  We propose a flexible statistical model for high-dimensional quantitative
data on a hypercube. Our model, called the structural gradient model (SGM), is
based on a one-to-one map on the hypercube that is a solution for an optimal
transport problem. As we show with many examples, SGM can describe various
dependence structures including correlation and heteroscedasticity. The maximum
likelihood estimation of SGM is effectively solved by the
determinant-maximization programming. In particular, a lasso-type estimation is
available by adding constraints. SGM is compared with graphical Gaussian models
and mixture models.


  We present and analyze long-term optical photometric measurements of the
three active stars V2253 Oph, IT Com and IS Vir. All three systems are
single-lined spectroscopic binaries with an early K giant as primary component
but in different stages of orbital-rotational synchronization. Our photometry
is supplemented by 2MASS and WISE near-IR and mid-IR magnitudes and then used
to obtain more accurate effective temperatures and extinctions. For V2253 Oph
and IT Com, we found their spectral energy distributions consistent with pure
photospheric emission. For IS Vir, we detect a marginal mid-IR excess which
hints towards a dust disk. The orbital and rotational planes of IT Com appear
to be coplanar, contrary to previous findings in the literature. We apply a
multiple frequency analysis technique to determine photometric periods, and
possibly changes of periods, ranging from days to decades. New rotational
periods of 21.55+-0.03d, 65.1+-0.3d, and 23.50+-0.04d were determined for V2253
Oph, IT Com, and IS Vir, respectively. Splitting of these periods led to
tentative detections of differential surface rotations of delta P/P ~0.02 for
V2253 Oph and 0.07 for IT Com. Using a time-frequency technique based on
short-term Fourier transforms we present evidence of cyclic light variations of
length ~10yrs for V2253 Oph and 5-6yrs for IS Vir. A single flip-flop event has
been observed for IT Com of duration 2-3yrs. Its exchange of the dominant
active longitude had happened close to a time of periastron passage, suggesting
some response of the magnetic activity from the orbital dynamics. The 21.55-d
rotational modulation of V2253 Oph showed phase coherence also with the orbital
period, which is 15 times longer than the rotational period, thus also
indicating a tidal feedback with the stellar magnetic activity.


  Results from the new Monte Carlo event generator Herwig++ are presented. This
first version simulates Hadron Emission Reactions With Interfering Gluons in
electron-positron annihilation. The parton shower evolution is carried out
using new evolution variables suited to describing radiation from heavy quarks
as well as light partons. The partonic final state is fragmented into hadrons
by means of an improved cluster hadronization model. The results are compared
with a wide variety of data from LEP and SLC.


  During its lifetime, a program suffers several changes that seek to improve
or to augment some parts of its functionality. However, these modifications
usually also introduce errors that affect the already-working code. There are
several approaches and tools that help to spot and find the source of these
errors. However, most of these errors could be avoided beforehand by using some
of the knowledge that the programmers had when they were writing the code. This
is the idea behind the design-by-contract approach, where users can define
contracts that can be checked during runtime. In this paper, we apply the
principles of this approach to Erlang, enabling, in this way, a runtime
verification system in this language. We define two types of contracts. One of
them can be used in any Erlang program, while the second type is intended to be
used only in concurrent programs. We provide the details of the implementation
of both types of contracts. Moreover, we provide an extensive explanation of
each contract as well as examples of their usage. All the ideas presented in
this paper have been implemented in a contract-based runtime verification
system named EDBC. Its source code is available at GitHub as an open-source and
free project.


  Given a compact complex $n$-fold $X$ satisfying the
$\partial\bar\partial$-lemma and supposed to have a trivial canonical bundle
$K_X$ and to admit a balanced (=semi-K\"ahler) Hermitian metric $\omega$, we
introduce the concept of deformations of $X$ that are {\bf co-polarised} by the
balanced class $[\omega^{n-1}]\in H^{n-1,\,n-1}(X,\,\C)\subset
H^{2n-2}(X,\,\C)$ and show that the resulting theory of balanced co-polarised
deformations is a natural extension of the classical theory of K\"ahler
polarised deformations in the context of Calabi-Yau or even holomorphic
symplectic compact complex manifolds. The concept of Weil-Petersson metric
still makes sense in this strictly more general, possibly non-K\"ahler context,
while the Local Torelli Theorem still holds.


  2+1 gravity for spacetimes with topology RxT^2 has been much studied. We add
a description of how to extend these spacetimes across a Cauchy horizon into a
region where the torus becomes Lorentzian. The result is a one parameter family
of tori given by a geodesic in the "Teichmueller space" of Lorentzian tori. We
describe this in detail. We also point out that if the modular group is
regarded as part of the gauge group then these spacetimes offer a nice toy
model for the dynamics of Bianchi IX models; in the region where the tori are
spacelike the dynamics is described exactly by a hyperbolic billiard. On the
other hand the modular group acts ergodically on the Teichmueller space of
Lorentzian tori.


  In this note we study advection diffusion equations associated to
incompressible $W^{1,p}$ velocity fields with $p>2$. We present new estimates
on the energy dissipation rate and we discuss applications to the study of
upper bounds on the enhancing dissipation rate, lower bounds on the $L^2$ norm
of the density, and quantitative vanishing viscosity estimates. The key tools
employed in our argument are a propagation of regularity result, coming from
the study of transport equations, and a new result connecting the energy
dissipation rate to regularity estimates for transport equations. Eventually we
provide examples which underline the sharpness of our estimates.


  In recent literature, it has been argued that a mild form of the Weak Gravity
Conjecture (WGC) is satisfied by wide classes of effective field theories in
which higher-derivative corrections can be shown to shift the charge-to-mass
ratios of extremal black holes to larger values. However, this mild form does
not directly constrain low-energy physics because the black holes satisfying
the WGC have masses above the cutoff of the effective theory. In this note, we
point out that in string theory modular invariance can connect a light
superextremal state to heavy superextremal states; the latter collapse into
black holes at small string coupling. In the context of heterotic string
theory, we show that these states are black holes that have $\alpha'$-exact
charge-to-mass ratios exceeding the classical extremality bound. This suggests
that modular invariance of the string partition function can be used to relate
the existence of a light superextremal particle to the positive shift in
charge-to-mass ratio of extremal black holes.


  In the present work, the application of the method of underwater arc
discharge of graphite electrodes for obtaining several carbon nanostructures is
described. The analysis of the obtained products by Transmission Electron
Microscopy (TEM), Scanning Electron Microscopy (SEM), Raman spectroscopy,
Atomic Force Microscopy (AFM) and X-Ray Diffraction (XRD) showed that the
samples collected from the material floating on the water surface were composed
mainly by polyhedral onion-like particles, while those taken from the
precipitate were a mixture multiwalled nano-tubes, onion-like particles and
other graphitic structures. The main features of the obtained nanostructures
are discussed.


  Stars do not form in isolation but together with other stars, and often in a
clustered environment. Depending on the initial conditions in these
environments, such as initial density and substructure, the distances of
encounters between stars will differ. These encounters can also affect
just-formed exoplanetary systems. Using N-body simulations, we show the effect
of a single fly-by on a common type of exoplanetary system: close-in
Super-Earths/sub-Neptunes with or without a distant Giant planet. Even a single
encounter can significantly modify the architecture of these exoplanetary
systems over their long lifetimes. We test fly-bys with different
characteristics, such as distance and mass, and show how they perturb the inner
planets long after the encounter, leading to collisions and mutual inclination
excitation, which can significantly modify the observed architecture of these
systems in transit. We find that our initially four-planet inner systems reduce
to three or two inner planets depending on their initial separation and that
the mutual inclinations of these remaining planets can be high enough to reduce
the number of observable, transiting planets. In our 500 Myr simulations, we
show that this reduction in the number of transiting planets due to stellar
fly-bys can contribute to the observed excess of single-transit systems.


  This paper addresses a decision problem highlighted by Grigorchuk,
Nekrashevich, and Sushchanskii, namely the finiteness problem for automaton
(semi)groups.
  For semigroups, we give an effective sufficient but not necessary condition
for finiteness and, for groups, an effective necessary but not sufficient
condition. The efficiency of the new criteria is demonstrated by testing all
Mealy automata with small stateset and alphabet. Finally, for groups, we
provide a necessary and sufficient condition that does not directly lead to a
decision procedure.


  We present a dispersive analysis of the decay amplitude for
$\eta'\to\eta\pi\pi$ that is based on the fundamental principles of analyticity
and unitarity. In this framework, final-state interactions are fully taken into
account. Our dispersive representation relies only on input for the $\pi\pi$
and $\pi\eta$ scattering phase shifts. Isospin symmetry allows us to describe
both the charged and neutral decay channel in terms of the same function. The
dispersion relation contains subtraction constants that cannot be fixed by
unitarity. We determine these parameters by a fit to Dalitz-plot data from the
VES and BES-III experiments. We study the prediction of a low-energy theorem
and compare the dispersive fit to variants of chiral perturbation theory.


  A rack on $[n]$ can be thought of as a set of maps $(f_x)_{x \in [n]}$, where
each $f_x$ is a permutation of $[n]$ such that $f_{(x)f_y} = f_y^{-1}f_xf_y$
for all $x$ and $y$. In 2013, Blackburn showed that the number of isomorphism
classes of racks on $[n]$ is at least $2^{(1/4 - o(1))n^2}$ and at most $2^{(c
+ o(1))n^2}$, where $c \approx 1.557$; in this paper we improve the upper bound
to $2^{(1/4 + o(1))n^2}$, matching the lower bound. The proof involves
considering racks as loopless, edge-coloured directed multigraphs on $[n]$,
where we have an edge of colour $y$ between $x$ and $z$ if and only if $(x)f_y
= z$, and applying various combinatorial tools.


  We have studied the reconstruction formalism of the DBI-essence dark energy
scalar field model with the help of non-metricity of gravity or f(Q) gravity.
The critical analysis has been done on the reconstructed model. The Black hole
and Wormhole mass accretions have been studied with this reconstructed model.
We have analyzed the validities of thermodynamic energy conditions. In our
reconstructed model, we have assumed four types of singularity resolutions of
scale factor and investigated the black hole and wormhole masses due to
accretion of reconstructed dark energy. Diagrammatically, we have analyzed the
nature of physical quantities with the kinetic and potential energies as well
as the mass due to accretion in the reconstructed DBI-essence dark energy in
the background of f(Q) gravity.


  We consider a static brane in the background of a topological black hole, in
arbitrary dimensions. For hyperbolic horizons, we find a solution only when the
black hole mass assumes its minimum negative value. In this case, the tension
of the brane vanishes, and the brane position coincides with the location of
the horizon. For an elliptic horizon, we show that the massless mode of
Randall-Sundrum is recovered in the limit of large black hole mass.


  In the complex multi-state system (MSS), reliability analysis is a
significant research content, both for equipment design, manufacturing, usage
and maintenance. Universal Generating Function (UGF) is an important method in
the reliability analysis, which efficiently obtains the system reliability by a
fast algebraic procedure. However, when structural relationships between
subsystems or components are not clear or without explicit expressions, the UGF
method is difficult to use or not applicable at all. Bayesian Network (BN) has
a natural advantage in terms of uncertainty inference for the relationship
without explicit expressions. For the number of components is extremely large,
though, it has the defects of low efficiency. To overcome the respective
defects of UGF and BN, a novel reliability analysis method called UGF-BN is
proposed for the complex MSS. In the UGF-BN framework, the UGF method is
firstly used to analyze the bottom components with a large number. Then
probability distributions obtained are taken as the input of BN. Finally, the
reliability of the complex MSS is modeled by the BN method. This proposed
method improves the computational efficiency, especially for the MSS with the
large number of bottom components. Besides, the aircraft reliability-based
design optimization based on the UGF-BN method is further studied with budget
constraints on mass, power, and cost. Finally, two cases are used to
demonstrate and verify the proposed method.


  Resonance relations among periodic orbits on given energy hypersurfaces are
very important for getting deeper understanding of the dynamics of the
corresponding Hamiltonian systems. In this paper, we establish two new
resonance identities for closed characteristics on every compact star-shaped
hypersurface $\Sigma$ in ${\bf R}^{2n}$ when the number of geometrically
distinct closed characteristics on $\Sigma$ is finite, which extend those
identities established by C. Viterbo in 1989 for star-shaped hypersurfaces
assuming in addition that all the closed characteristics and their iterates are
non-degenerate, and that by W. Wang, X. Hu and Y. Long in 2007 for strictly
convex hypersurfaces in ${\bf R}^{2n}$.


  We discuss a possible one-dimensional trapping and cooling of atoms and
molecules due to their non-resonant interaction with the counter-propagating
light pulses trains. The counter-propagating pulses form a one-dimensional trap
for atoms and molecules, and properly chosen the carrier frequency detuning
from the transition frequency of the atoms or molecules keeps the "temperature"
of the atomic or molecular ensemble close to the Doppler cooling limit. The
calculation by the Monte-Carlo wave function method is carried out for the
two-level and three-level schemes of the atom's and the molecule's interaction
with the field, correspondingly. The discussed models are applicable to atoms
and molecules with almost diagonal Frank-Condon factor arrays. Illustrative
calculations where carried out for ensemble averaged characteristics for sodium
atoms and SrF molecules in the trap. Perspective for the nanoparticle light
pulses's trap formed by counter-propagating light pulses trains is also
discussed.


  We identify a light echo candidate from Hubble Space Telescope (HST) imaging
of NGC 2441, the host galaxy of the Type Ia supernova 1995E. From the echo's
angular size and the estimated distance to the host galaxy, we find a distance
of 207 +/- 35 pc between the dust and the site of the supernova. If confirmed,
this echo brings the total number of observed non-historical Type Ia light
echoes to three -- the others being SN 1991T and SN 1998bu -- suggesting they
are not uncommon. We compare the properties of the known Type Ia supernova
echoes and test models of light echoes developed by Patat et al. (2005). HST
photometry of the SN 1991T echo shows a fading which is consistent with
scattering by dust distributed in a sphere or shell around the supernova. Light
echoes have the potential to answer questions about the progenitors of Type Ia
supernovae and more effort should be made for their detection given the
importance of Type Ia supernovae to measurements of dark energy.


  S. -R. Kim and F. S. Roberts (2002) introduced the following conditions
$C(p)$ and $C'(p)$ for digraphs as generalizations of the condition for
digraphs to be semiorders. The condition $C(p)$ (resp. $C'(p)$) is: For any set
$S$ of $p$ vertices in $D$, there exists $x \in S$ such that $N^+_D(x)
\subseteq N^+_D(y)$ (resp. $N^-_D(x) \subseteq N^-_D(y)$) for all $y \in S$,
where $N^+_D(x)$ (resp. $N^-_D(x)$) is the set of out-neighbors (resp.
in-neighbors) of $x$ in $D$. The competition graph of a digraph $D$ is the
(simple undirected) graph which has the same vertex set as $D$ and has an edge
between two distinct vertices $x$ and $y$ if $N^+_D(x) \cap N^+_D(y) \neq
\emptyset$. Kim and Roberts characterized the competition graphs of digraphs
which satisfy Condition $C(p)$. The competition-common enemy graph of a digraph
$D$ is the graph which has the same vertex set as $D$ and has an edge between
two distinct vertices $x$ and $y$ if it holds that both $N^+_D(x) \cap N^+_D(y)
\neq \emptyset$ and $N^-_D(x) \cap N^-_D(y) \neq \emptyset$. In this note, we
characterize the competition-common enemy graphs of digraphs satisfying
Conditions $C(p)$ and $C'(p)$.


  The evidence for associations between neutron stars and supernova remnants is
reviewed. After summarizing the situation for young radio pulsars, I consider
the evidence from associations that young neutron stars can have properties
very different from those of radio pulsars. This, though still controversial,
shakes our simple perception of the Crab pulsar as prototypical of the young
neutron star population.


  Smoothed AIC (S-AIC) and Smoothed BIC (S-BIC) are very widely used in model
averaging and are very easily to implement. Especially, the optimal model
averaging method MMA and JMA have only been well developed in linear models.
Only by modifying, they can be applied to other models. But S-AIC and S-BIC can
be used in all situations where AIC and BIC can be calculated. In this paper,
we study the asymptotic behavior of two commonly used model averaging
estimators, the S-AIC and S-BIC estimators, under the standard asymptotic with
general fixed parameter setup. In addition, the resulting coverage probability
in Buckland et al. (1997) is not studied accurately, but it is claimed that it
will be close to the intended. Our derivation make it possible to study
accurately. Besides, we also prove that the confidence interval construction
method in Hjort and Claeskens (2003) still works in linear regression with
normal distribution error. Both the simulation and applied example support our
theory conclusion.


  A topological dynamical system $(X,f)$ induces two natural systems, one is on
the probability measure spaces and other one is on the hyperspace.
  We introduce a concept for these two spaces, which is called entropy order,
and prove that it coincides with topological entropy of $(X,f)$. We also
consider the entropy order of an invariant measure and a variational principle
is established.


  This paper discusses our investigation into the evolution of cooperative
players in an online business environment. We explain our design of an
incentive based system with its foundation over binary reputation system whose
proportion of reward or punishment is a function of transaction value and the
players past history of cooperation. We compare the evolution of cooperation in
our setting with non-incentive based environment and our findings show that the
incentive based method is more suitable for the evolution of trustworthy
players.


  We solve the analytic Cauchy problem for the generalized two-component
Camassa-Holm system introduced by R. M. Chen and Y. Liu. We show the existence
of a unique local/global-in-time analytic solution under certain conditions.
This is the first result about global analyticity for a Camassa-Holm-like
system. The method of proof is basically that developed by Barostichi, Himonas
and Petronilho. The main differences of their proof and ours are twofold: (i)
the system of Chen and Liu is not symmetic in the two unknowns and our
estimates are not trivial generalization of those in their articles, (ii) we
have simplified their argument by using fewer function spaces and the main
result is stated in a simple and natural way.


  (Abridged) We investigate the morphology dependence of the Tully-Fisher
relation, and the expansion of the relation into a three-dimensional manifold
defined by luminosity, total circular velocity and a third dynamical parameter,
to fully characterise spiral galaxies across all morphological types. We use a
semi-analytic hierarchical model of galaxy evolution to build the theoretical
TF relation. With this tool, we analyse a unique dataset of galaxies for which
we cross-match luminosity with total circular velocity and central velocity
dispersion. We provide a theoretical framework to calculate such measurable
quantities from semi-analytic models. We establish the morphology dependence of
the TF relation in both model and data. We analyse the dynamical properties of
the model galaxies and determine that the parameter 'sigma/Vc', i.e. the ratio
between random and total motions defined by velocity dispersion and circular
velocity, accurately characterises the varying slope of the TF relation for
different model galaxy types. We apply these dynamical cuts to the observed
galaxies and find that such selection produces a differential slope of the TF
relation. The TF slope in different ranges of 'sigma/Vc' is consistent with
that for the photometric classification in Sa, Sb, Sc. We conclude that
'sigma/Vc' is a good parameter to classify galaxy type, and we argue that such
classification based on dynamics more closely mirrors the physical properties
of the observed galaxies, compared to visual classification. We also argue that
dynamical classification is useful for samples where eye inspection is not
reliable or impractical. We conclude that 'sigma/Vc' is a suitable parameter to
characterise the hierarchical assembly history that determines the
disk-to-bulge ratio, and to expand the TF relation into a three-dimensional
manifold, defined by luminosity, circular velocity and 'sigma/Vc'.


  Large Language Models (LLMs) are continuously being applied in a more diverse
set of contexts. At their current state, however, even state-of-the-art LLMs
such as Generative Pre-Trained Transformer 4 (GTP-4) have challenges when
extracting information from real-world technical documentation without a heavy
preprocessing. One such area with real-world technical documentation is
telecommunications engineering, which could greatly benefit from
domain-specific LLMs. The unique format and overall structure of
telecommunications internal specifications differs greatly from standard
English and thus it is evident that the application of out-of-the-box Natural
Language Processing (NLP) tools is not a viable option. In this article, we
outline the limitations of out-of-the-box NLP tools for processing technical
information generated by telecommunications experts, and expand the concept of
Technical Language Processing (TLP) to the telecommunication domain.
Additionally, we explore the effect of domain-specific LLMs in the work of
Specification Engineers, emphasizing the potential benefits of adopting
domain-specific LLMs to speed up the training of experts in different
telecommunications fields.


  Efficient textual data distributions (TDD) alignment and generation are open
research problems in textual analytics and NLP. It is presently difficult to
parsimoniously and methodologically confirm that two or more natural language
datasets belong to similar distributions, and to identify the extent to which
textual data possess alignment. This study focuses on addressing a segment of
the broader problem described above by applying multiple supervised and
unsupervised machine learning (ML) methods to explore the behavior of TDD by
(i) topical alignment, and (ii) by sentiment alignment. Furthermore we use
multiple text generation methods including fine-tuned GPT-2, to generate text
by topic and by sentiment. Finally we develop a unique process driven variation
of Kullback-Leibler divergence (KLD) application to TDD, named KL Textual
Distributions Contrasts(KL-TDC) to identify the alignment of machine generated
textual corpora with naturally occurring textual corpora. This study thus
identifies a unique approach for generating and validating TDD by topic and
sentiment, which can be used to help address sparse data problems and other
research, practice and classroom situations in need of artificially generated
topic or sentiment aligned textual data.


  We study the effects of short- and long-range correlations on the charge
radii of Ca isotopes. We start our investigation with an independent particle
model consisting in Hartree-Fock plus Bardeen-Cooper-Schrieffer calculations
with finite-range effective nucleon-nucleon interactions of Gogny type. The
short-range correlations effects are evaluated by considering all the terms of
a cluster expansion containing a single correlation line. The long-range
correlations are taken into account by including the coupling with the
quasi-particle random phase approximation phonons. While the effects of the
short-range correlations are negligible, those of the long-range correlations
largely modify the independent particle model results and improve the agreement
with the experimental data.


  A thin Hafnium film is shown to act both as an effective diffusion barrier
for manganese at a thickness of 0.7 nm, and as an effective exchange coupling
layer in a sandwich structure with perpendicular magnetic anisotropy. The
magnetic layers are Co$_{20}$Fe$_{60}$B$_{20}$ and the low moment ferrimagnet
Mn$_2$Ru$_x$Ga (MRG). The coupling changes sign at the compensation temperature
of MRG and the exchange energy reaches 0.11 mJm$^{-2}$ for the thinnest Hf
interlayers. Ruthenium, the usual metal of choice for coupling ferromagnetic
layers in thin film heterostructures, cannot be used with the zero-moment half
metal MRG because of Ru interdiffusion. Due to its large coercivity near
compensation, the MRG can act as an effective source of exchange pinning.


  Two different types of generalized solutions, namely viscosity and
variational solutions, were introduced to solve the first-order evolutionary
Hamilton--Jacobi equation. They coincide if the Hamiltonian is convex in the
momentum variable. In this paper we prove that there exists no other class of
integrable Hamiltonians sharing this property. To do so, we build for any
non-convex non-concave integrable Hamiltonian a smooth initial condition such
that the graph of the viscosity solution is not contained in the wavefront
associated with the Cauchy problem. The construction is based on a new example
for a saddle Hamiltonian and a precise analysis of the one-dimensional case,
coupled with reduction and approximation arguments.


  A link stream is a sequence of pairs of the form $(t,\{u,v\})$, where
$t\in\mathbb N$ represents a time instant and $u\neq v$. Given an integer
$\gamma$, the $\gamma$-edge between vertices $u$ and $v$, starting at time $t$,
is the set of temporally consecutive edges defined by $\{(t',\{u,v\}) | t' \in
[t,t+\gamma-1]\}$. We introduce the notion of temporal matching of a link
stream to be an independent $\gamma$-edge set belonging to the link stream. We
show that the problem of computing a temporal matching of maximum size is
NP-hard as soon as $\gamma>1$. We depict a kernelization algorithm
parameterized by the solution size for the problem. As a byproduct we also give
a $2$-approximation algorithm.
  Both our $2$-approximation and kernelization algorithms are implemented and
confronted to link streams collected from real world graph data. We observe
that finding temporal matchings is a sensitive question when mining our data
from such a perspective as: managing peer-working when any pair of peers $X$
and $Y$ are to collaborate over a period of one month, at an average rate of at
least two email exchanges every week. We furthermore design a link stream
generating process by mimicking the behaviour of a random moving group of
particles under natural simulation, and confront our algorithms to these
generated instances of link streams. All the implementations are open source.


  Supersonic turbulence is a large reservoir of suprathermal energy in the
interstellar medium. Its dissipation, because it is intermittent in space and
time, can deeply modify the chemistry of the gas. We further explore a hybrid
method to compute the chemical and thermal evolution of a magnetized
dissipative structure, under the energetic constraints provided by the observed
properties of turbulence in the cold neutral medium. For the first time, we
model a random line of sight by taking into account the relative duration of
the bursts with respect to the thermal and chemical relaxation timescales of
the gas. The key parameter is the turbulent rate of strain "a" due to the
ambient turbulence. With the gas density, it controls the size of the
dissipative structures, therefore the strength of the burst. For a large range
of rates of strain and densities, the models of turbulent dissipation regions
(TDR) reproduce the CH+ column densities observed in the diffuse medium and
their correlation with highly excited H2. They do so without producing an
excess of CH. As a natural consequence, they reproduce the abundance ratios of
HCO+/OH and HCO+/H2O, and their dynamic range of about one order of magnitude
observed in diffuse gas. Large C2H and CO abundances, also related to those of
HCO+, are another outcome of the TDR models that compare well with observed
values. The abundances and column densities computed for CN, HCN and HNC are
one order of magnitude above PDR model predictions, although still
significantly smaller than observed values.


  We explicitly map the N-body one dimensional Calogero eigenstates in a
harmonic well to the lowest Landau level sector of N-body eigenstates of the
two dimensional anyon model in a harmonic well. The mapping is achieved in
terms of a convolution kernel that uses as input the scattering eigenstates of
the free Calogero model on the infinite line, which are obtained in an operator
formulation.


  We introduce a general and fast convolution-based method (FCBM) for
peridynamics (PD). Expressing the PD integrals in terms of convolutions and
computing them by fast Fourier transform (FFT), we reduce the computational
complexity of PD models from O(N^2) to O(Nlog_2 N), with N being the total
number of discretization nodes. Initial neighbor identification and storing
neighbor information is not required, and, as a consequence, memory allocation
scales with O(N) instead of O(N^2), common for existing methods. The method is
applicable to bounded domains with arbitrary shapes and boundary conditions via
an embedded constraint (EC) approach. We explain the FCBM-EC formulation for
certain bond-based and state-based, linear and nonlinear PD models of
elasticity and dynamic brittle fracture, as applications. We solve a 3D
elastostatic problem and show that the FCBM reduces the computational time from
days to hours and from years to days, compared with the original meshfree
discretization for PD models. Large-scale computations of PD models are
feasible with the new method, and we demonstrate its versatility by simulating,
with ease, the difficult problem of multiple crack branching in a brittle
plate.


  In this paper, we develop a concise but efficient network architecture called
linear compressing based skip-connecting network (LCSCNet) for image
super-resolution. Compared with two representative network architectures with
skip connections, ResNet and DenseNet, a linear compressing layer is designed
in LCSCNet for skip connection, which connects former feature maps and
distinguishes them from newly-explored feature maps. In this way, the proposed
LCSCNet enjoys the merits of the distinguish feature treatment of DenseNet and
the parameter-economic form of ResNet. Moreover, to better exploit hierarchical
information from both low and high levels of various receptive fields in deep
models, inspired by gate units in LSTM, we also propose an adaptive
element-wise fusion strategy with multi-supervised training. Experimental
results in comparison with state-of-the-art algorithms validate the
effectiveness of LCSCNet.


  Stochastic resets have lately emerged as a mechanism able to generate finite
equilibrium mean square displacement (MSD) when they are applied to diffusive
motion. Furthermore, walkers with an infinite mean first arrival time (MFAT) to
a given position $x$, may reach it in a finite time when they reset their
position. In this work we study these emerging phenomena from a unified
perspective. On one hand we study the existence of a finite equilibrium MSD
when resets are applied to random motion with $\langle x^2(t)\rangle _m\sim
t^p$ for $0<p\leq2$. For exponentially distributed reset times, a compact
formula is derived for the equilibrium MSD of the overall process in terms of
the mean reset time and the motion MSD. On the other hand, we also test the
robustness of the finiteness of the MFAT for different motion dynamics which
are subject to stochastic resets. Finally, we study a biased Brownian
oscillator with resets with the general formulas derived in this work, finding
its equilibrium first moment and MSD, and its MFAT to the minimum of the
harmonic potential.


  We present a detailed study of the centre of NGC4654, a Milky Way-like spiral
galaxy in the Virgo cluster that has been reported to host a double stellar
nucleus, thus promising a rare view of ongoing star cluster infall into a
galaxy nucleus. Analysing JWST NIRSpec integral-field spectroscopic data and
Hubble Space Telescope imaging of the inner 330 $\times$ 330 pc, we find that
the nucleus harbours in fact three massive star clusters. Maps of infrared
emission lines from NIRSpec show different morphologies for the ionised and
molecular gas components. The emission from molecular hydrogen gas is
concentrated at the NSC location, while emission from hydrogen recombination
lines is more extended beyond the central cluster. The velocity fields of both
gas and stars indicate that the three clusters are part of a complicated
dynamical system, with the NSC having an elevated velocity dispersion in line
with its high stellar mass. To investigate the stellar populations of the three
clusters in more detail, we use surface brightness modelling to measure their
fluxes from ultraviolet to mid-infrared wavelengths and fit their spectral
energy distributions (SEDs). Two of the clusters are UV-bright and well
described by single stellar populations with young ages ($\sim$ 3 and 5 Myr)
and low masses ($M_\ast \sim 4 \times 10^{4} - 10^{5} M_\odot$), whereas the
central cluster is much more massive ($3 \times 10^7 M_\odot$), and cannot be
fitted by a single stellar population. Instead, we find that a minor young
population ($\sim$ 1 Myr) embedded in a dominant old population ($\sim$ 8 Gyr)
is needed to explain its SED. Given its complex composition and the close
proximity of two young star clusters that are likely to merge with it within a
few hundred million years, we consider NGC4654 a unique laboratory to study NSC
growth from both in-situ star formation and the infall of star clusters.


  A result of Spencer states that every collection of $n$ sets over a universe
of size $n$ has a coloring of the ground set with $\{-1,+1\}$ of discrepancy
$O(\sqrt{n})$. A geometric generalization of this result was given by Gluskin
(see also Giannopoulos) who showed that every symmetric convex body $K\subseteq
R^n$ with Gaussian measure at least $e^{-\epsilon n}$, for a small
$\epsilon>0$, contains a point $y\in K$ where a constant fraction of
coordinates of $y$ are in $\{-1,1\}$. This is often called a partial coloring
result. While both these results were inherently non-algorithmic, recently
Bansal (see also Lovett-Meka) gave a polynomial time algorithm for Spencer's
setting and Rothvo\ss gave a randomized polynomial time algorithm obtaining the
same guarantee as the result of Gluskin and Giannopoulos.
  This paper has several related results. First we prove another constructive
version of the result of Gluskin and Giannopoulos via an optimization of a
linear function. This implies a linear programming based algorithm for
combinatorial discrepancy obtaining the same result as Spencer. Our second
result gives a new approach to obtains partial colorings and shows that every
convex body $K\subseteq R^n$, possibly non-symmetric, with Gaussian measure at
least $e^{-\epsilon n}$, for a small $\epsilon>0$, contains a point $y\in K$
where a constant fraction of coordinates of $y$ are in $\{-1,1\}$. Finally, we
give a simple proof that shows that for any $\delta >0$ there exists a constant
$c>0$ such that given a body $K$ with $\gamma_n(K)\geq \delta$, a uniformly
random $x$ from $\{-1,1\}^n$ is in $cK$ with constant probability. This gives
an algorithmic version of a special case of the result of Banaszczyk.


  A design concept is introduced for the building block, a dot, of programmable
braille readers utilizing bistable shell buckling, magnetic actuation, and
pneumatic loading. The design process is guided by Finite Element simulations,
which are initially validated through precision experiments conducted on a
scaled-up, single-shell model system. Then, the simulations are leveraged to
systematically explore the design space, adhering to the standardized geometric
and physical specifications of braille systems. The findings demonstrate the
feasibility of selecting design parameters that satisfy both geometric
requirements and blocking forces under moderate magnetic fields, facilitated by
pneumatic loading to switch between the two stable states. The advantages of
the proposed design include the reversible bistability of the actuators and
fast state-switching via a transient magnetic field. While the study is focused
on experimentally validated numerical simulations, several manufacturing
challenges that need to be resolved for future physical implementations are
identified.


  We study soft limits of correlation functions for the density and velocity
fields in the theory of structure formation. First, we re-derive the (resummed)
consistency conditions at unequal times using the eikonal approximation. These
are solely based on symmetry arguments and are therefore universal. Then, we
explore the existence of equal-time relations in the soft limit which, on the
other hand, depend on the interplay between soft and hard modes. We scrutinize
two approaches in the literature: The time-flow formalism, and a background
method where the soft mode is absorbed into a locally curved cosmology. The
latter has been recently used to set up (angular averaged) `equal-time
consistency relations'. We explicitly demonstrate that the time-flow relations
and `equal-time consistency conditions' are only fulfilled at the linear level,
and fail at next-to-leading order for an Einstein de-Sitter universe. While
applied to the velocities both proposals break down beyond leading order, we
find that the `equal-time consistency conditions' quantitatively approximates
the perturbative results for the density contrast. Thus, we generalize the
background method to properly incorporate the effect of curvature in the
density and velocity fluctuations on short scales, and discuss the reasons
behind this discrepancy. We conclude with a few comments on practical
implementations and future directions.


  We demonstrate, by analogy with electromagnetism, that the geometric content
in the theory of gravity is an indirect consequence of the fact that the gauge
group in question is the Lorentz group SO(1,3). We hence construct field
equations for gravity and a spin-1/2 particle in a gravitational field based on
gauge considerations. Furthermore, we derive the weak field and Schroedinger
limits of the Dirac equation of the particle in the gravitational field,
especially in Fermi normal coordinates and on the equatorial plane of the Kerr
geometry, following which we identify the terms to which the electromagnetic
potentials A and Phi are analogous.


  We investigate a theoretical model for effective carrier mobility to
comprehensively describe the behavior of the perpendicular carrier transport
across multiple quantum well (MQW) structures under applied electric field. The
analytical expressions of effective mobilities for thermionic emission, direct
tunneling, and thermally-assisted tunneling are derived based on the
quasi-thermal equilibrium approximation and the semi-classical approach.
Effective electron and hole mobilities in InGaAs/GaAsP MQWs predicted from our
model are in good agreement with the experimental results obtained from the
carrier time-of-flight measurement near room temperature. With this concept,
the complicated carrier dynamics inside MQWs can be simplified to an effective
mobility, an equivalent parameter which is more straightforward to handle and
can be easily incorporated in the conventional drift-diffusion model.


  Partially synchronous Byzantine consensus protocols typically structure their
execution into a sequence of views, each with a designated leader process. The
key to guaranteeing liveness in these protocols is to ensure that all correct
processes eventually overlap in a view with a correct leader for long enough to
reach a decision. We propose a simple view synchronizer abstraction that
encapsulates the corresponding functionality for Byzantine consensus protocols,
thus simplifying their design. We present a formal specification of a view
synchronizer and its implementation under partial synchrony, which runs in
bounded space despite tolerating message loss during asynchronous periods. We
show that our synchronizer specification is strong enough to guarantee liveness
for single-shot versions of several well-known Byzantine consensus protocols,
including HotStuff, Tendermint, PBFT and SBFT. We furthermore give precise
latency bounds for these protocols when using our synchronizer. By factoring
out the functionality of view synchronization we are able to specify and
analyze the protocols in a uniform framework, which allows comparing them and
highlights trade-offs.


  We show that each $p$-block of ${\rm SL}(2,p^n)$ and ${\rm GL}(2,p^n)$ over
an arbitrary complete discrete valuation ring is splendidly Rickard equivalent
to its Brauer correspondent, hence give new evidence for a refined version of
Brou\'{e}'s abelian defect group conjecture proposed by Kessar and Linckelmann.


  The growth and success of deep learning approaches can be attributed to two
major factors: availability of hardware resources and availability of large
number of training samples. For problems with large training databases, deep
learning models have achieved superlative performances. However, there are a
lot of \textit{small sample size or $S^3$} problems for which it is not
feasible to collect large training databases. It has been observed that deep
learning models do not generalize well on $S^3$ problems and specialized
solutions are required. In this paper, we first present a review of deep
learning algorithms for small sample size problems in which the algorithms are
segregated according to the space in which they operate, i.e. input space,
model space, and feature space. Secondly, we present Dynamic Attention Pooling
approach which focuses on extracting global information from the most
discriminative sub-part of the feature map. The performance of the proposed
dynamic attention pooling is analyzed with state-of-the-art ResNet model on
relatively small publicly available datasets such as SVHN, C10, C100, and
TinyImageNet.


  In this paper we continue our studies of the one dimensional conformal metric
flows, which were introduced in [8]. In this part we mainly focus on evolution
equations involving fourth order derivatives. The global existence and
exponential convergence of metrics for the 1-Q and 4-Q flows are obtained.


  This is the author's Ph.D. thesis. We introduce two related invariants for
local (and standard graded) rings called differential and syzygy symmetric
signature. These are defined by looking at the maximal free splitting of the
module of K\"ahler differentials and of the the top-dimensional syzygy module
of the residue field respectively. We study and compute them for different
classes of rings: two-dimensional ADE singularities, two-dimensional cyclic
singularities, and cones over plane elliptic curves (for the differential
symmetric signature). The values obtained coincide with the F-signature of such
rings in positive characteristic. The thesis contains also a short survey on
the Auslander correspondence for quotient singularities.


  The DENIS and 2MASS near infrared surveys are presented. Their applications
in extragalactic astronomy and cosmology are listed. The prospects for a rapid
spectroscopic followup survey of a near infrared selected sample of nearly
$10^5$ galaxies are illustrated with Monte-Carlo simulations.


  Consider the universal gate set for quantum computing consisting of the gates
X, CX, CCX, omega^dagger H, and S. All of these gates have matrix entries in
the ring Z[1/2,i], the smallest subring of the complex numbers containing 1/2
and i. Amy, Glaudell, and Ross proved the converse, i.e., any unitary matrix
with entries in Z[1/2,i] can be realized by a quantum circuit over the above
gate set using at most one ancilla. In this paper, we give a finite
presentation by generators and relations of U_n(Z[1/2,i]), the group of unitary
nxn-matrices with entries in Z[1/2,i].


  We define the category of partitioned binary relations and show that it
contains many classical diagram categories, including categories of binary
relations, maps, injective maps, partitions, (oriented) Brauer diagrams and
(oriented) Temperley-Lieb diagrams. We construct a one-parameter deformation of
the category of partitioned binary relations and show that it gives rise to
classical one-parameter deformations of partition, Brauer and Temperley-Lieb
categories. Finally, we describe a factorization of partitioned binary
relations into a product of certain idempotents and pairs of usual binary
relations.


  Let $G$ be an unmixed bipartite graph of dimension $d-1$. Assume that
$K_{n,n}$, with $n\ge 2$, is a maximal complete bipartite subgraph of $G$ of
minimum dimension. Then $G$ is Cohen-Macaulay in codimension $d-n+1$. This
generalizes a characterization of Cohen-Macaulay bipartite graphs by Herzog and
Hibi and a result of Cook and Nagel on unmixed Buchsbaum graphs. Furthermore,
we show that any unmixed bipartite graph $G$ which is Cohen-Macaulay in
codimension $t$, is obtained from a Cohen-Macaulay graph by replacing certain
edges of $G$ with complete bipartite graphs. We provide some examples.


  An evergreen scientific feature is the ability for scientific works to be
reproduced. This feature allows researchers to understand, enhance, or even
question works that have been developed by other scientists. In control theory
the importance of modeling and simulation of systems is widely recognized.
Despite this recognition, less attention is paid to the effects of finite
precision of computers on the simulation reproducibility of nonlinear dynamic
systems. In this work, a case study of reproducibility is presented in the
simulation of a chaotic Jerk circuit, using the software LtSpice. In order to
do so, we performed simulations of the circuit in the same version of the
software on different computers, in order to collect the data and compare them
with experimental results. The comparison was made with the NRMSE (Normalized
Root Mean Square Error), in order to identify the computer with the highest
prediction horizon. Tests performed in 4 different configurations showed the
difficulties of simulation reproducibility in LtSpice. The methodology
developed was efficient in identifying the computer with better performance,
which allows applying it to other cases in the literature.


  This paper proposes an arrayed-waveguide grating (AWG) based
wavelength-division-multiplexing (WDM) shuffle network. Compared with previous
optical shuffle networks, our proposal is compact, easy to implement, highly
scalable, and cost effective.


  In the vicinity of a massive black hole, stars move on precessing Keplerian
orbits. The mutual stochastic gravitational torques between the stellar orbits
drive a rapid reorientation of their orbital planes, through a process called
vector resonant relaxation. We derive, from first principles, the correlation
of the potential fluctuations in such a system, and the statistical properties
of random walks undergone by the stellar orbital orientations. We compare this
new analytical approach with effective $N$-body simulations. We also provide a
simple scheme to generate the random walk of a test star's orbital orientation
using a stochastic equation of motion. We finally present quantitative
estimations of this process for a nuclear stellar cluster such as the one of
the Milky Way.


  End user privacy is a critical concern for all organizations that collect,
process and store user data as a part of their business. Privacy concerned
users, regulatory bodies and privacy experts continuously demand organizations
provide users with privacy protection. Current research lacks an understanding
of organizational characteristics that affect an organization's motivation
towards user privacy. This has resulted in a "one solution fits all" approach,
which is incapable of providing sustainable solutions for organizational issues
related to user privacy. In this work, we have empirically investigated 40
diverse organizations on their motivations and approaches towards user privacy.
Resources such as newspaper articles, privacy policies and internal privacy
reports that display information about organizational motivations and
approaches towards user privacy were used in the study. We could observe
organizations to have two primary motivations to provide end users with privacy
as voluntary driven inherent motivation, and risk driven compliance motivation.
Building up on these findings we developed a taxonomy of organizational privacy
approaches and further explored the taxonomy through limited exclusive
interviews. With his work, we encourage authorities and scholars to understand
organizational characteristics that define an organization's approach towards
privacy, in order to effectively communicate regulations that enforce and
encourage organizations to consider privacy within their business practices.


  We study the average asymptotic growth rate of cells in randomly fluctuating
environments, with multiple viable phenotypes per environment. We show that any
information processing strategy has an asymptotic growth rate, which is the sum
of: (i) the maximal growth rate at the worst possible distribution of
environments, (ii) relative information between the actual distribution of
environments to the worst one, and (iii) information utilization rate, which is
the information rate of the sensory devices minus the "information dissipation
rate", the amount of information not utilized by the cell for growth. In
non-stationary environments, we find that the optimal phenotypic switching
times equally partition the information dissipation rate between consecutive
switching intervals.


  Positivity constraints have proved to be important for spin observables of
exclusive reactions involving polarized initial and final particles. Attention
is focused in this note on the photoproduction of pseudoscalar mesons from spin
1/2 baryons, more specifically gamma+ N -> K+ Lambda, gamma+ N -> K Sigma, for
which new experimental data are becoming available.


  A method for treating ferromagnetic chains coupled with antiferromagnetic
interactions on an hexagonal lattice is presented in this paper. The solution
of the $1D$ part of the problem is obtained by classical transfer-matrix while
the coupling between the chains is processed by mean-field theory. This method
is applied with success to the phase diagram and angular dependence of the
critical field of CsNiF$_3$. Results concerning the general influence of
single-ion anisotropy on the magnetic ordering of such systems are also
presented.


  We study a model of $N$ fermions in a quantum dot, coupled to $M$ bosons by a
disorder-induced complex Yukawa coupling (Yukawa-SYK model), in order to
explore the interplay between non-Fermi liquid and superconductivity in a
strongly coupled, (quantum-)critical environment. We analyze the phase diagram
of the model for an arbitrary complex interaction and arbitrary ratio of $N/M$,
with special focus on the two regimes of non-Fermi-liquid behavior: an SYK-like
behavior with a power-law frequency dependence of the fermionic self-energy and
an impurity-like behavior with frequency independent self-energy. We show that
the crossover between the two. can be reached by varying either the strength of
the fermion-boson coupling or the ratio $M/N$. We next argue that in both
regimes the system is unstable to superconductivity if the strength of
time-reversal-symmetry-breaking disorder is below a certain threshold. We show
how the corresponding onset temperatures vary between the two regimes. We argue
that the superconducting state is highly unconventional with an infinite set of
minima of the condensation energy at $T=0$, corresponding to topologically
different gap functions. We discuss in detail similarities and differences
between this model and the model of dispersion-full fermions tuned to a
metallic quantum-critical point, with an effective singular dynamical
interaction $V(\Omega) \propto 1/|\Omega|^\gamma$ (the $\gamma-$model).


  We consider the problem of designing waveforms for mitigating single tone
jamming (STJ) signals with an estimated jamming frequency in time-hopping
spread spectrum (TH SS) systems. The proposed design of waveforms optimizes the
anti-jamming (AJ) performance of TH SS systems by minimizing the correlation
between the template and STJ signals, in which the problem of waveform
optimization is simplified by employing a finite number of rectangular pulses.
The simplification eventually makes the design of waveforms be converted into a
problem of finding eigenvalues and eigenvectors of a matrix. Simulation results
show that the waveforms designed by the proposed scheme provide us with
  performance superior not only to the conventional waveforms but also to the
clipper receiver in the mitigation of STJ. The waveforms from the proposed
design also exhibit a desirable AJ capability even when the estimated frequency
of the STJ is not perfect.


  We show that in finite dimensions, the Berezin expectation on an exterior
algebra corresponds to the trace on a Clifford algebra, the correspondence
being mediated by what is effectively a version of antinormal ordering.


  We report on a spectral principal component analysis (SPCA) of a sample of
816 quasars, selected to have small Fe II velocity shifts with spectral
coverage in the rest wavelength range 3500--5500 \AA. The sample is explicitly
designed to mitigate spurious effects on SPCA induced by Fe II velocity shifts.
We improve the algorithm of SPCA in the literature and introduce a new
quantity, \emph{the fractional-contribution spectrum}, that effectively
identifies the emission features encoded in each eigenspectrum. The first
eigenspectrum clearly records the power-law continuum and very broad Balmer
emission lines. Narrow emission lines dominate the second eigenspectrum. The
third eigenspectrum represents the Fe II emission and a component of the Balmer
lines with kinematically similar intermediate velocity widths. Correlations
between the weights of the eigenspectra and parametric measurements of line
strength and continuum slope confirm the above interpretation for the
eigenspectra. Monte Carlo simulations demonstrate the validity of our method to
recognize cross talk in SPCA and firmly rule out a single-component model for
broad Hbeta. We also present the results of SPCA for four other samples that
contain quasars in bins of larger Fe II velocity shift; similar eigenspectra
are obtained. We propose that the Hbeta-emitting region has two kinematically
distinct components: one with very large velocities whose strength correlates
with the continuum shape, and another with more modest, intermediate velocities
that is closely coupled to the gas that gives rise to Fe II emission.


  We determine the homotopy types of the independence complexes of $(n \times
4)$ and $(n \times 5)$-square grid graphs. In fact, they are homotopy
equivalent to wedges of spheres.


  In this paper we construct and classify novel Drukker-Trancanelli (DT) type
BPS Wilson loops along infinite straight lines and circles in $\mathcal N=2,3$
quiver superconformal Chern-Simons-matter theories,
Aharony-Bergman-Jafferis-Maldacena (ABJM) theory, and $\mathcal N=4$ orbifold
ABJM theory. Generally we have four classes of Wilson loops, and all of them
preserve the same supersymmetries as the BPS Gaiotto-Yin (GY) type Wilson
loops. There are several free complex parameters in the DT type BPS Wilson
loops, and for two classes of Wilson loops in ABJM theory and $\mathcal N=4$
orbifold ABJM theory there are supersymmetry enhancements at special values of
the parameters. We check that the differences of the DT type and GY type Wilson
loops are $Q$-exact with $Q$ being some supercharges preserved by both the DT
type and GY type Wilson loops. The results would be useful to calculate vacuum
expectation values of the DT type Wilson loops in matrix models if they are
still BPS quantum mechanically.


  This paper responds to suggestions that the standard approach to collective
neutrino oscillations leaves out potentially important quantum many-body
correlations. Arguments in favor of this idea have been based on calculations
that, on close scrutiny, offer no evidence either way. Inadequacies of the
usual quantum-kinetic formalism are not currently supported by the literature.


  In this paper a new design of MMIC based LNA is outlined. This design uses a
discrete 100-nm InP HEMT placed in front of an existing InP MMIC LNA to lower
the overall noise temperature of the LNA. This new approach known as the
Transistor in front of MMIC (T+MMIC) LNA, possesses a gain in excess of 40dB
and an average noise temperature of 9.4K compared to 14.5K for the equivalent
MMIC-only LNA measured across a 27-33GHz bandwidth at a physical temperature of
8K. A simple ADS model offering further insights into the operation of the LNA
is also presented and a potential radio astronomy application is discussed


  One problem of non-crystalline condensed matter (soft matter) is creating the
right equilibrium between elasticity and viscosity, referred to as
viscoelasticity. Manifestations of that can be found in everyday live, where
the viscoelasticity in a tire needs to be balanced so it is still flexible and
can dissipate shock-energy, yet hard enough for energy-saving operation.
Similarly, the cartilage in joints needs to absorb shocks while operating at
low- level friction with high elasticity. Two such examples with a biological
applicability are stiff membranes, which allow for the sliding of joints and
therefore maintain their function over the lifetime of the corresponding
individual (decades) and the softening of cell membranes, for example for
antimicrobial effects by dissolution in the case of bacteria (seconds). While
the first should allow for low- friction operation at high elasticity, in the
second scenario energy dissipated into the membrane eventually leads to
membrane destruction. Here we address the intrinsic difference between these
two types of membranes, differing in stiffness and displaying different
relaxation behavior on the nanosecond time scale. The harder membranes show
additional elastic modes, capillary waves, that indicate the high degree of
elasticity necessary for instance in cartilage or red blood cells. The energy
of these modes is in the order of 1 micro-eV. As model systems we chose a hard
phospholipidmembrane of SoyPC lipids and a D2O/C10E4/decane microemulsion
system representing soft surfactant membranes. Our results help to explain
properties observed for many membranes in nature, where hard membranes
lubricate joints or stay intact as red blood particles in tiniest capillaries,
both with extremely long lifetimes. Contrarily, softened membranes can be
destroyed easily under little shear stress within seconds.


  Seymour Second Neighborhood Conjecture (SSNC) asserts that every finite
oriented graph has a vertex whose second out-neighborhood is at least as large
as its first out-neighborhood. Such a vertex is called a Seymour vertex. A
digraph $D = (V, E)$ is $k$-anti-transitive if for every pair of vertices $u, v
\in V$, the existence of a directed path of length $k$ from $u$ to $v$ implies
that $(u, v) \notin E$. An $m$-free digraph is digraph having no directed
cycles with length at most $m$. In this paper, we prove that if $D$ is
$k$-anti-transitive and $(k-4)$-free digraph, then $D$ has a Seymour vertex. As
a consequence, a special case of Caccetta-Haggkvist Conjecture holds on
7-anti-transitive oriented graphs. This work extends recently known results.


  I present an overview of the ridge phenomenon in proton-proton and
proton-lead collisions. This novel collimation between rapidity separated
hadron pairs is a consequence of non-linear gluon dynamics within the small-x
wave-function of the colliding hadrons.


  We study optical cycling in the polar free radical calcium monohydroxide
(CaOH) and establish an experimental path towards scattering $\sim$$10^4$
photons. We report rovibronic branching ratio measurements with precision at
the $\sim10^{-4}$ level and observe weak symmetry-forbidden decays to bending
modes with non-zero vibrational angular momentum. Calculations are in excellent
agreement with these measurements and predict additional decay pathways.
Additionally, we perform high-resolution spectroscopy of the
$\widetilde{\text{X}}\,^2\Sigma^+(12^00)$ and
$\widetilde{\text{X}}\,^2\Sigma^+(12^20)$ hybrid vibrational states of CaOH.
These advances establish a path towards radiative slowing, 3D magneto-optical
trapping, and sub-Doppler cooling of CaOH.


  We present the X-ray point source population of NGC 7457 based on 124 ks of
Chandra observations. Previous deep Chandra observations of low mass X-ray
binaries (LMXBs) in early-type galaxies have typically targeted the large
populations of massive galaxies. NGC 7457 is a nearby, early-type galaxy with a
stellar luminosity of $1.7\times10^{10} L_{K\odot}$, allowing us to investigate
the populations in a relatively low mass galaxy. We classify the detected X-ray
sources into field LMXBs, globular cluster LMXBs, and background AGN based on
identifying optical counterparts in new HST/ACS images. We detect 10 field
LMXBs within the $r_{ext}$ ellipse of NGC 7457 (with semi-major axis $\sim$ 9.1
kpc, ellipticity = 0.55). The corresponding number of LMXBs with
$L_{x}>2\times10^{37}erg/s$ per stellar luminosity is consistent with that
observed in more massive galaxies, $\sim 7$ per $10^{10} L_{K\odot}$. We detect
a small globular cluster population in these HST data and show that its colour
distribution is likely bimodal and that its specific frequency is similar to
that of other early type galaxies. However, no X-ray emission is detected from
any of these clusters. Using published data for other galaxies, we show that
this non-detection is consistent with the small stellar mass of these clusters.
We estimate that 0.11 (and 0.03) LMXBs are expected per $10^{6}M_{\odot}$ in
metal-rich (and metal-poor) globular clusters. This corresponds to 1100 (and
330) LMXBs per $10^{10} L_{K\odot}$, highlighting the enhanced formation
efficiency of LMXBs in globular clusters. A nuclear X-ray source is detected
with $L_{x}$ varying from $2.8-6.8\times10^{38}erg/s$. Combining this $L_{x}$
with a published dynamical mass estimate for the central SMBH in NGC 7457, we
find that $L_{x}/L_{Edd}$ varies from $0.5-1.3\times10^{-6}$.


  The problem of determining the thermomechanical characteristics of the system
of closely spaced bodies considered by many authors. For scalar problems, such
as problems of heat, electrostatic, etc., the localization effect was found (so
called Tamm's shielding effect), which consists in the fact that in a system of
closely spaced highly conductive bodies, most energy is localized in the region
between adjacent bodies. We can assume that the localization of energy is a
general property of closely spaced bodies. The aim is to study the effect of
localization of energy in a system of closely spaced rigid bodies in an elastic
medium.


  Atomic collapse in graphene nanoribbons behaves in a fundamentally different
way as compared to monolayer graphene, due to the presence of multiple energy
bands and the effect of edges. For armchair nanoribbons we find that bound
states gradually transform into atomic collapse states with increasing impurity
charge. This is very different in zig-zag nanoribbons where multiple
quasi-one-dimensional \emph{bound states} are found that originates from the
zero energy zig-zag edge states. They are a consequence of the flat band and
the electron distribution of these bound states exhibits two peaks. The lowest
energy edge state transforms from a bound state into an atomic collapse
resonance and shows a distinct relocalization from the edge to the impurity
position with increasing impurity charge.


  Probabilistic models with hierarchical-latent-variable structures provide
state-of-the-art results amongst non-autoregressive, unsupervised density-based
models. However, the most common approach to training such models based on
Variational Autoencoders (VAEs) often fails to leverage deep-latent
hierarchies; successful approaches require complex inference and optimisation
schemes. Optimal Transport is an alternative, non-likelihood-based framework
for training generative models with appealing theoretical properties, in
principle allowing easier training convergence between distributions. In this
work we propose a novel approach to training models with deep-latent
hierarchies based on Optimal Transport, without the need for highly bespoke
models and inference networks. We show that our method enables the generative
model to fully leverage its deep-latent hierarchy, avoiding the well known
"latent variable collapse" issue of VAEs; therefore, providing qualitatively
better sample generations as well as more interpretable latent representation
than the original Wasserstein Autoencoder with Maximum Mean Discrepancy
divergence.


  Neighborhood-prime labeling is a variation of prime labeling. A labeling
$f:V(G) \to [|V(G)|]$ is a neighborhood-prime labeling if for each vertex $v\in
V(G)$ with degree greater than $1$, the greatest common divisor of the set of
labels in the neighborhood of $v$ is $1$. In this paper, we introduce
techniques for finding neighborhood-prime labelings based on the Hamiltonicity
of the graph, by using conditions on possible degrees of vertices, and by
examining a neighborhood graph. In particular, classes of graphs shown to be
neighborhood-prime include all generalized Petersen graphs, grid graphs of any
size, and lobsters given restrictions on the degree of the vertices. In
addition, we show that almost all graphs and almost all regular graphs have are
neighborhood-prime, and we find all graphs of order $10$ or less that have a
neighborhood-prime labeling. We give several conjectures for future work in
this area.


  The well-known Batty's theorem states that if a $C_0$-semigroup $T(t)$ is
bounded and the spectrum of the generator $A$ is contained in the open
left-half plane of $\mathbb{C}$, then $\|T(t)A^{-1}\|$ tends to $0$. This can
be thought of as a particular case of a more general property that, for
$\omega_0>-\infty$ and $(\omega_0+i\mathbb{R})\cap \sigma(A)=\emptyset$ it
holds $\|T(t)(A-\omega_0 I)^{-1}\|/\|T(t)\|$ tends to 0. We show that it is
true for $\|T(t)\|$ regular enough, however we give examples of unbounded
semigroups, with the spectrum of the generator not contained in the open
left-half plane of $\mathbb{C}$, with the above property. Moreover we give a
more general sufficient condition for this property to hold, thus extending
Batty's theorem.


  We study constrained clustering, where constraints guide the clustering
process. In existing works, two categories of constraints have been widely
explored, namely pairwise and cardinality constraints. Pairwise constraints
enforce the cluster labels of two instances to be the same (must-link
constraints) or different (cannot-link constraints). Cardinality constraints
encourage cluster sizes to satisfy a user-specified distribution. Most existing
constrained clustering models can only utilize one category of constraints at a
time. We enforce the above two categories into a unified clustering model
starting with the integer program formulation of the standard K-means. As the
two categories provide different useful information, utilizing both allow for
better clustering performance. However, the optimization is difficult due to
the binary and quadratic constraints in the unified formulation. To solve this,
we utilize two techniques: equivalently replacing the binary constraints by the
intersection of two continuous constraints; the other is transforming the
quadratic constraints into bi-linear constraints by introducing extra
variables. We derive an equivalent continuous reformulation with simple
constraints, which can be efficiently solved by Alternating Direction Method of
Multipliers. Extensive experiments on both synthetic and real data demonstrate
when: (1) utilizing a single category of constraint, the proposed model is
superior to or competitive with SOTA constrained clustering models, and (2)
utilizing both categories of constraints jointly, the proposed model shows
better performance than the case of the single category. The experiments show
that the proposed method exploits the constraints to achieve perfect clustering
performance with improved clustering to 2%-5% in classical clustering metrics,
e.g. Adjusted Random, Mirkin's, and Huber's, indices outerperfomring other
methods.


  At very large tilt of the magnetic (B) field with respect to the plane of a
two-dimensional electron system the transport in the integer quantum Hall
regime at $\nu$ = 4, 6, and 8 becomes strongly anisotropic. At these filling
factors the usual {\em deep minima} in the magneto-resistance occur for the
current flowing {\em perpendicular} to the in-plane B field direction but
develop into {\em strong maxima} for the current flowing {\em parallel} to the
in-plane B field. The origin of this anisotropy is unknown but resembles the
recently observed anisotropy at half-filled Landau levels.


  Applications in quantum information theory and quantum tomography have raised
current interest in complex Hadamard matrices. In this note we investigate the
connection between tiling Abelian groups and constructions of complex Hadamard
matrices. First, we recover a recent very general construction of complex
Hadamard matrices due to Dita via a natural tiling construction. Then we find
some necessary conditions for any given complex Hadamard matrix to be
equivalent to a Dita-type matrix. Finally, using another tiling construction,
due to Szabo, we arrive at new parametric families of complex Hadamard matrices
of order 8, 12 and 16, and we use our necessary conditions to prove that these
families do not arise with Dita's construction. These new families complement
the recent catalogue of complex Hadamard matrices of small order.


  We establish a new version of the stochastic Strichartz estimate for the
stochastic convolution driven by jump noise which we apply to the stochastic
nonlinear Schr\"{o}dinger equation with nonlinear multiplicative jump noise in
the Marcus canonical form. With the help of the deterministic Strichartz
estimates, we prove the existence and uniqueness of a global solution to
stochastic nonlinear Schr\"{o}dinger equation in $L^2(\RR^n)$ with either
focusing or defocusing nonlinearity in the full subcritical range of exponents
as in the deterministic case.


  We show that all CP violation in the MSSM could originate in the
supersymmetry breaking sector rather than the CKM matrix, and discuss the
important consequences for $B$-physics.


  The Computer-Assisted Diagnosis systems could save workloads and give
objective diagnostic to ophthalmologists. At first, feature extraction is a
fundamental step. One of these retinal features is the fovea. The fovea is a
small fossa on the fundus. The main vessels diverge from the optic nerve head
and follow a specific course that can be geometrically modeled as a parabola,
with a common vertex inside the optic nerve head and the fovea located along
the apex of this parabola curve. Therefore, based on this assumption, the main
retinal blood vessels are segmented and fitted to a parabolic model. With
respect to the core vascular structure, we can thus detect fovea in the fundus
images. For the vessel segmentation, our algorithm addresses the image locally
where homogeneity of features is more likely to occur. The algorithm is
composed of 4 steps: multi-overlapping windows, local Radon transform, vessel
validation, and parabolic fitting. In order to extract blood vessels,
sub-vessels should be extracted in local windows. The high contrast between
blood vessels and image background in the images cause the vessels to be
associated with peaks in the Radon space. The largest vessels, using a high
threshold of the Radon transform, determine the main course or overall
configuration of the blood vessels which when fitted to a parabola, leads to
the future localization of the fovea. In effect, with an accurate fit, the
fovea normally lies along the slope joining the vertex and the focus. The
darkest region along this line is indicative of the fovea. To evaluate our
method, we used 220 fundus images from a rural database (MUMS-DB) and one
public one (DRIVE). The results show that among 20 images of the first public
database (DRIVE) we detected fovea in 85\% of them. Also for the MUMS-DB
database among 200 images, we detect fovea correctly in 83% on them.


  Velocity anisotropy induced by MHD turbulence is investigated using
computational simulations and molecular line observations of the Taurus
molecular cloud. A new analysis method is presented to evaluate the degree and
angle of velocity anisotropy using spectroscopic imaging data of interstellar
clouds. The efficacy of this method is demonstrated on model observations
derived from three dimensional velocity and density fields from the set of
numerical MHD simulations that span a range of magnetic field strengths. The
analysis is applied to 12CO J=1-0 imaging of a sub-field within the Taurus
molecular cloud. Velocity anisotropy is identified that is aligned within 10
degrees of the mean local magnetic field direction derived from optical
polarization measurements. Estimated values of the field strength based on
velocity anisotropy are consistent with results from other methods. When
combined with new column density measurements for Taurus, our magnetic field
strength estimate indicates that the envelope of the cloud is magnetically
subcritical. These observations favor strong MHD turbulence within the low
density, sub-critical, molecular gas substrate of the Taurus cloud.


  We study simple examples of ensemble-averaged holography in free compact
boson CFTs with rational values of the radius squared. These well-known
rational CFTs have an extended chiral algebra generated by three currents. We
consider the modular average of the vacuum character in these theories, which
results in a weighted average over all modular invariants. In the simplest
case, when the chiral algebra is primitive (in a sense we explain), the weights
in this ensemble average are all equal. In the non-primitive case the ensemble
weights are governed by a semigroup structure on the space of modular
invariants.
  These observations can be viewed as evidence for a holographic duality
between the ensemble of CFTs and an exotic gravity theory based on a compact
$U(1) \times U(1)$ Chern-Simons action. In the bulk description, the extended
chiral algebra arises from soliton sectors, and including these in the path
integral on thermal AdS$_3$ leads to the vacuum character of the chiral
algebra. We also comment on wormhole-like contributions to the multi-boundary
path integral.


  The exact suppression of backscattering from rotationally symmetric objects
requires dual symmetric materials where ${\epsilon_r} = {\mu_r}$. This prevents
their design at many frequency bands, including the optical one, because
magnetic materials are not available. Electromagnetically small non-magnetic
spheres of large permittivity offer an alternative. They can be tailored to
exhibit balanced electric and magnetic dipole polarizabilities, which result in
approximate zero backscattering. In this case, the effect is inherently
narrowband. Here, we put forward a different alternative that allows broadband
functionality: Electromagnetically large spheres made from low permittivity
materials. The effect occurs in a parameter regime that approaches the trivial
${\epsilon_r} \to {\mu_r} =1$ case, where approximate duality is met in a
weakly wavelength dependence fashion. Despite the low permittivity, the overall
scattering response of the spheres is still significant. Radiation patterns
from these spheres are shown to be highly directive across an octave spanning
band. The effect is analytically and numerically shown using the Mie
coefficients.


  We propose a non-intrusive Deep Learning-based Reduced Order Model (DL-ROM)
capable of capturing the complex dynamics of mechanical systems showing inertia
and geometric nonlinearities. In the first phase, a limited number of high
fidelity snapshots are used to generate a POD-Galerkin ROM which is
subsequently exploited to generate the data, covering the whole parameter
range, used in the training phase of the DL-ROM. A convolutional autoencoder is
employed to map the system response onto a low-dimensional representation and,
in parallel, to model the reduced nonlinear trial manifold. The system dynamics
on the manifold is described by means of a deep feedforward neural network that
is trained together with the autoencoder. The strategy is benchmarked against
high fidelity solutions on a clamped-clamped beam and on a real micromirror
with softening response and multiplicity of solutions. By comparing the
different computational costs, we discuss the impressive gain in performance
and show that the DL-ROM truly represents a real-time tool which can be
profitably and efficiently employed in complex system-level simulation
procedures for design and optimisation purposes.


  The effect of the collinear photon radiation by charged particles is
considered in the second order of the perturbation theory. Double and single
photon radiation is evaluated. The corresponding radiation factors are
obtained. The QED renormalization group approach is exploited in the
next-to-leading order. The results are suited to perform a systematic treatment
of the second order next-to-leading logarithmic radiative corrections to
various processes either analytically or numerically.


  Adiabatic quantum computing enables the preparation of many-body ground
states. This is key for applications in chemistry, materials science, and
beyond. Realisation poses major experimental challenges: Direct analog
implementation requires complex Hamiltonian engineering, while the digitised
version needs deep quantum gate circuits. To bypass these obstacles, we suggest
an adiabatic variational hybrid algorithm, which employs short quantum circuits
and provides a systematic quantum adiabatic optimisation of the circuit
parameters. The quantum adiabatic theorem promises not only the ground state
but also that the excited eigenstates can be found. We report the first
experimental demonstration that many-body eigenstates can be efficiently
prepared by an adiabatic variational algorithm assisted with a multi-qubit
superconducting coprocessor. We track the real-time evolution of the ground and
exited states of transverse-field Ising spins with a fidelity up that can reach
about 99%.


  We present the first joint observation of a small microflare in X-rays with
the Nuclear Spectroscopic Telescope ARray (NuSTAR), UV with the Interface
Region Imaging Spectrograph (IRIS) and EUV with the Solar Dynamics
Observatory/Atmospheric Imaging Assembly (SDO/AIA). These combined observations
allows us to study the microflare's hot coronal and cooler
chromospheric/transition region emission. This small microflare peaks from
SOL2016-07-26T23:35 to 23:36UT, in both NuSTAR, SDO/AIA and IRIS. Spatially
this corresponds to a small loop visible in the SDO/AIA Fe XVIII emission,
which matches a similar structure lower in the solar atmosphere seen by IRIS in
SJI1330{\AA} and 1400\AA. The NuSTAR emission in both 2.5-4 keV and 4-6 keV, is
located in a small source at this loop location. The IRIS slit was over the
microflaring loop, and fits show little change in Mg II but do show intensity
increases, slight width enhancements and redshifts in Si IV andO IV, indicating
that this microflare had most significance in and above the upper chromosphere.
The NuSTAR microflare spectrum is well fitted by a thermal component of 5.8MK
and $2.3\times10^{44}$ cm$^{-3}$, which corresponds to a thermal energy of
$10^{26}$ erg, making it considerably smaller than previously studied X-ray
microflares. No non-thermal emission was detected but this could be due to the
limited effective exposure time of the observation. This observation shows that
even ordinary features seen in UV and EUV, can remarkably have a higher energy
component that is clear in X-rays.


  In this article I generalise previous computations (by K. Kato, T. Hara and
myself) of K_1 (only up to p-power torsion) of p-adic group rings of finite
non-abelian p-groups in terms of p-adic group rings of abelian subquotients of
the group. Such computation have applications in non-commutative Iwasawa theory
due to a strategy proposed by D. Burns, K. Kato (and a modification by T. Hara)
for deducing non-commutative main conjectures from commutative main conjectures
and certain congruences between special L-values. However, I do not say
anything about Iwasawa theory in this article. The details of applications in
Iwasawa theory will be presented in a separate paper.


  In this note we show that the maximum number of edges in a $3$-uniform
hypergraph without a Berge cycle of length four is at most
$(1+o(1))\frac{n^{3/2}}{\sqrt{10}}$. This improves earlier estimates by
Gy\H{o}ri and Lemons and by F\"uredi and \"Ozkahya.


  We present an effective model, which is an extension of the usual linear
sigma model, that contains a low energy multiplet for every hadronic particle
type. These multiplets are a scalar nonet, a pseudoscalar nonet, a vector
nonet, an axialvector nonet, a baryon octet and a baryon decuplet. Tree level
baryon masses and possible two body decuplet decays are calculated. The baryon
masses are generated through spontaneous symmetry breaking. The calculated
quantities are used to determine the model parameters through a multiparametric
minimalization process, which compares the calculated physical quantities with
their experimental values. We found that the calculated quantities are in good
agreement with the experimental data.


  We study particle current in a recently proposed model for coherent quantum
transport. In this model a system connected to mesoscopic Fermi reservoirs
(meso-reservoir) is driven out of equilibrium by the action of super reservoirs
thermalized to prescribed temperatures and chemical potentials by a simple
dissipative mechanism described by the Lindblad equation. We compare exact
(numerical) results with theoretical expectations based on the Landauer formula


  The Planck collaboration has measured the temperature and polarization of the
cosmic microwave background well enough to determine the locations of eight
peaks in the temperature (TT) power spectrum, five peaks in the polarization
(EE) power spectrum and twelve extrema in the cross (TE) power spectrum. The
relative locations of these extrema give a striking, and beautiful,
demonstration of what we expect from acoustic oscillations in the plasma; e.g.,
that EE peaks fall half way between TT peaks. We expect this because the
temperature map is predominantly sourced by temperature variations in the last
scattering surface, while the polarization map is predominantly sourced by
gradients in the velocity field, and the harmonic oscillations have temperature
and velocity 90 degrees out of phase. However, there are large differences in
expectations for extrema locations from simple analytic models vs. numerical
calculations. Here we quantitatively explore the origin of these differences in
gravitational potential transients, neutrino free-streaming, the breakdown of
tight coupling, the shape of the primordial power spectrum, details of the
geometric projection from three to two dimensions, and the thickness of the
last scattering surface. We also compare the peak locations determined from
Planck measurements to expectations under the $\Lambda$CDM model. Taking into
account how the peak locations were determined, we find them to be in
agreement.


  Decreasing magnetic resonance (MR) image acquisition times can potentially
make MR examinations more accessible. Prior arts including the deep learning
models have been devoted to solving the problem of long MRI imaging time.
Recently, deep generative models have exhibited great potentials in algorithm
robustness and usage flexibility. Nevertheless, none of existing schemes can be
learned or employed to the k-space measurement directly. Furthermore, how do
the deep generative models work well in hybrid domain is also worth being
investigated. In this work, by taking advantage of the deep energy-based
models, we propose a k-space and image domain collaborative generative model to
comprehensively estimate the MR data from under-sampled measurement.
Experimental comparisons with the state-of-the-arts demonstrated that the
proposed hybrid method has less error in reconstruction accuracy and is more
stable under different acceleration factors


  Let $1\le p<q\le\infty$ and let $T$ be a subadditive operator acting on
  $L^p$ and $L^q$. We prove that $T$ is bounded on the Orlicz space
  $L^\phi$, where $\phi^{-1}(u)=u^{1/p}\rho(u^{1/q-1/p})$ for some concave
function $\rho$ and \[ \|T\|_{L^\phi\to L^\phi}\le C\max\{\|T\|_{L^p\to
L^p},\|T\|_{L^q\to L^q}\}. \] The interpolation constant $C$, in general, is
less than 4 and, in many cases, we can give much better estimates for $C$. In
particular, if $p=1$ and $q=\infty$, then the classical Orlicz interpolation
theorem holds for subadditive operators with the interpolation constant C=1.
These results generalize our results for linear operators obtained in
\cite{KM01}.


  We consider the KdV equation on a circle and its Lie-Poisson reconstruction,
which is reminiscent of an equation of motion for fluid particles. For periodic
waves, the stroboscopic reconstructed motion is governed by an iterated map
whose Poincar\'e rotation number yields the drift velocity. We show that this
number has a geometric origin: it is the sum of a dynamical phase, a Berry
phase, and an "anomalous phase". The last two quantities are universal: they
are solely due to the underlying Virasoro group structure. The Berry phase, in
particular, was previously described in [arXiv:1703.06142] for two-dimensional
conformal field theories, and follows from adiabatic deformations produced by
the propagating wave. We illustrate these general results with cnoidal waves,
for which all phases can be evaluated in closed form thanks to a uniformizing
map that we derive. Along the way, we encounter "orbital bifurcations"
occurring when a wave becomes non-uniformizable: there exists a resonance
wedge, in the cnoidal parameter space, where particle motion is locked to the
wave, while no such locking occurs outside of the wedge.


  Large Language Models (LLMs) are essential tools to collaborate with users on
different tasks. Evaluating their performance to serve users' needs in
real-world scenarios is important. While many benchmarks have been created,
they mainly focus on specific predefined model abilities. Few have covered the
intended utilization of LLMs by real users. To address this oversight, we
propose benchmarking LLMs from a user perspective in both dataset construction
and evaluation designs. We first collect 1846 real-world use cases with 15 LLMs
from a user study with 712 participants from 23 countries. These self-reported
cases form the User Reported Scenarios(URS) dataset with a categorization of 7
user intents. Secondly, on this authentic multi-cultural dataset, we benchmark
10 LLM services on their efficacy in satisfying user needs. Thirdly, we show
that our benchmark scores align well with user-reported experience in LLM
interactions across diverse intents, both of which emphasize the overlook of
subjective scenarios. In conclusion, our study proposes to benchmark LLMs from
a user-centric perspective, aiming to facilitate evaluations that better
reflect real user needs. The benchmark dataset and code are available at
https://github.com/Alice1998/URS.


  The paper contains a complete theory of factors for ray representations
acting in a Hilbert bundle, which is a generalization of the known Bargmann's
theory. With the help of it we have reformulated the standard quantum theory
such that the gauge freedom emerges naturally from the very nature of quantum
laws. The theory is of primary importance in the investigations of covariance
(in contradistinction to symmetry) of a quantum theory which possesses a
nontrivial gauge freedom. In that case the group in question is not any
symmetry group but it is a covariance group only - that case which has not been
deeply investigated. It is shown on the paper that the factor of its
representation depends on space and time when the system in question possesses
a gauge freedom. In the nonrelativistic theories the factor depends on the time
only. In the relativistic theory the Hilbert bundle is over the spacetime in
the nonrelativistic one it is over the time.
  We explain two applications of this generalization: in a theory of a quantum
particle in the nonrelativistic limit and in the quantum electrodynamics.


  We prove a quenched central limit theorem for balanced random walks in time
dependent ergodic random environments which is not necessarily
nearest-neigbhor. We assume that the environment satisfies appropriate
ergodicity and ellipticity conditions. The proof is based on the use of a
maximum principle for parabolic difference operators.


  In this letter we propose a reduction of the $H_0$ tension puzzle by means of
a theory of minimally modified gravity which is dubbed VCDM. After confronting
the theory with the experiments, we find that the data allow for a low-redshift
transition in the expansion history of the universe at either $z\simeq 0.3 $ or
$z \simeq 1.8\,$, corresponding to one of the two local minima of the total
$\chi^2$. From the bestfit values the total fitness parameter is improved by
$\Delta \chi^2 \simeq 12$, for the data set considered. We then infer the local
Hubble expansion rate today within this theory by means of low redshift
Pantheon data. The resulting local Hubble expansion rate today is
$H^{\rm{loc}}_0=73.6\pm1.4$. We find the tension is reduced within the VCDM
theory.


  We present a cut elimination argument that witnesses the conservativity of
the compositional axioms for truth (without the extended induction axiom) over
any theory interpreting a weak subsystem of arithmetic. In doing so we also fix
a critical error in Halbach's original presentation. Our methods show that the
admission of these axioms determines a hyper-exponential reduction in the size
of derivations of truth-free statements.


  Parsing accuracy using efficient greedy transition systems has improved
dramatically in recent years thanks to neural networks. Despite striking
results in dependency parsing, however, neural models have not surpassed
state-of-the-art approaches in constituency parsing. To remedy this, we
introduce a new shift-reduce system whose stack contains merely sentence spans,
represented by a bare minimum of LSTM features. We also design the first
provably optimal dynamic oracle for constituency parsing, which runs in
amortized O(1) time, compared to O(n^3) oracles for standard dependency
parsing. Training with this oracle, we achieve the best F1 scores on both
English and French of any parser that does not use reranking or external data.


  We investigate the recently proposed nonlinear equation for the unintegrated
gluon distribution function which includes the subleading effects at small $x$.
We obtained numerically the solution to this equation in $(x,k)$ space, and
also the integrated gluon density. The subleading effects affect strongly the
normalization and the $x$ and $k$ dependence of the gluon distribution. We show
that the saturation scale $Q_s(x)$, which is obtained from this model, is
consistent with the one used in the saturation model by Golec-Biernat and
W\"usthoff. We also estimate the nonlinear effects by looking at the relative
normalization of the solutions to the linear and nonlinear equations. It turns
out that the differences are quite large even in the nominally dilute regime,
that is when $Q^2 \gg Q_s^2$. Finally, we calculate the dipole-nucleon cross
section.


  To accurately analyze changes of anatomical structures in longitudinal
imaging studies, consistent segmentation across multiple time-points is
required. Existing solutions often involve independent registration and
segmentation components. Registration between time-points is used either as a
prior for segmentation in a subsequent time point or to perform segmentation in
a common space. In this work, we propose a novel hybrid convolutional neural
network (CNN) that integrates segmentation and registration into a single
procedure. We hypothesize that the joint optimization leads to increased
performance on both tasks. The hybrid CNN is trained by minimizing an
integrated loss function composed of four different terms, measuring
segmentation accuracy, similarity between registered images, deformation field
smoothness, and segmentation consistency. We applied this method to the
segmentation of white matter tracts, describing functionally grouped axonal
fibers, using N=8045 longitudinal brain MRI data of 3249 individuals. The
proposed method was compared with two multistage pipelines using two existing
segmentation methods combined with a conventional deformable registration
algorithm. In addition, we assessed the added value of the joint optimization
for segmentation and registration separately. The hybrid CNN yielded
significantly higher accuracy, consistency and reproducibility of segmentation
than the multistage pipelines, and was orders of magnitude faster. Therefore,
we expect it can serve as a novel tool to support clinical and epidemiological
analyses on understanding microstructural brain changes over time.


  We have measured the spin injection efficiency and spin lifetime in
Co$_2$FeSi/$n$-GaAs lateral nonlocal spin valves from 20 to 300 K. We observe
large ($\sim$40 $\mu$V) spin valve signals at room temperature and injector
currents of $10^3~$A/cm$^2$, facilitated by fabricating spin valve separations
smaller than the 1 $\mu$m spin diffusion length and applying a forward bias to
the detector contact. The spin transport parameters are measured by comparing
the injector-detector contact separation dependence of the spin valve signal
with a numerical model accounting for spin drift and diffusion. The apparent
suppression of the spin injection efficiency at the lowest temperatures
reflects a breakdown of the ordinary drift-diffusion model in the regime of
large spin accumulation. A theoretical calculation of the D'yakonov-Perel spin
lifetime agrees well with the measured $n$-GaAs spin lifetime over the entire
temperature range.


  Traditional Lp spaces are fundamental in functional analysis, demarcated by
the relationship $1/p + 1/q = 1$. This research pioneers the concept of
$\theta$-Lebesgue space, stemming from a simultaneous weakening of both the
classical $L_p$ relation and its $\theta$-variant, $1/(\theta(p)) +
1/(\theta(q)) = 1$. This conceptual shift addresses a gap in existing
mathematical frameworks, aiming to create a space that encompasses a broader
range of mathematical purpose. The primary objective is to rigorously demarcate
the $\theta$-Lebesgue space within this new context, explore its foundational
properties, and articulate its theoretical significance in the realm of
functional analysis.


  If the baryon asymmetry of the Universe is produced by leptogenesis, CP
violation is required in the lepton sector. In the seesaw extension of the
Standard Model with three hierarchical right-handed neutrinos, we show that the
baryon asymmetry is insensitive to the PMNS phases: thermal leptogenesis can
work for any value of the observable phases. This result was well-known when
there are no flavour effects in leptogenesis; we show that it remains true when
flavour effects are included.


  In the Type II superstring the 4-point function for massless NS-NS bosons at
one-loop is well known [1][14]. The overall constant factor in this amplitude
is very important because it needs to satisfy the unitarity and S-duality
conditions [14]. This coefficient has not been computed in the pure spinor
formalism due to the difficulty to solve the integrals on the pure spinors
space. In this paper we compute it by using the non-minimal pure spinor
formalism and we will show that the answer is in perfect agreement with the one
given in [14].