  In an excitable Delaunay triangulation every node takes three states
(resting, excited and refractory) and updates its state in discrete time
depending on a ratio of excited neighbours. All nodes update their states in
parallel. By varying excitability of nodes we produce a range of phenomena,
including reflection of excitation wave from edge of triangulation, backfire of
excitation, branching clusters of excitation and localized excitation domains.
Our findings contribute to studies of propagating perturbations and waves in
non-crystalline substrates.


  The paper presents a detailed description of duality for braided algebras,
coalgebras, bialgebras, Hopf algebras and their modules and comodules in the
infinite setting. Assuming that the dual objects exist, it is shown how a given
braiding induces compatible braidings for the dual objects, and how actions
(resp. coactions) can be turned into coactions (resp. actions) of the dual
coalgebra (resp. algebra), with an emphasis on braided bialgebras and their
braided (co)module algebras.


  We examine the possibility of artificial Hawking radiation by proposing a
non-PT - symmetric weakly pseudo-Hermitian two band model containing a tilting
parameter. We also determine the tunneling probability using our Hamiltonian
through the event horizon that acts as a classically forbidden barrier.


  Models with an extra dimension generally contain background scalar fields in
a non-trivial configuration, whose stability must be ensured. With gravity
present, the extra dimension is warped by the scalars, and the spin-0 degrees
of freedom in the metric mix with the scalar perturbations. Where possible, we
formally solve the coupled Schrodinger equations for the zero modes of these
spin-0 perturbations. When specialising to the case of two scalars with a
potential generated by a superpotential, we are able to fully solve the system.
We show how these zero modes can be used to construct a solution matrix, whose
eigenvalues tell whether a normalisable zero mode exists, and how many negative
mass modes exist. These facts are crucial in determining stability of the
corresponding background configuration. We provide examples of the general
analysis for domain-wall models of an infinite extra dimension and domain-wall
soft-wall models. For 5D models with two scalars constructed using a
superpotential, we show that a normalisable zero mode survives, even in the
presence of warped gravity. Such models, which are widely used in the
literature, are therefore phenomenologically unacceptable.


  We present updated predictions for the cross-sections for pair production of
squarks and gluinos at the LHC Run II. First of all, we update the calculations
based on NLO+NLL partonic cross-sections by using the NNPDF3.0NLO global
analysis. This study includes a full characterization of theoretical
uncertainties from higher orders, PDFs and the strong coupling. Then, we
explore the implications for this calculation of the recent NNPDF3.0 PDFs with
NLO+NLL threshold resummation. We find that the shift in the results induced by
the threshold-improved PDFs is within the total theory uncertainty band of the
calculation based on NLO PDFs. However, we also observe that the central values
of the cross-sections are modified both in a qualitative and a quantitative
way, illustrating the relevance and impact of using threshold-improved PDFs
together with resummed partonic cross-sections. The updated NLO+NLL
cross-sections based on NNPDF3.0NLO are publicly available in the NLL-fast
format, and should be an important ingredient for the interpretation of the
searches for supersymmetric particles at Run II.


  Four problems about recovery of a high-frequency source in the one-dimension
heat equation with homogeneous initial-boundary conditions by some information
about partial asymptotic of its solution have solved. It is shown, that the
source can be completely recovered from a specific data about incomplete
(two-terms) asymptotic of the solution. Before formulation of each problem
about recovery of a source, construction and justification of the asymptotic of
the solution of original initial-boundary problem is given.


  Astrometry and photometry from {\it Gaia} and spectroscopic data from the
{\it Gaia}-ESO Survey (GES) are used to identify the lithium depletion boundary
(LDB) in the young cluster NGC 2232. A specialised spectral line analysis
procedure was used to recover the signature of undepleted lithium in very low
luminosity cluster members. An age of $38\pm 3$ Myr is inferred by comparing
the LDB location in absolute colour-magnitude diagrams (CMDs) with the
predictions of standard models. This is more than twice the age derived from
fitting isochrones to low-mass stars in the CMD with the same models. Much
closer agreement between LDB and CMD ages is obtained from models that
incorporate magnetically suppressed convection or flux-blocking by dark,
magnetic starspots. The best agreement is found at ages of $45-50$\,Myr for
models with high levels of magnetic activity and starspot coverage fractions
$>50$ per cent, although a uniformly high spot coverage does not match the CMD
well across the full luminosity range considered.


  We investigate the phase structure of two-component Bose-Einstein condensates
(BECs) with repulsive intra- and interspecies interactions in the presence of
respective vortex-antivortex superposition states (VAVSS). We show that
different winding numbers of vortex and antivortex and different intra- and
interspecies interaction strengths may lead to different phase configurations,
such as fully separated phases, inlaid separated phases, asymmetric separated
phase, and partially mixed phases, where the density profile of each component
displays a petal-like (or modulated petal-like) structure. A phase diagram is
given for the case of equal unit winding numbers of the vortex and antivortex
in respective components, and it is shown that conventional criterion for phase
separation of two-component BECs is not applicable for the present system due
to the VAVSS. In addition, our nonlinear stability analysis indicates that the
typical phase structures of two-component BECs with VAVSS allow to be detected
in experiments. Moreover, for the case of unequal winding numbers of the vortex
and antivortex in respective components, we find that each component in any of
the possible phase structures is in a cluster state of vortices and
antivortices, where the topological defects appear in the form of singly
quantized visible vortex, or hidden vortex, or ghost vortex, depending on the
specific parameters of the system. Finally, a general rule between the
vortex-antivortex cluster state and the winding numbers of vortex and
antivortex is revealed.


  We theoretically study the dynamics of an adiabatic sweep through a Feshbach
resonance, thereby converting a degenerate quantum gas of fermionic atoms into
a degenerate quantum gas of bosonic dimers. Our analysis relies on a zero
temperature mean-field theory which accurately accounts for initial molecular
quantum fluctuations, triggering the association process. The structure of the
resulting semiclassical phase space is investigated, highlighting the dynamical
instability of the system towards association, for sufficiently small detuning
from resonance. It is shown that this instability significantly modifies the
finite-rate efficiency of the sweep, transforming the single-pair exponential
Landau-Zener behavior of the remnant fraction of atoms Gamma on sweep rate
alpha, into a power-law dependence as the number of atoms increases. The
obtained nonadiabaticity is determined from the interplay of characteristic
time scales for the motion of adiabatic eigenstates and for fast periodic
motion around them. Critical slowing-down of these precessions near the
instability leads to the power-law dependence. A linear power law $Gamma\propto
alpha$ is obtained when the initial molecular fraction is smaller than the 1/N
quantum fluctuations, and a cubic-root power law $Gamma\propto alpha^{1/3}$ is
attained when it is larger. Our mean-field analysis is confirmed by exact
calculations, using Fock-space expansions. Finally, we fit experimental low
temperature Feshbach sweep data with a power-law dependence. While the
agreement with the experimental data is well within experimental error bars,
similar accuracy can be obtained with an exponential fit, making additional
data highly desirable.


  We consider the cones of curves and divisors on the moduli space of stable
pointed rational curves,M_n, and on the quotient by the symmetric group, Q_n,
which is a moduli space of pairs. We find generators for contractible extremal
rays of the cone of curves NE_1(M_n), and for the cone of divisors NE^1(Q_n).
This second cone turns out to be simplicial. We give complete descriptions of
NE_1(M_n) and NE_1(Q_n) for small n (< 8 in the first case, < 11 in the
second). We also have results of independent interest on when curves in a
divisor generate the cone of curves of the ambient variety.


  Existing approaches for visuomotor robotic control typically require
characterizing the robot in advance by calibrating the camera or performing
system identification. We propose MAVRIC, an approach that works with minimal
prior knowledge of the robot's morphology, and requires only a camera view
containing the robot and its environment and an unknown control interface.
MAVRIC revolves around a mutual information-based method for self-recognition,
which discovers visual "control points" on the robot body within a few seconds
of exploratory interaction, and these control points in turn are then used for
visual servoing. MAVRIC can control robots with imprecise actuation, no
proprioceptive feedback, unknown morphologies including novel tools, unknown
camera poses, and even unsteady handheld cameras. We demonstrate our method on
visually-guided 3D point reaching, trajectory following, and robot-to-robot
imitation.


  We consider a definition of mathematics as the art of thinking in terms of
formalized systems, and the science of relations, structures and algorithms. We
also touch upon the relation of mathematics to other sciences, in particular
through modelling and scientific computing. We discuss mathematics as a martial
art and a key to paradigm changes.


  Recent measurements of coherent electron spin dynamics reveal an
antiferromagnetic s-d exchange coupling between conduction band electrons and
electrons localized on Mn{2+} impurities in GaMnAs quantum wells. Here we
discuss systematic measurements of the s-d exchange interaction in
GaMnAs/AlGaAs quantum wells with different confinement potentials using
time-resolved Kerr rotation. Extending previous investigations of the
dependence of the s-d exchange, N{0}alpha, on well width, we find that its
magnitude also depends on well depth. Both phenomena reduce to a general
dependence on confinement energy, described by a band-mixing model of
confinement-induced kinetic exchange in the conduction band.


  The theory of substellar evolution predicts that there is a sharp mass
boundary between lithium and non-lithium brown dwarfs, not far below the
substellar-mass limit. The imprint of thermonuclear burning is carved on the
surface lithium abundance of substellar-mass objects during the first few
hundred million years of their evolution, leading to a sharp boundary between
lithium and non-lithium brown dwarfs, so-called, the lithium test. New optical
spectroscopic observations of the binaries DENIS+J063001.4-184014 and
DENIS+J225210.7-173013 obtained using the 10.4-m Gran Telescopio de Canarias
are reported here. They allow us to re-determine their combined optical
spectral types (M9.5 and L6.5, respectively) and to search for the presence of
the LiI resonance doublet. The non detection of the LiI feature in the combined
spectrum of DENIS\,J063001.4$-$184014AB is converted into estimates for the
depletion of lithium in the individual components of this binary system. In
DENIS\,J225210.7$-$173013AB we report the detection of a weak LiI feature which
we tentatively ascribe as arising from the contribution of the T3.5-type
secondary. Combining our results with data for seven other brown dwarf binaries
in the literature treated in a self-consistent way, we confirm that there is
indeed a sharp transition in mass for lithium depletion in brown dwarfs, as
expected from theoretical calculations. We estimate such mass boundary is
observationally located at 51.48$^{+0.22}_{-4.00}$ $M_\mathrm{Jup}$, which is
lower than the theoretical determinations.


  Velocity distribution functions link the micro- and macro-level theories of
fluid flow through porous media. Here we study them for the fluid absolute
velocity and its longitudinal and lateral components relative to the
macroscopic flow direction in a model of a random porous medium. We claim that
all distributions follow the power exponential law controlled by an exponent
$\gamma$ and a shift parameter $u_0$ and examine how these parameters depend on
the porosity. We find that $\gamma$ has a universal value $1/2$ at the
percolation threshold and grows with the porosity, but never exceeds 2.


  Generated texts from large language models (LLMs) have been shown to exhibit
a variety of harmful, human-like biases against various demographics. These
findings motivate research efforts aiming to understand and measure such
effects. Prior works have proposed benchmarks for identifying and techniques
for mitigating these stereotypical associations. However, as recent research
pointed out, existing benchmarks lack a robust experimental setup, hindering
the inference of meaningful conclusions from their evaluation metrics. In this
paper, we introduce a list of desiderata for robustly measuring biases in
generative language models. Building upon these design principles, we propose a
benchmark called OCCUGENDER, with a bias-measuring procedure to investigate
occupational gender bias. We then use this benchmark to test several
state-of-the-art open-source LLMs, including Llama, Mistral, and their
instruction-tuned versions. The results show that these models exhibit
substantial occupational gender bias. We further propose prompting techniques
to mitigate these biases without requiring fine-tuning. Finally, we validate
the effectiveness of our methods through experiments on the same set of models.


  Recently Hod proposes a lower bound on the relaxation time of a perturbed
thermodynamic system. For gravitational systems this bound transforms into a
condition on the fundamental quasinormal frequency. We test the bound in some
spacetimes whose quasinormal frequencies are calculated exactly, as the
three-dimensional BTZ black hole, the D-dimensional de Sitter spacetime, and
the D-dimensional Nariai spacetime. We find that for some of these spacetimes
their fundamental quasinormal frequencies do not satisfy the bound proposed by
Hod.


  Different stellar sub-populations of the Milky Way's stellar disk are known
to have different vertical scale heights, their thickness increasing with age.
Using SEGUE spectroscopic survey data, we have recently shown that
mono-abundance sub-populations, defined in the [\alpha/Fe]-[Fe/H] space, are
well described by single exponential spatial-density profiles in both the
radial and the vertical direction; therefore any star of a given abundance is
clearly associated with a sub-population of scale height h_z. Here, we work out
how to determine the stellar surface-mass density contributions at the solar
radius R_0 of each such sub-population, accounting for the survey selection
function, and for the fraction of the stellar population mass that is reflected
in the spectroscopic target stars given populations of different abundances and
their presumed age distributions. Taken together, this enables us to derive
\Sigma_{R_0}(h_z), the surface-mass contributions of stellar populations with
scale height h_z. Surprisingly, we find no hint of a thin-thick disk
bi-modality in this mass-weighted scale-height distribution, but a smoothly
decreasing function, approximately \Sigma_{R_0}(h_z)\propto \exp(-h_z), from
h_z ~ 200 pc to h_z ~ 1 kpc. As h_z is ultimately the structurally defining
property of a thin or thick disk, this shows clearly that the Milky Way has a
continuous and monotonic distribution of disk thicknesses: there is no 'thick
disk' sensibly characterized as a distinct component. We discuss how our result
is consistent with evidence for seeming bi-modality in purely geometric disk
decompositions, or chemical abundances analyses. We constrain the total visible
stellar surface-mass density at the Solar radius to be \Sigma^*_{R_0} = 30 +/-
1 M_\odot pc^{-2}.


  This paper deals with well-known extensions of the Prufer domain concept to
arbitrary commutative rings. We investigate the transfer of these notions in
trivial ring extensions (also called idealizations) of commutative rings by
modules and then generate original families of rings with zerodivisors subject
to various Prufer conditions. The new examples give further evidence for the
validity of Bazzoni-Glaz conjecture on the weak dimension of Gaussian rings.
Moreover, trivial ring extensions allow us to widen the scope of validity of
Kaplansky-Tsang conjecture on the content ideal of Gaussian polynomials.


  A quadratic optimal transport metric on the set of probability measure over
$\R^2$ is introduced. The quadratic cost is given by the euclidean norm on
$\R^2$ associated to some well chosen symmetric positive matrix, which makes
the metric equivalent to the usual Wasserstein-2 metric. The dissipation of the
distance to the equilibrium along the kinetic Fokker-Planck flow, is bounded by
below in terms of the distance itself. It enables to obtain some new type of
trend to equilibrium estimate in Wasserstein-2 like metric, in the case of
non-convex confinement potential.


  Polar metals based on binary and ternary compounds have been demonstrated in
literature. Here, we propose a design principle for ferroelectric-like
elemental polar metals and relate it to real materials. The design principle is
that, to be an elemental polar metal, atoms should occupy at least two
inequivalent Wyckoff positions in a crystal with a polar space group, where
inversion symmetry is spontaneously broken. According to this rule, we propose
the first class of potential ferroelectric-like elemental polar metals in a
distorted {\alpha}-La-like structure with a polar space group P63mc in which
two inequivalent Wyckoff positions 2a (0, 0, z) and 2b (1/3, 2/3, z) are
occupied by group-V elements (phosphorus, arsenic, antimony, and bismuth).
Analyses based on first-principles calculations indicate that the dynamically
stable polar phase results from a lone pair driven polar distortion of the
nonploar phase in P63/mmc symmetry where two inequivalent Wyckoff positions 2a
(0, 0, 0) and 2c (1/3, 2/3, 1/4) are occupied. This ferroelectric-like
transition involves a transition from a metallic state to a semimetallic state.
These predicted polar phases are metastable with respect to their corresponding
ground phases. Moreover, ionic bonding characters are found due to the
inequivalence in Wyckoff positions between group-V atoms. Our work opens a
route to single-element parity-breaking phases.


  We review the coronal visible and infrared lines, collecting previous
observations, and comparing, whenever available, observed radiances with those
predicted by various models: the quiet Sun, a moderately active Sun, and an
active region as observed near the limb, around 1.1R$_{\odot}$. We also model
the off-limb radiances for the quiet Sun case. We used the most up-to-date
atomic data in CHIANTI version 8. The comparison is satisfactory, in that all
of the strong visible lines now have a firm identification. We revise several
previous identifications and suggest some new ones. We also list the large
number of observed lines for which we do not currently have atomic data, and
therefore still await firm identifications. We also show that a significant
number of coronal lines should be observable in the near-infrared region of the
spectrum by the upcoming Daniel K. Inouye Solar Telescope (DKIST) and the
AIR-Spec instrument, which observed the corona during the 2017 August 21 solar
eclipse. We also briefly discuss the many potential spectroscopic diagnostics
available to the visible and infrared, with particular emphasis on measurements
of electron densities and chemical abundances. We briefly point out some of the
potential diagnostics that could be available with the future infrared
instrumentation that is being built for DKIST and planned for the
  Coronal Solar Magnetism Observatory (COSMO). Finally, we highlight the need
for further improvements in the atomic data.


  We analyze the opportunistic relaying based on HARQ transmission over the
block-fading channel with absence of channel state information (CSI) at the
transmitter nodes. We assume that both the source and the relay are allowed to
vary their transmission rate between the HARQ transmission rounds. We solve the
problem of throughput maximization with respect to the transmission rates using
double-recursive Dynamic Programming. Simplifications are also proposed to
diminish the complexity of the optimization. The numerical results confirm that
the variable-rate HARQ can increase the throughput significantly comparing to
its fixed-rate counterpart.


  We present the design, architecture and detailed performance of a
three-dimensional (3D) underwater acoustic carpet cloak (UACC). The proposed
system of the 3D UACC is an octahedral pyramid which is composed of periodical
steel strips. This underwater acoustic device, placed over the target to hide,
is able to manipulate the scattered wavefront to mimic a reflecting plane. The
effectiveness of the prototype is experimentally demonstrated in an anechoic
tank. The measured acoustic pressure distributions show that the 3D UACC can
work in all directions in a wide frequency range. This experimental
verification of 3D device paves the way for guidelines on future practical
applications.


  Distributed word representations have been shown to be very useful in various
natural language processing (NLP) application tasks. These word vectors learned
from huge corpora very often carry both semantic and syntactic information of
words. However, it is well known that each individual user has his own language
patterns because of different factors such as interested topics, friend groups,
social activities, wording habits, etc., which may imply some kind of
personalized semantics. With such personalized semantics, the same word may
imply slightly differently for different users. For example, the word
"Cappuccino" may imply "Leisure", "Joy", "Excellent" for a user enjoying
coffee, by only a kind of drink for someone else. Such personalized semantics
of course cannot be carried by the standard universal word vectors trained with
huge corpora produced by many people. In this paper, we propose a framework to
train different personalized word vectors for different users based on the very
successful continuous skip-gram model using the social network data posted by
many individual users. In this framework, universal background word vectors are
first learned from the background corpora, and then adapted by the personalized
corpus for each individual user to learn the personalized word vectors. We use
two application tasks to evaluate the quality of the personalized word vectors
obtained in this way, the user prediction task and the sentence completion
task. These personalized word vectors were shown to carry some personalized
semantics and offer improved performance on these two evaluation tasks.


  Coalition forming is investigated among countries, which are coupled with
short range interactions, under the influence of external fields produced by
the existence of global alliances. The model rests on the natural model of
coalition forming inspired from Statistical Physics, where instabilities are a
consequence of decentralized maximization of the individual benefits of actors
within their long horizon of rationality as the ability to envision a way
through intermediate loosing states, to a better configuration. The effects of
those external incentives on the interactions between countries and the
eventual stabilization of coalitions are studied. The results shed a new light
on the understanding of the complex phenomena of stabilization and
fragmentation in the coalition dynamics and on the possibility to design stable
coalitions. In addition to the formal implementation of the model, the
phenomena is illustrated through some historical cases of conflicts in Western
Europe.


  For $X(n)$ a Steinhaus random multiplicative function, we study the maximal
size of the random Dirichlet polynomial $$ D_N(t) = \frac1{\sqrt{N}} \sum_{n
\leq N} X(n) n^{it}, $$ with $t$ in various ranges. In particular, for fixed
$C>0$ and any small $\varepsilon>0$ we show that, with high probability, $$
  \exp( (\log N)^{1/2-\varepsilon} ) \ll \sup_{|t| \leq N^C} |D_N(t)| \ll \exp(
(\log N)^{1/2+\varepsilon}). $$


  A two-state system (TSS) under time-periodic perturbations (to be regarded as
input signals) is studied in connection with self-tuning (ST) of threshold and
stochastic resonance (SR). By ST, we observe the improvement of signal-to-noise
ratio (SNR) in a weak noise region. Analytic approach to a tuning equation
reveals that SNR improvement is possible also for a large noise region and this
is demonstrated by Monte Carlo simulations of hopping processes in a TSS. ST
and SR are discussed from a little more physical point of energy transfer
(dissipation) rate, which behaves in a similar way as SNR. Finally ST is
considered briefly for a double-well potential system (DWPS), which is closely
related to the TSS.


  We look at the semigroup generated by a system of heat equations.
Applications to testing normality and option pricing are addressed.


  We develop a recursive formula for counting the number of rectangulations of
a square, i.e the number of combinatorially distinct tilings of a square by
rectangles. Our formula specializes to give a formula counting generic
rectangulations, as analyzed by Reading in [5]. Our computations agree with [5]
as far as was calculated and extend to the non-generic case. An interesting
feature of the number of rectangulations is that it appears to have an 8-fold
periodicity modulo 2. We verify this periodicity for small values of n, but the
general result remains elusive, perhaps hinting at some unseen structure on the
space of rectangulations, analogous to Reading's discovery that generic
rectangulations are in 1-1 correspondence with a certain class of permutations.
Finally, we use discrete Morse theory to show that the space of tilings by less
than or equal to n rectangles is homotopy-equivalent to a wedge of some number
of (n-1)-dimensional spheres. Combined with formulae for the number of tilings,
the exact homotopy type is computed for $n\leq 28$.


  We consider an idealized model in which individuals' changing opinions and
their social network coevolve, with disagreements between neighbors in the
network resolved either through one imitating the opinion of the other or by
reassignment of the discordant edge. Specifically, an interaction between $x$
and one of its neighbors $y$ leads to $x$ imitating $y$ with probability
$(1-\alpha)$ and otherwise (i.e., with probability $\alpha$) $x$ cutting its
tie to $y$ in order to instead connect to a randomly chosen individual.
Building on previous work about the two-opinion case, we study the
multiple-opinion situation, finding that the model has infinitely many phase
transitions. Moreover, the formulas describing the end states of these
processes are remarkably simple when expressed as a function of $\beta =
\alpha/(1-\alpha)$.


  We present LinkQ, a system that leverages a large language model (LLM) to
facilitate knowledge graph (KG) query construction through natural language
question-answering. Traditional approaches often require detailed knowledge of
complex graph querying languages, limiting the ability for users -- even
experts -- to acquire valuable insights from KG data. LinkQ simplifies this
process by first interpreting a user's question, then converting it into a
well-formed KG query. By using the LLM to construct a query instead of directly
answering the user's question, LinkQ guards against the LLM hallucinating or
generating false, erroneous information. By integrating an LLM into LinkQ,
users are able to conduct both exploratory and confirmatory data analysis, with
the LLM helping to iteratively refine open-ended questions into precise ones.
To demonstrate the efficacy of LinkQ, we conducted a qualitative study with
five KG practitioners and distill their feedback. Our results indicate that
practitioners find LinkQ effective for KG question-answering, and desire future
LLM-assisted systems for the exploratory analysis of graph databases.


  The purpose of this paper is to calculate the two-photon decay rate
corresponding to the two-photon transitions nS->1S and nD->1S in hydrogenlike
ions with a low nuclear charge number Z (for principal quantum numbers n =
2,...,8. Numerical results are obtained within a nonrelativistic framework, and
the results are found to scale approximately as (Z alpha)^6/n^3, where alpha is
the fine-structure constant. We also attempt to clarify a number of subtle
issues regarding the treatment of the coherent, quasi-simultaneous emission of
the two photons as opposed to one-photon cascades. In particular, the gauge
invariance of the decay rate is shown explicitly.


  Existing evaluation benchmarks of language models of code (code LMs) focus
almost exclusively on whether the LMs can generate functionally-correct code.
In real-world software engineering, developers think beyond functional
correctness. They have requirements on "how" a functionality should be
implemented to meet overall system design objectives like efficiency, security,
and maintainability. They would also trust the code LMs more if the LMs
demonstrate robust understanding of requirements and code semantics.
  We propose a new benchmark NoFunEval to evaluate code LMs on non-functional
requirements and simple classification instances for both functional and
non-functional requirements. We propose a prompting method, Coding Concepts
(CoCo), as a way for a developer to communicate the domain knowledge to the
LMs. We conduct an extensive evaluation of twenty-two code LMs. Our finding is
that they generally falter when tested on our benchmark, hinting at fundamental
blindspots in their training setups. Surprisingly, even the classification
accuracy on functional-correctness instances derived from the popular HumanEval
benchmark is low, calling in question the depth of their comprehension and the
source of their success in generating functionally-correct code in the first
place. We will release our benchmark and evaluation scripts publicly at
https://aka.ms/NoFunEval.


  Global localization is essential for robots to perform further tasks like
navigation. In this paper, we propose a new framework to perform global
localization based on a filter-based visual-inertial odometry framework MSCKF.
To reduce the computation and memory consumption, we only maintain the keyframe
poses of the map and employ Schmidt-EKF to update the state. This global
localization framework is shown to be able to maintain the consistency of the
state estimator. Furthermore, we introduce a re-linearization mechanism during
the updating phase. This mechanism could ease the linearization error of
observation function to make the state estimation more precise. The experiments
show that this mechanism is crucial for large and challenging scenes.
Simulations and experiments demonstrate the effectiveness and consistency of
our global localization framework.


  We report on recent results from our successful and pioneering observational
program with ALMA to study emerging ultracom pact HII regions of pre-Planetary
Nebulae (pPNe) using mm-wavelength recombination lines (mRRLs) as new optimal
tracers. We focus on our study of two poster-child pPNe, namely, M2-9 and
CRL618. We reveal the structure and kinematics of the en igmatic inner nebular
regions of these objects with an unprecedented angular resolution down to
20-30mas (~15-30AU). For both targets, the ionized central regions are
elongated along the main symmetry axis of the large-scale nebulae, consiste nt
with bipolar winds, and show notable axial velocity gradients with expansion
velocities of up to ~100km/s. The H30a pr ofiles exhibit time variability,
reflecting changes in the physical properties and kinematics on scales of a few
years. O ur ongoing analysis employs 3D, non-LTE radiative transfer modeling,
providing a detailed description of the innermost la yers of these well known
pPNe with exceptional clarity.


  Simulations have shown that space-charge effects can lead to regular
modulation of photoemitted beams in vacuum diodes with gap sizes on the order
of 1 micron and accelerating voltage on the order of 1V. These modulations are
in the THz regime and can be tuned by simply changing the emitter area or
accelerating vacuum field. The average current in the diode corresponds to the
Child-Langmuir current, but the amplitude of the oscillations is affected by
various factors. Given the small size and voltage of the system, the maximum
radiated AC power is expected to be small. In this work we show that an array
of small emitters produces higher frequency signals than a single large emitter
of same area, and how these emitters may be synchronized to produce higher
power signals.


  This paper develops a new Hilbert space method to characterize a family of
reproducing kernel Hilbert spaces of real harmonic functions in a bounded
Lipschitz domain $\Omega \subset \mathbb R^d, d\geq 2$ involving some families
of positive self-adjoint operators and making use of characterizations of their
trace data and of a special inner product on $H^1(\Omega).$ We also establish
boundary representation results for this family in terms of the $L^2-$ Bergman
kernel. In particular, a boundary integral representation for the very weak
solution of the Dirichlet problem for Laplace's equation with $L^2- $ boundary
data is provided. Reproducing kernels and orthonormal bases for the harmonic
spaces are also found.


  We perform a Dalitz plot analysis of the decay Ds to K+K-pi+ with the CLEO-c
data set of 586/pb of e+e- collisions accumulated at sqrt(s) = 4.17 GeV. This
corresponds to about 0.57 million D_s+D_s(*)- pairs from which we select 14400
candidates with a background of roughly 15%. In contrast to previous
measurements we find good agreement with our data only by including an
additional f_0(1370)pi+ contribution. We measure the magnitude, phase, and fit
fraction of K*(892) K+, phi(1020)pi+, K0*(1430)K+, f_0(980)pi+, f_0(1710)pi+,
and f_0(1370)pi+ contributions and limit the possible contributions of other KK
and Kpi resonances that could appear in this decay.


  We investigate the gravitational instability (GI) of dust-ring structures and
the formation of planetesimals by their gravitational collapse. The normalized
dispersion relation of a self-gravitating ring structure includes two
parameters that are related to its width and line mass (the mass per unit
length). We survey these parameters and calculate the growth rate and
wavenumber. Additionally, we investigate the planetesimal formation by growth
of the GI of the ring that is formed by the growth of the secular GI of the
protoplanetary disk. We adopt a massive, dust rich disk as a disk model. We
find the range of radii for the fragmentation by the ring GI as a function of
the width of the ring. The inner-most radius for the ring GI is smaller for the
smaller ring width. We also determine the range of the initial planetesimal
mass resulting from the fragmentation of the ring GI. Our results indicate that
the planetesimal mass can be as large as 10^28 g at its birth after the
fragmentation. It can be as low as about 10^25 g if the ring width is 0.1% of
the ring radius and the lower limit increases with the ring width. Furthermore,
we obtain approximate formulas for the upper and lower limits of the
planetesimal mass. We predict that the planetesimals formed by the ring GI have
prograde rotations because of the Coriolis force acting on the contracting
dust. This is consistent with the fact that many trans-Neptunian binaries
exhibit prograde rotation.


  Several mechanical realizations of PR-Boxes are discussed. Apart from
superluminal correlations, which are known not to be realizable by classical
devices, the requirements (1) PR-condition on input-output relations, (2)
non-signaling, and (3) allowing for independent measurements are discussed
separately. The examples show that internal signaling (inside the box) does not
invariably imply the possibility of external signaling and may externally be
attributed to contextuality. The proposed model requires two classical bits to
be exchanged internally in order to realize the defined requirements. However,
with EPR correlations this can be reduced to one classical bit.


  Recent results have shown the stability of frustration-free Hamiltonians to
weak local perturbations, assuming several conditions. In this paper, we prove
the stability of free fermion Hamiltonians which are gapped and local. These
free fermion Hamiltonians are not necessarily frustration-free, but we are able
to adapt previous work to prove stability. The key idea is to add an additional
copy of the system to cancel topological obstructions. We comment on
applications to quantization of Hall conductance in such systems.


  Thyroid hormone (TH) signalling, an evolutionary conserved pathway, is
crucial for brain function and cognition throughout life, from early
development to ageing. In humans, TH deficiency during pregnancy alters
offspring brain development, increasing the risk of cognitive disorders. How TH
regulates neurogenesis and subsequent behaviour and cognitive functions remains
a major research challenge. Cellular and molecular mechanisms underlying TH
signalling on proliferation, survival, determination, migration,
differentiation and maturation have been studied in mammalian animal models for
over a century. However, recent data show that THs also influence embryonic and
adult neurogenesis throughout vertebrates (from mammals to teleosts). These
latest observations raise the question of how TH availability is controlled
during neurogenesis and particularly in specific neural stem cell populations.
This review deals with the role of TH in regulating neurogenesis in the
developing and the adult brain across different vertebrate species. Such
evo-devo approaches can shed new light on (i) the evolution of the nervous
system and (ii) the evolutionary control of neurogenesis by TH across animal
phyla. We also discuss the role of thyroid disruptors on brain development in
an evolutionary context.


  Stellar rotation produces an internal mixing of the elements due to shear
instability and meridional circulation. This leads to observable $N/C$
enhancements in massive stars above about 7--9 $M_{\odot}$. Rotation also
favours mass loss by stellar winds. Mass loss effects dominate for masses above
30 $M_{\odot}$, while mixing dominates below that limit.
  The effects of mixing are also much larger at lower metallicity $Z$, because
the internal $\Omega$--gradients are steeper. This appears to be in agreement
with observations in the SMC.
  At very low $Z$ and Z=0, mixing between the He--burning core and the
H--burning shell leads to the production of primary N in intermediate mass
stars.
  Such enrichments increase the metallicity of the rotating star, also massive
Z=0 stars with moderate initial velocities currently reach break--up velocity
during a fraction of the MS phase. Both effects favour mass loss in Z=0 stars,
which have ejecta with abundance anomalies very similar to those of C--rich
very metal poor stars.


  This paper discusses the gravitational collapse of dynamical self-gravitating
fluid distribution in $f(\mathcal{R},\mathcal{T},\mathcal{Q})$ gravity, where
$\mathcal{Q}=\mathcal{R}_{\varphi\vartheta}\mathcal{T}^{\varphi\vartheta}$. In
this regard, we assume a charged anisotropic spherical geometry involving
dissipation flux and adopt standard model of the form
$\mathcal{R}+\Phi\sqrt{\mathcal{T}}+\Psi\mathcal{Q}$, where $\Phi$ and $\Psi$
symbolize real-valued coupling parameters. The Misner-Sharp as well as
M\"{u}ler-Israel Stewart mechanisms are employed to formulate the corresponding
dynamical and transport equations. We then interlink these evolution equations
which help to study the impact of state variables, heat dissipation, modified
corrections and charge on the collapse rate. The Weyl scalar is further
expressed in terms of the modified field equations. The necessary and
sufficient condition of conformal flatness of the considered configuration and
homogeneous energy density is obtained by applying some constraints on the
model along with disappearing charge and anisotropy. Finally, we discuss
different cases to investigate how the spherical matter source is affected by
the charge and modified corrections.


  In this work we want to study quasielastic (p, n) exchange reactions using a
semi-microscopic optical model derived in a previous work [1] based on a
nuclear matter approach where the real and imaginary parts are given by the
first and second order terms, respectively, of the mass operator obtained by a
Brueckner-Hartree-Fock calculation using a G-matrix built up with an effective
Gogny interaction. The study of these quasielastic reactions is performed
within a Distorted Wave Born Approximation (DWBA) to evaluate the wave
functions in the entrance and exit channels, which in turn are used to compute
the transition matrix elements. This model, which is free of adjustable
parameters, provide a reasonable good agreement with the considered
experimental data, namely differential cross sections, analyzing powers and
total cross sections, of different reactions spanned along the periodic table
at several energies.


  The propagation of Interplanetary Coronal Mass Ejections (ICMEs) in the
heliosphere is influenced by many physical phenomena, related to the internal
structure of the ICME and its interaction with the ambient solar wind and
magnetic field. As the solar magnetic field is modulated by the 11-year dynamo
cycle, our goal is to perform a theoretical exploratory study to assess the
difference of propagation of an ICME in typical minimum and maximum activity
backgrounds. We define a median representative CME at 0.1~au, using both
observations and numerical simulations, and describe it using a spheromak
model. We use the heliospheric propagator European Heliospheric FORecasting
Information Asset (EUHFORIA) to inject the same ICME in two different
background wind environments. We then study how the environment and the
internal CME structure impact the propagation of the ICME towards Earth, by
comparison with an unmagnetized CME. At minimum of activity, the structure of
the heliosphere around the ecliptic causes the ICME to slow down, creating a
delay with the polar parts of the ejecta. This delay is more important if the
ICME is faster. At maximum of activity, a southern coronal hole causes a
northward deflection. For these cases, we always find that the ICME at maximum
of activity arrives first, while the ICME at minimum of activity is actually
more geo-effective. The helicity sign of the ICME is also a crucial parameter
but at minimum of activity only, since it affects the magnetic profile and the
arrival time of up to 8 hours.


  We study the influence of many-particle interaction in a system which, in the
single particle case, exhibits a metal-insulator transition induced by a finite
amount of onsite pontential fluctuations. Thereby, we consider the problem of
interacting particles in the one-dimensional quasiperiodic Aubry-Andre chain.
We employ the density-matrix renormalization scheme to investigate the finite
particle density situation. In the case of incommensurate densities, the
expected transition from the single-particle analysis is reproduced. Generally
speaking, interaction does not alter the incommensurate transition. For
commensurate densities, we map out the entire phase diagram and find that the
transition into a metallic state occurs for attractive interactions and
infinite small fluctuations -- in contrast to the case of incommensurate
densities. Our results for commensurate densities also show agreement with a
recent analytic renormalization group approach.


  The weak noise limit of dissipative dynamical systems is often the most
fascinating one. In such a case fluctuations can interact with a rich
complexity frequently hidden in deterministic systems to give rise of
completely new phenomena that are absent for both noiseless and strong
fluctuations regimes. Unfortunately, this limit is also notoriously hard to
approach analytically or numerically. We reinvestigate in this context the
paradigmatic model of nonequlibrium statistical physics consisting of inertial
Brownian particle diffusing in a tilted periodic potential by exploiting the
state of the art computer simulations of unprecedented time scale. In contrast
to the previous results on this long standing problem we draw an inference that
in the parameter regime for which the particle velocity is bistable the
lifetime of ballistic diffusion diverges to infinity when thermal noise
intensity tends to zero, i.e. an everlasting ballistic diffusion emerges. As a
consequence the diffusion coefficient does not reach its stationary constant
value.


  We use exceptional field theory to describe locally non-geometric spaces of
M-theory of more than three dimensions. For these spaces, we find a new set of
locally non-geometric fluxes which lie in the R-R sector in the weak-coupling
limit and can typically be characterised by mixed symmetry tensors. These
spaces thus provide new examples of non-geometric backgrounds which go beyond
the NS-NS sector of string theory. Starting from twisted tori we construct
duality chains that lead to these new non-geometric backgrounds and we show
that, just as in the four-dimensional case, there are missing momenta
associated to the mixed symmetry tensors.


  The vector magnetic field characteristics of superactive regions (SARs) hold
the key for understanding why SARs are extremely active and provide the
guidance in space weather prediction. We aim to quantify the characteristics of
SARs using the vector magnetograms taken by the Solar Magnetic Field Telescope
at Huairou Solar Observatory Station. The vector magnetic field characteristics
of 14 SARs in solar cycles 22 and 23 were analyzed using the following four
parameters: 1) the magnetic flux imbalance between opposite polarities, 2) the
total photospheric free magnetic energy, 3) the length of the magnetic neutral
line with its steep horizontal magnetic gradient, and 4) the area with strong
magnetic shear. Furthermore, we selected another eight large and inactive
active regions (ARs), which are called fallow ARs (FARs), to compare them with
the SARs. We found that most of the SARs have a net magnetic flux higher than
7.0\times10^21 Mx, a total photospheric free magnetic energy higher than
1.0\times10^24 erg/cm, a magnetic neutral line with a steep horizontal magnetic
gradient (\geq 300 G/Mm) longer than 30 Mm, and an area with strong magnetic
shear (shear angle \geq 80\degree) greater than 100 Mm^2. In contrast, the
values of these parameters for the FARs are mostly very low. The Pearson
\c{hi}2 test was used to examine the significance of the difference between the
SARs and FARs, and the results indicate that these two types of ARs can be
fairly distinguished by each of these parameters. The significance levels are
99.55%, 99.98%, 99.98%, and 99.96%, respectively. However, no single parameter
can distinguish them perfectly. Therefore we propose a composite index based on
these parameters, and find that the distinction between the two types of ARs is
also significant with a significance level of 99.96%. These results are useful
for a better physical understanding of the SAR and FAR


  Recent approaches to distributed model fitting rely heavily on consensus
ADMM, where each node solves small sub-problems using only local data. We
propose iterative methods that solve {\em global} sub-problems over an entire
distributed dataset. This is possible using transpose reduction strategies that
allow a single node to solve least-squares over massive datasets without
putting all the data in one place. This results in simple iterative methods
that avoid the expensive inner loops required for consensus methods. To
demonstrate the efficiency of this approach, we fit linear classifiers and
sparse linear models to datasets over 5 Tb in size using a distributed
implementation with over 7000 cores in far less time than previous approaches.


  The physics search potential of the FEL {gamma} - Nucleus colliders is
analysed using excitations of the (232)Th nucleus. It is shown that, due to the
monochromacity of FEL {gamma} beam and high statistics, proposed colliders will
play an important role in the field of "traditional" nuclear physics.


  We propose a non-learning depth completion method for a sparse depth map
captured using a light detection and ranging (LiDAR) sensor guided by a pair of
stereo images. Generally, conventional stereo-aided depth completion methods
have two limiations. (i) They assume the given sparse depth map is accurately
aligned to the input image, whereas the alignment is difficult to achieve in
practice. (ii) They have limited accuracy in the long range because the depth
is estimated by pixel disparity. To solve the abovementioned limitations, we
propose selective stereo matching (SSM) that searches the most appropriate
depth value for each image pixel from its neighborly projected LiDAR points
based on an energy minimization framework. This depth selection approach can
handle any type of mis-projection. Moreover, SSM has an advantage in terms of
long-range depth accuracy because it directly uses the LiDAR measurement rather
than the depth acquired from the stereo. SSM is a discrete process; thus, we
apply variational smoothing with binary anisotropic diffusion tensor (B-ADT) to
generate a continuous depth map while preserving depth discontinuity across
object boundaries. Experimentally, compared with the previous state-of-the-art
stereo-aided depth completion, the proposed method reduced the mean absolute
error (MAE) of the depth estimation to 0.65 times and demonstrated
approximately twice more accurate estimation in the long range. Moreover, under
various LiDAR-camera calibration errors, the proposed method reduced the depth
estimation MAE to 0.34-0.93 times from previous depth completion methods.


  The cosmic microwave background (CMB), carrying the inhomogeneous information
of the very early universe, is of great significance for understanding the
origin and evolution of our universe. However, observational CMB maps contain
serious foreground contaminations from several sources, such as galactic
synchrotron and thermal dust emissions. Here, we build a deep convolutional
neural network (CNN) to recover the tiny CMB signal from various huge
foreground contaminations. Focusing on the CMB temperature fluctuations, we
find that the CNN model can successfully recover the CMB temperature maps with
high accuracy, and that the deviation of the recovered power spectrum $C_\ell$
is smaller than the cosmic variance at $\ell>10$. We then apply this method to
the current Planck observation, and find that the recovered CMB is quite
consistent with that disclosed by the Planck collaboration, which indicates
that the CNN method can provide a promising approach to the component
separation of CMB observations. Furthermore, we test the CNN method with
simulated CMB polarization maps based on the CMB-S4 experiment. The result
shows that both the EE and BB power spectra can be recovered with high
accuracy. Therefore, this method will be helpful for the detection of
primordial gravitational waves in current and future CMB experiments. The CNN
is designed to analyze two-dimensional images, thus this method is not only
able to process full-sky maps, but also partial-sky maps. Therefore, it can
also be used for other similar experiments, such as radio surveys like the
Square Kilometer Array.


  In this paper, we discuss how the integrated properties of intermediate-age
single burst population, especially in the near-infrared, behave as a function
of age and metallicity. Our models take into account all stellar evolutionary
phases that affect the evolution of the integrated optical and near-infrared
spectrum of such a population. Particular care was dedicated to the Asymptotic
Giant Brach stars, which can be dominant at near-infrared wavelengths. First we
present new synthetic model that takes into account the relevant physical
processes that control the evolution through the thermally pulsing AGB. In the
isochrone presented in this paper the lifetime and the nature of the AGB stars
are established as consequences of the interplay between the physical processes
that control the AGB star evolution. The contribution of these stars to the
integrated light of the population is thus obtained in a consistent way. We
optimize our models by using a new stellar library that explicitly takes into
account the spectral features thar characterize only AGB stars in comparison to
other cool and luminous stars (abriged)


  When a logical qubit is protected using a quantum error-correcting code, the
net effect of coding, decoherence (a physical channel acting on qubits in the
codeword) and recovery can be represented exactly by an effective channel
acting directly on the logical qubit. In this paper we describe a procedure for
deriving the map between physical and effective channels that results from a
given coding and recovery procedure. We show that the map for a concatenation
of codes is given by the composition of the maps for the constituent codes.
This perspective leads to an efficient means for calculating the exact
performance of quantum codes with arbitrary levels of concatenation. We present
explicit results for single-bit Pauli channels. For certain codes under the
symmetric depolarizing channel, we use the coding maps to compute exact
threshold error probabilities for achievability of perfect fidelity in the
infinite concatenation limit.


  We present a design and a top-down fabrication method for realizing diamond
nanowires in both bulk single crystal and polycrystalline diamond. Numerical
modeling was used to study coupling between a Nitrogen Vacancy (NV) color
center and optical modes of a nanowire, and to find an optimal range of
nanowire diameters that allows for large collection efficiency of emitted
photons. Inductively coupled plasma (ICP) reactive ion etching (RIE) with
oxygen is used to fabricate the nanowires. Drop-casted nanoparticles (including
$\mathrm{Au}$, $\mathrm{SiO_{2}}$ and $\mathrm{Al_2O_3}$) as well as electron
beam lithography defined spin-on glass and evaporated $\mathrm{Au}$ have been
used as an etch mask. We found $\mathrm{Al_2O_3}$ nanoparticles to be the most
etch resistant. At the same time FOx e-beam resist (spin-on glass) proved to be
a suitable etch mask for fabrication of ordered arrays of diamond nanowires. We
were able to obtain nanowires with near vertical sidewalls in both
polycrystalline and single crystal diamond. The heights and diameters of the
polycrystalline nanowires presented in this paper are $\unit[\approx1]{\mu m}$
and $\unit[120-340]{nm}$, respectively, having a $\unit[200]{nm/min}$ etch
rate. In the case of single crystal diamond (types Ib and IIa) nanowires the
height and diameter for different diamonds and masks shown in this paper were
$\unit[1-2.4]{\mu m}$ and $\unit[120-490]{nm}$ with etch rates between
$\unit[190-240]{nm/min}$.


  In this paper, we calculate mass and probability fractions of meson-meson
components of $X(3872)$ in an unquenched quark model. Different from most of
other unquenched quark models, the quark pairs creation operator from $^3P_0$
is modified by considering effects of the created quark pair energy and
separation between the created quark pair and the valence quark-pair. In the
calculation, all the wavefunctions of mesons and the relative motion between
two mesons are obtained by solving the corresponding Schr\"{o}dinger equation
with the help of gaussian expansion method. The multi-channel coupling of
quark-antiquark state with possible meson-meson states are performed. The
results show that the $X(3872)$ can be described as a mixing state of dominant
charmonium state (70\%) and meson-meson components (30\%).


  We describe in a simple setting how to extract a unitary braided fusion
category from a collection of superselection sectors of a two-dimensional
quantum spin system, corresponding to abelian anyons. The structure of the
unitary braided fusion category is given by F and R-symbols, which describe
fusion and braiding of the anyons. We then construct the double semion state in
infinite volume and extract the unitary braided fusion category describing its
semion, anti-semion, and bound state excitations. We verify that this category
corresponds to the representation category of the twisted quantum double of
Z_2.


  Given a Probabilistic Finite Automata (PFA), a set of states S, and an error
threshold e > 0, our algorithm approximates the infimum probability
(quantifying over all infinite words) that the automata reaches S. Our result
contrasts with the known result that the approximation problem is undecidable
if we consider the supremum instead of the infimum. Since we study the
probability of reaching a set of states, instead of the probability of ending
in an accepting state, our work is more related to model checking than to
formal languages.


  We have obtained deep, high spatial resolution images of the central region
of Abell 1795 at Halpha and [NII] (6583A) with the Maryland Magellan Tunable
Filter (MMTF), and in the far-ultraviolet (FUV) with the Advanced Camera for
Surveys Solar Blind Channel on the Hubble Space Telescope (HST). The superb
image quality of the MMTF data has made it possible to resolve the known SE
filament into a pair of thin, intertwined filaments extending for ~50 kpc, with
a width < 1 kpc. The presence of these thin, tangled strands is suggestive of a
cooling wake where runaway cooling is taking place, perhaps aided by an
enhanced magnetic field in this region. The HST data further resolve these
strands into chains of FUV-bright stellar clusters, indicating that these
filaments are indeed sites of on-going star formation, but at a rate ~2 orders
of magnitude smaller than the mass-deposition rates predicted from the X-ray
data. The elevated [NII]/Halpha ratio and large spatial variations of the
FUV/Halpha flux ratio across the filaments indicate that O-star photoionization
is not solely responsible for the ionization. The data favor collisional
heating by cosmic rays either produced in-situ by magnetohydrodynamical
processes or conducted in from the surrounding intracluster medium.


  In modern power systems, the operating point, at which the demand and supply
are balanced, may take different values due to changes in loads and renewable
generation levels. Understanding the dynamics of stressed power systems with a
range of operating points would be essential to assuring their reliable
operation, and possibly allow higher integration of renewable resources. This
letter introduces a non-traditional way to think about the stability assessment
problem of power systems. Instead of estimating the set of initial states
leading to a given operating condition, we characterize the set of operating
conditions that a power grid converges to from a given initial state under
changes in power injections and lines. We term this problem as "inverse
stability", a problem which is rarely addressed in the control and systems
literature, and hence, poorly understood. Exploiting quadratic approximations
of the system's energy function, we introduce an estimate of the inverse
stability region. Also, we briefly describe three important applications of the
inverse stability notion: (i) robust stability assessment of power systems
w.r.t. different renewable generation levels, (ii) stability-constrained
optimal power flow (sOPF), and (iii) stability-guaranteed corrective action
design.


  We present a systematic study of mid-infrared spectra of galaxies including
star-forming galaxies and Active Galactic Nuclei observed with JWST MIRI-MRS
and NIRSpec-IFU. We focus on the relative variations of the 3.3, 6.2, 7.7,
11.3, 12.7 and 17 micron Polycyclic Aromatic Hydrocarbon (PAH) features within
spatially resolved regions of galaxies including NGC 3256, NGC 7469, VV 114, II
Zw96 and NGC 5728. Using theoretical PAH models and extending our earlier work,
we introduce a new PAH diagnostic involving the 17 micron PAH feature. To
determine the drivers of PAH band variations in galaxies, we compare observed
PAH spectral bands to predictions from theoretical PAH models. We consider
extinction, dehydrogenation and PAH size and charge as possible drivers of PAH
band variations. We find a surprising uniformity in PAH size distribution among
the spatially resolved regions of the galaxies studied here, with no evidence
for preferential destruction of the smallest grains, contrary to earlier
findings. Neither extinction nor dehydrogenation play a crucial role in setting
the observed PAH bands. Instead, we find that PAH charge plays a significant
role in PAH inter-band variations. We find a tight relation between PAH charge
and the intensity of the radiation field as traced by the [NeIII]/[NeII] maps.
In agreement with recent JWST results, we find a predominance of neutral PAH
molecules in the nuclei of Active Galaxies and their outflows. Ionised PAHs are
the dominant population in star-forming galaxies. We discuss the implications
of our findings for the use of PAHs as ISM tracers in high redshift galaxies.


  In this paper we construct planar polynomials of the type
$f_{A,B}(x)=x(x^{q^2}+Ax^{q}+Bx)\in \mathbb{F}_{q^3}[x]$, with $A,B \in
\mathbb{F}_{q}$. In particular we completely classify the pairs $(A,B)\in
\mathbb{F}_{q}^2$ such that $f_{A,B}(x)$ is planar using connections with
algebraic curves over finite fields.


  Effective resource allocation is a crucial requirement to achieve the
stringent performance targets of ultra-reliable low-latency communication
(URLLC) services. Predicting future interference and utilizing it to design
efficient interference management algorithms is one way to allocate resources
for URLLC services effectively. This paper proposes an empirical mode
decomposition (EMD) based hybrid prediction method to predict the interference
and allocate resources for downlink based on the prediction results. EMD is
used to decompose the past interference values faced by the user equipment.
Long short-term memory and auto-regressive integrated moving average methods
are used to predict the decomposed components. The final predicted interference
value is reconstructed using individual predicted values of decomposed
components. It is found that such a decomposition-based prediction method
reduces the root mean squared error of the prediction by $20 - 25\%$. The
proposed resource allocation algorithm utilizing the EMD-based interference
prediction was found to meet near-optimal allocation of resources and
correspondingly results in $2-3$ orders of magnitude lower outage compared to
state-of-the-art baseline prediction algorithm-based resource allocation.


  We study the role of configuration mixing in the heavier even-even isotopes
of Argon. We begin by limiting the configurations of the even-even Ar isotopes
to $(d_{3/2}^2)_{\pi}$ $(f_{7/2}^n)_{\nu}$. There, due to the particular
location in this shell model space of $^{40}$Ar and $^{44}$Ar, we find that the
spectra, B(E2)'s and magnetic moments of these two nuclei are identical. Any
deviation from this equality is direct evidence of configuration mixing. In a
larger shell model space there are significant differences between these two
nuclei, with $^{44}$Ar being more collective. We also consider other even-even
isotopes of Argon and study how their nuclear structure effects evolve with N.
We compare in the full 0$\hbar \omega$ space $(sd)_{\pi}$ $(fp)_{\nu}$ the
results of calculations with the WBT interaction and with the newer SDPF,
denoted SDPF-U, interaction.


  We present a detailed study of the early phases of the peculiar supernova
2011ay based on BVRI photometry obtained at Konkoly Observatory, Hungary, and
optical spectra taken with the Hobby-Eberly Telescope at McDonald Observatory,
Texas. The spectral analysis carried out with SYN++ and SYNAPPS confirms that
SN 2011ay belongs to the recently defined class of SNe Iax, which is also
supported by the properties of its light and color curves. The estimated
photospheric temperature around maximum light, T_{phot} ~8,000 K, is lower than
in most Type Ia SNe, which results in the appearance of strong Fe II features
in the spectra of SN 2011ay, even during the early phases. We also show that
strong blending with metal features (those of Ti II, Fe II, Co II) makes the
direct analysis of the broad spectral features very difficult, and this may be
true for all SNe Iax. We find two alternative spectrum models that both
describe the observed spectra adequately, but their photospheric velocities
differ by at least 3,000 km/s. The quasi-bolometric light curve of SN~2011ay
has been assembled by integrating the UV-optical spectral energy distributions.
Fitting a modified Arnett-model to L_{bol}(t), the moment of explosion and
other physical parameters, i.e. the rise time to maximum, the ^{56}Ni mass and
the total ejecta mass are estimated as t_{rise} ~14 +/-1 days, M_{Ni} ~0.22 +/-
0.01 M_{sol} and M_{ej} ~0.8 M_{sol}, respectively.


  By conformally coupling vector and hyper multiplets in Minkowski space, we
obtain a class of field theories with extended rigid conformal supersymmetry on
any Lorentzian four-manifold admitting twistor spinors. We construct the
conformal symmetry superalgebras which describe classical symmetries of these
theories and derive an appropriate BRST operator in curved spacetime. In the
process, we elucidate the general framework of cohomological algebra which
underpins the construction. We then consider the corresponding perturbative
quantum field theories. In particular, we examine the conditions necessary for
conformal supersymmetries to be preserved at the quantum level, i.e. when the
BRST operator commutes with the perturbatively defined S-matrix, which ensures
superconformal invariance of amplitudes. To this end, we prescribe a
renormalization scheme for time-ordered products that enter the perturbative
S-matrix and show that such products obey certain Ward identities in curved
spacetime. These identities allow us to recast the problem in terms of the
cohomology of the BRST operator. Through a careful analysis of this cohomology,
and of the renormalization group in curved spacetime, we establish precise
criteria which ensure that all conformal supersymmetries are preserved at the
quantum level. As a by-product, we provide a rigorous proof that the
beta-function for such theories is one-loop exact. We also briefly discuss the
construction of chiral rings and the role of non-perturbative effects in curved
spacetime.


  In this short notes, we discuss monotonicity formulas under various rescaled
versions of Ricci flow. The main result is Theorem \ref{theo rescaled}.


  The recent LEP data for gauge coupling constants constrain many grand unified
models. In this paper, we study several possibilities for unification of gauge
coupling constants. Without an intermediate mass scale, the minimal
supersymmetric standard model is the only possibility. For one intermediate
mass scale, it is possible to have many routes toward grand unification:
$SO(10)\rightarrow SU(3)_c\times SU(2)_L\times SU(2)_R\times U(1) , SU(7),
SU(8)$, etc. We present also simple relations for the possibility of
unification.


  We discuss the quantization of the energy levels of two-particle scattering
states in a finite volume in the case of Bloch-type boundary conditions. A
generalization of the Luescher quantization condition is obtained that can be
used in order to calculate the scattering phases, resulting for example by the
strong elastic interaction of two pions, at fixed physical momentum transfers
on a sequence of volumes of growing sizes. We also give a generalization of the
Lellouch-Luescher formula to be used to extract the physical decay rate for a
kaon decaying into two pions below the inelastic threshold from finite volume
calculations. The formula is valid up to corrections exponentially vanishing in
the volume. By using this formula the calculation can in principle be performed
on different finite volumes of growing sizes in order to keep under control the
corrections.


  We show that when a monopolar current is passed through an n-i-n structure,
superlinear photocurrent response occurs when there is a polariton condensate.
This is in sharp contrast to the previously observed behavior for a standard
semiconductor laser. Theoretical modeling shows that this is due to a
stimulated exciton-exciton scattering process in which one exciton relaxes into
the condensate, while another one dissociates into an electron-hole pair.


  We consider the effects of the Faddeev-Popov determinant in the Coulomb gauge
on the confinement properties of the QCD vacuum. We show that the the
determinant is needed to regularize the otherwise divergent functional
integrals near the Gribov horizon but still enables large field configurations
to generate IR enhanced running coupling. The physical gluon propagator is
found to be strongly suppressed in the
  IR consistent with expectations from lattice gauge calculations.


  Motivated by the recent experimental data of the values of the Heavy Quark
Expansion parameters, in particular the spin-orbit and Darwin terms, we argue
that nature actually may be close to a limit of QCD which has been suggested by
Uraltsev more than ten years ago. Assuming that this limit is not accidental,
we derive the relations among the Heavy Quark Expansion parameters that occur
up to the order 1/mb^5.


  We survey the coevolutionary dynamics of network topology and group
interactions in opinion formation, grounded on a coevolving nonlinear voter
model. The coevolving nonlinear voter model incorporates two mechanisms: group
interactions implemented through nonlinearity in the voter model and network
plasticity demonstrated as the rewiring of links to remove connections between
nodes in different opinions. We show that the role of group interactions,
implemented by the nonlinearity can significantly impact both the dynamical
outcomes of nodes' state and the network topology. Additionally, we review
several variants of the coevolving nonlinear voter model considering different
rewiring mechanisms, noise of flipping nodes' state, and multilayer structures.
We portray the various aspects of the coevolving nonlinear voter model as an
example of network coevolution driven by group interactions, and finally,
present the implications and potential directions for future research.


  For a variety $X$ separated over a perfect field of characteristic $p>0$
which admits an embedding into a smooth variety, we establish an
anti-equivalence between the bounded derived categories of Cartier crystals on
$X$ and constructible $\mathbb Z/p \mathbb Z$-sheaves on the \'etale site
$X_{\text{\'et}}$. The key intermediate step is to extend the category of
locally finitely generated unit $\mathcal O_{F,X}$-modules for smooth schemes
introduced by Emerton and Kisin to embeddable schemes. On the one hand, this
category is equivalent to Cartier crystals. On the other hand, by using
Emerton-Kisin's Riemann-Hilbert correspondence, we show that it is equivalent
to Gabber's category of perverse sheaves in $D_c^b(X_{\text{\'et}},\mathbb Z/p
\mathbb Z)$.


  The latest results on charm-tagged jets and open-charm production obtained
with \mbox{ALICE} at the LHC are presented. The baryon-to-meson ratios for
$\mathrm{\Lambda^+_c}$, $\mathrm{\Sigma^{0,+,++}_c}$ and $\mathrm{\Xi^{0,+}_c}$
measured in pp collisions at $\sqrt{s}=13\ \mathrm{TeV}$ are discussed. The
measurements of the jet-momentum fraction carried by the $\mathrm{D^0}$ meson
and $\mathrm{\Lambda^+_c}$ baryon in pp collisions at $\sqrt{s}=13\
\mathrm{TeV}$ are reported, and the number of leading-parton splittings
$n_{SD}$ for $\mathrm{D^0}$-tagged and inclusive jets in pp collisions at
$\sqrt{s}=13\ \mathrm{TeV}$ are compared. Finally, the first direct measurement
of the dead-cone effect at hadron colliders is shown.


  An analytic method is presented which allows for the computation of the
self-force for a static particle with a scalar charge in the region of an
ultrastatic spacetime which one can call the long throat. The method is based
on the approximate WKB solution of a radial mode equation for a scalar field.
This field is assumed to be massless, with a coupling $\xi$ to the scalar
curvature is satisfying the condition $\xi>1/8$.


  We show by numerical simulations that a non rotationally symmetric body,
whose orientation is fixed and whose center of mass can only slide along a
rectilinear guide, under the effect of inelastic collisions with a surrounding
gas of particles, displays directed motion. We present a theory which explains
how the lack of time reversal induced by the inelasticity of collisions can be
exploited to generate a steady average drift. In the limit of an heavy ratchet,
we derive an effective Langevin equation whose parameters depend on the
microscopic properties of the system and obtain a fairly good quantitative
agreement between the theoretical predictions and simulations concerning
mobility, diffusivity and average velocity.


  Local bifurcation theory typically deals with the response of a degenerate
but isolated equilibrium state or periodic orbit of a dynamical system to
perturbations controlled by one or more independent parameters, and
characteristically uses tools from singularity theory. There are many
situations, however, in which the equilibrium state or periodic orbit is not
isolated but belongs to a manifold $S$ of such states, typically as a result of
continuous symmetries in the problem. In this case the bifurcation analysis
requires a combination of local and global methods, and is most tractable in
the case of normal nondegeneracy, that is when the degeneracy is only along $S$
itself and the system is nondegenerate in directions normal to $S$.
  In this paper we consider the consequences of relaxing normal nondegeneracy,
which can generically occur within 1-parameter families of such systems. We pay
particular attention to the simplest but important case where $\dim S=1$ and
where the normal degeneracy occurs with corank 1. Our main focus is on uniform
degeneracy along $S$, although we also consider aspects of the branching
structure for solutions when the degeneracy varies at different places on $S$.
The tools are those of singularity theory adapted to global topology of $S$,
which allow us to explain the bifurcation geometry in natural way. In
particular, we extend and give a clear geometric setting for earlier analytical
results of Hale and Taboas.


  Recently, the first author has extended the definition of the zeta function
associated with fractal strings to arbitrary bounded subsets $A$ of the
$N$-dimensional Euclidean space ${\mathbb R}^N$, for any integer $N\ge1$. It is
defined by $\zeta_A(s)=\int_{A_{\delta}}d(x,A)^{s-N}\,\mathrm{d} x$ for all
$s\in\mathbb{C}$ with $\operatorname{Re}\,s$ sufficiently large, and we call it
the distance zeta function of $A$. Here, $d(x,A)$ denotes the Euclidean
distance from $x$ to $A$ and $A_{\delta}$ is the $\delta$-neighborhood of $A$,
where $\delta$ is a fixed positive real number. We prove that the abscissa of
absolute convergence of $\zeta_A$ is equal to $\overline\dim_BA$, the upper box
(or Minkowski) dimension of $A$. Particular attention is payed to the principal
complex dimensions of $A$, defined as the set of poles of $\zeta_A$ located on
the critical line $\{\mathop{\mathrm{Re}} s=\overline\dim_BA\}$, provided
$\zeta_A$ possesses a meromorphic extension to a neighborhood of the critical
line. We also introduce a new, closely related zeta function,
$\tilde\zeta_A(s)=\int_0^{\delta} t^{s-N-1}|A_t|\,\mathrm{d} t$, called the
tube zeta function of $A$. Assuming that $A$ is Minkowski measurable, we show
that, under some mild conditions, the residue of $\tilde\zeta_A$ computed at
$D=\dim_BA$ (the box dimension of $A$), is equal to the Minkowski content of
$A$. More generally, without assuming that $A$ is Minkowski measurable, we show
that the residue is squeezed between the lower and upper Minkowski contents of
$A$. We also introduce transcendentally quasiperiodic sets, and construct a
class of such sets, using generalized Cantor sets, along with Baker's theorem
from the theory of transcendental numbers.


  We address two basic issues in the theory of galaxy formation from
fluctuations of quantum fields: 1) the nature and origin of noise and
fluctuations and 2) the conditions for using a classical stochastic equation
for their description. On the first issue, we derive the influence functional
for a $\lambda \phi^4 $ field in a zero-temperature bath in de Sitter universe
and obtain the correlator for the colored noises of vacuum fluctuations. This
exemplifies a new mechanism we propose for colored noise generation which can
act as seeds for galaxy formation with non-Gaussian distributions. For the
second issue, we present a (functional) master equation for the inflaton field
in de Sitter universe. By examining the form of the noise kernel we study the
decoherence of the long-wavelength sector and the conditions for it to behave
classically.


  We propose a natural inflation model driven by an imaginary or axionic
component of a K\"ahler modulus in string-inspired supergravity. The shift
symmetry of the axion is gauged under an anomalous $U(1)_X$ symmetry, which
leads to a modulus-dependent Fayet-Iliopoulos (FI) term. The matter fields are
stabilized by F-terms, and the real component of the modulus is stabilized by
the $U(1)_X$ D-term, while its axion remains light. Therefore, the masses of
real and imaginary components of the modulus are separated at different scales.
The scalar potential for natural inflation is realized by the superpotential
from the non-perturbative effects. The trans-Planckian axion decay constant,
which is needed to fit with BICEP2 observations, can be obtained naturally in
this model.


  We consider Campanato spaces with exponents $\lambda , p$ on domains of class
$C^{0,\gamma}$ in the N-dimensional Euclidean space endowed with a natural
anisotropic metric depending on $\gamma$. We discuss several results including
the appropriate Campanato's embedding theorem and we prove that functions of
those spaces can be extended to the whole of the Euclidean space without
deterioration of the exponents $\lambda, p$.


  A new method is introduced for analysis of interactions between
time-dependent coupled oscillators, based on the signals they generate. It
distinguishes unsynchronized dynamics from noise-induced phase slips, and
enables the evolution of the coupling functions and other parameters to be
followed. It is based on phase dynamics, with Bayesian inference of the
time-evolving parameters achieved by shaping the prior densities to incorporate
knowledge of previous samples. The method is tested numerically and applied to
reveal and quantify the time-varying nature of cardiorespiratory interactions.


  Given a natural language query, a phrase grounding system aims to localize
mentioned objects in an image. In weakly supervised scenario, mapping between
image regions (i.e., proposals) and language is not available in the training
set. Previous methods address this deficiency by training a grounding system
via learning to reconstruct language information contained in input queries
from predicted proposals. However, the optimization is solely guided by the
reconstruction loss from the language modality, and ignores rich visual
information contained in proposals and useful cues from external knowledge. In
this paper, we explore the consistency contained in both visual and language
modalities, and leverage complementary external knowledge to facilitate weakly
supervised grounding. We propose a novel Knowledge Aided Consistency Network
(KAC Net) which is optimized by reconstructing input query and proposal's
information. To leverage complementary knowledge contained in the visual
features, we introduce a Knowledge Based Pooling (KBP) gate to focus on
query-related proposals. Experiments show that KAC Net provides a significant
improvement on two popular datasets.


  We present a study of photometric redshift performance for galaxies and
active galactic nuclei detected in deep radio continuum surveys. Using two
multi-wavelength datasets, over the NOAO Deep Wide Field Survey Bo\"otes and
COSMOS fields, we assess photometric redshift (photo-z) performance for a
sample of $\sim 4,500$ radio continuum sources with spectroscopic redshifts
relative to those of $\sim 63,000$ non radio-detected sources in the same
fields. We investigate the performance of three photometric redshift template
sets as a function of redshift, radio luminosity and infrared/X-ray properties.
We find that no single template library is able to provide the best performance
across all subsets of the radio detected population, with variation in the
optimum template set both between subsets and between fields. Through a
hierarchical Bayesian combination of the photo-z estimates from all three
template sets, we are able to produce a consensus photo-z estimate which equals
or improves upon the performance of any individual template set.


  Empirical scoring functions based on either molecular force fields or
cheminformatics descriptors are widely used, in conjunction with molecular
docking, during the early stages of drug discovery to predict potency and
binding affinity of a drug-like molecule to a given target. These models
require expert-level knowledge of physical chemistry and biology to be encoded
as hand-tuned parameters or features rather than allowing the underlying model
to select features in a data-driven procedure. Here, we develop a general
3-dimensional spatial convolution operation for learning atomic-level chemical
interactions directly from atomic coordinates and demonstrate its application
to structure-based bioactivity prediction. The atomic convolutional neural
network is trained to predict the experimentally determined binding affinity of
a protein-ligand complex by direct calculation of the energy associated with
the complex, protein, and ligand given the crystal structure of the binding
pose. Non-covalent interactions present in the complex that are absent in the
protein-ligand sub-structures are identified and the model learns the
interaction strength associated with these features. We test our model by
predicting the binding free energy of a subset of protein-ligand complexes
found in the PDBBind dataset and compare with state-of-the-art cheminformatics
and machine learning-based approaches. We find that all methods achieve
experimental accuracy and that atomic convolutional networks either outperform
or perform competitively with the cheminformatics based methods. Unlike all
previous protein-ligand prediction systems, atomic convolutional networks are
end-to-end and fully-differentiable. They represent a new data-driven,
physics-based deep learning model paradigm that offers a strong foundation for
future improvements in structure-based bioactivity prediction.


  In this paper we give a proof via the contraction mapping principle of a
Bloch-type theorem for normalised Bochner-Takahashi $K$-mappings, which are
solutions to equations of the form $Lu=0$, where $L$ is the heat operator.


  We investigate the space complexity of solving linear systems of equations.
While all known deterministic or randomized algorithms solving a square system
of $n$ linear equations in $n$ variables require $\Omega(\log^2 n)$ space,
Ta-Shma (STOC 2013) recently showed that on a quantum computer an approximate
solution can be computed in logarithmic space, giving the first explicit
computational task for which quantum computation seems to outperform classical
computation with respect to space complexity. In this paper we show that for
systems of linear equations in the Laplacian matrix of graphs, the same
logarithmic space complexity can actually be achieved by a classical (i.e.,
non-quantum) algorithm. More precisely, given a system of linear equations
$Lx=b$, where $L$ is the (normalized) Laplacian matrix of a graph on $n$
vertices and $b$ is a unit-norm vector, our algorithm outputs a vector $\tilde
x$ such that $\left\lVert\tilde x -x\right\rVert\le 1/\mathrm{poly}(n)$ and
uses only $O(\log n)$ space if the underlying graph has polynomially bounded
weights. We also show how to estimate, again in logarithmic space, the smallest
non-zero eigenvalue of $L$.


  Robust tube-based model predictive control (MPC) methods address constraint
satisfaction by leveraging an a priori determined tube controller in the
prediction to tighten the constraints. This paper presents a system level
tube-MPC (SLTMPC) method derived from the system level parameterization (SLP),
which allows optimization over the tube controller online when solving the MPC
problem, which can significantly reduce conservativeness. We derive the SLTMPC
method by establishing an equivalence relation between a class of robust MPC
methods and the SLP. Finally, we show that the SLTMPC formulation naturally
arises from an extended SLP formulation and show its merits in a numerical
example.


  The research area of plasmonics promises devices with ultrasmall footprint
operating at ultrafast speeds and with lower energy consumption compared to
conventional electronics. These devices will operate with light and bridge the
gap between microscale dielectric photonic systems and nanoscale electronics.
Recent research advancements in nanotechnology and optics have led to the
creation of a plethora of new plasmonic designs. Among the most promising are
nanoscale antennas operating at optical frequencies, called nanoantennas.
Plasmonic nanoantennas can provide enhanced and controllable light-matter
interactions and strong coupling between far-field radiation and localized
sources at the nanoscale. After a brief introduction of several plasmonic
nanoantenna designs and their well-established radio-frequency antenna
counterparts, we review several linear and nonlinear applications of different
nanoantenna configurations. In particular, the possibility to tune the
scattering response of linear nanoantennas and create robust optical wireless
links is presented. In addition, the nonlinear and photodynamic responses of
different linear and nonlinear nanoantenna systems are reported. Several future
optical devices are envisioned based on these plasmonic nanoantenna
configurations, such as low-power nanoswitches, compact ultrafast light
sources, nanosensors and efficient energy harvesting systems.


  The tau function on the moduli space of generic holomorphic 1-differentials
on complex algebraic curves is interpreted as a section of a line bundle on the
projectivized Hodge bundle over the moduli space of stable curves. The
asymptotics of the tau function near the boundary of the moduli space of
1-differentials is computed, and an explicit expression for the pullback of the
Hodge class on the projectivized Hodge bundle in terms of the tautological
class and the classes of boundary divisors is derived. This expression is used
to clarify the geometric meaning of the Kontsevich-Zorich formula for the sum
of the Lyapunov exponents associated with the Teichm\"uller flow on the Hodge
bundle.


  Based on the results of applying the extended ADC emission model for low mass
X-ray binaries to three Z-track sources: GX340+0, GX5-1 and CygX-2, we propose
an explanation of the CygnusX-2 like Z-track sources. The Normal Branch is
dominated by the increasing radiation pressure of the neutron star caused by a
mass accretion rate that increases between the soft apex and the hard apex. The
radiation pressure continues to increase on the Horizontal Branch becoming
several times super-Eddington. We suggest that this disrupts the inner
accretion disk and that part of the accretion flow is diverted vertically
forming jets which are detected by their radio emission on this part of the
Z-track. We thus propose that high radiation pressure is the necessary
condition for the launching of jets. On the Flaring Branch there is a large
increase in the neutron star blackbody luminosity at constant mass accretion
rate indicating an additional energy source on the neutron star. We find that
there is good agreement between the mass accretion rate per unit emitting area
of the neutron star mdot at the onset of flaring and the theoretical critical
value at which burning becomes unstable. We thus propose that flaring in the
CygnusX-2 like sources consists of unstable nuclear burning. Correlation of
measurements of kilohertz QPO frequencies in all three sources with spectral
fitting results leads to the proposal that the upper kHz QPO is an oscillation
always taking place at the inner accretion disk edge, the radius of which
increases due to disruption of the disk by the high radiation pressure of the
neutron star.


  In this article we address a problem of determination of light pressure upon
space structures of the complex geometric shape. For the surface element, we
wrote a condition that this element can interact with light only from the front
side, not from the back side. This condition To in the form of series of
Chebyshev polynomials of the first kind. Chebyshev expansion lets us move to
the series of tensors of increasing rank for the problem of determination of
force and moment. We obtained expressions for the fiber method for
determination of light pressure on space structures of complex geometry taking
into account self--shadowing and reflections within the structure. We also give
the expressions for tensor parametrization by the specularity coefficient in
case of specular-diffuse reflection. For these expressions we calculated the
principal moment and force upon two-sided flat solar sail, spherical and
cylindrical bodies, and approximated light pressure upon a perspective space
observatory Millimetron. The proposed expressions can be used in the ballistic
analysis of solar sails and other space objects, which are significantly
affected by the radiation pressure. Also, these results can be used to analyze
the dynamics of movement of large-scale space structures around the center of
gravity under the light pressure.


  Let $M$ be a monoid that is embeddable in a group. We consider the topos
$\mathbf{PSh}(M)$ of sets equipped with a right $M$-action, and we study the
subtoposes that are of monoid type, i.e. the subtoposes that are again of the
form $\mathbf{PSh}(N)$ for $N$ a monoid. Our main result is that every subtopos
of monoid type can be obtained by localization at a prime ideal of $M$.
Conversely, we show that localization at a prime ideal produces a subtopos if
and only if $M$ has the right Ore property with respect to the complement of
the prime ideal. We demonstrate our calculations in some examples: free
monoids, two monoids related to the Connes-Consani Arithmetic Site, and torus
knot monoids.


  We study the phase diagram of mass- and spin-imbalanced unitary Fermi gases,
in search for the emergence of spatially inhomogeneous phases. To account for
fluctuation effects beyond the mean-field approximation, we employ
renormalization group techniques. We thus obtain estimates for critical values
of the temperature, mass and spin imbalance, above which the system is in the
normal phase. In the unpolarized, equal-mass limit, our result for the critical
temperature is in accordance with state-of-the-art Monte Carlo calculations. In
addition, we estimate the location of regions in the phase diagram where
inhomogeneous phases are likely to exist. We show that an intriguing relation
exists between the general structure of the many-body phase diagram and the
binding energies of the underlying two-body bound-state problem, which further
supports our findings. Our results suggest that inhomogeneous condensates form
for mass ratios of the spin-down and spin-up fermions greater than three. The
extent of the inhomogeneous phase in parameter space increases with increasing
mass imbalance.


  This paper aims to exploit the fundamental limits on the downlink coverage
and spatial throughput performances of a cellular network comprised of a tier
of unmanned aerial vehicle (UAV) base stations (BSs) using the millimeter wave
(mmWave) band and a tier of ground BSs using the ultra high frequency (UHF)
band. To reduce handover signaling overhead, the ground BSs take charge of
control signaling delivery whereas the UAVs are in charge of payload data
transmission so that users need to be simultaneously associated with a ground
BS and a UAV in this network with a control-data plane-split architecture. We
first propose a three-dimensional (3D) location distribution model of the UAVs
using stochastic geometry which is able to generally characterize the positions
of the UAVs in the sky. Using this 3D distribution model of UAVs, two
performance metrics, i.e., multi-cell coverage probability and volume spectral
efficiency, are proposed. Their explicit low-complexity expressions are derived
and their upper limits are found when each of the UAVs and ground BSs is
equipped with a massive antenna array. We further show that the multi-cell
coverage probability and the volume spectral efficiency can be maximized by
optimally deploying and positioning the UAVs in the sky and thereby their
fundamental maximal limits are found. These important analytical findings are
validated by numerical simulations.


  We study the probability that a random walk started inside a subgraph of a
larger graph exits that subgraph (or, equivalently, hits the exterior boundary
of the subgraph). Considering the chance a random walk started in the subgraph
never leaves the subgraph leads to a notion we call "survival" transience, or
$S$-transience. In the case where the heat kernel of the larger graph satisfies
two-sided Gaussian estimates, we prove an upper bound on the probability of
hitting the boundary of the subgraph. Under the additional hypothesis that the
subgraph is inner uniform, we prove a two-sided estimate for this probability.
The estimate depends upon a harmonic function in the subgraph. We also provide
two-sided estimates for related probabilities, such as the harmonic measure
(the chance the walk exits the subgraph at a particular point on its boundary).


  This report discusses the foundations of the VO approach. Then, it explores
multiple directions and argues about structure and applications.


  An M6.5-class flare was observed at N12E56 of the solar surface at 16:06 UT
on July 8, 2014. In association with this flare, solar neutron detectors
located on two high mountains, Mt. Sierra Negra and Chacaltaya and at the space
station observed enhancements in the neutral channel. The authors analysed
these data and a possible scenario of enhancements produced by high-energy
protons and neutrons is proposed, using the data from continuous observation of
a solar surface by the ultraviolet telescope onboard the Solar Dynamical
Observatory (SDO).


  The game of Spot it(R) is based on an order 7 finite projective plane. This
article presents a solitaire challenge: extract an order 7 affine plane and
arrange those 49 cards into a square such that the symmetries of the affine and
projective planes are obvious. The objective is not to simply create such a
deck already in this solved position. Rather, it is to solve the inverse
problem of arranging the cards of such a deck which has already been created
shuffled.


  In this article, the cohomology of the arithmetic group
$\mathrm{Sp}_4(\mathbb{Z})$ with coefficients in any finite dimensional highest
weight representation $\mathcal{M}_\lambda$ have been studied. Euler
characteristic with coefficients in $\mathcal{M}_\lambda$ have been carried out
in detail. Combining the results obtained on Euler characteristic and the work
of Harder on Eisenstein cohomology, the description of the cuspidal cohomology
has been achieved. At the end, we employ our study to compute the dimensions
for the cohomology spaces $H^{\bullet}(\mathrm{Sp}_4(\mathbb{Z}),
\mathcal{M}_\lambda)$.


  Time-dependent Lindblad master equations have important applications in areas
ranging from quantum thermodynamics to dissipative quantum computing. In this
paper we outline a general method for writing down exact solutions of
time-dependent Lindblad equations whose superoperators form closed algebras. We
focus on the particular case of a single qubit and study the exact solution
generated by both coherent and incoherent mechanisms. We also show that if the
time-dependence is periodic, the problem may be recast in terms of Floquet
theory. As an application, we give an exact solution for a two-levels quantum
heat engine operating in a finite-time.


  Model-independent description of nonleptonic decays of charmed mesons is a
challenging task due to large nonperturbative effects of strong interactions on
the transition amplitudes. We discuss the equivalence of two different
flavor-$SU(3)$-based descriptions of Cabibbo-favored non-leptonic decays of
charmed mesons to two-pseudoscalars final states including the $\eta$ and
$\eta^\prime$ mesons.


  The possibility of description of the experimental data for the astrophysical
S-factor of the proton radiative capture on 16O to the ground and first excited
states of 17F was considered in the frame of the modified potential cluster
model with forbidden states and classification of the states according to Young
tableaux. It was shown that on the basis of the E1 transitions from the P
states of p16O scattering to the bound states of 17F in the p16O channel, it
generally succeed to explain the value of measured astrophysical S-factors and
reaction rates at astrophysical energies.