  We present a numerical study of polyelectrolytes electrophoresing in free
solution while squeezed by an axisymmetric confinement force transverse to
their net displacement. Hybrid multi-particle collision dynamics and molecular
dynamics simulations with mean-field finite Debye layers show that even though
the polyelectrolyte chains remain "free-draining", their electrophoretic
mobility increases with confinement in nanoconfining potential wells. The
primary mechanism leading to the increase in mobility above the free-solution
value, despite long-range hydrodynamic screening by counterion layers, is the
orientation of polymer segments within Debye layers. The observed
length-dependence of the electrophoretic mobility arises due to secondary
effects of counterion condensation related to confinement compactification.


  The mechanisms of lithium electrodeposition, which overwhelmingly affect
lithium metal battery performance and safety, remain insufficiently understood
due to its electrochemical complexity. Novel, non-destructive and in situ
techniques to probe electrochemical interfaces during lithium electrodeposition
are highly desirable. In this work, we demonstrate the capability of transient
grating spectroscopy to monitor lithium electrodeposition at the micrometer
scale by generating and detecting surface acoustic waves that sensitively
interact with the deposited lithium. Specifically, we show that the evolution
of the frequency, velocity and damping rate of the surface acoustic waves
strongly correlate with the lithium nucleation and growth process. Our work
illustrates the sensitivity of high-frequency surface acoustic waves to
micrometer scale changes in electrochemical cells and establishes transient
grating spectroscopy as a versatile platform for future in situ investigation
of electrochemical inte


  We theoretically investigate polarization properties of a two-component
Bose-Einstein condensate (BEC) and influence of decoherence induced by
environment on BEC polarization through introducing four BEC Stokes operators
which are quantum analog of the classical Stokes parameters for a light field.
BEC polarization states can be geometrically described by a Poincar\'{e} sphere
defined by expectation values of BEC Stokes operators. Without decoherence, it
is shown that nonlinear inter-atomic interactions in the BEC induce periodic
polarization oscillations whose periods depend on the difference between
self-interaction in each component and inter-component interaction strengths.
In particular, when inter-atomic nonlinear self-interaction in each BEC
component equals inter-component nonlinear interaction, Stokes vector
associated with Stokes operators precesses around a fixed axis in the dynamic
evolution of the BEC. The value of the processing frequency is determined by
the strength of the linear coupling between two components of the BEC. When
decoherence is involved, we find each component of the Stokes vector decays
which implies that decoherence depolarizes the BEC.


  In this paper we study the Hilbert function HR of one-dimensional semigroup
rings R = k[[S]]. For some classes of semigroups, by means of the notion of
support of the elements in S, we give conditions on the generators of S in
order to have decreasing HR. When the embedding dimension v and the
multiplicity e verify v + 3 ? e ? v + 4, the decrease of HR gives explicit
description of the Apery set of S. In particular for e = v+3, we classify the
semigroups with e = 13 and HR decreasing, further we show that HR is
non-decreasing if e < 12. Finally we deduce that HR is non-decreasing for every
Gorenstein semigroup ring with e ? v + 4.


  Social events provide valuable insights into group social behaviors and
public concerns and therefore have many applications in fields such as product
recommendation and crisis management. The complexity and streaming nature of
social messages make it appealing to address social event detection in an
incremental learning setting, where acquiring, preserving, and extending
knowledge are major concerns. Most existing methods, including those based on
incremental clustering and community detection, learn limited amounts of
knowledge as they ignore the rich semantics and structural information
contained in social data. Moreover, they cannot memorize previously acquired
knowledge. In this paper, we propose a novel Knowledge-Preserving Incremental
Heterogeneous Graph Neural Network (KPGNN) for incremental social event
detection. To acquire more knowledge, KPGNN models complex social messages into
unified social graphs to facilitate data utilization and explores the
expressive power of GNNs for knowledge extraction. To continuously adapt to the
incoming data, KPGNN adopts contrastive loss terms that cope with a changing
number of event classes. It also leverages the inductive learning ability of
GNNs to efficiently detect events and extends its knowledge from previously
unseen data. To deal with large social streams, KPGNN adopts a mini-batch
subgraph sampling strategy for scalable training, and periodically removes
obsolete data to maintain a dynamic embedding space. KPGNN requires no feature
engineering and has few hyperparameters to tune. Extensive experiment results
demonstrate the superiority of KPGNN over various baselines.


  We present a construction for circuits with low gate count and depth,
implementing three- and four-body Pauli-Z product operators as they appear in
the form of plaquette-shaped constraints in QAOA when using the parity mapping.
The circuits can be implemented on any quantum device with nearest-neighbor
connectivity on a square-lattice, using only one gate type and one orientation
of two-qubit gates at a time. We find an upper bound for the circuit depth
which is independent of the system size. The procedure is readily adjustable to
hardware-specific restrictions, such as a minimum required spatial distance
between simultaneously executed gates, or gates only being simultaneously
executable within a subset of all the qubits, for example a single line.


  Let S be an abelian semigroup, and A a finite subset of S. The sumset hA
consists of all sums of h elements of A, with repetitions allowed. Let |hA|
denote the cardinality of hA. Elementary lattice point arguments are used to
prove that an arbitrary abelian semigroup has polynomial growth, that is, there
exists a polynomial p(t) such that |hA| = p(h) for all sufficiently large h.
Lattice point counting is also used to prove that sumsets of the form h_1A_1 +
>... + h_rA_r have multivariate polynomial growth.


  We present a new algorithmic framework for grouped variable selection that is
based on discrete mathematical optimization. While there exist several
appealing approaches based on convex relaxations and nonconvex heuristics, we
focus on optimal solutions for the $\ell_0$-regularized formulation, a problem
that is relatively unexplored due to computational challenges. Our methodology
covers both high-dimensional linear regression and nonparametric sparse
additive modeling with smooth components. Our algorithmic framework consists of
approximate and exact algorithms. The approximate algorithms are based on
coordinate descent and local search, with runtimes comparable to popular sparse
learning algorithms. Our exact algorithm is based on a standalone
branch-and-bound (BnB) framework, which can solve the associated mixed integer
programming (MIP) problem to certified optimality. By exploiting the problem
structure, our custom BnB algorithm can solve to optimality problem instances
with $5 \times 10^6$ features and $10^3$ observations in minutes to hours --
over $1000$ times larger than what is currently possible using state-of-the-art
commercial MIP solvers. We also explore statistical properties of the
$\ell_0$-based estimators. We demonstrate, theoretically and empirically, that
our proposed estimators have an edge over popular group-sparse estimators in
terms of statistical performance in various regimes. We provide an open-source
implementation of our proposed framework.


  Recent ALMA observations of high-redshift normal galaxies have been providing
a great opportunity to clarify the general origin of dust in the Universe, not
biased to very bright special objects even at $z>6$. To clarify what constraint
we can get for the dust enrichment in normal galaxies detected by ALMA, we use
a theoretical model that includes major processes driving dust evolution in a
galaxy; that is, dust condensation in stellar ejecta, dust growth by the
accretion of gas-phase metals, and supernova destruction. Using the dust
emission fluxes detected in two normal galaxies at $z>6$ by ALMA as a
constraint, we can get the range of the time-scales (or efficiencies) of the
above mentioned processes. We find that if we assume extremely high
condensation efficiency in stellar ejecta ($f_{\mathrm{in}} \ga 0.5$), rapid
dust enrichment by stellar sources in the early phase may be enough to explain
the observed ALMA flux, unless dust destruction by supernovae in those galaxies
is stronger than that in nearby galaxies. If we assume a condensation
efficiency expected from theoretical calculations ($f_{\mathrm{in}} \la 0.1$),
strong dust growth (even stronger than assumed for nearby galaxies if they are
metal-poor galaxies) is required. These results indicate that the normal
galaxies detected by ALMA at $z>6$ are biased to objects (i) with high dust
condensation efficiency in stellar ejecta, (ii) with strong dust growth in very
dense molecular clouds, or (iii) with efficient dust growth because of fast
metal enrichment up to solar metallicity. A measurement of metallicity is
crucial to distinguish among these possibilities.


  A generalized matrix function $d_\chi^G : M_n(\mathbb{C}) \rightarrow
\mathbb{C}$ is a function constructed by a subgroup $G$ of $S_n$ and a complex
valued function $\chi$ of $G$.
  The main purpose of this paper is to find a necessary and sufficient
condition for the equality of two generalized matrix functions on the set of
all symmetric matrices, $\mathbb{S}_n(\mathbb{C})$.
  In order to fulfill the purpose, a symmetric matrix $S_\sigma$ is constructed
and $d_\chi^G(S_\sigma)$ is evaluated for each $\sigma \in S_n$.
  By applying the value of $d_\chi^G(S_\sigma)$, it is shown that $d_\chi^G(AB)
= d_\chi^G(A)d_\chi^G(B)$ for each $A, B \in \mathbb{S}_n(\mathbb{C})$ if and
only if $d_\chi^G = \det$.
  Furthermore, a criterion when $d_\chi^G(AB) = d_\chi^G(BA)$ for every $A, B
\in \mathbb{S}_n(\mathbb{C})$, is established.


  Electric vehicles (EVs) represent the long-term green substitute for
traditional fuel-based vehicles. To encourage EV adoption, the trust of the
end-users must be assured. In this work, we focus on a recently emerging
privacy threat of profiling and identifying EVs via the analog electrical data
exchanged during the EV charging process. The core focus of our work is to
investigate the feasibility of such a threat at scale. To this end, we first
propose an improved EV profiling approach that outperforms the state-of-the-art
EV profiling techniques. Next, we exhaustively evaluate the performance of our
improved approach to profile EVs in real-world settings. In our evaluations, we
conduct a series of experiments including 25032 charging sessions from 530 real
EVs, sub-sampled datasets with different data distributions, etc. Our results
show that even with our improved approach, profiling and individually
identifying the growing number of EVs is not viable in practice; at least with
the analog charging data utilized throughout the literature. We believe that
our findings from this work will further foster the trust of potential users in
the EV ecosystem, and consequently, encourage EV adoption.


  If one attaches shifted copies of a skew tableau to the right of itself and
rectifies, at a certain point the copies no longer experience vertical slides,
a phenomenon called tableau stabilization. While tableau stabilization was
originally developed to construct the sufficiently large rectangular tableaux
fixed by given powers of promotion, the purpose of this paper is to improve the
original bound on tableau stabilization to the number of rows of the skew
tableau. In order to prove this bound, we encode increasing subsequences as
lattice paths and show that various operations on these lattice paths weakly
increase the maximum combined length of the increasing subsequences.


  We describe a mode sorter for two-dimensional parity of transverse spatial
states of light based on an out-of-plane Sagnac interferometer. Both
Hermite-Gauss (HG) and Laguerre-Gauss (LG) modes can be guided into one of two
output ports according to the two-dimensional parity of the mode in question.
Our interferometer sorts HG_nm input modes depending upon whether they have
even or odd order n+m; it equivalently sorts LG modes depending upon whether
they have an even or odd value of their orbital angular momentum. It functions
efficiently at the single-photon level, and therefore can be used to sort
single-photon states. Due to the inherent phase stability of this type of
interferometer as compared to those of the Mach-Zehnder type, it provides a
promising tool for the manipulation and filtering of higher order transverse
spatial modes for the purposes of quantum information processing. For example,
several similar Sagnacs cascaded together may allow, for the first time, a
stable measurement of the orbital angular momentum of a true single-photon
state. Furthermore, as an alternative to well-known holographic techniques, one
can use the Sagnac in conjunction with a multi-mode fiber as a spatial mode
filter, which can be used to produce spatial-mode entangled Bell states and
heralded single photons in arbitrary first-order (n+m=1) spatial states,
covering the entire Poincare sphere of first-order transverse modes.


  Natural data are often long-tail distributed over semantic classes. Existing
recognition methods tackle this imbalanced classification by placing more
emphasis on the tail data, through class re-balancing/re-weighting or
ensembling over different data groups, resulting in increased tail accuracies
but reduced head accuracies.
  We take a dynamic view of the training data and provide a principled model
bias and variance analysis as the training data fluctuates: Existing long-tail
classifiers invariably increase the model variance and the head-tail model bias
gap remains large, due to more and larger confusion with hard negatives for the
tail.
  We propose a new long-tailed classifier called RoutIng Diverse Experts
(RIDE). It reduces the model variance with multiple experts, reduces the model
bias with a distribution-aware diversity loss, reduces the computational cost
with a dynamic expert routing module. RIDE outperforms the state-of-the-art by
5% to 7% on CIFAR100-LT, ImageNet-LT and iNaturalist 2018 benchmarks. It is
also a universal framework that is applicable to various backbone networks,
long-tailed algorithms, and training mechanisms for consistent performance
gains. Our code is available at:
https://github.com/frank-xwang/RIDE-LongTailRecognition.


  We make a global vacuum neutrino oscillation analysis of solar neutrino data,
including the seasonal and energy dependence of the recent Super-Kamiokande
708-day results. The best fit parameters for \nu_e oscillations to an active
neutrino are \delta m^2 = 4.42\times10^{-10} eV^2, \sin^2 2\theta = 0.93. The
allowed mixing angle region is consistent with bi-maximal mixing of three
neutrinos. Oscillations to a sterile neutrino are disfavored. Allowing an
enhanced hep neutrino flux does not significantly alter the oscillation
parameters.


  The single and collective particle interaction with spatially localized
wavepackets is analytically and numerically studied. The role of the finite
spatial width of the wavepacket on the momentum and energy variation of
particles passing through the wavepacket is investigated. The range of validity
of analytical results, based on a perturbative approach, is investigated and
clearly defined. Strongly nonlinear effects are shown to qualitatively
differentiate the collective particle dynamics, for larger interaction
strengths. These effects are manifested through the complex dependency of
averaged momentum variations on the initial particle momentum, as shown by
dissecting a particle distribution in terms of partitioning the ensemble of
particles with respect to their initial momentum. The results provide
understanding on the relation between single and collective particle dynamics
and the emerging of complexity for weak and strong particle interactions with
localized wavepackets.


  Ising spins put onto a Barabasi-Albert scale-free network show an effective
phase transition from ferromagnetism to paramagnetism upon heating, with an
effective critical temperature increasing as the logarithm of the system size.
Starting with all spins up and upon equilibration pinning the few
most-connected spins down nucleates the phase with most of the spins down.


  False discovery rate (FDR) is a common way to control the number of false
discoveries in multiple testing. There are a number of approaches available for
controlling FDR. However, for functional test statistics, which are discretized
into $m$ highly correlated hypotheses, the methods must account for changes in
distribution across the functional domain and correlation structure. Further,
it is of great practical importance to visualize the test statistic together
with its rejection or acceptance region. Therefore, the aim of this paper is to
find, based on resampling principles, a graphical envelope that controls FDR
and detects the outcomes of all individual hypotheses by a simple rule: the
hypothesis is rejected if and only if the empirical test statistic is outside
of the envelope. Such an envelope offers a straightforward interpretation of
the test results, similarly as the recently developed global envelope testing
which controls the family-wise error rate. Two different adaptive single
threshold procedures are developed to fulfill this aim. Their performance is
studied in an extensive simulation study. The new methods are illustrated by
three real data examples.


  The frequency with which the letters of the English alphabet appear in
writings has been applied to the field of cryptography, the development of
keyboard mechanics, and the study of linguistics. We expanded on the
statistical analysis of the English alphabet by examining the average frequency
which each letter appears in different categories of writings. We evaluated
news articles, novels, plays, scientific publications and calculated the
frequency of each letter of the alphabet, the information density of each
letter, and the overall letter distribution. Furthermore, we developed a metric
known as distance, d that can be used to algorithmically recognize different
categories of writings. The results of our study can be applied to information
transmission, large data curation, and linguistics.


  For the in-ice component of the next generation neutrino observatory at the
South Pole, IceCube-Gen2, a new sensor module is being developed, which is an
evolution of the D-Egg and mDOM sensors developed for the IceCube Upgrade. The
sensor design features up to 18 4-inch PMTs distributed homogeneously in a
borosilicate glass pressure vessel. Challenges arise for the mechanical design
from the tight constraints on the bore hole diameter (which will be 2 inches
smaller than for IceCube Upgrade) and from the close packing of the PMTs. The
electronics design must meet the space constraints posed by the mechanical
design as well as the power consumption and cost considerations from over
10,000 optical modules being deployed. This contribution presents
forward-looking solutions to these design considerations. Prototype modules
will be installed and integrated in the IceCube Upgrade.


  Supervised training of neural networks requires large, diverse and well
annotated data sets. In the medical field, this is often difficult to achieve
due to constraints in time, expert knowledge and prevalence of an event.
Artificial data augmentation can help to prevent overfitting and improve the
detection of rare events as well as overall performance. However, most
augmentation techniques use purely spatial transformations, which are not
sufficient for video data with temporal correlations. In this paper, we present
a novel methodology for workflow augmentation and demonstrate its benefit for
event recognition in cataract surgery. The proposed approach increases the
frequency of event alternation by creating artificial videos. The original
video is split into event segments and a workflow graph is extracted from the
original annotations. Finally, the segments are assembled into new videos based
on the workflow graph. Compared to the original videos, the frequency of event
alternation in the augmented cataract surgery videos increased by 26%. Further,
a 3% higher classification accuracy and a 7.8% higher precision was achieved
compared to a state-of-the-art approach. Our approach is particularly helpful
to increase the occurrence of rare but important events and can be applied to a
large variety of use cases.


  We present spectral synthesis calculations of the solar extreme UV (EUV) in
spherical symmetry carried out with the 'Solar Modeling in 3D' code. The
calculations are based on one-dimensional atmospheric structures that represent
a temporal and spatial mean of the chromosphere, transition region, and corona.
The synthetic irradiance spectra are compared with the recent calibration
spectrum taken with the EUV Variability Experiment during the Whole
Heliospheric Interval. The good agreement between the synthetic and observed
quiet Sun spectrum shows that the employed atmospheric structures are suitable
for irradiance calculations. The validation of the quiet Sun spectrum for the
present solar minimum is the first step towards the modeling of the EUV
variations.


  Periodic orbit quantization requires an analytic continuation of
non-convergent semiclassical trace formulae. We propose two different methods
for semiclassical quantization. The first method is based upon the harmonic
inversion of semiclassical recurrence functions. A band-limited periodic orbit
signal is obtained by analytical frequency windowing of the periodic orbit sum.
The frequencies of the periodic orbit signal are the semiclassical eigenvalues,
and are determined by either linear predictor, Pade approximant, or signal
diagonalization. The second method is based upon the direct application of the
Pade approximant to the periodic orbit sum. The Pade approximant allows the
resummation of the, typically exponentially, divergent periodic orbit terms.
Both techniques do not depend on the existence of a symbolic dynamics, and can
be applied to bound as well as to open systems. Numerical results are presented
for two different systems with chaotic and regular classical dynamics, viz. the
three-disk scattering system and the circle billiard.


  The confrontation between general relativity (and its theoretically most
plausible deviations) and experimental or observational results is summarized.
Some discussion is devoted to the various methodologies used in confronting
theory and experiment. Both weak-field (solar system) and strong-field (binary
pulsar) tests are discussed in detail. A special discussion is devoted to the
cosmology of moduli fields, i.e. scalar fields having only
gravitational-strength couplings to matter.


  This paper is concerned with linear stochastic Hamiltonian (LSH) systems
subject to random external forces. Their dynamics are modelled by linear
stochastic differential equations, parameterised by stiffness, mass, damping
and coupling matrices. A class of physical couplings is discussed for such
systems using inerters, springs and dampers. We consider a problem of
minimising a steady-state quadratic cost functional over the coupling
parameters for the interconnection of two LSH systems, one of which plays the
role of an analog controller. For this mean square optimal
control-by-interconnection setting, we outline first-order necessary conditions
of optimality which employ variational methods developed previously for
constrained linear quadratic Gaussian control problems.


  One of the powerful techniques to analyze the 5 dimensional Super Yang Mills
theory with a massive hypermultiplet (N=1*) is provided by the AdS/CFT
correspondence. It predicts that, for certain special values of the
hypermultiplet mass, this theory develops nonperturbative branches of the
moduli space as well as new light degrees of freedom.
  We use the higher dimensional generalization of the matrix model/gauge theory
correspondence and recover all the prediction of the supergravity analysis. We
construct the map between the four dimensional holomorphic superpotential and
the five dimensional action and explicitly show that the superpotential is flat
along the nonperturbative branches. This is the first instance in which the
Dijkgraaf-Vafa method is used to analyze intrinsically higher dimensional
phenomena.


  Based on phase retrieval, lensless coherent imaging and in particular
holography offers quantitative phase and amplitude images. This is of
particular importance for spectral ranges where suitable lenses are
challenging, such as for hard x-rays. Here, we propose a phase retrieval
approach for inline x-ray holography based on Tikhonov regularization applied
to the full nonlinear forward model of image formation. The approach can be
seen as a nonlinear generalization of the well-established
contrast-transfer-function (CTF) reconstruction method. While similar methods
have been proposed before, the current work achieves nonlinear, constrained
phase retrieval at competitive computation times. We thus enable
high-throughput imaging of optically strong objects beyond the scope of CTF.
Using different examples of inline holograms obtained from illumination by a
x-ray waveguide-source, we demonstrate superior image quality even for samples
which do not obey the assumption of a weakly varying phase. Since the presented
approach does not rely on linearization, we expect it to be well suited also
for other probes such as visible light or electrons, which often exhibit strong
phase interaction.


  We give a new algorithm using linear approximation and lattice reduction to
efficiently calculate all rational points of small height near a given plane
curve C. For instance, when C is the Fermat cubic, we find all integer
solutions of |x^3+y^3-z^3|<M with 0<x<=y<z<N in heuristic time << L(N) M [where
L(X):= (log X)^O(1)] provided M>>N, using only O(log N) space. Since the number
of solutions should be asymptotically proportional to M log N (as long as
M<N^3), the computational costs are essentially as low as possible. Moreover
the algorithm readily parallelizes. It not only yields new numerical examples
but leads to theoretical results, difficult open questions, and natural
generalizations. We also adapt our algorithm to investigate Hall's conjecture:
we find all integer solutions of 0<|x^3-y^2|<<x^(1/2) with x<X in time
O(X^(1/2) L(X)). By implementing this algorithm with X=10^18 we shattered the
previous record for x^(1/2)/|x^3-y^2|. The O(X^{1/2} L(X)) bound is rigorous;
its proof also yields new estimates on the distribution mod 1 of sqrt(cx^3) for
any positive rational c.


  Chas and Sullivan recently defined an intersection product on the homology
$H_*(LM)$ of the space of smooth loops in a closed, oriented manifold $M$. In
this paper we will use the homotopy theoretic realization of this product
described by the first two authors to construct a second quadrant spectral
sequence of algebras converging to the loop homology multiplicatively, when $M$
is simply connected. The $E_2$ term of this spectral sequence is
$H^*(M;H_*(\Omega M))$ where the product is given by the cup product on the
cohomology of the manifold $H^* (M)$ with coefficients in the Pontryagin ring
structure on the homology of its based loop space $H_*(\Omega M)$. We then use
this spectral sequence to compute the ring structures of $H_* (LS^n)$ and $H_*
(L\bcp^n)$.


  The rate of merger events observed by LIGO/Virgo can be used in order to
probe the fraction $f$ of dark mater in the form of Primordial Black Holes.
Here, we consider the merger rate of PBH binaries, accounting for the effect of
cosmological perturbations on their initial eccentricity $e$. The torque on the
binaries receives significant contributions from a wide range of scales, that
goes from the size of the horizon at the time when the binary forms, down to
the co-moving size of the binary. In scenarios where PBH are formed from
adiabatic perturbations, it is natural to expect an enhancement of the power
spectrum $P_\Phi$ at small scales, where it is poorly constrained
observationally. The effect can then be quite significant. For instance, a
nearly flat spectrum with amplitude $P_\Phi \gtrsim 10^{-7}$ on scales smaller
than $\sim 10 Mpc^{-1}$ gives a contribution $\langle j^2 \rangle \sim 10^3
P_\Phi$, where $j= (1-e^2)^{1/2}$ is the dimensionless angular momentum
parameter of the binaries. This contribution can dominate over tidal torques
from neighboring PBHs for any value of $f$. Current constraints allow for a
power spectrum as large as $P_\Phi \sim 10^{-5}$ at the intermediate scales
$10^3-10^5 Mpc^{-1}$, comparable to the co-moving size of the binaries at the
time of formation. In particular, this can relax current bounds on the PBH
abundance based on the observed LIGO/Virgo merger rate, allowing for a fraction
$f\sim 10\%$ of dark matter in PBH of mass $\sim 30 M_\odot$. We investigate
the differential merger rate $\Delta\Gamma(m_1,m_2)$, as a function of the
masses of the binary components, and the corresponding ``universality"
coefficient $\alpha = -(m_1+m_2)^2 \partial^2 \ln \Delta\Gamma/\partial
m_1\partial m_2$, concluding that merger rates may provide valuable information
on the spectrum of primordial cosmological perturbations at currently uncharted
lengthscales.


  In this note it is proved that the complete spectral data of selfadjoint
Schr\"odinger operators on unbounded domains can be described with an
associated Dirichlet-to-Neumann map. In particular, a characterization of the
isolated and embedded eigenvalues, the corresponding eigenspaces, as well as
the continuous and absolutely continuous spectrum in terms of the limiting
behaviour of the Dirichlet-to-Neumann map is obtained. Furthermore, a
sufficient criterion for the absence of singular continuous spectrum is
provided. The results are natural multidimensional analogues of classical facts
from singular Sturm-Liouville theory.


  This paper presents a substructural logic of sequents with very restricted
exchange and weakening rules. It is sound with respect to sequences of
measurements of a quantic system. A sound and complete semantics is provided.
The semantic structures include a binary relation that expresses orthogonality
between elements and enables the definition of an operation that generalizes
the projection operation in Hilbert spaces. The language has a unitary
connective, a sort of negation, and two dual binary connectives that are
neither commutative nor associative, sorts of conjunction and disjunction. This
provides a logic for quantum measurements whose proof theory is aesthetically
pleasing.


  A short proof of the Caratheodory conjecture about index of an isolated
umbilic on the convex 2-dimensional sphere is suggested. The argument is based
on the study of geodesic lines near cone-type singularity of a metric induced
by holomorphic quadratic differentials.


  We consider effects of spatial dispersion in noncentrosymmetric time-reversal
invariant Weyl metals in the presence of a static magnetic field. In
particular, we study currents that are linear in both the spatial derivatives
of an applied electric field, and the static magnetic field, which are
responsible for the phenomenon of gyrotropic birefringence. We show that the
chiral anomaly and the chiral magnetic effect make the leading contribution to
this class of phenomena in metals. We apply the obtained results to the problem
of electromagnetic wave transmission through a thin slab of a Weyl semimetal,
and show that the transmission coefficient contains a component that is odd in
the applied static magnetic field. As such, it can be easily distinguished from
conventional Ohmic magnetotransport effects, which are quadratic in the applied
magnetic field. The relative magnitude of the effect can reach a few percent in
Weyl materials subject to magnetic fields of 0.1Tesla, while the effect is
several orders of magnitude smaller in metals without Berry monopoles. We
conclude that the nonreciprocal optical and magnetotransport effects can be a
robust probe of band topology in metals.


  In this paper, we review the recently formulated quantum laws of motion and
provide new observations. We also extend these laws to higher dimensions. By
applying in two dimensions the obtained relations to charge submitted to an
electric central potential, we decide between these laws. Furthermore, we
extend the selected law to the relativistic case in higher dimensions.


  Many neural-based recommender systems were proposed in recent years and part
of them used Generative Adversarial Networks (GAN) to model user-item
interactions. However, the exploration of Wasserstein GAN with Gradient Penalty
(WGAN-GP) on recommendation has received relatively less scrutiny. In this
paper, we focus on two questions: 1- Can we successfully apply WGAN-GP on
recommendation and does this approach give an advantage compared to the best
GAN models? 2- Are GAN-based recommender systems relevant? To answer the first
question, we propose a recommender system based on WGAN-GP called CFWGAN-GP
which is founded on a previous model (CFGAN). We successfully applied our
method on real-world datasets on the top-k recommendation task and the
empirical results show that it is competitive with state-of-the-art GAN
approaches, but we found no evidence of significant advantage of using WGAN-GP
instead of the original GAN, at least from the accuracy point of view. As for
the second question, we conduct a simple experiment in which we show that a
well-tuned conceptually simpler method outperforms GAN-based models by a
considerable margin, questioning the use of such models.


  In this work we estimate rates of the linear transient growth of the
perturbations of cellular flames governed by the Sivashinsky equation. The
possibility and significance of such a growth was indicated ear- lier in both
computational and analytical investigations. Numerical investigation of the
norm of the resolvent of the linear operator asso- ciated with the Sivashinsky
equation linearized in a neighbourhood of the steady coalescent pole solution
was undertaken. The results are presented in the form of the pseudospectra and
the lower bound of possible transient amplification. This amplification is
strong enough to make the round-off errors visible in the numerical simulations
in the form of small cusps appearing on the flame surface randomly in time.
Performance of available numerical approaches was compared to each other and
the results are checked versus directly calculated norms of the evolution
operator.


  We calculate the production of massive Kaluza-Klein(KK) modes via
nucleon-nucleon gravi-bremsstrahlung in the early universe. Overproduction of
these states would result in early matter domination and therefore a low age
for the universe so it is possible to place constraints on the number and size
of large extra dimensions. The constraints are stronger than those from Sn1987a
- for 2 large extra dimensions and T_QCD=170 MeV, we show the fundamental scale
must be larger than 1,000 TeV.


  We study the synthesis of lithium isotopes in the hot tori formed around
stellar mass black holes by accretion of the companion star. We find that
sizable amounts of both stable isotopes 6Li and 7Li can be produced, the exact
figures varying with the characteristics of the torus and reaching as much as
1e-2 Msun for each isotope. This mass output is enough to contaminate the
entire Galaxy at a level comparable with the original, pre-galactic amount of
lithium and to overcome other sources such as cosmic-ray spallation or stellar
nucleosynthesis.


  The spin-liquid candidate $\kappa$-(BEDT-TTF)$_{2}$Cu$_{2}$(CN)$_{3}$ has
been studied by measuring the uniaxial expansion coefficients $\alpha_{i}$, the
specific heat, and magnetic susceptibility. Special emphasis was placed on the
mysterious anomaly around 6 K - a potential spin-liquid instability. Distinct
and strongly anisotropic lattice effects have been observed at 6 K, clearly
identifying this feature as a second-order phase transition. Owing to the large
anomalies in $\alpha_{i}$, the application of Gr\"{u}neisen scaling has enabled
us to determine the corresponding specific heat contribution and the entropy
release. Comparison of the latter with available spin models suggests that spin
degrees of freedom alone cannot account for the phase transition. Scenarios,
involving charge degrees of freedom, are discussed. charge degrees of freedom,
are discussed.


  We investigate matter couplings in massive bigravity. We find a new family of
such consistent couplings, including and extending known consistent matter
couplings, and we investigate their decoupling limits, ADM decompositions,
Higuchi bounds and further aspects. We show that differences to previous known
consistent couplings only arise beyond the $\Lambda_3$ decoupling limit and
discuss the uniqueness of consistent matter couplings and how this is related
to the so-called symmetric vielbein condition. Since we work in a vielbein
formulation, these results easily generalise to multi-gravity.


  We investigate the link sharing behavior of Twitter users following the
temporary halt of AstraZeneca COVID-19 vaccine development in September 2020.
During this period, we show the presence of malicious and low credibility
information sources shared on Twitter messages in multiple languages. The
malicious URLs, often in shortened forms, are increasingly hosted in content
delivery networks and shared cloud hosting infrastructures not only to improve
reach but also to avoid being detected and blocked. There are potential signs
of coordination to promote both malicious and low credibility URLs on Twitter.
Our findings suggest the need to develop a system that monitors the low-quality
URLs shared in times of crisis.


  $M$-Lipschitz mappings of graphs (or equivalently graph-indexed random walks)
are a generalization of standard random walk on $\mathbb{Z}$. For $M \in \N$,
an \emph{$M$-Lipschitz mapping} of a connected rooted graph $G = (V,E)$ is a
mapping $f: V \to \Z$ such that root is mapped to zero and for every edge
$(u,v) \in E$ we have $|f(u) - f(v)| \le M$.
  We study two natural problems regarding graph-indexed random walks. -
Computing the maximum range of a graph-indexed random walk for a given graph. -
Deciding if we can extend a partial GI random walk into a full GI random walk
for a given graph.
  We show that both these problems are polynomial-time solvable and we show
efficient algorithms for them. To our best knowledge, this is the first
algorithmic treatment of Lipschitz mappings of graphs. Furthermore, our problem
of extending partial mappings is connected to the problem of \emph{list
homomorphism} and yields a better run-time complexity for a specific family of
its instances.


  Despite the considerable advancements achieved by deep neural networks, their
performance tends to degenerate when the test environment diverges from the
training ones. Domain generalization (DG) solves this issue by learning
representations independent of domain-related information, thus facilitating
extrapolation to unseen environments. Existing approaches typically focus on
formulating tailored training objectives to extract shared features from the
source data. However, the disjointed training and testing procedures may
compromise robustness, particularly in the face of unforeseen variations during
deployment. In this paper, we propose a novel and holistic framework based on
causality, named InPer, designed to enhance model generalization by
incorporating causal intervention during training and causal perturbation
during testing. Specifically, during the training phase, we employ
entropy-based causal intervention (EnIn) to refine the selection of causal
variables. To identify samples with anti-interference causal variables from the
target domain, we propose a novel metric, homeostatic score, through causal
perturbation (HoPer) to construct a prototype classifier in test time.
Experimental results across multiple cross-domain tasks confirm the efficacy of
InPer.


  The Generalized Integral Representation Method (GIRM) for
Space-Time-Separated Method (STSM) and Space-Time-Unified Method (STUM) are
discussed. STSM and STUM give explicit and implicit time evolutions,
respectively. The algorithm of STSM is much simpler than STUM. However, the
implicit time evolution of STUM could give us much more efficient computation.
Numerical calculations using STUM for Dirichlet and Neumann problems in 2D
space-time are conducted using a Traditional Fundamental Solution (TFS). The
results seem very satisfactory. However, in case of Neumann problem, the time
increment must be smaller than in case of Dirichlet problem.


  One of the main issues for underwater robots navigation is their accurate
positioning, which heavily depends on the orientation estimation phase. The
systems employed to this scope are affected by different noise typologies,
mainly related to the sensors and to the irregular noise of the underwater
environment. Filtering algorithms can reduce their effect if opportunely
configured, but this process usually requires fine techniques and time. In this
paper we propose DANAE, a deep Denoising AutoeNcoder for Attitude Estimation
which works on Kalman filter IMU/AHRS data integration with the aim of reducing
any kind of noise, independently of its nature. This deep learning-based
architecture showed to be robust and reliable, significantly improving the
Kalman filter results. Further tests could make this method suitable for
real-time applications on navigation tasks.


  We report the thermoelectric (TE) properties of
Na$_{0.74}$Co$_{0.95}$Nb$_{0.05}$O$_{2}$ in the temperature range $300-1200$ K,
as a potential candidate for p-type thermoelectric material. The experimental
values of Seebeck coefficient (S) are $ \sim $ $82-121$ $ \mu $V/K measured in
the temperature range $300-620$ K. The positive values of S in the entire
temperature range indicates p-type behaviour of the compound. At 300 K the
experimental value of thermal conductivity ($ \kappa $) is $ \sim $ 1.88 W/m-K
that increases up to $ \sim $ 420 K, then decreases till 620 K with
corresponding value $ \sim $ 1.86 W/m-K. To understand the experimentally
observed transport properties, we have calculated S and $\rho$ of this
compound. Then, based on theoretical understanding, we have estimated
\textit{figure-of-merit} (ZT) up to 1200 K by using calculated S and $\rho$
values with extrapolated experimental $\kappa$. The value of ZT is found to be
$\sim$ 0.03 at 300 K, whereas, the highest value is observed as $\sim$ 1.7 at
1200 K. Finally, we have calculated the efficiency ($\eta$) by keeping the cold
end temperature (T$_{c}$) fixed at 500 K and varying hot end temperature
(T$_{h}$) from 500 to 1200 K, respectively. The maximum value of $\eta$ is
found to be $\sim$ 8 %, when T$_{c}$ and T$_{h}$ are fixed at 500 and 1200 K,
respectively. This result suggests that
Na$_{0.74}$Co$_{0.95}$Nb$_{0.05}$O$_{2}$ compound can be used as a p-leg for
making high temperature TE generator (TEG).


  Building future wireless systems that support services like digital twins
(DTs) is challenging to achieve through advances to conventional technologies
like meta-surfaces. While artificial intelligence (AI)-native networks promise
to overcome some limitations of wireless technologies, developments still rely
on AI tools like neural networks. Such tools struggle to cope with the
non-trivial challenges of the network environment and the growing demands of
emerging use cases. In this paper, we revisit the concept of AI-native wireless
systems, equipping them with the common sense necessary to transform them into
artificial general intelligence (AGI)-native systems. These systems acquire
common sense by exploiting different cognitive abilities such as perception,
analogy, and reasoning, that enable them to generalize and deal with unforeseen
scenarios. Towards developing the components of such a system, we start by
showing how the perception module can be built through abstracting real-world
elements into generalizable representations. These representations are then
used to create a world model, founded on principles of causality and
hyper-dimensional (HD) computing, that aligns with intuitive physics and
enables analogical reasoning, that define common sense. Then, we explain how
methods such as integrated information theory play a role in the proposed
intent-driven and objective-driven planning methods that maneuver the
AGI-native network to take actions. Next, we discuss how an AGI-native network
can enable use cases related to human and autonomous agents: a) analogical
reasoning for next-generation DTs, b) synchronized and resilient experiences
for cognitive avatars, and c) brain-level metaverse experiences like
holographic teleportation. Finally, we conclude with a set of recommendations
to build AGI-native systems. Ultimately, we envision this paper as a roadmap
for the beyond 6G era.


  The movement of grain boundaries in pure metals and alloys with a low
concentration of dislocations has been historically proved to follow curvature
flow behavior. This mechanism is typically known as grain growth (GG). However,
recent 3D in-situ experimental results tend to question this global picture
concerning the influence of the curvature on the kinetics of interface
migration. This article explains, thanks to 2D anisotropic full-field
simulations, how the torque effects can complexify these discussions. It is
then illustrated that neglecting torque effects in full-field formulations
remains potentially a strong hypothesis. The apparent mobility can be much more
complex than expected without necessarily questioning the influence of the
curvature on the local kinetic equation.


  The theoretical analysis of many problems in physics, astronomy and applied
mathematics requires an efficient numerical exploration of multimodal parameter
spaces that exhibit broken ergodicity. Monte Carlo methods are widely used to
deal with these classes of problems, but such simulations suffer from a
ubiquitous sampling problem: the probability of sampling a particular state is
proportional to its entropic weight. Devising an algorithm capable of sampling
efficiently the full phase space is a long-standing problem. Here we report a
new hybrid method for the exploration of multimodal parameter spaces exhibiting
broken ergodicity. Superposition enhanced nested sampling (SENS) combines the
strengths of global optimization with the unbiased/athermal sampling of nested
sampling, greatly enhancing its efficiency with no additional parameters. We
report extensive tests of this new approach for atomic clusters that are known
to have energy landscapes for which conventional sampling schemes suffer from
broken ergodicity. We also introduce a novel parallelization algorithm for
nested sampling.


  Out-of-time-ordered correlators (OTOC) have been proposed to characterize
quantum chaos in generic systems. However, they can also show interesting
behavior in integrable models, resembling the OTOC in chaotic systems in some
aspects. Here we study the OTOC for different operators in the exactly-solvable
one-dimensional quantum Ising spin chain. The OTOC for spin operators that are
local in terms of the Jordan-Wigner fermions has a "shell-like" structure:
after the wavefront passes, the OTOC approaches its original value in the
long-time limit, showing no signature of scrambling; the approach is described
by a $t^{-1}$ power law at long time $t$. On the other hand, the OTOC for spin
operators that are nonlocal in the Jordan-Wigner fermions has a "ball-like"
structure, with its value reaching zero in the long-time limit, looking like a
signature of scrambling; the approach to zero, however, is described by a slow
power law $t^{-1/4}$ for the Ising model at the critical coupling. These
long-time power-law behaviors in the lattice model are not captured by
conformal field theory calculations. The mixed OTOC with both local and
nonlocal operators in the Jordan-Wigner fermions also has a "ball-like"
structure, but the limiting values and the decay behavior appear to be
nonuniversal. In all cases, we are not able to define a parametrically large
window around the wavefront to extract the Lyapunov exponent.


  To achieve fast computation, it is crucial to reset the memory to a desired
state within a limited time. However, the inherent delay in the system's
response often prevents reaching the desired state once the control process is
completed in finite time. To address this challenge, we propose a shortcut
strategy that incorporates an auxiliary control to guide the system towards an
equilibrium state that corresponds to the intended control, thus enabling
accurate memory reset. Through the application of thermodynamic geometry, we
derive an optimal shortcut protocol for erasure processes that minimizes the
energy cost. This research provides an effective design principle for realizing
the finite-time erasure process while simultaneously reducing the energy cost,
thereby alleviating the burden of heat dissipation.


  Let {\phi} be a Drinfeld A-module of characteristic p0 over a finitely
generated field K. Previous articles determined the image of the absolute
Galois group of K up to commensurability in its action on all prime-to-p0
torsion points of {\phi}, or equivalently, on the prime-to-p0 adelic Tate
module of {\phi}. In this article we consider in addition a finitely generated
torsion free A-submodule M of K for the action of A through {\phi}. We
determine the image of the absolute Galois group of K up to commensurability in
its action on the prime-to-p0 division hull of M, or equivalently, on the
extended prime-to-p0 adelic Tate module associated to {\phi} and M.


  The translocation dynamics of a polymer chain through a nanopore in the
absence of an external driving force is analyzed by means of scaling arguments,
fractional calculus, and computer simulations. The problem at hand is mapped on
a one dimensional {\em anomalous} diffusion process in terms of reaction
coordinate $s$ (i.e. the translocated number of segments at time $t$) and shown
to be governed by an universal exponent $\alpha = 2/(2\nu+2-\gamma_1)$ whose
value is nearly the same in two- and three-dimensions. The process is described
by a {\em fractional} diffusion equation which is solved exactly in the
interval $0 <s < N$ with appropriate boundary and initial conditions. The
solution gives the probability distribution of translocation times as well as
the variation with time of the statistical moments: $<s(t)>$, and $<s^2(t)> - <
s(t)>^2$ which provide full description of the diffusion process. The
comparison of the analytic results with data derived from extensive Monte Carlo
(MC) simulations reveals very good agreement and proves that the diffusion
dynamics of unbiased translocation through a nanopore is anomalous in its
nature.


  We propose and analyse new stabilized time marching schemes for Phase Fields
model such as Allen-Cahn and Cahn-Hillard equations, when discretized in space
with high order finite differences compact schemes. The stabilization applies
to semi-implicit schemes for which the linear part is simplified using sparse
pre-conditioners. The new methods allow to significant obtain a gain of CPU
time. The numerical illustrations we give concern applications on pattern
dynamics and on image processing (inpainting, segmentation) in two and three
dimension cases.


  Timed automata and register automata are well-known models of computation
over timed and data words respectively. The former has clocks that allow to
test the lapse of time between two events, whilst the latter includes registers
that can store data values for later comparison. Although these two models
behave in appearance differently, several decision problems have the same
(un)decidability and complexity results for both models. As a prominent
example, emptiness is decidable for alternating automata with one clock or
register, both with non-primitive recursive complexity. This is not by chance.
  This work confirms that there is indeed a tight relationship between the two
models. We show that a run of a timed automaton can be simulated by a register
automaton, and conversely that a run of a register automaton can be simulated
by a timed automaton. Our results allow to transfer complexity and decidability
results back and forth between these two kinds of models. We justify the
usefulness of these reductions by obtaining new results on register automata.


  We study the low-rank phase retrieval problem, where the objective is to
recover a sequence of signals (typically images) given the magnitude of linear
measurements of those signals. Existing solutions involve recovering a matrix
constructed by vectorizing and stacking each image. These algorithms model this
matrix to be low-rank and leverage the low-rank property to decrease the sample
complexity required for accurate recovery. However, when the number of
available measurements is more limited, these low-rank matrix models can often
fail. We propose an algorithm called Tucker-Structured Phase Retrieval (TSPR)
that models the sequence of images as a tensor rather than a matrix that we
factorize using the Tucker decomposition. This factorization reduces the number
of parameters that need to be estimated, allowing for a more accurate
reconstruction in the under-sampled regime. Interestingly, we observe that this
structure also has improved performance in the over-determined setting when the
Tucker ranks are chosen appropriately. We demonstrate the effectiveness of our
approach on real video datasets under several different measurement models.


  We define subscripted unstable higher Toda brackets and study their
elementary properties. This paper is the continuation of our previous paper in
which we defined the non-subscripted unstable higher Toda brackets.


  Choice designs for the main effects model, broader main effects model and
main effects plus specified interaction effects model are discussed in this
paper. Universally optimal choice designs are obtained for all of these models
using Hadamard matrix and other combinatorial techniques. Choice experiments
under the multinomial logit model for equally attractive options are assumed
for finding universally optimal choice designs.


  We show that if every module W for a vertex operator algebra V satisfies the
condition that the dimension of W/C_1(W) is less than infinity, where C_1(W) is
the subspace of W spanned by elements of the form u_{-1}w for u in V of
positive weight and w in W, then matrix elements of products and iterates of
intertwining operators satisfy certain systems of differential equations.
Moreover, for prescribed singular points, there exist such systems of
differential equations such that the prescribed singular points are regular.
The finiteness of the fusion rules is an immediate consequence of a result used
to establish the existence of such systems. Using these systems of differential
equations and some additional reducibility conditions, we prove that products
of intertwining operators for V satisfy the convergence and extension property
needed in the tensor product theory for V-modules. Consequently, when a vertex
operator algebra V satisfies all the conditions mentioned above, we obtain a
natural structure of vertex tensor category (consequently braided tensor
category) on the category of V-modules and a natural structure of intertwining
operator algebra on the direct sum of all (inequivalent) irreducible V-modules.


  In a recent paper it was shown that No Free Lunch results hold for any subset
F of the set of all possible functions from a finite set X to a finite set Y
iff F is closed under permutation of X. In this article, we prove that the
number of those subsets can be neglected compared to the overall number of
possible subsets. Further, we present some arguments why problem classes
relevant in practice are not likely to be closed under permutation.


  Small perturbations in the dielectric environment around a high quality
whispering gallery mode resonator usually lead to a frequency shift of the
resonator modes directly proportional to the polarizability of the
perturbation. Here, we report experimental observations of strong frequency
shifts that can be opposite and even exceed the contribution of the
perturbations' polarizability. The mode frequencies of a lithium niobate
whispering gallery mode resonator are shifted using substrates of refractive
indices ranging from 1.50 to 4.22. Both blue- and red-shifts are observed, as
well as an increase in mode linewidth, when substrates are moved into the
evanescent field of the whispering gallery mode. We compare the experimental
results to a theoretical model by Foreman et al. and provide an additional
intuitive explanation based on the Goos-H\"anchen shift for the optical domain.


  Detection of pulmonary nodules by CT is used for screening lung cancer in
early stages.omputer aided diagnosis (CAD) based on deep-learning method can
identify the suspected areas of pulmonary nodules in CT images, thus improving
the accuracy and efficiency of CT diagnosis. The accuracy and robustness of
deep learning models. Method:In this paper, we explore (1) the data
augmentation method based on the generation model and (2) the model structure
improvement method based on the embedding mechanism. Two strategies have been
introduced in this study: a new data augmentation method and a embedding
mechanism. In the augmentation method, a 3D pixel-level statistics algorithm is
proposed to generate pulmonary nodule and by combing the faked pulmonary nodule
and healthy lung, we generate new pulmonary nodule samples. The embedding
mechanism are designed to better understand the meaning of pixels of the
pulmonary nodule samples by introducing hidden variables. Result: The result of
the 3DVNET model with the augmentation method for pulmonary nodule detection
shows that the proposed data augmentation method outperforms the method based
on generative adversarial network (GAN) framework, training accuracy improved
by 1.5%, and with embedding mechanism for pulmonary nodules classification
shows that the embedding mechanism improves the accuracy and robustness for the
classification of pulmonary nodules obviously, the model training accuracy is
close to 1 and the model testing F1-score is 0.90.Conclusion:he proposed data
augmentation method and embedding mechanism are beneficial to improve the
accuracy and robustness of the model, and can be further applied in other
common diagnostic imaging tasks.


  Conveying human goals to autonomous systems (AS) occurs both when the system
is being designed and when it is being operated. The design-step conveyance is
typically mediated by robotics and AI engineers, who must appropriately capture
end-user requirements and concepts of operations, while the operation-step
conveyance is mediated by the design, interfaces, and behavior of the AI.
However, communication can be difficult during both these periods because of
mismatches in the expectations and expertise of the end-user and the
roboticist, necessitating more design cycles to resolve. We examine some of the
barriers in communicating system design requirements, and develop an
augmentation for applied cognitive task analysis (ACTA) methods, that we call
robot task analysis (RTA), pertaining specifically to the development of
autonomous systems. Further, we introduce a top-down view of an underexplored
area of friction between requirements communication -- implied human
expectations -- utilizing a collection of work primarily from experimental
psychology and social sciences. We show how such expectations can be used in
conjunction with task-specific expectations and the system design process for
AS to improve design team communication, alleviate barriers to user rejection,
and reduce the number of design cycles.


  We reinterpret Kim's non-abelian reciprocity maps for algebraic varieties as
obstruction towers of mapping spaces of etale homotopy types, removing
technical hypotheses such as global basepoints and cohomological constraints.
We then extend the theory by considering alternative natural series of
extensions, one of which gives an obstruction tower whose first stage is the
Brauer--Manin obstruction, allowing us to determine when Kim's maps recover the
Brauer-Manin locus. A tower based on relative completions yields non-trivial
reciprocity maps even for Shimura varieties; for the stacky modular curve,
these take values in Galois cohomology of modular forms, and give obstructions
to an adelic elliptic curve with global Tate module underlying a global
elliptic curve.


  In this paper, I try to tame "Basu's elephants" (data with extreme selection
on observables). I propose new practical large-sample and finite-sample methods
for estimating and inferring heterogeneous causal effects (under
unconfoundedness) in the empirically relevant context of limited overlap. I
develop a general principle called "Stable Probability Weighting" (SPW) that
can be used as an alternative to the widely used Inverse Probability Weighting
(IPW) technique, which relies on strong overlap. I show that IPW (or its
augmented version), when valid, is a special case of the more general SPW (or
its doubly robust version), which adjusts for the extremeness of the
conditional probabilities of the treatment states. The SPW principle can be
implemented using several existing large-sample parametric, semiparametric, and
nonparametric procedures for conditional moment models. In addition, I provide
new finite-sample results that apply when unconfoundedness is plausible within
fine strata. Since IPW estimation relies on the problematic reciprocal of the
estimated propensity score, I develop a "Finite-Sample Stable Probability
Weighting" (FPW) set-estimator that is unbiased in a sense. I also propose new
finite-sample inference methods for testing a general class of weak null
hypotheses. The associated computationally convenient methods, which can be
used to construct valid confidence sets and to bound the finite-sample
confidence distribution, are of independent interest. My large-sample and
finite-sample frameworks extend to the setting of multivalued treatments.


  Biological systems perceive the world by simultaneously processing
high-dimensional inputs from modalities as diverse as vision, audition, touch,
proprioception, etc. The perception models used in deep learning on the other
hand are designed for individual modalities, often relying on domain-specific
assumptions such as the local grid structures exploited by virtually all
existing vision models. These priors introduce helpful inductive biases, but
also lock models to individual modalities. In this paper we introduce the
Perceiver - a model that builds upon Transformers and hence makes few
architectural assumptions about the relationship between its inputs, but that
also scales to hundreds of thousands of inputs, like ConvNets. The model
leverages an asymmetric attention mechanism to iteratively distill inputs into
a tight latent bottleneck, allowing it to scale to handle very large inputs. We
show that this architecture is competitive with or outperforms strong,
specialized models on classification tasks across various modalities: images,
point clouds, audio, video, and video+audio. The Perceiver obtains performance
comparable to ResNet-50 and ViT on ImageNet without 2D convolutions by directly
attending to 50,000 pixels. It is also competitive in all modalities in
AudioSet.


  We prove that a self-similar free abelian group has finite rank. We apply the
result to self-similar wreath products of abelian groups $G=BwrX$. We show that
if $X$ is torsion-free, then $B$ is torsion of finite exponent. Furthemore, we
construct a self-similar group $G=BwrC_{2}$ where $B$ is free abelian of
infinite rank.


  In this paper, we explain our methodology to identify replacement patterns.
The main purpose of this article is to show that with replacement methods on
plain texts, it is possible to have more success rates when trying to
recovering hashed passwords.


  Calculations of the inner mass function of the Hayward regular black hole
with fluxes are reviewed and rederived. We present detailed calculations of the
inner mass function in two forms of the Ori approach (the ingoing flux is
continuous, the outgoing flux is modeled by a thin null shell) and compare them
with calculations in Reissner-Nordstrom black hole. A formal reason of
different results is discussed. The energy density of scalar perturbations
propagating from the event horizon into the Hayward black hole measured by a
free falling observer near the inner horizon is calculated.


  Traditional Answer Set Programming (ASP) rests upon one-shot solving. A logic
program is fed into an ASP system and its stable models are computed. The high
practical relevance of dynamic applications led to the development of
multi-shot solving systems. An operative system solves continuously changing
logic programs. Although this was primarily aiming at dynamic applications in
assisted living, robotics, or stream reasoning, where solvers interact with an
environment, it also opened up the opportunity of interactive ASP, where a
solver interacts with a user. We begin with a formal characterization of
interactive ASP in terms of states and operations on them. In turn, we describe
the interactive ASP shell aspic along with its basic functionalities.


  The Bogoliubov-Dirac-Fock (BDF) model is a no-photon, mean-field approxi-
mation of quantum electrodynamics. It describes relativistic electrons in the
Dirac sea. In this model, a state is fully characterized by its one-body
density matrix, an infinite rank nonnegative operator. We prove the existence
of the positronium, the bound state of an electron and a positron, represented
by a critical point of the energy functional in the absence of external field.
This state is interpreted as the ortho-positronium, where the two particles
have parallel spins.


  We obtain the asymptotics for the speed of a particular case of a particle
system with branching and selection introduced by B\'erard and Gou\'er\'e
(2010). The proof is based on a connection with a supercritical Galton-Watson
process censored at a certain level.


  In this paper we define and investigate Z/2-homology cobordism invariants of
Z/2-homology 3-spheres which turn out to be related to classical invariants of
knots. As an application we show that many lens spaces have infinite order in
the Z/2-homology cobordism group and we prove a lower bound for the slice genus
of a knot on which integral surgery yields a given Z/2-homology sphere. We also
give some new examples of 3-manifolds which cannot be obtained by integral
surgery on a knot.


  Recently a boundary string field theory that had been proposed some time ago,
was used to calculate correctly the ratios of D-brane (both BPS and non-BPS)
tensions. We discuss how this work is related to the boundary state formalism
and open string closed string duality, and argue that the latter clarifies why
the correct tension ratios are obtained in these recent calculations.


  Sparse decision trees are one of the most common forms of interpretable
models. While recent advances have produced algorithms that fully optimize
sparse decision trees for prediction, that work does not address policy design,
because the algorithms cannot handle weighted data samples. Specifically, they
rely on the discreteness of the loss function, which means that real-valued
weights cannot be directly used. For example, none of the existing techniques
produce policies that incorporate inverse propensity weighting on individual
data points. We present three algorithms for efficient sparse weighted decision
tree optimization. The first approach directly optimizes the weighted loss
function; however, it tends to be computationally inefficient for large
datasets. Our second approach, which scales more efficiently, transforms
weights to integer values and uses data duplication to transform the weighted
decision tree optimization problem into an unweighted (but larger) counterpart.
Our third algorithm, which scales to much larger datasets, uses a randomized
procedure that samples each data point with a probability proportional to its
weight. We present theoretical bounds on the error of the two fast methods and
show experimentally that these methods can be two orders of magnitude faster
than the direct optimization of the weighted loss, without losing significant
accuracy.


  We find a simple relation between the first subleading terms in the
asymptotic expansion of the metric field in AdS$_3$, obeying the Brown-Henneaux
boundary conditions, and the stress tensor of the underlying Liouville theory
on the boundary. We can also provide an more explicit relation between the bulk
metric and the boundary conformal field theory when it is described in terms of
a free field with a background charge.


  An improved unified formulation based on the effective field theory is
introduced for a spin-1/2 Ising model with nearest neighbor interactions with
arbitrary coordination number z. Present formulation is capable of calculating
all the multi-spin correlations systematically in a representative manner, as
well as its single site counterparts in the system and gives results for the
critical temperature of the system much better than those of the other works in
the literature. The formulation can be easily applied to various extensions of
s-1/2 Ising models, as long as the system contains only the nearest neighbor
interactions as spin-spin interactions.


  Studies based on Hubble Space Telescope ($HST$) photometry in F275W, F336W,
and F438W have shown that the incidence and complexity of multiple populations
(MPs) in Globular Clusters (GCs) depend on cluster mass. This result, however,
is based on nearby, low-reddening Galactic GCs, for which we can obtain
accurate F275W photometry. In this work we exploit $HST$ photometry in F336W,
F438W, and F814W to characterize MPs in 68 Galactic and extragalactic GCs by
using the pseudo-color $C_{F336W,F438W,F814W}$, which is more efficient in
terms of observation time than the pseudo-color $C_{F275W,F336W,F438W}$ adopted
in previous works. We first analyzed the Galactic GCs alone and find that the
RGB color width strongly correlates with [Fe/H]. After removing the dependence
from metallicity, we obtain a strong correlation with cluster mass, thus
confirming previous findings. We then exploited the RGB width to compare MPs in
Galactic and extragalactic GCs. Similarly to Galactic GCs, the RGB width of
Magellanic Cloud GCs correlates with clusters mass, after removing the
dependence from metallicity. This fact demonstrates that cluster mass is the
main factor affecting the properties of MPs. Magellanic Cloud clusters exhibit,
on average, narrower RGBs than Galactic GCs with similar mass and metallicity.
We suggest that this difference is a signature of stellar mass loss in Galactic
GCs. As an alternative, the mass-RGB-width relation would depend on the host
galaxy. Finally, we used ground-based photometry to investigate Terzan\,7
through the $C_{U,B,I}$ pseudo-color, ground-based analogous of
$C_{F336W,F438W,F814W}$, and find that this cluster is consistent with a simple
population.


  The existence of hadronic string is derived as a consequence of confinement
in QCD. A state of ``stretched glue'', created by a Polyakov loop operator, is
shown to have translational zero-modes which are stringy degrees of freedom.
These modes are described by an effective string theory, valid for world-
sheets which are locally flat on length scales of order $\Lambda_{QCD}^{-1}$,
the dominant behavior being given by the Nambu-Goto action. In a subsequent
paper, these effective strings will be shown to emerge in mesons stretched by
their orbital angular momentum, thereby deriving some aspects of Regge
phenomenology directly from QCD and confinement.


  Explicit calibration-based methods have dominated RAW image denoising under
extremely low-light environments. However, these methods are impeded by several
critical limitations: a) the explicit calibration process is both labor- and
time-intensive, b) challenge exists in transferring denoisers across different
camera models, and c) the disparity between synthetic and real noise is
exacerbated by digital gain. To address these issues, we introduce a
groundbreaking pipeline named Lighting Every Darkness (LED), which is effective
regardless of the digital gain or the camera sensor. LED eliminates the need
for explicit noise model calibration, instead utilizing an implicit fine-tuning
process that allows quick deployment and requires minimal data. Structural
modifications are also included to reduce the discrepancy between synthetic and
real noise without extra computational demands. Our method surpasses existing
methods in various camera models, including new ones not in public datasets,
with just a few pairs per digital gain and only 0.5% of the typical iterations.
Furthermore, LED also allows researchers to focus more on deep learning
advancements while still utilizing sensor engineering benefits. Code and
related materials can be found in https://srameo.github.io/projects/led-iccv23/ .


  Let E be a real quadratic field with discriminant d and let p be an odd prime
not dividing d. For \rho=1 or -1, we determine $\prod_{0<c<d, (d/c)=\rho}
binomial coeff.{p-1}{\lfloor pc/d\rfloor}$ modulo p^2 in terms of Lucas
numbers, the fundamental unit and the class number of E, where (d/c) is the
Kronecker symbol.


  In user-generated recipe websites, users post their-original recipes. Some
recipes, however, are very similar in major components such as the cooking
instructions to other recipes. We refer to such recipes as "near-duplicate
recipes". In this study, we propose a method that extends the "Word Mover's
Distance", which calculates distances between texts based on word embedding, to
character 3-gram embedding. Using a corpus of over 1.21 million recipes, we
learned the word embedding and the character 3-gram embedding by using a
Skip-Gram model with negative sampling and fastText to extract candidate pairs
of near-duplicate recipes. We then annotated these candidates and evaluated the
proposed method against a comparison method. Our results demonstrated that
near-duplicate recipes that were not detected by the comparison method were
successfully detected by the proposed method.


  Intrigued by the product formula prod_{i=1}^{n-2} C_i for the volume of the
Chan-Robbins-Yuen polytope CRY_n, where C_i is the ith Catalan number, we
construct a family of polytopes P_{m,n}, whose volumes are given by the product
\prod_{i=m+1}^{m+n-2}\frac{1}{2i+1}{{m+n+i} \choose {2i}}. The
Chan-Robbins-Yuen polytope CRY_n coincides with P_{0,n-1}. Our construction of
the polytopes P_{m,n} is an application of a systematic method we develop for
expressing volumes of a class of flow polytopes as the number of certain
triangular arrays. This method can also be used as a heuristic technique for
constructing polytopes with combinatorial volumes. As an illustration of this
we construct polytopes whose volumes equal the number of r-ary trees on n
internal nodes, \frac{1}{(r-1)n+1} {{rn} \choose n}. Using triangular arrays we
also express the volumes of flow polytopes as constant terms of formal Laurent
series.


  Unique word-orthogonal frequency division multiplexing (UW-OFDM) is known to
provide various performance benefits over conventional OFDM using cyclic
prefixes (CP). Most important, UW-OFDM features excellent spectral sidelobe
suppression properties and an outstanding bit error ratio performance. Current
research has mainly focused on principle performance bounds of UW-OFDM, with
less attention on challenges aside from idealized communication scenarios, such
as system parameter estimation tasks. In this work we present an approach for
including frequency pilots tones into the UW-OFDM signaling scheme, which can
then be utilized for these estimation tasks. Suitable optimization criteria are
presented and interactions of pilots with data symbols are highlighted. Pilot
tone based estimation of a carrier frequency offset (CFO) is conducted as an
estimation example, revealing considerable differences to conventional OFDM.
Simulation results in a multipath environment demonstrate a significantly
increased estimation accuracy in UW-OFDM over CP-OFDM, which becomes even more
dominant with an increasing CFO. This performance difference is due to the
inherent redundancy present in an UW-OFDM signal.


  We consider possible interpretations of the recently detected X- ray
afterglow from the gamma-ray burst source GRB 970228. Cosmological and Galactic
models of gamma-ray bursts predict different flux and spectral evolution of
X-ray afterglows. We show that models based on adiabatic expansion of
relativistic forward shocks require very efficient particle energization or
post-burst re-acceleration during the expansion. Cooling neutron star models
predict a very distinctive spectral and flux evolution that can be tested in
current X-ray data.


  We present the catalog of clusters found in the area of ~2.4 square degree in
the central regions of the Small Magellanic Cloud. The catalog contains data
for 238 clusters, 72 of them are new objects. For each cluster equatorial
coordinates, radii, approximate number of members, cross-identification,
finding chart and color magnitude diagrams: V-(B-V) and V-(V-I) are provided.
Photometric data for all clusters presented in the catalog are available from
the OGLE Internet archive.


  Packings of frictionless athermal particles that interact only when they
overlap experience a jamming transition as a function of packing density. Such
packings provide the foundation for the theory of jamming. This theory rests on
the observation that, despite the multitude of disordered configurations, the
mechanical response to linear order depends only on the distance to the
transition. We investigate the validity and utility of such measurements that
invoke the harmonic approximation and show that, despite particles coming in
and out of contact, there is a well-defined linear regime in the thermodynamic
limit.


  Recent methods in speech and language technology pretrain very LARGE models
which are fine-tuned for specific tasks. However, the benefits of such LARGE
models are often limited to a few resource rich languages of the world. In this
work, we make multiple contributions towards building ASR systems for low
resource languages from the Indian subcontinent. First, we curate 17,000 hours
of raw speech data for 40 Indian languages from a wide variety of domains
including education, news, technology, and finance. Second, using this raw
speech data we pretrain several variants of wav2vec style models for 40 Indian
languages. Third, we analyze the pretrained models to find key features:
codebook vectors of similar sounding phonemes are shared across languages,
representations across layers are discriminative of the language family, and
attention heads often pay attention within small local windows. Fourth, we
fine-tune this model for downstream ASR for 9 languages and obtain
state-of-the-art results on 3 public datasets, including on very low-resource
languages such as Sinhala and Nepali. Our work establishes that multilingual
pretraining is an effective strategy for building ASR systems for the
linguistically diverse speakers of the Indian subcontinent. Our code, data and
models are available publicly at https://indicnlp.ai4bharat.org/indicwav2vec/
and we hope they will help advance research in ASR for Indic languages.


  Cosmic-ray (CR) sources temporarily enhance the relativistic particle density
in their vicinity over the background distribution accumulated from the
Galaxy-wide past injection activity and propagation. If individual sources are
close enough to the solar system, their localised enhancements may present as
features in the measured spectra of the CRs and in the associated secondary
electromagnetic emissions. Large scale loop like structures visible in the
radio sky are possible signatures of such nearby CR sources. If so, these loops
may also have counterparts in the high-latitude $\gamma$-ray sky. Using
$\sim$10 years of data from the Fermi Large Area Telescope, applying Bayesian
analysis including Gaussian Processes, we search for extended enhanced emission
associated with putative nearby CR sources in the energy range from 1 GeV to 1
TeV for the sky region $|b| > 30^\circ$. We carefully control the systematic
uncertainty due to imperfect knowledge of the interstellar gas distribution.
Radio Loop~IV is identified for the first time as a $\gamma$-ray emitter and we
also find significant emission from Loop~I. Strong evidence is found for
asymmetric features about the Galactic $l = 0^\circ$ meridian that may be
associated with parts of the so-called "Fermi Bubbles", and some evidence is
also found for $\gamma$-ray emission from other radio loops. Implications for
the CRs producing the features and possible locations of the sources of the
emissions are discussed.


  We study the variability mechanism of active galactic nuclei (AGN) within the
framework of the flare model. To this end we examine the case of Seyfert/LINER
galaxy NGC 4258, which is observed at high inclination angle and exhibits rapid
fluctuations of the X-ray light curve. We construct a model light curve based
on the assumption of magnetic flares localized in the equatorial plane and
orbiting with Keplerian speed at each given radius. We calculate the level of
variability as a function of the inclination of an observer, taking into
account all effects of general relativity near a rotating supermassive black
hole. The variability level is a monotonic function of the source inclination.
It rises more rapidly for larger values of the black hole spin (Kerr parameter)
and for steeper emissivity (index beta of the radial profile). We compare the
expected level of variability for the viewing angle 81.6 deg, as inferred for
NGC 4258, with the case of moderate viewing angles about 30 deg, typical for
Seyfert type-1 galaxies. Highly inclined sources such as this one are
particularly suitable to test the flare model because the effects of orbital
motion, Doppler boosting and light bending are all expected to have maximum
when the accretion disk is seen almost edge-on. The model is consistent with
the NGC 4258 variability, where the obscuring material is thought to be
localized mainly towards the equatorial plane rather than forming a
geometrically thick torus. Once the intrinsic time-scales of the flare duration
are determined to better precision, this kind of highly inclined objects with a
precisely known mass of the black hole can be used to set independent
constraints on the spin parameter.


  The measurement of azimuthal correlations between two particles is a powerful
tool to investigate the properties of strongly-interacting nuclear matter
created in ultra-relativistic heavy-ion collisions. We present measurements of
di-hadron correlations in azimuth angle and pseudorapidity in Pb-Pb collisions
at $\sqrt{s_{\rm NN}} = 2.76 \tev$ and photon-hadron correlations in pp
collisions at $\sqrt{s} = 7 \tev$ with the ALICE detector, respectively. In
di-hadron correlations, the near-side jet shape in the short-range correlation
region is quantitatively analyzed at $\ptt < 8 \gmom$, and the modification of
jet-particle yield, $I_{\rm AA}$ and $I_{\rm CP}$, is measured at $8 < \ptt <
15 \gmom$. In photon-hadron correlations, isolated leading photon and
associated hadrons in its opposite azimuthal direction correlations are used to
estimate the jet fragmentation function via the imbalance parameter, $x_{\rm E}
\equiv -\frac{\vec{p}_{\rm T}^{\gamma}\cdot\vec{p}_{\rm T}^{\rm
h^{\pm}}}{|\vec{p}_{\rm T}^{\gamma}|^{2}}$.


  We consider the Minimal Supersymmetric Standard Model (MSSM) without imposing
relations on the superpartner masses that arise in grand unified theories.
Given an arbitrary pattern of superpartner masses (consistent with experimental
constraints), it may happen that the scalar potential is actually unstable,
even though all scalar masses-squared are positive at the weak scale $M_W$.
This is most likely to happen if the running mass-squared in a ``flat''
direction in field space becomes negative at some scale $Q_0$ which is well
below the GUT scale. In this case, either this pattern of masses is ruled out,
or there must be new physics (beyond the MSSM) at or below the scale $Q_0$.


  In the dynamical gauge-Higgs unification in the Randall-Sundrum warped
spacetime, where the 4D Higgs field is unified with gauge fields and the
electroweak symmetry is dynamically broken by the Hosotani mechanism, the
trilinear couplings for WWZ, WWH, and ZZH, where H stands for the Higgs field,
are evaluated. The latter two couplings are suppressed by a factor of \cos
\theta_H where \theta_H is the Yang-Mills Aharonov-Bohm phase in the extra
dimension, while the WWZ couplings remain the same as in the standard model to
good accuracy.


  While direct statemets for kernel based approximation on domains $\Omega
\subset \mathbb{R}^d$ using radial basis functions are well researched, there
still seems to be a gap in comparison with corresponding inverse statements. In
this paper we sharpen inverse statements and by this close a ``gap of $d/2$"
which was raised in the literature. In particular we show that for a large
class of finitely smooth radial basis function kernels such as Mat\'ern or
Wendland kernels, there exists a one-to-one correspondence between the
smoothness of a function and its $L^2(\Omega)$ approximation rate via kernel
interpolation: If a function can be approximation with a given rate, it has a
corresponding smoothness and vice versa


  Artificial neural networks have revolutionized machine learning in recent
years, but a complete theoretical framework for their learning process is still
lacking. Substantial progress has been made for infinitely wide networks. In
this regime, two disparate theoretical frameworks have been used, in which the
network's output is described using kernels: one framework is based on the
Neural Tangent Kernel (NTK) which assumes linearized gradient descent dynamics,
while the Neural Network Gaussian Process (NNGP) kernel assumes a Bayesian
framework. However, the relation between these two frameworks has remained
elusive. This work unifies these two distinct theories using a Markov proximal
learning model for learning dynamics in an ensemble of randomly initialized
infinitely wide deep networks. We derive an exact analytical expression for the
network input-output function during and after learning, and introduce a new
time-dependent Neural Dynamical Kernel (NDK) from which both NTK and NNGP
kernels can be derived. We identify two learning phases characterized by
different time scales: gradient-driven and diffusive learning. In the initial
gradient-driven learning phase, the dynamics is dominated by deterministic
gradient descent, and is described by the NTK theory. This phase is followed by
the diffusive learning stage, during which the network parameters sample the
solution space, ultimately approaching the equilibrium distribution
corresponding to NNGP. Combined with numerical evaluations on synthetic and
benchmark datasets, we provide novel insights into the different roles of
initialization, regularization, and network depth, as well as phenomena such as
early stopping and representational drift. This work closes the gap between the
NTK and NNGP theories, providing a comprehensive framework for understanding
the learning process of deep neural networks in the infinite width limit.


  Recently, adversarial training has been incorporated in self-supervised
contrastive pre-training to augment label efficiency with exciting adversarial
robustness. However, the robustness came at a cost of expensive adversarial
training. In this paper, we show a surprising fact that contrastive
pre-training has an interesting yet implicit connection with robustness, and
such natural robustness in the pre trained representation enables us to design
a powerful robust algorithm against adversarial attacks, RUSH, that combines
the standard contrastive pre-training and randomized smoothing. It boosts both
standard accuracy and robust accuracy, and significantly reduces training costs
as compared with adversarial training. We use extensive empirical studies to
show that the proposed RUSH outperforms robust classifiers from adversarial
training, by a significant margin on common benchmarks (CIFAR-10, CIFAR-100,
and STL-10) under first-order attacks. In particular, under
$\ell_{\infty}$-norm perturbations of size 8/255 PGD attack on CIFAR-10, our
model using ResNet-18 as backbone reached 77.8% robust accuracy and 87.9%
standard accuracy. Our work has an improvement of over 15% in robust accuracy
and a slight improvement in standard accuracy, compared to the
state-of-the-arts.


  Utilising optical and near-infrared broadband photometry covering $> 5\,{\rm
deg}^2$ in two of the most well-studied extragalactic legacy fields (COSMOS and
XMM-LSS), we measure the galaxy stellar mass function (GSMF) between $0.1 < z <
2.0$. We explore in detail the effect of two source extraction methods
(SExtractor and ProFound) in addition to the inclusion/exclusion of Spitzer
IRAC 3.6 and 4.5$\mu$m photometry when measuring the GSMF. We find that
including IRAC data reduces the number of massive ($\log_{10}(M/M_\odot) >
11.25$) galaxies found due to improved photometric redshift accuracy, but has
little effect on the more numerous lower-mass galaxies. We fit the resultant
GSMFs with double Schechter functions down to $\log_{10}(M/M_\odot)$ = 7.75
(9.75) at z = 0.1 (2.0) and find that the choice of source extraction software
has no significant effect on the derived best-fit parameters. However, the
choice of methodology used to correct for the Eddington bias has a larger
impact on the high-mass end of the GSMF, which can partly explain the spread in
derived $M^*$ values from previous studies. Using an empirical correction to
model the intrinsic GSMF, we find evidence for an evolving characteristic
stellar mass with $\delta \log_{10}(M^*/M_\odot)/\delta z$ = $-0.16\pm0.05 \,
(-0.11\pm0.05)$, when using SExtractor (ProFound). We argue that with widely
quenched star formation rates in massive galaxies at low redshift ($z<0.5$),
additional growth via mergers is required in order to sustain such an evolution
to a higher characteristic mass.


  Let $\mathcal{A}$ be a finite subset of $\mathbb{N}$ including $0$ and
$f_\mathcal{A}(n)$ be the number of ways to write
$n=\sum_{i=0}^{\infty}\epsilon_i2^i$, where $\epsilon_i\in\mathcal{A}$. The
sequence $\left(f_\mathcal{A}(n)\right) \bmod 2$ is always periodic, and
$f_\mathcal{A}(n)$ is typically more often even than odd. We give four families
of sets $\left(\mathcal{A}_m\right)$ with $\left|\mathcal{A}_m\right|=4$ such
that the proportion of odd $f_{\mathcal{A}_m}(n)$'s goes to $1$ as
$m\to\infty$.


  Recommender systems are important and powerful tools for various personalized
services. Traditionally, these systems use data mining and machine learning
techniques to make recommendations based on correlations found in the data.
However, relying solely on correlation without considering the underlying
causal mechanism may lead to various practical issues such as fairness,
explainability, robustness, bias, echo chamber and controllability problems.
Therefore, researchers in related area have begun incorporating causality into
recommendation systems to address these issues. In this survey, we review the
existing literature on causal inference in recommender systems. We discuss the
fundamental concepts of both recommender systems and causal inference as well
as their relationship, and review the existing work on causal methods for
different problems in recommender systems. Finally, we discuss open problems
and future directions in the field of causal inference for recommendations.


  The aim of this work is to investigate the lunisolar perturbations affecting
the long-term dynamics of a Molniya satellite. Some numerical experiments on
the doubly-averaged model, including the expansion of the lunisolar disturbing
functions up to the third order, are carried out in order to detect the terms
dominating the long-term evolution. The analysis focuses on the following
significant indicators: the amplitude of the harmonic coefficients, the periods
of the arguments involved and, in particular, the ratio between the amplitudes
and the corresponding frequency. The results show that the second-order
lunisolar perturbation gives the dominant contribution to the long-term
dynamics. The second part of this work aims to study the resonant regions
associated to the dominant terms identified so far by using both the ideal
resonance model and an alternative approach. The results obtained show when the
standard method does not catch the main features of the dynamical structure of
the resonant regions. Finally, the maximum overlapping region is identified in
the proximity of the Molniya orbital environment.


  We show the existence of free dense subgroups, generated by 2 elements, in
the holomorphic shear and overshear group of complex-Euklidean space and extend
this result to the group of holomorphic automorphisms of Stein manifolds with
Density Property, provided there exists a generalized translation. The
conjugation operator associated to this generalized translation is hypercyclic
on the topological space of holomorphic automorphisms.


  Historically studies of behaviour on networks have focused on the behaviour
of individuals (node-based) or on the aggregate behaviour of the entire
network. We propose a new method to decompose a temporal network into
macroscale components and to analyse the behaviour of these components, or
collectives of nodes, across time. This method utilises all available
information in the temporal network (i.e. no temporal aggregation), combining
both topological and temporal structure using temporal motifs and inter-event
times. This allows us create an embedding of a temporal network in order to
describe behaviour over time and at different timescales. We illustrate this
method using an example of digital communication data collected from an online
social network.


  Self-diffusion and interdiffusion coefficients of binary ionic mixtures are
evaluated using the Effective Potential Theory (EPT), and the predictions are
compared with the results of molecular dynamics simulations. We find that EPT
agrees with molecular dynamics from weak coupling well into the strong coupling
regime, which is a similar range of coupling strengths as previously observed
in comparisons with the one-component plasma. Within this range, typical
relative errors of approximately 20% and worst-case relative errors of
approximately 40% are observed. We also examine the Darken model, which
approximates the interdiffusion coefficients based on the self-diffusion
coefficients.


  Many useful properties of dilute Bose gases at ultra-low temperature are
predicted precisely by the (mean-field) product-state Ansatz, in which all
particles are in the same quantum state. Yet, in situations where
particle-particle correlations become important, the product Ansatz fails. To
include correlations nonperturbatively, we consider a new set of states: the
particle-correlated state of $N=l\times n$ bosons is derived by symmetrizing
the $n$-fold product of an $l$-particle quantum state. The particle-correlated
states can be simulated efficiently for large $N$, because their parameter
spaces, which depend on $l$, do not grow with $n$. Here we formulate and
develop in great detail the pure-state case for $l=2$, where the many-body
state is constructed from a two-particle pure state. These paired wave
functions, which we call pair-correlated states (PCS), were introduced by A. J.
Leggett [Rev. Mod. Phys. ${\bf 73}$, 307 (2001)] as a
particle-number-conserving version of the Bogoliubov approximation. We present
an iterative algorithm that solves for the reduced (marginal) density matrices
(RDMs), i.e., the correlation functions, associated with PCS in time $O(N)$.
The RDMs can also be derived from the normalization factor of PCS, which is
derived analytically in the large-$N$ limit. To test the efficacy of PCS, we
analyze the ground state of the two-site Bose-Hubbard model by minimizing the
energy of the PCS~state, both in its exact form and in its large-$N$
approximate form, and comparing with the exact ground state. For $N=1\,000$,
the relative errors of the ground-state energy for both cases are within
$10^{-5}$ over the entire parameter region from a single condensate to a Mott
insulator. We present numerical results that suggest that PCS might be useful
for describing the dynamics in the strongly interacting regime.


  An analytical study is presented of the double resonant Raman scattering
process in graphene, responsible for the D and D$^{\prime}$ features in the
Raman spectra. This work yields analytical expressions for the D and
D$^{\prime}$ integrated Raman intensities that explicitly show the dependencies
on laser energy, defect concentration, and electronic lifetime. Good agreement
is obtained between the analytical results and experimental measurements on
samples with increasing defect concentrations and at various laser excitation
energies. The use of Raman spectroscopy to identify the nature of defects is
discussed. Comparison between the models for the edge-induced and the
disorder-induced D band intensity suggests that edges or grain boundaries can
be distinguished from disorder by the different dependence of their Raman
intensity on laser excitation energy. Similarly, the type of disorder can
potentially be identified not only by the intensity ratio
$I_{\mathrm{D}}/I_{\mathrm{D}^{\prime}}$, but also by its laser energy
dependence. Also discussed is a quantitative analysis of quantum interference
effects of the graphene wavefunctions, which determine the most important
phonon wavevectors and scattering processes responsible for the D and
D$^{\prime}$ bands.