  We have used spin-polarized neutron reflectometry to investigate the
magnetization profile of superlattices composed of ferromagnetic Gd and
superconducting Nb layers. We have observed a partial suppression of
ferromagnetic (F) order of Gd layers in [Gd($d_F$)/Nb(25nm)]$_{12}$
superlattices below the superconducting (S) transition of the Nb layers. The
amplitude of the suppression decreases with increasing $d_F$. By analyzing the
neutron spin asymmetry we conclude that the observed effect has an
electromagnetic origin - the proximity-coupled S layers screen out the external
magnetic field and thus suppress the F response of the Gd layers inside the
structure. Our investigation demonstrates the considerable influence of
electromagnetic effects on the magnetic properties of S/F systems.


  Atomic vapors are systems well suited for nonlinear optics studies but very
few direct measurements of their nonlinear refractive index have been reported.
Here we use the z-scan technique to measure the Kerr coefficient, $n_2$, for a
Cs vapor. Our results are analyzed through a four-level model, and we show that
coherence between excited levels as well as cross-population effects contribute
to the Kerr-nonlinearity.


  Within supersymmetric SU(5) GUT we suggest mechanisms for suppression of
baryon number violating dimension five and six operators. The mechanism is
based on the idea of split multiplets (i.e. quarks and leptons are not coming
from a single GUT state) which is realized by an extension with additional
vector-like matter. The construction naturally avoids wrong asymptotic relation
$\hat{M}_D=\hat{M}_E$. Thus, the long standing problems of the minimal SUSY
SU(5) GUT can be resolved.
  In a particular example of flavor structure and with additional ${\cal
U}(1)\tm {\cal Z}_{3N}$ symmetry we demonstrate how the split multiplet
mechanism works out. Namely, the considered model is compatible with successful
gauge coupling unification and realistic fermion mass pattern. The nucleon
decay rates are relatively suppressed and can be well compatible with current
experimental bounds.


  The recent reported gravitational wave detection motivates one to investigate
the properties of different black hole models, especially their behavior under
(axial) gravitational perturbation. Here, we study the quasinormal modes of
black holes in Weyl gravity. We derive the master equation describing the
quasinormal radiation by using a relation between the Schwarzschild-anti de
Sitter black holes and Weyl solutions, and also the conformal invariance
property of the Weyl action. It will be observed that the quasinormal mode
spectra of the Weyl solutions deviate from those of the Schwarzschild black
hole due to the presence of an additional linear $r$-term in the metric
function. We also consider the evolution of the Maxwell field on the background
spacetime and obtain the master equation of electromagnetic perturbations.
Then, we use the WKB approximation and asymptotic iteration method to calculate
the quasinormal frequencies. Finally, the time evolution of modes is studied
through the time-domain integration of the master equation.


  In previous publications [arXiv:1608.08430, arXiv:1704.06502], the authors
have proposed Debye-H\"uckel-approximate free-energy functionals of the pair
distribution functions for one-component fluid and two-component plasmas. These
functionals yield the corresponding Debye-H\"uckel integral equations when they
are minimized with respect to the pair distribution functions, lead to correct
thermodynamic relations and fulfill the virial theorem. In the present
addendum, we update our results by providing simpler functionals that have the
same properties. We relate these functionals to the approaches of Lado [Phys.
Rev. A 8:2548, 1973] and of Olivares and McQuarrie [J. Chem. Phys. 65:3604,
1976]. We also discuss briefly the non-uniqueness issue that is raised by these
results.


  We introduce a scheme for linear optics quantum computation, that makes no
use of teleported gates, and requires stable interferometry over only the
coherence length of the photons. We achieve a much greater degree of efficiency
and a simpler implementation than previous proposals. We follow the "cluster
state" measurement based quantum computational approach, and show how cluster
states may be efficiently generated from pairs of maximally polarization
entangled photons using linear optical elements. We demonstrate the
universality and usefulness of generic parity measurements, as well as
introducing the use of redundant encoding of qubits to enable utilization of
destructive measurements - both features of use in a more general context.


  The recently discovered Neural Collapse (NC) phenomenon occurs pervasively in
today's deep net training paradigm of driving cross-entropy (CE) loss towards
zero. During NC, last-layer features collapse to their class-means, both
classifiers and class-means collapse to the same Simplex Equiangular Tight
Frame, and classifier behavior collapses to the nearest-class-mean decision
rule. Recent works demonstrated that deep nets trained with mean squared error
(MSE) loss perform comparably to those trained with CE. As a preliminary, we
empirically establish that NC emerges in such MSE-trained deep nets as well
through experiments on three canonical networks and five benchmark datasets. We
provide, in a Google Colab notebook, PyTorch code for reproducing MSE-NC and
CE-NC: at
https://colab.research.google.com/github/neuralcollapse/neuralcollapse/blob/main/neuralcollapse.ipynb.
The analytically-tractable MSE loss offers more mathematical opportunities than
the hard-to-analyze CE loss, inspiring us to leverage MSE loss towards the
theoretical investigation of NC. We develop three main contributions: (I) We
show a new decomposition of the MSE loss into (A) terms directly interpretable
through the lens of NC and which assume the last-layer classifier is exactly
the least-squares classifier; and (B) a term capturing the deviation from this
least-squares classifier. (II) We exhibit experiments on canonical datasets and
networks demonstrating that term-(B) is negligible during training. This
motivates us to introduce a new theoretical construct: the central path, where
the linear classifier stays MSE-optimal for feature activations throughout the
dynamics. (III) By studying renormalized gradient flow along the central path,
we derive exact dynamics that predict NC.


  Social participation is known to bring great benefits to the health and
well-being of people as they age. From being in contact with others to engaging
in group activities, keeping socially active can help slow down the effects of
age-related declines, reduce risks of loneliness and social isolation and even
mortality in old age. There are unfortunately a variety of barriers that make
it difficult for older adults to engage in social activities in a regular
basis. In this chapter, we give an overview of the challenges to social
participation and discuss how technology can help overcome these barriers and
promote participation in social activities. We examine two particular research
threads and designs, exploring ways in which technology can support co-located
and virtual participation: i) an application that motivates the virtual
participation in group training programs, and ii) a location-based game that
supports co-located intergenerational ICT training classes. We discuss the
effectiveness and limitations of various design choices in the two use cases
and outline the lessons learned


  Shape-constrained functional data encompass a wide array of application
fields especially in the life sciences, such as activity profiling, growth
curves, healthcare and mortality. Most existing methods for general functional
data analysis often ignore that such data are subject to inherent shape
constraints, while some specialized techniques rely on strict distributional
assumptions. We propose an approach for modeling such data that harnesses the
intrinsic geometry of functional trajectories by decomposing them into size and
shape components. We focus on the two most prevalent shape constraints,
positivity and monotonicity, and develop individual-level estimators for the
size and shape components. Furthermore, we demonstrate the applicability of our
approach by conducting subsequent analyses involving Fr\'{e}chet mean and
Fr\'{e}chet regression and establish rates of convergence for the empirical
estimators. Illustrative examples include simulations and data applications for
activity profiles for Mediterranean fruit flies during their entire lifespan
and for data from the Z\"{u}rich longitudinal growth study.


  The construction of Generalized Intelligent States (GIS) for the $x^4$%
-anharmonic oscillator is presented. These GIS families are required to
minimize the Robertson-Schr\"odinger uncertainty relation. As a particular
case, we will get the so-called Gazeau-Klauder coherent states. The properties
of the latters are discussed in detail. Analytical representation is also
considered and its advantage is shown in obtaining the GIS in an analytical
way. Further extensions are finally proposed.


  In recent years, neural implicit surface reconstruction methods have become
popular for multi-view 3D reconstruction. In contrast to traditional multi-view
stereo methods, these approaches tend to produce smoother and more complete
reconstructions due to the inductive smoothness bias of neural networks.
State-of-the-art neural implicit methods allow for high-quality reconstructions
of simple scenes from many input views. Yet, their performance drops
significantly for larger and more complex scenes and scenes captured from
sparse viewpoints. This is caused primarily by the inherent ambiguity in the
RGB reconstruction loss that does not provide enough constraints, in particular
in less-observed and textureless areas. Motivated by recent advances in the
area of monocular geometry prediction, we systematically explore the utility
these cues provide for improving neural implicit surface reconstruction. We
demonstrate that depth and normal cues, predicted by general-purpose monocular
estimators, significantly improve reconstruction quality and optimization time.
Further, we analyse and investigate multiple design choices for representing
neural implicit surfaces, ranging from monolithic MLP models over single-grid
to multi-resolution grid representations. We observe that geometric monocular
priors improve performance both for small-scale single-object as well as
large-scale multi-object scenes, independent of the choice of representation.


  We show that two operator algebras are strongly Morita equivalent (in the
sense of Blecher, Muhly and Paulsen) if and only if their categories of
operator modules are equivalent via completely contractive functors. Moreover,
any such functor is completely isometrically isomorphic to the Haagerup tensor
product (= interior tensor product) with a strong Morita equivalence bimodule.


  We show that transport in low-dimensional carbon structures with finite
concentrations of scatterers can be modeled by utilising scaling theory and
effective cross sections. Our reults are based on large scale numerical
simulations of carbon nanotubes and graphene nanoribbons, using a tightbinding
model with parameters obtained from first principles electronic structure
calculations. As shown by a comprehensive statistical analysis, the scattering
cross sections can be used to estimate the conductance of a quasi-1D system
both in the Ohmic and localized regimes. They can be computed with good
accuracy from the transmission functions of single defects, greatly reducing
the computational cost and paving the way towards using first principles
methods to evaluate the conductance of mesoscopic systems, consisting of
millions of atoms.


  A systematic study of holomorphic gauge invariant operators in general
$\mathcal{N}=1$ quiver gauge theories, with unitary gauge groups and
bifundamental matter fields, was recently presented in [1]. For large ranks a
simple counting formula in terms of an infinite product was given. We extend
this study to quiver gauge theories with fundamental matter fields, deriving an
infinite product form for the refined counting in these cases. The infinite
products are found to be obtained from substitutions in a simple building block
expressed in terms of the weighted adjacency matrix of the quiver. In the case
without fundamentals, it is a determinant which itself is found to have a
counting interpretation in terms of words formed from partially commuting
letters associated with simple closed loops in the quiver. This is a new
relation between counting problems in gauge theory and the Cartier-Foata
monoid. For finite ranks of the unitary gauge groups, the refined counting is
given in terms of expressions involving Littlewood-Richardson coefficients.


  We study the probability that a random polynomial with integer coefficients
is reducible when factored over the rational numbers. Using computer-generated
data, we investigate a number of different models, including both monic and
non-monic polynomials. Our data supports conjectures made by Odlyzko and Poonen
and by Konyagin, and we formulate a universality heuristic and new conjectures
that connect their work with Hilbert's Irreducibility Theorem and work of van
der Waerden. The data indicates that the probability that a random polynomial
is reducible divided by the probability that there is a linear factor appears
to approach a constant and, in the large-degree limit, this constant appears to
approach one. In cases where the model makes it impossible for the random
polynomial to have a linear factor, the probability of reducibility appears to
be close to the probability of having a non-linear, low-degree factor. We also
study characteristic polynomials of random matrices with +1 and -1 entries.


  We derive frame estimates for vector-valued Gabor systems with window
functions belonging to Schwartz space. The main result provides frame bound
estimates for windows composed of Hermite functions. The proof is based on a
recently established sampling theorem for the simply connected Heisenberg
group, which is translated to a family of frame estimates via a direct integral
decomposition.


  A small-scale, two-phase (liquid/gas) xenon time projection chamber (Xurich
II) was designed, constructed and is under operation at the University of
Zurich. Its main purpose is to investigate the microphysics of particle
interactions in liquid xenon at energies below 50 keV, which are relevant for
rare event searches using xenon as target material. Here we describe in detail
the detector, its associated infrastructure, and the signal identification
algorithm developed for processing and analysing the data. We present the first
characterisation of the new instrument with calibration data from an internal
83m-Kr source. The zero-field light yield is 15.0 and 14.0 photoelectrons/keV
at 9.4 keV and 32.1 keV, respectively, and the corresponding values at an
electron drift field of 1 kV/cm are 10.8 and 7.9 photoelectrons/keV. The charge
yields at these energies are 28 and 31 electrons/keV, with the proportional
scintillation yield of 24 photoelectrons per one electron extracted into the
gas phase, and an electron lifetime of 200 $\mu$s. The relative energy
resolution, $\sigma/E$, is 11.9 % and 5.8 % at 9.4 keV and 32.1 keV,
respectively using a linear combination of the scintillation and ionisation
signals. We conclude with measurements of the electron drift velocity at
various electric fields, and compare these to literature values.


  Propane steam reforming using a sliding discharge reactor was investigated
under atmospheric pressure and low temperature (420 K). Non-thermal plasma
steam reforming proceeded efficiently and hydrogen was formed as a main product
(H2 concentration up to 50%). By-products (C2-hydrocarbons, methane, carbon
dioxide) were measured with concentrations lower than 6%. The mean electrical
power injected in the discharge is less than 2 kW. The process efficiency is
described in terms of propane conversion rate, steam reforming and cracking
selectivity, as well as by-products production. Chemical processes modelling
based on classical thermodynamic equilibrium reactor is also proposed.
Calculated data fit quiet well experimental results and indicate that the
improvement of C3H8 conversion and then H2 production can be achieved by
increasing the gas fraction through the discharge. By improving the reactor
design, the non-thermal plasma has a potential for being an effective way for
supplying hydrogen or synthesis gas.


  We consider the four waves spatial homogeneous kinetic equation arising in
wave turbulence theory. We study the long-time behaviour and existence of
solutions around the Rayleigh-Jeans equilibrium solutions. For cut-off'd
frequencies, we show that for dispersion relations weakly perturbed around the
quadratic case, the linearized operator around the Rayleigh-Jeans equilibria is
coercive. We then pass to the fully nonlinear operator, showing an $L^2$ -
stability for initial data close to Rayleigh-Jeans.


  The partial interference cancellation (PIC) group decoding has recently been
proposed to deal with the decoding complexity and code rate trade-off on the
basis of space-time block code (STBC) design criterion when full diversity is
achieved. It provides a framework to arrange the rate-complexity-performance
tradeoff by choosing a suitable size of information symbol groups. In this
paper, a simple design of a linear dispersive space-time-frequency (STF) code
is proposed with a design criterion to achieve high rate for
frequency-selective channels in terms of multipath when the PIC group decoding
is applied at receiver. With an appropriate grouping scheme as well as the PIC
group decoding, the proposed STF code is shown to obtain the similar diversity
gain as the maximum likelihood (ML) decoding, namely full-dimensional sphere
decoding, but have a low decoding complexity. It seems as an intermediate
decoding between the ML receiver and zero-forcing (ZF) receiver. The proposed
grouping design criterion for the PIC group decoding to achieve full diversity
deploying the orthogonal-frequency-division multiplexing (OFDM) technique is
also an intermediate condition between the loosest ML full rank criterion of
codewords and the strongest ZF linear independence condition of the column
vectors for the equivalent frequency-selective channel matrix. It can achieves
full diversity with the PIC group decoding for any number of sub-carriers and
the data rate can be made high. Several code design examples are illustrated
for the feasibility of this coding scheme. Simulation results show that the
proposed STF code can well address the rate-performance-complexity tradeoff of
the multiple-input multiple-output orthogonal frequency division multiplexing
(MIMO-OFDM) communication system.


  Microstates of colinear black holes embedded in a multi-center Taub-NUT
spacetime are sought in 4 dimensions. A set of coupled ordinary partial
differential equations are obtained and solved for almost-BPS states, where
some supersymmetry is preserved in the context of N=2 supergravity in 4
dimensions. The regularity of solutions is being carefully considered and we
ensure that no CTC (closed time-like curves) are present. The larger framework
is that of 11-dimensional N=2 supergravity and the current theory is obtained
by compactifying down to 4 dimensions.


  The nonperturbative aspects of string theory are explored for non-critical
string in two distinct formulations: loop equations and matrix models. The
effects corresponding to D-brane in these formulations are especially
investigated in detail. It is shown that matrix models can universally yield a
definite value of the chemical potential for an instanton while loop equations
can not. This implies that string theory may not be nonperturbatively
formulated solely in terms of closed strings.


  This is a brief overview of a few selected chapters on automorphism groups of
affine varieties. It includes some open questions.


  Due to the complex attention mechanisms and model design, most existing
vision Transformers (ViTs) can not perform as efficiently as convolutional
neural networks (CNNs) in realistic industrial deployment scenarios, e.g.
TensorRT and CoreML. This poses a distinct challenge: Can a visual neural
network be designed to infer as fast as CNNs and perform as powerful as ViTs?
Recent works have tried to design CNN-Transformer hybrid architectures to
address this issue, yet the overall performance of these works is far away from
satisfactory. To end these, we propose a next generation vision Transformer for
efficient deployment in realistic industrial scenarios, namely Next-ViT, which
dominates both CNNs and ViTs from the perspective of latency/accuracy
trade-off. In this work, the Next Convolution Block (NCB) and Next Transformer
Block (NTB) are respectively developed to capture local and global information
with deployment-friendly mechanisms. Then, Next Hybrid Strategy (NHS) is
designed to stack NCB and NTB in an efficient hybrid paradigm, which boosts
performance in various downstream tasks. Extensive experiments show that
Next-ViT significantly outperforms existing CNNs, ViTs and CNN-Transformer
hybrid architectures with respect to the latency/accuracy trade-off across
various vision tasks. On TensorRT, Next-ViT surpasses ResNet by 5.5 mAP (from
40.4 to 45.9) on COCO detection and 7.7% mIoU (from 38.8% to 46.5%) on ADE20K
segmentation under similar latency. Meanwhile, it achieves comparable
performance with CSWin, while the inference speed is accelerated by 3.6x. On
CoreML, Next-ViT surpasses EfficientFormer by 4.6 mAP (from 42.6 to 47.2) on
COCO detection and 3.5% mIoU (from 45.1% to 48.6%) on ADE20K segmentation under
similar latency. Our code and models are made public at:
https://github.com/bytedance/Next-ViT


  We obtain black hole rotating solutions for Horndesky theory (specific
partial case), bumblebee model and Gauss-Bonnet scalar gravity using the
specially improved Newman-Janis algorithm. The shadow profiles for these
metrics were calculated. Applying the limitations from the Event Horizon
Telescope we find the opportunity to constrain model parameters from considered
extended gravity theories. We show that for three considered models two of them
(Horndesky theory and Gauss-Bonnet scalar gravity) weaken the effect of
rotation and bumblebee model enhances it. This conclusion matches the
previously obtained one that extended gravity theories by themselves correct
the effect of rotation in both directions.


  Contributing to the toolbox for interpreting election results, we evaluate
the robustness of election winners to random noise. We compare the robustness
of different voting rules and evaluate the robustness of real-world election
winners from the Formula 1 World Championship and some variant of political
elections. We find many instances of elections that have very non-robust
winners and numerous delicate robustness patterns that cannot be identified
using classical and simpler approaches.


  Results on hard diffraction from HERA and proton-antiproton Colliders are
reviewed with emphasis on the factorization properties of the diffractive
structure function of the proton and on the structure of the pomeron.


  We present high-resolution multiwavelength radio continuum images of the
region within 150$"$ of Sgr A*, revealing a number of new extended features and
stellar sources in this region. First, we detect a continuous 2" east-west
ridge of radio emission, linking Sgr A* and a cluster of stars associated with
IRS 13N and IRS 13E. The ridge suggests that an outflow of east-west blob-like
structures is emerging from Sgr A*. We also find arc-like features within the
ridge with morphologies suggestive of photoevaporative protoplanetary disks. We
use near-IR fluxes to show that the emission has similar characteristics to
those of a protoplanetary disk irradiated by the intense radiation field at the
Galactic center. This suggests that star formation has taken place within the S
cluster 2$"$ from Sgr A*. We suggest that the diffuse X-ray emission associated
with Sgr A* is due to an expanding hot wind produced by the mass loss from
B-type main sequence stars, and/or the disks of photoevaporation of low mass
YSOs at a rate ~10^{-6} solar mass per year. The proposed model naturally
reduces the inferred accretion rate and is an alternative to the inflow-outflow
style models to explain the underluminous nature of Sgr A*. Second, we detect
new cometary radio and nea-IR sources and a striking tower of radio emission
suggesting that they are tracing interaction sites of a mildly relativistic jet
from Sgr A* with the atmosphere of stars and the nonthermal Sgr A East shell at
a PA$\sim50-60^\circ$ with ~10^{-7} solar mass per year, and opening angle 10
degrees.


  We study the moduli spaces of rational curves on prime Fano threefolds of
index 1. For general threefolds of most genera we compute the dimension and the
number of irreducible components of these moduli spaces. Our results confirm
Geometric Manin's Conjecture in these examples and show the enumerativity of
certain Gromov-Witten invariants.


  Granular surfaces subjected to forces due to rolling wheels develop ripples
above a critical speed. The resulting pattern, known as "washboard" or
"corrugated" road, is common on dry, unpaved roads. We investigated this
phenomenon theoretically and experimentally, using laboratory-scale apparatus
and beds of dry sand. A thick layer of sand on a circular track was forced by a
rolling wheel on an arm whose weight and moment of inertia could be varied. We
compared the ripples made by the rolling wheel to those made using a simple
inclined plow blade. We investigated the dependence of the critical speed on
various parameters, and describe a scaling argument which leads to a
dimensionless ratio, analogous to the hydrodynamic Froude number, which
controls the instability. This represents the crossover between conservative,
dynamic forces and dissipative, static forces. Above onset, wheel-driven
ripples move in the direction of motion of the wheel, but plow-driven ripples
move in the reverse direction for a narrow range of Froude numbers.


  We investigate the following vertex percolation process. Starting with a
random regular graph of constant degree, delete each vertex independently with
probability p, where p=n^{-alpha} and alpha=alpha(n) is bounded away from 0. We
show that a.a.s. the resulting graph has a connected component of size n-o(n)
which is an expander, and all other components are trees of bounded size.
Sharper results are obtained with extra conditions on alpha. These results have
an application to the cost of repairing a certain peer-to-peer network after
random failures of nodes.


  We prove a rigidity theorem for morphisms from products of open subschemes of
the projective line into solvable groups not containing a copy of $\Ga$ (for
example, wound unipotent groups). As a consequence, we deduce several
structural results about unirational group schemes, including that
unirationality for group schemes descends through separable extensions. We also
apply the main result to prove that permawound unipotent groups are unirational
and -- when wound -- commutative.


  We find the entanglement entropy of a subregion of the vacuum state in scalar
quantum electrodynamics, working perturbatively to the 2-loops level. Doing so
leads us to derive the Maxwell-Proca propagator in conical Euclidean space. The
area law of entanglement entropy is recovered in both the massive and massless
limits of the theory, as is expected. These results yield the renormalisation
group flow of entanglement entropy, and we find that loop contributions
suppress entanglement entropy. We highlight these results in the light of the
renormalization group flow of couplings and correlators, which are increased in
scalar quantum electrodynamics, so that the potential tension between the
increase in correlations between two points of spacetime and the decrease in
entanglement entropy between two regions of spacetime with energy is discussed.
We indeed show that the vacuum of a subregion of spacetime purifies with energy
in scalar quantum electrodynamics, which is related to the concept of
screening.


  Due to its critical role in cybersecurity, digital forensics has received
significant attention from researchers and practitioners alike. The ever
increasing sophistication of modern cyberattacks is directly related to the
complexity of evidence acquisition, which often requires the use of several
technologies. To date, researchers have presented many surveys and reviews on
the field. However, such articles focused on the advances of each particular
domain of digital forensics individually. Therefore, while each of these
surveys facilitates researchers and practitioners to keep up with the latest
advances in a particular domain of digital forensics, the global perspective is
missing. Aiming to fill this gap, we performed a qualitative review of reviews
in the field of digital forensics, determined the main topics on digital
forensics topics and identified their main challenges. Our analysis provides
enough evidence to prove that the digital forensics community could benefit
from closer collaborations and cross-topic research, since it is apparent that
researchers and practitioners are trying to find solutions to the same problems
in parallel, sometimes without noticing it.


  We formulate a notion of modular form on the double half-plane for
half-integral weights and explain its relationship to the usual notion of
modular form. The construction we provide is compatible with certain physical
considerations due to the second author.


  We show that if $u$ is a compactly supported distribution on the complex
plane such that, for every pair of entire functions $f,g$, \[ \langle
u,f\overline{g}\rangle=\langle u,f\rangle\langle u,\overline{g}\rangle, \] then
$u$ is supported at a single point. As an application, we complete the
classification of all weighted Dirichlet spaces on the unit disk that are de
Branges-Rovnyak spaces by showing that, for such spaces, the weight is
necessarily a superharmonic function.


  We investigate the role of boundary conditions in gauge theories in AdS4. The
presence of the boundary can break the gauge symmetry consistently with AdS4
isometries. We show that, as a consequence, the gauge bosons associated to the
broken symmetries become massive at one loop. In particular chiral gauge
theories such us the Standard Model are necessarily massive in AdS4. We briefly
discuss similarities with the Schwinger model and implications for CFTs in
three dimensions.


  The low-temperature conductivity of low-density, high-mobility,
two-dimensional hole systems in GaAs was studied. We explicitly show that the
metal-insulator transition, observed in these systems, is characterized by a
well-defined critical density, p_0c. We also observe that the low-temperature
conductivity of these systems depends linearly on the hole density, over a wide
density range. The high-density linear conductivity extrapolates to zero at a
density close to the critical density.


  Cluster states are a new type of multiqubit entangled states with
entanglement properties exceptionally well suited for quantum computation. In
the present work, we experimentally demonstrate that correlations in a
four-qubit linear cluster state cannot be described by local realism. This
exploration is based on a recently derived Bell-type inequality [V. Scarani et
al., Phys. Rev A 71, 042325 (2005)] which is tailored, by using a combination
of three- and four-particle correlations, to be maximally violated by cluster
states but not violated at all by GHZ states. We observe a cluster state Bell
parameter of $2.59\pm 0.08$, which is more than 7 standard deviations larger
than the threshold of 2 imposed by local realism.


  Cerulli Irelli and Lanini have shown that PBW degenerations of flag varieties
in type A and C are actually Schubert varieties of higher rank. We introduce
Dynkin cones to parameterise specific abelianisations of classical Lie
algebras. Within this framework, we generalise their result to all
degenerations of flag varieties defined by degree vectors originating from a
Dynkin cone. This framework allows us to determine the extent to which a flag
variety can be degenerate while still naturally being a Schubert variety of the
same Lie type. Furthermore, we compute the defining relations for the
corresponding degenerate simple modules in all classical types.


  Many-body Green's functions encode all the properties and excitations of
interacting electrons. While these are challenging to be evaluated accurately
on a classical computer, recent efforts have been directed towards finding
quantum algorithms that may provide a quantum advantage for this task,
exploiting architectures that will become available in the near future. In this
work we introduce a novel near-term quantum algorithm for computing
one-particle Green's functions via their Lehmann representation. The method is
based on a generalization of the quantum equation of motion algorithm that
gives access to the charged excitations of the system. We demonstrate the
validity of the present proposal by computing the Green's function of a
two-site Fermi-Hubbard model on a IBM quantum processor.


  In the paper "The Steenrod algebra and its dual", J.Milnor determined the
structure of the dual Steenrod algebra which is a graded commutative Hopf
algebra of finite type. We consider the affine group scheme $G_p$ represented
by the dual Hopf algebra of the mod $p$ Steenrod algebra. Then, $G_p$ assigns a
graded commutative algebra $A_*$ over a prime field of finite characteristic
$p$ to a set of isomorphisms of the additive formal group law over $A_*$, whose
group structure is given by the composition of formal power series. The aim of
this paper is to show some group theoretic properties of $G_p$ by making use of
this presentation of $G_p(A_*)$. We give a decreasing filtration of subgroup
schemes of $G_p$ which we use for estimating the length of the lower central
series of finite subgroup schemes of $G_p$. We also give a successive quotient
maps
$G_p\xrightarrow{\rho_0}G_p^{\langle1\rangle}\xrightarrow{\rho_1}G_p^{\langle2\rangle}\xrightarrow{\rho_2}\cdots\xrightarrow{\rho_{k-1}}
G_p^{\langle k\rangle}\xrightarrow{\rho_k}G_p^{\langle
k+1\rangle}\xrightarrow{\rho_{k+1}}\cdots$ of affine group schemes over a prime
field ${\boldsymbol F}_p$ such that the kernel of $\rho_k$ is a maximal abelian
subgroup.


  We prove that the KLR algebra associated with the cyclic quiver of length $e$
is a subquotient of the KLR algebra associated with the cyclic quiver of length
$e+1$. We also give a geometric interpretation of this fact. This result has an
important application in the theory of categorical representations. We prove
that a category with an action of $\widetilde{\mathfrak{sl}}_{e+1}$ contains a
subcategory with an action of $\widetilde{\mathfrak{sl}}_{e}$. We also give
generalizations of these results to more general quivers and Lie types.


  In recent years, the direction of the study of networks in which connections
correspond to the mutual influences of nodes has been developed. Many works
have been devoted to the study of such complex networks, but most often they
relate to the spread of one type of activity (influence). In the process of
development of the newest technologies various mathematical models are
developed and investigated: models with thresholds, models of independent
cascades, models of distribution of epidemics, models of Markov processes.
  The paper proposes to use hypercomplex number systems, which are a
mathematical apparatus that allows you to model some network problems and solve
them at a new level, ie to consider a complex network with several properties
in each node. In this paper, we consider networks where the edges correspond to
the mutual influences of the nodes. It is proposed to match the number of
properties in each node and the measurability of a hypercomplex number
system(HNS) with the same number of basic elements. Each HNS corresponds to the
Kelly table, which corresponds to the law of multiplication of these CSF. The
properties of the CSF allow you to build an isomorphic transition from a filled
Kelly table to a less filled one, which simplifies the calculation.
  To model the problem using hypercomplex number systems, we offer a
specialized software package of hypercomplex computations based on the system
of computer algebra Maple. All this made it easy to model a complex system with
several effects.


  The novel coronavirus disease 2019 (COVID-19) has been spreading rapidly
around the world and caused significant impact on the public health and
economy. However, there is still lack of studies on effectively quantifying the
lung infection caused by COVID-19. As a basic but challenging task of the
diagnostic framework, segmentation plays a crucial role in accurate
quantification of COVID-19 infection measured by computed tomography (CT)
images. To this end, we proposed a novel deep learning algorithm for automated
segmentation of multiple COVID-19 infection regions. Specifically, we use the
Aggregated Residual Transformations to learn a robust and expressive feature
representation and apply the soft attention mechanism to improve the capability
of the model to distinguish a variety of symptoms of the COVID-19. With a
public CT image dataset, we validate the efficacy of the proposed algorithm in
comparison with other competing methods. Experimental results demonstrate the
outstanding performance of our algorithm for automated segmentation of COVID-19
Chest CT images. Our study provides a promising deep leaning-based segmentation
tool to lay a foundation to quantitative diagnosis of COVID-19 lung infection
in CT images.


  In this paper, we connect some recent papers on smoothing of energy
landscapes and scored-based generative models of machine learning to classical
work in stochastic control. We clarify these connections providing rigorous
statements and representations which may serve as guidelines for further
learning models.


  Within the framework of the NJL model, we investigate the modification of the
pion damping width in a hot pion gas for temperatures ranging from 0 to 180
MeV. The pion is found to broaden noticeably at T > 60 MeV. Near the chiral
phase transition T ~ 180 MeV, the pion width is saturated and amounts to 70
MeV. The main contribution to the width comes from pion-pion collisions. Other
contributions are found negligibly small.


  Raga is a fundamental melodic concept in Indian Art Music (IAM). It is
characterized by complex patterns. All performances and compositions are based
on the raga framework. Raga and tonic detection have been a long-standing
research problem in the field of Music Information Retrieval. In this paper, we
attempt to detect the raga using a novel feature to extract sequential or
temporal information from an audio sample. We call these Sequential Pitch
Distributions (SPD), which are distributions taken over pitch values between
two given pitch values over time. We also achieve state-of-the-art results on
both Hindustani and Carnatic music raga data sets with an accuracy of 99% and
88.13%, respectively. SPD gives a great boost in accuracy over a standard pitch
distribution. The main goal of this paper, however, is to present an
alternative approach to modeling the temporal aspects of the melody and thereby
deducing the raga.


  We study metamaterials known as hyperbolic media that in the usual
local-response approximation exhibit hyperbolic dispersion and an associated
broadband singularity in the density of states. Instead, from the more
microscopic hydrodynamic Drude theory we derive qualitatively different optical
properties of these metamaterials, due to the free-electron nonlocal optical
response of their metal constituents. We demonstrate that nonlocal response
gives rise to a large-wavevector cutoff in the dispersion that is inversely
proportional to the Fermi velocity of the electron gas, but also for small
wavevectors we find differences for the hyperbolic dispersion. Moreover, the
size of the unit cell influences effective parameters of the metamaterial even
in the deep sub-wavelength regime. Finally, instead of the broadband
super-singularity in the local density of states, we predict a large but finite
maximal enhancement proportional to the inverse cube of the Fermi velocity.


  Recently single-beam intracavity optical tweezers have been reported and
achieved orders-of-magnitude higher confinement than standard optical tweezers.
However, there is only one feedback loop between the trapped particle's
three-dimensional position and the scattering loss of the intracavity laser.
That leads to the coupling effect between the particle's radial and axial
motion, and aggravates the axial confinement efficiency. Here, we present and
demonstrate the dual-beam intracavity optical trap enabling independent radial
and axial self-feedback control of the trapped particle, through offsetting the
foci of the clockwise and counter-clockwise beams. We have achieved the axial
confinement efficiency of 1.6*10^(-4) mW^(-1) experimentally at very low
numerical aperture (NA=0.25), which is the highest axial confinement efficiency
of the optical trap to date, to the best of our knowledge. The dual-beam
intracavity optical trap will significantly expand the range of applications in
the further studies of biology and physics, especially for a sample that is
extremely sensitive to heat.


  The optimal control of unitary transformations is a fundamental problem in
quantum control theory and quantum information processing. The feasibility of
performing such optimizations is determined by the computational and control
resources required, particularly for systems with large Hilbert spaces. Prior
work on unitary transformation control indicates that (i) for controllable
systems, local extrema in the search landscape for optimal control of quantum
gates have null measure, facilitating the convergence of local search
algorithms; but (ii) the required time for convergence to optimal controls can
scale exponentially with Hilbert space dimension. Depending on the control
system Hamiltonian, the landscape structure and scaling may vary. This work
introduces methods for quantifying Hamiltonian-dependent and kinematic effects
on control optimization dynamics in order to classify quantum systems according
to the search effort and control resources required to implement arbitrary
unitary transformations.


  Recently, there is growing concern that machine-learning models, which
currently assist or even automate decision making, reproduce, and in the worst
case reinforce, bias of the training data. The development of tools and
techniques for certifying fairness of these models or describing their biased
behavior is, therefore, critical. In this paper, we propose a perfectly
parallel static analysis for certifying causal fairness of feed-forward neural
networks used for classification of tabular data. When certification succeeds,
our approach provides definite guarantees, otherwise, it describes and
quantifies the biased behavior. We design the analysis to be sound, in practice
also exact, and configurable in terms of scalability and precision, thereby
enabling pay-as-you-go certification. We implement our approach in an
open-source tool and demonstrate its effectiveness on models trained with
popular datasets.


  When agents with independent priors bid for a single item, Myerson's optimal
auction maximizes expected revenue, whereas Vickrey's second-price auction
optimizes social welfare. We address the natural question of trade-offs between
the two criteria, that is, auctions that optimize, say, revenue under the
constraint that the welfare is above a given level. If one allows for
randomized mechanisms, it is easy to see that there are polynomial-time
mechanisms that achieve any point in the trade-off (the Pareto curve) between
revenue and welfare. We investigate whether one can achieve the same guarantees
using deterministic mechanisms. We provide a negative answer to this question
by showing that this is a (weakly) NP-hard problem. On the positive side, we
provide polynomial-time deterministic mechanisms that approximate with
arbitrary precision any point of the trade-off between these two fundamental
objectives for the case of two bidders, even when the valuations are correlated
arbitrarily. The major problem left open by our work is whether there is such
an algorithm for three or more bidders with independent valuation
distributions.


  The 11 Mpc H-alpha and Ultraviolet Galaxy (11HUGS) Survey traces the star
formation activity of nearby galaxies. In addition within this volume the
detection completeness of core-collapse supernovae (CCSNe) is high therefore by
comparing these observed stellar births and deaths we can make a sensitive test
of our understanding of how stars live and die. In this paper, we use the
results of the Binary Population and Spectral Synthesis (BPASS) code to
simulate the 11HUGS galaxies H-alpha and far-ultraviolet (FUV) star formation
rate indicators (SFRIs) and simultaneously match the core-collapse supernova
(CCSN) rate. We find that stellar population including interacting binary stars
makes little difference to the total CCSN rate but increases the H-alpha and
FUV fluxes for a constant number of stars being formed. In addition they
significantly increase the predicted rate of type Ibc supernovae (SNe) relative
to type II SNe to the level observed in the 11HUGS galaxies. We also find that
instead of assuming a constant star formation history (SFH) for the galaxies
our best fitting models have a star formation rate (SFR) that peaked more than
3 Myrs ago.


  We report observation of a large-amplitude filament oscillation followed by
an eruption. This is used to probe the pre-eruption condition and the trigger
mechanism of solar eruptions. We used the EUV images from the
Extreme-Ultraviolet Imaging Telescope on board SOHO satellite and the H-alpha
images from the Flare Monitoring Telescope at Hida Observatory. The observed
event is a polar crown filament that erupted on 15 Oct. 2002. The filament
clearly exhibited oscillatory motion in the slow-rising, pre-eruption phase.
The amplitude of the oscillation was larger than 20 km/s, and the motion was
predominantly horizontal. The period was about 2 hours and seemed to increase
during the oscillation, indicating weakening of restoring force. These results
strongly indicate that, even in the slow-rise phase before the eruption, the
filament retained equilibrium and behaved as an oscillator, and the equilibrium
is stable to nonlinear perturbation. Moreover, the transition from such
nonlinear stability to either instabilities or a loss of equilibrium that leads
to the eruption occurred in the Alfven time scale. This suggests that the onset
of the eruption was triggered by a fast magnetic reconnection that stabilized
the pre-eruption magnetic configuration, rather than by the slow shearing
motion at the photosphere.


  The development of open-source, multilingual medical language models can
benefit a wide, linguistically diverse audience from different regions. To
promote this domain, we present contributions from the following: First, we
construct a multilingual medical corpus, containing approximately 25.5B tokens
encompassing 6 main languages, termed as MMedC, enabling auto-regressive domain
adaptation for general LLMs; Second, to monitor the development of multilingual
medical LLMs, we propose a multilingual medical multi-choice question-answering
benchmark with rationale, termed as MMedBench; Third, we have assessed a number
of open-source large language models (LLMs) on our benchmark, along with those
further auto-regressive trained on MMedC. Our final model, MMed-Llama 3, with
only 8B parameters, achieves superior performance compared to all other
open-source models on both MMedBench and English benchmarks, even rivaling
GPT-4. In conclusion, in this work, we present a large-scale corpus, a
benchmark and a series of models to support the development of multilingual
medical LLMs.


  We study the spectrum of the QCD Dirac operator near zero virtuality for $N_c
=2$. According to a universality argument, it can be described by a random
matrix theory with the chiral structure of QCD, but with $real$ matrix
elements. Using results derived by Mehta and Mahoux and Nagao and Wadati, we
are able to obtain an analytical result for the microscopic spectral density
that in turn is the generating function for Leutwyler-Smilga type spectral sum
rules.


  In this paper, we deal with the asymptotic distribution of the maximum
increment of a random walk with a regularly varying jump size distribution.
This problem is motivated by a long-standing problem on change point detection
for epidemic alternatives. It turns out that the limit distribution of the
maximum increment of the random walk is one of the classical extreme value
distributions, the Fr\'{e}chet distribution. We prove the results in the
general framework of point processes and for jump sizes taking values in a
separable Banach space.


  In this paper, we consider a class of second-order evolution differential
inclusions in Hilbert spaces. This paper deals with the approximate
controllability for a class of second-order control systems. First, we
establish a set of sufficient conditions for the approximate controllability
for a class of second-order evolution differential inclusions in Hilbert
spaces. We use Bohnenblust-Karlin's fixed point theorem to prove our main
results. Further, we extend the result to study the approximate controllability
concept with nonlocal conditions and extend the result to study the approximate
controllability for impulsive control systems with nonlocal conditions. An
example is also given to illustrate our main results.


  We study the moduli functor of flat bundles on smooth, possibly non-proper,
algebraic variety $X$ (over a field of characteristic zero). For this we
introduce the notion of \emph{formal boundary} of $X$, denoted by $\partial X$,
which is a formal analogue of the boundary at infinity of the Betti topological
space associated to $X$. We explain how to construct two derived moduli
functors $Vect^{\nabla}(X)$ and $Vect^{\nabla}(\partial X)$, of flat bundles on
$X$ and on $\partial X$, as well as a restriction map $R : Vect^{\nabla}(X)
\rightarrow Vect^\nabla(\partial X)$ from the former to the later.
  This work contains two main results. First we prove that the morphism R comes
equipped with a canonical shifted Lagrangian structure in the sense of [PTVV].
This first result can be understood as the de Rham analogue of the existence of
Poisson structures on moduli of local systems previously studied by the
authors. As a second statement, we prove that the geometric fibers of $R$ are
representable by "quasi-algebraic spaces", a slight weakening of the notion of
algebraic spaces.


  Spontaneous emission is one of the most fundamental out-of-equilibrium
processes in which an excited quantum emitter relaxes to the ground state due
to quantum fluctuations. In this process, a photon is emitted that can interact
with other nearby emitters and establish quantum correlations between them,
e.g., via super and subradiance effects. One way to modify these
photon-mediated interactions is to alter the dipole radiation patterns of the
emitter, e.g., by placing photonic crystals near them. One recent example is
the generation of strong directional emission patterns-key to enhancing super
and subradiance effects-in two dimensions by employing photonic crystals with
band structures characterized by linear isofrequency contours and
saddle-points. However, these studies have predominantly used oversimplified
toy models, overlooking the electromagnetic field's intricacies in actual
materials, including aspects like geometrical dependencies, emitter positions,
and polarization. Our study delves into the interaction between these
directional emission patterns and the aforementioned variables, revealing the
untapped potential to fine-tune collective quantum optical phenomena.


  The dispersion relation of surface plasmon polaritons in graphene that
includes optical losses is often obtained for complex wave vectors while the
frequencies are assumed to be real. This approach, however, is not suitable for
describing the temporal dynamics of optical excitations and the spectral
properties of graphene. Here, we propose an alternative approach that
calculates the dispersion relation in the complex frequency and real wave
vector space. This approach provides a clearer insight into the optical
properties of a graphene layer and allows us to find the surface plasmon modes
of a graphene sheet in the full frequency range, thus removing the earlier
reported limitation (1.667 < $\hbar\omega/\mu$ < 2) for the transverse-electric
mode. We further develop a simple analytic approximation which accurately
describes the dispersion of the surface plasmon polariton modes in graphene.
Using this approximation, we show that transverse-electric surface plasmon
polaritons propagate along the graphene sheet without losses even at finite
temperature.


  Deep learning (DL) based supervised change detection (CD) models require
large labeled training data. Due to the difficulty of collecting labeled
multi-temporal data, unsupervised methods are preferred in the CD literature.
However, unsupervised methods cannot fully exploit the potentials of
data-driven deep learning and thus they are not absolute alternative to the
supervised methods. This motivates us to look deeper into the supervised DL
methods and investigate how they can be adopted intelligently for CD by
minimizing the requirement of labeled training data. Towards this, in this work
we show that geographically diverse training dataset can yield significant
improvement over less diverse training datasets of the same size. We propose a
simple confidence indicator for verifying the trustworthiness/confidence of
supervised models trained with small labeled dataset. Moreover, we show that
for the test cases where supervised CD model is found to be less
confident/trustworthy, unsupervised methods often produce better result than
the supervised ones.


  We show that the action of the Lie algebra HH^1(A) of outer derivations of an
associative algebra A on the Hochschild cohomology HH^*(A) of A given by the
Gerstenhaber bracket can be computed in terms of an arbitrary projective
resolution of A as an A-bimodule, without having recourse to comparison maps
between the resolution and the bar resolution.


  We present an approach for identifying the most walkable direction for
navigation using a hand-held camera. Our approach extracts semantically rich
contextual information from the scene using a custom encoder-decoder
architecture for semantic segmentation and models the spatial and temporal
behavior of objects in the scene using a spatio-temporal graph. The system
learns to minimize a cost function over the spatial and temporal object
attributes to identify the most walkable direction. We construct a new
annotated navigation dataset collected using a hand-held mobile camera in an
unconstrained outdoor environment, which includes challenging settings such as
highly dynamic scenes, occlusion between objects, and distortions. Our system
achieves an accuracy of 84% on predicting a safe direction. We also show that
our custom segmentation network is both fast and accurate, achieving mIOU (mean
intersection over union) scores of 81 and 44.7 on the PASCAL VOC and the PASCAL
Context datasets, respectively, while running at about 21 frames per second.


  The main results of this article are asymptotic formulas for the variance of
the number of zeros of a Gaussian random polynomial of degree $N$ in an open
set $U \subset C$ as the degree $N \to \infty$, and more generally for the
zeros of random holomorphic sections of high powers of any positive line bundle
over any Riemann surface. The formulas were conjectured in special cases by
Forrester and Honner. In higher dimensions, we give similar formulas for the
variance of the volume inside a domain $U$ of the zero hypersurface of a random
holomorphic section of a high power of a positive line bundle over any compact
K\"ahler manifold. These results generalize the variance asymptotics of Sodin
and Tsirelson for special model ensembles of chaotic analytic functions in one
variable to any ample line bundle and Riemann surface. We also combine our
methods with those of Sodin-Tsirelson to generalize their asymptotic normality
results for smoothed number statistics.


  We prove the existence of two-dimensional good lattice points in thick
multiplicative subgroups modulo $p$.


  Tensor network (TN), a young mathematical tool of high vitality and great
potential, has been undergoing extremely rapid developments in the last two
decades, gaining tremendous success in condensed matter physics, atomic
physics, quantum information science, statistical physics, and so on. In this
lecture notes, we focus on the contraction algorithms of TN as well as some of
the applications to the simulations of quantum many-body systems. Starting from
basic concepts and definitions, we first explain the relations between TN and
physical problems, including the TN representations of classical partition
functions, quantum many-body states (by matrix product state, tree TN, and
projected entangled pair state), time evolution simulations, etc. These
problems, which are challenging to solve, can be transformed to TN contraction
problems. We present then several paradigm algorithms based on the ideas of the
numerical renormalization group and/or boundary states, including density
matrix renormalization group, time-evolving block decimation,
coarse-graining/corner tensor renormalization group, and several distinguished
variational algorithms. Finally, we revisit the TN approaches from the
perspective of multi-linear algebra (also known as tensor algebra or tensor
decompositions) and quantum simulation. Despite the apparent differences in the
ideas and strategies of different TN algorithms, we aim at revealing the
underlying relations and resemblances in order to present a systematic picture
to understand the TN contraction approaches.


  Half life values for $\alpha$-decay in the mass region $A=150-200$ have been
calculated in the Microscopic Super Asymmetric Fission Model. The interaction
between the $\alpha$-particle and the daughter nucleus has been obtained in the
double folding model with the microscopic interaction DDM3Y1. Theoretical
densities for the nuclei involved have been calculated in Relativistic Mean
Field approach with the Lagrangian density FSU Gold. Spectroscopic factors for
$\alpha$-decay, calculated as the ratios of the theoretically calculated and
experimentally measured half life values, show a simple dependence on the mass
number and the product of the number of valence protons and neutrons. The
implications of the parameterization have been discussed. Finally, based on
this simple relation, $\alpha$-decay half life values in a number of nuclei
have been predicted.


  The transfer of neutrons onto 24Ne has been measured using a reaccelerated
radioactive beam of 24Ne to study the (d,p) reaction in inverse kinematics. The
unusual raising of the first 3/2+ level in 25Ne and its significance in terms
of the migration of the neutron magic number from N=20 to N=16 is put on a firm
footing by confirmation of this state's identity. The raised 3/2+ level is
observed simultaneously with the intruder negative parity 7/2- and 3/2- levels,
providing evidence for the reduction in the N=20 gap. The coincident gamma-ray
decays allowed the assignment of spins as well as the transferred orbital
angular momentum. The excitation energy of the 3/2+ state shows that the
established USD shell model breaks down well within the sd model space and
requires a revised treatment of the proton-neutron monopole interaction.


  In this paper we consider single leptoquark resonance production associated
with the emission of a hard photon. We have obtained analytical formulae for
differential and total cross sections for the cases of scalar and vector
leptoquarks. We have found that in reactions with scalar leptoquarks there is
no photon radiation in some directions depending on the leptoquark electric
charge (the radiative amplitude zero - the RAZ effect).
  For vector leptoquarks the exact RAZ is present only in the case of
Yang-Mills coupling. We propose to use the RAZ effect to determine the types of
leptoquarks. We conclude also that this effect opens a possibility to measure
the leptoquark anomalous magnetic moment.


  The zero-temperature ordering kinetics of conserved XY models in spatial
dimensions $d=2$ and 3 is studied using cell dynamical simulations. The growth
of the characteristic length scale $L(t)$ is fully consistent with recent
theoretical predictions: $L(t) \sim t^{1/4}$ for $d=2$ and $L(t) \sim (t\ln
t)^{1/4}$ for $d=3$. A gaussian closure approximation describes the form of the
structure factor rather well for $d=3$.


  Ideals are used to define homological functors for additive categories. In
abelian categories the ideals corresponding to the usual universal objects are
principal, and the construction reduces, in a choice dependent way, to homology
groups.
  Applications are considered: derived categories and functors.


  K Nearest Neighbor (KNN) joins are used in scientific domains for data
analysis, and are building blocks of several well-known algorithms. KNN-joins
find the KNN of all points in a dataset. This paper focuses on a hybrid CPU/GPU
approach for low-dimensional KNN-joins, where the GPU may not yield substantial
performance gains over parallel CPU algorithms. We utilize a work queue that
prioritizes computing data points in high density regions on the GPU, and low
density regions on the CPU, thereby taking advantage of each architecture's
relative strengths. Our approach, HybridKNN-Join, effectively augments a
state-of-the-art multi-core CPU algorithm. We propose optimizations that $(i)$
maximize GPU query throughput by assigning the GPU large batches of work;
$(ii)$ increase workload granularity to optimize GPU utilization; and, $(iii)$
limit load imbalance between CPU and GPU architectures. We compare
HybridKNN-Join to one GPU and two parallel CPU reference implementations.
Compared to the reference implementations, we find that the hybrid algorithm
performs best on larger workloads (dataset size and K). The methods employed in
this paper show promise for the general division of work in other hybrid
algorithms.


  The systems of nonlinear Volterra integral equations of the first kind with
jump discontinuous kernels are studied. The iterative numerical method for such
nonlinear systems is proposed. Proposed method employs the modified
Newton-Kantorovich iterative process for the integral operators linearization.
On each step of the iterative process the linear system of integral equations
is obtained and resolved using the discontinuity driven piecewise constant
approximation of the exact solution. The convergence theorem is proved. The
polynomial collocation technique is also applied to solve such systems as the
alternative method. The accuracy of proposed numerical methods is discussed.
The model examples are examined in order to demonstrate the efficiency of
proposed numerical methods and illustrate the constructed theory.


  Compact Galactic binaries where at least one member is a white dwarf or
neutron star constitute the majority of individually detectable sources for
future low-frequency space-based gravitational-wave (GW) observatories; they
also form an unresolved continuum, the dominant Galactic foreground at
frequencies below a few mHz. Due to the paucity of electromagnetic
observations, the majority of studies of Galactic-binary populations so far
have been based on population-synthesis simulations. However, recent surveys
have reported several new detections of white-dwarf binaries, providing new
constraints for population estimates. In this article, we evaluate the impact
of revised local densities of interacting white-dwarf binaries on future GW
observations. Specifically: we consider five scenarios that explain these
densities with different assumptions on the formation of interacting systems;
we simulate corresponding populations of detached and interacting white-dwarf
binaries; we estimate the number of individually detectable GW sources and the
magnitude of the confusion-noise foreground, as observed by space-based
detectors with 5- and 1-Mkm arms. We confirm earlier estimates of thousands of
detached-binary detections, but project only few ten to few hundred detections
of interacting systems. This reduction is partly due to our assessment of
detection prospects, based on the iterative identification and subtraction of
bright sources with respect to both instrument and confusion noise. We also
confirm earlier estimates for the confusion-noise foreground, except in one
scenario that explains smaller local densities of interacting systems with
smaller numbers of progenitor detached systems.


  We investigate single-electron transport through quantum dots with negative
charging energy induced by a polaronic energy shift. For weak dot-lead tunnel
couplings, we demonstrate a bipolaronic blockade effect at low biases which
suppresses the oscillating linear conductance, while the conductance resonances
under large biases are enhanced. Novel conductance plateau develops when the
coupling asymmetry is introduced, with its height and width tuned by the
coupling strength and external magnetic field. It is further shown that the
amplitude ratio of magnetic-split conductance peaks changes from 3 to 1for
increasing coupling asymmetry. Though we demonstrate all these transport
phenomena in the low-order single-electron tunneling regime, they are already
strikingly different from the usual Coulomb blockade physics and are easy to
observe experimentally.


  We revisit earlier studies on Berry phases suggested to appear in certain
cavity QED settings. It has been especially argued that a non-trivial geometric
phase is achievable even in the situation of no cavity photons. We, however,
show that such results hinge on imposing the {\it rotating wave approximation}
(RWA), while without the RWA no Berry phases occur in these schemes. A
geometrical interpretation of our results is obtained by introducing
semi-classical energy surfaces which in a simple way brings out the phase space
dynamics. With the RWA, a conical intersection between the surfaces emerges and
encircling it gives rise to the Berry phase. Without the RWA, the conical
intersection is absent and therefore the Berry phase vanishes. It is believed
that this is a first example showing how the application of the RWA in the
Jaynes-Cummings model may lead to false conclusions, regardless mutual
strengths between the system parameters.


  Collaborative edge computing (CEC) is an emerging paradigm where
heterogeneous edge devices (stakeholders) collaborate to fulfill computation
tasks, such as model training or video processing, by sharing communication and
computation resources. Nevertheless, the optimal data/result routing and
computation offloading strategy in CEC with arbitrary topology still remains an
open problem. In this paper, we formulate a partial-offloading and multi-hop
routing model for arbitrarily divisible tasks. Each node individually decides
the computation of the received data and the forwarding of data/result traffic.
In contrast to most existing works, our model applies to tasks with
non-negligible result size, and enables separable data sources and result
destinations. We propose a network-wide cost minimization problem with
congestion-aware cost to jointly optimize routing and computation offloading.
This problem covers various performance metrics and constraints, such as
average queueing delay with limited processor capacity. Although the problem is
non-convex, we provide non-trivial necessary and sufficient conditions for the
global-optimal solution, and devise a fully distributed algorithm that
converges to the optimum in polynomial time, allows asynchronous individual
updating, and is adaptive to changes in network topology or task pattern.
Numerical evaluation shows that our proposed method significantly outperforms
other baseline algorithms in multiple network instances, especially in
congested scenarios.


  We perform an exact spherical geometry finite-size diagonalization
calculation for the fractional quantum Hall ground state in three different
experimentally relevant GaAs-Al_{x}Ga_{1-x}As systems: a wide parabolic quantum
well, a narrow square quantum well, and a heterostructure. For each system we
obtain the Coulomb pseudopotential parameters entering the exact
diagonalization calculation by using the realistic subband wave function from a
self-consistent electronic structure calculation within the local density
approximation (LDA) for a range of electron densities. We compare our realistic
LDA pseudopotential parameters with those from widely used simpler model
approximations in order to estimate the accuracies of the latter. We also
calculate the overlap between the exact numerical ground state and the
analytical Laughlin state as well as the excitation gap as a function of
density. For the three physical systems we consider the calculated overlap is
found to be large in the experimental electron density range. We compare our
calculated excitation gap energy to the experimentally obtained activated
transport energy gaps after subtracting out the effect of level broadening due
to collisions. The agreement between our calculated excitation gaps and the
experimental measurements is excellent.


  We study periodic magnetic Schr\"odinger operators on covers of closed
manifolds in relation to Ma\~n\'e's critical energy values of the corresponding
classical Hamiltonian systems. In particular, we show that if the covering
transformation group is amenable, then the bottom of the spectrum is bounded
from above by Ma\~n\'e's critical energy value. We also determine the spectra
for various homogeneous spaces with left-invariant magnetic fields.


  We study (slope-)stability properties of syzygy bundles on a projective space
P^N given by ideal generators of a homogeneous primary ideal. In particular we
give a combinatorial criterion for a monomial ideal to have a semistable syzygy
bundle. Restriction theorems for semistable bundles yield the same stability
results on the generic complete intersection curve. From this we deduce a
numerical formula for the tight closure of an ideal generated by monomials or
by generic homogeneous elements in a generic two-dimensional complete
intersection ring.


  It has become common understanding that the recession of galaxies and the
corresponding redshift of light received from them can only be explained by an
expansion of the space between them and us. In this paper, for the presently
favored case of a universe without spatial curvature, it is shown that this
interpretation is restricted to comoving coordinates. It is proven by
construction that within the framework of general relativity other coordinates
exist in relation to which these phenomena can be explained by a motion of the
cosmic substrate across space, caused by an explosion like big bang or by
inflation preceding an almost big bang. At the place of an observer, this
motion occurs without any spatial expansion. It is shown that in these
"explosion coordinates" the usual redshift comes about by a Doppler shift and a
subsequent gravitational shift. Making use of this interpretation, it can
easily be understood why in comoving coordinates light rays of short spatial
extensions expand and thus constitute an exemption from the rule that small
objects up to the size of the solar system or even galaxies do not participate
in the expansion of the universe. It is also discussed how the two
interpretations can be reconciled with each other.


  We review recent theoretical progress and observational constraints on
multifractional spacetimes, geometries that change with the probed scale. On
the theoretical side, the basic structure of the Standard Model and of the
gravitational action is discussed. On the experimental side, we recall the
bounds on the scales of the geometry coming from particle physics,
astrophysics, and the cosmic microwave background.


  We report on the collision-coalescence dynamics of drops in Leidenfrost state
using liquids with different physicochemical properties. Drops of the same
liquid deposited on a hot concave surface coalesce practically at contact, but
when drops of different liquids collide, they can bounce several times before
finally coalescing when the one that evaporates faster reaches a critical size,
of the order of the capillary length. The bouncing dynamics is produced because
the drops are not only in Leidenfrost state with the substrate, they also
experience Leidenfrost effect between them at the moment of collision. This
happens due to their different boiling temperatures, and therefore, the hotter
drop works as a hot surface for the drop with lower boiling point, producing
three contact zones of Leidenfrost state simultaneously. We called this
scenario the triple Leidenfrost effect.


  The existence of $D^0-\overline{D^0}$ mixing at a detectable level requires
new physics, which effectively yields a $\Delta c = 2$ superweak interaction.
In general this interaction may involve significant CP violation. For small
values of the mixing it may be much easier to detect the CP-violating part of
the mixing than the CP-conserving part.


  Variational extremization of the relative Fisher information (RFI, hereafter)
is performed. Reciprocity relations, akin to those of thermodynamics are
derived, employing the extremal results of the RFI expressed in terms of
probability amplitudes. A time independent Schr\"{o}dinger-like equation
(Schr\"{o}dinger-like link) for the RFI is derived. The concomitant Legendre
transform structure (LTS, hereafter) is developed by utilizing a generalized
RFI-Euler theorem, which shows that the entire mathematical structure of
thermodynamics translates into the RFI framework, both for equilibrium and
non-equilibrium cases. The qualitatively distinct nature of the present results
\textit{vis-\'{a}-vis} those of prior studies utilizing the Shannon entropy
and/or the Fisher information measure (FIM, hereafter) is discussed. A
principled relationship between the RFI and the FIM frameworks is derived. The
utility of this relationship is demonstrated by an example wherein the energy
eigenvalues of the Schr\"{o}dinger-like link for the RFI is inferred solely
using the quantum mechanical virial theorem and the LTS of the RFI.


  Web development is a challenging research area for its creativity and
complexity. The existing raised key challenge in web technology technologic
development is the presentation of data in machine read and process able format
to take advantage in knowledge based information extraction and maintenance.
Currently it is not possible to search and extract optimized results using full
text queries because there is no such mechanism exists which can fully extract
the semantic from full text queries and then look for particular knowledge
based information.


  In this note we study the approach to equilibrium of a chain of anharmonic
oscillators. We find indications that a sufficiently large system always
relaxes to the usual equilibrium distribution. There is no sign of an
ergodicity threshold. The time however to arrive to equilibrium diverges when
$g \to 0$, $g$ being the anharmonicity.


  We propose a solution to the hyperelliptic Schottky problem, based on the use
of Jacobian Nullwerte and symmetric models for hyperelliptic curves. Both
ingredients are interesting on its own, since the first provide period matrices
which can be geometrically described, and the second have remarkable arithmetic
properties.


  Depending on whether electroweak physics beyond the Standard Model is based
on a linear or on a non-linear implementation of the electroweak symmetry
breaking, a linear or a chiral Effective Lagrangian is more appropriate. In
this talk, the main low-energy signals that allow to recognize whether the
observed Higgs scalar is a dynamical (composite) particle or rather an
elementary one are presented, in a model-independent way. The patterns of
effective couplings produced upon the assumption of specific composite Higgs
models are also discussed.


  Understanding the fundamental structure of matter requires an understanding
of how quarks and gluons are assembled to form hadrons and of the structure of
the protons which are the colliding particles at LHC. The arrangement of quarks
and gluons inside nucleons can be probed by accelerating electrons, hadrons or
nuclei to precisely controlled energies, smashing them into a target nucleus
and examining in detail the final products. The LHC physics program is rich and
has been widely described. It encompasses the searches for new particles up to
masses of several TeV, including the elucidation of electroweak symmetry
breaking and the possible observation of new symmetries at higher scales, and
precision measurements of fundamental parameters in the electroweak and strong
gauge sectors. Obviously, this program requires a precise understanding of the
structure of the proton in terms of quarks and gluons, obtained from HERA and
Tevatron. However, the knowledge on parton distribution functions (PDFs) is
still limited for many aspects of LHC physics and the discovery potential is
thus reduced. In this proceeding, we show on one example that it is possible to
find some observables less sensitive to PDF uncertainties to probe with a high
efficency new physics beyond the standard model.


  We discuss new ideas for consideration of loop diagrams and angular integrals
in $D$-dimensions in QCD. In case of loop diagrams, we propose the covariant
formalism of expansion of tensorial loop integrals into the orthogonal basis of
linear combinations of external momenta. It gives a very simple presentation
for the final results and is more convenient for calculations on computer
algebra systems. In case of angular integrals we demonstrate how to simplify
the integration of differential cross sections over polar angles. Also we
derive the recursion relations, which allow to reduce all occurring angular
integrals to a short set of basic scalar integrals. All order
$\epsilon$-expansion is given for all angular integrals with up to two
denominators based on the expansion of the basic integrals and using recursion
relations. A geometric picture for partial fractioning is developed which
provides a new rotational invariant algorithm to reduce the number of
denominators.


  To date a number of studies have shown that receptive field shapes of early
sensory neurons can be reproduced by optimizing coding efficiency of natural
stimulus ensembles. A still unresolved question is whether the efficient coding
hypothesis explains formation of neurons which explicitly represent
environmental features of different functional importance. This paper proposes
that the spatial selectivity of higher auditory neurons emerges as a direct
consequence of learning efficient codes for natural binaural sounds. Firstly,
it is demonstrated that a linear efficient coding transform - Independent
Component Analysis (ICA) trained on spectrograms of naturalistic simulated
binaural sounds extracts spatial information present in the signal. A simple
hierarchical ICA extension allowing for decoding of sound position is proposed.
Furthermore, it is shown that units revealing spatial selectivity can be
learned from a binaural recording of a natural auditory scene. In both cases a
relatively small subpopulation of learned spectrogram features suffices to
perform accurate sound localization. Representation of the auditory space is
therefore learned in a purely unsupervised way by maximizing the coding
efficiency and without any task-specific constraints. This results imply that
efficient coding is a useful strategy for learning structures which allow for
making behaviorally vital inferences about the environment.


  Fourier Ptychographic Microscopy (FPM) is a recent technique to overcome the
diffraction limit of a low numerical aperture (NA) objective lens by
algorithmic post-processing of several lower resolved images. It can increase
the space-bandwidth product of an optical system by computationally combining
images captured under different illumination conditions. Vignetting determines
the spatial extent of the bright field and dark field regions in the captured
images that contain information about low and high frequency image content,
respectively. State-of-the-art analyses treat vignetting as a nuisance that
needs to be reduced or excluded from algorithmic consideration by means of
ad-hoc decision rules [1]. In contrast, this work investigates vignetting
effects as a tool to infer a range of properties of the optical system. To
achieve this, we characterize the individual system components of the
experimental setup and compare experimental data to both, geometrical and wave
optical simulations. We demonstrate that using vignetting as an analytical tool
enables the modeling of the geometric and coherence properties of the optical
system as evidenced by the good agreement between our simulation and
experiment. Moreover, our work investigates pupil aberrations in the FPM setup
and enables their partial characterization, despite not yet encompassing all
aspects.


  Quantum tomography has become an indispensable tool in order to compute the
density matrix $\rho$ of quantum systems in Physics. Recently, it has further
gained importance as a basic step to test entanglement and violation of Bell
inequalities in High-Energy Particle Physics. In this work, we present the
theoretical framework for reconstructing the helicity quantum initial state of
a general scattering process. In particular, we perform an expansion of $\rho$
over the irreducible tensor operators $\{T^L_M\}$ and compute the corresponding
coefficients uniquely by averaging, under properly chosen Wigner D-matrices
weights, the angular distribution data of the final particles. Besides, we
provide the explicit angular dependence of both the normalised differential
cross section and the generalised production matrix $\Gamma$. Finally, we
re-derive all our previous results from a quantum-information perspective using
the Weyl-Wigner-Moyal formalism and we obtain in addition simple analytical
expressions for the Wigner $P$ and $Q$ symbols.


  Every quadratic form represents 0; therefore, if we take any number of
quadratic forms and ask which integers are simultaneously represented by all
members of the collection, we are guaranteed a nonempty set. But when is that
set more than just the "trivial" 0? We address this question in the case of
integral, positive- definite, reduced, binary quadratic forms. For forms of the
same discriminant, we can use the structure of the underlying class group. If,
however, the forms have different discriminants, we must apply class field
theory.


  An optical-lattice quantum simulator is an ideal experimental platform to
investigate non-equilibrium dynamics of a quantum many-body system, which is in
general hard to simulate with classical computers. Here, we use our quantum
simulator of the Bose-Hubbard model to study dynamics far from equilibrium
after a quantum quench. We successfully confirm the energy conservation law in
the one- and three-dimensional systems and extract the propagation velocity of
the single-particle correlation in the one- and two-dimensional systems. We
corroborate the validity of our quantum simulator through quantitative
comparisons between the experiments and the exact numerical calculations in one
dimension. In the computationally hard cases of two or three dimensions, by
using the quantum-simulation results as references, we examine the performance
of a numerical method, namely the truncated Wigner approximation, revealing its
usefulness and limitation. This work constitutes an exemplary case for the
usage of analog quantum simulators.


  We give an explicit bound for the Wasserstein distance with quadratic cost
between the solutions of Boltzmann's and Landau's equations in the case of soft
and Coulomb potentials. This gives an explicit rate of convergence for the
grazing collisions limit. Our result is local in time for very soft and Coulomb
potentials and global in time for moderately soft potentials.


  YouTube is a popular video platform for sharing creative content and ideas,
targeting different demographics. Adults, older children, and young children
are all avid viewers of YouTube videos. Meanwhile, countless young-kid-oriented
channels have produced numerous instructional and age appropriate videos for
young children. However, inappropriate content for young children, such as
violent or sexually suggestive content, still exists. And children lack the
ability to decide whether a video is appropriate for them or not, which then
causes a huge risk to children's mental health. Prior works have focused on
identifying YouTube videos that are inappropriate for children. However, these
works ignore that not only the actual video content influences children, but
also the advertisements that are shown with those videos.
  In this paper, we quantify the influence of inappropriate advertisements on
YouTube videos that are appropriate for young children to watch. We analyze the
advertising patterns of 24.6 K diverse YouTube videos appropriate for young
children. We find that 9.9% of the 4.6 K unique advertisements shown on these
24.6 K videos contain inappropriate content for young children. Moreover, we
observe that 26.9% of all the 24.6 K appropriate videos include at least one ad
that is inappropriate for young children. Additionally, we publicly release our
datasets and provide recommendations about how to address this issue.


  We establish doubly-exponential degree bounds for Gr\"obner bases in certain
algebras of solvable type over a field (as introduced by Kandri-Rody and
Weispfenning). The class of algebras considered here includes commutative
polynomial rings, Weyl algebras, and universal enveloping algebras of
finite-dimensional Lie algebras. For the computation of these bounds, we adapt
a method due to Dub\'e based on a generalization of Stanley decompositions. Our
bounds yield doubly-exponential degree bounds for ideal membership and
syzygies, generalizing the classical results of Hermann and Seidenberg (in the
commutative case) and Grigoriev (in the case of Weyl algebras).


  It is a natural consequence of fundamental properties of the Casson invariant
that the Rokhlin invariant of an amphichiral integral homology 3-sphere M
vanishes. In this paper, we give a new direct proof of this vanishing property.
For such an M, we construct a manifold pair (Y,Q) of dimensions 6 and 3
equipped with some additional structure (6-dimensional spin e-manifold), such
that Q = M \cup M \cup (-M) and (Y,Q) \cong (-Y,-Q). We prove that (Y,Q) bounds
a 7-dimensional spin e-manifold (Z,X) by studying the cobordism group of
6-dimensional spin e-manifolds and the Z/2-actions on the two--point
configuration space of M minus one point. For any such (Z,X), the signature of
X vanishes, and this implies the vanishing of the Rokhlin invariant. The idea
of the construction of (Y,Q) comes from the definition of the
Kontsevich-Kuperberg-Thurston invariant for rational homology 3-spheres.


  Cooperative transmission is an emerging communication technique that takes
advantage of the broadcast nature of wireless channels. However, due to low
spectral efficiency and the requirement of orthogonal channels, its potential
for use in future wireless networks is limited. In this paper, by making use of
multiuser detection (MUD) and network coding, cooperative transmission
protocols with high spectral efficiency, diversity order, and coding gain are
developed. Compared with the traditional cooperative transmission protocols
with single-user detection, in which the diversity gain is only for one source
user, the proposed MUD cooperative transmission protocols have the merit that
the improvement of one user's link can also benefit the other users. In
addition, using MUD at the relay provides an environment in which network
coding can be employed. The coding gain and high diversity order can be
obtained by fully utilizing the link between the relay and the destination.
  From the analysis and simulation results, it is seen that the proposed
protocols achieve higher diversity gain, better asymptotic efficiency, and
lower bit error rate, compared to traditional MUD schemes and to existing
cooperative transmission protocols. From the simulation results, the
performance of the proposed scheme is near optimal as the performance gap is
0.12dB for average bit error rate (BER) 10^{-6} and 1.04dB for average BER
10^(-3), compared to two performance upper bounds.


  The normal or Gaussian distribution plays a prominent role in almost all
fields of science. However, it is well known that the Gauss (or Euler--Poisson)
integral over a finite boundary, as it is necessary for instance for the error
function or the cumulative distribution of the normal distribution, cannot be
expressed by analytic functions. This is proven by the Risch algorithm. Still,
there are proposals for approximate solutions. In this paper, we give a new
solution in terms of normal distributions by applying a geometric procedure
iteratively to the problem.


  Human evaluation is increasingly critical for assessing large language
models, capturing linguistic nuances, and reflecting user preferences more
accurately than traditional automated metrics. However, the resource-intensive
nature of this type of annotation process poses significant challenges. The key
question driving our work: "is it feasible to minimize human-in-the-loop
feedback by prioritizing data instances which most effectively distinguish
between models?" We evaluate several metric-based methods and find that these
metrics enhance the efficiency of human evaluations by minimizing the number of
required annotations, thus saving time and cost, while ensuring a robust
performance evaluation. We show that our method is effective across widely used
model families, reducing instances of indecisive (or "tie") outcomes by up to
54% compared to a random sample when focusing on the top-20 percentile of
prioritized instances. This potential reduction in required human effort
positions our approach as a valuable strategy in future large language model
evaluations.


  We consider planar lattice walks that start from (0,0), remain inthe first
quadrant i, j >= 0, and are made of three types of steps: North-East, West and
South. These walks are known to have remarkable enumerative and probabilistic
properties: -- they are counted by nice numbers (Kreweras 1965), -- the
generating function of these numbers is algebraic (Gessel 1986), -- the
stationary distribution of the corresponding Markov chain in the quadrant has
an algebraic probability generating function (Flatto and Hahn 1984). These
results are not well understood, and have been established via complicated
proofs. Here we give a uniform derivation of all of them, whichis more
elementary that those previously published.We then go further by computing the
full law of the Markov chain. This helps to delimit the border of algebraicity:
the associated probability generating function is no longer algebraic, unless a
diagonal symmetry holds. Our proofs are based on the solution of certain
functional equations,which are very simple to establish. Finding purely
combinatorial proofs remains an open problem.


  As a lot of studies have declared, the proton structure function $F_2$
explicitly satisfies a power-law mathematical formation. We describe the
behavior of proton structure function $F_2$ at small-$x$ as well as large $Q^2$
using the analytical solution of the Balitsky-Kovchegov equation. We obtain the
effective slope value $\lambda$ of the structure function with $Q^2$. Our
results come from fitting the HERA experimental data at low $Q^2$ region and we
also give the prediction for the effective slope of $F_2$ at the high $Q^2$
region.


  Fault-tolerant protocols enable large and precise quantum algorithms. Many
such protocols rely on a feed-forward processing of data, enabled by a hybrid
of quantum and classical logic. Representing the control structure of such
programs can be a challenge. Here we explore two such fault-tolerant
subroutines and analyze the performance of the subroutines using Quantum
Intermediate Representation (QIR) as their underlying intermediate
representation. First, we look at QIR's ability to leverage the LLVM compiler
toolchain to unroll the quantum iteration logic required to perform magic state
distillation on the $[[5,1,3]]$ quantum error-correcting code as originally
introduced by Bravyi and Kitaev [Phys. Rev. A 71, 022316 (2005)]. This allows
us to not only realize the first implementation of a real-time magic state
distillation protocol on quantum hardware, but also demonstrate QIR's ability
to optimize complex program structures without degrading machine performance.
Next, we investigate a different fault-tolerant protocol that was first
introduced by Paetznick and Svore [arXiv:1311.1074 (2013)], that reduces the
amount of non-Clifford gates needed for a particular algorithm. We look at four
different implementations of this two-stage repeat-until-success algorithm to
analyze the performance changes as the results of programming choices. We find
the QIR offers a viable representation for a compiled high-level program that
performs nearly as well as a hand-optimized version written directly in quantum
assembly. Both of these results demonstrate QIR's ability to accurately and
efficiently expand the complexity of fault-tolerant protocols that can be
realized today on quantum hardware.


  We define an infinite series of translation coverings of Veech's double-n-gon
for odd n greater or equal to 5 which share the same Veech group. Additionally
we give an infinite series of translation coverings with constant Veech group
of a regular n-gon for even n greater or equal to 8. These families give rise
to explicit examples of infinite translation surfaces with lattice Veech group.


  This paper is a survey on the works [MS77, MS79, MS81] on maximal subgroups
in finitely generated linear groups, and the works that followed it [GG08,
GG13b, GG13a, Kap03, Iva92, HO16, GM16, AGS14, Sf90, Sf98, Per05, AKT16, FG18,
GS17] concerning maximal subgroups of infinite index in linear groups as well
as in various other groups possessing a suitable geometry or dynamics.


  Multimodal contents have become commonplace on the Internet today, manifested
as news articles, social media posts, and personal or business blog posts.
Among the various kinds of media (images, videos, graphics, icons, audio) used
in such multimodal stories, images are the most popular. The selection of
images from a collection - either author's personal photo album, or web
repositories - and their meticulous placement within a text, builds a succinct
multimodal commentary for digital consumption. In this paper we present a
system that automates the process of selecting relevant images for a story and
placing them at contextual paragraphs within the story for a multimodal
narration. We leverage automatic object recognition, user-provided tags, and
commonsense knowledge, and use an unsupervised combinatorial optimization to
solve the selection and placement problems seamlessly as a single unit.


  In this letter we revisit general dark matter (DM)-bound-electron
interactions studied previously in the influential work of [Catena et al.,
Phys. Rev. Res. 2, 033195 (2020)]. We derive the DM-electron response functions
and find a crucial minus sign was missed for the second atomic response
function $W_2$ defined in that work. The minus sign has significant
phenomenological consequences when explaining experimental bounds on specific
DM scenarios. Furthermore, for the most general DM-electron nonrelativistic or
relativistic interactions for DM with spin up to one, we find there are three
DM response functions ($a_{0,1,2}$) whose corresponding atomic response
functions ($\widetilde W_{0,1,2}$) are linear combinations of the four response
functions ($W_{1,2,3,4}$) given in that work, $$ \widetilde W_0 = W_1, \,
\widetilde W_2 = |\mathbf{v}_0^\perp|^2 W_1+ W_3 - 2 {m_e\, \mathbf{q}\cdot
\mathbf{v}_0^\perp \over \mathbf{q}^2} W_2,\, \widetilde W_3 = {
(\mathbf{q}\cdot \mathbf{v}_0^\perp)^2 \over \mathbf{q}^2} W_1 + {m_e^2 \over
\mathbf{q}^2}W_4 - 2 {m_e\, \mathbf{q}\cdot \mathbf{v}_0^\perp \over
\mathbf{q}^2} W_2. $$ Due to the minus sign correction for $W_2$, there can be
significant cancellations between the $W_2$ and $W_{3,4}$ terms, so that
$\widetilde W_{2,3}$ are dominated by the usual response function $W_1$ in some
cases. Ignoring the sign could thus result in misinterpretation of the
experimental data in some DM scenarios. As an example, we show that the recent
XENON1T constraint on the fermionic DM anapole moment is weakened by a factor
of 2 or so. Many DM scenarios involving DM or electron axial-vector current can
yield $W_2$ and thus are potentially affected by the sign.


  We study three special Dirichlet series, two of them alternating, related to
the Riemann zeta function. These series are shown to have extensions to the
entire complex plane and we find their values at the negative integers (or
residues at poles). These values are given in terms of Bernoulli and Euler
numbers.


  Operator learning refers to the application of ideas from machine learning to
approximate (typically nonlinear) operators mapping between Banach spaces of
functions. Such operators often arise from physical models expressed in terms
of partial differential equations (PDEs). In this context, such approximate
operators hold great potential as efficient surrogate models to complement
traditional numerical methods in many-query tasks. Being data-driven, they also
enable model discovery when a mathematical description in terms of a PDE is not
available. This review focuses primarily on neural operators, built on the
success of deep neural networks in the approximation of functions defined on
finite dimensional Euclidean spaces. Empirically, neural operators have shown
success in a variety of applications, but our theoretical understanding remains
incomplete. This review article summarizes recent progress and the current
state of our theoretical understanding of neural operators, focusing on an
approximation theoretic point of view.