  We study the buckling of elastic spherical shells under osmotic pressure with
the osmolyte concentration of the exterior solution as control parameter. We
compare our results for the bifurcation behavior with results for buckling
under mechanical pressure control, that is, with an empty capsule interior. We
find striking differences for the buckling states between osmotic and
mechanical buckling. Mechanical pressure control always leads to fully
collapsed states with opposite sides in contact, whereas uncollapsed states
with a single finite dimple are generic for osmotic pressure control. For
sufficiently large interior osmolyte concentrations, osmotic pressure control
is qualititatively similar to buckling under volume control with the volume
prescribed by the osmolyte concentrations inside and outside the shell. We
present a quantitative theory which also captures the influence of shell
elasticity on the relation between osmotic pressure and volume. These findings
are relevant for the control of buckled shapes in applications. We show how the
osmolyte concentration can be used to control the volume of buckled shells. An
accurate analytic formula is derived for the relation between the osmotic
pressure, the elastic moduli and the volume of buckled capsules. This also
allows to use elastic capsules as osmotic pressure sensors or to deduce elastic
properties and the internal osmolyte concentration from shape changes in
response to osmotic pressure changes. We apply our findings to published
experimental data on polyelectrolyte capsules.


  We study the quantum synchronization between a pair of two-level systems
inside two coupled cavities. By using a digital-analog decomposition of the
master equation that rules the system dynamics, we show that this approach
leads to quantum synchronization between both two-level systems. Moreover, we
can identify in this digital-analog block decomposition the fundamental
elements of a quantum machine learning protocol, in which the agent and the
environment (learning units) interact through a mediating system, namely, the
register. If we can additionally equip this algorithm with a classical feedback
mechanism, which consists of projective measurements in the register,
reinitialization of the register state and local conditional operations on the
agent and environment subspace, a powerful and flexible quantum machine
learning protocol emerges. Indeed, numerical simulations show that this
protocol enhances the synchronization process, even when every subsystem
experience different loss/decoherence mechanisms, and give us the flexibility
to choose the synchronization state. Finally, we propose an implementation
based on current technologies in superconducting circuits.


  Harmonic inpainting with optimised data is very popular for inpainting-based
image compression. We improve this approach in three important aspects.
Firstly, we replace the standard finite differences discretisation by a finite
element method with triangle elements. This does not only speed up inpainting
and data selection, but even improves the reconstruction quality. Secondly, we
propose highly efficient algorithms for spatial and tonal data optimisation
that are several orders of magnitude faster than state-of-the-art methods. Last
but not least, we show that our algorithms also allow working with very large
images. This has previously been impractical due to the memory and runtime
requirements of prior algorithms.


  The effectiveness of neural processes (NPs) in modelling posterior prediction
maps -- the mapping from data to posterior predictive distributions -- has
significantly improved since their inception. This improvement can be
attributed to two principal factors: (1) advancements in the architecture of
permutation invariant set functions, which are intrinsic to all NPs; and (2)
leveraging symmetries present in the true posterior predictive map, which are
problem dependent. Transformers are a notable development in permutation
invariant set functions, and their utility within NPs has been demonstrated
through the family of models we refer to as TNPs. Despite significant interest
in TNPs, little attention has been given to incorporating symmetries. Notably,
the posterior prediction maps for data that are stationary -- a common
assumption in spatio-temporal modelling -- exhibit translation equivariance. In
this paper, we introduce of a new family of translation equivariant TNPs that
incorporate translation equivariance. Through an extensive range of experiments
on synthetic and real-world spatio-temporal data, we demonstrate the
effectiveness of TE-TNPs relative to their non-translation-equivariant
counterparts and other NP baselines.


  This is the second of a series of papers where we study the plurigenera, the
Kodaira dimension and the Iitaka dimension on compact almost complex manifolds.
By using the pseudoholomorphic pluricanonical map, we define the second version
of Kodaira dimension as well as Iitaka dimension on compact almost complex
manifolds. We show the almost complex structures with the top Kodaira dimension
are integrable. For compact almost complex 4-manifolds with Kodaira dimension
one, we obtain elliptic fibration like structural description. Some vanishing
theorems in complex geometry are generalized to the almost complex setting.
  For tamed symplectic $4$-manifolds, we show that the almost Kodaira dimension
is bounded above by the symplectic Kodaira dimension, by using a probabilistic
combinatorics style argument. The appendix also contains a few results
including answering a question of the second author that there is a unique
subvariety in exceptional curve classes for irrational symplectic
$4$-manifolds, as well as extending Evans-Smith's constraint on symplectic
embeddings of certain rational homology balls by removing the assumption on the
intersection form.


  We introduce notions such as cdp presheaf, cds precosheaf, Mayer-Vietoris
system, and investigate their properties. As applications, we study
cohomologies with values in local systems on smooth manifolds and Dolbeault
cohomologies with values in locally free sheaves on complex manifolds, where
the compactness is not necessary for both cases. In particular, we write out
explicit blow-up formulas for these cohomologies. Moreover, we compare the
blow-up formula given by Rao, S., Yang, S. and Yang, X.-D. with ours, and then
deduce that their formula is still an isomorphism in the noncompact case.


  Evolutionary algorithms (EAs) have been successfully applied to optimize the
policies for Reinforcement Learning (RL) tasks due to their exploration
ability. The recently proposed Negatively Correlated Search (NCS) provides a
distinct parallel exploration search behavior and is expected to facilitate RL
more effectively. Considering that the commonly adopted neural policies usually
involves millions of parameters to be optimized, the direct application of NCS
to RL may face a great challenge of the large-scale search space. To address
this issue, this paper presents an NCS-friendly Cooperative Coevolution (CC)
framework to scale-up NCS while largely preserving its parallel exploration
search behavior. The issue of traditional CC that can deteriorate NCS is also
discussed. Empirical studies on 10 popular Atari games show that the proposed
method can significantly outperform three state-of-the-art deep RL methods with
50% less computational time by effectively exploring a 1.7 million-dimensional
search space.


  The critical behavior of pinned charge density waves (CDW's) is studied as
the threshold for sliding is approached. Using the Fukuyama-Lee-Rice
Hamiltonian with relaxational dynamics, the polarization and linear response
are calculated numerically. ... On the irreversible approach to threshold, the
response due to avalanches triggered by local instabilities dominates the
polarizability, which diverges in one and two dimensions. Characteristic
diverging length scales are studied using finite-size scaling of the
sample-to-sample variations of the threshold field in finite systems and
finite-size effects in the linear polarizability and the irreversible
polarization. A dominant diverging correlation length is found which controls
the threshold field distribution, finite-size effects in the irreversible
polarization, and a cutoff size for the avalanche size distribution. Our
results are compared with those for related models and questions are raised
concerning the relationship of the static critical behavior below threshold to
the dynamic critical behavior in the sliding state above threshold.


  We find, using high resolution numerical relativistic simulations, that the
tail of the dynamical ejecta of neutron star mergers extends to mildly
relativistic velocities faster than $0.7c$. The kinetic energy of this fast
tail is $\sim 10^{47}$--$10^{49}$ erg, depending on the neutron star equation
of state and on the binary masses. The synchrotron flare arising from the
interaction of this fast tail with the surrounding ISM can power the observed
non-thermal emission that followed GW170817, provided that the ISM density is
$\sim 10^{-2}\,{\rm cm^{-3}}$, the two neutron stars had roughly equal masses
and the neutron star equation of state is soft (small neutron star radii). One
of the generic predictions of this scenario is that the cooling frequency
crosses the X-ray band on a time scale of a few months to a year, leading to a
cooling break in the X-ray light curve. If this dynamical ejecta scenario is
correct, we expect that the synchrotron radio flare from the ejecta that have
produced the macronova/kilonova emission will be observable on time scales of
$10^3$ to $10^5$ days. Further multi-frequency observations will confirm or
rule out this dynamical ejecta scenario.


  We reduce the question whether a given quantum mixed state is separable or
entangled to the problem of existence of a certain full family of commuting
normal matrices whose matrix elements are partially determined by components of
the pure states constituting a decomposition of the considered mixture. The
method reproduces many known entanglement and/or separability criteria, and
provides yet another geometrical characterization of mixed separable states.


  We study model predictive control for singular differential-algebraic
equations with higher index. This is a novelty when compared to the literature
where only regular differential-algebraic equations with additional assumptions
on the index and/or controllability are considered. By regularization
techniques, we are able to derive an equivalent optimal control problem for an
ordinary differential equation to which well-known model predictive control
techniques can be applied. This allows the construction of terminal constraints
and costs such that the origin is asymptotically stable w.r.t. the resulting
closed-loop system.


  In this paper, we study distributed methods for solving a Sylvester equation
in the form of AX+XB=C for matrices A, B, C$\in R^{n\times n}$ with X being the
unknown variable. The entries of A, B and C (called data) are partitioned into
a number of pieces (or sometimes we permit these pieces to overlap). Then a
network with a given structure is assigned, whose number of nodes is consistent
with the partition. Each node has access to the corresponding set of data and
holds a dynamic state. Nodes share their states among their neighbors defined
from the network structure, and we aim to design flows that can asymptotically
converge to a solution of this equation. The decentralized data partitions may
be resulted directly from networks consisting of physically isolated
subsystems, or indirectly from artificial and strategic design for processing
large data sets. Natural partial row/column partitions, full row/column
partitions and clustering block partitions of the data A, B and C are assisted
by the use of the vectorized matrix equation. We show that the existing
"consensus + projection" flow and the "local conservation + global consensus"
flow for distributed linear algebraic equations can be used to drive
distributed flows that solve this kind of equations. A "consensus + projection
+ symmetrization" flow is also developed for equations with symmetry
constraints on the solution matrices. We reveal some fundamental convergence
rate limitations for such flows regardless of the choices of node interaction
strengths and network structures. For a special case with B=A$^T$, where the
equation mentioned is reduced to a classical Lyapunov equation, we demonstrate
that by exploiting the symmetry of data, we can obtain flows with lower
complexity for certain partitions.


  Various pion and photon production mechanisms in high-energy nuclear
collisions at RHIC and LHC are discussed. Comparison with RHIC data is done
whenever possible. The prospect of using electromagnetic probes to characterize
quark-gluon plasma formation is assessed.


  The intricate pattern of chemical modifications on DNA and histones, the
"histone code", is considered to be a key gene regulation factor. Multivalency
is seen by many as an essential instrument to transmit the "encoded"
information to the transcription machinery via multi-domain effector proteins
and chromatin-associated complexes. However, as examples of multivalent histone
engagement accumulate, an apparent contradiction is emerging. The isolated
effector domains are notably weak binders, thus it is often asserted that the
entropic cost of orienting multiple domains can be "prepaid" by a rigid tether.
Meanwhile, evidence suggests that the tethers are largely disordered and offer
little rigidity. Here we consider a mechanism to "prepay" the entropic costs of
orienting the domains for binding, not through rigidity of the tether but
through the careful spacing of the modifications on chromatin. An all-atom
molecular dynamics study of the most fully characterized multivalent chromatin
effector conforms to the conditions for an optimal free-energy payout, as
predicted by the model discussed here.


  We study the question of when we can provide direct access to the k-th answer
to a Conjunctive Query (CQ) according to a specified order over the answers in
time logarithmic in the size of the database, following a preprocessing step
that constructs a data structure in time quasilinear in database size.
Specifically, we embark on the challenge of identifying the tractable answer
orderings, that is, those orders that allow for such complexity guarantees. To
better understand the computational challenge at hand, we also investigate the
more modest task of providing access to only a single answer (i.e., finding the
answer at a given position), a task that we refer to as the selection problem,
and ask when it can be performed in quasilinear time. We also explore the
question of when selection is indeed easier than ranked direct access.
  We begin with lexicographic orders. For each of the two problems, we give a
decidable characterization (under conventional complexity assumptions) of the
class of tractable lexicographic orders for every CQ without self-joins. We
then continue to the more general orders by the sum of attribute weights and
establish the corresponding decidable characterizations, for each of the two
problems, of the tractable CQs without self-joins. Finally, we explore the
question of when the satisfaction of Functional Dependencies (FDs) can be
utilized for tractability, and establish the corresponding generalizations of
our characterizations for every set of unary FDs.


  In advanced manufacturing, the incorporation of sensing technology provides
an opportunity to achieve efficient in-situ process monitoring using machine
learning methods. Meanwhile, the advances of information technologies also
enable a connected and decentralized environment for manufacturing systems,
making different manufacturing units in the system collaborate more closely. In
a decentralized manufacturing system, the involved units may fabricate same or
similar products and deploy their own machine learning model for online process
monitoring. However, due to the possible inconsistency of task progress during
the operation, it is also common that some units have more informative data
while some have less informative data. Thus, the monitoring performance of
machine learning model for each unit may highly vary. Therefore, it is
extremely valuable to achieve efficient and secured knowledge sharing among the
units in a decentralized manufacturing system for enhancement of poorly
performed models. To realize this goal, this paper proposes a novel knowledge
distillation-based information sharing (KD-IS) framework, which could distill
informative knowledge from well performed models to improve the monitoring
performance of poorly performed models. To validate the effectiveness of this
method, a real-world case study is conducted in a connected fused filament
fabrication (FFF)-based additive manufacturing (AM) platform. The experimental
results show that the developed method is very efficient in improving model
monitoring performance at poorly performed models, with solid protection on
potential data privacy.


  Code Smell, similar to a bad smell, is a surface indication of something
tainted but in terms of software writing practices. This metric is an
indication of a deeper problem lies within the code and is associated with an
issue which is prominent to experienced software developers with acceptable
coding practices. Recent studies have often observed that codes having code
smells are often prone to a higher probability of change in the software
development cycle. In this paper, we developed code smell prediction models
with the help of features extracted from source code to predict eight types of
code smell. Our work also presents the application of data sampling techniques
to handle class imbalance problem and feature selection techniques to find
relevant feature sets. Previous studies had made use of techniques such as
Naive - Bayes and Random forest but had not explored deep learning methods to
predict code smell. A total of 576 distinct Deep Learning models were trained
using the features and datasets mentioned above. The study concluded that the
deep learning models which used data from Synthetic Minority Oversampling
Technique gave better results in terms of accuracy, AUC with the accuracy of
some models improving from 88.47 to 96.84.


  We analyze the asymptotic behavior of Regge trajectories of non-strange
mesons. In contrast to an existing belief, it is demonstrated that for the
asymptotically linear Regge trajectories the width of heavy hadrons cannot
linearly depend on their mass. Using the data on masses and widths of rho_J,
omega_J, a_J and f_J mesons for the spin values J \leq 6, we extract the
parameters of the asymptotically linear Regge trajectory predicted by the
finite width model of quark gluon bags. As it is shown the obtained parameters
for the data set B correspond to the cross-over temperature lying in the
interval 170.9-175.3 MeV which is consistent with the kinetic freeze-out
temperature of early hadronizing particles found in relativistic heavy ion
collisions at and above the highest SPS energy.


  In this article we introduce an algorithm for mitigating the adverse effects
of noise on gradient descent in variational quantum algorithms. This is
accomplished by computing a {\emph{regularized}} local classical approximation
to the objective function at every gradient descent step. The computational
overhead of our algorithm is entirely classical, i.e., the number of circuit
evaluations is exactly the same as when carrying out gradient descent using the
parameter-shift rules. We empirically demonstrate the advantages offered by our
algorithm on randomized parametrized quantum circuits.


  The minimum number of NOT gates in a logic circuit computing a Boolean
function is called the inversion complexity of the function. In 1957, A. A.
Markov determined the inversion complexity of every Boolean function and proved
that $\lceil\log_{2}(d(f)+1)\rceil$ NOT gates are necessary and sufficient to
compute any Boolean function $f$ (where $d(f)$ is the maximum number of value
changes from greater to smaller over all increasing chains of tuples of
variables values). This result is extended to $k$-valued functions computing in
this paper. Thereupon one can use monotone functions "for free" like in the
Boolean case. It is shown that the minimum sufficient number of non-monotone
gates for the realization of the arbitrary $k$-valued logic function $f$ is
equal to $\lceil\log_{2}(d(f)+1)\rceil$ if Post negation (function $x+1
\pmod{k}$) is used in NOT nodes and is also equal to
$\lceil\log_{k}(d(f)+1)\rceil$, if {\L}ukasiewicz negation (function $k-1-x$)
is used in NOT nodes. Similar extension for another classical result of A. A.
Markov for the inversion complexity of a system of Boolean functions to
$k$-valued logic functions has been obtained.


  The remarkable generative capabilities of denoising diffusion models have
raised new concerns regarding the authenticity of the images we see every day
on the Internet. However, the vast majority of existing deepfake detection
models are tested against previous generative approaches (e.g. GAN) and usually
provide only a "fake" or "real" label per image. We believe a more informative
output would be to augment the per-image label with a localization map
indicating which regions of the input have been manipulated. To this end, we
frame this task as a weakly-supervised localization problem and identify three
main categories of methods (based on either explanations, local scores or
attention), which we compare on an equal footing by using the Xception network
as the common backbone architecture. We provide a careful analysis of all the
main factors that parameterize the design space: choice of method, type of
supervision, dataset and generator used in the creation of manipulated images;
our study is enabled by constructing datasets in which only one of the
components is varied. Our results show that weakly-supervised localization is
attainable, with the best performing detection method (based on local scores)
being less sensitive to the looser supervision than to the mismatch in terms of
dataset or generator.


  I review various theoretical questions that arise from data from HERA and the
Tevatron, and which are relevant for the LHC. They range from soft physics,
such as the total cross section, to hard physics, such as Higgs production. In
particular, I argue that the proton's gluon density is somewhat larger at small
$x$ than is currently accepted.


  We confirm TOI-4201 b as a transiting Jovian mass planet orbiting an early M
dwarf discovered by the Transiting Exoplanet Survey Satellite. Using ground
based photometry and precise radial velocities from NEID and the Planet Finder
Spectrograph, we measure a planet mass of 2.59$^{+0.07}_{-0.06}$ M$_{J}$,
making this one of the most massive planets transiting an M-dwarf. The planet
is $\sim$0.4\% the mass of its 0.63 M$_{\odot}$ host and may have a heavy
element mass comparable to the total dust mass contained in a typical Class II
disk. TOI-4201 b stretches our understanding of core-accretion during the
protoplanetary phase, and the disk mass budget, necessitating giant planet
formation to either take place much earlier in the disk lifetime, or perhaps
through alternative mechanisms like gravitational instability.


  This paper proposes an effective emotion control method for an end-to-end
text-to-speech (TTS) system. To flexibly control the distinct characteristic of
a target emotion category, it is essential to determine embedding vectors
representing the TTS input. We introduce an inter-to-intra emotional distance
ratio algorithm to the embedding vectors that can minimize the distance to the
target emotion category while maximizing its distance to the other emotion
categories. To further enhance the expressiveness of a target speech, we also
introduce an effective interpolation technique that enables the intensity of a
target emotion to be gradually changed to that of neutral speech. Subjective
evaluation results in terms of emotional expressiveness and controllability
show the superiority of the proposed algorithm to the conventional methods.


  Gravitational-wave detection has been pursued relentlessly for over 40 years.
With the imminent operation of a new generation of laser interferometers, it is
expected that detections will become a common occurrence. The research into
more ambitious detectors promises to allow the field to move beyond detection
and into the realm of precision science using gravitational radiation. In this
article, I review the state of the art for the detectors and describe an
outlook for the coming decades.


  In this paper we give an affirmative answer to an open question mentioned in
[Le Bris and Lions, Comm. Partial Differential Equations 33 (2008),
1272--1317], that is, we prove the well-posedness of the Fokker-Planck type
equations with Sobolev diffusion coefficients and BV drift coefficients.


  In the last decade, Deep Learning has rapidly infiltrated the consumer end,
mainly thanks to hardware acceleration across devices. However, as we look
towards the future, it is evident that isolated hardware will be insufficient.
Increasingly complex AI tasks demand shared resources, cross-device
collaboration, and multiple data types, all without compromising user privacy
or quality of experience. To address this, we introduce a novel paradigm
centered around EdgeAI-Hub devices, designed to reorganise and optimise compute
resources and data access at the consumer edge. To this end, we lay a holistic
foundation for the transition from on-device to Edge-AI serving systems in
consumer environments, detailing their components, structure, challenges and
opportunities.


  The thickness of freshly made soap films is usually in the micron range, and
interference colors make thickness fluctuations easily visible. Circular
patterns of constant thickness are commonly observed, either a thin film disc
in a thicker film or the reverse. In this Letter, we evidence the line tension
at the origin of these circular patterns. Using a well controlled soap film
preparation, we produce a piece of thin film surrounded by a thicker film. The
thickness profile, measured with a spectral camera, leads to a line tension of
the order of 0.1 nN which drives the relaxation of the thin film shape,
initially very elongated, toward a circular shape.A balance between line
tension and air friction leads to a quantitative prediction of the relaxation
process. Such a line tension is expected to play a role in the production of
marginal regeneration patches, involved in soap film drainage and stability.


  Any medium can be represented as an isometric subgraph of the hypercube, with
each token of the medium represented by a particular equivalence class of arcs
of the subgraph. Such a representation, although useful, is not especially
revealing of the structure of a particular medium. We propose an axiomatic
definition of the concept of a `mediatic graph'. We prove that the graph of any
medium is a mediatic graph. We also show that, for any non-necessarily finite
set S, there exists a bijection from the collection M of all the media on a
given set S (of states) onto the collection G of all the mediatic graphs on S.


  We propose an iterative algorithm for incomplete quantum process tomography,
with the help of quantum state estimation, based on the combined principles of
maximum-likelihood and maximum-entropy. The algorithm yields a unique estimator
for an unknown quantum process when one has less than a complete set of
linearly independent measurement data to specify the quantum process uniquely.
We apply this iterative algorithm adaptively in various situations and so
optimize the amount of resources required to estimate the quantum process with
incomplete data.


  In this note Levinson theorems for Schroedinger operators in R^n with one
point interaction at 0 are derived using the concept of winding numbers. These
results are based on new expressions for the associated wave operators.


  (Abridged) METHODS: We performed SMA observations at 1.3 mm with both the
most extended and compact array configurations, providing sub-arcsecond and
high sensitivity maps of various molecular lines, including both hot-core and
outflow tracers. We also reconstruct the spectral energy distribution of the
region from millimeter to near infrared wavelengths, using the Herschel/Hi-GAL
maps, as well as archival data. RESULTS: From the spectral energy distribution,
we derive a bolometric luminosity of about 4x10^4 Lsun. Our interferometric
observations reveal that the distribution of dense gas and dust in the HMC is
significantly flattened and extends up to a radius of 8000 AU from the center
of radio continuum and maser emission in the region. The equatorial plane of
this HMC is strictly perpendicular to the elongation of the collimated bipolar
outflow, as imaged on scales of about 0.1-0.5 pc in the main CO isotopomers as
well as in the SiO(5-4) line. In the innermost HMC regions (ca. 1000 AU), the
velocity field traced by the CH3CN(12_K-11_K) line emission shows that
molecular gas is both expanding along the outflow direction following a
Hubble-law, and rotating about the outflow axis, in agreement with the (3-D)
velocity field traced by methanol masers. The velocity field associated with
rotation indicates a dynamical mass of 19 Msun at the center of the core. The
latter is likely to be concentrated in a single O9.5 ZAMS star, consistent with
the estimated bolometric luminosity of G023.01-00.41. The physical properties
of the CO(2-1) outflow emission, such as its momentum rate 6x10^-3 Msun km/s
/yr and its outflow rate 2x10^-4 Msun/yr, support our estimates of the
luminosity (and mass) of the embedded young stellar object.


  We give a short argument that yields a new lower bound on the number of
subsampled rows from a bounded, orthonormal matrix necessary to form a matrix
with the restricted isometry property. We show that a matrix formed by
uniformly subsampling rows of an $N \times N$ Walsh matrix contains a
$K$-sparse vector in the kernel, unless the number of subsampled rows is
$\Omega(K \log K \log (N/K))$ -- our lower bound applies whenever $\min(K, N/K)
> \log^C N$. Containing a sparse vector in the kernel precludes not only the
restricted isometry property, but more generally the application of those
matrices for uniform sparse recovery.


  In this paper we fix $1\le p<\infty$ and consider $(\Om,d,\mu)$ be an
unbounded, locally compact, non-complete metric measure space equipped with a
doubling measure $\mu$ supporting a $p$-Poincar\'e inequality such that $\Om$
is a uniform domain in its completion $\bar\Om$. We realize the trace of
functions in the Dirichlet-Sobolev space $D^{1,p}(\Om)$ on the boundary
$\partial\Om$ as functions in the homogeneous Besov space
$HB^\alpha_{p,p}(\partial\Om)$ for suitable $\alpha$; here, $\partial\Om$ is
equipped with a non-atomic Borel regular measure $\nu$. We show that if $\nu$
satisfies a $\theta$-codimensional condition with respect to $\mu$ for some
$0<\theta<p$, then there is a bounded linear trace operator
$T:D^{1,p}(\Om)\rightarrow HB^{1-\theta/p}(\partial\Om)$ and a bounded linear
extension operator $E:HB^{1-\theta/p}(\partial\Om)\rightarrow D^{1,p}(\Om)$
that is a right-inverse of $T$.


  In 2023, a series of intense Thunderstorm Ground Enhancements (TGEs) were
recorded on Mount Aragats in Armenia, with five events exceeding the
fair-weather cosmic ray flux by more than 100 percent. This study
comprehensively analyzes these TGEs, investigating the atmospheric conditions
and electric fields contributing to their occurrence. Key insights include
discovering relationships between TGEs and atmospheric electric fields,
recovering electron and gamma-ray energy spectra, and the impact of nearby
lightning activity. The findings offer a deeper understanding of TGEs' role in
atmospheric physics and its synergy with high energy astrophysics.


  The constitutive relations of a dense granular flow composed of
self-propelling frictional hard particles are investigated by means of DEM
numerical simulations. We show that the rheology, which relates the dynamical
friction $\mu$ and the volume fraction $\phi$ to the inertial number $I$,
depends on a dimensionless number $\mathcal{A}$, which compares the active
force to the confining pressure. Two liquid/solid transitions -- in the Maxwell
rigidity sense -- are observed. As soon as the activity is turned on, the
packing becomes an `active solid' with a mean number of particle contacts
larger than the isostatic value. The quasi-static values of $\mu$ and $\phi$
decrease with $\mathcal{A}$. At a finite value of the activity $\mathcal{A}_t$,
corresponding to the isostatic condition, a second `active rigidity transition'
is observed beyond which the quasi-static values of the friction vanishes and
the rheology becomes Newtonian. For $\mathcal{A}>\mathcal{A}_t$, we provide
evidence for a highly intermittent dynamics of this 'active fluid'.


  The seek for a new universal formulation for describing various
non-equilibrium processes is a central task of modern non-equilibrium
thermodynamics. In this paper, a novel steady-state thermodynamic formalism was
established for general Markov processes described by the Chapman-Kolmogorov
equation. Furthermore, corresponding formalisms of steady-state thermodynamics
for master equation and Fokker-Planck equation could be rigorously derived in
mathematics. To be concrete, we proved that: 1) in the limit of continuous
time, the steady-state thermodynamic formalism for the Chapman-Kolmogorov
equation fully agrees with that for the master equation; 2) a similar
one-to-one correspondence could be established rigorously between the master
equation and Fokker-Planck equation in the limit of large system size; 3) when
a Markov process is restrained to one-step jump, the steady-state thermodynamic
formalism for the Fokker-Planck equation with discrete state variables also
goes to that for master equations, as the discretization step gets smaller and
smaller. Our analysis indicated that, with respect to the steady state, general
Markov processes admit a unified and self-consistent non-equilibrium
thermodynamic formulation, regardless of underlying detailed models.


  Context:Quality requirements (QRs) describe the desired quality of software,
and they play an important role in the success of software projects. In agile
software development (ASD), QRs are often ill-defined and not well addressed
due to the focus on quickly delivering functionality. Rapid software
development (RSD) approaches (e.g., continuous delivery and continuous
deployment), which shorten delivery times, are more prone to neglect QRs.
Despite the significance of QRs in both ASD and RSD, there is limited
synthesized knowledge on their management in those approaches. Objective:This
study aims to synthesize state-of-the-art knowledge about QR management in ASD
and RSD, focusing on three aspects: bibliometric, strategies, and challenges.
Research method:Using a systematic mapping study with a snowballing search
strategy, we identified and structured the literature on QR management in ASD
and RSD. Check the PDF file to see the full abstract and document.


  The presence of a magnetic field can have a strong impact on the evolution of
a binary star. However, only a dozen of magnetic OB binaries are known as of
today and available to study this effect, including very few magnetic pulsating
spectroscopic OB binaries. We aim at checking for the presence of a magnetic
field in the B5IV hierarchical triple system HD 1976 with spectropolarimetric
data obtained with Narval at the Bernard Lyot Telescope (TBL). We use orbital
parameters of HD 1976 available in the literature to disentangle the Narval
intensity spectra. We compute Stokes V profiles with the Least Square
Deconvolution (LSD) technique to search for magnetic signatures. We then derive
an estimate of the longitudinal magnetic field strength for each observation
and for various line lists. Our disentangling of the intensity spectra shows
that HD 1976 is a double-lined spectroscopic (SB2) binary, with the lines of
the secondary component about twice broader than the ones of the primary
component. We do not identify the third component. Moreover, we find that clear
magnetic signatures are present in the spectropolarimetric measurements of HD
1976 and seem to be associated with the primary component. We conclude that HD
1976 is a magnetic slowly-pulsating double-lined spectroscopic binary star,
with an undetected third component. It is the second such example known (with
HD 25558).


  We define the Ricci curvature, as a measure, for certain singular
torsion-free connections on the tangent bundle of a manifold. The definition
uses an integral formula and vector-valued half-densities. We give relevant
examples in which the Ricci measure can be computed. In the time dependent
setting, we give a weak notion of a Ricci flow solution on a manifold.


  These proceedings review the differential decay rates and the branching
ratios of the tau and muon decays $\tau \to \ell \ell' \ell' \nu \bar\nu$ (with
$\ell,\ell'=\mu,e$) and $\mu \to e e e \nu \bar \nu$ in the Standard Model at
NLO. These five-body leptonic decays are a tool to study the Lorentz structure
of weak interactions and to test lepton flavour universality. They are also a
source of SM background to searches for the lepton-flavour-violating decays
$\mu \to e e e$ and $\tau \to \ell \ell' \ell'$. Even if the shift in the
branching ratios induced by radiative corrections turns out to be small and of
order 1% --- mainly due to a running effect of the fine structure constant ---
locally in the phase space these corrections can reach the 5 - 10% level,
depending on the applied cuts. We found for instance that in the phase space
region where the neutrino energies are small, and the momenta of the three
charged leptons have a similar signature as in $\mu \to eee$ and $\tau \to \ell
\ell'\ell'$, the NLO corrections decrease the leading-order prediction by about
10 - 20%.


  Artificial Intelligence (AI) has huge impact on our daily lives with
applications such as voice assistants, facial recognition, chatbots,
autonomously driving cars, etc. Natural Language Processing (NLP) is a
cross-discipline of AI and Linguistics, dedicated to study the understanding of
the text. This is a very challenging area due to unstructured nature of the
language, with many ambiguous and corner cases. In this thesis we address a
very specific area of NLP that involves the understanding of entities (e.g.,
names of people, organizations, locations) in text. First, we introduce a
radically different, entity-centric view of the information in text. We argue
that instead of using individual mentions in text to understand their meaning,
we should build applications that would work in terms of entity concepts. Next,
we present a more detailed model on how the entity-centric approach can be used
for the entity linking task. In our work, we show that this task can be
improved by considering performing entity linking at the coreference cluster
level rather than each of the mentions individually. In our next work, we
further study how information from Knowledge Base entities can be integrated
into text. Finally, we analyze the evolution of the entities from the evolving
temporal perspective.


  Non-local, time-dependent convection models have been used to explain the
location of double-mode pulsations in Cepheids in the HR diagram as well as the
existence and location of the red edge of the instability strip. These
properties are highly sensitive to model parameters. We use 2D radiation
hydrodynamical simulations with realistic microphysics and grey
radiative-transfer to model a short period Cepheid. The simulations show that
the strength of the convection zone varies significantly over the pulsation
period and exhibits a phase shift relative to the variations in radius. We
evaluate the convective flux and the work integral as predicted by the most
common convection models. It turns out that over one pulsation cycle the model
parameter $\alpha_{\rm c}$, has to be varied by up to a factor of beyond 2 to
match the convective flux obtained from the simulations. To bring convective
fluxes integrated over the He II convection zone and the overshoot zone below
into agreement, this parameter has to be varied by a factor of up to $\sim 7.5$
(Kuhfu{\ss}). We then present results on the energetics of the convection and
overshoot zone by radially symmetric and fluctuating quantities. To
successfully model this scenario by a static, one dimensional or even by a
simple time-dependent model appears extremely challenging. We conclude that
significant improvements are needed to make predictions based on 1D models more
robust and to improve the reliability of conclusions on the
convection-pulsation coupling drawn from them. Multidimensional simulations can
provide guidelines for developing descriptions of convection then applied in
traditional 1D modelling.


  Using limited observations of the velocity field of the two-dimensional
Navier-Stokes equations, we successfully reconstruct the steady body force that
drives the flow. The number of observed data points is less than 10\% of the
number of modes that describes the full flow field, indicating that the method
introduced here is capable of identifying complicated forcing mechanisms from a
relatively small collection of observations. In addition to demonstrating the
efficacy of this method on turbulent flow data generated by simulations of the
two-dimensional Navier-Stokes equations, we also rigorously justify convergence
of the derived algorithm. Beyond the practical applicability of such an
algorithm, the reliance of this method on the dynamical evolution of the system
yields physical insight into the turbulent cascade.


  Significant effort has been devoted to searching for new fundamental forces
of nature. At short length scales (below approximately 10 nm), the strongest
experimental constraints come from neutron scattering from individual nuclei in
gases. The leading experiments at longer length scales instead measure forces
between macroscopic test masses. We propose a hybrid of these two approaches:
scattering neutrons off of a target that has spatial structure at nanoscopic
length scales. Such structures will give a coherent enhancement to small-angle
scattering, where the new force is most significant. This can considerably
improve the sensitivity of neutron scattering experiments for new forces in the
0.1 - 100 nm range. We discuss the backgrounds due to Standard Model
interactions and a variety of potential target structures that could be used,
estimating the resulting sensitivities. We show that, using only one day of
beam time at a modern neutron scattering facility, our proposal has the
potential to detect new forces as much as two orders of magnitude beyond
current laboratory constraints at the appropriate length scales.


  In this work we introduce two different generalizations of the Fokker-Planck
equation in (1+1) dimensions by replacing the spatial derivatives in terms of
generalized Dunkl-type derivatives involving reflection operators. As
applications of these results, we solve exactly the generalized Fokker-Planck
equations for the harmonic oscillator and the centrifugal-type potentials.


  In 1959 Ya. B. Zel'dovich predicted that the bound-state spectrum of the
non-relativistic Coulomb problem distorted at small distances by a short-range
potential undergoes a peculiar reconstruction whenever this potential alone
supports a low-energy scattering resonance. However documented experimental
evidence of this effect has been lacking. Previous theoretical studies of this
phenomenon were confined to the regime where the range of the short-ranged
potential is much smaller than Bohr's radius of the Coulomb field. We go beyond
this limitation by restricting ourselves to highly-excited s states. This
allows us to demonstrate that along the Periodic Table of elements the
Zel'dovich effect manifests itself as systematic periodic variation of the
Rydberg spectra with a period proportional to the cubic root of the atomic
number. This dependence, which is supported by analysis of experimental and
numerical data, has its origin in the binding properties of the ionic core of
the atom.


  We review briefly the sphaleron and list some of its properties. We summarize
some of the results in models which have an extended scalar sector. We also
present our work on models dealing with physics beyond the standard model. We
focus on the energy of the sphaleron which is important in determining the rate
of baryon number violation at the electroweak scale.


  After the Observing Campaign of Eta Carinae carried out during 2003, we have
continued the CCD observations using the 0.8 m Reflector telescope at La Plata
Observatory, in the BVRI bands. Here, we present the results obtained since
November 2003 until August 2004. In addition, we present differential
photometry of other objects included in the Eta Car's frames, belonging to the
open cluster Trumpler 16.


  We review the application of the critical point large N_f self-consistency
method to QCD. In particular we derive the O(1/N_f) d-dimensional critical
exponents whose epsilon-expansion determines the perturbative coefficients in
MSbar of the field dimensions, beta-function and various twist-2 operators
which occur in the operator product expansion of deep inelastic scattering.


  Observations of planetary material polluting the atmospheres of white dwarfs
are an important probe of the bulk composition of exoplanetary material.
Medium- and high-resolution optical and ultraviolet spectroscopy of seven white
dwarfs with known circumstellar dust and gas emission are presented. Detections
or meaningful upper limits for photospheric absorption lines are measured for:
C, O, Na, S, P, Mg, Al, Si, Ca, Ti, Cr, Fe, and Ni. For 16 white dwarfs with
known observable gaseous emission discs (and measured photospheric abundances),
there is no evidence that their accretion rates differ, on average, from those
without detectable gaseous emission. This suggests that, typically, accretion
is not enhanced by gas drag. At the effective temperature range of the white
dwarfs in this sample (16,000-25,000K) the abundance ratios of elements are
more consistent than absolute abundances when comparing abundances derived from
spectroscopic white dwarf parameters versus photometric white dwarf parameters.
Crucially, this highlights that the uncertainties on white dwarf parameters do
not prevent white dwarfs from being utilised to study planetary composition.
The abundances of oxygen and silicon for the three hydrogen-dominated white
dwarfs in the sample with both optical and ultraviolet spectra differ by 0.62
dex depending on if they are derived from the optical or ultraviolet spectra.
This optical/ultraviolet discrepancy may be related to differences in the
atmospheric depth of line formation; further investigations into the white
dwarf atmospheric modelling are needed to understand this discrepancy.


  Research on a large-area, cost-effective Muon Telescope Detector has been
carried out for RHIC and for next generation detectors at future QCD Lab. We
utilize state-of-the-art multi-gap resistive plate chambers with large modules
and long readout strips in detector design \cite{MTDLDRD}. The results from
cosmic ray and beam test will be presented to address intrinsic timing and
spatial resolution for a Long-MRPC. The prototype performance of a novel muon
telescope detector at STAR will be reported, including muon identification
capability, timing and spatial resolution.


  In this paper, we propose a new of coding/decoding algorithm using Padovan
Q-matrices. This method is based on blocked message matrices. an advantage of
this method is that the encryption of each message matrix will use a different
key and that will increase the security of the method.


  The origin of the Lyman-${\alpha}$ (Ly${\alpha}$) emission in galaxies is a
long-standing issue: despite several processes known to originate this line
(e.g. AGN, star formation, cold accretion, shock heating), it is difficult to
discriminate among these phenomena based on observations. Recent studies have
suggested that the comparison of the ultraviolet (UV) and optical properties of
these sources could solve the riddle. For this reason, we investigate the
rest-frame UV and optical properties of A2895b, a strongly lensed
Ly${\alpha}$-emitter at redshift z ~ 3.7. From this study, we find that our
target is a compact (r ~ 1.2 pkpc) star-forming (star formation rate ~ 11
M$_{\odot}$/yr) galaxy having a young stellar population. Interestingly, we
measure a high ratio of the H${\beta}$ and the UV continuum monochromatic
luminosities (L(H${\beta}$)/L(UV) ~ 100). Based on tracks of theoretical
stellar models (Starburst99, BPASS), we can only partially explain this result
by assuming a recent (< 10 Myr), bursty episode of star-formation and
considering models characterised by binary stars, a top-heavy initial-mass
function (IMF) and sub-solar metallicities (Z < 0.01 Z$_{\odot}$). These
assumptions also explain the observed low (C/O) abundance of our target (~
0.23(C/O)$_{\odot}$). By comparing the UV and optical datasets, we find that
the Ly${\alpha}$ and UV continuum are more extended (x2) than the Balmer lines,
and that the peak of the Ly${\alpha}$ is offset (~ 0.6 pkpc). The
multi-wavelength results of our analysis suggest that the observed Ly${\alpha}$
emission originates from a recent star-formation burst, likely taking place in
an off-centre clump.


  Pole-skipping is a recently discovered signature of many-body quantum chaos
in collective energy dynamics. It establishes a precise connection between
resummed, all-order hydrodynamics and the underlying microscopic chaos. In this
paper, we demonstrate the existence of pole-skipping in holographic conformal
field theories with higher-derivative gravity duals. In particular, we first
consider Einstein-Hilbert gravity deformed by curvature-squared ($R^2$)
corrections and then type IIB supergravity theory with the $\alpha'^3 R^4$
term, where $\alpha'$ is set by the length of the fundamental string. The
former case allows us to discuss the effects of leading-order $1/N_c$
corrections (with $N_c$ being the number of colours of the dual gauge group)
and phenomenological coupling constant dependence. In Einstein-Gauss-Bonnet
theory, pole-skipping turns out to be valid non-perturbatively in the
Gauss-Bonnet coupling. The $\alpha'^3 R^4$ deformation enables us to study
perturbative inverse 't Hooft coupling corrections ($\alpha'^3 \sim 1 /
\lambda^{3/2}$) in $SU(N_c)$, $\mathcal{N} = 4$ supersymmetric Yang-Mills
theory with infinite $N_c$. While the maximal Lyapunov exponent characterising
quantum chaos remains uncorrected, the butterfly velocity is shown to depend
both on $N_c$ and the coupling. Several implications of the relation between
hydrodynamics and chaos are discussed, including an intriguing similarity
between the dependence of the butterfly velocity and the ratio of shear
viscosity to entropy density on stringy corrections.


  We discuss possible acceleration scenarios and methods for a mu+ mu-
collider. The accelerator must take the beams from ~100 MeV to 2 TeV within the
muon lifetime (2.2 x 10**(-6) E(mu)/m(mu) uS), while compressing bunches of
10**(12) muons from m to cm bunch lengths. Linac, recirculating linac, and very
rapid-cycling synchrotron approaches are studied. Multiple recirculating linac
approaches are matched to the muon lifetime and appear readily feasible.
Rapid-cycling approaches require innovations in magnet designs and layouts, but
could be much more affordable.


  Minkowski Functionals (MF) are excellent tools to investigate the statistical
properties of the cosmic background radiation (CMB) maps. Between their
notorious advantages is the possibility to use them efficiently in patches of
the CMB sphere, which allow studies in masked skies, inclusive analyses of
small sky regions. Then, possible deviations from Gaussianity are investigated
by comparison with MF obtained from a set of Gaussian isotropic simulated CMB
maps to which are applied the same cut-sky masks. These analyses are sensitive
enough to detect contaminations of small intensity like primary and secondary
CMB anisotropies. Our methodology uses the MF, widely employed to study
non-Gaussianities in CMB data, and asserts Gaussian deviations only when all of
them points out an exceptional $\chi^2$ value, at more than $2.2 \sigma$
confidence level, in a given sky patch. Following this rigorous procedure, we
find 13 regions in the foreground-cleaned Planck maps that evince such high
levels of non-Gaussian deviations. According to our results, these non-Gaussian
contributions show signatures that can be associated to the presence of hot or
cold spots in such regions. Moreover, some of these non-Gaussian deviations
signals suggest the presence of foreground residuals in those regions located
near the galactic plane. Additionally, we confirm that most of the regions
revealed in our analyses, but not all, have been recently reported in studies
done by the Planck collaboration. Furthermore, we also investigate whether
these non-Gaussian deviations can be possibly sourced by systematics, like
inhomogeneous noise and beam effect in the released Planck data, or perhaps due
to residual galactic foregrounds.


  A theoretical investigation of the possible existence of the chiral polaron
formation in graphene is reported. We present an analytical method to calculate
the ground-state of the electron-phonon system within the framework of the
Lee-Low and Pines theory. On the basis of our model, the influence of
electron-optical phonon interaction onto the graphene electronic spectrum is
examined. In this paper, we only considered doubly degenerate optical phonon
modes of E_2g symmetry near the zone center Gamma. We show analytically that
the energy dispersions of both valance and conduction bands of the pristine
graphene differ significantly than those obtained through the standard electron
self energy calculations due to the electron-phonon interactions. Furthermore,
we prove that the degenerate band structure of the graphene promote the chiral
polaron formation.


  We introduce two numerical invariants, the waist and the trunk of knots. The
waist of a closed incompressible surface in the complement of a knot is defined
as the minimal intersection number of all compressing disks for the surface in
the 3-sphere and the knot. Then the waist of a knot is defined as the maximal
waist of all closed incompressible surfaces in the complement of the knot. On
the other hand, the trunk of a knot is defined as the minimal number of the
intersection of the most thick level 2-sphere and the knot over all Morse
positions of the knot. In this paper, we obtain an inequality between the waist
and the trunk of knots and show that the inequality is best possible. We also
define the supertrunk of a knot and relate it to the hull number and the
3-width.


  Context: The expansion of network magnetic fields with height is a
fundamental property of flux tube models. A rapid expansion is required to form
a magnetic canopy. Aims: We characterize the observed expansion properties of
magnetic network elements and compare them with the thin flux tube and sheet
approximations, as well as with magnetoconvection simulations. Methods: We used
data from the Hinode SOT NFI NaD1 channel and spectropolarimeter to study the
appearance of magnetic flux concentrations seen in circular polarization as a
function of position on the solar disk. We compared the observations with
synthetic observables from models based on the thin flux tube approximation and
magnetoconvection simulations with two different upper boundary conditions for
the magnetic field (potential and vertical). Results: The observed circular
polarization signal of magnetic flux concentrations changes from unipolar at
disk center to bipolar near the limb, which implies an expanding magnetic
field. The observed expansion agrees with expansion properties derived from the
thin flux sheet and tube approximations. Magnetoconvection simulations with a
potential field as the upper boundary condition for the magnetic field also
produce bipolar features near the limb while a simulation with a vertical field
boundary condition does not. Conclusions: The near-limb apparent bipolar
magnetic features seen in high-resolution Hinode observations can be
interpreted using a simple flux sheet or tube model. This lends further support
to the idea that magnetic features with vastly varying sizes have similar
relative expansion rates. The numerical simulations presented here are less
useful in interpreting the expansion since the diagnostics we are interested in
are strongly influenced by the choice of the upper boundary condition for the
magnetic field in the purely photospheric simulations.


  We propose M\"obius transformations as the natural rotation and scaling tools
for editing spherical images. As an application we produce spherical Droste
images. We obtain other self-similar visual effects using rational functions,
elliptic functions, and Schwarz-Christoffel maps.


  This paper aims to provide an optimization framework for coded caching that
accounts for various heterogeneous aspects of practical systems. An
optimization theoretic perspective on the seminal work on the fundamental
limits of caching by Maddah Ali and Niesen is first developed, whereas it is
proved that the coded caching scheme presented in that work is the optimal
scheme among a large, non-trivial family of possible caching schemes. The
optimization framework is then used to develop a coded caching scheme capable
of handling simultaneous non-uniform file length, non-uniform file popularity,
and non-uniform user cache size. Although the resulting full optimization
problem scales exponentially with the problem size, this paper shows that
tractable simplifications of the problem that scale as a polynomial function of
the problem size can still perform well compared to the original problem. By
considering these heterogeneities both individually and in conjunction with one
another, insights into their interactions and influence on optimal cache
content are obtained.


  Results of the investigations of the yield of high-spin and low-spin isomers
in reactions $^{41}$K($\alpha $,n)$^{44}$Sc, $^{86}$Sr ($\alpha $,n)$^{89}$Zr,
$^{112}$Sn($\alpha$,n)$^{115}$Te, and $^{134}$Ba($\alpha$,n)$^{137}$Ce in the
energy range of the alpha particles 15 $\div$ 31 MeV based on off-beam
measurements of induced activity of members of the isomeric pair are presented.
The anomalous behavior of the isomeric cross-section ratios for the first of
these reactions is confirmed. Uniquely large isomeric cross-section ratios for
the second and third ones are obtained. The features of the fourth reaction,
which are promising for its application in fundamental research, are revealed.
Quality of the description of this dynamics by popular computer codes is
analyzed.


  We define in an axiomatic fashion a \emph{Coxeter datum} for an arbitrary
Coxeter group $W$. This Coxeter datum will specify a pair of reflection
representations of $W$ in two vector spaces linked only by a bilinear paring
without any integrality and non-degeneracy requirements. These representations
are not required to be embeddings of $W$ in the orthogonal group of any vector
space, and they give rise to a pair of inter-related root systems generalizing
the classical root systems of Coxeter groups. We obtain comparison results
between these non-orthogonal root systems and the classical root systems.
Further, we study the equivalent of the Tits cone in these non-orthogonal
representations, and we show that strong results on the geometry in the
equivalent of the Tits cone can be obtained.


  We will describe algebro-geometric solutions of the KdV hierarchy whose
$\tau$-functions in addition satisfy a generalization of the Virasoro
constraints (and, in particular, a generalization of the string equation). We
show that these solutions are closely related to embeddings of the positive
half of the Virasoro algebra into the Lie algebra of differential operators on
the circle. Our results are tested against the case of Witten-Kontsevich
$\tau$-function. As by-products, we exhibit certain links of our methods with
double covers of the projective line equipped with a line bundle and with ${\rm
Gl}(n)$-opers on the punctured disk.


  Recent studies of quantum circuit models have theoretically shown that
frequent measurements induce a transition in a quantum many-body system, which
is characterized by the change of the scaling law of the entanglement entropy
from a volume law to an area law. In order to propose a way for experimentally
observing this measurement-induced transition, we present numerical analyses
using matrix-product states on quench dynamics of a dissipative Bose-Hubbard
model with controllable two-body losses, which has been realized in recent
experiments with ultracold atoms. We find that when the strength of dissipation
increases, there occurs a measurement-induced transition from volume-law
scaling to area-law scaling with a logarithmic correction in a region of
relatively small dissipation. We also find that the strong dissipation leads to
a revival of the volume-law scaling due to a continuous quantum Zeno effect. We
show that dynamics starting with the area-law states exhibits the breaking of
ergodicity, which can be used in experiments for distinguishing them from the
volume-law states.


  In this paper, using techniques of value distribution theory, we give a
uniqueness theorem for meromorphic mappings of C^m into P^n with truncated
multiplicities and "few" targets. We also give a theorem of linear degeneration
for such maps with truncated multiplicities and moving targets.


  The existing experimental data on the d(n,p)nn and d(p,n)pp cross sections in
the forward direction are reviewed in terms of the Dean sum rule. It is shown
that the measurement of the ratio of the charge exchange on the deuteron to
that on the proton might, if taken together with other experimental data, allow
a direct construction of the np -> np scattering amplitude in the backward
direction with few ambiguities.


  For $n \geq 1$, the twistor space $\mathfrak{Z}(\mathbb{S}^{2n})$ of the
conformal $2n$-sphere is biholomorphic to the Zariski closure, taken in the
complex Grassmannian manifold $\mathbf{G}(n+1, 2n+2)$, of the set of graphs of
skew-symmetric linear endomorphism of $\mathbb{C}^{n+1}$. We use this fact to
describe a natural stratification of the twistor space
$\mathfrak{Z}(\mathbb{S}^{2n})$ with $n \geq 3$, in terms of what we have
called {\it generalised complex orthogonal Stiefel manifolds} of
$\mathbb{C}^{n+1}$. In particular, the twistor space
$\mathfrak{Z}(\mathbb{S}^{6})$ is biholomorphic to a non-singular complex
quadric hypersurface in $\mathbb{P}^{7}$. We explicitly construct a
real-analytic foliation, by linear 3-folds, of this quadric hypersurface such
that the quotient space is isomorphic to the 6-sphere with its standard metric.
This foliation is Riemannian with respect to the Fubini-Study metric and
isometrically equivalent to the twistor fibration over the 6-sphere.


  A Cech closure space $(X,u)$ is a set $X$ with a (Cech) closure operator $u$
which need not be idempotent. Many properties which hold in topological spaces
hold in Cech closure spaces as well. The notions of proper (splitting) and
admissible (jointly continuous) topologies are introduced on the sets of
continuous functions between Cech closure spaces. It is shown that some
well-known results of Arens and Dugundji and of Iliadis and Papadopoulos are
true in this setting. We emphasize that Theorems 1--10 encompass the results of
A. di Concilio and of Georgiou and Papadopoulos for the spaces of
continuous-like functions as $\theta$-continuous, strongly and weakly
$\theta$-continuous, weakly and super-continuous.


  We investigate inertial frames in the absence of Lorentz invariance,
reconsidering the usual group structure implied by the relativity principle. We
abandon the relativity principle, discarding the group structure for the
transformations between inertial frames, while requiring these transformations
to be at least linear (to preserve homogeneity). In theories with a preferred
frame (aether), the set of transformations between inertial frames forms a
groupoid/pseudogroup instead of a group, a characteristic essential to evading
the von Ignatowsky theorems. In order to understand the dynamics, we also
demonstrate that the transformation rules for energy and momentum are in
general affine. We finally focus on one specific and compelling model
implementing a minimalist violation of Lorentz invariance.


  We construct Type IIB supergravity solutions with geometry $AdS_6\times S^2$
warped over a disc with two boundary points where 5-branes emerge and punctures
with 7-brane monodromy. They describe $(p,q)$ 5-brane junctions with two groups
of like-charged external 5-branes that are unconstrained by the $s$-rule and an
additional group of constrained 5-branes. The dual 5d SCFTs include various
theories discussed previously in the literature. We match SCFT operators with
scaling dimension of $\mathcal O(N)$ with their representation in supergravity
to support the proposed dualities.


  This article deals with an initial-boundary value problem for the coupled
chemotaxis-haptotaxis system with nonlinear diffusion \begin{align*}
  u_t=&\nabla\cdot(D(u)\nabla u)-\chi\nabla\cdot(u\nabla
v)-\xi\nabla\cdot(u\nabla w)+\mu u(1-u-w),\\ v_t=&\Delta v-v+u,\\
w_t=&-vw\end{align*} under homogeneous Neumann boundary conditions in a bounded
smooth domain $\Omega\subset\mathbb{R}^n$, $n=2, 3, 4$, where $\chi, \xi$ and
$\mu$ are given nonnegative parameters. The diffusivity $D(u)$ is assumed to
satisfy $D(u)\geq\delta u^{m-1}$ for all $u>0$ with some $\delta>0$. It is
proved that for sufficiently regular initial data global bounded solutions
exist whenever $m>2-\frac{2}{n}$. For the case of non-degenerate diffusion
(i.e. $D(0)>0$) the solutions are classical; for the case of possibly
degenerate diffusion ($D(0)\geq 0$), the existence of bounded weak solutions is
shown.


  Preliminary results on $\rho(770)^0 \to \pi^{+}\pi^{-}$, K$^{*}(892)^{0} \to
\pi$K and $f_{0}(980) \to \pi^{+}\pi^{-}$ production using the mixed-event
technique are presented. The measurements are performed at mid-rapidity by the
STAR detector in $\sqrt{s_{NN}}$= 200 GeV Au-Au and pp interactions at RHIC.
The results are compared to different measurements at various energies.


  The isotropic Dunkl oscillator model in the plane is investigated. The model
is defined by a Hamiltonian constructed from the combination of two independent
parabosonic oscillators. The system is superintegrable and its symmetry
generators are obtained by the Schwinger construction using parabosonic
creation/annihilation operators. The algebra generated by the constants of
motion, which we term the Schwinger-Dunkl algebra, is an extension of the Lie
algebra u(2) with involutions. The system admits separation of variables in
both Cartesian and polar coordinates. The separated wavefunctions are
respectively expressed in terms of generalized Hermite polynomials and products
of Jacobi and Laguerre polynomials. Moreover, the so-called Jacobi-Dunkl
polynomials appear as eigenfunctions of the symmetry operator responsible for
the separation of variables in polar coordinates. The expansion coefficients
between the Cartesian and polar bases (overlap coefficients) are given as
linear combinations of dual -1 Hahn polynomials. The connection with the
Clebsch-Gordan problem of the sl_{-1}(2) algebra is explained.


  Bistable nanomagnets store a binary bit of information. Exchange coupled
nanomagnets can increase the thermal stability at low dimensions. Here we show
that the antiferromagnetically (AFM) coupled nanomagnets can be highly stable
at low dimensions than that of the ferromagnetically (FM) coupled nanomagnets.
By solving stochastic Landau-Lifshitz-Gilbert equation of magnetization
dynamics at room temperature, we analyze the stability of the exchange coupled
nanomagnets in the presence of correlated, uncorrelated, and anti-correlated
noise. The results show that the correlated noise can make the stability of the
AFM coupled nanomagnets very high. Such finding will lead to very high-density
non-volatile storage and logic devices in our future information processing
systems.


  Decays of Higgs boson-like particles into multileptons is a well-motivated
process for investigating physics beyond the Standard Model (SM). A unique
feature of this final state is the precision with which the SM is known. As a
result, simulations are used directly to estimate the background. Current
searches consider specific models and typically focus on those with a single
free parameter to simplify the analysis and interpretation. In this paper, we
explore recent proposals for signal model agnostic searches using machine
learning in the multilepton final state. These tools can be used to
simultaneously search for many models, some of which have no dedicated search
at the Large Hadron Collider. We find that the machine learning methods offer
broad coverage across parameter space beyond where current searches are
sensitive, with a necessary loss of performance compared to dedicated searches
by only about one order of magnitude.


  Using the new equipment of the Shanghai Tian Ma Radio Telescope, we have
searched for carbon-chain molecules (CCMs) towards five outflow sources and six
Lupus I starless dust cores, including one region known to be characterized by
warm carbon-chain chemistry (WCCC), Lupus I-1 (IRAS 15398-3359), and one TMC-1
like cloud, Lupus I-6 (Lupus-1A). Lines of HC3N J=2-1, HC5N J=6-5, HC7N
J=14-13, 15-14, 16-15 and C3S J=3-2 were detected in all the targets except in
the outflow source L1660 and the starless dust core Lupus I-3/4. The column
densities of nitrogen-bearing species range from 10$^{12}$ to 10$^{14}$
cm$^{-2}$ and those of C$_3$S are about 10$^{12}$ cm$^{-2}$. Two outflow
sources, I20582+7724 and L1221, could be identified as new
carbon-chain--producing regions. Four of the Lupus I dust cores are newly
identified as early quiescent and dark carbon-chain--producing regions similar
to Lup I-6, which together with the WCCC source, Lup I-1, indicate that
carbon-chain-producing regions are popular in Lupus I which can be regard as a
Taurus like molecular cloud complex in our Galaxy. The column densities of C3S
are larger than those of HC7N in the three outflow sources I20582, L1221 and
L1251A. Shocked carbon-chain chemistry (SCCC) is proposed to explain the
abnormal high abundances of C3S compared with those of nitrogen-bearing CCMs.
Gas-grain chemical models support the idea that shocks can fuel the environment
of those sources with enough $S^+$ thus driving the generation of S-bearing
CCMs.


  After a brief introduction to the Painlev\'{e} property for ordinary
differential equations, we present a concise review of the various methods of
singularity analysis which are commonly referred to as Painlev\'{e} tests. The
tests are applied to several different examples, and we discuss the connection
between singularity structure and integrability for ordinary and partial
differential equations.


  Multiple raters are often needed to be used interchangeably in practice for
measurement or evaluation. Assessing agreement among these multiple raters via
agreement indices are necessary before their participation. While the
intuitively appealing agreement indices such as coverage probability and total
deviation index, and relative area under coverage probability curve, have been
extended for assessing overall agreement among multiple raters, these
extensions have limitations. The existing overall agreement indices either
require normality and homogeneity assumptions or did not preserve the intuitive
interpretation of the indices originally defined for two raters. In this paper,
we propose a new set of overall agreement indices based on maximum pairwise
differences among all raters. The proposed new overall coverage probability,
overall total deviation index and relative area under overall coverage
probability curve retain the original intuitive interpretation from the
pairwise version. Without making any distributional assumption, we also propose
a new unified nonparametric estimation and inference approach for the overall
indices based on generalized estimating equations that can accommodate
replications made by the same rater. Under mild assumptions, the proposed
variance estimator is shown to achieve efficiency bound under independent
working correlation matrix. Simulation studies under different scenarios are
conducted to assess the performance of the proposed estimation and inference
approach with and without replications. We illustrate the methodology by using
a blood pressure data with three raters who made three replications on each
subjects.


  Learning linear combinations of multiple kernels is an appealing strategy
when the right choice of features is unknown. Previous approaches to multiple
kernel learning (MKL) promote sparse kernel combinations to support
interpretability and scalability. Unfortunately, this 1-norm MKL is rarely
observed to outperform trivial baselines in practical applications. To allow
for robust kernel mixtures, we generalize MKL to arbitrary norms. We devise new
insights on the connection between several existing MKL formulations and
develop two efficient interleaved optimization strategies for arbitrary norms,
like p-norms with p>1. Empirically, we demonstrate that the interleaved
optimization strategies are much faster compared to the commonly used wrapper
approaches. A theoretical analysis and an experiment on controlled artificial
data experiment sheds light on the appropriateness of sparse, non-sparse and
$\ell_\infty$-norm MKL in various scenarios. Empirical applications of p-norm
MKL to three real-world problems from computational biology show that
non-sparse MKL achieves accuracies that go beyond the state-of-the-art.


  The coupling between Zeeman spin splitting and Rashba spin-orbit terms has
been studied experimentally in a gated InGaAs/InP quantum well structure by
means of simultaneous measurements of the weak antilocalization (WAL) effect
and beating in the SdH oscillations. The strength of the Zeeman splitting was
regulated by tilting the magnetic field with the spin-zeros in the SdH
oscillations, which are not always present, being enhanced by the tilt. In
tilted fields the spin-orbit and Zeeman splittings are not additive, and a
simple expression is given for the energy levels. The Rashba parameter and the
electron g-factor were extracted from the position of the spin zeros in tilted
fields. A good agreement is obtained for the spin-orbit coupling strength from
the spin-zeros and weak antilocalization measurements.


  Floquet higher order topological insulators (FHOTIs) are a novel topological
phase that can occur in periodically driven lattices. An appropriate
experimental platform to realize FHOTIs has not yet been identified. We
introduce a periodically-driven bipartite (two-band) system that hosts FHOTI
phases, and predict that this lattice can be realized in
experimentally-realistic optical waveguide arrays, similar to those previously
used to study anomalous Floquet insulators. The model exhibits interesting
phase transitions from first-order to second-order topological matter by tuning
a coupling strength parameter, without breaking lattice symmetry. In the FHOTI
phase, the lattice hosts corner modes at eigenphase $0$ or $\pi$, which are
robust against disorder in the individual couplings.


  The Milky Way nuclear star cluster (NSC) is located within the nuclear
stellar disc (NSD) in the Galactic centre. It is not fully understood if the
formation and evolution of these two components are connected, and how they
influence each other. We study the stellar populations in the transition region
of NSC and NSD. We observed two $\sim$4.3 pc$^2$ fields with the integral-field
spectrograph KMOS (VLT), located at r$\sim$20 pc (> 4 R$_e$) to the Galactic
East and West of the NSC. We extract and analyse medium-resolution stellar
spectra of >200 stars per field. The data contain in total nine young star
candidates. We use stellar photometry to estimate the stellar masses, effective
temperatures, and spectral types of the young stars. The stars are consistent
with an age of 4-6 Myr, they may have formed inside the Quintuplet cluster, but
were dispersed in dynamical interactions. Most stars in the two fields are red
giant stars, and we measure their stellar metallicities [M/H] using full
spectral fitting. We compare our [M/H] distributions to the NSC and NSD, using
data from the literature, and find that the overall metallicity decreases from
the central NSC, over the transition region, to the NSD. The steep decrease of
[M/H] from the NSC to the region dominated by the NSD indicates that the two
components have distinct stellar populations and formation histories.


  We discuss the relation between the solutions of the Skyrme model of lower
degrees and the corresponding axially symmetric Hopfions which is given by the
projection onto the coset space SU(2)/U(1). The interaction energy of the
Hopfions is evaluated directly from the product ansatz. Our results show that
if the separation between the constituents is not very small, the product
ansatz can be considered as a relatively good approximation to the general
pattern of the charge one Hopfions interaction both in repulsive and attractive
channel.


  We consider random walks in dynamic random environments, with an environment
generated by the time-reversal of a Markov process from the oriented
percolation universality class. If the influence of the random medium on the
walk is small in space-time regions where the medium is typical, we obtain a
law of large numbers and an averaged central limit theorem for the walk via a
regeneration construction under suitable coarse-graining.
  Such random walks occur naturally as spatial embeddings of ancestral lineages
in spatial population models with local regulation. We verify that our
assumptions hold for logistic branching random walks when the population
density is sufficiently high.


  In this paper we adapt the broken replica interpolation technique (developed
by Francesco Guerra to deal with the Sherrington-Kirkpatrick model, namely a
pairwise mean-field spin-glass whose couplings are i.i.d. standard Gaussian
variables) in order to work also with the Hopfield model (i.e., a pairwise
mean-field neural-network whose couplings are drawn according to Hebb's
learning rule): this is accomplished by grafting Guerra's telescopic averages
on the transport equation technique, recently developed by some of the Authors.
As an overture, we apply the technique to solve the Sherrington-Kirkpatrick
model with i.i.d. Gaussian couplings centered at $J_0$ and with finite variance
$J$; the mean $J_0$ plays the role of a signal to be detected in a noisy
environment tuned by $J$, hence making this model a natural test-case to be
investigated before addressing the Hopfield model. For both the models, an
explicit expression of their quenched free energy in terms of their natural
order parameters is obtained at the K-th step (K arbitrary, but finite) of
replica-symmetry-breaking. In particular, for the Hopfield model, by assuming
that the overlaps respect Parisi's decomposition (following the ziqqurat
ansatz) and that the Mattis magnetization is self-averaging, we recover
previous results obtained via replica-trick by Amit, Crisanti and Gutfreund
(1RSB) and by Steffan and K\"{u}hn (2RSB).


  Optical pump-terahertz probe differential transmission measurements of
as-prepared single layer graphene (AG)(unintentionally hole doped with Fermi
energy $E_F$ at $\sim$180 meV), nitrogen doping compensated graphene (NDG) with
$E_F$ $\sim$10 meV and thermally annealed doped graphene (TAG) are examined
quantitatively to understand the opposite signs of photo-induced dynamic
terahertz conductivity $\Delta\sigma$. It is negative for AG and TAG but
positive for NDG. We show that the recently proposed mechanism of multiple
generations of secondary hot carriers due to Coulomb interaction of
photoexcited carriers with the existing carriers together with the intraband
scattering can explain the change of photoinduced conductivity sign and its
magnitude. We give a quantitative estimate of $\Delta\sigma$ in terms of
controlling parameters - the Fermi energy $E_F$ and momentum relaxation time
$\tau$. Further, the cooling of photoexcited carriers is analyzed using
super-collision model which involves defect mediated collision of the hot
carriers with the acoustic phonons, thus giving an estimate of the deformation
potential.


  A two-dimensional electrodynamic model is used to study particle acceleration
and non-thermal emission mechanisms in the pulsar magnetospheres.
  We solve distribution of the accelerating electric field with the emission
process and the pair-creation process in meridional plane, which includes the
rotational axis and the magnetic axis. By solving the evolutions of the Lorentz
factor, and of the pitch angle, we calculate spectrum in optical through
$\gamma$-ray bands with the curvature radiation, synchrotron radiation, and
inverse-Compton process not only for outgoing particles, but also for ingoing
particles, which were ignored in previous studies. We apply the theory to the
Vela pulsar. We find that the curvature radiation from the outgoing particles
is the major emission process above 10 MeV bands. In soft $\gamma$-ray to hard
X-ray bands, the synchrotron radiation from the ingoing primary particles in
the gap dominates in the spectrum. Below hard X-ray bands, the synchrotron
emissions from both outgoing and ingoing particles contribute to the calculated
spectrum. The calculated spectrum is consistent with the observed
phase-averaged spectrum of the Vela pulsar. We show that the observed five-peak
pulse profile in the X-ray bands of the Vela pulsar is reproduced by the inward
and outward emissions, and the observed double-peak pulse profile in
$\gamma$-ray bands is explained by the outward emissions.


  Quantum correlations may be measured by means of the distance of the state to
the subclass of states $\Omega$ having well defined classical properties. In
particular, a geometric measure of asymmetric discord [Dakic et al., Phys. Rev.
Lett. 105, 190502 (2010)] was recently defined as the Hilbert-Schmidt distance
of a given two-qubit state to the closest classical-quantum (CQ) correlated
state. We analyze a geometric measure of symmetric discord defined as the
Hilbert-Schmidt distance of a given state to the closest classical-classical
(CC) correlated state. The optimal member of $\Omega$ is just specially
measured original state both for the CQ and CC discords. This implies that this
measure is equal to quantum deficit of post-measurement purity. We discuss some
general relations between the CC discords and explain why an analytical formula
for the CC discord, contrary to the CQ discord, can hardly be found even for a
general two-qubit state. Instead of such exact formula, we find simple
analytical measurement-based upper bounds for the CC discord which, as we show,
are very efficient in the case of two qubits and may serve as independent
indicators of two-party quantum correlations. In particular, we propose an
adaptive upper bound, which corresponds to the optimal states induced by
single-party measurements: optimal measurement on one of the parties determines
an optimal measurement on the other party. We discuss how to refine the
adaptive upper bound by nonoptimal single-party measurements and by an
iterative procedure which usually rapidly converges to the CC discord. We also
raise the question of optimality of the symmetric measurements realising the CC
discord on symmetric states, and give partial answer for the qubit case.


  The U.S. Census Bureau collects and publishes detailed demographic data about
Americans which are heavily used by researchers and policymakers. The Bureau
has recently adopted the framework of differential privacy in an effort to
improve confidentiality of individual census responses. A key output of this
privacy protection system is the Noisy Measurement File (NMF), which is
produced by adding random noise to tabulated statistics. The NMF is critical to
understanding any errors introduced in the data, and performing valid
statistical inference on published census data. Unfortunately, the current
release format of the NMF is difficult to access and work with. We describe the
process we use to transform the NMF into a usable format, and provide
recommendations to the Bureau for how to release future versions of the NMF.
These changes are essential for ensuring transparency of privacy measures and
reproducibility of scientific research built on census data.


  Anomaly detection requires detecting abnormal samples in large unlabeled
datasets. While progress in deep learning and the advent of foundation models
has produced powerful zero-shot anomaly detection methods, their deployment in
practice is often hindered by the lack of labeled data -- without it, their
detection performance cannot be evaluated reliably. In this work, we propose
SWSA (Selection With Synthetic Anomalies): a general-purpose framework to
select image-based anomaly detectors with a generated synthetic validation set.
Our proposed anomaly generation method assumes access to only a small support
set of normal images and requires no training or fine-tuning. Once generated,
our synthetic validation set is used to create detection tasks that compose a
validation framework for model selection. In an empirical study, we find that
SWSA often selects models that match selections made with a ground-truth
validation set, resulting in higher AUROCs than baseline methods. We also find
that SWSA selects prompts for CLIP-based anomaly detection that outperform
baseline prompt selection strategies on all datasets, including the challenging
MVTec-AD and VisA datasets.


  Whilst recent face-recognition (FR) techniques have made significant progress
on recognising constrained high-resolution web images, the same cannot be said
on natively unconstrained low-resolution images at large scales. In this work,
we examine systematically this under-studied FR problem, and introduce a novel
Complement Super-Resolution and Identity (CSRI) joint deep learning method with
a unified end-to-end network architecture. We further construct a new
large-scale dataset TinyFace of native unconstrained low-resolution face images
from selected public datasets, because none benchmark of this nature exists in
the literature. With extensive experiments we show there is a significant gap
between the reported FR performances on popular benchmarks and the results on
TinyFace, and the advantages of the proposed CSRI over a variety of
state-of-the-art FR and super-resolution deep models on solving this largely
ignored FR scenario. The TinyFace dataset is released publicly at:
https://qmul-tinyface.github.io/.


  We analytically determine the quasinormal mode (QNM) frequencies of a black
hole with quadrupole moment in the eikonal limit using the light-ring method.
The generalized black holes that are discussed in this work possess arbitrary
quadrupole and higher mass moments in addition to mass and angular momentum.
Static collapsed configurations with mass and quadrupole moment are treated in
detail and the QNM frequencies associated with two such configurations are
evaluated to linear order in the quadrupole moment. Furthermore, we touch upon
the treatment of rotating systems. In particular, the generalized black hole
that we consider for our extensive QNM calculations is a completely collapsed
configuration whose exterior gravitational field can be described by the
Hartle-Thorne spacetime [Astrophys. J. 153, 807-834 (1968)]. This collapsed
system as well as its QNMs is characterized by mass $M$, quadrupole moment $Q$
and angular momentum $J$, where the latter two parameters are treated to first
and second orders of approximation, respectively. When the quadrupole moment is
set equal to the relativistic quadrupole moment of the corresponding Kerr black
hole, $J^2/(Mc^2)$, the Hartle-Thorne QNMs reduce to those of the Kerr black
hole to second order in angular momentum $J$. Using ringdown frequencies, one
cannot observationally distinguish a generalized Hartle-Thorne black hole with
arbitrary quadrupole moment from a Kerr black hole provided the dimensionless
parameter given by $|QMc^2-J^2|c^2/(G^2M^4)$ is sufficiently small compared to
unity.


  A programmable quantum processor is a fundamental model of quantum
computation. In this model, any quantum channel can be approximated by applying
a fixed universal quantum operation onto an input state and a quantum `program'
state, whose role is to condition the operation performed by the processor. It
is known that perfect channel simulation is only possible in the limit of
infinitely large program states, so that finding the best program state
represents an open problem in the presence of realistic finite-dimensional
resources. Here we prove that the search for the optimal quantum program is a
convex optimization problem. This can be solved either exactly, by minimizing a
diamond distance cost function via semi-definite programming, or approximately,
by minimizing other cost functions via gradient-based machine learning methods.
We apply this general result to a number of different designs for the
programmable quantum processor, from the shallow protocol of quantum
teleportation, to deeper schemes relying on port-based teleportation and
parametric quantum circuits. We benchmark the various designs by investigating
their optimal performance in simulating arbitrary unitaries, Pauli and
amplitude damping channels.


  Let $M \in M_n (\mathbb Z)$ denote any matrix. Thinking of $M$ as a linear
map $M:{\mathbb Z}^n \to {\mathbb Z}^n$, we denote by ${\Image}(M)$ the
$\mathbb Z$-span of the column vectors of $M$. Let $e_1, ..., e_n,$ denote the
standard basis of ${\mathbb Z}^n$, and let $E_{ij}: = e_i - e_j$, $ (i \neq
j)$. In this article, we are interested in the group ${\mathbb Z}^n
/{\Image}(M)$, and in particular in the elements of this group defined by the
images $\tau_{ij}$ of the vectors $E_{ij}$ under the quotient ${\mathbb Z}^n
\to {\mathbb Z}^n / {\Image} (M)$. Most of this article is devoted to the study
of the case where $M$ is the laplacian of a graph. In this case, the elements
$\tau_{ij}$ have finite order, and we study how the geometry of the graph
relates to these orders. Applications to the theory of semistable reduction of
curves will appear in a forthcoming article.


  A macroscopic model of the tumor Gompertzian growth is proposed. The new
approach is based on the energetic balance among the different cell activities,
described by methods of statistical mechanics and related to the growth
inhibitor factors. The model is successfully applied to the multicellular tumor
spheroid data.


  Magnetic resonance studies of nuclear spins in solids are exceptionally well
suited to probe the limits of statistical physics. We report experimental
results indicating that isolated macroscopic systems of interacting nuclear
spins possess the following fundamental property: spin decays that start from
different initial configurations quickly evolve towards the same long-time
behavior. This long-time behavior is characterized by the shortest ballistic
microscopic timescale of the system and therefore falls outside of the validity
range for conventional approximations of statistical physics. We find that the
nuclear free induction decay and different solid echoes in hyperpolarized solid
xenon all exhibit sinusoidally modulated exponential long-time behavior
characterized by identical time constants. This universality was previously
predicted on the basis of analogy with resonances in classical chaotic systems.


  Generally, identifying the spiral arms of a spiral galaxy is not a hard task.
However, defining the main characteristics, width and length of those structure
is not a common task. Previous studies have used different tracers: Star
clusters, Massers, H$\alpha$. It was until recently that individual stars were
used as tracers of spiral structures. The basic method of measuring the width
of spiral arms assumes a Gaussian distribution around the mean concentration,
either of gas or other tracer. In this work we use NGC 5236's stars as tracers.
We estimated the surface stellar density of arms and inter-arm regions to
measure the width of the arms. As a test case, this works focused on NGC 5236
(M83). We find that field stellar populations can trace the (two) main spiral
arms of NGC 5236. We find a correlation between the arm width and the
galactocentric radii, found using other tracers. The slope of the growth of the
width of the arm correlates with the morphological types of spiral galaxies. A
second finding of our study suggest the possible correlation between the width
of the arms and the corrotation radius, result that will be presented in a
follow up paper.


  We show that $\N=1$ gauge theories with an adjoint chiral multiplet admit a
wide class of large-N double-scaling limits where $N$ is taken to infinity in a
way coordinated with a tuning of the bare superpotential. The tuning is such
that the theory is near an Argyres-Douglas-type singularity where a set of
non-local dibaryons becomes massless in conjunction with a set of confining
strings becoming tensionless. The doubly-scaled theory consists of two
decoupled sectors, one whose spectrum and interactions follow the usual large-N
scaling whilst the other has light states of fixed mass in the large-N limit
which subvert the usual large-N scaling and lead to an interacting theory in
the limit. $F$-term properties of this interacting sector can be calculated
using a Dijkgraaf-Vafa matrix model and in this context the double-scaling
limit is precisely the kind investigated in the "old matrix model'' to describe
two-dimensional gravity coupled to $c<1$ conformal field theories. In
particular, the old matrix model double-scaling limit describes a sector of a
gauge theory with a mass gap and light meson-like composite states, the
approximate Goldstone boson of superconformal invariance, with a mass which is
fixed in the double-scaling limit. Consequently, the gravitational $F$-terms in
these cases satisfy the string equation of the KdV hierarchy.


  We revisit the apparent correlation between soft X-ray band photon index and
spin-down rate nudot previously reported for Anomalous X-ray Pulsars (AXPs) and
Soft Gamma Repeaters (SGRs) by Marsden & White (2001). Our analysis, improved
thanks to new source discoveries, better spectral parameter measurements in
previously known sources, and the requirement of source quiescence for
parameter inclusion, shows evidence for the previously noted trend, although
with greater scatter. This trend supports the twisted magnetosphere model of
magnetars although the scatter suggests that factors other than nudot are also
important. We also note possible correlations involving the spectra of AXPs and
SGRs in the hard X-ray band. Specifically, the hard-band photon index shows a
possible correlation with inferred nudot and B, as does the degree of spectral
turnover. If the former trend is correct, then the hard-band photon index for
AXP 1E 1048.1-5937 should be ~0--1. This may be testable with long integrations
by INTEGRAL, or by the upcoming focussing hard X-ray mission NuSTAR.


  We theoretically study the formation of Brillouin precursors in Debye media.
We point out that the precursors are visible only at propagation distances such
that the impulse response of the medium is essentially determined by the
frequency dependence of its absorption and is practically Gaussian. By simple
convolution, we then obtain explicit analytical expressions of the transmitted
waves generated by reference incident waves, distinguishing precursor and main
signal by a simple examination of the long-time behavior of the overall signal.
These expressions are in good agreement with the signals obtained in numerical
or real experiments performed on water in the radio-frequency domain and
explain in particular some observed shapes of the precursor. Results are
obtained for other remarkable incident waves. In addition, we show quite
generally that the shape of the Brillouin precursor appearing alone at
sufficiently large propagation distance and the law giving its amplitude as a
function of this distance do not depend on the precise form of the incident
wave but only on its integral properties. The incidence of a static
conductivity of the medium is also examined and explicit analytical results are
again given in the limit of weak and strong conductivities.


  We present ALMA deep spectroscopy for a lensed galaxy at $z_{\rm spec}=8.496$
with $\log(M_{\rm star}/M_{\odot})\sim7.8$ whose optical nebular lines and
stellar continuum are detected by JWST/NIRSpec and NIRCam Early Release
Observations in SMACS0723. Our ALMA spectrum shows [OIII]88$\mu$m and
[CII]158$\mu$m line detections at $4.0\sigma$ and $4.5\sigma$, respectively.
The redshift and position of the [OIII] line coincide with those of the JWST
source, while the [CII] line is blue-shifted by 90 km s$^{-1}$ with a spatial
offset of $0.''5$ ($\approx0.5$ kpc in source plane) from the JWST source. The
NIRCam F444W image, including [OIII]$\lambda$5007 and H$\beta$ line emission,
spatially extends beyond the stellar components by a factor of $>8$. This
indicates that the $z=8.5$ galaxy has already experienced strong outflows whose
oxygen and carbon produce the extended [OIII]$\lambda$5007 and the offset [CII]
emission, which would promote ionizing photon escape and facilitate
reionization. With careful slit-loss corrections and removals of emission
spatially outside the galaxy, we evaluate the [OIII]88$\mu$m/$\lambda$5007 line
ratio, and derive the electron density $n_{\rm e}$ by photoionization modeling
to be $220^{+170}_{-100}$ cm$^{-3}$, which is comparable with those of
$z\sim2-3$ galaxies. We estimate an [OIII]88$\mu$m/[CII]158$\mu$m line ratio in
the galaxy of $>4$, as high as those of known $z\sim6-9$ galaxies. This high
[OIII]88$\mu$m/[CII]158$\mu$m line ratio is generally explained by the high
$n_{\rm e}$ as well as the low metallicity ($Z_{\rm
gas}/Z_{\odot}=0.04^{+0.02}_{-0.02}$), high ionization parameter ($\log U >
-2.27$), and low carbon-to-oxygen abundance ratio ($\log$(C/O)
$=[-0.52:-0.24]$) obtained from the JWST/NIRSpec data; further [CII] follow-up
observations will constrain the covering fraction of photodissociation regions.