  XMM-Newton observations of the bright Seyfert 1.9 galaxy MCG-5-23-16 have
revealed a broad FeKalpha emission line which is nearly symmetric in contrast
to the broad and red-shifted asymmetric FeKalpha line sometimes observed from
Seyfert 1 galaxies. The FeKalpha line has two distinct components - a narrow
unresolved component with equivalent width of 40 eV and a broad component with
full width at half maximum of 40000 km/s and equivalent width of 120 eV. An
absorption feature at 7.1 keV has also been observed. The energies of the
emission and absorption features are consistent with those arising from neutral
iron. The broad component is consistent with an FeKalpha emission line expected
from a relativistic accretion disk around a Schwarzschild or a Kerr black hole.
Alternatively, most of the flux in the broad component could also be modeled as
reflection emission which mimics emission line like feature due to the presence
of iron K-shell edge at 7.1eV, however, the reflection fraction is much higher
than that inferred from the BeppoSax observations. The disk inclination angle
of about 47 deg, inferred from the disk-line fits, and the absorption column of
about 10^{22} cm^{-2}, inferred from the low-energy spectral curvature due to
photoelectric absorption, suggest that our line of sight passes through the
outer edge of a putative torus and are consistent with those expected for a
Seyfert 1.9 galaxy falling within the unification scheme. The strength of the
narrow iron Kalpha emission and the optical depth of the iron K absorption edge
suggest their origin in the putative torus with N_H about 10^{24} cm^{-2} in
the inner regions and N_H about 10^{22} cm^{-2} in the outer edges.


  We present deep observations of the nearby T-type brown dwarf binary
$\epsilon$ Indi Bab in radio with the Australia Telescope Compact Array and in
X-rays with the Chandra X-ray Observatory. Despite long integration times, the
binary (composed of T1 and T6 dwarfs) was not detected in either wavelength
regime. We reached $3\sigma$ upper limits of $1.23 \times 10^{12}$ and $1.74
\times 10^{12}$ erg/s/Hz for the radio luminosity at 4.8 GHz and 8.64 GHz,
respectively; in the X-rays, the upper limit in the $0.1-10$ keV band was $3.16
\times 10^{23}$ erg/s. We discuss the above results in the framework of
magnetic activity in ultracool, low-mass dwarfs.


  In many machine learning applications, it is important for the model to
provide confidence scores that accurately capture its prediction uncertainty.
Although modern learning methods have achieved great success in predictive
accuracy, generating calibrated confidence scores remains a major challenge.
Mixup, a popular yet simple data augmentation technique based on taking convex
combinations of pairs of training examples, has been empirically found to
significantly improve confidence calibration across diverse applications.
However, when and how Mixup helps calibration is still a mystery. In this
paper, we theoretically prove that Mixup improves calibration in
\textit{high-dimensional} settings by investigating natural statistical models.
Interestingly, the calibration benefit of Mixup increases as the model capacity
increases. We support our theories with experiments on common architectures and
datasets. In addition, we study how Mixup improves calibration in
semi-supervised learning. While incorporating unlabeled data can sometimes make
the model less calibrated, adding Mixup training mitigates this issue and
provably improves calibration. Our analysis provides new insights and a
framework to understand Mixup and calibration.


  Given a collection of objects and an associated similarity measure, the
all-pairs similarity search problem asks us to find all pairs of objects with
similarity greater than a certain user-specified threshold. Locality-sensitive
hashing (LSH) based methods have become a very popular approach for this
problem. However, most such methods only use LSH for the first phase of
similarity search - i.e. efficient indexing for candidate generation. In this
paper, we present BayesLSH, a principled Bayesian algorithm for the subsequent
phase of similarity search - performing candidate pruning and similarity
estimation using LSH. A simpler variant, BayesLSH-Lite, which calculates
similarities exactly, is also presented. BayesLSH is able to quickly prune away
a large majority of the false positive candidate pairs, leading to significant
speedups over baseline approaches. For BayesLSH, we also provide probabilistic
guarantees on the quality of the output, both in terms of accuracy and recall.
Finally, the quality of BayesLSH's output can be easily tuned and does not
require any manual setting of the number of hashes to use for similarity
estimation, unlike standard approaches. For two state-of-the-art candidate
generation algorithms, AllPairs and LSH, BayesLSH enables significant speedups,
typically in the range 2x-20x for a wide variety of datasets.


  We study the semileptonic decays of the lowest-lying bc baryons to the
lowest-lying cc baryons (Xi_{bc}^{(\prime*)}--> Xi_{cc}^{(*)} and
Omega_{bc}^{(\prime*)}--> Omega_{cc}^{(*)}), in the limit m_b, m_c >>
Lambda_{QCD} and close to the zero recoil point. The separate heavy quark spin
symmetries make it possible to describe all these decays using a single form
factor. We recover results derived previously by White and Savage in a manner
which we think is more straightforward and parallels the method applied later
to study Bc semileptonic decays. We further discuss the resemblance between the
bc baryon decays and those of Bc mesons to eta_c and J/\psi mesons and comment
on the relation between the slopes of the single functions describing each set
of decays. Our results can straightforwardly be applied to the decays of bb
baryons to bc baryons.


  The engineering of light confinement is a topic with a long history in optics
and with significant implications for the control of light-matter interaction.
In inhomogeneous and disordered media, however, multiple scattering prevents
the application of conventional approaches for the design of light fields with
desired properties. This is because any local change to such a medium typically
affects these fields in a non-local and complicated fashion. Here, we present a
theoretical methodology for tailoring an inhomogeneous one-dimensional (1D)
Hermitian dielectric index distribution, such that the intensity profile of an
incoming light field can be controlled purely locally, i.e., with little or no
influence on the field profile outside of a designated region of interest.
Strongly increasing or decreasing the light's intensity at arbitrary positions
inside the medium thereby becomes possible without, in fact, changing the
external reflectance or transmittance of the medium. These local modifications
of the medium can thus be made undetectable to unidirectional far field
measurements. We apply our approach to locally control the confinement of light
inside 1D materials with inhomogeneous continuous refractive index profiles and
extend it to multilayer films as well as to chains of coupled micro-resonators.


  Jokes are intentionally written to be funny, but not all jokes are created
the same. Some jokes may be fit for a classroom of kindergarteners, but others
are best reserved for a more mature audience. While recent work has shown
impressive results on humor detection in text, here we instead investigate the
more nuanced task of detecting humor subtypes, especially of the less innocent
variety. To that end, we introduce a novel jokes dataset filtered from Reddit
and solve the subtype classification task using a finetuned Transformer dubbed
the Naughtyformer. Moreover, we show that our model is significantly better at
detecting offensiveness in jokes compared to state-of-the-art methods.


  We study the drag force and diffusion coefficient with respect to a moving
heavy quark in a D-instanton background, which corresponds to the Yang-Mills
theory in the deconfining, high-temperature phase. It is shown that the
presence of the D-instanton density tends to increase the drag force and
decrease the diffusion coefficient, reverse to the effects of the velocity and
the temperature. Moreover, the inclusion of the D-instanton density makes the
medium less viscous.


  A search for new light bosons decaying into muon pairs is presented using a
data sample corresponding to an integrated luminosity of 35.9 fb$^{-1}$ of
proton-proton collisions at a center-of-mass energy $\sqrt{s} =$ 13 TeV,
collected with the CMS detector at the CERN LHC. The search is model
independent, only requiring the pair production of a new light boson and its
subsequent decay to a pair of muons. No significant deviation from the
predicted background is observed. A model independent limit is set on the
product of the production cross section times branching fraction to dimuons
squared times acceptance as a function of new light boson mass. This limit
varies between 0.15 and 0.39 fb over a range of new light boson masses from
0.25 to 8.5 GeV. It is then interpreted in the context of the next-to-minimal
supersymmetric standard model and a dark supersymmetry model that allows for
nonnegligible light boson lifetimes. In both cases, there is significant
improvement over previously published limits.


  We relate possible cosmological variations in the mass ratio mu \equiv
m_p/m_e and the fine structure constant alpha to long-range
composition-dependent forces mediated by a scalar field. The differential
acceleration eta in Eotvos-type experiments is bounded below by 10^{-14},
except in cases where one or more scalar couplings vanish. We consider what
values for these couplings could arise from unified theories. By considering
the contribution of the scalar field to the cosmological energy density we use
bounds on eta to put upper bounds on the current rate of change of mu and
alpha.


  This paper reports on modern approaches in Information Extraction (IE) and
its two main sub-tasks of Named Entity Recognition (NER) and Relation
Extraction (RE). Basic concepts and the most recent approaches in this area are
reviewed, which mainly include Machine Learning (ML) based approaches and the
more recent trend to Deep Learning (DL) based methods.


  Coded distributed computing (CDC) is a new technique proposed with the
purpose of decreasing the intense data exchange required for parallelizing
distributed computing systems. Under the famous MapReduce paradigm, this coded
approach has been shown to decrease this communication overhead by a factor
that is linearly proportional to the overall computation load during the
mapping phase. Nevertheless, it is widely accepted that this overhead remains a
main bottleneck in distributed computing. To address this, we take a new
approach and we explore a new system model which, for the same aforementioned
overall computation load of the mapping phase, manages to provide astounding
reductions of the communication overhead and, perhaps counterintuitively, a
substantial increase of the computational parallelization. In particular, we
propose multi-access distributed computing (MADC) as a novel generalization of
the original CDC model, where now mappers and reducers are distinct computing
nodes that are connected through a multi-access network topology. Focusing on
the MADC setting with combinatorial topology, which implies $\Lambda$ mappers
and $K$ reducers such that there is a unique reducer connected to any $\alpha$
mappers, we propose a novel coded scheme and a novel information-theoretic
converse, which jointly identify the optimal inter-reducer communication load
to within a constant gap of $1.5$. Additionally, a modified coded scheme and
converse identify the optimal max-link communication load across all existing
links to within a gap of $4$. The unparalleled coding gains reported here
should not be simply credited to having access to more mapped data, but rather
to the powerful role of topology in effectively aligning mapping outputs. This
realization raises the open question of which multi-access network topology
guarantees the best possible performance in distributed computing.


  A cost effectively method to fabricate nanopores in silicon by only using the
conventional wet-etching technique is developed in this research. The main
concept of the proposed method is a two-step etching process, including a
premier double-sided wet etching and a succeeding track-etching. A special
fixture is designed to hold the pre-etched silicon wafer inside it such that
the track-etching can be effectively carried out. An electrochemical system is
employed to detect and record the ion diffusion current once the pre-etched
cavities are etched into a through nanopore. Experimental results indicate that
the proposed method can cost effectively fabricate nanopores in silicon.


  In this work, we present EvoK, a new way of sharing one's heart rate with
feedback from their close contacts to alleviate social isolation and
loneliness. EvoK consists of a pair of wearable prototype devices (i.e., sender
and receiver). The sender is designed as a headband enabling continuous sensing
of heart rate with aesthetic designs to maximize social acceptance. The
receiver is designed as a wristwatch enabling unobtrusive receiving of the
loved one's continuous heart rate with multi-modal notification systems.


  The `Chern-Simons Quantum Mechanics' of a particle on CP(n|m) is shown to
yield the fuzzy descriptions of these superspaces, for which we construct the
non-(anti)commuting position operators. For a particle on the supersphere
CP(1|1) = SU(2|1)/U(1|1), the particle's wave-function at fuzziness level 2s is
shown to be a degenerate irrep of SU(2|1) describing a supermultiplet of SU(2)
spins (s-1\2, s).


  A new method based on continuous wavelet transform with the complex Morlet
wavelet to analyze Saturn main rings is presented. It allows to investigate in
detail the resonance zones and reveal the coexistence of waves with stable
periods and the wave trains with a variable instant period. This method is
based on the replacing the integration of the fast--oscillation function by the
solution of the partial differential equations. It is shown that such an
approach is an effective tool for the study the radial structure of Saturn's A,
B, and C rings. All the analyzed images were obtained from the Cassini
spacecraft during 2004--2005 years.


  Recently, continuous cache models were proposed as extensions to recurrent
neural network language models, to adapt their predictions to local changes in
the data distribution. These models only capture the local context, of up to a
few thousands tokens. In this paper, we propose an extension of continuous
cache models, which can scale to larger contexts. In particular, we use a large
scale non-parametric memory component that stores all the hidden activations
seen in the past. We leverage recent advances in approximate nearest neighbor
search and quantization algorithms to store millions of representations while
searching them efficiently. We conduct extensive experiments showing that our
approach significantly improves the perplexity of pre-trained language models
on new distributions, and can scale efficiently to much larger contexts than
previously proposed local cache models.


  Game theoretic approaches have gained traction as robust methodologies for
designing distributed local algorithms that induce a desired overall system
configuration in multi-agent settings. However, much of the emphasis in these
approaches is on providing asymptotic guarantees on the performance of a
network of agents, and there is a gap in the study of efficiency guarantees
along transients of these distributed algorithms. Therefore, in this paper, we
study the transient efficiency guarantees of a natural game-theoretic algorithm
in the class of set covering games, which have been used to model a variety of
applications. Our main results characterize the optimal utility design that
maximizes the guaranteed efficiency along the transient of the natural
dynamics. Furthermore, we characterize the Pareto-optimal frontier with regards
to guaranteed efficiency in the transient and the asymptote under a class of
game-theoretic designs. Surprisingly, we show that there exists an extreme
trade-off between the long-term and short-term guarantees in that an
asymptotically optimal game-theoretic design can perform arbitrarily bad in the
transient.


  The trace metals and mineralogical composition of harmattan dust carried out
on the samples collected at Jos ((9 55'N, 8 55'E)) and Potiskum ((11 43'N, 11
02'E) as revealed by PIXE and AAS machine using clean Petri Dishes and Plastic
bowls of 10 cm in diameter aimed on the characteristics of the mineralogical
and elemental composition of the harmattan dust carried out in Nigeria.
Thirteen trace elements, Na, K, Ca, Mg, Fe, Cd, Zn, Mn, Cu, Si, Al, Ti, and Zr
were determined and their concentrations were evaluated in different
proportion. Minerals such as Quartz [SiO2], Corundum [Al2O3], Hematite [Fe2O3],
Lime [CaO], Periclase [MgO], Rutile [TiO2], Zincite [MnO], Bunsenite [NiO],
Cuprite [Cu2O], Zincite [ZnO], Baddeleyite [ZrO2], Litharge [PbO], Monazite
[P2O5], Montrodydite [HgO] and Petzite [Au2O3] were also determined in
different concentrations. The particle weight of the sample for the residential
and commercial areas were calculated to be Jos (18.95g/m2, 19.25g/m2), Potiskum
(24.24 g/m2, 2515g/m2) respectively. The results shows that the harmattan dust
that blows across the two stations in Nigeria comprise of high elements and
more minerals.


  In this paper, we introduce a modification of the Szasz-Mirakjan-Kantorovich
operators as well as Stancu operators [9] (or a Dunkl generalization of
modified Szasz-Mirakjan-Kantrovich operators [5]) which preserve the linear
functions. These types of operators modification enables better error
estimation than the classical Dunkl Szasz-MirakjanKantrovich as well as Stancu
operators. We obtain some approximation results via well known Korovkin's type
theorem, weighted Korovkin's type theorem convergence properties by using the
modulus of continuity and the rate of convergence of the operators for
functions belonging to the Lipschitz class


  We construct the pair of logarithmic operators associated with the recoil of
a $D$-brane. This construction establishes a connection between a translation
in time and a world-sheet rescaling. The problem of measuring the centre of
mass coordinate of the $D$-brane is considered and the relation between the
string uncertainty principle and the logarithmic operators is discussed.


  We examine the prospects of detecting demagnified images of gravitational
lenses in observations of strongly lensed mm-wave molecular emission lines with
ALMA. We model the lensing galaxies as a superposition of a dark matter
component, a stellar component, and a central supermassive black hole and
assess the detectability of the central images for a range of relevant
parameters (e.g., stellar core, black hole mass, and source size). We find that
over a large range of plausible parameters, future deep observations of lensed
molecular lines with ALMA should enable detection of the central images at
$\gtrsim 3\sigma$ significance. We use a Fisher analysis to examine the
constraints that could be placed on these parameters in various scenarios and
find that for large stellar cores, both the core size and the mass of the
central SMBHs can be accurately measured. We also study the prospects for
detecting binary SMBHs with such observations and find that only under rare
conditions and with very long integrations ($\sim$40-hr) the masses of both
SMBHs may be measured using the distortions of central images.


  Let s_q(n) denote the base q sum of digits function, which for n<x, is
centered around (q-1)/2 log_q x. In Drmota, Mauduit and Rivat's 2009 paper,
they look at sum of digits of prime numbers, and provide asymptotics for the
size of the set {p<x, p prime : s_q(p)=alpha(q-1)log_q x} where alpha lies in a
tight range around 1/2. In this paper, we examine the tails of this
distribution, and provide the lower bound |{p < x, p prime :
s_q(p)>alpha(q-1)log_q x}| >>x^{2(1-alpha)}e^{-c(log x)^{1/2+epsilon}} for
1/2<alpha<0.7375. To attain this lower bound, we note that the multinomial
distribution is sharply peaked, and apply results regarding primes in short
intervals. This proves that there are infinitely many primes with more than
twice as many ones than zeros in their binary expansion.


  With the next generation of interferometric telescopes, such as the Square
Kilometre Array (SKA), the need for highly computationally efficient
reconstruction techniques is particularly acute. The challenge in designing
learned, data-driven reconstruction techniques for radio interferometry is that
they need to be agnostic to the varying visibility coverages of the telescope,
since these are different for each observation. Because of this, learned
post-processing or learned unrolled iterative reconstruction methods must
typically be retrained for each specific observation, amounting to a large
computational overhead. In this work we develop learned post-processing and
unrolled iterative methods for varying visibility coverages, proposing training
strategies to make these methods agnostic to variations in visibility coverage
with minimal to no fine-tuning. Learned post-processing techniques are heavily
dependent on the prior information encoded in training data and generalise
poorly to other visibility coverages. In contrast, unrolled iterative methods,
which include the telescope measurement operator inside the network, achieve
state-of-the-art reconstruction quality and computation time, generalising well
to other coverages and require little to no fine-tuning. Furthermore, they
generalise well to realistic radio observations and are able to reconstruct the
high dynamic range of these images.


  In order to become aware of inconsistencies, one must first construe of the
world in a way that reflects its consistencies. This paper begins with a
tentative model for how a set of discrete memories transforms into an
interconnected worldview wherein relationships between memories are forged by
way of abstractions. Inconsistencies prompt the invention of new abstractions.
In regions of the conceptual network where inconsistencies abound, a cognitive
analog of simulated annealing is in order; there is a willingness to question
previous assumptions--to 'loosen' conceptual relationships--so as to let new
concepts thoroughly percolate through the worldview and exert the needed
revolutionary effect. In so doing there is a risk of assimilating dangerous
concepts. Repression arrests the process by which dangerous thoughts infiltrate
the conceptual network, and deception blocks thoughts that have already been
assimilated. These forms of self-initiated worldview inconsistency may evoke
feelings of fragmentation at the level of the individual or the society.


  We study the problem of covariant separation between first and second class
constraints for the $D=10$ Brink-Schwarz superparticle. Opposite to the
supersymmetric light-cone frame separation, we show here that there is a
Lorentz covariant way to identify the second class constraints such that,
however, supersymmetry is broken. Consequences for the $D=10$ superstring are
briefly discussed.


  Particular strain geometry in graphene could leads to a uniform
pseudo-magnetic field of order 10T and might open up interesting applications
in graphene nano-electronics. Through quantum transport calculations of
realistic strained graphene flakes of sizes of 100nm, we examine possible means
of exploiting this effect for practical electronics and valleytronics devices.
First, we found that elastic backscattering at rough edges leads to the
formation of well defined transport gaps of order 100meV under moderate maximum
strain of 10%. Second, the application of a real magnetic field induced a
separation, in space and energy, of the states arising from different valleys,
leading to a way of inducing bulk valley polarization which is insensitive to
short range scattering.


  We compare the results of constructing binary black hole initial data with
three different decompositions of the constraint equations of general
relativity. For each decomposition we compute the initial data using a
superposition of two Kerr-Schild black holes to fix the freely specifiable
data. We find that these initial-data sets differ significantly, with the ADM
energy varying by as much as 5% of the total mass. We find that all
initial-data sets currently used for evolutions might contain unphysical
gravitational radiation of the order of several percent of the total mass. This
is comparable to the amount of gravitational-wave energy observed during the
evolved collision. More astrophysically realistic initial data will require
more careful choices of the freely specifiable data and boundary conditions for
both the metric and extrinsic curvature. However, we find that the choice of
extrinsic curvature affects the resulting data sets more strongly than the
choice of conformal metric.


  A search for quark compositeness in the form of quark contact interactions,
based on hadronic jet pairs (dijets) produced in proton-proton collisions at
sqrt(s)=7 TeV, is described. The data sample of the study corresponds to an
integrated luminosity of 2.9 inverse picobarns collected with the CMS detector
at the LHC. The dijet centrality ratio, which quantifies the angular
distribution of the dijets, is measured as a function of the invariant mass of
the dijet system and is found to agree with the predictions of the Standard
Model. A statistical analysis of the data provides a lower limit on the energy
scale of quark contact interactions. The sensitivity of the analysis is such
that the expected limit is 2.9 TeV; because the observed value of the
centrality ratio at high invariant mass is below the expectation, the observed
limit is 4.0 TeV at the 95% confidence level.


  Attention mechanisms are widely used in salient object detection models based
on deep learning, which can effectively promote the extraction and utilization
of useful information by neural networks. However, most of the existing
attention modules used in salient object detection are input with the processed
feature map itself, which easily leads to the problem of `blind
overconfidence'. In this paper, instead of applying the widely used
self-attention module, we present an output-guided attention module built with
multi-scale outputs to overcome the problem of `blind overconfidence'. We also
construct a new loss function, the intractable area F-measure loss function,
which is based on the F-measure of the hard-to-handle area to improve the
detection effect of the model in the edge areas and confusing areas of an
image. Extensive experiments and abundant ablation studies are conducted to
evaluate the effect of our methods and to explore the most suitable structure
for the model. Tests on several data sets show that our model performs very
well, even though it is very lightweight.


  The end-to-end ASR model is often desired in the streaming multilingual
scenario since it is easier to deploy and can benefit from pre-trained speech
models such as powerful foundation models. Meanwhile, the heterogeneous nature
and imbalanced data abundance of different languages may cause performance
degradation, leading to asynchronous peak performance for different languages
during training, especially on tail ones. Sometimes even the data itself may
become unavailable as a result of the enhanced privacy protection. Existing
work tend to significantly increase the model size or learn language-specific
decoders to accommodate each language separately. In this study, we explore
simple yet effective Language-Dependent Adapter (LDA) finetuning under a
cascaded Conformer transducer framework enhanced by teacher pseudo-labeling for
tail languages in the streaming multilingual ASR. The adapter only accounts for
0.4% of the full model per language. It is plugged into the frozen foundation
model and is the only trainable module during the finetuning process with noisy
student training. The final model merges the adapter parameters from different
checkpoints for different languages. The model performance is validated on a
challenging multilingual dictation dataset, which includes 39 tail languages
across Latin, Greek, Arabic, etc. Our proposed method brings 12.2% word error
rate reduction on average and up to 37.5% on a single locale. Furthermore, we
show that our parameter-efficient LDA can match the quality of the full model
finetuning, thus greatly alleviating the asynchronous peak performance issue.


  We investigate the constraints on basic cosmological parameters set by the
first compact-configuration observations of the Very Small Array (VSA), and
other cosmological data sets, in the standard inflationary LambdaCDM model.
Using a weak prior 40 < H_0 < 90 km/s/Mpc and 0 < tau < 0.5 we find that the
VSA and COBE_DMR data alone produce the constraints Omega_tot =
1.03^{+0.12}_{-0.12}, Omega_bh^2 = 0.029^{+0.009}_{-0.009}, Omega_cdm h^2 =
0.13^{+0.08}_{-0.05} and n_s = 1.04^{+0.11}_{-0.08} at the 68 per cent
confidence level. Adding in the type Ia supernovae constraints, we additionally
find Omega_m = 0.32^{+0.09}_{-0.06} and Omega_Lambda = 0.71^{+0.07}_{-0.07}.
These constraints are consistent with those found by the BOOMERanG, DASI and
MAXIMA experiments. We also find that, by combining all the recent CMB
experiments and assuming the HST key project limits for H_0 (for which the
X-ray plus Sunyaev--Zel'dovich route gives a similar result), we obtain the
tight constraints Omega_m=0.28^{+0.14}_{-0.07} and Omega_Lambda=
0.72^{+0.07}_{-0.13}, which are consistent with, but independent of, those
obtained using the supernovae data.


  CAT(0) metric spaces and hyperbolic spaces play an important role in
combinatorial and geometric group theory. In this paper, we present efficient
algorithms for distance problems in CAT(0) planar complexes. First of all, we
present an algorithm for answering single-point distance queries in a CAT(0)
planar complex. Namely, we show that for a CAT(0) planar complex K with n
vertices, one can construct in O(n^2 log n) time a data structure D of size
O(n^2) so that, given a point x in K, the shortest path gamma(x,y) between x
and the query point y can be computed in linear time. Our second algorithm
computes the convex hull of a finite set of points in a CAT(0) planar complex.
This algorithm is based on Toussaint's algorithm for computing the convex hull
of a finite set of points in a simple polygon and it constructs the convex hull
of a set of k points in O(n^2 log n + nk log k) time, using a data structure of
size O(n^2 + k).


  All Rota-Baxter operators of weight zero on split octonion algebra over
a~field of characteristic not 2 are classified up to conjugation by
automorphisms and antiautomorphisms. Thus, the classification of Rota-Baxter
operators on composition algebras is finished. There are two descriptions:
a~common description over arbitratry field of characteristic not 2 and more
accurate description over a~quadratically closed field of characteristic not 2.


  Brain computer interfaces (BCI) using EEG, fNIRS and body motion (MoCap) data
are getting more attention due to the fact that fNIRS and MoCap are not prone
to movement artifacts similar to other brain imaging techniques such as EEG.
Advancements in deep learning (neural networks) would allow the use of raw data
for efficient feature extraction without any pre-/post-processing. In this
work, we are performing human activity recognition (BCI classification task)
for 5 activity classes using an end-to-end (deep) neural network (NN) (from
input all the way to the output) on raw fNIRS, EEG and MoCap data. Our core
contribution is focused on applying an end-to-end NN model without any
pre-/post-processing on the data. The entire NN model is being trained using
backpropagation algorithm. Our end-to-end model is composed of a four-layered
MLP: input layer, two hidden layers (using fully connected (dense) layer, batch
normalization and leaky-RELU as non-linearity and activation function), and
output layer using softmax. We have reached minimum 90\% accuracy on the test
dataset for the classification task on 10 subjects data and 5 classes of
activity.


  Our main task in this note is to prove the existence and to classify the
exact growth at infinity of radial positive $C^6$-solutions of $(-\Delta )^3 u
= u^p$ in $\mathbf{R}^n$, where $n\geqslant 15$ and $p$ is bounded from below
by the sixth-order Joseph-Lundgren exponent. Following the main work of
Winkler, we introduce the sub- and super-solution method and comparision
principle to conclude the asymptotic behavior of solutions.


  In this paper we study both experimentally and numerically the intermittent
behavior taking place near the boundary of the synchronous time scales of
chaotic oscillators being in the regime of time scale synchronization. We have
shown that the observed type of the intermittent behavior should be classified
as the ring intermittency.


  We introduce a trisection axiom for mathematical origami and descibe the
totally real origami numbers. We also discuss the solution of Alhazen's problem
and its relation to trisections.


  We investigate quantum computational complexity of calculating partition
functions of Ising models. We construct a quantum algorithm for an additive
approximation of Ising partition functions on square lattices. To this end, we
utilize the overlap mapping developed by Van den Nest, D\"ur, and Briegel
[Phys. Rev. Lett. 98, 117207 (2007)] and its interpretation through
measurement-based quantum computation (MBQC). We specify an algorithmic domain,
on which the proposed algorithm works, and an approximation scale, which
determines the accuracy of the approximation. We show that the proposed
algorithm does a nontrivial task, which would be intractable on any classical
computer, by showing the problem solvable by the proposed quantum algorithm are
BQP-complete. In the construction of the BQP-complete problem coupling
strengths and magnetic fields take complex values. However, the Ising models
that are of central interest in statistical physics and computer science
consist of real coupling strengths and magnetic fields. Thus we extend the
algorithmic domain of the proposed algorithm to such a real physical parameter
region and calculate the approximation scale explicitly. We found that the
overlap mapping and its MBQC interpretation improves the approximation scale
exponentially compared to a straightforward constant depth quantum algorithm.
On the other hand, the proposed quantum algorithm also provides us a partial
evidence that there exist no efficient classical algorithm for a multiplicative
approximation of the Ising partition functions even on the square lattice. This
result supports that the proposed quantum algorithm does a nontrivial task also
in the physical parameter region.


  The results of density functional theory (DFT) calculations and measurements
of X-ray photoelectron (XPS) and X-ray emission (XES) spectra of
Co-nanoparticles dispersed on graphene/Cu composites are presented. It is found
that for 0.02nm and 0.06nm Co coverage the Co atoms form islands which are
strongly oxidized under exposure at the air. For Co (2nm) coverage the upper
Co-layers is oxidized whereas the lower layers contacting with graphene is in
metallic state. Therefore Co (2 nm) coverage induces the formation of
protective oxide layer providing the ferromagnetic properties of Co
nanoparticles which can be used as spin filters in spintronics devices.


  We provide progenitor models for electron capture supernovae (ECSNe) with
detailed evolutionary calculation. We include minor electron capture nuclei
using a large nuclear reaction network with updated reaction rates. For
electron captures, the Coulomb correction on the rates is treated and
contribution of neutron-rich nuclei is taken into account in the nuclear
statistical equilibrium (NSE) composition. We calculate the evolution of the
most massive super asymptotic giant branch stars and show that these stars
undergo off-center carbon burnings and form ONe cores at the center. These
cores get heavier up to the critical mass of 1.367 Msun and keep contracting
even after the initiation of O+Ne deflagration. Though inclusion of minor
electron capture nuclei causes convective URCA process at the contraction
phase, such process will have minor effect on the evolution. On the other hand,
electron captures by neutron-rich nuclei in the NSE region have more
significant effect. Also, we discuss the uniqueness of the critical core mass
for ECSNe and the effect of mass loss on the plausibility of our models for
ECSN progenitors.


  When developers use different keywords such as TODO and FIXME in source code
comments to describe self-admitted technical debt (SATD), we refer it as
Keyword-Labeled SATD (KL-SATD). We study KL-SATD from 33 software repositories
with 13,588 KL-SATD comments. We find that the median percentage of KL-SATD
comments among all comments is only 1,52%. We find that KL-SATD comment
contents include words expressing code changes and uncertainty, such as remove,
fix, maybe and probably. This makes them different compared to other comments.
KL-SATD comment contents are similar to manually labeled SATD comments of prior
work. Our machine learning classifier using logistic Lasso regression has good
performance in detecting KL-SATD comments (AUC-ROC 0.88). Finally, we
demonstrate that using machine learning we can identify comments that are
currently missing but which should have a SATD keyword in them. Automating SATD
identification of comments that lack SATD keywords can save time and effort by
replacing manual identification of comments. Using KL-SATD offers a potential
to bootstrap a complete SATD detector.


  In this paper the main consequences of the vector theory of excitation of
resonators by particle beams are presented. Some features of excitation of
broadband radiation in longitudinal modes of the enclosed and open resonators
are discussed.


  Recent breakthroughs have opened the possibility to intermediate-scale
quantum computing with tens to hundreds of qubits, and shown the potential for
solving classical challenging problems, such as in chemistry and condensed
matter physics. However, the extremely high accuracy needed to surpass
classical computers poses a critical demand to the circuit depth, which is
severely limited by the non-negligible gate infidelity, currently around
0.1-1%. Here, by incorporating a virtual Heisenberg circuit, which acts
effectively on the measurement observables, to a real shallow Schr\"odinger
circuit, which is implemented realistically on the quantum hardware, we propose
a paradigm of Schr\"odinger-Heisenberg variational quantum algorithms to
resolve this problem. We choose a Clifford virtual circuit, whose effect on the
Hamiltonian can be efficiently and classically implemented according to the
Gottesman-Knill theorem. Yet, it greatly enlarges the state expressivity,
realizing much larger unitary t-designs. Our method enables accurate quantum
simulation and computation that otherwise is only achievable with much deeper
and more accurate circuits conventionally. This has been verified in our
numerical experiments for a better approximation of random states and a
higher-fidelity solution to the ground state energy of the XXZ model. Together
with effective quantum error mitigation, our work paves the way for realizing
accurate quantum computing algorithms with near-term quantum devices.


  We study the masses and radii of 65 exoplanets smaller than 4 Earth radii
with orbital periods shorter than 100 days. We calculate the weighted mean
densities of planets in bins of 0.5 Earth radii and identify a density maximum
of 7.6 g/cc at 1.4 Earth radii. Planets with radii up to R = 1.5 Earth radii
increase in density with increasing radius. Above 1.5 Earth radii, planet
density rapidly decreases with increasing radius, indicating that these planets
have a large fraction of volatiles by volume overlying a rocky core. Including
the solar system terrestrial planets with the exoplanets below 1.5 Earth radii,
we find \rho = 2.43 + 3.39 (R/R_E) g cm^-3 for R < 1.5 Earth radii, which is
consistent with rocky compositions. For exoplanets between 1.5 and 4 Earth
radii, we find M/M_E = 2.69 (R/R_E)^0.93. The RMS of planet masses to the fit
between 1.5 and 4 Earth radii is 4.3 M_E with reduced \chi^2 = 6.2. The large
scatter indicates a diversity in planet composition at a given radius. The
compositional diversity can be due to planets of a given volume (as determined
by their large H/He envelopes) containing rocky cores of different masses or
compositions.


  In a wireless system with Intelligent Reflective Surfaces (IRS) containing
many passive elements, we consider the problem of channel estimation. All the
links from the transmitter to the receiver via each IRS elements (or groups)
are estimated. As the estimation performance are dependent on the setting of
the IRS, we design an optimal channel estimation scheme where the IRS elements
follow an optimal series of activation patterns. The optimal design is guided
by results for the minimum variance unbiased estimation. The IRS setting during
the channel estimation period mimics a series of discrete Fourier transforms.
We show theoretically and with simulations that the estimation variance is one
order smaller compared to existing on/off methods proposed in the literature.


  Accretion-powered X-ray pulsars are among the most luminous X-ray sources in
the Galaxy. However, despite decades of theoretical and observational work
since their discovery, no satisfactory model for the formation of the observed
X-ray spectra has emerged. In particular, the previously available theories are
unable to reproduce the power-law variation observed at high energies in many
sources. In this paper, we present the first self-consistent calculation of the
spectrum emerging from a pulsar accretion column that includes an explicit
treatment of the energization occurring in the shock. Using a rigorous
eigenfunction expansion method based on the exact dynamical solution for the
velocity profile in the column, we obtain a closed-form expression for the
Green's function describing the upscattering of radiation injected into the
column from a monochromatic source located at the top of the thermal mound,
near the base of the flow. The Green's function is convolved with a Planck
distribution to calculate the radiation spectrum resulting from the
reprocessing of blackbody photons emitted by the thermal mound. We demonstrate
that the energization of the photons in the shock naturally produces an X-ray
spectrum with a power-law shape at high energies and a blackbody shape at low
energies, in agreement with many observations of accreting X-ray pulsars.


  In the stable homotopy groups
  $\pi_{q(p^n+p^m+1)-3}(S)$ of the sphere spectrum $S$ localized at the prime
$p$ greater than three, J. Lin constructed an essential family $\xi_{m,n}$ for
$n \geq m + 2 >5$. In this paper, the authors show that the composite
$\xi_{m,n}\beta_{s}\in \pi_{q(p^n+p^m+sp+s)-5}(S)$ for $2 \leq s < p$ is
non-trivial, where $q=2(p-1)$ and $\beta_s \in \pi_{q(sp+s-1)-2}(S)$ is the
known $\beta$-family. We show our result by explicit combinatorial analysis of
the (modified) May spectral sequence.


  This paper proposes a high-throughput short reference differential chaos
shift keying cooperative communication system with the aid of code index
modulation, referred to as CIM-SR-DCSK-CC system. In the proposed
CIM-SR-DCSK-CC system, the source transmits information bits to both the relay
and destination in the first time slot, while the relay not only forwards the
source information bits but also sends new information bits to the destination
in the second time slot. To be specific, the relay employs an $N$-order Walsh
code to carry additional ${{\log }_{2}}N$ information bits, which are
superimposed onto the SR-DCSK signal carrying the decoded source information
bits. Subsequently, the superimposed signal carrying both the source and relay
information bits is transmitted to the destination. Moreover, the theoretical
bit error rate (BER) expressions of the proposed CIM-SR-DCSK-CC system are
derived over additive white Gaussian noise (AWGN) and multipath Rayleigh fading
channels. Compared with the conventional DCSK-CC system and SR-DCSK-CC system,
the proposed CIM-SR-DCSK-CC system can significantly improve the throughput
without deteriorating any BER performance. As a consequence, the proposed
system is very promising for the applications of the 6G-enabled low-power and
high-rate communication.


  A spanner of a graph is a subgraph that preserves lengths of shortest paths
up to a multiplicative distortion. For every $k$, a spanner with size
$O(n^{1+1/k})$ and stretch $(2k+1)$ can be constructed by a simple centralized
greedy algorithm, and this is tight assuming Erd\H{o}s girth conjecture.
  In this paper we study the problem of constructing spanners in a local
manner, specifically in the Local Computation Model proposed by Rubinfeld et
al. (ICS 2011).
  We provide a randomized Local Computation Agorithm (LCA) for constructing
$(2r-1)$-spanners with $\tilde{O}(n^{1+1/r})$ edges and probe complexity of
$\tilde{O}(n^{1-1/r})$ for $r \in \{2,3\}$, where $n$ denotes the number of
vertices in the input graph. Up to polylogarithmic factors, in both cases, the
stretch factor is optimal (for the respective number of edges). In addition,
our probe complexity for $r=2$, i.e., for constructing a $3$-spanner, is
optimal up to polylogarithmic factors. Our result improves over the probe
complexity of Parter et al. (ITCS 2019) that is $\tilde{O}(n^{1-1/2r})$ for $r
\in \{2,3\}$. Both our algorithms and the algorithms of Parter et al. use a
combination of neighbor-probes and pair-probes in the above-mentioned LCAs.
  For general $k\geq 1$, we provide an LCA for constructing $O(k^2)$-spanners
with $\tilde{O}(n^{1+1/k})$ edges using $O(n^{2/3}\Delta^2)$ neighbor-probes,
improving over the $\tilde{O}(n^{2/3}\Delta^4)$ algorithm of Parter et al.
  By developing a new randomized LCA for graph decomposition, we further
improve the probe complexity of the latter task to be
$O(n^{2/3-(1.5-\alpha)/k}\Delta^2)$, for any constant $\alpha>0$. This latter
LCA may be of independent interest.


  This article aims to provide the information retrieval community with some
reflections on recent advances in retrieval learning by analyzing the
reproducibility of image-text retrieval models. Due to the increase of
multimodal data over the last decade, image-text retrieval has steadily become
a major research direction in the field of information retrieval. Numerous
researchers train and evaluate image-text retrieval algorithms using benchmark
datasets such as MS-COCO and Flickr30k. Research in the past has mostly focused
on performance, with multiple state-of-the-art methodologies being suggested in
a variety of ways. According to their assertions, these techniques provide
improved modality interactions and hence more precise multimodal
representations. In contrast to previous works, we focus on the reproducibility
of the approaches and the examination of the elements that lead to improved
performance by pretrained and nonpretrained models in retrieving images and
text. To be more specific, we first examine the related reproducibility
concerns and explain why our focus is on image-text retrieval tasks. Second, we
systematically summarize the current paradigm of image-text retrieval models
and the stated contributions of those approaches. Third, we analyze various
aspects of the reproduction of pretrained and nonpretrained retrieval models.
To complete this, we conducted ablation experiments and obtained some
influencing factors that affect retrieval recall more than the improvement
claimed in the original paper. Finally, we present some reflections and
challenges that the retrieval community should consider in the future. Our
source code is publicly available at
https://github.com/WangFei-2019/Image-text-Retrieval.


  Particle creation at the expense of gravitational field might be sufficient
to explain the cosmic evolution history, without the need of dark energy at
all. This phenomena has been investigated in a recent work by Lima et-al,
assuming particle creation at the cost of gravitational energy in the late
Universe. However, the model does not satisfy the WMAP constraint on
matter-radiation equality. Here, we have suggested a model, in the same
framework, which fits perfectly with SNIa data at low redshift as well as early
Integrated Sachs-Wolfe effect on matter-radiation equality determined by WMAP
at high redshift. Such a model, requires the presence of nearly 26% primeval
matter in the form of baryons and CDM.


  The growth of N,N'-dimethylperylene-3,4,9,10-bis(dicarboximide) (DiMe-PTCDI)
on KBr(001) and NaCl(001) surfaces has been studied. Experimental results have
been achieved using frequency modulation atomic force microscopy at room
temperature under ultra-high vacuum conditions. On both substrates, DiMe-PTCDI
forms molecular wires with a width of 10 nm, typically, and a length of up to
600 nm at low coverages. All wires grow along the [110] direction (or
[1$\bar{1}$0] direction, respectively) of the alkali halide (001) substrates.
There is no wetting layer of molecules: Atomic resolution of the substrates can
be achieved between the wires. The wires are mobile on KBr surface but
substantially more stable on NaCl. A p(2 x 2) superstructure in brickwall
arrangement on the ionic crystal surfaces is proposed based on electrostatic
considerations. Calculations and Monte-Carlo simulations using empirical
potentials reveal possible growth mechanisms for molecules within the first
layer for both substrates, also showing a significantly higher binding energy
for NaCl(001). For KBr, the p(2 x 2) superstructure is confirmed by the
simulations, for NaCl, a less dense, incommensurate superstructure is
predicted.


  Using dynamical computer simulation we have investigated vortex matters in
glass states. A genuine continuous depinning transition is observed at zero
temperature, which also governs the low-temperature creep motion. With the
notion of scaling, we evaluate in high accuracy critical exponents and scaling
functions; we observe a non-Arrhenius creep motion for weak collective pinning
where Bragg glass (BrG) is stabilized at equilibrium, while for strong pinning
the well-known Arrhenius law is recovered. In both cases, a sharp crossover
takes place between depinning and creep at low temperatures. The possible
relation between the present results and a recent experimental observation of a
second-order like phase boundary inside the BrG phase is discussed.


  Amorphous materials have a rich relaxation spectrum, which is usually
described in terms of a hierarchy of relaxation mechanisms. In this work, we
investigate the local dynamic modulus spectra in a model glass just above the
glass transition temperature by performing a mechanical spectroscopy analysis
with molecular dynamics simulations. We find that the spectra, at the local as
well as on the global scale, can be well described by the Cole-Davidson formula
in the frequency range explored with simulations. Surprisingly, the
Cole-Davidson stretching exponent does not change with the size of the local
region that is probed. The local relaxation time displays a broad distribution,
as expected based on dynamic heterogeneity concepts, but the stretching is
obtained independently of this distribution. We find that the size dependence
of the local relaxation time and moduli can be well explained by the elastic
shoving model.


  Budker INP hosts two e+e- colliders, VEPP-4M operating in the beam energy
range of 1-5.5 GeV and the low-energy machine VEPP-2000, collecting data at
160-1000 MeV per beam. The latter uses a novel concept of round colliding
beams. The paper presents an overview of observed beam-beam effects and
obtained luminosities.


  The QCD quark cyclobutadiene (ring-like), a new color structure of tetraquark
system, is proposed and studied in the flux tube model with multi-body
confinement potential. The QCD quark cyclobutadiene and other flux tube
structures of tetraquark states have similar energies and they can be regarded
as QCD isomeric compounds. The light tetraquark spectra ($u, d, s$ only) with
ring-like and diquark-antidiquark structures are calculated in the flux tube
model. The results show that many experimental states have the masses close to
the calculated values if they are taken as tetraquark states. The isotensor
states with $J^{PC}=1^{--}$ and $J^{PC}=2^{++}$ are studied and predicted that
the masses are around 1500 MeV. The multi-body interaction plays a important
role to reduce the energy of the multiquark state.


  We propose a definition of when a triangulated category should be considered
a complete intersection. We show (using work of Avramov and Gulliksen) that for
the derived category of a complete local Noetherian commutative ring R, the
condition on the derived category D(R) holds precisely when R is a complete
intersection in the classical sense.


  As an alternative perspective on the injectivity of a pure-injective module,
a pure-injective module M is said to be pi-indigent if its subinjectivity
domain is smallest possible, namely, consisting of exactly the absolutely pure
modules. A module M is called subinjective relative to a module N if for every
extension K of N, every homomorphism N \to M can be extended to a homomorphism
K \to M. The subinjectivity domain of the module M is defined to be the class
of modules N such that M is N-subinjective. Basic properties of the
subinjectivity domains of pure-injective modules and of pi-indigent modules are
studied. The structure of a ring over which every pure-injective (resp. simple,
uniform, indecomposable) module is injective or subinjective relative only to
the smallest possible family of modules is investigated. This work is a natural
continuation to recent papers that have embraced the systematic study of the
subinjective and subprojective domains of modules.


  If a theory has more than one classically stable vacuum, quantum tunneling
and thermal jumps make the transition between the vacua possible. The
transition happens through a first order phase transition started by nucleation
of a bubble of the new vacuum. The outward pressure of the truer vacuum makes
the bubble expand and consequently eat away more of the old phase. In the
presence of gravity this phenomenon gets more complicated and meanwhile more
interesting. It can potentially have important cosmological consequences. Some
aspects of this decay are studied in this thesis. Solutions with different
symmetry than the generically used O(4) symmetry are studied and their actions
calculated. Vacuum decay in a spatial vector field is studied and novel
features like kinky domain walls are presented. The question of stability of
vacua in a landscape of potentials is studied and the possible instability in
large dimension of fields is shown. Finally a compactification of the
Einstein-Maxwell theory is studied which can be a good lab to understand the
decay rates in compactification models of arbitrary dimensions.


  The objective function of a matrix factorization model usually aims to
minimize the average of a regression error contributed by each element.
However, given the existence of stochastic noises, the implicit deviations of
sample data from their true values are almost surely diverse, which makes each
data point not equally suitable for fitting a model. In this case, simply
averaging the cost among data in the objective function is not ideal.
Intuitively we would like to emphasize more on the reliable instances (i.e.,
those contain smaller noise) while training a model. Motivated by such
observation, we derive our formula from a theoretical framework for optimal
weighting under heteroscedastic noise distribution. Specifically, by modeling
and learning the deviation of data, we design a novel matrix factorization
model. Our model has two advantages. First, it jointly learns the deviation and
conducts dynamic reweighting of instances, allowing the model to converge to a
better solution. Second, during learning the deviated instances are assigned
lower weights, which leads to faster convergence since the model does not need
to overfit the noise. The experiments are conducted in clean recommendation and
noisy sensor datasets to test the effectiveness of the model in various
scenarios. The results show that our model outperforms the state-of-the-art
factorization and deep learning models in both accuracy and efficiency.


  The amount of texture can be rich or deficient depending on the objects and
the structures of the building. The conventional mono visual-initial navigation
system (VINS)-based localization techniques perform well in environments where
stable features are guaranteed. However, their performance is not assured in a
changing indoor environment. As a solution to this, we propose Adaptive Line
and point feature-based Visual Inertial Odometry (ALVIO) in this paper. ALVIO
actively exploits the geometrical information of lines that exist in abundance
in an indoor space. By using a strong line tracker and adaptive selection of
feature-based tightly coupled optimization, it is possible to perform robust
localization in a variable texture environment. The structural characteristics
of ALVIO are as follows: First, the proposed optical flow-based line tracker
performs robust line feature tracking and management. By using epipolar
geometry and trigonometry, accurate 3D lines are recovered. These 3D lines are
used to calculate the line re-projection error. Finally, with the
sensitivity-analysis-based adaptive feature selection in the optimization
process, we can estimate the pose robustly in various indoor environments. We
validate the performance of our system on public datasets and compare it
against other state-of the-art algorithms (S-MSKCF, VINS-Mono). In the proposed
algorithm based on point and line feature selection, translation RMSE increased
by 16.06% compared to VINS-Mono, while total optimization time decreased by up
to 49.31%. Through this, we proved that it is a useful algorithm as a real-time
pose estimation algorithm.


  It is shown that the two-level correlation function $R(s,s')$ in the
invariant random matrix ensembles (RME) with soft confinement exhibits a "ghost
peak" at $s\approx -s'$. This lifts the sum rule prohibition for the level
number variance to have a Poisson-like term ${\rm var}(n)=\eta n$ that is
typical of RME with broken U(N) symmetry. Thus we conclude that the U(N)
invariance is broken spontaneously in the RME with soft confinement, $\eta$
playing the role of an order-parameter.


  As a variant of the much studied Tur\'an number, $ex(n,F)$, the largest
number of edges that an $n$-vertex $F$-free graph may contain, we introduce the
connected Tur\'an number $ex_c(n,F)$, the largest number of edges that an
$n$-vertex connected $F$-free graph may contain. We focus on the case where the
forbidden graph is a tree. The celebrated conjecture of Erd\H{o}s and S\'os
states that for any tree $T$, we have $ex(n,T)\le(|T|-2)\frac{n}{2}$. We
address the problem how much smaller $ex_c(n,T)$ can be, what is the smallest
possible ratio of $ex_c(n,T)$ and $(|T|-2)\frac{n}{2}$ as $|T|$ grows. We also
determine the exact value of $ex_c(n,T)$ for small trees, in particular for all
trees with at most six vertices. We introduce general constructions of
connected $T$-free graphs based on graph parameters as longest path, matching
number, branching number, etc.


  We show that, assuming GCH, if $\kappa$ is a Ramsey or a strongly Ramsey
cardinal and $F$ is a class function on the regular cardinals having a closure
point at $\kappa$ and obeying the constraints of Easton's theorem, namely,
$F(\alpha)\leq F(\beta)$ for $\alpha\leq\beta$ and $\alpha<\cf(F(\alpha))$,
then there is a cofinality preserving forcing extension in which $\kappa$
remains Ramsey or strongly Ramsey respectively and $2^\delta=F(\delta)$ for
every regular cardinal $\delta$.


  A novel, non-invasive method of measuring the beam energy at the
International Linear Collider is proposed. Laser light collides head-on with
beam particles and either the energy of the Compton scattered electrons near
the kinematic end-point is measured or the positions of the Compton
backscattered $\gamma$-rays, the edge electrons and the unscattered beam
particles are recorded. A compact layout for the Compton spectrometer is
suggested. It consists of a bending magnet and position sensitive detectors
operating in a large radiation environment. Several options for high spatial
resolution detectors are discussed. Simulation studies support the use of an
infrared or green laser and quartz fiber detectors to monitor the backscattered
photons and edge electrons. Employing a cavity monitor, the beam particle
position downstream of the magnet can be recorded with submicrometer precision.
Such a scheme provides a feasible and promising method to access the incident
beam energy with precisions of $10^{-4}$ or better on a bunch-to-bunch basis
while the electron and positron beams are in collision.


  Interference alignment is a transmission technique for exploiting all
available degrees of freedom in the interference channel with an arbitrary
number of users. Most prior work on interference alignment, however, neglects
interference from other nodes in the network not participating in the alignment
operation. This paper proposes three generalizations of interference alignment
for the multiple-antenna interference channel with multiple users that account
for colored noise, which models uncoordinated interference. First, a minimum
interference-plus-noise leakage algorithm is presented, and shown to be
equivalent to previous subspace methods when noise is spatially white or
negligible. A joint minimum mean squared error design is then proposed that
jointly optimizes the transmit precoders and receive spatial filters, whereas
previous designs neglect the receive spatial filter. This algorithm is shown to
be a generalization of previous joint MMSE designs for other system
configurations such as the broadcast channel. Finally, a maximum
signal-to-interference-plus-noise ratio algorithm is developed that is proven
to converge, unlike previous maximum SINR algorithms. The latter two designs
are shown to have increased complexity due to non-orthogonal precoders, more
required iterations, or more channel state knowledge than the min INL or
subspace methods. The sum throughput performance of these algorithms is
simulated in the context of a network with uncoordinated co-channel interferers
not participating in the alignment protocol. It is found that a network with
cochannel interference can benefit from employing precoders designed to
consider that interference, but in some cases, ignoring the co-channel
interference is advantageous.


  Neutron stars may sustain a non-axisymmetric deformation due to magnetic
distortion and are potential sources of continuous gravitational waves (GWs)
for ground-based interferometric detectors. With decades of searches using
available GW detectors, no evidence of a GW signal from any pulsar has been
observed. Progressively stringent upper limits of ellipticity have been placed
on Galactic pulsars. In this work, we use the ellipticity inferred from the
putative millisecond magnetars in short gamma-ray bursts (SGRBs) to estimate
their detectability by current and future GW detectors. For $\sim 1$ ms
magnetars inferred from the SGRB data, the detection horizon is $\sim 30$ Mpc
and $\sim 600$ Mpc for advanced LIGO (aLIGO) and Einstein Telescope (ET),
respectively. Using the ellipticity of SGRB millisecond magnetars as
calibration, we estimate the ellipticity and gravitational wave strain of
Galactic pulsars and magnetars assuming that the ellipticity is
magnetic-distortion-induced. We find that the results are consistent with the
null detection results of Galactic pulsars and magnetars with the aLIGO O1. We
further predict that the GW signals from these pulsars/magnetars may not be
detectable by the currently designed aLIGO detector. The ET detector may be
able to detect some relatively low frequency signals ($<50$ Hz) from some of
these pulsars. Limited by its design sensitivity, the eLISA detector seems not
suitable for detecting the signals from Galactic pulsars and magnetars.


  Reinforcement learning (RL) often faces the challenges of uninformed search
problems where the agent should explore without access to the domain knowledge
such as characteristics of the environment or external rewards. To tackle these
challenges, this work proposes a new approach for curriculum RL called
Diversify for Disagreement & Conquer (D2C). Unlike previous curriculum learning
methods, D2C requires only a few examples of desired outcomes and works in any
environment, regardless of its geometry or the distribution of the desired
outcome examples. The proposed method performs diversification of the
goal-conditional classifiers to identify similarities between visited and
desired outcome states and ensures that the classifiers disagree on states from
out-of-distribution, which enables quantifying the unexplored region and
designing an arbitrary goal-conditioned intrinsic reward signal in a simple and
intuitive way. The proposed method then employs bipartite matching to define a
curriculum learning objective that produces a sequence of well-adjusted
intermediate goals, which enable the agent to automatically explore and conquer
the unexplored region. We present experimental results demonstrating that D2C
outperforms prior curriculum RL methods in both quantitative and qualitative
aspects, even with the arbitrarily distributed desired outcome examples.


  Karyotyping is a process in which chromosomes in a dividing cell are properly
stained, identified and displayed in a standard format, which helps geneticist
to study and diagnose genetic factors behind various genetic diseases and for
studying cancer. M-FISH (Multiplex Fluorescent In-Situ Hybridization) provides
color karyotyping. In this paper, an automated method for M-FISH chromosome
segmentation based on watershed transform followed by naive Bayes
classification of each region using the features, mean and standard deviation,
is presented. Also, a post processing step is added to re-classify the small
chromosome segments to the neighboring larger segment for reducing the chances
of misclassification. The approach provided improved accuracy when compared to
the pixel-by-pixel approach. The approach was tested on 40 images from the
dataset and achieved an accuracy of 84.21 %.


  Solar prominences represent large-scale condensations suspended against
gravity within the solar atmosphere. The Rayleigh-Taylor (RT) instability is
proposed to be one of the important fundamental processes leading to the
generation of dynamics at many spatial and temporal scales within these
long-lived, cool, and dense structures amongst the solar corona. We run 2.5D
ideal magnetohydrodynamic (MHD) simulations with the open-source MPI-AMRVAC
code far into the nonlinear evolution of an RT instability perturbed at the
prominence-corona interface. Our simulation achieves a resolution down to $\sim
23$ km on a 2D $(x,y)$ domain of size 30 Mm $\times$ 30 Mm. We follow the
instability transitioning from a multi-mode linear perturbation to its
nonlinear, fully turbulent state. Over the succeeding $\sim 25$ minute period,
we perform a statistical analysis of the prominence at a cadence of $\sim
0.858$ s. We find the dominant guiding $B_z$ component induces coherent
structure formation predominantly in the vertical velocity $V_y$ component,
consistent with observations, demonstrating an anisotropic turbulence state
within our prominence. We find power-law scalings in the inertial range for the
velocity, magnetic, and temperature fields. The presence of intermittency is
evident from the probability density functions of the field fluctuations, which
depart from Gaussianity as we consider smaller and smaller scales. In exact
agreement, the higher-order structure functions quantify the multifractality,
in addition to different scale characteristics and behavior between the
longitudinal and transverse directions. Thus, the statistics remain consistent
with the conclusions from previous observational studies, enabling us to
directly relate the RT instability to the turbulent characteristics found
within quiescent prominence.


  The field-induced quantum criticality of compounds with ferromagnetically
coupled structural spin units (as dimers and ladders) is explored by applying
Wilson's renormalization group framework to an appropriate effective action. We
determine the low-temperature phase boundary and the behavior of relevant
quantities decreasing the temperature with the applied magnetic field fixed at
its quantum critical point value. In this context, a plausible interpretation
of some recent experimental results is also suggested.


  Quantum algorithms have the potential to outperform their classical
counterparts in a variety of tasks. The realization of the advantage often
requires the ability to load classical data efficiently into quantum states.
However, the best known methods require $\mathcal{O}\left(2^n\right)$ gates to
load an exact representation of a generic data structure into an $n$-qubit
state. This scaling can easily predominate the complexity of a quantum
algorithm and, thereby, impair potential quantum advantage. Our work presents a
hybrid quantum-classical algorithm for efficient, approximate quantum state
loading. More precisely, we use quantum Generative Adversarial Networks (qGANs)
to facilitate efficient learning and loading of generic probability
distributions -- implicitly given by data samples -- into quantum states.
Through the interplay of a quantum channel, such as a variational quantum
circuit, and a classical neural network, the qGAN can learn a representation of
the probability distribution underlying the data samples and load it into a
quantum state. The loading requires
$\mathcal{O}\left(poly\left(n\right)\right)$ gates and can, thus, enable the
use of potentially advantageous quantum algorithms, such as Quantum Amplitude
Estimation. We implement the qGAN distribution learning and loading method with
Qiskit and test it using a quantum simulation as well as actual quantum
processors provided by the IBM Q Experience. Furthermore, we employ quantum
simulation to demonstrate the use of the trained quantum channel in a quantum
finance application.


  A non-commutative differential calculus on the $h$-superplane is presented
via a contraction of the $q$-superplane. An R-matrix which satisfies both
ungraded and graded Yang-Baxter equations is obtained and a new deformation of
the $(1+1)$ dimensional classical phase space (the super-Heisenberg algebra) is
introduced.


  Twisted modules for N=2 supersymmetric vertex operator superalgebras are
classified for the vertex operator superalgebra automorphisms which are lifts
of a finite automorphism of the N=2 Neveu-Schwarz Lie superalgebra
representation. These include the Ramond-twisted sectors and mirror-twisted
sectors for N=2 vertex operator superalgebras, as well as twisted modules
related to more general "spectral flow" representations of the N=2
Neveu-Schwarz algebra. We present the construct of twisted modules for free N=2
vertex operator superalgebras for all of the N=2 Neveu-Schwarz Lie superalgebra
automorphisms of finite order. We show how to extend these to lattice N=2
vertex operator superalgebras. As a consequence, we also construct the
Ramond-twisted sectors for free and lattice N=1 supersymmetric vertex operator
superalgebras. We show that the lifting of the mirror automorphism for the N=2
Neveu-Schwarz algebra to an N=2 vertex operator superalgebra is not unique and
that different mirror map vertex operator superalgebra automorphisms of an N=2
vertex operator superalgebra can lead to non-isomorphic categories of
mirror-twisted modules, as in the case of free and lattice N=2 vertex operator
superalgebras.


  Molecular representation learning is fundamental for many drug related
applications. Most existing molecular pre-training models are limited in using
single molecular modality, either SMILES or graph representation. To
effectively leverage both modalities, we argue that it is critical to capture
the fine-grained 'semantics' between SMILES and graph, because subtle
sequence/graph differences may lead to contrary molecular properties. In this
paper, we propose a universal SMILE-graph representation learning model, namely
UniMAP. Firstly, an embedding layer is employed to obtain the token and
node/edge representation in SMILES and graph, respectively. A multi-layer
Transformer is then utilized to conduct deep cross-modality fusion. Specially,
four kinds of pre-training tasks are designed for UniMAP, including Multi-Level
Cross-Modality Masking (CMM), SMILES-Graph Matching (SGM), Fragment-Level
Alignment (FLA), and Domain Knowledge Learning (DKL). In this way, both global
(i.e. SGM and DKL) and local (i.e. CMM and FLA) alignments are integrated to
achieve comprehensive cross-modality fusion. We evaluate UniMAP on various
downstream tasks, i.e. molecular property prediction, drug-target affinity
prediction and drug-drug interaction. Experimental results show that UniMAP
outperforms current state-of-the-art pre-training methods.We also visualize the
learned representations to demonstrate the effect of multi-modality
integration.


A digest of my closing overview talk at DIS2013


  The zCOSMOS-bright 10k spectroscopic sample reveals a strong environmental
dependence of close kinematic galaxy pair fractions in the redshift range 0.2 <
z < 1. The fraction of close pairs is three times higher in the top density
quartile than in the lowest one. This environmental variation in pair fractions
will translate into merger fractions since merger timescales are shown, based
on Millennium simulation catalogs, to be largely independent of environment.
While galactic properties of close kinematic pairs (morphologies and star
formation rates) may seem to be non-representative of an underlying galaxy
population, they can be explained by taking into account well-known effects of
environment, and changes caused by interactions. The latter is responsible for
an increase of irregular galaxies in pairs by a factor of 50-75%, with a
disproportionate increase in the number of irregular-irregular pairs (4-8
times), due to disturbance of about 15% of the disk galaxies in pairs. Another
sign of interaction is an observed boost in specific star formation rate
(factor 2-4) for the closest pairs. While significant for paired galaxies, this
triggered star-formation due to interactions represents only about 5% of the
integrated star-formation activity in our volume-limited sample. Although
majority of close kinematic pairs are in dense environments, the effects of
interactions appear to be strongest in the lower density environments. This may
introduce strong biases into observational studies of mergers, especially those
based on morphological criteria. Relative excess of post-starburst galaxies
observed in paired galaxies (factor \sim2) as well as excess of AGNs (factor of
over 2), linked with environmental dependence of the pair fractions could
indicate that early phases of interactions and merging are plausible candidates
for environmental quenching, observed in the global galaxy populations.


  Neural networks are widely known to be vulnerable to backdoor attacks, a
method that poisons a portion of the training data to make the target model
perform well on normal data sets, while outputting attacker-specified or random
categories on the poisoned samples. Backdoor attacks are full of threats.
Poisoned samples are becoming more and more similar to corresponding normal
samples, and even the human eye cannot easily distinguish them. On the other
hand, the accuracy of models carrying backdoors on normal samples is no
different from that of clean models.In this article, by observing the
characteristics of backdoor attacks, We provide a new model training method
(PT) that freezes part of the model to train a model that can isolate
suspicious samples. Then, on this basis, a clean model is fine-tuned to resist
backdoor attacks.


  We have analyzed the quasiparticle dispersion and ARPES-spectral density for
Sr2CuO2Cl2 and Ca2CuO2Cl2 antiferromagnetic insulators along basic symmetric
directions of the Brillouin zone (BZ) in a framework of an extended tight
binding method (ETBM) with explicit account for intracell strong electron
correlations. The quasiparticle dispersion is in a good agreement with ARPES-
data. At the top of valence band we found a narrow impurity-like virtual level
with the spectral weight proportional to the concentration of spin
fluctuations. A pseudogap between the virtual level and the top of the valence
band has dispersion similar to 'remnant Fermi surface' in Ca2CuO2Cl2 and to a
pseudogap in the underdoped Bi2212 samples. A calculated parity of the
polarized ARPES-spectra in (0,0),(pi/2,pi/2),(pi,0) - points in the AFM- phase
is even with regard to relative magnitudes of the partial contributions by
different orbitals to the total ARPES- spectral density. Conditions of an
observability for the different partial contributions in the polarized ARPES-
experiments are determined also.


  There are many equivalent ways to describe the p-torsion of a principally
polarized abelian variety in characteristic p. We briefly explain these methods
and then illustrate them for abelian varieties A of arbitrary dimension g in
several important cases, including when A has p-rank f and a-number 1 and when
A has p-rank f and a-number g-f. We provide complete tables for abelian
varieties of dimension up to four.


  Perception systems for autonomous driving have seen significant advancements
in their performance over last few years. However, these systems struggle to
show robustness in extreme weather conditions because sensors like lidars and
cameras, which are the primary sensors in a sensor suite, see a decline in
performance under these conditions. In order to solve this problem,
camera-radar fusion systems provide a unique opportunity for all weather
reliable high quality perception. Cameras provides rich semantic information
while radars can work through occlusions and in all weather conditions. In this
work, we show that the state-of-the-art fusion methods perform poorly when
camera input is degraded, which essentially results in losing the all-weather
reliability they set out to achieve. Contrary to these approaches, we propose a
new method, RadSegNet, that uses a new design philosophy of independent
information extraction and truly achieves reliability in all conditions,
including occlusions and adverse weather. We develop and validate our proposed
system on the benchmark Astyx dataset and further verify these results on the
RADIATE dataset. When compared to state-of-the-art methods, RadSegNet achieves
a 27% improvement on Astyx and 41.46% increase on RADIATE, in average precision
score and maintains a significantly better performance in adverse weather
conditions


  We propose a mechanism for instanton induced chiral symmetry breaking in QCD
with fundamental scalars. The model Lagragian that we use has the same symmetry
properties as QCD. The scalar fields develop vacuum expectation values at a
non-trivial minimum and generate masses for thhe light quarks. The minimization
condition is also used to break the $SU(N_f)$ flavour symmetry in order to make
the $s$ quark heavier than the two lighter ones. Thus a vacuum of the theory
that is not chirally invariant is obtained.


  The effect of fluctuation induced weakly first order phase transition known
for three dimensional (3D) type I superconductors appears in a modified and
strongly enhanced variant in thin (quasi-2D) superconducting films. The unusual
thermodynamic properties of this new type of first order phase transitions and
the possibility for an experimental verification of the effect are established
and discussed.


  Efficiently sampling from the P\'olya-Gamma distribution, ${PG}(b,z)$, is an
essential element of P\'olya-Gamma data augmentation. Polson et. al (2013) show
how to efficiently sample from the ${PG}(1,z)$ distribution. We build two new
samplers that offer improved performance when sampling from the ${PG}(b,z)$
distribution and $b$ is not unity.


  Electron microscopy, while reliable, is an expensive, slow, and inefficient
technique for thorough size distribution characterization of both mono- and
polydisperse colloidal nanoparticles. If rapid in-situ characterization of
colloid samples is to be achieved, a different approach, based on fast, widely
accessible, and inexpensive optical measurements such as UV-Vis spectroscopy in
combination with spectra interpretation related to Mie scattering theory, is
needed. In this article, we present a tandem deep neural network (DNN) for the
size distribution and concentration prediction of close to spherical silver
colloidal nanoparticle batches synthesized via the seeded growth method. The
first DNN identified the dipole component of the localized surface plasmon
resonance and the second one determined the size distribution from the isolated
spectral component. The training data was engineered to be bias-free and
generated numerically. High prediction accuracy with root mean square
percentage error of mean size down to 1.2% was achieved, spanning the entire
prediction range from 1 nm up to 150 nm in radius, suggesting the possible
extension limits of the effective medium theory used for simulating the
spectra. The DNN-predicted nanoparticle concentrations also were very close to
the ones expected based on synthesis precursor contents as well as measured by
atomic absorption spectroscopy.


  Recently, a theory for the tropicalization of a spherical homogeneous space
$G/H$ was developed by Tassos Vogiannou. We extend his ideas to define the
tropicalization of a spherical $G/H$-embedding. This generalizes the
construction of tropicalization of toric varieties. We also extend an alternate
definition of spherical tropicalization via Gr\"obner theory developed by
Kiumars Kaveh and Christopher Manon and show that the two notions of extended
tropicalization coincide.


  The Einstein-Podolsky-Rosen paradox (1935) is reexamined in the light of
Shannon's information theory (1948). The EPR argument did not take into account
that the observers' information was localized, like any other physical object.
General relativity introduces new problems: there are horizons which act as
one-way membranes for the propagation of quantum information, in particular
black holes which act like sinks.


  The effects of the tilt of the crystallographic orientation with respect to
an incident electron probe on high-angle annular dark field (HAADF) imaging in
aberration-corrected scanning transmission electron microscopy (STEM) have been
investigated with experiments and simulations. A small specimen tilt can lead
to unequal deviations of different atom species in the HAADF image and result
in further relative displacement between anions and cations. Simulated HAADF
images also confirm that the crystal tilt causes an artifact in atom
polarization as well. The effect is derived from the scattering ability of
different atoms.


  We make use of the unprecedented depth, spatial resolution, and field of view
of the Euclid Early Release Observations of the Perseus galaxy cluster to
detect and characterise the dwarf galaxy population in this massive system. The
Euclid high resolution VIS and combined VIS+NIR colour images were visually
inspected and dwarf galaxy candidates were identified. Their morphologies, the
presence of nuclei, and their globular cluster (GC) richness were visually
assessed, complementing an automatic detection of the GC candidates. Structural
and photometric parameters, including Euclid filter colours, were extracted
from 2-dimensional fitting. Based on this analysis, a total of 1100 dwarf
candidates were found across the image, with 638 appearing to be new
identifications. The majority (96%) are classified as dwarf ellipticals, 53%
are nucleated, 26% are GC-rich, and 6% show disturbed morphologies. A
relatively high fraction of galaxies, 8%, are categorised as ultra-diffuse
galaxies. The majority of the dwarfs follow the expected scaling relations.
Globally, the GC specific frequency, S_N, of the Perseus dwarfs is intermediate
between those measured in the Virgo and Coma clusters. While the dwarfs with
the largest GC counts are found throughout the Euclid field of view, those
located around the east-west strip, where most of the brightest cluster members
are found, exhibit larger S_N values, on average. The spatial distribution of
the dwarfs, GCs, and intracluster light show a main iso-density/isophotal
centre displaced to the west of the bright galaxy light distribution. The ERO
imaging of the Perseus cluster demonstrates the unique capability of Euclid to
concurrently detect and characterise large samples of dwarfs, their nuclei, and
their GC systems, allowing us to construct a detailed picture of the formation
and evolution of galaxies over a wide range of mass scales and environments.


  Building on the fundamentals introduced in part I, we employ the Bethe ansatz
to study some ground-state properties (energy, magnetization, susceptibility)
of the one-dimensional s=1/2 Heisenberg antiferromagnet in zero and nonzero
magnetic field. The 2-spinon triplet and singlet excitations from the
zero-field ground state are discussed in detail, and their energies are
calculated for finite and infinite chains. Procedures for the numerical
calculation of real and complex solutions of the Bethe ansatz equations are
discussed and applied. The paper is designed as a tutorial for beginning
graduate students. It includes 10 problems for further study.


  This paper considers the distributed bandit convex optimization problem with
time-varying inequality constraints over a network of agents, where the goal is
to minimize network regret and cumulative constraint violation. Existing
distributed online algorithms require that each agent broadcasts its decision
to its neighbors at each iteration. To better utilize the limited communication
resources, we propose a distributed event-triggered online primal--dual
algorithm with two-point bandit feedback. Under several classes of
appropriately chosen decreasing parameter sequences and non-increasing
event-triggered threshold sequences, we establish dynamic network regret and
network cumulative constraint violation bounds. These bounds are comparable to
the results achieved by distributed event-triggered online algorithms with
full-information feedback. Finally, a numerical example is provided to verify
the theoretical results.


  We show that multiple point contacts on a barrier separating two laterally
coupled quantum Hall fluids induce Aharonov-Bohm (AB) oscillations in the
tunneling conductance. These quantum coherence effects provide new evidence for
the Luttinger liquid behavior of the edge states of quantum Hall fluids. For a
two point contact, we identify coherent and incoherent regimes determined by
the relative magnitude of their separation and the temperature. We analyze both
regimes in the strong and weak tunneling amplitude limits as well as their
temperature dependence. We find that the tunneling conductance should exhibit
AB oscillations in the coherent regime, both at strong and weak tunneling
amplitude with the same period but with different functional form.


  When ${\cal{D}}:\xi \rightarrow \eta$ is a linear differential operator, a
"direct problem " is to find the generating compatibility conditions (CC) in
the form of an operator ${\cal{D}}_1:\eta \rightarrow \zeta$ such that
${\cal{D}}\xi=\eta$ implies ${\cal{D}}_1\eta=0$. When ${\cal{D}}$ is
involutive, the procedure provides successive first order involutive operators
${\cal{D}}_1, ... , {\cal{D}}_n$ when the ground manifold has dimension $n$.
Conversely, when ${\cal{D}}_1$ is given, a more difficult " inverse problem "
is to look for an operator ${\cal{D}}: \xi \rightarrow \eta$ having the
generating CC ${\cal{D}}_1\eta=0$. If this is possible, that is when the
differential module defined by ${\cal{D}}_1$ is torsion-free, one shall say
that the operator ${\cal{D}}_1$ is parametrized by ${\cal{D}}$ and there is no
relation in general between ${\cal{D}}$ and ${\cal{D}}_2$. The parametrization
is said to be " minimum " if the differential module defined by ${\cal{D}}$ has
a vanishing differential rank and is thus a torsion module. The parametrization
of the Cauchy stress operator in arbitrary dimension $n$ has attracted many
famous scientists (G.B. Airy in 1863 for $n=2$, J.C. Maxwell in 1863, G. Morera
and E. Beltrami in 1892 for $n=3$, A. Einstein in 1915 for $n=4$) . This paper
proves that all these works are using the Einstein operator and not the Ricci
operator. As a byproduct, they are all based on a confusion between the
so-called $div$ operator induced from the Bianchi operator ${\cal{D}}_2$ and
the Cauchy operator which is the formal adjoint of the Killing operator
${\cal{D}}$ parametrizing the Riemann operator ${\cal{D}}_1$ for an arbitrary
$n$. Like the Michelson and Morley experiment, it is an open historical problem
to know whether Einstein was aware of these previous works or not, as the
comparison needs no comment.


  Accurate local Kohn-Sham potentials have been constructed for the ground
$1s^2 ^1S$ state and, in particular, for the lowest triplet $1s2s ^{3}S$ state
of the helium atom, using electron densities from many-body calculations and
the procedure of van Leeuwen and Baerends (Phys. Rev. A{\bf49}, 2138 (1994)).
The resulting Kohn-Sham orbitals reproduce the many-body densities very
accurately, and furthermore we have demonstrated that the negative of the
energy eigenvalue of the outermost electron orbital agrees with the
corresponding ionization energy with extreme accuracy. The procedure is also
applied to the Hartree-Fock density of the $1s2s ^{3}S$ state, and the
Kohn-Sham eigenvalue of the $2s$ orbital is found to agree very well with the
corresponding Hartree-Fock eigenvalue, which is the negative of the ionization
energy in this model due to Koopmans' theorem. The results for the $1s2s ^{3}S$
state clearly demonstrate that there is no conflict between the locality of the
Kohn-Sham potential and the exclusion principle, as claimed by Nesbet (Phys.
Rev. A{\bf58}, R12 (1998)).


  We describe a new method to map the requested error tolerance on an H-matrix
approximation to the block error tolerances. Numerical experiments show that
the method produces more efficient approximations than the standard method for
kernels having singularity order greater than one, often by factors of 1.5 to 5
and at a lower computational cost.


  Exact solutions, in terms of special functions, of all wave equations $%
u_{xx} - u_{tt} = V(x) u(t,x)$, characterised by eight inequivalent time
independent potentials and by variable separation, have been found. The real
valueness of the solutions from computer algebra programs is not always
manifest and in this work we provide ready to use solutions. We discussed
especially the potential $\cosh^{-2}x (m_1 + m_2 \sinh x)$. Such potential
approximates the Schwarzschild black hole potential for even parity.


  We derive theta function representations of algebro-geometric solutions of a
discrete system governed by a transfer matrix associated with (an extension of)
the trigonometric moment problem studied by Szego and Baxter. We also derive a
new hierarchy of coupled nonlinear difference equations satisfied by these
algebro-geometric solutions.


  Recent advances in implicit neural representations have achieved impressive
results by sampling and fusing individual points along sampling rays in the
sampling space. However, due to the explosively growing sampling space, finely
representing and synthesizing detailed textures remains a challenge for
unbounded large-scale outdoor scenes. To alleviate the dilemma of using
individual points to perceive the entire colossal space, we explore learning
the surface distribution of the scene to provide structural priors and reduce
the samplable space and propose a Point Diffusion implicit Function, PDF, for
large-scale scene neural representation. The core of our method is a
large-scale point cloud super-resolution diffusion module that enhances the
sparse point cloud reconstructed from several training images into a dense
point cloud as an explicit prior. Then in the rendering stage, only sampling
points with prior points within the sampling radius are retained. That is, the
sampling space is reduced from the unbounded space to the scene surface.
Meanwhile, to fill in the background of the scene that cannot be provided by
point clouds, the region sampling based on Mip-NeRF 360 is employed to model
the background representation. Expensive experiments have demonstrated the
effectiveness of our method for large-scale scene novel view synthesis, which
outperforms relevant state-of-the-art baselines.


  The Born cross sections for the process $e^{+}e^{-}\to \omega\eta^{\prime}$
are measured at 22 center-of-mass energies from 2.000 to 3.080 GeV using data
collected with the BESIII detector at the BEPCII collider. A resonant structure
is observed with a statistical significance of 9.6$\sigma$. A Breit-Wigner fit
determines its mass to be $M_R=(2153\pm30\pm31)~{\rm{MeV}}/c^{2}$ and its width
to be $\Gamma_{R}=(167\pm77\pm7)~\rm{MeV}$, where the first uncertainties are
statistical and the second are systematic.


  The spin dependent charge transport in zigzag graphene nanoribbons (ZGNRs)
has been investigated by the nonequilibrium Green's function method combined
with the density functional theory at the local spin density approximation. The
current versus voltage curve shows distinguished behaviors for symmetric and
asymmetric ZGNRs and the doping on the ZGNR edges can manipulate the spin
transport. In special cases that a Be atom is substitutionally doped on one
edge of the symmetric ZGNRs, one spin current shows negative differential
resistance while the other increases monotonically with the bias. This property
might be used to design spin oscillators or other devices for spintronics.


  How should we evaluate the effect of a policy on the likelihood of an
undesirable event, such as conflict? The significance test has three
limitations. First, relying on statistical significance misses the fact that
uncertainty is a continuous scale. Second, focusing on a standard point
estimate overlooks the variation in plausible effect sizes. Third, the
criterion of substantive significance is rarely explained or justified. A new
Bayesian decision-theoretic model, "causal binary loss function model,"
overcomes these issues. It compares the expected loss under a policy
intervention with the one under no intervention. These losses are computed
based on a particular range of the effect sizes of a policy, the probability
mass of this effect size range, the cost of the policy, and the cost of the
undesirable event the policy intends to address. The model is more applicable
than common statistical decision-theoretic models using the standard loss
functions or capturing costs in terms of false positives and false negatives. I
exemplify the model's use through three applications and provide an R package.


  Hyperfine-structure constants of odd Ra$^{+}$ due to the interactions of
nuclear magnetic dipole, electric quadrupole, and magnetic octupole moments
with the electrons are investigated in the framework of relativistic
coupled-cluster method within single- and double-excitation approximation. The
calculated energies and magnetic dipole hyperfine-structure constants $A$
exhibit a good agreement with available experimental values. Combining with the
experimental electric quadrupole hyperfine-structure constant, we also
extracted the electric quadrupole moments $Q$ of $^{209,211,221,223}$Ra. Our
$Q$($^{221}$Ra) and $Q$($^{223}$Ra) are consistent with the referenced values
from a semi-empirical analysis (Z. Phys. D: At., Mol. Clusters 11, 105 (1988)),
but $Q(^{211}$Ra)=$0.33(2)$ is smaller than the referenced value $0.48(4)$ by
about 30\%. Furthermore, we also performed a procedure for assessing the
contributions of magnetic octupole moment to the hyperfine splitting. The
sensitivity of hyperfine-structure interval measurements in $^{223}$Ra$^{+}$
that can reveal the effect caused by the nuclear octupole moment are found to
be on the order of kHz.


  We summarize the ongoing scientific program of the 12 GeV Continuous Electron
Beam Accelerator Facility (CEBAF) and give an outlook into future scientific
opportunities. The program addresses important topics in nuclear, hadronic, and
electroweak physics including nuclear femtography, meson and baryon
spectroscopy, quarks and gluons in nuclei, precision tests of the standard
model, and dark sector searches. Potential upgrades of CEBAF are considered,
such as higher luminosity, polarized and unpolarized positron beams, and
doubling the beam energy.


  At the heart of differential geometry is the construction of the tangent
bundle of a manifold. There are various abstractions of this construction, and
this paper seeks to compare two of them: Synthetic Differential Geometry (SDG)
and Tangent Structures.
  Tangent structure is defined via giving an underlying category M and a
tangent functor T along with a list of natural transformations satisfying a set
of axioms, then detailing the behaviour of T in the category End(M). SDG on the
other hand is defined through the use of Weil algebras.
  The aim of this paper is to present a more precise relationship between the
two approaches for describing tangent structures.