$Au. Bulk Mn$_2$Au
crystals have a room-temperature resistivity of 16-19 $\mu\Omega$-cm and a
residual resistivity ratio of 41. Mn$_2$Au crystals have a dimensionless
susceptibility on the order of 10$^{-4}$, comparable to calculated and
experimental reports on powder samples. Single-crystal neutron diffraction
confirms the in-plane magnetic structure. The tetragonal symmetry of Mn$_2$Au
constrains the $ab$-plane magnetic susceptibility to be constant, meaning that
$\chi_{100}=\chi_{110}$ in the low-field limit, below any spin-flop transition.
We find that three measured magnetic susceptibilities $\chi_{100}$,
$\chi_{110}$, and $\chi_{001}$ are the same order of magnitude and agree with
the calculated prediction, meaning the low-field susceptibility of Mn$_2$Au is
quite isotropic, despite clear differences in $ab$-plane and $ac$-plane
magnetocrystalline anisotropy. Mn$_2$Au is calculated to have an extremely high
in-plane spin-flop field above 30 T, which is much larger than that of another
in-plane antiferromagnet Fe$_2$As (less than 1 T). The subtle anisotropy of
intrinsic susceptibilities may lead to dominating effects from shape,
crystalline texture, strain, and defects in devices that attempt spin readout
in Mn$_2$Au.


  We present a 2.5 sigma detection of the Integrated Sachs-Wolfe (ISW) effect
and discuss the constraints it places on cosmological parameters. We
cross-correlate microwave temperature maps from the WMAP satellite with a 4000
deg^2 luminous red galaxy (LRG) overdensity map measured by the Sloan Digital
Sky Survey. Accurate photometric redshifts allow us to perform a reliable
auto-correlation analysis of the LRGs, eliminating the uncertainty in the
galaxy bias, and combined with cross correlation signal, constrains
cosmological parameters -- in particular, the matter density. We find a 2.5
sigma signal in the Ka, Q, V, and W WMAP bands, after combining the information
from multipoles 2 <= l < 400. This is consistent with the expected amplitude of
the ISW effect, but requires a lower matter density than is usually assumed:
the amplitude, parametrized by the galaxy bias assuming \Omega_M=0.3,
\Omega_\Lambda=0.7 and \sigma_8=0.9, is b_g = 4.05 \pm 1.54 for V band, with
similar results for the other bands. This should be compared to b_g = 1.82 \pm
0.02 from the auto-correlation analysis. These data provide only a weak
confirmation (2.5 sigma) of dark energy, but provide a significant upper limit:
\Omega_\Lambda=0.80_{-0.06}^{+0.03} (1 sigma)_{-0.19}^{+0.05} (2 sigma),
assuming a cosmology with \Omega_M+\Omega_\Lambda=1, \Omega_b = 0.05, and
\sigma_8=0.9, and w=-1. The weak cross-correlation signal rules out low matter
density/high dark energy density universes and, in combination with other data,
strongly constrains models with w<-1.3. We provide a simple prescription to
incorporate these constraints into cosmological parameter estimation methods
for (\Omega_M, \sigma_8,w). (abridged)


  We perform canonical analysis of non-relativistic particle in Newton-Cartan
Background. Then we extend this analysis to the case of non-relativistic
superparticle in the same background. We determine constraints structure of
this theory and find generator of \kappa-symmetry.


  We study effective potentials coming from compactifications of string theory.
We show that, under mild assumptions, such potentials are bounded from below in
four dimensions, giving an affirmative answer to a conjecture proposed by the
second author in arXiv:0911.3378v4 [hep-th]. We also derive some sufficient
conditions for the existence of critical points. All proofs and mathematical
hypotheses are discussed in the context of their relevance to the physics of
the problem.


  Far-infrared Herschel PACS imaging and spectroscopic observations of the
nebula around the luminous blue variable (LBV) star AG Car have been obtained
along with optical imaging in the Halpha+[NII] filter. In the infrared light,
the nebula appears as a clumpy ring shell that extends up to 1.2 pc with an
inner radius of 0.4 pc. It coincides with the Halpha nebula, but extends
further out. Dust modeling of the nebula was performed and indicates the
presence of large grains. The dust mass is estimated to be ~ 0.2 Msun. The
infrared spectrum of the nebula consists of forbidden emission lines over a
dust continuum. Apart from ionized gas, these lines also indicate the existence
of neutral gas in a photodissociation region that surrounds the ionized region.
The abundance ratios point towards enrichment by processed material. The total
mass of the nebula ejected from the central star amounts to ~ 15 Msun, assuming
a dust-to-gas ratio typical of LBVs. The abundances and the mass-loss rate were
used to constrain the evolutionary path of the central star and the epoch at
which the nebula was ejected, with the help of available evolutionary models.
This suggests an ejection during a cool LBV phase for a star of ~ 55 Msun with
little rotation.


  This review provides a conceptual and technical survey of methods for
parameter estimation of gravitational wave signals in ground-based
interferometers such as LIGO and Virgo. We introduce the framework of Bayesian
inference and provide an overview of models for the generation and detection of
gravitational waves from compact binary mergers, focusing on the essential
features that are observable in the signals. Within the traditional
likelihood-based paradigm, we describe various approaches for enhancing the
efficiency and robustness of parameter inference. This includes techniques for
accelerating likelihood evaluations, such as heterodyne/relative binning,
reduced-order quadrature, multibanding and interpolation. We also cover methods
to simplify the analysis to improve convergence, via reparametrization,
importance sampling and marginalization. We end with a discussion of recent
developments in the application of likelihood-free (simulation-based) inference
methods to gravitational wave data analysis.


  The $N=2$ supersymmetric continuum limit is investigated in the SU(2) adjoint
Higgs-Yukawa model using lattice perturbation theory. In the one-loop
renormalization group equations a non-trivial infrared fixed point of coupling
ratios is found. The phase structure at weak couplings is determined by a
numerical study of the one-loop effective potential.


  We give an explicit realization of the "String Axiverse" discussed in
Arvanitaki et. al \cite{Arvanitaki:2009fg} by extending our previous results on
moduli stabilization in $M$ theory to include axions. We extend the analysis of
\cite{Arvanitaki:2009fg} to allow for high scale inflation that leads to a
moduli dominated pre-BBN Universe. We demonstrate that an axion which solves
the strong-CP problem naturally arises and that both the axion decay constants
and GUT scale can consistently be around $2\times 10^{16}$ GeV with a much
smaller fine tuning than is usually expected. Constraints on the Axiverse from
cosmological observations, namely isocurvature perturbations and tensor modes
are described. Extending work of Fox et. al \cite{Fox:2004kb}, we note that
{\it the observation of tensor modes at Planck will falsify the Axiverse
completely.} Finally we note that Axiverse models whose lightest axion has mass
of order $10^{-15}$ eV and with decay constants of order $5\times 10^{14}$ GeV
require no (anthropic) fine-tuning, though standard unification at $10^{16}$
GeV is difficult to accommodate.


  Numerical simulation codes are very common tools to study complex phenomena,
but they are often time-consuming and considered as black boxes. For some
statistical studies (e.g. asset management, sensitivity analysis) or
optimization problems (e.g. tuning of a molecular model), a high number of runs
of such codes is needed. Therefore it is more convenient to build a
fast-running approximation - or metamodel - of this code based on a design of
experiments. The topic of this paper is the definition of metamodels for
stochastic codes. Contrary to deterministic codes, stochastic codes can give
different results when they are called several times with the same input. In
this paper, two approaches are proposed to build a metamodel of the probability
density function of a stochastic code output. The first one is based on kernel
regression and the second one consists in decomposing the output density on a
basis of well-chosen probability density functions, with a metamodel linking
the coefficients and the input parameters. For the second approach, two types
of decomposition are proposed, but no metamodel has been designed for the
coefficients yet. This is a topic of future research. These methods are applied
to two analytical models and three industrial cases.


  Non-terrestrial networks have been attracting much interest from the industry
and academia. Satellites and high altitude platform station (HAPS) systems are
expected to be the key enablers of next-generation wireless networks. In this
paper, we introduce a novel downlink satellite communication (SatCom) model
where free-space optical (FSO) communication is adopted between a satellite and
a HAPS node. A hybrid FSO/radio-frequency (RF) transmission model is used
between the HAPS node and ground station (GS). In the first phase of
transmission, the satellite selects the HAPS node that provides the highest
signal-to-noise ratio (SNR). In the second phase, the selected HAPS decodes and
forwards the signal to the GS. To evaluate the performance of the proposed
system, outage probability expressions are derived for exponentiated Weibull
(EW) and shadowed-Rician fading models while considering the atmospheric
turbulence, stratospheric attenuation, and attenuation due to scattering, path
loss, and pointing errors. Additionally, asymptotic analysis is carried out and
diversity gain is provided. Furthermore, the impact of aperture averaging
technique, temperature, and wind speed are investigated. We also provide some
important guidelines that can be helpful for the design of practical HAPS-aided
SatCom. Finally, the results show that the use of HAPS improves the system
performance and that the proposed model performs better than all other existing
models.


  In spite of the fact that photons do not interact with an external magnetic
field, the latter field may indirectly affect photons in the presence of a
charged environment. This opens up an interesting possibility to continuously
control the entanglement of photon beams without using any crystalline devices.
We study this possibility in the framework of an adequate QED model. In an
approximation it was discovered that such entanglement has a resonant nature,
namely, a peak behavior at certain magnetic field strengths, depending on
characteristics of photon beams direction of the magnetic field and parameters
of the charged medium. Numerical calculations illustrating the above-mentioned
resonant behavior of the entanglement measure and some concluding remarks are
presented.


  The flag curvature of a Finsler metric is called a Riemannian quantity
because it is an extension of sectional curvature in Riemannian geometry. In
Finsler geometry, there are several non-Riemannian quantities such as the
(mean) Cartan torsion, the (mean) Landsberg curvature and the S-curvature,
which all vanish for Riemannian metrics. It is important to understand the
geometric meanings of these quantities. In this paper, we study Finsler metrics
of scalar curvature (i.e., the flag curvature is a scalar function on the slit
tangent bundle) and partially determine the flag curvature when certain
non-Riemannian quantities are isotropic. Using the obtained formula for the
flag curvature, we classify locally projectively flat Randers metrics with
isotropic S-curvature.


  Fierz transformations for four-fermion operators are generalized to the
one-loop level. A general renormalization scheme is used to compute QCD and QED
corrections to the tree-level relations, which result from Fierz-evanescent
operators. The results can be used to perform general one-loop basis
transformations involving four-fermi and evanescent operators. We illustrate
the usefulness of our results by discussing two examples from a matching
calculation and a one-loop basis change.


  We give a simple proof of the matrix Spencer conjecture up to
poly-logarithmic rank: given symmetric $d \times d$ matrices $A_1,\ldots,A_n$
each with $\|A_i\|_{\mathsf{op}} \leq 1$ and rank at most $n/\log^3 n$, one can
efficiently find $\pm 1$ signs $x_1,\ldots,x_n$ such that their signed sum has
spectral norm $\|\sum_{i=1}^n x_i A_i\|_{\mathsf{op}} = O(\sqrt{n})$. This
result also implies a $\log n - \Omega( \log \log n)$ qubit lower bound for
quantum random access codes encoding $n$ classical bits with advantage $\gg
1/\sqrt{n}$.
  Our proof uses the recent refinement of the non-commutative Khintchine
inequality in [Bandeira, Boedihardjo, van Handel, 2022] for random matrices
with correlated Gaussian entries.