  We revisit the pairing model of state spaces with new emergent states
introduced in J. Phys. A: Math. Theor. 51 375002, 2018.
  We facilitate our analysis by introducing a simplified pairing model
consisting of balls able to form pairs but without any internal structure.
  For both the simplified and the original model we compute exactly the
probability distribution for observing a state with $n_p$ pairs. We show this
distribution satisfies a large deviation principle with speed $n \ln(n)$. We
present closed form expressions for a variety of statistical quantities
including moments and marginal distributions.


  Non-supersymmetric heterotic strings share various properties with their
supersymmetric counterparts. Torus compactifications of the latter live in a
component of the moduli space of string vacua with 16 supercharges, and various
asymmetric orbifolds thereof realize vacua in other components, exhibiting
qualitative differences such as rank reduction. We set out to study the
analogous problem for non-supersymmetric heterotic strings, framing it in
relation to chiral fermionic CFTs with central charge 24, which were classified
recently. We find that for the case analogous to the so-called CHL string,
which has gauge group rank reduced by 8, there are in total four
non-supersymmetric versions. These include the well known $E_8$ string and
three other constructions a la CHL, which can be distinguished qualitatively by
how tachyons appear in their classical moduli spaces. We also discuss the
classification problem for lower rank theories and the relationship between
MSDS models and Scherk-Schwarz reductions.


  Thermodynamic resources, beyond their well-known usefulness in work
extraction and other thermodynamic tasks, are often important also in tasks
that are not evidently thermodynamic. Here we develop a framework for
identifying such resources in diverse applications of bosonic
continuous-variable systems. Introducing the class of bosonic linear thermal
operations to model operationally-feasible processes, we apply this model to
identify uniquely quantum properties of bosonic states that refine classical
notions of thermodynamic resourcefulness. Among these are (1) a suite of
temperature-like quantities generalizing the equilibrium temperature to
quantum, non-equilibrium scenarios; (2) signal-to-noise ratios quantifying a
system's capacity to carry information in phase-space displacement; and (3)
well-established non-classicality measures quantifying the resolution in
sensing and parameter estimation tasks.


  Social recommender systems (SocialRS) simultaneously leverage the
user-to-item interactions as well as the user-to-user social relations for the
task of generating item recommendations to users. Additionally exploiting
social relations is clearly effective in understanding users' tastes due to the
effects of homophily and social influence. For this reason, SocialRS has
increasingly attracted attention. In particular, with the advance of graph
neural networks (GNN), many GNN-based SocialRS methods have been developed
recently. Therefore, we conduct a comprehensive and systematic review of the
literature on GNN-based SocialRS. In this survey, we first identify 84 papers
on GNN-based SocialRS after annotating 2151 papers by following the PRISMA
framework (preferred reporting items for systematic reviews and meta-analyses).
Then, we comprehensively review them in terms of their inputs and architectures
to propose a novel taxonomy: (1) input taxonomy includes 5 groups of input type
notations and 7 groups of input representation notations; (2) architecture
taxonomy includes 8 groups of GNN encoder notations, 2 groups of decoder
notations, and 12 groups of loss function notations. We classify the GNN-based
SocialRS methods into several categories as per the taxonomy and describe their
details. Furthermore, we summarize benchmark datasets and metrics widely used
to evaluate the GNN-based SocialRS methods. Finally, we conclude this survey by
presenting some future research directions. GitHub repository with the curated
list of papers are available at
https://github.com/claws-lab/awesome-GNN-social-recsys.


  The minimum modulus problem on covering systems was posed by Erd\H{o}s in
1950, who asked whether the minimum modulus of a covering system with distinct
moduli is bounded. In 2007, Filaseta, Ford, Konyagin, Pomerance and Yu affirmed
it if the reciprocal sum of the moduli of a covering system is bounded. Later
in 2015, Hough resolved this problem by showing that the minimum modulus is at
most $10^{16}$. In 2022, Balister, Bollob\'as, Morris, Sahasrabudhe and Tiba
reduced this bound to $616,000$ by developing a versatile method called the
distortion method. Recently, Klein, Koukoulopoulos and Lemieux generalized
Hough's result by using this method. In this paper, we develop the distortion
method by introducing the theory of probability measures associated to an
inverse system. Following Klein et al.'s work, we derive an analogue of their
theorem in the setting of number fields, which provides a solution to
Erd\H{o}s' minimum modulus problem in number fields.


  We demonstrate that the latest constraints on inflationary observables,
namely the tensor-to-scalar ratio $r$ and the scalar spectral index $n_{_S}$,
from the Cosmic Background Radiation (CMB) observations are already strong
enough to rule out the model of a scalar field with a power law potential even
in the presence of kinetic coupling to gravity with a positive coupling
constant. The case for a negative coupling constant needs special treatment.


  Diffusion magnetic resonance imaging (dMRI) provides a unique tool for
noninvasively probing the microstructure of the neuronal tissue. The NODDI
model has been a popular approach to the estimation of tissue microstructure in
many neuroscience studies. It represents the diffusion signals with three types
of diffusion in tissue: intra-cellular, extra-cellular, and cerebrospinal fluid
compartments. However, the original NODDI method uses a computationally
expensive procedure to fit the model and could require a large number of
diffusion gradients for accurate microstructure estimation, which may be
impractical for clinical use. Therefore, efforts have been devoted to efficient
and accurate NODDI microstructure estimation with a reduced number of diffusion
gradients. In this work, we propose a deep network based approach to the NODDI
microstructure estimation, which is named Microstructure Estimation using a
Deep Network (MEDN). Motivated by the AMICO algorithm which accelerates the
computation of NODDI parameters, we formulate the microstructure estimation
problem in a dictionary-based framework. The proposed network comprises two
cascaded stages. The first stage resembles the solution to a dictionary-based
sparse reconstruction problem and the second stage computes the final
microstructure using the output of the first stage. The weights in the two
stages are jointly learned from training data, which is obtained from training
dMRI scans with diffusion gradients that densely sample the q-space. The
proposed method was applied to brain dMRI scans, where two shells each with 30
gradient directions (60 diffusion gradients in total) were used. Estimation
accuracy with respect to the gold standard was measured and the results
demonstrate that MEDN outperforms the competing algorithms.


  Besides many interesting application to the study of foundations of quantum
mechanics, entangled state are now assuming a large relevance for some
practical application. In particular, we discuss most recent results obtained
in our laboratory on the use of two photons entangled states produced in
parametric down conversion for absolute quantum efficiency calibration of
photodetectors, in photon counting regime.


  In this paper, we present a new variable selection method for regression and
classification purposes. Our method, called Subsampling Ranking Forward
selection (SuRF), is based on LASSO penalised regression, subsampling and
forward-selection methods. SuRF offers major advantages over existing variable
selection methods in terms of both sparsity of selected models and model
inference. We provide an R package that can implement our method for
generalized linear models. We apply our method to classification problems from
microbiome data, using a novel agglomeration approach to deal with the special
tree-like correlation structure of the variables. Existing methods arbitrarily
choose a taxonomic level a priori before performing the analysis, whereas by
combining SuRF with these aggregated variables, we are able to identify the key
biomarkers at the appropriate taxonomic level, as suggested by the data. We
present simulations in multiple sparse settings to demonstrate that our
approach performs better than several other popularly used existing approaches
in recovering the true variables. We apply SuRF to two microbiome data sets:
one about prediction of pouchitis and another for identifying samples from two
healthy individuals. We find that SuRF can provide a better or comparable
prediction with other methods while controlling the false positive rate of
variable selection.


  Hamilton-Jacobi theory provides a natural starting point for a covariant
description of the gravitational field. Using a spatial gradient expansion, one
may solve for the phase of the wavefunction by using a line-integral in
superspace. Each contour of integration corresponds to a particular choice of
time-hypersurface, and each yields the same answer. In this way, one can
describe all time choices simultaneously. In an interesting application to
cosmology, I compute large-angle microwave background anisotropies and the
galaxy-galaxy correlation function associated with the scalar and tensor
fluctuations of power-law inflation.


  We implement an iSWAP gate with two transmon qubits using a flux-tunable
coupler. Precise control of the relative phase of the qubit-control pulses and
the parametric-coupler drive is achieved with a multi-channel instrument called
Presto using direct digital synthesis (DDS), a promising technique for scaling
up quantum systems. We describe the process of tuning and benchmarking the
iSWAP gate, where the relative phase of the pulses is controlled via software.
We perform the iSWAP gate in 290 ns, validate it with quantum-state tomography,
and measure 2\% error with interleaved randomized benchmarking.


  It is well-known that in dimension 4 any framed link $(L,c)$ uniquely
represents the PL 4-manifold $M^4(L,c)$ obtained from $\mathbb D^4$ by adding
2-handles along $(L,c)$. Moreover, if trivial dotted components are also
allowed (i.e. in case of a Kirby diagram $(L^{(*)},d)$), the associated PL
4-manifold $M^4(L^{(*)},d)$ is obtained from $\mathbb D^4$ by adding 1-handles
along the dotted components and 2-handles along the framed components. In this
paper we study the relationships between framed links and/or Kirby diagrams and
the representation theory of compact PL manifolds by edge-colored graphs: in
particular, we describe how to construct algorithmically a (regular) 5-colored
graph representing $M^4(L^{(*)},d)$, directly "drawn over" a planar diagram of
$(L^{(*)},d)$, or equivalently how to algorithmically obtain a triangulation of
$M^4(L^{(*)},d)$. As a consequence, the procedure yields triangulations for any
closed (simply-connected) PL 4-manifold admitting handle decompositions without
3-handles. Furthermore, upper bounds for both the invariants gem-complexity and
regular genus of $M^4(L^{(*)},d)$ are obtained, in terms of the combinatorial
properties of the Kirby diagram.


  We reconsider semiclassical quantization of folded string spinning in AdS_3
part of AdS_5 X S^5 using integrability-based (algebraic curve) method. We
focus on the "short string" (small spin S) limit with the angular momentum J in
S^5 scaled down according to \cal J = rho \sqrt \cal S in terms of the
variables \cal J = J/\sqrt\lambda, \cal S = S/\sqrt\lambda. The semiclassical
string energy in this particular scaling limit admits the double expansion E =
\sum_{n=0}^{\infty}\sum_{p=0}^{\infty} (\sqrt\lambda)^{1-n}\,a_{n,p}(rho)\,
\cal S^{p+1/2}. It behaves smoothly as J -> 0 and partially resums recent
results by Gromov and Valatka. We explicitly compute various one-loop
coefficients a_{1,p}(rho) by summing over the fluctuation frequencies for
integrable perturbations around the classical solution. For the simple folded
string, the result agrees with what could be derived exploiting a recent
conjecture of Basso. However, the method can be extended to more general
situations. As an example, we consider the m-folded string where Basso's
conjecture fails. For this classical solution, we present the exact values of
a_{1,0}(rho) and a_{1,1}(rho) for m=2, 3, 4, 5 and explain how to work out the
general case.


  Building on insights from the theory of integrable lattices, the
integrability is claimed for nonlinear replica sigma models derived in the
context of real symmetric random matrices. Specifically, the fermionic and the
bosonic replica partition functions are proven to form a single
(supersymmetric) Pfaff-KP hierarchy whose replica limit is shown to reproduce
the celebrated nonperturbative formula for the density-density eigenvalue
correlation function in the infinite-dimensional Gaussian Orthogonal Ensemble.
Implications of the formalism outlined are briefly discussed.


  We consider the job assignment problem in a multi-server system consisting of
$N$ parallel processor sharing servers, categorized into $M$ ($\ll N$)
different types according to their processing capacity or speed. Jobs of random
sizes arrive at the system according to a Poisson process with rate $N
\lambda$. Upon each arrival, a small number of servers from each type is
sampled uniformly at random. The job is then assigned to one of the sampled
servers based on a selection rule. We propose two schemes, each corresponding
to a specific selection rule that aims at reducing the mean sojourn time of
jobs in the system.
  We first show that both methods achieve the maximal stability region. We then
analyze the system operating under the proposed schemes as $N \to \infty$ which
corresponds to the mean field. Our results show that asymptotic independence
among servers holds even when $M$ is finite and exchangeability holds only
within servers of the same type. We further establish the existence and
uniqueness of stationary solution of the mean field and show that the tail
distribution of server occupancy decays doubly exponentially for each server
type. When the estimates of arrival rates are not available, the proposed
schemes offer simpler alternatives to achieving lower mean sojourn time of
jobs, as shown by our numerical studies.


  Let $M$ be a pseudoconvex, oriented, bounded and closed CR submanifold of
$\mathbb{C}^{n}$ of hypersurface type. We show that Sobolev estimates for the
complex Green operator hold simultaneously for forms of symmetric bidegrees,
that is, they hold for $(p,q)$--forms if and only if they hold for
$(m-p,m-1-q)$--forms. Here $m$ equals the CR dimension of $M$ plus one.
Symmetries of this type are known to hold for compactness estimates. We further
show that with the usual microlocalization, compactness estimates for the
positive part percolate up the complex, i.e. if they hold for $(p,q)$--forms,
they also hold for $(p,q+1)$--forms. Similarly, compactness estimates for the
negative part percolate down the complex. As a result, if the complex Green
operator is compact on $(p,q_{1})$--forms and on $(p,q_{2})$--forms ($q_{1}\leq
q_{2}$), then it is compact on $(p,q)$--forms for $q_{1}\leq q\leq q_{2}$. It
is interesting to contrast this behavior of the complex Green operator with
that of the $\overline{\partial}$--Neumann operator on a pseudoconvex domain.


  We provide necessary and sufficient conditions for stochastic invariance of
finite dimensional submanifolds with boundary in Hilbert spaces for stochastic
partial differential equations driven by Wiener processes and Poisson random
measures.


  The null distributed controllability of the semilinear heat equation
$y_t-\Delta y + g(y)=f \,1_{\omega}$, assuming that $g$ satisfies the growth
condition $g(s)/(\vert s\vert \log^{3/2}(1+\vert s\vert))\rightarrow 0$ as
$\vert s\vert \rightarrow \infty$ and that $g^\prime\in
L^\infty_{loc}(\mathbb{R})$ has been obtained by Fern\'andez-Cara and Zuazua in
2000. The proof based on a fixed point argument makes use of precise estimates
of the observability constant for a linearized heat equation. It does not
provide however an explicit construction of a null control. Assuming that
$g^\prime\in W^{s,\infty}(\mathbb{R})$ for one $s\in (0,1]$, we construct an
explicit sequence converging strongly to a null control for the solution of the
semilinear equation. The method, based on a least-squares approach, generalizes
Newton type methods and guarantees the convergence whatever be the initial
element of the sequence. In particular, after a finite number of iterations,
the convergence is super linear with a rate equal to $1+s$. Numerical
experiments in the one dimensional setting support our analysis.


  We construct a Baum-Douglas type model for $K$-homology with coefficients in
$\mathbb{Z}/k\mathbb{Z}$. The basic geometric object in a cycle is a $spin^c$
$\mathbb{Z}/k\mathbb{Z}$-manifold. The relationship between these cycles and
the topological side of the Freed-Melrose index theorem is discussed in detail.
Finally, using inductive limits, we construct geometric models for $K$-homology
with coefficients in any countable abelian group.


  A fundamental conflict of many proof-of-work systems is that they want to
achieve inclusiveness and security at the same time. We analyze and resolve
this conflict with a theory of proof-of-work quorums, which enables a new
bridge between Byzantine and Nakamoto consensus. The theory yields stochastic
uniqueness of quorums as a function of a security parameter. We employ the
theory in HotPoW, a scalable permissionless distributed log protocol that
supports finality based on the pipelined three-phase commit previously
presented for HotStuff. We evaluate HotPoW and variants with adversarial
modifications by simulation. Results show that the protocol can tolerate
network latency, churn, and targeted attacks on consistency and liveness with a
small storage overhead compared to plain Nakamoto consensus and less complexity
than protocols that rely on sidechains for finality.


  Inspirals of an Intermediate Mass Black Hole (IMBH) and a solar mass type
object will be observable by space based gravitational wave detectors such as
The Laser Interferometer Space Antenna (LISA). A dark matter overdensity around
an IMBH - a dark matter spike - can affect the orbital evolution of the system.
We consider here such Intermediate Mass Ratio Inspirals on eccentric orbits,
experiencing dynamical friction of the dark matter spike. We find that by
including the phase space distribution of the dark matter, the dynamical
friction tends to circularize the orbit, in contrast to previous inquiries. We
derive a general condition for circularization or eccentrification for any
given dissipative force. In addition to the dephasing, we suggest using the
circularization rate as another probe of the dark matter spike. Observing these
effects would be an indicator for the particle nature of dark matter.


  Cooling a range of molecules to ultracold temperatures (<1 mK) is a difficult
but important challenge in molecular physics and chemistry. Collective cavity
cooling of molecules is a promising method that does not rely on molecular
energy level and thus can be applied to all molecules in principle. However,
the initial lack of cold molecules leads to the difficulty in its experimental
implementation. We show that efficient collective sympathetic cooling of
molecules to sub-mK temperatures using a large ensemble of atoms within a
cavity is feasible. This approach is a new type of sympathetic cooling which
does not rely on direct collisions between atoms and molecules, but utilizes
thermalization via their mutual interaction with a cavity field. Two important
mechanisms are identified. This include: (1) giant enhancement of cavity
optical field from the efficient scattering of the pump light by the atoms; (2)
cavity-mediated collective interaction between the atoms and the molecules. We
show an optimal cavity detuning for maximizing cooling, which is dependent on
the atom and molecule numbers. We determine a threshold for the molecular pump
strength and show that it is independent of molecule number when the number of
atoms is much greater than the molecules. This can be reduced by orders of
magnitude when compared to cavity cooling of single molecular species only.
Using this new sympathetic cavity cooling technique, cooling molecules to
sub-mK within a high-Q cavity could be within reach of experimental
demonstration.


  The EU ESCAPE project is developing ESAP, ESFRI 1 Scientific Analysis
Platform, as an API gateway that enables the seamless integration of
independent services accessing distributed data and computing resources. In
ESCAPE we are exploring the possibility of exploiting EGI's OpenStack cloud
computing services through ESAP. In our contribution we briefly describe ESCAPE
and ESAP, the the use cases, the work done to automate a virtual machine
creation in EGI's OpenStack cloud computing, drawbacks and possible solutions.


  Molecular interactions are key to many chemical and biological processes like
protein function. In many signaling processes they occur in sub-cellular areas
displaying nanoscale organizations and involving molecular assemblies. The
nanometric dimensions and the dynamic nature of the interactions make their
investigations complex in live cells. While super-resolution fluorescence
microscopies offer live-cell molecular imaging with sub-wavelength resolutions,
they lack specificity for distinguishing interacting molecule populations. Here
we combine super-resolution microscopy and single-molecule F\"orster Resonance
Energy Transfer (FRET) to identify dimers of receptors induced by ligand
binding and provide super-resolved images of their membrane distribution in
live cells. By developing a two-color
universal-Point-Accumulation-In-the-Nanoscale-Topography (uPAINT) method,
dimers of epidermal growth factor receptors (EGFR) activated by EGF are studied
at ultra-high densities, revealing preferential cell-edge sub-localization.
This methodology which is specifically devoted to the study of molecules in
interaction, may find other applications in biological systems where
understanding of molecular organization is crucial.


  We study the bulk viscosity of dense matter, taking into account non-linear
effects which arise in the large amplitude "supra-thermal" region where the
deviation $\mu_\Delta$ of the chemical potentials from chemical equilibrium
fulfills $\mu_\Delta>T$. This regime is relevant to unstable modes such as
r-modes, which grow in amplitude until saturated by non-linear effects. We
study the damping due to direct and modified Urca processes in hadronic matter,
and due to nonleptonic weak interactions in strange quark matter. We give
general results valid for an arbitrary equation of state of dense matter and
find that the viscosity can be strongly enhanced by supra-thermal effects. Our
study confirms previous results on quark matter and shows that the non-linear
enhancement is even stronger in the case of hadronic matter. Our results can be
applied to calculations of the r-mode-induced spin-down of fast-rotating
neutron stars, where the spin-down time will depend on the saturation amplitude
of the r-mode


  A search for dark matter is conducted in events with large missing transverse
momentum and a hadronically decaying, Lorentz-boosted top quark. This study is
performed using proton-proton collisions at a center-of-mass energy of 13 TeV,
in data recorded by the CMS detector in 2016 at the LHC, corresponding to an
integrated luminosity of 36 fb$^{-1}$. New substructure techniques, including
the novel use of energy correlation functions, are utilized to identify the
decay products of the top quark. With no significant deviations observed from
predictions of the standard model, limits are placed on the production of new
heavy bosons coupling to dark matter particles. For a scenario with purely
vector-like or purely axial-vector-like flavor changing neutral currents,
mediator masses between 0.20 and 1.75 TeV are excluded at 95% confidence level,
given a sufficiently small dark matter mass. Scalar resonances decaying into a
top quark and a dark matter fermion are excluded for masses below 3.4 TeV,
assuming a dark matter mass of 100 GeV.


  Given a dense countable set in a metric space, the infinite random geometric
graph is the random graph with the given vertex set and where any two points at
distance less than 1 are connected, independently, with some fixed probability.
It has been observed by Bonato and Janssen that in some, but not all, such
settings, the resulting graph does not depend on the random choices, in the
sense that it is almost surely isomorphic to a fixed graph. While this notion
makes sense in the general context of metric spaces, previous work has been
restricted to sets in Banach spaces. We study the case when the underlying
metric space is a circle of circumference $L$, and find a surprising dependency
of behavior on the rationality of $L$.


  Event detection (ED) is aimed to identify the key trigger words in
unstructured text and predict the event types accordingly. Traditional ED
models are too data-hungry to accommodate real applications with scarce labeled
data. Besides, typical ED models are facing the context-bypassing and disabled
generalization issues caused by the trigger bias stemming from ED datasets.
Therefore, we focus on the true few-shot paradigm to satisfy the low-resource
scenarios. In particular, we propose a multi-step prompt learning model
(MsPrompt) for debiasing few-shot event detection, that consists of the
following three components: an under-sampling module targeting to construct a
novel training set that accommodates the true few-shot setting, a multi-step
prompt module equipped with a knowledge-enhanced ontology to leverage the event
semantics and latent prior knowledge in the PLMs sufficiently for tackling the
context-bypassing problem, and a prototypical module compensating for the
weakness of classifying events with sparse data and boost the generalization
performance. Experiments on two public datasets ACE-2005 and FewEvent show that
MsPrompt can outperform the state-of-the-art models, especially in the strict
low-resource scenarios reporting 11.43% improvement in terms of weighted
F1-score against the best-performing baseline and achieving an outstanding
debiasing performance.


  We prove that the generalized rational blowdown, a surgery on smooth
4-manifolds, can be performed in the symplectic category.


  We study entire solutions to homogeneous reaction-diffusion equations in
several dimensions with Fisher-KPP reactions. Any entire solution $0<u<1$ is
known to satisfy \[ \lim_{t\to -\infty} \sup_{|x|\le c|t|} u(t,x) = 0 \qquad
\text{for each $c<2\sqrt{f'(0)}\,$,} \] and we consider here those satisfying
\[ \lim_{t\to -\infty} \sup_{|x|\le c|t|} u(t,x) = 0 \qquad \text{for some
$c>2\sqrt{f'(0)}\,$.} \] When $f$ is $C^2$ and concave, our main result
provides an almost complete characterization of transition fronts as well as
transition solutions with bounded width within this class of solutions.


  Recent developments in the commercial open source community have catalysed
the use of Linux containers for scalable deployment of web-based applications
to the cloud. Scientific software can be containerized with dependencies,
configuration files, post-processing tools and even simulation results,
referred to as containerized computing. This new approach promises to
significantly improve sustainability, productivity and reproducibility. We
present our experiences, technology, and future plans for open source
containerization of software used to model particle and radiation beams.
Vagrant is central to our approach, using Docker for cloud deployment and
VirtualBox virtual machines for deployment to Mac OS and Windows computers. Our
technology enables seamless switching between the desktop and the cloud to
simplify simulation development and execution.


  Prior benchmarks have analyzed models' answers to questions about videos in
order to measure visual compositional reasoning. Action Genome Question
Answering (AGQA) is one such benchmark. AGQA provides a training/test split
with balanced answer distributions to reduce the effect of linguistic biases.
However, some biases remain in several AGQA categories. We introduce AGQA 2.0,
a version of this benchmark with several improvements, most namely a stricter
balancing procedure. We then report results on the updated benchmark for all
experiments.


  Quantum key distribution (QKD) offers the promise of absolutely secure
communications. However, proofs of absolute security often assume perfect
implementation from theory to experiment. Thus, existing systems may be prone
to insidious side-channel attacks that rely on flaws in experimental
implementation. Here we replace all real channels with virtual channels in a
QKD protocol, making the relevant detectors and settings inside private spaces
inaccessible while simultaneously acting as a Hilbert space filter to eliminate
side-channel attacks. By using a quantum memory we find that we are able to
bound the secret-key rate below by the entanglement-distillation rate computed
over the distributed states.


  Context: NOTT (formerly Hi-5) is a new high-contrast L' band (3.5-4.0 \textmu
m) beam combiner for the VLTI with the ambitious goal to be sensitive to young
giant exoplanets down to 5 mas separation around nearby stars. The performance
of nulling interferometers in these wavelengths is affected both by fundamental
noise from the background and by the contributions of instrumental noises. This
motivates the development of end-to-end simulations to optimize these
instruments. Aims: To enable the performance evaluation and inform the design
of such instruments on the current and future infrastructures, taking into
account the different sources of noise, and their correlation. Methods:
SCIFYsim is an end-to-end simulator for single mode filtered beam combiners,
with an emphasis on nulling interferometers. It is used to compute a covariance
matrix of the errors. Statistical detection tests based on likelihood ratios
are then used to compute compound detection limits for the instrument. Results:
With the current assumptions on the performance of the wavefront correction
systems, the errors are dominated by correlated instrumental errors down to
stars of magnitude 6-7 in the L band, beyond which thermal background from the
telescopes and relay system becomes dominant. Conclusions: SCIFYsim is suited
to anticipate some of the challenges of design, tuning, operation and signal
processing for integrated optics beam combiners. The detection limits found for
this early version of NOTT simulation with the unit telescopes are compatible
with detections at contrasts up to $10^5$ in the L band at separations of 5 to
80 mas around bright stars.


  It is crucial to determine masses and radii of extrasolar planets with high
precision to have constraints on their chemical composition, internal structure
and thereby their formation and evolution. In order to achieve this goal, we
apply the defocus technique in the observations of selected planetary systems
with the 1 m Turkish telescope T100 in TUBITAK National Observatory (TUG). With
this contribution, we aim to present preliminary analyses of transit light
curves of the selected exoplanets KELT-3b, HAT-P-10b/WASP-11b, HAT-P-20b, and
HAT-P-22b, observed with this technique using T100.


  Given a speaker's speech, it is interesting to see if it is possible to
generate this speaker's face. One main challenge in this task is to alleviate
the natural mismatch between face and speech. To this end, in this paper, we
propose a novel Attention-based Residual Speech Portrait Model (AR-SPM) by
introducing the ideal of the residual into a hybrid encoder-decoder
architecture, where face prior features are merged with the output of speech
encoder to form the final face feature. In particular, we innovatively
establish a tri-item loss function, which is a weighted linear combination of
the L2-norm, L1-norm and negative cosine loss, to train our model by comparing
the final face feature and true face feature. Evaluation on AVSpeech dataset
shows that our proposed model accelerates the convergence of training,
outperforms the state-of-the-art in terms of quality of the generated face, and
achieves superior recognition accuracy of gender and age compared with the
ground truth.


  The linearized Einstein equations in D spacetime dimensions can be written as
twisted self-duality equations expressing that the linearized curvature tensor
of the graviton described by a rank-two symmetric tensor, is dual to the
linearized curvature tensor of the "dual graviton" described by a tensor of
(D-3,1) Young symmetry type. In the case of 4 dimensions, both the graviton and
its dual are rank-two symmetric tensors (Young symmetry type (1,1)), while in
the case of 11 space-time dimensions relevant to M-theory, the dual graviton is
described by a tensor of (8,1) Young symmetry type. We provide in this paper an
action principle that yields the twisted self-duality conditions as equations
of motion, keeping the graviton and its dual on equal footing. In order to
construct a local, quadratic, variational principle for the twisted linear
self-duality equations, it is necessary to introduce two "prepotentials". These
are also tensors of mixed Young symmetry types and are obtained by solving the
Hamiltonian constraints of the Hamiltonian formulation either of the
Pauli-Fierz action for the graviton or of the Curtright action for its dual,
the resulting actions being identical. The prepotentials enjoy interesting
gauge invariance symmetries, which are exhibited and generalize the gauge
symmetries found in D=4. A variational principle where the basic variables are
the original Pauli-Fierz field and its dual can also be given but contrary to
the prepotential action, the corresponding action is non-local in space --
while remaining local in time. We also analyze in detail the Hamiltonian
structure of the theory and show that the graviton and its dual are canonically
conjugate in a sense made precise in the text.


  An algebraic theory, sometimes called an equational theory, is a theory
defined by finitary operations and equations, such as the theories of groups
and of rings. It is well known that algebraic theories are equivalent to
finitary monads on $\mathbf{Set}$. In this paper, we generalize this phenomenon
to locally finitely presentable categories using partial Horn logic. For each
locally finitely presentable category $\mathscr{A}$, we define an "algebraic
concept" relative to $\mathscr{A}$, which will be called an
$\mathscr{A}$-relative algebraic theory, and show that $\mathscr{A}$-relative
algebraic theories are equivalent to finitary monads on $\mathscr{A}$. In
establishing such equivalence, a generalized Birkhoff's variety theorem plays
an important role.


  The Bi-Te binary system, characterized by the homologous series of the
(Bi2)m(Bi2Te3)n, has always attracted research interest for its layered
structures and potential in advanced materials applications. Despite Bi2Te3 has
been extensively studied, exploration of other compounds has been constrained
by synthesis challenges. This study reports the molecular beam epitaxy (MBE)
growth of FeTe on Bi2Te3, demonstrating that varying growth conditions can turn
the Bi2Te3 layer into different Bi-Te phases and form corresponding FeTe/Bi-Te
heterostructures. Our combined analysis using reflection high-energy electron
diffraction (RHEED), high-resolution X-ray diffraction (HRXRD), and
high-resolution scanning transmission electron microscopy (HR-STEM), indicates
that specific growth conditions used for the growth of the FeTe layer can
facilitate the extraction of Te from Bi2Te3, leading to the formation of Bi4Te3
and Bi6Te3. Additionally, by lowering the FeTe growth temperature to 230 oC, Te
extraction from the Bi2Te3 layer could be avoided, preserving the Bi2Te3
structure. Notably, all the three FeTe/Bi-Te structures exhibit
superconductivity with the FeTe/Bi2Te3 heterostructure enjoying the highest
superconductivity quality. These findings introduce a novel method for
realizing Bi4Te3 and Bi6Te3 through Te extraction by growing FeTe on Bi2Te3,
driven by the high reactivity between Fe and Te. This approach holds promise
for synthesizing other members of the Bi-Te series, expanding the functional
potential of these materials.


  We analyze the small-scale clustering in "MegaZ-LRG", a large
photometric-redshift catalogue of Luminous Red Galaxies extracted from the
imaging dataset of the Sloan Digital Sky Survey. MegaZ-LRG, presented in a
companion paper, spans the redshift range 0.4 < z < 0.7 with an r.m.s. redshift
error dz ~ 0.03(1+z), covering 5,914 deg^2 to map out a total cosmic volume 2.5
h^-3 Gpc^3. In this study we use 380,000 photometric redshifts to measure
significant deviations from the canonical power-law fit to the angular
correlation function in a series of narrow redshift slices, in which we
construct volume-limited samples. These deviations are direct signatures of the
manner in which these galaxies populate the underlying network of dark matter
haloes. We cleanly delineate the separate contributions of the "1-halo" and
"2-halo" clustering terms and fit our measurements by parameterizing the halo
occupation distribution N(M) of the galaxies. Our results are successfully fit
by a "central" galaxy contribution with a "soft" transition from zero to one
galaxies, combined with a power-law "satellite" galaxy component, the slope of
which is a strong function of galaxy luminosity. The large majority of galaxies
are classified as central objects of their host dark matter haloes rather than
satellites in more massive systems. The effective halo mass of MegaZ-LRG
galaxies lies in the range log_10 (M_eff / h^-1 M_sol) = 13.61 - 13.8
(increasing with redshift, assuming large-scale normalization sigma_8 = 0.8)
for corresponding number densities in the range n_g = 5.03 - 0.56 x 10^-4 h^3
Mpc^-3. Our results confirm the usefulness of the halo model for gaining
physical insight into the patterns of galaxy clustering.


  Arbitrary-shaped text detection is a challenging task since curved texts in
the wild are of the complex geometric layouts. Existing mainstream methods
follow the instance segmentation pipeline to obtain the text regions. However,
arbitraryshaped texts are difficult to be depicted through one single
segmentation network because of the varying scales. In this paper, we propose a
two-stage segmentation-based detector, termed as NASK (Need A Second looK), for
arbitrary-shaped text detection. Compared to the traditional single-stage
segmentation network, our NASK conducts the detection in a coarse-to-fine
manner with the first stage segmentation spotting the rectangle text proposals
and the second one retrieving compact representations. Specifically, NASK is
composed of a Text Instance Segmentation (TIS) network (1st stage), a
Geometry-aware Text RoI Alignment (GeoAlign) module, and a Fiducial pOint
eXpression (FOX) module (2nd stage). Firstly, TIS extracts the augmented
features with a novel Group Spatial and Channel Attention (GSCA) module and
conducts instance segmentation to obtain rectangle proposals. Then, GeoAlign
converts these rectangles into the fixed size and encodes RoI-wise feature
representation. Finally, FOX disintegrates the text instance into serval
pivotal geometrical attributes to refine the detection results. Extensive
experimental results on three public benchmarks including Total-Text,
SCUTCTW1500, and ICDAR 2015 verify that our NASK outperforms recent
state-of-the-art methods.


  Vehicular networks enable vehicles support real-time vehicular applications
through training data. Due to the limited computing capability, vehicles
usually transmit data to a road side unit (RSU) at the network edge to process
data. However, vehicles are usually reluctant to share data with each other due
to the privacy issue. For the traditional federated learning (FL), vehicles
train the data locally to obtain a local model and then upload the local model
to the RSU to update the global model, thus the data privacy can be protected
through sharing model parameters instead of data. The traditional FL updates
the global model synchronously, i.e., the RSU needs to wait for all vehicles to
upload their models for the global model updating. However, vehicles may
usually drive out of the coverage of the RSU before they obtain their local
models through training, which reduces the accuracy of the global model. It is
necessary to propose an asynchronous federated learning (AFL) to solve this
problem, where the RSU updates the global model once it receives a local model
from a vehicle. However, the amount of data, computing capability and vehicle
mobility may affect the accuracy of the global model. In this paper, we jointly
consider the amount of data, computing capability and vehicle mobility to
design an AFL scheme to improve the accuracy of the global model. Extensive
simulation experiments have demonstrated that our scheme outperforms the FL
scheme


  By requiring invariance directly under the Yangian symmetry, we rederive
Beisert's quantum R-matrix, in a form that carries explicit dependence on the
representation labels, the braiding factors, and the spectral parameters u_i.
In this way, we demonstrate that there exist a rewriting of its entries, such
that the dependence on the spectral parameters is purely of difference form.
Namely, the latter enter only in the combination u_1-u_2, as indicated by the
shift automorphism of the Yangian. When recasted in this fashion, the entries
exhibit a cleaner structure, which allows to spot new interesting relations
among them. This permits to package them into a practical tensorial expression,
where the non-diagonal entries are taken care by explicit combinations of
symmetry algebra generators.


  In this paper we study an invariant for oriented three-manifolds with
$b_1>0$, which is defined using Heegaard splittings and the theta divisor of a
Riemann surface. The paper is divided into two parts, the first of which gives
the definition of the invariant, and the second of which identifies it with
more classical (torsion) invariants of three-manifolds. Its close relationship
with Seiberg-Witten theory is also addressed.


  A 2-dimensional discrete Boltzmann model for combustion is presented.
Mathematically, the model is composed of two coupled discrete Boltzmann
equations for two species and a phenomenological equation for chemical reaction
process. Physically, the model is equivalent to a reactive Navier-Stokes model
supplemented by a coarse-grained model for the thermodynamic nonequilibrium
behaviours. This model adopts 16 discrete velocities. It works for both
subsonic and supersonic combustion phenomena with flexible specific heat ratio.
To discuss the physical accuracy of the coarse-grained model for nonequilibrium
behaviours, three other discrete velocity models are used for comparisons.
Numerical results are compared with analytical solutions based on both the
first-order and second-order truncations of the distribution function. It is
confirmed that the physical accuracy increases with the increasing moment
relations needed by nonequlibrium manifestations. Furthermore, compared with
the single distribution function model, this model can simulate more details of
combustion.


  The workflow concept, proliferated through the recently emergent computer
supported cooperative work (CSCW) systems and workflow systems, advances
information systems (IS) implementation models by incorporating aspects of
collaboration and coordination in business processes. Under traditional
implementation models, applications are partitioned into discrete units of
functionality, with (typically) operational procedures used to describe how
human and computerised actions of business processes combine to deliver
business services. In this paper, a number of essential modelling concepts and
features for business transaction workflows are developed.


  The cosmic star formation rate density first increases with time towards a
pronounced peak 10 Gyrs ago (or z=1-2) and then slows down, dropping by more
than a factor 10 since z=1. The processes at the origin of the star formation
quenching are not yet well identified, either the gas is expelled by supernovae
and AGN feedback, or prevented to inflow. Morphological transformation or
environment effects are also invoked. Recent IRAM/NOEMA and ALMA results are
reviewed about the molecular content of galaxies and its dynamics, as a
function of redshift. Along the main sequence of massive star forming galaxies,
the gas fraction was higher in the past (up to 80\%), and galaxy disks were
more unstable and more turbulent.
  The star formation efficiency increases with redshift, or equivalently the
depletion time decreases, whatever the position of galaxies, either on the main
sequence or above. Attempts have been made to determine the cosmic evolution of
the H_2 density, but deeper ALMA observations are needed to effectively compare
with models.


  A new fit is done to obtain numerical values for the order $p^4$
low-energy-constants $L_i^r$ in Chiral Perturbation Theory. This includes both
new data and new calculated observables. We take into account masses, decay
constants, $K_{\ell4}$, $\pi\pi$ and $\pi K$ scattering lengths and slopes and
the slope of the pion scalar formfactor. We compare in detail where the changes
w.r.t. to the 10 year old "fit 10" come from. We discuss several scenarios for
estimating the order $p^6$ constants $C_i^r$ and search for possible values of
them that provide a good convergence for the ChPT series. We present two such
sets. One big change is that the fits do not have the expected behaviour in the
limit of large $N_c$ as well as before.


  Applications of large language models often involve the generation of
free-form responses, in which case uncertainty quantification becomes
challenging. This is due to the need to identify task-specific uncertainties
(e.g., about the semantics) which appears difficult to define in general cases.
This work addresses these challenges from a perspective of Bayesian decision
theory, starting from the assumption that our utility is characterized by a
similarity measure that compares a generated response with a hypothetical true
response. We discuss how this assumption enables principled quantification of
the model's subjective uncertainty and its calibration. We further derive a
measure for epistemic uncertainty, based on a missing data perspective and its
characterization as an excess risk. The proposed measures can be applied to
black-box language models. We demonstrate the proposed methods on question
answering and machine translation tasks, where they extract broadly meaningful
uncertainty estimates from GPT and Gemini models and quantify their
calibration.


  We prove that for extended Dynkin quivers, simple perverse sheaves in Lusztig
category are characterized by the nilpotency of their singular support. This
proves a conjecture of Lusztig in the case of affine quivers. For cyclic
quivers, we prove a similar result for a larger nilpotent variety and a larger
class of perverse sheaves. We formulate conjectures for similar results for
quivers with loops, for which we have to use the appropriate notion of
nilpotent variety, due to Bozec, Schiffmann and Vasserot. We prove our
conjecture for $g$-loops quivers ($g\geq 2$).


  It is shown that `bipartite' wave functions can present a mathematical
formalism of quantum theory for a single particle, in which the associated
Schr\"{o}dinger's wave functions correspond to those `bipartite' wave functions
of product forms. This extension of Schr\"{o}dinger's form establishes a
mathematical expression of wave-particle duality and that von Neumann's entropy
is a quantitative measure of complementarity between wave-like and
particle-like behaviors. In particular, this formalism suggests that collapses
of Schr\"{o}dinger's wave functions can be regarded as the simultaneous
transition of the particle from many levels to one. Our results shed
considerable light on the basis of quantum mechanics, including quantum
measurement.


  The Calabi-Yau differential equations of degree 2 and 3 are listed. The idea
is to bring some order into the "big table" into the "big table" (math.
AG/0507430). The author has benefitted from an unpublished result by Yifan
Yang, which reduces the degree of many equations. Also difference equations
(giving rise to Calabi-Yau differential equations) of order 2 and 3 are
studied.


  Some thoughts regarding pairing in atomic Fermi gases were considered, meant
for starting discussion on the topic.


  We have proposed and demonstrated an effective scheme to steer both the
electronic and molecular motions of hydrogen molecule and its isotopes. Our
scheme lies in the idea of sub-cycle waveform shaping (SWS) with synthesizing
coherent IR pulses of different wavelengths. The quantum model simulation
indicates a remarkable enhancement of the electron localization asymmetry
compared with the few-cycle pulse. 68% and 89% electrons of the dissociating
fragmentation can be localized to one nucleus for H_2^+ and H_2, respectively.


  The doping dependence of the critical current density, $J_{c}$, was measured
in a series of high quality c-axis oriented ${\rm Bi_2Sr_2CaCu_2O_{8+\delta}}$
thin films. For each doping level we measured the temperature dependence of
$J_{c}$. We find that all samples have the same temperature dependence, but the
critical current at zero temperature, $J_{c}(0)$, has a non-trivial doping
dependence with a maximum at a unique doping level in the overdoped side of the
superconducting dome.


  We derive an upper bound for the expected gain of informed traders in the
Glosten-Milgrom model with finite horizon, fully analogous to a generalized
second law of thermodynamics. This result extends that obtained by Touzo et al.
a couple of years ago. The proof relies on Bayesian inference (exploiting the
invariance of the problem under consecutive game sequences) and an interesting
entropic inequality. We also provide numerical results both supporting the
existence of a characteristic timescale in the model and illustrating the
magnitude of gain fluctuations. Other possible extensions are discussed.


  This paper describes a novel scheme for integrating a coherent THz source in
the baseline of the LCLS facility. Any method relying on the spent electron
beam downstream of the baseline undulator should provide a way of transporting
the radiation up to the experimental floor. Here we propose to use the dump
area access maze. In this way the THz output must propagate with limited size
at least for one hundred meters in a maze, following many turns, to reach the
near experimental hall. The use of a standard, discrete, open beam-waveguide
formed by periodic reflectors, that is a mirror guide, would lead to
unacceptable size of the system. To avoid these problems, in this paper we
propose an alternative approach based on periodically spaced metallic screens
with holes. This quasi-optical transmission line is referred to as an iris
line. We present complete calculations for the iris line using both analytical
and numerical methods, which we find in good agreement. We present a design of
a THz edge radiation source based on the use of an iris line. The proposed
setup takes almost no cost nor time to be implemented at the LCLS baseline, and
can be used at other facilities as well. The edge radiation source is limited
in maximally achievable field strength at the sample. An extension based on the
use of an undulator in the presence of the iris line, which is feasible at the
LCLS energies, is proposed as a possible upgrade of the baseline THz source.


  A space is called Dieudonn\'{e} complete if it is complete relative to the
maximal uniform structure compatible with its topology. In this paper, we
investigated when the function space $C(X,Y)$ of all continuous functions from
a topological space $X$ into a uniform space $Y$ with the topology of uniform
convergence on a family of subsets of $X$ is Dieudonn\'{e} complete. Also we
proved a generalization of the Eberlein-\v{S}mulian theorem to the class of
Banach spaces.


  We study how the presence of a background magnetic field, of intensity
compatible with current observation constraints, affects the linear evolution
of cosmological density perturbations at scales below the Hubble radius. The
magnetic field provides an additional pressure that can prevent the growth of a
given perturbation; however, the magnetic pressure is confined only to the
plane orthogonal the field. As a result, the "Jeans length" of the system not
only depends on the wavelength of the fluctuation but also on its direction,
and the perturbative evolution is anisotropic. We derive this result
analytically and back it up with direct numerical integration of the relevant
ideal magnetohydrodynamics equations during the matter-dominated era. Before
recombination, the kinetic pressure dominates and the perturbations evolve in
the standard way, whereas after that time magnetic pressure dominates and we
observe the anisotropic evolution. We quantify this effect by estimating the
eccentricity $\epsilon$ of a Gaussian perturbation in the coordinate space that
was spherically symmetric at recombination. For perturbations at the
sub-galactic scale, we find that $\epsilon = 0.7$ at $z=10$ taking the
background magnetic field of order $10^{-9}$ gauss.


  Let $M = G/H$ be a connected simply connected homogeneous manifold of a
compact, not necessarily connected Lie group $G$. We will assume that the
isotropy $H$-module $\mathfrak {g/h}$ has a simple spectrum, i.e. irreducible
submodules are mutually non-equivalent.
  There exists a convex Newton polytope $N=N(G,H)$, which was used for the
estimation of the number of isolated complex solutions of the algebraic
Einstein equation for invariant metrics on $G/H$ (up to scaling). Using the
moment map, we identify the space $\mathcal{M}_1$ of invariant Riemannian
metrics of volume 1 on $G/H$ with the interior of this polytope $N$.
  We associate with a point ${x \in \partial N}$ of the boundary a homogeneous
Riemannian space (in general, only local) and we extend the Einstein equation
to $\bar{\mathcal{M}_1}= N$. As an application of the Aleksevsky--Kimel'fel'd
theorem, we prove that all solutions of the Einstein equation associated with
points of the boundary are locally Euclidean.
  We describe explicitly the set $T\subset \partial N$ of solutions at the
boundary together with its natural triangulation.
  Investigating the compactification $\bar{\mathcal{M}_1} $ of $\mathcal{M}_1$,
we get an algebraic proof of the deep result by B\"ohm, Wang and Ziller about
the compactness of the set $ \mathcal{E}_1 \subset \mathcal{M}_1$ of Einstein
metrics. The original proof by B\"ohm, Wang and Ziller was based on a different
approach and did not use the simplicity of the spectrum.
  In Appendix we consider the non-symmetric K\"ahler homogeneous spaces $G/H$
with the second Betti number $b_2=1$. We write the normalized volumes
$2,6,20,82,344$ of the corresponding Newton polytopes and discuss the number of
complex solutions of the algebraic Einstein equation and the finiteness
problem.


  Ultra-high dose rate radiation therapy (FLASH) based on proton irradiation is
of major interest for cancer treatments but creates new challenges for dose
monitoring. Amorphous hydrogenated silicon is known to be one of the most
radiation-hard semiconductors. In this study, detectors based on this material
are investigated at proton dose rates similar to or exceeding those required
for FLASH therapy. Tested detectors comprise two different types of contacts,
two different thicknesses deposited either on glass or on polyimide substrates.
All detectors exhibit excellent linear behaviour as a function of dose rate up
to a value of 20 kGy/s. Linearity is achieved independently of the depletion
condition of the device and remarkably in passive (unbiased) conditions. The
degradation of the performance as a function of the dose rate and its recovery
are also discussed.


  Galama et al. have recently reported their follow-up measurements of the
radio afterglow (AG) of the Gamma Ray Burst (GRB) 991208, up to 293 days after
burst, and their reanalysis of the broad-band AG, in the framework of standard
fireball models. They advocate a serious revision of their prior analysis and
conclusions, based on optical data and on their earlier observations during the
first two weeks of the AG. We comment on their work and fill a lacuna: these
authors have overlooked the possibility of comparing their new data to the
available predictions of the cannonball (CB) model, based --like their
incorrect predictions-- on the first round of data. The new data are in good
agreement with these CB-model predictions. This is in spite of the fact that,
in comparison to the fireball models, the CB model is much simpler, much more
predictive, has many fewer parameters, practically no free choices... and it
describes well --on a universal basis-- all the measured AGs of GRBs of known
redshift.


  The reversible Markov chains that drive the data augmentation (DA) and
sandwich algorithms define self-adjoint operators whose spectra encode the
convergence properties of the algorithms. When the target distribution has
uncountable support, as is nearly always the case in practice, it is generally
quite difficult to get a handle on these spectra. We show that, if the
augmentation space is finite, then (under regularity conditions) the operators
defined by the DA and sandwich chains are compact, and the spectra are finite
subsets of $[0,1)$. Moreover, we prove that the spectrum of the sandwich
operator dominates the spectrum of the DA operator in the sense that the
ordered elements of the former are all less than or equal to the corresponding
elements of the latter. As a concrete example, we study a widely used DA
algorithm for the exploration of posterior densities associated with Bayesian
mixture models [J. Roy. Statist. Soc. Ser. B 56 (1994) 363--375]. In
particular, we compare this mixture DA algorithm with an alternative algorithm
proposed by Fr\"{u}hwirth-Schnatter [J. Amer. Statist. Assoc. 96 (2001)
194--209] that is based on random label switching.


  Residue complexes were introduced by Grothendieck in algebraic geometry.
These are canonical complexes of injective modules that enjoy remarkable
functorial properties (traces).
  In this paper we study residue complexes over noncommutative rings. These
objects are even more complicated than in the commutative case, since they are
complexes of bimodules. We develop methods to prove uniqueness, existence and
functoriality of residue complexes.
  For a noetherian affine PI algebra over a field (admitting a noetherian
connected filtration) we prove existence of the residue complex and describe
its structure in detail.


  We study dynamics of an artificial two-level atom in an open 1D space by
measuring evolution of its coherent and incoherent emission. States of the atom
-- a superconducting flux qubit coupled to a transmission line -- are fully
controlled by resonant excitation microwave pulses. The coherent emission -- a
direct measure of superposition in the atom -- exhibits decaying oscillations
shifted by $\pi/2$ from oscillations of the incoherent emission, which, in
turn, is proportional to the atomic population. The emission dynamics provides
information about states and properties of the atom. By measuring the coherent
dynamics, we derive two-time correlation function of fluctuations and, using
quantum regression formula, reconstruct the incoherent spectrum of the
resonance fluorescence triplet, which is in a good agreement with the directly
measured one.


  In this paper we give characterizations of mappings generate embeddings of
Sobolev spaces in the terms of ring capacity inequalities. In addition we prove
that such mappings are Lipschitz mappings in the sub-hyperbolic type capacitory
metrics.


  Our research is concerned with studying behavioural changes within a dynamic
system, i.e. health care, and their effects on the decision-making process.
Evolutionary Game theory is applied to investigate the most probable
strategy(ies) adopted by individuals in a finite population based on the
interactions among them with an eye to modelling behaviour using the following
metrics: cost of investment, cost of management, cost of treatment, reputation
benefit for the provider(s), and the gained health benefit for the patient.


  The propagation of infectious diseases and its impact on individuals play a
major role in disease dynamics, and it is important to incorporate population
heterogeneity into efforts to study diseases. As a simplistic but illustrative
example, we examine interactions between urban and rural populations in the
dynamics of disease spreading. Using a compartmental framework of
susceptible--infected--susceptible ($\mathrm{SI\widetilde{S}}$) dynamics with
some level of immunity, we formulate a model that allows nonlinear reinfection.
We investigate the effects of population movement in the simplest scenario: a
case with two patches, which allows us to model movement between urban and
rural areas. To study the dynamics of the system, we compute a basic
reproduction number for each population (urban and rural). We also compute
steady states, determine the local stability of the disease-free steady state,
and identify conditions for the existence of endemic steady states. From our
analysis and computational experiments, we illustrate that population movement
plays an important role in disease dynamics. In some cases, it can be rather
beneficial, as it can enlarge the region of stability of a disease-free steady
state.


  For any positive integer r, the r-associated Stirling number of the second
kind enumerates the number of partitions of the set{1,2,3,...,n} into k
non-empty disjoint subsets such that each subset contains at least r elements.
We introduce the degenerate r-associated Stirling numbers of the second kind
and of the first kind. They are degenerate versions of the r-associated
Stirling numbers of the second kind and of the first kind, and reduce to the
degenerate Stirling numbers of the second kind and of the first kind for r=1.
The aim of this paper is to derive recurrence relations for both of those
numbers.


  In this paper, we let $\Hecke$ be the Hecke algebra associated with a finite
Coxeter group $W$ and with one-parameter, over the ring of scalars
$\Alg=\mathbb{Z}(q, q^{-1})$. With an elementary method, we introduce a
cellular basis of $\Hecke$ indexed by the sets $E_J (J\subseteq S)$ and obtain
a general theory of "Specht modules". We provide an algorithm for $W\!$-graphs
for the "generic Specht module", which associates with the Kazhdan and Lusztig
cell ( or more generally, a union of cells of $W$ ) containing the longest
element of a parabolic subgroup $W_J$ for appropriate $J\subseteq S$. As an
example of applications, we show a construction of $W\!$-graphs for the Hecke
algebra of type $A$.


  A Nitche's method is presented to couple different mechanical models. They
include coupling of a solid and a beam and of a solid and a plate. Both
conforming and non-conforming formulations are presented. In a non-conforming
for- mulation, the structure domain is overlapped by a refined solid model.
Applications can be found in multi-dimensional analyses in which parts of a
structure are modeled with solid elements and others are modeled using a
coarser model with beam and/or plate elements. Discretisations are performed
using both standard Lagrange elements and high order NURBS (Non Uniform
Rational Bsplines) based isogeometric elements. We present various examples to
demonstrate the performance of the method.


  Measurements of normalized differential top-quark-pair ($t\bar{t}$)
production cross sections are performed using final states with two leptons
($e^+e^-$, $\mu^+\mu^-$, and $e^\pm\mu^\mp$) in proton-proton ($pp$) collisions
at $\sqrt{s}$ = 13 TeV at the CERN LHC. The data were recorded in 2015 with the
CMS detector and correspond to an integrated luminosity of 2.2 fb$^{-1}$. The
$t\bar{t}$ production cross section is measured as a function of kinematic
properties of the top quarks and the $t\bar{t}$ system in the full phase space,
as well as of the jet multiplicity in the event in the fiducial phase space.
Several perturbative quantum chromodynamics (QCD) calculations are confronted
with the data and are found to be broadly in agreement with the measured
results.


  This paper presents a geoneutrino measurement using 3262.74 days of data
taken with the Borexino detector at LNGS in Italy. By observing $52.6
^{+9.4}_{-8.6} ({\rm stat}) ^{+2.7}_{-2.1}({\rm sys})$ geoneutrinos (68%
interval) from $^{238}$U and $^{232}$Th, a signal of $47.0^{+8.4}_{-7.7}\,({\rm
stat)}^{+2.4}_{-1.9}\,({\rm sys})$ TNU with $^{+18.3}_{-17.2}$% total precision
was obtained. This result assumes the same Th/U mass ratio found in chondritic
CI meteorites but compatible results were found when contributions from
$^{238}$U and $^{232}$Th were fit as free parameters. Antineutrino background
from reactors is fit unconstrained and found compatible with the expectations.
The null-hypothesis of observing a signal from the mantle is excluded at a
99.0% C.L. when exploiting the knowledge of the local crust. Measured mantle
signal of $21.2 ^{+9.6}_{-9.0} ({\rm stat})^{+1.1}_{-0.9} ({\rm sys})$ TNU
corresponds to the production of a radiogenic heat of $24.6 ^{+11.1}_{-10.4}$
TW (68% interval) from $^{238}$U and $^{232}$Th in the mantle. Assuming 18%
contribution of $^{40}$K in the mantle and $8.1^{+1.9}_{-1.4}$ TW of radiogenic
heat of the lithosphere, the Borexino estimate of the total Earth radiogenic
heat is $38.2 ^{+13.6}_{-12.7}$ TW, corresponding to a convective Urey ratio of
0.78$^{+0.41}_{-0.28}$. These values are compatible with different geological
models, however there is a 2.4$\sigma$ tension with those which predict the
lowest concentration of heat-producing elements. By fitting the data with a
constraint on the reactor antineutrino background, the existence of a
hypothetical georeactor at the center of the Earth having power greater than
2.4 TW at 95% C.L. is excluded. Particular attention is given to all analysis
details, which should be of interest for the next generation geoneutrino
measurements.


  The Universal Feature Selection Tool (UniFeat) is an open-source tool
developed entirely in Java for performing feature selection processes in
various research areas. It provides a set of well-known and advanced feature
selection methods within its significant auxiliary tools. This allows users to
compare the performance of feature selection methods. Moreover, due to the
open-source nature of UniFeat, researchers can use and modify it in their
research, which facilitates the rapid development of new feature selection
algorithms.


  Sequential recommendation systems are integral to discerning temporal user
preferences. Yet, the task of learning from abbreviated user interaction
sequences poses a notable challenge. Data augmentation has been identified as a
potent strategy to enhance the informational richness of these sequences.
Traditional augmentation techniques, such as item randomization, may disrupt
the inherent temporal dynamics. Although recent advancements in reverse
chronological pseudo-item generation have shown promise, they can introduce
temporal discrepancies when assessed in a natural chronological context. In
response, we introduce a sophisticated approach, Bidirectional temporal data
Augmentation with pre-training (BARec). Our approach leverages bidirectional
temporal augmentation and knowledge-enhanced fine-tuning to synthesize
authentic pseudo-prior items that \emph{retain user preferences and capture
deeper item semantic correlations}, thus boosting the model's expressive power.
Our comprehensive experimental analysis confirms the superiority of BARec
across both short and elongated sequence contexts. Moreover, theoretical
examination and visual representation of item embeddings offer further insight
into the model's logical processes and interpretability. The source code for
our study is available at
\textcolor{blue}{\href{https://github.com/juyongjiang/BARec}{https://github.com/juyongjiang/BARec}}.


  In this paper we use current and proposed final doublet magnet technologies
to reoptimise the interaction region of the International Linear Collider and
reduce the power losses. The result is a set of three new final doublet layouts
with improved beam transport properties. The effect of localised power
deposition is considered, and its reduction using Tungsten liners.


  Self-supported electrocatalysts being generated and employed directly as
electrode for energy conversion has been intensively pursued in the fields of
materials chemistry and energy. Herein, we report a synthetic strategy to
prepare freestanding hierarchically structured, nitrogen-doped nanoporous
graphitic carbon membranes functionalized with Janus-type Co/CoP nanocrystals
(termed as HNDCM-Co/CoP), which were successfully applied as a
highly-efficient, binder-free electrode in hydrogen evolution reaction (HER).
Benefited from multiple structural merits, such as high degree of
graphitization, three-dimensionally interconnected micro-/meso-/macropores,
uniform nitrogen-doping, well-dispersed Co/CoP nanocrystals as well as the
confinement effect of the thin carbon layer on the nanocrystals, HNDCM-Co/CoP
exhibited superior electrocatalytic activity and long-term operation stability
for HER under both acid and alkaline conditions. As a proof-of-concept of
practical usage, a macroscopic piece of HNDCM-Co/CoP of 5.6 cm x 4 cm x 60 um
in size was prepared in our laboratory. Driven by a solar cell,
electroreduction of water in alkaline condition (pH 14) was performed, and H2
has been produced at a rate of 16 ml/min, demonstrating its potential as
real-life energy conversion systems.


  Denoising Diffusion Models (DDM) are emerging as the cutting-edge technology
in the realm of deep generative modeling, challenging the dominance of
Generative Adversarial Networks. However, effectively exploring the latent
space's semantics and identifying compelling trajectories for manipulating and
editing important attributes of the generated samples remains challenging,
primarily due to the high-dimensional nature of the latent space. In this
study, we specifically concentrate on face rotation, which is known to be one
of the most intricate editing operations. By leveraging a recent embedding
technique for Denoising Diffusion Implicit Models (DDIM), we achieve, in many
cases, noteworthy manipulations encompassing a wide rotation angle of $\pm
30^o$, preserving the distinct characteristics of the individual. Our
methodology exploits the computation of trajectories approximating clouds of
latent representations of dataset samples with different yaw rotations through
linear regression. Specific trajectories are obtained by restricting the
analysis to subsets of data sharing significant attributes with the source
image. One of these attributes is the light provenance: a byproduct of our
research is a labeling of CelebA, categorizing images into three major groups
based on the illumination direction: left, center, and right.


  We associate a fractal in $\RPn$ to each vector basis of $\bR^{n+1}$ and we
study its measure and asymptotic properties. Then we discuss and study
numerically in detail the cases $n=1,2,3$, evaluating in particular their
Hausdorff dimension.


  We present $^{56}$Ni mass estimates for 110 normal Type II supernovae (SNe
II), computed here from their luminosity in the radioactive tail. This sample
consists of SNe from the literature, with at least three photometric
measurements in a single optical band within 95-320 d since explosion. To
convert apparent magnitudes to bolometric ones, we compute bolometric
corrections (BCs) using 15 SNe in our sample having optical and near-IR
photometry, along with three sets of SN II atmosphere models to account for the
unobserved flux. We find that the $I$- and $i$-band are best suited to estimate
luminosities through the BC technique. The $^{56}$Ni mass distribution of our
SN sample has a minimum and maximum of 0.005 and 0.177 M$_{\odot}$,
respectively, and a selection-bias-corrected average of $0.037\pm0.005$
M$_{\odot}$. Using the latter value together with iron isotope ratios of two
sets of core-collapse (CC) nucleosynthesis models, we calculate a mean iron
yield of $0.040\pm0.005$ M$_{\odot}$ for normal SNe II. Combining this result
with recent mean $^{56}$Ni mass measurements for other CC SN subtypes, we
estimate a mean iron yield $<$0.068 M$_{\odot}$ for CC SNe, where the
contribution of normal SNe II is $>$36 per cent. We also find that the
empirical relation between $^{56}$Ni mass and steepness parameter ($S$) is
poorly suited to measure the $^{56}$Ni mass of normal SNe II. Instead, we
present a correlation between $^{56}$Ni mass, $S$, and absolute magnitude at 50
d since explosion. The latter allows to measure $^{56}$Ni masses of normal SNe
II with a precision around 30 per cent.


  The combination of two-dimensional (2D) materials into heterostructures
enabled the formation of atomically thin devices with designed properties. To
achieve a high density, bottom-up integration, the growth of these 2D
heterostructures via van der Waals epitaxy (vdWE) is an attractive alternative
to the currently mostly employed mechanical transfer, which is still
problematic in terms of scaling and reproducibility. However, controlling the
location of the nuclei formation remains a key challenge in vdWE. Here, we use
a focused He ion beam for a deterministic placement of defects in graphene
substrates, which act as preferential nucleation sites for the growth of
insulating, 2D hexagonal boron nitride (h-BN). We demonstrate a mask-free,
selective-area vdWE (SAvdWE), where nucleation yield and crystal quality of
h-BN is controlled by the ion beam parameter used for the defect formation.
Moreover, we show that h-BN grown via SAvdWE has electron tunneling
characteristics comparable to those of mechanically transferred layers, thereby
lying the foundation for a reliable, high density array fabrication of 2D
heterostructures for device integration via defect engineering in 2D
substrates.


  This article focuses on finding the eigenvalues of the Laplacian matrix of
the comaximal graph $\Gamma(\mathbb Z_n)$ of the ring $\mathbb Z_n$ for $n> 2$.
We determine the eigenvalues of $\Gamma(\mathbb Z_n)$ for various $n$ and also
provide a procedure to find the eigenvalues of $\Gamma(\mathbb Z_n)$ for any
$n> 2$. We show that $\Gamma(\mathbb Z_n)$ is Laplacian Integral for
$n=p^\alpha q^\beta$ where $p,q$ are primes and $\alpha, \beta$ are
non-negative integers. The algebraic and vertex connectivity of $\Gamma(\mathbb
Z_n)$ have been shown to be equal for all $n> 2$. An upper bound on the second
largest eigenvalue of $\Gamma(\mathbb Z_n)$ has been obtained and a necessary
and sufficient condition for its equality has also been determined. Finally we
discuss the multiplicity of the spectral radius and the multiplicity of the
algebraic connectivity of $\Gamma(\mathbb Z_n)$. Some problems have been
discussed at the end of this article for further research.


  Contribution of nearby pulsars to the cosmic rays observed at Earth has been
studied. It is found that the experimental bound on amplitude of cosmic ray
anisotropy may produce significant constraint on the efficiency of converting
pulsar rotational energy to emitted particles kinetic energy. Cosmic ray fluxes
from two well known nearby gamma ray pulsars, namely the Vela and Geminga
pulsars, are estimated. The analysis suggests that observed bound on cosmic ray
anisotropy restricts the contributions of the Vela and the Geminga pulsars to
at most 1 % of the observed cosmic rays below the knee.


  For every $n\ge 2$, we construct a body $U_n$ of constant width $2$ in
$\mathbb{E}^n$ with small volume and symmetries of a regular $n$-simplex. $U_2$
is the Reuleaux triangle. To the best of our knowledge, $U_3$ was not
previously constructed, and its volume is smaller than the volume of other
three-dimensional bodies of constant width with tetrahedral symmetries. While
the volume of $U_3$ is slightly larger than the volume of Meissner's bodies of
width $2$, it exceeds the latter by less than $0.137\%$. For all large $n$, the
volume of $U_n$ is smaller than the volume of the ball of radius $0.891$.


  Recently, we have been witnessing the scale-up of superconducting quantum
computers; however, the noise of quantum bits (qubits) is still an obstacle for
real-world applications to leveraging the power of quantum computing. Although
there exist error mitigation or error-aware designs for quantum applications,
the inherent fluctuation of noise (a.k.a., instability) can easily collapse the
performance of error-aware designs. What's worse, users can even not be aware
of the performance degradation caused by the change in noise. To address both
issues, in this paper we use Quantum Neural Network (QNN) as a vehicle to
present a novel compression-aided framework, namely QuCAD, which will adapt a
trained QNN to fluctuating quantum noise. In addition, with the historical
calibration (noise) data, our framework will build a model repository offline,
which will significantly reduce the optimization time in the online adaption
process. Emulation results on an earthquake detection dataset show that QuCAD
can achieve 14.91% accuracy gain on average in 146 days over a noise-aware
training approach. For the execution on a 7-qubit IBM quantum processor,
IBM-Jakarta, QuCAD can consistently achieve 12.52% accuracy gain on earthquake
detection.


  Recently, the combination of machine learning (ML) and simulation is gaining
a lot of attention. This paper presents a novel application of ML within the
simulation to improve patient flow within an emergency department (ED). An ML
model used within a real ED simulation model to quantify the effect of
detouring a patient out of the ED on the length of stay (LOS) and
door-to-doctor time (DTDT) as a response to the prediction of patient admission
to the hospital from the ED. The ML model trained using a set of six features
including the patient age, arrival day, arrival hour of the day, and the triage
level. The prediction model used a decision tree (DT) model, which is trained
using historical data achieves a 75% accuracy. The set of rules extracted from
the DT are coded within the simulation model. Given a certain probability of
free inpatient beds, the predicted admitted patient is then pulled out from the
ED to inpatient units to alleviate the crowding within the ED. The used policy
combined with adding specific ED resources achieve 9.39% and 8.18% reduction in
LOS and DTDT, respectively.


  Thermodynamic description of a model system with magnetoelastic coupling is
presented. The elastic, vibrational, electronic and magnetic energy
contributions are taken into account. The long-range RKKY interaction is
considered together with the nearest-neighbour direct exchange. The generalized
Gibbs potential and the set of equations of state are derived, from which all
thermodynamic functions are self-consistently obtained. Thermodynamic
properties are calculated numerically for FCC structure for arbitrary external
pressure, magnetic field and temperature, and widely discussed. In particular,
for some parameters of interaction potential and electron concentration
corresponding to antiferromagnetic phase, the existence of negative thermal
expansion coefficient is predicted.


  This work aims to provide an alternative approach to modeling a two-state
system (qubit) coupled to a nonlinear oscillator. Within a single algebraic
scheme based upon the f-deformed oscillator description, hard and soft
nonlinearities are proposed to be simulated by making use of fitting algebraic
models extracted from the trigonometric and modified P\"oschl-Teller
potentials, respectively. In the regime where the strength of the coupling is
considered to be moderate, this approach allows for an analytic, albeit
approximate, diagonalization process of the proposed Hamiltonian through using
the Van Vleck perturbation theory and embracing the two types of nonlinear
features. In the ultrastrong-coupling regime, the effect of such nonlinearities
upon the squeezing and phase space properties of the ground state of the
composite system is also explored by numerical means.


  The blockchain data structure maintained via the longest-chain
rule---popularized by Bitcoin---is a powerful algorithmic tool for consensus
algorithms. Such algorithms achieve consistency for blocks in the chain as a
function of their depth from the end of the chain. While the analysis of
Bitcoin guarantees consistency with error $2^{-k}$ for blocks of depth $O(k)$,
the state-of-the-art of proof-of-stake (PoS) blockchains suffers from a
quadratic dependence on $k$: these protocols, exemplified by Ouroboros (Crypto
2017), Ouroboros Praos (Eurocrypt 2018) and Sleepy Consensus (Asiacrypt 2017),
can only establish that depth $\Theta(k^2)$ is sufficient. Whether this
quadratic gap is an intrinsic limitation of PoS---due to issues such as the
nothing-at-stake problem---has been an urgent open question, as deployed PoS
blockchains further rely on consistency for protocol correctness.
  We give an axiomatic theory of blockchain dynamics that permits rigorous
reasoning about the longest-chain rule and achieve, in broad generality,
$\Theta(k)$ dependence on depth in order to achieve consistency error $2^{-k}$.
In particular, for the first time, we show that PoS protocols can match
proof-of-work protocols for linear consistency. We analyze the associated
stochastic process, give a recursive relation for the critical functionals of
this process, and derive tail bounds in both i.i.d. and martingale settings via
associated generating functions.


  We study pseudo Yang-Mills fields on a compact strictly pseudoconvex CR
manifold.


  We present an algebraic approach to the internal structure of baryons in
terms of three constituents. We investigate a collective model in which the
nucleon is regarded as a rotating and vibrating oblate top with a prescribed
distribution of charges and magnetization. We contrast the collective and
single-particle descriptions of baryons and compare the predictions of the
model with existing data on masses, electromagnetic elastic and transition form
factors and strong decays widths.


  This paper introduces a generalized few-shot segmentation framework with a
straightforward training process and an easy-to-optimize inference phase. In
particular, we propose a simple yet effective model based on the well-known
InfoMax principle, where the Mutual Information (MI) between the learned
feature representations and their corresponding predictions is maximized. In
addition, the terms derived from our MI-based formulation are coupled with a
knowledge distillation term to retain the knowledge on base classes. With a
simple training process, our inference model can be applied on top of any
segmentation network trained on base classes. The proposed inference yields
substantial improvements on the popular few-shot segmentation benchmarks,
PASCAL-$5^i$ and COCO-$20^i$. Particularly, for novel classes, the improvement
gains range from 7% to 26% (PASCAL-$5^i$) and from 3% to 12% (COCO-$20^i$) in
the 1-shot and 5-shot scenarios, respectively. Furthermore, we propose a more
challenging setting, where performance gaps are further exacerbated. Our code
is publicly available at https://github.com/sinahmr/DIaM.


  We study the tail asymptotic of the stationary joint queue length
distribution for a generalized Jackson network (GJN for short), assuming its
stability. For the two station case, this problem has been recently solved in
the logarithmic sense for the marginal stationary distributions under the
setting that arrival processes and service times are of phase-type. In this
paper, we study similar tail asymptotic problems on the stationary
distribution, but problems and assumptions are different. First, the
asymptotics are studied not only for the marginal distribution but also the
stationary probabilities of state sets of small volumes. Second, the
interarrival and service times are generally distributed and light tailed, but
of phase type in some cases. Third, we also study the case that there are more
than two stations, although the asymptotic results are less complete. For them,
we develop a martingale method, which has been recently applied to a single
queue with many servers by the author.


  Training self-driving systems to be robust to the long-tail of driving
scenarios is a critical problem. Model-based approaches leverage simulation to
emulate a wide range of scenarios without putting users at risk in the real
world. One promising path to faithful simulation is to train a forward model of
the world to predict the future states of both the environment and the
ego-vehicle given past states and a sequence of actions. In this paper, we
argue that it is beneficial to model the state of the ego-vehicle, which often
has simple, predictable and deterministic behavior, separately from the rest of
the environment, which is much more complex and highly multimodal. We propose
to model the ego-vehicle using a simple and differentiable kinematic model,
while training a stochastic convolutional forward model on raster
representations of the state to predict the behavior of the rest of the
environment. We explore several configurations of such decoupled models, and
evaluate their performance both with Model Predictive Control (MPC) and direct
policy learning. We test our methods on the task of highway driving and
demonstrate lower crash rates and better stability. The code is available at
https://github.com/vladisai/pytorch-PPUU/tree/ICLR2022.


  We propose an adaptive threshold multi secret sharing scheme based solely on
cryptographically secure hash functions. We show that the proposed scheme is
also: perfect, ideal, verifiable, and proactive. Moreover the proposed scheme
has a low computational complexity comparing to the most common schemes
operating over finite fields.


  ImageNet serves as the primary dataset for evaluating the quality of
computer-vision models. The common practice today is training each architecture
with a tailor-made scheme, designed and tuned by an expert. In this paper, we
present a unified scheme for training any backbone on ImageNet. The scheme,
named USI (Unified Scheme for ImageNet), is based on knowledge distillation and
modern tricks. It requires no adjustments or hyper-parameters tuning between
different models, and is efficient in terms of training times. We test USI on a
wide variety of architectures, including CNNs, Transformers, Mobile-oriented
and MLP-only. On all models tested, USI outperforms previous state-of-the-art
results. Hence, we are able to transform training on ImageNet from an
expert-oriented task to an automatic seamless routine. Since USI accepts any
backbone and trains it to top results, it also enables to perform methodical
comparisons, and identify the most efficient backbones along the speed-accuracy
Pareto curve. Implementation is available
at:https://github.com/Alibaba-MIIL/Solving_ImageNet


  We present observations of the singly and doubly deuterated species of
thioformaldehyde, HDCS and D$_2$CS, towards the dark cloud Barnard 1. This is
the first detection of D$_2$CS in Space and in dense and cold prestellar
regions. Column densities obtained using rotational diagrams and a Large
Velocity Gradient model show an extremely high D-enhancement in
thioformaldehyde in Barnard 1. Although the column density of H$_2$CS is
smaller than that of H$_2$CO, both species show similar D-enhancements in their
singly and doubly deuterated species. A chemical model -including multiply
deuterated species- has been used in order to interpret the observations.
  Predicted rotational frequencies from laboratory data for HDCS and D$_2$CS
are significantly in error when compared to the observed frequencies in Space.
Consequently, we have derived new rotational constants for these two species
and for H$_2$CS and H$_2$C$^{34}$S using the observed frequencies in Barnard 1.
The new rotational constants allow to predict the rotational transitions of
these species with the accuracy needed for the narrow line emerging from dark
clouds. Rotational constants for HDCS and D$_2$CS have been obtained from the
observed transitions in the laboratory and in Space.


  The complete point symmetry group of the barotropic vorticity equation on the
sphere is determined. The method we use relies on the invariance of megaideals
of the maximal Lie invariance algebra of a system of differential equations
under automorphisms generated by the associated group. A convenient set of
megaideals is found for the maximal Lie invariance algebra of the spherical
vorticity equation. We prove that there are only two independent (up to
composition with continuous point symmetry transformations) discrete symmetries
for this equation.


  The mobility of a Kaehler metric is the dimension of the space of metrics
with which it is c-projectively equivalent. The mobility is at least two if and
only if the Kaehler metric admits a nontrivial hamiltonian 2-form. After
summarizing this relationship, we present necessary conditions for a Kaehler
metric to have mobility at least three: its curvature must have nontrivial
nullity at every point. Using the local classification of Kaehler metrics with
hamiltonian 2-forms, we describe explicitly the Kaehler metrics with mobility
at least three and hence show that the nullity condition on the curvature is
also sufficient, up to some degenerate exceptions. In an Appendix, we explain
how the classification may be related, generically, to the holonomy of a
complex cone metric.


  This paper contains four main results associated with an attractor of a
projective iterated function system (IFS). The first theorem characterizes when
a projective IFS has an attractor which avoids a hyperplane. The second theorem
establishes that a projective IFS has at most one attractor. In the third
theorem the classical duality between points and hyperplanes in projective
space leads to connections between attractors that avoid hyperplanes and
repellers that avoid points as well as hyperplane attractors that avoid points
and repellers that avoid hyperplanes. Finally, an index is defined for
attractors which avoid a hyperplane. This index is shown to be a nontrivial
projective invariant.


  In the previous paper (Inverse Problems, 32, 015010, 2016), a new heuristic
mathematical model was proposed for accurate forecasting of prices of stock
options for 1-2 trading days ahead of the present one. This new technique uses
the Black-Scholes equation supplied by new intervals for the underlying stock
and new initial and boundary conditions for option prices. The Black-Scholes
equation was solved in the positive direction of the time variable, This
ill-posed initial boundary value problem was solved by the so-called
Quasi-Reversibility Method (QRM). This approach with an added trading strategy
was tested on the market data for 368 stock options and good forecasting
results were demonstrated. In the current paper, we use the geometric Brownian
motion to provide an explanation of that effectivity using computationally
simulated data for European call options. We also provide a convergence
analysis for QRM. The key tool of that analysis is a Carleman estimate.


  This paper is concerned with quasilinear systems of partial differential
equations consisting of two hyperbolic operators interacting dissipatively. Its
main theorem establishes global-in-time existence and asymptotic stability of
strong solutions to the Cauchy problem close to homogeneous reference states.
Notably, the operators are not required to be symmetric hyperbolic, instead
merely the existence of symbolic symmetrizers is assumed. The dissipation is
characterized by conditions equivalent to the uniform decay of all Fourier
modes at the reference state. On a technical level, the theory developed herein
uses para-differential operators as its main tool. Apparently being the first
to apply such operators in the context of global-in-time existence for
quasi-linear hyperbolic systems, the present work contains new results in the
field of para-differential calculus. In the context of theoretical physics, the
theorem applies to recent formulations for the relativistic dynamics of
viscous, heat-conductive fluids notably such as that of Bemfica, Disconzi and
Noronha (Phys. Rev. D, 98:104064, 2018.)


  We study a cohomology theory $H^{\bullet}_{\varphi}$, called the $\mathcal
L_B$-cohomology, on compact torsion-free $\mathrm{G}_2$-manifolds. We show that
$H^k_{\varphi} \cong H^k_{\mathrm{dR}}$ for $k \neq 3, 4$, but that
$H^k_{\varphi}$ is infinite-dimensional for $k = 3,4$. Nevertheless there is a
canonical injection $H^k_{\mathrm{dR}} \to H^k_{\varphi}$. The $\mathcal
L_B$-cohomology also satisfies a Poincar\'e duality induced by the Hodge star.
The establishment of these results requires a delicate analysis of the
interplay between the exterior derivative $\mathrm{d}$ and the derivation
$\mathcal L_B$, and uses both Hodge theory and the special properties of
$\mathrm{G}_2$-structures in an essential way. As an application of our
results, we prove that compact torsion-free $\mathrm{G}_2$-manifolds are
'almost formal' in the sense that most of the Massey triple products
necessarily must vanish.


  The clear-cut experimental identification of Majorana bound states in
transport measurements still poses experimental challenges. We here show that
the zero-energy Majorana state formed at a junction of three topological
superconductor wires is directly responsible for giant shot noise amplitudes,
in particular at low voltages and for small contact transparency. The only
intrinsic noise limitation comes from the current-induced dephasing rate due to
multiple Andreev reflection processes.


  In this note we study order reversing quasi involutions and their properties.
These maps are dualities (order reversing involutions) on their image. We prove
that any order reversing quasi involution is induced by a cost. Invariant sets
of order reversing quasi involutions are of special interest and we provide
several results regarding their existence and uniqueness. We determine when an
order reversing quasi involution on a sub-class can be extended to the whole
space and discuss the uniqueness of such an extension. We also provide several
ways for constructing new order reversing quasi involutions from given ones. In
particular, we define the dual of an order reversing quasi involution. Finally,
throughout the paper we exhibit a "zoo" of illustrative examples. Some of them
are classical, some have recently attracted attention of the convexity
community and some are new. We study in depth the new example of dual polarity
and obtain a Blaschke-Santal\'o type inequality for a corresponding Gaussian
volume product. The unified point of view on order reversing quasi involutions
presented in this paper gives a deeper understanding of the underlying
principles and structures, offering a new and exciting perspective on the
topic, exposing many new research directions.


  The early-R stars are carbon-rich K-type giants. They are enhanced in C12,
C13 and N14, have approximately solar oxygen, magnesium isotopes, s-process and
iron abundances, have the luminosity of core-helium burning stars, are not
rapid rotators, are members of the Galactic thick disk and, most peculiarly of
all, are all single stars. Conventional single-star stellar evolutionary models
cannot explain such stars, but mergers in binary systems have been proposed to
explain their origin.
  We have synthesized binary star populations to calculate the number of merged
stars with helium cores which could be early-R stars. We find many possible
evolutionary channels. The most common of which is the merger of a helium white
dwarf with a hydrogen-burning red giant branch star during a common envelope
phase followed by a helium flash in a rotating core which mixes carbon to the
surface. All the channels together give ten times more early-R stars than we
require to match recent Hipparcos observations - we discuss which channels are
likely to be the true early-R stars and which are not. For the first time we
have constructed a viable model of the early-R stars with which we can test
some of our ideas regarding common envelope evolution in giants, stellar
mergers, rotation, the helium flash and the origin of the early-R stars.


  For a Euclidean building $X$ of type $A_{2}$, we classify the 0-dimensional
subbuildings $A$ of $\partial_{T}X$ that occur as the asymptotic boundary of
closed convex subsets. In particular, we show that triviality of the holonomy
of a triple (of points of $A$) is (essentially) sufficient.
  To prove this, we construct new convex subsets as the union of convex sets.


  In this exploratory study, I present, for the first time, the implications of
the charge symmetry breaking (CSB) that arise from the $u$ and $d$ quark mass
differences on gluon and sea quark distribution functions of the pion and kaon
in the framework of the Nambu--Jona-Lasino (NJL) model, which is a quark-level
chiral effective theory of QCD, with the help of the proper-time regularization
scheme to simulate color confinement of QCD. From the analysis, one finds that
the charge symmetry (CS) gluon distribution for the pion has a good agreement
with the prediction results obtained from the recent lattice QCD simulation and
JAM global fit QCD analysis at a higher scale of $Q^2 =$ 5 GeV$^2$. The size of
the CSB effects on gluon and sea quark distributions for the pion with the
realistic ratios of $m_u/m_d = 0.5$ at $Q^2 =$ 5 GeV$^2$ are respectively
estimated by 1.3\% and 2.0\% at $x \simeq 1$ in comparison with those for
$m_u/m_d = 1.0$, while those for the kaon are approximately about 0.3\% and
0.5\% at $ x \simeq 1$, respectively. A remarkable result is found that the CSB
effects on gluon distribution for the kaon are smaller than that for the pion,
which has a similar prediction result as that for the CS case.