  A topological bifurcation in chaotic scattering is characterized by a sudden
change in the topology of the infinite set of unstable periodic orbits embedded
in the underlying chaotic invariant set. We uncover a scaling law for the
fractal dimension of the chaotic set for such a bifurcation. Our analysis and
numerical computations in both two- and three-degrees-of-freedom systems
suggest a striking feature associated with these subtle bifurcations: the
dimension typically exhibits a sharp, cusplike local minimum at the
bifurcation.


  We investigate the regularity of semi-stable, radially symmetric, and
decreasing solutions for a class of quasilinear reaction-diffusion equations in
the inhomogeneous context of Riemannian manifolds. We prove uniform
boundedness, Lebesgue and Sobolev estimates for this class of solutions for
equations involving the p-Laplace Beltrami operator and locally Lipschitz
non-linearity. We emphasize that our results do not depend on the boundary
conditions and the specific form of the non-linearities and metric. Moreover,
as an application, we establish regularity of the extremal solutions for
equations involving the p-Laplace Beltrami operator with zero Dirichlet
boundary conditions.


  The orbital period of the binary pulsar PSR 1913+16 has been observed to
decrease at the rate of $2.40\times 10^{-12}$ s/s which agrees with the
prediction of the quadropole formula for gravitational radiation to within one
percent. The decrease in orbital period may also occur by radiation of other
massless particles like scalars and pseudoscalar Nambu-Goldstone bosons.
Assuming that this energy loss is less than one percent of the gravitational
radiation, we can establish bounds on couplings of these particles to nucleons.
For a scalar nucleon coupling of the form $g_s~\phi~\bar\psi~\psi$ we find that
$g_s< 3\times 10^{-19}$. From the radiation loss of massless Goldstone bosons
we establish the upper bound $\theta /f< 7.5\times 10^{-16}$ GeV$^{-1}$ on the
QCD vacuum angle $\theta$ and the scale $f$ at which the baryon number symmetry
can be broken spontaneously.


  Contrastive representation learning seeks to acquire useful representations
by estimating the shared information between multiple views of data. Here, the
choice of data augmentation is sensitive to the quality of learned
representations: as harder the data augmentations are applied, the views share
more task-relevant information, but also task-irrelevant one that can hinder
the generalization capability of representation. Motivated by this, we present
a new robust contrastive learning scheme, coined R\'enyiCL, which can
effectively manage harder augmentations by utilizing R\'enyi divergence. Our
method is built upon the variational lower bound of R\'enyi divergence, but a
na\"ive usage of a variational method is impractical due to the large variance.
To tackle this challenge, we propose a novel contrastive objective that
conducts variational estimation of a skew R\'enyi divergence and provide a
theoretical guarantee on how variational estimation of skew divergence leads to
stable training. We show that R\'enyi contrastive learning objectives perform
innate hard negative sampling and easy positive sampling simultaneously so that
it can selectively learn useful features and ignore nuisance features. Through
experiments on ImageNet, we show that R\'enyi contrastive learning with
stronger augmentations outperforms other self-supervised methods without extra
regularization or computational overhead. Moreover, we also validate our method
on other domains such as graph and tabular, showing empirical gain over other
contrastive methods.


  Collaborative creativity is the approach of employing crowd to accomplish
creative tasks. In this paper, we present a collaborative crowdsourcing
platform for writing stories by means of connecting a series of `images'. These
connected images are termed as Image Chains, reflecting successive scenarios.
Users can either start or extend an Image Chain by uploading their own image or
choosing from the available ones. These users are allowed to pen their stories
from the Image Chains. Finally, stories get published based on the number of
votes obtained. This provides an organized framework of story writing unlike
most of the state-of-the-art collaborative editing platforms. Our experiments
on 25 contributors highlight their interest in growing shorter Image Chains but
voting longer Image Chains.


  Using a procedure based on interpolation via continued fractions supplemented
by statistical sampling, we analyse proton magnetic form factor data obtained
via electron+proton scattering on $Q^2 \in [0.027,0.55]\,$GeV$^2$ with the goal
of determining the proton magnetic radius. The approach avoids assumptions
about the function form used for data interpolation and ensuing extrapolation
onto $Q^2\simeq 0$ for extraction of the form factor slope. In this way, we
find $r_M = 0.817(27)\,$fm. Regarding the difference between proton electric
and magnetic radii calculated in this way, extant data are seen to be
compatible with the possibility that the slopes of the proton Dirac and Pauli
form factors, $F_{1,2}(Q^2)$, are not truly independent observables; to wit,
the difference $F_1^\prime(0)-F_2^\prime(0)/\kappa_p = [1+\kappa_p]/[4 m_p^2]$,
viz. the proton Foldy term.


  We consider gluon condensation (GC) at finite temperature using AdS/CFT. We
first show that in the presence of regular horizon, the GC is forbidden in high
temperature. Then we consider gravity back-reaction to dilaton coupling and
show that the back-reaction develops an singularity, and non-vanishing value of
gluon condensation is allowed. We also study thermodynamic quantities and the
trace anomaly in the presence of the GC. We discuss how to define a temperature
in the presence of the singularity which forbids Hawking temperature. Finally
we describe the thermodynamics of the gluon condensation including the effect
of the Hawking-Page transition.


  More and more claims of having detected WIMP dark matter are being put
forward. Some are discussed here, stressing the importance of exploiting
distinctive signatures to ascertain their WIMP origin. The best signals for
WIMP discovery are characterized by special features that make them
recognizable as due to WIMPs and nothing else. Sometimes, however, a single
feature, although accountable for in theoretical models, may not be enough to
make sure that we have detected WIMPs. This is because the theory of WIMPs and
their distribution in the galaxy is still very uncertain, and allows for many
possibilities. What are needed are experimental verifications of the claimed
signals, either by discovering unmistakable features, or by detecting several
kinds of signals that can all be explained by the same WIMP model.


  For any asymptotically flat spacetime with a suitable causal structure
obeying (a weak form of) Penrose's cosmic censorship conjecture and satisfying
conditions guaranteeing focusing of complete null geodesics, we prove that
active topological censorship holds. We do not assume global hyperbolicity, and
therefore make no use of Cauchy surfaces and their topology. Instead, we
replace this with two underlying assumptions concerning the causal structure:
that no compact set can signal to arbitrarily small neighbourhoods of spatial
infinity (``$i^0$-avoidance''), and that no future incomplete null geodesic is
visible from future null infinity. We show that these and the focusing
condition together imply that the domain of outer communications is simply
connected. Furthermore, we prove lemmas which have as a consequence that if a
future incomplete null geodesic were visible from infinity, then given our
$i^0$-avoidance assumption, it would also be visible from points of spacetime
that can communicate with infinity, and so would signify a true naked
singularity.


  We argue that there exists a new class of completely smooth 1/8-BPS,
three-charge bound state configurations that depend upon arbitrary functions of
two variables. These configurations are locally 1/2-BPS objects in that if they
form an infinite flat sheet then they preserve 16 supersymmetries but even with
arbitrary two-dimensional shape modes they still preserve 4 supersymmetries.
They have three electric charges and can be thought of the result of two
successive supertube transitions that involve adding two independent dipole
moments and giving rise to the arbitrary two-dimensional shape modes. We
further argue that in the D1-D5-P duality frame this construction will give
rise to smooth, horizonless solutions, or microstate geometries. We expect
these solutions to be extremely important in the semi-classical and holographic
descriptions of black-hole entropy.


  In this note we show that the Riemann moduli spaces $M_{g, n}$ equipped with
the Weil--Petersson metric are quantum ergodic for $3g+n \geq 4$. We also
provide other examples of singular spaces with ergodic geodesic flow for which
quantum ergodicity holds.


  It is proved that the action for nonlinear Beltrami equation (quasiclassical
dbar-problem) evaluated on its solution gives a tau-function for dispersionless
KP hierarchy. Infinitesimal transformations of tau-function corresponding to
variations of dbar-data are found. Determinant equations for the function
generating these transformations are derived. They represent a dispersionless
analogue of singular manifold (Schwarzian) KP equations. Dispersionless 2DTL
hierarchy is also considered.


  We study a general class of multiplicative functions by relating "short
averages" to its "long average". More precisely, we estimate asymptotically the
variance of such a class of functions in short intervals using Fourier analysis
and counting rational points on certain binary forms.
  Our result is applicable to the interesting multiplicative functions
$\mu_k(n),\frac{\phi(n)}{n}, \frac{n}{\phi(n)},$ $\mu^2(n)\frac{\phi(n)}{n}$,
$\sigma_{\alpha}(n)$, $(-1)^{\#\{p\,: \, p^k|n\}}$ and many others that
establish various new results and improvements in short intervals to the
literature.


  In this paper, we investigate the impact of objects on gender bias in image
captioning systems. Our results show that only gender-specific objects have a
strong gender bias (e.g., women-lipstick). In addition, we propose a visual
semantic-based gender score that measures the degree of bias and can be used as
a plug-in for any image captioning system. Our experiments demonstrate the
utility of the gender score, since we observe that our score can measure the
bias relation between a caption and its related gender; therefore, our score
can be used as an additional metric to the existing Object Gender Co-Occ
approach. Code and data are publicly available at
\url{https://github.com/ahmedssabir/GenderScore}.


  Purpose: Self-supervised learning has been gaining attention in the medical
field for its potential to improve computer-aided diagnosis. One popular method
of self-supervised learning is masked image modeling (MIM), which involves
masking a subset of input pixels and predicting the masked pixels. However,
traditional MIM methods typically use a random masking strategy, which may not
be ideal for medical images that often have a small region of interest for
disease detection. To address this issue, this work aims to improve MIM for
medical images and evaluate its effectiveness in an open X-ray image dataset.
Methods: In this paper, we present a novel method called region-guided masked
image modeling (RGMIM) for learning meaningful representation from X-ray
images. Our method adopts a new masking strategy that utilizes organ mask
information to identify valid regions for learning more meaningful
representations. The proposed method was contrasted with five self-supervised
learning techniques (MAE, SKD, Cross, BYOL, and, SimSiam). We conduct
quantitative evaluations on an open lung X-ray image dataset as well as masking
ratio hyperparameter studies. Results: When using the entire training set,
RGMIM outperformed other comparable methods, achieving a 0.962 lung disease
detection accuracy. Specifically, RGMIM significantly improved performance in
small data volumes, such as 5% and 10% of the training set (846 and 1,693
images) compared to other methods, and achieved a 0.957 detection accuracy even
when only 50% of the training set was used. Conclusions: RGMIM can mask more
valid regions, facilitating the learning of discriminative representations and
the subsequent high-accuracy lung disease detection. RGMIM outperforms other
state-of-the-art self-supervised learning methods in experiments, particularly
when limited training data is used.


  Faradaic deionization (FDI) is a promising technology for energy-efficient
water desalination using porous electrodes containing redox-active materials.
Herein, we demonstrate for the first time the capability of a symmetric FDI
flow cell to produce freshwater (<17.1 mM NaCl) from concentrated brackish
water (118mM), to produce effluent near freshwater salinity (19.1 mM) from
influent with seawater-level salinity (496 mM), and to reduce the salinity of
hypersaline brine from 781 mM to 227 mM. These remarkable salt-removal levels
were enabled by using flow-through electrodes with high areal-loading of nickel
hexacyanoferrate (NiHCF) Prussian Blue analogue intercalation material. The
pumping energy consumption due to flow-through electrodes was mitigated by
embedding an interdigitated array of <100 $\mu$m wide channels in the
electrodes using laser micromachining. The micron-scale dimensions of the
resulting embedded, micro-interdigitated flow fields (e$\mu$-IDFFs) facilitate
flow-through electrodes with high apparent permeability while minimizing
active-material loss. Our modeling shows that these e$\mu$-IDFFs are more
suitable for our intercalation electrodes because they have >100X lower
permeability compared to common redox-flow battery electrodes, for which
millimetric flow-channel widths were used exclusively in the past. Total
desalination thermodynamic energy efficiency (TEE) was improved by more than
ten-fold relative to unpatterned electrodes: 40.0% TEE for brackish water,
11.7% TEE for hypersaline brine, and 7.4% TEE for seawater-salinity feeds.
Water transport between diluate and brine streams and charge efficiency losses
resulting from (electro)chemical effects are implicated as limiting energy
efficiency and water recovery, motivating their investigation for enhancing
future FDI performance.


  Dissolution testing is part of the target product quality that is essential
in approving new products in the pharmaceutical industry. The prediction of the
dissolution profile based on spectroscopic data is an alternative to the
current destructive and time-consuming method. Raman and near-infrared (NIR)
spectroscopies are two fast and complementary methods that provide information
on the tablets' physical and chemical properties and can help predict their
dissolution profiles. This work aims to compare the information collected by
these spectroscopy methods to support the decision of which measurements should
be used so that the accuracy requirement of the industry is met. Artificial
neural network models were created, in which the spectroscopy data and the
measured compression curves were used as an input individually and in different
combinations in order to estimate the dissolution profiles. Results showed that
using only the NIR transmission method along with the compression force data or
the Raman and NIR reflection methods, the dissolution profile was estimated
within the acceptance limits of the f2 similarity factor. Adding further
spectroscopy measurements increased the prediction accuracy.


  We consider the interpretation and the numerical construction of the inverse
branches of $n$ factor Blaschke-products on the disk and show that these
provide a generalization of the $n$-th root function. The inverse branches can
be defined on pairwise disjoint regions, whose union provides the disk. An
explicit formula can be given for the $n$ factor Blaschke-products on the
torus, which can be used to provide the inverses on the torus. The inverse
branches can be thought of as the solutions $z=z_t(r) (0\le r\le 1)$ to the
equation $B(z )=re^{it}$, where $B$ denotes an $n$ factor Blaschke-product. We
show that starting from a known value $z_t(1)$, any $z_t(r)$ point of the
solution trajectory can be reached in finite steps. The appropriate grouping of
the trajectories leads to two natural interpretations of the inverse branches
(see Figure 2). We introduce an algorithm which can be used to find the points
of the trajectories.


  In this note, we study the connection between Gray tensor product and
suspension. We derive a characterization of weak equivalences as fully faithful
and essentially surjective functors. We construct the $co$ duality, a weak
involution that reverses the direction of even dimensional cells. We conclude
by studying Grothendieck fibrations of complicial sets.


  Giant exoplanets have been directly imaged over orders of magnitude of
orbital separations, prompting theoretical and observational investigations of
their formation pathways. In this paper, we present new VLTI/GRAVITY
astrometric data of HIP 65426 b, a cold, giant exoplanet which is a particular
challenge for most formation theories at a projected separation of 92 au from
its primary. Leveraging GRAVITY's astrometric precision, we present an updated
eccentricity posterior that disfavors large eccentricities. The eccentricity
posterior is still prior-dependent, and we extensively interpret and discuss
the limits of the posterior constraints presented here. We also perform updated
spectral comparisons with self-consistent forward-modeled spectra, finding a
best fit ExoREM model with solar metallicity and C/O=0.6. An important caveat
is that it is difficult to estimate robust errors on these values, which are
subject to interpolation errors as well as potentially missing model physics.
Taken together, the orbital and atmospheric constraints paint a preliminary
picture of formation inconsistent with scattering after disk dispersal. Further
work is needed to validate this interpretation. Analysis code used to perform
this work is available at https://github.com/sblunt/hip65426.


  We propose a Variational Time Series Feature Extractor (VTSFE), inspired by
the VAE-DMP model of Chen et al., to be used for action recognition and
prediction. Our method is based on variational autoencoders. It improves
VAE-DMP in that it has a better noise inference model, a simpler transition
model constraining the acceleration in the trajectories of the latent space,
and a tighter lower bound for the variational inference. We apply the method
for classification and prediction of whole-body movements on a dataset with 7
tasks and 10 demonstrations per task, recorded with a wearable motion capture
suit. The comparison with VAE and VAE-DMP suggests the better performance of
our method for feature extraction. An open-source software implementation of
each method with TensorFlow is also provided. In addition, a more detailed
version of this work can be found in the indicated code repository. Although it
was meant to, the VTSFE hasn't been tested for action prediction, due to a lack
of time in the context of Maxime Chaveroche's Master thesis at INRIA.


  We present a method for applying spatially resolved adiabatic and radiative
loss processes to synthetic radio emission from hydrodynamic simulations of
radio sources from active galactic nuclei (AGN). Lagrangian tracer particles,
each representing an ensemble of electrons, are injected into simulations and
the position, grid pressure, and time since the last strong shock are recorded.
These quantities are used to track the losses of the electron packet through
the radio source in a manner similar to the Radio AGN in Semi-analytic
Environments (RAiSE) formalism, which uses global source properties to
calculate the emissivity of each particle ex-situ. Freedom in the choice of
observing parameters, including redshift, is provided through the
post-processing nature of this approach. We apply this framework to simulations
of jets in different environments, including asymmetric ones. We find a strong
dependence of radio source properties on frequency and redshift, in good
agreement with observations and previous modelling work. There is a strong
evolution of radio spectra with redshift due to the more prominent
inverse-Compton losses at high redshift. Radio sources in denser environments
have flatter spectral indices, suggesting that spectral index asymmetry may be
a useful environment tracer. We simulate intermediate Mach number jets that
disrupt before reaching the tip of the lobe, and find that these retain an
edge-brightened Fanaroff-Riley Type II morphology, with the most prominent
emission remaining near the tip of the lobes for all environments and redshifts
we study.


  The sector of decay constants of the octet of light pseudoscalar mesons in
the framework of 'resummed' $SU(3)$ chiral perturbation theory is investigated.
A theoretical prediction for the decay constant of $\eta$-meson is compared to
a range of available determinations. Compatibility of these determinations with
the latest fits of the $SU(3)$ low energy coupling constants is discussed.
Using a Bayesian statistical approach, constraints on the low energy coupling
constants $L_4^r$ and $L_5^r$, as well as higher order remainders to the decay
constants $F_K$ and $F_\eta$, are extracted from the most recent experimental
and lattice QCD inputs for the values of the decay constants.


  Data competitions rely on real-time leaderboards to rank competitor entries
and stimulate algorithm improvement. While such competitions have become quite
popular and prevalent, particularly in supervised learning formats, their
implementations by the host are highly variable. Without careful planning, a
supervised learning competition is vulnerable to overfitting, where the winning
solutions are so closely tuned to the particular set of provided data that they
cannot generalize to the underlying problem of interest to the host. This paper
outlines some important considerations for strategically designing relevant and
informative data sets to maximize the learning outcome from hosting a
competition based on our experience. It also describes a post-competition
analysis that enables robust and efficient assessment of the strengths and
weaknesses of solutions from different competitors, as well as greater
understanding of the regions of the input space that are well-solved. The
post-competition analysis, which complements the leaderboard, uses exploratory
data analysis and generalized linear models (GLMs). The GLMs not only expand
the range of results we can explore, they also provide more detailed analysis
of individual sub-questions including similarities and differences between
algorithms across different types of scenarios, universally easy or hard
regions of the input space, and different learning objectives. When coupled
with a strategically planned data generation approach, the methods provide
richer and more informative summaries to enhance the interpretation of results
beyond just the rankings on the leaderboard. The methods are illustrated with a
recently completed competition to evaluate algorithms capable of detecting,
identifying, and locating radioactive materials in an urban environment.


  The hypothetical photonic origin of the most energetic air shower detected by
the Fly's Eye experiment is discussed. The method used for the analysis is
based on Monte Carlo simulations including the effect of precascading of
ultra-high energy (UHE) photons in the geomagnetic field. The application of
this method to data expected from the Pierre Auger Observatory is discussed.
The importance of complementing the southern Auger location by a northern site
for UHE photon identification is pointed out.


  Helium burning is one of the most fundamental steps of stellar
nucleosynthesis, as it describes the formation of life-determining element of
carbon, while it plays a key role in the evolution of Red Giant, accreting
White Dwarfs and Neutron Stars. In this work we develop a generalized
statistical theory for the 3{\alpha} reaction, which is based on the use of the
Imaginary Time Method, along with the semi-classical Hybrid {\alpha}-Clustering
(H{\alpha}C) and Neck Model (NM) frameworks. The results compared to the
methodology and data of the NACRE collaboration, following in several orders of
magnitude discrepancies, especially at low temperatures. This may be crucial
for the early dynamics of helium burning stars.


  If a positive definite Hermitian lattice represents all positive integers, we
call it universal. Several mathematicians, including the author, found 25
universal binary Hermitian lattices. But their ad hoc proofs are complicated.
We give simple and unified proofs.


  We investigate the phase difference of the sunspot cycles in the two
hemispheres and compare it with the latitudinal sunspot distribution. If the
north-south phase difference exhibits a long-term tendency, it should not be
regarded as a stochastic phenomenon.
  We use datasets of historical sunspot records and drawings made by
Staudacher, Hamilton, Gimingham, Carrington, Spouml;rer, and Greenwich
observers, as well as the sunspot activity during the Maunder minimum
reconstructed by Ribes and Nesme-Ribes.
  We employ cross-recurrence plots to analyse north-south phase differences. We
show that during the last 300 years, the persistence of phase-leading in one of
the hemispheres exhibits a secular variation. Changes from one hemisphere to
the other leading in phase were registered near 1928 and 1968 as well as two
historical ones near 1783 and 1875.
  A long-term anticorrelation between the hemispheric phase differences in the
sunspot cycles and the latitudinal distribution of sunspots was traced since
1750.


  We study convergence of a finite volume scheme for the compressible
(barotropic) Navier--Stokes system. First we prove the energy stability and
consistency of the scheme and show that the numerical solutions generate a
dissipative measure-valued solution of the system. Then by the dissipative
measure-valued-strong uniqueness principle, we conclude the convergence of the
numerical solution to the strong solution as long as the latter exists.
Numerical experiments for standard benchmark tests support our theoretical
results.


  We present a Sugawara-type construction for boundary charges in 4d BF theory
and in a general family of related TQFTs. Starting from the underlying current
Lie algebra of boundary symmetries, this gives rise to well-defined quadratic
charges forming an algebra of vector fields. In the case of 3d BF theory (i.e.
3d gravity), it was shown in [PRD 106 (2022), arXiv:2012.05263 [hep-th]] that
this construction leads to a two-dimensional family of diffeomorphism charges
which satisfy a certain modular duality. Here we show that adapting this
construction to 4d BF theory first requires to split the underlying gauge
algebra. Surprisingly, the space of well-defined quadratic generators can then
be shown to be once again two-dimensional. In the case of tangential vector
fields, this canonically endows 4d BF theory with a
$\mathrm{diff}(S^2)\times\mathrm{diff}(S^2)$ or
$\mathrm{diff}(S^2)\ltimes\mathrm{vect}(S^2)_\mathrm{ab}$ algebra of boundary
symmetries depending on the gauge algebra. The prospect is to then understand
how this can be reduced to a gravitational symmetry algebra by imposing
Pleba\'nski simplicity constraints.


  Let $X$ be a smooth complex projective variety of dimension three and let $L$
be an ample line bundle on $X$. In this paper, we provide a lower bound of the
dimension of the global sections of $m(K_{X}+L)$ under the assumption that
$\kappa(K_{X}+L)$ is non-negative. In particular, we get the following: (1) if
$\kappa(K_{X}+L)$ is greater than or equal to zero and less than or equal to
two, then $h^{0}(K_{X}+L)$ is positive. (2) If $\kappa(K_{X}+L)$ is equal to
three, then $h^{0}(2(K_{X}+L))$ is greater than or equal to three. Moreover we
get a classification of $(X,L)$ such that $\kappa(K_{X}+L)$ is equal to three
and $h^{0}(2(K_{X}+L))$ is equal to three or four.


  We develop a coarse-grained protein model with a simplified amino acid
interaction potential. We perform discrete molecular dynamics folding
simulations of a small 20 residue protein - Trp-cage - from a fully extended
conformation. We demonstrate the ability of the Trp-cage model to consistently
reach conformations within 2angstrom backbone root-mean-square distance (RMSD)
from the corresponding NMR structures. The minimum RMSD of Trp-cage
conformations in the simulation can be smaller than 1.00angstrom. Our findings
suggest that, at least for the case of Trp-cage, a detailed all-atom protein
model with a physical molecular mechanics force field is not necessary to reach
the native state of a protein. Our results also suggest that the success
folding Trp-cage in our simulations and in the reported all-atom molecular
mechanics simulations studies may be mainly due to the special stabilizing
features specific to this miniprotein.


  The observation of the coherent elastic neutrino-nucleus scattering
(CE$\nu$NS) provides us opportunities to explore a wide class of new physics.
In the Standard Model (SM), the CE$\nu$NS process arises from the vector and
axial-vector neutral currents through the exchange of $Z$ boson and the
axial-vector current contribution turns out to be subdominant. It is thus
natural to consider the extra contributions to CE$\nu$NS from more generic new
physics beyond the SM with (axial-)vector interactions associated with a new
vector mediator $Z'$. Besides the ordinary CE$\nu$NS, the active neutrinos can
convert into a new exotic fermion $\chi$ through the process $\nu N\to \chi N$
mediated by $Z'$ without violating the coherence. It would be interesting to
consider the implication of this conversion for the new fermion sector beyond
the SM. We consider the framework of a simplified neutrino model in which a new
Dirac fermion $\chi$ interacts with active neutrinos and a leptophobic vector
mediator $Z'$. We evaluate both the tree-level and loop-level contributions to
the CE$\nu$NS and in particular the loop diagrams produce active neutrino
elastic scattering process $\nu N\to \nu N$ with the fermion $\chi$ inside the
loops. When the interaction between $Z'$ and the SM quarks is vector type and
axial-vector type, the CE$\nu$NS processes are respectively dominated by the
tree-level and loop-level contributions. We investigate the constraints on the
model parameters by fitting to the COHERENT data, assuming a wide range of
$m_\chi$. The parameter space with $m_\chi$ larger than the maximal energy of
incoming neutrinos can be constrained by including the loop-level contribution.
More importantly, the inclusion of loop diagrams can place constraint on
axial-vector interaction whose tree-level process is absent in the coherent
neutrino-nucleus scattering.


  Hyperspectral stimulated Raman scattering (SRS) microscopy is a label-free
technique for biomedical and mineralogical imaging which can suffer from low
signal to noise ratios. Here we demonstrate the use of an unsupervised deep
learning neural network for rapid and automatic denoising of SRS images: UHRED
(Unsupervised Hyperspectral Resolution Enhancement and Denoising). UHRED is
capable of one-shot learning; only one hyperspectral image is needed, with no
requirements for training on previously labelled datasets or images.
Furthermore, by applying a k-means clustering algorithm to the processed data,
we demonstrate automatic, unsupervised image segmentation, yielding, without
prior knowledge of the sample, intuitive chemical species maps, as shown here
for a lithium ore sample.


  Class-conditional noise commonly exists in machine learning tasks, where the
class label is corrupted with a probability depending on its ground-truth. Many
research efforts have been made to improve the model robustness against the
class-conditional noise. However, they typically focus on the single label case
by assuming that only one label is corrupted. In real applications, an instance
is usually associated with multiple labels, which could be corrupted
simultaneously with their respective conditional probabilities. In this paper,
we formalize this problem as a general framework of learning with
Class-Conditional Multi-label Noise (CCMN for short). We establish two unbiased
estimators with error bounds for solving the CCMN problems, and further prove
that they are consistent with commonly used multi-label loss functions.
Finally, a new method for partial multi-label learning is implemented with
unbiased estimator under the CCMN framework. Empirical studies on multiple
datasets and various evaluation metrics validate the effectiveness of the
proposed method.


  The probability density function of the arrival time of \v{C}erenkov light on
a photo-multiplier tube has been studied. This study covers light production,
transmission and detection. The light production includes the light from a
muon, the light from a shower and the light due to the energy loss of a muon.
For the transmission of light, the effects of dispersion, absorption and
scattering in the medium are considered. For the detection of light, the
angular acceptance and the quantum efficiency of the photo-multiplier tube are
taken into account.


  We calculate the cross-correlation function (CCF) between damped Ly-a systems
(DLAs) and Lyman break galaxies (LBGs) using cosmological hydrodynamic
simulations at z=3. We compute the CCF with two different methods. First, we
assume that there is one DLA in each dark matter halo if its DLA cross section
is non-zero. In our second approach we weight the pair-count by the DLA cross
section of each halo, yielding a cross-section-weighted CCF. We also compute
the angular CCF for direct comparison with observations. Finally, we calculate
the auto-correlation functions of LBGs and DLAs, and their bias against the
dark matter distribution. For these different approaches, we consistently find
that there is good agreement between our simulations and observational
measurements by Cooke et al. and Adelberger et al. Our results thus confirm
that the spatial distribution of LBGs and DLAs can be well described within the
framework of the concordance Lambda CDM model. We find that the correlation
strengths of LBGs and DLAs are consistent with the actual observations, and in
the case of LBGs it is higher than would be predicted by low-mass galaxy merger
models.


  The increased flexibility requirement needs a flexibility market at the
distribution grid level operated by the distribution system operators (DSOs) to
resolve challenges to ensure secure operation and, to integrate new renewable
productions or loads in the grid. Therefore, the network visibility and
monitoring are paramount to distribution network operation. This paper presents
a methodology demonstrating the value distribution grid monitoring can bring
for the realisation of a local flexibility market. This paper further
illustrates the reduction of costs of operation of a DSO with the help of grid
monitoring and local flexibility market while maintaining a secure and reliable
operation. The methodology has been applied on a real 35 node MV network of a
Swiss DSO with several GridEye measurement devices. The performance in terms of
losses and voltage and flow violation costs is compared with sub-optimal
operation without monitoring.


  We prove Gronwall-type estimates for the distance of integral curves of
smooth vector fields on a Riemannian manifold. Such estimates are of central
importance for all methods of solving ODEs in a verified way, i.e., with full
control of roundoff errors. Our results may therefore be seen as a prerequisite
for the generalization of such methods to the setting of Riemannian manifolds.


  This paper introduces a novel hybrid optimisation algorithm that combines
elements of both metaheuristic search and integer programming. This new
matheuristic combines elements of Benders decomposition and the Bees Algorithm,
to create the Bee-Benders Hybrid Algorithm (BBHA) which retains many of the
advantages both of the methods. Specifically it is designed to be easily
parallelizable, to produce good solutions quickly while still retaining a
guarantee of optimality when run for a sufficiently long time. The algorithm is
tested using a transmission network expansion and energy storage planning
model, a challenging and very large scale mixed integer linear programming
problem. Transmission network planning problems are already difficult on their
own. When including the planning for storage systems in the network, the
variation of demand over time has to be taken into account significantly
increasing the size and difficulty of the optimization problem. The BBHA is
shown to be highly effective hybrid matheuristic algorithm that performs at
least as well as either Benders decomposition or the Bees Algorithm where these
are effective on their own, and significantly improves upon the individual
approaches where neither component part has a pronounced advantage. While the
paper demonstrates the effectiveness in terms of the concrete electricity
network planning problem, the algorithm could be readily applied to any mixed
integer linear program, and is expected to work particularly well whenever this
has a structure that is amenable to Benders decomposition.


  We analyze the psu(2,2|4) supersymmetry algebra of a superstring propagating
in the AdS_5 x S^5 background in the uniform light-cone gauge. We consider the
off-shell theory by relaxing the level-matching condition and take the limit of
infinite light-cone momentum, which decompactifies the string world-sheet. We
focus on the psu(2|2)+psu(2|2) subalgebra which leaves the light-cone
Hamiltonian invariant and show that it undergoes extension by a central element
which is expressed in terms of the level-matching operator. This result is in
agreement with the conjectured symmetry algebra of the dynamic S-matrix in the
dual N=4 gauge theory.


  We derive, by introducing restrictions to the lesser self energy, a Monte
Carlo scheme that solves the NEGF equations for electron transport. In doing so
we formally prove that the Monte Carlo estimator has an expectation value equal
to the lead current of the NEGF solution, and we provide a simple test of the
Monte Carlo scheme by calculating conductivity in nanowires within Buttiker's
approximation of scattering. Good agreement between the Monte Carlo simulations
and the alternative approaches are obtained, and we also demonstrate the
existence of a regime where the Monte Carlo method is the fastest method. In
our tests this regime is to extreme to be of practical use. We discuss various
ways in which to speed up our prototype and how it can be extended to include
more physics. Although the full applicability range of our assumptions about
the lesser self energy remains to be better understood, we argue that they
should apply as long as the transport process can be considered stationary.


  We study the cost of improving the goodput, or the useful data rate, to user
in a wireless network. We measure the cost in terms of number of base stations,
which is highly correlated to the energy cost as well as capital and
operational costs of a network provider.We show that increasing the available
bandwidth, or throughput, may not necessarily lead to increase in goodput,
particularly in lossy wireless networks in which TCP does not perform well. As
a result, much of the resources dedicated to the user may not translate to high
goodput, resulting in an inefficient use of the network resources. We show that
using protocols such as TCP/NC, which are more resilient to erasures and
failures in the network, may lead to a goodput commensurate the throughput
dedicated to each user. By increasing goodput, users' transactions are
completed faster; thus, the resources dedicated to these users can be released
to serve other requests or transactions. Consequently, we show that translating
efficiently throughput to goodput may bring forth better connection to users
while reducing the cost for the network providers.


  Off-policy evaluation and learning (OPE/L) use offline observational data to
make better decisions, which is crucial in applications where online
experimentation is limited. However, depending entirely on logged data, OPE/L
is sensitive to environment distribution shifts -- discrepancies between the
data-generating environment and that where policies are deployed.
\citet{si2020distributional} proposed distributionally robust OPE/L (DROPE/L)
to address this, but the proposal relies on inverse-propensity weighting, whose
estimation error and regret will deteriorate if propensities are
nonparametrically estimated and whose variance is suboptimal even if not. For
standard, non-robust, OPE/L, this is solved by doubly robust (DR) methods, but
they do not naturally extend to the more complex DROPE/L, which involves a
worst-case expectation. In this paper, we propose the first DR algorithms for
DROPE/L with KL-divergence uncertainty sets. For evaluation, we propose
Localized Doubly Robust DROPE (LDR$^2$OPE) and show that it achieves
semiparametric efficiency under weak product rates conditions. Thanks to a
localization technique, LDR$^2$OPE only requires fitting a small number of
regressions, just like DR methods for standard OPE. For learning, we propose
Continuum Doubly Robust DROPL (CDR$^2$OPL) and show that, under a product rate
condition involving a continuum of regressions, it enjoys a fast regret rate of
$\mathcal{O}\left(N^{-1/2}\right)$ even when unknown propensities are
nonparametrically estimated. We empirically validate our algorithms in
simulations and further extend our results to general $f$-divergence
uncertainty sets.


  We explain how the so-called Einstein locality is to be understood in the
Schr\"odinger picture of quantum mechanics. This notion is perfectly compatible
with the Bell non-locality exhibited by entangled states. Contrary to some
beliefs that quantum mechanics is incomplete, it is, in fact, its
overcompleteness as exemplified by different pictures of quantum physics, that
points to the same underlying reality.


  In this paper we compute the collision strengths and their thermally-averaged
Maxwellian values for electron transitions between the fifteen lowest levels of
doubly-ionised cobalt, Co^{2+}, which give rise to forbidden emission lines in
the visible and infrared region of spectrum. The calculations also include
transition probabilities and predicted relative line emissivities. The data are
particularly useful for analysing the thermodynamic conditions of supernova
ejecta.


  We present wide-field optical imaging covering the entire neutral hydrogen
disc of the Local Group dwarf galaxy NGC 6822. These observations reveal the
presence of numerous blue, young stars at large galactocentric radii well
beyond R_25. Blue stars are also found that are associated with NGC 6822's
companion HI cloud, indicating that star formation was triggered in the
companion in the last 10^8 yr. In general, blue stars are present where the HI
surface densities reach values > 5 x 10^20 cm^(-2). However, over one-third of
the blue stars detected are found at lower surface densities. The young stars
trace the distribution of the neutral hydrogen surprisingly well, but seem to
be avoiding the supergiant HI shell in NGC 6822, setting a lower limit for its
age of 10^8 yr. The extended distribution of young stars implies that stars can
form at large galactocentric radii in dwarf galaxies; the HI is therefore not
necessarily much more extended than the stellar population. This finding has
important consequences for the chemical enrichment of the interstellar medium
throughout (dwarf) galaxies


  We develop a multimodal classifier for the cultural heritage domain using a
late fusion approach and introduce a novel dataset. The three modalities are
Image, Text, and Tabular data. We based the image classifier on a ResNet
convolutional neural network architecture and the text classifier on a
multilingual transformer architecture (XML-Roberta). Both are trained as
multitask classifiers and use the focal loss to handle class imbalance. Tabular
data and late fusion are handled by Gradient Tree Boosting. We also show how we
leveraged specific data models and taxonomy in a Knowledge Graph to create the
dataset and to store classification results. All individual classifiers
accurately predict missing properties in the digitized silk artifacts, with the
multimodal approach providing the best results.


  In mediation analysis, the effect of an exposure (or treatment) on an outcome
variable is decomposed into two components: a direct effect, which pertains to
an immediate influence of the exposure on the outcome, and an indirect effect,
which the exposure exerts on the outcome through a third variable called
mediator. Our motivating example concerns the relationship between maternal
smoking (the exposure, $X$), birthweight (the mediator, $M$), and infant
mortality (the outcome, $Y$), which has attracted the interest of
epidemiologists and statisticians for many years. We introduce new causal
estimands, named $u$-specific direct and indirect effects, which describe the
direct and indirect effects of the exposure on the outcome at a specific
quantile $u$ of the mediator, $0 < u < 1$. Under sequential ignorability we
derive an interesting and novel decomposition of $u$-specific indirect effects.
The components of this decomposition have a straightforward interpretation and
can provide new insights into the complexity of the mechanisms underlying the
indirect effect. We illustrate the proposed methods using data on infant
mortality in the US population. We provide analytical evidence that supports
the hypothesis that the risk of sudden infant death syndrome is not predicted
by changes in the birthweight distribution.


  Let $\Sigma$ be a smooth compact connected oriented surface with boundary. A
metric on $\Sigma$ is said to be of Anosov type if it has strictly convex
boundary, no conjugate points, and a hyperbolic trapped set. We prove that two
metrics of Anosov type with the same marked boundary distance are isometric
(via a boundary-preserving isometry isotopic to the identity). As a corollary,
we retrieve the boundary distance rigidity result for simple disks of Pestov
and Uhlmann [arXiv:math/0305280]. The proof rests on a new transfer principle
showing that, in any dimension, the marked length spectrum rigidity conjecture
implies the marked boundary distance rigidity conjecture under the existence of
a suitable isometric embedding into a closed Anosov manifold. Such an isometric
embedding result for open surfaces of Anosov type was proved by the first
author with Chen and Gogolev in [arXiv:2009.13665] while the marked length
spectrum rigidity for closed Anosov surfaces was established by the second
author with Guillarmou and Paternain in [arXiv:2303.12007].


  Estimating and optimizing Mutual Information (MI) is core to many problems in
machine learning; however, bounding MI in high dimensions is challenging. To
establish tractable and scalable objectives, recent work has turned to
variational bounds parameterized by neural networks, but the relationships and
tradeoffs between these bounds remains unclear. In this work, we unify these
recent developments in a single framework. We find that the existing
variational lower bounds degrade when the MI is large, exhibiting either high
bias or high variance. To address this problem, we introduce a continuum of
lower bounds that encompasses previous bounds and flexibly trades off bias and
variance. On high-dimensional, controlled problems, we empirically characterize
the bias and variance of the bounds and their gradients and demonstrate the
effectiveness of our new bounds for estimation and representation learning.


  We study the set of directions asymptotically explored by a spatially
homogeneous random walk in $d$-dimensional Euclidean space. We survey some
pertinent results of Kesten and Erickson, make some further observations, and
present some examples. We also explore links to the asymptotics of
one-dimensional projections, and to the growth of the convex hull of the random
walk.


  The energy and structure of dilute hard- and soft-sphere Bose gases are
systematically studied in the framework of several many-body approaches, as the
variational correlated theory, the Bogoliubov model and the uniform limit
approximation, valid in the weak interaction regime. When possible, the results
are compared with the exact diffusion Monte Carlo ones. A Jastrow type
correlation provides a good description of the systems, both hard- and
soft-spheres, if the hypernetted chain energy functional is freely minimized
and the resulting Euler equation is solved. The study of the soft-spheres
potentials confirms the appearance of a dependence of the energy on the shape
of the potential at gas paremeter values of $x \sim 0.001$. For quantities
other than the energy, such as the radial distribution functions and the
momentum distributions, the dependence appears at any value of $x$. The
occurrence of a maximum in the radial distribution function, in the momentum
distribution and in the excitation spectrum is a natural effect of the
correlations when $x$ increases. The asymptotic behaviors of the functions
characterizing the structure of the systems are also investigated. The uniform
limit approach results very easy to implement and provides a good description
of the soft-sphere gas. Its reliability improves when the interaction weakens.


  In the study of high-mass star formation, hot cores are empirically defined
stages where chemically rich emission is detected toward a massive YSO. It is
unknown whether the physical origin of this emission is a disk, inner envelope,
or outflow cavity wall and whether the hot core stage is common to all massive
stars. We investigate the chemical make up of several hot molecular cores to
determine physical and chemical structure. We use high spectral and spatial
resolution Cycle 0 ALMA observations to determine how this stage fits into the
formation sequence of a high mass star. We observed the G35.20-0.74N and
G35.03+0.35 hot cores at 350 GHz. We analyzed spectra and maps from four
continuum peaks (A, B1, B2 and B3) in G35.20, separated by 1000-2000 AU, and
one continuum peak in G35.03. We made all possible line identifications across
8 GHz of spectral windows of molecular emission lines and determined column
densities and temperatures for as many as 35 species assuming local
thermodynamic equilibrium. In comparing the spectra of the four peaks, we find
each has a distinct chemical composition expressed in over 400 different
transitions. In G35.20, B1 and B2 contain oxygen- and sulfur-bearing organic
and inorganic species but few nitrogen-bearing species whereas A and B3 are
strong sources of O, S, and N-bearing species (especially those with the
CN-bond). CH$_2$DCN is clearly detected in A and B3 with D/H ratios of 8 and
13$\%$, respectively, but is much weaker at B1 and undetected at B2. No
deuterated species are detected in G35.03, but similar molecular abundances to
G35.20 were found in other species. We also find co-spatial emission of HNCO
and NH$_2$CHO in both sources indicating a strong chemical link between the two
species. The chemical segregation between N-bearing organic species and others
in G35.20 suggests the presence of multiple protostars, surrounded by a disk or
torus.


  We use high resolution N-body/SPH simulations to study the hydrodynamical
interaction between the Large Magellanic Cloud (LMC) and the hot halo of the
Milky Way. We investigate whether ram-pressure acting on the satellite's ISM
can explain the peculiarities observed in the HI distribution and the location
of the recent star formation activity. Due to the present nearly edge-on
orientation of the disk with respect to the orbital motion, compression at the
leading edge can explain the high density region observed in HI at the
south-east border. In the case of a face-on disk (according to Mastropietro et
al. 2008 the LMC was moving almost face-on before the last perigalactic
passage), ram-pressure directed perpendicularly to the disk produces a clumpy
structure characterized by voids and high density filaments that resemble those
observed by the Parkes HI survey. As a consequence of the very recent edge-on
motion, the H-alpha emission is mainly concentrated on the eastern side where
30 Doradus and most of the supergiant shells are located, although some H-alpha
complexes form a patchy distribution on the entire disk. In this scenario only
the youngest stellar complexes show a progression in age along the leading
border of the disk.


  Helioseismology shows that the regions occupied by convection and
differential rotation inside the sun almost coincide. This supports the leading
theoretical concept for the origin of differential rotation as a result of
interaction between convection and rotation. This talk outlines the current
state of the differential rotation theory. Numerical models based on the theory
reproduce the observed solar rotation quite closely. The models also compute
meridional flow and predict that the flow at the bottom of the convection zone
is not small compared to the surface. Theoretical predictions for stellar
differential rotation as a function of the stellar mass and rotation rate are
discussed and compared with observations. The implications of the differential
rotation models for solar and stellar dynamos are briefly discussed.


  We present a significantly improved scheme of entanglement detection inspired
by local uncertainty relations for a system consisting of two qubits.
Developing the underlying idea of local uncertainty relations, namely
correlations, we demonstrate that it's possible to define a measure which is
invariant under local unitary transformations and which is based only on local
measurements. It is quite simple to implement experimentally and it allows
entanglement quantification in a certain range for mixed states and exactly for
pure states, without first obtaining full knowledge (e.g. through tomography)
of the state.


  Poincare gauge theories that, in the absence of spinning matter, reduce to
the one-parameter teleparallel theory are investigated with respect to their
mathematical consistency and experimental viability. It is argued that the
theories can be consistently coupled to the known standard model particles.
Moreover, we establish the result that in the classical limit, such theories
share a large class of solutions with general relativity, containing, among
others, the four classical black hole solutions (Schwarzschild,
Reisner-Nordstrom, Kerr and Kerr-Newman), as well as the complete class of
Friedman-Robertson-Walker cosmological solutions, thereby extending older
viability results that were restricted to the correct Newtonian limit and to
the existence of the Schwarzschild solution.


  The degenerate four-wave mixing spectroscopy of uniaxially strained GaN
layers is demonstrated using colinearly polarized laser pulses. The nonlinear
response of FWM signal on exciton oscillator strength enhances the sensitivity
for polarized exciton, allowing for mapping out the in-plane anisotropy of the
strain field. The observed high-contrast spectral polarization clearly shows
fine structure splittings of excitons, which are also confirmed in the change
of quantum beating periods of time.


  This paper expresses the structure of artificial neural network (ANN) as a
functional form, using the activation integral concept derived from the
activation function. In this way, the structure of ANN can be represented by a
simple function, and it is possible to find the mathematical solutions of ANN.
Thus, it can be recognized that the current ANN can be placed in a more
reasonable framework. Perhaps all questions about ANN will be eliminated.


  Reparametrization-invariant theories of point relativistic particle
interaction with fields of arbitrary tensor dimension are considered. It has
been shown that the equations of motion obtained by Kalman [G. Kalman, Phys.
Rev. vol.123, p.384 (1961)] are reproduced as the Euler - Lagrange equations
for reparametrization-invariant theory in the propertime gauge. The formalism
is developed that conserves manifest reparametrization invariance at each stage
of calculations. Using the above formalism, the equations of motion are being
analyzed and the dynamical variable theories are being constructed. It has been
shown that the remained invariance kept after gauge fixation gives an
identically-zero invariant Hamiltonian.


  The use of galaxy clusters as cosmological probes relies on a detailed
understanding of their properties. We aim to update the spectroscopic cluster
identification of CODEX by running the spectroscopic group finder on the
follow-up spectroscopy results and connecting the dynamical state of clusters
to their scaling relations. We implemented a reproducible spectroscopic
membership determination and cleaning procedures, based on the redMaPPer
membership, running the spectroscopic group finder on the follow-up
spectroscopy results and cleaning the membership for spectroscopic outliers. We
applied the Anderson-Darling test for velocity substructure and analysed its
influence on the scaling relations. We also tested the effect of the
X-ray-to-optical centre offset on the scaling relations. We report on the
scaling relations between richness, X-ray luminosity, and velocity dispersion
for a complete sample of clusters with at least 15 members. Clusters with
velocity substructure exhibit enhanced velocity dispersion for a given richness
and are characterized by 2.5 times larger scatter. Clusters that have a strong
offset in X-ray-to-optical centres have comparable scaling relations as
clusters with substructure. We demonstrate that there is a consistency in the
parameters of the scaling relations for the low- and high-richness galaxy
clusters. Splitting the clusters by redshift, we note a decrease in scatter
with redshift in all scaling relations. We localize the redshift range where a
high scatter is observed to $z<0.15$, which is in agreement with the literature
results on the scatter. We note that the increase in scatter for both high- and
low-luminosity clusters is $z<0.15$, suggesting that both cooling and the
resulting active galactic nucleus feedback are at the root of this scatter.
Abridged.


  Using the AKSZ prescription we construct 2D and 3D topological field theories
associated to generalized complex manifolds. These models can be thought of as
2D and 3D generalizations of A- and B-models. Within the BV framework we show
that the 3D model on a two-manifold cross an interval can be reduced to the 2D
model.


  During phase transitions certain properties of a material change, such as
composition field and lattice-symmetry distortions. These changes are typically
coupled, and affect the microstructures that form in materials. Here, we
propose a 2D theoretical framework that couples a Cahn-Hilliard (CH) model
describing the composition field of a material system, with a phase field
crystal (PFC) model describing its underlying microscopic configurations. We
couple the two continuum models via coordinate transformation coefficients. We
introduce the transformation coefficients in the PFC method, to describe affine
lattice deformations. These transformation coefficients are modeled as
functions of the composition field. Using this coupled approach, we explore the
effects of coarse-grained lattice symmetry and distortions on a phase
transition process. In this paper, we demonstrate the working of the CH-PFC
model through three representative examples: First, we describe base cases with
hexagonal and square lattice symmetries for two composition fields. Next, we
illustrate how the CH-PFC method interpolates lattice symmetry across a diffuse
composition phase boundary. Finally, we compute a Cahn-Hilliard type of
diffusion and model the accompanying changes to lattice symmetry during a phase
transition process.


  The basic result of Oka theory, due to Gromov, states that every continuous
map $f$ from a Stein manifold $S$ to an elliptic manifold $X$ can be deformed
to a holomorphic map. It is natural to ask whether this can be done for all $f$
at once, in a way that depends continuously on $f$ and leaves $f$ fixed if it
is holomorphic to begin with. In other words, is $\scrO(S,X)$ a deformation
retract of $\scrC(S,X)$? We prove that it is if $S$ has a strictly
plurisubharmonic Morse exhaustion with finitely many critical points; in
particular, if $S$ is affine algebraic. The only property of $X$ used in the
proof is the parametric Oka property with approximation with respect to finite
polyhedra, so our theorem holds under the weaker assumption that $X$ is an Oka
manifold. Our main tool, apart from Oka theory itself, is the theory of
absolute neighbourhood retracts. We also make use of the mixed model structure
on the category of topological spaces.


  Gyrokinetic validation studies are crucial in developing confidence in the
model incorporated in numerical simulations and thus improving their predictive
capabilities. As one step in this direction, we simulate an ASDEX Upgrade
discharge with the GENE code, and analyze various fluctuating quantities and
compare them to experimental measurements. The approach taken is the following.
First, linear simulations are performed in order to determine the turbulence
regime. Second, the heat fluxes in nonlinear simulations are matched to
experimental fluxes by varying the logarithmic ion temperature gradient within
the expected experimental error bars. Finally, the dependence of various
quantities with respect to the ion temperature gradient is analyzed in detail.
It is found that density and temperature fluctuations can vary significantly
with small changes in this parameter, thus making comparisons with experiments
very sensitive to uncertainties in the experimental profiles. However,
cross-phases are more robust, indicating that they are better observables for
comparisons between gyrokinetic simulations and experimental measurements.


  We propose a unified framework to generate both homophonic and homographic
puns to resolve the split-up in existing works. Specifically, we incorporate
three linguistic attributes of puns to the language models: ambiguity,
distinctiveness, and surprise. Our framework consists of three parts: 1) a
context words/phrases selector to promote the aforementioned attributes, 2) a
generation model trained on non-pun sentences to incorporate the context
words/phrases into the generation output, and 3) a label predictor that learns
the structure of puns which is used to steer the generation model at inference
time. Evaluation results on both pun types demonstrate the efficacy of our
model over strong baselines.


  Masked Autoencoders is a simple yet powerful self-supervised learning method.
However, it learns representations indirectly by reconstructing masked input
patches. Several methods learn representations directly by predicting
representations of masked patches; however, we think using all patches to
encode training signal representations is suboptimal. We propose a new method,
Masked Modeling Duo (M2D), that learns representations directly while obtaining
training signals using only masked patches. In the M2D, the online network
encodes visible patches and predicts masked patch representations, and the
target network, a momentum encoder, encodes masked patches. To better predict
target representations, the online network should model the input well, while
the target network should also model it well to agree with online predictions.
Then the learned representations should better model the input. We validated
the M2D by learning general-purpose audio representations, and M2D set new
state-of-the-art performance on tasks such as UrbanSound8K, VoxCeleb1,
AudioSet20K, GTZAN, and SpeechCommandsV2. We additionally validate the
effectiveness of M2D for images using ImageNet-1K in the appendix.


  Difficulties with finding the general exact solutions to the Wheeler-DeWitt
equation, i.e. the wave functions of the Universe, are known and well
documented. However, the present paper draws attention to a completely
different matter, which is rarely if ever discussed in relation to this
equation, namely, the time complexity of the Wheeler-DeWitt equation, that is,
the time required to exactly solve the equation for a given universe. As it is
shown in the paper, whatever generic exact algorithm is used to solve the
equation, most likely such an algorithm cannot be faster than brute force,
which makes the wave functions of the Universe infeasible.


  We are concerned with the convergence of numerical schemes for the initial
value problem associated to the Keyfitz-Kranzer system of equations. This
system is a toy model for several important models such as in elasticity
theory, magnetohydrodynamics, and enhanced oil recovery. In this paper we prove
the convergence of three difference schemes. Two of these schemes is shown to
converge to the unique entropy solution. Finally, the convergence is
illustrated by several examples.


  The design of reliable indicators to anticipate critical transitions in
complex systems is an im portant task in order to detect a coming sudden regime
shift and to take action in order to either prevent it or mitigate its
consequences. We present a data-driven method based on the estimation of a
parameterized nonlinear stochastic differential equation that allows for a
robust anticipation of critical transitions even in the presence of strong
noise levels like they are present in many real world systems. Since the
parameter estimation is done by a Markov Chain Monte Carlo approach we have
access to credibility bands allowing for a better interpretation of the
reliability of the results. By introducing a Bayesian linear segment fit it is
possible to give an estimate for the time horizon in which the transition will
probably occur based on the current state of information. This approach is also
able to handle nonlinear time dependencies of the parameter controlling the
transition. In general the method could be used as a tool for on-line analysis
to detect changes in the resilience of the system and to provide information on
the probability of the occurrence of a critical transition in future.


  Let $n$, $k$, and $t$ be integers satisfying $n>k>t\ge2$. A Steiner system
with parameters $t$, $k$, and $n$ is a $k$-uniform hypergraph on $n$ vertices
in which every set of $t$ distinct vertices is contained in exactly one edge.
An outstanding problem in Design Theory is to determine whether a nontrivial
Steiner system exists for $t\geq6$.
  In this note we prove that for every $k>t\ge2$ and sufficiently large $n$,
there exists an almost Steiner system with parameters $t$, $k$, and $n$; that
is, there exists a $k$-uniform hypergraph on $n$ vertices such that every set
of $t$ distinct vertices is covered by either one or two edges.


  Recently Sanwal et al. (2002) reported the first clear detection of
absorption features in an isolated neutron star, 1E1207.4-5209. Remarkably
their spectral modeling demonstrates that the atmosphere cannot be Hydrogen.
They speculated that the neutron star atmosphere is indicative of ionized
Helium in an ultra-strong (~1.5x10^{14} G) magnetic field. We have applied our
recently developed atomic model (Mori & Hailey 2002) for strongly-magnetized
neutron star atmospheres to this problem. We find that this model, along with
some simp le atomic physics arguments, severely constrains the possible
composition of the atmosphere. In particular we find that the absorption
features are naturally associated with He-like Oxygen or Neon in a magnetic
field of ~10^{12} G, comparable to the magnetic field derived from the spin
parameters of the neutron star. This interpretation is consistent with the
relative line strengths and widths and is robust. Our model predicts possible
substructure in the spectral features, which has now been reported by
XMM-Newton (Mereghetti et al. 2002). However we show the Mereghetti et al.
claim that the atmosphere is Iron or some comparable high-Z element at ~
10^{12} G is easily ruled out by the Chandra and XMM-Newton data.


  Consider a rational family of planar rational curves in a certain region of
interest. We are interested in finding an approximation to the implicit
representation of the envelope. Since exact implicitization methods tend to be
very costly, we employ an adaptation of approximate implicitization to envelope
computation. Moreover, by utilizing an orthogonal basis in the construction
process, the computational times can be shortened and the numerical condition
improved. We provide an example to illustrate the performance of our approach.


  We consider a swarm of mobile robots evolving in a bidimensional Euclidean
space. We study a variant of the crash-tolerant gathering problem: if no robot
crashes, robots have to meet at the same arbitrary location, not known
beforehand, in finite time; if one or several robots crash at the same
location, the remaining correct robots gather at the crash location to rescue
them. Motivated by impossibility results in the semi-synchronous setting, we
present the first solution to the problem for the fully synchronous setting
that operates in the vanilla Look-Compute-Move model with no additional
hypotheses: robots are oblivious, disoriented, have no multiplicity detection
capacity, and may start from arbitrary positions (including those with
multiplicity points). We furthermore show that robots gather in a time that is
proportional to the initial maximum distance between robots.


  We are interested in path decompositions of a perturbed reflecting Brownian
motion (PRBM) at the hitting times and at the minimum. Our study relies on the
loop soups developed by Lawler and Werner [10] and Le Jan [13]-[14], in
particular on a result discovered by Lupu [15] identifying the law of the
excursions of the PRBM above its past minimum with the loop measure of Brownian
bridges.


  We prove here that the polynomial <nabla(C_p(1)), e_a h_b h_c> q,
t-enumerates, by the statistics dinv and area, the parking functions whose
supporting Dyck path touches the main diagonal according to the composition p
of size a + b + c and have a reading word which is a shuffle of one decreasing
word and two increasing words of respective sizes a, b, c. Here Cp(1) is a
rescaled Hall-Littlewood polynomial and "nabla" is the Macdonald eigenoperator
introduced in [1]. This is our latest progress in a continued effort to settle
the decade old shuffle conjecture of [14]. It includes as special cases all
previous results connected with this conjecture such as the q, t-Catalan [3]
and the Schroder and h, h results of Haglund in [12] as well as their
compositional refinements recently obtained in [9] and [10]. It also confirms
the possibility that the approach adopted in [9] and [10] has the potential to
yield a resolution of the shuffle parking function conjecture as well as its
compositional refinement more recently proposed by Haglund, Morse and Zabrocki
in [15].


  Non-Hermitian nodal knot metals (NKMs) contains intricate complex-valued
energy bands gives rise to knotted exceptional loops and new topological
surface states. We introduce a formalism that connects the algebraic,
geometric, and topological aspects of these surface states with their parent
knots, and provide an optimized constructive ansatz for tight-binding models
for non-Hermitian NKMs of arbitrary knot complexity and minimal hybridization
range. Specifically, various representative non-Hermitian torus knots
Hamiltonians are constructed in real-space, and their nodal topologies studied
via winding numbers that avoid the explicit construction of generalized
Brillouin zones. In particular, we identify the surface state boundaries as
"tidal" intersections of the complex band structure in a marine landscape
analogy. Beyond topological quantities based on Berry phases, we further find
these tidal surface states to be intimately connected to the band vorticity and
the layer structure of their dual Seifert surface, and as such provide a
fingerprint for non-Hermitian NKMs.


  Distributed adaptive conforming refinement requires multiple iterations of
the serial refinement algorithm and global communication as the refinement can
be propagated over several processor boundaries. We show bounds on the maximum
number of iterations. The algorithm is implemented within the software package
DUNE-ALUGrid.


  We present the results of ALMA observations toward the low-mass Class-0
binary system, VLA 1623Aab in the Ophiuchus molecular cloud in $^{12}$CO,
$^{13}$CO, and C$^{18}$O(2--1) lines. Our $^{12}$CO ($J$=2--1) data reveal that
the VLA 1623 outflow consists of twin spatially overlapped outflows/jets. The
redshifted northwestern jet exhibits the three cycles of wiggle with a spatial
period of 1360$\pm$10 au, corresponding to a time period of 180 yr. The
wiggle-like structure is also found in the position-velocity (PV) diagram,
showing an amplitude in velocity of about 0.9 km s$^{-1}$. Both the period and
the velocity amplitude of the wiggle are roughly consistent with those expected
from the binary parameters, i.e., the orbital period (460$\pm$20 yr) and the
Keplerian velocity (2.2 km s$^{-1}$). Our $^{13}$CO and C$^{18}$O images reveal
the nature of the dense gas in the two cm/mm sources, VLA 1623-B and -W, and
its relation to the outflows, and strongly support the previous interpretation
that both are shocked cloudlets. The driving sources of the twin molecular
outflows are, therefore, likely to be within the VLA 1623Aab binary. The axes
of the two molecular outflows are estimated to be inclined by 70$\arcdeg$ from
each other across the plane of sky, implying that the associated protostellar
disks are also misaligned by $70\arcdeg$. Such a misalignment, together with a
small binary separation of 34 au in the one of the youngest protobinary systems
known, is difficult to explain by models of disk fragmentation in quiescent
environments. Instead, other effects such as turbulence probably play roles in
misaligning the disks.


  We introduce the notion of power lattices that unifies and extends the
equicardinal geometric lattices, Cartesian products of subspace lattices, and
multiset subset lattices, among several others. The notions of shellability for
simplicial complexes, q-complexes, and multicomplexes are then unified and
extended to that of complexes in power lattices, which we name as P-complexes.
A nontrivial class of shellable P-complexes are obtained via P-complexes of the
independent sets of a matroid in power lattice, which we introduce to
generalize matroids in Boolean lattices, q-matroids in subspace lattices, and
sum-matroids in Cartesian products of subspace lattices. We also prove that
shellable P-complexes in a power lattice yield shellable order complexes,
extending the celebrated result of shellability of order complexes of
(equicardinal) geometric lattices by Bj\"orner and also, a recent result on
shellability of order complexes of lexicographically shellable q-complexes.
Finally, we provide a construction of matroids on the lattice of multiset
subsets from weighted graphs. We also consider a variation of Stanley-Reisner
rings associated with shellable multicomplexes than the one considered by
Herzog and Popescu and proved that these rings are sequentially Cohen-Macaulay.


  Unsupervised domain adaptation (UDA) methods intend to reduce the gap between
source and target domains by using unlabeled target domain and labeled source
domain data, however, in the medical domain, target domain data may not always
be easily available, and acquiring new samples is generally time-consuming.
This restricts the development of UDA methods for new domains. In this paper,
we explore the potential of UDA in a more challenging while realistic scenario
where only one unlabeled target patient sample is available. We call it
Few-shot Unsupervised Domain adaptation (FUDA). We first generate target-style
images from source images and explore diverse target styles from a single
target patient with Random Adaptive Instance Normalization (RAIN). Then, a
segmentation network is trained in a supervised manner with the generated
target images. Our experiments demonstrate that FUDA improves the segmentation
performance by 0.33 of Dice score on the target domain compared with the
baseline, and it also gives 0.28 of Dice score improvement in a more rigorous
one-shot setting. Our code is available at
\url{https://github.com/MingxuanGu/Few-shot-UDA}.


  Izergin-Korepin's lattice discretization of the non-linear Schr\"odinger
model along with Oota's inverse problem provides one with determinant
representations for the form factors of the lattice discretized conjugated
field operator. We prove that these form factors converge, in the zero lattice
spacing limit, to those of the conjugated field operator in the continuous
model. We also compute the large-volume asymptotic behavior of such form
factors in the continuous model. These are in particular characterized by
Fredholm determinants of operators acting on closed contours. We provide a way
of defining these Fredholm determinants in the case of generic parameters.


  The NA61/SHINE experiment aims to discover the critical point of strongly
interacting matter and study the properties of the onset of deconfinement.
These goals are to be achieved by performing a two dimensional phase diagram
(T-\mu_B) scan by measurements of hadron production properties in
proton-proton, proton-nucleus and nucleus-nucleus interactions as a function of
collision energy and system size. Close to the critical point an increase of
fluctuations is predicted. In this contribution preliminary results on
transverse momentum fluctuations and two-particle pseudorapidity/azimuthal
angle correlations from the NA61/SHINE energy scan of p+p collisions will be
presented. These new results will be compared with NA49 data on central Pb+Pb
collisions and model predictions.


  Hybrid dynamical systems can exhibit many unique phenomena, such as Zeno
behavior. Zeno behavior is the occurrence of infinite discrete transitions in
finite time. Zeno behavior has been likened to a form of finite-time asymptotic
stability, and corresponding Lyapunov theorems have been developed. In this
paper, we propose a method to construct Lyapunov functions to prove Zeno
stability of compact sets in cyclic hybrid systems with parametric
uncertainties in the vector fields, domains and guard sets, and reset maps
utilizing sum-of-squares programming. This technique can easily be applied to
cyclic hybrid systems without parametric uncertainties as well. Examples
illustrating the use of the proposed technique are also provided.


  We analyze the prospect for observing the lightest and heaviest CP-even
neutral Higgs bosons ($\phi=h,\;H$) in their decays to flavor violating
$b\bar{s}$ (with charge conjugate) final states at the future Large Hadron
electron Collider (LHeC), in the framework of the Two Higgs Doublet Model type
III (2HDM-III) assuming a four-zero texture in the Yukawa matrices and a
general Higgs potential. We consider the charge current production processes
$e^- p \to \nu_e \phi q_f$ ($\phi= h, \; H$), with the flavor violating decays
of the Higgs bosons. We consider scenarios of the model which are consistent
with current experimental data from flavor and Higgs physics. We also consider
the most relevant Standard Model (SM) backgrounds. We find that the lightest
(SM-like) CP-even Higgs boson $h$ and the heaviest one $ H$ (with mass up to
150 GeV) would have 1--2 $\Sigma$ and 1 $\Sigma$ significances, respectively,
with 100 fb$^{-1}$ of data. At the end of the LHeC running, the significances
would be increased by ten times and the detection of both Higgs bosons ($h, H$)
would be guaranteed.


  Recently, in Axioms 10(2): 119 (2021), a nonclassical first-order theory T of
sets and functions has been introduced as the collection of axioms we have to
accept if we want a foundational theory for (all of) mathematics that is not
weaker than ZF, that is finitely axiomatized, and that does not have a
countable model (if it has a model at all, that is). Here we prove that T is
relatively consistent with ZF. We conclude that this is an important step
towards showing that T is an advancement in the foundations of mathematics.


  The diffusive motion of colloidal particles dispersed in a premelting solid
is analyzed within the framework of irreversible thermodynamics. We determine
the mass diffusion coefficient, thermal diffusion coefficient and Soret
coefficient of the particles in the dilute limit, and find good agreement with
experimental data. In contrast to liquid suspensions, the unique nature of
premelting solids allows us to derive an expression for the Dufour coefficient
and independently verify the Onsager reciprocal relation coupling diffusion to
the flow of heat.


  The aim of the current work is to investigate structural properties of the
sandpile group of a special class of self-similar graphs. More precisely, we
consider Abelian sandpiles on Sierpinski gasket graphs and for the choice of
normal boundary conditions, we give a characterization of the identity element
and a recursive description of the sandpile group. Finally, we consider Abelian
sandpile Markov chains on the aforementioned graphs and we improve the existing
bounds on the speed of convergence to stationarity.


  It is proved that a norm-decreasing homomorphism of commutative Banach
algebras is an effective descent morphism for Banach modules if and only if it
is a weak retract.


  A number of protoplanetary disks observed with ALMA potentially provide
direct examples of initial conditions for planetary systems. In particular, the
HL Tau disk has been intensively studied, and its rings/gaps are conventionally
interpreted to be a result of unseen massive planets embedded in the gaps.
Based on this interpretation, we carried out N-body simulations to investigate
orbital evolution of planets within the protoplanetary disk and after the disk
dispersal. Before the disk dispersal, our N-body simulations include both
migration and mass-growth of the planet coupled with evolution of the disk. By
varying the disk parameters, we produce a variety of widely-separated planetary
systems consisting of three super-Jupiters at the end of disk dispersal. We
found the outer planet is more massive than the inner one, and the migration of
the innermost planet is inefficient due to the accretion of outer planet(s). We
also showed how the final configuration and the final planetary mass depend on
disk parameters. The migration is found to be convergent and no planet-pair has
a period ratio less than 2. After the disk dispersal, we switch to pure
gravitational N-body simulations and integrate the orbits up to 10 Gyr. Most
simulated systems remain stable for at least 10 Gyr. We discuss implications of
our result in terms of the observed widely-separated planetary systems HR 8799
and PDS 70.


  Saturn's C ring contains multiple structures that appear to be density waves
driven by time-variable anomalies in the planet's gravitational field.
Semi-empirical extensions of density wave theory enable the observed wave
properties to be translated into information about how the pattern speeds and
amplitudes of these gravitational anomalies have changed over time. Combining
these theoretical tools with wavelet-based analyses of data obtained by the
Visual and Infrared Mapping Spectrometer (VIMS) onboard the Cassini spacecraft
reveals a suite of structures in Saturn's gravity field with azimuthal
wavenumber 3, rotation rates between 804 degrees/day and 842 degrees/day and
local gravitational potential amplitudes between 30 and 150 cm^2/s^2. Some of
these anomalies are transient, appearing and disappearing over the course of a
few Earth years, while others persist for decades. Most of these persistent
patterns appear to have roughly constant pattern speeds, but there is at least
one structure in the planet's gravitational field whose rotation rate steadily
increased between 1970 and 2010. This gravitational field structure appears to
induce two different asymmetries in the planet's gravity field, one with
azimuthal wavenumber 3 that rotates at roughly 810 degrees/day and another with
azimuthal wavenumber 1 rotating three times faster. The atmospheric processes
responsible for generating the latter pattern may involve solar tides.


  This contribution aims to shed light on mathematical epidemic dynamics
modelling from the viewpoint of analytical mechanics. To set the stage, it
recasts the basic SIR model of mathematical epidemic dynamics in an analytical
mechanics setting. Thereby, it considers two possible re-parameterizations of
the basic SIR model. On the one hand, it is proposed to re-scale time, while on
the other hand, to transform the coordinates, i.e.\ the independent variables.
In both cases, Hamilton's equations in terms of a suited Hamiltonian as well as
Hamilton's principle in terms of a suited Lagrangian are considered in minimal
and extended phase and state space coordinates, respectively. The corresponding
Legendre transformations relating the various options for the Hamiltonians and
Lagrangians are detailed. Ultimately, this contribution expands on a multitude
of novel vistas on mathematical epidemic dynamics modelling that emerge from
the analytical mechanics viewpoint. As result, it is believed that interesting
and relevant new research avenues open up when exploiting in depth the
analogies between analytical mechanics and mathematical epidemic dynamics
modelling.


  This technical report describes two methods that were developed for Task 2 of
the DCASE 2020 challenge. The challenge involves an unsupervised learning to
detect anomalous sounds, thus only normal machine working condition samples are
available during the training process. The two methods involve deep
autoencoders, based on dense and convolutional architectures that use
melspectogram processed sound features. Experiments were held, using the six
machine type datasets of the challenge. Overall, competitive results were
achieved by the proposed dense and convolutional AE, outperforming the baseline
challenge method.


  We show how excited states in QCD can be profitably used to build up the
Polyakov loop in the fundamental representation at temperatures below the
hadron-quark-gluon crossover. The conditions under which a Hagedorn temperature
for the Polyakov loop can be defined are analysed.


  Existing research on task incremental learning in continual learning has
primarily focused on preventing catastrophic forgetting (CF). Although several
techniques have achieved learning with no CF, they attain it by letting each
task monopolize a sub-network in a shared network, which seriously limits
knowledge transfer (KT) and causes over-consumption of the network capacity,
i.e., as more tasks are learned, the performance deteriorates. The goal of this
paper is threefold: (1) overcoming CF, (2) encouraging KT, and (3) tackling the
capacity problem. A novel technique (called SPG) is proposed that soft-masks
(partially blocks) parameter updating in training based on the importance of
each parameter to old tasks. Each task still uses the full network, i.e., no
monopoly of any part of the network by any task, which enables maximum KT and
reduction in capacity usage. To our knowledge, this is the first work that
soft-masks a model at the parameter-level for continual learning. Extensive
experiments demonstrate the effectiveness of SPG in achieving all three
objectives. More notably, it attains significant transfer of knowledge not only
among similar tasks (with shared knowledge) but also among dissimilar tasks
(with little shared knowledge) while mitigating CF.


  The approximation properties of infinitely wide shallow neural networks
heavily depend on the choice of the activation function. To understand this
influence, we study embeddings between Barron spaces with different activation
functions. These embeddings are proven by providing push-forward maps on the
measures $\mu$ used to represent functions $f$. An activation function of
particular interest is the rectified power unit ($\operatorname{RePU}$) given
by $\operatorname{RePU}_s(x)=\max(0,x)^s$. For many commonly used activation
functions, the well-known Taylor remainder theorem can be used to construct a
push-forward map, which allows us to prove the embedding of the associated
Barron space into a Barron space with a $\operatorname{RePU}$ as activation
function. Moreover, the Barron spaces associated with the
$\operatorname{RePU}_s$ have a hierarchical structure similar to the Sobolev
spaces $H^m$.


  We demonstrate that the electrical property of a single layer molybdenum
disulfide (MoS2) can be significantly tuned from semiconducting to insulating
regime via controlled exposure to oxygen plasma. The mobility, on-current and
resistance of single layer MoS2 devices were varied up to four orders of
magnitude by controlling the plasma exposure time. Raman spectroscopy, X-ray
photoelectron spectroscopy and density functional theory studies suggest that
the significant variation of electronic properties is caused by the creation of
insulating MoO3-rich disordered domains in the MoS2 sheet upon oxygen plasma
exposure, leading to an exponential variation of resistance and mobility as a
function of plasma exposure time. The resistance variation calculated using an
effective medium model is in excellent agreement with the measurements. The
simple approach described here can be used for the fabrication of tunable two
dimensional nanodevices on MoS2 and other transition metal dichalcogenides.


  We present a novel Structure from Motion pipeline that is capable of
reconstructing accurate camera poses for panorama-style video capture without
prior camera intrinsic calibration. While panorama-style capture is common and
convenient, previous reconstruction methods fail to obtain accurate
reconstructions due to the rotation-dominant motion and small baseline between
views. Our method is built on the assumption that the camera motion
approximately corresponds to motion on a sphere, and we introduce three novel
relative pose methods to estimate the fundamental matrix and camera distortion
for spherical motion. These solvers are efficient and robust, and provide an
excellent initialization for bundle adjustment. A soft prior on the camera
poses is used to discourage large deviations from the spherical motion
assumption when performing bundle adjustment, which allows cameras to remain
properly constrained for optimization in the absence of well-triangulated 3D
points. To validate the effectiveness of the proposed method we evaluate our
approach on both synthetic and real-world data, and demonstrate that camera
poses are accurate enough for multiview stereo.


  This work discusses how to derive upper bounds for the expected
generalisation error of supervised learning algorithms by means of the chaining
technique. By developing a general theoretical framework, we establish a
duality between generalisation bounds based on the regularity of the loss
function, and their chained counterparts, which can be obtained by lifting the
regularity assumption from the loss onto its gradient. This allows us to
re-derive the chaining mutual information bound from the literature, and to
obtain novel chained information-theoretic generalisation bounds, based on the
Wasserstein distance and other probability metrics. We show on some toy
examples that the chained generalisation bound can be significantly tighter
than its standard counterpart, particularly when the distribution of the
hypotheses selected by the algorithm is very concentrated.
  Keywords: Generalisation bounds; Chaining; Information-theoretic bounds;
Mutual information; Wasserstein distance; PAC-Bayes.


  This paper describes searches for the pair production of first or second
generation scalar leptoquarks using 35/pb of proton-proton collision data
recorded by the ATLAS detector at sqrt(s)=7 TeV. Leptoquarks are seached in
events with two oppositely charged muons or electrons and at least two jets,
and in events with one muon or electron, missing transverse momentum and at
least two jets. After event selection, the observed yields are consistent with
the predicted backgrounds. Leptoquark production is excluded at the 95% CL for
masses mLQ<376 (319) GeV and mLQ<422 (362) GeV for first and second generation
scalar leptoquarks, respectively, when assuming the branching fraction of a
leptoquark to a charged lepton is equal to 1.0 (0.5).


  We study the equivariant category associated to a finite group action on the
derived category of coherent sheaves of a smooth projective variety. We discuss
decompositions of the equivariant category and faithful actions, prove the
existence of a Serre functor, give a criterion for the equivariant category to
be Calabi--Yau, and describe an obstruction for a subgroup of the group of
auto-equivalences to act. As application we show that the equivariant category
of any symplectic action on the derived category of an elliptic curve is
equivalent to the derived category of an elliptic curve.


  We use the formalism of Gould and Raffelt to compute the dimensionless
thermal conduction coefficients for scattering of dark matter particles with
standard model nucleons via cross-sections that depend on the relative velocity
or momentum exchanged between particles. Motivated by models invoked to
reconcile various recent results in direct detection, we explicitly compute the
conduction coefficients $\alpha$ and $\kappa$ for cross-sections that go as
$v_{\rm rel}^2$, $v_{\rm rel}^4$, $v_{\rm rel}^{-2}$, $q^2$, $q^4$ and
$q^{-2}$, where $v_{\rm rel}$ is the relative DM-nucleus velocity and $q$ is
the momentum transferred in the collision. We find that a $v_{\rm rel}^{-2}$
dependence can significantly enhance energy transport from the inner solar core
to the outer core. The same can true for any $q$-dependent coupling, if the
dark matter mass lies within some specific range for each coupling. This effect
can complement direct searches for dark matter; combining these results with
state-of-the-art Solar simulations should greatly increase sensitivity to
certain DM models. It also seems possible that the so-called Solar Abundance
Problem could be resolved by enhanced energy transport in the solar core due to
such velocity- or momentum-dependent scatterings.


  We elucidate the mechanisms that underly the formation of temporal localized
states and frequency combs in vertical external-cavity Kerr-Gires-Tournois
interferometers. We reduce our first principle model based upon delay algebraic
equations to a minimal pattern formation scenario. It consists in a real cubic
Ginzburg-Landau equation modified by high-order effects such as third order
dispersion and nonlinear drift. The latter are responsible for generating
localized states via the locking of domain walls connecting the high and low
intensity levels of the injected micro-cavity. We interpret the effective
parameters of the normal form in relation with the configuration of the optical
setup. Comparing the two models, we observe an excellent agreement close to the
onset of bistability.


  Assur graphs are a tool originally developed by mechanical engineers to
decompose mechanisms for simpler analysis and synthesis. Recent work has
connected these graphs to strongly directed graphs, and decompositions of the
pinned rigidity matrix. Many mechanisms have initial configurations which are
symmetric, and other recent work has exploited the orbit matrix as a symmetry
adapted form of the rigidity matrix. This paper explores how the decomposition
and analysis of symmetric frameworks and their symmetric motions can be
supported by the new symmetry adapted tools.


  This paper is the third paper of a series devoted to higher dimensional
transition systems. The preceding paper proved the existence of a left
determined model structure on the category of cubical transition systems. In
this sequel, it is proved that there exists a model category of labelled
symmetric precubical sets which is Quillen equivalent to the Bousfield
localization of this left determined model category by the cubification
functor. The realization functor from labelled symmetric precubical sets to
cubical transition systems which was introduced in the first paper of this
series is used to establish this Quillen equivalence. However, it is not a left
Quillen functor. It is only a left adjoint. It is proved that the two model
categories are related to each other by a zig-zag of Quillen equivalences of
length two. The middle model category is still the model category of cubical
transition systems, but with an additional family of generating cofibrations.
The weak equivalences are closely related to bisimulation. Similar results are
obtained by restricting the constructions to the labelled symmetric precubical
sets satisfying the HDA paradigm.


  We consider the problem of diversity enhancing clustering, i.e, developing
clustering methods which produce clusters that favour diversity with respect to
a set of protected attributes such as race, sex, age, etc. In the context of
fair clustering, diversity plays a major role when fairness is understood as
demographic parity. To promote diversity, we introduce perturbations to the
distance in the unprotected attributes that account for protected attributes in
a way that resembles attraction-repulsion of charged particles in Physics.
These perturbations are defined through dissimilarities with a tractable
interpretation. Cluster analysis based on attraction-repulsion dissimilarities
penalizes homogeneity of the clusters with respect to the protected attributes
and leads to an improvement in diversity. An advantage of our approach, which
falls into a pre-processing set-up, is its compatibility with a wide variety of
clustering methods and whit non-Euclidean data. We illustrate the use of our
procedures with both synthetic and real data and provide discussion about the
relation between diversity, fairness, and cluster structure. Our procedures are
implemented in an R package freely available at
https://github.com/HristoInouzhe/AttractionRepulsionClustering.