  Text-based 2D diffusion models have demonstrated impressive capabilities in
image generation and editing. Meanwhile, the 2D diffusion models also exhibit
substantial potentials for 3D editing tasks. However, how to achieve consistent
edits across multiple viewpoints remains a challenge. While the iterative
dataset update method is capable of achieving global consistency, it suffers
from slow convergence and over-smoothed textures. We propose SyncNoise, a novel
geometry-guided multi-view consistent noise editing approach for high-fidelity
3D scene editing. SyncNoise synchronously edits multiple views with 2D
diffusion models while enforcing multi-view noise predictions to be
geometrically consistent, which ensures global consistency in both semantic
structure and low-frequency appearance. To further enhance local consistency in
high-frequency details, we set a group of anchor views and propagate them to
their neighboring frames through cross-view reprojection. To improve the
reliability of multi-view correspondences, we introduce depth supervision
during training to enhance the reconstruction of precise geometries. Our method
achieves high-quality 3D editing results respecting the textual instructions,
especially in scenes with complex textures, by enhancing geometric consistency
at the noise and pixel levels.


  The equilibrium free energy landscape of off-lattice model heteropolymers as
a function of an internal coordinate, namely the end-to-end distance, is
reconstructed from out-of-equilibrium steered molecular dynamics data. This
task is accomplished via two independent methods: by employing an extended
version of the Jarzynski equality (EJE) and the inherent structure (IS)
formalism. A comparison of the free energies estimated with these two schemes
with equilibrium results obtained via the umbrella sampling technique reveals a
good quantitative agreement among all the approaches in a range of temperatures
around the ``folding transition'' for the two examined sequences. In
particular, for the sequence with good foldability properties, the mechanically
induced structural transitions can be related to thermodynamical aspects of
folding. Moreover, for the same sequence the knowledge of the landscape profile
allows for a good estimation of the life times of the native configuration for
temperatures ranging from the folding to the collapse temperature. For the
random sequence, mechanical and thermal unfolding appear to follow different
paths along the landscape.


  We address the problem of the information-disturbance trade-off associated to
the estimation of a quantum transformation, and show how the extraction of
information about the a black box causes a perturbation of the corresponding
input-output evolution. In the case of a black box performing a unitary
transformation, randomly distributed according to the invariant measure, we
give a complete solution of the problem, deriving the optimal trade-off curve
and presenting an explicit construction of the optimal quantum network.


  In the previous paper arXiv:2003.06470 we introduced the notion of ${\mathbb
Z}_2\times{\mathbb Z}_2$-graded classical mechanics and presented a general
framework to construct, in the Lagrangian setting, the worldline sigma models
invariant under a ${\mathbb Z}_2\times{\mathbb Z}_2$-graded superalgebra. In
this work we discuss at first the classical Hamiltonian formulation of some of
these models and later present their canonical quantization. As the simplest
application of the construction we recover the ${\mathbb Z}_2\times{\mathbb
Z}_2$-graded quantum Hamiltonian introduced by Bruce and Duplij in
arXiv:1904.06975. We prove that this is the first example of a large class of
${\mathbb Z}_2\times{\mathbb Z}_2$-graded quantum models. We derive in
particular interacting multiparticle quantum Hamiltonians given by Hermitian,
matrix, differential operators. The interacting terms appear as non-diagonal
entries in the matrices. The construction of the Noether charges, both
classical and quantum, is presented. A comprehensive discussion of the
different ${\mathbb Z}_2\times{\mathbb Z}_2$-graded symmetries possessed by the
quantum Hamiltonians is given.


  Focusing properties of a novel type photoresist microlens are studied. A
specific character of the microlens is its mushroom shape. Recently it was
predicted and experimentally revealed that such a lens integrated with a
light-emitting diode is capable of enhancing its output efficiency and
directivity. In our paper we describe the true electromagnetic performance of a
mushroom lens by applying a mathematically rigorous method of boundary integral
equations. Numerical results are presented for the mushroom lens illuminated
with a plane E-polarized wave and include figures describing the evolution of
the lens focal spot and near field maps.


  In the last few years it has become possible to study low energy pi pi
scattering in kaon decays to three pions, thanks to the high statistics
measurement of K+- -> pi+- pi0 pi0 decays performed by the NA48/2 experiment at
the CERN SPS. At the pi+ pi- threshold, the pi0 pi0 mass spectrum exhibits a
Wigner-cusp, from which the S-wave pi pi scattering lengths are extracted with
high precision. This measurement is complementary to the extraction of the
scattering lengths from K_e4 decays, which is also performed by the NA48/2
experiment.


  We introduce the notion of Point in Time Economic Scenario Generation (PiT
ESG) with a clear mathematical problem formulation to unify and compare
economic scenario generation approaches conditional on forward looking market
data. Such PiT ESGs should provide quicker and more flexible reactions to
sudden economic changes than traditional ESGs calibrated solely to long periods
of historical data. We specifically take as economic variable the S&P500 Index
with the VIX Index as forward looking market data to compare the nonparametric
filtered historical simulation, GARCH model with joint likelihood estimation
(parametric), Restricted Boltzmann Machine and the conditional Variational
Autoencoder (Generative Networks) for their suitability as PiT ESG. Our
evaluation consists of statistical tests for model fit and benchmarking the out
of sample forecasting quality with a strategy backtest using model output as
stop loss criterion. We find that both Generative Networks outperform the
nonparametric and classic parametric model in our tests, but that the CVAE
seems to be particularly well suited for our purposes: yielding more robust
performance and being computationally lighter.


  We compute the second coefficient of the composition of two Berezin-Toeplitz
operators associated with the $\text{spin}^c$ Dirac operator on a symplectic
manifold, making use of the full-off diagonal expansion of the Bergman kernel.


  We show the following geometric generalization of a classical theorem of W.H.
Gottschalk and G.A. Hedlund: a skew action induced by a cocycle of (affine)
isometries of a Hilbert space over a minimal dynamics has a continuous
invariant section if and only if the cocycle is bounded. Equivalently, the
associated twisted cohomological equation has a continuous solution if and only
if the cocycle is bounded. We interpret this as a version of the Bruhat-Tits
center lemma in the space of continuous functions. Our result also holds when
the fiber is a proper CAT(0) space. One of the appplications concerns matrix
cocycles. Using the action of $\mathrm{GL} (n,\mathbb{R})$ on the
(nonpositively curved) space of positively definite matrices, we show that
every bounded linear cocycle over a minimal dynamics is cohomologous to a
cocycle taking values in the orthogonal group.


  We study algorithmic questions for concurrent systems where the transitions
are labeled from a complete, closed semiring, and path properties are algebraic
with semiring operations. The algebraic path properties can model dataflow
analysis problems, the shortest path problem, and many other natural problems
that arise in program analysis. We consider that each component of the
concurrent system is a graph with constant treewidth, a property satisfied by
the controlflow graphs of most programs. We allow for multiple possible
queries, which arise naturally in demand driven dataflow analysis. The study of
multiple queries allows us to consider the tradeoff between the resource usage
of the one-time preprocessing and for each individual query. The traditional
approach constructs the product graph of all components and applies the
best-known graph algorithm on the product. In this approach, even the answer to
a single query requires the transitive closure, which provides no room for
tradeoff between preprocessing and query time.
  Our main contributions are algorithms that significantly improve the
worst-case running time of the traditional approach, and provide various
tradeoffs depending on the number of queries. For example, in a concurrent
system of two components, the traditional approach requires hexic time in the
worst case for answering one query as well as computing the transitive closure,
whereas we show that with one-time preprocessing in almost cubic time, each
subsequent query can be answered in at most linear time, and even the
transitive closure can be computed in almost quartic time. Furthermore, we
establish conditional optimality results showing that the worst-case running
time of our algorithms cannot be improved without achieving major breakthroughs
in graph algorithms.


  We describe the nonzero temperature (T), low frequency (\omega) dynamics of
the order parameter near quantum critical points in two spatial dimensions (d),
with a special focus on the regime \hbar\omega << k_B T. For the case of a
`relativistic', O(n)-symmetric, bosonic quantum field theory we show that, for
small \epsilon=3-d, the dynamics is described by an effective classical model
of waves with a quartic interaction. We provide analytical and numerical
analyses of the classical wave model directly in d=2. We describe the crossover
from the finite frequency, "amplitude fluctuation", gapped quasiparticle mode
in the quantum paramagnet (or Mott insulator), to the zero frequency "phase" (n
>= 2) or "domain wall" (n=1) relaxation mode near the ordered state. For static
properties, we show how a surprising, duality-like transformation allows an
exact treatment of the strong-coupling limit for all n. For n=2, we compute the
universal T dependence of the superfluid density below the Kosterlitz-Thouless
temperature, and discuss implications for the high temperature superconductors.
For n=3, our computations of the dynamic structure factor relate to neutron
scattering experiments on La_{1.85}Sr_{0.15}CuO_4, and to light scattering
experiments on double layer quantum Hall systems. We expect that closely
related effective classical wave models will apply also to other quantum
critical points in d=2.


  A new approach to prove the one-dimensional Cauchy problem's weakly
discontinuous solutions for hyperbolic PDEs are on the characteristics is
discussed in this paper. To do so, I use wavelet singularity detection methods
or WTMM [1] based on two-dimensional wavelet transform and combine it with the
Lipschitz index to strengthen the detection.


  In this paper, we introduce GrAVITree, a tree- and sampling-based algorithm
to compute a near-optimal value function and corresponding feedback policy for
indefinite time-horizon, terminal state-constrained nonlinear optimal control
problems. Our algorithm is suitable for arbitrary nonlinear control systems
with both state and input constraints. The algorithm works by sampling feasible
control inputs and branching backwards in time from the terminal state to build
the tree, thereby associating each vertex in the tree with a feasible control
sequence to reach the terminal state. Additionally, we embed this stochastic
tree within a larger graph structure, rewiring of which enables rapid
adaptation to changes in problem structure due to, e.g., newly detected
obstacles. Because our method reasons about global problem structure without
relying on (potentially imprecise) derivative information, it is particularly
well suited to controlling a system based on an imperfect deep neural network
model of its dynamics. We demonstrate this capability in the context of an
inverted pendulum, where we use a learned model of the pendulum with actuator
limits and achieve robust stabilization in settings where competing graph-based
and derivative-based techniques fail.


  We present the MARD-Y3 catalog of between 1086 and 2171 galaxy clusters (52\%
and 65\% new) produced using multi-component matched filter (MCMF) followup in
5000\,deg$^2$ of DES-Y3 optical data of the $\sim$20000 overlapping 2RXS X-ray
sources. Optical counterparts are identified as peaks in galaxy richness as a
function of redshift along the line of sight toward each 2RXS source within a
search region informed by an X-ray prior. All peaks are assigned a probability
\fcont\ of being a random superposition. The clusters lie at $0.02<z<1.1$ with
more than 100 clusters at $z>0.5$. Residual contamination is 2.6\% and 9.6\%
for the cuts adopted here. For each cluster we present the optical center,
redshift, rest frame X-ray luminosity, $M_{500}$ mass, coincidence with NWAY
infrared sources and estimators of dynamical state. About 2\% of MARD-Y3
clusters have multiple possible counterparts, the photo-z's are high quality
with $\sigma_{\Delta z/(1+z)}=0.0046$, and $\sim$1\% of clusters exhibit
evidence of X-ray luminosity boosting from emission by cluster AGN. Comparison
with other catalogs (MCXC, RM, SPT-SZ, Planck) is performed to test consistency
of richness, luminosity and mass estimates. We measure the MARD-Y3 X-ray
luminosity function and compare it to the expectation from a fiducial cosmology
and externally calibrated luminosity- and richness-mass relations. Agreement is
good, providing evidence that MARD-Y3 has low contamination and can be
understood as a simple two step selection-- X-ray and then optical-- of an
underlying cluster population described by the halo mass function.


  A neuromorphic SLAM system shows potential for more efficient implementation
than its traditional counterpart. We demonstrate a mixed-mode implementation
for spatial encoding neurons including theta cells, vector cells, and place
cells. Together, they form a biologically plausible network that could
reproduce the localization functionality of place cells. The system consists of
a theta chip with 128 units and an FPGA encoding 4 networks for vector cells
formation that provides the capability for tracking on a 11 by 11 place cell
grid. Experimental results validate the robustness of our model when suffering
from 18% standard deviation from mathematical models induced by variations of
analog circuits. We provide a foundation for implementing dynamic neuromorphic
SLAM systems for nonhomogeneous mapping and inspirations for the formation of
spatial cells in biology.


  In the Milky Way, the thick disk can be defined using individual stellar
abundances, kinematics, or age; or geometrically, as stars high above the
mid-plane. In nearby galaxies, where only a geometric definition can be used,
thick disks appear to have large radial scale-lengths, and their red colors
suggest that they are uniformly old. The Milky Way's geometrically thick disk
is also radially extended, but it is far from chemically uniform:
alpha-enhanced stars are confined within the inner Galaxy. In simulated
galaxies, where old stars are centrally concentrated, geometrically thick disks
are radially extended, too. Younger stellar populations flare in the simulated
disks' outer regions, bringing those stars high above the mid-plane. The
resulting geometrically thick disks therefore show a radial age gradient, from
old in their central regions to younger in their outskirts. Based on our age
estimates for a large sample of giant stars in the APOGEE survey, we can now
test this scenario for the Milky Way. We find that the geometrically-defined
thick disk in the Milky Way has indeed a strong radial age gradient: the median
age for red clump stars goes from ~9 Gyr in the inner disk to 5 Gyr in the
outer disk. We propose that at least some nearby galaxies could also have thick
disks that are not uniformly old, and that geometrically thick disks might be
complex structures resulting from different formation mechanisms in their inner
and outer parts.


  The nature of phase transitions involving the questions why and how phase
transitions take place has not been sufficiently touched in the literature. In
contrast, the current attention to certain extent still focus on the
description of critical phenomena and the classification of the associated
phase transition along with the Ginzburg-Landau-Wilson paradigm, where the key
issue is to identify phenomenologically order parameters and related
symmetries. This brings the question to topological phase transitions (TPTs),
where no obvious order parameter and the broken symmetry are identified. Here
we present a unified pattern description of the second-order quantum phase
transition (QPT) and TPT, both involved in the one-dimensional anisotropic
quantum XY model in a transverse field, which contains the transverse Ising
model (TIM) as a limit case. Away from the TIM, the XY model enters the
ferromagnetic phase (marked by a second-order QPT or a direct TPT) as
increasing ferromagentic exchange coupling, a series of TPTs occur, which are
absent in the TIM. The TPTs behave like the first-order QPTs. In the isotropic
and large exchange coupling cases, the ground state of the XY model is
dominated by two topologically different vortices along positive and negative
direction of the transverse field. We confirm the above conclusion by analyzing
the energy contributions of the patterns to the ground state and calculating
the ground state pattern occupations of the XY model. The results have been
obtained in a unified and self-evident way and answer the questions why and how
the QPT and TPTs take place in the XY model.


  Three challenges, however, can hinder the application of Feedback
Linearization: over-intensive control signals, singular decoupling matrix, and
saturation. Activating any of these three issues can challenge the stability
proof. To solve these three challenges, first, this research proposed the drone
gait plan. The gait plan was initially used to figure out the control problems
in quadruped (four-legged) robots; applying this approach, accompanied by
Feedback Linearization, the quality of the control signals was enhanced. Then,
we proposed the concept of unacceptable attitude curves, which are not allowed
for the tiltrotor to travel to. The Two Color Map Theorem was subsequently
established to enlarge the supported attitude for the tiltrotor. These theories
were employed in the tiltrotor tracking problem with different references.
Notable improvements in the control signals were witnessed in the tiltrotor
simulator. Finally, we explored the control theory, the stability proof of the
novel mobile robot (tilt vehicle) stabilized by Feedback Linearization with
saturation. Instead of adopting the tiltrotor model, which is over-complicated,
we designed a conceptual mobile robot (tilt-car) to analyze the stability
proof. The stability proof (stable in the sense of Lyapunov) was found for a
mobile robot (tilt vehicle) controlled by Feedback Linearization with
saturation for the first time. The success tracking result with the promising
control signals in the tiltrotor simulator demonstrates the advances of our
control method. Also, the Lyapunov candidate and the tracking result in the
mobile robot (tilt-car) simulator confirm our deductions of the stability
proof. These results reveal that these three challenges in Feedback
Linearization are solved, to some extents.


  A nonlinear vector supersymmetry for three-dimensional topological massive
Yang-Mills is obtained by making use of a nonlinear but local and covariant
redefinition of the gauge field.


  This paper deals with a polymeric matrix composite material. The matrix
behaviour is described by the modified Rabotnov's nonlinear viscoelastic model
assuming the material is nonlinear viscoelastic. The parameters of creep and
stress-relaxation kernels of the model are determined. From the experimental
data related to kernels approximated by spline functions and by means of the
method of weighted residual, the formulas for the determination of viscoelastic
parameters are derived.


  We study anomalous scaling and multiscaling of two-dimensional crack profiles
in the random fuse model using both periodic and open boundary conditions. Our
large scale and extensively sampled numerical results reveal the importance of
crack branching and coalescence of microcracks, which induce jumps in the
solid-on-solid crack profiles. Removal of overhangs (jumps) in the crack
profiles eliminates the multiscaling observed in earlier studies and reduces
anomalous scaling. We find that the probability density distribution $p(\Delta
h(\ell))$ of the height differences $\Delta h(\ell) = [h(x+\ell) - h(x)]$ of
the crack profile obtained after removing the jumps in the profiles has the
scaling form $p(\Delta h(\ell)) = <\Delta h^2(\ell)>^{-1/2} ~f(\frac{\Delta
h(\ell)}{<\Delta h^2(\ell)>^{1/2}})$, and follows a Gaussian distribution even
for small bin sizes $\ell$. The anomalous scaling can be summarized with the
scaling relation $[\frac{<\Delta h^2(\ell)>^{1/2}}{<\Delta
h^2(L/2)>^{1/2}}]^{1/\zeta_{loc}} + \frac{(\ell-L/2)^2}{(L/2)^2} = 1$, where
$<\Delta h^2(L/2)>^{1/2} \sim L^{\zeta}$.


  In urban environments, where line-of-sight signals from GNSS satellites are
frequently blocked by high-rise objects, GNSS receivers are subject to large
errors in measuring satellite ranges. Heuristic methods are commonly used to
estimate these errors and reduce the impact of noisy measurements on
localization accuracy. In our work, we replace these error estimation
heuristics with a deep learning model based on Graph Neural Networks.
Additionally, by analyzing the cost function of the multilateration process, we
derive an optimal method to utilize the estimated errors. Our approach
guarantees that the multilateration converges to the receiver's location as the
error estimation accuracy increases. We evaluate our solution on a real-world
dataset containing more than 100k GNSS epochs, collected from multiple cities
with diverse characteristics. The empirical results show improvements from 40%
to 80% in the horizontal localization error against recent deep learning
baselines as well as classical localization approaches.


  We present a sequent calculus for abstract focussing, equipped with
proof-terms: in the tradition of Zeilberger's work, logical connectives and
their introduction rules are left as a parameter of the system, which collapses
the synchronous and asynchronous phases of focussing as macro rules. We go
further by leaving as a parameter the operation that extends a context of
hypotheses with new ones, which allows us to capture both classical and
intuitionistic focussed sequent calculi. We then define the realisability
semantics of (the proofs of) the system, on the basis of Munch-Maccagnoni's
orthogonality models for the classical focussed sequent calculus, but now
operating at the higher level of abstraction mentioned above. We prove, at that
level, the Adequacy Lemma, namely that if a term is of type A, then in the
model its denotation is in the (set-theoretic) interpretation of A. This
exhibits the fact that the universal quantification involved when taking the
orthogonal of a set, reflects in the semantics Zeilberger's universal
quantification in the macro rule for the asynchronous phase. The system and its
semantics are all formalised in Coq.


  We theoretically analyse the hybrid Mie-exciton optical modes arising from
the strong coupling of excitons in organic dyes or transition-metal
dichalcogenides with the Mie resonances of high-index dielectric nanoparticles.
Detailed analytic calculations show that silicon--exciton core--shell
nanoparticles are characterised by a richness of optical modes which can be
tuned through nanoparticle dimensions to produce large anticrossings in the
visible or near infrared, comparable to those obtained in plexcitonics. The
complex magnetic-excitonic nature of these modes is understood through spectral
decomposition into Mie-coefficient contributions, complemented by electric and
magnetic near-field profiles. In the frequency range of interest, absorptive
losses in silicon are sufficiently low to allow observation of several periods
of Rabi oscillations in strongly coupled emitter-particle architectures, as
confirmed here by discontinuous Galerkin time-domain calculations for the
electromagnetic field beat patterns. These results suggest that Mie resonances
in high-index dielectrics are promising alternatives for plasmons in
strong-coupling applications in nanophotonics, while the coupling of magnetic
and electric modes opens intriguing possibilities for external control.


  Performing Monte Carlo simulations we study the temperature dependent
self--organization of magnetic moments coupled to itinerant electrons in a
finite--size one--dimensional nanostructure proximitized to a superconducting
reservoir. At low temperature an effective interaction between the localized
magnetic moments, that is mediated by itinerant electrons, leads to their
helical ordering. This ordering, in turn, affects the itinerant electrons,
inducing the topologically nontrivial superconducting phase that hosts the
Majorana modes. In a~wide range of system parameters, the spatial periodicity
of a spiral order that minimizes the ground state energy turns out to promote
the topological phase. We determine the correlation length of such spiral order
and study how it is reduced by thermal fluctuations. This reduction is
accompanied by suppression of the topological gap (which separates the
zero-energy mode from continuum), setting the upper (critical) temperature for
existence of the Majorana quasiparticles. Monte Carlo simulations do not rely
on any ansatz for configurations of the localized moments, therefore they can
be performed for arbitrary model parameters, also beyond the perturbative
regime.


  Activation cross sections of deuteron induced reactions on ytterbium for
production of $^{177g,173,172,171,170,169,167}$Lu, $^{177,175,169}$Yb and
$^{173,168,167,165}$Tm were extended up to 50 MeV deuteron energy. The new data
are in acceptable agreement with the earlier experimental data in the
overlapping energy region. The experimental data are compared with the
predictions of the ALICE-D, EMPIRE-D and TALYS 1.4 (TENDL-2013 on-line library
results) codes.


  We propose an entropic geometrical model of crowd behavior dynamics (with
dissipative crowd kinematics), using Feynman action--amplitude formalism that
operates on three synergetic levels: macro, meso and micro. The intent is to
explain the dynamics of crowds simultaneously and consistently across these
three levels, in order to characterize their geometrical properties
particularly with respect to behavior regimes and the state changes between
them. Its most natural statistical descriptor (order parameter) is crowd
entropy $S$ that satisfies the Prigogine's extended second law of
thermodynamics, $\partial_t S\geq 0$ (for any nonisolated multi-component
system). Qualitative similarities and superpositions between individual and
crowd configuration manifolds motivate our claim that \emph{goal-directed crowd
movement} operates under entropy conservation, $\partial_t S = 0$, while
\emph{naturally chaotic crowd dynamics} operates under (monotonically)
increasing entropy function, $\partial_t S > 0$. Between these two distinct
topological phases lies a phase transition with a chaotic inter-phase. Both
inertial crowd dynamics and its dissipative kinematics represent diffusion
processes on the crowd manifold governed by the Ricci flow.
  Keywords: Crowd behavior dynamics, action--amplitude formalism, entropic
crowd manifold, crowd turbulence, Ricci flow, topological phase transitions.


  Given a polynomial map f on the Euclidean n-space and a vector q, the
polynomial complementarity problem, PCP(f,q), is the nonlinear complementarity
problem of finding a nonnegative vector x such that y=f(x)+q is nonnegative and
orthogonal to x. It is called a tensor complementarity problem if the
polynomial map is homogeneous. In this paper, we establish results connecting
the polynomial complementarity problem PCP(f,q) and the tensor complementarity
problem PCP(f*,0), where f* is the leading term in the decomposition of f as a
sum of homogeneous polynomial maps. We show, for example, that PCP(f,q) has a
nonempty compact solution set for every q when zero is the only solution of
PCP(f*,0)and the local (topological) degree of min{x,f*(x)} at the origin is
nonzero. As a consequence, we establish Karamardian type results for polynomial
complementarity problems. By identifying a tensor A of order m and dimension n
with its corresponding homogeneous polynomial F(x):= Ax^{m-1}, we relate our
results to tensor complementarity problems. These results show that under
appropriate conditions, PCP(F+P,q) has a nonempty compact solution set for all
polynomial maps P of degree less than m-1 and for all vectors q, thereby
substantially improving the existing tensor complementarity results where only
problems of the type PCP(F,q) are considered. We introduce the concept of
degree of an R_0-tensor and show that the degree of an R-tensor is one. We
illustrate our results by constructing matrix based tensors.


  Let $R$ be a factorial domain. In this work we investigate the connections
between the arithmetic of ${\rm Int}(R)$ (i.e., the ring of integer-valued
polynomials over $R$) and its monadic submonoids (i.e., monoids of the form
$\{g\in {\rm Int}(R)\mid g\mid_{{\rm Int}(R)} f^k$ for some
$k\in\mathbb{N}_0\}$ for some nonzero $f\in {\rm Int}(R)$). Since every monadic
submonoid of ${\rm Int}(R)$ is a Krull monoid it is possible to describe the
arithmetic of these monoids in terms of their divisor-class group. We give an
explicit description of these divisor-class groups in several situations and
provide a few techniques that can be used to determine them. As an application
we show that there are strong connections between ${\rm Int}(R)$ and its
monadic submonoids. If $R=\mathbb{Z}$ or more generally if $R$ has sufficiently
many "nice" atoms, then we prove that the infinitude of the elasticity and the
tame degree of ${\rm Int}(R)$ can be explained by using the structure of
monadic submonoids of ${\rm Int}(R)$.


  Canonical quantisation of constrained systems with first class constraints
via Dirac's operator constraint method proceeds by the thory of Rigged Hilbert
spaces, sometimes also called Refined Algebraic Quantisation (RAQ). This method
can work when the constraints form a Lie algebra. When the constraints only
close with nontrivial structure functions, the Rigging map can no longer be
defined.
  To overcome this obstacle, the Master Constraint Method has been proposed
which replaces the individual constraints by a weighted sum of absolute squares
of the constraints. Now the direct integral decomposition methods (DID), which
are closely related to Rigged Hilbert spaces, become available and have been
successfully tested in various situations.
  It is relatively straightforward to relate the Rigging Inner Product to the
path integral that one obtains via reduced phase space methods. However, for
the Master Constraint this is not at all obvious. In this paper we find
sufficient conditions under which such a relation can be established. Key to
our analysis is the possibility to pass to equivalent, Abelian constraints, at
least locally in phase space. Then the Master Constraint DID for those Abelian
constraints can be directly related to the Rigging Map and therefore has a path
integral formulation.


  We investigate transmission energy minimization via optimizing wireless relay
selection in orthogonal-frequency-division multiple access (OFDMA) networks. We
take into account the impact of the load of cells on transmission energy. We
prove the NP-hardness of the energy-aware wireless relay selection problem. To
tackle the computational complexity, a partial optimality condition is derived
for providing insights in respect of designing an effective and efficient
algorithm. Numerical results show that the resulting algorithm achieves high
energy performance.


  A high-precision test of the Glauber formula for the amplitude of
nucleon-deuteron scattering is performed. Nucleon-nucleon amplitudes used in
the calculations depend on the spins of interacting particles, phase shifts,
and mixing parameters. These amplitudes were derived by using the Nijmegen
potentials. The differential cross sections for nucleon-deuteron scattering
were calculated for the projectile-nucleon energies of 65, 95, 135, 150, 190,
and 250~MeV, and the results of these calculations were compared with
experimental data.


  Structural, mechanical, electronic, and thermodynamic properties of fluorite
and tetragonal phases of ZrH$_{2}$ are systematically studied by employing the
density functional theory within generalized gradient approximation. The
existence of the bistable structure for ZrH$_{2}$ is mainly due to the
tetragonal distortions. And our calculated lattice constants for the stable
face-centered tetragonal (fct) phase with \emph{c/a}=0.885 are consistent well
with experiments. Through calculating elastic constants, the mechanically
unstable characters of face-centered cubic (fcc) phase and fct structure with
\emph{c/a}=1.111 are predicted. As for fct0.885 structure, our calculated
elastic constants explicitly indicate that it is mechanically stable. Elastic
moduli, Poisson's ratio, and Debye temperature are derived from elastic
constants. After analyzing total and partial densities of states and valence
electron charge distribution, we conclude that the Zr$-$H bonds in ZrH$_{2}$
exhibit weak covalent feature. But the ionic property is evident with about 1.5
electrons transferring from each Zr atom to H. Phonon spectrum results indicate
that fct0.885 and fct1.111 structures are dynamically stable, while the fcc
structure is unstable.


  Five essential spectra of linear relations are defined in terms of
semi-Fredholm properties and the index. Basic properties of these sets are
established and the perturbation theory for semi-Fredholm relations is then
applied to verify a generalisation of Weyl's theorem for single-valued
operators. We conclude with a spectral mapping theorem.


  Periodic and quasi-periodic solutions of the n-body problem can be found as
minimizers of the Lagrangian action functional restricted to suitable spaces of
symmetric paths. The main purpose of this paper is to develop a systematic
approach to the equivariant minimization for the three-body problem in the
three-dimensional space. First we give a finite complete list of symmetry
groups fit to the minimization of the action, with the property that any other
symmetry group can be reduced to be isomorphic to one of these representatives.
A second step is to prove that the resulting (local and global) symmetric
action-minimizers are always collisionless (when they are not already bound to
collisions). Furthermore, we prove some results addressed to the question
whether minimizers are planar or non-planar; as a consequence of the theory we
will give general criteria for a symmetry group to yield planar or homographic
minimizers (either homographic or not, as in the Chenciner-Montgomery eight
solution); on the other hand we will provide a rigorous proof of the existence
of some interesting one-parameter families of periodic and quasi-periodic
non-planar orbits. These include the choreographic Marchal's $P_{12}$ family
with equal masses -- together with a less-symmetric choreographic family (which
anyway probably coincides with the $P_{12}$).


  Currently, High-Definition (HD) maps are a prerequisite for the stable
operation of autonomous vehicles. Such maps contain information about all
static road objects for the vehicle to consider during navigation, such as road
edges, road lanes, crosswalks, and etc. To generate such an HD map, current
approaches need to process pre-recorded environment data obtained from onboard
sensors. However, recording such a dataset often requires a lot of time and
effort. In addition, every time actual road environments are changed, a new
dataset should be recorded to generate a relevant HD map.
  This paper addresses a novel approach that allows to continuously generate or
update the HD map using onboard sensor data. When there is no need to
pre-record the dataset, updating the HD map can be run in parallel with the
main autonomous vehicle navigation pipeline.
  The proposed approach utilizes the VectorMapNet framework to generate vector
road object instances from a sensor data scan. The PolyMerge technique is aimed
to merge new instances into previous ones, mitigating detection errors and,
therefore, generating or updating the HD map.
  The performance of the algorithm was confirmed by comparison with ground
truth on the NuScenes dataset. Experimental results showed that the mean error
for different levels of environment complexity was comparable to the
VectorMapNet single instance error.


  We show that several interpretations of quantum mechanics admit an ontology
of objects and events. This ontology reduces the breach between mind and
matter. When humans act, their actions do not appear explainable in mechanical
terms but through mental activity: motives, desires or needs that propel them
to action. These are examples of what in the last few decades have come to be
called "downward causation". Basically, downward causation is present when the
disposition of the whole to behave in a certain way cannot be predicted from
the dispositions of the parts. The event ontology of quantum mechanics allow us
to show that systems in entangled states present emergent new properties and
downward causation.


  Large language models (LLMs) have become pivotal in recent research. However,
during the inference process, LLMs still require substantial resources. In this
paper, we propose CliqueParcel, a method designed to improve the efficiency of
LLMs via prompt batching. Existing strategies to optimize inference efficiency
often compromise on output quality, leading to a discounted output problem.
This issue might result in reduced accuracy or outputs that are less detailed.
CliqueParcel is our answer to this challenge. While ensuring accuracy and
minimizing deviations from the original outputs (i.e., faithfulness), our
method significantly improves efficiency during inference.
  To lay the groundwork, we first redefine efficiency measurements by excluding
the reduction in running time due to shorter lengths. Then, we provide a
comprehensive trade-off between efficiency and faithfulness to clarify the
nature of the 'discounted output' problem. Within the CliqueParcel framework,
we suggest multiple batching sub-methods and discuss the specific scenarios in
which they can be applied. During evaluation, CliqueParcel is tested on eight
widely recognized datasets, which can be classified into three types: reading
comprehension, open-source question-answering, and reasoning. Our experiments
explore the performance of CliqueParcel, including efficiency, faithfulness,
and the trade-off between them. This work provides novel insights into
inference efficiency and demonstrates promising performance.


  The diffuse interstellar medium is dynamic, and its chemistry and evolution
is determined by shock fronts as well as photodissociation. Shocks are implied
by the supersonic motions and velocity dispersion often statistically called
"turbulence". We compare models of magnetohydrodynamic (MHD) shocks, with
speeds typical of cloud motions through the ISM (3-25 km/s) and densities
typical of cold neutral gas (~ 100 cm-3), to archival observations of the
atomic hydrogen 21-cm line for gas kinematics, far-infrared emission for dust
mass, and mid-infrared emission for high-resolution morphology, to identify
shock fronts in three high-latitude clouds pairs with masses of order 50 suns.
The clouds have `heads' with extended `tails', and high-resolution images show
arcs on the leading edges of the "heads" that could be individual shocks. The
HI shows higher-velocity gas at the leading edges due to shock-accelerated
material. For two cloud pairs, one cloud has an active shock indicated by broad
and offset HI, while the other cloud has already been shocked and is
predominantly `CO-dark' molecular hydrogen. Two-dimensional MHD simulations for
shocks parallel to the magnetic field for pairs of clouds show a remarkable
similarity to observed cloud features, including merged "tails" due to aligned
flow and magnetic field, which leads to lateral confinement downstream. A
parallel alignment between magnetic field and gas flow may lead to formation of
small molecular clouds.


  Hybrid board games (HBGs) augment their analog origins digitally (e.g.,
through apps) and are an increasingly popular pastime activity. Continuous
world and character development and customization, known to facilitate
engagement in video games, remain rare in HBGs. If present, they happen
digitally or imaginarily, often leaving physical aspects generic. We developed
DungeonMaker, a fabrication-augmented HBG bridging physical and digital game
elements: 1) the setup narrates a story and projects a digital game board onto
a laser cutter; 2) DungeonMaker assesses player-crafted artifacts; 3)
DungeonMaker's modified laser head senses and moves player- and non-player
figures, and 4) can physically damage figures. An evaluation (n=4x3) indicated
that DungeonMaker provides an engaging experience, may support players'
connection to their figures, and potentially spark novices' interest in
fabrication. DungeonMaker provides a rich constellation to play HBGs by
blending aspects of craft and automation to couple the physical and digital
elements of an HBG tightly.


  Aggregation in relational databases is accomplished through hashing and
sorting interval data, which is computationally expensive and scales poorly as
the data volumes grow.
  In this paper, we show how quantitative interval and time-series data in
relational attributes can be represented using delta summary values rather than
absolute values. The need for sorting to determine the row corresponding to
some maximum timestamp is negated, reducing the time complexity from at least
O(n log(n)) towards O(n) and improving query execution times. We illustrate
this new method in the relational algebra, present the implementation
algorithmically, and test an implementation in two leading RDBMS products
against the use of normal equivalents.
  We found this delta summation technique to be most effective for use cases
with additive, numerical data upon which it is necessary to frequently obtain
the latest values, and where the row cardinalities are in the order of 10^5.
Our experiments found the proposed new delta summation technique could execute
faster than the equivalent standard selection method by up to 22.4%, reducing
the overall query cost in some circumstances by up to 24.0%, reducing I/O load
by up to 60.6%, but with increased query costs for write operations, an
increase in CPU time and memory allocation, uncertain performance with very low
or very high cardinalities and inconsistent results across different RDBMS
platforms.


  We consider the problem of option pricing and hedging when stock returns are
correlated in time. Within a quadratic-risk minimisation scheme, we obtain a
general formula, valid for weakly correlated non-Gaussian processes. We show
that for Gaussian price increments, the correlations are irrelevant, and the
Black-Scholes formula holds with the volatility of the price increments on the
scale of the re-hedging. For non-Gaussian processes, further non trivial
corrections to the `smile' are brought about by the correlations, even when the
hedge is the Black-Scholes Delta-hedge. We introduce a compact notation which
eases the computations and could be of use to deal with more complicated
models.


  The EM algorithm is a novel numerical method to obtain maximum likelihood
estimates and is often used for practical calculations. However, many of
maximum likelihood estimation problems are nonconvex, and it is known that the
EM algorithm fails to give the optimal estimate by being trapped by local
optima. In order to deal with this difficulty, we propose a deterministic
quantum annealing EM algorithm by introducing the mathematical mechanism of
quantum fluctuations into the conventional EM algorithm because quantum
fluctuations induce the tunnel effect and are expected to relax the difficulty
of nonconvex optimization problems in the maximum likelihood estimation
problems. We show a theorem that guarantees its convergence and give numerical
experiments to verify its efficiency.


  The microscopic description of alpha decay from the nucleons' degree of
freedom involves a two-step process. The first consists of the clusterization
of neutron and proton pairs; the second involves the tunneling process. A
robust protocol for calculating the normalized spectroscopic factor, as defined
by Fliessbach, and its error is established and used for calculating the
alpha-width for the $0^+$ states of the nucleus $^{44}$Ti. The Gamow Shell
Model is used to calculate the structure part of the alpha-decay, while the
Gamow wave function determines the reaction part. The conventional and
normalized spectroscopic factors are calculated for the ground and excited
$0^+$ states of $^{44}$Ti and the alpha-width and half-life of the excited
states. A near alpha-threshold state has an alpha half-life of 5 $\mu$sec. The
normalization does not appreciably modify the ground-state clusterization,
while the excited states do. The non-resonant continuum significantly increases
the clustering of some of the excited states, particularly the $T=2$ state. The
normalized formation amplitude looks like a single-particle wave function.


  Rotating Radio Transients (RRATs) are neutron stars emitting sporadic radio
pulses. The unique emission of RRATs has been proposed to resemble those of
known pulsar types, such as extreme nulling pulsars or pulsars with giant
pulses. However, the presence of additional radiation beyond these sporadic
pulses remains unclear. Through high-sensitivity observations and extended
tracking, we detected the sequential weak emissions in two RRATs with
relatively high surface magnetic fields (Bs > 10^13 G): J1846-0257 and
J1854+0306. These emissions show peak flux densities of 0.15 and 0.41 mJy, up
to 687 and 512 times weaker than our detected RRAT single pulses, respectively.
The weak emissions contribute small fractions (~ 16% and 5%) to the total radio
pulse energy releases, contrasting significantly with giant-pulse pulsars where
normal pulses dominate. Polarization analysis of J1854+0306 suggests that its
sporadic RRAT pulses may originate from intermittent enhanced sparking
processes due to magnetospheric evolution. Our findings indicate that some
RRATs may represent a novel class of pulsars, distinct from any previously
known subclass. Further observations of sources with similar rotational
properties using high-sensitivity instruments could validate the generality of
these hidden emissions.


  The empirical analysis of discrete complete-information games has relied on
behavioral restrictions in the form of solution concepts, such as Nash
equilibrium. Choosing the right solution concept is crucial not just for
identification of payoff parameters, but also for the validity and
informativeness of counterfactual exercises and policy implications. We say
that a solution concept is discernible if it is possible to determine whether
it generated the observed data on the players' behavior and covariates. We
propose a set of conditions that make it possible to discern solution concepts.
In particular, our conditions are sufficient to tell whether the players'
choices emerged from Nash equilibria. We can also discern between
rationalizable behavior, maxmin behavior, and collusive behavior. Finally, we
identify the correlation structure of unobserved shocks in our model using a
novel approach.


  Gaia DR2 has revealed new small-scale and large-scale patterns in the
phase-space distribution of stars in the Milky Way. In cylindrical Galactic
coordinates $(R,\phi,z)$, ridge-like structures can be seen in the \vphiR{}
plane and asymmetric arch-like structures in the \vphivR{} plane. We show that
the ridges are also clearly present when the third dimension of the \vphiR{}
plane is represented by $\langle z \rangle$, $\langle V_z \rangle$, $\langle
V_R \rangle$, $\langle$[Fe/H]$\rangle$ and $\langle[\alpha/{\rm Fe}]\rangle$.
The maps suggest that stars along the ridges lie preferentially close to the
Galactic midplane ($|z|<0.2$ kpc), and have metallicity and $\alpha$ elemental
abundance similar to that of the Sun. We show that phase mixing of disrupting
spiral arms can generate both the ridges and the arches. It also generates
discrete groupings in orbital energy $-$ the ridges and arches are simply
surfaces of constant energy. We identify 8 distinct ridges in the \gaia{} data:
six of them have constant energy while two have constant angular momentum.
Given that the signature is strongest for stars close to the plane, the
presence of ridges in $\langle z \rangle$ and $\langle V_z \rangle$ suggests a
coupling between planar and vertical directions. We demonstrate, using N-body
simulations that such coupling can be generated both in isolated discs and in
discs perturbed by an orbiting satellite like the Sagittarius dwarf galaxy.


  It is conjectured that the coefficients of the Jones polynomial can be
computed by counting solutions of the KW equations on a four-dimensional
half-space, with certain boundary conditions that depend on a knot. The
boundary conditions are defined by a "Nahm pole" away from the knot with a
further singularity along the knot. In a previous paper, we gave a precise
formulation of the Nahm pole boundary condition in the absence of knots, in the
present paper, we do this in the more general case with knots included. We show
that the KW equations with generalized Nahm pole boundary conditions are
elliptic, and that the solutions are polyhomogeneous near the boundary and near
the knot, with exponents determined by solutions of appropriate indicial
equations. This involves the analysis of a "depth two incomplete iterated edge
operator." As in our previous paper, a key ingredient in the analysis is a
convenient new Weitzenb\"ock formula that is well-adapted to the specific
problem.}


  Adversarial attack has recently become a tremendous threat to deep learning
models. To improve the robustness of machine learning models, adversarial
training, formulated as a minimax optimization problem, has been recognized as
one of the most effective defense mechanisms. However, the non-convex and
non-concave property poses a great challenge to the minimax training. In this
paper, we empirically demonstrate that the commonly used PGD attack may not be
optimal for inner maximization, and improved inner optimizer can lead to a more
robust model. Then we leverage a learning-to-learn (L2L) framework to train an
optimizer with recurrent neural networks, providing update directions and steps
adaptively for the inner problem. By co-training optimizer's parameters and
model's weights, the proposed framework consistently improves the model
robustness over PGD-based adversarial training and TRADES.


  This paper is devoted to explore some relativistic configurations of stellar
objects for static spherically symmetric structures in the context of modified
$f(\mathcal{G})$ gravity, by exploiting the Tolman-Kuchowicz spacetime [1,2].
We develop the equations of motion for spherically symmetric spacetime in the
presence of anisotropic matter distribution by considering the physically valid
expressions of the metric potentials, $\nu=Br^2+2lnC$ and $\lambda=ln(1 +
ar^2+br^4)$. To attain the values of the unknown constants we consider the
observational data of $Cen~ X-3$, $EXO ~1785-248$ and $LMC~ X-4$ star models.
Further, by using evaluated form of the solutions we provide many aspects which
are described by the physical status like effective energy density, components
of radial and transverse pressure, energy conditions, stability against
equilibrium of the forces, speed of sound, mass-radius relation, surface
redshift, compactness parameter, adiabatic index and anisotropic measurement.
It is observed that all these features follow physically accepted patterns and
the resulting outcome is in the experimental range which depicts the viability
of our presented $f(\mathcal{G})$ gravity models.


  Consider a $N\times n$ random matrix $Z_n=(Z^n_{j_1 j_2})$ where the
individual entries are a realization of a properly rescaled stationary gaussian
random field.
  The purpose of this article is to study the limiting empirical distribution
of the eigenvalues of Gram random matrices such as $Z_n Z_n ^*$ and $(Z_n
+A_n)(Z_n +A_n)^*$ where $A_n$ is a deterministic matrix with appropriate
assumptions in the case where $n\to \infty$ and $\frac Nn \to c \in
(0,\infty)$.
  The proof relies on related results for matrices with independent but not
identically distributed entries and substantially differs from related works in
the literature (Boutet de Monvel et al., Girko, etc.).


  We investigate the close connection between the quantum phase space Wigner
distribution of small-$x$ gluons and the color dipole scattering amplitude, and
propose to study it experimentally in the hard diffractive dijet production at
the planned electron-ion collider. The angular correlation between the nucleon
recoiled momentum and the dijet transverse momentum will probe the nontrivial
correlation in the phase space Wigner distribution. This experimental study
will not only provide us with three-dimensional tomographic pictures of gluons
inside high energy proton, but also give a unique and interesting signal for
the small-$x$ dynamics with QCD evolution effects.


  Scattering encounters between binaries and single stars play a central role
in determining the dynamical evolution of a star cluster. In addition,
three-body scattering can give rise to many interesting exceptional objects:
merging can produce blue stragglers; exchange can produce binaries containing
millisecond pulsars in environments quite different from those in which the
pulsars were spun up; various types of X-ray binaries can be formed, and their
activity can be either shut off or triggered as a result of triple
interactions.
  To date, all published results on three-body scattering have relied on human
guidance for determining the correct parameter range for the envelope within
which to perform Monte--Carlo scattering experiments. In this paper, we
describe the first fully automatic determination of cross sections and reaction
rates for binary--single-star scattering. Rather than relying on human
inspection of pilot calculations, we have constructed a feedback system that
ensures near-optimal coverage of parameter space while guaranteeing
completeness. We illustrate our approach with a particular example, in which we
describe the results of a three-body encounter between three main-sequence
stars of different masses. We provide total cross sections, as well as
branching ratios for the various different types of two-body mergers,
three-body mergers, and exchanges, both non-resonant and resonant. The
companion paper in this series, Paper VII, provides a full survey of
unequal-mass three-body scattering for hard binaries in the point-mass limit.


  Based on the concept of annotation-based agents, this report introduces tools
and a formal notation for defining and running text mining experiments using a
statically typed domain-specific language embedded in Scala. Using machine
learning for classification as an example, the framework is used to develop and
document text mining experiments, and to show how the concept of generic,
typesafe annotation corresponds to a general information model that goes beyond
text processing.


  We show that the four-dimensional extreme dilaton black hole with dilaton
coupling constant $a= \sqrt{p/(p+2)}$ can be interpreted as a {\it completely
non-singular}, non-dilatonic, black $p$-brane in $(4+p)$ dimensions provided
that $p$ is {\it odd}. Similar results are obtained for multi-black holes and
dilatonic extended objects in higher spacetime dimensions. The non-singular
black $p$-brane solutions include the self-dual three brane of ten-dimensional
N=2B supergravity and a multi-fivebrane solution of eleven-dimensional
supergravity. In the case of a supersymmetric non-dilatonic $p$-brane solution
of a supergravity theory, we show that it saturates a bound on the energy per
unit $p$-volume.


  Complex event processing systems process the input event streams on-the-fly.
Since input event rate could overshoot the system's capabilities and results in
violating a defined latency bound, load shedding is used to drop a portion of
the input event streams. The crucial question here is how many and which events
to drop so the defined latency bound is maintained and the degradation in the
quality of results is minimized. In stream processing domain, different load
shedding strategies have been proposed but they mainly depend on the importance
of individual tuples (events). However, as complex event processing systems
perform pattern detection, the importance of events is also influenced by other
events in the same pattern. In this paper, we propose a load shedding framework
called eSPICE for complex event processing systems. eSPICE depends on building
a probabilistic model that learns about the importance of events in a window.
The position of an event in a window and its type are used as features to build
the model. Further, we provide algorithms to decide when to start dropping
events and how many events to drop. Moreover, we extensively evaluate the
performance of eSPICE on two real-world datasets.


  We describe the locus of stable bundles on a smooth genus $g$ curve that fail
to be globally generated. For each rank $r$ and degree $d$ with $rg<d<r(2g-1)$,
we exhibit a component of the expected dimension. We show moreover that no
component has larger dimension and give an explicit description of those
families of smaller dimension than expected. For large enough degrees, we show
that the locus is irreducible.


  Optical isolators, while commonplace in bulk- and fiber-optic systems, remain
a key missing component in integrated photonic systems. Isolation using
magneto-optic effects has been difficult to implement due to fabrication
restraints, motivating use of other non-reciprocal effects such as temporal
modulation. We demonstrate a non-reciprocal modulator comprising a pair of
microring modulators and a microring phase shifter in an active silicon
photonic process which, in combination with standard frequency filters,
facilitates isolation. Isolation up to 13 dB is measured with a 3 dB bandwidth
of 2 GHz and insertion loss of 18 dB. As one potential application is
cross-talk suppression in bi-directional communication links, we also show
transmission of a 4 Gbps data signal through the isolator while retaining a
wide-open eye diagram. This compact design, in combination with increased
modulation efficiency, could enable modulator-based isolators to become a
standard `black-box' component in integrated photonics foundry platform
component library.


  We argue that effective 1D models of stripes in the cuprate superconductors
can be constructed by studying ground states and elementary excitations of
domain walls in 2D model antiferromagnets. This method, applied to the t-J
model with Ising anisotropy, yields two such limiting cases: an ordinary 1D
electron gas and a 1D gas of holons strongly coupled to transversal
fluctuations of the stripe.


  This report describes a new version of the OntoSpec methodology for ontology
building. Defined by the LaRIA Knowledge Engineering Team (University of
Picardie Jules Verne, Amiens, France), OntoSpec aims at helping builders to
model ontological knowledge (upstream of formal representation). The
methodology relies on a set of rigorously-defined modelling primitives and
principles. Its application leads to the elaboration of a semi-informal
ontology, which is independent of knowledge representation languages. We
recently enriched the OntoSpec methodology by endowing it with a new resource,
the DOLCE top-level ontology defined at the LOA (IST-CNR, Trento, Italy). The
goal of this integration is to provide modellers with additional help in
structuring application ontologies, while maintaining independence
vis-\`{a}-vis formal representation languages. In this report, we first provide
an overview of the OntoSpec methodology's general principles and then describe
the DOLCE re-engineering process. A complete version of DOLCE-OS (i.e. a
specification of DOLCE in the semi-informal OntoSpec language) is presented in
an appendix.


  Grover's algorithm for quantum searching is generalized to deal with
arbitrary initial complex amplitude distributions. First order linear
difference equations are found for the time evolution of the amplitudes of the
marked and unmarked states. These equations are solved exactly. New expressions
are derived for the optimal time of measurement and the maximal probability of
success. They are found to depend on the averages and variances of the initial
amplitude distributions of the marked and unmarked states, but not on higher
moments. Our results imply that Grover's algorithm is robust against modest
noise in the amplitude initialization procedure.


  We study the distribution of the number of rational points in a family of
curves over a finite field of characteristic 2. This distribution determines
the coset weight distribution of a certain BCH code.


  General relations for nonequilibrium spin transport at a magnetic junction
between a normal metal and a ferromagnetic insulator are derived from the
quantum fluctuation theorem. They include the extended Onsager relations
between the spin conductance and the spin-current noise that hold for
nonequilibrium states driven by an external current. These relations, that are
valid for a general setup of spin Hall magnetoresistance, provide a
comprehensive viewpoint for understanding of unidirectional spin Hall
magnetoresistance in insulating ferromagnetic junctions.


  Counterfactually-Augmented Data (CAD) has the potential to improve language
models' Out-Of-Distribution (OOD) generalization capability, as CAD induces
language models to exploit causal features and exclude spurious correlations.
However, the empirical results of OOD generalization on CAD are not as
efficient as expected. In this paper, we attribute the inefficiency to Myopia
Phenomenon caused by CAD: language models only focus on causal features that
are edited in the augmentation and exclude other non-edited causal features. As
a result, the potential of CAD is not fully exploited. Based on the structural
properties of CAD, we design two additional constraints to help language models
extract more complete causal features contained in CAD, thus improving the OOD
generalization capability. We evaluate our method on two tasks: Sentiment
Analysis and Natural Language Inference, and the experimental results
demonstrate that our method could unlock CAD's potential and improve language
models' OOD generalization capability.


  Let D be a bounded, finitely connected domain in the complex plane without
isolated points in the boundary and let f be a continuous function on the
boundary bD. Let F be a continuous extension of f to the closure of D. We prove
that f extends holomorphically through D if and only if the degree of F+h is
nonnegative for every holomorphic function h on D such that F+h is bounded away
from zero near bD.


  Deep Chandra exposures reveal the presence of diffuse X-ray emission with a
luminosity of 1.3x10^{39} ergs s^{-1} from the spiral galaxy NGC 3184. This
appears to be truly diffuse thermal emission distinct from the low-luminosity
LMXB emission. While the unresolved emission from older LMXBs is more uniformly
distributed across the galaxy, the diffuse X-ray emission is concentrated in
areas of younger stellar populations and star forming regions. The surface
brightness of the diffuse emission over the spiral arms is five times greater
than in off-arm regions, and eight times brighter in H II regions than in non-H
II regions. Spectral fits to the diffuse thermal emission are consistent with a
low temperature component, T ~ 1.5 x 10^6 K, plus a higher temperature
component, T ~ 5 x 10^6 K.


  This paper presents the first formalisation of the precise subtyping relation
for asynchronous multiparty sessions. We show that our subtyping relation is
sound (i.e., guarantees safe process replacement) and also complete: any
extension of the relation is unsound. To achieve our results, we develop a
novel session decomposition technique, from full session types (including
internal/external choices) into single input/output session trees (without
choices). Previous work studies precise subtyping for binary sessions (with
just two participants), or multiparty sessions (with any number of
participants) and synchronous interaction. Here, we cover multiparty sessions
with asynchronous interaction, where messages are transmitted via FIFO queues
(as in the TCP/IP protocol), and prove that our subtyping is both operationally
and denotationally precise. In the asynchronous multiparty setting, finding the
precise subtyping relation is a highly complex task: this is because, under
some conditions, participants can permute the order of their inputs and
outputs, by sending some messages earlier or receiving some later, without
causing errors; the precise subtyping relation must capture all such valid
permutations -- and consequently, its formalisation, reasoning and proofs
become challenging. Our session decomposition technique overcomes this
complexity, expressing the subtyping relation as a composition of refinement
relations between single input/output trees, and providing a simple reasoning
principle for asynchronous message optimisations.


  This paper aims to extend the BML method proposed in Wang et al. [22] to make
it applicable to more general coupled nonlinear FBSDEs. We interpret BML from
the fixed-point iteration perspective and show that optimizing BML is
equivalent to minimizing the distance between two consecutive trial solutions
in a fixed-point iteration. Thus, this paper provides a theoretical foundation
for an optimization-based approach to solving FBSDEs. We also empirically
evaluate the method through four numerical experiments.


  Current theoretical physics suggests the flow of time is an illusion: the
entire universe just is, with no special meaning attached to the present time.
This paper points out that this view, in essence represented by usual
space-time diagrams, is based on time-reversible microphysical laws, which fail
to capture essential features of the time-irreversible nature of decoherence
and the quantum measurement process, as well as macro-physical behaviour and
the development of emergent complex systems, including life, which exist in the
real universe. When these are taken into account, the unchanging block universe
view of spacetime is best replaced by an evolving block universe which extends
as time evolves, with the potential of the future continually becoming the
certainty of the past; spacetime itself evolves, as do the entities within it.
However this time evolution is not related to any preferred surfaces in
spacetime; rather it is associated with the evolution of proper time along
families of world lines. The default state of fundamental physics should not be
taken to be a time irreversible evolution of physical states: it is an ongoing
irreversible development of time itself.


  We study the kinetics of crystallization in deeply supercooled liquid silicon
employing computer simulations and the Stillinger-Weber three body potential.
The free energy barriers to crystallisation are computed using umbrella
sampling Monte Carlo simulations, and for selected low temperature and zero
pressure state points, using unconstrained molecular dynamics simulations to
reconstruct the free energy from a mean first passage time formulation. We
focus on state points that have been described in earlier work [Sastry and
Angell, Nature Mater., 2, 739, 2003] as straddling a first order liquid-liquid
phase transition (LLPT) between two metastable liquid states. It was argued
subsequently [Ricci et al., Mol. Phys., 117, 3254, 2019] that the apparent
phase transition is in fact due the loss of metastability of the liquid state
with respect to the globally stable crystalline state. The presence or absence
of a barrier to crystallization for these state points is therefore of
importance to ascertain, with due attention to ambiguities that may arise from
the choice of order parameters. We discuss our choice of order parameters and
also our choice of methods to calculate the free energy at deep supercooling.
We find a well-defined free energy barrier to crystallisation and demonstrate
that both umbrella sampling and mean first passage time methods yield results
that agree quantitatively. Our results thus provide strong evidence against the
possibility that the liquids at state points close to the reported LLPT exhibit
slow, spontaneous crystallisation, but they do not address the existence of a
LLPT (or lack thereof). We also compute the free energy barriers to
crystallisation at other state points over a broad range of temperatures and
pressures, and discuss the effect of changes in the microscopic structure of
the metastable liquid on the free energy barrier heights.


  In this paper, we introduce the notion of derivations of Lie 2-algebras and
construct the associated derivation Lie 3-algebra. We prove that isomorphism
classes of non-abelian extensions of Lie 2-algebras are classified by
equivalence classes of morphisms from a Lie 2-algebra to a derivation Lie
3-algebra.


  We establish a partial regularity result for solutions of parabolic systems
with general $\varphi$-growth, where $\varphi$ is an Orlicz function. In this
setting we can develop a unified approach that is independent of the degeneracy
of system and relies on two caloric approximation results: the
$\varphi$-caloric approximation, which was introduced in Diening, Schwarzacher,
Stroffolini and Verde (2017) (arXiv:1606.01706), and an improved version of the
\mathcal{A}-caloric approximation, which we prove without using the classical
compactness method.


  Homomorphic encryption (HE) is a privacy-preserving computation technique
that enables computation on encrypted data. Today, the potential of HE remains
largely unrealized as it is impractically slow, preventing it from being used
in real applications. A major computational bottleneck in HE is the
key-switching operation, accounting for approximately 70% of the overall HE
execution time and involving a large amount of data for inputs, intermediates,
and keys. Prior research has focused on hardware accelerators to improve HE
performance, typically featuring large on-chip SRAMs and high off-chip
bandwidth to deal with large scale data. In this paper, we present a novel
approach to improve key-switching performance by rigorously analyzing its
dataflow. Our primary goal is to optimize data reuse with limited on-chip
memory to minimize off-chip data movement. We introduce three distinct
dataflows: Max-Parallel (MP), Digit-Centric (DC), and Output-Centric (OC), each
with unique scheduling approaches for key-switching computations. Through our
analysis, we show how our proposed Output-Centric technique can effectively
reuse data by significantly lowering the intermediate key-switching working set
and alleviating the need for massive off-chip bandwidth. We thoroughly evaluate
the three dataflows using the RPU, a recently published vector processor
tailored for ring processing algorithms, which includes HE. This evaluation
considers sweeps of bandwidth and computational throughput, and whether keys
are buffered on-chip or streamed. With OC, we demonstrate up to 4.16x speedup
over the MP dataflow and show how OC can save 12.25x on-chip SRAM by streaming
keys for minimal performance penalty.


  The current paper proposes a novel variational Bayes predictive coding RNN
model, which can learn to generate fluctuated temporal patterns from exemplars.
The model learns to maximize the lower bound of the weighted sum of the
regularization and reconstruction error terms. We examined how this weighting
can affect development of different types of information processing while
learning fluctuated temporal patterns. Simulation results show that strong
weighting of the reconstruction term causes the development of deterministic
chaos for imitating the randomness observed in target sequences, while strong
weighting of the regularization term causes the development of stochastic
dynamics imitating probabilistic processes observed in targets. Moreover,
results indicate that the most generalized learning emerges between these two
extremes. The paper concludes with implications in terms of the underlying
neuronal mechanisms for autism spectrum disorder and for free action.


  Tigerlily is a TigerGraph based system designed to solve the drug interaction
prediction task. In this machine learning task, we want to predict whether two
drugs have an adverse interaction. Our framework allows us to solve this highly
relevant real-world problem using graph mining techniques in these steps:
  (a) Using PyTigergraph we create a heterogeneous biological graph of drugs
and proteins.
  (b) We calculate the personalized PageRank scores of drug nodes in the
TigerGraph Cloud.
  (c) We embed the nodes using sparse non-negative matrix factorization of the
personalized PageRank matrix.
  (d) Using the node embeddings we train a gradient boosting based drug
interaction predictor.


  A correlation term ${{ \sigma}_{n} }\cdot ({ k_{n}\times k_\gamma}) $ in the
${}^{139}{\rm La}(\vec{n},\gamma)$ reaction has been studied utilizing
epithermal polarized neutrons and germanium detectors. The transverse asymmetry
for single $\gamma$-ray transition was measured to be $0.60\pm0.19$ in the
$p$-wave resonance.


  Recent advances in fluorescence microscopy techniques and tissue clearing,
labeling, and staining provide unprecedented opportunities to investigate brain
structure and function. These experiments' images make it possible to catalog
brain cell types and define their location, morphology, and connectivity in a
native context, leading to a better understanding of normal development and
disease etiology. Consistent annotation of metadata is needed to provide the
context necessary to understand, reuse, and integrate these data. This report
describes an effort to establish metadata standards for 3D microscopy datasets
for use by the Brain Research through Advancing Innovative Neurotechnologies
(BRAIN) Initiative and the neuroscience research community. These standards
were built on existing efforts and developed with input from the brain
microscopy community to promote adoption. The resulting Essential Metadata for
3D BRAIN Microscopy includes 91 fields organized into seven categories:
Contributors, Funders, Publication, Instrument, Dataset, Specimen, and Image.
Adoption of these metadata standards will ensure that investigators receive
credit for their work, promote data reuse, facilitate downstream analysis of
shared data, and encourage collaboration.


  Context. The S\'ersic profile is a widely-used model to describe the surface
brightness distribution of galaxies. Spiral galaxies, however, are
qualitatively different from a S\'ersic model.
  Aims. The goal of this study is to assess how accurately the total flux and
half-light radius of a galaxy with spiral arms can be recovered when fitted
with a S\'ersic profile.
  Methods. I selected a sample of bulge-dominated galaxies with spiral arms.
Using photometric data from the Hyper Suprime-Cam survey, I estimated the
contribution of the spiral arms to their total flux. Then I generated simulated
images of galaxies with similar characteristics, fitted them with a S\'ersic
model, and quantified the error on the determination of the total flux and
half-light radius.
  Results. Spiral arms can introduce biases on the photometry of galaxies in a
way that depends on the underlying smooth surface brightness profile, the
location of the arms, and the depth of the photometric data. A set of spiral
arms accounting for 10% of the flux of a bulge-dominated galaxy typically
causes the total flux and the half-light radius to be overestimated by 15% and
30%, respectively. This bias, however, is much smaller if the galaxy is
disk-dominated.
  Conclusions. Galaxies with a prominent bulge and a non-zero contribution from
spiral arms are the most susceptible to biases in the total flux and half-light
radius, when fitted with a S\'ersic profile. If photometric measurements with
high accuracy are required, then measurements over finite apertures are to be
preferred over global estimates of the flux.


  We give a geometric realization of a subcategory of the $m$-cluster category
$\mathcal{C}^m$ of type $\widetilde{A}_{p,q}$, by using $(m+2)$-angulations of
an annulus with $p+q$ marked points. We also give a bijection between an
equivalence class of $(m+2)$-angulations and the mutation class of coloured
quivers of type $\widetilde{A}_{p,q}$.


  In medical imaging, organ/pathology segmentation models trained on current
publicly available and fully-annotated datasets usually do not well-represent
the heterogeneous modalities, phases, pathologies, and clinical scenarios
encountered in real environments. On the other hand, there are tremendous
amounts of unlabelled patient imaging scans stored by many modern clinical
centers. In this work, we present a novel segmentation strategy,
co-heterogenous and adaptive segmentation (CHASe), which only requires a small
labeled cohort of single phase imaging data to adapt to any unlabeled cohort of
heterogenous multi-phase data with possibly new clinical scenarios and
pathologies. To do this, we propose a versatile framework that fuses appearance
based semi-supervision, mask based adversarial domain adaptation, and
pseudo-labeling. We also introduce co-heterogeneous training, which is a novel
integration of co-training and hetero modality learning. We have evaluated
CHASe using a clinically comprehensive and challenging dataset of multi-phase
computed tomography (CT) imaging studies (1147 patients and 4577 3D volumes).
Compared to previous state-of-the-art baselines, CHASe can further improve
pathological liver mask Dice-Sorensen coefficients by ranges of $4.2\% \sim
9.4\%$, depending on the phase combinations: e.g., from $84.6\%$ to $94.0\%$ on
non-contrast CTs.


  The overdamped Brownian motion of a self-propelled particle which is driven
by a projected internal force is studied by solving the Langevin equation
analytically. The "active" particle under study is restricted to move along a
linear channel. The direction of its internal force is orientationally
diffusing on a unit circle in a plane perpendicular to the substrate. An
additional time-dependent torque is acting on the internal force orientation.
The model is relevant for active particles like catalytically driven Janus
particles and bacteria moving on a substrate. Analytical results for the first
four time-dependent displacement moments are presented and analysed for several
special situations. For vanishing torque, there is a significant dynamical
non-Gaussian behaviour at finite times t as signalled by a non-vanishing
normalized kurtosis in the particle displacement which approaches zero for long
time with a 1/t long-time tail.


  Sensor devices have been increasingly used in engineering and health studies
recently, and the captured multi-dimensional activity and vital sign signals
can be studied in association with health outcomes to inform public health. The
common approach is the scalar-on-function regression model, in which health
outcomes are the scalar responses while high-dimensional sensor signals are the
functional covariates, but how to effectively interpret results becomes
difficult. In this study, we propose a new Functional Adaptive Double-Sparsity
(FadDoS) estimator based on functional regularization of sparse group lasso
with multiple functional predictors, which can achieve global sparsity via
functional variable selection and local sparsity via zero-subinterval
identification within coefficient functions. We prove that the FadDoS estimator
converges at a bounded rate and satisfies the oracle property under mild
conditions. Extensive simulation studies confirm the theoretical properties and
exhibit excellent performances compared to existing approaches. Application to
a Kinect sensor study that utilized an advanced motion sensing device tracking
human multiple joint movements and conducted among community-dwelling elderly
demonstrates how the FadDoS estimator can effectively characterize the detailed
association between joint movements and physical health assessments. The
proposed method is not only effective in Kinect sensor analysis but also
applicable to broader fields, where multi-dimensional sensor signals are
collected simultaneously, to expand the use of sensor devices in health studies
and facilitate sensor data analysis.


  In this paper, we prove the stability of shear flows of Prandtl type as $
\big(U(y/\sqrt{\nu}),0\big)$ for the steady Navier-Stokes equations under a
natural spectral assumption on the linearized NS operator. We develop a direct
energy method combined with compact method to solve the Orr-Sommerfeld
equation.


  Let theta = p/q with p and q relatively prime and u and v a pair of unitaries
such that u v = e^{i theta} v u, where u and v generate the rotation C*-algebra
A_theta. Let h_{theta, lambda} = u + u^{-1} + lambda/2(v + v^{-1}) be the
almost Mathieu operator. By proving an identity of rational functions we show
that for q even, the constant term in the characteristic polynomial of
h_{\theta, \lambda} is (-1)^{q/2}(1 + (\lambda/2)^q) - (z_1^q + z_1^{-q} +
(\lambda/2)^q(z_2^q + z_2^{-q})).


  A determination of the dynamical evolution of the asteroid belt is difficult
because the asteroid belt has evolved since the time of asteroid formation
through mechanisms that include: (1) catastrophic collisions, (2) rotational
disruption, (3) chaotic orbital evolution and (4) orbital evolution driven by
Yarkovsky radiation forces. The timescales of these loss mechanisms are
uncertain and there is a need for more observational constraints. In the inner
main belt, the mean size of the non-family asteroids increases with increasing
inclination. Here, we use that observation to show that all inner main belt
asteroids originate from either the known families or from ghost families, that
is, old families with dispersed orbital elements. We estimate that the average
age of the asteroids in the ghost families is a factor of 1/3 less than the
Yarkovsky orbital evolution timescale. However, this orbital evolution
timescale is a long-term average that must allow for the collisional evolution
of the asteroids and for stochastic changes in their spin directions. By
applying these constraints on the orbital evolution timescales to the evolution
of the size-frequency distribution of the Vesta asteroid family, we estimate
that the age of this family is greater than 1.3 $Gyr$ and could be comparable
with the age of the solar system. By estimating the number of ghost families,
we calculate that the number of asteroids that are the root sources of the
meteorites and the near-Earth asteroids that originate from the inner main belt
is about 20.


  The electrical double layer at infinite flat solid surface was discussed with
respect to the triple layer model. Charge density at the outer Helmholtz plane
is assumed to be zero usually. However, the assumption causes the position of
the outer Helmholtz plane to be obscure. The charge density was calculated and
the condition that the charge density is negligible was discussed.


  We report on the enhancement of surface plasmon resonances in a holey
bidimensional grating of subwavelength size, drilled in a gold thin film coated
by a graphene sheet. The enhancement originates from the coupling between
charge carriers in graphene and gold surface plasmons. The main plasmon
resonance peak is located around 1.5 microns. A lower constraint on the
gold-induced doping concentration of graphene is specified and the interest of
this architecture for molecular sensing is also highlighted.


  We report the possible detection (99.3% of statistical significance) of
redshifted Fe iron line emission in the X-ray afterglow of Gamma-ray burst
GRB970508 observed by BeppoSAX. Its energy is consistent with the redshift of
the putative host galaxy determined from optical spectroscopy. The line
disappeared about 1 day after the burst. We have also analyzed the spectral
variability during the outburst event that characterizes the X-ray afterglow of
this GRB. The spectrum gets harder during the flare, turning to steep when the
flux decreases. The variability, intensity and width of the line indicate that
the emitting region should have a mass approximately greater than 0.5 solar
masses (assuming the iron abundance similar to its solar value), a size of
about 3 times 10^15 cm, be distributed anisotropically, and be moving with
sub-relativistic speed. In contrast to the fairly clean environment expected in
the merging of two neutron stars, the observed line properties would imply that
the site of the burst is embedded in a large mass of material, consistent with
pre-explosion ejecta of a very massive star. This material could be related
with the outburst observed in the afterglow 1 day after the GRB and with the
spectral variations measured during this phase.


  Three different analysis techniques for Atmospheric Imaging System are
presented. The classical Hillas parameters based technique is shown to be
robust and efficient, but more elaborate techniques can improve the sensitivity
of the analysis. A comparison of the different analysis techniques shows that
they use different information for gamma-hadron separation, and that it is
possible to combine their qualities.


  We prove the conjectured compatibility of $p$-adic fundamental lines with
specializations at motivic points for a wide class of $p$-adic families of
$p$-adic Galois representations (for instance, the families which arise from
$p$-adic families of automorphic representations of the unit group of a
quaternion algebra or of a totally definite unitary groups) and deduce the
compatibility of the Equivariant Tamagawa Number Conjectures for them. However,
we also show that fundamental lines are not compatible with arbitrary
characteristic zero specializations with values in a domain in general. This
points to the need to modify some conjectures on $p$-adic variation of special
values using completed cohomology.


  Learning the continuous dynamics of a system from snapshots of its temporal
marginals is a problem which appears throughout natural sciences and machine
learning, including in quantum systems, single-cell biological data, and
generative modeling. In these settings, we assume access to cross-sectional
samples that are uncorrelated over time, rather than full trajectories of
samples. In order to better understand the systems under observation, we would
like to learn a model of the underlying process that allows us to propagate
samples in time and thereby simulate entire individual trajectories. In this
work, we propose Action Matching, a method for learning a rich family of
dynamics using only independent samples from its time evolution. We derive a
tractable training objective, which does not rely on explicit assumptions about
the underlying dynamics and does not require back-propagation through
differential equations or optimal transport solvers. Inspired by connections
with optimal transport, we derive extensions of Action Matching to learn
stochastic differential equations and dynamics involving creation and
destruction of probability mass. Finally, we showcase applications of Action
Matching by achieving competitive performance in a diverse set of experiments
from biology, physics, and generative modeling.


  We have monitored the polarized radiation of the Type IIb SN 1993J in M81
over a period of 41 days, starting from 7 days after the explosion on 1993
March 27.5 (UT). Our data show clear evidence that the intrinsic continuum
polarization of SN 1993J evolved from being essentially negligible on April
3-4, to a peak value of ~ 1% in late April 1993, and started to decline by the
middle of May. The polarized flux spectrum in late April strongly resembled
spectra of Type Ib supernovae, with prominent He I lines but redshifted ~ 3380
km/s relative to the total flux spectrum. These data are consistent with models
of Hoflich; they suggest that the polarization was most likely produced by
either an asymmetric helium core configuration of material and/or flux, or
scattering from an asymmetric circumstellar distribution of dusty material. A
combination of electron and dust scattering, as well as a clumpy or stratified
distribution of the emitting gas, are possible as the polarization mechanism of
the continuum and emission lines. The latter interpretation is supported by the
fact that 1-2 months after the explosion, the observed rotations of
polarization position angle across prominent line features remain even after
correction for effects of interstellar polarization. This indicates that
emission lines of He I, Fe II, [O I], and H are all intrinsically polarized at
position angles different from that of the continuum, with the non-Balmer lines
generally being most highly polarized. If the supernova had an oblate geometry,
our data are consistent with a small viewing angle (i.e., more or less
equator-on), although the degree of asphericity that gave rise to the
polarization at early times is probably smaller (minor to major axis ratio >
0.7) than has been previously suggested.


  Propagation character of spin wave was investigated for chiral magnets FeGe
and Co-Zn-Mn alloys, which can host magnetic skyrmions near room temperature.
On the basis of the frequency shift between counter-propagating spin waves, the
magnitude and sign of Dzyaloshinskii-Moriya (DM) interaction were directly
evaluated. The obtained magnetic parameters quantitatively account for the size
and helicity of skyrmions as well as their materials variation, proving that
the DM interaction plays a decisive role in the skyrmion formation in this
class of room-temperature chiral magnets. The propagating spin-wave
spectroscopy can thus be an efficient tool to study DM interaction in bulk
single-phase compounds. Our results also demonstrate a function of spin-wave
diode based on chiral crystal structures at room temperature.


  We investigate the dynamics of Landau-Zener transitions in an anisotropic,
dissipative three-level model (3-LZM) using the numerically accurate multiple
Davydov D2 Ansatz in the framework of time-dependent variation. It is
demonstrated that a non-monotonic relationship exists between the Landau-Zener
transition probability and the phonon coupling strength when the 3-LZM is
driven by a linear external field. Under the influence of a periodic driving
field, phonon coupling may induce peaks in contour plots of the transition
probability when the magnitude of the system anisotropy matches the phonon
frequency. Dynamics of the 3-LZM have also been probed in the presence of a
super-ohmic phonon bath when driven by a periodic driving field. It is found
that both the period and the amplitude of the Rabi cycle decay exponentially
with the increasing bath coupling strength.


  The recent discovery of the ability to perform direct epitaxial growth of
graphene layers on semiconductor Ge surfaces led to the huge interest to this
topic. One of the reasons for this interest is the chance to overcome several
present-day drawbacks on the way of the graphene integration in the modern
semiconductor technology. The other one is connected with the fundamental
studies of the new graphene-semiconductor interfaces, that might help with the
deeper understanding of mechanisms, which governs graphene growth on different
substrates as well as shed light on the interaction of graphene with these
substrates, which range is now spread from metals to insulators. The present
minireview gives a timely overview of the state-of-the-art in the field of
studies of the graphene-Ge epitaxial interfaces and draw some perspective
directions in this research area.


  The feasibility of a CLIC-LHC based FEL-nucleus collider is investigated. It
is shown that the proposed scheme satisfies all requirements of an ideal photon
source for the Nuclear Resonance Fluorescence method. The tunability,
monochromaticity and high polarization of the FEL beam together with high
statistics and huge energy of LHC nucleus beams will give an unique opportunity
to determine different characteristics of excited nuclear levels. The physics
potential of the proposed collider is illustrated for a beam of Pb nuclei.


  A subset $S\subseteq V$ in a graph $G=(V,E)$ is a $k$-quasiperfect dominating
set (for $k\geq 1$) if every vertex not in $S$ is adjacent to at least one and
at most $k$ vertices in $S$. The cardinality of a minimum $k$-quasiperfect
dominating set in $G$ is denoted by $\gamma_ {\stackrel{}{1k}}(G)$. Those sets
were first introduced by Chellali et al. (2013) as a generalization of the
perfect domination concept and allow us to construct a decreasing chain of
quasiperfect dominating numbers $ n \ge \gamma_ {\stackrel{}{11}}(G) \ge
\gamma_ {\stackrel{}{12}}(G)\ge \ldots \ge \gamma_
{\stackrel{}{1\Delta}}(G)=\gamma(G)$ in order to indicate how far is $G$ from
being perfectly dominated. In this paper we study properties, existence and
realization of graphs for which the chain is short, that is, $\gamma_
{\stackrel{}{12}}(G)=\gamma (G)$. Among them, one can find cographs, claw-free
graphs and graphs with extremal values of $\Delta(G)$.


  This is a study of a possible alternative procedure for adding a potential
energy to the free electron Dirac equation. When Dirac added potentials to his
free electron equation, there were two alternatives (here called D1 and D2). He
chose D1 and lost charge conjugation symmetry, found Ehrenfest equations that
depended on the sign of the energy of the state determining the expectation
value, encountered Klein tunneling, zitterbewegung and the Klein paradox. The
D1 alternative also predicted that deep potentials should pull positive energy
states down into the negative energy continuum, possibly creating an unstable
vacuum. Extensive experiments (1975-1997) found no evidence for this
instability, but did find low energy electron-positron pairs with sharply
defined energies and unusually low counting statistics. These pairs tended to
disappear with higher beam currents. This paper explores the other alternative,
here called D2 and finds charge conjugation symmetry preserved, Ehrenfest
equations are classical, Klein tunneling is not present, unstable vacuua are
forbidden, zitterbewegung is absent in the charge current density, new
excitations of bound electron-positron pairs are possible in atoms, and the
energies at which low energy electron-positron pair production in heavy ion
scattering occurs is well described. Also all of the positive energy
calculations, including those with the Coulomb potential, the hydrogen-like
atom, are retained exactly the same as found in alternative D1. It might have
been better if Dirac had chosen alternative D2.


  We construct a large class of examples of the cyclic sieving phenomenon by
expoiting the representation theory of semi-simple Lie algebras. Let $M$ be a
finite dimensional representation of a semi-simple Lie algebra and let $B$ be
the associated Kashiwara crystal. For $r\ge 0$, the triple $(X,c,P)$ which
exhibits the cyclic sieving phenomenon is constructed as follows: the set $X$
is the set of isolated vertices in the crystal $\otimes^rB$; the map $c\colon
X\rightarrow X$ is a generalisation of promotion acting on standard tableaux of
rectangular shape and the polynomial $P$ is the fake degree of the Frobenius
character of a representation of $\mathfrak{S}_r$ related to the natural action
of $\mathfrak{S}_r$ on the subspace of invariant tensors in $\otimes^rM$.
Taking $M$ to be the defining representation of $\mathrm{SL}(n)$ gives the
cyclic sieving phenomenon for rectangular tableaux.


  t-SNE and hierarchical clustering are popular methods of exploratory data
analysis, particularly in biology. Building on recent advances in speeding up
t-SNE and obtaining finer-grained structure, we combine the two to create
tree-SNE, a hierarchical clustering and visualization algorithm based on
stacked one-dimensional t-SNE embeddings. We also introduce alpha-clustering,
which recommends the optimal cluster assignment, without foreknowledge of the
number of clusters, based off of the cluster stability across multiple scales.
We demonstrate the effectiveness of tree-SNE and alpha-clustering on images of
handwritten digits, mass cytometry (CyTOF) data from blood cells, and
single-cell RNA-sequencing (scRNA-seq) data from retinal cells. Furthermore, to
demonstrate the validity of the visualization, we use alpha-clustering to
obtain unsupervised clustering results competitive with the state of the art on
several image data sets. Software is available at
https://github.com/isaacrob/treesne.


  Structural fluctuations and dynamic cross-correlations in the mouse eugenol
olfactory receptor (Olfr73) were studied by molecular dynamics (MD) simulation
to characterize the dynamic response of the protein upon ligand binding. The
initial structure was generated by the artificial intelligence tool AlfaFold2
due to the current lack of experimental data. We focused on the hydrogen (H)
bond of the odorant eugenol to Ser113, Asn207, and Tyr260 of the receptor
protein, the importance of which has been suggested by previous experimental
studies. The H-bond was not observed in docking simulations, but in subsequent
MD simulations the H-bond to Ser113 was formed in 2--4 ns. The lifetime of the
H-bond was in the range of 1--20 ns. On the trajectory with the most stable (20
ns) H-bond, the structural fluctuation of the $\alpha$-carbon atoms of the
receptor main chain was studied by calculating the root mean square
fluctuations, the dynamic cross-correlation map, and the time-dependent dynamic
cross-correlation. The analysis suggested a correlation transfer pathway Ser113
$\to$ Phe182 $\to$ (Leu259 or Tyr260) $\to$ Tyr291 induced by the ligand
binding with a time scale of 4--6 ns.