  It is pointed out that the traditional explanation for the observation of a
non-zero energy h nu for light in free space does not apply for the analogous
situation in dispersive media. Because the speed of light u is no longer equal
to c in this case, the key quantity, gamma = (1-u2/c2)-0.5, is finite as a
result. Since the rest energy of photons is believed to always be equal to
zero, multiplying it with gamma in analogy to the usual procedure employed in
the special theory of relativity (STR) does not produce a nonzero result for
photons in dispersive media. The experimental evidence of the Fizeau light-drag
and Cerenkov radiation phenomena indicate that the Lorentz transformation in
free space is nonetheless valid for light in dispersive media. Instead, the
energy and momentum of photons in transparent media can be obtained from
observations of the frequency, wavelength and index of refraction of the light.
A modification of the Lorentz transformation in which the observed speed of
light does appear explicitly is required, however, in order to accurately
predict the results of measurements made when the observer is at a different
gravitational potential than the object.


  Geometric transformations of the training data as well as the test data
present challenges to the use of deep neural networks to vision-based learning
tasks. In order to address this issue, we present a deep neural network model
that exhibits the desirable property of transformation-robustness. Our model,
termed RobustCaps, uses group-equivariant convolutions in an improved capsule
network model. RobustCaps uses a global context-normalised procedure in its
routing algorithm to learn transformation-invariant part-whole relationships
within image data. This learning of such relationships allows our model to
outperform both capsule and convolutional neural network baselines on
transformation-robust classification tasks. Specifically, RobustCaps achieves
state-of-the-art accuracies on CIFAR-10, FashionMNIST, and CIFAR-100 when the
images in these datasets are subjected to train and test-time rotations and
translations.


  Models of the chemical evolution of our Galaxy are extended to include radial
migration of stars and flow of gas through the disc. The models track the
production of both iron and alpha elements. A model is chosen that provides an
excellent fit to the metallicity distribution of stars in the Geneva-Copenhagen
survey (GCS) of the solar neighbourhood, and a good fit to the local Hess
diagram. The model provides a good fit to the distribution of GCS stars in the
age-metallicity plane although this plane was not used in the fitting process.
Although this model's star-formation rate is monotonic declining, its disc
naturally splits into an alpha-enhanced thick disc and a normal thin disc. In
particular the model's distribution of stars in the ([O/Fe],[Fe/H]) plane
resembles that of Galactic stars in displaying a ridge line for each disc. The
thin-disc's ridge line is entirely due to stellar migration and there is the
characteristic variation of stellar angular momentum along it that has been
noted by Haywood in survey data. Radial mixing of stellar populations with high
sigma_z from inner regions of the disc to the solar neighbourhood provides a
natural explanation of why measurements yield a steeper increase of sigma_z
with age than predicted by theory. The metallicity gradient in the ISM is
predicted to be steeper than in earlier models, but appears to be in good
agreement with data for both our Galaxy and external galaxies. The models are
inconsistent with a cutoff in the star-formation rate at low gas surface
densities. The absolute magnitude of the disc is given as a function of time in
several photometric bands, and radial colour profiles are plotted for
representative times.


  With the previous results for the analytical blowup solutions of the
N-dimensional Euler-Poisson equations, we extend the similar structure to
construct an analytical family of solutions for the isothermal Navier-Stokes
equations and pressureless Navier-Stokes equations with density-dependent
viscosity.


  Anomalies in the abundance measurements of short lived radionuclides in
meteorites indicate that the protosolar nebulae was irradiated by a large
number of energetic particles ($E\gtrsim10\,$MeV), often called solar cosmic
rays. The particle flux of the contemporary Sun cannot explain these anomalies,
but, similar to \mbox{T Tauri} stars, the young Sun was more active and
probably produced enough high energy particles. However, the stellar particle
(SP) flux of young stars is essentially unknown. We model the impact of
high-energy ionization sources on the chemistry of the circumstellar
environment (disks and envelopes). The model includes X-ray radiative transfer
and makes use of particle transport models to calculate the individual
molecular hydrogen ionization rates. We study the impact on the chemistry via
the ionization tracers HCO$^+$ and N$_2$H$^+$. We argue that spatially resolved
observations of those molecules combined with detailed models allow for
disentangling the contribution of the individual high-energy ionization sources
and to put constraints on the SP flux in young stars.


  We perform a Bayesian analysis of NANOGrav 15yr and IPTA DR2 pulsar timing
residuals and show that the recently detected stochastic gravitational-wave
background (SGWB) is compatible with a SGWB produced by bubble dynamics during
a cosmological first-order phase transition. The timing data suggests that the
phase transition would occur around QCD confinement temperature and would have
a slow rate of completion. This scenario can naturally lead to the abundant
production of primordial black holes (PBHs) with solar masses. These PBHs can
potentially be detected by current and advanced gravitational wave detectors
LIGO-Virgo-Kagra, Einstein Telescope, Cosmic Explorer, by astrometry with GAIA
and by 21-cm survey.


  We apply the bulk holographic dark energy in general 5D two-brane models. We
extract the Friedmann equation on the physical brane and we show that in the
general moving-brane case the effective 4D holographic dark energy behaves as a
quintom for a large parameter-space area of a simple solution subclass. We find
that $w_\Lambda$ was larger than -1 in the past while its present value is
$w_{\Lambda_0}\approx-1.05$, and the phantom bound $w_\Lambda=-1$ was crossed
at $z_{p}\approx0.41$, a result in agreement with observations. Such a behavior
arises naturally, without the inclusion of special fields or potential terms,
but a fine-tuning between the 4D Planck mass and the brane tension has to be
imposed.


  We present a detailed analysis of 99 optically thin C III absorption systems
at redshift, $0.2 \le z \le 0.9$ associated with neutral hydrogen column
densities in the range, $15 \le {\rm log}$ $N_{\rm H\,I}$ ($cm^{-2}$) $\le
16.2$. Using photoionization models, we infer the number density ($n_{\rm H}$),
C-abundance ($[C/H]$) and line-of-sight thickness ($L$) of these systems in the
ranges, $-3.4 \le$ log $n_{\rm H}$ (in $cm^{-3}$) $\le -1.6$, $-1.6 \le [C/H]
\le 0.4$, and 1.3 pc $\le L \le$ 10 kpc, respectively with most of the systems
having sub-kpc scale thickness. We combine the low$-z$ and previously reported
high$-z$ ($2.1\le z\le 3.3$) optically thin C III systems to study the redshift
evolution and various correlation between the derived physical parameters. We
see a significant redshift evolution in $n_{\rm H}$, $[C/H]$ and $L$. We
compare the redshift evolution of metallicity in C III systems with those of
various types of absorption systems. We find that the slope of $[C/H]$ vs. $z$
for C III absorbers is stepper compared to the redshift evolution of cosmic
metallicity of the damped \lya\ sample (DLAs) but consistent with that of
sub$-$DLAs. We find the existence of strong anti-correlation between $L$ vs.
$[C/H]$ for the combined sample with a significance level of 8.39$\sigma$. We
see evidence of two distinct $[C/H]$ branch C III populations (low$-[C/H]$
branch, $[C/H]$ $\le -1.2$ and high$-[C/H]$ branch, $[C/H]$ $> -1.2$) in the
combined C III sample when divided appropriately in the $L$ vs. $N_{\rm
C\,III}$ plane. Further studies of C III absorbers in the redshift range, $1.0
\le z \le 2.0$ is important to map the redshift evolution of these absorbers
and gain insights into the time evolution physical conditions of the
circumgalactic medium.


  We show that the resonant dipole-dipole interaction can give rise to bound
states between two and three Rydberg atoms with non-overlapping electron
clouds. The dimer and trimer states arise from avoided level crossings between
states converging to different fine structure manifolds in the limit of
separated atoms. We analyze the angular dependence of the potential wells,
characterize the quantum dynamics in these potentials and discuss methods for
their production and detection. Typical distances between the atoms are of the
order of several micrometers which can be resolved in state-of-the-art
experiments. The potential depths and typical oscillation frequencies are about
one order of magnitude larger as compared to the dimer and trimer states
investigated in [PRA $\textbf{86}$ 031401(R) (2012)] and [PRL $\textbf{111}$
233003 (2014)], respectively. We find that the dimer and trimer molecules can
be aligned with respect to the axis of a weak electric field.


  Over the last 50 years a steady stream of accounts have been written on the
separation principle of stochastic control. Even in the context of the
linear-quadratic regulator in continuous time with Gaussian white noise, subtle
difficulties arise, unexpected by many, that are often overlooked. In this
paper we propose a new framework for establishing the separation principle.
This approach takes the viewpoint that stochastic systems are well-defined maps
between sample paths rather than stochastic processes per se and allows us to
extend the separation principle to systems driven by martingales with possible
jumps. While the approach is more in line with "real-life" engineering thinking
where signals travel around the feedback loop, it is unconventional from a
probabilistic point of view in that control laws for which the feedback
equations are satisfied almost surely, and not deterministically for every
sample path, are excluded.


  The rapid spread of misinformation through social media platforms has raised
concerns regarding its impact on public opinion. While misinformation is
prevalent in other languages, the majority of research in this field has
concentrated on the English language. Hence, there is a scarcity of datasets
for other languages, including Turkish. To address this concern, we have
introduced the FCTR dataset, consisting of 3238 real-world claims. This dataset
spans multiple domains and incorporates evidence collected from three Turkish
fact-checking organizations. Additionally, we aim to assess the effectiveness
of cross-lingual transfer learning for low-resource languages, with a
particular focus on Turkish. We demonstrate in-context learning (zero-shot and
few-shot) performance of large language models in this context. The
experimental results indicate that the dataset has the potential to advance
research in the Turkish language.


  Observations of galactic BHCs made by the Compton GRO in the hard X-ray and
gamma-ray bands have significantly enhanced our knowledge of the emission
properties of these objects. Understanding these observations presents a
formidable challenge to theoretical models of the accretion flow onto the
compact object and of the physical mechanisms that generate high-energy
radiation. Here we summarize the current state of observations and theoretical
interpretation of the emission from BHCs above 20 keV.
  The all-sky monitoring capability of BATSE allows nearly continuous studies
of the high-energy emission from more than a dozen BHCs. These long-term
datasets are particularly well-suited to multi-wavelength studies. Energy
spectral evolution and/or state transitions have been observed from many of the
BHCs.
  Observations above 50 keV from OSSE demonstrate the existence of two gamma
ray spectral states that appear to be the extensions of the X-ray low/hard and
high/soft (or perhaps very high) states. The former state, the "breaking"
state, cuts off with e-folding energy ~100 keV and has its peak luminosity near
this energy. In contrast, the latter state has luminosity peaking in the soft
X-rays and an unbroken power law spectrum, even up to energies above 500 keV in
some cases.
  The breaking gamma-ray spectrum can be well modeled by Comptonization of soft
photons in a hot thermal plasma. The power-law state creates more significant
theoretical challenges. It has been suggested that in this state the high-
energy emission arises from bulk-motion Comptonization in the convergent
accretion flow from the inner edge of the accretion disk.


  In this study, to perform the robotic stroke motions following the shape of
the human back similar to the stroke motions by humans, in contrast to the
conventional robotic stroke motion with a linear trajectory, we propose a
trajectory generation method for a robotic stroke motion following the shape of
the human back. We confirmed that the accuracy of the method's trajectory was
close to that of the actual stroking motion by a human. Furthermore, we
conducted a subjective experiment to evaluate the psychological effects of the
proposed stroke motion in contrast to those of the conventional stroke motion
with a linear trajectory. The experimental results showed that the actual
stroke motion following the shape of the human back tended to evoke more
pleasant and active feelings than the conventional stroke motion.


  We investigate the quantum-state transfer on spin-chian channels with random
imperfections.Through combining the advantages of two known schemes, the
dual-rail spin-chain channels[9] and the particular ihhomogenous spin-chain
channel[10], we propose a protocol that can avoid the quantum noises introduced
by many unnecessary measurements and can enhance the anti-decoherence ability.
The results show that our protocol is more efficient to transfer an arbitrary
quantum state than the original one. In particular, we discuss the effects of
couplings fluctuations and imperfect initialization on both of the improved
scheme and original one.


  Neural language models (LMs) based on recurrent neural networks (RNN) are
some of the most successful word and character-level LMs. Why do they work so
well, in particular better than linear neural LMs? Possible explanations are
that RNNs have an implicitly better regularization or that RNNs have a higher
capacity for storing patterns due to their nonlinearities or both. Here we
argue for the first explanation in the limit of little training data and the
second explanation for large amounts of text data. We show state-of-the-art
performance on the popular and small Penn dataset when RNN LMs are regularized
with random dropout. Nonetheless, we show even better performance from a
simplified, much less expressive linear RNN model without off-diagonal entries
in the recurrent matrix. We call this model an impulse-response LM (IRLM).
Using random dropout, column normalization and annealed learning rates, IRLMs
develop neurons that keep a memory of up to 50 words in the past and achieve a
perplexity of 102.5 on the Penn dataset. On two large datasets however, the
same regularization methods are unsuccessful for both models and the RNN's
expressivity allows it to overtake the IRLM by 10 and 20 percent perplexity,
respectively. Despite the perplexity gap, IRLMs still outperform RNNs on the
Microsoft Research Sentence Completion (MRSC) task. We develop a slightly
modified IRLM that separates long-context units (LCUs) from short-context units
and show that the LCUs alone achieve a state-of-the-art performance on the MRSC
task of 60.8%. Our analysis indicates that a fruitful direction of research for
neural LMs lies in developing more accessible internal representations, and
suggests an optimization regime of very high momentum terms for effectively
training such models.


  Discrete data are collected in many application areas and are often
characterised by highly skewed and power-lawlike distributions. An example of
this, which is considered in this paper, is the number of visits to a
specialist, often taken as a measure of demand in healthcare. A discrete
Weibull regression model was recently proposed for regression problems with a
discrete response and it was shown to possess two important features: the
ability to capture over and under-dispersion simultaneously and a closed-form
analytical expression of the quantiles of the conditional distribution. In this
paper, we propose the first Bayesian implementation of a discrete Weibull
regression model. The implementation considers a novel parameterization, where
both parameters of the discrete Weibull distribution can be made dependent on
the predictors. In addition, prior distributions can be imposed that encourage
parameter shrinkage and that lead to variable selection. As with Bayesian
procedures, the full posterior distribution of the parameters is returned, from
which credible intervals can be readily calculated. A simulation study and the
analysis of four real datasets of medical records show promises for the wide
applicability of this approach to the analysis of count data. The method is
implemented in the R package BDWreg.


  Text-guided image generation has witnessed unprecedented progress due to the
development of diffusion models. Beyond text and image, sound is a vital
element within the sphere of human perception, offering vivid representations
and naturally coinciding with corresponding scenes. Taking advantage of sound
therefore presents a promising avenue for exploration within image generation
research. However, the relationship between audio and image supervision remains
significantly underdeveloped, and the scarcity of related, high-quality
datasets brings further obstacles. In this paper, we propose a unified
framework 'Align, Adapt, and Inject' (AAI) for sound-guided image generation,
editing, and stylization. In particular, our method adapts input sound into a
sound token, like an ordinary word, which can plug and play with existing
powerful diffusion-based Text-to-Image (T2I) models. Specifically, we first
train a multi-modal encoder to align audio representation with the pre-trained
textual manifold and visual manifold, respectively. Then, we propose the audio
adapter to adapt audio representation into an audio token enriched with
specific semantics, which can be injected into a frozen T2I model flexibly. In
this way, we are able to extract the dynamic information of varied sounds,
while utilizing the formidable capability of existing T2I models to facilitate
sound-guided image generation, editing, and stylization in a convenient and
cost-effective manner. The experiment results confirm that our proposed AAI
outperforms other text and sound-guided state-of-the-art methods. And our
aligned multi-modal encoder is also competitive with other approaches in the
audio-visual retrieval and audio-text retrieval tasks.


  The performances of lithium-ion batteries are set by the electrodes materials
capacity to exchange lithium ions and electrons faster and reversibly. To this
goal Ni-rich layered metal oxides, especially LiNiO2, are attractive electrode
candidate to achieve both high voltage and capacities. Despite its
attractiveness, several drawbacks for its industrialization are related to
different form of surface and bulk instabilities. These instabilities are due
to redox process involving the charge transfer between cations and anions.
Therefore, a fundamental understanding based on further experimental evidence
is required to resolve of charge transfer between the cation and anion from the
surface to the bulk in LiNiO2. Herein, we resolve the role of nickel and oxygen
in the charge compensation process in LixNiO2 electrodes from the extreme
surface down to 30 nm by energy-dependent core-level HAXPES supported by ab
initio simulation. We emphasize the central role of oxygen in the bulk charge
compensation mechanism from LiNiO2 to NiO2 due to the negative charge transfer
and bond/charge-disproportionation characters of LiNiO2. This bulk behavior is
in turn responsible for surface deoxygenation and nickel reduction upon
delithiation.


  We develop an analytical model for ultraintense attosecond pulse emission in
the highly relativistic laser-plasma interaction. In this model, the attosecond
pulse is emitted by a strongly compressed electron layer around the instant
when the layer transverse current changes the sign and its longitudinal
velocity approaches the maximum. The emitted attosecond pulse has a broadband
exponential spectrum and a stabilized constant spectral phase
$\psi(\omega)=\pm\pi/2-\psi_{A_m}$. The waveform of the attosecond pulse is
also given explicitly, to our knowledge, for the first time. We validate the
analytical model via particle-in-cell (PIC) simulations for both normal and
oblique incidence. Based on this model, we highlight the potential to generate
an isolated ultraintense phase-stabilized attosecond pulse


  Smoothly varying magnetization textures such as domain walls, skyrmions or
hopfions serve as promising candidates for the information bits of the future.
Understanding their physical properties is both a major field of interest and a
theoretical challenge, involving the physics on different length scales. Here,
we apply the phase space formulation of quantum mechanics to magnetic
insulators and metals in the limit of zero temperature to obtain a gradient
expansion in terms of real-space derivatives of the magnetization. Our primary
focus is the anomalous Hall effect in noncollinear magnets which serves as an
important proxy in the detection of localized magnetic structures. We formulate
the problem in the language of noncommutative fiber bundles and make the
central finding that the semiclassical expansion of the density matrix and the
Berry curvature is governed by a construction from string theory which is known
as the Seiberg-Witten map. Originally discovered in the effective low-energy
behavior of D-branes, this map now gives a geometrical underpinning to gradient
expansion techniques in noncollinear magnets and offers a radically new
perspective on their electronic properties.


  Let f:C -> A be an entire holomorphic curve into a semi-Abelian variety A.
Then the Zariski closure of f(C) is a translate of a semi-Abelian subvariety of
A (logarithmic Bloch-Ochiai's theorem). The purpose of the present paper is to
establish a quantitative version of the above result for such f i.e., the
second main theorem and the defect relation.


  Formation of significant number of primordial black holes (PBHs) is realized
if and only if primordial density fluctuations have a large amplitude, which
means that tensor perturbations generated from these scalar perturbations as a
second order effect are also large and comparable to the observational data. We
show that pulsar timing observation could find/rule out PBHs with \sim 10^2
M_solar which are considered as a candidate of intermediate-mass black holes
and that PBHs with mass range 10^{20-26} g, which serves as a candidate of dark
matter, may be probed by future space-based laser interferometers and atomic
interferometers.


  Graph partitioning (GP), a.k.a. community detection, is a classic problem
that divides the node set of a graph into densely-connected blocks. Following
prior work on the IEEE HPEC Graph Challenge benchmark and recent advances in
graph machine learning, we propose a novel RAndom FasT Graph Partitioning
(RaftGP) method based on an efficient graph embedding scheme. It uses the
Gaussian random projection to extract community-preserving features from
classic GP objectives. These features are fed into a graph neural network (GNN)
to derive low-dimensional node embeddings. Surprisingly, our experiments
demonstrate that a randomly initialized GNN even without training is enough for
RaftGP to derive informative community-preserving embeddings and support
high-quality GP. To enable the derived embeddings to tackle GP, we introduce a
hierarchical model selection algorithm that simultaneously determines the
number of blocks and the corresponding GP result. We evaluate RaftGP on the
Graph Challenge benchmark and compare the performance with five baselines,
where our method can achieve a better trade-off between quality and efficiency.
In particular, compared to the baseline algorithm of the IEEE HPEC Graph
Challenge, our method is 6.68x -- 23.9x faster on graphs with 1E3 -- 5E4 nodes
and at least 64.5x faster on larger (1E5 node) graphs on which the baseline
takes more than 1E4 seconds. Our method achieves better accuracy on all test
cases. We also develop a new graph generator to address some limitations of the
original generator in the benchmark.


  In a two-player game, two cooperating but non communicating players, Alice
and Bob, receive inputs taken from a probability distribution. Each of them
produces an output and they win the game if they satisfy some predicate on
their inputs/outputs. The entangled value $\omega^*(G)$ of a game $G$ is the
maximum probability that Alice and Bob can win the game if they are allowed to
share an entangled state prior to receiving their inputs.
  The $n$-fold parallel repetition $G^n$ of $G$ consists of $n$ instances of
$G$ where Alice and Bob receive all the inputs at the same time and must
produce all the outputs at the same time. They win $G^n$ if they win each
instance of $G$. Recently, there has been a series of works showing parallel
repetition with exponential decay for projection games [DSV13], games on the
uniform distribution [CS14] and for free games, i.e. games on a product
distribution [JPY13].
  This article is meant to be a follow up of [CS14], where we improve and
simplify several parts of our previous paper. Our main result is that for any
free game $G$ with value $\omega^*(G)=1-\varepsilon$, we have $\omega^*(G^n)
\le (1 - \varepsilon^2)^{\Omega(\frac{n}{\log(l)})}$ where $l$ is the size of
the output set of the game. This result improves on both the results in [JPY13]
and [CS14]. The framework we use can also be extended to free projection games.
We show that for a free projection game $G$ with value
$\omega^*(G)=1-\varepsilon$, we have $\omega^*(G^n) \le (1 -
\varepsilon)^{\Omega(n)}$.


  In this paper, the author studies quaternionic Monge-Amp\`ere equations and
obtain the existence of the solutions to the Dirichlet problem for such
equations in strictly pesudoconvex domains in quaternionic space. The stability
and subsolution theorems are established for quaternionic Monge-Amp\`ere
equations.


  Realistic mathematical modeling of voice production has been recently boosted
by applications to different fields like bioprosthetics, quality speech
synthesis and pathological diagnosis. In this work, we revisit a two-mass model
of the vocal folds that includes accurate fluid mechanics for the air passage
through the folds and nonlinear properties of the tissue. We present the
bifurcation diagram for such a system, focusing on the dynamical properties of
two regimes of interest: the onset of oscillations and the normal phonation
regime. We also show theoretical support to the nonlinear nature of the elastic
properties of the folds tissue by comparing theoretical isofrequency curves
with reported experimental data.


  Geostatistical methods are powerful tools for understanding the spatial
structure of the metallicity distribution of galaxies, and enable construction
of accurate predictive models of the 2D metallicity distribution. However, so
far these methods have only been applied to very high spatial resolution
metallicity maps, leaving it uncertain if they will work on lower quality data.
In this study, we apply geostatistical techniques to high-resolution
spectroscopic maps of three local galaxies convolved to eight different spatial
resolutions ranging from ~40pc to ~1 kpc per pixel. We fit a geostatistical
model to the data at all resolutions, and find that for metallicity maps where
small scale structure is visible by eye (with > ~10 resolution elements per
Re), all parameters, including the metallicity correlation scale, can be
recovered accurately. At all resolutions tested, we find that point metallicity
predictions from such a geostatistical model outperform a circularly symmetric
metallicity gradient model. We also explore dependence on the number of data
points, and find that N > ~100 spatially resolved metallicity values are
sufficient to train a geostatistical model that yields more accurate
metallicity predictions than a radial gradient model. Finally, we investigate
the potential detrimental effects of having spaxels smaller than an individual
Hii region by repeating our analysis with metallicities integrated over Hii
regions. We see that spaxel-based measurements have more noise, as expected,
but the underlying spatial metallicity distribution can be recovered regardless
of whether spaxels or integrated regions are used.


  Preliminary results on strange particle production versus collision
centrality are presented. STAR measurements from \sqrts = 200 GeV heavy-ion and
\pp collisions are compared to SPS measurements. A systematic study of strange
particle production is presented with the aim of establishing how the
correlation volume of the produced source affects the scale of strange particle
creation, including that of the multi-strange baryons. A linear increase of
strangeness production with volume has been suggested by thermal models as an
indication that the collision region has reached sufficient size such that
small volume effects can be neglected. Analysis of preliminary results from
STAR show that, using the assumption that the number of participants is
linearly correlated with the volume, no such regime was obtained. This suggests
that the correlation volume ''seen" by strange quarks is not merely that of the
initial overlap.


  In this note we first give a new bound on $e_{HK}(\sim)$ the Hilbert-Kunz
multiplicity of invariant rings, by the help of the Noether's bound. Then, we
simplify, extend and present applications of the reciprocity formulae due to L.
Smith. He proved the formula over polynomial rings and his result is tight in
the following sense: Over complete intersection rings with isolated singularity
we show that the reciprocity formulae "$e_{HK}(R/I)+ e_{HK}(R/J) =
e_{HK}(R/\underline{f})$" is equivalent with $\pd(I)<\infty$ when $I$ is an
$\fm$-primary unmixed ideal linked to $J$ along with a regular sequence
$\underline{f}$.


  The relationship between the exactness of a first order differential calculus
on a comodule algebra $P$ and the Galois property of $P$ is investigated.


  We sketch an effective theory for the deconfined state of QCD near Tc. This
relates the behavior of the expectation value of the Polyakov loop, and its
two-point functions, to the pressure. Defining the ``mass'' of three and two
gluon states from the imaginary and real parts of the Polyakov loop, while this
ratio is 3:2 in perturbation theory, at Tc it is 3:1. We also discuss the decay
of the deconfined state into hadrons.


  In recent years, the rapid development of deep learning technology has
brought new prospects to the field of vulnerability detection. Many
vulnerability detection methods involve converting source code into images for
detection, yet they often overlook the quality of the generated images. Due to
the fact that vulnerability images lack clear and continuous contours, unlike
images used in object detection, Convolutional Neural Networks (CNNs) tend to
lose semantic information during the convolution and pooling processes.
Therefore, this paper proposes a pixel row oversampling method based on code
line concatenation to generate more continuous code features, addressing the
issue of discontinuity in code image coloration.Building upon these
contributions, we propose the vulnerability detection system VulMCI and conduct
tests on the SARD and NVD datasets. Experimental results demonstrate that
VulMCI outperforms seven state-of-the-art vulnerability detectors (namely
Checkmarx, FlawFinder, RATS, VulDeePecker, SySeVR, VulCNN, and Devign).
Compared to other image-based methods, VulMCI shows improvements in various
metrics, including a 2.877\% increase in True Positive Rate (TPR), a 5.446\%
increase in True Negative Rate (TNR), and a 5.91\% increase in Accuracy (ACC).
On the NVD real-world dataset, VulMCI achieves an average accuracy of 5.162\%,
confirming its value in practical vulnerability detection applications.


  We study the renormalization of non-commutative gauge theories with matter.
  As in the scalar field theory cases, there are logarithmic infrared
divergences resulting from integrating out high momentum modes. In order to
reproduce the correct infrared behaviour, the Wilsonian effective action has to
include certain ''closed string`` modes with prescribed couplings.
  In the case of quiver gauge theories, realized in string theory on orbifolds,
we identify the required modes with a set of twisted sector fields. These
closed string modes have exactly the prescribed couplings to correct the
Wilsonian effective action. This provides a concrete origin for the appearance
of closed string modes in noncommutative field theories.


  In this paper, we investigate the problem of scheduling parallel Kalman
filters for multiple processes, where each process is observed by a Kalman
filter and at each time step only one Kalman filter could obtain observation
due to practical constraints. To solve the problem, two novel notions,
permissible consecutive observation loss (PCOL) and least consecutive
observation (LCO), are introduced as criteria to describe feasible observation
sequences for a process ensuring desired estimation qualities. Then two
methods, namely, threshold method and periodic method, are proposed to
calculate PCOL and LCO for each process. Based on the derived PCOL and LCO
requirements, we develop two algorithms that are applicable to different
situations: Sxy algorithm from the pinwheel problem for the case of LCO = 1 and
tree search algorithm for general cases. Also, to reduce the computational
complexity of tree search algorithm, several useful pruning conditions are
obtained. Both rigorous analysis and simulation results are provided to
validate the approaches.


  Helical magnetic fields are injected into the cosmic medium during
cosmological baryogenesis and can potentially provide a useful probe of the
early universe. We construct a model to study the injection process during a
first order phase transition and to determine the power spectra of the injected
magnetic field. By Monte Carlo simulations we evaluate the Fourier space
symmetric and helical power spectra of the magnetic field at the time the phase
transition completes. The spectra are peaked at the scale given by the inverse
size of bubbles at percolation and with a comparable width. These injected
magnetic fields set the initial conditions for further cosmological
magneto-hydrodynamical evolution.


  This paper provides a new similarity detection algorithm. Given an input set
of multi-dimensional data points, where each data point is assumed to be
multi-dimensional, and an additional reference data point for similarity
finding, the algorithm uses kernel method that embeds the data points into a
low dimensional manifold. Unlike other kernel methods, which consider the
entire data for the embedding, our method selects a specific set of kernel
eigenvectors. The eigenvectors are chosen to separate between the data points
and the reference data point so that similar data points can be easily
identified as being distinct from most of the members in the dataset.


  We analyze optical and X-ray observations of GRB 050904 obtained with TAROT
and SWIFT. We perform temporal and spectral analysis of the X-ray and optical
data. We find significant absorption in the early phase of the X-ray light
curve, with some evidence (3 sigma level) of variability. We interpret this as
a progressive photo-ionization. We investigate the environment of the burst and
constrain its density profile. We find that the overall behavior of the
afterglow is compatible with a fireball expanding in a wind environment during
the first 2000 seconds after the burst (observer frame). On the other hand, the
late (after 0.5 days, observer frame) afterglow is consistent with an
interstellar medium, suggesting the possible presence of a termination shock.
We estimate the termination shock position to be R_t ~ 1.8 x 10^{-2} pc, and
the wind density parameter to be A_* ~ 1.8. We try to explain the simultaneous
flares observed in optical and X-ray bands in light of different models :
delayed external shock from a thick shell, inverse Compton emission from
reverse shock, inverse Compton emission from late internal shocks or a very
long internal shock activity. Among these models, those based on a single
emission mechanism, are unable to account for the broad-band observations.
Models invoking late internal shocks, with the inclusion of IC emission, or a
properly tuned very long internal shock activity, offer possible explanations.


  Evaluating the efficiency of organizations and branches within an
organization is a challenging issue for managers. Evaluation criteria allow
organizations to rank their internal units, identify their position concerning
their competitors, and implement strategies for improvement and development
purposes. Among the methods that have been applied in the evaluation of bank
branches, non-parametric methods have captured the attention of researchers in
recent years. One of the most widely used non-parametric methods is the data
envelopment analysis (DEA) which leads to promising results. However, the
static DEA approaches do not consider the time in the model. Therefore, this
paper uses a dynamic DEA (DDEA) method to evaluate the branches of a private
Iranian bank over three years (2017-2019). The results are then compared with
static DEA. After ranking the branches, they are clustered using the K-means
method. Finally, a comprehensive sensitivity analysis approach is introduced to
help the managers to decide about changing variables to shift a branch from one
cluster to a more efficient one.


  Effective monopole action at finite temperature in SU(2) gluodynamics is
studied on anisotropic lattices. Using an inverse Monte-Carlo method and the
blockspin transformation for space directions, we determine 4-dimensional
effective monopole action at finite temperature. We get an almost perfect
action in the continuum limit under the assumption that the action is composed
of two-point interactions alone. It depends on a physical scale $b_s$ and the
temperature $T$. The temperature-dependence appears with respect to the
spacelike monopole couplings in the deconfinement phase, whereas the timelike
monopole couplings do not show any appreciable temperature-dependence. The
dimensional reduction of the 4-dimensional SU(2) gluodynamics ((SU(2))$_{4D}$)
at high temperature is the 3-dimensional Georgi-Glashow model ($(GG)_{3D}$).
The latter is studied at the parameter region obtained from the dimensional red
uction. We compare the effective instanton action of $(GG)_{3D}$ with the
timelike monopole action obtained from (SU(2))$_{4D}$. We find that both agree
very well for $T \ge 2.4T_c$ at large $b$ region. The dimensional reduction
works well also for the effective action.


  Software Defined Radio (SDR) platforms are valuable for research and
development activities or high-end systems that demand real-time adaptable
wireless protocols. While low latency can be achieved using the dedicated
digital processing unit of a state-of-the-art SDR platform, its Radio Frequency
(RF) front-end often poses a limitation in terms of turnaround time (TT), the
time needed for switching from the receiving to the transmitting mode (or vice
versa). Zero Intermediate Frequency (ZIF) transceivers are favorable for SDR,
but suffer from self-interference even if the device is not currently
transmitting. The strict MAC-layer requirements of Time Division Duplex (TDD)
protocols like Wi-Fi cannot be achieved using configurable ZIF transceivers
without having to compromise receiver sensitivity. Using a novel approach, we
show that the TT using the AD9361 RF front-end can be as low as 640 ns, while
the self-interference is at the same level as achieved by the conventional TDD
mode, which has a TT of at least 55 {\mu}s. As compared to Frequency Division
Duplex (FDD) mode, a decrease of receiver noise floor by about 13 dB in the 2.4
GHz band and by about 4.5 dB in the 5 GHz band is achieved.


  We prove a Littlewood-type theorem on random analytic functions for not
necessarily independent Gaussian processes. We show that if we randomize a
function in the Hardy space $H^2(\dd)$ by a Gaussian process whose covariance
matrix $K$ induces a bounded operator on $l^2$, then the resulting random
function is almost surely in $H^p(\dd)$ for any $p>0$. The case $K=\text{Id}$,
the identity operator, recovers Littlewood's theorem. A new ingredient in our
proof is to recast the membership problem as the boundedness of an operator.
This reformulation enables us to use tools in functional analysis and is
applicable to other situations. The sharpness of the new condition and several
ramifications are discussed.


  Using a combination of resonant soft x-ray scattering, magnetometry, x-ray
reflectivity and microscopy techniques we have investigated the magnetic
properties and microstructure of a series of perpendicular anisotropy Co/Pt
multilayer films with respect to structural disorder tuned by varying the
sputtering deposition pressure. The observed magnetic changes in domain size,
shape and correlation length originate from structural and chemical variations
in the samples, such as chemical segregation and grain formation as well as
roughness at the surface and interfaces, which are all impacted by the
deposition pressure. For low pressure samples we find evidence of a random
"gas-like" distribution of magnetic domains, while in the higher pressure
samples the domain structure exhibits only short range "liquid-like" positional
ordering. The structural and chemical disorder induced by the higher deposition
pressure first leads to an increase in the number of magnetic point defects
that limit free domain wall propagation. Then, as the sputtering pressure is
further increased, the domain wall energy density is lowered due to the
formation of local regions with reduced magnetic moment, and finally
magnetically void regions appear that confine the magnetic domains and
clusters, similar to segregated granular magnetic recording media.


  We describe a protocol for perfectly transferring a quantum state from one
party to another under the dynamics of a fixed, engineered Hamiltonian. Our
protocol combines the concepts of fractional revival, dual rail encoding, and a
rare glimpse of the anti-Zeno effect. Remarkably, the transfer happens faster
than the speed limit for perfect quantum state transfer [1, 2].


  This article introduces a method, which starting from simple and quite
general mathematical data, allows to construct linear algebras of operators
which are, each of them, endowed with a bialgebra structure (coproduct and
counity). Moreover under some explicit and natural conditions on theses
mathematical data we obtain linear algebras of operators with the following
property: each of them, is either a Hopf algebra, or its bialgebra structure
determines a more abstract Hopf algebra associated with it. Finally, we
describe a more general abstract condition for theses bialgebras to admit a
unique associated Hopf algebra. The presentation is adapted to the cases where
the algebras of linear operators are not finitely generated. This article is
restricted to the exposition of the method of construction and to the proofs of
existence and uniqueness of the structures associated with each algebra of
linear operators that are constructed.
  Nevertheless, it may be noticed that the ideals of relations associated with
bialgebras that are obtained determine an algebraic domain which is of
theoretical interest .


  We investigate the propagation of spin excitations in a one-dimensional (1D)
ferromagnetic Bose gas. While the spectrum of longitudinal spin waves in this
system is sound-like, the dispersion of transverse spin excitations is
quadratic making a direct application of the Luttinger Liquid (LL) theory
impossible. By using a combination of different analytic methods we derive the
large time asymptotic behavior of the spin-spin dynamical correlation function
for strong interparticle repulsion. The result has an unusual structure
associated with a crossover from the regime of trapped spin wave to an open
regime and does not have analogues in known low-energy universality classes of
quantum 1D systems.


  We describe a new model for studying intermittently connected mobile
networks, based on Markovian random temporal graphs, that captures the
influence of message size, maximum tolerated delay and link stability on the
delivery ratio.


  Heat exchange during laminar flow is studied at the fracture scale on the
basis of the Stokes equation. We used a synthetic aperture model (a self-affine
model) that has been shown to be a realistic geometrical description of the
fracture morphology. We developed a numerical modelling using a finite
difference scheme of the hydrodynamic flow and its coupling with an
advection/conduction description of the fluid heat. As a first step,
temperature within the surrounding rock is supposed to be constant. Influence
of the fracture roughness on the heat flux through the wall, is estimated and a
thermalization length is shown to emerge. Implications for the
Soultz-sous-For\^{e}ts geothermal project are discussed.


  We have recently detected CO lines in the well-known filaments around NGC
1275, the galaxy at the centre of the Perseus cluster of galaxies. These
previous observations, with the HERA multi-beam array at the IRAM 30m telescope
enabled us to make a large map of the CO(2-1) line and to see hints of
molecular gas far away from the cluster centre. To confirm the presence of CO
emission lines in the outer filaments and to study the CO(2-1)/CO(1-0) line
ratio, we observed seven regions of interest again with the 30m telescope in
both CO(1-0) and CO(2-1). The regions we observed were: the eastern filament,
the horseshoe, the northern filament and a southern extension, all selected
from Halpha emission line mapping. Molecular gas is detected in all the
observed regions. This result confirms the large extent of the cold molecular
gas filaments. We discuss the CO(2-1)/CO(1-0) ratios in the filaments. The
eastern filament has optically thick gas, whereas further away, the line ratio
increases close to values expected for a warmer optically thin medium. We also
show CO(1-0) and CO(2-1) lines in 9 regions closer to the centre. The
kinematics of the CO is studied here in more detail and confirms that it
follows the motions of the warm H_2 gas found in the near-infrared. Finally, we
searched for dense gas tracers around 3C84 and claim here the first detection
of HCN(3-2).


  I analyze statistics of the stellar population properties for stellar nuclei
and bulges of nearby lenticular galaxies in different environments by using
panoramic spectral data of the integral-field spectrograph SAURON retrieved
from the open archive of Isaac Newton Group. I estimate also the fraction of
nearby lenticular galaxies having inner polar gaseous disks by exploring the
volume-limited sample of early-type galaxies of the ATLAS-3D survey. By
inspecting the two-dimensional velocity fields of the stellar and gaseous
components with running tilted-ring technique, I have found 7 new cases of the
inner polar disks. Together with those, the frequency of inner polar disks in
nearby S0 galaxies reaches 10% that is much higher than the frequency of
large-scale polar rings. Interestingly, the properties of the nuclear stellar
populations in the inner polar ring hosts are statistically the same as those
in the whole S0 sample implying similar histories of multiple gas accretion
events from various directions.


  Two popular approaches for distributed training of SVMs on big data are
parameter averaging and ADMM. Parameter averaging is efficient but suffers from
loss of accuracy with increase in number of partitions, while ADMM in the
feature space is accurate but suffers from slow convergence. In this paper, we
report a hybrid approach called weighted parameter averaging (WPA), which
optimizes the regularized hinge loss with respect to weights on parameters. The
problem is shown to be same as solving SVM in a projected space. We also
demonstrate an $O(\frac{1}{N})$ stability bound on final hypothesis given by
WPA, using novel proof techniques. Experimental results on a variety of toy and
real world datasets show that our approach is significantly more accurate than
parameter averaging for high number of partitions. It is also seen the proposed
method enjoys much faster convergence compared to ADMM in features space.


  We developed the quasi-particle random phase approximation (QRPA) for the
neutrino scattering off even-even nuclei via neutral current (NC) and charged
cur- rent (CC). The QRPA has been successfully applied for the \beta and
\beta\beta decay of relevant nuclei. To describe neutrino scattering, general
multipole transitions by weak interactions with a finite momentum transfer are
calculated for NC and CC reaction with detailed formalism. Since we consider
neutron-proton (np) pairing as well as neutron-neutron (nn) and proton-proton
(pp) pairing correlations, the nn + pp QRPA and np QRPA are combined in a
framework, which enables to describe both NC and CC reactions in a consistent
way. Numerical results for \nu-^{12}C, -^{56}Fe and -^{56}Ni reactions are
shown to comply with other theoretical calculations and reproduce well
available experimental data.


  We introduce an integral structure in orbifold quantum cohomology associated
to the K-group and the Gamma-class. In the case of compact toric orbifolds, we
show that this integral structure matches with the natural integral structure
for the Landau-Ginzburg model under mirror symmetry. By assuming the existence
of an integral structure, we give a natural explanation for the specialization
to a root of unity in Y. Ruan's crepant resolution conjecture.


  We introduced least absolute shrinkage and selection operator (lasso) in
obtaining periodic signals in unevenly spaced time-series data. A very simple
formulation with a combination of a large set of sine and cosine functions has
been shown to yield a very robust estimate, and the peaks in the resultant
power spectra were very sharp. We studied the response of lasso to low
signal-to-noise data, asymmetric signals and very closely separated multiple
signals. When the length of the observation is sufficiently long, all of them
were not serious obstacles to lasso. We analyzed the 100-year visual
observations of delta Cep, and obtained a very accurate period of 5.366326(16)
d. The error in period estimation was several times smaller than in Phase
Dispersion Minimization. We also modeled the historical data of R Sct, and
obtained a reasonable fit to the data. The model, however, lost its predictive
ability after the end of the interval used for modeling, which is probably a
result of chaotic nature of the pulsations of this star. We also provide a
sample R code for making this analysis.


  We introduce a family of quasisymmetric functions called {\em Eulerian
quasisymmetric functions}, which have the property of specializing to
enumerators for the joint distribution of the permutation statistics, major
index and excedance number on permutations of fixed cycle type. This family is
analogous to a family of quasisymmetric functions that Gessel and Reutenauer
used to study the joint distribution of major index and descent number on
permutations of fixed cycle type. Our central result is a formula for the
generating function for the Eulerian quasisymmetric functions, which
specializes to a new and surprising $q$-analog of a classical formula for the
exponential generating function of the Eulerian polynomials. This $q$-analog
computes the joint distribution of excedance number and major index, the only
of the four important Euler-Mahonian distributions that had not yet been
computed. Our study of the Eulerian quasisymmetric functions also yields
results that include the descent statistic and refine results of Gessel and
Reutenauer. We also obtain $q$-analogs, $(q,p)$-analogs and quasisymmetric
function analogs of classical results on the symmetry and unimodality of the
Eulerian polynomials. Our Eulerian quasisymmetric functions refine symmetric
functions that have occurred in various representation theoretic and
enumerative contexts such as in MacMahon's study of multiset derangements, in
work of Procesi and Stanley on toric varieties of Coxeter complexes and in
Stanley's work on symmetric chromatic polynomials. Here we present yet another
occurence in connection with the homology of a poset introduced by Bj\"orner
and Welker.


  Dense linear algebra kernels, such as linear solvers or tensor contractions,
are fundamental components of many scientific computing applications. In this
work, we present a novel method of deriving parallel I/O lower bounds for this
broad family of programs. Based on the X-partitioning abstraction, our method
explicitly captures inter-statement dependencies. Applying our analysis to LU
factorization, we derive COnfLUX, an LU algorithm with the parallel I/O cost of
$N^3 / (P \sqrt{M})$ communicated elements per processor -- only $1/3\times$
over our established lower bound. We evaluate COnfLUX on various problem sizes,
demonstrating empirical results that match our theoretical analysis,
communicating asymptotically less than Cray ScaLAPACK or SLATE, and
outperforming the asymptotically-optimal CANDMC library. Running on $1$,$024$
nodes of Piz Daint, COnfLUX communicates 1.6$\times$ less than the second-best
implementation and is expected to communicate 2.1$\times$ less on a full-scale
run on Summit.


  Let $G_n$ be the genus of a two-dimensional surface obtained by gluing,
uniformly at random, the sides of an $n$-gon. Recently Linial and Nowik proved,
via an enumerational formula due to Harer and Zagier, that the expected value
of $G_n$ is asymptotic to $(n - \ln n)/2$ for $n\to\infty$. We prove a local
limit theorem for the distribution of $G_n$, which implies that $G_n$ is
asymptotically Gaussian, with mean $(n-\ln n)/2$ and variance $(\ln n)/4$.


  Achieving high performance in virtualized data centers requires both
deploying high throughput storage clusters, i.e. based on Solid State Disks
(SSDs), as well as optimally consolidating the workloads across storage nodes.
Nowadays, the only practical solution for cloud storage providers to offer
guaranteed performance is to grossly over-provision the storage nodes. The
current workload scheduling mechanisms used in production do not have the
intelligence to optimally allocate block storage volumes based on the
performance of SSDs. In this paper, we introduce Serifos, an autonomous
performance modeling and load balancing system designed for SSD-based cloud
storage. Serifos takes into account the characteristics of the SSD storage
units and constructs hardware dependent workload consolidation models. Thus
Serifos is able to predict the latency caused by workload interference and the
average latency of concurrent workloads. Furthermore, Serifos leverages an I/O
load balancing algorithm to dynamically balance the volumes across the cluster.
Experimental results indicate that Serifos consolidation model is able to
maintain the mean prediction error of around 10% for heterogeneous hardware. As
a result of Serifos load balancing, we found that the variance and the maximum
average latency are reduced by 82% and 52%, respectively. The supported Service
Level Objectives (SLOs) on the testbed improve 43% on average latency, 32% on
the maximum read and 63% on the maximum write latency.


  We studied the Near-Earth Asteroid (NEA) candidates posted on the Minor
Planet Center's Near-Earth Object Confirmation Page (NEOCP) between years 2013
and 2016. Out of more than 17,000 NEA candidates, while the majority became
either new discoveries or were associated with previously known objects, about
11% were unable to be followed-up or confirmed. We further demonstrate that of
the unconfirmed candidates, 926+/-50 are likely to be NEAs, representing 18% of
discovered NEAs in that period. Only 11% (~93) of the unconfirmed NEA
candidates were large (having absolute magnitude H<22). To identify the reasons
why these NEAs were not recovered, we analyzed those from the most prolific
asteroid surveys: Pan-STARRS, the Catalina Sky Survey, the Dark Energy Survey,
and the Space Surveillance Telescope. We examined the influence of plane-of-sky
positions and rates of motion, brightnesses, submission delays, and computed
absolute magnitudes, as well as correlations with the phase of the moon and
seasonal effects. We find that delayed submission of newly discovered NEA
candidate to the NEOCP drove a large fraction of the unconfirmed NEA
candidates. A high rate of motion was another significant contributing factor.
We suggest that prompt submission of suspected NEA discoveries and rapid
response to fast moving targets and targets with fast growing ephemeris
uncertainty would allow better coordination among dedicated follow-up
observers, decrease the number of unconfirmed NEA candidates, and increase the
discovery rate of NEAs.


  We study the the sharp interface limit of $\varepsilon$-dependent two
dimensional stochastic Cahn-Hilliard equation driven by space-time white noise
and conservative noise as $\varepsilon\to 0$. In the case when the noise is
sufficiently small, by comparing the solutions to equation (1.1) with the
approximation solution constructed in [ABC94], we show that the limit of the
solutions is also solutions to the deterministic Hele-Shaw problem.


  During the years 2009 to 2011, neutrino beams were fired repeatedly from CERN
towards a detector in Italy's Gran Sasso tunnel, some 4 deg south and 7 deg
east of CERN, at a distance of 730.5 km, in the shape of short bunches of
particles. Their time of flight (2.5 msec) was measured at high accuracy (nsec)
with caesium clocks (Reich 2011). Remarkably, the CNGS team found a deficit of
61 nsec compared with propagation at the speed of light, and concluded at
superluminal speeds, of order 10$^{-4.6}$. In this communication, I will argue
that this is the first experiment to test Einstein's theory for the (weak)
gravity field of Earth, with the result that the neutrinos propagated (just)
luminally.


  The relations between smooth and peaked soliton solutions are reviewed for
the Camassa-Holm (CH) shallow water wave equation in one spatial dimension. The
canonical Hamiltonian formulation of the CH equation in action-angle variables
is expressed for solitons by using the scattering data for its associated
isospectral eigenvalue problem, rephrased as a Riemann-Hilbert problem. The
momentum map from the action-angle scattering variables $T^*({\mathbb{T}^N})$
to the flow momentum ($\mathfrak{X}^*$) provides the Eulerian representation of
the $N$-soliton solution of CH in terms of the scattering data and squared
eigenfunctions of its isospectral eigenvalue problem. The dispersionless limit
of the CH equation and its resulting peakon solutions are examined by using an
asymptotic expansion in the dispersion parameter. The peakon solutions of the
dispersionless CH equation in one dimension are shown to generalize in higher
dimensions to peakon wave-front solutions of the EPDiff equation whose
associated momentum is supported on smoothly embedded subspaces. The Eulerian
representations of the singular solutions of both CH and EPDiff are given by
the (cotangent-lift) momentum maps arising from the left action of the
diffeomorphisms on smoothly embedded subspaces.


  In this paper we show that the irreducible representations of a finite
inverse semigroup $S$ over an algebraically closed field $F$ are in bijection
with the conjugacy classes of $S$ if the characteristic of $F$ is zero or a
prime number that does not divide the order of any maximal subgroup of $S$.


  Using the Hamilton Echelle Spectrograph at Lick Observatory, we have obtained
precise radial velocities (RVs) of a sample of 373 G- and K-giant stars over
more than 12 years, leading to the discovery of several single and multiple
planetary systems. The RVs of the long-period (~53 years) spectroscopic binary
$\epsilon$ Cyg (HIP 102488) are found to exhibit additional regular variations
with a much shorter period (~291 days). We intend to improve the orbital
solution of the $\epsilon$ Cyg system and attempt to identify the cause of the
nearly periodic shorter period variations, which might be due to an additional
substellar companion. We used precise RV measurements of the K-giant star
$\epsilon$ Cyg from Lick Observatory, in combination with a large set of RVs
collected more recently with the SONG telescope, as well as archival data sets.
Our Keplerian model to the RVs characterizes the orbit of the spectroscopic
binary to higher precision than achieved previously, resulting in a semi-major
axis of $a = 15.8 \mathrm{AU}$, an eccentricity of $e = 0.93$, and a minimum
mass of the secondary of $m \sin i = 0.265 M_\odot$. Additional short-period RV
variations closely resemble the signal of a Jupiter-mass planet orbiting the
evolved primary component with a period of $291 \mathrm{d}$, but the period and
amplitude of the putative orbit change strongly over time. Furthermore, in our
stability analysis of the system, no stable orbits could be found in a large
region around the best fit. Both of these findings deem a planetary cause of
the RV variations unlikely. Most of the investigated alternative scenarios,
such as an hierarchical triple or stellar spots, also fail to explain the
observed variability convincingly. Due to its very eccentric binary orbit, it
seems possible, however, that $\epsilon$ Cyg could be an extreme example of a
heartbeat system.


  Deep learning researchers commonly suggest that converged models are stuck in
local minima. More recently, some researchers observed that under reasonable
assumptions, the vast majority of critical points are saddle points, not true
minima. Both descriptions suggest that weights converge around a point in
weight space, be it a local optima or merely a critical point. However, it's
possible that neither interpretation is accurate. As neural networks are
typically over-complete, it's easy to show the existence of vast continuous
regions through weight space with equal loss. In this paper, we build on recent
work empirically characterizing the error surfaces of neural networks. We
analyze training paths through weight space, presenting evidence that apparent
convergence of loss does not correspond to weights arriving at critical points,
but instead to large movements through flat regions of weight space. While it's
trivial to show that neural network error surfaces are globally non-convex, we
show that error surfaces are also locally non-convex, even after breaking
symmetry with a random initialization and also after partial training.


  The classical embedding theorem of Carleson deals with finite positive Borel
measures $\mu$ on the closed unit disk for which there exists a positive
constant $c$ such that $|f|_{L^2(\mu)} \leq c |f|_{H^2}$ for all $f \in H^2$,
the Hardy space of the unit disk. Lef\'evre et al. examined measures $\mu$ for
which there exists a positive constant $c$ such that $\|f\|_{L^2(\mu)} \geq c
|f|_{H^2}$ for all $f \in H^2$. The first type of inequality above was explored
with $H^2$ replaced by one of the model spaces $(\Theta H^2)^{\perp}$ by
Aleksandrov, Baranov, Cohn, Treil, and Volberg. In this paper we discuss the
second type of inequality in $(\Theta H^2)^{\perp}$.


  A subsystem approach for obtaining electron binding energies in the valence
region and apply it to the case of halide ions (X$^-$, X = F-At) in water. This
approach is based on electronic structure calculations combining the
relativistic equation of motion coupled-cluster method for electron detachment
(EOM-IP-CCSD) and density functional theory via the frozen density embedding
(FDE) approach, using structures from classical molecular dynamics with
polarizable force fields for discrete systems (in the present study, droplets
containing the anion and 50 water molecules). Our results indicate one can
accurately capture both the large solvent effect observed for the halides as
well as the splitting of their ionization signals due to the increasingly large
spin-orbit coupling of the p$_{3/2}$-p$_{1/2}$ manifold across the series, at
an affordable computational cost. Furthermore, due to the quantum mechanical
treatment of both solute and solvent, electron binding energies of
semi-quantitative quality are also obtained also obtained for (bulk) water as
by-products of the calculations for the halogens (in droplets).


  This paper targets to study the effect of the Riemann-Liouville fractional
integral operator on unbounded variation points of a continuous function. In
particular, we show that the fractional integral preserves the bounded
variation points of a function. We also prove that the fractional integral
operator is a bounded linear operator on the class of bounded variation and
continuous functions.


  We propose a model to study quantum population transfer via a structural
continuum. The model is composed of two spins which are coupled to two bosonic
modes separately by two control pulses, and the two bosonic modes are coupled
to a common structural continuum. We show that efficient population transfer
can be achieved between the two spins by using a multi-level stimulated Raman
adiabatic passage (STIRAP) across the continuum, which we refer to as straddle
STIRAP via continuum. We also consider the stability of this model against
different control parameters and show that efficient population transfer can be
achieved even in presence a moderate dissipation.


  We consider a random walk in random environment with random holding times,
that is, the random walk jumping to one of its nearest neighbors with some
transition probability after a random holding time. Both the transition
probabilities and the laws of the holding times are randomly distributed over
the integer lattice. Our main result is a quenched large deviation principle
for the position of the random walk. The rate function is given by the Legendre
transform of the so-called Lyapunov exponents for the Laplace transform of the
first passage time. By using this representation, we derive some asymptotics of
the rate function in some special cases.


  We provide a proof of a recently conjectured universal bound on current
fluctuations in Markovian processes. This bound establishes a link between the
fluctuations of an individual observable current, the cycle affinities driving
the system into a non-equilibrium steady state, and the topology of the
network. The proof is based on a decomposition of the network into independent
cycles with both positive affinity and positive stationary cycle current. This
formalism allows for a refinement of the bound for systems in equilibrium or
with locally vanishing affinities.


  Recovering the 3D scene geometry from a single view is a fundamental yet
ill-posed problem in computer vision. While classical depth estimation methods
infer only a 2.5D scene representation limited to the image plane, recent
approaches based on radiance fields reconstruct a full 3D representation.
However, these methods still struggle with occluded regions since inferring
geometry without visual observation requires (i) semantic knowledge of the
surroundings, and (ii) reasoning about spatial context. We propose KYN, a novel
method for single-view scene reconstruction that reasons about semantic and
spatial context to predict each point's density. We introduce a vision-language
modulation module to enrich point features with fine-grained semantic
information. We aggregate point representations across the scene through a
language-guided spatial attention mechanism to yield per-point density
predictions aware of the 3D semantic context. We show that KYN improves 3D
shape recovery compared to predicting density for each 3D point in isolation.
We achieve state-of-the-art results in scene and object reconstruction on
KITTI-360, and show improved zero-shot generalization compared to prior work.
Project page: https://ruili3.github.io/kyn.


  In this paper we study the formal algebraic structure underlying the
intrinsic classification algorithm, recently introduced by Hadani, Shkolnisky,
Singer and Zhao, for classifying noisy projection images of similar viewing
directions in three-dimensional cryo-electron microscopy (cryo-EM). This
preliminary classification is of fundamental importance in determining the
three-dimensional structure of macromolecules from cryo-EM images. Inspecting
this algebraic structure we obtain a conceptual explanation for the
admissibility (correctness) of the algorithm and a proof of its numerical
stability, thus putting it on firm mathematical grounds. The proof relies on
studying the spectral properties of an integral operator of geometric origin on
the two dimensional sphere, called the localized parallel transport operator.
Along the way, we develop further the representation theoretic set-up for
three-dimensional cryo-EM.


  We construct an algebra of dimension $2^{\aleph_0}$ consisting only of
functions which in no point possess a finite one-sided derivative. We further
show that some well known nowhere differentiable functions generate algebras,
which contain functions which are differentiable at some points, but where for
all functions in the algebra the set of points of differentiability is quite
small.


  Following systematically the generalized Hamiltonian approach of Batalin and
Fradkin, we demonstrate the equivalence of a self-dual model with the
Maxwell-Chern-Simons theory by embedding the former second-class theory into a
first-class theory.


  Robot control problems are often structured with a policy function that maps
state values into control values, but in many dynamic problems the observed
state can have a difficult to characterize relationship with useful policy
actions. In this paper we present a new method for learning state embeddings
from plans or other forms of demonstrations such that the embedding space has a
specified geometric relationship with the demonstrations. We present a novel
variational framework for learning these embeddings that attempts to optimize
trajectory linearity in the learned embedding space. We show how these
embedding spaces can then be used as an augmentation to the robot state in
reinforcement learning problems. We use kinodynamic planning to generate
training trajectories for some example environments, and then train embedding
spaces for these environments. We show empirically that observing a system in
the learned embedding space improves the performance of policy gradient
reinforcement learning algorithms, particularly by reducing the variance
between training runs. Our technique is limited to environments where
demonstration data is available, but places no limits on how that data is
collected. Our embedding technique provides a way to transfer domain knowledge
from existing technologies such as planning and control algorithms, into more
flexible policy learning algorithms, by creating an abstract representation of
the robot state with meaningful geometry.


  The group testing problem asks for efficient pooling schemes and algorithms
that allow to screen moderately large numbers of samples for rare infections.
The goal is to accurately identify the infected samples while conducting the
least possible number of tests. Exploring the use of techniques centred around
the Belief Propagation message passing algorithm, we suggest a new test design
that significantly increases the accuracy of the results. The new design comes
with Belief Propagation as an efficient inference algorithm. Aiming for results
on practical rather than asymptotic problem sizes, we conduct an experimental
study.


  In this article, we present a corpus of dialogues between a schizophrenic
speaker and an interlocutor who drives the dialogue. We had identified specific
discontinuities for paranoid schizophrenics. We propose a modeling of these
discontinuities with S-DRT (its pragmatic part)


  We report a numerical study of transport properties of a quantum dot with
superconducting leads. We introduce a general phenomenological model of quantum
dot transport, in which electron tunnel rates are computed within the Fermi's
Golden Rule approach. The low temperature current-voltage (I-V) characteristics
are in qualitative agreement with experimental observations of Ralph et al.
[Phys. Rev. Lett., 74, 3241 (1995)]. At higher temperatures, our results reveal
new effects due to the thermal excitation of quasiparticles in the leads as
well as the thermal population of excited quantum levels in the dot. We also
study the photon-assisted tunneling phenomena in our system and point out its
potential for millimeter wave applications.


  Interventions play a pivotal role in the study of complex biological systems.
In drug discovery, genetic interventions (such as CRISPR base editing) have
become central to both identifying potential therapeutic targets and
understanding a drug's mechanism of action. With the advancement of CRISPR and
the proliferation of genome-scale analyses such as transcriptomics, a new
challenge is to navigate the vast combinatorial space of concurrent genetic
interventions. Addressing this, our work concentrates on estimating the effects
of pairwise genetic combinations on the cellular transcriptome. We introduce
two novel contributions: Salt, a biologically-inspired baseline that posits the
mostly additive nature of combination effects, and Peper, a deep learning model
that extends Salt's additive assumption to achieve unprecedented accuracy. Our
comprehensive comparison against existing state-of-the-art methods, grounded in
diverse metrics, and our out-of-distribution analysis highlight the limitations
of current models in realistic settings. This analysis underscores the
necessity for improved modelling techniques and data acquisition strategies,
paving the way for more effective exploration of genetic intervention effects.


  We study a model for orbitally degenerate Mott insulators, where localized
electrons possess t_2g degrees of freedom coupled by several, competing,
exchange mechanisms. We provide evidence for two distinct strongly fluctuating
regimes, depending on whether superexchange or direct exchange mechanism
predominates. In the superexchange-dominated regime, the ground state is
dimerized, with nearest neighbor orbital singlets covering the lattice. By
deriving an effective quantum dimer model and analyzing it numerically, we
characterize this dimerized phase as a valence bond crystal stabilized by
singlet resonances within a large unit cell. In the opposite regime, with
predominant direct exchange, the combined analysis of the original model and
another effective model adapted to the local constraints, shows that subleading
perturbations select a highly resonating ground state, with coexisting diagonal
and off-diagonal long-range orbital orders.


  We investigate the existence of globally generated vector bundles of rank 2
with $c_1\leq 3$ on a smooth quadric threefold and determine their Chern
classes. As an automatic consequence, every rank 2 globally generated vector
bundle on $Q$ with $c_1=3$ is an odd instanton up to twist.


  We say that a metric space $(X,d)$ possesses the \emph{Banach Fixed Point
Property (BFPP)} if every contraction $f:X\to X$ has a fixed point. The Banach
Fixed Point Theorem says that every complete metric space has the BFPP.
However, E. Behrends pointed out \cite{Be1} that the converse implication does
not hold; that is, the BFPP does not imply completeness, in particular, there
is a non-closed subset of $\RR^2$ possessing the BFPP. He also asked \cite{Be2}
if there is even an open example in $\RR^n$, and whether there is a 'nice'
example in $\RR$. In this note we answer the first question in the negative,
the second one in the affirmative, and determine the simplest such examples in
the sense of descriptive set theoretic complexity.
  Specifically, first we prove that if $X\su\RR^n$ is open or $X\su\RR$ is
simultaneously $F_\si$ and $G_\de$ and $X$ has the BFPP then $X$ is closed.
Then we show that these results are optimal, as we give an $F_\si$ and also a
$G_\de$ non-closed example in $\RR$ with the BFPP.
  We also show that a nonmeasurable set can have the BFPP. Our non-$G_\de$
examples provide metric spaces with the BFPP that cannot be remetrised by any
compatible complete metric. All examples are in addition bounded.


  We show that a large scale mass mortality results in increased numbers of
suicides. As a case in point, we consider the influenza epidemic of October
1918 in the United States. In this month, suicides peaked at a level of over 4s
(where s denotes the desaisonalized standard deviation of the suicide rate)
which means that one would expect such a jump to occur merely by chance only
once in several centuries. The mechanism that we propose to explain this effect
relies on two steps (i) Mass mortalities break family bonds for instance
between parents and children or husbands and wives. (ii) Increased numbers of
suicides then result from the well known fact that the severance of family
bonds invariably produces more suicides.


  We present the results of a comprehensive wide field search for transiting
``Hot Jupiter'' planets (1d<P<16d) in the globular cluster 47 Tucanae.
Motivated by the core null result of Gilliland and coworkers, this work further
addresses the question of giant planet frequency in 47 Tuc by observing, from
the ground, a 52'x52' field centered on the cluster for 30.4 nights. Hence this
work is most sensitive to the uncrowded outer regions of the cluster and
concentrates on 21,920 main sequence stars (~solar in mass). This work
comprises the largest ground-based transit search of a globular cluster to
date.
  Monte Carlo simulations predict that seven planets should be present in our
dataset, if 47 Tuc has the same planetary frequency observed in the solar
neighbourhood. A detailed search with a custom developed detection algorithm
found no transit events. Being consistent with the cluster core null detection
of Gilliland and coworkers, our result indicates that system metallicity is the
dominant effect inhibiting Hot Jupiter formation in this environment.


  We consider the perturbative stability of non-supersymmetric configurations
in N=1 supergravity models with a spectator sector not involved in
supersymmetry breaking. Motivated by the supergravity description of complex
structure moduli in Large Volume Compactifications of type IIB-superstrings, we
concentrate on models where the interactions are consistent with the
supersymmetric truncation of the spectator fields, and we describe their
couplings by a random ensemble of generic supergravity theories. We
characterise the mass spectrum of the spectator fields in terms of the
statistical parameters of the ensemble and the geometry of the scalar manifold.
Our results show that the non-generic couplings between the spectator and the
supersymmetry breaking sectors can stabilise all the tachyons which typically
appear in the spectator sector before including the supersymmetry breaking
effects, and we find large regions of the parameter space where the
supersymmetric sector remains stable with probability close to one. We discuss
these results about the stability of the supersymmetric sector in two
physically relevant situations: non-supersymmetric Minkowski vacua, and
slow-roll inflation driven by the supersymmetry breaking sector. For the class
of models we consider, we have reproduced the regimes in which the KKLT and
Large Volume Scenarios stabilise all supersymmetric moduli. We have also
identified a new regime in which the supersymmetric sector is stabilised at a
very robust type of dS minimum without invoking a large mass hierarchy.


  In this paper we develop a new method which is a generalization of the
Obreshkoff -Ehrlich method for the cases of algebraic, trigonometric and
exponential polynomials. This method has a cubic rate of convergence. It is
efficient from the computational point of view and can be used for simultaneous
finding all roots if the roots have known multiplicities. This new method in
spite of the arbitrariness of multiplicities is of the same complexity as the
methods for simultaneous finding all roots of simple roots. We do not use
divided differences with multiple knots and this fact does not lead to
calculation of derivatives of the given polynomial of higher order, but only of
first ones.


  For arbitrary closed countable subsets $Z$ of the unit circle examples of
topologically mixing operators on Hilbert spaces are given which have a densely
spanning set of unimodular eigenvectors with eigenvalues restricted to $Z$. In
particular, these operators cannot be ergodic in the Gaussian sense.


  We present X-ray observations of the BL Lacertae (BL Lac) object Markarian
501 (Mrk 501), taken with the Rossi X-ray Timing Explorer in 1998 May as part
of a multi-wavelength campaign. The X-ray light curve shows a very rapid flare
in which the 2-10 keV flux increased by ~60% in <200 seconds. This rapid rise
is followed by a drop-off in the 2-10 keV flux of ~40% in <600 seconds. The
10-15 keV variation in this flare is roughly a factor of two on similar
time-scales. During the rise of the flare, the 3-15 keV spectral index hardened
from 2.02 +/- 0.03 to 1.87 +/- 0.04, where it remained during the decay of the
flare. This is the fastest variation ever seen in X-rays from Mrk 501 and among
the fastest seen at any wavelength for this object. The shift in the energy at
which the spectral power peaks (from <3 keV before the flare to >30 keV during
the flare) is also among the most rapid shifts seen from this object. This
flare occurs during an emission state (2-10 keV flux approximately 1.2e-10 erg
cm^-2 s^-1) that is approximately 25% of the peak flux observed in 1997 April
from this object but which is still high compared to its historical average
X-ray flux. The variations in the hardness ratio are consistent with the low
energy variations leading those at high energies during the development and
decay of the flare. This pattern is rare among high frequency peaked BL Lac
objects like Mrk 501, but has been seen recently in two other TeV emitting BL
Lacs, Mrk 421 and PKS 2155-304. The hard lag is consistent with a flare
dominated by the acceleration time-scale for a simple relativistic shock model
of flaring.


  We argue that models in which an observable variation of the fine structure
constant is explained by motion of a cosmic scalar field, are not stable under
renormalization, and require massive fine tuning that cannot be explained by
any known mechanism.


  We propose a new 2D shape decomposition method based on the short-cut rule.
The short-cut rule originates from cognition research, and states that the
human visual system prefers to partition an object into parts using the
shortest possible cuts. We propose and implement a computational model for the
short-cut rule and apply it to the problem of shape decomposition. The model we
proposed generates a set of cut hypotheses passing through the points on the
silhouette which represent the negative minima of curvature. We then show that
most part-cut hypotheses can be eliminated by analysis of local properties of
each. Finally, the remaining hypotheses are evaluated in ascending length
order, which guarantees that of any pair of conflicting cuts only the shortest
will be accepted. We demonstrate that, compared with state-of-the-art shape
decomposition methods, the proposed approach achieves decomposition results
which better correspond to human intuition as revealed in psychological
experiments.


  We propose an extended version of the gauge-mediated SUSY breaking models
where extra $SU(2)_L$ doublets and singlet field are introduced. These fields
are assumed to be parity-odd under an additional matter parity. In this model,
the lightest parity-odd particle among them would be dark matter in the
Universe. In this paper, we discuss direct detection of the dark matter and the
collider signatures of the model


  We investigate the behaviour of a relativistic spherically symmetric
radiative star with an accelerating, expanding and shearing interior matter
distribution in the presence of anisotropic pressures. The junction condition
can be written in standard form in three cases: linear, Bernoulli and Riccati
equations. We can integrate the boundary condition in each case and three
classes of new solutions are generated. For particular choices of the metric we
investigate the physical properties and consider the limiting behaviour for
large values of time. The causal temperature can also be found explicitly.


  Recently the new interest arised (hep-ph/0403139) to the chiral coefficients
$L_{11}, L_{12}, L_{13}$ in the low-energy ChPT lagrangian describing the
pseudoscalar meson coupling to gravity and/or light singlet dilatons. In 90ties
we estimated these coefficients within the Chiral and Conformal Bosonization
Model but published the results in the journal not easily accessible for the
physics community. We put now our old paper to the E-archives.


  High energy physics experiments in KEK/Japan rush into over KHz trigger
stage. Thus, we need a successor of the data acquisition(DAQ) system that
replaces the CAMAC or FASTBUS systems. To meet these needs, we have developed a
DAQ system which includes a crate, base-board modules, daughter cards for
front-end A/D or T/D conversion, and back-end communication cards for data
transfer and timing control. The size of the crate is for the 9U Euro-cards
with the standard VME32 bus and extension connectors for power supply. The
base-board comprises of a local bus with the sequencer connected to the
front-end daughter cards via event buffering FIFOs, and the standard PMC (PCI
mezzanine card) bus to be set a PMC processor unit to reduce data size from the
front-end daughter cards. A data transfer module, which is connected to the
event building system, and a trigger control unit, which communicates with the
central timing controller are installed on the back-end communication card
connected to the rear end of the base-board. We describe the design of this DAQ
system and evaluate the performance of it.


  3D hand pose estimation from monocular videos is a long-standing and
challenging problem, which is now seeing a strong upturn. In this work, we
address it for the first time using a single event camera, i.e., an
asynchronous vision sensor reacting on brightness changes. Our EventHands
approach has characteristics previously not demonstrated with a single RGB or
depth camera such as high temporal resolution at low data throughputs and
real-time performance at 1000 Hz. Due to the different data modality of event
cameras compared to classical cameras, existing methods cannot be directly
applied to and re-trained for event streams. We thus design a new neural
approach which accepts a new event stream representation suitable for learning,
which is trained on newly-generated synthetic event streams and can generalise
to real data. Experiments show that EventHands outperforms recent monocular
methods using a colour (or depth) camera in terms of accuracy and its ability
to capture hand motions of unprecedented speed. Our method, the event stream
simulator and the dataset are publicly available; see
https://4dqv.mpi-inf.mpg.de/EventHands/


  It is known that Flux Corrected Transport algorithms can produce
entropy-violating solutions of hyperbolic conservation laws. Our purpose is to
design flux correction with maximal antidiffusive fluxes to obtain entropy
solutions of scalar hyperbolic conservation laws. To do this we consider a
hybrid difference scheme that is a linear combination of a monotone scheme and
a scheme of high-order accuracy. Flux limiters for the hybrid scheme are
calculated from a corresponding optimization problem. Constraints for the
optimization problem consist of inequalities that are valid for the monotone
scheme and applied to the hybrid scheme. We apply the discrete cell entropy
inequality with the proper numerical entropy flux to single out a physically
relevant solution of scalar hyperbolic conservation laws. A nontrivial
approximate solution of the optimization problem yields expressions to compute
the required flux limiters. We present examples that show that not all
numerical entropy fluxes guarantee to single out a physically correct solution
of scalar hyperbolic conservation laws.


  Let $p$ be a fixed prime, and let $v(a)$ stand for the exponent of $p$ in the
prime factorization of the integer $a$. Let $f$ and $g$ be two monic
polynomials with integer coefficients and nonzero resultant $r$. Write $S$ for
the maximum of $v(\gcd (f(n), g(n)))$ over all integers $n$. It is known that
$S \le v(r)$. We give various lower and upper bounds for the least possible
value of $v(r)-S$ provided that a given power $p^s$ divides both $f(n)$ and
$g(n)$ for all $n$. In particular, the least possible value is $ps^2-s$ for
$s\le p$ and is asymptotically $(p-1)s^2$ for large $s$.


  We investigate the existence and multiplicity of solutions for higher order
discrete boundary value problems via critical point theory.


  Let $(M^3,g_0)$ be a complete noncompact Riemannian 3-manifold with
nonnegative Ricci curvature and with injectivity radius bounded away from zero.
Suppose that the scalar curvature $R(x)\to 0$ as $x\to \infty$. Then the Ricci
flow with initial data $(M^3,g_0)$ has a long time solution. This extends a
recent result of Ma and Zhu. We also have a higher dimensional version, and we
reprove a K$\ddot{a}$hler analogy due to Chau, Tam and Yu.


  Anderson localization of matter waves was recently observed with cold atoms
in a weak 1D disorder realized with laser speckle potential [J. Billy et al.,
Nature 453, 891 (2008)]. The latter is special in that it does not have spatial
frequency components above certain cutoff $q_{c}$. As a result, the Lyapunov
exponent (LE), or inverse localization length, vanishes in Born approximation
for particle wavevector $k>{1/2}q_{c}$, and higher orders become essential.
These terms, up to the order four, are calculated analytically and compared
with numerical simulations. For very weak disorder, LE exhibits a sharp drop at
$k$ $={1/2}q_{c}$. For moderate disorder (a) the drop is less dramatic than
expected from the fourth order approximation and (b) LE becomes very sensitive
to the sign of the disorder skewness (which can be controlled in cold atom
experiments). Both observations are related to the strongly non-Gaussian
character of the speckle intensity.


  The edge blow-up of a graph $G$, denoted by $G^{p+1}$, is obtained by
replacing each edge of $G$ with a clique of order $p+1$, where the new vertices
of the cliques are all distinct. Yuan [J. Comb. Theory, Ser. B, 152 (2022)
379-398] determined the range of the Tur\'{a}n numbers for edge blow-up of all
bipartite graphs and the exact Tur\'{a}n numbers for edge blow-up of all
non-bipartite graphs. In this paper we prove that the graphs with the maximum
spectral radius in an $n$-vertex graph without any copy of edge blow-up of star
forests are the extremal graphs for edge blow-up of star forests when $n$ is
sufficiently large.


  The positions in the H-R diagram of strongly magnetic Ap and Bp stars are
compared with those of normal main sequence stars of types B7 to F2, with a
view to investigating possible differences in evolutionary status between
magnetic and non-magnetic stars. The normal B7-F2 stars fill the whole width of
the main sequence band with some concentration towards the ZAMS, whereas the
magnetic stars are only rarely found close to either the zero-age or
terminal-age sequences.


  Scientific data has been growing in both size and complexity across the
modern physical, engineering, life and social sciences. Spatial structure, for
example, is a hallmark of many of the most important real-world complex
systems, but its analysis is fraught with statistical challenges. Topological
data analysis can provide a powerful computational window on complex systems.
Here we present a framework to extend and interpret persistent homology
summaries to analyse spatial data across multiple scales. We introduce
hyperTDA, a topological pipeline that unifies local (e.g. geodesic) and global
(e.g. Euclidean) metrics without losing spatial information, even in the
presence of noise. Homology generators offer an elegant and flexible
description of spatial structures and can capture the information computed by
persistent homology in an interpretable way. Here the information computed by
persistent homology is transformed into a weighted hypergraph, where hyperedges
correspond to homology generators. We consider different choices of generators
(e.g. matroid or minimal) and find that centrality and community detection are
robust to either choice. We compare hyperTDA to existing geometric measures and
validate its robustness to noise. We demonstrate the power of computing
higher-order topological structures on spatial curves arising frequently in
ecology, biophysics, and biology, but also in high-dimensional financial
datasets. We find that hyperTDA can select between synthetic trajectories from
the landmark 2020 AnDi challenge and quantifies movements of different animal
species, even when data is limited.


  We report on the direct observation of interface superconductivity in
single-unit-cell SnSe2 films grown on graphitized SiC(0001) substrate by means
of van der Waals epitaxy. Tunneling spectrum in the superconducting state
reveals rather conventional character with a fully gapped order parameter. The
occurrence of superconductivity is further confirmed by the presence of
vortices under external magnetic field. Through interface engineering, we
unravel the mechanism of superconductivity that originates from a
two-dimensional electron gas formed at the interface of SnSe2 and graphene. Our
finding opens up novel strategies to hunt for and understand interface
superconductivity based on van der Waals heterostructures.


  A number of categories is presented that are algebraically complete and
cocomplete, i.e., every endofunctor has an initial algebra and a terminal
coalgebra. For all finitary (and, more generally, all precontinuous) set
functors the initial algebra and terminal coalgebra are proved to carry a
canonical partial order with the same ideal CPO-completion. And they also both
carry a canonical ultrametric with the same Cauchy completion.


  We discuss thermal rectification and thermoelectric energy conversion from
the perspective of nonequilibrium statistical mechanics and dynamical systems
theory. After preliminary considerations on the dynamical foundations of the
phenomenological Fourier law in classical and quantum mechanics, we illustrate
ways to control the phononic heat flow and design thermal diodes. Finally, we
consider the coupled transport of heat and charge and discuss several general
mechanisms for optimizing the figure of merit of thermoelectric efficiency.


  We present a renormalization group analysis to Einstein-Rosen waves or vacuum
spacetimes with whole-cylinder symmetry. It is found that self-similar
solutions appear as fixed points in the renormalization group transformation.
These solutions correspond to the explosive gravitational waves and the
collapsing gravitational waves at late times and early times, respectively.
Based on the linear perturbation analysis of the self-similar solutions, we
conclude that the self-similar evolution is stable as explosive gravitational
waves under the condition of no incoming waves, while it is weakly unstable as
collapsing gravitational waves. The result implies that self-similar solutions
can describe the asymptotic behavior of more general solutions for exploding
gravitational waves and thus extends the similarity hypothesis in general
relativity from spherical symmetry to cylindrical symmetry.


  As a direct source of information on chiral symmetry breaking within QCD, the
sigma commutator is of considerable importance. With recent advances in the
calculation of hadron masses within full QCD it is of interest to see whether
the sigma commutator can be calculated directly from the dependence of the
nucleon mass on the input quark mass. We show that provided the correct chiral
behaviour of QCD is respected in the extrapolation to realistic quark masses
one can indeed obtain a fairly reliable determination of the sigma commutator
using present lattice data. Within two-flavour, dynamical-fermion QCD the value
obtained lies in the range 45 to 55 MeV.


  Let $F$ be a field of characteristic $p > 0$. We study the structure of the
finite groups $G$ for which the socle of the center of $FG$ is an ideal in $FG$
and classify the finite $p$-groups $G$ with this property. Moreover, we give an
explicit description of the finite groups $G$ for which the Reynolds ideal of
$FG$ is an ideal in $FG$.


  We introduce Longitudinal Predictive Conformal Inference (LPCI), a novel
distribution-free conformal prediction algorithm for longitudinal data. Current
conformal prediction approaches for time series data predominantly focus on the
univariate setting, and thus lack cross-sectional coverage when applied
individually to each time series in a longitudinal dataset. The current
state-of-the-art for longitudinal data relies on creating infinitely-wide
prediction intervals to guarantee both cross-sectional and asymptotic
longitudinal coverage. The proposed LPCI method addresses this by ensuring that
both longitudinal and cross-sectional coverages are guaranteed without
resorting to infinitely wide intervals. In our approach, we model the residual
data as a quantile fixed-effects regression problem, constructing prediction
intervals with a trained quantile regressor. Our extensive experiments
demonstrate that LPCI achieves valid cross-sectional coverage and outperforms
existing benchmarks in terms of longitudinal coverage rates. Theoretically, we
establish LPCI's asymptotic coverage guarantees for both dimensions, with
finite-width intervals. The robust performance of LPCI in generating reliable
prediction intervals for longitudinal data underscores its potential for broad
applications, including in medicine, finance, and supply chain management.