  We report magnetic behaviour of MnCr$_2$O$_4$, which belongs to a special
class of spinel, known as chromite. Bulk MnCr$_2$O$_4$ shows a sequence of
magnetic states, which follows paramagnetic (PM) to collinear ferrimagnetic
(FM) state below T$_C$ $\sim$ 45 K and collinear FM state to non-collinear FM
state below T$_S$ $\sim$ 18 K. The non-collinear spin structure has been
modified on decreasing the particle size, and magnetic transition at T$_S$
decreases in nanoparticle samples. However, ferrimagnetic order is still
dominating in nanoparticles, except the observation of superparamagnetic like
blocking and decrease of spontaneous magnetization for nanoparticle. This may,
according to the core-shell model of ferrimagnetic nanoparticle, be the surface
disorder effect of nanoparticle. The system also show the increase of T$_C$ in
nanoparticle samples, which is not consistent with the core-shell model. The
analysis of the M(T) data, applying spin wave theory, has shown an unusual
Bloch exponent value 3.35 for bulk MnCr$_2$O$_4$, which decreases and
approaches to 1.5, a typical value for any standard ferromagnet, with
decreasing the particle size. MnCr$_2$O$_4$ has shown a few more unusual
behaviour. For example, lattice expansion in nanoparticle samples. The present
work demonstrates the correlation between a systematic increase of lattice
parameter and the gradual decrease of B site non-collinear spin structure in
the light of magnetism of MnCr$_2$O$_4$ nanoparticles.


  A new core hypothesis on laughter is presented. It has been built by putting
together ideas from several disciplines: neurodynamics, evolutionary
neurobiology, paleoanthropology, social networks, and communication studies.
The hypothesis contributes to ascertain the evolutionary origins of human
laughter in connection with its cognitive emotional signaling functions. The
new behavioral and neurodynamic tenets introduced about this unusual sound
feature of our species justify the ubiquitous presence it has in social
interactions and along the life cycle of the individual. Laughter, far from
being a curious evolutionary relic or a rather trivial innate behavior, should
be considered as a highly efficient tool for inter-individual problem solving
and for maintenance of social bonds.


  We present interferometric measurements of the Sunyaev-Zel'dovich (SZ) effect
towards the galaxy cluster Abell 370. These measurements, which directly probe
the pressure of the cluster's gas, show the gas distribution to be strongly
aspherical, as do the x-ray and gravitational lensing observations. We
calculate the cluster's gas mass fraction in two ways. We first compare the gas
mass derived from the SZ measurements to the lensing-derived gravitational mass
near the critical lensing radius. We also calculate the gas mass fraction from
the SZ data by deprojecting the three-dimensional gas density distribution and
deriving the total mass under the assumption that the gas is in hydrostatic
equilibrium (HSE). We test the assumptions in the HSE method by comparing the
total cluster mass implied by the two methods and find that they agree within
the errors of the measurement. We discuss the possible systematic errors in the
gas mass fraction measurement and the constraints it places on the matter
density parameter, OmegaM.


  Differential chains are a proper subspace of de Rham currents given as an
inductive limit of Banach spaces endowed with a geometrically defined strong
topology. Boundary is a continuous operator, as are operators that dualize to
Hodge star, Lie derivative, pullback and interior product. Partitions of unity
exist in this setting, as does Cartesian wedge product. Subspaces of finitely
supported Dirac chains and polyhedral chains are both dense, leading to a
unification of the discrete with the smooth continuum. We conclude with an
application generalizing a simple version of the Reynolds' Transport Theorem to
rough domains.


  In this paper we discuss the possibility of measuring the anomalous magnetic
and electric dipole moments of the $\tau$ lepton. The method consists in
studying the spin precession induced by the strong effective magnetic field
inside channels of a bent crystal with a dedicated setup at the CERN Large
Hadron Collider.


  In this work we present some results on existence of Weyl almost periodic
selections of multivalued maps taking values in a complete metric space.


  Traders in a stock market exchange stock shares and form a stock trading
network. Trades at different positions of the stock trading network may contain
different information. We construct stock trading networks based on the limit
order book data and classify traders into $k$ classes using the $k$-shell
decomposition method. We investigate the influences of trading behaviors on the
price impact by comparing a closed national market (A-shares) with an
international market (B-shares), individuals and institutions, partially filled
and filled trades, buyer-initiated and seller-initiated trades, and trades at
different positions of a trading network. Institutional traders professionally
use some trading strategies to reduce the price impact and individuals at the
same positions in the trading network have a higher price impact than
institutions. We also find that trades in the core have higher price impacts
than those in the peripheral shell.


  Uniform random generation of Latin squares is a classical problem. In this
paper we prove that both Latin squares and Sudoku designs are maximum cliques
of properly defined graphs. We have developed a simple algorithm for uniform
random sampling of Latin squares and Sudoku designs. It makes use of recent
tools for graph analysis. The corresponding SAS code is annexed.


  Pretraining auto-regressive large language models~(LLMs) with retrieval
demonstrates better perplexity and factual accuracy by leveraging external
databases. However, the size of existing pretrained retrieval-augmented LLM is
still limited (e.g., Retro has 7.5B parameters), which limits the effectiveness
of instruction tuning and zero-shot generalization. In this work, we introduce
Retro 48B, the largest LLM pretrained with retrieval. Specifically, we continue
to pretrain a 43B GPT model on additional 100 billion tokens using the Retro
augmentation method by retrieving from 1.2 trillion tokens. Notably, the
obtained foundation model, Retro 48B, largely outperforms the counterpart GPT
43B trained on 1.2T tokens in terms of perplexity with only 2.58% additional
GPU hours, demonstrating the significant scaling potential of the method. After
instruction tuning on Retro, InstructRetro demonstrates significant improvement
over the instruction tuned GPT on a wide range of zero-shot tasks.
Specifically, the average improvement of InstructRetro is 7% over its GPT
counterpart across 8 short-form QA and reading comprehension tasks, 10% over
GPT across 4 challenging long-form QA tasks, and 16% over GPT across 3
summarization tasks. Surprisingly, we find that one can ablate the encoder from
InstructRetro architecture and directly use its decoder backbone, while
achieving comparable results. Our results highlight the promising direction to
obtain a better GPT decoder through continued pretraining with retrieval before
instruction tuning. Our code and checkpoints are publicly available at:
https://huggingface.co/nvidia/retro-48b-instruct-4k.


  There is a wide range of eruptions in the solar atmosphere which contribute
to space weather, including the major explosions of radiation known as flares.
To examine pre-event behavior in delta-spot regions, we use here a method based
on the weighted horizontal gradient of magnetic field (WG_M), defined between
opposite polarity umbrae at the polarity inversion line of active regions (ARs)
as measured using from the Debrecen Heliophysical Observatory catalogues. In
this work, we extend the previous analysis of high-energy flares to include
both medium (M) and low-energy (C and B) flares. First, we found a logarithmic
relationship between the log value of highest flare class intensity (from B- to
X-class) in a $\delta$-spot AR and the maximum value of WG_M of the 127 ARs
investigated. We confirm a trend in the convergence-divergence phase of the
barycenters of opposite polarities in the vicinity of the polarity inversion
line. The extended sample (i) affirms the linear connection between the
durations of the convergence-divergence phases of barycenters of opposite
polarities in delta-spot regions up to flare occurrence and (ii) provides a
geometric constraint for the location of flare emission around the polarity
inversion line. The method provides a tool to possibly estimate the likelihood
of a subsequent flare of the same or larger energy.


  The expected performance of GAIA satellite on eclipsing binaries is reviewed
on the basis of (a) combined Hipparcos and ground-based observations mimicking
GAIA data harvest, and (b) accurate simulations using the latest instrument
model. It is found that for a large majority of the 16000 SB2 eclipsing
binaries that GAIA will discover at magnitudes V<13, the orbital solutions and
physical parameters will be derived with formal accuracies better than 2%. For
the same stars the GAIA parallax errors will be about 5 micro-arcsec, i.e. an
error of 0.5% at 1 kpc, which will allow to iteratively refine of the
parameters and physics used in orbital modeling. The detectability of SB2
binaries by the already up and running spectral survey RAVE is discussed. It is
found that all F-to-M SB2 binaries showing a velocity separation >=35 km/sec
and a luminosity ratio >=0.5 will be recognized as such.


  In this article, we extend our previous study of the $\pi$-$\pi$ scattering
lengths under the presence of an external magnetic field, including finite
temperature effects. The novelty of this work is precisely the introduction of
temperature into the discussion, and its interplay with the magnetic field. As
in the previous article, we base our analysis in the linear sigma-model, and
our calculations are exact within this context. Although the effects are
comparatively small, it is interesting to remark that magnetic field and
temperature display opposite effects over the scattering lengths.


  In this paper we develop a measure-theoretic method to treat problems in
hypergraph theory. Our central theorem is a correspondence principle between
three objects: An increasing hypergraph sequence, a measurable set in an
ultraproduct space and a measurable set in a finite dimensional Lebesgue space.
Using this correspondence principle we build up the theory of dense hypergraphs
from scratch. Along these lines we give new proofs for the Hypergraph Removal
Lemma, the Hypergraph Regularity Lemma, the Counting Lemma and the Testability
of Hereditary Hypergraph Properties. We prove various new results including a
strengthening of the Regularity Lemma and an Inverse Counting Lemma. We also
prove the equivalence of various notions for convergence of hypergraphs and we
construct limit objects for such sequences. We prove that the limit objects are
unique up to a certain family of measure preserving transformations. As our
main tool we study the integral and measure theory on the ultraproduct of
finite measure spaces which is interesting on its own right.


  The thermal properties of $f_{2}(1270)$, $a_{2}(1320)$ and $K_2^*(1430)$
light tensor mesons are investigated in the framework of QCD sum rules at
finite temperature. In particular, the masses and decay constants of the light
tensor mesons are calculated taking into account the new operators appearing at
finite temperature. The numerical results show that at the point which the
temperature-dependent continuum threshold vanishes, the decay constants
decrease with amount of $(70-85)\%$ compared to their vacuum values, while the
masses diminish about $(60-72)\%$ depending on the kinds of the mesons under
consideration. The results obtained at zero temperature are in good consistency
with the experimental data as well as existing theoretical predictions.


  Based on a data sample of 60 pb$^{-1}$ collected at the $\psi(3770)$
resonance with the CLEO-c detector at CESR, we present improved measurements of
absolute branching fractions for exclusive $D^0$ semileptonic decays into
$K^-e^+\nu$, $\pi^-e^+\nu$ and $K^{*-}e^+\nu$, and the first observation and
measurement of $D^0 \to \rho^-e^+\nu$. The determinations of the CKM matrix
elements $V_{cs}$ and $V_{cd}$ are reviewed.


  This paper is devoted to prove the existence of one or multiple solutions of
a wide range of nonlinear differential boundary value problems.
  To this end, we obtain some new fixed point theorems for a class of integral
operators. We follow the well-known Krasnoselski\u{\i}'s fixed point Theorem
together with two fixed point results of Leggett-Williams type.
  After obtaining a general existence result for a one parameter family of
nonlinear differential equations, are proved, as particular cases, existence
results for second and fourth order nonlinear boundary value problems.


  We determine a next-to-leading order result for the shear channel thermal
spectral function in SU(N) Yang-Mills theory, working in the limit of vanishing
external three-momentum. The result is subsequently applied to the evaluation
of the corresponding imaginary time correlator, and its use in the context of
sum rules is discussed. Our hope is that the calculation will eventually find
use in the nonperturbative determination of the shear viscosity of the theory.


  The Unruh effect is the prediction that an accelerating object perceives its
surroundings as a bath of thermal radiation even if it accelerates in vacuum.
The Unruh effect is believed to be very difficult to observe in the experiment,
since an observer accelerating at g=9.8 m/s2 should see vacuum temperature of
only 4x10^-20 K. Here we demonstrate that photons in metamaterial waveguides
may behave as massive quasi-particles accelerating at up to 10^24 g, which is
about twelve orders of magnitude larger than the surface acceleration near a
stellar black hole. These record high accelerations may enable experimental
studies of the Unruh effect and the loss of quantum entanglement in strongly
accelerated reference frames.


  In the canonical seesaw mechanism of neutrino mass, lepton number is only
multiplicatively conserved, which enables the important phenomenon of
leptogenesis to occur, as an attractive explanation of the present baryon
asymmetry of the Universe. A parallel possibility, hitherto unrecognized, also
holds for baryon number and baryogenesis. This new idea is shown to be
naturally realized in the context of a known supersymmetric string-inspired
extension of the Standard Model, based on E(6) particle content, and having an
extra U(1)_N gauge symmetry. Within this framework, two-loop radiative neutrino
masses are also possible, together with a new form of very long-lived matter.


  Quantum mechanics describes the relation between different measurement
contexts in terms of superpositions of the potential measurement outcomes. This
relation between measurement contexts makes it impossible to determine context
independent realities. Here, I illustrate the problem using three path
interferences that implement the three box paradox and show that the
representation of the final measurement outcome as a superposition of
intermediate paths describes well-defined coherences between seemingly empty
paths.


  We propose in this paper a new method to compute the characteristic function
(CF) of generalized Gaussian (GG) random variable in terms of the Fox H
function. The CF of the sum of two independent GG random variables is then
deduced. Based on this results, the probability density function (PDF) and the
cumulative distribution function (CDF) of the sum distribution are obtained.
These functions are expressed in terms of the bivariate Fox H function. Next,
the statistics of the distribution of the sum, such as the moments, the
cumulant, and the kurtosis, are analyzed and computed. Due to the complexity of
bivariate Fox H function, a solution to reduce such complexity is to
approximate the sum of two independent GG random variables by one GG random
variable with suitable shape factor. The approximation method depends on the
utility of the system so three methods of estimate the shape factor are studied
and presented.


  We contribute a third-party survey of sparse matrix-vector (SpMV) product
performance on industrial-strength, large matrices using: (1) The SpMV
implementations in Intel MKL, the Trilinos project (Tpetra subpackage), the
CUSPARSE library, and the CUSP library, each running on modern architectures.
(2) NVIDIA GPUs and Intel multi-core CPUs (supported by each software package).
(3) The CSR, BSR, COO, HYB, and ELL matrix formats (supported by each software
package).


  The formation of coherently strained three-dimensional islands on top of the
wetting layer in Stranski-Krastanov mode of growth is considered in a model in
1+1 dimensions accounting for the anharmonicity and non-convexity of the real
interatomic forces. It is shown that coherent 3D islands can be expected to
form in compressed rather than in expanded overlayers beyond a critical lattice
misfit. In the latter case the classical Stranski-Krastanov growth is expected
to occur because the misfit dislocations can become energetically favored at
smaller island sizes. The thermodynamic reason for coherent 3D islanding is the
incomplete wetting owing to the weaker adhesion of the edge atoms. Monolayer
height islands with a critical size appear as necessary precursors of the 3D
islands. The latter explains the experimentally observed narrow size
distribution of the 3D islands. The 2D-3D transformation takes place by
consecutive rearrangements of mono- to bilayer, bi- to trilayer islands, etc.,
after exceeding the corresponding critical sizes. The rearrangements are
initiated by nucleation events each next one requiring to overcome a lower
energetic barrier. The model is in good qualitative agreement with available
experimental observations.


  We prove an invariance principle for a class of zero-drift spatially
non-homogeneous random walks in $\mathbb{R}^d$, which may be recurrent in any
dimension. The limit $\mathcal{X}$ is an elliptic martingale diffusion, which
may be point-recurrent at the origin for any $d\geq2$. To characterise
$\mathcal{X}$, we introduce a (non-Euclidean) Riemannian metric on the unit
sphere in $\mathbb{R}^d$ and use it to express a related spherical diffusion as
a Brownian motion with drift. This representation allows us to establish the
skew-product decomposition of the excursions of $\mathcal{X}$ and thus develop
the excursion theory of $\mathcal{X}$ without appealing to the strong Markov
property. This leads to the uniqueness in law of the stochastic differential
equation for $\mathcal{X}$ in $\mathbb{R}^d$, whose coefficients are
discontinuous at the origin. Using the Riemannian metric we can also detect
whether the angular component of the excursions of $\mathcal{X}$ is
time-reversible. If so, the excursions of $\mathcal{X}$ in $\mathbb{R}^d$
generalise the classical Pitman-Yor splitting-at-the-maximum property of Bessel
excursions.


  The detection of optical/infrared counterparts to Anomalous X-ray Pulsars
(AXPs) has greatly increased our understanding of these systems. Models for the
AXP phenomenon were based upon their X-ray emission, and all but the magnetar
model made predictions for the optical/infrared that have now been falsified.
  With detections in hand, detailed studies of the optical/infrared to X-ray
flux ratios, variability, and the spectral energy distributions have become
possible. We present new data on two AXPs taken with Keck and Magellan, and
compare the results with predictions made in the context of the magnetar model,
in which the emission is due to ion currents flowing in the >10e14 G
magnetosphere of young neutron stars.


  We develop a general framework to (numerically) study adiabatic braiding of
quasiholes in fractional quantum Hall systems. Specifically, we investigate the
Moore-Read (MR) state at $\nu=1/2$ filling factor, a known candidate for
non-Abelian statistics, which appears to actually occur in nature. The
non-Abelian statistics of MR quasiholes is demonstrated explicitly for the
first time, confirming the results predicted by conformal field theories.


  Homographs, words with the same spelling but different meanings, remain
challenging in Neural Machine Translation (NMT). While recent works leverage
various word embedding approaches to differentiate word sense in NMT, they do
not focus on the pivotal components in resolving ambiguities of homographs in
NMT: the hidden states of an encoder. In this paper, we propose a novel
approach to tackle homographic issues of NMT in the latent space. We first
train an encoder (aka "HDR-encoder") to learn universal sentence
representations in a natural language inference (NLI) task. We further
fine-tune the encoder using homograph-based synset sentences from WordNet,
enabling it to learn word-level homographic disambiguation representations
(HDR). The pre-trained HDR-encoder is subsequently integrated with a
transformer-based NMT in various schemes to improve translation accuracy.
Experiments on four translation directions demonstrate the effectiveness of the
proposed method in enhancing the performance of NMT systems in the BLEU scores
(up to +2.3 compared to a solid baseline). The effects can be verified by other
metrics (F1, precision, and recall) of translation accuracy in an additional
disambiguation task. Visualization methods like heatmaps, T-SNE and translation
examples are also utilized to demonstrate the effects of the proposed method.


  The various types of communication technologies and mobility features in
Internet of Things (IoT) on the one hand enable fruitful and attractive
applications, but on the other hand facilitates malware propagation, thereby
raising new challenges on handling IoT-empowered malware for cyber security.
Comparing with the malware propagation control scheme in traditional wireless
networks where nodes can be directly repaired and secured, in IoT, compromised
end devices are difficult to be patched. Alternatively, blocking malware via
patching intermediate nodes turns out to be a more feasible and practical
solution. Specifically, patching intermediate nodes can effectively prevent the
proliferation of malware propagation by securing infrastructure links and
limiting malware propagation to local device-to-device dissemination. This
article proposes a novel traffic-aware patching scheme to select important
intermediate nodes to patch, which applies to the IoT system with limited
patching resources and response time constraint. Experiments on real-world
trace datasets in IoT networks are conducted to demonstrate the advantage of
the proposed traffic-aware patching scheme in alleviating malware propagation.


  There exists a connection between the creation of toroidal moments (TM) and
the breaking of the one-cell relativistic crystalline symmetry (RCS) associated
to any given crystal into which non-trivial magnetoelectric coupling effects
(ME) exist. Indeed, in this kind of crystals, any interaction between a charge
carrier and an elementary magnetic cell can breaks the RCS of this previous
given cell by varying, in the simplest case, the continuous defining parameters
of the initial RCS. This breaking can be associated to a change of the initial
Galilean proper frame of any given carrier to an "effective" one, into which
the RCS of the interacting cell is kept. We can speak of a kind of "inverse"
kineto-magnetoelectric effect. The magnetic groups compatible with such process
have been computed. Moreover, one can notice that the TM's break the P and T
symmetries but not the PT one as in anyons theories. This breaking creates
so-called Nambu-Goldstone bosons generating "effective" magnetic monopoles.
These consequences allow us to claim, first, that anyons are charge carriers
associated with "effective" magnetic monopoles, both with TM's, and second,
that ME can be highly considered in superconductors theory.


  Double-beta processes play a key role in the exploration of neutrino and weak
interaction properties, and in the searches for effects beyond the Standard
Model. During the last half century many attempts were undertaken to search for
double-beta decay with emission of two electrons, especially for its
neutrinoless mode ($0\nu2\beta^-$), the latter being still not observed.
Double-electron capture (2EC) was not in focus so far because of its in general
lower transition probability. However, the rate of neutrinoless double-electron
capture ($0\nu2$EC) can experience a resonance enhancement by many orders of
magnitude in case the initial and final states are energetically degenerate. In
the resonant case, the sensitivity of the $0\nu2$EC process can approach the
sensitivity of the $0\nu2\beta^-$ decay in the search for the Majorana mass of
neutrinos, right-handed currents, and other new physics. We present an overview
of the main experimental and theoretical results obtained during the last
decade in this field. The experimental part outlines search results of 2EC
processes and measurements of the decay energies for possible resonant
$0\nu$2EC transitions. An unprecedented precision in the determination of decay
energies with Penning traps has allowed one to refine the values of the
degeneracy parameter for all previously known near-resonant decays and has
reduced the rather large uncertainties in the estimate of the $0\nu2$EC
half-lives. The theoretical part contains an updated analysis of the electron
shell effects and an overview of the nuclear structure models, in which the
nuclear matrix elements of the $0\nu2$EC decays are calculated. One can
conclude that the decay probability of $0\nu$2EC can experience a significant
enhancement in several nuclides.


  Most benchmarks for studying surgical interventions focus on a specific
challenge instead of leveraging the intrinsic complementarity among different
tasks. In this work, we present a new experimental framework towards holistic
surgical scene understanding. First, we introduce the Phase, Step, Instrument,
and Atomic Visual Action recognition (PSI-AVA) Dataset. PSI-AVA includes
annotations for both long-term (Phase and Step recognition) and short-term
reasoning (Instrument detection and novel Atomic Action recognition) in
robot-assisted radical prostatectomy videos. Second, we present Transformers
for Action, Phase, Instrument, and steps Recognition (TAPIR) as a strong
baseline for surgical scene understanding. TAPIR leverages our dataset's
multi-level annotations as it benefits from the learned representation on the
instrument detection task to improve its classification capacity. Our
experimental results in both PSI-AVA and other publicly available databases
demonstrate the adequacy of our framework to spur future research on holistic
surgical scene understanding.


  In the present work we systematically study $\mathcal{\alpha}$ decay
half-lives of $Z>51$ nuclei using the modified Gamow-like model which includes
the effects of the centrifugal potential and electrostatic shielding. For the
case of even-even nuclei, this model contains two adjustable parameters: the
parameter $a$ related to the screened electrostatic barrier and the radius
constant $r_0$, while for the case of odd-odd and odd-A nuclei, it is added a
new parameter i.e. hindrance factor $h$ which is used to describe the effect of
an odd-proton and/or an odd-neutron. Our calculations can well reproduce the
experimental data. In addition, we use this modified Gamow-like model to
predict the $\mathcal{\alpha}$-decay half-lives of seven even-even nuclei with
$Z=120$ and some un-synthesized nuclei on their $\mathcal{\alpha}$ decay
chains.


  We study the long wavelength shear modes (Tkachenko waves) of triangular
lattices of singly quantized vortices in neutron star interiors taking into
account the mutual friction between the superfluid and the normal fluid and the
shear viscosity of the normal fluid. The set of Tkachenko modes that propagate
in the plane orthogonal to the spin vector are weakly damped if the coupling
between the superfluid and normal fluid is small. In strong coupling, their
oscillation frequencies are lower and are undamped for small and moderate shear
viscosities. The periods of these modes are consistent with the observed
~100-1000 day variations in spin of PSR 1828-11.


  Supernova explosions inject a considerable amount of energy into the
interstellar medium (ISM) in regions with high to moderate star formation
rates. In order to assess whether the driving of turbulence by supernovae is
also important in the outer Galactic disk, where the star formation rates are
lower, we study the spatial distribution of molecular cloud (MC) inclinations
with respect to the Galactic plane. The latter contains important information
on the nature of the mechanism of energy injection into the ISM. We analyze the
spatial correlations between the position angles (PAs) of a selected sample of
MCs (the largest clouds in the catalogue of the outer Galaxy published by Heyer
et al. 2001). Our results show that when the PAs of the clouds are all mapped
to values into the [0,90]degrees interval, there is a significant degree of
spatial correlation between the $PA$s on spatial scales in the range of 100-800
pc. These scales are of the order of the sizes of individual SN shells in low
density environments such as those prevailing in the outer Galaxy and where the
metallicity of the ambient gas is of the order of the solar value or smaller.
These findings suggest that individual SN explosions, occurring in the outer
regions of the Galaxy and in likewise spiral galaxies, albeit at lower rates,
continue to play an important role in shaping the structure and dynamics of the
ISM in those regions. The SN explosions we postulate here are likely associated
with the existence of young stellar clusters in the far outer regions of the
Galaxy and the UV emission and low levels of star formation observed with the
GALEX satellite in the outer regions of local galaxies.


  Motivation: Flow Injection Analysis coupled to High-Resolution Mass
Spectrometry (FIA-HRMS) is a promising approach for high-throughput
metabolomics. FIA-HRMS data, however, cannot be preprocessed with current
software tools which rely on liquid chromatography separation, or handle low
resolution data only. Results: We thus developed the proFIA package, which
implements a suite of innovative algorithms to preprocess FIA-HRMS raw files,
and generates the table of peak intensities. The workflow consists of 3 steps:
i) noise estimation, peak detection and quantification, ii) peak grouping
across samples, and iii) missing value imputation. In addition, we have
implemented a new indicator to quantify the potential alteration of the feature
peak shape due to matrix effect. The preprocessing is fast (less than 15 s per
file), and the value of the main parameters (ppm and dmz) can be easily
inferred from the mass resolution of the instrument. Application to two
metabolomics datasets (including spiked serum samples) showed high precision
(96%) and recall (98%) compared with manual integration. These results
demonstrate that proFIA achieves very efficient and robust detection and
quantification of FIA-HRMS data, and opens new opportunities for
high-throughput phenotyping. Availability: The proFIA software (as well as the
plasFIA data set) is available as an R package on the Bioconductor repository
(http://bioconductor.org/packages/proFIA), and as a Galaxy module on the Main
Toolshed (https://toolshed.g2.bx.psu.edu/) and on the Workflow4Metabolomics
online infrastructure (http://workflow4metabolomics.org). Contacts:
<EMAIL_ADDRESS>and<EMAIL_ADDRESS>


  We thoroughly investigate vibrational quantum dynamics of dimers attached to
He droplets motivated by recent measurements with K-2 [1]. For those
femtosecond pump-probe experiments, crucial observed features are not
reproduced by gas phase calculations but agreement is found using a description
based on dissipative quantum dynamics, as briefly shown in [2]. Here we present
a detailed study of the influence of possible effects induced by the droplet.
The helium droplet causes electronic decoherence, shifts of potential surfaces,
and relaxation of wave packets in attached dimers. Moreover, a realistic
description of (stochastic) desorption of dimers off the droplet needs to be
taken into account. Step by step we include and study the importance of these
effects in our full quantum calculation. This allows us to reproduce and
explain all major experimental findings. We find that desorption is fast and
occurs already within 2-10 ps after electronic excitation. A further finding is
that slow vibrational motion in the ground state can be considered
frictionless.


  We study the noise, in the sense of Tsirelson, generated by Harris flows. A
criterion is given for the noise to be non-white, and in this case we study the
associated spectral sets.


  Dimensionality is an important aspect for analyzing and understanding
(high-dimensional) data. In their 2006 ICDM paper Tatti et al. answered the
question for a (interpretable) dimension of binary data tables by introducing a
normalized correlation dimension. In the present work we revisit their results
and contrast them with a concept based notion of intrinsic dimension (ID)
recently introduced for geometric data sets. To do this, we present a novel
approximation for this ID that is based on computing concepts only up to a
certain support value. We demonstrate and evaluate our approximation using all
available datasets from Tatti et al., which have between 469 and 41271
extrinsic dimensions.


  It is shown that the geometry of quantum theory can be derived from
geometrical structure that may be considered more fundamental. The basic
elements of this reconstruction of quantum theory are the natural metric on the
space of probabilities (information geometry), the description of dynamics
using a Hamiltonian formalism (symplectic geometry), and requirements of
consistency (K\"{a}hler geometry). The theory that results is standard quantum
mechanics, but in a geometrical formulation that includes also a particular
case of a family of nonlinear gauge transformations introduced by Doebner and
Goldin. The analysis is carried out for the case of discrete quantum mechanics.
The work presented here relies heavily on, and extends, previous work done in
collaboration with M. J. W. Hall.


  This article follows our previous work on Campbell-Hausdorff formula. We
study the case of symmetric spaces. We recover, by using a Kontsevich's
deformation of the Baker-Campbell-Hausdorff formula, Rouviere's results on the
convolution of invariant distributions, for solvable symmetric spaces and "very
symmetric spaces".


  Recently, there has been great interest in the field of audio style transfer,
where a stylized audio is generated by imposing the style of a reference audio
on the content of a target audio. We improve on the current approaches which
use neural networks to extract the content and the style of the audio signal
and propose a new autoencoder based architecture for the task. This network
generates a stylized audio for a content audio in a single forward pass. The
proposed network architecture proves to be advantageous over the quality of
audio produced and the time taken to train the network. The network is
experimented on speech signals to confirm the validity of our proposal.


  Alzheimer's Disease (AD) is a progressive neurodegenerative disease. Amnestic
mild cognitive impairment (MCI) is a common first symptom before the conversion
to clinical impairment where the individual becomes unable to perform
activities of daily living independently. Although there is currently no
treatment available, the earlier a conclusive diagnosis is made, the earlier
the potential for interventions to delay or perhaps even prevent progression to
full-blown AD. Neuroimaging scans acquired from MRI and metabolism images
obtained by FDG-PET provide in-vivo view into the structure and function
(glucose metabolism) of the living brain. It is hypothesized that combining
different image modalities could better characterize the change of human brain
and result in a more accuracy early diagnosis of AD. In this paper, we proposed
a novel framework to discriminate normal control(NC) subjects from subjects
with AD pathology (AD and NC, MCI subjects convert to AD in future). Our novel
approach utilizing a multimodal and multiscale deep neural network was found to
deliver a 85.68\% accuracy in the prediction of subjects within 3 years to
conversion. Cross validation experiments proved that it has better
discrimination ability compared with results in existing published literature.


  We describe a code designed for hot media {(T $\ge$} a few 10$^4$ K),
optically thick to Compton scattering. It computes the structure of a
plane-parallel slab of gas in thermal and ionization equilibrium, illuminated
on one or on both sides by a given spectrum. Contrary to the other
photoionization codes, it solves the transfer of the continuum and of the lines
in a two stream approximation, without using the local escape probability
formalism to approximate the line transfer. We stress the importance of taking
into account the returning flux even for small column densities (10$^{22}$
cm$^{-2}$), and we show that the escape probability approximation can lead to
strong errors in the thermal and ionization structure, as well as in the
emitted spectrum, for a Thomson thickness larger than a few tenths. The
transfer code is coupled with a Monte Carlo code which allows to take into
account Compton and inverse Compton diffusions, and to compute the spectrum
emitted up to MeV energies, in any geometry. Comparisons with {\sc{cloudy}}
show that it gives similar results for small column densities. Several
applications are mentioned.


  Discounting future costs and rewards is a common practice in accounting, game
theory, and machine learning. In spite of this, existing logics for reasoning
about strategies with cost and resource constraints do not account for
discounting. The paper proposes a sound and complete logical system for
reasoning about budget-constrained strategic abilities that incorporates
discounting into its semantics.


  We study the ground state properties of antiferromagnetic $J_1$-$J_2$ chains
with half-integer spins ranging from $S=\frac{3}{2}$ to $S=\frac{11}{2}$ using
the density-matrix renormalization group method. We map out the ground-state
phase diagrams as a function of $\frac{J_2}{J_1}$ containing topological phases
with alternating $\frac{2S-1}{2}$ and $\frac{2S+1}{2}$ valence bonds. We
identify these topological phases and their boundaries by calculating the
string order parameter, the dimer order parameter, and the spin gap for those
high-$S$ systems in thermodynamic limit (finite size scaling). We find that
these topological regions narrow down inversely with $S$ and converge to a
single point at $\frac{J_2}{J_1}=\frac{1}{4}$ in the classical limit -- a
critical threshold between commensurate and incommensurate orders. In addition,
we extend the discussion of the Majumder-Ghosh state, previously noted only for
$S=\frac{1}{2}$, and speculate its possible presence as a ground state in
half-integer high spin systems over a substantial range of $\frac{J_2}{J_1}$
values.


  We give optimally fast $O(\log p)$ time (per processor) algorithms for
computing round-optimal broadcast schedules for message-passing parallel
computing systems. This affirmatively answers difficult questions posed in a
SPAA 2022 BA and a CLUSTER 2022 paper. We observe that the computed schedules
and circulant communication graph can likewise be used for reduction,
all-broadcast and all-reduction as well, leading to new, round-optimal
algorithms for these problems. These observations affirmatively answer open
questions posed in a CLUSTER 2023 paper.
  The problem is to broadcast $n$ indivisible blocks of data from a given root
processor to all other processors in a (subgraph of a) fully connected network
of $p$ processors with fully bidirectional, one-ported communication
capabilities. In this model, $n-1+\lceil\log_2 p\rceil$ communication rounds
are required. Our new algorithms compute for each processor in the network
receive and send schedules each of size $\lceil\log_2 p\rceil$ that determine
uniquely in $O(1)$ time for each communication round the new block that the
processor will receive, and the already received block it has to send. Schedule
computations are done independently per processor without communication. The
broadcast communication subgraph is an easily computable, directed,
$\lceil\log_2 p\rceil$-regular circulant graph also used elsewhere. We show how
the schedule computations can be done in optimal time and space of $O(\log p)$,
improving significantly over previous results of $O(p\log^2 p)$ and $O(\log^3
p)$, respectively. The schedule computation and broadcast algorithms are simple
to implement, but correctness and complexity are not obvious. The schedules are
used for new implementations of the MPI (Message-Passing Interface) collectives
MPI_Bcast, MPI_Allgatherv, MPI_Reduce and MPI_Reduce_scatter. Preliminary
experimental results are given.


  In this paper we study two different ways of coupling a local operator with a
nonlocal one in such a way that the resulting equation is related to an energy
functional. In the first strategy the coupling is given via source terms in the
equation and in the second one a flux condition in the local part appears. For
both models we prove existence and uniqueness of a solution that is obtained
via direct minimization of the related energy functional. In the second part of
this paper we extend these ideas to deal with local/nonlocal elasticity models
in which we couple classical local elasticity with nonlocal peridynamics.


  The nondegenerate two-orbital Hubbard model is studied within the dynamic
mean-field theory to reveal the influence of two important factors, i.e.
crystal field splitting and interorbital hopping, on orbital selective Mott
transition (OSMT) and realistic compound Ca$_{2-x}$Sr$_{x}$RuO$_{4}$. A
distinctive feature of the optical conductivity of the two nondegenerate bands
is found in OSMT phase, where the metallic character of the wide band is
indicated by a nonzero Drude peak, while the insulating narrow band has its
Drude peak drop to zero in the mean time. We also find that the OSMT regime
expands profoundly with the increase of interorbital hopping integrals. On the
contrary, it is shown that large and negative level splitting of the two
orbitals diminishes the OSMT regime completely. Applying the present findings
to compound Ca$_{2-x}$Sr$_{x}$RuO$_{4}$, we demonstrate that in the doping
region from $x=0.2$ to 2.0, the negative level splitting is unfavorable to the
OSMT phase.


  We give reasons in support of the use of an effective intensity-dependent
pion-nucleon coupling Hamiltonian for describing the properties of the pion
multiplicity distribution and the corresponding factorial moments within the
thermal-density matrix approach.We explain the appearance of the
negative-binomial (NB) distribution for pions and the well-known empi- rical
relation of Wroblewski.Our model Hamiltonian is written as a linear combination
of the generators of the SU(1,1) group.We find the generating function for the
pion multiplicity distribution at finite temperature T and discuss the
properties of the second-order factorial moment.Also, we show that an
intensity-dependent pion-nucleon coupling generates the squeezed states of the
pion field. At T=0, these squeezed states become an inherent property of the NB
distribution.


  We extend the threshold resummation exponents G^N in Mellin-N space to the
fourth logarithmic (N^3LL) order collecting the terms alpha_s^2 (alpha_s ln
N)^n to all orders in the strong coupling constant as. Comparing the results to
our previous three-loop calculations for deep-inelastic scattering (DIS), we
derive the universal coefficients B_q and B_g governing the final-state jet
functions to order alpha_s^3, extending the previous quark and gluon results by
one and two orders. A curious relation is found at second order between these
quantities, the splitting functions and the large-angle soft emissions in
Drell-Yan type processes. We study the numerical effect of the N^3LL
corrections using both the fully exponentiated form and the expansion of the
coefficient function in towers of logarithms.


  We prove that $F$-injectivity localizes, descends under faithfully flat
homomorphisms, and ascends under flat homomorphisms with Cohen-Macaulay and
geometrically $F$-injective fibers, all for arbitrary Noetherian rings of prime
characteristic. As a consequence, we show that the $F$-injective locus is open
on most rings arising in arithmetic and geometry. As a geometric application,
we prove that over an algebraically closed field of characteristic $p > 3$,
generic projection hypersurfaces associated to suitably embedded smooth
projective varieties of dimension $\le 5$ are $F$-pure, and hence
$F$-injective. This geometric result is the positive characteristic analogue of
a theorem of Doherty.


  The H$\alpha$ profile varies with the orbital period. The two strong shell
type emission peaks are identified as from one single broad emission feature
with an absorption centered around -7.5~\kms. The intensity variations are
largely attributed to a differential amount of reddening towards the H$\alpha$
emitting region and the stellar continuum. The radial velocities suggest that
the H$\alpha$ emission moves in phase with the primary, but with a slightly
lower velocity amplitude.
  We propose two competing models that could account for the observed velocity
and intensity variations of the H$\alpha$ profile. Model I: light from the
primary reflects on a localized spot near the inner radius of the circumbinary
disc which is closest to the primary. Model II: H$\alpha$ emission originates
in the outer layers of the extended atmosphere of the primary due to activity.
These activities are locked to the position of the primary in its orbit.
  We discuss the similarities of variability and shape of the H$\alpha$
emission of HR~4049 with those of early type T-Tauri stars (e.g SU~Aur).


  We construct $\theta$-deformations of the classical groups SL(2,H) and Sp(2).
Coacting on the basic instanton on a noncommutative four-sphere $S^4_\theta$,
we construct a noncommutative family of instantons of charge 1. The family is
parametrized by the quantum quotient of $SL_\theta(2,H)$ by $Sp_\theta(2)$.


  The multi-armed bandit (MAB) problem is a classical learning task that
exemplifies the exploration-exploitation tradeoff. However, standard
formulations do not take into account {\em risk}. In online decision making
systems, risk is a primary concern. In this regard, the mean-variance risk
measure is one of the most common objective functions. Existing algorithms for
mean-variance optimization in the context of MAB problems have unrealistic
assumptions on the reward distributions. We develop Thompson Sampling-style
algorithms for mean-variance MAB and provide comprehensive regret analyses for
Gaussian and Bernoulli bandits with fewer assumptions. Our algorithms achieve
the best known regret bounds for mean-variance MABs and also attain the
information-theoretic bounds in some parameter regimes. Empirical simulations
show that our algorithms significantly outperform existing LCB-based algorithms
for all risk tolerances.


  Compact boson star binaries are hypothetical sources for ground-based and
space gravitational-wave detectors. Their signal would be a messenger for novel
fundamental fields and could shed light on the dark matter. In this work, we
further develop our analysis in Phys. Rev. D 102, 083002 (2020), aimed at
constraining the properties of these objects with future observations. We use a
coherent waveform template for the inspiral stage of boson star binaries with
large quartic self interactions, including tidal deformability and the
nonlinear dependence of the quadrupole moments on the spin in terms of the
fundamental couplings of the scalar field theory. Performing a Bayesian
analysis, we investigate the ability of a third-generation gravitational-wave
detector such as the Einstein Telescope to distinguish these exotic sources
from black holes and infer constraints on the fundamental couplings of the
model.


  The total entropy production of a trajectory can be split into an adiabatic
and a non-adiabatic contribution, deriving respectively from the breaking of
detailed balance via nonequilibrium boundary conditions or by external driving.
We show that each of them, the total, the adiabatic and the non-adiabatic
trajectory entropy, separately satisfies a detailed fluctuation theorem.


  We study the time evolution of a large-scale magnetic flux threading an
accretion disk. Induction equation of the mean poloidal field is solved under
the standard viscous disk model. Magnetic flux evolution is controlled by the
two timescales: One is the timescale of the inward advection of the magnetic
flux, tau_{adv}. This is induced by the dragging of the flux by the accreting
gas. The other is the outward diffusion timescale of the magnetic flux
tau_{dif}. We consider diffusion due to the Ohmic resistivity. These timescales
can be significantly different from the disk viscous timescale tau_{disk}. The
behaviors of the magnetic flux evolution is quite different depending on the
magnitude relationship of the timescales tau_{adv}, \tau_{dif}, and tau_{disk}.
The most interesting phenomena occurs when tau_{adv} << tau_{dif}, tau_{disk}.
In such a case, the magnetic flux distribution approaches a quasi-steady
profile much faster than the viscous evolution of the gas disk, and also the
magnetic flux has been tightly bundled to the inner part of the disk. In the
inner part, although the poloidal magnetic field becomes much stronger than the
interstellar magnetic field, the field strength is limited to the maximum value
that is analytically given by our previous work (Okuzumi et al. 2014, ApJ, 785,
127). We also find a condition for that the initial large magnetic flux, which
is a fossil of the magnetic field dragging during the early phase of star
formation, survives for a duration in which significant gas disk evolution
proceeds.


  In this work we consider the operator
  \[
  (\mathbf{T} G) (x)= \int_{\mathbb{S}^2} G(x\cdot \omega, \omega) d\omega,
\quad x\in \mathbb{R}^3, \; G\in L^2(\mathbb{R}\times \mathbb{S}^2).
  \]
  This is the adjoint operator of the Radon transform. We manage to give an
optimal $L^6$ decay estimate of $\mathbf{T} G$ near the infinity by a geometric
method, if the function $G$ is compactly supported. As an application we give
decay estimate of non-radiative solutions to the 3D linear wave equation in the
exterior region $\{(x,t)\in \mathbb{R}^3 \times \mathbb{R}: |x|>R+|t|\}$. This
kind of decay estimate is useful in the channel of energy method for wave
equations


  In order to resist the adverse effect of viewpoint variations for improving
vehicle re-identification performance, we design quadruple directional deep
learning networks to extract quadruple directional deep learning features
(QD-DLF) of vehicle images. The quadruple directional deep learning networks
are with similar overall architecture, including the same basic deep learning
architecture but different directional feature pooling layers. Specifically,
the same basic deep learning architecture is a shortly and densely connected
convolutional neural network to extract basic feature maps of an input square
vehicle image in the first stage. Then, the quadruple directional deep learning
networks utilize different directional pooling layers, i.e., horizontal average
pooling (HAP) layer, vertical average pooling (VAP) layer, diagonal average
pooling (DAP) layer and anti-diagonal average pooling (AAP) layer, to compress
the basic feature maps into horizontal, vertical, diagonal and anti-diagonal
directional feature maps, respectively.
  Finally, these directional feature maps are spatially normalized and
concatenated together as a quadruple directional deep learning feature for
vehicle re-identification. Extensive experiments on both VeRi and VehicleID
databases show that the proposed QD-DLF approach outperforms multiple
state-of-the-art vehicle re-identification methods.


  We present a continuous-space version of Infotaxis, a search algorithm where
a searcher greedily moves to maximize the gain in information about the
position of the target to be found. Using a combination of analytical and
numerical tools we study the nature of the trajectories in two and three
dimensions. The probability that the search is successful and the running time
of the search are estimated. A possible extension to non-greedy search is
suggested.


  A simple formula is given for generating Chern characters by repeated
exterior differentiation for n-dimensional differentiable manifolds having a
general linear connection.


  The geometric entropy in quantum field theory is not a Lorentz scalar and has
no invariant meaning, while the black hole entropy is invariant.
Renormalization of entropy and energy for reduced density matrices may lead to
the negative free energy even if no boundary conditions are imposed. Presence
of particles outside the horizon of a uniformly accelerated observer prevents
the description in terms of a single Unruh temperature.


  It is shown that the multiplicity distribution associated to self-shadowing
events satisfies an universal equation in terms of the minimum bias
distribution. The number of elementary collisions, basic in the structure of
any multiple scattering, is reduced if a collective effect like percolation of
strings takes place. The main consequences of the percolation are briefly
discussed.


  This is the first of several monographs to be devoted to the optics of
accelerated systems. They are being published for the benefit of those who may
wish to have another way of looking at kineoptical problems, and also to
demonstrate that the laws of optics are unwavering in their support of the view
that extragalactic redshifts need not be velocity doppler shifts nor
cosmological recession shifts. In the latter context the first few monographs
of the series may be viewed as providing a basis for the demonstration to be
given in a latter monograph.


  We investigate how the topological charge density in lattice QCD simulations
is affected by violations of chiral symmetry in different fermion actions. To
this end we compare lattice configurations generated with a number of different
actions including first configurations generated with exact overlap quarks. We
visualize the topological profiles after mild smearing. In the topological
charge correlator we measure the size of the positive core, which is known to
vanish in the continuum limit. To leading order we find the core size to scale
linearly with the lattice spacing with the same coefficient for all actions,
even including quenched simulations. In the subleading term the different
actions vary over a range of about 10 %. Our findings suggest that non-chiral
lattice actions at current lattice spacings do not differ much for this
specific observable related to topology, both among themselves and compared to
overlap fermions.


  Through the use of cutting-edge unsupervised classification techniques from
statistics and machine learning, we characterise symptom phenotypes among
symptomatic SARS-CoV-2 PCR-positive community cases. We first analyse each
dataset in isolation and across age bands, before using methods that allow us
to compare multiple datasets. While we observe separation due to the total
number of symptoms experienced by cases, we also see a separation of symptoms
into gastrointestinal, respiratory and other types, and different symptom
co-occurrence patterns at the extremes of age. In this way, we are able to
demonstrate the deep structure of symptoms of COVID-19 without usual biases due
to study design. This is expected to have implications for the identification
and management of community SARS-CoV-2 cases and could be further applied to
symptom-based management of other diseases and syndromes.


  We investigate the stellar and ionized gas kinematics, and stellar
populations of NGC3182 galaxy using integral field spectrograph data from the
Calar Alto Legacy Integral Field Area survey. We try to clarify the nature of
the ring structure in NGC 3182. We find a negative stellar age gradient out to
the ring, while [{\alpha}/Fe] considerably enhanced in the ring. The stellar
metallicity shows a smooth negative gradient. From the line ratio diagnostic
diagrams, we confirm that NGC 3182 is a Seyfert galaxy from emission line flux
ratio, while the gas in the inner ring is ionized mostly by young stars.
However, any obvious feature of outflows is not found in its gas kinematics. In
the ring, star formation seems to have recently occurred and the gas
metallicity is slightly enhanced compared to the center. From our results, we
conclude that star formation has occurred in the circumnuclear region within a
short period and this may result from a positive feedback by AGN radiation
pressure.


  We prove a condition on f \in C^2(\R+,\R) for the convexity of (f o det) on
PSym(n), namely that f o det is convex on PSym(n) if and only if
f"(s)+(n-1)/(ns) f'(s) >= 0 and f'(s)<= 0 \forall s \in \R+. This generalizes
the observation that C --> -ln det C is convex as a function of C.


  The transition from AI/ML models to production-ready AI-based systems is a
challenge for both data scientists and software engineers. In this paper, we
report the results of a workshop conducted in a consulting company to
understand how this transition is perceived by practitioners. Starting from the
need for making AI experiments reproducible, the main themes that emerged are
related to the use of the Jupyter Notebook as the primary prototyping tool, and
the lack of support for software engineering best practices as well as data
science specific functionalities.


  We show that every k-dichromatic vertex-critical digraph on at most 2k-2
vertices has a disconnected complement. This answers a question of Bang-Jensen
et al., and generalises a classical theorem of Gallai on undirected
vertex-critical graphs.


  We study the asymptotic behavior as L \to \infty of the finite-volume
spectral shift function for a positive, compactly-supported perturbation of a
Schr\"odinger operator in d-dimensional Euclidean space, restricted to a cube
of side length L with Dirichlet boundary conditions. The size of the support of
the perturbation is fixed and independent of L. We prove that the Ces\`aro mean
of finite-volume spectral shift functions remains pointwise bounded along
certain sequences L_n \to \infty for Lebesgue-almost every energy. In deriving
this result, we give a short proof of the vague convergence of the
finite-volume spectral shift functions to the infinite-volume spectral shift
function as L \to\infty . Our findings complement earlier results of W. Kirsch
[Proc. Amer. Math. Soc. 101, 509 - 512 (1987), Int. Eqns. Op. Th. 12, 383 - 391
(1989)] who gave examples of positive, compactly-supported perturbations of
finite-volume Dirichlet Laplacians for which the pointwise limit of the
spectral shift function does not exist for any given positive energy. Our
methods also provide a new proof of the Birman--Solomyak formula for the
spectral shift function that may be used to express the measure given by the
infinite-volume spectral shift function directly in terms of the potential.


  Sonification is the transformation of data into acoustic signals, achievable
through different techniques. Sonification can be defined as a way to represent
data values and relations as perceivable sounds, aiming at facilitating their
communication and interpretation. Like data visualization provides meaning via
images, sonification conveys meaning via sound. Sonification approaches are
useful in a number of scenario. A first case is the possibility to receive
information while keeping other sensory channels free, like in medical
environment, in driving experience, etc. Another scenario addresses an easier
recognition of patterns when data present high dimensionality and cardinality.
Finally, sonification can be applied to presentation and dissemination
initiatives, also with artistic goals. The zCOSMOS dataset contains detailed
data about almost 20000 galaxies, describing the evolution of a relatively
small portion of the universe in the last 10 million years in terms of galaxy
mass, absolute luminosity, redshift, distance, age, and star formation rate.
The present paper proposes a sonification for the mentioned dataset, with the
following goals: i) providing a general description of the dataset, accessible
via sound, which could also make unnoticed patterns emerge; ii) realizing an
artistic but scientifically accurate sonic portrait of a portion of the
universe, thus filling the gap between art and science in the context of
scientific dissemination and so-called "edutainment"; iii) adding value to the
dataset, since also scientific data and achievements must be considered as a
cultural heritage that needs to be preserved and enhanced. Both scientific and
technological aspects of the sonification are addressed.


  We study the Prime Graph Question for integral group rings. This question can
be reduced to almost simple groups by a result of Kimmerle and Konovalov. We
prove that the Prime Graph Question has an affirmative answer for all almost
simple groups having a socle isomorphic to $\operatorname{PSL}(2, p^f)$ for $f
\leq 2$, establishing the Prime Graph Question for the first time for all
automorphic extensions of series of simple groups. Using this, we determine
exactly how far the so-called HeLP-method can take us for (almost simple)
groups having an order divisible by at most $4$ different primes.


  We introduce a new invariant, the \textit{positive idempotent group}, for
strongly asymptotically dynamically convex contact manifolds. This invariant
can be used to distinguish different contact structures. As an application, for
any complex dimension $n>8$ and any positive integer $k$, we can construct
$n-$dimensional Stein manifolds $V_0,V_1,\cdots,V_k$ such that
$\tilde{H}_j(V_i)=0, j\neq n-1,n$, $V_i's$ are almost symplectomorphic, their
boundaries are in the same almost contact class but not contactomorphic.


  We show that the Aut-invariant word norm on right angled Artin and right
angled Coxeter groups is unbounded (except in few special cases). To prove
unboundedness we exhibit certain characteristic subgroups. This allows us to
find unbounded quasimorphisms which are Lipschitz with respect to the
Aut-invariant word norm.


  We give a topological description of the space of quadratic rational maps
with superattractive two-cycles: its "non-escape locus" M2 (the analog of the
Mandelbrot set M) is locally connected, it is the continuous image of M under a
canonical map, and it can be described as M (minus the 1/2-limb), mated with
the lamination of the basilica. The latter statement is a refined version of a
conjecture of Ben Wittner, which in its original version requires local
connectivity of M to even be stated. Our methods of mating with a lamination
also apply to dynamical matings of certain non-locally connected Julia sets.


  We introduce a new logic programming language T-PRISM based on tensor
embeddings. Our embedding scheme is a modification of the distribution
semantics in PRISM, one of the state-of-the-art probabilistic logic programming
languages, by replacing distribution functions with multidimensional arrays,
i.e., tensors. T-PRISM consists of two parts: logic programming part and
numerical computation part. The former provides flexible and interpretable
modeling at the level of first order logic, and the latter part provides
scalable computation utilizing parallelization and hardware acceleration with
GPUs. Combing these two parts provides a remarkably wide range of high-level
declarative modeling from symbolic reasoning to deep learning. To embody this
programming language, we also introduce a new semantics, termed tensorized
semantics, which combines the traditional least model semantics in logic
programming with the embeddings of tensors. In T-PRISM, we first derive a set
of equations related to tensors from a given program using logical inference,
i.e., Prolog execution in a symbolic space and then solve the derived equations
in a continuous space by TensorFlow. Using our preliminary implementation of
T-PRISM, we have successfully dealt with a wide range of modeling. We have
succeeded in dealing with real large-scale data in the declarative modeling.
This paper presents a DistMult model for knowledge graphs using the FB15k and
WN18 datasets.


  We study the asymptotic behavior of solutions to an ODE - Schr\"{o}dinger
type system that models the interaction of a particle with a Bose gas. We show
that the particle has a ballistic trajectory asymptotically, and that the wave
function describing the Bose gas converges to a soliton in $L^{\infty}.$


  We report on our recent study of flavor singlet matrix elements calculated
with the wall source method without gauge fixing. Results are presented for the
mass difference between $\eta^{\prime}$ and pseudoscalar octet mesons, the
$\pi$-N $\sigma$ term and the proton axial vector matrix elements. An
exploratory calculation of the N-N scattering lengths is also discussed
including a phenomenological study with one-boson exchange potentials.


  Let f be an orientation preserving homeomorphism of the disc D2 which
possesses a periodic point of period 3. Then either f is isotopic, relative the
periodic orbit, to a homeomorphism g which is conjugate to a rotation by 2 pi
/3 or 4 pi /3, or f has a periodic point of least period n for each n in N*.


  The rotational evolution of cool dwarfs is poorly constrained after around
1-2 Gyr due to a lack of precise ages and rotation periods for old
main-sequence stars. In this work we use velocity dispersion as an age proxy to
reveal the temperature-dependent rotational evolution of low-mass Kepler
dwarfs, and demonstrate that kinematic ages could be a useful tool for
calibrating gyrochronology in the future. We find that a linear gyrochronology
model, calibrated to fit the period-Teff relationship of the Praesepe cluster,
does not apply to stars older than around 1 Gyr. Although late-K dwarfs spin
more slowly than early-K dwarfs when they are young, at old ages we find that
late-K dwarfs rotate at the same rate or faster than early-K dwarfs of the same
age. This result agrees qualitatively with semi-empirical models that vary the
rate of surface-to-core angular momentum transport as a function of time and
mass. It also aligns with recent observations of stars in the NGC 6811 cluster,
which indicate that the surface rotation rates of K dwarfs go through an epoch
of inhibited evolution. We find that the oldest Kepler stars with measured
rotation periods are late-K and early-M dwarfs, indicating that these stars
maintain spotted surfaces and stay magnetically active longer than more massive
stars. Finally, based on their kinematics, we confirm that many rapidly
rotating GKM dwarfs are likely to be synchronized binaries.


  A seller with one unit of a good faces N\geq3 buyers and a single competitor
who sells one other identical unit in a second-price auction with a reserve
price. Buyers who do not get the seller's good will compete in the competitor's
subsequent auction. We characterize the optimal mechanism for the seller in
this setting. The first-order approach typically fails, so we develop new
techniques. The optimal mechanism features transfers from buyers with the two
highest valuations, allocation to the buyer with the second-highest valuation,
and a withholding rule that depends on the highest two or three valuations. It
can be implemented by a modified third-price auction or a pay-your-bid auction
with a rebate. This optimal withholding rule raises significantly more revenue
than would a standard reserve price. Our analysis also applies to procurement
auctions. Our results have implications for sequential competition in
mechanisms.


  We study non-supersymmetric solutions of five dimensional N=2 supergravity
theories coupled to an arbitrary number of abelian vector multiplets. The
solutions constructed can be considered as deformations of known supersymmetric
black hole and string solutions. General constraints coming from the analysis
of the equations of motion are derived. These represent explicit conditions on
the charges of the black holes and strings. The constraints are analyzed for
theories where the scalar manifolds are symmetric spaces and explicit solutions
are constructed in cases where the prepotential of the theory factorizes into a
linear and a quadratic term.


  Multiplicity fluctuations in rings around the jet axis and in off-axis cones
have been measured by the DELPHI collaboration in $e^+e^-$ annihilations into
hadrons at LEP energies. The measurements are compared with analytical
perturbative QCD calculations for the corresponding multiparton system, using
the concept of Local Parton Hadron Duality. Some qualitative features are
confirmed by the data but substantial quantitative deviations are observed.


  It can be shown on observational grounds that two basic effects of dynamo
theory for solar activity - production of the toroidal field from the poloidal
one by differential rotation and reverse conversion of the toroidal field to
the poloidal configuration by helical motions - are operating in the Sun. These
two effects, however, do not suffice for constructing a realistic model for the
solar dynamo. Only when a non-local version of the alpha-effect is applied, is
downward diamagnetic pumping included and field advection by the equatorward
meridional flow near the base of the convection zone allowed for, can the
observed activity cycles be closely reproduced. Fluctuations in the
alpha-effect can be estimated from sunspot data. Dynamo models with fluctuating
parameters reproduce irregularities of solar cycles including the grand
activity minima. The physics of parametric excitation of irregularities
remains, however, to be understood.


  Common grounding is the process of creating, repairing and updating mutual
understandings, which is a fundamental aspect of natural language conversation.
However, interpreting the process of common grounding is a challenging task,
especially under continuous and partially-observable context where complex
ambiguity, uncertainty, partial understandings and misunderstandings are
introduced. Interpretation becomes even more challenging when we deal with
dialogue systems which still have limited capability of natural language
understanding and generation. To address this problem, we consider reference
resolution as the central subtask of common grounding and propose a new
resource to study its intermediate process. Based on a simple and general
annotation schema, we collected a total of 40,172 referring expressions in
5,191 dialogues curated from an existing corpus, along with multiple judgements
of referent interpretations. We show that our annotation is highly reliable,
captures the complexity of common grounding through a natural degree of
reasonable disagreements, and allows for more detailed and quantitative
analyses of common grounding strategies. Finally, we demonstrate the advantages
of our annotation for interpreting, analyzing and improving common grounding in
baseline dialogue systems.


  There is an infinitely generated free subgroup of the smooth knot concordance
group with the property that no nontrivial element in this subgroup can be
represented by an alternating knot. This subgroup has the further property that
every element is represented by a topologically slice knot.


  A great challenge in video-language (VidL) modeling lies in the disconnection
between fixed video representations extracted from image/video understanding
models and downstream VidL data. Recent studies try to mitigate this
disconnection via end-to-end training. To make it computationally feasible,
prior works tend to "imagify" video inputs, i.e., a handful of sparsely sampled
frames are fed into a 2D CNN, followed by a simple mean-pooling or
concatenation to obtain the overall video representations. Although achieving
promising results, such simple approaches may lose temporal information that is
essential for performing downstream VidL tasks. In this work, we present
VIOLET, a fully end-to-end VIdeO-LanguagE Transformer, which adopts a video
transformer to explicitly model the temporal dynamics of video inputs. Further,
unlike previous studies that found pre-training tasks on video inputs (e.g.,
masked frame modeling) not very effective, we design a new pre-training task,
Masked Visual-token Modeling (MVM), for better video modeling. Specifically,
the original video frame patches are "tokenized" into discrete visual tokens,
and the goal is to recover the original visual tokens based on the masked
patches. Comprehensive analysis demonstrates the effectiveness of both explicit
temporal modeling via video transformer and MVM. As a result, VIOLET achieves
new state-of-the-art performance on 5 video question answering tasks and 4
text-to-video retrieval tasks.


  In this paper we consider the Cauchy problem on the angular cutoff Boltzmann
equation near global Maxwillians for soft potentials either in the whole space
or in the torus. We establish the existence of global unique mild solutions in
the space $L^p_vL^{\infty}_{T}L^{\infty}_{x}$ with polynomial velocity weights
for suitably large $p\leq \infty$, whenever for the initial perturbation the
weighted $L^p_vL^{\infty}_x$ norm can be arbitrarily large but the
$L^1_xL^\infty_v$ norm and the defect mass, energy and entropy are sufficiently
small. The proof is based on the local in time existence as well as the uniform
a priori estimates via an interplay in $L^p_vL^{\infty}_{T}L^{\infty}_{x}$ and
$L^{\infty}_{T}L^{\infty}_{x}L^1_v$.


  In this paper, a mechanistic data-driven approach is proposed to accelerate
structural topology optimization, employing an in-house developed finite
element convolutional neural network (FE-CNN). Our approach can be divided into
two stages: offline training, and online optimization. During offline training,
a mapping function is built between high and low resolution representations of
a given design domain. The mapping is expressed by a FE-CNN, which targets a
common objective function value (e.g., structural compliance) across design
domains of differing resolutions. During online optimization, an arbitrary
design domain of high resolution is reduced to low resolution through the
trained mapping function. The original high-resolution domain is thus designed
by computations performed on only the low-resolution version, followed by an
inverse mapping back to the high-resolution domain. Numerical examples
demonstrate that this approach can accelerate optimization by up to an order of
magnitude in computational time. Our proposed approach therefore shows great
potential to overcome the curse-of-dimensionality incurred by density-based
structural topology optimization. The limitation of our present approach is
also discussed.


  We consider active learning for binary classification in the agnostic
pool-based setting. The vast majority of works in active learning in the
agnostic setting are inspired by the CAL algorithm where each query is
uniformly sampled from the disagreement region of the current version space.
The sample complexity of such algorithms is described by a quantity known as
the disagreement coefficient which captures both the geometry of the hypothesis
space as well as the underlying probability space. To date, the disagreement
coefficient has been justified by minimax lower bounds only, leaving the door
open for superior instance dependent sample complexities. In this work we
propose an algorithm that, in contrast to uniform sampling over the
disagreement region, solves an experimental design problem to determine a
distribution over examples from which to request labels. We show that the new
approach achieves sample complexity bounds that are never worse than the best
disagreement coefficient-based bounds, but in specific cases can be
dramatically smaller. From a practical perspective, the proposed algorithm
requires no hyperparameters to tune (e.g., to control the aggressiveness of
sampling), and is computationally efficient by means of assuming access to an
empirical risk minimization oracle (without any constraints). Empirically, we
demonstrate that our algorithm is superior to state of the art agnostic active
learning algorithms on image classification datasets.


  For a locally finite set, $A \subseteq \mathbb{R}^d$, the $k$-th Brillouin
zone of $a \in A$ is the region of points $x \in \mathbb{R}^d$ for which
$\|x-a\|$ is the $k$-th smallest among the Euclidean distances between $x$ and
the points in $A$. If $A$ is a lattice, the $k$-th Brillouin zones of the
points in $A$ are translates of each other, which tile space. Depending on the
value of $k$, they express medium- or long-range order in the set. We study
fundamental geometric and combinatorial properties of Brillouin zones, focusing
on the integer lattice and its perturbations. Our results include the stability
of a Brillouin zone under perturbations, a linear upper bound on the number of
chambers in a zone for lattices in $\mathbb{R}^2$, and the convergence of the
maximum volume of a chamber to zero for the integer lattice.


  Some functorial properties are studied for the H\"{o}rmander classes defined
for symplectic bundles. The behaviour of the Chern first form on a Lagrangian
submanifold in an almost Hermitian manifold is also studied, and Fomenko's
conjecture about the behaviour of a Maslov class on minimal Lagrangian
submanifolds is considered.


  We study the formation of quasi-one- (quasi-1D) and quasi-two-dimensional
(quasi-2D) symbiotic solitons bound by an interspecies dipolar interaction in a
binary dipolar Bose-Einstein condensate. These binary solitons have a repulsive
intraspecies contact interaction stronger than the intraspecies dipolar
interaction, so that they can not be bound in isolation in the absence of an
interspecies dipolar interaction. These symbiotic solitons are bound in the
presence of an interspecies dipolar interaction and zero interspecies contact
interaction. The quasi-1D solitons are free to move along the polarization $z$
direction of the dipolar atoms, whereas the quasi-2D solitons move in the
$x$-$z$ plane. To illustrate these, we consider a $^{164}$Er-$^{166}$Er mixture
with scattering lengths $a$($^{164}$Er)$ =81a_0$ and $a$($^{166}$Er)$ =68a_0$
and with dipolar lengths $a_{\mathrm{dd}}$($^{164}$Er)$\approx
a_{\mathrm{dd}}$($^{166}$Er)$\approx 65a_0$, where $a_0$ is the Bohr radius. In
each of the two components $a> a_{\mathrm{dd}}$, which stops the binding of
solitons in each component in isolation, whereas a binary quasi-1D or a
quasi-2D $^{164}$Er-$^{166}$Er soliton is bound in the presence of an
interspecies dipolar interaction. The stationary states were obtained by
imaginary-time propagation of the underlying mean-field model; dynamical
stability of the solitons was established by real-time propagation over a long
period of time.


  Anaphora resolution is one of the most active research areas in natural
language processing. This study examines focusing as a tool for the resolution
of pronouns which are a kind of anaphora. Focusing is a discourse phenomenon
like anaphora. Candy Sidner formalized focusing in her 1979 MIT PhD thesis and
devised several algorithms to resolve definite anaphora including pronouns. She
presented her theory in a computational framework but did not generally
implement the algorithms. Her algorithms related to focusing and pronoun
resolution are implemented in this thesis. This implementation provides a
better comprehension of the theory both from a conceptual and a computational
point of view. The resulting program is tested on different discourse segments,
and evaluation and analysis of the experiments are presented together with the
statistical results.


  In this paper we extend the micromagnetic theory of magnetostatic surface
waves in insulating ferromagnetic thin films to include the applied electric
field effects. We start by identifying the two main effects on the dispersion
relation: the first one is of relativistic nature and emerges as a consequence
of the Ahronov-Casher effect, while the second one is a consequence of the
electric field induced symmetry breaking operating at the level of magnetic
exchange interactions. We support our theory by comparing its predictions with
experimental data on ittrium iron garnet thin films taken from the literature.
The main result is to evidence the limitations of using the same value of the
applied electric field to address both effects and to emphasize that crystal
symmetry breaking due to the applied electric field brings about the
contributions of the crystal field and determines different amplitudes for the
two effects.


  We present EasyCritics, an algorithm to detect strongly-lensing groups and
clusters in wide-field surveys without relying on a direct recognition of arcs.
EasyCritics assumes that light traces mass in order to predict the most likely
locations of critical curves from the observed fluxes of luminous red
early-type galaxies in the line of sight. The positions, redshifts and fluxes
of these galaxies constrain the idealized gravitational lensing potential as a
function of source redshift up to five free parameters, which are calibrated on
few known lenses. From the lensing potential, EasyCritics derives the critical
curves for a given, representative source redshift. The code is highly
parallelized, uses fast Fourier methods and, optionally, GPU acceleration in
order to process large datasets efficiently. The search of a $\smash{1 \,
\mathrm{deg}^2}$ field of view requires less than 1 minute on a modern
quad-core CPU, when using a pixel resolution of $0.25''/\mathrm{px}$. In this
first part of a paper series on EasyCritics, we describe the main underlying
concepts and present a first demonstration on data from the
Canada-France-Hawaii-Telescope Lensing Survey. We show that EasyCritics is able
to identify known group- and cluster-scale lenses, including a cluster with two
giant arc candidates that were previously missed by automated arc detectors.


  We study the connection between the cumulants of a time-integrated observable
of a quantum system and the PT-symmetry properties of the non-Hermitian
deformation of the Hamiltonian from which the generating function of these
cumulants is obtained. This non-Hermitian Hamiltonian can display regimes of
broken and of unbroken PT-symmetry, depending on the parameters of the problem
and on the counting field that sets the strength of the non-Hermitian
perturbation. This in turn determines the analytic structure of the long-time
cumulant generating function (CGF) for the time-integrated observable. We
consider in particular the case of the time-integrated (longitudinal)
magnetisation in the one-dimensional Ising model in a transverse field. We show
that its long-time CGF is singular on a curve in the magnetic field/counting
field plane that delimits a regime where PT-symmetry is spontaneously broken
(which includes the static ferromagnetic phase), from one where it is preserved
(which includes the static paramagnetic phase). In the paramagnetic phase,
conservation of PT -symmetry implies that all cumulants are sub-linear in time,
a behaviour usually associated to the absence of decorrelation.


  We explicitly construct and study the statistics of flux vacua for type IIB
string theory on an orientifold of the Calabi-Yau hypersurface
$P^4_{[1,1,2,2,6]}$, parametrised by two relevant complex structure moduli. We
solve for these moduli and the dilaton field in terms of the set of integers
defining the 3-form fluxes and examine the distribution of vacua. We compare
our numerical results with the predictions of the Ashok-Douglas density $\det
(-R - \omega)$, finding good overall agreement in different regions of moduli
space. The number of vacua are found to scale with the distance in flux space.
Vacua cluster in the region close to the conifold singularity. Large
supersymmetry breaking is more generic but supersymmetric and hierarchical
supersymmetry breaking vacua can also be obtained. In particular, the small
superpotentials and large dilaton VEVs needed to obtain de Sitter space in a
controllable approximation are possible but not generic. We argue that in a
general flux compactification, the rank of the gauge group coming from D3
branes could be statistically preferred to be very small.


  A set of 45 dust envelopes of carbon stars has been modeled. Among them, 34
were selected according to their dust envelope class (as suggested by Sloan,
Little-Marenin & Price, 1998) and 11 are extreme carbon stars. The models were
performed using a code that describes the radiative transfer in dust envelopes
considering core/mantle grains composed by an alpha-SiC core and an amorphous
carbon (A.C.) mantle. In addition, we have also computed models with a code
that considers two kinds of grains - alpha-SiC and A.C. - simultaneously.
Core-mantle grains seem to fit dust envelopes of evolved carbon stars, while
two homogeneous grains are more able to reproduce thinner dust envelopes. Our
results suggest that there exists an evolution of dust grains in the carbon
star sequence. In the beginning of the sequence, grains are mainly composed of
SiC and amorphous carbon; with dust envelope evolution, carbon grains are
coated in SiC. This phenomena could perhaps explain the small quantity of SiC
grains observed in the interstellar medium. However, in this work we consider
only alpha-SiC grains, and the inclusion of beta-SiC grains can perhaps change
some of there results.


  With the rapid growth of electric vehicles (EVs), EV aggregators have been
playing a increasingly vital role in power systems by not merely providing
charging management but also participating in wholesale electricity markets.
This work studies the optimal real-time bidding strategy for an EV aggregator.
Since the charging process of EVs is time-coupled, it is necessary for EV
aggregators to consider future operational conditions (e.g., future EV
arrivals) when deciding the current bidding strategy. However, accurately
forecasting future operational conditions is challenging under the inherent
uncertainties. Hence, there demands a real-time bidding strategy based solely
on the up-to-date information, which is the main goal of this work. We start by
developing an online optimal EV charging management algorithm for the EV
aggregator via Lyapunov optimization. Based on this, an optimal real-time
bidding strategy (bidding cost curve and bounds) for the aggregator is derived.
Then, an efficient yet practical algorithm is proposed to obtain the bidding
strategy. It shows that with the proposed bidding strategy, the aggregator's
profit is nearly offline optimal. Moreover, the wholesale electricity market
clearing result aligns with the individual aggregator's optimal charging
strategy given the prices. Case studies against several benchmarks are
conducted to evaluate the performance of the proposed method.


  This study aims to increase awareness concerning the pernicious effects of
photometric contamination (crowding/blending), since it can propagate an
undesirable systematic offset into the cosmic distance scale. The latest
Galactic Cepheid W_VIc and Spitzer calibrations were employed to establish
distances for classical Cepheids in IC 1613 and NGC 6822, thus enabling the
impact of photometric contamination to be assessed in concert with metallicity.
Distances (W_VIc, [3.6]) for Cepheids in IC 1613 exhibit a galactocentric
dependence, whereby Cepheids near the core appear (spuriously) too bright (r_g
< 2'). That effect is attributed to photometric contamination from neighboring
(unresolved) stars, since the stellar density and surface brightness may
increase with decreasing galactocentric distance. The impact is relatively
indiscernible for a comparison sample of Cepheids occupying NGC 6822, a result
which is partly attributable to that sample being nearer than the metal-poor
galaxy IC 1613. W_VIc and [3.6] distances for relatively uncontaminated
Cepheids in each galaxy are comparable, thus confirming that period-magnitude
relations (Leavitt Law) in those bands are relatively insensitive to
metallicity (d[Fe/H] ~ 1).


  In his article "Arithmetic Fujita Approximations", Huayi Chen introduces the
notion of an approximable graded algebra and asks if any such algebra is a
subalgebra of the graded section ring of a big line bundle on an algebraic
variety. We give a counter-example showing this is not the case.


  Understanding planet formation requires to discern how dust grows in
protoplanetary disks. An important parameter to measure in disks is the maximum
dust grain size present. This is usually estimated through measurements of the
dust opacity at different millimeter wavelengths assuming optically thin
emission and dust opacity dominated by absorption. However, ALMA observations
have shown that these assumptions might not be correct in the case of
protoplanetary disks, leading to overestimation of particle sizes and to
underestimation of the disk's mass. Here, we present an analysis of high
quality ALMA and VLA images of the HL Tau protoplanetary disk, covering a wide
range of wavelengths, from 0.8 mm to 1 cm, and with a physical resolution of
$\sim$7.35 au. We describe a procedure to analyze a set of millimeter images
without any assumption about the optical depth of the emission, and including
the effects of absorption and scattering in the dust opacity. This procedure
allows us to obtain the dust temperature, the dust surface density and the
maximum particle size at each radius. In the HL Tau disk, we found that
particles have already grown up to a few millimeters in size. We detect
differences in the dust properties between dark and bright rings, with dark
rings containing low dust density and small dust particles. Different features
in the HL Tau disk seem to have different origins. Planet-disk interactions can
explain substructure at the external half of the disk, but the internal rings
seem to be associated to the presence of snow lines of several molecules.


  With the help of a model of magnetohydrodynamic (MHD) turbulence tested
previously, we explore high Reynolds number regimes up to equivalent
resolutions of 6000^3 grid points in the absence of forcing and with no imposed
uniform magnetic field. For the given initial condition chosen here, with equal
kinetic and magnetic energy, the flow ends up being dominated by the magnetic
field, and the dynamics leads to an isotropic Iroshnikov-Kraichnan energy
spectrum. However, the locally anisotropic magnetic field fluctuations
perpendicular to the local mean field follow a Kolmogorov law. We find that the
ratio of the eddy turnover time to the Alfven time increases with wavenumber,
contrary to the so-called critical balance hypothesis. Residual energy and
helicity spectra are also considered; the role played by the conservation of
magnetic helicity is studied, and scaling laws are found for the magnetic
helicity and residual helicity spectra. We put these results in the context of
the dynamics of a globally isotropic MHD flow which is locally anisotropic
because of the influence of the strong large-scale magnetic field, leading to a
partial equilibration between kinetic and magnetic modes for the energy and the
helicity.


  We report a precise measurement of the isotope shifts in the $4^2$S$_{1/2}
\rightarrow 3^2$D$_{3/2}$ electric quadrupole transition at 732~nm in $^{40 -
42,44,48}$Ca$^+$ via high-resolution laser spectroscopy of co-trapped ions,
finding measured shifts of 2,775,392,374.8(6.0), 5,347,679,835.1(5.9), and
10,003,129,115.1(5.7)\,Hz between $^{42,44,48}$Ca$^+$and $^{40}$Ca$^+$,
respectively. When combined with prior measurements on the $4^2$S$_{1/2}
\rightarrow 3^2$D$_{5/2}$ transition [Phys. Rev. A 100, 022514 (2019),
https://journals.aps.org/pra/abstract/10.1103/PhysRevA.100.022514] a King Plot
analysis shows the data to be consistent with linearity below the level of
parts per billion. This observed linearity, which is free of nuclear
systematics, improves the previous isotope-shift based limits of Ca$^+$ for
couplings of a scalar boson beyond the Standard Model to electrons and neutrons
by a factor of 3. Our new limit excludes part of the coupling range remaining
for a new physics interpretation after accounting for one higher-order nuclear
term in the nonlinear King plot of Yb/Yb$^+$.


  Lagrangian averaging plays an important role in the analysis of
wave--mean-flow interactions and other multiscale fluid phenomena. The
numerical computation of Lagrangian means, e.g. from simulation data, is
however challenging. Typical implementations require tracking a large number of
particles to construct Lagrangian time series which are then averaged using a
low-pass filter. This has drawbacks that include large memory demands, particle
clustering and complications of parallelisation. We develop a novel approach in
which the Lagrangian means of various fields (including particle positions) are
computed by solving partial differential equations (PDEs) that are integrated
over successive averaging time intervals. We propose two strategies,
distinguished by their spatial independent variables. The first, which
generalises the algorithm of Kafiabad (2022, J. Fluid Mech. 940, A2), uses
end-of-interval particle positions; the second directly uses the Lagrangian
mean positions. The PDEs can be discretised in a variety of ways, e.g. using
the same discretisation as that employed for the governing dynamical equations,
and solved on-the-fly to minimise the memory footprint. We illustrate the new
approach with a pseudospectral implementation for the rotating shallow-water
model. Two applications to flows that combine vortical turbulence and Poincare
waves demonstrate the superiority of Lagrangian averaging over Eulerian
averaging for wave--vortex separation.


  In many contexts, particularly when study subjects are adolescents, peer
effects can invalidate typical statistical requirements in the data. For
instance, it is plausible that a student's academic performance is influenced
both by their own mother's educational level as well as that of their peers.
Since the underlying social network is measured, the Add Health study provides
a unique opportunity to examine the impact of maternal college education on
adolescent school performance, both direct and indirect. However, causal
inference on populations embedded in social networks poses technical
challenges, since the typical no interference assumption no longer holds. While
inverse probability-of-treatment weighted (IPW) estimators have been developed
for this setting, they are often highly unstable. Motivated by the question of
maternal education, we propose doubly robust (DR) estimators combining models
for treatment and outcome that are consistent and asymptotically normal if
either model is correctly specified. We present empirical results that
illustrate the DR property and the efficiency gain of DR over IPW estimators
even when the treatment model is misspecified. Contrary to previous studies,
our robust analysis does not provide evidence of an indirect effect of maternal
education on academic performance within adolescents' social circles in Add
Health.


  We carry out a systematic classification and computation of next-to-leading
order kinematic power corrections to the fully differential cross section in
the parton shower. To do this we devise a map between ingredients in a parton
shower and operators in a traditional effective field theory framework using a
chain of soft-collinear effective theories. Our approach overcomes several
difficulties including avoiding double counting and distinguishing
approximations that are coordinate choices from true power corrections.
Branching corrections can be classified as hard-scattering, that occur near the
top of the shower, and jet-structure, that can occur at any point inside it.
Hard-scattering corrections include matrix elements with additional hard
partons, as well as power suppressed contributions to the branching for the
leading jet. Jet-structure corrections require simultaneous consideration of
potential 1 -> 2 and 1 -> 3 branchings. The interference structure induced by
collinear terms with subleading powers remains localized in the shower.


  We show that the Grothendieck-Chow motive of a smooth hyperplane section $Y$
of an inner twisted form $X$ of a Milnor hypersurface splits as a direct sum of
shifted copies of the motive of the Severi-Brauer variety of the associated
cyclic algebra $A$ and the motive of its maximal commutative subfield $L\subset
A$. The proof is based on the non-triviality of the (monodromy) Galois action
on the equivariant Chow group of $Y_L$.


  We determine the cosmic abundance of molecular hydrogen (H2) in the local
universe from the xCOLD GASS survey. To constrain the H2 mass function at low
masses and correct for the effect of the lower stellar mass limit of 10^9 Msun
in the xCOLD GASS survey, we use an empirical approach based on an observed
scaling relation between star formation rate and gas mass. We also constrain
the HI and HI+H2 mass functions using the xGASS survey, and compare it to the
HI mass function from the ALFALFA survey. We find the cosmic abundance of
molecular gas in the local Universe to be Omega_H2=(5.34+/-0.47)x10^-5 h^-1.
Molecular gas accounts for 19.6 +/- 3.9% of the total abundance of cold gas,
Omega_HI+H2=(4.66+/-0.70)x10^-4 h^-1. Galaxies with stellar masses in excess of
10^9 Msun account for 89% of the molecular gas in the local Universe, while in
comparison such galaxies only contain 73% of the cold atomic gas as traced by
the HI 21cm line. The xCOLD GASS CO, molecular gas and cold gas mass functions
and Omega_H2 measurements provide constraints for models of galaxy evolution
and help to anchor blind ALMA and NOEMA surveys attempting to determine the
abundance of molecular gas at high redshifts.