  Near-ideal four wave mixing dynamics are observed in a nonlinear
Schr{\"o}dinger equation system using a new experimental technique associated
with iterated sequential initial conditions in optical fiber. This novel
approach mitigates against unwanted sideband generation and optical loss,
extending the effective propagation distance by two orders of magnitude,
allowing Kerr-driven coupling dynamics to be seen over 50 km of optical fiber
using only one short fiber segment of 500 m. Our experiments reveal the full
dynamical phase space topology in amplitude and phase, showing characteristic
features of multiple Fermi-Pasta-Ulam recurrence cycles, stationary wave
existence, and the system separatrix boundary. Experiments are shown to be in
excellent quantitative agreement with numerical solutions of the canonical
differential equation system describing the wave evolution.


  We characterize the star formation in the low-metallicity galaxy NGC 6822
over the past few hundred million years, using GALEX far-UV (FUV, 1344-1786 A)
and near-UV (NUV, 1771-2831 A) imaging, and ground-based Ha imaging. From GALEX
FUV image, we define 77 star-forming (SF) regions with area >860 pc^2, and
surface brightness <=26.8 mag(AB)arcsec^-2, within 0.2deg (1.7kpc) of the
center of the galaxy. We estimate the extinction by interstellar dust in each
SF region from resolved photometry of the hot stars it contains: E(B-V) ranges
from the minimum foreground value of 0.22mag up to 0.66+-0.21mag. The
integrated FUV and NUV photometry, compared with stellar population models,
yields ages of the SF complexes up to a few hundred Myr, and masses from 2x10^2
Msun to 1.5x10^6 Msun. The derived ages and masses strongly depend on the
assumed type of interstellar selective extinction, which we find to vary across
the galaxy. The total mass of the FUV-defined SF regions translates into an
average star formation rate (SFR) of 1.4x10^-2 Msun/yr over the past 100 Myr,
and SFR=1.0x10^-2 Msun/yr in the most recent 10 Myr. The latter is in agreement
with the value that we derive from the Ha luminosity, SFR=0.008 Msun/yr. The
SFR in the most recent epoch becomes higher if we add the SFR=0.02 Msun/yr
inferred from far-IR measurements, which trace star formation still embedded in
dust (age <= a few Myr).


  The sign problem is a widespread numerical hurdle preventing us from
simulating the equilibrium behavior of various problems at the forefront of
physics. Focusing on an important sub-class of such problems, bosonic
$(2+1)$-dimensional topological quantum field theories, here we provide a
simple criterion to diagnose intrinsic sign problems---that is, sign problems
that are inherent to that phase of matter and cannot be removed by any local
unitary transformation. Explicitly, \textit{if the exchange statistics of the
anyonic excitations do not form complete sets of roots of unity, then the model
has an intrinsic sign problem}. This establishes a concrete connection between
the statistics of anyons, contained in the modular $S$ and $T$ matrices, and
the presence of a sign problem in a microscopic Hamiltonian. Furthermore, it
places constraints on the phases that can be realised by stoquastic
Hamiltonians. We prove this and a more restrictive criterion for the large set
of gapped bosonic models described by an abelian topological quantum field
theory at low-energy, and offer evidence that it applies more generally with
analogous results for non-abelian and chiral theories.


  Let V be an algebraic variety embedded in a power of an elliptic curve, both
defined over the algebraic numbers. We show that the set of algebraic points of
V which are of bounded height and which satisfy certain algebraic conditions
are a non-dense subset of V. This result has implications in the context of the
Pink-Zilber Conjecture and Mordel-Lang plus Bogomolov Theorem.


  In this paper, we propose an improvement of Adversarial Transformation
Networks(ATN) to generate adversarial examples, which can fool white-box models
and black-box models with a state of the art performance and won the 2rd place
in the non-target task in CAAD 2018.


  Different authors have done analysis regarding sums of powers References
number 1,2 and 3, but systematic approach for solving Diophantine equations
having sums of many biquadratics equal to a quartic has not been done before.
In this paper we give methods for finding numerical solutions to equation A
given above in section one. Next in section two, we give methods for finding
numerical solutions for equation B given above. As is known that finding
parametric solutions to biquadratic equations is not easy by conventional
method. So the authors have found numerical solutions to equation A and B using
elliptic curve theory.


  We investigate multiparty communication scenarios where information is sent
from several sender to several receivers. We establish a relation between the
quantum capacity of multiparty communication channels and their distillability
properties which enables us to show that the quantum capacity of such channels
is not additive.


  We present the Mixed Likelihood Gaussian process latent variable model
(GP-LVM), capable of modeling data with attributes of different types. The
standard formulation of GP-LVM assumes that each observation is drawn from a
Gaussian distribution, which makes the model unsuited for data with e.g.
categorical or nominal attributes. Our model, for which we use a sampling based
variational inference, instead assumes a separate likelihood for each observed
dimension. This formulation results in more meaningful latent representations,
and give better predictive performance for real world data with dimensions of
different types.


  Can a graph specifying the pattern of connections of a dynamical network be
reconstructed from statistical properties of a signal generated by such a
system? In this model study, we present an evolutionary algorithm for
reconstruction of graphs from their Laplacian spectra. Through a stochastic
process of mutations and selection, evolving test networks converge to a
reference graph. Applying the method to several examples of random graphs,
clustered graphs, and small-world networks, we show that the proposed
stochastic evolution allows exact reconstruction of relatively small networks
and yields good approximations in the case of large sizes.


  We prove that when Hodge theory survives on non-compact symplectic manifolds,
a compact symplectic Lie group action having fixed points is necessarily
Hamiltonian, provided the associated almost complex structure preserves the
space of harmonic one-forms. For example, this is the case for complete
K\"ahler manifolds for which the symplectic form has an appropriate decay at
infinity. This extends a classical theorem of Frankel for compact K\"ahler
manifolds to complete non-compact K\"ahler manifolds.


  As a departure from existing continuum approaches for describing the
stability and evolution of surfaces of crystalline materials, this article
provides a description of surface evolution based on the physics of the main
feature imposed by the discrete nature of the material, namely,
crystallographic surface steps. It is shown that the formation energy of
surface steps depends on the sign of extensional strain of the crystal surface,
and this behavior plays a crucial role in surface evolution. The nature of this
dependence implies that there is no energetic barrier to nucleation of islands
on the growth surface during deposition, and that island faces tend toward
natural orientations which have no counterpart in unstrained materials. This
behavior is expressed in terms of a small number of parameters that can be
estimated through atomistic analysis of stepped surfaces. The continuum
framework developed is then applied to study the time evolution of surface
shape of an epitaxial film being deposited onto a substrate. The kinetic
equation for mass transport is enforced in a weak form by means of a
variational formulation [...].


  A continuous time cluster algorithm for two-level systems coupled to a
dissipative bosonic bath is presented and applied to the sub-ohmic spin-Boson
model. When the power s of the spectral function J(w) \propto w^s is smaller
than 1/2, the critical exponents are found to be classical, mean-field like.
Potential sources for the discrepancy with recent renormalization group
predictions are traced back to the effect of a dangerously irrelevant variable.


  I discuss some aspects of the Disc Instability Model applied to outbursts in
various types of binary systems. I lament the general lack of interest in the
subject.


  We consider a spin 1/2 charged particle on the Lobachevsky plane subjected to
a magnetic field corresponding to a discrete system of Aharonov-Bohm solenoids.
Let $H^+$ and $H^-$ be the two components of the Pauli operator for spin up and
down, respectively. We show that neither $H^+$ nor $H^-$ has a zero mode if the
number of solenoids is finite. On the other hand, a construction is described
of an infinite periodic system of solenoids for which either $H^+$ or $H^-$ has
zero modes depending on the value of the flux carried by the solenoids.


  We interpolate cohomology classes attached to families of Hilbert modular
forms. Using this we construct a two variable $p$-adic L-function which
interpolates one variable $p$-adic L-functions.


  We obtain the asymptotic orders of entropy numbers of Sobolev classes on the
unit sphere with Dunkl weight which associates with the finite reflection
group. Moreover, the asymptotic order of entropy numbers of weighted Sobolev
classes on the unit ball and on the standard simplex are discussed.


  We propose a method for a weak continuous measurement of the energy
eigenstates of a fast quantum system by means of a "slow" detector. Such a
detector is only sensitive to slowly-changing variables, e. g. energy, while
its back-action can be limited solely to decoherence of the eigenstate
superpositions. We apply this scheme to the problem of detection of quantum
jumps between energy eigenstates in a harmonic oscillator.


  Optogenetics is a rapidly growing field of biotechnology, potentially
allowing a deeper understanding and control of complex biological networks. The
major challenge is the multiplexed control of several optogenetic components in
the presence of significant spectral cross talk. We propose and demonstrate
through simulations a new control approach of Stimulated Depletion Quenching.
This approach is applied to the phytochrome Cph8 bidirectional optogenetic
switch, and the results show significant improvement of its dynamic range.


  Bosons hopping across sites and interacting on-site are the essence of the
Bose-Hubbard model (BHM). Inspired by the success of BHM simulators with atoms
in optical lattices, proposals for implementing the BHM with photons in coupled
nonlinear cavities have emerged. Two coupled semiconductor microcavities
constitute a model system where the hopping, interaction, and decay of exciton
polaritons --- mixed light-matter quasiparticles --- can be engineered in
combination with site-selective coherent driving to implement the
driven-dissipative two-site optical BHM. Here we explore the interplay of
interference and nonlinearity in this system, in a regime where three distinct
density profiles can be observed under identical driving conditions. We
demonstrate how the phase acquired by polaritons hopping between cavities can
be controlled through effective polariton-polariton interactions. Our results
open new perspectives for synthesizing density-dependent gauge fields for
polaritons in two-dimensional multicavity systems.


  Exact analytical solutions for start-up and cessation flows are obtained for
the affine linear Phan-Thien--Tanner fluid model. They include the results for
start-up and cessation of steady shear flows, of steady uniaxial and biaxial
extensional flows, and of steady planar extensional flows. The solutions
obtained show that at start-up of steady shear flows, the stresses go through
quasi-periodic exponentially damped oscillations while approaching their
steady-flow values (so that stress overshoots are present); at start-up of
steady extensional flows, the stresses grow monotonically, while at cessation
of steady shear and extensional flows, the stresses decay quickly and
non-exponentially. The steady-flow rheology of the fluid is also reviewed, the
exact analytical solutions obtained in this work for steady shear and
extensional flows being simpler than the alternative formulas found in the
literature. The properties of steady and transient solutions, including their
asymptotic behavior at low and high Weissenberg numbers, are investigated in
detail. Generalization to the multimode version of the Phan-Thien--Tanner model
is also discussed. Thus, this work provides a complete analytical description
of the rheology of the affine linear Phan-Thien--Tanner fluid in start-up,
cessation, and steady regimes of shear and extensional flows.


  The Kerr geometry is believed to represent the exterior spacetime of
astrophysical black holes. We here re-analyze the geometry of Kerr-like metrics
(Kerr, Kerr-Newman, Kerr-de Sitter, and Kerr-anti de Sitter), paying particular
attention to the region near the singular set. We find that, although the
Kretschmann scalar vanishes at the singular set along a given direction, a
certain combination of curvature invariants diverges regardless of the
direction of approach. We also find that the two-dimensional geometry induced
by the spacetime metric on the orbits of the isometry group also possesses a
singularity regardless of the direction of approach. Likewise, the
two-dimensional geometry in the directions orthogonal to the isometry orbits is
$C^{2}$-divergent, but extends continuously at the singular set as a cone with
opening angle $4\pi$. We conclude by showing that tidal forces lead to infinite
stresses on neighboring geodesics that approach the singular set, destroying
any such observers in finite proper time. Those geodesics that come in from
infinity and do not hit the singular set but approach it are found to need
tremendous energy to get close to the singular set, experiencing an
acceleration transversal to the equatorial plane which grows without bound when
the minimal distance of approach goes to zero. While establishing these
results, we also present an alternative description of some other known
properties, as well as introducing toroidal coordinates that provide a hands-on
description of the double-covering for the geometry near the singular set.


  Multi-wavelength spectroscopy of NGC 5548 revealed remarkable changes due to
presence of an obscuring wind from the accretion disk. This broadened our
understanding of obscuration and outflows in AGN. Swift monitoring of NGC 5548
shows that over the last 10 years the obscuration has gradually declined. This
provides a valuable opportunity for analyses that have not been feasible before
because of too much obscuration. The lowered obscuration, together with the
high energy spectral coverage of Chandra HETG, facilitate the first study of
X-ray absorption lines in the obscured state. The comparison of the lines (Mg
XI, Mg XII, Si XIII, and Si XIV) between the new and historical spectra reveals
interesting changes, most notably the He-like absorption being significantly
diminished in 2022. Our study finds that the changes are caused by an increase
in both the ionization parameter and the column density of the warm-absorber
outflow in the obscured state. This is contrary to the shielding scenario that
is evident in the appearance of the UV lines, where the inner obscuring wind
shields outflows that are located further out, thus lowering their ionization.
The X-ray absorption lines in the HETG spectra appear to be unaffected by the
obscuration. The results suggest that the shielding is complex since various
components of the ionized outflow are impacted differently. We explore various
possibilities for the variability behavior of the X-ray absorption lines and
find that the orbital motion of a clumpy ionized outflow traversing our line of
sight is the most likely explanation.


  We consider dislocations in a vortex lattice that is driven in a
two-dimensional superconductor with random impurities. The structure and
dynamics of dislocations is studied in this genuine nonequilibrium situation on
the basis of a coarse-grained equation of motion for the displacement field.
The presence of dislocations leads to a characteristic anisotropic distortion
of the vortex density that is controlled by a Kardar-Parisi-Zhang nonlinearity
in the coarse-grained equation of motion. This nonlinearity also implies a
screening of the interaction between dislocations and thereby an instability of
the vortex lattice to the proliferation of free dislocations.


  The production of hidden-bottom pentaquark $P_{b}$ states via $\gamma p$ and
$\pi ^{-}p$ scatterings is studied within an effective Lagrangian approach and
the vector-meson-dominance mechnism. For the $P_{b}$ production in the process
$\gamma p\rightarrow \Upsilon p$, the dipole Pomeron model is employed to
calculate the background contribution, and the experimental data can be well
described. For the process $\pi ^{-}p\rightarrow \Upsilon n$, the Reggeized
$t$-channel with $\pi $ exchange is considered as the main background for the
$P_{b}$ production. Near the threshold, two-peak structure from the states
$P_{b (11080)$ and $P_{b}(11125)$ can be observed if energy bin width is chosen
as 0.01 GeV, and the same result is obtained in the $\pi ^{-}p$ scattering.
Moreover, by taking the branching ratio of Br$[{P_{b}\rightarrow \pi N}]\simeq
0.05\%$, the numerical result shows that the average value of cross section
from the $P_{b}(11080)$ state produced in the $\gamma p$ or $\pi ^{-}p$
scattering reaches at least 0.1 nb with a bin of 0.1 GeV. Even if we reduce the
branching ratio of the $P_{b}$ state into $\pi N$ channel by one order, the
theoretical average of the cross section from $P_{b}(11080)$ production in $\pi
^{-}p$ scattering can reach the order of 0.01 nb with a bin of 0.1 GeV, which
means that the signal can still be clearly distinguished from the background.
The experimental measurements and studies on the hidden-bottom pentaquark
$P_{b}$ state production in the $\gamma p $ or $\pi ^{-}p$ scattering
near-threshold energy region around $W\simeq 11$ GeV are strongly suggested,
which are accessible at COMPASS and JPARC. Particularly, the result of the
photoproduction suggests that it is very promising to observe the hidden-bottom
pentaquark at proposed EicC facility in China.


  Prior studies on covert communication with noise uncertainty adopted a
worst-case approach from the warden's perspective. That is, the worst-case
detection performance of the warden is used to assess covertness, which is
overly optimistic. Instead of simply considering the worst limit, in this work,
we take the distribution of noise uncertainty into account to evaluate the
overall covertness in a statistical sense. Specifically, we define new metrics
for measuring the covertness, which are then adopted to analyze the maximum
achievable rate for a given covertness requirement under both bounded and
unbounded noise uncertainty models.


  We present some results on the structure of line graphs of triangle-free
graphs and a homogenization of the line graph of the universal homogeneous
triangle-free graph in a finite relational language with arity 4. This result
is relevant to the study of the relational complexity of structures defined by
forbidden embeddings.


  Most Globular Clusters (GC) show chemical inhomogeneities in the composition
of their stars, apparently due to a second stellar generation (SG) in which the
forming gas is enriched by hot-CNO cycled material processed in stars belonging
to a first stellar generation (FG). We propose to use the horizontal branch
(HB) to infer which is today the relative number fraction of ''normal" and
anomalous stars in clusters. We assume that the anomalies also include enhanced
helium abundance. Helium variations have been recognized to be able to explain
several puzzling peculiarities (gaps, RR Lyr periods and period distribution,
ratio of blue to red stars, blue tails) in HBs. We extend the analysis to as
many clusters as possible. We show that, with few exceptions, 50% or more of
the stars belong to the SG. In other cases, where one would think of a simple
stellar population, we suggest that the stars might all belong to the SG. We
fit the optical and UV data of NGC2808, including a reproduction of the main
sequence splittings and an exam of the problem of "blue hook" stars. We also
show a detailed fit of the totally blue HB of M13, one among the clusters that
are possibly fully made up by SG stars. We conclude that the formation of the
SG is a crucial event in the life of GCs. A high fraction of SG stars can be
achieved only if the initial cluster was much more massive than the present one
and most of the FG low mass stars have been lost. As shown by D'Ercole et al.,
the mass loss due to type II supernovae of the FG may be the process
responsible for triggering the expansion of the cluster, the stripping of its
outer layers and the loss of most of the FG low-mass stars.


  The measurement of transverse single spin asymmetries ($A_N$) provides
insight into the structure of the nucleon. Several mechanisms have been
proposed that attempt to explain $A_N$ based on QCD, and additional
measurements of $A_N$ for different processes further constrain these models.
Using the PHENIX detector at the Relativistic Heavy Ion Collider (RHIC), we
study transversely polarized p+p collisions. Results from PHENIX and other
experiments show significant asymmetries in the forward region, which could be
due to contributions from both the Sivers and the Collins effects. Studying the
species as well as the kinematic dependencies of these transverse single spin
asymmetries will help to disentangle the origin of the observed asymmetries.
Therefore, measurements of $A_N$ with inclusive $\eta$ mesons at forward
rapidities are an important tool for the understanding of these asymmetries. In
2008, the PHENIX experiment collected 5.2 pb$^{-1}$ integrated luminosity in
$p^\uparrow+p$ collisions at $\sqrt{s}$ = 200 GeV. The status of the asymmetry
analysis of $\eta$ mesons at forward rapidity will be shown.


  We generalize two well-known game-theoretic models by introducing multiple
partners matching games, defined by a graph $G=(N,E)$, with an integer vertex
capacity function $b$ and an edge weighting $w$. The set $N$ consists of a
number of players that are to form a set $M\subseteq E$ of 2-player coalitions
$ij$ with value $w(ij)$, such that each player $i$ is in at most $b(i)$
coalitions. A payoff vector is a mapping $p: N \times N \rightarrow {\mathbb
R}$ with $p(i,j)+p(j,i)=w(ij)$ if $ij\in M$ and $p(i,j)=p(j,i)=0$ if $ij\notin
M$. The pair $(M,p)$ is called a solution. A pair of players $i,j$ with $ij\in
E\setminus M$ blocks a solution $(M,p)$ if $i,j$ can form, possibly only after
withdrawing from one of their existing 2-player coalitions, a new 2-player
coalition in which they are mutually better off. A solution is stable if it has
no blocking pairs.
  We give a polynomial-time algorithm that either finds that a given multiple
partners matching game has no stable solution, or obtains a stable solution for
it. We characterize the set of stable solutions of a multiple partners matching
game in two different ways and show how this leads to simple proofs for a
number of known results of Sotomayor (1992,1999,2007) for multiple partners
ssignment games and to generalizations of some of these results to multiple
partners matching games. We also perform a study on the core of the
corresponding cooperative game, where coalitions of any size may be formed. In
particular we show that the standard relation between the existence of a stable
solution and the non-emptiness of the core, which holds in the other models
with payments, is no longer valid for our (most general) model. We also prove
that the problem of deciding if an allocation belongs to the core jumps from
being polynomial-time solvable for $b\leq 2$ to NP-complete for $b\equiv 3$.


  Bayesian Neural Networks (BNNs) provide a probabilistic interpretation for
deep learning models by imposing a prior distribution over model parameters and
inferring a posterior distribution based on observed data. The model sampled
from the posterior distribution can be used for providing ensemble predictions
and quantifying prediction uncertainty. It is well-known that deep learning
models with lower sharpness have better generalization ability. However,
existing posterior inferences are not aware of sharpness/flatness in terms of
formulation, possibly leading to high sharpness for the models sampled from
them. In this paper, we develop theories, the Bayesian setting, and the
variational inference approach for the sharpness-aware posterior. Specifically,
the models sampled from our sharpness-aware posterior, and the optimal
approximate posterior estimating this sharpness-aware posterior, have better
flatness, hence possibly possessing higher generalization ability. We conduct
experiments by leveraging the sharpness-aware posterior with state-of-the-art
Bayesian Neural Networks, showing that the flat-seeking counterparts outperform
their baselines in all metrics of interest.


  Consideration is given to the continuous-time supercritical branching random
walk over a multidimensional lattice with a finite number of particle
generation sources of the same intensity both with and without constraint on
the variance of jumps of random walk underlying the process. Asymptotic
behavior of the Green function and eigenvalue of the evolution operator of the
mean number of particles under source intensity close to the critical one was
established.


  In this paper, we establish existence and uniqueness of weak solutions to
general time fractional equations and give their probabilistic representations.
We then derive sharp two-sided estimates for fundamental solutions of a family
of time fractional equations in metric measure spaces.


  Let \pi :Z\to X be a holomorphic submersion of a complex manifold Z onto a
complex manifold X and D\Subset X a 1-convex domain with strongly pseudoconvex
boundary. We prove that under certain conditions there always exists a spray of
\pi -sections over \bar{D} which has prescribed core, it fixes the exceptional
set E of D, and is dominating on \bar{D}\setminus E. Each section in this spray
is of class C^k(\bar{D}) and holomorphic on D. As a consequence we obtain
several approximation results for \pi -sections. In particular, we prove that
\pi -sections which are of class C^k(\bar{D}) and holomorphic on D can be
approximated in the C^k(\bar{D}) topology by \pi -sections that are holomorphic
in open neighborhoods of \bar{D}. Under additional assumptions on the
submersion we also get approximation by global holomorphic \pi -sections and
the Oka principle over 1-convex manifolds. We include an application to the
construction of proper holomorphic maps of 1-convex domains into q-convex
manifolds.


  The quantum Monte Carlo methods represent a powerful and broadly applicable
computational tool for finding very accurate solutions of the stationary
Schroedinger equation for atoms, molecules, solids and a variety of model
systems. The algorithms are intrinsically parallel and are able to take full
advantage of the present-day high-performance computing systems. This review
article concentrates on the fixed-node/fixed-phase diffusion Monte Carlo method
with emphasis on its applications to electronic structure of solids and other
extended many-particle systems.


  The Solar System Notification Alert Processing System (SNAPS) is a ZTF and
Rubin Observatory alert broker that will send alerts to the community regarding
interesting events in the Solar System. SNAPS is actively monitoring Solar
System objects and one of its functions is to compare objects (primarily main
belt asteroids) to one another to find those that are outliers relative to the
population. In this paper, we use the SNAPShot1 dataset which contains 31,693
objects from ZTF and derive outlier scores for each of these objects. SNAPS
employs an unsupervised approach; consequently, to derive outlier rankings for
each object, we propose four different outlier metrics such that we can explore
variants of outlier scores and add confidence to outlier rankings. We also
provide outlier scores for each object in each permutation of 15 feature
spaces, between 2 and 15 features, which yields 32,752 total feature spaces. We
show that we can derive population outlier rankings each month at Rubin
Observatory scale using four Nvidia A100 GPUs, and present several avenues of
scientific investigation that can be explored using population outlier
detection.


  At VAST 2016, a characterization of guidance has been presented. It includes
a definition of guidance and a model of guidance based on van Wijk's model of
visualization. This note amends the original characterization of guidance in
two aspects. First, we provide a clarification of what guidance actually is
(and is not). Second, we insert into the model a conceptually relevant link
that was missing in the original version.


  We propose and study the properties of a new potential demanded by the
self-consistency of the duality scheme in electromagnetic-like field theories
of totally anti-symmetric tensors in diverse dimensions. Physical implications
of this new potential is manifest under the presence of scalar condensates in
the Julia-Toulouse mechanism for the nucleation of topological defects with
consequences for the confinement phenomenon.


  A method for creating 3D texture coordinates for a sequence of polygon meshes
with changing topology and vertex motion vectors.


  We improve Levenshtein's upper bound for the cardinality of a code of length
four that is capable of correcting single deletions over an alphabet of even
size. We also illustrate that the new upper bound is sharp. Furthermore we
construct an optimal perfect code that is capable of correcting single
deletions for the same parameters.


  An effective method to compute a presentation of $Tor_k (M,N)$ for modules on
a not necessarily commutative algebra is proposed, more precisely when $R$ is a
PBW algebra, $M$ is a centralizing $R$-bimodule and $N$ is a finitely generated
left $R$-module.


  Degeneration and adaptation are two competing sides of the same coin called
resilience in the progressive processes of brain aging or diseases.
Degeneration accumulates during brain aging and other cerebral activities,
causing structural atrophy and dysfunction. At the same time, adaptation allows
brain network reorganize to compensate for structural loss to maintain
cognition function. Although hidden resilience mechanism is critical and
fundamental to uncover the brain aging law, due to the lack of datasets and
appropriate methodology, it remains essentially unknown how these two processes
interact dynamically across brain networks. To quantitatively investigate this
complex process, we analyze aging brains based on 6-year follow-up multimodal
neuroimaging database from 63 persons. We reveal the critical mechanism of
network resilience that various perturbation may cause fast brain structural
atrophy, and then brain can reorganize its functional layout to lower its
operational efficiency, which helps to slow down the structural atrophy and
finally recover its functional efficiency equilibrium. This empirical finding
could be explained by our theoretical model, suggesting one universal
resilience dynamical function. This resilience is achieved in the brain
functional network with evolving percolation and rich-club features. Our
findings can help to understand the brain aging process and design possible
mitigation methods to adjust interaction between degeneration and adaptation
from resilience viewpoint.


  Handel and Mosher define the axis bundle for a fully irreducible outer
automorphism in "Axes in Outer Space." In this paper we give a necessary and
sufficient condition for the axis bundle to consist of a unique periodic fold
line. As a consequence, we give a setting, and means for identifying in this
setting, when two elements of an outer automorphism group $Out(F_r)$ have
conjugate powers.


  We present a method for performing quantum state reconstruction on qubits and
qubit registers in the presence of decoherence and inhomogeneous broadening.
The method assumes only rudimentary single qubit rotations as well as knowledge
of decoherence and loss mechanisms. We show that full state reconstruction is
possible even in the case where single qubit rotations may only be performed
imperfectly. Furthermore we show that for ensemble quantum computing proposals,
quantum state reconstruction is possible even if the ensemble experiences
inhomogeneous broadening and if only imperfect qubit manipulations are
available during state preparation and reconstruction.


  Let $Y$ be an Ornstein-Uhlenbeck diffusion governed by an ergodic finite
state Markov process $X$: $dY_t=-\lambda(X_t)Y_tdt+\sigma(X_t)dB_t$, $Y_0$
given. Under ergodicity condition, we get quantitative estimates for the long
time behavior of $Y$. We also establish a trichotomy for the tail of the
stationary distribution of $Y$: it can be heavy (only some moments are finite),
exponential-like (only some exponential moments are finite) or Gaussian-like
(its Laplace transform is bounded below and above by Gaussian ones). The
critical moments are characterized by the parameters of the model.


  Let $\theta(n)$ denote the number of permutations of $\{1,2,\ldots,n\}$ that
do not contain a 3-term arithmetic progression as a subsequence. Such
permutations are known as 3-free permutations. We present a dynamic programming
algorithm to count all 3-free permutations of $\{1,2,\ldots,n\}$. We use the
output to extend and correct enumerative results in the literature for
$\theta(n)$ from $n=20$ out to $n=90$ and use the new values to inductively
improve existing bounds on $\theta(n)$.


  A generic and scalable Reinforcement Learning scheme for Artificial Neural
Networks is presented, providing a general purpose learning machine. By
reference to a node threshold three features are described 1) A mechanism for
Primary Reinforcement, capable of solving linearly inseparable problems 2) The
learning scheme is extended to include a mechanism for Conditioned
Reinforcement, capable of forming long term strategy 3) The learning scheme is
modified to use a threshold-based deep learning algorithm, providing a robust
and biologically inspired alternative to backpropagation. The model may be used
for supervised as well as unsupervised training regimes.


  The problem is to determine which processors are reliable in a remote
location by asking "Yes or No" questions. The processors are of three types:
those that always tell the truth, those that always lie, and those the
sometimes tell the truth and sometimes lie. Using self-referential reasoning,
along with earlier techniques, we can regard both the truth-tellers and liars
as reliable and thus the tackle situations when fewer than half the processors
are truth-tellers.


  Let $(X,\omega)$ be a compact symplectic manifold with a Hamiltonian action
of a compact Lie group $G$ and $\mu: X\to \mathfrak g$ be its moment map. In
this paper, we study the $L^2$-moduli spaces of symplectic vortices on Riemann
surfaces with cylindrical ends. We studied a circle-valued action functional
whose gradient flow equation corresponds to the symplectic vortex equations on
a cylinder $S^1\times \mathbb R$. Assume that $0$ is a regular value of the
moment map $\mu$, we show that the functional is of Bott-Morse type and its
critical points of the functional form twisted sectors of the symplectic
reduction (the symplecitc orbifold $[\mu^{-1}(0)/G]$).
  We show that any gradient flow lines approaches its limit point exponentially
fast. Fredholm theory and compactness property are then established for the
$L^2$-Moduli spaces of symplectic vortices on Riemann surfaces with cylindrical
ends.


  Wire cutting is a technique for partitioning large quantum circuits into
smaller subcircuits in such a way that observables for the original circuits
can be estimated from measurements on the smaller subcircuits. Such techniques
provide workarounds for the limited numbers of qubits that are available on
near-term quantum devices. Wire cutting, however, introduces multiplicative
factors in the number of times such subcircuits need to be executed in order to
estimate desired quantum observables to desired levels of statistical accuracy.
An optimal wire-cutting methodology has recently been reported that uses
ancilla qubits to minimize the multiplicative factors involved as a function of
the number of wire cuts. Until just recently, the best-known wire-cutting
technique that did not employ ancillas asymptotically converged to the same
multiplicative factors, but performed significantly worse for small numbers of
cuts. This latter technique also requires inserting measurement and
state-preparation subcircuits that are randomly sampled from Clifford 2-designs
on a per-shot basis. This paper presents a modified wire-cutting approach for
pairs of subcircuits that achieves the same optimal multiplicative factors as
wire cutting aided by ancilla qubits, but without requiring ancillas. The paper
also shows that, while unitary 2-designs provide a sufficient basis for
satisfying the decomposition, 2-designs are not mathematically necessary and
alternative unitary designs can be constructed for the decompositions that are
substantially smaller in size than 2-designs. As this paper was just about to
be released, a similar result was published, so we also include a comparison of
the two approaches.


  Can a machine understand the meanings of natural language? Recent
developments in the generative large language models (LLMs) of artificial
intelligence have led to the belief that traditional philosophical assumptions
about machine understanding of language need to be revised. This article
critically evaluates the prevailing tendency to regard machine language
performance as mere syntactic manipulation and the simulation of understanding,
which is only partial and very shallow, without sufficient referential
grounding in the world. The aim is to highlight the conditions crucial to
attributing natural language understanding to state-of-the-art LLMs, where it
can be legitimately argued that LLMs not only use syntax but also semantics,
their understanding not being simulated but duplicated; and determine how they
ground the meanings of linguistic expressions.


  We study quintessence models using low energy supergravity inspired from
string theory. We consider effective supergravity with two scales m_S, the
string scale, and m_PL, the Planck scale and show that quintessence naturally
arises from a supersymmetry breaking hidden sector. As long as supersymmetry is
broken by the $F$-term of a Polonyi-like field coupled to the quintessence
field in the K\"ahler potential we find that the Ratra-Peebles potential and
its supergravity version are generic predictions. This requires that the string
scale decouples from the Planck scale, m_S << m_PL. In the context of
supergravity, the potential possesses a minimum induced by the supergravity
corrections to the Ratra-Peebles potential at low redshifts. We study the
physical consequences of the presence of this minimum.


  Quasicrystals are metallic alloys that possess long-range, aperiodic
structures with diffraction symmetries forbidden to conventional crystals.
Since the discovery of quasicrystals by Schechtman et al. at 1984 (ref. 1),
there has been considerable progress in resolving their geometric structure.
For example, it is well known that the golden ratio of mathematics and art
occurs over and over again in their crystal structure. However, the
characteristic properties of the electronic states - whether they are extended
as in periodic crystals or localized as in amorphous materials - are still
unresolved. Here we report the first observation of quantum (T = 0) critical
phenomena of the Au-Al-Yb quasicrystal - the magnetic susceptibility and the
electronic specific heat coefficient arising from strongly correlated 4f
electrons of the Yb atoms diverge as T -> 0. Furthermore, we observe that this
quantum critical phenomenon is robust against hydrostatic pressure. By
contrast, there is no such divergence in a crystalline approximant, a phase
whose composition is close to that of the quasicrystal and whose unit cell has
atomic decorations (that is, icosahedral clusters of atoms) that look like the
quasicrystal. These results clearly indicate that the quantum criticality is
associated with the unique electronic state of the quasicrystal, that is, a
spatially confined critical state. Finally we discuss the possibility that
there is a general law underlying the conventional crystals and the
quasicrystals.


  PMN J1603$-$4904 is a likely member of the rare class of $\gamma$-ray
emitting young radio galaxies. Only one other source, PKS 1718$-$649, has been
confirmed so far. These objects, which may transition into larger radio
galaxies, are a stepping stone to understanding AGN evolution. It is not
completely clear how these young galaxies, seen edge-on, can produce
high-energy $\gamma$-rays. PMN J1603$-$4904 has been detected by TANAMI Very
Long Baseline Interferometry (VLBI) observations and has been followed-up with
multiwavelength observations. A Fermi/LAT $\gamma$-ray source has been
associated with it in the LAT catalogs. We have obtained Chandra observations
of the source in order to consider the possibility of source confusion, due to
the relatively large positional uncertainty of Fermi/LAT. The goal was to
investigate the possibility of other X-ray bright sources in the vicinity of
PMN J1603$-$4904 that could be counterparts to the $\gamma$-ray emission. With
Chandra/ACIS, we find no other sources in the uncertainty ellipse of Fermi/LAT
data, which includes an improved localization analysis of 8 years of data. We
further study the X-ray fluxes and spectra. We conclude that PMN J1603$-$4904
is indeed the second confirmed $\gamma$-ray bright young radio galaxy.


  Despite the popularity of explainable AI, there is limited work on effective
methods for unsupervised learning. We study algorithms for $k$-means
clustering, focusing on a trade-off between explainability and accuracy.
Following prior work, we use a small decision tree to partition a dataset into
$k$ clusters. This enables us to explain each cluster assignment by a short
sequence of single-feature thresholds. While larger trees produce more accurate
clusterings, they also require more complex explanations. To allow flexibility,
we develop a new explainable $k$-means clustering algorithm, ExKMC, that takes
an additional parameter $k' \geq k$ and outputs a decision tree with $k'$
leaves. We use a new surrogate cost to efficiently expand the tree and to label
the leaves with one of $k$ clusters. We prove that as $k'$ increases, the
surrogate cost is non-increasing, and hence, we trade explainability for
accuracy. Empirically, we validate that ExKMC produces a low cost clustering,
outperforming both standard decision tree methods and other algorithms for
explainable clustering. Implementation of ExKMC available at
https://github.com/navefr/ExKMC.


  For assignment problems where agents, specifying ordinal preferences, are
allocated indivisible objects, two widely studied randomized mechanisms are the
Random Serial Dictatorship (RSD) and Probabilistic Serial Rule (PS). These two
mechanisms both have desirable economic and computational properties, but the
outcomes they induce can be incomparable in many instances, thus creating
challenges in deciding which mechanism to adopt in practice. In this paper we
first look at the space of lexicographic preferences and show that, as opposed
to the general preference domain, RSD satisfies envyfreeness. Moreover, we show
that although under lexicographic preferences PS is strategyproof when the
number of objects is less than or equal agents, it is strictly manipulable when
there are more objects than agents. In the space of general preferences, we
provide empirical results on the (in)comparability of RSD and PS, analyze
economic properties, and provide further insights on the applicability of each
mechanism in different application domains.


  We discuss a simple, binary tree-based algorithm for the collective allreduce
(reduction-to-all, MPI_Allreduce) operation for parallel systems consisting of
$p$ suitably interconnected processors. The algorithm can be doubly pipelined
to exploit bidirectional (telephone-like) communication capabilities of the
communication system. In order to make the algorithm more symmetric, the
processors are organized into two rooted trees with communication between the
two roots. For each pipeline block, each non-leaf processor takes three
communication steps, consisting in receiving and sending from and to the two
children, and sending and receiving to and from the root. In a round-based,
uniform, linear-cost communication model in which simultaneously sending and
receiving $n$ data elements takes time $\alpha+\beta n$ for system dependent
constants $\alpha$ (communication start-up latency) and $\beta$ (time per
element), the time for the allreduce operation on vectors of $m$ elements is
$O(\log p+\sqrt{m\log p})+3\beta m$ by suitable choice of the pipeline block
size. We compare the performance of an implementation in MPI to similar reduce
followed by broadcast algorithms, and the native MPI_Allreduce collective on a
modern, small $36\times 32$ processor cluster. With proper choice of the number
of pipeline blocks, it is possible to achieve better performance than pipelined
algorithms that do not exploit bidirectional communication.


  In this paper, we study the normalised characteristic scale of transition to
cosmic homogeneity, $\mathcal{R}_H/d_V$, as a cosmological probe. We use a
compilation of SDSS galaxy samples, comprising more than $10^6$ galaxies in the
redshift range $0.17 \leq z \leq 2.2$ within the largest comoving volume to
date, $\sim 8 h^{-3}\mathrm{Gpc}^3$. We show that these samples can be
described by a single bias model as a function of redshift. By combining our
measurements with prior Cosmic Microwave Background and Lensing information
from the Planck satellite, we constrain the total matter density ratio of the
universe, $\Omega_m = 0.363 \pm 0.025$, and the Dark Energy density ratio,
$\Omega_{\Lambda} = 0.649 \pm 0.021$, improving the values from Planck alone by
31% and 28%, respectively. Our results are compatible with a flat $\Lambda$CDM
model. These results show the complementarity of the normalised homogeneity
scale with other cosmological probes and open new roads to cosmometry.


  We propose an importance-truncation scheme for the large-scale nuclear shell
model that extends its range of applicability to larger valence spaces and
mid-shell nuclei. It is based on a perturbative measure for the importance of
individual basis states that acts as an additional truncation for the many-body
model space in which the eigenvalue problem of the Hamiltonian is solved
numerically. Through a posteriori extrapolations of all observables to
vanishing importance threshold, the full shell-model results can be recovered.
In addition to simple threshold extrapolations, we explore extrapolations based
on the energy variance. We apply the importance-truncated shell model for the
study of 56-Ni in the pf valence space and of 60-Zn and 64-Ge in the pfg9/2
space. We demonstrate the efficiency and accuracy of the approach, which pave
the way for future shell-model calculations in larger valence spaces with
valence-space interactions derived in ab initio approaches.


  Current methods for end-to-end constructive neural combinatorial optimization
usually train a policy using behavior cloning from expert solutions or policy
gradient methods from reinforcement learning. While behavior cloning is
straightforward, it requires expensive expert solutions, and policy gradient
methods are often computationally demanding and complex to fine-tune. In this
work, we bridge the two and simplify the training process by sampling multiple
solutions for random instances using the current model in each epoch and then
selecting the best solution as an expert trajectory for supervised imitation
learning. To achieve progressively improving solutions with minimal sampling,
we introduce a method that combines round-wise Stochastic Beam Search with an
update strategy derived from a provable policy improvement. This strategy
refines the policy between rounds by utilizing the advantage of the sampled
sequences with almost no computational overhead. We evaluate our approach on
the Traveling Salesman Problem and the Capacitated Vehicle Routing Problem. The
models trained with our method achieve comparable performance and
generalization to those trained with expert data. Additionally, we apply our
method to the Job Shop Scheduling Problem using a transformer-based
architecture and outperform existing state-of-the-art methods by a wide margin.


  Let $G,H$ be graphs and $G*H$ represent a particular graph product of $G$ and
$H$. We define $im(G)$ to be the largest $t$ such that $G$ has a
$K_t$-immersion and ask: given $im(G)=t$ and $im(H)=r$, how large is $im(G*H)$?
Best possible lower bounds are provided when $*$ is the Cartesian or
lexicographic product, and a conjecture is offered for each of the direct and
strong products, along with some partial results.


  With the global effort to reduce carbon emissions, clean technologies such as
electric vehicles and heat pumps are increasingly introduced into electricity
distribution networks. These technologies considerably increase electricity
flows and can lead to more coincident electricity demand. In this paper, we
analyze how such increases in demand coincidence impact future distribution
network investments. For this purpose, we develop a novel model for designing
electricity distribution networks, called the distribution network
reconfiguration problem with line-specific demand coincidence (DNRP-LSDC). Our
analysis is two-fold: (1) We apply our model to a large sample of real-world
networks from a Swiss distribution network operator. We find that a high demand
coincidence due to, for example, a large-scale uptake of electric vehicles,
requires a substantial amount of new network line construction and increases
average network cost by 84 % in comparison to the status quo. (2) We use a set
of synthetic networks to isolate the effect of specific network
characteristics. Here, we show that high coincidence has a more detrimental
effect on large networks and on networks with low geographic consumer
densities, as present in, e. g., rural areas. We also show that expansion
measures are robust to variations in the cost parameters. Our results
demonstrate the necessity of designing policies and operational protocols that
reduce demand coincidence. Moreover, our findings show that operators of
distribution networks must consider the demand coincidence of new electricity
uses and adapt investment budgets accordingly. Here, our solution algorithms
for the DNRP-LSDC problem can support operators of distribution networks in
strategic and operational network design tasks.


  The Trojan asteroids of Jupiter and Neptune are likely to have been captured
from original heliocentric orbits in the dynamically excited ("hot") population
of the Kuiper belt. However, it has long been known that the optical color
distributions of the Jovian Trojans and the hot population are not alike. This
difference has been reconciled with the capture hypothesis by assuming that the
Trojans were resurfaced (for example, by sublimation of near-surface volatiles)
upon inward migration from the Kuiper belt (where blackbody temperatures are
$\sim$40 K) to Jupiter's orbit ($\sim$125 K). Here, we examine the optical
color distribution of the \textit{Neptunian} Trojans using a combination of new
optical photometry and published data. We find a color distribution that is
statistically indistinguishable from that of the Jovian Trojans but unlike any
sub-population in the Kuiper belt. This result is puzzling, because the
Neptunian Trojans are very cold (blackbody temperature $\sim$50 K) and a
thermal process acting to modify the surface colors at Neptune's distance would
also affect the Kuiper belt objects beyond, where the temperatures are nearly
identical. The distinctive color distributions of the Jovian and Neptunian
Trojans thus present us with a conundrum: they are very similar to each other,
suggesting either capture from a common source or surface modification by a
common process. However, the color distributions differ from any plausible
common source population, and there is no known modifying process that could
operate equally at both Jupiter and Neptune.


  In this paper, we consider first-order convergence theory and algorithms for
solving a class of non-convex non-concave min-max saddle-point problems, whose
objective function is weakly convex in the variables of minimization and weakly
concave in the variables of maximization. It has many important applications in
machine learning including training Generative Adversarial Nets (GANs). We
propose an algorithmic framework motivated by the inexact proximal point
method, where the weakly monotone variational inequality (VI) corresponding to
the original min-max problem is solved through approximately solving a sequence
of strongly monotone VIs constructed by adding a strongly monotone mapping to
the original gradient mapping. We prove first-order convergence to a nearly
stationary solution of the original min-max problem of the generic algorithmic
framework and establish different rates by employing different algorithms for
solving each strongly monotone VI. Experiments verify the convergence theory
and also demonstrate the effectiveness of the proposed methods on training
GANs.


  Shadows in scattered light images of protoplanetary disks are a common
feature and support the presence of warps or misalignments between disk
regions. These warps are possibly due to an inclined (sub-)stellar companion
embedded in the disk. We study the morphology of the protoplanetary disk around
the Herbig Ae star HD 139614 based on the first scattered light observations of
this disk, which we model with the radiative transfer code MCMax3D. We obtained
J- and H-band observations in polarized scattered light with VLT/SPHERE that
show strong azimuthal asymmetries. In the outer disk, beyond ~30 au, a broad
shadow spans a range of ~240{\deg} in position angle, in the East. A bright
ring at ~16 au also shows an azimuthally asymmetric brightness, with the
faintest side roughly coincidental with the brightest region of the outer disk.
Additionally, two arcs are detected at ~34 au and ~50 au. We created a simple
4-zone approximation to a warped disk model of HD 139614 in order to
qualitatively reproduce these features. The location and misalignment of the
disk components were constrained from the shape and location of the shadows
they cast. We find that the shadow on the outer disk covers a range of position
angle too wide to be explained by a single inner misaligned component. Our
model requires a minimum of two separate misaligned zones -- or a continuously
warped region -- to cast this broad shadow on the outer disk. A small
misalignment of ~4{\deg} between adjacent components can reproduce most of the
observed shadow features. Multiple misaligned disk zones, potentially mimicing
a warp, can explain the observed broad shadows in the HD 139614 disk. A
planetary mass companion in the disk, located on an inclined orbit, could be
responsible for such a feature and for the dust depleted gap responsible for a
dip in the SED.


  Background: Access to medical care is strongly dependent on resource
allocation, such as the geographical distribution of medical facilities.
Nevertheless, this data is usually restricted to country official
documentation, not available to the public. While some medical facilities' data
is accessible as semantic resources on the Web, it is not consistent in its
modeling and has yet to be integrated into a complete, open, and specialized
repository. This work focuses on generating a comprehensive semantic dataset of
medical facilities worldwide containing extensive information about such
facilities' geo-location.
  Results: For this purpose, we collect, align, and link various open-source
databases where medical facilities' information may be present. This work
allows us to evaluate each data source along various dimensions, such as
completeness, correctness, and interlinking with other sources, all critical
aspects of current knowledge representation technologies.
  Conclusions: Our contributions directly benefit stakeholders in the
biomedical and health domain (patients, healthcare professionals, companies,
regulatory authorities, and researchers), who will now have a better overview
of the access to and distribution of medical facilities.


  Photovoltaic optoelectronic tweezers (PVOT) have been proven to be an
efficient tool for the manipulation and massive assembly of micro/nano-objects.
The technique relies on the strong electric fields produced by certain
ferroelectric materials upon illumination due to the bulk photovoltaic effect
(customarily LiNbO3:Fe). Despite the rapid development of PVOT and the
achievement of high-quality 1D and 2D particle patterning, research efforts
aimed at the fabrication of combinatorial structures made up of multiple types
of particles have been scarce. Here, we have established the working principles
of three different methods to tackle this pending challenge. To that end,
dielectrophoresis and/or electrophoresis acting on neutral and charged
particles respectively, have been suitably exploited. Simple mixed structures
combining metallic and dielectric nanoparticles of different sizes have been
successfully obtained. The results lay the groundwork for future fabrication of
more complex combinatorial structures by PVOT, where micro/nanoparticles are
the basic building blocks of miniaturized functional devices.


  It has recently been shown that an interesting inverse relationship exists
between the strength of the overturning in the regional boreal Hadley
circulation and tropical cyclone genesis and lifetime maximum intensity
latitudes in the eastern North Pacific. One of the particularly curious aspects
of this association is its uniqueness to this ocean basin. We show here that
this result can be understood as the outcome of an equatorward shift in the
local Intertropical Convergence Zone (ITCZ) and a moderate reduction of
tropical vertical shear. These two factors are not necessarily concomitant. The
magnitude of the vertical shear change is low enough to suggest that the
primary physical mechanism behind this inverse relationship is the equatorward
shift in the ITCZ. Since a significant proportion of tropical cyclone genesis
results from aggregated convective cells forming into a coherent convective
vortex and being shed from the ITCZ, this shift is apparently sufficient to
explain the observed association. The equatorward shift in the ITCZ is
potentially the result of a relative warming of the Southern Hemisphere in the
boreal tropical cyclone season. This more equatorward ITCZ, located over warmer
surface waters, presumably explains the more intense Hadley circulation,
despite a reduction of the large-scale boreal meridional temperature gradient.
Although, these links require further research.


  The $p$-group generation algorithm is used to verify that the Hilbert
$3$-class field tower has length $3$ for certain imaginary quadratic fields $K$
with $3$-class group $\mathrm{Cl}_3(K) \cong [3,3]$. Our results provide the
first examples of finite $p$-class towers of length $> 2$ for an odd prime $p$.


  In May 2022 ICRANet organized the Workshop dedicated to the 80th anniversary
of Professor Ruffini. This paper is based on the talk delivered at the meeting.
  Professor Ruffini was well known for Soviet scientific community not only due
to his publications in leading journals but also due Russian translations of
his books where he was an author or a contributor in collection of articles.
  But only in 1988 I had an opportunity to watch and listen professor R.
Ruffini at the Conference dedicated to the century since the birthday of
Alexander Alexandrovich Friedmann. This conference was organized in Leningrad
(Soviet Union) in June during a short magic period when there are white nights
there. In June 2023 we celebrate the 135th anniversary of Friedmann's birth.
Friedmann and his closed friend V. K. Frederics were the founders of Soviet
school of general relativity and George Gamow was one of the brilliant
representative of the school and he was the author of the hot Universe model
which is the most popular now. In the USSR a development of general relativity
and relativistic cosmology was not smooth and only in sixties of the last
century these branches of science freed from the total control of
representatives of the ideology of Marxism -- Leninism. I also discussed a
Soviet contribution in a discovery of cosmic microwave background radiation
done by T. Shmaonov in 1957 and reasons why his supervisors did not connect
these results with the hot Universe models discussed by G. Gamow. Author's
results about observational features of supemassive black holes (including the
black hole in our Galactic Center) are also briefly discussed, it was
considered
  an opportunity to evaluate a (tidal) charge of Reissner -- Nordstr\"om black
hole from observational estimates of shadow size in the Galactic Center and
M87* done by the EHT Collaboration based its observations in April 2017.


  The combination of self-play and planning has achieved great successes in
sequential games, for instance in Chess and Go. However, adapting algorithms
such as AlphaZero to simultaneous games poses a new challenge. In these games,
missing information about concurrent actions of other agents is a limiting
factor as they may select different Nash equilibria or do not play optimally at
all. Thus, it is vital to model the behavior of the other agents when
interacting with them in simultaneous games. To this end, we propose Albatross:
AlphaZero for Learning Bounded-rational Agents and Temperature-based Response
Optimization using Simulated Self-play. Albatross learns to play the novel
equilibrium concept of a Smooth Best Response Logit Equilibrium (SBRLE), which
enables cooperation and competition with agents of any playing strength. We
perform an extensive evaluation of Albatross on a set of cooperative and
competitive simultaneous perfect-information games. In contrast to AlphaZero,
Albatross is able to exploit weak agents in the competitive game of
Battlesnake. Additionally, it yields an improvement of 37.6% compared to
previous state of the art in the cooperative Overcooked benchmark.


  Many biological materials consist of sparse networks of disordered fibres,
embedded in a soft elastic matrix. The interplay between rigid and soft
elements in such composite networks leads to mechanical properties that can go
far beyond the sum of those of the constituents. Here we present lattice-based
simulations to unravel the microscopic origins of this mechanical synergy. We
show that the competition between fibre stretching and bending and elastic
deformations of the matrix gives rise to distinct mechanical regimes, with
phase transitions between them that are characterized by critical behaviour and
diverging strain fluctuations and with different mechanisms leading to
mechanical enhancement.


  Users of Virtual Reality (VR) systems often experience vection, the
perception of self-motion in the absence of any physical movement. While
vection helps to improve presence in VR, it often leads to a form of motion
sickness called cybersickness. Cybersickness is a major deterrent to large
scale adoption of VR.
  Prior work has discovered that changing vection (changing the perceived speed
or moving direction) causes more severe cybersickness than steady vection
(walking at a constant speed or in a constant direction). Based on this idea,
we try to reduce the cybersickness caused by character movements in a First
Person Shooter (FPS) game in VR. We propose Rotation Blurring (RB), uniformly
blurring the screen during rotational movements to reduce cybersickness. We
performed a user study to evaluate the impact of RB in reducing cybersickness.
We found that the blurring technique led to an overall reduction in sickness
levels of the participants and delayed its onset. Participants who experienced
acute levels of cybersickness benefited significantly from this technique.


  The Sznajd model is an Ising spin model representing a simple mechanism of
making up decisions in a closed community. In the model each member of the
community can take two attitudes A or B represented by a spin up or spin down
state respectively. It has been shown that, in one-dimension starting from a
totally random initial state, three final fixed points can be obtained; all
spins up, all spins down or an antiferromagnetic state in which each site take
a state which is opposite from its two nearest neighbors. Here, a modification
of the updating rule of the Sznajd model is proposed in order to avoid such
antiferromagnetic state since it is considered to be an unrealistic state in a
real community.


  Currently engineering efficient and successful event-driven applications
based on the emerging Complex Event Processing (CEP) technology, is a laborious
trial and error process. The proposed CEP design pattern approach should
support CEP engineers in their design decisions to build robust and efficient
CEP solutions with well understood tradeoffs and should enable an
interdisciplinary and efficient communication process about successful CEP
solutions in different application domains.


  This paper introduces a control problem of regulation of energy flows in a
two-site electricity and heat supply system, where two Combined Heat and Power
(CHP) plants are interconnected via electricity and heat flows. The control
problem is motivated by recent development of fast operation of CHP plants to
provide ancillary services of power system on the order of tens of seconds to
minutes. Due to the physical constraint that the responses of the heat
subsystem are not necessary as fast as those of the electric subsystem, the
target controlled state is not represented by any isolated equilibrium point,
implying that stability of the system is lost in the long-term sense on the
order of hours. In this paper, we first prove in the context of nonlinear
control theory that the state-space model of the two-site system is non-minimum
phase due to nonexistence of isolated equilibrium points of the associated zero
dynamics.Instead, we locate a one-dimensional invariant manifold that
represents the target controlled flows completely. Then, by utilizing a virtual
output under which the state-space model becomes minimum phase, we synthesize a
controller that achieves not only the regulation of energy flows in the
short-term regime but also stabilization of an equilibrium point in the
long-term regime. Effectiveness of the synthesized controller is established
with numerical simulations with a practical set of model parameters.


  We construct a family of Markov processes with continuous sample trajectories
on an infinite-dimensional space, the Thoma simplex. The family depends on
three continuous parameters, one of which, the Jack parameter, is similar to
the beta parameter in random matrix theory. The processes arise in a scaling
limit transition from certain finite Markov chains, the so called up-down
chains on the Young graph with the Jack edge multiplicities. Each of the limit
Markov processes is ergodic and its stationary distribution is a symmetrizing
measure. The infinitesimal generators of the processes are explicitly computed;
viewed as selfadjoint operators in the L^2 spaces over the symmetrizing
measures, the generators have purely discrete spectrum which is explicitly
described.
  For the special value 1 of the Jack parameter, the limit Markov processes
coincide with those of the recent work by Borodin and the author (Prob. Theory
Rel. Fields 144 (2009), 281--318; arXiv:0706.1034). In the limit as the Jack
parameter goes to 0, our family of processes degenerates to the one-parameter
family of diffusions on the Kingman simplex studied long ago by Ethier and
Kurtz in connection with some models of population genetics.
  The techniques of the paper are essentially algebraic. The main computations
are performed in the algebra of shifted symmetric functions with the Jack
parameter and rely on the concept of anisotropic Young diagrams due to Kerov.


  The shearing instability of a dilute granular mixture composed of smooth
inelastic hard spheres or disks is investigated. By using the Navier-Stokes
hydrodynamic equations, it is shown that the scaled transversal velocity mode
exhibits a divergent behaviour, similarly to what happens in one-component
systems. The theoretical prediction for the critical size is compared with
direct Monte Carlo simulations of the Boltzmann equations describing the
system, and a good agreement is found. The total energy fluctuations in the
vicinity of the transition are shown to scale with the second moment of the
distribution. The scaling distribution function is the same as found in other
equilibrium and non-equilibrium phase transitions, suggesting the existence of
some kind of universality.


  In this paper, we introduce and study the notion of phase rank. Given a
matrix filled with phases, i.e., with complex entries of modulus $1$, its phase
rank is the smallest possible rank for a complex matrix with the same phase,
but possible different modulus. This notion generalizes the notion of sign
rank, and is the complementary notion to that of phaseless rank. It also has
intimate connections to the problem of ray nonsingularity and provides an
important class of examples for the study of coamoebas. Among other results, we
provide a new characterization of phase rank $2$ for $3 \times 3$ matrices,
that implies the new result that for the $3\times 3$ determinantal variety, its
coamoeba is determined solely by the colopsidedness criterion.


  For the coefficients of the amplitude a set of simultaneous equations is
derived in momentum space. By the auxiliary conditions they are equivalent to
nonrelativistic equations and suitable for the investigation of two-nucleon
system.


  Vibration injury in the hand-arm system from hand-held machines is one of the
most common occupational health injuries and causes severe and often chronic
nerve and vascular injury to the operator. Machines emitting shock vibrations,
e.g., impact wrenches have since long been identified as a special risk factor.
In legislative and standard texts the terms shock, impact, and transient
vibration are frequently used to underline the special risk associated with
these kinds of vibrations. In spite of this, there is no mathematically
stringent definition what a shock vibration is or how the amplitude of the
shock is defined. This lack of definitions is the subject of this article. This
document discusses a number of candidate definitions for a vibration shock
index (VSI) that quantifies different vibration signals in terms of how
localized they are in the time domain. The VSI is intended to be used to
classify and compare different vibration sources. The VSI is independent of the
vibration level, i.e., it is unchanged if the vibration signal is rescaled. The
traditional root mean square method to determine the vibration level will not
produce a value representative for the shocks occurring in a signal with high
VSI. Thus, there is a need for a complementing quantification method for the
localized signal parts. Possible definitions for such a vibration shock level
(VSL) are suggested. A problem formulation is first stated together with a
description of the approach used for designing the VSI and the VSL. After this,
model signals are defined, which are used to discuss and evaluate the different
candidate definitions. Then, a number of candidate definitions are discussed,
leading up to a conclusion on which candidate definitions that are promising
for experimental evaluation.


  We apply crystal theory to affine Schubert calculus, Gromov-Witten invariants
for the complete flag manifold, and the positroid stratification of the
positive Grassmannian. We introduce operators on decompositions of elements in
the type-$A$ affine Weyl group and produce a crystal reflecting the internal
structure of the generalized Young modules whose Frobenius image is represented
by stable Schubert polynomials. We apply the crystal framework to products of a
Schur function with a $k$-Schur function, consequently proving that a subclass
of 3-point Gromov-Witten invariants of complete flag varieties for $\mathbb
C^n$ enumerate the highest weight elements under these operators. Included in
this class are the Schubert structure constants in the (quantum) product of a
Schubert polynomial with a Schur function $s_\lambda$ for all $|\lambda^\vee|<
n$. Another by-product gives a highest weight formulation for various fusion
coefficients of the Verlinde algebra and for the Schubert decomposition of
certain positroid classes.


  Radio galaxies are a subclass of active galactic nuclei that drive
relativistic jets from their center and are observed in radio to
very-high-energy gamma rays. The emission mechanisms and regions are still
unknown. High-energy gamma rays can be explained by the emission from the
magnetically arrested disks (MADs) around the central supermassive black hole,
for which the magnetic flux threading the black hole is in a saturation level,
although the emission from the MADs does not explain the optical and X-ray
data. We construct a multi-wavelength emission model in which the optical and
X-ray emission is emitted by jets and the gamma rays by MADs. Our model takes
into account the particle injection by the magnetic reconnection at the jet
base close to the black hole and particle entrainment from the ambient gas at
the jet emission zone. We apply our model to M87 and find that our model can
explain the simultaneous multi-wavelength data. In our model, the emission from
the jets is the synchrotron radiation of the nonthermal electrons accelerated
by magnetic reconnection, and the emission from the MADs is the synchrotron
radiation mainly of the nonthermal protons accelerated by turbulence. We also
find that the strong plasma entrainment is necessary to explain the
multi-wavelength data. Our model will be tested by variability analysis among
the multi-wavelength data.


  This paper attempts to analyze the Korean sentence classification system for
a chatbot. Sentence classification is the task of classifying an input sentence
based on predefined categories. However, spelling or space error contained in
the input sentence causes problems in morphological analysis and tokenization.
This paper proposes a novel approach of Integrated Eojeol (Korean syntactic
word separated by space) Embedding to reduce the effect that poorly analyzed
morphemes may make on sentence classification. It also proposes two noise
insertion methods that further improve classification performance. Our
evaluation results indicate that the proposed system classifies erroneous
sentences more accurately than the baseline system by 17%p.0


  Given a graph $G=(V,E)$ of order $n$ and an $n$-dimensional non-negative
vector $d=(d(1),d(2),\ldots,d(n))$, called demand vector, the vector domination
(resp., total vector domination) is the problem of finding a minimum
$S\subseteq V$ such that every vertex $v$ in $V\setminus S$ (resp., in $V$) has
at least $d(v)$ neighbors in $S$. The (total) vector domination is a
generalization of many dominating set type problems, e.g., the dominating set
problem, the $k$-tuple dominating set problem (this $k$ is different from the
solution size), and so on, and its approximability and inapproximability have
been studied under this general framework. In this paper, we show that a
(total) vector domination of graphs with bounded branchwidth can be solved in
polynomial time. This implies that the problem is polynomially solvable also
for graphs with bounded treewidth. Consequently, the (total) vector domination
problem for a planar graph is subexponential fixed-parameter tractable with
respectto $k$, where $k$ is the size of solution.


  In this study, we propose a carrier time-of-flight technique to evaluate the
carrier transport time across a quantum structure in an active region of solar
cells. By observing the time-resolved photoluminescence signal with a
quantum-well probe inserted under the quantum structure at forward bias, the
carrier transport time can be efficiently determined at room temperature. The
averaged drift velocity shows linear dependence on the internal field, allowing
us to estimate the quantum structure as a quasi-bulk material with low
effective mobility containing the information of carrier dynamics. We show that
this direct and real-time observation is more sensitive to carrier transport
than other conventional techniques, providing better insights into microscopic
carrier transport dynamics to overcome a device design difficulty.


  In this work we conjecture the Coulomb branch partition function, including
flux and instanton contributions, for the $\mathcal{N}=2$ vector multiplet on
weighted projective space $\mathbb{CP}^2_{\boldsymbol{N}}$ for equivariant
Donaldson-Witten and ``Pestun-like'' theories. More precisely, we claim that
this partition function agrees with the one computed on a certain branched
cover of $\mathbb{CP}^2$ upon matching conical deficit angles with
corresponding branch indices. Our conjecture is substantiated by checking that
similar partition functions on spindles agree with their equivalent on certain
branched covers of $\mathbb{CP}^1$. We compute the one-loop determinant on the
branched cover of $\mathbb{CP}^2$ for all flux sectors via dimensional
reduction from the $\mathcal{N}=1$ vector multiplet on a branched five-sphere
along a free $S^1$-action. This work paves the way for obtaining partition
functions on more generic symplectic toric orbifolds.


  In this paper we prove that if $G(R)=G_\pi (\Phi,R)$ $(E(R)=E_{\pi}(\Phi,
R))$ is an (elementary) Chevalley group of rank $> 1$, $R$ is a local ring
(with $\frac{1}{2}$ for the root systems ${\mathbf A}_2, {\mathbf B}_l,
{\mathbf C}_l, {\mathbf F}_4, {\mathbf G}_2$ and with $\frac{1}{3}$ for
${\mathbf G}_{2})$, then the group $G(R)$ (or $(E(R)$) is regularly
bi-interpretable with the ring~$R$. As a consequence of this theorem, we show
that the class of all Chevalley groups over local rings (with the listed
restrictions) is elementary definable, i.\,e., if for an arbitrary group~$H$ we
have $H\equiv G_\pi(\Phi, R)$, than there exists a ring $R'\equiv R$ such that
$H\cong G_\pi(\Phi,R')$.


  We obtain the analytic solution of the Friedmann equation for fully realistic
cosmologies including radiation, non-relativistic matter, a cosmological
constant $\lambda$ and arbitrary spatial curvature $\kappa$. The general
solution for the scale factor $a(\tau)$, with $\tau$ the conformal time, is an
elliptic function, meromorphic and doubly periodic in the complex $\tau$-plane,
with one period along the real $\tau$-axis, and the other along the imaginary
$\tau$-axis. The periodicity in imaginary time allows us to compute the
thermodynamic temperature and entropy of such spacetimes, just as Gibbons and
Hawking did for black holes and the de Sitter universe. The gravitational
entropy favors universes like our own which are spatially flat, homogeneous,
and isotropic, with a small positive cosmological constant.


  We explore the highly non-perturbative hot region of the QCD phase diagram
close to Tc by use of an imaginary chemical potential mu which avoids the sign
problem. The number density and the quark number susceptibility are consistent
with a critical behaviour associated with the transition line in the negative
mu^2 half-plane. We compare the analytic continuation of these results with
various phenomenological models, none of which provides a satisfactory
description of data, a failure on which we make some comments. These results
complement and extend the information obtained via the analysis of the
susceptibilities evaluated at zero mu, yielding a simple description of the
candidate strongly interacting QGP phase. As a byproduct of our analysis we
investigate the Polyakov loop and its hermitian conjugate. Our data offer a
vivid evidence of the importance of the complex nature of the functional
integral measure, which results in L (mu) ne \bar L(mu) for a real chemical
potential.


  We introduce fast millimeter-wave base station (BS) and its antenna sector
selection for user equipment based on its location. Using a conditional random
field inference model with specially designed parameters, which are robust to
change of environment, InferBeam allows the use of measurement samples on best
beam selection at a small number of locations to infer the rest dynamically.
Compared to beam-sweeping based approaches in the literature, InferBeam can
drastically reduce the setup cost for beam alignment for a new environment, and
also the latency in acquiring a new beam under intermittent blockage. We have
evaluated InferBeam using a discrete event simulation. Our results indicate
that the system can make best beam selection for 98% of locations in test
environments comprising smallsized apartment or office spaces, while sampling
fewer than 1% of locations. InferBeam is a complete protocol for best beam
inference that can be integrated into millimeter-wave standards for
accelerating the much-needed fast and economic beam alignment capability.


  We present a description of saturation in small $x$ deep inelastic scattering
from power counting in a top-down effective theory derived from QCD. A
factorization formula isolates the universal physics of the nucleus at leading
power in $x$. The onset of saturation is then understood as a breakdown in the
expansion in an emergent power counting parameter, which is defined by the
matrix element of a gauge invariant operator. We identify a new radiation mode,
which enables us to extend previous literature by distinguishing the appearance
of the saturation scale from the transition to non-linear evolution.


  The high complexity of various inverse problems poses a significant challenge
to model-based reconstruction schemes, which in such situations often reach
their limits. At the same time, we witness an exceptional success of data-based
methodologies such as deep learning. However, in the context of inverse
problems, deep neural networks mostly act as black box routines, used for
instance for a somewhat unspecified removal of artifacts in classical image
reconstructions. In this paper, we will focus on the severely ill-posed inverse
problem of limited angle computed tomography, in which entire boundary sections
are not captured in the measurements. We will develop a hybrid reconstruction
framework that fuses model-based sparse regularization with data-driven deep
learning. Our method is reliable in the sense that we only learn the part that
can provably not be handled by model-based methods, while applying the
theoretically controllable sparse regularization technique to the remaining
parts. Such a decomposition into visible and invisible segments is achieved by
means of the shearlet transform that allows to resolve wavefront sets in the
phase space. Furthermore, this split enables us to assign the clear task of
inferring unknown shearlet coefficients to the neural network and thereby
offering an interpretation of its performance in the context of limited angle
computed tomography. Our numerical experiments show that our algorithm
significantly surpasses both pure model- and more data-based reconstruction
methods.


  Traditional query planners translate SQL queries into query plans to be
executed over relational data. However, it is impossible to query other data
modalities, such as images, text, or video stored in modern data systems such
as data lakes using these query planners. In this paper, we propose
Language-Model-Driven Query Planning, a new paradigm of query planning that
uses Language Models to translate natural language queries into executable
query plans. Different from relational query planners, the resulting query
plans can contain complex operators that are able to process arbitrary
modalities. As part of this paper, we present a first GPT-4 based prototype
called CEASURA and show the general feasibility of this idea on two datasets.
Finally, we discuss several ideas to improve the query planning capabilities of
today's Language Models.


  We provide a simple algorithm for construction of Brownian paths
approximating those of a L\'evy process on a finite time interval. It requires
knowledge of the L\'evy process trajectory on a chosen regular grid and the law
of its endpoint, or the ability to simulate from that. This algorithm is based
on reordering of Brownian increments, and it can be applied in a recursive
manner. We establish an upper bound on the mean squared maximal distance
between the paths and determine a suitable mesh size in various asymptotic
regimes. The analysis proceeds by reduction to the comonotonic coupling of
increments. Applications to model risk and multilevel Monte Carlo are discussed
in detail, and numerical examples are provided.


  Generative modelling has been a topic at the forefront of machine learning
research for a substantial amount of time. With the recent success in the field
of machine learning, especially in deep learning, there has been an increased
interest in explainable and interpretable machine learning. The ability to
model distributions and provide insight in the density estimation and exact
data likelihood is an example of such a feature. Normalizing Flows (NFs), a
relatively new research field of generative modelling, has received substantial
attention since it is able to do exactly this at a relatively low cost whilst
enabling competitive generative results. While the generative abilities of NFs
are typically explored, we focus on exploring the data distribution modelling
for Out-of-Distribution (OOD) detection. Using one of the state-of-the-art NF
models, GLOW, we attempt to detect OOD examples in the ISIC dataset. We notice
that this model under performs in conform related research. To improve the OOD
detection, we explore the masking methods to inhibit co-adaptation of the
coupling layers however find no substantial improvement. Furthermore, we
utilize Wavelet Flow which uses wavelets that can filter particular frequency
components, thus simplifying the modeling process to data-driven conditional
wavelet coefficients instead of complete images. This enables us to efficiently
model larger resolution images in the hopes that it would capture more relevant
features for OOD. The paper that introduced Wavelet Flow mainly focuses on its
ability of sampling high resolution images and did not treat OOD detection. We
present the results and propose several ideas for improvement such as
controlling frequency components, using different wavelets and using other
state-of-the-art NF architectures.


  Topic modeling is a well-established technique for exploring text corpora.
Conventional topic models (e.g., LDA) represent topics as bags of words that
often require "reading the tea leaves" to interpret; additionally, they offer
users minimal control over the formatting and specificity of resulting topics.
To tackle these issues, we introduce TopicGPT, a prompt-based framework that
uses large language models (LLMs) to uncover latent topics in a text
collection. TopicGPT produces topics that align better with human
categorizations compared to competing methods: it achieves a harmonic mean
purity of 0.74 against human-annotated Wikipedia topics compared to 0.64 for
the strongest baseline. Its topics are also interpretable, dispensing with
ambiguous bags of words in favor of topics with natural language labels and
associated free-form descriptions. Moreover, the framework is highly adaptable,
allowing users to specify constraints and modify topics without the need for
model retraining. By streamlining access to high-quality and interpretable
topics, TopicGPT represents a compelling, human-centered approach to topic
modeling.


  Recently the widely used multi-view learning model, Canonical Correlation
Analysis (CCA) has been generalised to the non-linear setting via deep neural
networks. Existing deep CCA models typically first decorrelate the feature
dimensions of each view before the different views are maximally correlated in
a common latent space. This feature decorrelation is achieved by enforcing an
exact decorrelation constraint; these models are thus computationally expensive
due to the matrix inversion or SVD operations required for exact decorrelation
at each training iteration. Furthermore, the decorrelation step is often
separated from the gradient descent based optimisation, resulting in
sub-optimal solutions. We propose a novel deep CCA model Soft CCA to overcome
these problems. Specifically, exact decorrelation is replaced by soft
decorrelation via a mini-batch based Stochastic Decorrelation Loss (SDL) to be
optimised jointly with the other training objectives. Extensive experiments
show that the proposed soft CCA is more effective and efficient than existing
deep CCA models. In addition, our SDL loss can be applied to other deep models
beyond multi-view learning, and obtains superior performance compared to
existing decorrelation losses.


  Following a glitch, a neutron star interior undergoes a transfer of angular
momentum from the star's crust to the core, resulting in the spin-up of the
latter. The crust-core coupling, which determines how quickly this spin-up
proceeds, can be achieved through various physical processes, including Ekman
pumping, superfluid vortex-mediated mutual friction, and magnetic fields. While
the complexity of the problem has hindered studies of the mechanisms' combined
action, analytical work on individual processes suggests different spin-up
timescales depending on the relative strength of Coriolis, viscous, and mutual
friction forces, and the magnetic field, respectively. However, experimental
and numerical validations of these results are limited. In this paper, we focus
on viscous effects and mutual friction and conduct non-linear hydrodynamical
simulations of the spin-up problem in a two-component fluid by solving the
incompressible Hall$-$Vinen$-$Bekarevich$-$Khalatnikov (HVBK) equations in the
full sphere (i.e., including $r=0$) for the first time. We find that the
viscous (normal) component accelerates due to Ekman pumping, although the
mutual friction coupling to the superfluid component alters the spin-up
dynamics compared to the single-fluid scenario. Close to the sphere's surface,
the response of the superfluid is accurately described by the mutual friction
timescale irrespective of its coupling strength with the normal component.
However, as we move deeper into the sphere, the superfluid accelerates on
different timescales due to the slow viscous spin-up of the internal normal
fluid layers. We discuss potential implications for neutron stars and
requirements for future work to build more realistic models.


  We present a pair of open smooth $4$-manifolds that are mutually
homeomorphic. One of them admits a Riemannian metric that possesses
quasi-cylindricity, and positivity of scalar curvature and of dimension of
certain $L^2$ harmonic forms. By contrast, for the other manifold, no
Riemannian metric can simultaneously satisfy these properties. Our method uses
Seiberg-Witten theory on compact $4$-manifolds and applies $L^2$ harmonic
theory on non-compact, complete Riemannian $4$-manifolds. We introduce a new
argument to apply Gauge theory, which arises from a discovery of an asymptotic
property of the range of the differential.


  In this paper, we provide a geometric analysis of a new hysteresis model that
is based upon singular perturbations. Here hysteresis refers to a type of
regularization of piecewise smooth differential equations where the past of a
trajectory, in a small neighborhood of the discontinuity set, determines the
vector-field at present. In fact, in the limit where the neighborhood of the
discontinuity {vanishes}, hysteresis converges in an appropriate sense to
Filippov's sliding vector-field. Recently {(2022)}, however, {Bonet and Seara}
showed that hysteresis, in contrast to regularization through smoothing, leads
to chaos in the regularization of grazing bifurcations, even in two dimensions.
The hysteresis model we analyze in the present paper -- which was developed by
{Bonet et al in a paper from 2017} as an attempt to unify different
regularizations of piecewise smooth systems -- involves two singular
perturbation parameters and includes a combination of slow-fast and nonsmooth
effects. The description of this model is therefore -- from the perspective of
singular perturbation theory -- challenging, even in two dimensions. Using
blowup as our main technical tool, we prove existence of an invariant cylinder
carrying fast dynamics in the azimuthal direction and a slow drift in the axial
direction. We find that the slow drift is given by Filippov's sliding
{vector-field} to leading order. Moreover, in the case of grazing, we identify
two important parameter regimes that relate the model to smoothing (through a
saddle-node bifurcation of limit cycles) and hysteresis (through chaotic
dynamics, due to a folded saddle and a novel return mechanism).


  Class imbalance is a challenging issue in practical classification problems
for deep learning models as well as traditional models. Traditionally
successful countermeasures such as synthetic over-sampling have had limited
success with complex, structured data handled by deep learning models. In this
paper, we propose Deep Over-sampling (DOS), a framework for extending the
synthetic over-sampling method to exploit the deep feature space acquired by a
convolutional neural network (CNN). Its key feature is an explicit, supervised
representation learning, for which the training data presents each raw input
sample with a synthetic embedding target in the deep feature space, which is
sampled from the linear subspace of in-class neighbors. We implement an
iterative process of training the CNN and updating the targets, which induces
smaller in-class variance among the embeddings, to increase the discriminative
power of the deep representation. We present an empirical study using public
benchmarks, which shows that the DOS framework not only counteracts class
imbalance better than the existing method, but also improves the performance of
the CNN in the standard, balanced settings.


  Atomtronics is an emerging field that aims to manipulate ultracold atom
moving in matter wave circuits for both fundamental studies in quantum science
and technological applications. In this colloquium, we review recent progress
in matter-wave circuitry and atomtronics-based quantum technology. After a
short introduction to the basic physical principles and the key experimental
techniques needed to realize atomtronic systems, we describe the physics of
matter-waves in simple circuits such as ring traps and two-terminal systems.
The main experimental observations and outstanding questions are discussed. We
also present possible applications to a broad range of quantum technologies,
from quantum sensing with atom interferometry to future quantum simulation and
quantum computation architectures.


  We derive symmetry-based conditions for tight-binding Hamiltonians with
flatbands to have compact localized eigenstates occupying a single unit cell.
The conditions are based on unitary operators commuting with the Hamiltonian
and associated with local symmetries that guarantee compact localized states
and a flatband. We illustrate the conditions for compact localized states and
flatbands with simple Hamiltonians with given symmetries. We also apply these
results to general cases such as the Hamiltonian with long-range hoppings and
higher-dimensional Hamiltonian.


  Background: Nuclear pasta phases, present in the inner crust of neutron
stars, are associated with nucleonic matter at sub-saturation densities
arranged in regular shapes. Those complex phases, residing in a layer which is
approximately 100 m thick, impact many features of neutron stars. Theoretical
quantum-mechanical simulations of nuclear pasta are usually carried out in
finite 3D boxes assuming periodic boundary conditions (PBC). The resulting
solutions are affected by spurious finite-size effects.
  Purpose: In order to remove spurious finite-size effects, it is convenient to
employ twist-averaged boundary conditions (TABC) used in condensed matter,
nuclear matter, and lattice QCD applications. In this work, we study the
effectiveness of TABC in the context of pasta phases simulations within nuclear
density functional theory.
  Methods: We perform Skyrme-Hartree-Fock calculations in three dimensions by
implementing Bloch boundary conditions. The TABC averages are obtained by means
of Gauss-Legendre integration over twist angles.
  Results: We benchmark the TABC for a free nucleonic gas and apply it to
simple cases such as the rod and slab phases, as well as to more elaborate
P-surface and gyroidal phases.
  Conclusions: We demonstrate that by applying TABC reliable results can be
obtained from calculations performed in relatively small volumes. By studying
various contributions to the total energy, we gain insights into pasta phases
in mid-density range.