  In a protocluster USS1558-003 at z=2.53, galaxies in the dense cores show
systematically elevated star-forming activities than those in less dense
regions. To understand its origin, we look into the gas properties of the
galaxies in the dense cores by conducting deep 1.1mm observations with Atacama
Large Millimeter/submillimeter Array (ALMA). We detect interstellar dust
continuum emissions from 12 member galaxies and estimate their molecular gas
masses. Comparing these gas masses with our previous measurements from CO(3-2)
line, we infer that the latter might be overestimated. We find that the gas to
stellar mass ratios of the galaxies in the dense cores tend to be higher (at M*
~ 10^{10} M_sun) where we see the enhanced star-forming activities), suggesting
that such large gas masses can sustain their high star-forming activities.
However, if we compare the gas properties of these protocluster galaxies with
the gas scaling relations constructed for field galaxies at similar cosmic
epoch, we find no significant environmental difference at the same stellar mass
and star formation rate. Although both gas mass ratios and star-forming
activities are enhanced in the majority of member galaxies, they appear to
follow the same scaling relation as field galaxies. Our results are consistent
with the scenario that the cold gas is efficiently supplied to protocluster
cores and to galaxies therein along surrounding filamentary structures, which
leads to the high gas mass fractions and thus the elevated star-formation
activities, but without changing the star formation law.


  In this work, we study the numerical approximation of local fluctuations of
certain classes of parabolic stochastic partial differential equations (SPDEs).
Our focus is on effects for small spatially-correlated noise on a time scale
before large deviation effects have occurred. In particular, we are interested
in the local directions of the noise described by a covariance operator. We
introduce a new strategy and prove a Combined ERror EStimate (CERES) for the
five main errors: the spatial discretization error, the local linearization
error, the noise truncation error, the local relaxation error to steady state,
and the approximation error via an iterative low-rank matrix algorithm. In
summary, we obtain one CERES describing, apart from modelling of the original
equations and standard round-off, all sources of error for a local fluctuation
analysis of an SPDE in one estimate. To prove our results, we rely on a
combination of methods from optimal Galerkin approximation of SPDEs, covariance
moment estimates, analytical techniques for Lyapunov equations, iterative
numerical schemes for low-rank solution of Lyapunov equations, and working with
related spectral norms for different classes of operators.


  Some afterglow light curves of gamma-ray bursts (GRBs) exhibit very complex
temporal and spectral features, such as a sudden intensity jump about one hour
after the prompt emission in the optical band. We assume that this feature is
due to the late collision of two relativistic shells and investigate the
corresponding high-energy neutrino emission within a multi-messenger framework,
while contrasting our findings with the ones from the classic afterglow model.
For a constant density circumburst medium, the total number of emitted
neutrinos can increase by about an order of magnitude when an optical jump
occurs with respect to the self-similar afterglow scenario. By exploring the
detection prospects with the IceCube Neutrino Observatory and future radio
arrays such as IceCube-Gen2 radio, RNO-G and GRAND200k, as well as the POEMMA
spacecraft, we conclude that the detection of neutrinos with IceCube-Gen2 radio
could enable us to constrain the fraction of GRB afterglows with a jump as well
as the properties of the circumburst medium. We also investigate the neutrino
signal expected for the afterglows of GRB 100621A and a GRB 130427A-like burst
with an optical jump. The detection of neutrinos from GRB afterglows could be
crucial to explore the yet-to-be unveiled mechanism powering the optical jumps.


  We have observed 26 interspecies Feshbach resonances at fields up to 2050 G
in ultracold $^6$Li+$^{23}$Na mixtures for different spin-state combinations.
Applying the asymptotic bound-state model to assign the resonances, we have
found that most resonances have d-wave character. This analysis serves as
guidance for a coupled-channel calculation, which uses modified interaction
potentials to describe the positions of the Feshbach resonances well within the
experimental uncertainty and to calculate their widths. The scattering length
derived from the improved interaction potentials is experimentally confirmed
and deviates from previously reported values in sign and magnitude. We give
prospects for $^7$Li+$^{23}$Na and predict broad Feshbach resonances suitable
for tuning.


  Generalization of neural networks is crucial for deploying them safely in the
real world. Common training strategies to improve generalization involve the
use of data augmentations, ensembling and model averaging. In this work, we
first establish a surprisingly simple but strong benchmark for generalization
which utilizes diverse augmentations within a training minibatch, and show that
this can learn a more balanced distribution of features. Further, we propose
Diversify-Aggregate-Repeat Training (DART) strategy that first trains diverse
models using different augmentations (or domains) to explore the loss basin,
and further Aggregates their weights to combine their expertise and obtain
improved generalization. We find that Repeating the step of Aggregation
throughout training improves the overall optimization trajectory and also
ensures that the individual models have a sufficiently low loss barrier to
obtain improved generalization on combining them. We shed light on our approach
by casting it in the framework proposed by Shen et al. and theoretically show
that it indeed generalizes better. In addition to improvements in In- Domain
generalization, we demonstrate SOTA performance on the Domain Generalization
benchmarks in the popular DomainBed framework as well. Our method is generic
and can easily be integrated with several base training algorithms to achieve
performance gains.


  Robert Harry Kraichnan {(1928-2008)} was one of the leaders in the theory of
turbulence for a span of about forty years (mid-fifties to mid-nineties). Among
his many contributions, he is perhaps best known for his work on the inverse
energy cascade (i.e. from small to large scales) for forced two-dimensional
turbulence. This is a review of Kraichnan's main scientific contributions.


  We derive multiscale statistics for deconvolution in order to detect
qualitative features of the unknown density. An important example covered
within this framework is to test for local monotonicity on all scales
simultaneously. We investigate the moderately ill-posed setting, where the
Fourier transform of the error density in the deconvolution model is of
polynomial decay. For multiscale testing, we consider a calibration, motivated
by the modulus of continuity of Brownian motion. We investigate the performance
of our results from both the theoretical and simulation based point of view. A
major consequence of our work is that the detection of qualitative features of
a density in a deconvolution problem is a doable task although the minimax
rates for pointwise estimation are very slow.


  In this paper, we study the real analyticity of the scattering operator for
the Hartree equation $ i\partial_tu=-\Delta u+u(V*|u|^2)$. To this end, we
exploit interior and exterior cut-off in time and space, and combining with the
compactness argument to overcome difficulties which arise from absence of good
properties for the nonlinear Klein-Gordon equation, such as the finite speed of
propagation and ideal time decay estimate. Additionally, the method in this
paper allows us to simplify the proof of analyticity of the scattering operator
for the nonlinear Klein-Gordon equation with cubic nonlinearity in Kumlin.


  The supermassive black hole in the center of our Galaxy, Sgr A*, is unique
because the angular size of the black hole is the largest in the sky thus
providing detailed boundary conditions on, and much less freedom for, accretion
flow models. In this paper I review advection-dominated accretion flow (ADAF;
another name is radiatively inefficient accretion flow) models for Sgr A*. This
includes the developments and dynamics of ADAFs, and how to explain
observational results including the multi-waveband spectrum, radio
polarization, IR and X-ray flares, and the size measurements at radio
wavebands.


  We consider the quintic one dimensional nonlinear Schr\"odinger equation with
forcing and both linear and nonlinear dissipation. Quintic nonlinearity results
in multiple collapse events randomly distributed in space and time forming
forced turbulence. Without dissipation each of these collapses produces finite
time singularity but dissipative terms prevents actual formation of
singularity. In statistical steady state of the developed turbulence the
spatial correlation function has a universal form with the correlation length
determined by the modulational instability scale. The amplitude fluctuations at
that scale are nearly-Gaussian while the large amplitude tail of probability
density function (PDF) is strongly non-Gaussian with power-like behavior. The
small amplitude nearly-Gaussian fluctuations seed formation of large collapse
events. The universal spatio-temporal form of these events together with the
PDF for their maximum amplitudes define the power-like tail of PDF for large
amplitude fluctuations, i.e., the intermittency of strong turbulence.


  In this article, the Galois groupoid of the first Painlev\'{e} equation is
computed. This computation use E. Cartan's classification of structural
equations of pseudogroups acting on $C^2$ and the degeneration of the first
Painlev\'{e} equation on an elliptic equation ($y'' = 6y^2$). A definition of
reducibility for singular holomorphic foliations is proposed. A
characterisation of reducible foliations on their Galois groupoid is given and
applied to prove the foliation irreducibility of the first Painlev\'{e}
equation.


  As digital technologies become more pervasive in society and the economy,
cybersecurity incidents become more frequent and impactful. According to the
NIS and NIS2 Directives, EU Member States and their Operators of Essential
Services must establish a minimum baseline set of cybersecurity capabilities
and engage in cross-border coordination and cooperation. However, this is only
a small step towards European cyber resilience. In this landscape,
preparedness, shared situational awareness, and coordinated incident response
are essential for effective cyber crisis management and resilience. Motivated
by the above, this paper presents PHOENI2X, an EU-funded project aiming to
design, develop, and deliver a Cyber Resilience Framework providing
Artificial-Intelligence-assisted orchestration, automation and response
capabilities for business continuity and recovery, incident response, and
information exchange, tailored to the needs of Operators of Essential Services
and the EU Member State authorities entrusted with cybersecurity.


  We introduce a particle model, that we call the $\textit{golf model}$.
Initially, on a graph $G$, balls and holes are placed at random on some
distinct vertices. Balls then move one by one, doing a random walk on $G$,
starting from their initial vertex and stopping at the first empty hole they
encounter, filling it. On finite graphs, under reasonable assumptions (if there
are more holes than balls, and if the Markov chain characterizing the random
walks is irreducible) a final configuration is reached almost surely. In the
paper, we are mainly interested in ${\bf H}^1$, the set of remaining holes. We
give the distribution of ${\bf H}^1$ on $\mathbb{Z}/n\mathbb{Z}$, and describe
a phase transition on the largest distance between two consecutive holes when
the number of remaining holes has order $\sqrt{n}$. We show that the model on
$\mathbb{Z}$ is well-defined when every vertex contains either a ball with
probability $d_{\sf b}$, a hole with probability $d_{\sf h}$, or nothing,
independently from the other vertices, as long as $d_{\sf b} \leq d_{\sf h}$,
and we describe the law of ${\bf H}^1$ in this case.


  The equilibrium oxygen isotope fractionation factor between calcite and water
(18{\alpha}calcite/H2O) is an important quantity in stable isotope geochemistry
and allows in principle to infer temperature variations from carbonate
{\delta}18O if carbonate formation occurred in thermodynamic equilibrium. For
this reason, many studies intended to determine the value of the oxygen isotope
fractionation factor between calcite and water (18{\alpha}calcite/H2O) for a
wide range of temperatures using modern cave calcite and the corresponding cave
drip water or ancient speleothem carbonate and fluid inclusion samples.
However, the picture that emerges from all of these studies indicates that
speleothem calcite is not formed in thermodynamic equilibrium but under kinetic
conditions, provoking a large variability of determined 18{\alpha}calcite/H2O
values. Here we present a conceptual framework that can explain the variability
of 18{\alpha}calcite/H2O values obtained by cave studies. Prior calcite
precipitation (PCP) is calcite precipitation before cave drip water is dripping
from the cave ceiling and impinges on the surface of a stalagmite or watch
glass. Prior to the karst water dripping from the cave ceiling, PCP can occur
in the karst above the cave as well as on the cave ceiling, the cave walls and
on the surface of stalactites. We argue that PCP leads to increasing the
{\delta}18O value of the dissolved HCO3- ({\delta}18OHCO3-), resulting in an
oxygen isotope disequilibrium of the {\delta}18OHCO3- values with respect to
the {\delta}18O value of water ({\delta}18OH2O). The oxygen isotope
disequilibrium between HCO3- and H2O is re-equilibrated by oxygen isotope
exchange between H2O and HCO3. Depending on the temperature, the
re-equilibration time varies from hours to days and is usually much longer than
the residence time of the drip water on stalactites, but much shorter than the
time ...


  We describe a procedure for determination of freeze-out parameters of
heavy-ion collisions through direct comparisons between experimentally measured
higher order cumulants of charge fluctuations and first principle (lattice) QCD
calculations.


  I report B physics results from the CLEO collaboration, highlighting
measurements of the Cabibbo-Kobayashi-Maskawa matrix elements |Vcb| and |Vub|.
I report a recent measurement of |Vub| through study of the q^2 dependence of B
-> pi l nu and B -> rho l nu. I also describe new measurements of the inclusive
semileptonic branching fraction BF(B -> X e nu) and of moments of the hadronic
invariant mass spectrum in B -> X l nu, with impact on |Vcb|.


  Both structural glasses and disordered crystals are known to exhibit
anomalous thermal, vibrational, and acoustic properties at low temperatures or
low energies, what is still a matter of lively debate. To shed light on this
issue, we studied the halomethane family C-Br_n-Cl_4-n (n = 0,1,2) at low
temperature where, despite being perfectly translationally ordered stable
monoclinic crystals, glassy dynamical features had been reported from
experiments and molecular dynamics simulations. For n = 1,2 dynamic disorder
originates by the random occupancy of the same lattice sites by either Cl or Br
atoms, but not for the ideal reference case of CCl4. Measurements of the
low-temperature specific heat (Cp) for all these materials are here reported,
which provide evidence of the presence of a broad peak in Debye-reduced Cp/T^3
and in the reduced density of states g(w)/w^2 determined by means of neutron
spectroscopy, as well as a linear term in Cp usually ascribed in glasses to
two-level systems in addition to the cubic term expected for a fully ordered
crystal. Being CCl4 a fully ordered crystal, we also performed density
functional theory (DFT) calculations, which provide unprecedented detailed
information about the microscopic nature of vibrations responsible for that
broad peak, much alike the boson peak of glasses, finding it to essentially
arise from a piling up (at around 3 - 4 meV) of low-energy optical modes
together with acoustic modes near the Brillouin-zone limits.


  Machine-learned potentials (MLPs) have exhibited remarkable accuracy, yet the
lack of general-purpose MLPs for a broad spectrum of elements and their alloys
limits their applicability. Here, we present a feasible approach for
constructing a unified general-purpose MLP for numerous elements, demonstrated
through a model (UNEP-v1) for 16 elemental metals and their alloys. To achieve
a complete representation of the chemical space, we show, via principal
component analysis and diverse test datasets, that employing one-component and
two-component systems suffices. Our unified UNEP-v1 model exhibits superior
performance across various physical properties compared to a widely used
embedded-atom method potential, while maintaining remarkable efficiency. We
demonstrate our approach's effectiveness through reproducing experimentally
observed chemical order and stable phases, and large-scale simulations of
plasticity and primary radiation damage in MoTaVW alloys. This work represents
a significant leap towards a unified general-purpose MLP encompassing the
periodic table, with profound implications for materials science.


  We explore proximity-induced magnetocaloric effect (MCE) on transition metal
dichalcogenides, focusing on a two-dimensional (2D) MoTe$_2$ monolayer
deposited on a ferromagnetic semiconductor EuO substrate connected to a heat
source. We model this heterostructure using a tight-binding model,
incorporating exchange and Rashba fields induced by proximity to EuO, and
including temperature through Fermi statistics. The MCE is induced on the 2D
MoTe$_2$ layer due to the EuO substrate, revealing large spin-polarized entropy
changes for energies out of the band gap of the MoTe$_2$-EuO system. By gating
the chemical potential, the MCE can be tuned to produce heating for spin up and
cooling for spin down across the $K$ and $K'$ valley splitting in the valence
band, whereas either heats or cools for both spins in the conduction band. The
Rashba field enhances the MCE in the valence zone while decreasing it in the
conduction bands. The exchange field-induced MCE could be useful to produce
tunable spin-polarized thermal responses in magnetic proximitized 2D materials.


  We investigate several key questions of plasma heating in open-field regions
of the corona that connect to the solar wind. We present results for a model of
Alfven-wave-driven turbulence for three typical open magnetic field structures:
a polar coronal hole, an open flux tube neighboring an equatorial streamer, and
an open flux tube near a strong-field active region. We compare time-steady,
one-dimensional turbulent heating models (Cranmer et al., 2007) against fully
time-dependent three-dimensional reduced-magnetohydrodynamics modeling of BRAID
(van Ballegooijen et al., 2011). We find that the time-steady results agree
well with time-averaged results from BRAID. The time-dependence allows us to
investigate the variability of the magnetic fluctuations and of the heating in
the corona. The high-frequency tail of the power spectrum of fluctuations forms
a power law whose exponent varies with height, and we discuss the possible
physical explanation for this behavior. The variability in the heating rate is
bursty and nanoflare-like in nature, and we analyze the amount of energy lost
via dissipative heating in transient events throughout the simulation. The
average energy in these events is 10^21.91 erg, within the "picoflare" range,
and many events reach classical "nanoflare" energies. We also estimated the
multithermal distribution of temperatures that would result from the
heating-rate variability, and found good agreement with observed widths of
coronal differential emission measure (DEM) distributions. The results of the
modeling presented in this paper provide compelling evidence that turbulent
heating in the solar atmosphere by Alfven waves accelerates the solar wind in
open flux tubes.


  The current cosmological dark sector (dark matter plus dark energy) is
challenging our comprehension about the physical processes taking place in the
Universe. Recently, some authors tried to falsify the basic underlying
assumptions of such dark matter-dark energy paradigm. In this Letter, we show
that oversimplifications of the measurement process may produce false positives
to any consistency test based on the globally homogeneous and isotropic LCDM
model and its expansion history based on distance measurements. In particular,
when local inhomogeneity effects due to clumped matter or voids are taken into
account, an apparent violation of the basic assumptions ("Copernican
Principle") seems to be present. Conversely, the amplitude of the deviations
also probes the degree of reliability underlying the phenomenological
Dyer-Roeder procedure by confronting its predictions with the accuracy of the
weak lensing approach. Finally, a new method is devised to reconstruct the
effects of the inhomogeneities in a LCDM model, and some suggestions of how to
distinguish between clumpiness (or void) effects from different cosmologies are
discussed.


  In this paper, a novel multi-view methodology for graph-based neural networks
is proposed. A systematic and methodological adaptation of the key concepts of
classical deep learning methods such as convolution, pooling and multi-view
architectures is developed for the context of non-Euclidean manifolds. The aim
of the proposed work is to present a novel multi-view graph convolution layer,
as well as a new view pooling layer making use of: a) a new hybrid Laplacian
that is adjusted based on feature distance metric learning, b) multiple
trainable representations of a feature matrix of a graph, using trainable
distance matrices, adapting the notion of views to graphs and c) a multi-view
graph aggregation scheme called graph view pooling, in order to synthesise
information from the multiple generated views. The aforementioned layers are
used in an end-to-end graph neural network architecture for graph
classification and show competitive results to other state-of-the-art methods.


  In general, nighttime thermospheric 557.7 nm emission over mid-latitudes is
predominantly masked by significantly larger mesospheric component, and hence,
F-region plasma structures are rarely observed in this emission. This paper
reports the first rare simultaneous detection of F-region plasma depleted
structure in O($^1$D) 630.0 nm and O($^1$S) 557.7 nm airglow images from Hanle,
India, a mid-latitude station (32.7{\deg}N, 78.9{\deg}E; Mlat. ~24.1{\deg}N) on
a geomagnetically quiet night (Ap=3) of 26 June 2021. This indicates
significant enhancement of thermospheric 557.7 nm emission. Interestingly,
thermospheric 557.7 nm emission was not significant on the following
geomagnetically quiet night as MSTID bands were only observed in 630.0 nm
images. We show that enhanced dissociative recombination caused by descent of
F-layer peak over the observation region coupled with the significant increase
of the electron density at thermospheric 557.7 nm emission altitude enabled the
detection of the plasma depleted structure on 26 June 2021.


  In this paper we provide a full characterization of cyclic composition
operators defined on the d-dimensional Fock space $\mathcal F(\mathbb C^d)$ in
terms of their symbol. Also, we study the supercyclicity and convex-cyclicity
of this type of operators. We end this work by computing the approximation
numbers of compact composition operators defined on $\mathcal F(\mathbb C^d)$.


  We have developed improved spectral models of relativistic reflection in the
lamppost and disc-corona geometries. The models calculate photon transfer in
the Kerr metric and give the observed photon-energy spectra produced by either
thermal Comptonization or an e-folded power law incident on a cold ionized
disc. Radiative processes in the primary X-ray source and in the disc are
described with the currently most precise available models. Our implementation
of the lamppost geometry takes into account the presence of primary sources on
both sides of the disc, which is important when the disc is truncated. We
thoroughly discuss the differences between our models and the previous ones.


  Hyperparameter optimization is the process of identifying the appropriate
hyperparameter configuration of a given machine learning model with regard to a
given learning task. For smaller data sets, an exhaustive search is possible;
However, when the data size and model complexity increase, the number of
configuration evaluations becomes the main computational bottleneck. A
promising paradigm for tackling this type of problem is surrogate-based
optimization. The main idea underlying this paradigm considers an incrementally
updated model of the relation between the hyperparameter space and the output
(target) space; the data for this model are obtained by evaluating the main
learning engine, which is, for example, a factorization machine-based model. By
learning to approximate the hyperparameter-target relation, the surrogate
(machine learning) model can be used to score large amounts of hyperparameter
configurations, exploring parts of the configuration space beyond the reach of
direct machine learning engine evaluation. Commonly, a surrogate is selected
prior to optimization initialization and remains the same during the search. We
investigated whether dynamic switching of surrogates during the optimization
itself is a sensible idea of practical relevance for selecting the most
appropriate factorization machine-based models for large-scale online
recommendation. We conducted benchmarks on data sets containing hundreds of
millions of instances against established baselines such as Random Forest- and
Gaussian process-based surrogates. The results indicate that surrogate
switching can offer good performance while considering fewer learning engine
evaluations.


  Large Language Models (LLMs) demonstrate remarkable potential across various
domains; however, they exhibit a significant performance gap in Information
Extraction (IE). Note that high-quality instruction data is the vital key for
enhancing the specific capabilities of LLMs, while current IE datasets tend to
be small in scale, fragmented, and lack standardized schema. To this end, we
introduce IEPile, a comprehensive bilingual (English and Chinese) IE
instruction corpus, which contains approximately 0.32B tokens. We construct
IEPile by collecting and cleaning 33 existing IE datasets, and introduce
schema-based instruction generation to unearth a large-scale corpus.
Experimentally, IEPile enhance the performance of LLMs for IE, with notable
improvements in zero-shot generalization. We open-source the resource and
pre-trained models, hoping to provide valuable support to the NLP community.


  Let $X$ be a compact Riemann surface, $\Sigma$ a finite set of points and $M
= X\setminus \Sigma$. We study the $L^2$ cohomology of a polarized complex
variation of Hodge structure on a Galois covering of the Riemann surface of
finite type $M$. In this article we treat the case when the covering comes from
a branched covering of $X$, and where $M$ is endowed with a metric asymptotic
to a Poincar\'e metric. We prove that after tensorisation with the algebra of
affiliated operators, the $L^2$ cohomology admits a pure Hodge structure.


  Business surveys are not generally considered to be longitudinal by design.
However, the largest businesses are almost always included in each wave of
recurrent surveys because they are essential for producing good estimates; and
short-period business surveys frequently make use of rotating panel designs to
improve the estimates of change by inducing sample overlaps between different
periods. These design features mean that business surveys share some
methodological challenges with longitudinal surveys. We review the longitudinal
methods and approaches which can be used to improve the design and operation of
business surveys, giving examples of their use. We also look in the other
direction, considering the aspects of longitudinal analysis which have the
potential to improve the accuracy, relevance and interpretation of business
survey outputs.


  We investigate the problem of reconfigurable intelligent surface (RIS)-aided
near-field localization of a user equipment (UE) served by a base station (BS)
under phase-dependent amplitude variations at each RIS element. Through a
misspecified Cram\'{e}r-Rao bound (MCRB) analysis and a resulting lower bound
(LB) on localization, we show that when the UE is unaware of amplitude
variations (i.e., assumes unit-amplitude responses), severe performance
penalties can arise, especially at high signal-to-noise ratios (SNRs).
Leveraging Jacobi-Anger expansion to decouple range-azimuth-elevation
dimensions, we develop a low-complexity approximated mismatched maximum
likelihood (AMML) estimator, which is asymptotically tight to the LB. To
mitigate performance loss due to model mismatch, we propose to jointly estimate
the UE location and the RIS amplitude model parameters. The corresponding
Cram\'{e}r-Rao bound (CRB) is derived, as well as an iterative refinement
algorithm, which employs the AMML method as a subroutine and alternatingly
updates individual parameters of the RIS amplitude model. Simulation results
indicate fast convergence and performance close to the CRB. The proposed method
can successfully recover the performance loss of the AMML under a wide range of
RIS parameters and effectively calibrate the RIS amplitude model online with
the help of a user that has an a-priori unknown location.


  We consider the bifurcating Markov chain model introduced by Guyon to detect
cellular aging from cell lineage. To take into account the possibility for a
cell to die, we use an underlying Galton-Watson process to describe the
evolution of the cell lineage. We give in this more general framework a weak
law of large number, an invariance principle and thus fluctuation results for
the average over one generation or up to one generation. We also prove the
fluctuations over each generation are independent. Then we present the natural
modifications of the tests given by Guyon in cellular aging detection within
the particular case of the auto-regressive model.


  We prove a modification as well as an improvement of a result of K. Ford, D.
R. Heath-Brown and S. Konyagin concerning prime avoidance of square-free
numbers and perfect powers of prime numbers.


  We employ projection operator techniques in Hilbert space to derive a
continuous sequence of effective Hamiltonians which describe the dynamics on
successively larger length scales. We show for the case of \phi^4 theory that
the masses and couplings in these effective Hamiltonians vary in accordance
with 1-loop renormalization group equations. This is evidence for an intimate
connection between Wilson's renormalization and the venerable Bloch-Feshbach
formalism.


  We study the dynamics of two gray solitons in a Bose-Einstein condensate
confined by a toroidal trap with a tight confinement in the radial direction.
Gross-Pitaevskii simulations show that solitons can be long living objects
passing through many collisional processes. We have observed quite different
behaviors depending on the soliton velocity. Very slow solitons, obtained by
perturbing the stationary solitonic profile, move with a constant angular
velocity until they collide elastically and move in the opposite direction
without showing any sign of lowering their energy. In this case the density
notches are always well separated and the fronts are sharp and straight. Faster
solitons present vortices around the notches, which play a central role during
the collisions. We have found that in these processes the solitons lose energy,
as the outgoing velocity turns out to be larger than the incoming one. To study
the dynamics, we model the gray soliton state with a free parameter that is
related to the soliton velocity. We further analyze the energy, soliton
velocity and turning points in terms of such a free parameter, finding that the
main features are in accordance with the infinite one-dimensional system.


  The Z Cam-type dwarf nova AT Cnc displays a classical nova (CN) shell,
demonstrating that mass transfer in cataclysmic binaries decreases
substantially after a CN eruption. The hibernation scenario of cataclysmic
binaries predicts such a decrease, on a timescale of a few centuries. In order
to measure the time since AT Cnc's last CN eruption, we have measured the
radial velocities of a hundred clumps in its ejecta with SITELLE, CFHT's
recently commissioned imaging Fourier transform spectrometer. These range from
-455 to +490 km/s. Coupled with the known distance to AT Cnc of 460 pc (Shara
2012), the size of AT Cnc's shell, and a simple model of nova ejecta
deceleration, we determine that the last CN eruption of this system occurred
$330_{-90}^{+135}$ years ago. This is the most rapid transition from a high
mass transfer rate, novalike variable to a low mass transfer rate, dwarf nova
yet measured, and in accord with the hibernation scenario of cataclysmic
binaries. We conclude by noting the similarity in deduced outburst date (within
a century of 1686 CE) of AT Cnc with a "guest star" reported in the
constellation Cancer by Korean observers in 1645 CE.


  In this work, we consider the hydrogen atom confined inside a penetrable
spherical potential. The confining potential is described by an
inverted-Gaussian function of depth $\omega_0$, width $\sigma$ and centered at
$r_c$. In particular, this model has been used to study atoms inside a $C_{60}$
fullerene. For the lowest values of angular momentum $l=0,1,2$, the spectra of
the system as a function of the parameters ($\omega_0,\sigma,r_c$) is
calculated using three distinct numerical methods: (i) Lagrange-mesh method,
(ii) fourth order finite differences and (iii) the finite element method.
Concrete results with not less than 11 significant figures are displayed. Also,
within the Lagrange-mesh approach the corresponding eigenfunctions and the
expectation value of $r$ for the first six states of $s, p$ and $d$ symmetries,
respectively, are presented. Our accurate energies are taken as initial data to
train an artificial neural network as well. It generates an efficient numerical
interpolation. The present numerical results improve and extend those reported
in the literature.


  A closed form formula (generating function) for the Euler characteristic of
the configuration space of $\scriptstyle n$ particles in a simplicial complex
is given.


  This submission has been removed by arXiv administrators because it is a
duplicate of astro-ph/0603735.


  In this paper, we prove a normal criteria for family of meromorphic
functions. As an application of that result, we establish a uniqueness theorem
for entire function concerning a conjecture of R. Bruck. The above uniqueness
theorem is an improvement of a problem studied by L. Z. Yang et. al [14].
However, our method differs the method of L. Z. Yang et. al [14]. We mainly use
normal family theory and combine it with Nevanlinna theory instead of using
only the Nevanlinna theory as in [14].


  We consider an active Ising model in which spins both diffuse and align on
lattice in one and two dimensions. The diffusion is biased so that plus or
minus spins hop preferably to the left or to the right, which generates a
flocking transition at low temperature/high density. We construct a
coarse-grained description of the model that predicts this transition to be a
first-order liquid-gas transition in the temperature-density ensemble, with a
critical density sent to infinity. In this first-order phase transition, the
magnetization is proportional to the liquid fraction and thus varies
continuously. Using microscopic simulations, we show that this theoretical
prediction holds in 2d whereas the fluctuations alter the transition in 1d,
preventing for instance any spontaneous symmetry breaking.


  We calculate the dilepton emissions as the decay product of the charm and
bottom quarks produced in heavy-ion collisions at RHIC energy. We take into
account the next-to-leading-order radiative corrections in perturbative QCD to
the heavy quark production from both an initial hard parton-parton scattering
and an ideal quark-gluon plasma. We find that the thermal charm decay dominates
the dilepton production in the low dilepton mass region ($<2$ GeV), while the
heavy quark production from the initial scattering takes over the intermediate
and high mass regions ($> 2$ GeV). Our result also indicates the importance of
the bottom quark in the high mass region ($>4 $ GeV ) due to its large mass and
cascade decay. If the initial scattering produced charm suffers a significant
energy loss due to the secondary interaction, the bottom decay constitutes the
major background for the thermal dileptons.


  In this paper, we introduce a novel approach to user-centric association and
feedback bit allocation for the downlink of a cell-free massive MIMO (CF-mMIMO)
system, operating under limited feedback constraints. In CF-mMIMO systems
employing frequency division duplexing, each access point (AP) relies on
channel information provided by its associated user equipments (UEs) for
beamforming design. Since the uplink control channel is typically shared among
UEs, we take account of each AP's total feedback budget, which is distributed
among its associated UEs. By employing the Saleh-Valenzuela multi-resolvable
path channel model with different average path gains, we first identify
necessary feedback information for each UE, along with an appropriate codebook
structure. This structure facilitates adaptive quantization of multiple paths
based on their dominance. We then formulate a joint optimization problem
addressing user-centric UE-AP association and feedback bit allocation. To
address this challenge, we analyze the impact of feedback bit allocation and
derive our proposed scheme from the solution of an alternative optimization
problem aimed at devising long-term policies, explicitly considering the
effects of feedback bit allocation. Numerical results show that our proposed
scheme effectively enhances the performance of conventional approaches in
CF-mMIMO systems.


  The properties of net quark number fluctuations in the vicinity of the QCD
chiral phase transition are discussed in terms of an effective chiral model in
the mean-field approximation. We focus on the ratio of the fourth- to second-
order cumulants (kurtosis) and the compressibility of the system and discuss
their dependence on the pion mass. It is shown that near the chiral phase
transition, both observables are sensitive to the value of $m_\pi$. For
physical $m_\pi$, the kurtosis exhibits a peak whereas the inverse
compressibility shows a dip at the pseudocritical temperature. These structures
disappear for large $m_\pi$. Our results, obtained in an effective model with
two flavors, are qualitatively consistent with recent results of 2+1 flavor
lattice gauge theory. We also discuss the high- and low-temperature properties
of these observables and the role of the coupling of the quark degrees of
freedom to the Polyakov loop.


  We review recent developments in the Casimir effect which arises in
quantization volumes restricted by material boundaries and in spaces with
non-Euclidean topology. The starting point of our discussion is the novel exact
solution for the electromagnetic Casimir force in the configuration of a
cylinder above a plate. The related work for the scalar Casimir effect in
sphere-plate configuration is also considered, and the application region of
the proximity force theorem is discussed. Next we consider new experiments on
the measurement of the Casimir force between metals and between metal and
semiconductor. The complicated problem connected with the theory of the thermal
Casimir force between real metals is analyzed in detail. The present situation
regarding different theoretical approaches to the resolution of this problem is
summarized. We conclude with new constraints on non-Newtonian gravity obtained
using the results of latest Casimir force measurements and compare them with
constraints following from the most recent gravitational experiments.


  Renormalization in quantum statistics in the presence of a charge associated
to a spontaneously broken symmetry is discussed for the scalar field model. In
contrast to the case of non-broken symmetry, the renormalization mass
counterterm depends on the chemical potential. We argue that this is connected
to the ill-defined character of the charge operator.


  Human-swarm interaction has recently gained attention due to its plethora of
new applications in disaster relief, surveillance, rescue, and exploration.
However, if the task difficulty increases, the performance of the human
operator decreases, thereby decreasing the overall efficacy of the human-swarm
team. Thus, it is critical to identify the task difficulty and adaptively
allocate the task to the human operator to maintain optimal performance. In
this direction, we study the classification of task difficulty in a human-swarm
interaction experiment performing a target search mission. The human may
control platoons of unmanned aerial vehicles (UAVs) and unmanned ground
vehicles (UGVs) to search a partially observable environment during the target
search mission. The mission complexity is increased by introducing adversarial
teams that humans may only see when the environment is explored. While the
human is completing the mission, their brain activity is recorded using an
electroencephalogram (EEG), which is used to classify the task difficulty. We
have used two different approaches for classification: A feature-based approach
using coherence values as input and a deep learning-based approach using raw
EEG as input. Both approaches can classify the task difficulty well above the
chance. The results showed the importance of the occipital lobe (O1 and O2)
coherence feature with the other brain regions. Moreover, we also study
individual differences (expert vs. novice) in the classification results. The
analysis revealed that the temporal lobe in experts (T4 and T3) is predominant
for task difficulty classification compared with novices.


  The notion of Higgs-de Rham flows was introduced by Lan-Sheng-Zuo, as an
analogue of Yang-Mills-Higgs flows in the complex nonabelian Hodge theory. In
this short note we investigate a small part of this theory, and study those
Higgs-de Rham flows which are of level zero. We improve the original definition
of level-zero Higgs-de Rham flows (which works for general levels), and
establish a Hitchin-Simpson-type correspondence between such objects and
certain representations of fundamental groups in positive characteristic, which
generalizes the classical results of Katz. We compare the deformation theories
of two sides in the correspondence, and translate the Galois action on the
geometric fundamental groups of algebraic varieties defined over finite fields
into the Higgs side.


  We prove a Bernstein theorem for $\Phi$-anisotropic minimal hypersurfaces in
all dimensional Euclidean spaces that the only entire smooth solutions $u:
\mathbb{R}^{n}\rightarrow \mathbb{R}$ of $\Phi$-anisotropic minimal
hypersurfaces equation are linear functions provided the anisotropic area
functional integrand $\Phi$ is sufficiently $C^{3}$-close to classical area
functional integrand and $|\nabla u(x)|=o(|x|^{\varepsilon})$ for
$\varepsilon\leq \varepsilon_{0}(n, \Phi)$ with the constant
$\varepsilon_{0}(n, \Phi)>0$.


  The scaling of entanglement entropy for the nearest neighbor
antiferromagnetic Heisenberg spin model is studied computationally for clusters
joined by a single bond. Bisecting the balanced three legged Bethe Cluster,
gives a second Renyi entropy and the valence bond entropy which scales as the
number of sites in the cluster. For the analogous situation with square
clusters, i.e. two $L \times L$ clusters joined by a single bond, numerical
results suggest that the second Renyi entropy and the valence bond entropy
scales as $L$. For both systems, the environment and the system are connected
by the single bond and interaction is short range. The entropy is not constant
with system size as suggested by the area law.


  The free-streaming length of dark matter depends on fundamental dark matter
physics, and determines the abundance and concentration of dark matter halos on
sub-galactic scales. Using the image positions and flux ratios from eight
quadruply-imaged quasars, we constrain the free-streaming length of dark matter
and the amplitude of the subhalo mass function (SHMF). We model both main
deflector subhalos and halos along the line of sight, and account for warm dark
matter (WDM) free-streaming effects on the mass function and mass-concentration
relation. By calibrating the scaling of the SHMF with host halo mass and
redshift using a suite of simulated halos, we infer a global normalization for
the SHMF. We account for finite-size background sources, and marginalize over
the mass profile of the main deflector. Parameterizing dark matter
free-streaming through the half-mode mass $m_{\rm{hm}}$, we constrain the
thermal relic particle mass $m_{\rm{DM}}$ corresponding to $m_{\rm{hm}}$. At
$95 \%$ CI: $m_{\rm{hm}} < 10^{7.8} M_{\odot}$ ($m_{\rm{DM}} > 5.2 \
\rm{keV}$). We disfavor $m_{\rm{DM}} = 4.0 \rm{keV}$ and $ m_{\rm{DM}} = 3.0
\rm{keV}$ with likelihood ratios of 7:1 and 30:1, respectively, relative to the
peak of the posterior distribution. Assuming cold dark matter, we constrain the
projected mass in substructure between $10^6 - 10^{9} M_{\odot}$ near lensed
images. At $68 \%$ CI, we infer $2.0 - 6.1 \times 10^{7} M_{\odot}
\rm{kpc^{-2}}$, corresponding to mean projected mass fraction
$\bar{f}_{\rm{sub}} = 0.035_{-0.017}^{+0.021}$. At $95 \%$ CI, we obtain a
lower bound on the projected mass of $0.6 \times 10^{7} M_{\odot}
\rm{kpc^{-2}}$, corresponding to $\bar{f}_{\rm{sub}} > 0.005$. These results
agree with the predictions of cold dark matter.


  We propose a feasible scheme to achieve quantum computation based on
geometric manipulation of ensembles of atoms, and analyze it for neutral
rubidium atoms magnetically trapped in planoconcave microcavities on an atom
chip. The geometric operations are accomplished by optical excitation of a
single atom into a Rydberg state in a constant electric field. Strong
dipole-dipole interactions and incident lasers drive the dark state of the atom
ensembles to undergo cyclic evolutions that realize a universal set of quantum
gates. Such geometric manipulation turns out naturally to protect the qubits
from the errors induced by non-uniform laser illumination as well as cavity
loss. The gate performance and decoherence processes are assessed by numerical
simulation.


  We improve the decay argument by [Bona and Li, J. Math. Pures Appl., 1997]
for solitary waves of general dispersive equations and illustrate it in the
proof for the exponential decay of solitary waves to steady Degasperis-Procesi
equation in the nonlocal formulation. In addition, we give a method which
confirms the symmetry of solitary waves of the maximum height. Finally, we
discover how the symmetric structure is connected to the steady structure of
solutions to the Degasperis-Procesi equation, and give a more intuitive proof
for symmetric solutions to be traveling waves. The improved argument and new
methods above can be used for the decay rate of solitary waves to many other
dispersive equations and will give new perspectives on symmetric solutions for
general evolution equations.


  In the view of massive content explosion in World Wide Web through diverse
sources, it has become mandatory to have content filtering tools. The filtering
of contents of the web pages holds greater significance in cases of access by
minor-age people. The traditional web page blocking systems goes by the Boolean
methodology of either displaying the full page or blocking it completely. With
the increased dynamism in the web pages, it has become a common phenomenon that
different portions of the web page holds different types of content at
different time instances. This paper proposes a model to block the contents at
a fine-grained level i.e. instead of completely blocking the page it would be
efficient to block only those segments which holds the contents to be blocked.
The advantages of this method over the traditional methods are fine-graining
level of blocking and automatic identification of portions of the page to be
blocked. The experiments conducted on the proposed model indicate 88% of
accuracy in filtering out the segments.


  In this paper, a lifelong learning problem is studied for an Internet of
Things (IoT) system. In the considered model, each IoT device aims to balance
its information freshness and energy consumption tradeoff by controlling its
computational resource allocation at each time slot under dynamic environments.
An unmanned aerial vehicle (UAV) is deployed as a flying base station so as to
enable the IoT devices to adapt to novel environments. To this end, a new
lifelong reinforcement learning algorithm, used by the UAV, is proposed in
order to adapt the operation of the devices at each visit by the UAV. By using
the experience from previously visited devices and environments, the UAV can
help devices adapt faster to future states of their environment. To do so, a
knowledge base shared by all devices is maintained at the UAV. Simulation
results show that the proposed algorithm can converge $25\%$ to $50\%$ faster
than a policy gradient baseline algorithm that optimizes each device's decision
making problem in isolation.


  Gram staining has been one of the most frequently used staining protocols in
microbiology for over a century, utilized across various fields, including
diagnostics, food safety, and environmental monitoring. Its manual procedures
make it vulnerable to staining errors and artifacts due to, e.g., operator
inexperience and chemical variations. Here, we introduce virtual Gram staining
of label-free bacteria using a trained deep neural network that digitally
transforms darkfield images of unstained bacteria into their Gram-stained
equivalents matching brightfield image contrast. After a one-time training
effort, the virtual Gram staining model processes an axial stack of darkfield
microscopy images of label-free bacteria (never seen before) to rapidly
generate Gram staining, bypassing several chemical steps involved in the
conventional staining process. We demonstrated the success of the virtual Gram
staining workflow on label-free bacteria samples containing Escherichia coli
and Listeria innocua by quantifying the staining accuracy of the virtual Gram
staining model and comparing the chromatic and morphological features of the
virtually stained bacteria against their chemically stained counterparts. This
virtual bacteria staining framework effectively bypasses the traditional Gram
staining protocol and its challenges, including stain standardization, operator
errors, and sensitivity to chemical variations.


  The conflict between pro-self and pro-social behaviour is at the core of many
key problems of our time, as, for example, the reduction of air pollution and
the redistribution of scarce resources. For the well-being of our societies, it
is thus crucial to find mechanisms to promote pro-social choices over egoistic
ones. Particularly important, because cheap and easy to implement, are those
mechanisms that can change people's behaviour without forbidding any options or
significantly changing their economic incentives, the so-called "nudges".
Previous research has found that moral nudges (e.g., making norms salient) can
promote pro-social behaviour. However, little is known about whether their
effect persists over time and spills across context. This question is key in
light of research showing that pro-social actions are often followed by selfish
actions, thus suggesting that some moral manipulations may backfire. Here we
present a class of simple moral nudges that have a great positive impact on
pro-sociality. In Studies 1-4 (total N = 1,400), we use economic games to
demonstrate that asking subjects to self-report "what they think is the morally
right thing to do" does not only increase pro-sociality in the choice
immediately after, but also in subsequent choices, and even when the social
context changes. In Study 5, we explore whether moral nudges promote charity
donations to humanitarian organisations in a large (N=1,800) crowdfunding
campaign. We find that, in this context, moral nudges increase donations by
about 44 percent.


  This is a report on a talk to high school mathematics students. It gives some
combinatorial connections for the entries of the boustrophedon triangle whose
sides are the Taylor coefficients for the tangent and secant functions.


  We consider the wave maps from $\mathbb{R}^{1+2}$ into $\mathbb{S}^2\subset
\mathbb{R}^3.$ Under an additional assumption of $k$-corotational symmetry, the
problem reduces to the one dimensional semilinear wave equation:
\begin{equation*}
  \partial_t^2 u-\partial_r^2 u-\frac{\partial_r u}{r}+k^2
\frac{\sin(2u)}{2r^2}=0. \end{equation*} Given any integer $k\ge 1$ and any
integer $m\ge 2k,$ we exhibit a set of initial data $(u_0,u_1)$ with energy
arbitrarily close to that of the ground state solution $Q$, such that the
corresponding solution $u$ blows up in finite time by concentrating its energy.
To be precise, the solution $u$ satisfies \begin{equation*}
  \lim\limits_{t\rightarrow T}
\left\|\left(u(t,r)-Q\left(\frac{r}{\lambda(t)}\right)-u_1^*(r), \partial_t
u-u_2^*(r)\right)\right\|_{H\times L^2}=0 \end{equation*} with a quantized
speed \begin{equation*}
  \lambda(t)=c(u_0,u_1)(1+o_{t\to
T}(1))\frac{(T-t)^{\frac{m}{k}}}{|\log(T-t)|^{\frac{m}{k(m-k)}}},
\end{equation*} where $\|u\|_{H}:=\int_{\mathbb{R}^2}\left(|\partial_r
u|^2+\frac{|u|^2}{r^2}\right).$


  We show that the distortion of the (2,q)-torus knot is not bounded linearly
from below.


  The "classical-quantum" ($\mathit{cq}$) discord of a bipartite state
$\rho^{AB}$ is the smallest difference between the mutual information
$S(\rho^{A:B})$ of $\rho$ and that of $\rho$ after a measurement channel is
applied on the $A$ system. Relating zero discord to the strong subadditivity of
the Von Neumann entropy, Datta proved that a state has zero $\mathit{cq}$
discord iff and only if it can be written in the form $\sum_i p_i\,
|i\rangle\langle i|\otimes \rho^B_i$ for $p_i$ a probability distribution,
$|i\rangle$ a basis of the $A$ system and $\rho^B_i$ states of the $B$ system.
We provide a simple proof of that same result using directly a theorem of Petz
on channels that leave unchanged the relative entropy of two given states.


  We argue in favor of dynamical mass generation in an SU(2)xU(1) electroweak
model with two complex scalar doublets with ordinary masses. The masses of
leptons and quarks are generated by ultraviolet-finite non-perturbative
solutions of the Schwinger-Dyson equations for full fermion propagators with
self-consistently modified scalar boson exchanges. The W and Z boson masses are
expressed in terms of spontaneously generated fermion proper self-energies in
the form of sum rules. The model predicts two charged and four real neutral
heavy scalars.


  Here, we examine the influence of surface chemical reactivity toward ambient
gases on the performance of nanodevices based on two-dimensional materials
"beyond graphene" and novel topological phases of matter. While surface
oxidation in ambient conditions was observed for silicene and phosphorene with
subsequent reduction of the mobility of charge carriers, nanodevices with
active channels of indium selenide, bismuth chalcogenides and transition-metal
dichalcogenides are stable in air. However, air-exposed indium selenide suffers
of p-type doping due to water decomposition on Se vacancies, whereas the low
mobility of charge carriers in transition-metal dichalcogenides increases the
response time of nanodevices. Conversely, bismuth chalcogenides require a
control of crystalline quality, which could represent a serious hurdle for up
scaling.


  Conversation agents, commonly referred to as chatbots, are increasingly
deployed in many domains to allow people to have a natural interaction while
trying to solve a specific problem. Given their widespread use, it is important
to provide their users with methods and tools to increase users awareness of
various properties of the chatbots, including non-functional properties that
users may consider important in order to trust a specific chatbot. For example,
users may want to use chatbots that are not biased, that do not use abusive
language, that do not leak information to other users, and that respond in a
style which is appropriate for the user's cognitive level.
  In this paper, we address the setting where a chatbot cannot be modified, its
training data cannot be accessed, and yet a neutral party wants to assess and
communicate its trustworthiness to a user, tailored to the user's priorities
over the various trust issues. Such a rating can help users choose among
alternative chatbots, developers test their systems, business leaders price
their offering, and regulators set policies. We envision a personalized rating
methodology for chatbots that relies on separate rating modules for each issue,
and users' detected priority orderings among the relevant trust issues, to
generate an aggregate personalized rating for the trustworthiness of a chatbot.
The method is independent of the specific trust issues and is parametric to the
aggregation procedure, thereby allowing for seamless generalization. We
illustrate its general use, integrate it with a live chatbot, and evaluate it
on four dialog datasets and representative user profiles, validated with user
surveys.


  We present a time-resolved photoluminescence (PL) study in real- and
momentum-space of a polariton condensate switch in a quasi-1D semiconductor
microcavity. The polariton flow across the ridge is gated by excitons inducing
a barrier potential due to repulsive interactions. A study of the device
operation dependence on the power of the pulsed gate beam obtains a
satisfactory compromise for the ON/OFF-signal ratio and -switching time of the
order of 0.3 and $\thicksim50$ ps, respectively. The opposite transition is
governed by the long-lived gate excitons, consequently the OFF/ON-switching
time is $\thicksim200$ ps, limiting the overall operation speed of the device
to $\thicksim3$ GHz. The experimental results are compared to numerical
simulations based on a generalized Gross-Pitaevskii equation, taking into
account incoherent pumping, decay and energy relaxation within the condensate.


  A construction of the noncommutative-geometric counterparts of classical
classifying spaces is presented, for general compact matrix quantum structure
groups. A quantum analogue of the classical concept of the classifying map is
introduced and analyzed. Interrelations with the abstract algebraic theory of
quantum characteristic classes are discussed. Various non-equivalent approaches
to defining universal characteristic classes are outlined.


  The c-axis tunneling properties of both pristine Bi2212 and its HgBr$_2$
intercalate have been measured in the temperature range 4.2 - 250 K.
Lithographically patterned 7-10 unit-cell heigh mesa structures on the surfaces
of these single crystals were investigated. Clear SIS-like tunneling curves for
current applied in the $\it c$-axis direction have been observed. The dynamic
conductance d$I/$d$V(V)$ shows both sharp peaks corresponding to a
superconducting gap edge and a dip feature beyond the gap, followed by a wide
maximum, which persists up to a room temperature. Shape of the temperature
dependence of the {\it c}-axis resistance does not change after the
intercalation suggesting that a coupling between $\rm CuO_2$-bilayers has
little effect on the pseudogap.


  There are only a few learning algorithms applicable to stochastic dynamic
teams and games which generalize Markov decision processes to decentralized
stochastic control problems involving possibly self-interested decision makers.
Learning in games is generally difficult because of the non-stationary
environment in which each decision maker aims to learn its optimal decisions
with minimal information in the presence of the other decision makers who are
also learning. In stochastic dynamic games, learning is more challenging
because, while learning, the decision makers alter the state of the system and
hence the future cost. In this paper, we present decentralized Q-learning
algorithms for stochastic games, and study their convergence for the weakly
acyclic case which includes team problems as an important special case. The
algorithm is decentralized in that each decision maker has access to only its
local information, the state information, and the local cost realizations;
furthermore, it is completely oblivious to the presence of other decision
makers. We show that these algorithms converge to equilibrium policies almost
surely in large classes of stochastic games.


  A linear but global numerical model for the magnetorotational instability
(MRI) in disk geometry is considered to estimate the instability parameters for
galaxies. Similarity rules suggested by a local analysis are applied to reveal
a universal behavior approached by the results of global calculations for large
magnetic Prandtl numbers. The findings are used to estimate the MRI
characteristics for galaxies with their very large magnetic Prandtl numbers
which cannot be attained in any numerical simulations. The resulting minimum
field for the instability, Bmin 10-25 G, is small compared to any seed fields
currently discussed. The growth times of MRI are estimated to be on the order
of the rotation period of the inner rigidly-rotating core, i.e. ~100 Myr.
Global MRI excites preferentially the magnetic field modes of quadrupolar
symmetry.


  The fundamental physical description of the Universe is based on two
theories: Quantum Mechanics and General Relativity. Unified theory of Quantum
Gravity (QG) is an open problem. Quantum Gravity Phenomenology (QGP) studies QG
effects in low-energy systems. The basis of one such phenomenological model is
the Generalized Uncertainty Principle (GUP), which is a modified Heisenberg
uncertainty relation and predicts a deformed position-momentum commutator.
  Relativistic Generalized Uncertainty Principle (RGUP) is proposed in this
thesis, which gives a Loerentz invariant minimum length and resolves the
composition law problem. RGUP modified Klein-Gordon, Schrodinger and Dirac
equations with QG corrections to several systems are presented. The Lagrangians
of Quantum Electrodynamics for the gauge, scalar, and spinor fields are
obtained. The RGUP corrections to scattering amplitudes are then calculated.
The results are applied to high energy scattering experiments providing much
needed window for testing minimum length and QG theories in the laboratory.


  Leveraging planning during learning and decision-making is central to the
long-term development of intelligent agents. Recent works have successfully
combined tree-based search methods and self-play learning mechanisms to this
end. However, these methods typically face scaling challenges due to the
sequential nature of their search. While practical engineering solutions can
partly overcome this, they often result in a negative impact on performance. In
this paper, we introduce SPO: Sequential Monte Carlo Policy Optimisation, a
model-based reinforcement learning algorithm grounded within the Expectation
Maximisation (EM) framework. We show that SPO provides robust policy
improvement and efficient scaling properties. The sample-based search makes it
directly applicable to both discrete and continuous action spaces without
modifications. We demonstrate statistically significant improvements in
performance relative to model-free and model-based baselines across both
continuous and discrete environments. Furthermore, the parallel nature of SPO's
search enables effective utilisation of hardware accelerators, yielding
favourable scaling laws.


  Bidirectional Encoder Representations from Transformers (BERT) has shown
marvelous improvements across various NLP tasks, and its consecutive variants
have been proposed to further improve the performance of the pre-trained
language models. In this paper, we aim to first introduce the whole word
masking (wwm) strategy for Chinese BERT, along with a series of Chinese
pre-trained language models. Then we also propose a simple but effective model
called MacBERT, which improves upon RoBERTa in several ways. Especially, we
propose a new masking strategy called MLM as correction (Mac). To demonstrate
the effectiveness of these models, we create a series of Chinese pre-trained
language models as our baselines, including BERT, RoBERTa, ELECTRA, RBT, etc.
We carried out extensive experiments on ten Chinese NLP tasks to evaluate the
created Chinese pre-trained language models as well as the proposed MacBERT.
Experimental results show that MacBERT could achieve state-of-the-art
performances on many NLP tasks, and we also ablate details with several
findings that may help future research. We open-source our pre-trained language
models for further facilitating our research community. Resources are
available: https://github.com/ymcui/Chinese-BERT-wwm


  High-order structures have been recognised as suitable models for systems
going beyond the binary relationships for which graph models are appropriate.
Despite their importance and surge in research on these structures, their
random cases have been only recently become subjects of interest. One of these
high-order structures is the oriented hypergraph, which relates couples of
subsets of an arbitrary number of vertices. Here we develop the
Erd\H{o}s-R\'enyi model for oriented hypergraphs, which corresponds to the
random realisation of oriented hyperedges of the complete oriented hypergraph.
A particular feature of random oriented hypergraphs is that the ratio between
their expected number of oriented hyperedges and their expected degree or size
is 3/2 for large number of vertices. We highlight the suitability of oriented
hypergraphs for modelling large collections of chemical reactions and the
importance of random oriented hypergraphs to analyse the unfolding of
chemistry.


  In a previous report (Raju et al.,2023) we concluded that, if the goal was to
preserve events such as saccades, microsaccades, and smooth pursuit in
eye-tracking recordings, data with sine wave frequencies less than 100 Hz
(-3db) were the signal and data above 100 Hz were noise. We compare 5 filters
in their ability to preserve signal and remove noise. Specifically, we compared
the proprietary STD and EXTRA heuristic filters provided by our EyeLink 1000
(SR-Research, Ottawa, Canada), a Savitzky-Golay (SG) filter, an infinite
impulse response (IIR) filter (low-pass Butterworth), and a finite impulse
filter (FIR). For each of the non-heuristic filters, we systematically searched
for optimal parameters. Both the IIR and the FIR filters were zero-phase
filters. Mean frequency response profiles and amplitude spectra for all 5
filters are provided. In addition, we examined the effect of our filters on a
noisy recording. Our FIR filter had the sharpest roll-off of any filter.
Therefore, it maintained the signal and removed noise more effectively than any
other filter. On this basis, we recommend the use of our FIR filter. Several
reports have shown that filtering increased the temporal autocorrelation of a
signal. To address this, the present filters were also evaluated in terms of
autocorrelation (specifically the first 3 lags). Of all our filters, the STD
filter introduced the least amount of autocorrelation.


  Let $\Sigma$ be a $\sigma$-algebra over $\Omega$, and let $M(\Sigma)$ denote
the Banach space of complex measures. Consider a representation $T_t$ for
$t\in\Bbb R$ acting on $M(\Sigma)$. We show that under certain, very weak
hypotheses, that if for a given $\mu \in M(\Sigma)$ and all $A \in \Sigma$ the
map $t \mapsto T_t \mu(A)$ is in $H^\infty(\Bbb R)$, then it follows that the
map $t \mapsto T_t \mu$ is Bochner measurable. The proof is based upon the idea
of the Analytic Radon Nikod\'ym Property.
  Straightforward applications yield a new and simpler proof of Forelli's main
result concerning analytic measures ({\it Analytic and quasi-invariant
measures}, Acta Math., {\bf 118} (1967), 33--59).


  Alice string is a topological defect with a very peculiar feature. When a
defect with a monopole charge encircles an Alice string, the monopole charge
changes sign. In this work, we generalize this notion to momentum space of
periodic media with loss and gain. In particular, we find that the generic
band-structure node for a three-dimensional non-Hermitian crystalline system
acts as an Alice string, which can flip the Chern number charge carried by Weyl
points and by exceptional-line rings. We discuss signatures of this topological
structure for a lattice model with one tuning parameter, including non-trivial
braiding of bulk band nodes, and the spectroscopic features of both the bulk
and the surface states. We also explore how an Alice string affects the
validity of the Nielsen-Ninomiya theorem, and present a mathematical
description of the braiding phenomenon.


  Critical points that can be suppressed to zero temperature are interesting
because quantum fluctuations have been shown to dramatically alter electron gas
properties. Here, the metal formed by Co doping the paramagnetic insulator
FeS$_2$, Fe$_{1-x}$Co$_x$S$_2$, is demonstrated to order ferromagnetically at
$x>x_c=0.01\pm0.005$ where we observe unusual transport, magnetic, and
thermodynamic properties. We show that this magnetic semiconductor undergoes a
percolative magnetic transition with distinct similarities to the Griffiths
phase, including singular behavior at $x_c$ and zero temperature.


  Developing generative models for interleaved image-text data has both
research and practical value. It requires models to understand the interleaved
sequences and subsequently generate images and text. However, existing attempts
are limited by the issue that the fixed number of visual tokens cannot
efficiently capture image details, which is particularly problematic in the
multi-image scenarios. To address this, this paper presents MM-Interleaved, an
end-to-end generative model for interleaved image-text data. It introduces a
multi-scale and multi-image feature synchronizer module, allowing direct access
to fine-grained image features in the previous context during the generation
process. MM-Interleaved is end-to-end pre-trained on both paired and
interleaved image-text corpora. It is further enhanced through a supervised
fine-tuning phase, wherein the model improves its ability to follow complex
multi-modal instructions. Experiments demonstrate the versatility of
MM-Interleaved in recognizing visual details following multi-modal instructions
and generating consistent images following both textual and visual conditions.
Code and models are available at
\url{https://github.com/OpenGVLab/MM-Interleaved}.


  This paper proposes a deep learning (DL) model for automatic sleep stage
classification based on single-channel EEG data. The DL model features a
convolutional neural network (CNN) and transformers. The model was designed to
run on energy and memory-constrained devices for real-time operation with local
processing. The Fpz-Cz EEG signals from a publicly available Sleep-EDF dataset
are used to train and test the model. Four convolutional filter layers were
used to extract features and reduce the data dimension. Then, transformers were
utilized to learn the time-variant features of the data. To improve
performance, we also implemented a subject specific training before the
inference (i.e., prediction) stage. With the subject specific training, the F1
score was 0.91, 0.37, 0.84, 0.877, and 0.73 for wake, N1-N3, and rapid eye
movement (REM) stages, respectively. The performance of the model was
comparable to the state-of-the-art works with significantly greater
computational costs. We tested a reduced-sized version of the proposed model on
a low-cost Arduino Nano 33 BLE board and it was fully functional and accurate.
In the future, a fully integrated wireless EEG sensor with edge DL will be
developed for sleep research in pre-clinical and clinical experiments, such as
real-time sleep modulation.


  We theoretically investigate coherent optical excitations of collective modes
in two-band BCS superconductors, which accommodate two Higgs modes and one
Leggett mode corresponding, respectively, to the amplitude and relative-phase
oscillations of the superconducting order parameters associated with the two
bands. We find, based on a mean-field analysis, that each collective mode can
be resonantly excited through a nonlinear light-matter coupling when the
doubled frequency of the driving field coincides with the frequency of the
corresponding mode. Among the two Higgs modes, the higher-energy one exhibits a
sharp resonance with light, while the lower-energy mode has a broadened
resonance width. The Leggett mode is found to be resonantly induced by a
homogeneous ac electric field because the leading nonlinear effect generates a
potential offset between the two bands that couples to the relative phase of
the order parameters. The resonance for the Leggett mode becomes sharper with
increasing temperature. All of these light-induced collective modes along with
density fluctuations contribute to the third-harmonic generation. We also
predict an experimental possibility of optical detection of the Leggett mode.


  The ability to observe the effects of actions performed by others and to
infer their intent, most likely goals, or course of action, is known as a plan
or intention recognition cognitive capability and has long been one of the
fundamental research challenges in AI. Deep learning has recently been making
significant inroads on various pattern recognition problems, except for
intention recognition. While extensively explored since the seventies, the
problem remains unsolved for most interesting cases in various areas, ranging
from natural language understanding to human behavior understanding based on
video feeds. This paper compares symbolic inverse planning, one of the most
investigated approaches to goal recognition, to deep learning using CNN and
LTSM neural network architectures, on five synthetic benchmarks often used in
the literature. The results show that the deep learning approach achieves
better goal-prediction accuracy and timeliness than the symbolic cost-based
plan recognizer in these domains. Although preliminary, these results point to
interesting future research avenues.


  Convex integration and the holonomic approximation theorem are two well-known
pillars of flexibility in differential topology and geometry. They may each
seem to have their own flavor and scope. The goal of this paper is to bring
some new perspective on this topic. We explain how to prove the holonomic
approximation theorem for first order jets using convex integration. More
precisely we first prove that this theorem can easily be reduced to proving
flexibility of some specific relation. Then we prove this relation is open and
ample, hence its flexibility follows from off-the-shelf convex integration.


  We investigate the exclusive electroproduction of pi^+ mesons from nucleons.
To leading twist, leading order alpha_s accuracy the corresponding production
amplitude can be decomposed into pseudovector and pseudoscalar parts. Both can
be expressed in terms of quark double distribution functions of the nucleon.
While the pseudovector contribution is connected to ordinary polarized quark
distributions, the pseudoscalar part can be related to one pion t-channel
exchange. We observe that the pseudovector part of the production amplitude is
important at x < 0.1. On the other hand, for 0.1 < x < 0.4 contributions from
one pion exchange dominate.


  We consider three different families of Vafa-Witten invariants of $K3$
surfaces. In each case, the partition function that encodes the Vafa-Witten
invariants is given by combinations of twisted Dedekind $\eta$-functions. By
utilising known properties of these $\eta$-functions, we obtain exact formulae
for each of the invariants and prove that they asymptotically satisfy all
higher-order Tur\'{a}n inequalities.


  There is a chance that singleton fields, that in the context of strings and
membranes have been regarded as topological gauge fields that can interact only
at the boundary of anti-De Sitter space, at spatial infinity, may have a more
physical manifestation as costituents of massless fields in space time. The
composite character of massless fields is expressed by field - current
identities that relate ordinary massless field operators to singleton currents
and stress-energy tensors. Naive versions of such identities do not make sense,
but when the singletons are described in terms of dipole structures, then such
constructions are at least formally possible. The new proposal includes and
generalizes an early composite version of QED, and includes quantum gravity,
super gravity and models of QCD. Unitarity of such theories is conjectural.


  The Green function plays an essential role in the Kohn-Korringa-Rostocker
(KKR) multiple scattering method. In practice, it is constructed from the
regular and irregular solutions of the local Kohn-Sham equation and robust
methods exist for spherical potentials. However, when applied to a
non-spherical potential, numerical errors from the irregular solutions give
rise to pathological behaviors of the charge density at small radius. Here we
present a full-potential implementation of the relativistic KKR method to
perform \textit{ab initio} self-consistent calculation by directly solving the
Dirac differential equations. The pathology around the origin is completely
eliminated with the help of an efficient pole-searching technique. This method
is utilized to investigate the crystal structures of polonium and their bulk
properties. The noble metals are also calculated, both as a test of our method
and to study the relativistic effects.


  Asymptotic Safety provides an elegant mechanism for obtaining a consistent
high-energy completion of gravity and gravity-matter systems. Following the
initial idea by Steven Weinberg, the construction builds on an interacting
fixed point of the theories renormalization group (RG) flow. In this work we
use the Wetterich equation for the effective average action to investigate the
RG flow of gravity supplemented by a real scalar field. We give a
non-perturbative proof that the subspace of interactions respecting the global
shift-symmetry of the scalar kinetic term is closed under RG transformations.
Subsequently, we compute the beta functions in an approximation comprising the
EinsteinHilbert action supplemented by the shift-symmetric quartic scalar
self-interaction and the two lowest order shift-symmetric interactions coupling
scalar-bilinears to the spacetime curvature. The computation utilizes the
background field method with an arbitrary background, demonstrating that the
results are manifestly background independent. Our beta functions exhibit an
interacting fixed point suitable for Asymptotic Safety, where all matter
interactions are non-vanishing. The presence of this fixed point is rooted in
the interplay of the matter couplings which our work tracks for the first time.
The relation of our findings with previous results in the literature is
discussed in detail and we conclude with a brief outlook on potential
phenomenological applications.


  Parikh and Wilczek have shown that Hawking radiation's spectrum cannot be
strictly thermal. Such a non-strictly thermal character implies that the
spectrum is also not strictly continuous and thus generates a natural
correspondence between Hawking radiation and black hole's quasinormal modes.
This issue endorses the idea that, in an underlying unitary quantum gravity
theory, black holes result highly excited states. We use this key point to
re-analyze the spectrum of black hole's quasinormal modes by introducing a
black hole's effective temperature. Our analysis changes the physical
understanding of such a spectrum and enables a re-examination of various
results in the literature which realizes important modifies on quantum physics
of black holes. In particular, the formula of the horizon's area quantization
and the number of quanta of area are modified becoming functions of the quantum
"overtone" number n. Consequently, Bekenstein-Hawking entropy, its sub-leading
corrections and the number of microstates, i.e. quantities which are
fundamental to realize unitary quantum gravity theory, are also modified. They
become functions of the quantum overtone number too. Previous results in the
literature are re-obtained in the very large n limit.


  Recent experiments have shown that the high temperature incommensurate (I)
charge density wave (CDW) phase of 1T-TaS2 can be photoinduced from the lower
temperature, nearly commensurate (NC) CDW state. Here we report a time-resolved
x-ray diffraction study of the growth process of the photoinduced I-CDW
domains. The layered nature of the material results in a marked anisotropy in
the size of the photoinduced domains of the I-phase. These are found to grow
self-similarly, their shape remaining unchanged throughout the growth process.
The photoinduced dynamics of the newly formed I-CDW phase was probed at various
stages of the growth process using a double pump scheme, where a first pump
creates I-CDW domains and a second pump excites the newly formed I-CDW state.
We observe larger magnitudes of the coherently excited I-CDW amplitude mode in
smaller domains, which suggests that the incommensurate lattice distortion is
less stable for smaller domain sizes.


  The different point defects formed by two hydrogen atoms or two helium atoms
in tungsten were investigated through first-principles calculation. The
energetically favorable site for a hydrogen atom is tetrahedral interstitial
site while substitutional site is the most preferred site for a helium atom.
The formation energies of two hydrogen or helium atoms are determined by their
positions, and there are not a multiple of a single atom's. After relaxation,
two adjacent hydrogen atoms are away from each other while helium atoms are
close to. The reasons for the interaction between two hydrogen or helium atoms
are also discussed.


  We study short sums of algebraic trace functions via the $q$-analogue of van
der Corput method, and develop methods of arithmetic exponent pairs that
coincide with the classical case while the moduli has sufficiently good
factorizations. As an application, we prove a quadratic analogue of
Brun-Titchmarsh theorem on average, bounding the number of primes $p\leqslant
X$ with $p^2+1\equiv0\pmod q$. The other two applications include a larger
level of distribution of divisor functions in arithmetic progressions and a
sub-Weyl subconvex bound of Dirichlet $L$-functions studied previously by
Irving.


  Let $E/\mathbb{Q}$ be an elliptic curve and let $K$ be an imaginary quadratic
field. Under a certain Heegner hypothesis, Kolyvagin constructed cohomology
classes for $E$ using $K$-CM points and conjectured they did not all vanish.
Conditional on this conjecture, he described the Selmer rank of $E$ using his
system of classes. We extend work of Wei Zhang to prove new cases of
Kolyvagin's conjecture by considering congruences of modular forms modulo large
powers of $p $. Additionally, we prove an analogous result, and give a
description of the Selmer rank, in a complementary "definite" case (using
certain modified $L$-values rather than CM points). Similar methods are also
used to improve known results on the Heegner point main conjecture of
Perrin-Riou. One consequence of our results is a new converse theorem, that
$p$-Selmer rank one implies analytic rank one, when the residual representation
has dihedral image.


  Given a finite irreducible set of real $d \times d$ matrices $A_1,\ldots,A_M$
and a real parameter $s>0$, there exists a unique shift-invariant equilibrium
state associated to $(A_1,\ldots,A_M,s)$. In this article we characterise the
ergodic properties of such equilibrium states in terms of the algebraic
properties of the semigroup generated by the associated matrices. We completely
characterise when the equilibrium state has zero entropy, when it gives
distinct Lyapunov exponents to the natural cocycle generated by
$A_1,\ldots,A_M$, and when it is a Bernoulli measure. We also give a general
sufficient condition for the equilibrium state to be mixing, and give an
example where the equilibrium state is ergodic but not totally ergodic.
Connections with a class of measures investigated by S. Kusuoka are explored in
an appendix.


  Bose-Einstein correlations (BEC) observed between identical bosons produced
in high energy multiparticle collisions are regarded as very important tool in
investigations of multiparticle production processes. We present here their
stochastic feature stressing the fact that they can be regarded as a reflection
of correlations of fluctuations present in hadronizing system. We show in
particular that such approach allows for simple modelling of BEC in numerical
event generators used to describe the multiparticle production processes at
high energy collisions.


  While recent advances in 3D-aware Generative Adversarial Networks (GANs) have
aided the development of near-frontal view human face synthesis, the challenge
of comprehensively synthesizing a full 3D head viewable from all angles still
persists. Although PanoHead proves the possibilities of using a large-scale
dataset with images of both frontal and back views for full-head synthesis, it
often causes artifacts for back views. Based on our in-depth analysis, we found
the reasons are mainly twofold. First, from network architecture perspective,
we found each plane in the utilized tri-plane/tri-grid representation space
tends to confuse the features from both sides, causing "mirroring" artifacts
(e.g., the glasses appear in the back). Second, from data supervision aspect,
we found that existing discriminator training in 3D GANs mainly focuses on the
quality of the rendered image itself, and does not care much about its
plausibility with the perspective from which it was rendered. This makes it
possible to generate "face" in non-frontal views, due to its easiness to fool
the discriminator. In response, we propose SphereHead, a novel tri-plane
representation in the spherical coordinate system that fits the human head's
geometric characteristics and efficiently mitigates many of the generated
artifacts. We further introduce a view-image consistency loss for the
discriminator to emphasize the correspondence of the camera parameters and the
images. The combination of these efforts results in visually superior outcomes
with significantly fewer artifacts. Our code and dataset are publicly available
at https://lhyfst.github.io/spherehead.


  We study the Riemann geometric approach to be aimed at unifying soliton
systems. The general two-dimensional Einstein equation with constant scalar
curvature becomes an integrable differential equation. We show that such
Einstein equation includes KdV/mKdV/sine-Gordon equations.


  Let $G$ be a finite group and $\rho:G \to \GL(V)$ a finite dimensional
representation of $G$. We say that $\rho$ is unisingular if $\det(1-\rho(g)) =
0$ for all $g \in G$. Building on previous work in \cite{cullinan}, we consider
the symmetric groups $S_n$ and prove that certain families of Specht modules
are always unisingular as well as raise new questions for future study.


  Adaptive grid generation is an active research topic for numer- ical solution
of differential equations. In this paper, we propose a variational method which
generates transformations with prescribed Jacobian determinant and curl. Then
we use this transformation to achieve adaptive grid generation task, and show
the importance of curl in a transformation.


  We introduce the Uchuu suite of large high-resolution cosmological $N$-body
simulations. The largest simulation, named Uchuu, consists of 2.1 trillion
($12800^3$) dark matter particles in a box of side-length 2.0 Gpc/h, with
particle mass $3.27 \times 10^{8}$ Msun/h. The highest resolution simulation,
Shin-Uchuu, consists of 262 billion ($6400^3$) particles in a box of
side-length 140 Mpc/h, with particle mass $8.97 \times 10^{5}$ Msun/h.
Combining these simulations we can follow the evolution of dark matter halos
and subhalos spanning those hosting dwarf galaxies to massive galaxy clusters
across an unprecedented volume. In this first paper, we present basic
statistics, dark matter power spectra, and the halo and subhalo mass functions,
which demonstrate the wide dynamic range and superb statistics of the Uchuu
suite. From an analysis of the evolution of the power spectra we conclude that
our simulations remain accurate from the Baryon Acoustic Oscillation scale down
to the very small. We also provide parameters of a mass-concentration model,
which describes the evolution of halo concentration and reproduces our
simulation data to within 5 per cent for halos with masses spanning nearly
eight orders of magnitude at redshift 0<z<14. There is an upturn in the
mass-concentration relation for the population of all halos and of relaxed
halos at z>0.5, whereas no upturn is detected at z<0.5. We make publicly
available various $N$-body products as part of Uchuu Data Release 1 on the
Skies & Universes site. Future releases will include gravitational lensing maps
and mock galaxy, X-ray cluster, and active galactic nuclei catalogues.


  We provide a smoothed analysis of Hoare's find algorithm and we revisit the
smoothed analysis of quicksort.
  Hoare's find algorithm - often called quickselect - is an easy-to-implement
algorithm for finding the k-th smallest element of a sequence. While the
worst-case number of comparisons that Hoare's find needs is quadratic, the
average-case number is linear. We analyze what happens between these two
extremes by providing a smoothed analysis of the algorithm in terms of two
different perturbation models: additive noise and partial permutations.
  Moreover, we provide lower bounds for the smoothed number of comparisons of
quicksort and Hoare's find for the median-of-three pivot rule, which usually
yields faster algorithms than always selecting the first element: The pivot is
the median of the first, middle, and last element of the sequence. We show that
median-of-three does not yield a significant improvement over the classic rule:
the lower bounds for the classic rule carry over to median-of-three.


  The motion of test membranes on which the group $G$ of isometries of a
spacetime $M$ acts has been considered in general settings. It has been shown
that the configuration of Nambu-Goto membranes is described by the Nambu-Goto
membranes in the quotient manifold $M/G$ with an appropriate projected metric
if (i) $G$ is Abelian, (ii) $G$ is semisimple and compact, or (iii) the
orthogonal distribution of the orbit of $G$ is integrable, but in general not.
  It has also been shown that a similar result holds when the membranes couple
with scalar maps or differential form fields.


  Line segment detection is an essential task in computer vision and image
analysis, as it is the critical foundation for advanced tasks such as shape
modeling and road lane line detection for autonomous driving. We present a
robust topological graph guided approach for line segment detection in low
quality binary images (hence, we call it TGGLines). Due to the graph-guided
approach, TGGLines not only detects line segments, but also organizes the
segments with a line segment connectivity graph, which means the topological
relationships (e.g., intersection, an isolated line segment) of the detected
line segments are captured and stored; whereas other line detectors only retain
a collection of loose line segments. Our empirical results show that the
TGGLines detector visually and quantitatively outperforms state-of-the-art line
segment detection methods. In addition, our TGGLines approach has the following
two competitive advantages: (1) our method only requires one parameter and it
is adaptive, whereas almost all other line segment detection methods require
multiple (non-adaptive) parameters, and (2) the line segments detected by
TGGLines are organized by a line segment connectivity graph.


  Hawking radiation has become experimentally testable thanks to the many
analogue systems which mimic the effects of the event horizon on wave
propagation. These systems are typically dominated by dispersion, and give rise
to a numerically soluble and stable ODE only if the rest-frame dispersion
relation $\Omega^{2}(k)$ is a polynomial of relatively low degree. Here we
present a new method for the calculation of wave scattering in a
one-dimensional medium of arbitrary dispersion. It views the wave equation as
an integral equation in Fourier space, which can be solved using standard and
efficient numerical techniques.


  Knowledge of how a body is oriented relative to the world is frequently
invaluable information in the field of robotics. An attitude estimator that
fuses 3-axis gyroscope, accelerometer and magnetometer data into a quaternion
orientation estimate is presented in this paper. The concept of fused yaw, used
by the estimator, is also introduced. The estimator, a nonlinear complementary
filter at heart, is designed to be uniformly robust and stable---independent of
the absolute orientation of the body---and has been implemented and released as
a cross-platform open source C++ library. Extensions to the estimator, such as
quick learning and the ability to deal dynamically with cases of reduced
sensory information, are also presented.


  The paper is concerned with dynamics of multi-phase media consisting of a
solid permeable material and a compressible Newtonian fluid. Governing
macroscopic equations are derived starting from the space-averaged microscopic
mass and momentum balances. The Reynolds stress models (i.e., momentum
dispersive fluxes) are discussed, and a suitable model is developed. In the
case of granular media the solid constituent is considered as an
elastic-plastic matrix, and the yield condition is approximated by Coulomb
friction law. It is revealed that the classical principle of maximum plastic
work is not, in general, valid for granular media, and an appropriate
variational principle is developed. This novel principle coincides with the
maximum plastic work principle for the case of cohesionless and free from
internal friction granular media.


  Accurate and explainable health event predictions are becoming crucial for
healthcare providers to develop care plans for patients. The availability of
electronic health records (EHR) has enabled machine learning advances in
providing these predictions. However, many deep learning based methods are not
satisfactory in solving several key challenges: 1) effectively utilizing
disease domain knowledge; 2) collaboratively learning representations of
patients and diseases; and 3) incorporating unstructured text. To address these
issues, we propose a collaborative graph learning model to explore
patient-disease interactions and medical domain knowledge. Our solution is able
to capture structural features of both patients and diseases. The proposed
model also utilizes unstructured text data by employing an attention regulation
strategy and then integrates attentive text features into a sequential learning
process. We conduct extensive experiments on two important healthcare problems
to show the competitive prediction performance of the proposed method compared
with various state-of-the-art models. We also confirm the effectiveness of
learned representations and model interpretability by a set of ablation and
case studies.


  A framework to systematically decouple high order elliptic equations into
combination of Poisson-type and Stokes-type equations is developed. The key is
to systematically construct the underling commutative diagrams involving the
complexes and Helmholtz decompositions in a general way. Discretizing the
decoupled formulation leads to a natural superconvergence between the Galerkin
projection and the decoupled approximation. Examples include but not limit to:
the primal formulations and mixed formulations of biharmonic equation, fourth
order curl equation, and triharmonic equation etc. As a by-product, Helmholtz
decompositions for many dual spaces are obtained.


  Let $H$ be a hyperexponential function in $n$ variables $x=(x_1,\dots,x_n)$
with coefficients in a field $\mathbb{K}$, $[\mathbb{K}:\mathbb{Q}] <\infty$,
and $\omega$ a rational differential $1$-form. Assume that $H\omega$ is closed
and $H$ transcendental. We prove using Schanuel conjecture that there exist a
univariate function $f$ and multivariate rational functions $F,R$ such that
$\int H\omega= f(F(x))+H(x)R(x)$. We present an algorithm to compute this
decomposition. This allows us to present an algorithm to construct a basis of
the cohomology of differential $1$-forms with coefficients in
$H\mathbb{K}[x,1/(SD)]$ for a given $H$, $D$ being the denominator of $dH/H$
and $S\in\mathbb{K}[x]$ a square free polynomial. As an application, we
generalize a result of Singer on differential equations on the plane: whenever
it admits a Liouvillian first integral $I$ but no Darbouxian first integral,
our algorithm gives a rational variable change linearising the system.


  In this paper we propose a new framework for point cloud instance
segmentation. Our framework has two steps: an embedding step and a clustering
step. In the embedding step, our main contribution is to propose a
probabilistic embedding space for point cloud embedding. Specifically, each
point is represented as a tri-variate normal distribution. In the clustering
step, we propose a novel loss function, which benefits both the semantic
segmentation and the clustering. Our experimental results show important
improvements to the SOTA, i.e., 3.1% increased average per-category mAP on the
PartNet dataset.