  Inverse problems arise in a multitude of applications, where the goal is to
recover a clean signal from noisy and possibly (non)linear observations. The
difficulty of a reconstruction problem depends on multiple factors, such as the
structure of the ground truth signal, the severity of the degradation and the
complex interactions between the above. This results in natural
sample-by-sample variation in the difficulty of a reconstruction task, which is
often overlooked by contemporary techniques. Our key observation is that most
existing inverse problem solvers lack the ability to adapt their compute power
to the difficulty of the reconstruction task, resulting in subpar performance
and wasteful resource allocation. We propose a novel method that we call
severity encoding, to estimate the degradation severity of noisy, degraded
signals in the latent space of an autoencoder. We show that the estimated
severity has strong correlation with the true corruption level and can give
useful hints at the difficulty of reconstruction problems on a sample-by-sample
basis. Furthermore, we propose a reconstruction method based on latent
diffusion models that leverages the predicted degradation severities to
fine-tune the reverse diffusion sampling trajectory and thus achieve
sample-adaptive inference times. Our framework acts as a wrapper that can be
combined with any latent diffusion-based baseline solver, imbuing it with
sample-adaptivity and acceleration. We perform numerical experiments on both
linear and nonlinear inverse problems and demonstrate that our technique
greatly improves the performance of the baseline solver and achieves up to
$10\times$ acceleration in mean sampling speed.


  Integrable Heisenberg ferromagnetic equations are an important subclass of
integrable systems. The M-XCIX equation is one of a generalizations of the
Heisenberg ferromagnetic equation and are integrable. In this paper, the
Darboux transformation of the M-XCIX equation is constructed. Using the DT, a
1-soliton solution of the M-XCIX equation is presented.


  A method for segmenting water bodies in optical and synthetic aperture radar
(SAR) satellite images is proposed. It makes use of the textural features of
the different regions in the image for segmentation. The method consists in a
multiscale analysis of the images, which allows us to study the images
regularity both, locally and globally. As results of the analysis, coarse
multifractal spectra of studied images and a group of images that associates
each position (pixel) with its corresponding value of local regularity (or
singularity) spectrum are obtained. Thresholds are then applied to the
multifractal spectra of the images for the classification. These thresholds are
selected after studying the characteristics of the spectra under the assumption
that water bodies have larger local regularity than other soil types.
Classifications obtained by the multifractal method are compared quantitatively
with those obtained by neural networks trained to classify the pixels of the
images in covered against uncovered by water. In optical images, the
classifications are also compared with those derived using the so-called
Normalized Differential Water Index (NDWI).


  We report the discovery of excess K-band radiation from a metal-rich DAV
white dwarf star, WD1150-153. Our near infrared spectroscopic observations show
that the excess radiation cannot be explained by a (sub)stellar companion, and
is likely to be caused by a debris disk similar to the other DAZ white dwarfs
with circumstellar debris disks. We find that the fraction of DAZ white dwarfs
with detectable debris disks is at least 14%. We also revisit the problem of
explaining the metals in white dwarf photospheres by accretion from the
interstellar medium (ISM). We use the observed interstellar column densities
toward stars in close angular proximity and similar distance as DAZ white
dwarfs to constrain the contribution of accretion from the ISM. We find no
correlation between the accretion density required to supply metals observed in
DAZs with the densities observed in their interstellar environment, indicating
that ISM accretion alone cannot explain the presence of metals in nearby DAZ
white dwarfs. Although ISM accretion will certainly contribute, our analysis
indicates that it is not the dominant source of metals for most DAZ white
dwarfs. Instead, the growing number of circumstellar debris disks around DAZs
suggests that circumstellar material may play a more dominant role in polluting
the white dwarf atmospheres.


  Quantum batteries are energy-storing devices, governed by quantum mechanics,
that promise high charging performance thanks to collective effects. Due to its
experimental feasibility, the Dicke battery - which comprises $N$ two-level
systems coupled to a common photon mode - is one of the most promising designs
for quantum batteries. Here, we use reinforcement learning to optimize the
charging process of a Dicke battery either by modulating the coupling strength,
or the system-cavity detuning. We find that the extractable energy (ergotropy)
and quantum mechanical energy fluctuations (charging precision) can be greatly
improved with respect to standard charging strategies. Notably, the collective
speedup of the charging time can be preserved even when nearly fully charging
the battery.


  The recent experimental synthesis of the two-dimensional (2D)boron-graphdiyne
(BGDY) nanosheet has motivated us to investigate its structural, electronic,and
energy storage properties. BGDY is a particularly attractive candidate for this
purpose due to uniformly distributed pores which can bind the light-metal
atoms. Our DFTcalculations reveal that BGDY can accommodate multiple
light-metal dopants (Li, Na, K, Ca)with significantly high binding energies.
The stabilities of metal functionalized BGDY monolayers have been confirmed
through ab initio molecular dynamics simulations. Furthermore, significant
charge-transfer between the dopantsand BGDY sheet renders the metal with a
significant positive charge, which is a prerequisite for adsorbing hydrogen
(H2) molecules with appropriate binding energies.This results in exceptionally
high H2 storage capacities of 14.29, 11.11, 9.10 and 8.99 wt% for the Li, Na, K
and Ca dopants, respectively. These H2storage capacities are much higher than
many 2D materials such as graphene, graphane, graphdiyne, graphyne, C2N,
silicene, and phosphorene. Average H2 adsorption energies for all the studied
systems fall within an ideal window of 0.17-0.40 eV/H2. We have also performed
thermodynamic analysis to study the adsorption/desorption behavior of H2, which
confirmsthat desorption of the H2molecules occurs at practical conditions of
pressure and temperature.


  The $H^*H\pi$ form factor for H = B and D mesons is evaluated in a QCD sum
rule calculation. We study the Borel sum rule for the three point function of
two pseudoscalar and one vector meson currents up to order four in the operator
product expansion. The double Borel transform is performed with respect to the
heavy meson momenta. We discuss the momentum dependence of the form factors and
two different approaches to extract the $H^*H\pi$ coupling constant.


  We have theoretically explored the intrinsic spin Hall effect (SHE) in the
iron-based superconductor family with a variety of materials. The study is
motivated by an observation that, in addition to an appreciable spin-orbit
coupling in the Fe 3d states, a character of the band structure in which Dirac
cones appear below the Fermi energy may play a crucial role in producing a
large SHE. Our investigation does indeed predict a substantially large spin
Hall conductivity in the heavily hole-doped regime such as KFe$_2$As$_2$. The
magnitude of the SHE has turned out to be comparable with that for Pt despite a
relatively small spin-orbit coupling, which we identify to come from a huge
contribution from the gap opening induced by the spin-orbit coupling at the
Dirac point, which can become close to the Fermi energy for the heavy hole
doping.


  The recent realization of epitaxial SrCoO$_3$ thin films has triggered a
renewed interest in their electronic, magnetic, and ionic properties. Here we
uncover several unusual magneto-transport properties of this compound,
suggesting that it hosts persistent spin fluctuation down to low temperatures.
We achieve the metallic SrCoO$_3$ with record-low resistivity from insulating
SrCoO$_{2.5}$ by the ionic liquid gating. We find a linear relationship between
the anomalous Hall resistivity and the longitudinal resistivity, which cannot
be accounted for by the conventional mechanisms. We theoretically propose that
the impurity induced chiral spin fluctuation gives rise to such a dependence.
The existence of spin fluctuation manifests itself as negatively enhanced
magneto-resistance of SrCoO$_3$ when the temperature approaches zero. Our study
brings further insight into the unique spin state of SrCoO$_3$ and unveils a
novel skew scattering mechanism for the anomalous Hall effect.


  Recently, an anomaly of W+jets events at large invariant masses has been
reported by CDF. Many interpretations as physics beyond the Standard Model are
being offered. We show how such an invariant mass peak can arise from a slight
shift in the relative normalization of the top and WW backgrounds.


  Proper motions for several Milky Way dwarf spheroidal (dSph) galaxies have
been determined using both ground and space-based imaging. These measurements
require long baselines and repeat observations and typical errors are of order
ten milli-arcseconds per century. In this paper, we utilize the effect of
"perspective rotation" to show that systematic proper motion of some dSphs can
be determined to a similar precision using only stellar line-of-sight
velocities. We show that including the effects of small intrinsic rotation in
dSphs increases the proper motion errors by about a factor of two. We provide
error projections for future data sets, and show that proposed thirty meter
class telescopes will measure the proper motion of a few dSphs with
milli-arcsecond per century precision.


  In the current age, human lifestyle has become more knowledge oriented
leading to generation of sedentary employment. This has given rise to a number
of health and mental disorders. Mental wellness is one of the most neglected
but crucial aspects of today's world. Mental health issues can, both directly
and indirectly, affect other sections of human physiology and impede an
individual's day-to-day activities and performance. However, identifying the
stress and finding the stress trend for an individual leading to serious mental
ailments is challenging and involves multiple factors. Such identification can
be achieved accurately by fusing these multiple modalities (due to various
factors) arising from behavioral patterns. Certain techniques are identified in
the literature for this purpose; however, very few machine learning-based
methods are proposed for such multimodal fusion tasks. In this work, a
multimodal AI-based framework is proposed to monitor a person's working
behavior and stress levels. We propose a methodology for efficiently detecting
stress due to workload by concatenating heterogeneous raw sensor data streams
(e.g., face expressions, posture, heart rate, computer interaction). This data
can be securely stored and analyzed to understand and discover personalized
unique behavioral patterns leading to mental strain and fatigue. The
contribution of this work is twofold; proposing a multimodal AI-based strategy
for fusion to detect stress and its level and secondly identify a stress
pattern over a period of time. We were able to achieve 96.09% accuracy on the
test set in stress detection and classification. Further, we reduce the stress
scale prediction model loss to 0.036 using these modalities. This work can
prove important for the community at large, specifically those working
sedentary jobs to monitor and identify stress levels, especially in current
times of COVID-19.


  In order to identify expertise, forecasters should not be tested by their
calibration score, which can always be made arbitrarily small, but rather by
their Brier score. The Brier score is the sum of the calibration score and the
refinement score; the latter measures how good the sorting into bins with the
same forecast is, and thus attests to "expertise." This raises the question of
whether one can gain calibration without losing expertise, which we refer to as
"calibeating." We provide an easy way to calibeat any forecast, by a
deterministic online procedure. We moreover show that calibeating can be
achieved by a stochastic procedure that is itself calibrated, and then extend
the results to simultaneously calibeating multiple procedures, and to
deterministic procedures that are continuously calibrated.


  We consider the reflectionless transport of solitons in networks. The system
is modeled in terms of the nonlinear Schr\"odinger equation on metric graphs,
for which transparent boundary conditions at the branching points are imposed.
This allows to derive simple constraints, which link equivalent usual
Kirchhoff-type vertex conditions to the transparent ones. Our approach is
applied to a metric star graph. An extension to more complicated graph
topologies is straight forward.


  We describe a novel method for producing Greenberger-Horne-Zeilinger states
in cold atoms coupled to a superconducting coplanar cavity. In the proposed
scheme, atoms interact between each other by virtual photon exchange via a
cavity mode. These interactions cause an asymmetric Rydberg blockade mechanism
that suppresses simultaneous excitations into different atomic Rydberg levels,
thus forcing all atoms to occupy the same Rydberg state. This mechanism has
effect even if the atoms are separated by distances of the order of
millimeters. The atomic populations are transferred adiabatically from the
ground state into the entangled state by following a collective dark state with
low dissipation rates.


  The norms associated with the gradients of the two non-differential
invariants of the Kerr vacuum are examined. Whereas both locally single out the
horizons, their global behavior is more interesting. Both reflect the
background angular momentum as the volume of space allowing a timelike gradient
decreases with increasing angular momentum becoming zero in the degenerate and
naked cases. These results extend directly to the Kerr-Newman geometry.


  Wireless data communications are always facing the risk of eavesdropping and
interception. Conventional protection solutions which are based on encryption
may not always be practical as is the case for wireless IoT networks or may
soon become ineffective against quantum computers. In this regard, Physical
Layer Security (PLS) presents a promising approach to secure wireless
communications through the exploitation of the physical properties of the
wireless channel. Cooperative Friendly Jamming (CFJ) is among the PLS
techniques that have received attention in recent years. However, finding an
optimal transmit power allocation that results in the highest secrecy is a
complex problem that becomes more difficult to address as the size of the
wireless network increases. In this paper, we propose an optimization approach
to achieve CFJ in large Wi-Fi networks by using a Reinforcement Learning
Algorithm. Obtained results show that our optimization approach offers better
secrecy results and becomes more effective as the network size and the density
of Wi-Fi access points increase.


  The grain boundaries (GBs) of a graphene surface were extensively studied
because GBs with specific defect configurations result in the formation of new
curved structures, which can be treated as new carbon allotropes. We studied
the structures and electronic spectra of two periodic GBs in graphene on highly
oriented pyrolytic graphite (HOPG) surfaces using scanning tunneling microscopy
and spectroscopy (STM/S). Our results demonstrated that a GB consisting of dual
parallel periodic dislocation cores of pentagonal-heptagonal (5-7) carbon rings
gives rise to an enhanced localized state at 0.45 eV above the Dirac point in
graphene surfaces, which is attributed to van Hove singularities (VHSs).
Moreover, the energy positions of the localized states are varied between 0.40
and 0.47 eV depending on the site and eventually decayed to 0.36 eV. The
variation of the energy positions is induced by two parallel GBs because of the
higher electron density at the GB as a defect center and the lower electron
away from the GB. Another periodic GB with a symmetric zigzag structural
feature induced VHSs at -0.038 and 0.12 eV near the Fermi level. Moreover,
intervalley scattering was observed on both these GBs. This means that carrier
concentration and thus, the conductance around the periodic GBs can be
significantly enhanced by localized density of states. This finding suggests
that graphene with a properly embedded ordered GB is promising for improving
the performance of graphene-based electronic devices.


  We examine the running vacuum model with $\Lambda (H) = 3 \nu H^2 +
\Lambda_0$, where $\nu$ is the model parameter and $\Lambda_0$ is the
cosmological constant. From the data of the cosmic microwave background
radiation, weak lensing and baryon acoustic oscillation along with the time
dependent Hubble parameter $H(z)$ and weighted linear growth $f (z)\sigma_8(z)$
measurements, we find that $\nu=(1.37^{+0.72}_{-0.95})\times 10^{-4}$ with the
best fitted $\chi^2$ value slightly smaller than that in the $\Lambda$CDM
model.


  We prove the $\mathbb{Q}$-factoriality of a nodal hypersurface in
$\mathbb{P}^{4}$ of degree $n$ with at most ${\frac{(n-1)^{2}}{4}}$ nodes and
the $\mathbb{Q}$-factoriality of a double cover of $\mathbb{P}^{3}$ branched
over a nodal surface of degree $2r$ with at most ${\frac{(2r-1)r}{3}}$ nodes.


  The Sparse Mixture of Experts (SMoE) has been widely employed to enhance the
efficiency of training and inference for Transformer-based foundational models,
yielding promising results. However, the performance of SMoE heavily depends on
the choice of hyper-parameters, such as the number of experts and the number of
experts to be activated (referred to as top-k), resulting in significant
computational overhead due to the extensive model training by searching over
various hyper-parameter configurations. As a remedy, we introduce the Dynamic
Mixture of Experts (DynMoE) technique. DynMoE incorporates (1) a novel gating
method that enables each token to automatically determine the number of experts
to activate. (2) An adaptive process automatically adjusts the number of
experts during training. Extensive numerical results across Vision, Language,
and Vision-Language tasks demonstrate the effectiveness of our approach to
achieve competitive performance compared to GMoE for vision and language tasks,
and MoE-LLaVA for vision-language tasks, while maintaining efficiency by
activating fewer parameters. Our code is available at
https://github.com/LINs-lab/DynMoE.


  We apply the metrical approach to Sobolev spaces, which arise in various
evolution PDEs. Functions from those spaces are defined on an interval and take
values in a family of Banach spaces. In this case we adapt the definition of
Newtonian spaces. For a monotone family, we show the existence of weak
derivative, obtain an isomorphism to the standard Sobolev space, and provide
some scalar characteristics.


  This paper describes the PySLHA package, a Python language module and program
collection for reading, writing and visualising SUSY model data in the SLHA
format. PySLHA can read and write SLHA data in a very general way, including
the official SLHA2 extension and user customisations, and with arbitrarily deep
indexing of data block entries and a dedicated, intuitive interface for
particle data and decay information. PySLHA can additionally read and write the
legacy ISAWIG model format, and provides format conversion scripts. The draft
SLHA3 XSECTION feature is also fully supported. A publication-quality mass
spectrum & decay chain plotting tool, slhaplot, is also included.


  Convex relaxations of the power flow equations and, in particular, the
Semi-Definite Programming (SDP), Second-Order Cone (SOC), and Convex DistFlow
(CDF) relaxations, have attracted significant interest in recent years. Thus
far, studies of the CDF model and its connection to the other relaxations have
been limited to power distribution systems, which omit several parameters
necessary for modeling transmission systems. To increase the applicability of
the CDF relaxation, this paper develops an extended CDF model that is suitable
for transmission systems by incorporating bus shunts, line charging, and
transformers. Additionally, a theoretical result shows that the established
equivalence of the SOC and CDF models for distribution systems also holds in
this transmission system extension.


  Two averaging algorithms are considered which are intended for choosing an
optimal plane and an optimal circle approximating a group of points in
three-dimensional Euclidean space.


  We discuss the physics of the mirror (shadow) world which is completely
analogous to the visible one except that its `weak' scale is larger by one or
two orders of magnitude than the weak scale in the standard model. The mirror
neutrinos can mix the ordinary ones through the Planck scale induced higher
order operators, which can help to reconcile the present neutrino puzzles that
are the solar and atmospheric neutrino deficits, the recent LSND anomaly and
the need in the $\sim$ eV mass neutrino as the hot dark matter. In particular,
oscillation of $\nu_e$ into its mirror partner $\nu'_e$ emerges with parameters
naturally in the MSW range. The nucleosynthesis constraint on the extra light
particle species can be fulfilled by assuming the asymmetric postinflationary
reheating between the usual and mirror worlds. One implication of our proposal
is that bulk of the dark matter in the universe may be a warm dark matter
consisting of the keV range mirror neutrinos rather than the conventional cold
dark matter, while the mirror baryons can also contribute as dissipative dark
matter. Implications of the mirror Machos for microlensing experiments are also
discussed. [Talk given at the XIX int. conference on `Particle Physics and
Astrophysics in the Standard Model and Beyond', Bystra, Poland, 19-26 September
1995 (to appear on Proceedings). Based on refs. \cite{BM,BDM} done in
collaboration with A.D. Dolgov and R.N. Mohapatra]


  This paper describes our experiments with automatically identifying native
accents from speech samples of non-native English speakers using low level
audio features, and n-gram features from manual transcriptions. Using a
publicly available non-native speech corpus and simple audio feature
representations that do not perform word/phoneme recognition, we show that it
is possible to achieve close to 90% classification accuracy for this task.
While character n-grams perform similar to speech features, we show that speech
features are not affected by prompt variation, whereas ngrams are. Since the
approach followed can be easily adapted to any language provided we have enough
training data, we believe these results will provide useful insights for the
development of accent recognition systems and for the study of accents in the
context of language learning.


  This paper provides two characterizations of the primitive roots of unity in
quadratic cyclotomic extensions over arbitrary fields. Firstly, we introduce a
mapping from $\mathbb{N}$ to $\mathbb{N}$ crucial for describing these roots,
closely tied to their order over the field. Secondly, for any prime $p$, we
determine the maximal natural number $n$ such that $\zeta_{p^n}$ defines a
quadratic cyclotomic extension over the field $F$. This characterization is
uniform across different fields, regardless of their characteristic, and
applies to both odd and even primes.


  New recursive equations designed for the G/G/m queue are presented. These
equations describe the queue in terms of recursions for the arrival and
departure times of customers, and involve only the operations of maximum,
minimum and addition.


  Thermal functional circuits are an interesting and perspectivic group of the
MEMS elements. A practical realization is called Quadratic Transfer
Characteristic (QTC) element which driving principle is the Seebeck-effect. In
this paper we present the analyses of a QTC element from different
perspectives. To check the real behavior of the device, we measured a few,
secondary properties of the structure which correspond to special behavior
because these properties can not be easily derived from the main
characteristics.


  Context. The XXL Survey is the largest survey carried out by the XMM-Newton
satellite and covers a total area of 50 square degrees distributed over two
fields. It primarily aims at investigating the large-scale structures of the
Universe using the distribution of galaxy clusters and active galactic nuclei
as tracers of the matter distribution.
  Aims. This article presents the XXL bright cluster sample, a subsample of 100
galaxy clusters selected from the full XXL catalogue by setting a lower limit
of $3\times 10^{-14}\,\mathrm{erg \,s^{-1}cm^{-2}}$ on the source flux within a
1$^{\prime}$ aperture.
  Methods. The selection function was estimated using a mixture of Monte Carlo
simulations and analytical recipes that closely reproduce the source selection
process. An extensive spectroscopic follow-up provided redshifts for 97 of the
100 clusters. We derived accurate X-ray parameters for all the sources. Scaling
relations were self-consistently derived from the same sample in other
publications of the series. On this basis, we study the number density,
luminosity function, and spatial distribution of the sample.
  Results. The bright cluster sample consists of systems with masses between
$M_{500}=7\times 10^{13}$ and $3\times 10^{14} M_\odot$, mostly located between
$z=0.1$ and 0.5. The observed sky density of clusters is slightly below the
predictions from the WMAP9 model, and significantly below the predictions from
the Planck 2015 cosmology. In general, within the current uncertainties of the
cluster mass calibration, models with higher values of $\sigma_8$ and/or
$\Omega_m$ appear more difficult to accommodate. We provide tight constraints
on the cluster differential luminosity function and find no hint of evolution
out to $z\sim1$. We also find strong evidence for the presence of large-scale
structures in the XXL bright cluster sample and identify five new
superclusters.


  The importance of collimator R&D with test beam facilities is demonstrated
with the example of ILC collimator studies at SLAC End Station A. Related LHC
collimator aspects and longer term plans are addressed.


  In this paper, we study the pooled data problem of identifying the labels
associated with a large collection of items, based on a sequence of pooled
tests revealing the counts of each label within the pool. In the noiseless
setting, we identify an exact asymptotic threshold on the required number of
tests with optimal decoding, and prove a phase transition between complete
success and complete failure. In addition, we present a novel noisy variation
of the problem, and provide an information-theoretic framework for
characterizing the required number of tests for general random noise models.
Our results reveal that noise can make the problem considerably more difficult,
with strict increases in the scaling laws even at low noise levels. Finally, we
demonstrate similar behavior in an approximate recovery setting, where a given
number of errors is allowed in the decoded labels.


  Inspired by the Borcherds' work on ``$G$-vertex algebras,'' we formulate and
study an axiomatic counterpart of Borcherds' notion of $G$-vertex algebra for
the simplest nontrivial elementary vertex group, which we denote by $G_{1}$.
Specifically, we formulate a notion of axiomatic $G_{1}$-vertex algebra, prove
certain basic properties and give certain examples, where the notion of
axiomatic $G_{1}$-vertex algebra is a nonlocal generalization of the notion of
vertex algebra. We also show how to construct axiomatic $G_{1}$-vertex algebras
from a set of compatible $G_{1}$-vertex operators.
  The results of this paper were reported in June 2001, at the International
Conference on Lie Algebras in the Morningside center, Beijing, China, and were
reported on November 30, 2001, in the Quantum Mathematics Seminar, at
Rutgers-New Brunswick. We noticed that a paper of Bakalov and Kac appeared
today (math.QA/0204282) on noncommutative generalizations of vertex algebras,
which has certain overlaps with the current paper. On the other hand, most of
their results are orthogonal to the results of this paper.


  Conservative Policy Iteration (CPI) is a founding algorithm of Approximate
Dynamic Programming (ADP). Its core principle is to stabilize greediness
through stochastic mixtures of consecutive policies. It comes with strong
theoretical guarantees, and inspired approaches in deep Reinforcement Learning
(RL). However, CPI itself has rarely been implemented, never with neural
networks, and only experimented on toy problems. In this paper, we show how CPI
can be practically combined with deep RL with discrete actions. We also
introduce adaptive mixture rates inspired by the theory. We experiment
thoroughly the resulting algorithm on the simple Cartpole problem, and validate
the proposed method on a representative subset of Atari games. Overall, this
work suggests that revisiting classic ADP may lead to improved and more stable
deep RL algorithms.


  We study the behavior of Range Voting and Normalized Range Voting with
respect to electoral control. Electoral control encompasses attempts from an
election chair to alter the structure of an election in order to change the
outcome. We show that a voting system resists a case of control by proving that
performing that case of control is computationally infeasible. Range Voting is
a natural extension of approval voting, and Normalized Range Voting is a simple
variant which alters each vote to maximize the potential impact of each voter.
We show that Normalized Range Voting has among the largest number of control
resistances among natural voting systems.


  We present a general method for privacy-preserving Bayesian inference in
Poisson factorization, a broad class of models that includes some of the most
widely used models in the social sciences. Our method satisfies limited
precision local privacy, a generalization of local differential privacy, which
we introduce to formulate privacy guarantees appropriate for sparse count data.
We develop an MCMC algorithm that approximates the locally private posterior
over model parameters given data that has been locally privatized by the
geometric mechanism (Ghosh et al., 2012). Our solution is based on two
insights: 1) a novel reinterpretation of the geometric mechanism in terms of
the Skellam distribution (Skellam, 1946) and 2) a general theorem that relates
the Skellam to the Bessel distribution (Yuan & Kalbfleisch, 2000). We
demonstrate our method in two case studies on real-world email data in which we
show that our method consistently outperforms the commonly-used naive approach,
obtaining higher quality topics in text and more accurate link prediction in
networks. On some tasks, our privacy-preserving method even outperforms
non-private inference which conditions on the true data.


  Asymmetric microcavities supporting Whispering-gallery modes (WGMs) are of
great significance for on-chip optical information processing. We define
asymmetric microcavities on topologically curved surfaces, where the geodesic
light trajectories completely reconstruct the cavity mode features. The quality
factors of the lossy chaotic and island modes in flat cavities can be increased
by up to ~200 times by the space curvature. Strong and weak coupling between
modes of very different origins occur when the space curvature brings them into
resonance, leading to a fine tailoring of the cavity photon energy and
lifetime. Finally, we prove that by varying the overall loss, an exceptional
point can be clearly observed at which both the cavity photon energy and
lifetime become degenerate. Our work is at the crosspoint of optical chaotic
dynamics, non-Hermitian physics and geodesic optical devices, and would open
the novel area of geodesic microcavity photonics.


  On the basis of morphological analysis of yearly values of the maximum CME
(coronal mass ejection) speed index, the sunspot number and total sunspot area,
sunspot magnetic field, and solar flare index, the solar wind speed and
interplanetary magnetic field strength, and the geomagnetic Ap and Dst indices,
we point out the particularities of solar and geomagnetic activity during the
last cycle 23, the long minimum which followed it and the ascending branch of
cycle 24. We also analyze temporal offset between the maximum CME speed index
and the above-mentioned solar, geomagnetic, and interplanetary indices. It is
found that this solar activity index, analyzed jointly with other solar
activity, interplanetary parameters, and geomagnetic activity indices, shows a
hysteresis phenomenon. It is observed that these parameters follow different
paths for the ascending and the descending phases of solar cycle 23. It is
noticed that the hysteresis phenomenon represents a clue in the search for
physical processes responsible for linking the solar activity to the near-Earth
and geomagnetic responses.


  I discuss possible identification of the recently discovered mesons
$D_{sJ}(2860)$ and $D_{sJ}(2700)$.
  This paper is dedicated to the memory of my professor, colleague and friend
Beppe Nardulli.


  We show that a standard conic bundle over a minimal rational surface is
rational and its Jacobian splits as the direct sum of Jacobians of curves if
and only if its derived category admits a semiorthogonal decomposition by
exceptional objects and the derived categories of those curves. Moreover, such
a decomposition gives the splitting of the intermediate Jacobian also when the
surface is not minimal.


  Let $R$ be a commutative ring with one and $q$ an invertible element of $R$.
The (specialized) quantum group ${\mathbf U} = U_q(\mathfrak{gl}_n)$ over $R$
of the general linear group acts on mixed tensor space $V^{\otimes r}\otimes
{V^*}^{\otimes s}$ where $V$ denotes the natural $\mathbf U$-module $R^n$,
$r,s$ are nonnegative integers and $V^*$ is the dual $\mathbf U$-module to $V$.
The image of $\mathbf U$ in $\mathrm{End}_R(V^{\otimes r}\otimes {V^*}^{\otimes
s})$ is called the rational $q$-Schur algebra $S_{q}(n;r,s)$. We construct a
bideterminant basis of $S_{q}(n;r,s)$. There is an action of a $q$-deformation
$\mathfrak{B}_{r,s}^n(q)$ of the walled Brauer algebra on mixed tensor space
centralizing the action of $\mathbf U$. We show that
$\mathrm{End}_{\mathfrak{B}_{r,s}^n(q)}(V^{\otimes r}\otimes {V^*}^{\otimes
s})=S_{q}(n;r,s)$. By \cite{dipperdotystoll} the image of
$\mathfrak{B}_{r,s}^n(q)$ in $\mathrm{End}_R(V^{\otimes r}\otimes
{V^*}^{\otimes s})$ is $\mathrm{End}_{\mathbf U}(V^{\otimes r}\otimes
{V^*}^{\otimes s})$. Thus mixed tensor space as $\mathbf
U$-$\mathfrak{B}_{r,s}^n(q)$-bimodule satisfies Schur-Weyl duality.


  The discovery of unconventional superconductivity in hole doped NdNiO2,
similar to CaCuO2, has received enormous attention. However, different from
CaCuO2, RNiO2 (R = Nd, La) has itinerant electrons in the rare-earth spacer
layer. Previous studies show that the hybridization between Ni-dx2-y2 and
rare-earth-d orbitals is very weak and thus RNiO2 is still a promising analog
of CaCuO2. Here, we perform first-principles calculations to show that the
hybridization between Ni-dx2-y2 orbital and itinerant electrons in RNiO2 is
substantially stronger than previously thought. The dominant hybridization
comes from an interstitial-s orbital rather than rare-earth-d orbitals, due to
a large inter-cell hopping. Because of the hybridization, Ni local moment is
screened by itinerant electrons and the critical U_Ni for long-range magnetic
ordering is increased. Our work shows that the electronic structure of RNiO2 is
distinct from CaCuO2, implying that the observed superconductivity in
infinite-layer nickelates does not emerge from a doped Mott insulator.


  Regret theory is a theory that describes human decision-making under risk.
The key of obtaining a quantitative model of regret theory is to measure the
preference in humans' mind when they choose among a set of options. Unlike
physical quantities, measuring psychological preference is not procedure
invariant, i.e. the readings alter when the methods change. In this work, we
alleviate this influence by choosing the procedure compatible with the way that
an individual makes a choice. We believe the resulting model is closer to the
nature of human decision-making. The preference elicitation process is
decomposed into a series of short surveys to reduce cognitive workload and
increase response accuracy. To make the questions natural and familiar to the
subjects, we follow the insight that humans generate, quantify and communicate
preference in natural language. The fuzzy-set theory is hence utilized to model
responses from subjects. Based on these ideas, a graphical human-computer
interface (HCI) is designed to articulate the information as well as to
efficiently collect human responses. The design also accounts for human
heuristics and biases, e.g. range effect and anchoring effect, to enhance its
reliability. The overall performance of the survey is satisfactory because the
measured model shows prediction accuracy equivalent to the revisit-performance
of the subjects.


  We consider the pulsar rotation assuming that the neutron star consists of
crust component (which rotation is observed) and two core components. One of
the core components contains pinned superfluid which can, for some reasons,
suddenly inject small fraction of stored angular momentum in it. In the
framework of this simple model the star can demonstrate glitch-like events
together with long period precession (with period $1-10^{4}$ years).


  Variational autoencoders (VAE) represent a popular, flexible form of deep
generative model that can be stochastically fit to samples from a given random
process using an information-theoretic variational bound on the true underlying
distribution. Once so-obtained, the model can be putatively used to generate
new samples from this distribution, or to provide a low-dimensional latent
representation of existing samples. While quite effective in numerous
application domains, certain important mechanisms which govern the behavior of
the VAE are obfuscated by the intractable integrals and resulting stochastic
approximations involved. Moreover, as a highly non-convex model, it remains
unclear exactly how minima of the underlying energy relate to original design
purposes. We attempt to better quantify these issues by analyzing a series of
tractable special cases of increasing complexity. In doing so, we unveil
interesting connections with more traditional dimensionality reduction models,
as well as an intrinsic yet underappreciated propensity for robustly dismissing
sparse outliers when estimating latent manifolds. With respect to the latter,
we demonstrate that the VAE can be viewed as the natural evolution of recent
robust PCA models, capable of learning nonlinear manifolds of unknown dimension
obscured by gross corruptions.


  We have monitored the 2014 superoutburst of the WZ Sge-type transient PNV
J03093063+2638031 for more than four months, from V=11.0 maximum brightness
down to V=18.4 mag, close to quiescence value, by obtaining BVRI photometry and
low resolution fluxed spectroscopy. The evolution was normal and no late-time
`echo' outbursts were observed. The absolute integrated flux of emission lines
kept declining along the superoutburst, and their increasing contrast with the
underlying continuum was simply the result of the faster decline of the
continuum compared to the emission lines. Inspection of historical Harvard
plates covering the 1899-1981 period did not reveal previous outbursts, neither
`normal' nor 'super'. We discovered an extended emission nebula (radius ~1
arcmin) around PNV J03093063+2638031, that became visible for a few months as
the result of photo-ionization from the superoutburst of the central star. It
is not present on Palomar I and II sky survey images and it quickly disappeared
when the outburst was over. From the rate at wich the inization front swept
through the nebula, we derive a distance of ~120 pc to the system. The nebula
is density bounded with an outer radius of 0.03 pc, and the absolute magnitude
of the central star in quiescence is M(V)~14.2 mag. The electron density in the
nebula is estimated to be 10(+5) cm(-3) from the observed recombination time
scale. Given the considerable substructures seen across the nebula, a low
filling factor is inferred. Similar nebulae have not been reported for other WZ
Sge objects and the challenges posed to models are considered.


  Recent results on rare kaon and pion decays are reviewed and prospects for
future experiments are discussed


  We study non-invertible piecewise hyperbolic maps in the plane. The Hausdorff
dimension of the attractor is calculated in terms of the Lyapunov exponents,
provided that the map satisfies a transversality condition. Explicit examples
of maps for which this condition holds are given.


  Textbooks state that the successful application of Maxwell's Equations in
physical optics problems requires light to interact with matter where any
inhomogeneities are spaced by less than or equal to the wavelength of light;
the 'dense' limit. This untested statement is proved correct in the experiment
reported here and a precise dense limit is found. A 'matter field microscope'
is used. The dense limit appears exactly when the (approximately fixed) optical
wavenumber coincides with the (rapidly increasing) spatial frequency for a
discontinuous matter field as it develops from a dilute to a concentrated
material system. It is inferred that in the dilute material system examined
here plane wave methods are only valid over a well-defined, but restricted,
transverse dimension which is introduced here as the 'wavewidth'. This appears
to reveal a natural sub-wavelength mode structure for light. This result then
allows the application of the uncertainty relation to describe a longitudinal
spatial restriction of the light when crossing matter density interfaces.
Physical optics using 'spatial' rays and 'spatial' photons can then be
described on this model for light.


  A cutting sequence is a symbolic coding of a linear trajectory on a
translation surface corresponding to the sequence of sides hit in a polygonal
representation of the surface. We characterize cutting sequences in a regular
hexagon with opposite sides identified by translations exploiting the same
procedure used by Smillie and Ulcigrai for the regular octagon. In the case of
the square, cutting sequences are the well known Sturmian sequences. We remark
the differences between the procedure used in the case of the square and the
one used in the cases of the regular hexagon and regular octagon. We also show
how to adapt the latter to work also in the case of the square, giving a new
characterization for this case. We also show how to create a dictionary to pass
from the symbolic coding with respect to the hexagon to the symbolic coding
with respect to the parallelogram representing it in the space of flat tori.
Finally we consider the Bouw-M\"oller surfaces $\mathscr M(3,4)$ and $\mathscr
M(4,3)$ and we use their semi-regular polygons representations to prove our
main result, which is a theorem analogous to the central step used to
characterize cutting sequences in the previous cases.


  In these lecture notes I discussed the importance of phase correlations for
the morphology of large-scale structure and how phase analysis can probe
primordial non-Gaussianity and/or foreground contamination in CMB temperature
maps. I illustrate the ideas with application to the preliminary WMAP
first-year data. I also briefly introduce topological characteristics such as
the genus and Minkowski functionals, and how they provide a real-space
diagnostic of phase correlations.


  We report on our progress towards continuum rate equation modeling, as well
as numerical simulations, of self-healing of fatigue in composites reinforced
with glue carrying nanoporous fibers. We conclude that with the proper choice
of the material parameters, effects of fatigue can be partially overcome and
degradation of mechanical properties can be delayed.


  An effective integration method based on the classical solution to the Jacobi
inversion problem, using Kleinian ultra-elliptic functions, is presented for
quasi-periodic two-phase solutions of the focusing nonlinear Schr\"odinger
equation. The two-phase solutions with real quasi-periods are known to form a
two-dimensional torus, modulo a circle of complex phase factors, that can be
expressed as a ratio of theta functions. In this paper, the two-phase solutions
are explicitly parametrized in terms of the branch points on the genus-two
Riemann surface of the theta functions. Simple formulas, in terms of the
imaginary parts of the branch points, are obtained for the maximum modulus and
the minimum modulus of the two-phase solution.


  For a long time, Collatz Conjecture has been assumed to be true, although a
formal proof has eluded all efforts to date. In this article, evidence is
presented that suggests such an assumption is incorrect. By analysing the
stopping times of various Collatz sequences, a pattern emerges that indicates
the existence of non-empty sets of integers with stopping times greater than
any given integer. This implies the existence of an infinite set of integers
with non-finite stopping times, thus indicating the conjecture is false.
Furthermore, a simple algorithm is constructed that finds integers with
ever-greater stopping times. Such an algorithm does not halt, further
supporting the conclusion that the conjecture is false.


  (abridged) In the frame of the search for extrasolar planets and brown dwarfs
around early-type main-sequence stars, we present the results obtained on the
early F-type star Theta Cygni. Elodie and Sophie at OHP were used to obtain the
spectra. Our dedicated radial-velocity measurement method was used to monitor
the star's radial velocities over five years. We also use complementary, high
angular resolution and high-contrast images taken with PUEO at CFHT. We show
that Theta Cygni radial velocities are quasi-periodically variable, with a
~150-day period. These variations are not due to the ~0.35-Msun stellar
companion that we detected in imaging at more than 46 AU from the star. The
absence of correlation between the bisector velocity span variations and the
radial velocity variations for this 7 km/s vsini star, as well as other
criteria indicate that the observed radial velocity variations are not due to
stellar spots. The observed amplitude of the bisector velocity span variations
also seems to rule out stellar pulsations. However, we observe a peak in the
bisector velocity span periodogram at the same period as the one found in the
radial velocity periodogram, which indicates a probable link between these
radial velocity variations and the low amplitude lineshape variations which are
of stellar origin. Long-period variations are not expected from this type of
star to our knowledge. If a stellar origin (hence of new type) was to be
confirmed for these long-period radial velocity variations, this would have
several consequences on the search for planets around main-sequence stars, both
in terms of observational strategy and data analysis. An alternative
explanation for these variable radial velocities is the presence of at least
one planet of a few Jupiter masses orbiting at less than 1 AU. (abridged)


  Because protein-protein interactions (PPIs) are crucial to understand living
systems, harvesting these data is essential to probe disease development and
discern gene/protein functions and biological processes. Some curated datasets
contain PPI data derived from the literature and other sources (e.g., IntAct,
BioGrid, DIP, and HPRD). However, they are far from exhaustive, and their
maintenance is a labor-intensive process. On the other hand, machine learning
methods to automate PPI knowledge extraction from the scientific literature
have been limited by a shortage of appropriate annotated data. This work
presents a unified, multi-source PPI corpora with vetted interaction
definitions augmented by binary interaction type labels and a Transformer-based
deep learning method that exploits entities' relational context information for
relation representation to improve relation classification performance. The
model's performance is evaluated on four widely studied biomedical relation
extraction datasets, as well as this work's target PPI datasets, to observe the
effectiveness of the representation to relation extraction tasks in various
data. Results show the model outperforms prior state-of-the-art models. The
code and data are available at:
https://github.com/BNLNLP/PPI-Relation-Extraction


  We investigate the impact of content sequencing on student learning outcomes
in a first-year university electromagnetism course. Using a custom-built online
system, the McGill Learning Platform (McLEAP), we test student problem-solving
performance as a function of the sequence in which the students are presented
aspects of new material. New material was divided into the three categories of
conceptual, theoretical and example-based content. Here, we present findings
from a two-year study with over 1000 students participating. We find that
content sequencing has a significant impact on learning outcomes in our study:
students presented with conceptual content first perform significantly better
on our assessment than those presented with theoretical content. To explain
these results, we propose the Content Cube as an extension to the the mental
model frameworks. Additionally, we find that instructors' preferences for
content sequencing differ significantly from that of students. We discuss how
this information can be used to improve course instruction and student
learning, and motivate future work building upon our presented results to study
the impact of additional factors on student performance.


  Very-high energy observations of blazars can be used to constrain the
strength of the intergalactic magnetic field. A simplifying assumption which is
often made is that of a magnetic field of constant strength composed by
randomly oriented and identical cells. In this paper, we demonstrate that a
more realistic description of the structure of the intergalactic magnetic field
is indeed needed. If such a description is adopted, the observational bounds on
the field strength are significantly affected in the limit of short field
correlation lengths: in particular, they acquire a dependence on the magnetic
field power spectrum. In the case of intergalactic magnetic fields which are
generated causally, for which the magnetic field large scale spectral index is
$n_B\geq 2$ and even, the observational lower bound becomes more constraining
by about a factor 3. If instead $-3<n_B<-2$, the lower bound is significantly
relaxed. Such magnetic fields with very red spectra can in principle be
produced during inflation, but remain up to now speculative.


  Spin motive force is a spin-dependent force on conduction electrons induced
by magnetization dynamics. In order to examine its effects on magnetization
dynamics, it is indispensable to take into account spin accumulation, spin
diffusion, and spin-flip scattering since the spin motive force is in general
nonuniform. We examine the effects of all these on the way the spin motive
force generates the charge and spin currents in conventional situations, where
the conduction electron spin relaxation dynamics is much faster than the
magnetization dynamics. When the spin-dependent electric field is spatially
localized, which is common in experimental situations, we find that the
conservative part of the spin motive force is unable to generate the charge
current due to the cancelation effect by the diffusion current. We also find
that the spin current is a nonlocal function of the spin motive force and can
be effectively expressed in terms of nonlocal Gilbert damping tensor. It turns
out that any spin independent potential such as Coulomb potential does not
affect our principal results. At the last part of this paper, we apply our
theory to current-induced domain wall motion.


  ALHAMBRA is a project to gather data to sample a fraction of the Universe
with enough precision to follow the evolution of its content and properties
with z, a kind of Cosmic Tomography. It is defined as a 4 square degrees
photometric survey with 20 contiguous, equal width, medium band filters
covering from 3500 to 9700 A, plus the JHKs NIR bands. It was optimized to get
(for a fixed observing time) the maximum number of objects with accurate
classification and redshift and to be sensitive to relatively faint emission
features. The observations will be carried out with the 3.5m telescope in Calar
Alto (Spain). We intend to reach the limit AB=25 in all the optical filters
from the bluest to 8300 A, and from 24.7 to 23.4 for the remainder. The
expected limit in the NIR is fixed at Ks=20, H=21, J=22. The homogeneous and
contiguous spectral coverage will result in several hundred thousand objects
with accurate SED identification and z-values. The accuracy of the survey will
allow to make detailed studies, including galactic, without the need for any
further follow-up. Indeed, it will provide exciting targets for large
telescopes, the GTC in particular.


  We measured spin transport in nonferromagnetic (NM) metallic multilayers from
the contribution to damping due to spin pumping from a ferromagnetic Co90Fe10
thin film. The multilayer stack consisted of NM1/NM2/Co90Fe10(2 nm)/NM2/NM3
with varying NM materials and thicknesses. Using conventional theory for one
dimensional diffusive spin transport in metals, we show that the effective
damping due to spin pumping can be strongly affected by the spin transport
properties of each NM in the multilayer, which permits the use of damping
measurements to accurately determine the spin transport properties of the
various NM layers in the full five-layer stack. We find that due to its high
electrical resistivity, amorphous Ta is a poor spin conductor, in spite of a
short spin-diffusion length of 1.0 nm, and that Pt is an excellent spin
conductor by virtue of its low electrical resistivity and a spin diffusion
length of only 0.5 nm. Spin Hall effect measurements may have underestimated
the spin Hall angle in Pt by assuming a much longer spin diffusion length.


  A monolithic process is a single recursive equation with data parameters,
which only uses non-determinism, action prefixing, and recursion. We present a
technique that decomposes such a monolithic process into multiple processes
where each process defines behaviour for a subset of the parameters of the
monolithic process. For this decomposition we can show that a composition of
these processes is strongly bisimilar to the monolithic process under a
suitable synchronisation context. Minimising the resulting processes before
determining their composition can be used to derive a state space that is
smaller than the one obtained by a monolithic exploration. We apply the
decomposition technique to several specifications to show that this works in
practice. Finally, we prove that state invariants can be used to further
improve the effectiveness of this decomposition technique.


  We investigate necessary conditions for Gorenstein projective varieties to
admit semiorthogonal decompositions introduced by Kawamata, with main emphasis
on threefolds with isolated compound $A_n$ singularities. We introduce
obstructions coming from Algebraic $\mathrm{K}$-theory and translate them into
the concept of maximal nonfactoriality.
  Using these obstructions we show that many classes of nodal threefolds do not
admit Kawamata type semiorthogonal decompositions. These include nodal
hypersurfaces and double solids, with the exception of a nodal quadric, and del
Pezzo threefolds of degrees $1 \le d \le 4$ with maximal class group rank.
  We also investigate when does a blow up of a smooth threefold in a singular
curve admit a Kawamata type semiorthogonal decomposition and we give a complete
answer to this question when the curve is nodal and has only rational
components.


  The aim of this paper is to study a wide class of non-convex sweeping
processes with moving constraint whose translation and deformation are
represented by regulated functions, i.e., functions of not necessarily bounded
variation admitting one-sided limits at every point. Assuming that the
time-dependent constraint is uniformly prox-regular and has uniformly non-empty
interior, we prove existence and uniqueness of solutions, as well as continuous
data dependence with respect to the sup-norm.


  We identify two broad types of noninvertibilities in quantum dynamical maps,
one necessarily associated with CP indivisibility and one not so. We study the
production of (non-)Markovian, invertible maps by the process of mixing
noninvertible Pauli maps, and quantify the fraction of the same. The memory
kernel perspective appears to be less transparent on the issue of invertibility
than the approaches based on maps or master equations. Here we consider a
related and potentially helpful issue: the identification of criteria of
parameterized families of maps leading to the existence of a well-defined
semigroup limit.


  In this work, we investigate a biased dollar exchange model with collective
debt limit, in which agents picked at random (with a rate depending on the
amount of dollars they have) give at random time a dollar to another agent
being picked uniformly at random, as long as they have at least one dollar in
their pockets or they can borrow a dollar from a central bank if the bank is
not empty. This dynamics enjoys a mean-field type interaction and partially
extends the recent work \cite{cao_uncovering_2022} on a related model. We
perform a formal mean-field analysis as the number of agents grows to infinity
and as a by-product we discover a two-phase (ODE) dynamics behind the
underlying stochastic $N$-agents dynamics. Numerical experiments on the
two-phase (ODE) dynamics are also conducted where we observe the convergence
towards its unique equilibrium in the large time limit.


  We give a formula for a cocycle generating the Hochschild cohomology of the
Weyl algebra with coefficients in its dual.It is given by an integral over the
configuration space of ordered points on a circle. Using this formula and a
non-commutative version of formal geometry, we obtain an explicit expression
for the canonical trace in deformation quantization of symplectic manifolds.


  Felix Klein's so-called Erlangen Program was published in 1872 as professoral
dissertation. It proposed a new solution to the problem how to classify and
characterize geometries on the basis of projective geometry and group theory.
The given translation was made in 1892 by Dr. M. W. Haskell and transcribed by
N. C. Rughoonauth. We replaced bibliographical data in text and footnotes with
pointers to a complete bibliography section.


  This paper explores the integration of deep learning techniques for joint
sensing and communications, with an extension to semantic communications. The
integrated system comprises a transmitter and receiver operating over a
wireless channel, subject to noise and fading effects. The transmitter employs
a deep neural network, namely an encoder, for joint operations of source
coding, channel coding, and modulation, while the receiver utilizes another
deep neural network, namely a decoder, for joint operations of demodulation,
channel decoding, and source decoding to reconstruct the data samples. The
transmitted signal serves a dual purpose, supporting communication with the
receiver and enabling sensing. When a target is present, the reflected signal
is received, and another deep neural network decoder is utilized for sensing.
This decoder is responsible for detecting the target's presence and determining
its range. All these deep neural networks, including one encoder and two
decoders, undergo joint training through multi-task learning, considering data
and channel characteristics. This paper extends to incorporate semantic
communications by introducing an additional deep neural network, another
decoder at the receiver, operating as a task classifier. This decoder evaluates
the fidelity of label classification for received signals, enhancing the
integration of semantics within the communication process. The study presents
results based on using the CIFAR-10 as the input data and accounting for
channel effects like Additive White Gaussian Noise (AWGN) and Rayleigh fading.
The results underscore the effectiveness of multi-task deep learning in
achieving high-fidelity joint sensing and semantic communications.


  Model checking is essential to evaluate the adequacy of statistical models
and the validity of inferences drawn from them. Particularly, hierarchical
models such as latent Gaussian models (LGMs) pose unique challenges as it is
difficult to check assumptions about the distribution of the latent parameters.
Discrepancy measures are often used to quantify the degree to which a model fit
deviates from the observed data. We construct discrepancy measures by (a)
defining an alternative model with relaxed assumptions and (b) deriving the
discrepancy measure most sensitive to discrepancies induced by this alternative
model. We also promote a workflow for model criticism that combines model
checking with subsequent robustness analysis. As a result, we obtain a general
recipe to check assumptions in LGMs and the impact of these assumptions on the
results. We demonstrate the ideas by assessing the latent Gaussianity
assumption, a crucial but often overlooked assumption in LGMs. We illustrate
the methods via examples utilising Stan and provide functions for easy usage of
the methods for general models fitted through R-INLA.


  This paper investigates the application of consensus clustering and
meta-clustering to the set of all possible partitions of a data set. We show
that when using a "complement" of Rand Index as a measure of cluster
similarity, the total-separation partition, putting each element in a separate
set, is chosen.


  Alignment algorithms usually rely on simplified models of gaps for
computational efficiency. Based on an isomorphism between alignments and
physical helix-coil models, we show in statistical mechanics that alignments
with realistic laws for gaps can be computed with fast algorithms. Improved
performances of probabilistic alignments with realistic models of gaps are
illustrated. Probabilistic and optimization formulations are compared, with
potential implications in many fields and perspectives for computationally
efficient extensions to Markov models with realistic long-range interactions.


  Photo-z errors, especially catastrophic errors, are a major uncertainty for
precision weak lensing cosmology. We find that the shear-(galaxy number)
density and density-density cross correlation measurements between photo-z
bins, available from the same lensing surveys, contain valuable information for
self-calibration of the scattering probabilities between the true-z and photo-z
bins. The self-calibration technique we propose does not rely on cosmological
priors nor parameterization of the photo-z probability distribution function,
and preserves all of the cosmological information available from shear-shear
measurement. We estimate the calibration accuracy through the Fisher matrix
formalism. We find that, for advanced lensing surveys such as the planned stage
IV surveys, the rate of photo-z outliers can be determined with statistical
uncertainties of 0.01-1% for $z<2$ galaxies. Among the several sources of
calibration error that we identify and investigate, the {\it galaxy
distribution bias} is likely the most dominant systematic error, whereby
photo-z outliers have different redshift distributions and/or bias than
non-outliers from the same bin. This bias affects all photo-z calibration
techniques based on correlation measurements. Galaxy bias variations of
$O(0.1)$ produce biases in photo-z outlier rates similar to the statistical
errors of our method, so this galaxy distribution bias may bias the
reconstructed scatters at several-$\sigma$ level, but is unlikely to completely
invalidate the self-calibration technique.


  We prove the existence of piecewise smooth MHD equilibria in
three-dimensional toroidal domains of $\mathbf{R}^3$ where the pressure is
constant on the boundary but not in the interior. The pressure is piecewise
constant and the plasma current exhibits an arbitrary number of current sheets.
We also establish the existence of free boundary steady states surrounded by
vacuum with an external surface current. The toroidal domains where these
equilibria are shown to exist do not need to be small perturbations of an
axisymmetric domain, and in fact they can have any knotted topology. The
building blocks we use in our construction are analytic toroidal domains
satisfying a certain nondegeneracy condition, which roughly states that there
exists a force-free field that is ergodic on the surface of the domain. The
proof involves three main ingredients: a gluing construction of piecewise
smooth MHD equilibria, a Hamilton-Jacobi equation on the two-dimensional torus
that can be understood as a nonlinear deformation of the cohomological equation
(so the nondegeneracy assumption plays a major role in the corresponding
analysis), and a new KAM theorem tailored for the study of divergence-free
fields in three dimensions whose Poincar\'e map cannot be computed explicitly.


  The dielectric properties of Bi$_2$Te$_3$, a layered compound crystallizing
in a rhombohedral structure, are investigated by means of first-principles
calculations at the random phase approximation level. A special attention is
devoted to the anisotropy in the dielectric function and to the local field
effects that strongly renormalize the optical properties in the UV-visible
range when the electric field is polarized along the stacking axis.
Furthermore, both the Born effective charges for each atom and the zone center
phonon frequencies and eigenvectors needed to describe the dielectric response
in the infrared range are computed. Our theoretical near-normal incidence
reflectivity spectras in both the UV-visible and infrared range are in fairly
good agreement with the experimental spectras, provided that the free carriers
Drude contribution arising from defects is included in the infrared response.
The anisotropic plasmon frequencies entering the Drude model are computed
within the rigid band approximation, suggesting that a measurement of the
reflectivity in the infrared range for both polarizations might allow to infer
not only the type of doping but also the level of doping.


  In the classical relativistic regime, the accretion of phantom energy onto a
black hole reduces the mass of the black hole. In this context, we have
investigated the evolution of a Schwarzschild black hole in the standard model
of cosmology using the phantom-like modified variable Chaplygin gas and the
viscous generalized Chaplygin gas. The corresponding expressions for accretion
time scale and evolution of mass have been derived. Our results indicate that
mass of the black hole will decrease if the accreting phantom Chaplygin gas
violates the dominant energy condition and will increase in the opposite case.
Thus our results are in agreement with the results of Babichev \textit{et al}
\cite{Babi1} who first proposed this scenario.


  Nonlinear optical features of a plane structure consisted of silicon disks
placed periodically on a silver substrate have been studied in the Littrow
reflection scenario. The structure manifests a bistable resonant reflective
ability. Values of both specular reflectance and reverse one can be tuned by
varying an intensity of incident light.


  We present the first results of a radio survey of 79 narrow-line Seyfert 1
(NLS1) carried out with the Karl G. Jansky Very Large Array (JVLA) at 5 GHz in
A configuration aimed at studying the radio properties of these sources. We
report the detection of extended emission in one object: Mrk 783. This is
intriguing, since the radio-loudness parameter R of this object is close to the
threshold between radio-quiet and radio-loud active galactic nuclei (AGN). The
galaxy is one of the few NLS1 showing such an extended emission at z < 0.1. The
radio emission is divided in a compact core component and an extended
component, observed on both sides of the nucleus and extending from 14 kpc
south-east to 12 kpc north-west. There is no sign of a collimated jet, and the
shape of the extended component is similar to those of some Seyfert galaxies.
The properties of the emission are compatible with a relic produced by the
intermittent activity cycle of the AGN.


  The pressure dependence, up to 11.3 kbar, of basic parameters of the
superconducting state, such as the critical temperature (Tc), the lower and the
upper critical fields, the coherence length, the penetration depth, and their
anisotropy, was determined from magnetic measurements performed for two
singlecrystalline samples of FeTe0.5Se0.5. We have found pressure-induced
enhancement of all of the superconducting state properties, which entails a
growth of the density of superconducting carriers. However, we noticed more
pronounced increase in superconducting carrier density under pressure than that
in the critical temperature what may indicate an appearance of a mechanism
limiting the increase of Tc with pressure. We have observed that the critical
current density increases under pressure by at least one order of magnitude.


  This paper is devoted to the investigation of the origin and mechanism of
randomization in late boundary layer transition over a flat plate without
pressure gradient. The flow randomization is a crucial phase before flow
transition to the turbulent state. According to existing literatures, the
randomization was caused by the big background noises and non-periodic spanwise
boundary conditions. It was assumed that the large ring structure is affected
by background noises first, and then the change of large ring structure affects
the small length scales quickly, which directly leads to randomization and
formation of turbulence. However, by careful analysis of our high order DNS
results, we believe that the internal instability of multiple ring cycles
structure is the main reason. What we observed is that randomization begins
when the third cycle overlaps the first and second cycles. A significant
asymmetric phenomenon is originated from the second cycle in the middle of both
streamwise and spanwise directions. More technically, a visible asymmetric
phenomenon in the middle vortex ring cycle starts at time step t=16.25T and
x=838.9{\delta}in where the top and bottom level rings are still completely
symmetric. The non-symmetric structure of middle level ring affects the small
length scale in boundary layer bottom quickly. The randomization phenomenon
spreads to top level through ejections. Finally, the whole flow domain becomes
randomized. A hypothesis of C- and K-types shift is given as a possible
mechanism of flow randomization.


  We study fluctuations in plasmonic electroluminescence at the single-atom
limit profiting from the precision of a low-temperature scanning tunneling
microscope. First, we investigate the influence of a controlled single-atom
transfer on the plasmonic properties of the junction. Next, we form a
well-defined atomic contact of several quanta of conductance. In contact, we
observe changes of the electroluminescence intensity that can be assigned to
spontaneous modifications of electronic conductance, plasmonic excitation and
optical antenna properties all originating from minute atomic rearrangements at
or near the contact. The observations are relevant for the understanding of
processes leading to spontaneous intensity variations in plasmon-enhanced
atomic-scale spectroscopies.


  A historical account of Einstein's 'Fernparallelismus' approach towards a
unified field theory of gravitation and electromagnetism is given. In this
theory, a space-time characterized by a curvature-free connection in
conjunction with a metric tensor field, both defined in terms of a dynamical
tetrad field, is investigated. The approach was pursued by Einstein in a number
of publications that appeared in the period from summer 1928 until spring 1931.
In the historical analysis special attention is given to the question of how
Einstein tried to find field equations for the tetrads. We claim that it was
the failure to find and justify a uniquely determined set of acceptable field
equations which eventually led to Einstein's abandoning of this approach. We
comment on some historical and systematic similarities between the
'Fernparallelismus' episode and the 'Entwurf' theory, i.e. the precursor theory
of general relativity pursued by Einstein in the years 1912-1915.


  Saturn was observed by Chandra ACIS-S on 20 and 26-27 January 2004 for one
full Saturn rotation (10.7 hr) at each epoch. We report here the first
observation of an X-ray flare from Saturn's non-auroral (low-latitude) disk,
which is seen in direct response to an M6-class flare emanating from a sunspot
that was clearly visible from both Saturn and Earth. Saturn's disk X-ray
emissions are found to be variable on time scales of hours to weeks to months,
and correlated with solar F10.7 cm flux. Unlike Jupiter, X-rays from Saturn's
polar (auroral) region have characteristics similar to those from its disk.
This report, combined with earlier studies, establishes that disk X-ray
emissions of the giant planets Saturn and Jupiter are directly regulated by
processes happening on the Sun. We suggest that these emissions could be
monitored to study X-ray flaring from solar active regions when they are on the
far side and not visible to Near-Earth space weather satellites.


  We demonstrate a quantum walk with time-dependent coin bias. With this
technique we realize an experimental single-photon one-dimensional quantum walk
with a linearly-ramped time-dependent coin flip operation and thereby
demonstrate two periodic revivals of the walker distribution. In our
beam-displacer interferometer, the walk corresponds to movement between
discretely separated transverse modes of the field serving as lattice sites,
and the time-dependent coin flip is effected by implementing a different angle
between the optical axis of half-wave plate and the light propagation at each
step. Each of the quantum-walk steps required to realize a revival comprises
two sequential orthogonal coin-flip operators, with one coin having constant
bias and the other coin having a time-dependent ramped coin bias, followed by a
conditional translation of the walker.


  Reliability estimation of Machine Learning (ML) models is becoming a crucial
subject. This is particularly the case when such \mbox{models} are deployed in
safety-critical applications, as the decisions based on model predictions can
result in hazardous situations. In this regard, recent research has proposed
methods to achieve safe, \mbox{dependable}, and reliable ML systems. One such
method consists of detecting and analyzing distributional shift, and then
measuring how such systems respond to these shifts. This was proposed in
earlier work in SafeML. This work focuses on the use of SafeML for time series
data, and on reliability and robustness estimation of ML-forecasting methods
using statistical distance measures. To this end, distance measures based on
the Empirical Cumulative Distribution Function (ECDF) proposed in SafeML are
explored to measure Statistical-Distance Dissimilarity (SDD) across time
series. We then propose SDD-based Reliability Estimate (StaDRe) and SDD-based
Robustness (StaDRo) measures. With the help of a clustering technique, the
similarity between the statistical properties of data seen during training and
the forecasts is identified. The proposed method is capable of providing a link
between dataset SDD and Key Performance Indicators (KPIs) of the ML models.


  In this paper, we study the characterization of geodesics for a class of
distances between probability measures introduced by Dolbeault, Nazaret and
Savar e. We first prove the existence of a potential function and then give
necessary and suffi cient optimality conditions that take the form of a coupled
system of PDEs somehow similar to the Mean-Field-Games system of Lasry and
Lions. We also consider an equivalent formulation posed in a set of probability
measures over curves.


  Topological states of matter exhibit many novel properties due to the
presence of robust topological invariants such as the Chern index. These global
characteristics pertain to the system as a whole and are not locally defined.
However, local topological markers can distinguish between topological phases,
and they can vary in space. In equilibrium, we show that the topological marker
can be used to extract the critical behavior of topological phase transitions.
Out of equilibrium, we show that the topological marker spreads via a flow of
currents, with a bounded maximum propagation speed. We discuss the
possibilities for measuring the topological marker and its flow in experiment.


  We propose the use of optical lattice clocks operated with fermionic
alkaline-earth-atoms to study spin-orbit coupling (SOC) in interacting
many-body systems. The SOC emerges naturally during the clock interrogation
when atoms are allowed to tunnel and accumulate a phase set by the ratio of the
"magic" lattice wavelength to the clock transition wavelength. We demonstrate
how standard protocols such as Rabi and Ramsey spectroscopy, that take
advantage of the sub-Hertz resolution of state-of-the-art clock lasers, can
perform momentum-resolved band tomography and determine SOC-induced $s$-wave
collisions in nuclear spin polarized fermions. By adding a second
counter-propagating clock beam a sliding superlattice can be implemented and
used for controlled atom transport and as a probe of $p$ and $s$-wave
interactions. The proposed spectroscopic probes provide clean and well-resolved
signatures at current clock operating temperatures.


  We model quantum space-time on the Planck scale as dynamical networks of
elementary relations or time dependent random graphs, the time dependence being
an effect of the underlying dynamical network laws. We formulate a kind of
geometric renormalisation group on these (random) networks leading to a
hierarchy of increasingly coarse-grained networks of overlapping lumps. We
provide arguments that this process may generate a fixed limit phase,
representing our continuous space-time on a mesoscopic or macroscopic scale,
provided that the underlying discrete geometry is critical in a specific sense
(geometric long range order). Our point of view is corroborated by a series of
analytic and numerical results, which allow to keep track of the geometric
changes, taking place on the various scales of the resolution of space-time. Of
particular conceptual importance are the notions of dimension of such random
systems on the various scales and the notion of geometric criticality.


  We study Maker/Breaker games on the edges of the complete graph, as
introduced by Chvatal and Erdos. We show that in the (m:b) clique game played
on K_{N}, the complete graph on N vertices, Maker can achieve a K_{q} for q =
(m/(log_{2}(b + 1)) - o(1)) * log N, which partially solves an open problem by
Beck. Moreover, we show that in the (1:1) clique game played on K_{N} for a
sufficiently large N, Maker can achieve a K_{q} in only 2^(2q/3) moves, which
improves the previous best bound and answers a question of Beck. Finally we
consider the so called tournament game. A tournament is a directed graph where
every pair of vertices is connected by a single directed edge. The tournament
game is played on K_{N}. At the beginning Breaker fixes an arbitrary tournament
T_{q} on q vertices. Maker and Breaker then alternately take turns at claiming
one unclaimed edge e and selecting one of the two possible orientations. Maker
wins if his graph contains a copy of the goal tournament T_{q}; otherwise
Breaker wins. We show that Maker wins the tournament game on K_{N} with q = (1
- o(1))*log_{2}(N) which supports the random graph intuition: the threshold for
q is asymptotically the same for the game played by two "clever'' players and
the game played by two ``random'' players.
  This last result solves an open problem of Beck which he included in his list
of the seven most humiliating open problems.


  When gravitational waves pass through the nuclear star clusters of galactic
lenses, they may be microlensed by the stars. Such microlensing can cause
potentially observable beating patterns on the waveform due to waveform
superposition and magnify the signal. On the one hand, the beating patterns and
magnification could lead to the first detection of a microlensed gravitational
wave. On the other hand, microlensing introduces a systematic error in strong
lensing use-cases, such as localization and cosmography studies. We show that
diffraction effects are important when we consider GWs in the LIGO frequency
band lensed by objects with masses $\lesssim 100 \, \rm M_\odot$. We also show
that the galaxy hosting the microlenses changes the lensing configuration
qualitatively, so we cannot treat the microlenses as isolated point mass lenses
when strong lensing is involved. We find that for stellar lenses with masses
$\sim 1 \, \rm M_\odot$, diffraction effects significantly suppress the
microlensing magnification. Thus, our results suggest that gravitational waves
lensed by typical galaxy or galaxy cluster lenses may offer a relatively clean
environment to study the lens system, free of contamination by stellar lenses.
We discuss potential implications for the strong lensing science case. More
complicated microlensing configurations will require further study.


  In the present paper we describe the computational implementation of some
integral terms that arise from mixed virtual element methods (mixed-VEM) in
two-dimensional pseudostress-velocity formulations. The implementation
presented here consider any polynomial degree $k \geq 0$ in a natural way by
building several local matrices of small size through the matrix multiplication
and the Kronecker product. In particular, we apply the foregoing mentioned
matrices to the Navier-Stokes equations with Dirichlet boundary conditions,
whose mixed-VEM formulation was originally proposed and analyzed in a recent
work using virtual element subspaces for $H(\text{div})$ and $H^1$,
simultaneously. In addition, an algorithm is proposed for the assembly of the
associated global linear system for the Newton's iteration. Finally, we present
a numerical example in order to illustrate the performance of the mixed-VEM
scheme and confirming the expected theoretical convergence rates.


  In this work, we present a new approach for fast tracking on multiwire
proportional chambers with neural networks. The tracking networks are developed
and adapted for the first-level trigger at hadron collider experiments. We use
Monte Carlo samples generated by Geant4 with a custom muon chamber, which
resembles part of the thin gap chambers from the ATLAS experiment, for training
and performance evaluations. The chamber has a total of seven gas gaps, where
the first and last gas gaps are displaced by ~1.5 m. Each gas gap has 50
channels with a size of 18-20 mm. Two neural network models are developed and
presented: a convolutional neural network and a neural network optimized for
the detector configuration of this study. In the latter network, a convolution
layer is provided for each of three groups formed from 2-3 gas gaps of the
chamber, and the outputs are fed into multilayer perceptrons in sequence. Both
networks are transformed into hardware description language and implemented in
Virtex UltraScale+ FPGA. The angular resolution is 2 mrad, which is comparable
to the maximum resolution of the detector estimated by the minimum chi2 method.
The latency achieved by the implemented firmware is less than 100 ns, and the
throughput rate is 160 MHz.


  In line with advances in recent years about realizing cryptographic
functionalities in an information-theoretically secure way from physical
phenomena and laws, we propose here to obtain useful tasks from the sole
assumption of limited free energy. Specifically, based on that assumption --
resulting in a setting loosely related to Maurer's bounded-storage model -- we
derive protocols for unconditional proofs-of-thermodynamical-work, secret
sharing of free energy, unforgeable money, and proofs-of-position. While our
schemes can be considered classical and not quantum per se, they are resistant
against both classes of adversaries.


  We discuss the difference between the distribution of secondaries measured in
terms of pseudorapidity and that using the correct rapidity variable. We show a
set of examples obtained using Monte Carlo simulations. We also consider the
production of particles of low transverse momentum where coherence effects may
occur, which are not yet included in the present Monte Carlos.


  X-ray reflection spectroscopy is a promising technique for testing general
relativity in the strong field regime, as it can be used to test the Kerr black
hole hypothesis. In this context, the parametrically deformed black hole
metrics proposed by Konoplya, Rezzolla \& Zhidenko (Phys. Rev. D93, 064015,
2016) form an important class of non-Kerr black holes. We implement this class
of black hole metrics in \textsc{relxill\_nk}, which is a framework we have
developed for testing for non-Kerr black holes using X-ray reflection
spectroscopy. We perform a qualitative analysis of the effect of the leading
order strong-field deformation parameters on typical observables like the
innermost stable circular orbits and the reflection spectra. We also present
the first X-ray constraints on some of the deformation parameters of this
metric, using \textit{Suzaku} data from the supermassive black hole in Ark~564,
and compare them with those obtained (or expected) from other observational
techniques like gravitational waves and black hole imaging.


  We present the results of a synthetic spectral analysis of HST STIS spectra
of five long period dwarf novae obtained during their quiescence to determine
the properties of their white dwarfs which are little known for systems above
the CV period gap. The five systems, TU Men, BD Pav, SS Aur, TT Crt, and V442
Cen were observed as part of an HST Snapshot project. The spectra are described
and fitted with combinations of white dwarf photospheres and accretion disks.
We provide evidence that the white dwarfs in all five systems are at least
partially exposed. We discuss the evolutionary implications of our model
fitting results and compare these dwarf novae to previously analyzed FUV
spectra of other dwarf novae above the period gap. The dispersion in CV WD
temperatures above the period gap is substantially greater than one finds below
the period gap where there is a surprisingly narrow dispersion in temperatures
around 15,000K. There appears to be a larger spread of surface temperatures in
dwarf novae above the period than is seen below the gap.


  Through a particularly chosen coordinate transformation, we propose an
optical carpet cloak that only requires homogeneous anisotropic dielectric
material. The proposed cloak could be easily imitated and realized by
alternative layers of isotropic dielectrics. To demonstrate the cloaking
performance, we have designed a two-dimensional version that a uniform silicon
grating structure fabricated on a silicon-on-insulator wafer could work as an
infrared carpet cloak. The cloak has been validated through full wave
electromagnetic simulations, and the non-resonance feature also enables a
broadband cloaking for wavelengths ranging from 1372 to 2000 nm.


  We consider an evolution equation with the Caputo-Dzhrbashyan fractional
derivative of order $\alpha \in (1,2)$ with respect to the time variable, and
the second order uniformly elliptic operator with variable coefficients acting
in spatial variables. This equation describes the propagation of stress pulses
in a viscoelastic medium. Its properties are intermediate between those of
parabolic and hyperbolic equations. In this paper, we construct and investigate
a fundamental solution of the Cauchy problem, prove existence and uniqueness
theorems for such equations.


  We revisit the description of ferromagnetic domain wall dynamics through an
extended one-dimensional model by allowing flexural distortions of the wall
during its motion. This is taken into account by allowing the domain wall
center and internal angle to be functions of position in the direction parallel
to the wall. In the limit of small applied fields, this model accounts for the
nonreciprocity in the propagation of wall modes and their stability in the
presence of the Dzyaloshinskii-Moriya interaction and in-plane magnetic field.


  Recently, several new results related to the evaluation of the series sum
(-1)^n zeta(n)/(n+k) were published. In this short note we show that this
series also possesses an interesting connection to the values of the
zeta-function on the critical line and to the Euler constant.


  The aim of this paper is to generalize some of the properties and results
regarding both the coincidence point set and the common fixed point set of any
two digitally continuous maps to the case of several (more than two) digitally
continuous mappings. Moreover, we study how rigidity may affect these
coincidence and homotopy coincidence point sets. Also, we investigate whether
an established result by Staecker in Nielsen classical topology regarding the
coincidence set for many maps still remains valid in the digital topological
setting.


  Although the primary objective of the keyboard to input data into the
computer, the advanced keyboards keep various other things in mind, such as,
how to use the same keyboard for various other purposes, or how to use the same
keyboard efficiently by using various other attachments to the keyboard. This
objective led to various inventions on keyboard attachments, some of which are
illustrated below in this article.
  This article illustrates 10 inventions on various keyboard attachments from
US patent database. Each different attachment improves the usability of the
keyboard in some way or other. Some attachments illustrated are template
holders, paper holders, pointing device attachments, mouse pad attachments,
wrist rest attachments, storage device attachments, and multimedia attachments.


  We demonstrate aqueous refractive index sensing with 15 to 30 {\mu}m diameter
silicon nitride microdisk resonators to detect small concentrations of Li salt.
A dimpled-tapered fiber is used to couple 780 nm visible light to the
microdisks, in order to perform spectroscopy their optical resonances. The
dimpled fiber probe allows testing of multiple devices on a chip in a single
experiment. This sensing system is versatile and easy to use, while remaining
competitive with other refractometric sensors. For example, from a 20 {\mu}m
diameter device we measure a sensitivity of 200 $\pm$ 30 nm/RIU with a loaded
quality factor of 1.5 $\times$ 10$^4$, and a limit of detection down to (1.3
$\pm$ 0.1) $\times$ 10$^{-6}$ RIU.


  Multi-task feature learning (MTFL) is a powerful technique in boosting the
predictive performance by learning multiple related
classification/regression/clustering tasks simultaneously. However, solving the
MTFL problem remains challenging when the feature dimension is extremely large.
In this paper, we propose a novel screening rule---that is based on the dual
projection onto convex sets (DPC)---to quickly identify the inactive
features---that have zero coefficients in the solution vectors across all
tasks. One of the appealing features of DPC is that: it is safe in the sense
that the detected inactive features are guaranteed to have zero coefficients in
the solution vectors across all tasks. Thus, by removing the inactive features
from the training phase, we may have substantial savings in the computational
cost and memory usage without sacrificing accuracy. To the best of our
knowledge, it is the first screening rule that is applicable to sparse models
with multiple data matrices. A key challenge in deriving DPC is to solve a
nonconvex problem. We show that we can solve for the global optimum efficiently
via a properly chosen parametrization of the constraint set. Moreover, DPC has
very low computational cost and can be integrated with any existing solvers. We
have evaluated the proposed DPC rule on both synthetic and real data sets. The
experiments indicate that DPC is very effective in identifying the inactive
features---especially for high dimensional data---which leads to a speedup up
to several orders of magnitude.


  Charmonia hadro- and photo-production are analyzed in the framework of the
color-octet model taking into account higher-order effects induced by
initial-state radiation of gluons. We argue that color-octet matrix elements
obtained from Tevatron data might be reconciled with those extracted from HERA
data on inelastic $J/\psi$ photoproduction. Finally we estimate cross sections
for events with muons from prompt $J/\psi$'s as a background for the B physics
programme at LHC experiments.


  In recent years, self-supervised learning has been studied to deal with the
limitation of available labeled-dataset. Among the major components of
self-supervised learning, the data augmentation pipeline is one key factor in
enhancing the resulting performance. However, most researchers manually
designed the augmentation pipeline, and the limited collections of
transformation may cause the lack of robustness of the learned feature
representation. In this work, we proposed Multi-Augmentations for
Self-Supervised Representation Learning (MA-SSRL), which fully searched for
various augmentation policies to build the entire pipeline to improve the
robustness of the learned feature representation. MA-SSRL successfully learns
the invariant feature representation and presents an efficient, effective, and
adaptable data augmentation pipeline for self-supervised pre-training on
different distribution and domain datasets. MA-SSRL outperforms the previous
state-of-the-art methods on transfer and semi-supervised benchmarks while
requiring fewer training epochs.


  A theorem on computation of the homological Conley index of an isolated
invariant set of the Poincar\'e map associated to a section in a rotating local
dynamical system $\phi$ is proved. Let $(N,L)$ be an index pair for a
discretization $\phi^h$ of $\phi$, where $h>0$, and let $S$ denote the
invariant part of $N\setminus L$; it follows that the section $S_0$ of $S$ is
an isolated invariant set of the Poincar\'e map. The theorem asserts that if
the sections $N_0$ of $N$ and $L_0$ of $L$ are ANRs, the homology classes
$[u_j]$ of some cycles $u_j$ form a basis of $H(N_0,L_0)$, and for some scalars
$a_{ij}$, the cycles $u_j$ and $\sum a_{ij}u_i$ are homologous in the covering
pair $(\widetilde N,\widetilde L)$ of $(N,L)$ and the homology relation is
preserved in $(\widetilde N,\widetilde L)$ under the transformation induced by
$\phi^t$ for $t\in [0,h]$ then the homological Conley index of $S_0$ is equal
to the Leray reduction of the matrix $[a_{ij}]$. In particular, no information
on the values of the Poincar\'e map or its approximations is required. In a
special case of the system generated by a $T$-periodic non-autonomous ordinary
differential equation with rational $T/h>1$, the theorem was proved in the
paper M.\,Mrozek, R.\,Srzednicki, and F.\,Weilandt, SIAM J. Appl. Dyn. Syst. 14
(2015), 1348-1386, and it motivated a construction of an algorithm for
determining the index.


  Lie's third theorem does not hold for Lie groupoids and Lie algebroids. In
this article, we show that Lie's third theorem is valid within a specific class
of diffeological groupoids that we call `singular Lie groupoids.' To achieve
this, we introduce a subcategory of diffeological spaces which we call
`quasi-etale.' Singular Lie groupoids are precisely the groupoid objects within
this category, where the unit space is a manifold.
  Our approach involves the construction of a functor that maps singular Lie
groupoids to Lie algebroids, extending the classical functor from Lie groupoids
to Lie algebroids. We prove that the \v{S}evera-Weinstein groupoid of an
algebroid is an example of a singular Lie groupoid, thereby establishing Lie's
third theorem in this context.


  A procedure for quantifying the U $5f$ electrons' covalence and degree of
localization in U intermetallic compounds is presented. To this end, bulk
sensitive hard and soft x-ray photoelectron spectroscopy were utilized in
combination with density-functional theory (DFT) plus dynamical mean-field
theory (DMFT) calculations. The energy dependence of the photoionization
cross-sections allows the disentanglement of the U\,$5f$ contribution to the
valence band from the various other atomic subshells so that the computational
parameters in the DFT\,+\,DMFT can be reliably determined. Applying this method
to UGa$_2$ and UB$_2$ as model compounds from opposite ends of the
(de)localization range, we have achieved excellent simulations of the valence
band and core-level spectra. The width in the distribution of atomic U\,$5f$
configurations contributing to the ground state, as obtained from the
calculations, quantifies the correlated nature and degree of localization of
the U\,5$f$. The findings permit answering the longstanding question why
different spectroscopic techniques give seemingly different numbers for the U
5$f$ valence in intermetallic U compounds.


  We study the classical Heisenberg model for spins on a pyrochlore lattice
interacting via long range dipole-dipole forces and nearest neighbor exchange.
Antiferromagnetic exchange alone is known not to induce ordering in this
system. We analyze low temperature order resulting from the combined
interactions, both by using a mean-field approach and by examining the energy
cost of fluctuations about an ordered state. We discuss behavior as a function
of the ratio of the dipolar and exchange interaction strengths and find two
types of ordered phase. We relate our results to the recent experimental work
and reproduce and extend the theoretical calculations on the pyrochlore
compound, Gd$_2$Ti$_2$O$_7$, by Raju \textit{et al.}, Phys. Rev. B {\bf 59},
14489 (1999).