  Motivated by recent advances in Donaldson-Thomas theory, four-dimensional
$\mathcal{N}=4$ string-string duality is examined in a reduced rank theory on a
less studied BPS sector. In particular we identify candidate partition
functions of "untwisted" quarter-BPS dyons in the heterotic $\mathbb{Z}_2$ CHL
model by studying the associated chiral genus two partition function, based on
the M-theory lift of string webs argument by Dabholkar and Gaiotto. This yields
meromorphic Siegel modular forms for the Iwahori subgroup $B(2) \subset
\text{Sp}_4 (\mathbb{Z}) $ which generate BPS indices for dyons with untwisted
sector electric charge, in contrast to twisted sector dyons counted by a
multiplicative lift of twisted-twining elliptic genera known from Mathieu
moonshine. The new partition functions are shown to satisfy the expected
constraints coming from wall-crossing and S-duality symmetry as well as the
black hole entropy based on the Gauss-Bonnet term in the effective action. In
these aspects our analysis confirms and extends work of Banerjee, Sen and
Srivastava, which only addressed a subset of the untwisted sector dyons
considered here. Our results are also compared with recently conjectured
formulae of Bryan and Oberdieck for the partition functions of primitive DT
invariants of the CHL orbifold $X=( \text{K3} \times T^2 )/ \mathbb{Z}_2$, as
suggested by string duality with type IIA theory on $X$.


  We adopt and analyze results on the incidence and physical properties of
damped Ly$\alpha$ systems (DLAs) to predict the astrophysical impact of gas in
galaxies on observations of Fast Radio Bursts (FRBs). Three DLA measures form
the basis of this analysis: (i) the HI column density distribution,
parameterized as a double power-law; (ii) the incidence of DLAs with redshift
(derived here), $\ell(z)=A+B \arctan(z-C)$ with $A=0.236_{-0.021}^{+0.016},
B=0.168_{-0.017}^{+0.010}, C=2.87_{-0.13}^{+0.17}$ and (iii) the electron
density, parameterized as a log-normal deviate with mean $10^{-2.6} cm^{-3}$
and dispersion 0.3dex. Synthesizing these results, we estimate that the average
rest-frame dispersion measure from the neutral medium of a single, intersecting
galaxy is DM$^{NM}_{DLA}=0.25$ pc/cm^3. Analysis of AlIII and CII* absorption
limits the putative warm ionized medium to contribute
DM$^{WIM}_{DLA}<20$pc/cm^3. Given the low incidence of DLAs, we find that a
population of FRBs at z=2 will incur DM(z=2)=0.01 pc/cm^3 on average, with a
99% c.l. upper bound of 0.22 pc/cm^3. Assuming that turbulence of the ISM in
external galaxies is qualitatively similar to our Galaxy, we estimate that the
angular broadening of an FRB by intersecting galaxies is negligible
($\theta<0.1$mas). The temporal broadening is also predicted to be small, $\tau
\approx 0.3$ms for a z=1 galaxy intersecting a z=2 FRB for an observing
frequency of $\nu=1$GHz. Even with $\nu=600$MHz, the fraction of sightlines
broadened beyond 25ms is only approximately 0.1%. We conclude that gas within
the ISM of intervening galaxies has a minor effect on the detection of FRBs and
their resultant DM distributions. Download the repository at
https://github.com/FRBs/FRB to repeat and extend the calculations presented
here.


  Automatic program repair (APR) is crucial to improve software reliability.
Recently, neural machine translation (NMT) techniques have been used to fix
software bugs automatically. While promising, these approaches have two major
limitations. Their search space often does not contain the correct fix, and
their search strategy ignores software knowledge such as strict code syntax.
Due to these limitations, existing NMT-based techniques underperform the best
template-based approaches.
  We propose CURE, a new NMT-based APR technique with three major novelties.
First, CURE pre-trains a programming language (PL) model on a large software
codebase to learn developer-like source code before the APR task. Second, CURE
designs a new code-aware search strategy that finds more correct fixes by
focusing on compilable patches and patches that are close in length to the
buggy code. Finally, CURE uses a subword tokenization technique to generate a
smaller search space that contains more correct fixes.
  Our evaluation on two widely-used benchmarks shows that CURE correctly fixes
57 Defects4J bugs and 26 QuixBugs bugs, outperforming all existing APR
techniques on both benchmarks.


  A decade ago, an electron-attachment process called interatomic Coulombic
electron capture has been predicted to be possible through energy transfer to a
nearby neighbor. It has been estimated to be competitive with
environment-independent photorecombination, but its general relevance has yet
to be established. Here, we evaluate the capability of alkali and alkaline
earth metal cations to capture a free electron by assistance from a nearby
water molecule. We introduce a characteristic distance $r_{IC}$ for this energy
transfer mechanism in equivalence to the F\"orster radius. Our results show
that water-assisted electron capture dominates over photorecombination beyond
the second hydration shell of each cation for electron energies above a
threshold. The assisted capture reaches distances equivalent to a fifth to
seventh solvation shell for the studied cations. The far reach of the assisted
electron capture is of significant general interest to the broad spectrum of
research fields dealing with low-energy electrons, in particular
radiation-induced damage of biomolecules. The here introduced distance measure
will enable quantification of the role of the environment for assisted electron
attachment.


  We study a class of Hamilton-Jacobi partial differential equations in the
space of probability measures. In the first part of this paper, we prove
comparison principles (implying uniqueness) for this class. In the second part,
we establish the existence of a solution and give a representation using a
family of partial differential equations with control. A large part of our
analysis exploits special structures of the Hamiltonian, which might look
mysterious at first sight. However, we show that this Hamiltonian structure
arises naturally as limit of Hamiltonians of microscopical models. Indeed, in
the third part of this paper, we informally derive the Hamiltonian studied
before, in a context of fluctuation theory on the hydrodynamic scale. The
analysis is carried out for a specific model of stochastic interacting
particles in gas kinetics, namely a version of the Carleman model. We use a
two-scale averaging method on Hamiltonians defined in the space of probability
measures to derive the limiting Hamiltonian.


  In industry as well as education as well as academics we see a growing need
for knowledge on how to apply machine learning in software applications. With
the educational programme ICT & AI at Fontys UAS we had to find an answer to
the question: "How should we educate software engineers to become AI
engineers?" This paper describes our educational programme, the open source
tools we use, and the literature it is based on. After three years of
experience, we present our lessons learned for both educational institutions
and software engineers in practice.


  Presented is a new method for calculating the time-optimal guidance control
for a multiple vehicle pursuit-evasion system. A joint differential game of k
pursuing vehicles relative to the evader is constructed, and a
Hamilton-Jacobi-Isaacs (HJI) equation that describes the evolution of the value
function is formulated. The value function is built such that the terminal cost
is the squared distance from the boundary of the terminal surface.
Additionally, all vehicles are assumed to have bounded controls. Typically, a
joint state space constructed in this way would have too large a dimension to
be solved with existing grid-based approaches. The value function is computed
efficiently in high-dimensional space, without a discrete grid, using the
generalized Hopf formula. The optimal time-to-reach is iteratively solved, and
the optimal control is inferred from the gradient of the value function.


  We consider the problem of estimating bounds on parameters representing tasks
being performed by individual robots in a multirobot system. In our previous
work, we derived necessary conditions based on persistency of excitation
analysis for the exact identification of these parameters. We concluded that
depending on the robot's task, the dynamics of individual robots may fail to
satisfy these conditions, thereby preventing exact inference. As an extension
to that work, this paper focuses on estimating bounds on task parameters when
such conditions are not satisfied. Each robot in the team uses
optimization-based controllers for mediating between task satisfaction and
collision avoidance. We use KKT conditions of this optimization and SVD of
active collision avoidance constraints to derive explicit relations between
Lagrange multipliers, robot dynamics, and task parameters. Using these
relations, we are able to derive bounds on each robot's task parameters.
Through numerical simulations, we show how our proposed region based
identification approach generates feasible regions for parameters when a
conventional estimator such as a UKF fails. Additionally, empirical evidence
shows that this approach generates contracting sets which converge to the true
parameters much faster than the rate at which a UKF based estimate converges.
Videos of these results are available at https://bit.ly/2JDMgeJ


  Multimodal deep learning foundation models can learn the relationship between
images and text. In the context of medical imaging, mapping images to language
concepts reflects the clinical task of diagnostic image interpretation, however
current general-purpose foundation models do not perform well in this context
because their training corpus have limited medical text and images. To address
this challenge and account for the range of cardiac physiology, we leverage
1,032,975 cardiac ultrasound videos and corresponding expert interpretations to
develop EchoCLIP, a multimodal foundation model for echocardiography. EchoCLIP
displays strong zero-shot (not explicitly trained) performance in cardiac
function assessment (external validation left ventricular ejection fraction
mean absolute error (MAE) of 7.1%) and identification of implanted intracardiac
devices (areas under the curve (AUC) between 0.84 and 0.98 for pacemakers and
artificial heart valves). We also developed a long-context variant (EchoCLIP-R)
with a custom echocardiography report text tokenizer which can accurately
identify unique patients across multiple videos (AUC of 0.86), identify
clinical changes such as orthotopic heart transplants (AUC of 0.79) or cardiac
surgery (AUC 0.77), and enable robust image-to-text search (mean cross-modal
retrieval rank in the top 1% of candidate text reports). These emergent
capabilities can be used for preliminary assessment and summarization of
echocardiographic findings.


  We present the results of a long-term (1999--2010) spectral optical
monitoring campaign of the active galactic nucleus (AGN) Ark 564, which shows a
strong Fe II line emission in the optical. This AGN is a narrow line Seyfert 1
(NLS1) galaxies, a group of AGNs with specific spectral characteristics. We
analyze the light curves of the permitted Ha, Hb, optical Fe II line fluxes,
and the continuum flux in order to search for a time lag between them.
Additionally, in order to estimate the contribution of iron lines from
different multiplets, we fit the Hb and Fe II lines with a sum of Gaussian
components. We found that during the monitoring period the spectral variation
(F_max/F_min) of Ark 564 was between 1.5 for Ha to 1.8 for the Fe II lines. The
correlation between the Fe II and Hb flux variations is of higher significance
than that of Ha and Hb (whose correlation is almost absent). The permitted-line
profiles are Lorentzian-like, and did not change shape during the monitoring
period. We investigated, in detail, the optical Fe II emission and found
different degrees of correlation between the Fe II emission arising from
different spectral multiplets and the continuum flux. The relatively weak and
different degrees of correlations between permitted lines and continuum fluxes
indicate a rather complex source of ionization of the broad line emission
region.


  This paper pursues the study of the Calabi-Yau equation on certain symplectic
non-Kaehler 4-manifolds, building on a key example of Tosatti-Weinkove in which
more general theory had proved less effective. Symplectic 4-manifolds admitting
a 2-torus fibration over a 2-torus base are modelled on one of three solvable
Lie groups. Having assigned an invariant almost-Kaehler structure and a volume
form that effectively varies only on the base, one seeks a symplectic form with
this volume. Our approach simplifies the previous analysis of the problem, and
establishes the existence of solutions in various other cases.


  In this paper, we study the dynamical uniform boundedness principle over a
family of rational maps with certain nontrivial automorphisms. Specifically, we
consider a family of rational maps of an arbitrary degree $d\ge 2$ whose
automorphism group contains the cyclic group of order $d$. We prove that a
subfamily of this family satisfies the dynamical uniform boundedness principle.


  Rotational bands of positive and negative parity are frequently found
experimentally in heavy deformed even-even nuclei along with their
corresponding $E2$ intra-band and $E1$ inter-band transitions. In $SU(3)$
symmetry-based models, calculating the $B(E2)$ strengths is relatively
straightforward due to the relation between the $E2$ operator and the
quadrupole generator of the algebra. However, calculating the $B(E1)$ strengths
is a more difficult task, requiring computations involving the shell-model
expansion of the dipole operator and multi-shell matrix elements. In this work
the $E1$ operator is expanded in $SU(3)$ second quantization and applied to
calculate the inter-band $B(E1)$ strengths of the isotope $^{224}$Th using the
semi-microscopic algebraic quartet model (SAQM) based on the recently proposed
proxy-$SU(3)$ scheme.


  We present a coordinated study of the paramagnetic-to-antiferromagnetic,
rhombohedral-to-monoclinic, and metal-to-insulator transitions in thin-film
specimens of the classic Mott insulator V$_2$O$_3$ using low-energy muon spin
relaxation, x-ray diffraction, and nanoscale-resolved near-field infrared
spectroscopic techniques. The measurements provide a detailed characterization
of the thermal evolution of the magnetic, structural, and electronic phase
transitions occurring in a wide temperature range, including quantitative
measurements of the high- and low-temperature phase fractions for each
transition. The results reveal a stable coexistence of the high- and
low-temperature phases over a broad temperature range throughout the
transition. Careful comparison of temperature dependence of the different
measurements, calibrated by the resistance of the sample, demonstrates that the
electronic, magnetic, and structural degrees of freedom remain tightly coupled
to each other during the transition process. We also find evidence for
antiferromagnetic fluctuations in the vicinity of the phase transition,
highlighting the important role of the magnetic degree of freedom in the
metal-insulator transition.


  We consider directed random polymers in $(d+1)$ dimensions with nearly gamma
i.i.d. disorder. We study the partition function $Z_{N,\omega}$ and establish
exponential concentration of $\log Z_{N,\omega}$ about its mean on the
subgaussian scale $\sqrt{N/\log N}$ . This is used to show that $\mathbb{E}[
\log Z_{N,\omega}]$ differs from $N$ times the free energy by an amount which
is also subgaussian (i.e. $o(\sqrt{N})$), specifically $O(\sqrt{\frac{N}{\log
N}}\log \log N)$.


  We compute the massless spectra of a set of flux vacua of the heterotic
string. The vacua we study include well-known non-Kahler T^2-fibrations over K3
with SU(3) structure and intrinsic torsion. Following gauged linear sigma
models of these vacua into phases governed by asymmetric Landau-Ginzburg
orbifolds allows us to compute the spectrum using generalizations of familiar
LG-orbifold techniques. We study several four- and six-dimensional examples
with N=2 spacetime supersymmetry in detail.


  The deformation-related energy budget is usually considered in the simplest
form or even completely omitted from the energy balance equation. We derive a
full energy balance equation that accounts not only for heat energy but also
for mechanical (elastic, plastic and viscous) work. The derived equation is
implemented in DES3D, an unstructured finite element solver for long-term
tectonic deformation. We verify the implementation by comparing numerical
solutions to the corresponding semi-analytic solutions in three benchmarks
extended from the classical oedometer test. Two of the benchmarks are designed
to evaluate the temperature change in a Mohr-Coulomb elasto-plastic square
governed by a simplified equation involving plastic power only and by the full
temperature evolution equation, respectively. The third benchmark differs in
that it computes thermal stresses associated with a prescribed uniform
temperature increase. All the solutions from DES3D show relative error less
than 0.1%. We also investigate the long-term effects of deformation energetics
on the evolution of large offset normal faults. We find that the models
considering the full energy balance equation tend to produce more secondary
faults and an elongated core complex. Our results for the normal fault system
confirm that persistent inelastic deformation has a significant impact on the
long-term evolution of faults, motivating further exploration of the role of
the full energy balance equation in other geodynamic systems.


  In the medical image analysis field, organizing challenges with associated
workshops at international conferences began in 2007 and has grown to include
over 150 challenges. Several of these challenges have had a major impact in the
field. However, whereas well-designed challenges have the potential to unite
and focus the field on creating solutions to important problems, poorly
designed and documented challenges can equally impede a field and lead to
pursuing incremental improvements in metric scores with no theoretic or
clinical significance. This is supported by a critical assessment of challenges
at the international MICCAI conference. In this assessment the main observation
was that small changes to the underlying challenge data can drastically change
the ranking order on the leaderboard. Related to this is the practice of
leaderboard climbing, which is characterized by participants focusing on
incrementally improving metric results rather than advancing science or solving
the driving problem of a challenge. In this abstract we look beyond the
leaderboard of a challenge and instead look at the conclusions that can be
drawn from a challenge with respect to the research problem that it is
addressing. Research study design is well described in other research areas and
can be translated to challenge design when viewing challenges as research
studies on algorithm performance that address a research problem. Based on the
two main types of scientific research study design, we propose two main
challenge types, which we think would benefit other research areas as well: 1)
an insight challenge that is based on a qualitative study design and 2) a
deployment challenge that is based on a quantitative study design. In addition
we briefly touch upon related considerations with respect to statistical
significance versus practical significance, generalizability and data
saturation.


  The Kepler spacecraft observed the hot subdwarf star PHL 417 during its
extended K2 mission, and the high-precision photometric lightcurve reveals the
presence of 17 pulsation modes with periods between 38 and 105 minutes. From
follow-up ground-based spectroscopy we find that the object has a relatively
high temperature of 35 600 K, a surface gravity of $\log g / {\rm
cm\,s^{-2}}\,=\,5.75$ and a super-solar helium abundance. Remarkably, it also
shows strong zirconium lines corresponding to an apparent +3.9 dex
overabundance compared with the Sun. These properties clearly identify this
object as the third member of the rare group of pulsating heavy-metal stars,
the V366 Aquarii pulsators. These stars are intriguing in that the pulsations
are inconsistent with the standard models for pulsations in hot subdwarfs,
which predicts that they should display short-period pulsations rather than the
observed longer periods. We perform a stability analysis of the pulsation modes
based on data from two campaigns with K2. The highest amplitude mode is found
to be stable with a period drift, $\dot{P}$, of less than $1.1\cdot10^{-9}$
s/s. This result rules out pulsations driven during the rapid stages of helium
flash ignition.


  It is believed that in knowledge distillation (KD), the role of the teacher
is to provide an estimate for the unknown Bayes conditional probability
distribution (BCPD) to be used in the student training process. Conventionally,
this estimate is obtained by training the teacher using maximum log-likelihood
(MLL) method. To improve this estimate for KD, in this paper we introduce the
concept of conditional mutual information (CMI) into the estimation of BCPD and
propose a novel estimator called the maximum CMI (MCMI) method. Specifically,
in MCMI estimation, both the log-likelihood and CMI of the teacher are
simultaneously maximized when the teacher is trained. Through Eigen-CAM, it is
further shown that maximizing the teacher's CMI value allows the teacher to
capture more contextual information in an image cluster. Via conducting a
thorough set of experiments, we show that by employing a teacher trained via
MCMI estimation rather than one trained via MLL estimation in various
state-of-the-art KD frameworks, the student's classification accuracy
consistently increases, with the gain of up to 3.32\%. This suggests that the
teacher's BCPD estimate provided by MCMI method is more accurate than that
provided by MLL method. In addition, we show that such improvements in the
student's accuracy are more drastic in zero-shot and few-shot settings.
Notably, the student's accuracy increases with the gain of up to 5.72\% when
5\% of the training samples are available to the student (few-shot), and
increases from 0\% to as high as 84\% for an omitted class (zero-shot). The
code is available at \url{https://github.com/iclr2024mcmi/ICLRMCMI}.


  We introduce a comprehensive numerical framework to generically infer the
emergent macroscopic properties of uniaxial nematic and cholesteric phases from
that of their microscopic constituent mesogens. This approach, based on the
full numerical resolution of the Poniewierski-Stecki equations in the weak
chirality limit, may expediently handle a wide range of particle models through
the use of Monte-Carlo sampling for all virial-type integrals. Its predictions
in terms of equilibrium cholesteric structures are found to be in excellent
agreement with previous full-functional descriptions, thereby demonstrating the
quantitative validity of the perturbative treatment of chirality for pitch
lengths as short as a few dozen particle diameters. Furthermore, the use of the
full angle-dependent virial coefficients in the Onsager-Parsons-Lee formalism
increases its numerical efficiency by several orders of magnitude over that of
these previous methods. The comparison of our results with numerical
simulations however reveals some shortcomings of the Parsons-Lee approximation
for systems of strongly non-convex particles, notwithstanding the accurate
inclusion of their full effective molecular volume. Further potential
limitations of our theory in terms of phase symmetry assumptions are also
examined, and prospective directions for future improvements discussed.


  In this paper we study spiderweb central configurations for the $N$-body
problem, i.e configurations given by $N=n \times \ell+1$ masses located at the
intersection points of $\ell$ concurrent equidistributed half-lines with $n$
circles and a central mass $m_0$, under the hypothesis that the $\ell$ masses
on the $i$-th circle are equal to a positive constant $m_i$; we allow the
particular case $m_0=0$. We focus on constructive proofs of the existence of
spiderweb central configurations, which allow numerical implementation.
Additionally, we prove the uniqueness of such central configurations when $\ell
\in \{2,\dots,9\}$ and arbitrary $n$ and $m_i$; under the constraint $m_1\geq
m_2\geq \ldots \geq m_n$ we also prove uniqueness for $\ell \in
\{10,\dots,18\}$ and $n$ not too large. We also give an algorithm providing a
rigorous proof of the existence and local unicity of such central
configurations when given as input a choice of $n$, $\ell$ and $m_0, . . .
,m_n$. Finally, our numerical simulations highlight some interesting properties
of the mass distribution.


  We provide exact analytical expressions for the magnetic susceptibility
function in the high temperature expansion for finite Heisenberg spin systems
with an arbitrary coupling matrix, arbitrary single-spin quantum number, and
arbitrary number of spins. The results can be used to determine unknown
exchange parameters from zero-field magnetic susceptibility measurements
without diagonalizing the system Hamiltonian. We demonstrate the possibility of
reconstructing the exchange parameters from simulated data for two specific
model systems. We examine the accuracy and stability of the proposed method.


  Soft robots are made of compliant materials that perform their tasks by
deriving motion from elastic deformations. They are used in various
applications, e.g., for handling fragile objects, navigating sensitive/complex
environments, etc., and are typically actuated by Pneumatic/hydraulic loads.
Though demands for soft robots are continuously increasing in various
engineering sectors, due to the lack of systematic approaches, they are
primarily designed manually. This paper presents a systematic density-based
topology optimization approach to designing soft robots while considering the
design-dependent behavior of the actuating loads. We use the Darcy law with the
conceptualized drainage term to model the design-dependent nature of the
applied pressure loads. The standard finite element is employed to evaluate the
consistent nodal loads from the obtained pressure field. The robust topology
optimization formulation is used with the multi-criteria objective. The success
of the presented approach is demonstrated by designing a member/soft robot of
the pneumatic networks (PneuNets). The optimized member is combined in several
series to get different PneuNets. Their CAD models are generated, and they are
studied with high-pressure loads in a commercial software. Depending upon the
number of members in the PneuNets, different output motions are noted.


  We present explicit expressions for Fock-space projection operators that
correspond to realistic final states in scattering experiments. Our operators
automatically sum over unobserved quanta and account for non-emission into
sub-regions of momentum space.


  Given a finite set of points $S\subset\mathbb{R}^d$, a $k$-set of $S$ is a
subset $A \subset S$ of size $k$ which can be strictly separated from $S
\setminus A $ by a hyperplane. Similarly, a $k$-facet of a point set $S$ in
general position is a subset $\Delta\subset S$ of size $d$ such that the
hyperplane spanned by $\Delta$ has $k$ points from $S$ on one side. For a
probability distribution $P$ on $\mathbb{R}^d$, we study $E_P(k,n)$, the
expected number of $k$-facets of a sample of $n$ random points from $P$. When
$P$ is a distribution on $\mathbb{R}^2$ such that the measure of every line is
0, we show that $E_P(k,n) = O(n(k+1)^{1/4})$. Our argument is based on a
technique by B\'{a}r\'{a}ny and Steiger. We study how it may be possible to
improve this bound using the continuous version of the polynomial partitioning
theorem. This motivates a question concerning the points of intersection of an
algebraic curve and the $k$-edge graph of a set of points.
  We also study a variation on the $k$-set problem for the set system whose set
of ranges consists of all translations of some strictly convex body in the
plane. The motivation is to show that the technique by B\'{a}r\'{a}ny and
Steiger is tight for a natural family of set systems. For any such set system,
we determine bounds for the expected number of $k$-sets which are tight up to
logarithmic factors.


  The second author has shown that existence of extremal K\"ahler metrics on
semisimple principal toric fibrations is equivalent to a notion of weighted
uniform K-stability, read off from the moment polytope. The purpose of this
article is to prove various sufficient conditions of weighted uniform
K-stability which can be checked effectively and explore the low dimensional
new examples of extremal K\"ahler metrics it provides.


  We show that engineered diffraction gratings can considerably simplify the
design and performance of acoustic devices. Acoustic reflecting gratings based
on rectangular cavities drilled on an acoustically rigid surface are designed
in such a way that all the incident energy is channeled towards the diffracted
mode traveling in the oposite direction of the incident field (retroreflection
effect), and this effect is used to cloak an object placed over a rigid
surface. Axisymmetric gratings consisting in rigid surfaces with just one
groove per unit cell are used to design acoustic thin acoustic carpet cloaks.
Finally, full wave numerical simulations are performed and a conical carpet
cloak is experimentally tested, showing an excellent scattering cancellation
effect.


  A positive level Kazhdan-Lusztig functor is defined using Arkhipov-Gaitsgory
duality for affine Lie algebras. The functor sends objects in the DG category
of G(O)-equivariant positive level affine Lie algebra modules to objects in the
DG category of modules over Lusztig's quantum group at a root of unity. We
prove that the semi-infinite cohomology functor for positive level modules
factors through the Kazhdan-Lusztig functor at positive level and the quantum
group cohomology functor with respect to the positive part of Lusztig's quantum
group.


  The many low energy modes near a black hole horizon give the thermal
atmosphere a divergent entropy which becomes of order $A/4G$ with a Planck
scale cut-off. However, Sorkin has given a Newtonian argument for 3+1
Schwarzschild black holes to the effect that fluctuations of such modes provide
the horizon with a non-zero quantum mechanical width. This width then
effectively enforces a cut-off at much larger distances so that the entropy of
the thermal atmosphere is negligible in comparison with $A/4G$ for large black
holes. We generalize and improve this result by giving a relativistic argument
valid for any spherical black hole in any dimension. The result is again a
cut-off $L_c$ at a geometric mean of the Planck scale and the black hole
radius; in particular, $L_c^d \sim \frac{R}{T_H} \ell_p^{d-2}$. With this
cut-off, the entropy of the thermal atmosphere is again parametrically small in
comparison with the Bekenstein-Hawking entropy of the black hole. The effect of
a large number $N$ of fundamental fields and the discrepancies from naive
predictions of a stretched horizon model are also discussed.


  Deep neural networks (DNNs) have become increasingly popular in recent years.
However, despite their many successes, DNNs may also err and produce incorrect
and potentially fatal outputs in safety-critical settings, such as autonomous
driving, medical diagnosis, and airborne collision avoidance systems. Much work
has been put into detecting such erroneous behavior in DNNs, e.g., via testing
or verification, but removing these errors after their detection has received
lesser attention. We present here a new tool, called 3M-DNN, for repairing a
given DNN, which is known to err on some set of inputs. The novel repair
procedure implemented in 3M-DNN computes a modification to the network's
weights that corrects its behavior, and attempts to minimize this change via a
sequence of calls to a backend, black-box DNN verification engine. To the best
of our knowledge, our method is the first one that allows repairing the network
by simultaneously modifying multiple layers. This is achieved by splitting the
network into sub-networks, and applying a single-layer repairing technique to
each component. We evaluated 3M-DNN tool on an extensive set of benchmarks,
obtaining promising results.


  Coulomb bound electron-hole pairs, excitons, govern the optical properties of
semi-conducting transition metal dichalcogenides like MoS$_2$ and WSe$_2$. We
study optical transitions at the K-point for 2H homobilayer MoS$_2$ in Density
Functional Theory (DFT) including excitonic effects and compare with
reflectivity measurements in high quality samples encapsulated in hexagonal BN.
In both calculated and measured spectra we find a strong interlayer exciton
transition in energy between A and B intralayer excitons, observable for T$=4
-300$ K, whereas no such transition is observed for the monolayer in the same
structure in this energy range. The interlayer excitons consist of an electron
localized in one layer and a hole state delocalized over the bilayer, which
results in the unusual combination of high oscillator strength and a static
dipole moment. We also find signatures of interlayer excitons involving the
second highest valence band (B) and compare absorption calculations for
different bilayer stackings. For homotrilayer MoS$_2$ we also observe
interlayer excitons and an energy splitting between different intralayer
A-excitons originating from the middle and outer layers, respectively.


  The recent progress in embedding inflation in string theory has made it clear
that the problem of moduli stabilization cannot be ignored in this context. In
many models a special role is played by the volume modulus, which is modified
in the presence of mobile branes. The challenge is to stabilize this modified
volume while keeping the inflaton mass small compared to the Hubble parameter.
It is then crucial to know not only how the volume modulus is modified, but
also to have control over the dependence of the potential on the inflaton
field. We address these questions within a simple setting: toroidal N=1 type
IIB orientifolds. We calculate corrections to the superpotential and show how
the holomorphic dependence on the properly modified volume modulus arises. The
potential then explicitly involves the inflaton, leaving room for lowering the
inflaton mass through moderate fine-tuning of flux quantum numbers.


  The flux of high-energy astrophysical neutrinos observed by the present
generation of neutrino detectors has already indicated a few hints of new
physics beyond the Standard Model. In this work, we show that high-energy
gamma-ray observations can also be considered as a complementary probe for
unveiling the source of high-energy astrophysical neutrino events and new
physics. Recently, the LHAASO collaboration has reported O(5000) gamma-ray
events in the energy range between 0.5 TeV -18 TeV from gamma-ray burst
GRB221009A within 2000 seconds after the initial outburst. We showed that
attenuated high-energy gamma rays can be produced from the interaction of
astrophysical neutrinos with CMB neutrinos through non-standard
self-interaction of neutrinos mediated by light scalar bosons. The non-standard
interaction of neutrinos recently took a lot of attention in cosmology for its
role in reducing Hubble tension. We have constrained the parameter space of
non-standard self-interacting neutrinos from the flux of photons observed by
LHAASO and showed consistency of the same with the resulting parameter space
from Hubble tension requirements and other recent constraints from
laboratory/cosmology.


  We investigate the structure attained by neutron star matter with proton to
neutron ratios ranging from x=0.1 to 0.5, densities in the range of 0.02 fm-3
to 0.085 fm-3, and temperatures T<4 MeV. In particular we study the pasta
shapes and the phase changes previously observed in nuclear matter, as well as
the behavior of the symmetry energy. We corroborate the existence of
homogeneous to non-homogeneous phase transitions, and the different values of
the symmetry energy at different densities and temperatures.


  Ollivier and Lin--Lu--Yau established the theory of graph Ricci curvature
(LLY curvature) via optimal transport on graphs.
Ikeda--Kitabeppu--Takai--Uehara introduced a new distance called the
Kantorovich difference on hypergraphs and generalized the LLY curvature to
hypergraphs (IKTU curvature). As the LLY curvature can be represented by the
graph Laplacian by M\"unch--Wojciechowski, Ikeda--Kitabeppu--Takai--Uehara
conjectured that the IKTU curvature has a similar expression in terms of the
hypergraph Laplacian. In this paper, we introduce a variant of the Kantorovich
difference inspired by the above conjecture and study the Ricci curvature
associated with this distance ($\mathsf{wIKTU}$ curvature). Moreover, for
hypergraphs with a specific structure, we analyze a quantity $\mathcal{C}(x,y)$
at two distinct vertices $x,y$ defined by using the hypergraph Laplacian. If
the resolvent operator converges uniformly to the identity, then
$\mathcal{C}(x,y)$ coincides with the $\mathsf{wIKTU}$ curvature along $x,y$.


  A calculation of the photonic Green's tensor of a structure is at the heart
of many photonic problems, but for non-trivial nanostructures, it is typically
a prohibitively time-consuming task. Recently, a general normal mode expansion
(GENOME) was implemented to construct the Green's tensor from eigenpermittivity
modes. Here, we employ GENOME to the study the response of a cluster of
nanoparticles. To this end, we use the rigorous mode hybridization theory
derived earlier by D. J. Bergman [Phys. Rev. B 19, 2359 (1979)], which
constructs the Green's tensor of a cluster of nanoparticles from the sole
knowledge of the modes of the isolated constituent. The method is applied, for
the first time, to a scatterer with a non-trivial shape (namely, a pair of
elliptical wires) within a fully electrodynamic setting, and for the
computation of the Purcell enhancement and F\"{o}rster Resonant Energy Transfer
(FRET) rate enhancement, showing a good agreement with direct simulations. The
procedure is general, trivial to implement using standard electromagnetic
software, and holds for arbitrary shapes and number of scatterers forming the
cluster. Moreover, it is orders of magnitude faster than conventional direct
simulations for applications requiring the spatial variation of the Green's
tensor, promising a wide use in quantum technologies, free-electron light
sources and heat transfer, among others.


  At the beginning of the 20th century the classical electron theory (or,
perhaps more appropriately, the classical electromagnetic mass theory) - the
first physical theory that dared ask the question of what inertia and mass were
- was gaining momentum and there were hopes that physics would be finally able
to explain their origin. It is argued in this paper that if that promising
research path had not been inexplicably abandoned after the advent of
relativity and quantum mechanics, the contemporary physics would have revealed
not only the nature of inertia, mass, and gravitation, but most importantly
would have outlined the ways of their manipulation. Another goal of the paper
is to try to stimulate the search for the mechanism responsible for inertia and
gravitation by outlining a research direction, which demonstrates that the
classical electromagnetic mass theory in conjunction with the principle of
equivalence offers such a mechanism.


  We consider the modification of Newton's gravity law in Dolgov's higher spin
models designed to compensate the cosmological constant. We find that the
effective Planck mass is unacceptably large in these models. We also point out
that the properties of gravitational waves are entirely different in these
models as compared to general relativity.


  Recent theoretical predictions on DNA mechanical separation induced by
pulling forces are numerically tested within a model in which self-avoidance
for DNA strands is fully taken into account. DNA strands are described by
interacting pairs of self avoiding walks (SAW) which are pulled apart by a
force applied at the two extremities. The whole phase diagram is spanned by
extensive Monte Carlo (MC) simulations and the existence of a low temperature
denaturation is confirmed. The basic features of the phase diagram and the
re-entrant phase boundary are also obtained with a simple heuristic argument
based on an energy-entropy estimate.


  We discuss the domain variation solutions notion for some degenerate elliptic
two-phase free boundary problems as well as the viscosity definition of the
problem when the operator is degenerate.


  Standard deep reinforcement learning methods such as Deep Q-Networks (DQN)
for multiple tasks (domains) face scalability problems. We propose a method for
multi-domain dialogue policy learning---termed NDQN, and apply it to an
information-seeking spoken dialogue system in the domains of restaurants and
hotels. Experimental results comparing DQN (baseline) versus NDQN (proposed)
using simulations report that our proposed method exhibits better scalability
and is promising for optimising the behaviour of multi-domain dialogue systems.


  Chalcogenides, which refer to chalcogen anions, have attracted considerable
attention in multiple fields of applications, such as optoelectronics,
thermoelectrics, transparent contacts, and thin film transistors. In comparison
to oxide counterparts, chalcogenides have demonstrated higher mobility and
\textit{p}-type dopability, owing to larger orbital overlaps between metal-X
covalent chemical bondings and higher-energy valence bands derived by
p-orbitals. Despite the potential of chalcogenides, the number of successfully
synthesized compounds remains relatively low compared to oxides, suggesting the
presence of numerous unexplored chalcogenides with fascinating physical
characteristics. In this study, we implemented a systematic high-throughput
screening process combined with first-principles calculations on ternary
chalcogenides using 34 crystal structure prototypes. We generated a
computational material database containing over 400,000 compounds by exploiting
the ion-substitution approach at different atomic sites with elements in the
periodic table. The thermodynamic stabilities of the candidates were validated
using the chalcogenides included in the Open Quantum Materials Database.
Moreover, we trained a model based on Crystal Graph Convolutional Neural
Networks to predict the thermodynamic stability of novel materials.
Furthermore, we theoretically evaluated the electronic structures of the stable
candidates using accurate hybrid functionals. A series of in-depth
characteristics, including the carrier effective masses, electronic
configuration, and photovoltaic conversion efficiency, was also investigated.
Our work provides useful guidance for further experimental research in the
synthesis and characterization of such chalcogenides as promising candidates,
as well as charting the stability and optoelectronic performance of ternary
chalcogenides.


  We investigate effect of position-dependent mass profiles on dynamical
breaking of N-fold supersymmetry in several type B and type X_2 models. We find
that N-fold supersymmetry in rational potentials in the constant-mass
background are steady against the variation of mass profiles. On the other
hand, some physically relevant mass profiles can change the pattern of
dynamical N-fold supersymmetry breaking in trigonometric, hyperbolic, and
exponential potentials of both type B and type X_2. The latter results open the
possibility of detecting experimentally phase transition of N-fold as well as
ordinary supersymmetry at a realistic energy scale.


  A pair $(a, b)$ of positive integers is a pythagorean pair if $a^2 + b^2 =
\Box$ (i.e., $a^2 + b^2$ is a square). A pythagorean pair $(a, b)$ is called a
double-pythapotent pair if there is another pythagorean pair $(k,l)$ such that
$(ak,bl)$ is a pythagorean pair, and it is called a quadratic pythapotent pair
if there is another pythagorean pair $(k,l)$ which is not a multiple of
$(a,b)$, such that $(a^2k,b^2l)$ is a pythagorean pair. To each pythagorean
pair $(a, b)$ we assign an elliptic curve $\Gamma_{a,b}$ with torsion group
$\mathbb Z/2\mathbb Z\times\mathbb Z/4\mathbb Z$, such that $\Gamma_{a,b}$ has
positive rank if and only if $(a, b)$ is a double-pythapotent pair. Similarly,
to each pythagorean pair $(a, b)$ we assign an elliptic curve $\Gamma_{a^2
,b^2}$ with torsion group $\mathbb Z/2\mathbb Z\times\mathbb Z/8\mathbb Z$,
such that $\Gamma_{a^2,b^2}$ has positive rank if and only if $(a,b)$ is a
quadratic pythapotent pair. Moreover, in the later case we obtain that every
elliptic curve $\Gamma$ with torsion group $\mathbb Z/2\mathbb Z\times\mathbb
Z/8\mathbb Z$ is isomorphic to a curve of the form $\Gamma_{a^2 ,b^2}$ , where
$(a,b)$ is a pythagorean pair. As a side-result we get that if $(a,b)$ is a
double-pythapotent pair, then there are infinitely many pythagorean pairs $(k,
l)$, not multiples of each other, such that $(ak, bl)$ is a pythagorean pair;
the analogous result holds for quadratic pythapotent pairs.


  We study the dimension and construct a basis for $C^1$-smooth isogeometric
function spaces over two-patch domains. In this context, an isogeometric
function is a function defined on a B-spline domain, whose graph surface also
has a B-spline representation. We consider constructions along one interface
between two patches. We restrict ourselves to a special case of planar B-spline
patches of bidegree (p,p) with $p \geq 3$, so-called analysis-suitable $G^1$
geometries, which are derived from a specific geometric continuity condition.
This class of two-patch geometries is exactly the one which allows, under
certain additional assumptions, $C^1$ isogeometric spaces with optimal
approximation properties (Collin et al., 2016).
  Such spaces are of interest when solving numerically fourth-order PDE
problems, such as the biharmonic equation, using the isogeometric method. In
particular, we analyze the dimension of the $C^1$-smooth isogeometric space and
present an explicit representation for a basis of this space. Both the
dimension of the space and the basis functions along the common interface
depend on the considered two-patch parameterization. Such an explicit, geometry
dependent basis construction is important for an efficient implementation of
the isogeometric method. The stability of the constructed basis is numerically
confirmed for an example configuration.


  An anomaly free non-universal $U(1)_{X}$ extension to the Minimal
Supersymmetric Standard Model is proposed, where additional two $SU(2)$ doublet
superfields and four singlet superfields complement the scalar sector of the
model. The fermion sector is extended by considering additional superfields
containing three quark singlets, two charged lepton singlet superfields and six
neutral leptons. A tree-level massless electron is found so radiative
corrections are considered to match the mass spectrum with both SUSY and
non-SUSY contributions. Likewise, a massless neutrino is found and analytic
expressions for massive mass eigenstates are obtained via inverse-seesaw
mechanism, which implies a known neutrino mass spectrum for both normal and
inverse ordering. Lastly, a numerical fitting of the model parameters to the
PMNS matrix is done.


  Context. While in serverless computing, application resource management and
operational concerns are generally delegated to the cloud provider, ensuring
that serverless applications meet their performance requirements is still a
responsibility of the developers. Performance testing is a commonly used
performance assessment practice; however, it traditionally requires visibility
of the resource environment.
  Objective. In this study, we investigate whether performance tests of
serverless applications are stable, that is, if their results are reproducible,
and what implications the serverless paradigm has for performance tests.
  Method. We conduct a case study where we collect two datasets of performance
test results: (a) repetitions of performance tests for varying memory size and
load intensities and (b) three repetitions of the same performance test every
day for ten months.
  Results. We find that performance tests of serverless applications are
comparatively stable if conducted on the same day. However, we also observe
short-term performance variations and frequent long-term performance changes.
  Conclusion. Performance tests for serverless applications can be stable;
however, the serverless model impacts the planning, execution, and analysis of
performance tests.


  Unsupervised blind source separation methods do not require a training phase
and thus cannot suffer from a train-test mismatch, which is a common concern in
neural network based source separation. The unsupervised techniques can be
categorized in two classes, those building upon the sparsity of speech in the
Short-Time Fourier transform domain and those exploiting non-Gaussianity or
non-stationarity of the source signals. In this contribution, spatial mixture
models which fall in the first category and independent vector analysis (IVA)
as a representative of the second category are compared w.r.t. their separation
performance and the performance of a downstream speech recognizer on a
reverberant dataset of reasonable size. Furthermore, we introduce a serial
concatenation of the two, where the result of the mixture model serves as
initialization of IVA, which achieves significantly better WER performance than
each algorithm individually and even approaches the performance of a much more
complex neural network based technique.


  In the last few years, Motor Current Signature Analysis (MCSA) has proven to
be an effective method for electrical machines condition monitoring. Indeed,
many mechanical and electrical faults manifest as side-band spectral components
generated around the fundamental frequency component of the motor current.
These components are called interharmonics and they are a major focus of fault
detection using MCSA. However, the main drawback of this approach is that the
interference of other more prevalent components can obstruct the effect of
interharmonics in the spectrum and may therefore impede fault detection
accuracy. Thus, we propose in this paper an alternative approach that
decomposes the different current components based on the Vandermonde model and
implements the tracking of each distinct component in time and spectral
domains. This is achieved by estimating their respective relevant parameters
using the Gradient Descent algorithm. The results of this work prove to be
promising and establish the parametric tracking of the electrical current
components using the Gradient Descent algorithm as a reliable monitoring
approach.


  Consider a $C^{\infty}$ closed connected Riemannian manifold $(M, g)$ with
negative curvature. The unit tangent bundle $SM$ is foliated by the (weak)
stable foliation $\mathcal{W}^s$ of the geodesic flow. Let $\Delta^s$ be the
leafwise Laplacian for $\mathcal{W}^s$ and let $\overline{X}$ be the geodesic
spray, i.e., the vector field that generates the geodesic flow. For each
$\lambda$, the operator $\mathcal{L}_{\lambda}:=\Delta^s+\lambda \overline{X}$
generates a diffusion for $\mathcal{W}^s$. We show that, as $\lambda\to
-\infty$, the unique stationary probability measure for the leafwise diffusion
of $\mathcal{L}_{\lambda}$ converges to the normalized Lebesgue measure on
$SM$.


  Recommendation problems with large numbers of discrete items, such as
products, webpages, or videos, are ubiquitous in the technology industry. Deep
neural networks are being increasingly used for these recommendation problems.
These models use embeddings to represent discrete items as continuous vectors,
and the vocabulary sizes and embedding dimensions, although heavily influence
the model's accuracy, are often manually selected in a heuristical manner. We
present Neural Input Search (NIS), a technique for learning the optimal
vocabulary sizes and embedding dimensions for categorical features. The goal is
to maximize prediction accuracy subject to a constraint on the total memory
used by all embeddings. Moreover, we argue that the traditional Single-size
Embedding (SE), which uses the same embedding dimension for all values of a
feature, suffers from inefficient usage of model capacity and training data. We
propose a novel type of embedding, namely Multi-size Embedding (ME), which
allows the embedding dimension to vary for different values of the feature.
During training we use reinforcement learning to find the optimal vocabulary
size for each feature and embedding dimension for each value of the feature. In
experiments on two common types of large scale recommendation problems, i.e.
retrieval and ranking problems, NIS automatically found better vocabulary and
embedding sizes that result in $6.8\%$ and $1.8\%$ relative improvements on
Recall@1 and ROC-AUC over manually optimized ones.


  We study the heat kernel of the sub-Laplacian L on the CR sphere S2n+1. An
explicit and geometrically meaningful formula for the heat kernel is obtained.
As a by-product we recover in a simple way the Green function of the conformal
sub- Laplacian -L + n2 that was obtained by Geller [12], and also get an
explicit formula for the sub-Riemannian distance. The key point is to work in a
set of coordinates that reflects the symmetries coming from the fibration S2n+1
\rightarrow CPn.


  In this work we study the dynamics of spinning binary black hole systems in
the strong field regime. For this purpose we extract from numerical relativity
simulations the binding energy, specific orbital angular momentum, and
gauge-invariant orbital frequency. The goal of our work is threefold: First, we
extract the individual spin contributions to the binding energy, in particular
the spin-orbit, spin-spin, and cubic-in-spin terms. Second, we compare our
results with predictions from waveform models and find that while
post-Newtonian approximants are not capable of representing the dynamics during
the last few orbits before merger, there is good agreement between our data and
effective-one-body approximants as well as the numerical relativity surrogate
models. Finally, we present phenomenological representations for the binding
energy for non-spinning systems with mass ratios up to $q = 10$ and for the
spin-orbit interaction for mass ratios up to $q = 8$ obtaining accuracies of
$\lesssim 0.1\%$ and $\lesssim 6\%$, respectively.


  This paper introduces an interpretable contextual bandit algorithm using
Tsetlin Machines, which solves complex pattern recognition tasks using
propositional logic. The proposed bandit learning algorithm relies on
straightforward bit manipulation, thus simplifying computation and
interpretation. We then present a mechanism for performing Thompson sampling
with Tsetlin Machine, given its non-parametric nature. Our empirical analysis
shows that Tsetlin Machine as a base contextual bandit learner outperforms
other popular base learners on eight out of nine datasets. We further analyze
the interpretability of our learner, investigating how arms are selected based
on propositional expressions that model the context.


  The 2000 outburst of V445 Puppis shows unique properties, such as absence of
hydrogen, enrichment of helium and carbon, slow development of the light curve
with a small amplitude that does not resemble any classical novae. This object
has been suggested to be the first example of helium novae. We calculate
theoretical light curves of helium novae and reproduce the observational light
curve of V445 Pup. Modeling indicates a very massive white dwarf (WD), more
massive than 1.3 Msun. The companion star is possibly either a helium star or a
helium-rich main-sequence star. We estimate the ignition mass as several times
10^{-5} Msun, the corresponding helium accretion rate as several times 10^{-7}
Msun yr^{-1}, and the recurrence period as several tens of years. These values
suggest that the WD is growing in mass and ends up either a Type Ia supernova
or an accretion induced collapse to a neutron star.


  We analyze the thermodynamical potential of a lattice gas model with three
components and five parameters using the methods of Catastrophe Theory. We find
the highest singularity, which has codimension five, and establish its
transversality. Hence the corresponding seven-degree Landau potential, the
canonical form Wigwam or $A_6$, constitutes the adequate starting point to
study the overall phase diagram of this model.


  The recent progress in studies of two-nucleon~(2N) short-range
correlations~(SRCs) are reviewed with the main emphasize given to the
observation of the strong dominance of proton-neutron~(pn) SRCs in nuclei as
compared to proton-proton and neutron-neutron SRCs. Based on the pn SRC
dominance a specific prediction is made for the dynamical structure of 3N- SRCs
for inclusive $A(e,e^\prime)X$ reactions, according to which the 3N- SRCs are
generated through the sequence of two short range $pn$ interactions. This
allowed us to predict that the height of the plateau in the ratios of inclusive
eA cross sections to that of $^3He$ in the 3N-SRC region is related to the
height of the plateau in the 2N-SRC region by a quadratic relation. The
analysis of the available experimental data supports validity of such a
relation.


  Empirical evidence for the Heckscher-Ohlin model has been inconclusive. We
test whether the predictions of the Heckscher-Ohlin Theorem with respect to
labor and capital find support in value-added trade. Defining labor-capital
intensities and endowments as the ratio of hours worked to the nominal capital
stock, we find evidence against Heckscher-Ohlin. However, taking the ratio of
total factor compensations, and thus accounting for differences in
technologies, we find strong support for it. That is, labor-abundant countries
tend to export value-added in goods of labor-intensive industries. Moreover,
differentiating between broad industries, we find support for nine out of
twelve industries.


  We prove a Hermitian matrix version of Bougerol's identity. Moreover, we
construct the Hua-Pickrell measures on Hermitian matrices, as stochastic
integrals with respect to a drifting Hermitian Brownian motion and with an
integrand involving a conjugation by an independent, matrix analogue of the
exponential of a complex Brownian motion with drift.


  The elegance and usefulness of a complex formulation of the basic lensing
equations is demonstrated with a number of applications. Using standard tools
of complex function theory, we present, for instance, a new proof of the fact
that the number of images produced by a regular lens is always odd, provided
that the source is not located on a caustic. Several differential and integral
relations between the mean curvature and the (reduced) shear are also derived.
These emerge almost automatically from complex differentiations of the
differential of the lens map, together with Stokes' theorem for complex valued
1-forms.


  Target space symmetries are studied for orbifold compactified string theories
containing Wilson line background fields. The symmetries determined are for
those moduli which contribute to the string loop threshold corrections of the
gauge coupling constants. The groups found are subgroups of the modular group
$PSL(2, Z)$ and depend on the choice of discrete Wilson lines and the shape of
the underlying six-dimensional lattice.


  Let $R$ be a commutative noetherian ring, $\fa$ an ideal of $R$ and $M,N$
finite $R$--modules. We prove that the following statements are equivalent.
\begin{enumerate} \item[(i)] $\lc^{i}_{\fa}(M,N)$ is finite for all $i< n$.
\item[(ii)] $\Coass_R(\lc^{i}_{\fa}(M,N)) \subset \V{(\fa)}$ for all $i< n$.
\item[(iii)] $\lc^{i}_{\fa}(M,N)$ is coatomic for all $i< n$. \end{enumerate}
If $\pd M$ is finite and $r$ be a non-negative integer such that $r>\pd M$ and
$\lc^{i}_{\fa}(M,N)$ is finite (resp. minimax) for all $i\geq r$, then
$\lc^{i}_{\fa}(M,N)$ is zero (resp. artinian) for all $i\geq r$.


  We consider corrections to the Penrose limit of AdS_3 \times S^3 with NS-NS
flux which are due to the terms next to leading order in inverse radius
expansion. The worldsheet theory of a lightcone string is interacting due to
the presence of quartic terms in the action. Perturbative corrections to the
spectrum are shown to agree with the results from the exact quantization in
AdS_3 \times S^3.


  Theoretical studies of the metamagnetism and anomalous phase of Sr3Ru2O7 have
focused on the role of van Hove singularities, although much experimental
evidence points towards quantum criticality having a large effect. We
investigate the magnetic and thermodynamic properties of systems where magnetic
field tunes through such a peak in the electronic density of states. We study
the generic case of a van Hove singularity in 2D. We see that in combination
with the requirement of number conservation and interaction effects the peak in
the density of states produces several interesting phenomena including raising
the critical field of the transition above naive estimates, altering the
relationship between temperature and field scales and creating a distinctive
double-peak structure in the electronic specific heat. We show that this
apparent non-Fermi liquid behaviour can be caused at mean-field level by a peak
in the density of states.


  We study the Bishop-Phelps-Bollob\'as property (BPBp for short) for compact
operators. We present some abstract techniques which allows to carry the BPBp
for compact operators from sequence spaces to function spaces. As main
applications, we prove the following results. Let $X$, $Y$ be Banach spaces. If
$(c_0,Y)$ has the BPBp for compact operators, then so do $(C_0(L),Y)$ for every
locally compact Hausdorff topological space $L$ and $(X,Y)$ whenever $X^*$ is
isometrically isomorphic to $\ell_1$. If $X^*$ has the Radon-Nikod\'ym property
and $(\ell_1(X),Y)$ has the BPBp for compact operators, then so does
$(L_1(\mu,X),Y)$ for every positive measure $\mu$; as a consequence,
$(L_1(\mu,X),Y)$ has the the BPBp for compact operators when $X$ and $Y$ are
finite-dimensional or $Y$ is a Hilbert space and $X=c_0$ or $X=L_p(\nu)$ for
any positive measure $\nu$ and $1< p< \infty$. For $1\leqslant p <\infty$, if
$(X,\ell_p(Y))$ has the BPBp for compact operators, then so does
$(X,L_p(\mu,Y))$ for every positive measure $\mu$ such that $L_1(\mu)$ is
infinite-dimensional. If $(X,Y)$ has the BPBp for compact operators, then so do
$(X,L_\infty(\mu,Y))$ for every $\sigma$-finite positive measure $\mu$ and
$(X,C(K,Y))$ for every compact Hausdorff topological space $K$.


  We investigate the dynamics of a two-dimensional array of oscillators with
phase-shifted coupling. Each oscillator is allowed to interact with its
neighbors within a finite radius. The system exhibits various patterns
including squarelike pinwheels, (anti)spirals with phase-randomized cores, and
antiferro patterns embedded in (anti)spirals. We consider the symmetry
properties of the system to explain the observed behaviors, and estimate the
wavelengths of the patterns by linear analysis. Finally, we point out the
implications of our work for biological neural networks.


  We prove that any quasirandom uniform hypergraph $H$ can be approximately
decomposed into any collection of bounded degree hypergraphs with almost as
many edges. In fact, our results also apply to multipartite hypergraphs and
even to the sparse setting when the density of $H$ quickly tends to $0$ in
terms of the number of vertices of $H$. Our results answer and address
questions of Kim, K\"uhn, Osthus and Tyomkyn; and Glock, K\"uhn and Osthus as
well as Keevash.
  The provided approximate decompositions exhibit strong quasirandom properties
which is very useful for forthcoming applications. Our results also imply
approximate solutions to natural hypergraph versions of long-standing graph
decomposition problems, as well as several decomposition results for
(quasi)random simplicial complexes into various more elementary simplicial
complexes such as triangulations of spheres and other manifolds.


  Conventional optimal power flow (OPF) solvers assume full observability of
the involved system states. However, in practice, there is a lack of reliable
system monitoring devices in the distribution networks. To close the gap
between the theoretic algorithm design and practical implementation, this work
proposes to solve the OPF problems based on the state estimation (SE) feedback
for the distribution networks where only a part of the involved system states
are physically measured. The SE feedback increases the observability of the
under-measured system and provides more accurate system states monitoring when
the measurements are noisy. We analytically investigate the convergence of the
proposed algorithm. The numerical results demonstrate that the proposed
approach is more robust to large pseudo measurement variability and inherent
sensor noise in comparison to the other frameworks without SE feedback.


  We construct topological Wess-Zumino term for supercoset sigma-models on
various AdS(3) backgrounds. For appropriately chosen set of parameters, the
sigma-model remains integrable when the Wess-Zumino term is added to the
action. Moreover, the conditions for integrability, kappa-symmetry and
conformal invariance are equivalent to each other.


  $^{96}_{44}$Ru+$^{96}_{44}$Ru and $^{96}_{40}$Zr+$^{96}_{40}$Zr collisions at
$\sqrt{s_{_{\rm NN}}}=200$ GeV provide unique opportunities to study the
geometry and fluctuations raised from the deformation of the colliding nuclei.
Using iEBE-VISHNU hybrid model, we predict ${\rm ac}_{2}\{3\}$ ratios between
these two collision systems and demonstrate that the ratios of ${\rm
ac}_{2}\{3\}$, as well as the ratios of the involving flow harmonics and
event-plane correlations, are sensitive to quadrupole and octupole
deformations, which could provide strong constrains on the shape differences
between $^{96}$Ru and $^{96}$Zr. We also study the nonlinear response
coefficients $\chi_{4,22}$, which show insensitivity to the deformation effect.


  For Lax-pair isospectral deformations whose associated spectrum, for given
initial data, consists of the disjoint union of a finitely denumerable discrete
spectrum (solitons) and a continuous spectrum (continuum), the matrix
Riemann-Hilbert problem approach is used to derive the leading-order
asymptotics as $| t | \to \infty$ $(x/t \sim \mathcal{O} (1))$ of solutions $(u
= u(x,t))$ to the Cauchy problem for the defocusing non-linear Schr\"{o}dinger
equation (D${}_{f}$NLSE), $\mi \partial_{t}u + \partial_{x}^{2}u - 2(| u |^{2}
- 1) u = 0$, with finite-density initial data $u(x,0) =_{x \to \pm \infty} \exp
(\tfrac{\mi (1 \mp 1) \theta}{2})(1 + o(1))$, $\theta \in [0,2\pi)$. The
D${}_{f}$NLSE dark soliton position shifts in the presence of the continuum are
also obtained.


  We investigate ultrathin superconducting TiN films, which are very close to
the localization threshold. Perpendicular magnetic field drives the films from
the superconducting to an insulating state, with very high resistance. Further
increase of the magnetic field leads to an exponential decay of the resistance
towards a finite value. In the limit of low temperatures, the saturation value
can be very accurately extrapolated to the universal quantum resistance h/e^2.
Our analysis suggests that at high magnetic fields a new ground state, distinct
from the normal metallic state occurring above the superconducting transition
temperature, is formed. A comparison with other studies on different materials
indicates that the quantum metallic phase following the magnetic-field-induced
insulating phase is a generic property of systems close to the disorder-driven
superconductor-insulator transition.


  We explore particle physics beyond accelerator energies, motivated by
questions exposed in astroparticle physics observations: 1) Are there
reasonable modifications to the standard extrapolations of LHC-tuned hadronic
interaction models, so that ultrahigh energy cosmic ray (UHECR) showers are
well-described with a purely protonic primary composition rather than requiring
a tuned, energy-dependent composition mixture as needed in conventional models?
2) What modifications to standard models can solve the deficiency in the
predicted ground signal found in hybrid UHECR observations? We find that a pure
proton composition provides an excellent fit to shower observations, if the QCD
inelastic cross section increases more rapidly above $E_{\rm cm} \approx 60$
TeV than in conventional models, and speculate as to possible reasons this may
happen; the "muon deficiency" can be cured by relatively minor modifications to
particle ratios in unexplored kinematic regimes below and above LHC energies.


  For compact Riemannian manifolds with convex boundary, B.White proved the
following alternative: Either there is an isoperimetric inequality for minimal
hypersurfaces or there exists a closed minimal hypersurface, possibly with a
small singular set. There is the natural question if a similar result is true
for submanifolds of higher codimension. Specifically, B.White asked if the
non-existence of an isoperimetric inequality for k-varifolds implies the
existence of a nonzero, stationary, integral k-varifold. We present examples
showing that this is not true in codimension greater than two. The key step is
the construction of a Riemannian metric on the closed four-dimensional ball B
with the following properties: (1) B has strictly convex boundary. (2) There
exists a complete nonconstant geodesic. (3) There does not exist a closed
geodesic in B.


  Using optical dipole forces we have realized controlled transport of a single
or any desired small number of neutral atoms over a distance of a centimeter
with sub-micrometer precision. A standing wave dipole trap is loaded with a
prescribed number of cesium atoms from a magneto-optical trap. Mutual detuning
of the counter-propagating laser beams moves the interference pattern, allowing
us to accelerate and stop the atoms at preselected points along the standing
wave. The transportation efficiency is close to 100%. This optical "single-atom
conveyor belt" represents a versatile tool for future experiments requiring
deterministic delivery of a prescribed number of atoms on demand.


  Approximately half of the nearby E+A galaxies followed up with 21-cm
observations have detectable HI emission. The optical spectra of these galaxies
show strong post-starburst stellar populations but no optical emission lines
implying star-formation is not ongoing despite the presence of significant gas
reservoirs. We have obtained integral field spectroscopic follow up
observations of the two brightest, and nearest, of the six E+A galaxies with HI
21-cm emission in the recent sample of Zwaan et al. (2013). In the central
regions of both galaxies the observations are consistent with a post-starburst
population with little emission. However, outside the central regions both
galaxies have strong optical emission lines, with a clumpy or knot-like
distribution, indicating ongoing star-formation. We conclude that in these two
cases the presence of optical spectra lacking evidence for star-formation while
a large gas mass is present can be explained by an aperture effect in selecting
the nearby E+A galaxies using single-fibre spectroscopy that probes only the
galaxy core.


  SDSS-V will be an all-sky, multi-epoch spectroscopic survey of over six
million objects. It is designed to decode the history of the Milky Way, trace
the emergence of the chemical elements, reveal the inner workings of stars, and
investigate the origin of planets. It will also create an integral-field
spectroscopic map of the gas in the Galaxy and the Local Group that is 1,000x
larger than the current state of the art and at high enough spatial resolution
to reveal the self-regulation mechanisms of galactic ecosystems. SDSS-V will
pioneer systematic, spectroscopic monitoring across the whole sky, revealing
changes on timescales from 20 minutes to 20 years. The survey will thus track
the flickers, flares, and radical transformations of the most luminous
persistent objects in the universe: massive black holes growing at the centers
of galaxies.
  The scope and flexibility of SDSS-V will be unique among extant and future
spectroscopic surveys: it is all-sky, with matched survey infrastructures in
both hemispheres; it provides near-IR and optical multi-object fiber
spectroscopy that is rapidly reconfigurable to serve high target densities,
targets of opportunity, and time-domain monitoring; and it provides optical,
ultra-wide-field integral field spectroscopy. SDSS-V, with its programs
anticipated to start in 2020, will be well-timed to multiply the scientific
output from major space missions (e.g., TESS, Gaia, eROSITA) and ground-based
projects. SDSS-V builds on the 25-year heritage of SDSS's advances in data
analysis, collaboration infrastructure, and product deliverables. The project
is now refining its science scope, optimizing the survey strategies, and
developing new hardware that builds on the SDSS-IV infrastructure. We present
here an overview of the current state of these developments as we seek to build
our worldwide consortium of institutional and individual members.


  In this work, we introduce a personalised and age-specific Net Benefit
function, composed of benefits and costs, to recommend optimal timing of risk
assessments for cardiovascular disease prevention. We extend the 2-stage
landmarking model to estimate patient-specific CVD risk profiles, adjusting for
time-varying covariates. We apply our model to data from the Clinical Practice
Research Datalink, comprising primary care electronic health records from the
UK. We find that people at lower risk could be recommended an optimal
risk-assessment interval of 5 years or more. Time-varying risk-factors are
required to discriminate between more frequent schedules for higher-risk
people.


  For the quintom models with arbitrary potential $V=V(\phi,\sigma)$, the
asymptotic value of equation of state parameter w is obtained by a new method.
In this method, w of stable attractors are calculated by using the ratio (d ln
V)/(d ln a) in asymptotic region. All the known results, have been obtained by
other methods, are reproduced by this method as specific examples.


  Nanocrystalline silicon and silicon-germanium alloys are promising
thermoelectric materials that have achieved substantially improved figure of
merits compared to their bulk counterparts. This enhancement is typically
attributed to a reduction in lattice thermal conductivity by phonon scattering
at grain boundaries. However, further improvements are difficult to achieve
because grain boundary scattering is poorly understood, with recent
experimental observations suggesting that the phonon transmissivity may depend
on phonon frequency rather than being constant as in the commonly used gray
model. Here, we examine the impact of frequency-dependent grain boundary
scattering in nanocrystalline silicon and silicon-germanium alloys in a
realistic 3D geometry using frequency-dependent variance-reduced Monte Carlo
simulations. We find that the grain boundary may not be as effective as
predicted by the gray model in scattering certain phonons, with a substantial
amount of heat being carried by low frequency phonons with mean free paths
longer than the grain size. Our result will help guide the design of more
efficient thermoelectrics.


  We analyse the anisotropy of homogeneous turbulence in an electrically
conducting fluid submitted to a uniform magnetic field, for low magnetic
Reynolds number, in the quasi- static approximation. We interpret disagreeing
previous predictions between linearized theory and simulations: in the linear
limit, the kinetic energy of transverse velocity components, normal to the
magnetic field, decays faster than the kinetic energy of the axial component,
along the magnetic field (Moffatt (1967)); whereas many numerical studies
predict a final state characterised by dominant energy of transverse velocity
components. We investigate the corresponding nonlinear phenomenon using Direct
Numerical Simulations of freely-decaying turbulence, and a two-point
statistical spectral closure based on the Eddy Damped Quasi-Normal Markovian
model. The transition from the three-dimensional turbulent flow to a
"two-and-a-half-dimensional" flow (Montgomery & Turner (1982)) is a result of
the combined effects of short-time linear Joule dissipation and longer time
nonlinear creation of polarisation anisotropy. It is this combination of linear
and nonlinear effects which explains the disagreement between predictions from
linearized theory and results from numerical simulations. The transition is
characterized by the elongation of turbulent structures along the applied
magnetic field, and by the strong anisotropy of directional two-point
correlation spectra, in agreement with experimental evidence. Inertial
equatorial transfers in both DNS and the model are presented to describe in
detail the most important equilibrium dynamics. Spectral scalings are
maintained in high Reynolds number turbulence attainable only with the EDQNM
model, which also provides simplified modelling of the asymptotic state of
quasi-static MHD turbulence.


  We have studied the effect of free space nucleon radius on the nuclear matter
and slowly rotating neutron star properties within a relativistic mean field
model with the inclusion of omega-rho mixing nonlinear term. We use the same
density dependent radius as in our previous work. However, in the present work
we utilize the parameter sets with more proper symmetric nuclear matter (SNM)
predictions for a number of different nucleon radii. To this end, the isoscalar
parameters in each parameter set and the cutoff parameter $\beta$ are adjusted
by fitting the corresponding SNM properties at sub-saturation density to the
prediction of IUFSU parameter set. We have obtained that the assumption of
composite nucleons with free space radius $r \le 0.83$ fm is still compatible
with the currently acceptable nuclear matter (NM) properties beyond the
saturation density. We have also found that the effect of free space nucleon
radius could be imprinted in the radius, moment of inertia, and crust
properties of the slowly rotating neutron star.


  This study investigated e-resources use, storage, the preferred format for
reading, and difficulties faced while accessing e-resources. Electronic
resources are playing a crucial role all over the world, and they are
increasing widely in all age groups of the academic community. The main aim of
the law academics' role is to know the effective use of electronic resources.
For this study, we adopted a descriptive survey research design that was used
to collect feedback from the respondents through the survey and Google form.
The study samples are Progressive Education Society's Modern Law College
affiliated with Savitribai Phule Pune University. BA LLB students are samples
of the study.


  Locally, a screen integrable globally null manifold $M$ splits through a
Riemannian leaf $M'$ of its screen distribution and a null curve $\mathcal{C}$
tangent to its radical distribution. The leaf $M'$ carries a lot of geometric
information about $M$ and, in fact, forms a basis for the study of expanding
and non-expanding horizons in black hole theory. In the present paper, we
introduce a degenerate Ricci-type flow in $M'$ via the intrinsic Ricci tensor
of $M$. Several new gradient estimates regarding the flow are proved.


  We consider a type of Quantum Electro-Mechanical System, known as the shuttle
system, first proposed by Gorelik et al., [Phys. Rev. Lett., 80, 4526, (1998)].
We use a quantum master equation treatment and compare the semi-classical
solution to a full quantum simulation to reveal the dynamics, followed by a
discussion of the current noise of the system. The transition between
tunnelling and shuttling regime can be measured directly in the spectrum of the
noise.


  Deep learning algorithms lack human-interpretable accounts of how they
transform raw visual input into a robust semantic understanding, which impedes
comparisons between different architectures, training objectives, and the human
brain. In this work, we take inspiration from neuroscience and employ
representational approaches to shed light on how neural networks encode
information at low (visual saliency) and high (semantic similarity) levels of
abstraction. Moreover, we introduce a custom image dataset where we
systematically manipulate salient and semantic information. We find that
ResNets are more sensitive to saliency information than ViTs, when trained with
object classification objectives. We uncover that networks suppress saliency in
early layers, a process enhanced by natural language supervision (CLIP) in
ResNets. CLIP also enhances semantic encoding in both architectures. Finally,
we show that semantic encoding is a key factor in aligning AI with human visual
perception, while saliency suppression is a non-brain-like strategy.


  The minimum distance graph of an extended Preparata code P(m) has vertices
corresponding to codewords and edges corresponding to pairs of codewords that
are distance 6 apart. The clique structure of this graph is investigated and it
is established that the minimum distance graphs of two extended Preparata codes
are isomorphic if and only if the codes are equivalent.


  Heat capacity is an invaluable quantity in condensed matter physics, yet it
has been so far experimentally inaccessible in two-dimensional (2D) van der
Waals (vdW) materials, owing to their ultra-fast thermal relaxation times and
the lack of suitable nano-scale thermometers. Here, we demonstrate a novel
thermal relaxation calorimetry scheme that allows the first measurements of the
electronic heat capacity of graphene Ce. It is enabled by the grouping of a
radio-frequency Johnson noise thermometer, which can measure the electronic
temperature Te with a measurement sensitivity of {\delta}Te ~ 20 mK, and an
ultra-fast photo-mixed optical heater, which can simultaneously modulate Te
with a frequency of up to {\Omega}=0.2 THz. This combination allows record
sensitive and record fast measurements of the electronic heat capacity Ce <
10^(-19) J/K, with an electronic thermal relaxation time {\tau}e < 10^(-13),
representing orders of magnitude improvements as compared to previous
state-of-the-art calorimeters. These features embody a breakthrough in heat
capacity metrology of nano-scale and low-dimensional systems, and provide a new
avenue for the investigation of their thermodynamic quantities.


  We study the evolution of vortex sheets according to the Birkhoff-Rott
equation, which describe the motion of sharp shear interfaces governed by the
incompressible Euler equation in two dimensions. In a recent work, the authors
demonstrated within this context a marginal linear stability of circular vortex
sheets, standing in sharp contrast with classical instability of the flat
vortex sheet, which is known as the Kelvin-Helmholtz instability. This article
continues that analysis by investigating how non-linear effects induce
singularity formation near the circular vortex sheet. In high-frequency
regimes, the singularity formation is primarily driven by a complex-valued,
conjugated Burgers equation, which we study by modifying a classical argument
from hyperbolic conservation laws. This provides a deeper understanding of the
mechanisms driving the breakdown of circular vortex sheets, which are observed
both numerically and experimentally.


  Image Classification is a fundamental task in the field of computer vision
that frequently serves as a benchmark for gauging advancements in Computer
Vision. Over the past few years, significant progress has been made in image
classification due to the emergence of deep learning. However, challenges still
exist, such as modeling fine-grained visual information, high computation
costs, the parallelism of the model, and inconsistent evaluation protocols
across datasets. In this paper, we conduct a comprehensive survey of existing
papers on Vision Transformers for image classification. We first introduce the
popular image classification datasets that influenced the design of models.
Then, we present Vision Transformers models in chronological order, starting
with early attempts at adapting attention mechanism to vision tasks followed by
the adoption of vision transformers, as they have demonstrated success in
capturing intricate patterns and long-range dependencies within images.
Finally, we discuss open problems and shed light on opportunities for image
classification to facilitate new research ideas.


  Many corner cube prisms, or retroreflectors, employ total internal reflection
(TIR) via uncoated rear surfaces. The different elliptical polarization states
emerging from the six unique paths through the corner cube complicate the
far-field diffraction pattern by introducing various phase delays between the
six paths. In this paper, we present a computational framework to evaluate
polarization through TIR corner cubes for arbitrary incidence angles and input
polarization states, presenting example output for key normal-incidence
conditions. We also describe a method to produce far-field diffraction patterns
resulting from the polarization analysis, presenting representative
images---broken into orthogonal polarizations, and characterizing key cases.
Laboratory confirmation is also presented for both polarization states and
far-field diffraction patterns.


  We investigate the formation of weakly bound, electronically excited,
heteronuclear 6Li40K* molecules by single-photon photoassociation in a
magneto-optical trap. We performed trap loss spectroscopy within a range of 325
GHz below the Li(2S_(1/2))+K(4P_(3/2)) and Li(2S_(1/2))+K(4P_(1/2)) asymptotic
states and observed more than 60 resonances, which we identify as rovibrational
levels of 7 of 8 attractive long-range molecular potentials. The long-range
dispersion coefficients and rotational constants are derived. We find large
molecule formation rates of up to ~3.5x10^7s^(-1), which are shown to be
comparable to those for homonuclear 40K_2*. Using a theoretical model we infer
decay rates to the deeply bound electronic ground-state vibrational level
X^1\Sigma^+(v'=3) of ~5x10^4s^(-1). Our results pave the way for the production
of ultracold bosonic ground-state 6Li40K molecules which exhibit a large
intrinsic permanent electric dipole moment.


  As high-average power ultrafast lasers become increasingly available for
nonlinear conversion, the temperature dependence of the material properties of
nonlinear crystals becomes increasingly relevant. Here, we present
temperature-dependent THz complex refractive index measurements of the organic
crystal BNA over a wide range of temperatures from 300 K down to 80 K for THz
frequencies up to 4 THz for the first time. Our measurements show that whereas
the temperature-dependent refractive index has only minor deviation from room
temperature values, the temperature-dependent absorption coefficient decreases
at low temperature. We additionally compare these measurements with conversion
efficiency and spectra observed during THz generation experiments in the same
temperature range and using the same crystal, using an ultrafast Yb-laser for
excitation. Surprisingly, the damage threshold of the material does not improve
significantly upon cooling, pointing to a nonlinear absorption mechanism being
responsible for damage. However, we observe a significant increase in THz yield
at lower temperatures, which is most likely due to the reduced THz absorption.
These findings will be useful for future designs of high average power pumped
organic-crystal based THz-TDS systems.


  We developed an algorithm to find and characterize gravitationally lensed
galaxies (arcs) to perform a comparison of the observed and simulated arc
abundance. Observations are from the Cluster Lensing And Supernova survey with
Hubble (CLASH). Simulated CLASH images are created using the MOKA package and
also clusters selected from the high resolution, hydrodynamical simulations,
MUSIC, over the same mass and redshift range as the CLASH sample. The
algorithm' s arc elongation accuracy, completeness and false positive rate are
determined and used to compute an estimate of the true arc abundance. We derive
a lensing efficiency of $4 \pm 1$ arcs (with length $\ge 6"$ and
length-to-width ratio $\ge 7$) per cluster for the X-ray selected CLASH sample,
$4 \pm 1$ arcs per cluster for the MOKA simulated sample and $3 \pm 1$ arcs per
cluster for the MUSIC simulated sample. The observed and simulated arc
statistics are in full agreement. We measure the photometric redshifts of all
detected arcs and find a median redshift $z_s = 1.9$ with 33% of the detected
arcs having $z_s > 3$. We find that the arc abundance does not depend strongly
on the source redshift distribution but is sensitive to the mass distribution
of the dark matter halos (e.g. the $c-M$ relation). Our results show that
consistency between the observed and simulated distributions of lensed arc
sizes and axial ratios can be achieved by using cluster-lensing simulations
that are carefully matched to the selection criteria used in the observations.


  Some properties of characteristic curves in connection with viscosity
solutions of Hamilton-Jacobi equations defined by Hopf-type formula are
studied. We investigate the points where the Hopf-type formula $u(t,x)$ is
differentiable, and the strip of the form $(0,t_0)\times \R^n$ of the domain
$\Omega$ where the viscosity solution $u(t,x)$ is continuously differentiable.
Moreover, we present the propagation of singularity in forward of $u(t,x).$


  Based on PYTHIA6.428, event-by-event fluctuations of the mean transverse
momentum in proton- proton collisions at sqrt_s = 7 TeV are studied using
several measures of the fluctuations. The study compares results of the
fluctuations for events where color reconnection is turned on, with those where
color reconnection is turned off. The comparison reveals that some of the
fluctuation measures are much more sensitive to color reconnection than others.
Through the comparison it is demonstrated for the first time that for
proton-proton collisions at the Large Hadron Collider, these sensitive measures
of the mean transverse momentum fluctuations can serve as alternative probes to
color reconnection and color reconnection is a non-trivial source of the
event-by-event fluctuations.


  We develop an obstruction theory for the existence and uniqueness of a
solution to the gluing problem for a destriction functor and apply it to some
well-known biset functors. The obstruction groups for this theory are reduced
cohomology groups of a category ${\mathcal D}_G$, whose objects are the
sections $(U,V)$ of $G$ with $V\neq 1$, and whose morphisms are defined as a
generalization of morphisms in the orbit category. Using this obstruction
theory, we calculate the obstruction group for the Dade group of a $p$-group
when $p$ is odd.


  Words (phrases or symbols) play a key role in human life. Word (phrase or
symbol) representation is the fundamental problem for knowledge representation
and understanding. A word (phrase or symbol) usually represents a name of a
category. However, it is always a challenge that how to represent a category
can make it easily understood. In this paper, a new representation for a
category is discussed, which can be considered a generalization of classic set.
In order to reduce representation complexity, the economy principle of category
representation is proposed. The proposed category representation provides a
powerful tool for analyzing conceptual systems, relations between words,
communication, knowledge, situations. More specifically, the conceptual system,
word relations and communication are mathematically defined and classified such
as ideal conceptual system, perfect communication and so on; relation between
words and sentences is also studied, which shows that knowledge are words.
Furthermore, how conceptual systems and words depend on situations is
presented, and how truth is defined is also discussed.


  Using spin-polarized scanning tunneling microscopy and density functional
theory we demonstrate the occurrence of a novel type of noncollinear spin
structure in Rh/Fe atomic bilayers on Ir(111). We find that higher-order
exchange interactions depend sensitively on the stacking sequence. For
fcc-Rh/Fe/Ir(111) frustrated exchange interactions are dominant and lead to the
formation of a spin spiral ground state with a period of about 1.5 nm. For
hcp-Rh/Fe/Ir(111) higher-order exchange interactions favor a double-row wise
antiferromagnetic or "uudd" state. However, the Dzyaloshinskii- Moriya
interaction at the Fe/Ir interface leads to a small angle of about 4{\deg}
between adjacent magnetic moments resulting in a canted "uudd" ground state.


  A relativistic radio component, which moves in a direction close to the sky
plane, will increase in flux density when it decelerates. This effect is the
basis for the qualitative model for GPS galaxies we present in this paper,
which can explain their low-variability convex spectrum, their compact double
or compact symmetric morphology, and the lack of GPS quasars at similar
redshifts. Components are expelled from the nucleus at relativistic speeds at a
large angle to the line of sight, and are decelerated (eg. by ram-pressure or
entrainment of the external gas) before contributing to a mini-lobe. The young
components are Doppler boosted in the direction of motion but appear fainter
for the observer. The non-relativistic mini-lobes dominate the structure and
are responsible for the low variability in flux density and the convex radio
spectrum as well as the compact double angular morphology. Had the same source
been orientated at a small angle to the line of sight, the young components
would be boosted in the observer's direction resulting in a flat and variable
radio spectrum at high frequencies. Hence the characteristic convex spectrum of
a GPS source would not be seen. These sources at small angles to the line of
sight are probably identified with quasars, and are not recognized as GPS
sources, but are embedded in the large population of flat spectrum variable
quasars and BL Lac objects. This leads to a deficiency in GPS/CSOs identified
with quasars.


  Structural, electronic and thermodynamic properties of native defects in GaS
and GaSe monolayers are investigated by means of accurate ab-initio
calculations. Based on their charge transition levels we assess the influence
of the studied defects on the electrical properties of the monolayers.
Specifically, we show that native defects do not behave as shallow dopants and
their presence cannot account for the experimentally observed intrinsic doping.
In addition, we predict that native defects are efficient compensation and
recombination centers. Besides pointing out their detrimental nature, we also
calculate the corresponding finite temperature formation energies and provide a
window of growth conditions able to reduce the concentration of all relevant
native defects.


  Finding an agreement among diverse opinions is a challenging topic in
multiagent systems. Recently, large language models (LLMs) have shown great
potential in addressing this challenge due to their remarkable capabilities in
comprehending human opinions and generating human-like text. However, they
typically rely on extensive human-annotated data. In this paper, we propose
Self-Agreement, a novel framework for fine-tuning LLMs to autonomously find
agreement using data generated by LLM itself. Specifically, our approach
employs the generative pre-trained transformer-3 (GPT-3) to generate multiple
opinions for each question in a question dataset and create several agreement
candidates among these opinions. Then, a bidirectional encoder representations
from transformers (BERT)-based model evaluates the agreement score of each
agreement candidate and selects the one with the highest agreement score. This
process yields a dataset of question-opinion-agreements, which we use to
fine-tune a pre-trained LLM for discovering agreements among diverse opinions.
Remarkably, a pre-trained LLM fine-tuned by our Self-Agreement framework
achieves comparable performance to GPT-3 with only 1/25 of its parameters,
showcasing its ability to identify agreement among various opinions without the
need for human-annotated data.


  This review article presents historical developments and recent advances in
our understanding on the three-body forces and Efimov physics, from an
interdisciplinary viewpoint encompassing nuclear physics and cold atoms.
Theoretical attempts to elucidate the three-body force with the chiral
effective field theory are explained, followed by an overview of experiments
aimed at observing signatures of the nuclear three-body force. Some recent
experimental and theoretical works in the field of cold atoms devoted to
measuring and engineering three-body forces among atoms are also presented. As
a phenomenon arising from the three-body effect, Efimov physics in both cold
atoms and nuclear systems is reviewed.


  This paper presents a simple method to fabricate micro-ball lens and its
array. The key technology is to use the hydrophobic characteristics of
polyterafluoroethylene (PTFE) substrate. High contact angle between melted
photoresist pattern and PTFE can generate micro-ball lens and its array. PTFE
thin film was spun onto a silicon wafer and dried in oven. Photoresist AZ4620
was used to pattern micro-columns with different diameters 60, 70 and 80
$\mu$m. A thermal reflow process then was applied to melt these micro-column
patterns resulted in micro-ball lens array. The achieved micro-ball lens array
with diameter 98 $\mu$m was fabricated using 80 $\mu$m in diameter patterns.
This method provides a simple fabrication process and low material cost.


  In this paper, a finite-state mean-reverting model for the short-rate, based
on the continuous time Ehrenfest process, will be examined. Two explicit
pricing formulae for zero-coupon bonds will be derived in the general and the
special symmetric cases. Its limiting relationship to the Vasicek model will be
examined with some numerical results.