  The discovery of 1I/2017 U1 ('Oumuamua) has provided the first glimpse of a
planetesimal born in another planetary system. This interloper exhibits a
variable colour within a range that is broadly consistent with local small
bodies such as the P/D type asteroids, Jupiter Trojans, and dynamically excited
Kuiper Belt Objects. 1I/'Oumuamua appears unusually elongated in shape, with an
axial ratio exceeding 5:1. Rotation period estimates are inconsistent and
varied, with reported values between 6.9 and 8.3 hours. Here we analyse all
available optical photometry reported to date. No single rotation period can
explain the exhibited brightness variations. Rather, 1I/'Oumuamua appears to be
in an excited rotational state undergoing Non-Principal Axis (NPA) rotation, or
tumbling. A satisfactory solution has apparent lightcurve frequencies of 0.135
and 0.126 hr-1 and implies a longest-to-shortest axis ratio of 5:1, though the
available data are insufficient to uniquely constrain the true frequencies and
shape. Assuming a body that responds to NPA rotation in a similar manner to
Solar System asteroids and comets, the timescale to damp 1I/'Oumuamua's
tumbling is at least a billion years. 1I/'Oumuamua was likely set tumbling
within its parent planetary system, and will remain tumbling well after it has
left ours.


  We provide some additional evidence in favour of the strong - weak coupling
duality between the SO(32) heterotic and type I superstring theories by
comparing terms quartic in the gauge field strength in their low-energy
effective actions. We argue that these terms should not receive higher-loop
string corrections so that duality should relate the leading-order perturbative
coefficients in the two theories. In particular, we demonstrate that the
coefficient of the $F^4$-term in the one-loop (torus) part of the SO(32)
heterotic string action is exactly the same as the coefficient of the
$F^4$-term in the tree-level (disc) part of the type I action.


  We construct Jordan arcs of prescribed conformal dimension which are minimal
for conformal dimension. These curves are used to design fractal rugs, similar
to Rickman's rug, that are also minimal for conformal dimension. These fractal
rugs could potentially settle a standing conjecture regarding the existence of
metric spaces of prescribed topological conformal dimension.


  Solvent-solute interactions in precursor solutions of lead halide perovskites
(LHP) critically impact the quality of solution-processed materials, as they
lead to the formation of a variety of poly-iodoplumbates that act as building
blocks for LHP. The formation of [PbI$_{2+n}$]$^{n-}$ complexes is often
expected in diluted solutions while coordination occurring at high
concentrations is not well understood yet. In a combined \textit{ab initio} and
experimental work, we demonstrate that the optical spectra of the
quasi-one-dimensional iodoplumbate complexes PbI$_2$(DMSO)$_4$,
Pb$_2$I$_4$(DMSO)$_6$, and Pb$_3$I$_6$(DMSO)$_8$ formed in dimethyl sulfoxide
solutions are compatible with the spectral fingerprints measured at high
concentrations of lead iodide. This finding suggests that the formation of
polynuclear lead-halide complexes should be accounted for in the interpretation
of optical spectra of LHP precursor solutions.


  The holographic dual of self gravitating Julia-Zee dyon is discussed. It is
shown that the dual field theory is generally a field theory with a vortex
condensate. The vacuum expectation values of the dual operators, as functions
of the sources in the field theory, are studied in a class of bulk solutions.
In these solutions the sign of the vacuum expectation values of the dual
operators change, by changing the sources in the model.


  The solution to the Poisson equation arising from the spectral element
discretization of the incompressible Navier-Stokes equation requires robust
preconditioning strategies. One such strategy is multigrid. To realize the
potential of multigrid methods, effective smoothing strategies are needed.
Chebyshev polynomial smoothing proves to be an effective smoother. However,
there are several improvements to be made, especially at the cost of symmetry.
For the same cost per iteration, a full V-cycle with $k$ order Chebyshev
polynomial smoothing may be substituted with a half V-cycle with order $2k$
Chebyshev polynomial smoothing, wherein the smoother is omitted on the up-leg
of the V-cycle. The choice of omitting the post-smoother in favor of higher
order Chebyshev pre-smoothing is shown to be advantageous in cases where the
multigrid approximation property constant, $C$, is large. Results utilizing
Lottes's fourth-kind Chebyshev polynomial smoother are shown. These methods
demonstrate substantial improvement over the standard Chebyshev polynomial
smoother. The authors demonstrate the effectiveness of this scheme in
$p$-geometric multigrid, as well as a 2D model problem with finite differences.


  We generalize the known equivalence between higher order gravity theories and
scalar tensor theories to a new class of theories. Specifically, in the context
of a first order or Palatini variational principle where the metric and
connection are treated as independent variables, we consider theories for which
the Lagrangian density is a function f of (i) the Ricci scalar computed from
the metric, and (ii) a second Ricci scalar computed from the connection. We
show that such theories can be written as tensor-multi-scalar theories with two
scalar fields with the following features: (i) the two dimensional sigma-model
metric that defines the kinetic energy terms for the scalar fields has
constant, negative curvature; (ii) the coupling function determining the
coupling to matter of the scalar fields is universal, independent of the choice
of function f; and (iii) if both mass eigenstates are long ranged, then the
Eddington post-Newtonian parameter has value 1/2. Therefore in order to be
compatible with solar system experiments at least one of the mass eigenstates
must be short ranged.


  I present a new phenomenological model for the normal state transport
properties of high-Tc cuprates. In particular, I identify a form of scattering
rate that may account, qualitatively and quantitatively, for the normal state
(magneto)-transport properties of Tl2Ba2CuO6+\delta and Bi2Sr2CaCu2O8+\delta
from optimal doping through to the overdoped side of the phase diagram. The
form of the scattering rate is also consistent with features seen in
photoemission spectroscopy in Bi2Sr2CaCu2O8+\delta and offers a new intuitive
way to understand the evolution of the temperature dependence of the inverse
Hall angle with disorder and with carrier concentration.


  The paper deals with the asymptotic properties of a random jump process in a
high contrast periodic medium in $\mathbb R^d$, $d\geq 1$. We show that if the
coordinates of the random jump process in $\mathbb R^d$ are equipped with an
extra variable that characterizes the position of the process inside the
period, then the limit dynamics of this two-component process is Markov. We
describe the limit process and prove the convergence in law in the path space.
We show that the components of the limit process are coupled and derive the
evolution equation with a memory term for the spatial component of the process.
We also discuss the construction of the limit process in the $L^2$ space and
study the spectrum of the generator of the limit semigroup.


  Huang's Lemma is an important tool in CR geometry to study rigidity problems.
This paper introduces a generalization of Huang's Lemma based on the rigidity
properties of holomorphic mappings preserving certain orthogonality on
projective spaces, which is optimal for the case of partial linearity. By
exploring the intricate relationship between rigidity and Huang's Lemma, we
establish that the rigidity properties of Segre maps or proper holomorphic
mappings between generalized balls with Levi-degenerate boundaries can be
inferred from those between generalized balls with Levi-non-degenerate
boundaries by in a coordinate-free and more geometric manner.


  One of the main advantages of proposed by P. Raimondi "Crab Waist" collision
scheme is a strong suppression of betatron resonances excited by beam-beam
interaction. Some qualitative explanations with numerical examples, describing
beam-beam resonances for different collision schemes, were given in
arXiv:physics/0702033. This paper can be considered as an "appendix"
(additional illustration) to that one. We performed a number of full 2D
betatron tune scans (beam-beam simulations) for different collision schemes, so
one can easily see how the beam-beam resonances appear and disappear, depending
on the colliding conditions.


  The phase space for Hamiltonians of two degrees of freedom is usually divided
into stochastic and integrable components. Even when well into the stochastic
regime, integrable orbits may surround small stable regions or islands. The
effect of these islands on the correlation function for the stochastic
trajectories is examined. Depending on the value of the parameter describing
the rotation number for the elliptic fixed point at the center of the island,
the long-time correlation function may decay as t^-5 or exponentially, but more
commonly it decays much more slowly (roughly as t^-1). As a consequence these
small islands may have a profound effect on the properties of the stochastic
orbits. In particular, there is evidence that the evolution of a distribution
of particles is no longer governed by a diffusion equation.


  We present a supersymmetric model of leptogenesis in which the right-handed
neutrinos have weak scale masses and O(10-2-10-3) yukawa couplings. The model
employs an R-symmetry at the weak scale that forces neutrino masses to be
proportional to the gravitino mass. We predict that the lightest right-handed
neutrino decays to a displaced Higgs and neutrino and that the NLSP is
long-lived on collider scales. These could be striking signatures at the LHC
if, for instance, the right-handed neutrino is produced in a cascade decay.


  A new index for high-impact weather forecasting is introduced and assessed in
comparison with the well-established extreme forecast index (EFI). Two other
ensemble summary statistics are also included in this comparison study: the
shift-of-tail and a standardised ensemble mean anomaly. All these forecasts are
based on the same ingredients: the ensemble forecast run at the European Centre
for Medium-Range Weather Forecasts and the corresponding model climatology
derived from a set of reforecasts. The new index emerges from recent
developments in forecast verification of extreme events: it is derived as a
consistent forecast with the diagonal score, a weighted version of the
continuous ranked probability score targetting high-impact events. In this
study, we emphasise the importance of forecast discretisation for communication
purposes and decision-making. A forecast is actionable in the situation where a
user can decide to take action when a threshold is exceeded by the forecast.
Forecast verification is performed to assess both the potential skill of the
different indices as well as their specific skill as actionable forecasts.
Among the investigated actionable forecasts, the new proposed index
demonstrates the strongest discrimination power, in particular at longer lead
times, paving the way for seamless predictions of high-impact weather across
time ranges.


  We show that all nonnegative solutions of the critical semilinear elliptic
equation involving the regional fractional Laplacian are locally universally
bounded. This strongly contrasts with the standard fractional Laplacian case.
Second, we consider the fractional critical elliptic equations with nonnegative
potentials. We prove compactness of solutions provided the potentials only have
non-degenerate zeros. Corresponding to Schoen's Weyl tensor vanishing
conjecture for the Yamabe equation on manifolds, we establish a Laplacian
vanishing rate of the potentials at blow-up points of solutions.


  Recent progress in the on-surface synthesis of graphene nanoribbons (GNRs)
has given access to atomically precise narrow GNRs with tunable electronic band
gaps that makes them excellent candidates for room-temperature switching
devices such as field-effect transistors (FET). However, in spite of their
exceptional properties, significant challenges remain for GNR processing and
characterization. This contribution addresses some of the most important
challenges, including GNR fabrication scalability, substrate transfer,
long-term stability under ambient conditions and ex situ characterization. We
focus on 7- and 9-atom wide armchair graphene nanoribbons (i.e, 7-AGNR; and
9-AGNR) grown on 200 nm Au(111)/mica substrates using a high throughput system.
Transfer of both, 7- and 9-AGNRs from their Au growth sub-strate onto various
target substrates for additional characterization is accomplished utilizing a
polymer-free method that avoids residual contamination. This results in a
homogeneous GNR film morphology with very few tears and wrinkles, as examined
by atomic force microscopy. Raman spectroscopy indicates no significant
degradation of GNR quality upon substrate transfer, and reveals that GNRs have
remarkable stability under ambient conditions over a 24-month period. The
transferred GNRs are analyzed using multi-wavelength Raman spectroscopy, which
provides detailed insight into the wavelength dependence of the width-specific
vibrational modes. Finally, we characterize the optical properties of 7- and
9-AGNRs via ultra-violet-visible (UV-Vis) spectroscopy


  We address estimation of temperature for a micromechanical oscillator lying
arbitrarily close to its quantum ground state. Motivated by recent experiments,
we assume that the oscillator is coupled to a probe qubit via Jaynes-Cummings
interaction and that the estimation of its effective temperature is achieved
via quantum limited measurements on the qubit. We first consider the ideal
unitary evolution in a noiseless environment and then take into account the
noise due to non dissipative decoherence. We exploit local quantum estimation
theory to assess and optimize the precision of estimation procedures based on
the measurement of qubit population, and to compare their performances with the
ultimate limit posed by quantum mechanics. In particular, we evaluate the
Fisher information (FI) for population measurement, maximize its value over the
possible qubit preparations and interaction times, and compare its behavior
with that of the quantum Fisher information (QFI). We found that the FI for
population measurement is equal to the QFI, i.e., population measurement is
optimal, for a suitable initial preparation of the qubit and a predictable
interaction time. The same configuration also corresponds to the maximum of the
QFI itself. Our results indicate that the achievement of the ultimate bound to
precision allowed by quantum mechanics is in the capabilities of the current
technology.


  Effect of replacing the classical game object with a quantum object is
analyzed. We find this replacement requires a throughout reformation of the
framework of Game Theory. If we use density matrix to represent strategy state
of players, they are full-structured density matrices with off-diagonal
elements for the new games, while reduced diagonal density matrix will be
enough for the traditional games on classical objects. In such formalism, the
payoff function of every player becomes Hermitian Operator acting on the
density matrix. Therefore, the new game looks really like Quantum Mechanics
while the traditional game becomes Classical Mechanics.


  We describe the first known mean-field study of landing probabilities for
random walks on hypergraphs. In particular, we examine clique-expansion and
tensor methods and evaluate their mean-field characteristics over a class of
random hypergraph models for the purpose of seed-set community expansion. We
describe parameter regimes in which the two methods outperform each other and
propose a hybrid expansion method that uses partial clique-expansion to reduce
the projection distortion and low-complexity tensor methods applied directly on
the partially expanded hypergraphs.


  While polar metals are a metallic analogue of ferroelectrics, magnetic polar
metals can be considered as a metallic analogue of multiferroics. There have
been a number of attempts to integrate magnetism into a polar metal by
synthesizing new materials or heterostructures. Here we use a simple yet widely
used approach--epitaxial strain in the search for intrinsic magnetic polar
metals. Via first-principles calculations, we study strain engineering of a
ferromagnetic metallic oxide SrCoO$_3$, whose bulk form crystallizes in a cubic
structure. We find that under an experimentally feasible biaxial strain on the
$ab$ plane, collective Co polar displacements are stabilized in SrCoO$_3$.
Specifically, a compressive strain stabilizes Co polar displacements along the
$c$ axis, while a tensile strain stabilizes Co polar displacements along the
diagonal line in the $ab$ plane. In both cases, we find an intrinsic
ferromagnetic polar metallic state in SrCoO$_3$. In addition, we also find that
a sufficiently large biaxial strain ($> 4\%$) can yield a
ferromagnetic-to-antiferromagnetic transition in SrCoO$_3$. Our work
demonstrates that in addition to yielding emergent multiferroics, epitaxial
strain is also a viable approach to inducing magnetic polar metallic states in
quantum materials.


  Scattering interactions between dark matter and Standard Model states
mediated by pseudoscalars are generically challenging to uncover at direct
detection experiments due to rates suppressed by powers of the local dark
matter velocity v ~ 0.001 c. However, they may be observed in the dark
matter-induced heating of neutron stars, whose steep gravitational potentials
prevent such suppression by accelerating infalling particles to
semi-relativistic speeds. We investigate this phenomenon in the context of two
specific, self-consistent scenarios for pseudoscalars coupled to dark matter,
and compare the sensitivity of neutron star heating to bounds from direct
searches for the mediators and dark matter. The first "lighter" scenario
consists of sub-10 GeV mass dark matter mediated by an axion-like particle
(ALP), while the second "heavier" scenario has dark matter above 10 GeV
mediated by a dark pseudoscalar that mixes with a pseudoscalar from a two-Higgs
doublet (the so-called 2HDM+a model). In both frameworks, we show that imminent
measurements of neutron stars will be able to test pseudoscalar-mediated dark
matter beyond the reach of direct dark matter searches as well as bounds on the
mediators from flavor observables, beam dump experiments, and high-energy
colliders.


  As a consequence of his numerical local Langlands correspondence for $GL(n)$,
Henniart deduced the following theorem: If $F$ is a nonarchimedean local field
and if $\pi$ is an irreducible admissible representation of $GL(n,F)$, then,
after a finite sequence of cyclic base changes, the image of $\pi$ contains a
vector fixed under an Iwahori subgroup. This result was indispensable in all
proofs of the local Langlands correspondence. Scholze later gave a different
proof, based on the analysis of nearby cycles in the cohomology of the
Lubin-Tate tower.
  Let $G$ be a reductive group over $F$. Assuming a theory of stable cyclic
base change exists for $G$, we define an incorrigible supercuspidal
representation $\pi$ of $G(F)$ to be one with the property that, after any
sequence of cyclic base changes, the image of $\pi$ contains a supercuspidal
member. If F is of positive characteristic then we define $\pi$ to be pure if
the Langlands parameter attached to $\pi$ by Genestier and Lafforgue is pure in
an appropriate sense. We conjecture that no pure supercuspidal representation
is incorrigible. We prove this conjecture for $GL(n)$ and for classical groups,
using properties of standard $L$-functions; and we show how this gives rise to
a proof of Henniart's theorem and the local Langlands correspondence for
$GL(n)$ based on V. Lafforgue's Langlands parametrization, and thus independent
of point-counting on Shimura or Drinfel'd modular varieties.


  This paper presents aims at mobility improvement of flexible underwater
robots. For this purpose, a novel propulsion method using planar structural
vibration pattern is proposed, and tested on two kinds of prototypes. The
result of experiments showed the possibility of the movements for multiple
directions: forward, backward, turn, rotation, drift, and their combination.
These movements are achieved by only one structure with two actuators. The
results also indicated the possibility of driving using eigenmodes since
movements were concentrated on low driving frequency area. To investigate the
relation between movement and structural vibration pattern, we established a
simulation model.


  Some foundational results on the geometry of Lorentz-Minkowski spaces and
Finsler spacetimes are obtained. We prove that the local light cone structure
of a reversible Finsler spacetime with more than two dimensions is
topologically the same as that of Lorentzian spacetimes: at each point we have
just two strictly convex causal cones which intersect only at the origin.
Moreover, we prove a reverse Cauchy-Schwarz inequality for these spaces and a
corresponding reverse triangle inequality. The Legendre map is proved to be a
diffeomorphism in the general pseudo-Finsler case provided the dimension is
larger than two.


  A novel cesium (Cs) two-color magneto-optical trap (TC-MOT), which partially
employs the optical radiation forces due to photon scattering of the 6P3/2
(F'=5) - 7S1/2 (F"=4) excited-state transition in the Cs 6S1/2 - 6P3/2 - 7S1/2
(852 + 1470 nm) ladder-type system, has been proposed and experimentally
investigated. One of the three pairs of 852 nm cooling/trapping beams (CTBs) in
a conventional Cs MOT is replaced with a pair of the 1470 nm CTBs (type-I) or
with one 852 nm CTB plus another counter-propagating 1470 nm CTB (type-II).
Both the type-I and type-II Cs TC-MOTs can cool and trap atoms on both the red-
and blue-detuning sides of the two-photon resonance. The Cs TC-MOT demonstrated
in this work may have applications in the background-free detection of cooled
and trapped atoms, and the photon-pair sources compatible with the
ensemble-based quantum memory and the long-distance quantum communication via
optical fiber.


  Each quiver corresponds to a path semigroup, and such a path semigroup also
corresponds to an associative K-algebra over an algebraically closed field K.
Let Q be a quiver and S_Q, KQ be its path semigroup, path algebra,
respectively. In this paper, we study some properties of the congruence lattice
of S_Q. First, we show that there is a one-to-one correspondence between
congruences on S and certain algebraic ideals of KQ. Based on such a
description, we consider acyclic quivers and show that the congruence latices
of such path semigroups are strong upper semimodular but not necessarily lower
semimodular. Moreover, we provide some equivalent conditions for the congruence
lattices to be modular and distributive.


  This work adopts a Banach-valued time series framework for component-wise
estimation and prediction, from temporal correlated functional data, in
presence of exogenous variables. The strong-consistency of the proposed
functional estimator and associated plug-in predictor is formulated. The
simulation study undertaken illustrates their large-sample size properties. Air
pollutants PM10 curve forecasting, in the Haute-Normandie region (France), is
addressed by implementation of the functional time series approach presented


  We study the problem of finding all $k$-periods of a length-$n$ string $S$,
presented as a data stream. $S$ is said to have $k$-period $p$ if its prefix of
length $n-p$ differs from its suffix of length $n-p$ in at most $k$ locations.
  We give a one-pass streaming algorithm that computes the $k$-periods of a
string $S$ using $\text{poly}(k, \log n)$ bits of space, for $k$-periods of
length at most $\frac{n}{2}$. We also present a two-pass streaming algorithm
that computes $k$-periods of $S$ using $\text{poly}(k, \log n)$ bits of space,
regardless of period length. We complement these results with comparable lower
bounds.


  This study provides an account of the bulk preparation of
TlBa2Ca2Cu3O9-{\delta} (Tl-1223) superconductor at ambient pressure, and the Tc
features under thermal-annealing conditions. The as-prepared Tl-1223 (Tc =106
K) presents a significantly higher Tc = 125 K after annealing the
polycrystalline material in either flowing Ar+4% H2, or N2 gases. In order to
understand the fundamental reasons for a particular Tc, we refined the average
bulk structures using powder X-ray diffraction data. Although Ar+4%H2 annealed
Tl-1223 shows an increased c lattice parameter, it is approximately unchanged
upon N2-anneal. Due to such indeterminate conclusions on the average structural
changes, local structures were investigated at using aberration-corrected
scanning-transmission electron microscopy technique. Similar compositional
changes in the atomic arrangements of both annealed-samples of Tl-1223 were
detected in which the plane containing Ca atomic layer gives a non-uniform
contrast, due to substitution of some heavier Tl. In this report, extensive
bulk properties are summarized through temperature-dependent resistivity, and
shielding and Meissner fractions of magnetic susceptibility results; the bulk
and local structures are investigated to correlate to properties.


  The minimality of the penalization function associated with a convex risk
measure is analyzed in this paper. First, in a general static framework, we
provide necessary and sufficient conditions for a penalty function defined in a
convex and closed subset of the absolutely continuous measures with respect to
some reference measure $\mathbb{P}$ to be minimal. When the probability space
supports a L\'{e}vy process, we establish results that guarantee the minimality
property of a penalty function described in terms of the coefficients
associated with the density processes. The set of densities processes is
described and the convergence of its quadratic variation is analyzed.


  We suggest that electromagnetic chirality, generally displayed by 3D or 2D
complex chiral structures, can occur in 1D patterned composites whose
components are achiral. This feature is highly unexpected in a 1D system which
is geometrically achiral since its mirror image can always be superposed onto
it by a 180 deg rotation. We analytically evaluate from first principles the
bi-anisotropic response of multilayered metamaterials and we show that the
chiral tensor is not vanishing if the system is geometrically one-dimensional
chiral, i.e. its mirror image can not be superposed onto it by using
translations without resorting to rotations. As a signature of 1D chirality, we
show that 1D chiral metamaterials support optical activity and we prove that
this phenomenon undergoes a dramatic non-resonant enhancement in the
epsilon-near-zero regime where the magneto-electric coupling can become
dominant in the constitutive relations.


  Conventional magnetic domain walls are characterized by the reorientation of
local moments. However, what occurs at the boundary of itinerant magnets is
largely unknown. Here using spin-sensitive scanning tunneling microscopy, we
investigated the microscopic boundaries of spin-density-wave (SDW) state in a
prototypical itinerant anti-ferromagnet of Cr. We find at the boundary of two
incommensurate SDW domains, the spins display finite-scale decay rather than
reorientation. A novel double-Q SDW is generated with a second-order charge
modulation. In commensurate SDW domains, a clear SDW gap is observed. Screw
dislocations induced novel "half" vortex and anti-vortex that are connected by
antiphase domain wall. This domain wall is characterized by vanishing spin
density, where intriguing SDW in-gap states emerge, resembling the Andreev
bound states in superconductors. All these unique SDW boundary structures can
be viewed as consequences of local interference of two SDW, either with
different Q or reversed phases. Therefore, our study revealed a new category of
magnetic domain wall, the "interference wall", with a mechanism rooted in
itinerant nature.


  It is well known that static spherically symmetric spacetimes can admit
foliations by flat spacelike hypersurfaces, which are best described in terms
of the Painlev\`{e}--Gullstrand coordinates. The uniqueness and existence of
such foliations were addressed earlier. In this paper, we prove, purely
geometrically, that any possible foliation of a static spherically symmetric
spacetime by an arbitrary codimension-one spherical spacelike geometry, up to
time translation and rotation, is unique, and we find the algebraic condition
under which it exists. This leads us to what can be considered as the most
natural generalization of the Painlev\`{e}--Gullstrand coordinate system for
static spherically symmetric metrics, which, in turn, makes it easy to derive
generic conclusions on foliation and to study specific cases as well as to
easily reproduce previously obtained generalizations as special cases. In
particular, we note that the existence of foliation by flat hypersurfaces
guarantees the existence of foliation by hypersurfaces whose Ricci curvature
tensor is everywhere non-positive (constant negative curvature is a special
case). The study of uniqueness and the existence concurrently solves the
question of embeddability of a spherical spacelike geometry in one-dimensional
higher static spherically symmetric spacetimes, and this produces known and new
results geometrically, without having to go through the momentum and
Hamiltonian constraints.


  This is a manuscript of a chapter prepared for a book. The good codes possess
large information length and large minimum distance. A class of codes is said
to be asymptotically good if there exists a positive real $\delta$ such that,
for any positive integer $N$ we can find a code in the class with code length
greater than $N$, and with both the rate and the relative minimum distance
greater than $\delta$. The linear codes over any finite field are
asymptotically good. More interestingly, the (asymptotic) GV-bound is a phase
transition point for the linear codes; i.e., asymptotically speaking, the
parameters of most linear codes attain the GV-bound. It is a long-standing open
question: whether or not the cyclic codes over a finite field (which are an
important class of codes) are asymptotically good? However, from a long time
ago the quasi-cyclic codes of index $2$ were proved to be asymptotically good.
This chapter consists of some of our studies on the asymptotic properties of
several classes of quasi-group codes. We'll explain the studies in a consistent
and self-contained style. We begin with the classical results on linear codes.
In many cases we consider the quasi-group codes over finite abelian groups
(including the cyclic case as a subcase of course), and study their asymptotic
properties along two directions: (1) the order of the group (the coindex) is
fixed while the index is going to infinity; (2) the index is small while the
order of the group (the coindex) is going to infinity. Finally we describe the
story on dihedral codes. The dihedral groups are non-abelian but near to cyclic
groups (they have cyclic subgroups of index $2$). The asymptotic goodness of
binary dihedral codes was obtained in the beginning of this century, and
extended to the general dihedral codes recently.


  This work provides linear control-oriented state space models of gas flow
through standard equipment, such as valves, compressors, manifolds and
non-trivial pipe geometries. After presenting the catalog of components, we
show how to interconnect them: we briefly recall the matrix methodology derived
elsewhere, accompanied by a Matlab example for a gas loop; secondly for the
same example we provide an alternative approach using Matlab's connect
function. All the aforementioned models are suited to model-based MIMO control
design tools as they are in state-space form and they can be physically
parametrized. Conservation of mass is the source of the algebraic constraints
in and is a property subsumed in these new models. This is characterized by
model transfer function properties at frequency zero. Each of the component
models is shown to posses this property.


  The subtle interplay of randomness and quantum fluctuations at low
temperatures gives rise to a plethora of unconventional phenomena in systems
ranging from quantum magnets and correlated electron materials to ultracold
atomic gases. Particularly strong disorder effects have been predicted to occur
at zero-temperature quantum phase transitions. Here, we demonstrate that the
composition-driven ferromagnetic-to-paramagnetic quantum phase transition in
Sr1-xCaxRuO3 is completely destroyed by the disorder introduced via the
different ionic radii of the randomly distributed Sr and Ca ions. Using a
magneto-optical technique, we map the magnetic phase diagram in the
composition-temperature space. We find that the ferromagnetic phase is
significantly extended by the disorder and develops a pronounced tail over a
broad range of the composition x. These findings are explained by a microscopic
model of smeared quantum phase transitions in itinerant magnets. Moreover, our
theoretical study implies that correlated disorder is even more powerful in
promoting ferromagnetism than random disorder.


  In the present paper we prove that the $3$-fold projective tensor product of
$c_0$, $c_{0} \widehat{\otimes}_\pi c_{0}\widehat{\otimes}_\pi c_{0}$, is not
isomorphic to a subspace of $c_{0} \widehat{\otimes}_\pi c_{0}$. In particular,
this settles the long-standing open problem of whether $c_{0}
\widehat{\otimes}_\pi c_{0}$ is isomorphic to $c_{0} \widehat{\otimes}_\pi
c_{0}\widehat{\otimes}_\pi c_{0}$. The origin of this problem goes back to Joe
Diestel who mentioned it in a private communication to the authors of paper
"Unexpected subspaces of tensor products" published in 2006.


  A simple analytical way of creating superpositions of Bessel-Gaussian light
beams with knotted nodal lines is proposed. It is based on the equivalence
between the paraxial wave equation and the two-dimensional Schr\"odinger
equation for a free particle. The $2D$ Schr\"odinger propagator is expressed in
terms of Bessel functions, which allows to obtain directly superpositions of
beams with a desired topology of nodal lines. Four types of knots are
constructed in the explicit way: the unknot, the Hopf link, the Borromean rings
and the trefoil. It is also shown, using the example of the figure-eight knot,
that more complex structures require larger number of constituent beams as well
as high precision both from the numerical and the experimental side. A tiny
change of beam's intensity can lead to the knot "switching".


  Various possibilities of polar self-organisation in low molar mass nematic,
smectic and columnar liquid crystals are discussed with particular focus on the
underlying molecular symmetries and interactions. Distinction is made between
vector and pseudovector polarities, their quantification in terms of molecular
order parameters and their relation to spontaneous electric polarisation and to
molecular chirality. The understanding of the molecular mechanisms that give
rise to polar ordering in existing lamellar and columnar phases may be useful
for the design of new polar variants of common a-polar liquid crystals.
Keywords:Polar Nematics; Ferroelectric Liquid Crystals; Polar Ordering.


  We investigate the decay of vortices in a rotating cylindrical sample of
3He-B, after rotation has been stopped. With decreasing temperature vortex
annihilation slows down as the damping in vortex motion, the mutual friction
dissipation \alpha(T), decreases almost exponentially. Remanent vortices then
survive for increasingly long periods, while they move towards annihilation in
zero applied flow. After a waiting period \Delta t at zero flow, rotation is
reapplied and the remnants evolve to rectilinear vortices. By counting these
lines, we measure at temperatures above the transition to turbulence ~0.6T_c
the number of remnants as a function of \alpha(T) and \Delta t. At temperatures
below the transition to turbulence T \lesssim 0.55 T_c, remnants expanding in
applied flow become unstable and generate in a turbulent burst the equilibrium
number of vortices. Here we measure the onset temperature T_on of turbulence as
a function of \Delta t, applied flow velocity, and length of sample L.


  If a Kerr black hole is connected to a disk rotating around it by a magnetic
field, the rotational energy of the Kerr black hole provides an energy source
for the radiation of the disk in addition to disk accretion. The black hole
exerts a torque on the disk, which transfers energy and angular momentum
between the black hole and the disk. If the black hole rotates faster than the
disk, energy and angular momentum are extracted from the black hole and
transfered to the disk. The energy deposited into the disk is eventually
radiated away by the disk, which will increase the efficiency of the disk. If
the black hole rotates slower than the disk, energy and angular momentum are
transfered from the disk to the black hole, which will lower the efficiency of
the disk. With suitable boundary conditions, quasi-steady state solutions are
obtained for a thin Keplerian disk magnetically coupled to a Kerr black hole.
By ``quasi-steady state'' we mean that any macroscopic quantity at a given
radius in the disk slowly changes with time: the integrated change within one
rotation period of the disk is much smaller than the quantity itself. We find
that, the torque produced by the magnetic coupling propagates only outward in
the disk, the total radiation flux of the disk is a superposition of the
radiation flux produced by the magnetic coupling and that produced by
accretion. Most interestingly, a disk magnetically coupled to a rapidly
rotating black hole can radiate without accretion. Such a disk has an infinite
efficiency. For a specific example that the magnetic field touches the disk at
the inner boundary, the radial radiation profile is very different from that of
a standard accretion disk: the emissivity index is significantly bigger, most
radiation comes from a region which is closer to the center of the disk.


  Influence maximization (IM) aims to select a small number of nodes that are
able to maximize their influence in a network and covers a wide range of
applications. Despite numerous attempts to provide effective solutions in
ordinary networks, higher-order interactions between entities in various
real-world systems are not usually taken into account. In this paper, we
propose a versatile meta-heuristic approach, hyper genetic algorithm (HGA), to
tackle the IM problem in hypergraphs, which is based on the concept of genetic
evolution. Systematic validations in synthetic and empirical hypergraphs under
both simple and complex contagion models indicate that HGA achieves universal
and plausible performance compared to baseline methods. We explore the cause of
the excellent performance of HGA through ablation studies and correlation
analysis. The findings show that the solution of HGA is distinct from that of
other prior methods. Moreover, a closer look at the local topological features
of the seed nodes acquired by different algorithms reveals that the selection
of seed nodes cannot be based on a single topological characteristic, but
should involve a combination of multiple topological features to address the IM
problem.


  Let $g$ be an element of a finite group $G$ and let $R_{n}(g)$ be the
subgroup generated by all the right Engel values $[g,{}_{n}x]$ over $x\in G$.
In the case when $G$ is soluble we prove that if, for some $n$, the Fitting
height of $R_{n}(g)$ is equal to $k$, then $g$ belongs to the $(k+1)$th Fitting
subgroup $F_{k+1}(G)$. For nonsoluble $G$, it is proved that if, for some $n$,
the generalized Fitting height of $R_n(g)$ is equal to $k$, then $g$ belongs to
the generalized Fitting subgroup $F^*_{f(k,m)}(G)$ with $f(k,m)$ depending only
on $k$ and $m$, where $|g|$ is the product of $m$ primes counting
multiplicities. It is also proved that if, for some $n$, the nonsoluble length
of $R_n(g)$ is equal to $k$, then $g$ belongs to a normal subgroup whose
nonsoluble length is bounded in terms of $k$ and $m$. Earlier similar
generalizations of Baer's theorem (which states that an Engel element of a
finite group belongs to the Fitting subgroup) were obtained by the first two
authors in terms of left Engel-type subgroups.


  We report the discovery of a substellar companion to the nearby solar-type
star HD 46588 (F7V, 17.9 pc, ~3 Gyr). HD 46588 B was found through a survey for
common proper motion companions to nearby stars using data from the Wide-field
Infrared Survey Explorer and the Two-Micron All-Sky Survey. It has an angular
separation of 79.2" from its primary, which corresponds to a projected physical
separation of 1420 AU. We have measured a spectral type of L9 for this object
based on near-infrared spectroscopy performed with TripleSpec at Palomar
Observatory. We estimate a mass of 0.064+0.008/-0.019 Msun from a comparison of
its luminosity to the values predicted by theoretical evolutionary models for
the age of the primary. Because of its companionship to a well-studied star, HD
46588 B is one of the few known brown dwarfs at the L/T transition for which
both age and distance estimates are available. Thus, it offers new constraints
on the properties of brown dwarfs during this brief evolutionary phase. The
discovery of HD 46588 B also illustrates the value of the Wide-field Infrared
Survey Explorer for identifying brown dwarfs in the solar neighborhood via
their proper motions.


  For a number of reasons, computational intelligence and machine learning
methods have been largely dismissed by the professional community. The reasons
for this are numerous and varied, but inevitably amongst the reasons given is
that the systems designed often do not perform as expected by their designers.
The reasons for this lack of performance is a direct result of mistakes that
are commonly seen in market-prediction systems. This paper examines some of the
more common mistakes, namely dataset insufficiency; inappropriate scaling;
time-series tracking; inappropriate target quantification and inappropriate
measures of performance. The rationale that leads to each of these mistakes is
examined, as well as the nature of the errors they introduce to the analysis /
design. Alternative ways of performing each task are also recommended in order
to avoid perpetuating these mistakes, and hopefully to aid in clearing the way
for the use of these powerful techniques in industry.


  We study the Ginzburg-Landau model of type-I superconductors in the regime of
small external magnetic fields. We show that, in an appropriate asymptotic
regime, flux patterns are described by a simplified branched transportation
functional. We derive the simplified functional from the full Ginzburg-Landau
model rigorously via $\Gamma$-convergence. The detailed analysis of the
limiting procedure and the study of the limiting functional lead to a precise
understanding of the multiple scales contained in the model.


  Transverse and parallel static susceptibilities of in-plane uniaxial
anisotropic ferromagnetic films are calculated within many-body Green's
function theory on the basis of an Heisenberg model. The importance of
collective magnetic excitations in particular in the paramagnetic regime are
stressed by comparing with mean field calculations. The paper generalizes the
work of Jensen et al. [1] to the multilayer case and to spins with S>1/2.


  We study the phase diagram of S=3/2 and S=2 bond-alternating spin chains
numerically. In previous papers, the phase diagram of S=1 XXZ spin chain with
bond-alternation was shown to reflect the hidden $Z_{2}\times Z_{2}$ symmetry.
But for the higher S Heisenberg spin chain, the successive dimerization
transition occurs, and for anisotropic spin chains the phase structure will be
more colorful than the S=1 case. Using recently developed methods, we show
directly that the phase structure of the anisotropic spin chains relates to the
$Z_{2}\times Z_{2}$ symmetry.


  We study algebraic and topological properties of the convolution semigroups
of probability measures on a topological groups and show that a compact
Clifford topological semigroup $S$ embeds into the convolution semigroup $P(G)$
over some topological group $G$ if and only if $S$ embeds into the semigroup
$\exp(G)$ of compact subsets of $G$ if and only if $S$ is an inverse semigroup
and has zero-dimensional maximal semilattice. We also show that such a Clifford
semigroup $S$ embeds into the functor-semigroup $F(G)$ over a suitable compact
topological group $G$ for each weakly normal monadic functor $F$ in the
category of compacta such that $F(G)$ contains a $G$-invariant element (which
is an analogue of the Haar measure on $G$).


  We describe a way of solving a partial differential equation using the
differential invariants of its point symmetries. By first solving its quotient
PDE, which is given by the differential syzygies in the algebra of differential
invariants, we obtain new differential constraints which are compatible with
the PDE under consideration. Adding these constraints to our system makes it
overdetermined, and thus easier to solve. We focus on second-order scalar PDEs
whose quotients are first-order scalar PDEs. This situation occurs only when
the Lie algebra of symmetries of the second-order PDE is infinite-dimensional.
We apply this idea to several different PDEs, one of which is the Hunter-Saxton
equation.


  A model that combines celestial geometry and atmospheric physics is used to
calculate the dimming of artificial satellites as they enter and exit the
Earth's shadow. Refraction of sunlight by the terrestrial atmosphere can
illuminate a satellite while it is inside the eclipse region determined from
geometry alone. Meanwhile, refraction combines with atmospheric absorption to
dim the satellites for tens of km outside of that region. Spacecraft brightness
is reduced more in blue light than in red because absorption of sunlight is
stronger at shorter wavelengths. Observations from the MMT-9 robotic
observatory are consistent with the model predictions. Tables of satellite
brightness as functions of their location in the eclipse region are provided.


  The zeta function regularization technique is used to study the finite
temperature Casimir effect for a massless Majorana fermion field confined
between parallel plates and satisfying bag boundary conditions. A magnetic
field perpendicular to the plates is included. An expression for the zeta
function is obtained, which is exact to all orders in the magnetic field
strength, temperature and plate distance. The zeta function is used to
calculate the Helmholtz free energy of the Majorana field and the pressure on
the plates, in the case of weak magnetic field and strong magnetic field. In
both cases, simple analytic expressions are obtained for the free energy and
pressure which are very accurate and valid for all values of the temperature
and plate distance.


  We analyze a generalization of the hard sphere dipole system in two
dimensions in which the interaction range of the interaction can be varied. We
focus on the system in the limit the interaction becomes increasingly
short-ranged, while the temperature becomes low. By using a cluster expansion
and taking advantage of low temperatures to perform saddle-point
approximations, we argue that a well defined double limit exists in which the
only structures which contribute to the free energy are chains. We then argue
that the dominance of chain structures is equivalent to the dominance of chain
diagrams in a cluster expansion, but only if the expansion is performed around
a hard sphere system (rather than the standard ideal gas). We show that this
leads to non-standard factorization rules for diagrams, and use this to
construct a closed-form expression for the free energy at low densities. We
then compare this construction to several models previously developed for the
hard sphere dipole system in the regime where chain structures dominate, and
argue that the comparison provides evidence in favor of one model over the
others. We also use this construction to incorporate some finite density
effects though the hard sphere radial distribution function, and analyze the
impact of these effects on chain length and the equation of state.


  As the inevitable development trend of quantum key distribution, quantum
networks have attracted extensive attention, and many prototypes have been
deployed over recent years. Existing quantum networks based on optical fibers
or quantum satellites can realize the metro and even global communications.
However, for some application scenarios that require emergency or temporary
communications, such networks cannot meet the requirements of rapid deployment,
low cost, and high mobility. To solve this problem, we introduce an important
concept of classical networks, i.e., self-organization, to quantum networks,
and give two simple network prototypes based on acquisition, tracking, and
pointing systems. In these networks, the users only need to deploy the network
nodes, which will rapidly, automatically, and adaptively organize and mange a
quantum network. Our method expands the application scope of quantum networks,
and gives a new approach for the design and implementation of quantum networks.
It also provides users with a low-cost access network solution, and can be used
to fundamentally solve the security problem of classical self-organizing
networks.


  Documentation enables sharing knowledge between the developers of a
technology and its users. Creating quality documents, however, is challenging:
Documents must satisfy the needs of a large audience without being overwhelming
for individuals. We address this challenge with a new document format, named
Casdoc. Casdoc documents are interactive resources centered around code
examples for programmers. Explanations of the code elements are presented as
annotations that the readers reveal based on their needs. We evaluated Casdoc
in a field study with over 300 participants who used 126 documents as part of a
software design course. The majority of participants adopted Casdoc instead of
a baseline format during the study. We observed that interactive documents can
contain more information than static documents without being distracting to
readers. We also gathered insights into five aspects of Casdoc that can be
applied to other formats, and propose five guidelines to improve navigability
in online documents.


  Gaussian processes (GPs) are an important tool in machine learning and
statistics with applications ranging from social and natural science through
engineering. They constitute a powerful kernelized non-parametric method with
well-calibrated uncertainty estimates, however, off-the-shelf GP inference
procedures are limited to datasets with several thousand data points because of
their cubic computational complexity. For this reason, many sparse GPs
techniques have been developed over the past years. In this paper, we focus on
GP regression tasks and propose a new approach based on aggregating predictions
from several local and correlated experts. Thereby, the degree of correlation
between the experts can vary between independent up to fully correlated
experts. The individual predictions of the experts are aggregated taking into
account their correlation resulting in consistent uncertainty estimates. Our
method recovers independent Product of Experts, sparse GP and full GP in the
limiting cases. The presented framework can deal with a general kernel function
and multiple variables, and has a time and space complexity which is linear in
the number of experts and data samples, which makes our approach highly
scalable. We demonstrate superior performance, in a time vs. accuracy sense, of
our proposed method against state-of-the-art GP approximation methods for
synthetic as well as several real-world datasets with deterministic and
stochastic optimization.


  We present a generic tree-interpolation algorithm in the SMT context with
quantifiers. The algorithm takes a proof of unsatisfiability using resolution
and quantifier instantiation and computes interpolants (which may contain
quantifiers). Arbitrary SMT theories are supported, as long as each theory
itself supports tree interpolation for its lemmas. In particular, we show this
for the theory combination of equality with uninterpreted functions and linear
arithmetic. The interpolants can be tweaked by virtually assigning each literal
in the proof to interpolation partitions (colouring the literals) in arbitrary
ways. The algorithm is implemented in SMTInterpol.


  Abridged: We present a detailed multi-wavelength study of the bright-rimmed
cloud SFO 75, including 1.3cm and 1.2mm continuum, and 13CO and ammonia
spectral line observations. The 13CO and 1.2 mm emission reveals the presence
of a dense core located behind the bright rim of the cloud which is
approximately coincident with that of the IRAS point source. From an analysis
of the IRAS and 1.2mm fluxes we derive a dust temperature of ~30 K, a
luminosity of 1.6x10^4 L\odot and estimate the core mass to be ~570 M\odot. The
higher resolution ammonia observations resolve the 1.2mm core into two distinct
cores, one directly behind the cloud's rim (Core A) and the second located
slightly farther back (Core B). Comparing the morphology of Core A with that of
the photon-dominated region and ionised boundary layer leaves little doubt that
it is being strongly affected by the ionisation front. 2MASS and GLIMPSE
archive data which reveal a small cluster of three deeply embedded high- and
intermediate-mass young stellar objects towards Core A leads us to conclude
that the star formation found towards this core has been triggered. In stark
contrast, Core B appears to have a much simpler, almost spherical, morphology.
No stars are found towards Core B. The scenario that emerges from our analysis
is one where the two ammonia cores pre-date the arrival of the ionisation
front. Since its arrival the over-pressure of the ionised gas at the surface of
the cloud has driven shocks into the surface layers of the cloud. The
propagation of these shocks through Core A have triggered the formation of a
small cluster of massive stars, however, the shock front has not yet propagated
deeply enough into the cloud to have affected the evolution of Core B.


  We consider the $XYZ$ chain model of arbitrary spin $S$ in the high
temperature region, with external magnetic field and single-ion anisotropy
term. Our high-temperature expansion of the Helmholtz free energy is analytic
in the parameters of the model for $S$, which may range from 1/2 to the
classical limit of infinite spin ($S\to \infty$). Our expansion is carried out
up to order $(J \beta)^5$. Our results agree with numerical results of the
specific heat per site for $S=1/2$, obtained by the Bethe ansatz, with $h=0$
and D=0. Finally, we show that the magnetic susceptibility and magnetization of
the quantum model can be well approximated by their classical analog in this
region of temperature.


  We investigate the boundedness of Fourier multipliers on a compact Lie group
when acting on Triebel-Lizorkin spaces. Criteria are given in terms of the
H\"ormander-Mihlin-Marcinkiewicz condition. In our analysis, we use the
difference structure of the unitary dual of a compact Lie group. Our results
cover the sharp H\"ormander-Mihlin theorem on Lebesgue spaces and also other
historical results on the subject.


  In this Letter, we proposed and experimentally demonstrated a method to
detect vector magnetic field with a single nitrogen vacancy (NV) center in
diamond. The magnetic field in parallel with the axis of the NV center can be
obtained by detecting the electron Zeeman shift, while the Larmor precession of
an ancillary nuclear spin close to the NV center can be used to measure the
field perpendicular to the axis. Experimentally, both the Zeeman shift and
Larmor precession can be measured through the fluorescence from the NV center.
By applying additional calibrated magnetic fields, complete information of the
vector magnetic field can be achieved with such a method. This vector magnetic
field detection method is insensitive to temperature fluctuation and it can be
applied to nanoscale magnetic measurement.


  Whereas machine learning models typically learn language by directly training
on language tasks (e.g., next-word prediction), language emerges in human
children as a byproduct of solving non-language tasks (e.g., acquiring food).
Motivated by this observation, we ask: can embodied reinforcement learning (RL)
agents also indirectly learn language from non-language tasks? Learning to
associate language with its meaning requires a dynamic environment with varied
language. Therefore, we investigate this question in a multi-task environment
with language that varies across the different tasks. Specifically, we design
an office navigation environment, where the agent's goal is to find a
particular office, and office locations differ in different buildings (i.e.,
tasks). Each building includes a floor plan with a simple language description
of the goal office's location, which can be visually read as an RGB image when
visited. We find RL agents indeed are able to indirectly learn language. Agents
trained with current meta-RL algorithms successfully generalize to reading
floor plans with held-out layouts and language phrases, and quickly navigate to
the correct office, despite receiving no direct language supervision.


  Time irreversibility (temporal asymmetry) is one of fundamental properties
that characterize the nonlinearity of complex dynamical processes, and our
brain is a typical complex dynamical system manifested with nonlinearity. Two
subtraction-based parameters, Ys and X2, are employed to measure the
probabilistic differences of permutations instead of raw vectors for the
simplified quantification of time irreversibility, which is validated by
chaotic and reversible processes and the surrogate data. We show that it is
equivalent to quantify time irreversibility by measuring probabilistic
difference between the forward and its backward processes and between the
symmetric permutations. And we detect time irreversibility of two groups of
epileptic EEGs, from the Nanjing General Hospital (NJGH) and from the public
Bonn epileptic database. In our contribution, NJGH epileptic EEGs during
seizure-free intervals of have lower time irreversibility than the control data
while those of the Bonn data sets have higher nonlinearity than the healthy
brain electrical activities. For the inconsistent results, we conduct
multi-scale analysis and elucidate from the circadian rhythms in epileptic
nonlinearity, however, more targeted researches are needed to verify our
assumptions or to determine if there are other reasons leading to the
inconsistency.


  The nonlinear interaction of waves in a driven medium may lead to wave
turbulence, a state such that energy is transferred from large to small
lengthscales. Here, wave turbulence is observed in experiments on a vibrating
plate. The frequency power spectra of the normal velocity of the plate may be
rescaled on a single curve, with power-law behaviors that are incompatible with
the weak turbulence theory of D{\"u}ring et al. [Phys. Rev. Lett. 97, 025503
(2006)]. Alternative scenarios are suggested to account for this discrepancy --
in particular the occurrence of wave breaking at high frequencies. Finally, the
statistics of velocity increments do not display an intermittent behavior.


  Frenkel excitons, the primary photoexcitations in organic semiconductors that
are unequivocally responsible for the optical properties of this materials
class, are predicted to form \emph{bound} exciton pairs, i.e., biexcitons.
These are key intermediates, ubiquitous in many relevant photophysical
processes; for example, they determine the exciton bimolecular annihilation
dynamics in such systems. Deciphering the details of biexciton correlations is,
thus, of utmost importance to understand the optical processes in these
semiconductors. To date, however, due to their spectral ambiguity, there has
been only scant direct evidence of bound biexcitons, limiting the insights that
can be gained. Moreover, a quantum-mechanical basis describing biexciton
correlation/stability has so far been lacking. By employing nonlinear coherent
spectroscopy, we identify here bound biexcitons in a model polymeric
semiconductor. We find, unexpectedly, that excitons with \emph{interchain}
vibronic dispersion reveal \emph{intrachain} biexciton correlations and vice
versa. Moreover, using a Frenkel exciton model, we can relate the biexciton
binding energy to molecular parameters quantified by quantum chemistry,
including the magnitude and sign of the exciton-exciton interaction the
inter-site hopping energies. Therefore, our work promises a window towards
general insights into the many-body electronic structure in polymeric
semiconductors and beyond; e.g., other excitonic systems such as organic
semiconductor crystals, molecular aggregates, photosynthetic light-harvesting
complexes, or DNA.


  The geometric multigrid algorithm is an efficient numerical method for
solving a variety of elliptic partial differential equations (PDEs). The method
damps errors at progressively finer grid scales, resulting in faster
convergence compared to iterative methods such as Gauss-Seidel. The
prolongation or coarse-to-fine interpolation operator within the multigrid
algorithm, lends itself to a data-driven treatment with deep learning
super-resolution, commonly used to increase the resolution of images. We (i)
propose the integration of a super-resolution generative adversarial network
(GAN) model with the multigrid algorithm as the prolongation operator and (ii)
show that the GAN-interpolation can improve the convergence properties of
multigrid in comparison to cubic spline interpolation on a class of multiscale
PDEs typically solved in fluid mechanics and engineering simulations. We also
highlight the importance of characterizing hybrid (machine
learning/traditional) algorithm parameters.


  We apply two independent data analysis methodologies to locate stable climate
states in an intermediate complexity climate model and analyze their interplay.
First, drawing from the theory of quasipotentials, and viewing the state space
as an energy landscape with valleys and mountain ridges, we infer the relative
likelihood of the identified multistable climate states, and investigate the
most likely transition trajectories as well as the expected transition times
between them. Second, harnessing techniques from data science, specifically
manifold learning, we characterize the data landscape of the simulation output
to find climate states and basin boundaries within a fully agnostic and
unsupervised framework. Both approaches show remarkable agreement, and reveal,
apart from the well known warm and snowball earth states, a third intermediate
stable state in one of the two climate models we consider. The combination of
our approaches allows to identify how the negative feedback of ocean heat
transport and entropy production via the hydrological cycle drastically change
the topography of the dynamical landscape of Earth's climate.


  Motivated by surprisingly good generalization properties of learned deep
neural networks in overparameterized scenarios and by the related double
descent phenomenon, this paper analyzes the relation between smoothness and low
generalization error in an overparameterized linear learning problem. We study
a random Fourier series model, where the task is to estimate the unknown
Fourier coefficients from equidistant samples. We derive exact expressions for
the generalization error of both plain and weighted least squares estimators.
We show precisely how a bias towards smooth interpolants, in the form of
weighted trigonometric interpolation, can lead to smaller generalization error
in the overparameterized regime compared to the underparameterized regime. This
provides insight into the power of overparameterization, which is common in
modern machine learning.


  We present the explicit de Sitter supergravity action describing the
interaction of supergravity with an arbitrary number of chiral and vector
multiplets as well as one nilpotent chiral multiplet. The action has a
non-Gaussian dependence on the auxiliary field of the nilpotent multiplet,
however, it can be integrated out for an arbitrary matter-coupled supergravity.
The general supergravity action with a given Kahler potential $K$,
superpotential $W$ and vector matrix $f_{AB}$ interacting with a nilpotent
chiral multiplet consists of the standard supergravity action defined by $K$,
$W$ and $f_{AB}$ where the scalar in the nilpotent multiplet has to be replaced
by a bilinear combination of the fermion in the nilpotent multiplet divided by
the Gaussian value of the auxiliary field. All additional contributions to the
action start with terms quartic and higher order in the fermion of the
nilpotent multiplet. These are given by a simple universal closed form
expression.


  We consider the problem of stable recovery of sparse signals of the form
$$F(x)=\sum_{j=1}^d a_j\delta(x-x_j),\quad x_j\in\mathbb{R},\;a_j\in\mathbb{C},
$$ from their spectral measurements, known in a bandwidth $\Omega$ with
absolute error not exceeding $\epsilon>0$. We consider the case when at most
$p\le d$ nodes $\{x_j\}$ of $F$ form a cluster whose extent is smaller than the
Rayleigh limit ${1\over\Omega}$, while the rest of the nodes are well
separated. Provided that $\epsilon \lessapprox SRF^{-2p+1}$, where
$SRF=(\Omega\Delta)^{-1}$ and $\Delta$ is the minimal separation between the
nodes, we show that the minimax error rate for reconstruction of the cluster
nodes is of order ${1\over\Omega}SRF^{2p-1}\epsilon$, while for recovering the
corresponding amplitudes $\{a_j\}$ the rate is of the order
$SRF^{2p-1}\epsilon$. Moreover, the corresponding minimax rates for the
recovery of the non-clustered nodes and amplitudes are ${\epsilon\over\Omega}$
and $\epsilon$, respectively. These results suggest that stable
super-resolution is possible in much more general situations than previously
thought. Our numerical experiments show that the well-known Matrix Pencil
method achieves the above accuracy bounds.


  Matter and dark matter are unified under the framework of $SU(6)\to SU(5)
\times U(1)_N$. A dark-matter candidate is possible, not because it is stable,
but because it has a very long lifetime, in analogy to that of the proton in
theories of grand unification. A specific example is presented.


  Realising de Sitter vacua in string theory is challenging. For this reason it
has been conjectured that de Sitter vacua inhabit the Swampland of inconsistent
low-energy effective theories coupled to gravity. Since de Sitter is an
attractor for $\Lambda$CDM, the conjecture calls $\Lambda$CDM into question.
Reality appears sympathetic to this idea as local measurements of the Hubble
constant $H_0$ are also at odds with $\Lambda$CDM analysis of Planck data. This
tension suggests that the de Sitter state is unstable, thereby implying a
turning point in the Hubble parameter. We present a model relieving this
tension, which predicts a turning at small positive redshift $z_*$ that is
dictated by present-day matter density $\omega_m$. This feature is easily
identified by homogeneous surveys covering redshifts $z \leq 0.1$. We comment
on the implications for the Swampland program.


  Arrival directions of 40 neutrino events with energies >~100 TeV, observed by
the IceCube experiment, are studied. Their distribution in the Galactic
latitude and in the angular distance to the Galactic Center allow to search for
the Milky-Way disk and halo-related components, respectively. No statistically
significant evidence for the disk component is found, though even 100% disk
origin of the flux is allowed at the 90% confidence level. Contrary, the
Galactic Center-Anticenter dipole anisotropy, specific for dark-matter decays
(annihilation) or for interactions of cosmic rays with the extended halo of
circumgalactic gas, is clearly favoured over the isotropic distribution (the
probability of a fluctuation of the isotropic signal is ~2%).


  Coreference resolution (CR), identifying expressions referring to the same
real-world entity, is a fundamental challenge in natural language processing
(NLP). This paper explores the latest advancements in CR, spanning coreference
and anaphora resolution. We critically analyze the diverse corpora that have
fueled CR research, highlighting their strengths, limitations, and suitability
for various tasks. We examine the spectrum of evaluation metrics used to assess
CR systems, emphasizing their advantages, disadvantages, and the need for more
nuanced, task-specific metrics. Tracing the evolution of CR algorithms, we
provide a detailed overview of methodologies, from rule-based approaches to
cutting-edge deep learning architectures. We delve into mention-pair,
entity-based, cluster-ranking, sequence-to-sequence, and graph neural network
models, elucidating their theoretical foundations and performance on benchmark
datasets. Recognizing the unique challenges of Persian CR, we dedicate a
focused analysis to this under-resourced language. We examine existing Persian
CR systems and highlight the emergence of end-to-end neural models leveraging
pre-trained language models like ParsBERT. This review is an essential resource
for researchers and practitioners, offering a comprehensive overview of the
current state-of-the-art in CR, identifying key challenges, and charting a
course for future research in this rapidly evolving field.


  Given a finite set of $r$ points in a closed surface of genus $g$, we
consider the torsion elements in the mapping class group of the surface leaving
the finite set invariant. We show that the torsion elements generate the
mapping class group if and only if $(g, r) \neq (2, 5k+4)$ for some integer
$k$.


  It is understood that the Supernovae (SNe) associated to Gamma Ray Bursts
(GRBs) are of type Ib/c. The temporal coincidence of the GRB and the SN
represents still a major enigma of Relativistic Astrophysics. We elaborate
here, from the earlier paradigm, that the concept of induced gravitational
collapse is essential to explain the GRB-SN connection. The specific case of a
close (orbital period <1 h) binary system composed of an evolved star with a
Neutron Star (NS) companion is considered. We evaluate the accretion rate onto
the NS of the material expelled from the explosion of the core progenitor as a
type Ib/c SN, and give the explicit expression of the accreted mass as a
function of the nature of the components and binary parameters. We show that
the NS can reach, in a few seconds, the critical mass and consequently
gravitationally collapses to a Black Hole. This gravitational collapse process
leads to the emission of the GRB.


  We investigate in how far the hysteresis-free behavior of perovskite solar
cells can be reproduced using particular pre-conditioning and measurement
conditions. As there are currently more and more reports of perovskite solar
cells without J-V hysteresis it is crucial to distinguish between genuine
performance improvements and measurement artifacts. We focus on two of the
parameters that influence the dynamic J-V scans, namely the bias scan rate and
and the bias poling voltage, and point out measurement conditions for achieving
a hysteresis-free behavior. In this context we discuss the suitability of
defining a hysteresis index (HI) for the characterization of dynamic J-V scans.
Using HI, aging effects are also investigated, establishing a potential
connection between the sample degradation and the variation of the maximal
hysteresis on one hand, and relaxation time scale of the slow process, on the
other hand. Pre-poling induced recombinations effects are identified. In
addition, our analysis based on sample pre-biasing reveals potential indication
regarding two types of slow processes, with two different relaxation time
scales, which provides further insight regarding ionic migration.


  Objective: We propose a semiautomatic pipeline for radiation therapy
treatment planning, combining ideas from machine learning-automated planning
and multicriteria optimization (MCO).
  Approach: Using knowledge extracted from historically delivered plans,
prediction models for spatial dose and dose statistics are trained and
furthermore systematically modified to simulate changes in tradeoff priorities,
creating a set of differently biased predictions. Based on the predictions, an
MCO problem is subsequently constructed using previously developed dose
mimicking functions, designed in such a way that its Pareto surface spans the
range of clinically acceptable yet realistically achievable plans as exactly as
possible. The result is an algorithm outputting a set of Pareto optimal plans,
either fluence-based or machine parameter-based, which the user can navigate
between in real time to make adjustments before a final deliverable plan is
created.
  Main results: Numerical experiments performed on a dataset of prostate cancer
patients show that one may often navigate to a better plan than one produced by
a single-plan-output algorithm.
  Significance: We demonstrate the potential of merging MCO and a data-driven
workflow to automate labor-intensive parts of the treatment planning process
while maintaining a certain extent of manual control for the user.


  Neutron irradiation progressively changes the properties of zirconium alloys:
they harden and their average c/a lattice parameter ratio decreases with
fluence. The bombardment by neutrons produces point defects, which evolve into
dislocation loops that contribute to a non-uniform growth phenomenon called
irradiation-induced growth (IIG). To gain insights into these dislocation loops
in Zr we studied them using atomistic simulation. We constructed and relaxed
dislocation loops of various types. We find that the energies of <a>-loops on
different habit planes are similar, but our results indicate that they are most
likely to form on the 1st prismatic plane and then reduce their energy by
rotating onto the 2nd prismatic plane. By simulating loops of different aspect
ratios, we find that, based on energetics alone, the shape of <a>-loops does
not depend on character, and that these loops become increasingly elliptical as
their size increases. Additionally, we find that interstitial <c/2+p>-loops and
vacancy <c>-loops are both energetically feasible and so the possibility of
these should be considered in future work. Our findings offer important
insights into loop formation and evolution, which are difficult to probe
experimentally.


  We propose a low complexity list successive cancellation (LCLSC) decoding
algorithm to reduce complexity of traditional list successive cancellation
(LSC) decoding of polar codes while trying to maintain the LSC decoding
performance at the same time. By defining two thresholds, namely "likelihood
ratio (LR) threshold" and "Bhattacharyya parameter threshold", we classify the
reliability of each received information bit and the quality of each bit
channel. Based on this classification, we implement successive cancellation
(SC) decoding instead of LSC decoding when the information bits from "bad"
subchannels are received reliably and further attempt to skip LSC decoding for
the rest information bits in order to achieve a lower complexity compared to
full LSC decoding. Simulation results show that the complexity of LCLSC
decoding is much lower than LSC decoding and can be close to that of SC
decoding, especially in low code rate regions.


  In this work we study a phenomenological non-gravitational interaction
between dark matter and dark energy. The scenario studied in this work extends
the usual interaction model proportional to the derivative of the dark
component density adding to the coupling a non-linear term of the form $Q =
\rho'/3(\alpha + \beta \rho)$. This dark sector interaction model could be
interpreted as a particular case of a running vacuum model of the type
$\Lambda(H) = n_0 + n_1 H^2 + n_2 H^4$ in which the vacuum decays into dark
matter. For a flat FRW Universe filled with dark energy, dark matter and
decoupled baryonic matter and radiation we calculate the energy density
evolution equations of the dark sector and solve them. The different sign
combinations of the two parameters of the model show clear qualitative
different cosmological scenarios, from basic cosmological insights we discard
some of them. The linear scalar perturbation equations of the dark matter were
calculated. Using the CAMB code we calculate the CMB and matter power spectra
for some values of the parameters $\alpha$ and $\beta$ and compare it with
$\Lambda$CDM. The model modify mainly the lower multipoles of the CMB power
spectrum remaining almost the same the high ones. The matter power spectrum for
low wave numbers is not modified by the interaction but after the maximum it is
clearly different. Using observational data from Planck, and various galaxy
surveys we obtain the constraints of the parameters, the best fit values
obtained are the combinations $\alpha = (3.7 \pm 7 )\times 10^{-4} $,
$-(1.5\times10^{-5} {\rm eV}^{-1})^{4} \ll \beta < (0.07 {\rm eV}^{-1})^4$.


  We show that with spatially incoherent illumination, the point spread
function width of an imaging interferometer like that used in full-field
optical coherence tomography (FFOCT) is almost insensitive to aberrations that
mostly induce a reduction of the signal level without broadening. This is
demonstrated by comparison with traditional scanning OCT and wide-field OCT
with spatially coherent illuminations. Theoretical analysis, numerical
calculation as well as experimental results are provided to show this specific
merit of incoherent illumination in full-field OCT. To the best of our
knowledge, this is the first time that such result has been demonstrated.


  We present precision calculations of dark radiation in the form of gravitons
coming from Hawking evaporation of spinning primordial black holes (PBHs) in
the early Universe. Our calculation incorporates a careful treatment of
extended spin distributions of a population of PBHs, the PBH reheating
temperature, and the number of relativistic degrees of freedom. We compare our
precision results with those existing in the literature, and show constraints
on PBHs from current bounds on dark radiation from BBN and the CMB, as well as
the projected sensitivity of CMB Stage 4 experiments. As an application, we
consider the case of PBHs formed during an early matter-dominated era (EMDE).
We calculate graviton production from various PBH spin distributions pertinent
to EMDEs, and find that PBHs in the entire mass range up to $10^9\,$g will be
constrained by measurements from CMB Stage 4 experiments, assuming PBHs come to
dominate the Universe prior to Hawking evaporation. We also find that for PBHs
with monochromatic spins $a^*>0.81$, all PBH masses in the range $10^{-1}\,{\rm
g} < M_{\rm BH} <10^9\,$g will be probed by CMB Stage 4 experiments.


  Affordance-Centric Question-driven Task Completion (AQTC) has been proposed
to acquire knowledge from videos to furnish users with comprehensive and
systematic instructions. However, existing methods have hitherto neglected the
necessity of aligning spatiotemporal visual and linguistic signals, as well as
the crucial interactional information between humans and objects. To tackle
these limitations, we propose to combine large-scale pre-trained
vision-language and video-language models, which serve to contribute stable and
reliable multimodal data and facilitate effective spatiotemporal visual-textual
alignment. Additionally, a novel hand-object-interaction (HOI) aggregation
module is proposed which aids in capturing human-object interaction
information, thereby further augmenting the capacity to understand the
presented scenario. Our method achieved first place in the CVPR'2023 AQTC
Challenge, with a Recall@1 score of 78.7\%. The code is available at
https://github.com/tomchen-ctj/CVPR23-LOVEU-AQTC.


  We determine the factor generated by the GNS-representation defined by a
KMS-weight for a generalized gauge action on a simple graph C*-algebra when the
corresponding measure on the path space of the graph is conservative for the
shift. This is an improvment of Theorem 3.2 in arXives 1412.6762.


  The validity of two fundamental concepts of classical chemical kinetics - the
notion of "Chemical Equilibrium" and the "Law of Mass Action" - are re-examined
for reversible \textit{diffusion-limited} reactions (DLR), as exemplified here
by association/dissociation $A+A \rightleftharpoons B$ reactions. We consider a
general model of long-ranged reactions, such that any pair of $A$ particles,
separated by distance $\mu$, may react with probability $\omega_+(\mu)$, and
any $B$ may dissociate with probability $\omega_-(\lambda)$ into a geminate
pair of $A$s separated by distance $\lambda$. Within an exact analytical
approach, we show that the asymptotic state attained by reversible DLR at $t =
\infty$ is generally \textit{not a true thermodynamic equilibrium}, but rather
a non-equilibrium steady-state, and that the Law of Mass Action is invalid. The
classical picture holds \text{only} in physically unrealistic case when
$\omega_+(\mu) \equiv \omega_-(\mu)$ for any value of $\mu$.


  Can one learn to diagnose COVID-19 under extreme minimal supervision? Since
the outbreak of the novel COVID-19 there has been a rush for developing
Artificial Intelligence techniques for expert-level disease identification on
Chest X-ray data. In particular, the use of deep supervised learning has become
the go-to paradigm. However, the performance of such models is heavily
dependent on the availability of a large and representative labelled dataset.
The creation of which is a heavily expensive and time consuming task, and
especially imposes a great challenge for a novel disease. Semi-supervised
learning has shown the ability to match the incredible performance of
supervised models whilst requiring a small fraction of the labelled examples.
This makes the semi-supervised paradigm an attractive option for identifying
COVID-19. In this work, we introduce a graph based deep semi-supervised
framework for classifying COVID-19 from chest X-rays. Our framework introduces
an optimisation model for graph diffusion that reinforces the natural relation
among the tiny labelled set and the vast unlabelled data. We then connect the
diffusion prediction output as pseudo-labels that are used in an iterative
scheme in a deep net. We demonstrate, through our experiments, that our model
is able to outperform the current leading supervised model with a tiny fraction
of the labelled examples. Finally, we provide attention maps to accommodate the
radiologist's mental model, better fitting their perceptual and cognitive
abilities. These visualisation aims to assist the radiologist in judging
whether the diagnostic is correct or not, and in consequence to accelerate the
decision.


  We present an analytical solution of an effective field theory which, in one
of its formulations, is equivalent to the Ginzburg's $\Psi$-theory for the
behavior of the Casimir force in a film of $^4$He in equilibrium with its vapor
near the superfluid transition point. We consider three versions of the theory,
depending on the way one determines its parameters from the experimental
measurements. We present exact results for the behavior of the order parameter
profiles and of the Casimir force within this theory, which is characterized by
$d=3$, $\nu=2/3$ and $\beta=1/3$, where $d$ is the bulk spatial dimension and
$\nu$ and $\beta$ are the usual critical exponents. In addition, we revisit
relevant experiments \cite{GC99} and \cite{GSGC2006} in terms of our findings.
We find reasonably good agreement between our theoretical predictions and the
experimental data. We demonstrate analytically that our calculated force is
attractive. The position of the extremum is predicted to be at $x_{\rm
min}=\pi$, with $x=(L/\xi_0)(T/T_\lambda-1)^{1/\nu}$, which value effectively
coincides with the experimental finding $x_{\rm min}=3.2\pm 0.18$. Here $L$ is
the thickness of the film, $T_\lambda$ is the bulk critical temperature and
$\xi_0$ is the correlation length amplitude of the system for temperature
$T>T_\lambda$. The theoretically predicted position of the minimum does not
depend on the one adjustable parameter, $M$, entering the theory.


  Due to the significant resemblance in visual appearance, pill misuse is
prevalent and has become a critical issue, responsible for one-third of all
deaths worldwide. Pill identification, thus, is a crucial concern needed to be
investigated thoroughly. Recently, several attempts have been made to exploit
deep learning to tackle the pill identification problem. However, most
published works consider only single-pill identification and fail to
distinguish hard samples with identical appearances. Also, most existing pill
image datasets only feature single pill images captured in carefully controlled
environments under ideal lighting conditions and clean backgrounds. In this
work, we are the first to tackle the multi-pill detection problem in real-world
settings, aiming at localizing and identifying pills captured by users in a
pill intake. Moreover, we also introduce a multi-pill image dataset taken in
unconstrained conditions. To handle hard samples, we propose a novel method for
constructing heterogeneous a priori graphs incorporating three forms of
inter-pill relationships, including co-occurrence likelihood, relative size,
and visual semantic correlation. We then offer a framework for integrating a
priori with pills' visual features to enhance detection accuracy. Our
experimental results have proved the robustness, reliability, and
explainability of the proposed framework. Experimentally, it outperforms all
detection benchmarks in terms of all evaluation metrics. Specifically, our
proposed framework improves COCO mAP metrics by 9.4% over Faster R-CNN and
12.0% compared to vanilla YOLOv5. Our study opens up new opportunities for
protecting patients from medication errors using an AI-based pill
identification solution.


  We study cluster and hypernuclei production in heavy-ion collisions at
relativistic energies employing the Parton-Hadron-Quantum-Molecular-Dynamics
(PHQMD) approach, a microscopic n-body transport model based on the QMD
propagation of the baryonic degrees of freedom with density dependent 2-body
potential interactions. All other ingredients of PHQMD, including the collision
integral and the treatment of the quark-gluon plasma (QGP) phase, are adopted
from the Parton-Hadron-String Dynamics (PHSD) approach. In PHQMD the cluster
formation occurs dynamically, caused by the interactions. The clusters are
recognized by the Minimum Spanning Tree (MST) algorithm. We present the PHQMD
results for cluster and hypernuclei formation in comparison with the available
experimental data at AGS, SPS, RHIC-BES and RHIC fixed target energies. We also
provide predictions on cluster production for the upcoming FAIR and NICA
experiments. PHQMD allows to study the time evolution of formed clusters and
the origin of their production, which helps to understand how such weakly bound
objects are formed and survive in the rather dense and hot environment created
in heavy-ion collisions. It offers therefore an explanation of the 'ice in the
fire' puzzle.


  Krylov complexity is considered to provide a measure of the growth of
operators evolving under Hamiltonian dynamics. The main strategy is the
analysis of the structure of Krylov subspace $\mathcal{K}_M(\mathcal{H},\eta)$
spanned by the multiple applications of the Liouville operator $\mathcal{L}$
defined by the commutator in terms of a Hamiltonian $\mathcal{H}$,
$\mathcal{L}:=[\mathcal{H},\cdot]$ acting on an operator $\eta$,
$\mathcal{K}_M(\mathcal{H},\eta)=\text{span}\{\eta,\mathcal{L}\eta,\ldots,\mathcal{L}^{M-1}\eta\}$.
For a given inner product $(\cdot,\cdot)$ of the operators, the orthonormal
basis $\{\mathcal{O}_n\}$ is constructed from
$\mathcal{O}_0=\eta/\sqrt{(\eta,\eta)}$ by Lanczos algorithm. The moments
$\mu_m=(\mathcal{O}_0,\mathcal{L}^m\mathcal{O}_0)$ are closely related to the
important data $\{b_n\}$ called Lanczos coefficients. I present the exact and
explicit expressions of the moments $\{\mu_m\}$ for 16 quantum mechanical
systems which are {\em exactly solvable both in the Schr\"odinger and
Heisenberg pictures}. The operator $\eta$ is the variable of the
eigenpolynomials. Among them six systems show a clear sign of `non-complexity'
as vanishing higher Lanczos coefficients $b_m=0$, $m\ge3$.


  We show that quantum computers can be used for producing large $n$-partite
nonlocality, thereby providing a method to benchmark them. The main challenges
to overcome are: (i) The interaction topology might not allow arbitrary
two-qubit gates. (ii) Noise limits the Bell violation. (iii) The number of
combinations of local measurements grows exponentially with $n$. To overcome
(i), we point out that graph states that are compatible with the two-qubit
connectivity of the computer can be efficiently prepared. To mitigate (ii), we
note that, for specific graph states, there are $n$-partite Bell inequalities
whose resistance to white noise increases exponentially with $n$. To address
(iii) for any $n$ and any connectivity, we introduce an estimator that relies
on random sampling. As a result, we propose a method for producing $n$-partite
Bell nonlocality with unprecedented large $n$. This allows in return to
benchmark nonclassical correlations regardless of the number of qubits or the
connectivity. We test our approach by using a simulation for a noisy IBM
quantum computer, which predicts $n$-partite Bell nonlocality for at least
$n=24$ qubits.


  In the past decade, due to the experimental observation of many
charmonium-like states, there has been a revival of hadron spectroscopy. In
particular, the experimental observation of charged charmonium-like, $Z_c$
states, and bottomonium-like, $Z_b$ states, represents a challenge since they
can not be accommodated within the naive quark model. These charged states are
good candidates of either tetraquark or molecular states and their observation
motivated a vigorous theoretical activity. This is a rapidly evolving field
with enormous amount of new experimental information. In this work, we review
the current experimental progress and investigate various theoretical
interpretations of these candidates of the multiquark states. The present
review is written from the perspective of the QCD sum rules approach, where we
present the main steps of concrete calculations and compare the results with
other approaches and with experimental data.


  Dwarf galaxies populating the Galactic halo are assumed to host the largest
fractions of dark matter, as calculated from their velocity dispersions. Their
major axes are preferentially aligned with the Vast Polar Structure (VPOS) that
is perpendicular to the Galactic disk, and we find their velocity gradients
aligned as well. It suggests that tidal forces exerted by the Milky Way are
distorting dwarf galaxies.
  Here we demonstrate on the basis of the impulse approximation that the
Galactic gravitational acceleration induces the dwarf line-of-sight velocity
dispersion, which is also evidenced by strong dependences between both
quantities. Since this result is valid for any dwarf mass value, it implies
that dark matter estimate in Milky Way dwarfs cannot be deduced from the
product of their radius to the square of their line-of-sight velocity
dispersion. This questions the high dark-matter fractions reported for these
evanescent systems, and the universally adopted total-to-stellar mass
relationship in the dwarf regime. It suggests that many dwarfs are at their
first passage and are dissolving into the Galactic halo. It opens a promising
way to estimate the Milky Way total mass profile at large distances.


  This study uses 125 responses from companies of all sizes headquartered in
Germany, Switzerland, France and UK to reveal perceptions of the drivers of
organisational agility. It further investigates current understanding of
managing principles of multiple organisational dimensions such as culture,
values, leadership, organisational structure, processes and others to achieve
greater organisational agility. The data set is disaggregated into four major
profiles of agile organisations: laggards, execution specialists,
experimenters, and leaders. The approach to agile transformation is analysed by
each of those profiles. While the positive effect from a more holistic approach
is confirmed, leaders tend to focus more on processes and products rather than
project work. Respondents perceive that IT, product development and research
are most agile functions within their organisations, while human resources,
finance and administration are considered being not agile. Further,
organisations with higher levels of organisational agility tend use more than
one agile scaling framework. Implications on theories of agile transformations
and organisational design are discussed.


  For immersed surfaces in the four-space, we have a generating set of the
Swenton--Hughes--Kim--Miller spatial moves that relate singular banded diagrams
of ambient isotopic immersions of those surfaces. We also have
Yoshikawa--Kamada--Kawauchi--Kim--Lee planar moves that relate marked graph
diagrams of ambient isotopic immersions of those surfaces. One can ask if the
former moves form a minimal set and if the latter moves form a generating set.
In this paper, we derive a minimal generating set of spatial moves for diagrams
of surfaces immersed in the four-space, which translates into a generating set
of planar moves. We also show that the complements of two equivalent immersed
surfaces can be transformed one another by a Kirby calculus not requiring the
1-1-handle or 2-1-handle slides. We also discuss the fundamental group of the
immersed surface-link complement in the four-space and a quandle coloring
invariant of an oriented immersed surface-link.


  In this paper, we extend the study of concept ablation within pre-trained
models as introduced in 'Ablating Concepts in Text-to-Image Diffusion Models'
by (Kumari et al.,2022). Our work focuses on reproducing the results achieved
by the different variants of concept ablation proposed and validated through
predefined metrics. We also introduce a novel variant of concept ablation,
namely 'trademark ablation'. This variant combines the principles of
memorization and instance ablation to tackle the nuanced influence of
proprietary or branded elements in model outputs. Further, our research
contributions include an observational analysis of the model's limitations.
Moreover, we investigate the model's behavior in response to ablation
leakage-inducing prompts, which aim to indirectly ablate concepts, revealing
insights into the model's resilience and adaptability. We also observe the
model's performance degradation on images generated by concepts far from its
target ablation concept, documented in the appendix.


  In this paper, we provide a complete classification for the first-order
Goedel logics concerning the property that the formulas admit logically
equivalent prenex normal forms. We show that the only first-order Goedel logics
that admit such prenex forms are those with finite truth value sets since they
allow all quantifier-shift rules and the logic $G_\uparrow$ with only one
accumulation point at 1 in the infinite truth value set. In all the other
cases, there are generally no logically equivalent prenex normal forms. We will
also see that $G_\uparrow$ is the intersection of all finite first-order Goedel
logics.
  The second part of this paper investigates the existence of effective
equivalence between the validity of a formula and the validity of some prenex
normal form. The existence of such a normal form is obvious for finite valued
Goedel logic and $G_\uparrow$. Goedel logics with an uncountable truth value
set admit the prenex normal forms if and only if every surrounding of 0 is
uncountable or 0 is an isolated point. Otherwise, uncountable Goedel logics are
not recursively enumerable, however, the prenex fragment is always recursively
enumerable. Therefore, there is no effective translation between the valid
formula and the valid prenex normal form. However, the existence of effectively
constructible validity equivalent prenex forms for the countable case is still
up for debate.


  Neural network (NN) ensembles can reduce large prediction variance of NN and
improve prediction accuracy. For highly nonlinear problems with insufficient
data set, the prediction accuracy of NN models becomes unstable, resulting in a
decrease in the accuracy of ensembles. Therefore, this study proposes a
frequency distribution-based ensemble that identifies core prediction values,
which are expected to be concentrated near the true prediction value. The
frequency distribution-based ensemble classifies core prediction values
supported by multiple prediction values by conducting statistical analysis with
a frequency distribution, which is based on various prediction values obtained
from a given prediction point. The frequency distribution-based ensemble can
improve predictive performance by excluding prediction values with low accuracy
and coping with the uncertainty of the most frequent value. An adaptive
sampling strategy that sequentially adds samples based on the core prediction
variance calculated as the variance of the core prediction values is proposed
to improve the predictive performance of the frequency distribution-based
ensemble efficiently. Results of various case studies show that the prediction
accuracy of the frequency distribution-based ensemble is higher than that of
Kriging and other existing ensemble methods. In addition, the proposed adaptive
sampling strategy effectively improves the predictive performance of the
frequency distribution-based ensemble compared with the previously developed
space-filling and prediction variance-based strategies.