  Let $K$ be a connected compact semisimple group and $V_\lambda$ be an
irreducible unitary representation with highest weight $\lambda$. We study the
momentum map $\mu:\mathbb P(V_\lambda)\to\mathfrak k^*$. The intersection
$\mu(\mathbb P(V_\lambda))^+=\mu(\mathbb P(V_\lambda))\cap{\mathfrak t}^+$ of
the momentum image with a fixed Weyl chamber is a convex polytope called the
momentum polytope of $V_\lambda$. We construct an affine rational polyhedral
convex cone $\Upsilon_\lambda$ with vertex $\lambda$, such that $\mu(\mathbb
P(V_\lambda))^+\subset\Upsilon_\lambda \cap {\mathfrak t}^+$. We show that
equality holds for a class of representations, including those with regular
highest weight. For those cases, we obtain a complete combinatorial description
of the momentum polytope, in terms of $\lambda$. We also present some results
on the critical points of $||\mu||^2$. Namely, we consider the existence
problem for critical points in the preimages of Kirwan's candidates for
critical values. Also, we consider the secant varieties to the unique complex
orbit $\mathbb X\subset\mathbb P(V_\lambda)$, and prove a relation between the
momentum images of the secant varieties and the degrees of $K$-invariant
polynomials on $V_\lambda$.


  In this article we explain sonoluminescence from ideas borrowed from
superradiance. The model has no free parameters and the predicted energies of
quanta agree with experiment. It also hints why noble gases play a pivotal role
in the effect.


  The Multi-Scale Continuum and Line Exploration of W49 (MUSCLE W49) is a
comprehensive gas and dust survey of the giant molecular cloud (GMC) of W49A,
the most luminous star-formation region in the Milky Way. It covers the entire
GMC at different scales and angular resolutions. In this paper we present: 1)
an all-configuration SMA mosaic in the 230-GHz band covering the central 3
arcmin (10 pc, known as W49N), with most of the embedded massive stars; and 2)
PMO 14m telescope observations in the 90-GHz band, covering the entire GMC with
maps up to 35 arcmin in size, or 113 pc. We also make use of archival data from
the VLA, JCMT-SCUBA, IRAM 30m, and the CSO BOLOCAM GPS. Our main findings are:
1) The W49 GMC is one of the most massive in the Galaxy, with a total mass
~1.1x10^6 Msun within a radius of 60 pc. Within a radius of 6 pc, the total gas
mass is ~2x10^5 Msun. At these scales only 1% of the material is photoionized.
The mass reservoir is sufficient to form several young massive clusters (YMCs)
as massive as a globular cluster. 2) The mass of the GMC is distributed in a
hierarchical network of filaments. At scales <10 pc, a triple, centrally
condensed structure peaks toward the ring of HC HII regions in W49N. This
structure extends to scales from ~10 to 100 pc. The W49A starburst most likely
formed from global gravitational contraction with localized collapse in a
"hub-filament" geometry. 3) Currently, feedback from the central YMCs (with a
present mass Mcl > 5x10^4 Msun) is still not enough to entirely disrupt the
GMC, but further stellar mass growth could be enough to allow radiation
pressure to clear the cloud and halt star formation. 4) The resulting stellar
content will probably remain as a gravitationally bound massive star cluster,
or a small system of bound clusters. (ABRIDGED)


  The interaction between free electrons and nanoscale optical fields has
emerged as a unique platform to investigate ultrafast processes in matter and
explore fundamental quantum phenomena. In particular, optically modulated
electrons are employed in ultrafast electron microscopy as noninvasive probes
that push the limits of spatiotemporal and spectral resolution down to the
picometer--attosecond--microelectronvolt range. Electron kinetic energies well
above the involved photon energies are commonly employed, rendering the
electron--light coupling efficiency low and, thus, only providing limited
access to the wealth of quantum nonlinear phenomena underlying the dynamical
response of nanostructures. Here, we theoretically investigate electron--light
interactions when photons and electrons have comparable energies, revealing
strong quantum and recoil effects that include a nonvanishing coupling of
surface-scattered electrons to plane waves of light, inelastic electron
backscattering from localized optical fields, and strong electron--light
coupling under grazing electron diffraction by an illuminated crystal surface.
Our results open new vistas in electron--light--matter interactions with
promising applications in ultrafast electron microscopy.


  Technology videos contain rich multi-modal information. In cross-modal
information search, the data features of different modalities cannot be
compared directly, so the semantic gap between different modalities is a key
problem that needs to be solved. To address the above problems, this paper
proposes a novel Feature Fusion based Adversarial Cross-modal Retrieval method
(FFACR) to achieve text-to-video matching, ranking and searching. The proposed
method uses the framework of adversarial learning to construct a video
multimodal feature fusion network and a feature mapping network as generator, a
modality discrimination network as discriminator. Multi-modal features of
videos are obtained by the feature fusion network. The feature mapping network
projects multi-modal features into the same semantic space based on semantics
and similarity. The modality discrimination network is responsible for
determining the original modality of features. Generator and discriminator are
trained alternately based on adversarial learning, so that the data obtained by
the feature mapping network is semantically consistent with the original data
and the modal features are eliminated, and finally the similarity is used to
rank and obtain the search results in the semantic space. Experimental results
demonstrate that the proposed method performs better in text-to-video search
than other existing methods, and validate the effectiveness of the method on
the self-built datasets of technology videos.


  A detailed analysis of the coupled relativistic kinetic equations for two
domains separated by a hypersurface having both space- and time-like parts is
presented. Integrating the derived set of transport equations, we obtain the
correct system of the hydro+cascade equations to model the relativistic nuclear
collision process. Remarkably, the conservation laws on the boundary between
domains conserve separately both the incoming and outgoing components of
energy, momentum and baryonic charge. Thus, the relativistic kinetic theory
generates twice the number of conservation laws compared to traditional
hydrodynamics. Our analysis shows that these boundary conditions between
domains, the three flux discontinuity, can be satisfied only by a special
superposition of two cut-off distribution functions for the ``out'' domain. All
these results are applied to the case of the phase transition between quark
gluon plasma and hadronic matter. The possible consequences for an improved
hydro+cascade description of the relativistic nuclear collisions are discussed.
The unique properties of the three flux discontinuity and their effect on the
space-time evolution of the transverse expansion are also analyzed. The
possible modifications of both transversal radii from pion correlations
generated by a correct hydro+cascade approach are discussed.


  A few radio galaxies have been discovered to emit GeV-TeV gamma-ray emission
in spite of relatively large viewing angles of their jets. We consider a
scenario in which such large angle gamma-ray emission is preferentially
produced by isotropically distributed relativistic electrons in the kpc scale
jet. These electrons comptonize soft, non-thermal radiation from the inner jet
which is beamed due to its relativistic motion. In terms of such a model, we
interpret recently discovered TeV gamma-ray emission from the kpc scale jets in
Cen~A. Interestingly, due to the geometry of the inverse Compton scattering
process, intensity of the gamma-ray emission from the counter-jet is predicted
to be on a higher level than the emission from the jet. This is true provided
that both, a jet and a counter-jet, are twins, i.e. the physical processes in
the jet and counter-jet result in the acceleration of particles in a similar
way. However, in general, the jet and counter-jet can differ significantly.
Therefore, their relative contribution to the gamma-ray emission from the jets
in Cen~A can become more complicated. Investigation of the distribution of the
TeV gamma-ray emission along jets of nearby radio galaxies with the next
generation telescopes should provide constraints on the considered model and
the content of the kpc-scale jets.


  YMnO3 exhibits a ferroelectric transition at high temperature (~ 900 K) and
magnetic ordering at T_N ~ 70 K where the dielectric constant shows an anomaly
indicative of the magneto-dielectric effect. Here we report powder neutron
diffraction experiments in this compound that show that the magnetic moment at
saturation is reduced by application of hydrostatic pressure. Our results yield
further insight about the nature of the spin-lattice interaction in ferroic
materials.


  A system containing a pair of non-BPS D-strings of type IIA string theory on
an orbifold, representing a single D2-brane wrapped on a nonsupersymmetric
2-cycle of a Calabi-Yau 3-fold with $(h^{(1,1)},h^{(1,2)})$ = (11,11), is
analyzed. In certain region of the moduli space the configuration is stable. We
show that beyond the region of stability the system can decay into a pair of
non-BPS D3-branes. At one point on the boundary of the region of stability,
there exists a marginal deformation which connects the system of non-BPS
D-strings to the system of non-BPS D3-branes. Across any other point on the
boundary of the region of stability, the transition from the system of non-BPS
D-strings to the system of non-BPS D3-branes is first order. We discuss the
phase diagram in the moduli space for these configurations.


  Level energies, wavelengths, electric dipole, magnetic dipole, electric
quadrupole, and magnetic quadrupole transition rates, oscillator strengths, and
line strengths from combined relativistic configuration interaction and
many-body perturbation calculations are reported for the 201 fine-structure
states of the $2s^2 2p^6$, $2s^2 2p^5 3l$, $2s 2p^6 3l$, $2s^2 2p^5 4l$, $2s
2p^6 4l$, $2s^2 2p^5 5l$, and $2s^2 2p^5 6l$ configurations in all Ne-like ions
between Cr XV and Kr XXVII. Calculated level energies and transition data are
compared with experiments from the NIST and CHIANTI databases, and other recent
benchmark calculations. The mean energy difference with the NIST experiments is
only 0.05%. The present calculations significantly increase the amount of
accurate spectroscopic data for the $n >3$ states in a number of Ne-like ions
of astrophysics interest. A complete dataset should be helpful in analyzing new
observations from the solar and other astrophysical sources, and is also likely
to be useful for modeling and diagnosing a variety of plasmas including
astronomical and fusion plasma.


  We report on measurements of the angular dynamics of micron-sized
equilaterally triangular platelets suspended in a micro-channel shear flow. Our
measurements confirm that such particles spin and tumble like a spheroid in a
simple shear. Since the triangle has corners we can observe the spinning
directly. In general the spinning frequency is different from the tumbling
frequency, and the spinning is affected by tumbling. This gives rise to
doubly-periodic angular dynamics.


  Breaking of ensemble equivalence between the microcanonical ensemble and the
canonical ensemble may occur for random graphs whose size tends to infinity,
and is signaled by a non-zero specific relative entropy of the two ensembles.
In [3] and [4] it was shown that breaking occurs when the constraint is put on
the degree sequence (configuration model). It is not known what is the effect
on the relative entropy when the number of constraints is reduced, i.e., when
only part of the nodes are constrained in their degree (and the remaining nodes
are left unconstrained). Intuitively, the relative entropy is expected to
decrease. However, this is not a trivial issue because when constraints are
removed both the microcanonical ensemble and the canonical ensemble change. In
this paper a formula for the relative entropy valid for generic discrete random
structures, recently formulated by Squartini and Garlaschelli, is used to prove
that the relative entropy is monotone in the number of constraints when the
constraint is on the degrees of the nodes. It is further shown that the
expression for the relative entropy corresponds, in the dense regime, to the
degrees in the microcanonical ensemble being asymptotically multivariate Dirac
and in the canonical ensemble being asymptotically Gaussian.


  This report describes the methodology and results of an assessment study of
the performance of the Large Synoptic Survey Telescope (LSST) in its planned
efforts to detect and catalog near-Earth objects (NEOs). The baseline LSST
survey approach is designed to make only two visits to a given field in a given
night, leading to two possible NEO detections per night. These nightly pairs
must be linked across nights to derive orbits of moving objects. However, the
presence of false detections in the data stream leads to the possibility of
high rates of false tracklets, and the ensuing risk that the resulting orbit
catalog may be contaminated by false orbits. To understand the challenges
stemming from a two-visit-per-night cadence, we conducted high-fidelity linkage
tests on a full-density simulated LSST detection stream. We also sought to
quantify the overall performance of LSST as an NEO discovery system under the
hypothesis that detections from the baseline cadence can be successfully
linked. Our simulations revealed that in 10 years LSST would catalog ~60% of
NEOs with absolute magnitude H<22, which is a proxy for 140m and larger
objects. This results neglects linking losses and the contribution of any other
NEO surveys. Including our worst-case linking efficiency we reach a overall
performance assessment of 55% completeness of NEOs with H<22. We estimate that
survey mis-modeling could account for systematic errors of up to 5%. We find
that restricting the evaluation metric to so-called Potentially Hazardous
Asteroids (PHAs) increases the completeness by 3-4%, and that including the
benefits of past and expected future NEO survey activity increases completeness
at the end of the baseline LSST survey by 15-20%. Assembling these results
leads to a projection that by the end of the baseline LSST survey the NEO
catalog will be 80+/-5% complete for PHAs with H < 22.


  Solitonic boson stars (SBS) are compact shell-like objects with an inside
having a nearly constant value of scalar field bounded by a thin shell where
the scalar field rapidly changes. While the spherically symmetric SBS can be
described by an analytical approximation that works well in the thin-shell
case, no such approximation exists for rotating SBS and the investigation of
such stars poses a numerical challenge. We numerically investigate rotating SBS
in case if the relative thickness of the shell is small. We compute
Gerosh-Hansen multipole moments to study the structure of SBS spacetime in the
outside region and the closeness of SBS to the rotating black hole metric.


  The $SL_2(\mathbb{C})$ character variety $X(M)$ has emerged as an important
tool in studying the topology of hyperbolic 3-manifolds. Chinburg-Reid-Stover
constructed arithmetic invariants stemming from a canonical Azumaya algebra
over the normalization of an irreducible component of $X(M)$ containing a lift
of the holonomy representation of $M$. We provide an explicit topological
criterion for extending the canonical Azumaya algebra over an ideal point,
potentially leading to finer arithmetic invariants than those of
Chinburg-Reid-Stover. This topological criterion involves Culler-Shalen theory
and, in some cases, JSJ decompositions of toroidal Dehn fillings of knot
complements in the three-sphere. Inspired by the work of Paoluzzi-Porti and
Tillmann, we provide examples of several cases where these refined invariants
exist. Along the way, we show that certain families of Seifert surfaces in
hyperbolic knot complements can be associated to ideal points of character
varieties.


  The thesis deals with the effect of magnetic fields on elementary particle
interactions, of which the neutrino is of prime concern. The initial part
focuses on the quantum field theoretical description of scattering processes
which involves charged particles, in presence of a background uniform magnetic
field. A brief discussion on the charged particle propagators in an uniform
background magnetic field using Schwinger's method is presented. A general
analysis on neutrino self-energy in a background magnetic field (and in a
magnetized medium) alongwith its effect on neutrino oscillation phenomenology,
follows. The final part of the thesis deals with the topic of neutrino photon
interactions in a background magnetic field and finds an expression of the
effective electric charge of neutrinos in a magnetized medium.


  Since their inception in the 1980's, regression trees have been one of the
more widely used non-parametric prediction methods. Tree-structured methods
yield a histogram reconstruction of the regression surface, where the bins
correspond to terminal nodes of recursive partitioning. Trees are powerful, yet
susceptible to over-fitting. Strategies against overfitting have traditionally
relied on pruning greedily grown trees. The Bayesian framework offers an
alternative remedy against overfitting through priors. Roughly speaking, a good
prior charges smaller trees where overfitting does not occur. While the
consistency of random histograms, trees and their ensembles has been studied
quite extensively, the theoretical understanding of the Bayesian counterparts
has been missing. In this paper, we take a step towards understanding why/when
do Bayesian trees and their ensembles not overfit. To address this question, we
study the speed at which the posterior concentrates around the true smooth
regression function. We propose a spike-and-tree variant of the popular
Bayesian CART prior and establish new theoretical results showing that
regression trees (and their ensembles) (a) are capable of recovering smooth
regression surfaces, achieving optimal rates up to a log factor, (b) can adapt
to the unknown level of smoothness and (c) can perform effective dimension
reduction when p>n. These results provide a piece of missing theoretical
evidence explaining why Bayesian trees (and additive variants thereof) have
worked so well in practice.


  Host-side page victimizations can easily overflow the SSD internal buffer,
which interferes I/O services of diverse user applications thereby degrading
user-level experiences. To address this, we propose FastDrain, a co-design of
OS kernel and flash firmware to avoid the buffer overflow, caused by page
victimizations. Specifically, FastDrain can detect a triggering point where a
near-future page victimization introduces an overflow of the SSD internal
buffer. Our new flash firmware then speculatively scrubs the buffer space to
accommodate the requests caused by the page victimization. In parallel, our new
OS kernel design controls the traffic of page victimizations by considering the
target device buffer status, which can further reduce the risk of buffer
overflow. To secure more buffer spaces, we also design a latency-aware FTL,
which dumps the dirty data only to the fast flash pages. Our evaluation results
reveal that FastDrain reduces the 99th response time of user applications by
84%, compared to a conventional system.


  By employing the Pekeris approximation, the D-dimensional Schr\"odinger
equation is solved for the nuclear deformed Woods-Saxon potential plus double
ring-shaped potential within the framework of the Asymptotic Iteration Method
(AIM). The energy eingenvalues are given in a closed form and the corresponding
normalized eigenfunctions are obtained in terms of hypergeometric functions.
Our general results reproduce many predictions obtained in the literature,
using the Nikiforov-Uvarov method (NU) and the Improved Quantization Rule
approach, particulary those derived by considering Woods-Saxon potential
without deformation and/or without ring shape interaction.


  We define a set of fully Lorentz-invariant wave packets and show that it
spans the corresponding one-particle Hilbert subspace, and hence the whole Fock
space as well, with a manifestly Lorentz-invariant completeness relation
(resolution of identity). The position-momentum uncertainty relation for this
Lorentz-invariant wave packet deviates from the ordinary Heisenberg uncertainty
principle, and reduces to it in the non-relativistic limit.


  Recently, the conformal-bootstrap has been successfully used to obtain
generic bounds on the spectrum and OPE coefficients of unitary conformal field
theories. In practice, these bounds are obtained by assuming the existence of a
scalar operator in the theory and analyzing the crossing-symmetry constraints
of its 4-point function. In $\mathcal{N}=1$ superconformal theories with a
global symmetry there is always a scalar primary operator, which is the top of
the current-multiplet. In this paper we analyze the crossing-symmetry
constraints of the 4-point function of this operator for $\mathcal{N}=1$
theories with $SU(N)$ global symmetry. We analyze the current-current OPE, and
derive the superconformal blocks, generalizing the work of Fortin,
Intrilligator and Stergiou to the non-Abelian case and finding new
superconformal blocks which appear in the Abelian case. We then use these
results to obtain bounds on the coefficient of the current 2-point function.


  We propose a method to prepare a sample of fermionic atoms in a
three-dimensional (3D) optical lattice at unprecedentedly low temperatures and
uniform filling factors. The process involves adiabatic loading of atoms into
multiple energy bands of an optical lattice followed by a filtering stage
whereby atoms from all but the ground band are removed. Of critical importance
is the use of a non-harmonic trapping potential, taken here to be the radial
profile of a high-order Laguerre-Gaussian laser beam, to provide external
confinement for the atoms. For realistic experimental parameters, this
procedure should produce samples with temperatures $\sim10^{-3}$ of the Fermi
temperature. This would allow the investigation of the low-temperature phase
diagram of the Fermi-Hubbard model as well as the initialization of a
high-fidelity quantum register.


  A new form of Bethe ansatz equations is introduced. A version of a separation
of variables for the quantum $sl_3$ Gaudin model is presented.


  Knowledge distillation (KD) has demonstrated its effectiveness to boost the
performance of graph neural networks (GNNs), where its goal is to distill
knowledge from a deeper teacher GNN into a shallower student GNN. However, it
is actually difficult to train a satisfactory teacher GNN due to the well-known
over-parametrized and over-smoothing issues, leading to invalid knowledge
transfer in practical applications. In this paper, we propose the first
Free-direction Knowledge Distillation framework via Reinforcement learning for
GNNs, called FreeKD, which is no longer required to provide a deeper
well-optimized teacher GNN. The core idea of our work is to collaboratively
build two shallower GNNs in an effort to exchange knowledge between them via
reinforcement learning in a hierarchical way. As we observe that one typical
GNN model often has better and worse performances at different nodes during
training, we devise a dynamic and free-direction knowledge transfer strategy
that consists of two levels of actions: 1) node-level action determines the
directions of knowledge transfer between the corresponding nodes of two
networks; and then 2) structure-level action determines which of the local
structures generated by the node-level actions to be propagated. In essence,
our FreeKD is a general and principled framework which can be naturally
compatible with GNNs of different architectures. Extensive experiments on five
benchmark datasets demonstrate our FreeKD outperforms two base GNNs in a large
margin, and shows its efficacy to various GNNs. More surprisingly, our FreeKD
has comparable or even better performance than traditional KD algorithms that
distill knowledge from a deeper and stronger teacher GNN.


  Phase-space features of the Wigner flow for an anharmonic quantum system
driven by the harmonic oscillator potential modified by the addition of an
inverse square (one-dimension Coulomb-like) contribution are analytically
described in terms of Wigner functions and Wigner currents. Reporting about
three correlated continuity equations which quantify the flux of quantum
information in the phase-space, the non-classicality profile of such an
anharmonic system can be consistently obtained in terms of the fluxes of {\em
probability}, {\em purity} and {\em von Neumann-like entropy}. Considering that
quantum fluctuations can be identified from distortions over the classical
regime, they can be quantified through the above-mentioned information fluxes
whenever some {\em classically bounded} volume of the phase-space is selected.
Our results suggest that the Wigner flow approach works as a probe of
quantumness and classicality for a large set of anharmonic quantum systems
driven by quantum wells.


  We have investigated the spin wave dynamics of Permalloy (Py) thin films with
and without a Ta capping layer for varying Py thickness (15 nm, 20 nm and 30
nm) using all optical time-resolved magneto-optical Kerr effect measurements.
XPS measurements confirm the oxidation of the originally-prepared samples and
also that the removal of the Ta capping layer is achievable by a few sputtering
cycles. The magnetic field strength dependencies of the spin wave modes with
the variation of the Py film thickness for the samples are studied. We observe
that the presence of the Ta capping layer reduces the precessional frequencies
of the samples while the samples without a Ta capping layer enhance the role of
Py thickness. We also observe that the decay time of spin waves is highly
dependent on the top layer of the samples. The decay time increases with
increasing Py thicknesses for Ta/Py/Ta samples implying that the enhancement of
decay time is caused by the Ta/Py/Ta interfaces. Whereas, for Ta/Py samples the
decay time decreases with increasing Py thickness. The results of this work
extend the knowledge on the magnetization dynamics of Py thin films giving
information on how to resume and even enhance the spin mobility after a
deleterious oxidation process. This can open new scenarios on the building
process and on the maintenance of fast magnetic switching devices.


  Einstein-Boltzmann Solvers (EBSs) are run on a massive scale by the cosmology
community when fitting cosmological models to data. We present a new concept
for speeding up such codes with neural networks. The originality of our
approach stems from not substituting the whole EBS by a machine learning
algorithm, but only its most problematic and least parallelizable step: the
integration of perturbation equations over time. This approach offers two
significant advantages: the task depends only on a subset of cosmological
parameters, and it is blind to the characteristics of the experiment for which
the output must be computed (for instance, redshift bins). These allow us to
construct a fast and highly re-usable network. In this proof-of-concept paper,
we focus on the prediction of CMB source functions, and design our networks
according to physical considerations and analytical approximations. This allows
us to reduce the depth and training time of the networks compared to a
brute-force approach. Indeed, the calculation of the source functions using the
networks is fast enough so that it is not a bottleneck in the EBS anymore.
Finally, we show that their accuracy is more than sufficient for accurate MCMC
parameter inference from Planck data. This paves the way for a new project,
CosmicNet, aimed at gradually extending the use and the range of validity of
neural networks within EBSs, and saving massive computational time in the
context of cosmological parameter extraction.


  The interaction of atomic hydrogen with a single layer of hexagonal boron
nitride on rhodium leads to a removal of the h-BN surface corrugation. The
process is reversible as the hydrogen may be expelled by annealing to about 500
K whereupon the texture on the nanometer scale is restored. This effect is
traced back to hydrogen intercalation. It is expected to have implications for
applications, like the storage of hydrogen, the peeling of sp2-hybridized
layers from solid substrates or the control of the wetting angle, to name a
few.


  In this paper, a novel objective evaluation metric for image fusion is
presented. Remarkable and attractive points of the proposed metric are that it
has no parameter, the result is probability in the range of [0, 1] and it is
free from illumination dependence. This metric is easy to implement and the
result is computed in four steps: (1) Smoothing the images using Gaussian
filter. (2) Transforming images to a vector field using Del operator. (3)
Computing the normal distribution function ({\mu},{\sigma}) for each
corresponding pixel, and converting to the standard normal distribution
function. (4) Computing the probability of being well-behaved fusion method as
the result. To judge the quality of the proposed metric, it is compared to
thirteen well-known non-reference objective evaluation metrics, where eight
fusion methods are employed on seven experiments of multimodal medical images.
The experimental results and statistical comparisons show that in contrast to
the previously objective evaluation metrics the proposed one performs better in
terms of both agreeing with human visual perception and evaluating fusion
methods that are not performed at the same level.


  We report the regions where a signal-to-noise ratio (SNR) gain exceeding
unity exists in a parallel uncoupled array of identical bistable systems, for
both subthreshold and suprathreshold sinusoids buried in broadband Gaussian
white input noise. Due to independent noise in each element of the parallel
array, the SNR gain of the collective array response approaches its local
maximum exhibiting a stochastic resonant behavior. Moreover, the local maximum
SNR gain, at a non-zero optimal array noise intensity, increases as the array
size rises. This leads to the conclusion of the global maximum SNR gain being
obtained by an infinite array. We suggest that the performance of infinite
arrays can be closely approached by an array of two bistable oscillators
operating in different noisy conditions, which indicates a simple but effective
realization of arrays for improving the SNR gain. For a given input SNR, the
optimization of maximum SNR gains is touched upon in infinite arrays by tuning
both array noise levels and an array parameter. The nonlinear collective
phenomenon of SNR gain amplification in parallel uncoupled dynamical arrays,
i.e. array stochastic resonance, together with the possibility of the SNR gain
exceeding unity, represent a promising application in array signal processing.


  We consider an identity relating Fibonacci numbers to Pascal's triangle
discovered by G. E. Andrews. Several authors provided proofs of this identity,
all of them rather involved or else relying on sophisticated number theoretical
arguments. We not only give a simple and elementary proof, but also show the
identity generalizes to arrays other than Pascal's triangle. As an application
we obtain identities relating trinomial coefficients and Catalan's triangle to
Fibonacci numbers.


  As the first successful technique used to detect exoplanets orbiting distant
stars, the Radial Velocity Method aims to detect a periodic Doppler shift in a
star's spectrum. We introduce a new, mathematically rigorous, approach to
detect such a signal that accounts for functional relationships of neighboring
wavelengths, minimizes the role of wavelength interpolation, accounts for
heteroskedastic noise, and easily allows for statistical inference. Using
Hermite-Gaussian functions, we show that the problem of detecting a Doppler
shift in the spectrum can be reduced to linear regression in many settings. A
simulation study demonstrates that the proposed method is able to accurately
estimate an individual spectrum's radial velocity with precision below 0.3 m/s.
Furthermore, the new method outperforms the traditional Cross-Correlation
Function approach by reducing the root mean squared error up to 15 cm/s. The
proposed method is also demonstrated on a new set of observations from the
EXtreme PREcision Spectrometer (EXPRES) for the star 51 Pegasi, and
successfully recovers estimates that agree well with previous studies of this
planetary system. Data and Python3 code associated with this work can be found
at https://github.com/parkerholzer/hgrv_method. The method is also implemented
in the open source R package rvmethod.


  In CeCoIn$_5$, the thermal conductivity $\kappa_{xx}$ and Hall conductivity
$\kappa_{xy}$ below $T_c$ display large anomalies below $T_c$. The strong
suppression of the anomalies in weak fields implies the existence of long-lived
quasiparticles. We also discuss briefly the Wiedemann-Franz ratio and the
existence of a strongly field-dependent spin-fluctuation heat current.


  In this article, we prove results about the cohomology of compact unitary
group Shimura varieties at split places. In nonendoscopic cases, we are able to
give a full description of the cohomology, after restricting to integral Hecke
operators at p on the automorphic side. We allow arbitrary ramification at p;
even the PEL data may be ramified. This gives a description of the semisimple
local Hasse-Weil zeta function in these cases. We also treat cases of
nontrivial endoscopy. For this purpose, we give a general stabilization of the
expression given in previous work, following the stabilization given by
Kottwitz. This introduces endoscopic transfers of the functions $\phi_{\tau,h}$
which were introduced in previous work via deformation spaces of $p$-divisible
groups. We state a general conjecture relating these endoscopic transfers with
Langlands parameters. We verify this conjecture in all cases of EL type, and
deduce new results about the endoscopic part of the cohomology of Shimura
varieties. This allows us to simplify the construction of Galois
representations attached to conjugate self-dual regular algebraic cuspidal
automorphic representations of $\mathrm{GL}_n$, as previously constructed by
one of us.


  We study the problem of finding fake online news. This is an important
problem as news of questionable credibility have recently been proliferating in
social media at an alarming scale. As this is an understudied problem,
especially for languages other than English, we first collect and release to
the research community three new balanced credible vs. fake news datasets
derived from four online sources. We then propose a language-independent
approach for automatically distinguishing credible from fake news, based on a
rich feature set. In particular, we use linguistic (n-gram),
credibility-related (capitalization, punctuation, pronoun use, sentiment
polarity), and semantic (embeddings and DBPedia data) features. Our experiments
on three different testsets show that our model can distinguish credible from
fake news with very high accuracy.


  Recent theoretical investigations of two-body hadronic B decays have provided
justification for the use of the factorization ansatz to evaluate the B decay
matrix elements. Motivated by this, we present simplified formulae for a wide
range of B decays into the lowest mass pseudoscalar and vector mesons. These
formulae, valid in the heavy quark limit, involve a reduced set of soft QCD
parameters and, although resulting in some loss of accuracy, should still
provide an adequate and transparent tool with which to confront data for some
time to come. Finally, we confront these formulae with data on 19 channels.


  Multitasking optimization is an emerging research field which has attracted
lot of attention in the scientific community. The main purpose of this paradigm
is how to solve multiple optimization problems or tasks simultaneously by
conducting a single search process. The main catalyst for reaching this
objective is to exploit possible synergies and complementarities among the
tasks to be optimized, helping each other by virtue of the transfer of
knowledge among them (thereby being referred to as Transfer Optimization). In
this context, Evolutionary Multitasking addresses Transfer Optimization
problems by resorting to concepts from Evolutionary Computation for
simultaneous solving the tasks at hand. This work contributes to this trend by
proposing a novel algorithmic scheme for dealing with multitasking
environments. The proposed approach, coined as Coevolutionary Bat Algorithm,
finds its inspiration in concepts from both co-evolutionary strategies and the
metaheuristic Bat Algorithm. We compare the performance of our proposed method
with that of its Multifactorial Evolutionary Algorithm counterpart over 15
different multitasking setups, composed by eight reference instances of the
discrete Traveling Salesman Problem. The experimentation and results stemming
therefrom support the main hypothesis of this study: the proposed
Coevolutionary Bat Algorithm is a promising meta-heuristic for solving
Evolutionary Multitasking scenarios.


  COMPASS is a fixed-target experiment at the CERN SPS that studies the
spectrum of light-quark hadrons. In 2009, it collected a large dataset using a
$190\,$GeV$/c$ positive hadron beam impinging on a liquid-hydrogen target in
order to measure the central exclusive production of light scalar mesons. One
of the goals is the search for so-called glueballs, which are hypothetical
meson-like objects without valence-quark content. We study the decay of neutral
resonances by selecting centrally produced pion pairs from the COMPASS dataset.
The angular distributions of the two pseudoscalar mesons are decomposed in
terms of partial waves, where particular attention is paid to the inherent
mathematical ambiguities. The large dataset allows us to perform a detailed
analysis in bins of the two squared four-momentum transfers carried by the
exchange particles in the reaction. Possible parameterisations of the mass
dependence of the partial-wave amplitudes in terms of resonances are also
discussed.


  Aims: To try and clarify whether there are stars in the neighbourhood of
$\beta$ Lyrae which are physically connected to the famous prototype eclipsing
binary.
  Methods: Scrutinize the astrometric and photometric data (from Hipparcos and
Gaia DR2) of stars in a limited sky field around $\beta$~Lyrae.
  Results: A star cluster of about 100 members is discovered, nicely centered
on $\beta$~Lyrae in 5 dimensions. There are clear indications that the newly
discovered cluster belongs to a larger old (extinct) star formation complex,
including two already known star clusters and an extended strewn field of stars
at practically the same distance and space velocity.}
  Conclusions: This discovery opens up the possibility of determining a precise
distance and a precise age for $\beta$ Lyrae, using the combined properties of
the cluster members. This in turn may provide an important asset for an
improved astrophysical interpretation of the model binary $\beta$ Lyrae and its
kin. --- The larger old star formation complex is of scientific interest in its
own right.


  For any elliptic curve $E$ over $k\subset \Bbb R$ with $E({\Bbb C})={\Bbb
C}^\times/q^{\Bbb Z}$, $q=e^{2\pi iz}, \Im(z)>0$, we study the $q$-average
$D_{0,q}$, defined on $E({\Bbb C})$, of the function $D_0(z) = \Im(z/(1-z))$.
Let $\Omega^+(E)$ denote the real period of $E$. We show that there is a
rational function $R \in {\Bbb Q}(X_1(N))$ such that for any non-cuspidal real
point $s\in X_1(N)$ (which defines an elliptic curve $E(s)$ over $\Bbb R$
together with a point $P(s)$ of order $N$), $\pi D_{0,q}(P(s))$ equals
$\Omega^+(E(s))R(s)$. In particular, if $s$ is $\Bbb Q$-rational point of
$X_1(N)$, a rare occurrence according to Mazur, $R(s)$ is a rational number.


  A search is presented for high-mass exclusive diphoton production via
photon-photon fusion in proton-proton collisions at $\sqrt{s}$ = 13 TeV in
events where both protons survive the interaction. The analysis utilizes data
corresponding to an integrated luminosity of 103 fb$^{-1}$ collected in
2016-2018 with the central CMS detector and the CMS and TOTEM precision proton
spectrometer (PPS). Events that have two photons with high transverse momenta
($p_\mathrm{T}^\gamma > $ 100 GeV), back-to-back in azimuth, and with a large
diphoton invariant mass ($m_{\gamma\gamma} \gt$ 350 GeV) are selected. To
remove the dominant inclusive diphoton backgrounds, the kinematic properties of
the protons detected in PPS are required to match those of the central diphoton
system. Only events having opposite-side forward protons detected with a
fractional momentum loss between 0.035 and 0.15 (0.18) for the detectors on the
negative (positive) side of CMS are considered. One exclusive diphoton
candidate is observed for an expected background of 1.1 events. Limits at 95%
confidence level are derived for the four-photon anomalous coupling parameters
$\lvert\zeta_1\rvert \lt$ 0.073 TeV$^{-4}$ and $\lvert\zeta_2\rvert \lt$ 0.15
TeV$^{-4}$, using an effective field theory. Additionally, upper limits are
placed on the production of axion-like particles with coupling strength to
photons $f^{-1}$ that varies from 0.03 TeV$^{-1}$ to 1 TeV$^{-1}$ over the mass
range from 500 to 2000 GeV.


  Let $Di\langle X\rangle$ be the free dialgebra over a field generated by a
set $X$. Let $S$ be a monic subset of $Di\langle X\rangle$. A
Composition-Diamond lemma for dialgebras is firstly established by Bokut, Chen
and Liu in 2010 \cite{Di} which claims that if (i) $S$ is a
Gr\"{o}bner-Shirshov basis in $Di\langle X\rangle$, then (ii) the set of
$S$-irreducible words is a linear basis of the quotient dialgebra $Di\langle X
\mid S \rangle$, but not conversely. Such a lemma based on a fixed ordering on
normal diwords of $Di\langle X\rangle$ and special definition of composition
trivial modulo $S$. In this paper, by introducing an arbitrary monomial-center
ordering and the usual definition of composition trivial modulo $S$, we give a
new Composition-Diamond lemma for dialgebras which makes the conditions (i) and
(ii) equivalent. We show that every ideal of $Di\langle X\rangle$ has a unique
reduced Gr\"{o}bner-Shirshov basis. The new lemma is more useful and convenient
than the one in \cite{Di}. As applications, we give a method to find normal
forms of elements of an arbitrary disemigroup, in particular, A.V. Zhuchok's
(2010) and Y.V. Zhuchok's (2015) normal forms of the free commutative
disemigroups and the free abelian disemigroups, and normal forms of the free
left (right) commutative disemigroups.


  Interfacing atomistic-based with continuum-based simulation codes is now
required in many multiscale physical and biological systems. We present the
first results from coupled atomistic-continuum simulations on 190,000
processors. Platelet aggregation in the patient-specific model of an aneurysm
has been modeled using a high-order spectral/hp element Navier-Stokes solver
with a stochastic (coarse-grained) Molecular Dynamics solver based on
Dissipative Particle Dynamics (DPD).


  In this study, we propose a dense frequency-time attentive network (DeFT-AN)
for multichannel speech enhancement. DeFT-AN is a mask estimation network that
predicts a complex spectral masking pattern for suppressing the noise and
reverberation embedded in the short-time Fourier transform (STFT) of an input
signal. The proposed mask estimation network incorporates three different types
of blocks for aggregating information in the spatial, spectral, and temporal
dimensions. It utilizes a spectral transformer with a modified feed-forward
network and a temporal conformer with sequential dilated convolutions. The use
of dense blocks and transformers dedicated to the three different
characteristics of audio signals enables more comprehensive enhancement in
noisy and reverberant environments. The remarkable performance of DeFT-AN over
state-of-the-art multichannel models is demonstrated based on two popular noisy
and reverberant datasets in terms of various metrics for speech quality and
intelligibility.


  Surface characteristics are a major contributor to the in-service
performance, particularly fatigue life, of additively manufactured (AM)
components. Centrifugal disk finishing (CDF) is one of many rigid media,
abrasive machining processes employed to smooth the surfaces and edges of AM
components. Within the general family of abrasive machining processes currently
applied to AM, CDF is moderate in terms of material removal rate and the
inertial forces exerted. How CDF alters the underlying microstructure of the
processed surface is currently unknown. Here we employ white light profilometry
and high-energy X-ray diffraction to characterize surface finish,
crystallographic texture, and anisotropic distributions of residual microscale
strain as a function of depth in CDF-finished Inconel 718 manufactured with
laser powder bed fusion. Surfaces are finished using both unimodal and bimodal
finishing media size distributions. We find that CDF will remove surface
crystallographic textures (here a {111} fiber texture) from AM components, but
generally not alter the bulk texture (here a cube texture). CDF is also found
to impart significant amounts of residual microscale strain into the first 100
$\mu$m from the sample surface as evidenced by an approximately 50% increase in
diffraction peak widths at 20 $\mu$m from the surface in comparison to 120
$\mu$m.


  This paper addresses the problem of Over-The-Air (OTA) computation in
wireless networks which has the potential to realize huge efficiency gains for
instance in training of distributed ML models. We provide non-asymptotic,
theoretical guarantees for OTA computation in fast-fading wireless channels
where the fading and noise may be correlated. The distributions of fading and
noise are not restricted to Gaussian distributions, but instead are assumed to
follow a distribution in the more general sub-gaussian class. Furthermore, our
result does not make any assumptions on the distribution of the sources and
therefore, it can, e.g., be applied to arbitrarily correlated sources. We
illustrate our analysis with numerical evaluations for OTA computation of two
example functions in large wireless networks: the arithmetic mean and the
Euclidean norm.


  We present polarization images of Comet ISON (C/2012 S1) taken with the
Hubble Space Telescope (HST) on UTC 2013 May 8 (rh = 3.81 AU, Delta = 4.34 AU),
when the phase angle was alpha = 12.16 degrees. This phase angle is
approximately centered in the negative polarization branch for cometary dust.
The region beyond 1000 km from the nucleus shows a negative polarization
amplitude of p% -1.6%. Within 1000 km of the nucleus, the polarization position
angle rotates to be approximately perpendicular to the scattering plane, with
an amplitude p% +2.5%. Such positive polarization has been observed previously
as a characteristic feature of cometary jets, and we show that Comet ISON does
indeed harbor a jet-like feature. These HST observations of Comet ISON
represent the first visible light, imaging polarimetry with sub-arcsecond
spatial resolution of a Nearly Isotropic Comet (NIC) beyond 3.8 AU from the Sun
at a small phase angle. The observations provide an early glimpse of the
properties of the cometary dust preserved in this Oort-cloud comet.


  Let $\mu$ be a finite Borel measure on $[0,1)$. In this paper, we consider
the generalized integral type Hilbert operator
  $$\mathcal{I}_{\mu_{\alpha+1}}(f)(z)=\int_{0}^{1}\frac{f(t)}{(1-tz)^{\alpha+1}}d\mu(t)\
\ \ (\alpha>-1).$$ The operator $\mathcal{I}_{\mu_{1}}$ has been extensively
studied recently. The aim of this paper is to study the boundedness(resp.
compactness) of $\mathcal{I}_{\mu_{\alpha+1}}$ acting from the normal weight
Bloch space into another of the same kind. As consequences of our study, we get
completely results for the boundedness of $ \mathcal{I}_{\mu_{\alpha+1}}$
acting between Bloch type spaces, logarithmic Bloch spaces among others.


  In this work, we present a novel trajectory comparison algorithm to identify
abnormal vital sign trends, with the aim of improving recognition of
deteriorating health.
  There is growing interest in continuous wearable vital sign sensors for
monitoring patients remotely at home. These monitors are usually coupled to an
alerting system, which is triggered when vital sign measurements fall outside a
predefined normal range. Trends in vital signs, such as increasing heart rate,
are often indicative of deteriorating health, but are rarely incorporated into
alerting systems.
  We introduce a dynamic time warp distance-based measure to compare time
series trajectories. We split each multi-variable sign time series into 180
minute, non-overlapping epochs. We then calculate the distance between all
pairs of epochs. Each epoch is characterized by its mean pairwise distance
(average link distance) to all other epochs, with clusters forming with nearby
epochs.
  We demonstrate in synthetically generated data that this method can identify
abnormal epochs and cluster epochs with similar trajectories. We then apply
this method to a real-world data set of vital signs from 8 patients who had
recently been discharged from hospital after contracting COVID-19. We show how
outlier epochs correspond well with the abnormal vital signs and identify
patients who were subsequently readmitted to hospital.


  We consider the question of the amorphization of metallic alloys by melt
quenching, as predicted by molecular dynamics simulations with semi-empirical
potentials. The parametrization of the potentials is discussed on the example
of the ternary Cu-Ti-Zr transition metals alloy, using as reference the
ab-initio simulation. The pair structure in the amorphous state is computed
from a potential of the Stillinger Weber form. The transferability of the
parameters during the quench is investigated using two parametrizations: from
solid state data, as usual, and from a new parametrization on the liquid
structure. When the adjustment is made on the pair structure of the liquid, a
satisfactory transferability is found between the pure components and their
alloys. The liquid structure predicted in this way agrees well with experiment,
in contrast with the one obtained using the adjustment on the solid. The final
structure, after quenches down to the amorphous state, determined with the new
set of parameters is shown to be very close to the ab-initio one, the latter
being in excellent agreement with recent X-rays diffraction experiments. The
corresponding critical temperature of the glass transition is estimated from
the behavior of the heat capacity. Discussion of the consistency between the
structures predicted using semi-empirical potentials and ab-initio simulation,
and comparison of different experimental data underlines the question of the
dependence of the final structure on the thermodynamic path followed to reach
the amorphous state.


  Special-purpose Autonomous Underwater Vehicles (AUVs) are utilised for
benthic (seafloor) surveys, where the vehicle collects optical imagery of the
seafloor. Due to the small-sensor footprint of the cameras and the vast areas
to be surveyed, these AUVs can not feasibly collect full coverage imagery of
areas larger than a few tens of thousands of square meters. Therefore it is
necessary for AUV paths to sample the surveys areas sparsely, yet effectively.
Broad-scale acoustic bathymetric data is readily available over large areas,
and is often a useful prior of seafloor cover. As such, prior bathymetry can be
used to guide AUV data collection. This research proposes methods for planning
initial AUV surveys that efficiently explore a feature space representation of
the bathymetry, in order to sample from a diverse set of bathymetric terrain.
This will enable the AUV to visit areas that likely contain unique habitats and
are representative of the entire survey site. We propose several information
gathering planners that utilise a feature space exploration reward, to plan
freeform paths or to optimise the placement of a survey template. The
suitability of these methods to plan AUV surveys is evaluated based on the
coverage of the feature space and also the ability to visit all classes of
benthic habitat on the initial dive. Informative planners based on
Rapidly-expanding Random Trees (RRT) and Monte-Carlo Tree Search (MCTS) were
found to be the most effective. This is a valuable tool for AUV surveys as it
increases the utility of initial dives. It also delivers a comprehensive
training set to learn a relationship between acoustic bathymetry and
visually-derived seafloor classifications.


  The cultivated strawberry Fragaria ananassa Duch. is widely planted in
greenhouses in China. Its production heavily depends on pollination services.
Compared with artificial pollination, bee pollination can significantly improve
fruit quality and save considerable labor requirement. Multiple factors such as
bee foraging behavior, planting pattern and the spatial complexity of the
greenhouse environment interacting over time and space are major obstacles to
understanding of bee pollination dynamics. We propose a spatially-explicit
agent-based simulation model which allows users to explore how various factors
including bee foraging behavior and strawberry phenology conditions as well as
the greenhouse environment influence pollination efficiency and fruit quality.
Simulation experiments allowed us to compare pollination efficiencies in
different conditions. Especially, the cause of bee pollination advantage,
optimal bee density and bee hive location were discussed based on sensitivity
analysis. In addition, simulation results provide some insights for strawberry
planting in a greenhouse. The firmly validated open-source model is a useful
tool for hypothesis testing and theory development for strawberry pollination
research.


  I summarize and discuss some recent results on formulating actions of
six-dimensional superconformal field theories using the language of higher
gauge theory. The latter guarantees mathematical consistency of our
constructions and we review crucial aspects of this framework, such as
$L_\infty$-algebras and corresponding kinematical data given by higher
connections. We then show that there is a mathematically consistent non-Abelian
extension of the self-dual string equation which satisfies many physical
expectations. Our construction favors a particular higher gauge group leading
us to higher principal bundles known as string structures. Using these, we
manage to formulate a six-dimensional action which shares many properties with
the famous $(2,0)$-theory but also still differs from it in some key points.


  In order to design next-generation ferroelectrics, a microscopic
understanding of their macroscopic properties is critical. One means to
achieving an atomistic description of ferroelectric and dielectric phenomena is
classical molecular dynamics simulations. Previously, we have shown that
interatomic potentials based on the bond valence molecular dynamics (BVMD)
method can be used to study structural phase transitions, ferroelectric domain
nucleation, and domain wall migration in several perovskite oxides and
fixed-composition binary and ternary alloys. Most modern devices, however, use
variable-composition perovskite oxide alloys such as Ba$_x$Sr$_{1-x}$TiO$_3$
(BST). In this paper, we extend our bond valence approach to BST solid
solutions and, in so doing, show that the potential parameters for each element
are transferable between materials with different $x$. Using this potential, we
perform BVMD simulations investigating the temperature and composition
dependence of the lattice constants, Ti displacements, and ferroelectric
polarization of BST and find that our predictions match experiments and
first-principles theory. Additionally, based on a detailed analysis of local
dipole distributions, we demonstrate that substitution of Sr for Ba scrambles
dipoles, reduces global polarization, and enhances the order-disorder character
of the ferroelectric-paraelectric phase transition.


  It is well known that Zee type neutrino mass matrix can provide bi-maximal
neutrino mixing for three neutrinos. We study the reconciliation of this model
with the gauge mediated supersymmetry breaking scenario, which naturally
suppresses the large flavor changing neutral current and CP violation in the
supersymmetric standard model. When the messenger fields have suitable B-L
charges, the radiative correction naturally induces the Zee neutrino mass
matrix, which provides tiny neutrino masses and large lepton flavor mixings.
Our numerical results are consistent with the neutrino oscillation experiments
in both three and four neutrino models.


  Wireless connectivity has traditionally been regarded as an opaque data pipe
carrying messages, whose context-dependent meaning and effectiveness have been
ignored. Nevertheless, in emerging cyber-physical and autonomous networked
systems, acquiring, processing, and sending excessive amounts of distributed
real-time data, which ends up being stale or useless to the end user, will
cause communication bottlenecks, increased latency, and safety issues. We
envision a communication paradigm shift, which makes the Semantics of
Information, i.e., the significance and the usefulness of messages with respect
to the goal of data exchange, the underpinning of the entire communication
process. This entails a goal-oriented unification of information generation,
transmission, and usage, by taking into account process dynamics, signal
sparsity, data correlation, and semantic information attributes. We apply this
structurally new, synergetic approach to a communication scenario where the
destination is tasked with real-time source reconstruction for the purpose of
remote actuation. Capitalizing on semantics-empowered sampling and
communication policies, we show significant reduction in both reconstruction
error and cost of actuation error, as well as in the number of uninformative
samples generated.


  We study a bipartite collective spin-$1$ model with exchange interaction
between the spins. The bipartite nature of the model manifests itself by the
spins being divided into two equal-sized subsystems; within each subsystem the
spin-spin interactions are of the same strength, across the subsystems they are
also equal, but the two coupling values within and across the subsystem are
different. Such a set-up is inspired by recent experiments with ultracold
atoms. Using the $\mathrm{SU}(3)$-symmetry of the exchange interaction and the
permutation symmetry within the subsystems, we can employ representation
theoretic methods to diagonalize the Hamiltonian of the system in the entire
parameter space of the two coupling-strengths. These techniques then allow us
to explicitly construct and explore the ground-state phase diagram. The phase
diagram turns out to be rich containing both gapped and gapless phases. An
interesting observation is that one of the five phases features a strong
bipartite symmetry breaking, meaning that the two subsystems in the ground
states are in different $\mathrm{SU}(3)$ representations.


  This paper examines the velocity profile of fuel issuing from a high-pressure
single-orifice diesel injector. Velocities of liquid structures were determined
from time-resolved ultrafast shadow images, formed by an amplified two-pulse
laser source coupled to a double-frame camera. A statistical analysis of the
data over many injection events was undertaken to map velocities related to
spray formation near the nozzle outlet as a function of time after start of
injection. These results reveal a strong asymmetry in the liquid profile of the
test injector, with distinct fast and slow regions on opposite sides of the
orifice. Differences of ~100 m/s can be observed between the 'fast' and 'slow'
sides of the jet, resulting in different atomization conditions across the
spray. On average, droplets are dispersed at a greater distance from the nozzle
on the 'fast' side of the flow, and distinct macrostructure can be observed
under the asymmetric velocity conditions. The changes in structural velocity
and atomization behavior resemble flow structures which are often observed in
the presence of string cavitation produced under controlled conditions in
scaled, transparent test nozzles. These observations suggest that widely used
common-rail supply configurations and modern injectors can potentially generate
asymmetric interior flows which strongly influence diesel spray morphology. The
velocimetry measurements presented in this work represent an effective and
relatively straightforward approach to identify deviant flow behavior in real
diesel sprays, providing new spatially resolved information on fluid structure
and flow characteristics within the shear layers on the jet periphery.


  A spinning black hole with a much smaller black hole companion forms a
fundamental gravitational system, like a colossal classical analog to an atom.
In an appealing if imperfect analogy to atomic physics, this gravitational atom
can be understood through a discrete spectrum of periodic orbits. Exploiting a
correspondence between the set of periodic orbits and the set of rational
numbers, we are able to construct periodic tables of orbits and energy level
diagrams of the accessible states around black holes. We also present a closed
form expression for the rational q, thereby quantifying zoom-whirl behavior in
terms of spin, energy, and angular momentum. The black hole atom is not just a
theoretical construct, but corresponds to extant astrophysical systems
detectable by future gravitational wave observatories.


Recent lattice calculations of hadron structure functions are described.


  The stochastic system approach to causality is applied to situations where
the risk of death is not negligible. This approach grounds causality on
physical laws, distinguishes system and observation and represents the system
by multivariate stochastic processes. The particular role of death is
highlighted, and it is shown that local influences must be defined on the
random horizon of time of death. We particularly study the problem of
estimating the effect of a factor $V$ on a process of interest $Y$, taking
death into account. We unify the cases where $Y$ is a counting process
(describing an event) and the case where $Y$ is quantitative; we examine the
case of observations in continuous and discrete time and we give a typology of
cases where the mechanism leading to incomplete data can be ignored. Finally,
we give an example of a situation where we are interested in estimating the
effect of a factor (blood pressure) on cognitive ability in elderly.


  Neutron Zeeman spatial beam-splitting is considered at reflection from
magnetically noncollinear films. Two applications of Zeeman beam-splitting
phenomenon in polarized neutron reflectometry are discussed. One is the
construction of polarizing devices with high polarizing efficiency. Another one
is the investigations of magnetically noncollinear films with low spin-flip
probability. Experimental results are presented for illustration.


  The observed microwave background anisotropies in combination with the theory
of quantum mechanically generated cosmological perturbations predict a well
measurable amount of relic gravitational waves in the frequency intervals
tested by LISA and ground-based laser interferometers.


  In this work we address the development of a smart personal assistant that is
capable of anticipating a user's information needs based on a novel type of
context: the person's activity inferred from her check-in records on a
location-based social network. Our main contribution is a method that
translates a check-in activity into an information need, which is in turn
addressed with an appropriate information card. This task is challenging
because of the large number of possible activities and related information
needs, which need to be addressed in a mobile dashboard that is limited in
size. Our approach considers each possible activity that might follow after the
last (and already finished) activity, and selects the top information cards
such that they maximize the likelihood of satisfying the user's information
needs for all possible future scenarios. The proposed models also incorporate
knowledge about the temporal dynamics of information needs. Using a combination
of historical check-in data and manual assessments collected via crowdsourcing,
we show experimentally the effectiveness of our approach.


  This paper describes by example how astronomers can use cloud-computing
resources offered by Amazon Web Services (AWS) to create new datasets at scale.
We have created from existing surveys an atlas of the Galactic Plane at 16
wavelengths from 1 {\mu}m to 24 {\mu}m with pixels co-registered at spatial
sampling of 1 arcsec. We explain how open source tools support management and
operation of a virtual cluster on AWS platforms to process data at scale, and
describe the technical issues that users will need to consider, such as
optimization of resources, resource costs, and management of virtual machine
instances.


  We address the problem of state estimation, attack isolation, and control of
discrete-time linear time-invariant systems under (potentially unbounded)
actuator and sensor false data injection attacks. Using a bank of unknown input
observers, each observer leading to an exponentially stable estimation error
(in the attack-free case), we propose an observer-based estimator that provides
exponential estimates of the system state in spite of actuator and sensor
attacks. Exploiting sensor and actuator redundancy, the estimation scheme is
guaranteed to work if a sufficiently small subset of sensors and actuators are
under attack. Using the proposed estimator, we provide tools for reconstructing
and isolating actuator and sensor attacks; and a control scheme capable of
stabilizing the closed-loop dynamics by switching off isolated actuators.
Simulation results are presented to illustrate the performance of our tools.


  A holey Schr\"oder design of type $h_1^{n_1}h_4^{n_2}\cdots h^{n_k}_k$
(HSD$(h_1^{n_1}h_4^{n_2}\cdots h^{n_k}_k))$ is equivalent to a frame idempotent
Schr\"oder quasigroup (FISQ$(h_1^{n_1}h_4^{n_2}\cdots h^{n_k}_k))$ of order $n$
with $n_i$ missing subquasigroups (holes) of order $h_i, 1 \le i \le k$, which
are disjoint and spanning (i.e., $\sum_{1\le i \le k}n_ih_i = n$). The
existence of HSD$(h^nu^1)$ for $h=1, 2, 4$ has been known. In this paper, we
consider the existence of HSD$(3^nu^1)$ and show that for $0\le u \le 15$, an
HSD$(3^nu^1)$ exists if and only if $n(n + 2u -1) \equiv 0~(mod~4)$, $n\ge 4$
and $n\ge 1+2u/3$. For $0 \le u \le n$, an HSD$(3^nu^1)$ exists if and only if
$n(n + 2u -1) \equiv 0~(mod~4)$ and $n \ge 4$, with possible exceptions of $n =
29, 43$. We have also found six new HSDs of type $(4^nu^1)$.


  Sampling-based motion planning methods for manipulators in crowded
environments often suffer from expensive collision checking and high sampling
complexity, which make them difficult to use in real time. To address this
issue, we propose a new generalizable control barrier function (CBF)-based
steering controller to reduce the number of samples needed in a sampling-based
motion planner RRT. Our method combines the strength of CBF for real-time
collision-avoidance control and RRT for long-horizon motion planning, by using
CBF-induced neural controller (CBF-INC) to generate control signals that steer
the system towards sampled configurations by RRT. CBF-INC is learned as Neural
Networks and has two variants handling different inputs, respectively: state
(signed distance) input and point-cloud input from LiDAR. In the latter case,
we also study two different settings: fully and partially observed
environmental information. Compared to manually crafted CBF which suffers from
over-approximating robot geometry, CBF-INC can balance safety and goal-reaching
better without being over-conservative. Given state-based input, our neural
CBF-induced neural controller-enhanced RRT (CBF-INC-RRT) can increase the
success rate by 14% while reducing the number of nodes explored by 30%,
compared with vanilla RRT on hard test cases. Given LiDAR input where vanilla
RRT is not directly applicable, we demonstrate that our CBF-INC-RRT can improve
the success rate by 10%, compared with planning with other steering
controllers. Our project page with supplementary material is at
https://mit-realm.github.io/CBF-INC-RRT-website/.


  We present a technique for extracting Raman intensities from ab initio
molecular dynamics (MD) simulations at high temperature. The method is applied
to the highly anharmonic case of dense hydrogen up to 500 K for pressures
ranging from 180 GPa to 300 GPa. On heating or pressurizing we find first-order
phase transitions at the experimental conditions of the phase III - IV
boundary. Direct comparison of Raman vibrons with experiment provides excellent
discrimination between subtly different structures, found in MD. We find
candidate structures whose Raman spectra are in good agreement with experiment.
The new phase obtained in high temperature simulations adopts a dynamic, simple
hexagonal structure with three layer types: freely rotating hydrogen molecules,
static hexagonal trimers and rotating hexagonal trimers. We show that
previously calculated structures for phase IV are inconsistent with experiment,
and their appearance in simulation is due to finite size effects.


  The laser cooling of atoms is a result of the combined effect of doppler
shift, light shift and polarization gradient. These are basically undesirable
phenomena. However, they combine gainfully in realizing laser cooling and
trapping of the atoms. In this paper we discuss the laser cooling of atoms in
the presence of the squeezed light with the decay of atomic dipole moment into
noisy quadrature. We show that the higher decay rate of the atomic dipole
moment into the noisy quadrature, which is also an undesirable effect, may
contribute in realizing larger cooling force vis-a-vis normal laser light.


  Silicon (Si) is one of the most extensively studied materials owing to its
significance to semiconductor science and technology. While efforts to find a
new three-dimensional (3D) Si crystal with unusual properties have made some
progress, its two-dimensional (2D) phases have not yet been explored as much.
Here, based on a newly developed systematic $ab$ $initio$ materials searching
strategy, we report a series of novel 2D Si crystals with unprecedented
structural and electronic properties. The new structures exhibit perfectly
planar outermost surface layers of a distorted hexagonal network with their
thicknesses varying with the atomic arrangement inside. Dramatic changes in
electronic properties ranging from semimetal to semiconducting with indirect
energy gaps and even to one with direct energy gaps are realized by varying
thickness as well as by surface oxidation. Our predicted 2D Si crystals with
flat surfaces and tunable electronic properties will shed light on the
development of silicon-based 2D electronics technology.


  Let $M_n$ be the set of $n\times n$ complex matrices. In this note we
determine all the possible ranks of a bipartite state in $M_m\otimes M_n$ with
prescribed reduced states in the two subsystems. The results are used to
determine the Choi rank of quantum channels $\Phi: M_m \rightarrow M_n$ sending
$I/m$ to a specific state $\sigma_2 \in M_n$.


  We obtain an asymptotic formula for the mean value of the function
$\tau_k(n)$, which is the number of solutions of the equation $x_1...\, x_k=n$
in natural numbers $x_1,..., x_k$ in some special sequences of natural numbers.


  The functional form of the nuclear symmetry energy in the whole range of
densities relevant for the neutron stars is still unknown. Discrepancies
concern both the low as well as the high density behaviour of this function. By
use of Bezier curves three different families of the symmetry energy shapes,
relevant for different density range were introduced. Their consequences for
the crustal properties of neutron stars are presented.


  Hybridization of multi-junction concentrator photovoltaics with
single-junction flat plate solar cells (CPV/PV) can deliver the highest power
output per module area of any PV technology. Conversion efficiencies up to
34.2% have been published under the AM1.5g spectrum at standard test conditions
for the EyeCon module which combines Fresnel lenses and III-V four-junction
solar cells with bifacial c-Si. We investigate here its energy yield and
compare it to conventional CPV as well as flat plate PV. The advantage of the
hybrid CPV/PV module is that it converts direct sunlight with the most advanced
multi-junction cell technology, while accessing diffuse, lens-scattered and
back side irradiance with a Si cell that also serves as the heat distributor
for the concentrator cells. This article quantifies that hybrid bifacial CPV/PV
modules are expected to generate a 25 - 35% higher energy yield with respect to
their closest competitor in regions with a diffuse irradiance fraction around
50%. Additionally, the relative cost of electricity generated by hybrid CPV/PV
technology was calculated worldwide under certain economic assumptions.
Therefore, this article gives clear guidance towards establishing competitive
business cases for the technology.


  Let $\Lambda$ be an infinite connected graph, and let $v_0$ be a vertex of
$\Lambda$. We consider the following positional game. Two players, Maker and
Breaker, play in alternating turns. Initially all edges of $\Lambda$ are marked
as unsafe. On each of her turns, Maker marks $p$ unsafe edges as safe, while on
each of his turns Breaker takes $q$ unsafe edges and deletes them from the
graph. Breaker wins if at any time in the game the component containing $v_0$
becomes finite. Otherwise if Maker is able to ensure that $v_0$ remains in an
infinite component indefinitely, then we say she has a winning strategy. This
game can be thought of as a variant of the celebrated Shannon switching game.
Given $(p,q)$ and $(\Lambda, v_0)$, we would like to know: which of the two
players has a winning strategy?
  Our main result in this paper establishes that when $\Lambda = \mathbb{Z}^2$
and $v_0$ is any vertex, Maker has a winning strategy whenever $p\geq 2q$,
while Breaker has a winning strategy whenever $2p\leq q$. In addition, we
completely determine which of the two players has a winning strategy for every
pair $(p,q)$ when $\Lambda$ is an infinite $d$-regular tree. Finally, we give
some results for general graphs and lattices and pose some open problems.


  This paper investigates the stability of a class of differential systems
time-changed by $E_{t}$ which is the inverse of a $\beta$-stable subordinator.
In order to explore stability, a time-changed Gronwall's inequality and a
generalized It\^o formula related to both the natural time $t$ and the
time-change $E_{t}$ are developed. For different time-changed systems,
corresponding stability behaviors such as exponential sample-path stability,
$p$th moment asymptotic stability and $p$th moment exponential stability are
investigated. Also a connection between the stability of the time-changed
system and that of its corresponding non-time-changed system is revealed.


  Zeros of the $n$th moment of the partition function $[Z^n]$ are investigated
in a vanishing temperature limit $\beta \to \infty$, $n \to 0$ keeping $y=\beta
n \sim O(1)$. In this limit, the moment parameterized by $y$ characterizes the
distribution of the ground-state energy. We numerically investigate the zeros
for $\pm J$ Ising spin glass models with several ladder and tree systems, which
can be carried out with a feasible computational cost by a symbolic operation
based on the Bethe--Peierls method. For several tree systems we find that the
zeros tend to approach the real axis of $y$ in the thermodynamic limit implying
that the moment cannot be described by a single analytic function of $y$ as the
system size tends to infinity, which may be associated with breaking of the
replica symmetry. However, examination of the analytical properties of the
moment function and assessment of the spin-glass susceptibility indicate that
the breaking of analyticity is relevant to neither one-step or full replica
symmetry breaking.


  The measurement of a large tensor-to-scalar ratio by the BICEP2 experiment, r
= 0.20 (-0.05)(+0.07), severely restricts the landscape of viable inflationary
models and shifts attention once more towards models featuring large inflaton
field values. In this context, chaotic inflation based on a fractional
power-law potential that is dynamically generated by the dynamics of a strongly
coupled supersymmetric gauge theory appears to be particularly attractive. We
revisit this class of inflation models and find that, in the light of the
BICEP2 measurement, models with a non-minimal gauge group behind the dynamical
model seem to be disfavored, while the model with the simplest group, i.e.
SU(2), is consistent with all results. We also discuss how the dynamical model
can be distinguished from the standard chaotic inflation model based on a
quadratic inflaton potential.


  The launching mechanism of the jets of active galactic nuclei is
observationally poorly constrained, due to the large distances to these objects
and the very small scales (sub-parsec) involved. In order to better constrain
theoretical models, it is especially important to get information from the
region close to the physical base of the jet, where the plasma acceleration
takes place. In this paper, we report multi-epoch and multi-frequency continuum
observations of the z=2.5 blazar PKS1830-211 with ALMA, serendipitously
coincident with a strong $\gamma$-ray flare reported by Fermi-LAT. The blazar
is lensed by a foreground z=0.89 galaxy, with two bright images of the compact
core separated by 1". Our ALMA observations individually resolve these two
images (although not any of their substructures), and we study the change of
their relative flux ratio with time (four epochs spread over nearly three times
the time delay between the two lensed images) and frequency (between 350 and
1050 GHz, rest-frame of the blazar), during the $\gamma$-ray flare. In
particular, we detect a remarkable frequency-dependent behaviour of the flux
ratio, which implies the presence of a chromatic structure in the blazar (i.e.,
a core-shift effect). We rule out the possiblity of micro- and milli-lensing
effects and propose instead a simple model of plasmon ejection in the blazar's
jet to explain the time and frequency variability of the flux ratio. We suggest
that PKS1830-211 is likely one of the best sources to probe the activity at the
base of a blazar's jet at submillimeter wavelengths, thanks to the peculiar
geometry of the system. The implications of the core-shift in absorption
studies of the foreground z=0.89 galaxy (e.g., constraints on the cosmological
variations of fundamental constants) are discussed.


  Given a finite group $G,$ we denote by $\Delta(G)$ the graph whose vertices
are the elements $G$ and where two vertices $x$ and $y$ are adjacent if there
exists a minimal generating set of $G$ containing $x$ and $y.$ We prove that
$\Delta(G)$ is connected and classify the groups $G$ for which $\Delta(G)$ is a
planar graph.


  We study a practical yet hasn't been explored problem: how a drone can
perceive in an environment from different flight heights. Unlike autonomous
driving, where the perception is always conducted from a ground viewpoint, a
flying drone may flexibly change its flight height due to specific tasks,
requiring the capability for viewpoint invariant perception. Tackling the such
problem with supervised learning will incur tremendous costs for data
annotation of different flying heights. On the other hand, current
semi-supervised learning methods are not effective under viewpoint differences.
In this paper, we introduce the ground-to-aerial perception knowledge transfer
and propose a progressive semi-supervised learning framework that enables drone
perception using only labeled data of ground viewpoint and unlabeled data of
flying viewpoints. Our framework has four core components: i) a dense viewpoint
sampling strategy that splits the range of vertical flight height into a set of
small pieces with evenly-distributed intervals, ii) nearest neighbor
pseudo-labeling that infers labels of the nearest neighbor viewpoint with a
model learned on the preceding viewpoint, iii) MixView that generates augmented
images among different viewpoints to alleviate viewpoint differences, and iv) a
progressive distillation strategy to gradually learn until reaching the maximum
flying height. We collect a synthesized and a real-world dataset, and we
perform extensive experimental analyses to show that our method yields 22.2%
and 16.9% accuracy improvement for the synthesized dataset and the real world.
Code and datasets are available on
https://github.com/FreeformRobotics/Progressive-Self-Distillation-for-Ground-to-Aerial-Perception-Knowledge-Transfer.


  Meta-learning optimizes an inductive bias---typically in the form of the
hyperparameters of a base-learning algorithm---by observing data from a finite
number of related tasks. This paper presents an information-theoretic bound on
the generalization performance of any given meta-learner, which builds on the
conditional mutual information (CMI) framework of Steinke and Zakynthinou
(2020). In the proposed extension to meta-learning, the CMI bound involves a
training \textit{meta-supersample} obtained by first sampling $2N$ independent
tasks from the task environment, and then drawing $2M$ independent training
samples for each sampled task. The meta-training data fed to the meta-learner
is modelled as being obtained by randomly selecting $N$ tasks from the
available $2N$ tasks and $M$ training samples per task from the available $2M$
training samples per task. The resulting bound is explicit in two CMI terms,
which measure the information that the meta-learner output and the base-learner
output provide about which training data are selected, given the entire
meta-supersample. Finally, we present a numerical example that illustrates the
merits of the proposed bound in comparison to prior information-theoretic
bounds for meta-learning.


  AAT/WFI optical images of a candidate extragalactic HI cloud, HIPASS
J1712-64, are presented. The g and r-band CCD mosaic camera frames were
processed using a new data pipeline recently installed at the AAO. The
resultant stacked images reach significantly deeper levels than those of
previous published optical imaging of this candidate, providing a detection
limit M_g -7 at a distance of 3Mpc, the inferred distance to HIPASS J1712-64.
However, detailed analysis of the images fails to uncover any stellar
population associated with the HI emission. If this system is a member of the
Local Group then it is pathologically different to other members. Hence, our
observations reinforce earlier suggestions that this HI cloud is most likely
Galactic in origin and not a Local Volume dwarf galaxy.


  The theory of statistical thermodynamics tells us the equipartition law of
energy does not hold in the limit of very low temperatures. It is found the
Debye model is very successful in explaining the experimental results for most
of the solid objects. Motivated by this fact, we modify the entropic force
formula which is proposed very recently. Since the Unruh temperature is
proportional to the strength of gravitational field, so the modified entropic
force formula is an extension of the Newtonian gravity to weak field. On the
contrary, General Relativity extends Newtonian gravity to strong field case.
Corresponding to Debye temperature, there exists a Debye acceleration g_D. It
is found the Debye acceleration is g_D=10^{-15}N kg^{-1}. This acceleration is
very much smaller than the gravitational acceleration 10^{-4}N kg^{-1} which is
felt by the Neptune and the gravitational acceleration 10^{-10}N kg^{-1} felt
by the Sun. Therefore, the modified entropic force can be very well
approximated by the Newtonian gravity in the solar system and in the Galaxy.
With this Debye acceleration, we find the current cosmic speeding up can be
explained without invoking any kind of dark energy.


  We present a practical design and implementation of a broadband sample holder
suitable for microwave experiments with superconducting integrated circuits at
millikelvin temperatures. Proposed design can be easily integrated in standard
dilution cryostats, has flat pass band response in a frequency range from 0 to
32 GHz, allowing the RF testing of the samples with substrate size up to 4x4
mm. The parasitic higher modes interference in the holder structure is analyzed
and prevented via design considerations. The developed setup can be used for
characterization of superconducting parametric amplifiers, bolometers and
qubits. We tested the designed sample holder by characterizing of a
superconducting flux qubit at 20 mK temperature.


  We establish the most general form of the discrete elasticity of a 2D
triangular lattice embedded in three dimensions, taking into account up to
next-nearest neighbour interactions. Besides crystalline system, this is
relevant to biological physics (e.g., red blood cell cytoskeleton) and soft
matter (e.g., percolating gels, etc.). In order to correctly impose the
rotational invariance of the bulk terms, it turns out to be necessary to take
into account explicitly the elasticity associated with the vertices located at
the edges of the lattice. We find that some terms that were suspected in the
litterature to violate rotational symmetry are in fact admissible


  We observed the optical afterglow of the bright gamma-ray burst GRB030329 on
the nights of 2003 March 29, using the Kiso observatory (the University of
Tokyo) 1.05 m Schmidt telescope. Data were taken from March 29 13:21:26 UT to
17:43:16 (0.072 to 0.253 days after the burst), using an $Rc$-band filter. The
obtained $Rc$-band light curve has been fitted successfully by a single power
law function with decay index of $0.891\pm0.004$. These results remain
unchanged when incorporating two early photometric data points at 0.065 and
0.073 days, reported by Price et al.(2003) using the SSO 40 inch telescope, and
further including RTT150 data (Burenin et al. 2003) covering at about 0.3 days.
Over the period of 0.065-0.285 days after the burst, any deviation from the
power-law decay is smaller than $\pm$0.007 mag. The temporal structure reported
by Uemura et al. (2003) does not show up in our $R$-band light curve.


  Knowledge of an exoplanet's oblateness and obliquity would give clues about
its formation and internal structure. In principle, a light curve of a
transiting planet bears information about the planet's shape, but previous work
has shown that the oblateness-induced signal will be extremely difficult to
detect. Here we investigate the potentially larger signals due to planetary
spin precession. The most readily detectable effects are transit depth
variations (T$\delta$V) in a sequence of light curves. For a planet as oblate
as Jupiter or Saturn, the transit depth will undergo fractional variations of
order 1%. The most promising systems are those with orbital periods of
approximately 15--30 days, which is short enough for the precession period to
be less than about 40 years, and long enough to avoid spin-down due to tidal
friction. The detectability of the T$\delta$V signal would be enhanced by moons
(which would decrease the precession period) or planetary rings (which would
increase the amplitude). The Kepler mission should find several planets for
which precession-induced T$\delta$V signals will be detectable. Due to modeling
degeneracies, Kepler photometry would yield only a lower bound on oblateness.
The degeneracy could be lifted by observing the oblateness-induced asymmetry in
at least one transit light curve, or by making assumptions about the planetary
interior.


  We describe an approach to calculating the cohomology rings of stable map
spaces. The method we use is due to Akildiz-Carrell and employs a C^*-action
and a vector field which is equivariant with respect to this C^*-action. We
give an explicit description of the big Bialynicky-Birula cell of the
C^*-action on Mbar_00(P^n,d) as a vector bundle on Mbar_0d. This is used to
calculate explicitly the cohomology ring of Mbar_00(P^n,d) in the cases d=2 and
d=3. Of particular interest is the case as n approaches infinity.


  We introduce and study a semigroup structure on the set of irreducible
components of the Hurwitz space of marked coverings of a complex projective
curve with given Galois group of the coverings and fixed ramification type. As
application, we give new conditions on the ramification type that are
sufficient for irreducibility of the Hurwitz spaces, suggest some bounds on the
number of irreducibility components under certain more general conditions, and
show that the number of irreducible components coincides with the number of
topological classes of the coverings if the number of brunch points is big
enough.


  Although there have been many experimental and theoretical efforts to measure
and interpret small deviations from the standard model of particle physics, the
gap that the model leaves in understanding why there are only three generations
of elementary fermions, with hierarchical masses, has not received the
attention it deserves. I present here an attempt to fill this gap. Although our
findings are mostly only qualitative, they nevertheless may be of heuristic
value. Rules concerning the elementary fermions, some previously known and some
new, lead to a number of conclusions and questions that seem worth pursuing.
Some clarify the standard model, and others suggest possible modifications, the
implications of which are discussed.


  We solve for the spectrum of quantum spin chains based on representations of
the Temperley-Lieb algebra associated with the quantum groups ${\cal U}_q(X_n }
for $X_n = A_1,B_n,C_n$ and $D_n$. We employ a generalization of the coordinate
Bethe-Ansatz developed previously for the deformed biquadratic spin one chain.
As expected, all these models have equivalent spectra, i.e. they differ only in
the degeneracy of their eigenvalues. This is true for finite length and open
boundary conditions. For periodic boundary conditions the spectra of the lower
dimensional representations are containded entirely in the higher dimensional
ones. The Bethe states are highest weight states of the quantum group, except
for some states with energy zero.


  The log-aesthetic curve has a significant factor in the field of aesthetic
design to meet the high industrial requirements. It has much exceptional
property and a large number of research papers are published, since its
introduction. It can be parametrized by tangential angle, and it is
autoevolute, meaning that its evolute is also a log-aesthetic curve. In this
paper, we will examine the isoptics of the log-aesthetic curve and determine if
it is autoisoptic as well. We will show that the log-aesthetic curve only
coincides its isoptic in some specific cases. We will also provide a new
formula to calculate the isoptic curve of any tangential angle parametrized
curves.


  High-energy photon-proton interactions at the LHC offer interesting
possibilities for the study of top properties. Using a fast simulation of a
LHC-like detector, first results on the measurement of the |V_{tb}| matrix
element using Wt photoproduction are presented. Anomalous photoproduction of
single top due to Flavour-Changing Neutral Currents permits to improve the
current limits on the coupling parameters, k_{tu\gamma} and k_{tc\gamma} after
only 1 fb^{-1}.


  New formulas are given for Chow forms, discriminants and resultants arising
from (not necessarily normal) toric varieties of codimension 2. Exact
descriptions are also given for the secondary polygon and for the Newton
polygon of the discriminant.


  Different wavelength regimes and methods for estimating the space density of
the star-formation rate (SFR) result in discrepant values. While it is
recognised that ultra-violet (UV) and H-alpha emission line data must be
corrected for the effects of extinction, the magnitude of the required
correction is uncertain. Even when these corrections are made there remains a
significant discrepancy between SFRs derived from UV and H-alpha measurements
compared with those derived from far-infrared (FIR) and radio luminosities.
Since the FIR/radio derived SFRs are not affected by extinction, and simple
corrections to reconcile the UV and H-alpha measurement with these do not fully
account for the discrepancies, a more sophisticated correction may be required.
Recent results suggest that at least part of the solution may be a form of
extinction which increases with increasing SFR (or luminosity, given the common
assumption that SFR is proportional to luminosity). We present an analysis of
the effects of a dust reddening dependent on star formation rate applied to
estimators of SFR. We show (1) that the discrepancies between H-alpha and
FIR/radio SFR estimates may be explained by such an effect, and we present an
iterative method for applying the correction; and (2) UV-based estimates of SFR
are harder to reconcile with FIR/radio estimates using this method, although
the extent of the remaining discrepancy is less than for a non-SFR-dependent
correction. Particularly at high redshift, our understanding of extinction at
UV wavelengths may require a still more complex explanation.


  The kinetic energy of solid neon is calculated by a path-integral Monte Carlo
approach with a refined Trotter- and finite-size extrapolation. These accurate
data present significant quantum effects up to temperature T=20 K. They confirm
previous simulations and are consistent with recent experiments.


  It is well-known that theta characteristics on smooth plane curves over a
field of characteristic different from two are in bijection with certain smooth
complete intersections of three quadrics. We generalize this bijection to
possibly singular hypersurfaces of any dimension over arbitrary fields
including those of characteristic two. It is accomplished in terms of linear
orbits of tuples of symmetric matrices instead of smooth complete intersections
of quadrics. As an application of our methods, we give a description of the
projective automorphism groups of complete intersections of quadrics
generalizing Beauville's results.


  We run numerical simulations of strongly confined suspensions of model
spherical swimmers called "squirmers". Because of the confinement, the
Stokeslet dipoles generated by the particles are quickly screened and the
far-field flow is dominated by the source dipole for all the different kinds of
squirmers. However, we show that the collective behavior of the suspension
still depends on the self-propelling mechanism of the swimmers as polar states
can only be observed for neutral squirmers. We demonstrate that the near-field
hydrodynamic interactions play a crucial role in the alignment of the
orientation vectors of spherical particles. Moreover, we point out that the
enstrophy and the fluid fluctuations of an active suspension also depend on the
nature of the squirmers.


  Eye tracking data during reading is a useful source of information to
understand the cognitive processes that take place during language
comprehension processes. Different languages account for different brain
triggers , however there seems to be some uniform indicators. In this paper, we
describe our submission to the CMCL 2022 shared task on predicting human
reading patterns for multi-lingual dataset. Our model uses text representations
from transformers and some hand engineered features with a regression layer on
top to predict statistical measures of mean and standard deviation for 2 main
eye-tracking features. We train an end to end model to extract meaningful
information from different languages and test our model on two seperate
datasets. We compare different transformer models and show ablation studies
affecting model performance. Our final submission ranked 4th place for
SubTask-1 and 1st place for SubTask-2 for the shared task.


  Let $G$ be a finite 2-group and $K$ be a field satisfying that (i)
$\fn{char}K\ne 2$, and (ii) $\sqrt{a}\in K$ for any $a\in K$. If $G$ acts on
the rational function field $K(x,y,z)$ by monomial $K$-automorphisms, then the
fixed field $K(x,y,z)^G$ is rational (= purely transcendental) over $K$.
Applications of this theorem will be given.


  In this paper, we show how to construct for a given consistent theory $U$ a
$\Sigma^0_1$-predicate that both satisfies the L\"ob Conditions and the Kreisel
Condition ---even if $U$ is unsound. We do this in such a way that $U$ itself
can verify satisfaction of an internal version of the Kreisel Condition.


  We consider the oscillating dark energy with periodic equation of state in
two equivalent formulations: ideal fluid or scalar-tensor theory. It is shown
that such dark energy suggests the natural way for the unification of
early-time inflation with late-time acceleration. We demonstrate how it
describes the transition from deceleration to acceleration or from non-phantom
to phantom era and how it solves the coincidence problem. The occurence of
finite-time future singularity for the oscillating (phantom) universe is also
investigated.