  We present the discovery of a white dwarf companion at 3.6" from GJ3346, a
nearby ($\pi\sim$42 mas) K star observed with SPHERE@VLT as part of an open
time survey for faint companions to objects with significant proper motion
discrepancies ($\Delta\mu$) between Gaia DR1 and Tycho-2. Syrius-like systems
like GJ3346AB, which include a main sequence star and a white dwarf, can be
difficult to detect because of the intrinsic faintness of the latter. They
have, however, been found to be common contaminants for direct imaging
searches. White dwarfs have in fact similar brightness to sub-stellar
companions in the infrared, while being much brighter in the visible bands like
those used by Gaia. Combining our observations with Gaia DR2 and with several
additional archival data sets, we were able to fully constrain the physical
properties of GJ3346B, such as its effective temperature
(11$\times$10$^3\pm$500 K) as well as the cooling age of the system (648$\pm$58
Myrs). This allowed us to better understand the system history and to partially
explains the discrepancies previously noted in the age indicators for this
objects. Although further investigation is still needed, it seems that GJ3346,
which was previously classified as young, is in fact most likely to be older
than 4 Gyrs. Finally, given that the mass (0.58$\pm$0.01$M_{\odot}$)} and
separation (85 au) of GJ3346B are compatible with the observed $\Delta\mu$,
this discovery represents a further confirmation of the potential of this kind
of dynamical signatures as selection methods for direct imaging surveys
targeting faint, sub-stellar companions.


  In the article, new asymptotic approximation of the $n$th order is obtained
and proposed to be used in calculations of radiation propagation without
scattering in optically thick media; the asymptotic approximation is much
simpler and more precise than the known diffusion approximation. The rigorous
derivation of the diffusion approximation equation and the equation of the
radiation heat conduction approximation is obtained from the constructed
asymptotic solution of the kinetic equation of radiation propagation in
optically thick media. It is shown, that for optically thick media the
asymptotic solution of the kinetic equation of radiation propagation without
scattering is asymptotic expansion of the exact integral solution of that
kinetic equation. Improved boundary conditions, which are essential for
practical application in calculations of radiation propagation, are derived
(for inner boundaries and outer boundaries with vacuum).


  Limited data availability is a challenging problem in the latent fingerprint
domain. Synthetically generated fingerprints are vital for training data-hungry
neural network-based algorithms. Conventional methods distort clean
fingerprints to generate synthetic latent fingerprints. We propose a simple and
effective approach using style transfer and image blending to synthesize
realistic latent fingerprints. Our evaluation criteria and experiments
demonstrate that the generated synthetic latent fingerprints preserve the
identity information from the input contact-based fingerprints while possessing
similar characteristics as real latent fingerprints. Additionally, we show that
the generated fingerprints exhibit several qualities and styles, suggesting
that the proposed method can generate multiple samples from a single
fingerprint.


  We study the N-step binary stationary ergodic Markov chain and analyze its
differential entropy. Supposing that the correlations are weak we express the
conditional probability function of the chain through the pair correlation
function and represent the entropy as a functional of the pair correlator.
Since the model uses the two-point correlators instead of the block
probability, it makes it possible to calculate the entropy of strings at much
longer distances than using standard methods. A fluctuation contribution to the
entropy due to finiteness of random chains is examined. This contribution can
be of the same order as its regular part even at the relatively short lengths
of subsequences. A self-similar structure of entropy with respect to the
decimation transformations is revealed for some specific forms of the pair
correlation function. Application of the theory to the DNA sequence of the R3
chromosome of Drosophila melanogaster is presented.


  Accurate crop type maps are an essential source of information for monitoring
yield progress at scale, projecting global crop production, and planning
effective policies. To date, however, crop type maps remain challenging to
create in low and middle-income countries due to a lack of ground truth labels
for training machine learning models. Field surveys are the gold standard in
terms of accuracy but require an often-prohibitively large amount of time,
money, and statistical capacity. In recent years, street-level imagery, such as
Google Street View, KartaView, and Mapillary, has become available around the
world. Such imagery contains rich information about crop types grown at
particular locations and times. In this work, we develop an automated system to
generate crop type ground references using deep learning and Google Street View
imagery. The method efficiently curates a set of street view images containing
crop fields, trains a model to predict crop type by utilizing weakly-labelled
images from disparate out-of-domain sources, and combines predicted labels with
remote sensing time series to create a wall-to-wall crop type map. We show
that, in Thailand, the resulting country-wide map of rice, cassava, maize, and
sugarcane achieves an accuracy of 93%. We publicly release the first-ever crop
type map for all of Thailand 2022 at 10m-resolution with no gaps. To our
knowledge, this is the first time a 10m-resolution, multi-crop map has been
created for any smallholder country. As the availability of roadside imagery
expands, our pipeline provides a way to map crop types at scale around the
globe, especially in underserved smallholder regions.


  For many years, lunar laser ranging (LLR) observations using a green
wavelength have suffered an inhomogeneity problem both temporally and
spatially. This paper reports on the implementation of a new infrared detection
at the Grasse LLR station and describes how infrared telemetry improves this
situation. Our first results show that infrared detection permits us to densify
the observations and allows measurements during the new and the full Moon
periods. The link budget improvement leads to homogeneous telemetric
measurements on each lunar retro-reflector. Finally, a surprising result is
obtained on the Lunokhod 2 array which attains the same efficiency as Lunokhod
1 with an infrared laser link, although those two targets exhibit a
differential efficiency of six with a green laser link.


  We consider an elliptic self-adjoint first order pseudodifferential operator
acting on columns of m complex-valued half-densities over a connected compact
n-dimensional manifold without boundary. The eigenvalues of the principal
symbol are assumed to be simple but no assumptions are made on their sign, so
the operator is not necessarily semi-bounded. We study the spectral function,
i.e. the sum of squares of Euclidean norms of eigenfunctions evaluated at a
given point of the manifold, with summation carried out over all eigenvalues
between zero and a positive lambda. We derive a two-term asymptotic formula for
the spectral function as lambda tends to plus infinity. We then restrict our
study to the case when m=2, n=3, the operator is differential and has
trace-free principal symbol, and address the question: is our operator a
massless Dirac operator? We prove that it is a massless Dirac operator if and
only if the following two conditions are satisfied at every point of the
manifold: a) the subprincipal symbol is proportional to the identity matrix and
b) the second asymptotic coefficient of the spectral function is zero.


  We investigate the interplay between spatial anisotropy and further exchange
interactions in the spin-$\frac{1}{2}$ Heisenberg antiferromagnetic model on a
triangular lattice. We use the Schwinger boson theory by including Gaussian
fluctuations above the mean-field approach. The phase diagram exhibits a strong
reduction of the long range collinear and incommensurate spirals regions with
respect to the mean-field ones. This reduction is accompanied by the emergence
of its short range order counterparts, leaving an ample room for $0$-flux and
nematic spin liquid regions. Remarkably, within the neighborhood of the
spatially isotropic line, there is a range where the spirals are so fragile
that only the commensurate $120^{\circ}$ N\'eel ones survive. The good
agreement with recent variational Monte Carlo predictions gives support to the
rich phase diagram induced by spatial anisotropy.


  The sensitivity of the SKA enables a number of tests of theories of gravity.
A Galactic Census of pulsars will discover most of the active pulsars in the
Galaxy beamed toward us. In this census will almost certainly be pulsar-black
hole binaries as well as pulsars orbiting the super-massive black hole in the
Galactic centre. These systems are unique in their capability to probe the
ultra-strong field limit of relativistic gravity. These measurements can be
used to test the Cosmic Censorship Conjecture and the No-Hair theorem.
  The large number of millisecond pulsars discovered with the SKA will also
provide a dense array of precision clocks on the sky. These clocks will act as
the multiple arms of a huge gravitational wave detector, which can be used to
detect and measure the stochastic cosmological gravitational wave background
that is expected from a number of sources.


  As a baryon number violating process with $\Delta B=2$, neutron-antineutron
oscillation ($n\to\bar n$) provides a unique test of baryon number
conservation. We have performed a search for $n\to\bar n$ oscillation with
bound neutrons in Super-Kamiokande, with the full data set from its first four
run periods, representing an exposure of 0.37~Mton-years. The search used a
multivariate analysis trained on simulated $n\to\bar n$ events and atmospheric
neutrino backgrounds and resulted in 11 candidate events with an expected
background of 9.3 events. In the absence of statistically significant excess,
we derived a lower limit on $\bar n$ appearance lifetime in $^{16}$O nuclei of
$3.6\times{10}^{32}$ years and on the neutron-antineutron oscillation time of
$\tau_{n\to\bar n} > 4.7\times10^{8}$~s at 90\% C.L..


  We study the transmission properties of a nonlinear periodic structure
containing alternating slabs of a nonlinear right handed material and a linear
left handed material. We find that the transmission associated with the zero
averaged- refractive- index gap exhibits a bistable characteristic that is
relatively insensitive to incident angle. This is in contrast to the nonlinear
behavior of the usual Bragg gap


  The preliminary detection of the Galactic Center black hole Sgr A* in X-rays
by the Chandra mission, as well as recent mm-VLBI measurements, impose strict
constraints on this source. Using a relativistic jet model for Sgr A*, we
calculate the synchrotron and synchrotron self-Compton emission. The predicted
spectrum provides an excellent fit to the radio spectrum and the the X-ray
observations. Limits on the infrared flux and the low X-ray flux require a
high-energy cut-off in the electron spectrum at gamma_e ~< 100. The implied
lack of a significant power-law tail of high-energy electrons also suppresses
the appearance of the extended, optically thin radio emission usually seen in
astrophysical jets. The jet therefore appears rather compact and naturally
satisfies current VLBI limits. The initial parameters of the model are tightly
constrained by the radio spectrum and the "submm-bump" in particular. While the
jet most likely is coupled to some kind of accretion flow, we suggest that the
most visible signatures can be produced by this outflow. If SSC emission from
the jet contributes to the Sgr A* spectrum, significant variability in X-rays
would be expected. The model could be generic for other low-luminosity AGN or
even X-ray binaries.


  We give formulas for the Bruce-Roberts number $\mu_{BR}(f,X)$ and its
relative version $\mu_{BR}^{-}(f,X)$ of a function $f$ with respect to an ICIS
$(X,0)$. We show that $\mu_{BR}^{-}(f,X)=\mu(f^{-1}(0)\cap
X,0)+\mu(X,0)-\tau(X,0)$, where $\mu$ and $\tau$ are the Milnor and Tjurina
numbers, respectively, of the ICIS. The formula for $\mu_{BR}(f,X)$ is more
complicated and also involves $\mu(f)$ and some lengths in terms of the ideals
$I_X$ and $Jf$. We also consider the logarithmic characteristic variety,
$LC(X)$, and its relative version, $LC(X)^{-}$. We show that $LC(X)^{-}$ is
Cohen-Macaulay and that $LC(X)$ is Cohen-Macaulay at any point not in
$X\times\{0\}$. We generalize previous results presented by the authors when
$(X,0)$ has codimension one and by Bruce and Roberts when it is weighted
homogeneous of any codimension.


  Non-orthogonal multiple access (NOMA) is potentially capable of circumventing
the limitations of the classic orthogonal multiple access schemes, hence it has
recently received significant research attention both in industry and academia.
This article is focused on exploiting multiple antenna techniques in NOMA
networks, with an emphasis on investigating the rate region of multiple-input
multiple-output (MIMO)-NOMA, whist reviewing two popular multiple antennas
aided NOMA structures, as well as underlining resource management problems of
both single-carrier and multi-carrier MIMO-NOMA networks. This article also
points out several effective methods of tackling the practical implementation
constraints of multiple antenna NOMA networks. Finally, some promising open
research directions are provided in context of multiple antenna aided NOMA.


  The magnetization rotation transition occurs in the itinerant ferromagnet
URhGe when the field about 12T is applied in direction perpendicular to
spontaneous magnetization in the plane of the smallest magnetic anisotropy
energy.The transition is accompanied by the maximum of resistivity in the
normal state and by reentrance of superconductivity at lower temperatures in
the field interval between 8 and 13 Tesla [F.Levy et al, Science, to be
published (2005)].
  We discuss the magnetization orientation transition and the modification of
triplet pairing superconducting state coexisting with ferromagnetism up to the
fields about 2 Tesla and then reappearing in the broad vicinity of the
transition.
  The nonsymmorphic space group crystal symmetry of ferromagnetic URhGe allows
existance of antiferromagnetic ordering of magnetic moments of pairs of uranium
atoms along a-axis. We show that the amplitude of this weak antiferromagnetic
ordering increases below the phase transition into superconducting state due to
Cooper pairs spontaneous magnetism.


  The exploration of nontrivial transport phenomena associated with the
interplay between magnetic order and spin-orbit coupling (SOC), particularly in
van der Waals (vdW) systems has gained a resurgence of interest due to their
easy exfoliation, ideal for two-dimensional (2D) spintronics. We report the
near room temperature quasi-2D ferromagnet, Fe$_4$GeTe$_2$ from the iron-based
vdW family (Fe$_n$GeTe$_2$, $n$=3,4,5), exhibiting a large anomalous Hall
conductivity (AHC), $\sigma^A_{xy}$ $\sim$ 490 $\Omega^{-1}\textrm{cm}^{-1}$ at
2 K. The near quadratic behavior of anomalous Hall resistivity
($\rho^{A}_{xy}$) with the longitudinal resistivity ($\rho_{xx}$) suggests that
a dominant AHC contribution is coming from an intrinsic Berry curvature (BC)
mechanism. Concomitantly, the electronic structure calculations reveal a large
BC arising from SOC induced gaped nodal lines around the Fermi level, governing
such large AHC property. Moreover, we also report an exceptionally large
anomalous Hall angle ($\simeq$ 10.6\%) and Hall factor ($\simeq$ 0.22 V$^{-1}$)
values which so far, are the largest in compared to those for other members in
this vdW family.


  Improvements in data acquisition and processing techniques have lead to an
almost continuous flow of information for financial data. High resolution tick
data are available and can be quite conveniently described by a continuous time
process. It is therefore natural to ask for possible extensions of financial
time series models to a functional setup. In this paper we propose a functional
version of the popular ARCH model. We will establish conditions for the
existence of a strictly stationary solution, derive weak dependence and moment
conditions, show consistency of the estimators and perform a small empirical
study demonstrating how our model matches with real data.


  We present a high density disc reflection spectral analysis of a sample of 17
Seyfert 1 galaxies to study the inner disc densities at different black hole
mass scales and accretion rates. All the available XMM-Newton observations in
the archive are used. OM observations in the optical/UV band are used to
estimate their accretion rates. We find that 65% of sources in our sample show
a disc density significantly higher than 1e15 cm^{-3}, which was assumed in
previous reflection-based spectral analyses. The best-fit disc densities show
an anti-correlation with black hole mass and mass accretion rate. High density
disc reflection model can successfully explain the soft excess emission and
significantly reduce inferred iron abundances. We also compare our black hole
spin and disc inclination angle measurements with previous analyses.


  Large language models (LLMs) trained on a substantial corpus of human
knowledge and literature productively work with a large array of facts from
that corpus. Surprisingly, they are also able to re-create the behaviors of
personae that are captured within the corpus. By forming teams of simulated
personae, supplying contexts that set the stage, and providing gentle prompts,
one can move through scenarios that elicit expert behavior to perform
meaningful cognitive work. The power of this strategy is demonstrated with two
examples, one attacking factuality of LLM responses and the other reproducing a
very recently published result in quantum optics.


  Linear feature extraction at the presence of nonlinear dependencies among the
data is a fundamental challenge in unsupervised learning. We propose using a
probabilistic Gram-Schmidt (GS) type orthogonalization process in order to
detect and map out redundant dimensions. Specifically, by applying the GS
process over a family of functions which presumably captures the nonlinear
dependencies in the data, we construct a series of covariance matrices that can
either be used to identify new large-variance directions, or to remove those
dependencies from the principal components. In the former case, we provide
information-theoretic guarantees in terms of entropy reduction. In the latter,
we prove that under certain assumptions the resulting algorithms detect and
remove nonlinear dependencies whenever those dependencies lie in the linear
span of the chosen function family. Both proposed methods extract linear
features from the data while removing nonlinear redundancies. We provide
simulation results on synthetic and real-world datasets which show improved
performance over PCA and state-of-the-art linear feature extraction algorithms,
both in terms of variance maximization of the extracted features, and in terms
of improved performance of classification algorithms. Additionally, our methods
are comparable and often outperform the non-linear method of kernel PCA.


  Recently Pasetto et al. have proposed a new method to derive a convection
theory appropriate for the implementation in stellar evolution codes. Their
approach is based on the simple physical picture of spherical bubbles moving
within a potential flow in dynamically unstable regions, and a detailed
computation of the bubble dynamics. Based on this approach the authors derive a
new theory of convection which is claimed to be parameter free, non-local and
time-dependent. This is a very strong claim, as such a theory is the holy grail
of stellar physics.
  Unfortunately we have identified several distinct problems in the derivation
which ultimately render their theory inapplicable to any physical regime. In
addition we show that the framework of spherical bubbles in potential flows is
unable to capture the essence of stellar convection, even when equations are
derived correctly.


  We study the nature of the ground state of the strongly-coupled two
dimensional extended boson Hubbard model on a square lattice. We demonstrate
that strong but finite on-site interaction U along with a comparable
nearest-neighbor repulsion V result in a thermodynamically stable supersolid
ground state just above half-filling, and that the checker-board crystal is
unstable for smaller V, and for any V just below half-filling. The interplay
between these two interaction energies results in a rich phase diagram which is
studied in detail using quantum Monte Carlo methods.


  We present an independent estimate of the interstellar extinction law for the
Spitzer IRAC bands as well as a first attempt at extending the law to the
24micron MIPS band. The source data for these measurements are observations of
five nearby star-forming regions: the Orion A cloud, NGC 2068/71, NGC 2024/23,
Serpens and Ophiuchus. Color excess ratios E(H-Ks)/E(Ks-[lambda]) were measured
for stars without infrared excess dust emission from circumstellar
disks/envelopes.
  For four of these five regions, the extinction laws are similar at all
wavelengths and differ systematically from a previous determination of the
extinction law, which was dominated by the diffuse ISM, derived for the IRAC
bands. This difference could be due to the difference in the dust properties of
the dense molecular clouds observed here and those of the diffuse ISM. The
extinction law at longer wavelengths toward the Ophiuchus region lies between
that to the other four regions studied here and that for the ISM. In addition,
we extended our extinction law determination to 24micron for Serpens and NGC
2068/71 using Spitzer MIPS data. We compare these results against several ISO
extinction law determinations, although in each case there are assumptions
which make absolute comparison uncertain. However, our work confirms a
relatively flatter extinction curve from 4 - 8micron than the previously
assumed standard, as noted by all of these recent studies. The extinction law
at 24micron is consistent with previous measurements and models, although there
are relatively large uncertainties.


  We prove a strong form of the comparison principle for the elliptic
Monge-Ampere equation, with a Dirichlet boundary condition interpreted in the
viscosity sense. This comparison principle is valid when the equation admits a
Lipschitz continuous weak solution. The result is tight, as demonstrated by
examples in which the strong comparison principle fails in the absence of
Lipschitz continuity. This form of comparison principle closes a significant
gap in the convergence analysis of many existing numerical methods for the
Monge-Ampere equation. An important corollary is that any consistent, monotone,
stable approximation of the Dirichlet problem for the Monge-Ampere equation
will converge to the viscosity solution.


  The 2 nu double beta decay half-lives of six nuclei, whose decays were
previously reported as theoretically forbidden, are calculated by including the
pairing interaction, which mixes different occupations and opens up the
possibility of the decay. All allowed channels for the 0 nu double beta decay
are also computed. The estimated 2 nu double beta half-lives suggest that
measurements in 244Pu may find positive signals, and that planned experiments
would succeed in detecting the 2 nu double beta decay in 160Gd. Limits for the
zero neutrino mode, in the analyzed deformed emitters, are predicted.


  Let M be an orientable hyperbolic surface without boundary and let $\gamma$
be a closed geodesic in M. We prove that any side of any triangle formed by
distinct lifts of $\gamma$ in H2 is shorter than $\gamma$.


  We obtain systematic approximations for the modes of vibration of a string of
variable density, which is held fixed at its ends. These approximations are
obtained iteratively applying three theorems which are proved in the paper and
which hold regardless of the inhomogeneity of the string. Working on specific
examples we obtain very accurate approximations which are compared both with
the results of WKB method and with the numerical results obtained with a
collocation approach. Finally, we show that the asymptotic behaviour of the
energies of the string obtained with perturbation theory, worked to second
order in the inhomogeinities, agrees with that obtained with the WKB method and
implies a different functional dependence on the density that in two and higher
dimensions.


  Trustworthy language models should abstain from answering questions when they
do not know the answer. However, the answer to a question can be unknown for a
variety of reasons. Prior research has focused on the case in which the
question is clear and the answer is unambiguous but possibly unknown, but the
answer to a question can also be unclear due to uncertainty of the questioner's
intent or context. We investigate question answering from this perspective,
focusing on answering a subset of questions with a high degree of accuracy,
from a set of questions in which many are inherently ambiguous. In this
setting, we find that the most reliable approach to decide when to abstain
involves quantifying repetition within sampled model outputs, rather than the
model's likelihood or self-verification as used in prior work. We find this to
be the case across different types of uncertainty and model scales,and with or
without instruction tuning. Our results suggest that sampling-based confidence
scores help calibrate answers to relatively unambiguous questions, with more
dramatic improvements on ambiguous questions.


  The COVID-19 pandemic, which began in December 2019, progressed in a
complicated manner and thus caused problems worldwide. Seeking clues to the
reasons for the complicated progression is necessary but challenging in the
fight against the pandemic. We sought clues by investigating the relationship
between reactions on social media and the COVID-19 epidemic in Japan. Twitter
was selected as the social media platform for study because it has a large user
base in Japan and because it quickly propagates short topic-focused messages
("tweets"). Analysis using Japanese Twitter data suggests that reactions on
social media and the progression of the COVID-19 pandemic may have a close
relationship. Experiments to evaluate the potential of using tweets to support
the prediction of how an epidemic will progress demonstrated the value of using
epidemic-related social media data. Our findings provide insights into the
relationship between user reactions on social media, particularly Twitter, and
epidemic progression, which can be used to fight pandemics.


  Bounds for the maximal degree of certain Gr\"obner bases of simplicial toric
ideals are given. These bounds are close to the bound stated in Eisenbud-Goto's
Conjecture on the Castelnuovo-Mumford regularity.


  In this work, I discuss how Large Language Models can be applied in the legal
domain, circumventing their current drawbacks. Despite their large success and
acceptance, their lack of explainability hinders legal experts to trust in
their output, and this happens rightfully so. However, in this paper, I argue
in favor of a new view, Justifiable Artificial Intelligence, instead of
focusing on Explainable Artificial Intelligence. I discuss in this paper how
gaining evidence for and against a Large Language Model's output may make their
generated texts more trustworthy - or hold them accountable for misinformation.


  Magnetic skyrmion, a topological magnetic domain with complex non-coplanar
spin texture, appears a disk-like structure in two dimensions. Exploring
three-dimensional spin texture and related chirality switching has drawn
enormous interests from the perspective of fundamental research. Here, the
three-dimensional magnetic moment of the skyrmion bubbles in centrosymmetric
Mn-Ni-Ga were reconstructed with the vector field tomography approach via
Lorentz transmission electron microscopy. The type of the bubbles was
determined from investigating the magnetic vectors in entire space. We found
that the bubbles switched their chirality easily but still keep the polarity to
remain the singularity of the bubbles within the material. Our results offer
valuable insights into the fundamental mechanisms underlying the spin chirality
flips dynamics of skyrmion bubbles.


  In this manuscript we present a novel and efficient numerical method for the
compressible viscous and resistive MHD equations for all Mach number regimes.
The time-integration strategy is a semi-implicit splitting, combined with a
hybrid finite-volume and finite-element (FE) discretization in space. The
non-linear convection is solved by a robust explicit FV scheme, while the
magneto-acoustic terms are treated implicitly in time. The resulting CFL
stability condition depends only on the fluid velocity, and not on the
Alfv\'enic and acoustic modes. The magneto-acoustic terms are discretized by
compatible FE based on a continuous and a discrete de Rham complexes designed
using Finite Element Exterior Calculus (FEEC). Thanks to the use of FEEC,
energy stability, magnetic-helicity conservation and the divergence-free
conditions can be preserved also at the discrete level. A very efficient
splitting approach is used to separate the acoustic and the Alfv\'enic modes in
such a fashion that the original symmetries of the PDE governing equations are
preserved. In this way, the algorithm relies on the solution of linear,
symmetric and positive-definite algebraic systems, that are very efficiently
handled by the simple matrix-free conjugate-gradient method. The resulting
algorithm showed to be robust and accurate in low and high Mach regimes even at
large Courant numbers. Non-trivial tests are solved in one-, two- and three-
space dimensions to confirm the robustness, accuracy, and the low-dissipative
and conserving properties of the final algorithm. While the formulation of the
method is very general, numerical results for a second-order accurate FV-FE
scheme will be presented.


  We explore scenarios in which the graviton is not a fundamental degree of
freedom at short distances but merely emerges as an effective degree of freedom
at long distances. In general, the scale of such graviton `compositeness',
Lambda_g, can only be probed by measuring gravitational forces at short
distances, which becomes increasingly difficult and eventually impossible as
the distance is reduced. Here, however, we point out that if supersymmetry is
an underlying symmetry, the gravitino can be used as an alternative probe to
place a limit on Lambda_g in a collider environment, by demonstrating that
there is a model-independent relation, Lambda_g > m_{3/2}. In other words, the
gravitino knows that gravity is standard at least down to its Compton
wavelength, so this can also be viewed as a test of general relativity possible
at very short distances. If composite gravity is found first at some Lambda_g,
this would imply a model-independent upper bound on m_{3/2}.


  Interfacial interactions are crucial in a variety of fields and can greatly
affect the electric, magnetic, and chemical properties of materials. Among
them, interface orbital hybridization plays a fundamental role in the
properties of surface electrons such as dispersion, interaction, and ground
states. Conventional measurements of electronic states at interfaces such as
scanning tunneling microscopes are all based on electric interactions which,
however, suffer from strong perturbation on these electrons. Here we unveil a
new experimental detection of interface electrons based on the weak magnetic
interactions between them and the nitrogen-vacancy (NV) center in diamond. With
negligible perturbation on the interface electrons, their physical properties
can be revealed by the NV spin coherence time. In our system, the interface
interaction leads to significant decreases in both the density and coherence
time of the electron spins at the diamond-graphene interface. Furthermore,
together with electron spin resonance spectra and first-principle calculations,
we can retrieve the effect of interface electron orbital hybridization. Our
study opens a new pathway toward the microscopic probing of interfacial
electronic states with weak magnetic interactions and provides a new avenue for
future research on material interfaces.


  We show the following algebraicity result for a complex projective variety
$X$ with big representation of $\pi_1$ into a semi-simple algebraic group:
There exists a proper subvariety $Z \subset X$ such that for any algebraic
curve $C$, any holomorphic map $\gamma:\, C \to X$ with $\gamma(C) \not\subset
Z$ is induced from an algebraic morphism. As an application, we prove
pseudo-Brody hyperbolicity of certain varieties with big reductive
representations of $\pi_1$.


  The advance of image editing techniques allows users to create artistic
works, but the manipulated regions may be incompatible with the background.
Localizing the inharmonious region is an appealing yet challenging task.
Realizing that this task requires effective aggregation of multi-scale
contextual information and suppression of redundant information, we design
novel Bi-directional Feature Integration (BFI) block and Global-context Guided
Decoder (GGD) block to fuse multi-scale features in the encoder and decoder
respectively. We also employ Mask-guided Dual Attention (MDA) block between the
encoder and decoder to suppress the redundant information. Experiments on the
image harmonization dataset demonstrate that our method achieves competitive
performance for inharmonious region localization. The source code is available
at https://github.com/bcmi/DIRL.


  Visual speech recognition aims to identify the sequence of phonemes from
continuous speech. Unlike the traditional approach of using 2D image feature
extraction methods to derive features of each video frame separately, this
paper proposes a new approach using a 3D (spatio-temporal) Discrete Cosine
Transform to extract features of each feasible sub-sequence of an input video
which are subsequently classified individually using Support Vector Machines
and combined to find the most likely phoneme sequence using a tailor-made
Hidden Markov Model. The algorithm is trained and tested on the VidTimit
database to recognise sequences of phonemes as well as visemes (visual speech
units). Furthermore, the system is extended with the training on phoneme or
viseme pairs (biphones) to counteract the human speech ambiguity of
co-articulation. The test set accuracy for the recognition of phoneme sequences
is 20%, and the accuracy of viseme sequences is 39%. Both results improve the
best values reported in other papers by approximately 2%. The contribution of
the result is three-fold: Firstly, this paper is the first to show that 3D
feature extraction methods can be applied to continuous sequence recognition
tasks despite the unknown start positions and durations of each phoneme.
Secondly, the result confirms that 3D feature extraction methods improve the
accuracy compared to 2D features extraction methods. Thirdly, the paper is the
first to specifically compare an otherwise identical method with and without
using biphones, verifying that the usage of biphones has a positive impact on
the result.


  We show that Bunce-Deddens algebras, which are AT-algebras, are also limits
of circle algebras for Rieffel's quantum Gromov-Hausdorff distance, and
moreover, form a continuous family indexed by the Baire space. To this end, we
endow Bunce-Deddens algebras with a quantum metric structure, a step which
requires that we reconcile the constructions of the Latremoliere's
Gromov-Hausdorff propinquity and Rieffel's quantum Gromov-Hausdorff distance
when working on order-unit quantum metric spaces. This work thus continues the
study of the connection between inductive limits and metric limits.


  The cosmic ray spectrum has been shown to extend well beyond 10^20 eV. With
nearly 20 events observed in the last 40 years, it is now established that
particles are accelerated or produced in the universe with energy near 10^21
eV. In all production models neutrinos and photons are part of the cosmic ray
flux. In acceleration models (bottom-up models), they are produced as
secondaries of the possible interactions of the accelerated charged particle,
in direct production models (top-down models) they are a dominant fraction of
the decay chain. In addition, hadrons above the GZK threshold energy will also
produce, along their path in the Universe, neutrinos and photons as secondaries
of the pion photo-production processes. Therefore, photons and in particular
neutrinos, are very distinctive signatures of the nature and distribution of
the potential sources of ultra high energy cosmic rays. In the following we
expose the identification capabilities of the Auger observatories. In the
hypothesis of nu_mu-->nu_tau oscillations with full mixing, special emphasis is
placed on the observation of tau neutrinos, with which Auger is able to
establish the GZK cutoff as well as to provide a strong and model independant
constraint on the top-down sources of ultra high energy cosmic rays.


  Using existing classification results for the 7- and 8-cycles in the pancake
graph, we determine the number of permutations that require 4 pancake flips
(prefix reversals) to be sorted. A similar characterization of the 8-cycles in
the burnt pancake graph, due to the authors, is used to derive a formula for
the number of signed permutations requiring 4 (burnt) pancake flips to be
sorted. We furthermore provide an analogous characterization of the 9-cycles in
the burnt pancake graph. Finally we present numerical evidence that polynomial
formulae exist giving the number of signed permutations that require $k$ flips
to be sorted, with $5\leq k\leq9$.


  We propose a novel diffusion map particle system (DMPS) for generative
modeling, based on diffusion maps and Laplacian-adjusted Wasserstein gradient
descent (LAWGD). Diffusion maps are used to approximate the generator of the
corresponding Langevin diffusion process from samples, and hence to learn the
underlying data-generating manifold. On the other hand, LAWGD enables efficient
sampling from the target distribution given a suitable choice of kernel, which
we construct here via a spectral approximation of the generator, computed with
diffusion maps. Our method requires no offline training and minimal tuning, and
can outperform other approaches on data sets of moderate dimension.


  As a new type of self-healing material, room-temperature liquid metal (LM)
composed of Ga, In and Sn is a promising anode in lithium-ion batteries (LIBs).
It is difficult to directly prepare an electrode slurry with pure LM. Here, the
LM electrode slurry was successfully prepared by simple high-speed stirring
method. The LM in the slurry was evenly distributed in the form of liquid
particles (average size 100 {\mu}m) and no aggregation occurred. The initial
discharge specific capacity of LM is 1148 mAh g-1, and the stable discharge
specific capacity is 350 mAh g-1. Cyclic voltammetry measurements show that
three pairs of obvious reduction peaks and oxidation occur in LM anodes at 0.37
V,0.67 V,1.02 V and 0.72 V,0.79 V,0.97 V. In the process of lithium insertion,
the LM undergoes a liquid-solid phase transition, and when it is delithiated,
it will be converted into a liquid phase. The SEI film consumed active lithium
and electrolyte during the long cycle, resulting in loss of reversible
capacity.


  Inspired by a recent paper of Garcia, Stichtenoth and Xing [2000, Compositio
Math. 120, 137--170], we investigate the quotient curves of the Deligne-Lusztig
curve associated to the Suzuki group.


  In this paper, we prove the boundedness of all the solutions for the equation
$\ddot{x}+n^2x+g(x)+\psi'(x)=p(t)$ with the Lazer-Leach condition on $g$ and
$p$, where $n\in \mathbb{N^+}$, $p(t)$ and $\psi'(x)$ are periodic and $g(x)$
is bounded. For the critical situation that $\big |\int_0^{2\pi}p(t)e^{int}dt
\big|=2\big|g(+\infty)-g(-\infty)\big|$, we also prove a sufficient and
necessary condition for the boundedness if $\psi'(x)\equiv0$.


  We propose a novel experimental method to produce and detect weakly
interacting light vector bosons using coherent processes in refractive media. A
light vector boson would be produced by a laser photon scattered at a plane
interface between two media of different dielectric properties and will be
converted back to photon in the similar scattering process. The effect depends
strongly on the indices of refraction of the two media. If incident and
recovered photons were traveling through extremely high vacuums, limits on the
existence of several light vector bosons could be substantially improved.


  We investigate the ionic Hubbard model (IHM) at half-filling in the limit of
strong correlations and large ionic potential. The low energy effective
Hamiltonian in this limit, obtained by a similarity transformation, is a
modified $t-J$ model with effective second neighbour hopping terms. We explore
the possibilities of d-wave pairing and extended s-wave pairing superconducting
(SC) phases on a two dimensional square lattice at zero temperature within a
Gutzwiller projected renormalized mean field theory. In the sector of solutions
that forbid spin ordering, the system shows a finite non-zero d-wave as well as
extended s-wave pairing amplitude for $\Delta \sim U \gg t$. The width of the
superconducting phase in $U-\Delta$ regime shrinks with increase in $U$ and
$\Delta$, though the extended s-wave pairing phase is higher in energy than the
d-wave pairing superconducting phase. But in a spin resolved renormalized mean
field calculation, which allows for an antiferromagnetic (AF) order along with
the d-wave or extended s-wave pairing, the SC phase is no longer viable and the
system shows a direct transition from an AF ordered phase to a paramagnetic
band insulator. Except for a thin sliver of a half-metallic AF phase close to
the AF transition point, most of the AF ordered phase is a Mott insulator. We
benchmarked the AF Mott insulator to band insulator transition within the
Gutzwiller projected renormalized mean field theory against the dynamical mean
field theory (DMFT) solved using continuous time quantum Monte-Carlo (CTQMC).
Our work suggests that the ground state phase diagram of the IHM at
half-filling in the limit of extreme correlations does not have any SC phase.
The SC phase seen in the paramagnetic sector is a metastable phase, being
higher in energy than the AF Mott insulator phase.


  We revisit mean-risk portfolio selection in a one-period financial market
where risk is quantified by a positively homogeneous risk measure $\rho$. We
first show that under mild assumptions, the set of optimal portfolios for a
fixed return is nonempty and compact. However, unlike in classical
mean-variance portfolio selection, it can happen that no efficient portfolios
exist. We call this situation $\rho$-arbitrage, and prove that it cannot be
excluded -- unless $\rho$ is as conservative as the worst-case risk measure.
  After providing a primal characterisation of $\rho$-arbitrage, we focus our
attention on coherent risk measures that admit a dual representation and give a
necessary and sufficient dual characterisation of $\rho$-arbitrage. We show
that the absence of $\rho$-arbitrage is intimately linked to the interplay
between the set of equivalent martingale measures (EMMs) for the discounted
risky assets and the set of absolutely continuous measures in the dual
representation of $\rho$. A special case of our result shows that the market
does not admit $\rho$-arbitrage for Expected Shortfall at level $\alpha$ if and
only if there exists an EMM $\mathbb{Q} \approx \mathbb{P}$ such that $\Vert
\frac{\text{d}\mathbb{Q}}{\text{d}\mathbb{P}} \Vert_\infty < \frac{1}{\alpha}$.


  The first result of our article is another proof of Mertens' third theorem in
the number field setting, which generalises a method of Hardy. The second
result concerns the sign of the error term in Mertens' third theorem. Diamond
and Pintz showed that the error term in the classical case changes sign
infinitely often and in our article, we establish this result for number fields
assuming a reasonable technical condition. In order to do so, we needed to
prove Cram\'er's inequality for number fields, which is interesting in its own
right. Lamzouri built upon Diamond and Pintz's work to prove the existence of
the logarithmic density of the set of real numbers $x \ge 2$ such that the
error term in Mertens' third theorem is positive, so the third result of our
article generalises Lamzouri's results for number fields. We also include
numerical investigations for the number fields $\mathbb{Q}(\sqrt{5})$ and
$\mathbb{Q}(\sqrt{13})$, building upon similar work done by Rubinstein and
Sarnak in the classical case.


  The work concerns relativistic effects and the influence of an external
magnetic field on the transmission coefficient. The Fowler-Nordheim equation
has been relativistically generalized and effect of the Lorentz contraction of
a potential barrier at the metal-vacuum interface has been found. Influence of
the magnetic field parallel to a metal surface on the transmission coefficient
is taken into account when cB < E.


  In the present note, we discuss a simple example of a macroscopic quantum
many-body system in which the approach to thermal equilibrium from an arbitrary
initial state in the microcanonical energy shell is proved without relying on
any unproven assumptions. The model, which is equivalent to a free fermion
chain, is designed to be a toy model for a weakly heat-conducting
one-dimensional solid. We take a phenomenological point of view and perceive
that the system is in thermal equilibrium when the measured coarse-grained
energy distribution is uniform.
  The result on thermalization reported here is a variation (and an
improvement) of our previous result on the irreversible expansion in a free
fermion chain. As far as we know, this is the first concrete and rigorous
realization of the philosophy on the foundation of equilibrium statistical
mechanics proposed by von Neumann in 1929, and further developed recently by
Goldstein, Lebowitz, Mastrodonato, Tumulka, and Zangh\`\i and the present
author, namely, to characterize thermal equilibrium from a macroscopic
viewpoint and to make use of the strong ETH to control the long-time dynamics.
  This note will be the most technical part of my longer article on
thermalization, "What is thermal equilibrium and how do we get there?". I am
making this document public at this stage since I have already announced (and
will announce) the results at some of my talks.


  This study evaluates the effectiveness of various large language models
(LLMs) in performing tasks common among undergraduate computer science
students. Although a number of research studies in the computing education
community have explored the possibility of using LLMs for a variety of tasks,
there is a lack of comprehensive research comparing different LLMs and
evaluating which LLMs are most effective for different tasks. Our research
systematically assesses some of the publicly available LLMs such as Google
Bard, ChatGPT(3.5), GitHub Copilot Chat, and Microsoft Copilot across diverse
tasks commonly encountered by undergraduate computer science students in India.
These tasks include code explanation and documentation, solving class
assignments, technical interview preparation, learning new concepts and
frameworks, and email writing. Evaluation for these tasks was carried out by
pre-final year and final year undergraduate computer science students and
provides insights into the models' strengths and limitations. This study aims
to guide students as well as instructors in selecting suitable LLMs for any
specific task and offers valuable insights on how LLMs can be used
constructively by students and instructors.


  We study a one-dimensional classical stochastic kinetically constrained model
(KCM) inspired by Rydberg atoms in their "facilitated" regime, where sites can
flip only if a single of their nearest neighbours is excited. We call this
model "XOR-FA" to distinguish it from the standard Fredrickson-Andersen (FA)
model. We describe the dynamics of the XOR-FA model, including its relation to
simple exclusion processes in its domain wall representation. The interesting
relaxation dynamics of the XOR-FA is related to the prominence of large
dynamical fluctuations that lead to phase transitions between active and
inactive dynamical phases as in other KCMs. By means of numerical tensor
network methods we study in detail such transitions in the dynamical large
deviation regime.


  We study the sunset Feynman integral defined as the scalar two-point
self-energy at two-loop order in a two dimensional space-time.
  We firstly compute the Feynman integral, for arbitrary internal masses, in
terms of the regulator of a class in the motivic cohomology of a 1-parameter
family of open elliptic curves. Using an Hodge theoretic (B-model) approach, we
show that the integral is given by a sum of elliptic dilogarithms evaluated at
the divisors determined by the punctures.
  Secondly we associate to the sunset elliptic curve a local non-compact
Calabi-Yau 3-fold, obtained as a limit of elliptically fibered compact
Calabi-Yau 3-folds. By considering the limiting mixed Hodge structure of the
Batyrev dual A-model, we arrive at an expression for the sunset Feynman
integral in terms of the local Gromov-Witten prepotential of the del Pezzo
surface of degree 6. This expression is obtained by proving a strong form of
local mirror symmetry which identifies this prepotential with the second
regulator period of the motivic cohomology class.


  The principle "Every result in classical homological algebra should have a
counterpart in Gorenstein homological algebra" is given in [3]. There is a
remarkable body of evidence supporting this claim (cf. [2] and [3]). Perhaps
one of the most glaring exceptions is provided by the fact that tensor products
of Gorenstein projective modules need not be Gorenstein projective, even over
Gorenstein rings. So perhaps it is surprising that tensor products of
Gorenstein injective modules over Gorenstein rings of finite Krull dimension
are Gorenstein injective.
  Our main result is in support of the principle. Over commutative, noetherian
rings injective modules have direct sum decompositions into indecomposable
modules. We will show that Gorenstein injective modules over Gorenstein rings
of finite Krull dimension have filtrations analogous to those provided by these
decompositions. This result will then provide us with the tools to prove that
all tensor products of Gorenstein injective modules over these rings are
Gorenstein injective.


  We perform a complete classification of two-band $\bk\cdot\mathbf{p}$
theories at band crossing points in 3D semimetals with $n$-fold rotation
symmetry and broken time-reversal symmetry. Using this classification, we show
the existence of new 3D topological semimetals characterized by
$C_{4,6}$-protected double-Weyl nodes with quadratic in-plane (along $k_{x,y}$)
dispersion or $C_6$-protected triple-Weyl nodes with cubic in-plane dispersion.
We apply this theory to the 3D ferromagnet HgCr$_2$Se$_4$ and confirm it is a
double-Weyl metal protected by $C_4$ symmetry. Furthermore, if the direction of
the ferromagnetism is shifted away from the [001]- to the [111]-axis, the
double-Weyl node splits into four single Weyl nodes, as dictated by the point
group $S_6$ of that phase. Finally, we discuss experimentally relevant effects
including splitting of multi-Weyl nodes by applying $C_n$ breaking strain and
the surface Fermi arcs in these new semimetals.


  Many real-world data can be represented as heterogeneous graphs with
different types of nodes and connections. Heterogeneous graph neural network
model aims to embed nodes or subgraphs into low-dimensional vector space for
various downstream tasks such as node classification, link prediction, etc.
Although several models were proposed recently, they either only aggregate
information from the same type of neighbors, or just indiscriminately treat
homogeneous and heterogeneous neighbors in the same way. Based on these
observations, we propose a new heterogeneous graph neural network model named
HMSG to comprehensively capture structural, semantic and attribute information
from both homogeneous and heterogeneous neighbors. Specifically, we first
decompose the heterogeneous graph into multiple metapath-based homogeneous and
heterogeneous subgraphs, and each subgraph associates specific semantic and
structural information. Then message aggregation methods are applied to each
subgraph independently, so that information can be learned in a more targeted
and efficient manner. Through a type-specific attribute transformation, node
attributes can also be transferred among different types of nodes. Finally, we
fuse information from subgraphs together to get the complete representation.
Extensive experiments on several datasets for node classification, node
clustering and link prediction tasks show that HMSG achieves the best
performance in all evaluation metrics than state-of-the-art baselines.


  Let $\alpha,\beta$ be real numbers such that $\alpha>1$ is irrational and of
finite type, and let $c$ be a real number in the range $1<c<\frac{14}{13}$. In
this paper, it is shown that there are infinitely many Piatetski-Shapiro primes
$p = \left\lfloor n^c \right\rfloor$ in the non-homogenous Beatty sequence
$\big(\left\lfloor\alpha m+\beta\right\rfloor\big)_{m=1}^\infty$.


  By means of the experimental result on the present equipartition between
background microwave radiation energy and that of the interstellar magnetic
field, and by advancing a Machian relation for the magnetic field, which,
differently than in other authors' papers, is valid for the entire spanlife of
the Universe, implying that the magnetic field depends on the inverse radius of
the Universe, we obtain a general formula such that B depends on the inverse of
R . Our estimate for Planck's magnetic field is (1/1000) times the Sabbata and
Sivaram's one. It is shown that the energy densities involved in the above
problem are dependent on the inverse square of R . For radiation, this implies,
as we show, that the total entropy of the Universe is increasing with
expansion. In particular we show that R depends on the inverse square of T,
where T is the absolute temperature, and the entropy is proportional to the 3/2
power of R .


  Reservoir Computing (RC) is a powerful computational paradigm that allows
high versatility with cheap learning. While other artificial intelligence
approaches need exhaustive resources to specify their inner workings, RC is
based on a reservoir with highly non-linear dynamics that does not require a
fine tuning of its parts. These dynamics project input signals into
high-dimensional spaces, where training linear readouts to extract input
features is vastly simplified. Thus, inexpensive learning provides very
powerful tools for decision making, controlling dynamical systems,
classification, etc. RC also facilitates solving multiple tasks in parallel,
resulting in a high throughput. Existing literature focuses on applications in
artificial intelligence and neuroscience. We review this literature from an
evolutionary perspective. RC's versatility make it a great candidate to solve
outstanding problems in biology, which raises relevant questions: Is RC as
abundant in Nature as its advantages should imply? Has it evolved? Once
evolved, can it be easily sustained? Under what circumstances? (In other words,
is RC an evolutionarily stable computing paradigm?) To tackle these issues we
introduce a conceptual morphospace that would map computational selective
pressures that could select for or against RC and other computing paradigms.
This guides a speculative discussion about the questions above and allows us to
propose a solid research line that brings together computation and evolution
with RC as a working bench.


  The limiting mass of cold white dwarfs was first calculated by E. Stoner in
an approximate model of a uniform star and was soon reduced by ~20% in papers
by S. Chandrasekhar and L. D. Landau based on an exact solution of the
equations for the stellar equilibrium. Here we examine uniform models of white
dwarfs taking general relativity effects and the influence of finite
temperature into account. Solutions are obtained in the form of finite analytic
formulas and, for masses differing by no more than ~20% from the exact
solutions, found by numerical integration of the differential equations for the
stellar equilibrium.


  We derived a new speed limit in population dynamics, which is a fundamental
limit on the evolutionary rate. By splitting the contributions of selection and
mutation to the evolutionary rate, we obtained the new bound on the speed of
arbitrary observables, named the selection bound, that can be tighter than the
conventional Cram\'{e}r--Rao bound. Remarkably, the selection bound can be much
tighter if the contribution of selection is more dominant than that of
mutation. This tightness can be geometrically characterized by the correlation
between the observable of interest and the growth rate. We also numerically
illustrate the effectiveness of the selection bound in the transient dynamics
of evolutionary processes and discuss how to test our speed limit
experimentally.


  We report two-dimensional spectroscopic analysis of massive red spiral
galaxies ($M_{*}$ $>$ 10$^{10.5}$ $M_{\odot}$) and compare them to blue spiral
and red elliptical galaxies above the same mass limit based on the public SDSS
DR15 MaNGA observations. We find that the stellar population properties of red
spiral galaxies are more similar to those of elliptical galaxies than to blue
spiral galaxies. Red spiral galaxies show a shallow mass-weighted age profile,
and they have higher stellar metallicity and Mgb/${\rm \langle Fe \rangle}$
across the whole 1.5$R_{\rm e}$ as compared to blue spirals, but all these
properties are close to those of elliptical galaxies. One scenario to explain
this is that red spirals form as remnants of very gas-rich major mergers that
happened above $z$$\sim$1.


  Let $A \in \mathbb{Z}^{m \times n}$ be an integral matrix and $a$, $b$, $c
\in \mathbb{Z}$ satisfy $a \geq b \geq c \geq 0$. The question is to recognize
whether $A$ is $\{a,b,c\}$-modular, i.e., whether the set of $n \times n$
subdeterminants of $A$ in absolute value is $\{a,b,c\}$. We will succeed in
solving this problem in polynomial time unless $A$ possesses a duplicative
relation, that is, $A$ has nonzero $n \times n$ subdeterminants $k_1$ and $k_2$
satisfying $2 \cdot |k_1| = |k_2|$. This is an extension of the well-known
recognition algorithm for totally unimodular matrices. As a consequence of our
analysis, we present a polynomial time algorithm to solve integer programs in
standard form over $\{a,b,c\}$-modular constraint matrices for any constants
$a$, $b$ and $c$.


  We present SF3D, a novel method for rapid and high-quality textured object
mesh reconstruction from a single image in just 0.5 seconds. Unlike most
existing approaches, SF3D is explicitly trained for mesh generation,
incorporating a fast UV unwrapping technique that enables swift texture
generation rather than relying on vertex colors. The method also learns to
predict material parameters and normal maps to enhance the visual quality of
the reconstructed 3D meshes. Furthermore, SF3D integrates a delighting step to
effectively remove low-frequency illumination effects, ensuring that the
reconstructed meshes can be easily used in novel illumination conditions.
Experiments demonstrate the superior performance of SF3D over the existing
techniques. Project page: https://stable-fast-3d.github.io


  In an attempt to describe the change of topological structure of pure SU(2)
gauge theory near deconfinement a renormalization group inspired method is
tested. Instead of cooling, blocking and subsequent inverse blocking is applied
to Monte Carlo configurations to capture topological features at a well-defined
scale. We check that this procedure largely conserves long range physics like
string tension. UV fluctuations and lattice artefacts are removed which
otherwise spoil topological charge density and Abelian monopole currents. We
report the behaviour of topological susceptibility and monopole current
densities across the deconfinement transition and relate the two faces of
topology to each other. First results of a cluster analysis are described.


  The Ara OB1a association is one of the closest sites where triggered star
formation is visible for multiple generations of massive stars. At about 1.3
kpc distance, it contains complex environments including cleared young
clusters, embedded infrared clusters, CO clouds with no evidence of star
formation, and clouds with evidence of ongoing star formation. In this review
we discuss the research on this region spanning the last half-century. It has
been proposed that the current configuration is the result of an expanding wave
of neutral gas set in motion between 10--40 million years ago in combination
with photoionization from the current epoch.


  Problems in econometrics, insurance, reliability engineering, and statistics
quite often rely on the assumption that certain functions are non-decreasing.
To satisfy this requirement, researchers frequently model the underlying
phenomena using parametric and semi-parametric families of functions, thus
effectively specifying the required shapes of the functions. To tackle these
problems in a non-parametric way, in this paper we suggest indices for
measuring the lack of monotonicity in functions. We investigate properties of
the indices and also offer a convenient computational technique for practical
use.


  Despite the buzz around ChatGPT's potential, empirical studies exploring its
actual utility in the classroom for learning remain scarce. This study aims to
fill this gap by analyzing the lesson plans developed by 29 pre-service
elementary teachers from a Korean university and assessing how they integrated
ChatGPT into science learning activities. We first examined how the subject
domains and teaching and learning methods/strategies were integrated with
ChatGPT in the lesson plans. We then evaluated the lesson plans using a
modified TPACK-based rubric. We further examined pre-service teachers'
perceptions and concerns about integrating ChatGPT into science learning.
Results show diverse applications of ChatGPT in different science domains.
Fourteen types of teaching and learning methods/strategies were identified in
the lesson plans. On average, the pre-service teachers' lesson plans scored
high on the modified TPACK-based rubric, indicating a reasonable envisage of
integrating ChatGPT into science learning, particularly in 'instructional
strategies & ChatGPT'. However, they scored relatively lower on exploiting
ChatGPT's functions toward its full potential compared to other aspects. The
study also identifies both appropriate and inappropriate use cases of ChatGPT
in lesson planning. Pre-service teachers anticipated ChatGPT to afford
high-quality questioning, self-directed learning, individualized learning
support, and formative assessment. Meanwhile, they also expressed concerns
about its accuracy and the risks that students may be overly dependent on
ChatGPT. They further suggested solutions to systemizing classroom dynamics
between teachers and students. The study underscores the need for more research
on the roles of generative AI in actual classroom settings and provides
insights for future AI-integrated science learning.


  Edge computing is an emerging solution to support the future Internet of
Things (IoT) applications that are delay-sensitive, processing-intensive or
that require closer intelligence. Machine intelligence and data-driven
approaches are envisioned to build future Edge-IoT systems that satisfy IoT
devices' demands for edge resources. However, significant challenges and
technical barriers exist which complicate the resource management for such
Edge-IoT systems. IoT devices running various applications can demonstrate a
wide range of behaviors in the devices' resource demand that are extremely
difficult to manage. In addition, the management of multidimensional resources
fairly and efficiently by the edge in such a setting is a challenging task. In
this paper, we develop a novel data-driven resource management framework named
BEHAVE that intelligently and fairly allocates edge resources to heterogeneous
IoT devices with consideration of their behavior of resource demand (BRD).
BEHAVE aims to holistically address the management technical barriers by: 1)
building an efficient scheme for modeling and assessment of the BRD of IoT
devices based on their resource requests and resource usage; 2) expanding a new
Rational, Fair, and Truthful Resource Allocation (RFTA) model that binds the
devices' BRD and resource allocation to achieve fair allocation and encourage
truthfulness in resource demand; and 3) developing an enhanced deep
reinforcement learning (EDRL) scheme to achieve the RFTA goals. The evaluation
results demonstrate BEHAVE's capability to analyze the IoT devices' BRD and
adjust its resource management policy accordingly.


  Stress and depression are prevalent nowadays across people of all ages due to
the quick paces of life. People use social media to express their feelings.
Thus, social media constitute a valuable form of information for the early
detection of stress and depression. Although many research works have been
introduced targeting the early recognition of stress and depression, there are
still limitations. There have been proposed multi-task learning settings, which
use depression and emotion (or figurative language) as the primary and
auxiliary tasks respectively. However, although stress is inextricably linked
with depression, researchers face these two tasks as two separate tasks. To
address these limitations, we present the first study, which exploits two
different datasets collected under different conditions, and introduce two
multitask learning frameworks, which use depression and stress as the main and
auxiliary tasks respectively. Specifically, we use a depression dataset and a
stressful dataset including stressful posts from ten subreddits of five
domains. In terms of the first approach, each post passes through a shared BERT
layer, which is updated by both tasks. Next, two separate BERT encoder layers
are exploited, which are updated by each task separately. Regarding the second
approach, it consists of shared and task-specific layers weighted by attention
fusion networks. We conduct a series of experiments and compare our approaches
with existing research initiatives, single-task learning, and transfer
learning. Experiments show multiple advantages of our approaches over
state-of-the-art ones.


  Segmentation of brain structures from magnetic resonance (MR) scans plays an
important role in the quantification of brain morphology. Since 3D deep
learning models suffer from high computational cost, 2D deep learning methods
are favored for their computational efficiency. However, existing 2D deep
learning methods are not equipped to effectively capture 3D spatial contextual
information that is needed to achieve accurate brain structure segmentation. In
order to overcome this limitation, we develop an Anatomical Context-Encoding
Network (ACEnet) to incorporate 3D spatial and anatomical contexts in 2D
convolutional neural networks (CNNs) for efficient and accurate segmentation of
brain structures from MR scans, consisting of 1) an anatomical context encoding
module to incorporate anatomical information in 2D CNNs and 2) a spatial
context encoding module to integrate 3D image information in 2D CNNs. In
addition, a skull stripping module is adopted to guide the 2D CNNs to attend to
the brain. Extensive experiments on three benchmark datasets have demonstrated
that our method achieves promising performance compared with state-of-the-art
alternative methods for brain structure segmentation in terms of both
computational efficiency and segmentation accuracy.


  In this article, we present a method for approximating affine processes on
the cone of positive Hilbert-Schmidt operators using matrix-valued affine
processes. By leveraging results from the theory on affine processes with
values in the cone of symmetric and positive semi-definite matrices, we
construct sequences of finite-rank operator-valued affine processes that
converge weakly to the target processes and provide convergence rates for their
Laplace transforms using Galerkin approximations of the associated
operator-valued generalized Riccati equations. This article not only offers a
practical approximation scheme for operator-valued affine processes with error
bounds that hold uniformly in time, but also provides a novel existence proof
for this class of affine processes with c\`adl\`ag paths, including affine
pure-jump processes with infinite variation and state-dependent jump
intensities. In addition to the theoretical significance, the results of this
paper provide useful tools for analyzing and approximating infinite-dimensional
affine stochastic covariance models that were recently introduced in
mathematical finance.


  We focus on the problem of finding an optimal strategy for a team of two
players that faces an opponent in an imperfect-information zero-sum
extensive-form game. Team members are not allowed to communicate during play
but can coordinate before the game. In that setting, it is known that the best
the team can do is sample a profile of potentially randomized strategies (one
per player) from a joint (a.k.a. correlated) probability distribution at the
beginning of the game. In this paper, we first provide new modeling results
about computing such an optimal distribution by drawing a connection to a
different literature on extensive-form correlation. Second, we provide an
algorithm that computes such an optimal distribution by only using profiles
where only one of the team members gets to randomize in each profile. We can
also cap the number of such profiles we allow in the solution. This begets an
anytime algorithm by increasing the cap. We find that often a handful of
well-chosen such profiles suffices to reach optimal utility for the team. This
enables team members to reach coordination through a relatively simple and
understandable plan. Finally, inspired by this observation and leveraging
theoretical concepts that we introduce, we develop an efficient
column-generation algorithm for finding an optimal distribution for the team.
We evaluate it on a suite of common benchmark games. It is three orders of
magnitude faster than the prior state of the art on games that the latter can
solve and it can also solve several games that were previously unsolvable.


  Metallization and dissociation are key transformations in diatomic molecules
at high densities particularly significant for modeling giant planets. Using
X-ray absorption spectroscopy and atomistic modeling, we demonstrate that in
halogens, the formation of a \textit{connected} molecular structure takes place
at pressures well below metallization. Here we show that the iodine diatomic
molecule first elongates of $\sim$0.007 \AA~up to a critical pressure of $P_c$
$\backsim$7~GPa developing bonds between molecules. Then its length
continuously decreases with pressure up to 15-20~GPa. Universal trends in
halogens are shown and allow to predict for chlorine a pressure of 42$\pm$8~GPa
for molecular bond-length reversal. Our findings tackle the molecule
invariability paradigm in diatomic molecular phases at high pressures and may
be generalized to other abundant diatomic molecules in the universe, including
hydrogen.


  This paper focuses on convex constrained optimization problems, where the
solution is subject to a convex inequality constraint. In particular, we aim at
challenging problems for which both projection into the constrained domain and
a linear optimization under the inequality constraint are time-consuming, which
render both projected gradient methods and conditional gradient methods (a.k.a.
the Frank-Wolfe algorithm) expensive. In this paper, we develop projection
reduced optimization algorithms for both smooth and non-smooth optimization
with improved convergence rates under a certain regularity condition of the
constraint function. We first present a general theory of optimization with
only one projection. Its application to smooth optimization with only one
projection yields $O(1/\epsilon)$ iteration complexity, which improves over the
$O(1/\epsilon^2)$ iteration complexity established before for non-smooth
optimization and can be further reduced under strong convexity. Then we
introduce a local error bound condition and develop faster algorithms for
non-strongly convex optimization at the price of a logarithmic number of
projections. In particular, we achieve an iteration complexity of $\widetilde
O(1/\epsilon^{2(1-\theta)})$ for non-smooth optimization and $\widetilde
O(1/\epsilon^{1-\theta})$ for smooth optimization, where $\theta\in(0,1]$
appearing the local error bound condition characterizes the functional local
growth rate around the optimal solutions. Novel applications in solving the
constrained $\ell_1$ minimization problem and a positive semi-definite
constrained distance metric learning problem demonstrate that the proposed
algorithms achieve significant speed-up compared with previous algorithms.


  Recently we have proposed models of topological field theory including
gravity in Mod. Phys. Lett. A 31 (2016) no.37, 1650213 and Phys. Rev. D 96
(2017) no.2, 024009, in order to solve the problem of the cosmological
constant. The Lagrangian densities of the models are BRS (Becchi-Rouet-Stora)
exact and therefore the models can be regarded as topological theories. In the
models, the coupling constants, including the cosmological constant, look as if
they run with the scale of the universe and its behavior is very similar to the
renormalization group. Motivated by these models, we propose new models with an
the infrared fixed point, which may correspond to the late time universe, and
an ultraviolet fixed point, which may correspond to the early universe.
Especially we construct a model with the solutions corresponding to the de
Sitter space-time both in the ultraviolet and the infrared fixed points.


  This paper proposes a joint multi-task learning algorithm to better predict
attributes in images using deep convolutional neural networks (CNN). We
consider learning binary semantic attributes through a multi-task CNN model,
where each CNN will predict one binary attribute. The multi-task learning
allows CNN models to simultaneously share visual knowledge among different
attribute categories. Each CNN will generate attribute-specific feature
representations, and then we apply multi-task learning on the features to
predict their attributes. In our multi-task framework, we propose a method to
decompose the overall model's parameters into a latent task matrix and
combination matrix. Furthermore, under-sampled classifiers can leverage shared
statistics from other classifiers to improve their performance. Natural
grouping of attributes is applied such that attributes in the same group are
encouraged to share more knowledge. Meanwhile, attributes in different groups
will generally compete with each other, and consequently share less knowledge.
We show the effectiveness of our method on two popular attribute datasets.


  We formulate an effective theory for the atom-mediated photon-photon
interactions in a two-dimensional ``photon fluid'' confined in a Fabry-Perot
resonator. With the atoms modelled by a collection of anharmonic Lorentz
oscillators, the effective interaction is evaluated to second order in the
coupling constant (the anharmonicity parameter). The interaction has the form
of a renormalized two-dimensional delta-function potential, with the
renormalization scale determined by the physical parameters of the system, such
as density of atoms and the detuning of the photons relative to the resonance
frequency of the atoms. For realistic values of the parameters, the
perturbation series has to be resummed, and the effective interaction becomes
independent of the ``bare'' strength of the anharmonic term. The resulting
expression for the non-linear Kerr susceptibility, is parametrically equal to
the one found earlier for a dilute gas of two-level atoms. Using our result for
the effective interaction parameter, we derive conditions for the formation of
a photon fluid, both for Rydberg atoms in a microwave cavity and for alkali
atoms in an optical cavity.


  We consider the problem of recovering the rank of a set of $n$ items based on
noisy pairwise comparisons. We assume the SST class as the family of generative
models. Our analysis gave sharp information theoretic upper and lower bound for
the exact requirement, which matches exactly in the parametric limit. Our tight
analysis on the algorithm induced by the moment method gave better constant in
Minimax optimal rate than ~\citet{shah2017simple} and contribute to their open
problem. The strategy we used in this work to obtain information theoretic
bounds is based on combinatorial arguments and is of independent interest.


  We consider the dynamics of the open string tachyon condensation in a
framework of the cubic fermionic String Field Theory including a non-minimal
coupling with closed string massless modes, the graviton and the dilaton.
Coupling of the open string tachyon and the dilaton is motivated by the open
String Field Theory in a linear dilaton background and the flat space-time. We
note that the dilaton gravity provides several restrictions on the tachyon
condensation and show explicitly that the influence of the dilaton on the
tachyon condensation is essential and provides a significant effect:
oscillations of the Hubble parameter and the state parameter become of a
cosmological scale. We give an estimation for the period of these oscillations
(0.1-1) Gyr and note a good agreement of this period with the observed
oscillations with a period (0.15-0.65) Gyr in a distribution of quasar spectra.


  We use the largest homogeneous sample of globular clusters (GCs), drawn from
the ACSVCS and ACSFCS, to investigate the color gradients of GC systems in 76
early-type galaxies. We find that most GC systems possess an obvious negative
gradient in g-z color (bluer outwards). For GC systems displaying color
bimodality, both metal-rich and metal-poor GC subpopulations present shallower
but significant color gradients on average, and the mean gradients of these two
subpopulations are of roughly equal strength. The FOV of ACS mainly restricts
us to measuring the inner gradients of GC systems. These gradients, however,
can introduce an aperture bias when measuring the mean colors of GC
subpopulations from relatively narrow central pointings. Inferred corrections
to previous work imply a reduced significance for the relation between the mean
color of metal-poor GCs and their host galaxy luminosity. The GC color
gradients also show a dependence with host galaxy mass where the gradiens are
weakest at the ends of the mass spectrum--in massive galaxies and dwarf
galaxies--and strongest in galaxies of intermediate mass, around a stellar mass
of M_stellar~10^10M_sun. We also measure color gradients for field stars in the
host galaxies. We find that GC color gradients are systematically steeper than
field star color gradients, but the shape of the gradient-mass relation is the
same for both. If gradients are caused by rapid dissipational collapse and
weakened by merging, these color gradients support a picture where the inner GC
systems of most intermediate-mass and massive galaxies formed early and rapidly
with the most massive galaxies having experienced greater merging. The lack of
strong gradients in the GC systems of dwarfs, which probably have not
experienced many recent major mergers, suggests that low mass halos were
inefficient at retaining and mixing metals during the epoch of GC formation.


  We study the dynamics of a bulk deterministic Floquet model, the Rule 201
synchronous one-dimensional reversible cellular automaton (RCA201). The system
corresponds to a deterministic, reversible, and discrete version of the PXP
model, whereby a site flips only if both its nearest neighbours are unexcited.
We show that the RCA201/Floquet-PXP model exhibits ballistic propagation of
interacting quasiparticles - or solitons - corresponding to the domain walls
between non-trivial three-fold vacuum states. Starting from the quasiparticle
picture, we find the exact matrix product state form of the non-equilibrium
stationary state for a range of boundary conditions, including both periodic
and stochastic. We discuss further implications of the integrability of the
model.


  We show that when the Wald-Zoupas prescription is implemented, the resulting
charges realize the BMS symmetry algebra without any 2-cocycle nor central
extension, at any cut of future null infinity. We refine the covariance
prescription for application to the charge aspects, and introduce a new aspect
for Geroch's super-momentum with better covariance properties. For the extended
BMS symmetry with singular conformal Killing vectors we find that a Wald-Zoupas
symplectic potential exists, if one is willing to modify the symplectic
structure by a corner term. The resulting algebra of Noether currents between
two arbitrary cuts is center-less. The charge algebra at a given cut has a
residual field-dependent 2-cocycle, but time-independent and non-radiative.
More precisely, super-rotation fluxes act covariantly, but super-rotation
charges act covariantly only on global translations. The take home message is
that in any situation where 2-cocycles appears in the literature, covariance
has likely been lost in the charge prescription, and that the criterium of
covariance is a powerful one to reduce ambiguities in the charges, and can be
used also for ambiguities in the charge aspects.


  Various Hamiltonian actions of loop groups $\wt G$ and of the algebra
$\text{diff}_1$ of first order differential operators in one variable are
defined on the cotangent bundle $T^*\wt G$ of a Loop Group. The moment maps
generating the $\text{diff}_1$ actions are shown to factorize through those
generating the loop group actions, thereby defining commuting diagrams of
Poisson maps to the duals of the corresponding centrally extended algebras. The
maps are then used to derive a number of infinite commuting families of
Hamiltonian flows that are nonabelian generalizations of the dispersive water
wave hierarchies. As a further application, sets of pairs of generators of the
nonabelian mKdV hierarchies are shown to give a commuting hierarchy on $T^*\wt
G$ that contain the WZW system as its first element.


  We use bounds of mixed character sums modulo a prime $p$ to estimate the
density of integer points on the hypersurface $$ f_1(x_1) + \ldots + f_n(x_n)
=a x_1^{k_1} \ldots x_n^{k_n} $$ for some polynomials $f_i \in {\mathbb Z}[X]$,
nonzero integer $a$ and positive integers $k_i$ $i=1, \ldots, n$. In the case
of $$ f_1(X) = \ldots = f_n(X) = X^2 \quad \text{and}\quad k_1 = \ldots = k_n
=1 $$ the above congruence is known as the Markoff-Hurwitz hypersurface, while
for $$ f_1(X) = \ldots = f_n(X) = X^n\quad \text{and}\quad k_1 = \ldots = k_n
=1 $$ it is known as the Dwork hypersurface. Our result is substantially
stronger than those known for general hypersurfaces.


  In this paper we propose a quantum random number generator (QRNG) which
utilizes an entangled photon pair in a Bell singlet state, and is certified
explicitly by value indefiniteness. While "true randomness" is a mathematical
impossibility, the certification by value indefiniteness ensures the quantum
random bits are incomputable in the strongest sense. This is the first QRNG
setup in which a physical principle (Kochen-Specker value indefiniteness)
guarantees that no single quantum bit produced can be classically computed
(reproduced and validated), the mathematical form of bitwise physical
unpredictability. The effects of various experimental imperfections are
discussed in detail, particularly those related to detector efficiencies,
context alignment and temporal correlations between bits. The analysis is to a
large extent relevant for the construction of any QRNG based on beam-splitters.
By measuring the two entangled photons in maximally misaligned contexts and
utilizing the fact that two rather than one bitstring are obtained, more
efficient and robust unbiasing techniques can be applied. A robust and
efficient procedure based on XORing the bitstrings together---essentially using
one as a one-time-pad for the other---is proposed to extract random bits in the
presence of experimental imperfections, as well as a more efficient
modification of the von Neumann procedure for the same task. Some open problems
are also discussed.


  For an arbitrary tree we investigate the problems of constructing a maximum
matching which minimizes or maximizes the cardinality of a maximum matching of
the graph obtained from original one by its removal and present corresponding
polynomial algorithms.


  Some time ago, we showed that a weak (linear) massless spin 2 wave could only
propagate on a Ricci-flat or Ricci-constant background: it must necessarily be
a perturbation of General Relativity. This was just the continuation of the
higher spin chain: massless $s=3/2$ also required Ricci-flatness (which is the
basis of supergravity) while $s>2$ needs Riemann flatness. This note
re-analyzes the problem in a perhaps more physical way: by considering massless
and -- only apparently -- massive small excitations and showing how their
parameters relate to the cosmological constant. We will thus prove, in a simple
physical way, the necessity, as well as the sufficiency, of the known
supergravity results.


  The near horizon geometry of general black holes in equilibrium can be
conveniently characterized in the formalism of weakly isolated horizons in the
form of the Bondi-like expansions (Krishnan B, Class.\ Quantum Grav.\ 29,
205006, 2012). While the intrinsic geometry of the Kerr-Newman black hole has
been extensively investigated in the weakly isolated horizon framework, the
off-horizon description in the Bondi-like system employed by Krishnan has not
been studied. We extend Krishnan's work by explicit, non-perturbative
construction of the Bondi-like tetrad in the full Kerr-Newman spacetime.
Namely, we construct the Bondi-like tetrad which is parallelly propagated along
a nontwisting null geodesic congruence transversal to the horizon and provide
all Newman-Penrose scalars associated with this tetrad. This work completes the
description of the Kerr-Newman spacetime in the formalism of weakly isolated
horizons and is a starting point for the investigation of deformed black holes.


  Ultrasound-modulated optical tomography (UOT) is a technique that images
optical contrast deep inside scattering media. Heterodyne holography is a
promising tool able to detect the UOT tagged photons with high efficiency. In
this work, we describe theoretically the detection of the tagged photon in
heterodyne holography based UOT, show how to filter the untagged photon, and
discuss the effect of shot noise. The discussion considers also speckle
decorrelation. We show that optimal detection sensitivity can be reached, if
the frame exposure time of the camera used to perform the holographic detection
is of the order of the decorrelation time.


  The motion of Abrikosov vortices in type-II superconductors results in a
finite resistance in the presence of an applied electric current. Elimination
or reduction of the resistance via immobilization of vortices is the "holy
grail" of superconductivity research. Common wisdom dictates that an increase
in the magnetic field escalates the loss of energy since the number of vortices
increases. Here we show that this is no longer true if the magnetic field and
the current are applied parallel to each other.Our experimental studies on the
resistive behavior of a superconducting Mo$_{0.79}$Ge$_{0.21}$ nanostrip reveal
the emergence of a dissipative state with increasing magnetic field, followed
by a pronounced resistance drop, signifying a reentrance to the superconducting
state. Large-scale simulations of the 3D time-dependent Ginzburg-Landau model
indicate that the intermediate resistive state is due to an unwinding of
twisted vortices. When the magnetic field increases, this instability is
suppressed due to a better accommodation of the vortex lattice to the pinning
configuration. Our findings show that magnetic field and geometrical
confinement can suppress the dissipation induced by vortex motion and thus
radically improve the performance of superconducting materials.


  Major search engines deploy personalized Web results to enhance users'
experience, by showing them data supposed to be relevant to their interests.
Even if this process may bring benefits to users while browsing, it also raises
concerns on the selection of the search results. In particular, users may be
unknowingly trapped by search engines in protective information bubbles, called
"filter bubbles", which can have the undesired effect of separating users from
information that does not fit their preferences. This paper moves from early
results on quantification of personalization over Google search query results.
Inspired by previous works, we have carried out some experiments consisting of
search queries performed by a battery of Google accounts with differently
prepared profiles. Matching query results, we quantify the level of
personalization, according to topics of the queries and the profile of the
accounts. This work reports initial results and it is a first step a for more
extensive investigation to measure Web search personalization.


  A few matrix-vector multiplications with random vectors are often sufficient
to obtain reasonably good estimates for the norm of a general matrix or the
trace of a symmetric positive semi-definite matrix. Several such probabilistic
estimators have been proposed and analyzed for standard Gaussian and Rademacher
random vectors. In this work, we consider the use of rank-one random vectors,
that is, Kronecker products of (smaller) Gaussian or Rademacher vectors. It is
not only cheaper to sample such vectors but it can sometimes also be much
cheaper to multiply a matrix with a rank-one vector instead of a general
vector. In this work, theoretical and numerical evidence is given that the use
of rank-one instead of unstructured random vectors still leads to good
estimates. In particular, it is shown that our rank-one estimators multiplied
with a modest constant constitute, with high probability, upper bounds of the
quantity of interest. Partial results are provided for the case of lower
bounds. The application of our techniques to condition number estimation for
matrix functions is illustrated.


  A Lie bracket defined on the linear span of the free homotopy classes of
undirected closed curves was discovered in stages passing through Thurston's
earthquake deformations, Wolpert's corresponding calculations with Hamiltonian
vector fields and Goldman's algebraic treatment of the latter leading to a Lie
bracket on the span of directed closed curves. The purpose of this work is to
deepen the understanding of the former Lie bracket which will be referred to as
the Thurston-Wolpert-Goldman Lie bracket or, briefly, the TWG bracket.
  We give a local direct geometric definition of the TWG bracket and use this
geometric point of view to prove three results: firstly, the center of the
TWG-bracket is the Lie sub algebra generated by the class of the trivial loop
and the classes of loops parallel to boundary components or punctures; secondly
the analogous result hold for the centers of the universal enveloping algebra
and of the symmetric algebra determined by the TWG Lie algebra; and thirdly, in
terms of the natural basis, the TWG bracket of two non-central curves is always
a linear combination of non-central curves. We also give a brief and more
illuminating proof of a known result, namely, the TWG bracket counts
intersection.
  We conclude by discussing substantial computer evidence suggesting an
unexpected and strong conjectural statement relating the intersection structure
of curves and the TWG bracket, namely, if the TWG bracket of two distinct
undirected curves is zero then these curve classes have disjoint
representatives.
  The main tools are basic hyperbolic geometry and Thurston's earthquake
theory.


  We discuss generic limits posed by the trap in atomic systems on the accurate
determination of critical parameters for second-order phase transitions, from
which we deduce optimal protocols to extract them. We show that under current
experimental conditions the in-situ density profiles are barely suitable for an
accurate study of critical points in the strongly correlated regime. Contrary
to recent claims, the proper analysis of time-of-fight images yields critical
parameters accurately.


  Around 1980 Connes extended the notions of geometry to the non-commutative
setting. Since then {\it non-commutative geometry} has turned into a very
active area of mathematical research. As a first non-trivial example of a
non-commutative manifold Connes discussed subalgebras of rotation algebras, the
so-called {\it non-commutative tori}. In the last two decades researchers have
unrevealed the relevance of non-commutative tori in a variety of mathematical
and physical fields. In a recent paper we have pointed out that non-commutative
tori appear very naturally in Gabor analysis. In the present paper we show that
Janssen's result on good window classes in Gabor analysis has already been
proved in a completely different context and in a very disguised form by Connes
in 1980. Our treatment relies on non-commutative analogs of Wiener's lemma for
certain subalgebras of rotation algebras by Gr\"ochenig and Leinert.


  We show that any closed $n$-dimensional manifold $(M,g)$ can be embedded by a
map constructed using the heat kernels of the connection Laplacian as well as a
maps constructed using truncated heat kernel at a certain time $t$ from a
$\delta$-net $\{q_i\}_{i=1}^{N_0}$ via a rescaling trick. Both the time $t$ and
$N_0$ are bounded in terms of the dimension, bounds on the Ricci curvature and
its derivative, the injectivity radius, and the volume. Moreover, both maps can
be made arbitrarily close to an isometry.


  New chat AI applications like ChatGPT offer an advanced understanding of
question context and memory across multi-step tasks, such that experiments can
test its deductive reasoning. This paper proposes a multi-role and multi-step
challenge, where ChatGPT plays the classic twenty-questions game but
innovatively switches roles from the questioner to the answerer. The main
empirical result establishes that this generation of chat applications can
guess random object names in fewer than twenty questions (average, 12) and
correctly guess 94% of the time across sixteen different experimental setups.
The research introduces four novel cases where the chatbot fields the
questions, asks the questions, both question-answer roles, and finally tries to
guess appropriate contextual emotions. One task that humans typically fail but
trained chat applications complete involves playing bilingual games of twenty
questions (English answers to Spanish questions). Future variations address
direct problem-solving using a similar inquisitive format to arrive at novel
outcomes deductively, such as patentable inventions or combination thinking.
Featured applications of this dialogue format include complex protein designs,
neuroscience metadata, and child development educational materials.


  We show in this letter that gravity coupled to a massless scalar field with
full cylindrical symmetry can be exactly quantized by an extension of the
techniques used in the quantization of Einstein-Rosen waves. This system
provides a useful testbed to discuss a number of issues in quantum general
relativity such as the emergence of the classical metric, microcausality, and
large quantum gravity effects. It may also provide an appropriate framework to
study gravitational critical phenomena from a quantum point of view, issues
related to black hole evaporation, and the consistent definition of test fields
and particles in quantum gravity.


  During laparoscopic surgery, context-aware assistance systems aim to
alleviate some of the difficulties the surgeon faces. To ensure that the right
information is provided at the right time, the current phase of the
intervention has to be known. Real-time locating and classification the
surgical tools currently in use are key components of both an activity-based
phase recognition and assistance generation.
  In this paper, we present an image-based approach that detects and classifies
tools during laparoscopic interventions in real-time. First, potential
instrument bounding boxes are detected using a pixel-wise random forest
segmentation. Each of these bounding boxes is then classified using a cascade
of random forest. For this, multiple features, such as histograms over hue and
saturation, gradients and SURF feature, are extracted from each detected
bounding box.
  We evaluated our approach on five different videos from two different types
of procedures. We distinguished between the four most common classes of
instruments (LigaSure, atraumatic grasper, aspirator, clip applier) and
background. Our method succesfully located up to 86% of all instruments
respectively. On manually provided bounding boxes, we achieve a instrument type
recognition rate of up to 58% and on automatically detected bounding boxes up
to 49%.
  To our knowledge, this is the first approach that allows an image-based
classification of surgical tools in a laparoscopic setting in real-time.