  Deep learning models have gained increasing prominence in recent years in the
field of solar pho-tovoltaic (PV) forecasting. One drawback of these models is
that they require a lot of high-quality data to perform well. This is often
infeasible in practice, due to poor measurement infrastructure in legacy
systems and the rapid build-up of new solar systems across the world. This
paper proposes SolNet: a novel, general-purpose, multivariate solar power
forecaster, which addresses these challenges by using a two-step forecasting
pipeline which incorporates transfer learning from abundant synthetic data
generated from PVGIS, before fine-tuning on observational data. Using actual
production data from hundreds of sites in the Netherlands, Australia and
Belgium, we show that SolNet improves forecasting performance over data-scarce
settings as well as baseline models. We find transfer learning benefits to be
the strongest when only limited observational data is available. At the same
time we provide several guidelines and considerations for transfer learning
practitioners, as our results show that weather data, seasonal patterns, amount
of synthetic data and possible mis-specification in source location, can have a
major impact on the results. The SolNet models created in this way are
applicable for any land-based solar photovoltaic system across the planet where
simulated and observed data can be combined to obtain improved forecasting
capabilities.


  We obtain a theorem which allows to prove compact generation of derived
categories of Grothendieck categories, based upon certain coverings by
localizations. This theorem follows from an application of Rouquier's
cocovering theorem in the triangulated context, and it implies Neeman's result
on compact generation of quasi-compact separated schemes. We prove an
application of our theorem to non-commutative deformations of such schemes,
based upon a change from Koszul complexes to Chevalley-Eilenberg complexes.


  Knowledge graph embedding~(KGE) aims to represent entities and relations into
low-dimensional vectors for many real-world applications. The representations
of entities and relations are learned via contrasting the positive and negative
triplets. Thus, high-quality negative samples are extremely important in KGE.
However, the present KGE models either rely on simple negative sampling
methods, which makes it difficult to obtain informative negative triplets; or
employ complex adversarial methods, which requires more training data and
strategies. In addition, these methods can only construct negative triplets
using the existing entities, which limits the potential to explore harder
negative triplets. To address these issues, we adopt mixing operation in
generating harder negative samples for knowledge graphs and introduce an
inexpensive but effective method called MixKG. Technically, MixKG first
proposes two kinds of criteria to filter hard negative triplets among the
sampled negatives: based on scoring function and based on correct entity
similarity. Then, MixKG synthesizes harder negative samples via the convex
combinations of the paired selected hard negatives. Experiments on two public
datasets and four classical KGE methods show MixKG is superior to previous
negative sampling algorithms.


  The study of jets, collimated sprays of particles associated with hard
partons, is an important tool in testing perturbative quantum chromodynamics
(pQCD) and probing hot and dense nuclear matter created in high energy
heavy-ion collisions. Jets enable the study of hard scatterings, fragmentation
and hadronisation and their modification in the presence of a nuclear medium
with respect to baseline vacuum measurements, which is acquired from jet
measurements in proton-proton collisions. We have analysed data from
proton-proton collisions at s= \sqrt{s} = 7 TeV measured by the ALICE
experiment at the LHC and reconstructed the inclusive spectra of charged
particle jets at mid- rapidity using anti-kT clustering algorithm. We present
the jet spectra corrected for detector effects using several unfolding methods.
Furthermore, we examine various properties of jets, such as their charged
particle multiplicity and jet shapes.


  The evolution of transverse-momentum-dependent effective band offset
($V_{\mathrm{eff}}$) profile for heavy (\emph{hh})- and light-holes
(\emph{lh}), is detailed studied. Several new features in the metamorphosis of
the standardized fixed-height $V_{\mathrm{eff}}$ profile for holes, in the
presence of gradually increasing valence-band mixing and pseudomorphic strain,
are presented. In some $III-V$ unstrained semiconducting layered
heterostructures a fixed-height potential, is not longer valid for \emph{lh}.
Indeed, we found ---as predicted for electrons---, permutations of the
$V_{\mathrm{eff}}$ character for \emph{lh}, that resemble a "\emph{keyboard}",
together with bandgap changes, whenever the valence-band mixing varies from low
to large intensity. Strain is able to diminish the \emph{keyboard} effect on
$V_{\mathrm{eff}}$, and also makes it emerge or vanish occasionally. We found
that multiband-mixing effects and stress induced events, are competitors
mechanisms that can not be universally neglected by assuming a fixed-height
rectangular spatial distribution for fixed-character potential energy, as a
reliable test-run input for heterostructures. Prior to the present report,
neither direct transport-domain measurements, nor theoretical calculations
addressed to these $V_{\mathrm{eff}}$ evolutions and permutations, has been
reported for holes, as far as we know. Our results may be of relevance for
promising heterostructure's design guided by valence-band structure modeling to
enhance the hole mobility in $III-V$ materials.


  An improved update of the structure and decays of $\rho^0$, $\omega$ and
$\phi$ mesons based on a chiral SU(3) Lagrangian, including anomaly terms is
presented. We demonstrate that a consistent and quantitatively successful
description of both pion and kaon electromagnetic form factors can be achieved.
We also discuss the $e^+e^- \to \pi^+ \pi^0 \pi^-$ cross section, the Dalitz
decay $\omega \to \pi^0 \mu^+ \mu^-$ and aspects of $\rho^0 \omega$ and $\omega
\phi$ mixing. Relations to previous versions of the Vector Meson Dominance
model will be examined.


  Novel View Synthesis (NVS) is concerned with synthesizing views under camera
viewpoint transformations from one or multiple input images. NVS requires
explicit reasoning about 3D object structure and unseen parts of the scene to
synthesize convincing results. As a result, current approaches typically rely
on supervised training with either ground truth 3D models or multiple target
images. We propose Continuous Object Representation Networks (CORN), a
conditional architecture that encodes an input image's geometry and appearance
that map to a 3D consistent scene representation. We can train CORN with only
two source images per object by combining our model with a neural renderer. A
key feature of CORN is that it requires no ground truth 3D models or target
view supervision. Regardless, CORN performs well on challenging tasks such as
novel view synthesis and single-view 3D reconstruction and achieves performance
comparable to state-of-the-art approaches that use direct supervision. For
up-to-date information, data, and code, please see our project page:
https://nicolaihaeni.github.io/corn/.


  The oscillation of tunnel splitting are obtained by geometrical analysis of
the topological Wess-Zumino phase on the basis of tunneling paths in biaxial
nanomagnetic particles with magnetic field along the hard anisotropy axis. This
theory not only just yields the previous quantum interference results for the
ground state tunneling, but also gives the excited level splittings, all of
which agree well with the numerical diagonalization. Furthermore, the parity
effect in the asymmetric system which was recently discovered in experiment can
be derived by similar arguments, and is also certified by using the complex
periodic orbit theory. The possibility of improving the discrepancy with the
experiment in the periods of oscillations is discussed.


  We discuss the physics underlying an all-order resummation of logarithmic
enhanced contributions to dijet cross sections, and present preliminary results
for the distribution in the dijet transverse energy difference in DIS.


  With analytical treatment, the classical dynamics of an ultrarelativistic
electron in two counter-propagating circularly polarized strong laser beams
with either co-rotating or counter-rotating direction are considered. Assuming
that the particle energy is the dominant scale in the setup, an approximate
solution is derived and the influence of the rotational sense on the dynamics
is analyzed. Qualitative differences in both electron energy and momentum are
found for the laser beams being co-rotating or counter-rotating and are
confirmed by the exact numerical solution of the classical equation of motion.
Despite of these differences in the electron trajectory, the radiation spectra
of the electron do not deviate qualitatively from each other for configurations
with varying rotational directions of the laser beams. Here, the radiation of
an ultrarelativistic electron interacting with counterpropagating laser beams
is given in the framework of the Baier-Katkov semi-classical approximation.
Several parameter regimes are considered and the spectra resulting from the two
scenarios all have the same shape and only differ quantitatively by a few
percent.


  We present a study of the achievable rates for classical information
transmission via a lossy bosonic channel with memory, using homodyne detection.
A comparison with the memoryless case shows that the presence of memory
enhances the bit rate if information is encoded in collective states, i.e.
states which are entangled over different uses of the channel.


  We present a three-dimensional study of the plasma dynamics at the flank
magnetopause of the Earth's magnetosphere during mainly northward
interplanetary magnetic field (IMF) periods. Two-fluid simulations show that
the initial magnetic shear at the magnetopause and the field line bending
caused by the dynamics itself (in a configuration taken as representative of
the properties of the flank magnetopause) influence both the location where the
Kelvin-Helmholtz (KH) instability and the induced magnetic reconnection take
place and their nonlinear development. The KH vortices develop asymmetrically
with respect to the Earth's equatorial plane where the local KH linear growth
rate is maximal. Vortex driven reconnection processes take place at different
latitudes, ranging from the equatorial plane to mid-latitude regions, but only
in the hemisphere that turns out to be the less KH unstable. These results
suggest that KH-induced reconnection is not limited to specific regions around
the vortices (inside, below or above), but may be triggered over a broad and
continuous range of locations in the vicinity of the vortices.


  The time evolution and the asymptotic outcome of a
Landau-Zener-Stueckelberg-Majorana (LZ) process under continuous weak
non-selective measurement is analyzed. We compare two measurement protocols in
which the populations of either the adiabatic or the non-adiabatic levels are
(continuously and weakly) monitored. The weak measurement formalism, described
using a Gaussian Kraus operator, leads to a time evolution characterized by a
Markovian dephasing process, which, in the non-adiabatic measurement protocol
is similar to earlier studies of LZ dynamics in a dephasing environment.
Casting the problem in the language of measurement theory makes it possible for
us to compare diabatic and adiabatic measurement scenarios, to consider
engineered dephasing as a control device and to examine the manifestation of
the Zeno effect under the different measurement protocols. In particular, under
measurement of the non- adiabatic populations, the Zeno effect is manifested
not as a freezing of the measured system in its initial state, but rather as an
approach to equal asymptotic populations of the two diabatic states. This
behavior can be traced to the way by which the weak measurement formalism
behaves in the strong measurement limit, with a built-in relationship between
measurement time and strength.


  Context: Existing SWAS observations and future HIFI/Herschel data require a
clear sense of the information content of water emission and absorption lines.
Aims: Investigate wether the ground-state transition of ortho-H2O,
1_(10)-1_(01), at 557GHz can be used to measure the column density throughout
an interstellar cloud. Methods: We make use of a multi-zone escape probability
code suitable for the treatment of molecular line emission. Results: For low
abundances, i.e., X(H2O)=<10^(-9), the intensity of the 1_(10)-1_(01)
transition scales with the total column of H2. However, this relationship
breaks down with increasing abundance, i.e., optical depth, due to line
trapping and -- for T_(dust)>=25K, X(H2O)=<10^(-8) and n~10^4 cm^(-3) --
absorption of the dust continuum. Conclusions: An observed decline in intensity
per column, expected if H2O is a surface tracer, does not necessarily mean that
the water is absent in the gas phase at large columns, but can be caused by
line trapping and subsequent collisional de-excitation. To determine the amount
of water vapour in the interstellar medium, multiple line measurements of
optically thin transitions are needed to disentangle radiative transfer and
local excitation effects.


  This paper analyses Conversational AI multi-agent interoperability frameworks
and describes the novel architecture proposed by the Open Voice
Interoperability initiative (Linux Foundation AI and DATA), also known briefly
as OVON (Open Voice Network). The new approach is illustrated, along with the
main components, delineating the key benefits and use cases for deploying
standard multi-modal AI agency (or agentic AI) communications. Beginning with
Universal APIs based on Natural Language, the framework establishes and enables
interoperable interactions among diverse Conversational AI agents, including
chatbots, voicebots, videobots, and human agents. Furthermore, a new Discovery
specification framework is introduced, designed to efficiently look up agents
providing specific services and to obtain accurate information about these
services through a standard Manifest publication, accessible via an extended
set of Natural Language-based APIs. The main purpose of this contribution is to
significantly enhance the capabilities and scalability of AI interactions
across various platforms. The novel architecture for interoperable
Conversational AI assistants is designed to generalize, being replicable and
accessible via open repositories.


  In this paper, we derive the Jarzynski equality (JE) for an isolated quantum
system in three different cases: (i) the full evolution is unitary with no
intermediate measurements, (ii) with intermediate measurements of arbitrary
observables being performed, and (iii) with intermediate measurements whose
outcomes are used to modify the external protocol (feedback). We assume that
the measurements will involve errors that are purely classical in nature. Our
treatment is based on path probability in state space for each realization.
This is in contrast to the formal approach based on projection operator and
density matrices. We find that the JE remains unaffected in the second case,
but gets modified in the third case where the mutual information between the
measured values with the actual eigenvalues must be incorporated into the
relation.


  Thermalization of quark matter and antiquark matter is studied with
quark-quark-antiquark as well as quark-antiquark-antiquark elastic scatterings.
Squared amplitudes of qqqbar to qqqbar and qqbarqbar to qqbarqbar at order
alpha_s^4 are derived in perturbative QCD. Solved by a new technique, solutions
of transport equations with the squared amplitudes indicate that the
scatterings qqqbar to qqqbar and qqbarqbar to qqbarqbar shorten the
thermalization time of quark matter and antiquark matter. It is emphasized that
three-parton and other multi-parton scatterings become important at the high
parton number density achieved in RHIC Au-Au collisions.


  For a pair consisting of a gene tree and a species tree, the ancestral
configurations at an internal node of the species tree are the distinct sets of
gene lineages that can be present at that node. Ancestral configurations appear
in computations of gene tree probabilities under evolutionary models
conditional on fixed species trees, and the enumeration of root ancestral
configurations -- ancestral configurations at the root of the species tree --
assists in describing the complexity of these computations. In the case that
the gene tree matches the species tree in topology, we study the distribution
of the number of root ancestral configurations of a random labeled tree
topology under each of two models.


  Integrated optics is at the heart of a wide range of systems from remote
sensing and communications to computing and quantum information processing.
Demand for smaller and more energy efficient structures stimulates search for
more advanced material platforms. Here, we propose a concept of an all van der
Waals photonics, where we show that electronically bulk transition metal
dichalcogenide (TMDC) semiconductors are well fitted for the design of key
optical components for nanoscale and integrated photonics. Specifically, we
demonstrate theoretically that owing to low optical loss and high refractive
index across near-infrared and telecom frequency bands, components made of bulk
TMDCs can potentially outperform counterparts made of conventional 3D
semiconductors, such as Si and III/Vs. We discuss several key quantum and
classical optical components and show that bulk TMDCs may pave the way to
smaller footprint devices, more energy efficient electro-optical modulators,
and stronger quantum light-materials interaction. Enhanced optical performance,
ease of integration, and a wide selection of materials suggest that bulk TMDCs
may complement and, potentially, replace existing integrated photonics systems.


  The recent experimental realization of a high quality WSe$% _{2} $ leads to
the possibility of magneto-optical measurements and the manipulation of the
spin and valley degrees of freedom. We study the influence of the very strong
spin-orbit coupling and of the anisotropic lifting of the valley pseudospin
degeneracy on its magnetotransport properties. The energy spectrum of WSe$_{2}
$ is derived and discussed in the presence of a perpendicular magnetic field
$B$. Correspondingly we evaluate the magneto-optical Hall conductivity and the
optical longitudinal conductivity as functions of the frequency, magnetic
field, and Fermi energy. They are strongly influenced by the field $B$ and the
strong spin splitting. The former exhibits valley polarization and the latter
beatings of oscillations. The magneto-optical responses can be tuned in two
different regimes: the mictrowave-to-terahertz regime and the visible-frequency
one. The absorption peaks involving the $n=0$ LL appear in between these two
regimes and show a magnetic control of the spin and valley splittings. We also
evaluate the power absorption spectrum.


  The purpose of this paper is to study deformation theory of Hom-associative
algebra morphisms and Hom-Lie algebra morphisms. We introduce a suitable
cohomology and discuss Infinitesimal deformations, equivalent deformations and
obstructions. Moreover, we provide some examples.


  We report the observation of inverse-magnetic-field-periodic,
radiation-induced magnetoresistance oscillations in GaAs/AlGaAs
heterostructures prepared in W. Wegscheider's group, compare their
characteristics with similar oscillations in V. Umansky's material, and
describe the lineshape variation vs. the radiation power, $P$, in the two
systems. We find that the radiation-induced oscillatory $\Delta R_{xx}$, in
both materials, can be described by $\Delta R_{xx} = -A exp(-\lambda/B)sin(2
\pi F/B)$, where $A$ is the amplitude, $\lambda$ is the damping parameter, and
$F$ is the oscillation frequency. Both $\lambda$ and $F$ turn out to be
insensitive to $P$. On the other hand, $A$ grows nonlinearly with $P$.


  Since the emergence of the Transformer architecture, language model
development has increased, driven by their promising potential. However,
releasing these models into production requires properly understanding their
behavior, particularly in sensitive domains such as medicine. Despite this
need, the medical literature still lacks technical assessments of pre-trained
language models, which are especially valuable in resource-constrained settings
in terms of computational power or limited budget. To address this gap, we
provide a comprehensive survey of language models in the medical domain. In
addition, we selected a subset of these models for thorough evaluation,
focusing on classification and text generation tasks. Our subset encompasses 53
models, ranging from 110 million to 13 billion parameters, spanning the three
families of Transformer-based models and from diverse knowledge domains. This
study employs a series of approaches for text classification together with
zero-shot prompting instead of model training or fine-tuning, which closely
resembles the limited resource setting in which many users of language models
find themselves. Encouragingly, our findings reveal remarkable performance
across various tasks and datasets, underscoring the latent potential of certain
models to contain medical knowledge, even without domain specialization.
Consequently, our study advocates for further exploration of model applications
in medical contexts, particularly in resource-constrained settings. The code is
available on https://github.com/anpoc/Language-models-in-medicine.


  Sampling theory has benefited from a surge of research in recent years, due
in part to the intense research in wavelet theory and the connections made
between the two fields. In this survey we present several extensions of the
Shannon theorem, that have been developed primarily in the past two decades,
which treat a wide class of input signals as well as nonideal sampling and
nonlinear distortions. This framework is based on viewing sampling in a broader
sense of projection onto appropriate subspaces, and then choosing the subspaces
to yield interesting new possibilities. For example, our results can be used to
uniformly sample non-bandlimited signals, and to perfectly compensate for
nonlinear effects.


  We propose a general derivation of differential cross section in quark-quark
scatterings at fixed impact parameters. The derivation is well defined and free
of ambiguity in the conventional one. The approach can be applied to a variety
of partonic and hadronic scatterings in low or high energy particle collisions.


  Many modern video processing pipelines rely on edge-aware (EA) filtering
methods. However, recent high-quality methods are challenging to run in
real-time on embedded hardware due to their computational load. To this end, we
propose an area-efficient and real-time capable hardware implementation of a
high quality EA method. In particular, we focus on the recently proposed
permeability filter (PF) that delivers promising quality and performance in the
domains of HDR tone mapping, disparity and optical flow estimation. We present
an efficient hardware accelerator that implements a tiled variant of the PF
with low on-chip memory requirements and a significantly reduced external
memory bandwidth (6.4x w.r.t. the non-tiled PF). The design has been taped out
in 65 nm CMOS technology, is able to filter 720p grayscale video at 24.8 Hz and
achieves a high compute density of 6.7 GFLOPS/mm2 (12x higher than embedded
GPUs when scaled to the same technology node). The low area and bandwidth
requirements make the accelerator highly suitable for integration into SoCs
where silicon area budget is constrained and external memory is typically a
heavily contended resource.


  A new method of path averaging for waves propagating in a random dilute
system of identical scatterers is developed. The scattering matrix of such a
system is calculated. The method systematically takes into account repeating
scatterings on the same scatterer and effects of correlations. Results obtained
show the significant influence of new effects on the extinction of a coherent
field and are valid in both the diffusive and localized regimes.


  The era of big data has promoted the vigorous development of many industries,
boosting the full potential of holistic data-driven analysis. Hadoop has become
the primary choice for mainstream platforms used by stakeholders to process big
data. Thereafter, the security of Hadoop platform has arisen tremendous
attention worldwide. In this paper, we mainly concentrate on enforcing access
control on users to ensure platform security. First, we leverage access proxy
integrated with attribute-based access control (ABAC) model to implement
front-end authorization, which can fully reflect and cope with the flexible
nature of the complex access control process in Hadoop platform, as well as can
release back-end resources from complex authorization process through access
proxy. Moreover, in order to ensure the fine-granularity of authorization, the
access proxy maintains a list composed of trust threshold value provided by
each resource according to its importance. The access proxy interacts with the
blockchain network to obtain the user's trust evaluation value, which serves as
an important basis for dynamic authorization determination. More specifically,
blockchain network works together on-chain and off-chain modes. The user's
historical behavior data is stored off-chain, and the corresponding hash value
is anchored on-chain. Consequently, the user's trust value is evaluated based
on his historical behavior stored on the blockchain platform. Meanwhile, the
authenticity of user behavior data can be guaranteed, thereby ensuring the
reliability of trust assessment results. Our experiment demonstrates that the
proposed model can dynamically and flexibly adjust user permissions to ensure
the security of the platform, while time and money are consumed within a
reasonable range.


  We present a Chinese judicial reading comprehension (CJRC) dataset which
contains approximately 10K documents and almost 50K questions with answers. The
documents come from judgment documents and the questions are annotated by law
experts. The CJRC dataset can help researchers extract elements by reading
comprehension technology. Element extraction is an important task in the legal
field. However, it is difficult to predefine the element types completely due
to the diversity of document types and causes of action. By contrast, machine
reading comprehension technology can quickly extract elements by answering
various questions from the long document. We build two strong baseline models
based on BERT and BiDAF. The experimental results show that there is enough
space for improvement compared to human annotators.


  This paper proposes a squared smoothing Newton method via the Huber smoothing
function for solving semidefinite programming problems (SDPs). We first study
the fundamental properties of the matrix-valued mapping defined upon the Huber
function. Using these results and existing ones in the literature, we then
conduct rigorous convergence analysis and establish convergence properties for
the proposed algorithm. In particular, we show that the proposed method is
well-defined and admits global convergence. Moreover, under suitable regularity
conditions, i.e., the primal and dual constraint nondegenerate conditions, the
proposed method is shown to have a superlinear convergence rate. To evaluate
the practical performance of the algorithm, we conduct extensive numerical
experiments for solving various classes of SDPs. Comparison with the
state-of-the-art SDP solvers demonstrates that our method is also efficient for
computing accurate solutions of SDPs.


  OwnThink stands as the most extensive Chinese open-domain knowledge graph
introduced in recent times. Despite prior attempts in question answering over
OwnThink (OQA), existing studies have faced limitations in model representation
capabilities, posing challenges in further enhancing overall accuracy in
question answering. In this paper, we introduce UniOQA, a unified framework
that integrates two complementary parallel workflows. Unlike conventional
approaches, UniOQA harnesses large language models (LLMs) for precise question
answering and incorporates a direct-answer-prediction process as a
cost-effective complement. Initially, to bolster representation capacity, we
fine-tune an LLM to translate questions into the Cypher query language (CQL),
tackling issues associated with restricted semantic understanding and
hallucinations. Subsequently, we introduce the Entity and Relation Replacement
algorithm to ensure the executability of the generated CQL. Concurrently, to
augment overall accuracy in question answering, we further adapt the
Retrieval-Augmented Generation (RAG) process to the knowledge graph.
Ultimately, we optimize answer accuracy through a dynamic decision algorithm.
Experimental findings illustrate that UniOQA notably advances SpCQL Logical
Accuracy to 21.2% and Execution Accuracy to 54.9%, achieving the new
state-of-the-art results on this benchmark. Through ablation experiments, we
delve into the superior representation capacity of UniOQA and quantify its
performance breakthrough.


  We describe an extension of the axioms of quantization to the case of
2-plectic manifolds. We show how such quantum spaces can be obtained as stable
classical solutions in a zero-dimensional 3-algebra reduced model obtained by
dimensional reduction of the Bagger-Lambert-Gustavsson theory. We demonstrate
that the groupoid approach to geometric quantization proposed by Hawkins and
others can be useful for quantizing 2-plectic manifolds. We discuss our results
in the context of recent developments in the quantum geometry of M-branes, and
in the nonassociative deformation of spacetime induced by closed strings in the
presence of a 2-plectic form.


  Program code as a data source is gaining popularity in the data science
community. Possible applications for models trained on such assets range from
classification for data dimensionality reduction to automatic code generation.
However, without annotation number of methods that could be applied is somewhat
limited. To address the lack of annotated datasets, we present the Code4ML
corpus. It contains code snippets, task summaries, competitions and dataset
descriptions publicly available from Kaggle - the leading platform for hosting
data science competitions. The corpus consists of ~2.5 million snippets of ML
code collected from ~100 thousand Jupyter notebooks. A representative fraction
of the snippets is annotated by human assessors through a user-friendly
interface specially designed for that purpose. Code4ML dataset can potentially
help address a number of software engineering or data science challenges
through a data-driven approach. For example, it can be helpful for semantic
code classification, code auto-completion, and code generation for an ML task
specified in natural language.


  We present a timing and spectral analysis of the X-ray pulsar XTE J1946+274
observed with Suzaku during an outburst decline in 2010 October and compare
with previous results. XTE J1946+274 is a transient X-ray binary consisting of
a Be-type star and a neutron star with a 15.75 s pulse period in a 172 d orbit
with 2-3 outbursts per orbit during phases of activity. We improve the orbital
solution using data from multiple instruments. The X-ray spectrum can be
described by an absorbed Fermi-Dirac cutoff power law model along with a narrow
Fe K line at 6.4 keV and a weak Cyclotron Resonance Scattering Feature (CRSF)
at ~35 keV. The Suzaku data are consistent with the previously observed
continuum flux versus iron line flux correlation expected from fluorescence
emission along the line of sight. However, the observed iron line flux is
slightly higher, indicating the possibility of a higher iron abundance or the
presence of non-uniform material. We argue that the source most likely has only
been observed in the subcritical (non-radiation dominated) state since its
pulse profile is stable over all observed luminosities and the energy of the
CRSF is approximately the same at the highest (~$5 \times 10^{37} $erg
s$^{-1}$) and lowest (~$5 \times 10^{36} $erg s$^{-1}$) observed 3-60 keV
luminosities.


  Placing a large mass in a large spatial superposition, such as a
Schr\"odinger Cat state is a significant and important challenge. In
particular, the large spatial superposition (${\cal O}(10-100)$ $\mu$m) of
mesoscopic masses ($m\sim {\cal O}(10^{-14} -10^{-15})$ kg) makes it possible
to test the quantum nature of gravity via entanglement in the laboratory. To
date, the proposed methods of achieving this spatial delocalization are to use
wavepacket expansions or quantum ancilla (for example spin) dependent forces,
all of whose efficacy reduces with mass. Thus increasing the spatial splitting
independent of the mass is an important open challenge. In this paper, we
present a method of achieving a mass-independent enhancement of superposition
via diamagnetic repulsion from current-carrying wires. We analyse an example
system which uses the Stern-Gerlach effect to creating a small initial
splitting, and then apply the diamagnetic repulsion method to enhance the
superposition size ${\cal O}(400-600)$ $\mu$m from an initial modest split of
the wavefunction. We provide an analytic and numeric analysis of our scheme.


  In this study, we present and validate a variation of recently-developed
physically motivated sub-grid prescriptions for supernova feedback that account
for the unresolved energy-conserving phase of the bubble expansion. Our model
builds upon the implementation publicly available in the mesh-less hydrodynamic
code GIZMO, and is coupled with the chemistry library KROME. Here, we test it
against different setups, to address how it affects the formation/dissociation
of molecular hydrogen (H$_2$). First, we explore very idealised conditions, to
show that it can accurately reproduce the terminal momentum of the blast-wave
independent of resolution. Then, we apply it to a suite of numerical
simulations of an isolated Milky Way-like galaxy and compare it with a similar
run employing the delayed-cooling sub-grid prescription. We find that the
delayed-cooling model, by pressurising ad-hoc the gas, is more effective in
suppressing star formation. However, to get this effect, it must maintain the
gas warm/hot at densities where it is expected to cool efficiently,
artificially changing the thermo-chemical state of the gas, and reducing the
H$_2$ abundance even in dense gas. Mechanical feedback, on the other hand, is
able to reproduce the H$_2$ column densities without altering the gas
thermodynamics, and, at the same time, drives more powerful outflows. However,
being less effective in suppressing star formation, it over-predicts the
Kennicutt-Schmidt relation by a factor of about 2.5. Finally, we show that the
model is consistent at different resolution levels, with only mild differences.


  Using mixed analytical and numerical methods we investigate the development
of singularities in the heat flow for corotational harmonic maps from the
$d$-dimensional sphere to itself for $3\leq d\leq 6$. By gluing together
shrinking and expanding asymptotically self-similar solutions we construct
global weak solutions which are smooth everywhere except for a sequence of
times $T_1<T_2<...<T_k<\infty$ at which there occurs the type I blow-up at one
of the poles of the sphere. We show that in the generic case the continuation
beyond blow-up is unique, the topological degree of the map changes by one at
each blow-up time $T_i$, and eventually the solution comes to rest at the zero
energy constant map.


  Density probability distribution functions (PDFs) for turbulent
self-gravitating clouds should be convolutions of the local log-normal PDF,
which depends on the local average density rho-ave and Mach number M, and the
probability distribution functions for rho-ave and M, which depend on the
overall cloud structure. When self-gravity drives a cloud to increased central
density, the total PDF develops an extended tail. If there is a critical
density or column density for star formation, then the fraction of the local
mass exceeding this threshold becomes higher near the cloud center. These
elements of cloud structure should be in place before significant star
formation begins. Then the efficiency is high so that bound clusters form
rapidly, and the stellar initial mass function (IMF) has an imprint in the gas
before destructive radiation from young stars can erase it. The IMF could arise
from a power-law distribution of mass for cloud structure. These structures
should form stars down to the thermal Jeans mass MJ at each density in excess
of a threshold. The high-density tail of the PDF, combined with additional
fragmentation in each star-forming core, extends the IMF into the Brown Dwarf
regime. The core fragmentation process is distinct from the cloud structuring
process and introduces an independen core fragmentation mass function (CFMF).
The CFMF would show up primarily below the IMF peak.


  Finding efficient algorithms to explore large networks with the aim of
recovering information about their structure is an open problem. Here, we
investigate this challenge by proposing a model in which random walkers with
previously assigned home nodes navigate through the network during a fixed
amount of time. We consider that the exploration is successful if the walker
gets the information gathered back home, otherwise, no data is retrieved.
Consequently, at each time step, the walkers, with some probability, have the
choice to either go backward approaching their home or go farther away. We show
that there is an optimal solution to this problem in terms of the average
information retrieved and the degree of the home nodes and design an adaptive
strategy based on the behavior of the random walker. Finally, we compare
different strategies that emerge from the model in the context of network
reconstruction. Our results could be useful for the discovery of unknown
connections in large scale networks.


  Twin-Field Quantum Key Distribution(TF-QKD) protocol and its variants, such
as Phase-Matching QKD(PM-QKD), sending or not QKD(SNS-QKD) and No Phase
Post-Selection TF-QKD(NPP-TFQKD), are very promising for long-distance
applications. However, there are still some gaps between theory and practice in
these protocols. Concretely, a finite-key size analysis is still missing, and
the intensity fluctuations are not taken into account. To address the
finite-key size effect, we first give the key rate of NPP-TFQKD against
collective attack in finite-key size region and then prove it can be against
coherent attack. To deal with the intensity fluctuations, we present an
analytical formula of 4-intensity decoy state NPP-TFQKD and a practical
intensity fluctuation model. Finally, through detailed simulations, we show
NPP-TFQKD can still keep its superiority of high key rate and long achievable
distance.


  A dynamical process that takes a random time to complete, e.g., a chemical
reaction, may either be accelerated or hindered due to resetting. Tuning system
parameters such as temperature, viscosity or concentration, can invert the
effect of resetting on the mean completion time of the process, which leads to
a resetting transition. Though the resetting transition was recently studied
for diffusion in a handful of model potentials, it is yet unknown whether the
results follow any universality in terms of well-defined physical parameters.
To bridge this gap, we propose a general framework which reveals that the
resetting transition is governed by an interplay between thermal and potential
energy. This result is illustrated for different classes of potentials that are
used to model a wide variety of stochastic processes with numerous
applications.


  The predictions of mean-field electrodynamics can now be probed using direct
numerical simulations of random flows and magnetic fields. When modelling
astrophysical MHD, it is important to verify that such simulations are in
agreement with observations. One of the main challenges in this area is to
identify robust \it{quantitative} measures to compare structures found in
simulations with those inferred from astrophysical observations. A similar
challenge is to compare quantitatively results from different simulations.
Topological data analysis offers a range of techniques, including the Betti
numbers and persistence diagrams, that can be used to facilitate such a
comparison. After describing these tools, we first apply them to synthetic
random fields and demonstrate that, when the data are standardized in a
straightforward manner, some topological measures are insensitive to either
large-scale trends or the resolution of the data. Focusing upon one particular
astrophysical example, we apply topological data analysis to HI observations of
the turbulent interstellar medium (ISM) in the Milky Way and to recent MHD
simulations of the random, strongly compressible ISM. We stress that these
topological techniques are generic and could be applied to any complex,
multi-dimensional random field.


  This paper focuses on a class of zero-norm composite optimization problems.
For this class of nonconvex nonsmooth problems, we establish the
Kurdyka-Lojasiewicz property of exponent being a half for its objective
function under a suitable assumption, and provide some examples to illustrate
that such an assumption is not very restricted which, in particular, involve
the zero-norm regularized or constrained piecewise linear-quadratic function,
the zero-norm regularized or constrained logistic regression function, the
zero-norm regularized or constrained quadratic function over a sphere.


  The reconstruction of the large scale velocity field from the grouped
Cosmicflows-4 (CF4) database is presented. The lognormal bias of the inferred
distances and velocities data is corrected by the Bias Gaussianization
correction (BGc) scheme, and the linear density and velocity fields are
reconstructed by means of the Wiener filter (WF) and constrained realizations
(CRs) algorithm. These tools are tested against a suite of random and
constrained Cosmicflows-3-like mock data. The CF4 data consists of 3 main
subsamples - the 6dFGS and the SDSS data - and the `others'. The individual
contributions of the subsamples have been studied. The quantitative analysis of
the velocity field is done mostly by the mean overdensity ($\Delta_L(R)$) and
the bulk velocity ($V_{\mathrm{bulk}}(R)$) profiles of the velocity field out
to $300\, h^{-1}{\rm Mpc}$.
  The $V_{\mathrm{bulk}}(R)$ and $\Delta_{\mathrm L}(R)$ profiles of the CF4
data without its 6dFGS component are consistent with the cosmic variance to
within $1\sigma$. The 6dFGS sample dominates the $V_{\mathrm{bulk}}$
($\Delta_{\mathrm L}$) profile beyond $\sim120\, h^{-1}{\rm Mpc}$, and drives
it to roughly a $3.4\sigma$ ($-1.9\sigma$) excess (deficiency) relative to the
cosmic variance at $R\sim250\ (190)\ \, h^{-1}{\rm Mpc}$. The excess in the
amplitude of $V_{\mathrm{bulk}}$ is dominated by its Supergalactic X component,
roughly in the direction of the Shapley Concentration. The amplitude and
alignment of the inferred velocity field from the CF4 data is at
$\sim(2\,-\,3)\,\sigma$ discrepancy with respect to the $\Lambda$CDM model.
Namely, it is somewhat atypical but yet there is no compelling tension with the
model.


  Nonadiabatic dynamical simulations were carried out to study cis-to-trans
isomerization of azobenzene under laser irradiation and/or external mechanical
loads. We used a semiclassical electron-radiation-ion dynamics method that is
able to describe the coevolution of the structural dynamics and the underlying
electronic dynamics in a real-time manner. It is found that azobenzene
photoisomerization occurs predominantly by an out-of-plane rotation mechanism
even under a nontrivial resisting force of several tens of piconewtons. We have
repeated the simulations systematically for a broad range of parameters for
laser pulses, but could not find any photoisomerization event by a previously
suggested in-plane inversion mechanism. The simulations found that the
photoisomerization process can be held back by an external resisting force of
90 - 200 pN depending on the frequency and intensity of the lasers. This study
also found that a pure mechanical isomerization is possible from the cis state
if the azobenzene molecule is stretched by an external force of 1250 -1650 pN.
Remarkably, the mechanical isomerization first proceeds through a mechanically
activated inversion, and then is diverted to an ultrafast downhill rotation
that accomplishes the isomerization. Implications of these findings to
azobenzene-based nanomechanical devices are discussed.


  This paper formulates and solves a sequential detection problem that involves
the mutual information (stochastic observability) of a Gaussian process
observed in noise with missing measurements. The main result is that the
optimal decision is characterized by a monotone policy on the partially ordered
set of positive definite covariance matrices. This monotone structure implies
that numerically efficient algorithms can be designed to estimate and implement
monotone parametrized decision policies.The sequential detection problem is
motivated by applications in radar scheduling where the aim is to maintain the
mutual information of all targets within a specified bound. We illustrate the
problem formulation and performance of monotone parametrized policies via
numerical examples in fly-by and persistent-surveillance applications involving
a GMTI (Ground Moving Target Indicator) radar.


  We consider (4+D)-dimensional Kaluza-Klein cosmological model with two
scaling factors, as real, p-adic and adelic quantum mechanical one. One of the
scaling factors corresponds to the D-dimensional internal space, and second one
to the 4-dimensional universe. In standard quantum cosmology, i.e. over the
field of real numbers R, it leads to dynamical compactification of additional
dimensions and to the accelerating evolution of 4-dimensional universe. We
construct corresponding $p$-adic quantum model and explore existence of its
p-adic ground state. In addition, we explore evolution of this model and a
possibility for its adelic generalization. It is necessary for the further
investigation of space-time discreteness at very short distances, i.e. in a
very early universe


  The concept of an $I$-matrix in the full $2\times 2$ matrix ring $M_2(R/I)$,
where $R$ is an arbitrary UFD and $I$ is a nonzero ideal in $R$, is introduced.
We obtain a concrete description of the centralizer of an $I$-matrix $\hat B$
in $M_2(R/I)$ as the sum of two subrings $\mathcal S_1$ and $\mathcal S_2$ of
$M_2(R/I)$, where $\mathcal S_1$ is the image (under the natural epimorphism
from $M_2(R)$ to $M_2(R/I)$) of the centralizer in $M_2(R)$ of a pre-image of
$\hat B$, and where the entries in $\mathcal S_2$ are intersections of certain
annihilators of elements arising from the entries of $\hat B$. It turns out
that if $R$ is a PID, then every matrix in $M_2(R/I)$ is an $I$-matrix.
However, this is not the case if $R$ is a UFD in general. Moreover, for every
factor ring $R/I$ with zero divisors and every $n\ge 3$ there is a matrix for
which the mentioned concrete description is not valid.


  In this paper, we clarify a foundational loose end affecting the
phenomenological approach to quantum gravity centered around the generalization
of Heisenberg uncertainty principle. This misconception stems from a series of
recently published works in which perturbative and non-perturbative methods are
confused, thereby resulting in a blurring of the distinction between changes in
the deformed algebra and changes in the representation of operators.
Accordingly, this reasoning would render the existence of a minimal length
representation-dependent, and thus unphysical.


  We present the first results from a high resolution simulation with a focus
on galactic wind driving for an isolated galaxy with a halo mass of $\sim
10^{11}$ M$_{\odot}$ (similar to the Large Magellanic Cloud) and a total gas
mass of $\sim 6 \times 10^{8}$ M$_{\odot}$, resulting in $\sim 10^{8}$ gas
cells at $\sim 4$ M$_{\odot}$ mass resolution. We adopt a resolved stellar
feedback model with non-equilibrium cooling and heating, including
photoelectric heating and photo-ionizing radiation, as well as supernovae
(SNe), coupled to the second order meshless finite mass (MFM) method for
hydrodynamics. These features make this the largest resolved-ISM galaxy model
run to date. We find mean star formation rates around $0.05$ M$_{\odot}$
yr$^{-1}$ and evaluate typical time averaged loading factors for mass
($\eta_\mathrm{M}$ $\sim$ 1.0, in good agreement with recent observations) and
energy ($\eta_\mathrm{E}$ $\sim$ 0.01). The bulk of the mass of the wind is
transported by the warm ($T < 5 \times 10^5$K) phase, while there is a similar
amount of energy transported in the warm and the hot phases ($T > 5 \times
10^5$K). We find an average opening angle of 30 degrees for the wind,
decreasing with higher altitude above the midplane. The wind mass loading is
decreasing (flat) for the warm (hot) phase as a function of the star formation
surface rate density $\Sigma_{\rm SFR}$, while the energy loading shows
inverted trends with $\Sigma_{\rm SFR}$, decreasing for the warm wind and
increasing for the hot wind, although with very shallow slopes. These scalings
are in good agreement with previous simulations of resolved wind driving in the
multi-phase ISM.


  High-intensity proton beams impinging on a fixed target or beam dump allow to
probe new physics via the production of new weakly-coupled particles in hadron
decays. The CERN SPS provides opportunities to do so with the running NA62
experiment and the planned SHiP experiment. Reconstruction of kaon decay
kinematics (beam mode) allows NA62 to probe for the existence of right-handed
neutrinos and dark photons with masses below 0.45 GeV. Direct reconstruction of
displaced vertices from the decays of new neutral particles (dump mode) will
allow NA62 and SHiP to probe right-handed neutrinos with masses up to 5 GeV and
mixings down to several orders of magnitude smaller than current constraints,
in regions favoured in models which explain at once neutrino masses,
matter-antimatter asymmetry and dark matter.


  We describe epitaxial Ge/Si multilayers with cross-plane thermal
conductivities which can be systematically reduced to exceptionally low values,
as compared both with bulk and thin-film SiGe alloys of the same average
concentration, by simply changing the thicknesses of the constituent layers. Ab
initio calculations reveal that partial interdiffusion of Ge into the Si
spacers, which naturally results from Ge segregation during growth, plays a
determinant role, lowering the thermal conductivity below what could be
achieved without interdiffusion (perfect superlattice), or with total
interdiffusion (alloy limit). This phenomenon is similar to the one previously
observed in alloys with embedded nanoparticles, and it stresses the importance
of combining alloy and nanosized scatterers simultaneously to minimize thermal
conductivity. Our calculations thus suggest that superlattices with sharp
interfaces, which are commonly sought but difficult to realize, are worse than
compositionally-modulated Si1-xGex multilayers in the search for materials with
ultralow thermal conductivities.


  This paper discusses the mathematical aspects of band fitting and introduces
the mathematics of the Asymmetric Gaussian shape and its tangent space for the
first time. First, we derive an equation for an Asymmetric Gaussian shape. We
then use this equation to derive a rule for the resolution of two Gaussian
shaped bands. We then use the Asymmetrical Gaussian equation to derive a Master
Equation to fit two overlapping bands. We identify regions of the fitting space
where the Asymmetric Gaussian fit is optimal, sub optimal and not optimal. We
then demonstrate the use of the Asymmetric Gaussian to fit four overlapping
Gaussian bands, and show how this is relevant to the olivine spectral complex
at 1 micron. We develop a new model of the olivine family spectrum based on
previous work by Runciman and Burns. The limitations of the asymmetric band
fitting method and a critical assessment of three commonly used numerical
minimization methods are also provided.


  In recent years, the end-to-end (E2E) scheme based on deep learning (DL) has
been proposed as a potential scheme to jointly optimize the encoder and the
decoder parameters of the optical communication system. Compared with
conventional deep neural network (DNN) adopted in E2E design, center-oriented
Gated Recurrent Unit (Co-GRU) network has the ability to learn and compensate
for inter-symbol interference (ISI) with low computation cost while satisfying
the gradient backpropagation (BP) condition. In this paper, the Co-GRU
structure is adopted for both channel modeling and decoder implementation in
E2E design for long-haul coherent wavelength division multiplexing (WDM)
transmission systems, which can enhance the performance of general mutual
information (GMI) and Q2-factor. For the E2E system with Co-GRU based decoder,
the gain of GMI and Q2-factor are respectively improved 0.2 bits/sym and
0.48dB, compared to that of the conventional QAM system, for a 5-channel
dual-polarization coherent system transmitting over 960km standard single mode
fiber (SSMF). This work paves the way for further study of the application of
the Co-GRU structure for both the data-driven channel modeling and the decoder
performance improvement in E2E design.


  We propose a game theoretic framework for task allocation in mobile cloud
computing that corresponds to offloading of compute tasks to a group of nearby
mobile devices. Specifically, in our framework, a distributor node holds a
multidimensional auction for allocating the tasks of a job among nearby mobile
nodes based on their computational capabilities and also the cost of
computation at these nodes, with the goal of reducing the overall job
completion time. Our proposed auction also has the desired incentive
compatibility property that ensures that mobile devices truthfully reveal their
capabilities and costs and that those devices benefit from the task allocation.
To deal with node mobility, we perform multiple auctions over adaptive time
intervals. We develop a heuristic approach to dynamically find the best time
intervals between auctions to minimize unnecessary auctions and the
accompanying overheads. We evaluate our framework and methods using both real
world and synthetic mobility traces. Our evaluation results show that our game
theoretic framework improves the job completion time by a factor of 2-5 in
comparison to the time taken for executing the job locally, while minimizing
the number of auctions and the accompanying overheads. Our approach is also
profitable for the nearby nodes that execute the distributor's tasks with these
nodes receiving a compensation higher than their actual costs.


  I investigate the bound state problems of lowest-lying mesons and heavy
mesons. Chiral symmetry is essential when one consider lowest-lying mesons.
Heavy quark symmetry plays an central role in considering the semi-leptonic
form factors of heavy mesons. Various properties based on the symmetries are
revealed using Bethe-Salpeter equations.


  In this article we revisit the problem of numerical integration for monotone
bounded functions, with a focus on the class of nonsequential Monte Carlo
methods. We first provide new a lower bound on the maximal $L^p$ error of
nonsequential algorithms, improving upon a theorem of Novak when p > 1. Then we
concentrate on the case p = 2 and study the maximal error of two unbiased
methods-namely, a method based on the control variate technique, and the
stratified sampling method.


  In this paper, we develop a deep learning approach for the accurate solution
of challenging problems of near-field microscopy that leverages the powerful
framework of physics-informed neural networks (PINNs) for the inversion of the
complex optical parameters of nanostructured environments. Specifically, we
show that PINNs can be flexibly designed based on the full-vector Maxwell's
equations to inversely retrieve the spatial distributions of the complex
electric permittivity and magnetic permeability of unknown scattering objects
in the resonance regime from near-field data. Moreover, we demonstrate that
PINNs achieve excellent convergence to the true material parameters under both
plane wave and point source (localized) excitations, enabling parameter
retrieval in scanning near-field optical microscopy (SNOM). Our method is
computationally efficient compared to traditional data-driven deep learning
approaches as it requires only a single dataset for training. Furthermore, we
develop and successfully demonstrate adaptive PINNs with trainable loss weights
that largely improve the accuracy of the inverse reconstruction for high-index
materials compared to standard PINNs. Finally, we demonstrate the full
potential of our approach by retrieving the space-dependent permittivity of a
three-dimensional (3D) unknown object from near-field data. The presented
framework paves the way to the development of a computationally-driven,
accurate, and non-invasive platform for the simultaneous retrieval of the
electric and magnetic parameters of resonant nanostructures from measured
optical images, with applications to biomedical imaging, optical remote
sensing, and characterization of metamaterial devices.


  Let $\mathbb{K}$ be a field and $S=\mathbb{K}[x_1,\dots,x_n]$ be the
polynomial ring in $n$ variables over $\mathbb{K}$. In 1982, R. Stanley
associated a combinatorial invariant to any finitely generated
$\mathbb{Z}^n$-graded $S$-module which is now called Stanley depth. Stanley
conjectured that this invariant is an upper bound for the depth of module.
Stanley's conjecture has been disproved by Duval et al. \cite{abcj}, and the
counterexample is a quotient of squarefree monomial ideals. On the other hand,
there are evidences showing that Stanley's inequality can be true for high
powers of monomial ideals. In this survey article, we collect the recent
results in this direction. More precisely, we investigate the Stanley depth of
powers, integral closure of powers and symbolic powers of monomial ideals.


  We use a recent O(alpha_s^2) calculation of the differential cross section
for the production of heavy quarks in e+e- annihilation to compute a few
moments of the heavy quark single-inclusive production cross section. We verify
that, contrary to some recent claims, the leading and next-to-leading
logarithmic terms in this cross section are correctly given by the standard NLO
fragmentation function formalism for heavy quark production.


  Recently, the relationship between matroids and generalized rough sets based
on relations has been studied from the viewpoint of linear independence of
matrices. In this paper, we reveal more relationships by the predecessor and
successor neighborhoods from relations. First, through these two neighborhoods,
we propose a pair of matroids, namely predecessor relation matroid and
successor relation matroid, respectively. Basic characteristics of this pair of
matroids, such as dependent sets, circuits, the rank function and the closure
operator, are described by the predecessor and successor neighborhoods from
relations. Second, we induce a relation from a matroid through the circuits of
the matroid. We prove that the induced relation is always an equivalence
relation. With these two inductions, a relation induces a relation matroid, and
the relation matroid induces an equivalence relation, then the connection
between the original relation and the induced equivalence relation is studied.
Moreover, the relationships between the upper approximation operator in
generalized rough sets and the closure operator in matroids are investigated.


  High-redshift, luminous, dusty star forming galaxies (DSFGs) constrain the
extremity of galaxy formation theories. The most extreme are discovered through
follow-up on candidates in large area surveys. Here we present 850 $\mu$m
SCUBA-2 follow-up observations of 188 red DSFG candidates from the
\textit{Herschel} Multi-tiered Extragalactic Survey (HerMES) Large Mode Survey,
covering 274 deg$^2$. We detected 87 per cent with a signal-to-noise ratio $>$
3 at 850~$\mu$m. We introduce a new method for incorporating the confusion
noise in our spectral energy distribution fitting by sampling correlated flux
density fluctuations from a confusion limited map. The new 850~$\mu$m data
provide a better constraint on the photometric redshifts of the candidates,
with photometric redshift errors decreasing from $\sigma_z/(1+z)\approx0.21$ to
$0.15$. Comparison spectroscopic redshifts also found little bias ($\langle
(z-z_{\rm spec})/(1+z_{\rm spec})\rangle = 0.08 $). The mean photometric
redshift is found to be 3.6 with a dispersion of $0.4$ and we identify 21 DSFGs
with a high probability of lying at $z > 4$. After simulating our selection
effects we find number counts are consistent with phenomenological galaxy
evolution models. There is a statistically significant excess of WISE-1 and
SDSS sources near our red galaxies, giving a strong indication that lensing may
explain some of the apparently extreme objects. Nevertheless, our sample should
include examples of galaxies with the highest star formation rates in the
Universe ($\gg10^3$ M$_\odot$yr$^{-1}$).


  Given a maximal even-integral lattice $\cL$ of signature $(m+, 2-)$ with an
odd $m\geq 3$, we consider the holomorphic cusp forms $F$ of weight $l$ on the
bounded symmetric domain of type IV of dimension $m$ with respect to the
discriminant subgroup of the orthogonal group $O(\cL)$ defined by $\cL$. Under
a non-negativity assumption on the central $L$-values, we prove an
equidistribution result of Satake parameters in an ensemble constructed from
the central values of standard $L$-functions and the square of the
Whittaker-Bessel periods.


  Partial decay widths and branching fractions are calculated for the exclusive
decays of the Standard Model Higgs boson into a pair of vector quarkonium
states, $ H\to J/\psi J/\psi, H\to \Upsilon \Upsilon, H\to J/\psi \phi, H\to
J/\psi \Upsilon$, with relativistic corrections due to quark motion in mesons
taken into account.


  We present a new test of hypothesis in which we seek the probability of the
null conditioned on the data, where the null is a simplification undertaken to
counter the intractability of the more complex model, that the simpler null
model is nested within. With the more complex model rendered intractable, the
null model uses a simplifying assumption that capacitates the learning of an
unknown parameter vector given the data. Bayes factors are shown to be known
only up to a ratio of unknown data-dependent constants--a problem that cannot
be cured using prescriptions similar to those suggested to solve the problem
caused to Bayes factor computation, by non-informative priors. Thus, a new test
is needed in which we can circumvent Bayes factor computation. In this test, we
undertake generation of data from the model in which the null hypothesis is
true and can achieve support in the measured data for the null by comparing the
marginalised posterior of the model parameter given the measured data, to that
given such generated data. However, such a ratio of marginalised posteriors can
confound interpretation of comparison of support in one measured data for a
null, with that in another data set for a different null. Given an application
in which such comparison is undertaken, we alternatively define support in a
measured data set for a null by identifying the model parameters that are less
consistent with the measured data than is minimally possible given the
generated data, and realising that the higher the number of such parameter
values, less is the support in the measured data for the null. Then, the
probability of the null conditional on the data is given within an MCMC-based
scheme, by marginalising the posterior given the measured data, over parameter
values that are as, or more consistent with the measured data, than with the
generated data.


  Using a near-field microwave technique, two-dimensional images have been made
of the second and third order intermodulation distortion (IMD) of Tl2Ba2CaCu2O8
and YBa2Cu3O7 thin film microwave resonators. It was found that second and
third order IMD do not have identical spatial distributions, which indicates
that physical mechanisms play different roles in their generation. This
technique enables the investigation of the roles of these mechanisms. As an
illustration, the sensitivity to magnetic fluxons of the two orders is
described, with second order being more sensitive to fluxon density.


  We unify inflation and dark matter via a single scalar field phi. One of the
main difficulties for this unification is that between inflation and dark
matter one needs a successful reheating process and a long lasting period of
radiation. Therefore the amount of energy density in the inflaton-dark matter
field phi must be fine tune after reheating to give dark matter. Here we show
an alternative scheme in which the inflaton decays completely, disappearing
entirely from the spectrum. However, at low energies, before matter-radiation
equality, the same interaction term that leads to the inflaton decay,
regenerates phi. An essential feature is that the transition between the
intermediate radiation dominated to the dark matter phase is related to a
quantum generation of the scalar field \phi instead to purely classical
dynamics. Thanks to this quantum transition the inflation-dark matter
unification can take place naturally without fine tuning. The unification
scheme presented here has three parameters, the mass of the dark matter
particle m_o, the inflation parameter lambda and the coupling g for the
inflaton interaction. Phenomenology fixes the value for lambda and gives a
constraint between g and m_o, leaving only the mass of the dark matter particle
m_o as a free parameter. These same three parameters lambda, m_o, g are present
in models with inflation and a dark matter wimp particle but without
unification. Therefore our unification scheme does not increase the number of
parameters and it accomplishes the desired unification between inflaton and
dark matter for free.


  We propose an efficient framework with compatibility between normal printing
and printing with special color inks in this paper. Special color inks can be
used for printing to represent some particular colors and specific optical
properties, which are difficult to express using only CMYK inks. Special color
layers are required in addition to the general color layer for printing with
special color inks. We introduce a reversible data hiding (RDH) method to embed
the special color layers into the general color layer without visible
artifacts. The proposed method can realize both normal printing and printing
with special color inks by using a single layer. Our experimental results show
that the quality of the marked image is virtually identical to that of the
original image, i.e., the general color layer.


  Here we present the reasoning behind, and program to find, the generating
functions for the number of permutations in the title. The article duals as the
"accompanying" Maple package.


  The utilization of technology in second language learning and teaching has
become ubiquitous. For the assessment of writing specifically, automated
writing evaluation (AWE) and grammatical error correction (GEC) have become
immensely popular and effective methods for enhancing writing proficiency and
delivering instant and individualized feedback to learners. By leveraging the
power of natural language processing (NLP) and machine learning algorithms, AWE
and GEC systems have been developed separately to provide language learners
with automated corrective feedback and more accurate and unbiased scoring that
would otherwise be subject to examiners. In this paper, we propose an
integrated system for automated writing evaluation with corrective feedback as
a means of bridging the gap between AWE and GEC results for second language
learners. This system enables language learners to simulate the essay writing
tests: a student writes and submits an essay, and the system returns the
assessment of the writing along with suggested grammatical error corrections.
Given that automated scoring and grammatical correction are more efficient and
cost-effective than human grading, this integrated system would also alleviate
the burden of manually correcting innumerable essays.


  A systematic method is proposed for the determination of the statistical
properties of a field consisting of a coherent structure interacting with
turbulent linear waves. The explicit expression of the generating functional of
the correlations is obtained, performing the functional integration on a
neighbourhood in the function space around the soliton. The results show that
the non-gaussian fluctuations observed in the tokamak plasma edge can be
explained by the intermittent formation of nonlinear coherent structures.


  Analyzing the health status of patients based on Electronic Health Records
(EHR) is a fundamental research problem in medical informatics. The presence of
extensive missing values in EHR makes it challenging for deep neural networks
to directly model the patient's health status based on EHR. Existing deep
learning training protocols require the use of statistical information or
imputation models to reconstruct missing values; however, the protocols inject
non-realistic data into downstream EHR analysis models, significantly limiting
model performance. This paper introduces Learnable Prompt as Pseudo Imputation
(PAI) as a new training protocol. PAI no longer introduces any imputed data but
constructs a learnable prompt to model the implicit preferences of the
downstream model for missing values, resulting in a significant performance
improvement for all EHR analysis models. Additionally, our experiments show
that PAI exhibits higher robustness in situations of data insufficiency and
high missing rates. More importantly, in a real-world application involving
cross-institutional data with zero-shot evaluation, PAI demonstrates stronger
model generalization capabilities for non-overlapping features.


  Following Vinberg, we find the criterions for a subgroup generated by
reflections $\Gamma \subset \SL^{\pm}(n+1,\mathbb{R})$ and its finite-index
subgroups to be definable over $\mathbb{A}$ where $\mathbb{A}$ is an integrally
closed Noetherian ring in the field $\mathbb{R}$. We apply the criterions for
groups generated by reflections that act cocompactly on irreducible properly
convex open subdomains of the $n$-dimensional projective sphere. This gives a
method for constructing injective group homomorphisms from such Coxeter groups
to $\SL^{\pm}(n+1,\mathbb{Z})$. Finally we provide some examples of
$\SL^{\pm}(n+1,\mathbb{Z})$-representations of such Coxeter groups. In
particular, we consider simplicial reflection groups that are isomorphic to
hyperbolic simplicial groups and classify all the conjugacy classes of the
reflection subgroups in $\SL^{\pm}(n+1,\mathbb{R})$ that are definable over
$\mathbb{Z}$. These were known by Goldman, Benoist, and so on previously.


  Two dimensional pi conjugated metal porphyrin covalent organic frameworks
were produced in aqueous solution on an iodine-modified Au(111) surface by on
site azomethine coupling of Fe(III) 5,10,15,20 tetrakis(4 aminophenyl)porphyrin
(FeTAPP) with terephthal dicarboxaldehyde and investigated in detail using
in-situ scanning tunneling microscopy. Mixed covalent organic porphyrin
frameworks consisting of FeTAPP and metal-free TAPP (H2TAPP) were prepared
through simultaneous adsorption in a mixed solution as well as partial
replacement of FeTAPP by H2TAPP in an as prepared metal porphyrin framework. In
the mixed framework, the relative distribution of FeTAPP to H2TAPP was not
random and revealed a preference for homo-connection rather than
heteroconnection. The construction of substrate-supported, pi conjugated
covalent frameworks from multiple building blocks, including metal centers,
will be of significant utility in the design of functional molecular
nanoarchitectures.


  Let $\zeta(s)$ and $Z(t)$ be the Riemann zeta function and Hardy's function
respectively. We show asymptotic formulas for $\int_0^T Z(t)\zeta(1/2+it)dt$
and $\int_0^T Z^2(t) \zeta(1/2+it)dt$. Furthermore we derive an upper bound for
$\int_0^T Z^3(t)\chi^{\alpha}(1/2+it)dt$ for $-1/2<\alpha<1/2$, where $\chi(s)$
is the function which appears in the functional equation of the Riemann zeta
function: $\zeta(s)=\chi(s)\zeta(1-s)$.


  A subsequence of a word $w$ is a word $u$ such that $u = w[i_1] w[i_2] \dots
w[i_{k}]$, for some set of indices $1 \leq i_1 < i_2 < \dots < i_k \leq \lvert
w\rvert$. A word $w$ is $k$-subsequence universal over an alphabet $\Sigma$ if
every word in $\Sigma^k$ appears in $w$ as a subsequence. In this paper, we
study the intersection between the set of $k$-subsequence universal words over
some alphabet $\Sigma$ and regular languages over $\Sigma$. We call a regular
language $L$ \emph{$k$-$\exists$-subsequence universal} if there exists a
$k$-subsequence universal word in $L$, and \emph{$k$-$\forall$-subsequence
universal} if every word of $L$ is $k$-subsequence universal. We give
algorithms solving the problems of deciding if a given regular language,
represented by a finite automaton recognising it, is
\emph{$k$-$\exists$-subsequence universal} and, respectively, if it is
\emph{$k$-$\forall$-subsequence universal}, for a given $k$. The algorithms are
FPT w.r.t.~the size of the input alphabet, and their run-time does not depend
on $k$; they run in polynomial time in the number $n$ of states of the input
automaton when the size of the input alphabet is $O(\log n)$. Moreover, we show
that the problem of deciding if a given regular language is
\emph{$k$-$\exists$-subsequence universal} is NP-complete, when the language is
over a large alphabet. Further, we provide algorithms for counting the number
of $k$-subsequence universal words (paths) accepted by a given deterministic
(respectively, nondeterministic) finite automaton, and ranking an input word
(path) within the set of $k$-subsequence universal words accepted by a given
finite automaton.


  We consider a theory of massless reduced quantum electrodynamics
(RQED$_{d_\gamma,d_e}$), e.g., a quantum field theory where the U(1) gauge
field lives in $d_\gamma$-spacetime dimensions while the fermionic field lives
in a reduced spacetime of $d_e$ dimensions ($d_e \leqslant d_\gamma$). In the
case where $d_\gamma=4$ such RQEDs are renormalizable while they are
super-renormalizable for $d_\gamma <4$. The 2-loop electromagnetic current
correlation function is computed exactly for a general RQED$_{d_\gamma,d_e}$.
Focusing on RQED$_{4,3}$, the corresponding $\beta$-function is shown to vanish
which implies the scale invariance of the theory. Interaction correction to the
1-loop vacuum polarization, $\Pi_1$, of RQED$_{4,3}$ is found to be: $\Pi =
\Pi_1 (1 + 0.056 \al)$ where $\al$ is the fine structure constant. The scaling
dimension of the fermion field is computed at 1-loop and is shown to be
anomalous for RQED$_{4,3}$.


  It is shown that an aberrated wavefront incident upon a Fabry-Perot optical
cavity excites higher order spatial modes in the cavity, and that the spectral
width and distribution of these modes is indicative of the type and magnitude
of the aberration. The cavities are purely passive and therefore frequency
content is limited to that provided by the original light source, unless
time-varying content is introduced. To illustrate this concept, spatial mode
decomposition and transmission spectrum calculation are simulated on an example
cavity; the effects of various phase delays, in the form of two basic Seidel
aberrations and a composite of Zernike polynomial terms, are shown using both
Laguerre-Gaussian and plane wave incident beams. The aggregate spectral width
of the excited cavity modes is seen to widen as the magnitude of the phase
delay increases.


  This paper is the second in a series where we examine the generation and
filtering of internal gravity waves in stars and the consequences of wave
induced transport of angular momentum at various stages of the stellar
evolution.
  Here we concentrate on Pop II dwarf stars and we focus in particular on the
differential properties of internal gravity waves as a function of the stellar
mass. We show that, for the range of masses corresponding to the lithium
plateau, gravity waves are fully efficient and should thus lead to a
quasi-solid rotation state, similar to that of the Sun. In the slightly more
massive progenitors of currently observed horizontal branch star however,
internal wave generation is not efficient on the main sequence, and large
internal differential rotation can thus be maintained. This leads to a natural
explanation of the large rotational velocities measured on the horizontal
branch in some globular clusters.


  In this paper, we study pre-Lie analogues of Poisson-Nijenhuis structures and
introduce ON-structures on bimodules over pre-Lie algebras. We show that an
ON-structure gives rise to a hierarchy of pairwise compatible O-operators. We
study solutions of the strong Maurer-Cartan equation on the twilled pre-Lie
algebra associated to an O-operator, which gives rise to a pair of
ON-structures which are naturally in duality. We show that KVN-structures and
HN-structures on a pre-Lie algebra g are corresponding to ON-structures on the
bimodule $(\mathfrak g^*;\mathrm{ad}^*,-R^*)$, and $KV\Omega$-structures are
corresponding to solutions of the strong Maurer-Cartan equation on a twilled
pre-Lie algebra associated to an $s$-matrix.


  We elaborate on a novel model of N=4 supersymmetric mechanics with extra spin
variables. A dynamical linear (1,4,3) multiplet is coupled to a
"semi-dynamical" linear (3,4,1) multiplet representing spin degrees of freedom
in a Wess-Zumino action. The unique coupling of these two multiplets relates
the dynamical bosonic variable to an arbitrary harmonic function of the SU(2)
triplet of spin variables. As we prove at the classical and quantum level, N=4
supersymmetry is equivalent to the Nahm equations for the spin variables, with
the dynamical boson as evolution parameter. We treat in detail the one- and
two-monopole as well as some special multi-monopole configurations. While one
monopole exhibits superconformal OSp(4|2) symmetry and was worked out
previously, only N=4, d=1 Poincare supersymmetry survives for multi-monopole
configurations.


  We study state transfer in quantum walk on graphs relative to the adjacency
matrix. Our motivation is to understand how the addition of pendant subgraphs
affect state transfer. For two graphs $G$ and $H$, the Frucht-Harary corona
product $G \circ H$ is obtained by taking $|G|$ copies of the cone $K_{1} + H$
and by connecting the conical vertices according to $G$. Our work explores
conditions under which the corona $G \circ H$ exhibits state transfer. We also
describe new families of graphs with state transfer based on the corona
product. Some of these constructions provide a generalization of related known
results.


  We compute exact three and four point functions in the W_N minimal models
that were recently conjectured to be dual to a higher spin theory in AdS_3. The
boundary theory has a large number of light operators that are not only
invisible in the bulk but grow exponentially with N even at small conformal
dimensions. Nevertheless, we provide evidence that this theory can be
understood in a 1/N expansion since our correlators look like free-field
correlators corrected by a power series in 1/N . However, on examining these
corrections we find that the four point function of the two bulk scalar fields
is corrected at leading order in 1/N through the contribution of one of the
additional light operators in an OPE channel. This suggests that, to correctly
reproduce even tree-level correlators on the boundary, the bulk theory needs to
be modified by the inclusion of additional fields. As a technical by-product of
our analysis, we describe two separate methods -- including a Coulomb gas type
free-field formalism -- that may be used to compute correlation functions in
this theory.


  We prove the attainability of the best constant in the fractional
Hardy--Sobolev inequality with boundary singularity for the Spectral Dirichlet
Laplacian. The main assumption is the average concavity of the boundary at the
origin.


  We state and prove several characterizations of Thom's regularity condition
for stratified maps. In particular we extend to stratified maps some
characterizations of Whitney (a) regularity, due to the second author.


  We provide a quantum field theory based description of the nonperturbative
effects from hadronization for soft drop groomed jet mass distributions using
the soft-collinear effective theory and the coherent branching formalism. There
are two distinct regions of jet mass $m_J$ where grooming modifies
hadronization effects. In a region with intermediate $m_J$ an operator
expansion can be used, and the leading power corrections are given by three
universal nonperturbative parameters that are independent of all kinematic
variables and grooming parameters, and only depend on whether the parton
initiating the jet is a quark or gluon. The leading power corrections in this
region cannot be described by a standard normalized shape function. These power
corrections depend on the kinematics of the subjet that stops soft drop through
short distance coefficients, which encode a perturbatively calculable
dependence on the jet transverse momentum, jet rapidity, and on the soft drop
grooming parameters $z_{\rm cut}$ and $\beta$. Determining this dependence
requires a resummation of large logarithms, which we carry out at LL order. For
smaller $m_J$ there is a nonperturbative region described by a one-dimensional
shape function that is unusual because it is not normalized to unity, and has a
non-trivial dependence on $\beta$.


  As science and engineering have become increasingly data-driven, the role of
optimization has expanded to touch almost every stage of the data analysis
pipeline, from signal and data acquisition to modeling and prediction. The
optimization problems encountered in practice are often nonconvex. While
challenges vary from problem to problem, one common source of nonconvexity is
nonlinearity in the data or measurement model. Nonlinear models often exhibit
symmetries, creating complicated, nonconvex objective landscapes, with multiple
equivalent solutions. Nevertheless, simple methods (e.g., gradient descent)
often perform surprisingly well in practice.
  The goal of this survey is to highlight a class of tractable nonconvex
problems, which can be understood through the lens of symmetries. These
problems exhibit a characteristic geometric structure: local minimizers are
symmetric copies of a single "ground truth" solution, while other critical
points occur at balanced superpositions of symmetric copies of the ground
truth, and exhibit negative curvature in directions that break the symmetry.
This structure enables efficient methods to obtain global minimizers. We
discuss examples of this phenomenon arising from a wide range of problems in
imaging, signal processing, and data analysis. We highlight the key role of
symmetry in shaping the objective landscape and discuss the different roles of
rotational and discrete symmetries. This area is rich with observed phenomena
and open problems; we close by highlighting directions for future research.


  We investigate, via computer simulations, the time evolution of the
(Boltzmann) entropy of a dense fluid not in local equilibrium. The
macrovariables $M$ describing the system are the (empirical) particle density
$f=\{f(\un{x},\un{v})\}$ and the total energy $E$. We find that $S(f_t,E)$ is
monotone increasing in time even when its kinetic part is decreasing. We argue
that for isolated Hamiltonian systems monotonicity of $S(M_t) = S(M_{X_t})$
should hold generally for ``typical'' (the overwhelming majority of) initial
microstates (phase-points) $X_0$ belonging to the initial macrostate $M_0$,
satisfying $M_{X_0} = M_0$. This is a direct consequence of Liouville's theorem
when $M_t$ evolves autonomously.


  This paper develops an adaptive version of Mallat's scattering transform for
signals on graphs. The main results are norm bounds for the layers of the
transform, obtained from a version of a Beurling-Deny inequality that permits
to remove the nonlinear steps in the scattering transform. Under statistical
assumptions on the input signal, the norm bounds can be refined. The concepts
presented here are illustrated with an application to traffic counts which
exhibit characteristic daily and weekly periodicities. Anomalous traffic
patterns which deviate from these expected periodicities produce a response in
the scattering transform.


  The NASA K2 mission obtained high precision time-series photometry for four
young clusters, including the near-twin 600-800 Myr-old Praesepe and Hyades
clusters. Hot sub-Neptunes are highly prone to mass-loss mechanisms, given
their proximity to the the host star and the weakly bound gaseous envelopes,
and analyzing this population at young ages can provide strong constraints on
planetary evolution models. Using our automated transit detection pipeline, we
recover 15 planet candidates across the two clusters, including 10 previously
confirmed planets. We find a hot sub-Neptune occurrence rate of 79-107% for GKM
stars in the Praesepe cluster. This is 2.5-3.5 sigma higher than the occurrence
rate of 16.54+1.00-0.98% for the same planets orbiting the ~3-9 Gyr-old GKM
field stars observed by K2, even after accounting for the slightly super-solar
metallicity ([Fe/H]~0.2 dex) of the Praesepe cluster. We examine the effect of
adding ~100 targets from the Hyades cluster, and extending the planet parameter
space under examination, and find similarly high occurrence rates in both
cases. The high occurrence rate of young, hot sub-Neptunes could indicate
either that these planets are undergoing atmospheric evolution as they age, or
that planetary systems that formed when the Galaxy was much younger are
substantially different than from today. Under the assumption of the
atmospheric mass-loss scenario, a significantly higher occurrence rate of these
planets at the intermediate ages of Praesepe and Hyades appears more consistent
with the core-powered mass loss scenario sculpting the hot sub-Neptune
population, compared to the photoevaporation scenario.


  The recent discovery of J0737-3039A & B-two pulsars in a highly relativistic
orbit around one another - offers an unprecedented opportunity to study the
elusive physics of pulsar radio emission. The system contains a rapidly
rotating pulsar with a spin period of 22.7 ms and a slow companion with a spin
period of 2.77 s, hereafter referred to as 'A' and 'B', respectively. A unique
property of the system is that the pulsed radio flux from B increases
systematically by almost two orders-of-magnitude during two short portions of
each orbit. Here, we describe a geometrical model of the system that
simultaneously explains the intensity variations of B and makes definitive and
testable predictions for the future evolution of the emission properties of
both stars. Our model assumes that B's pulsed radio flux increases when
illuminated by emission from A. This model provides constraints on the spin
axis orientation and emission geometry of A and predicts that its pulse profile
will evolve considerably over the next several years due to geodetic precession
until it disappears entirely in 15-20 years.


  Decentralized federated learning (DFL) captures FL settings where both (i)
model updates and (ii) model aggregations are exclusively carried out by the
clients without a central server. Existing DFL works have mostly focused on
settings where clients conduct a fixed number of local updates between local
model exchanges, overlooking heterogeneity and dynamics in communication and
computation capabilities. In this work, we propose Decentralized Sporadic
Federated Learning (DSpodFL), a DFL methodology built on a generalized notion
of sporadicity in both local gradient and aggregation processes. DSpodFL
subsumes many existing decentralized optimization methods under a unified
algorithmic framework by modeling the per-iteration (i) occurrence of gradient
descent at each client and (ii) exchange of models between client pairs as
arbitrary indicator random variables, thus capturing heterogeneous and
time-varying computation/communication scenarios. We analytically characterize
the convergence behavior of DSpodFL for both convex and non-convex models, for
both constant and diminishing learning rates, under mild assumptions on the
communication graph connectivity, data heterogeneity across clients, and
gradient noises, and show how our bounds recover existing results as special
cases. Experiments demonstrate that DSpodFL consistently achieves improved
training speeds compared with baselines under various system settings.


  We obtain a family of functional identities satisfied by vector-valued
functions of two variables and their geometric inversions. For this we
introduce particular differential operators of arbitrary order attached to
Gegenbauer polynomials. These differential operators are symmetry breaking for
the pair of Lie groups $(SL(2,\mathbb C), SL(2,\mathbb R))$ that arise from
conformal geometry.


  Machine learning (ML) is successful in achieving human-level artificial
intelligence in various fields. However, it lacks the ability to explain an
outcome due to its black-box nature. While recent efforts on explainable AI
(XAI) has received significant attention, most of the existing solutions are
not applicable in real-time systems since they map interpretability as an
optimization problem, which leads to numerous iterations of time-consuming
complex computations. Although there are existing hardware-based acceleration
framework for XAI, they are implemented through FPGA and designed for specific
tasks, leading to expensive cost and lack of flexibility. In this paper, we
propose a simple yet efficient framework to accelerate various XAI algorithms
with existing hardware accelerators. Specifically, this paper makes three
important contributions. (1) The proposed method is the first attempt in
exploring the effectiveness of Tensor Processing Unit (TPU) to accelerate XAI.
(2) Our proposed solution explores the close relationship between several
existing XAI algorithms with matrix computations, and exploits the synergy
between convolution and Fourier transform, which takes full advantage of TPU's
inherent ability in accelerating matrix computations. (3) Our proposed approach
can lead to real-time outcome interpretation. Extensive experimental evaluation
demonstrates that proposed approach deployed on TPU can provide drastic
improvement in interpretation time (39x on average) as well as energy
efficiency (69x on average) compared to existing acceleration techniques.


  We study a discrete dynamical system designed to find a 'most holomorphic'
connection on a smooth complex vector bundle $E$. We examine the relation
between the distance of the chern classes of $E$ from the $(p,p)$ axis of the
Hodge diamond and singularity formation. Canonical connections and canonical
metrics pulled back from Grassmannians play a major role, and we review their
differential geometry. As an exercise in the geometry of canonical connections,
we include an expression for the curvature in terms of heat kernels.


  The problem of synchronization of coupled self-oscillators by external force
is studied. The charts of Lyapunov's exponents in the "frequency - amplitude"
parameter plane are obtained within the framework of the phase approximation.
We identified the characteristic configurations of the domains of complete
synchronization, two- and three-frequency quasi-periodic oscillations and
different variants of partial synchronization of oscillators by an external
force. The differences between regimes of mode locking and beats of partial
oscillators are revealed and discussed. To visualize and analyze the domains of
resonant two-frequency tori we construct the charts, in which regions of
dynamics with different winding numbers are represented by colors.


  We prove a well-posedness result for two pseudo-parabolic problems, which can
be seen as two models for the same electrical conduction phenomenon in
heterogeneous media, neglecting the magnetic field. One of the problems is the
concentration limit of the other one, when the thickness of the dielectric
inclusions goes to zero. The concentrated problem involves a transmission
condition through interfaces, which is mediated by a suitable Laplace-Beltrami
type equation.


  What does it mean for a clustering to be fair? One popular approach seeks to
ensure that each cluster contains groups in (roughly) the same proportion in
which they exist in the population. The normative principle at play is balance:
any cluster might act as a representative of the data, and thus should reflect
its diversity.
  But clustering also captures a different form of representativeness. A core
principle in most clustering problems is that a cluster center should be
representative of the cluster it represents, by being "close" to the points
associated with it. This is so that we can effectively replace the points by
their cluster centers without significant loss in fidelity, and indeed is a
common "use case" for clustering. For such a clustering to be fair, the centers
should "represent" different groups equally well. We call such a clustering a
group-representative clustering.
  In this paper, we study the structure and computation of group-representative
clusterings. We show that this notion naturally parallels the development of
fairness notions in classification, with direct analogs of ideas like
demographic parity and equal opportunity. We demonstrate how these notions are
distinct from and cannot be captured by balance-based notions of fairness. We
present approximation algorithms for group representative $k$-median clustering
and couple this with an empirical evaluation on various real-world data sets.


  The shape and tails of partial distribution functions (PDF) for a
climatological signal, i.e. the El Nino SOI and the turbulent nature of the
ocean-atmosphere variability are linked through a model encompassing Tsallis
nonextensive statistics and leading to evolution equations of the Langevin and
Fokker-Planck type. A model originally proposed to describe the intermittent
behavior of turbulent flows describes the behavior of the normalized
variability for such a climatological index, for small and large time windows,
both for small and large variability. This normalized variabil- ity
distributions can be sufficiently well fitted with a chi-square-distribution.
The transition between the small time scale model of nonextensive, intermittent
process and the large scale Gaussian exten- sive homogeneous fluctuation
picture is found to occur at above ca. a 48 months time lag. The intermittency
exponent ($\kappa$) in the framework of the Kolmogorov log-normal model is
found to be related to the scaling exponent of the PDF moments. The value of
$\kappa$ (= 0.25) is in agreement with the intermittency exponent recently
obtained for other atmospheric data.


  We revisit the analysis of the improved ladder Schwinger-Dyson (SD) equation
for the dynamical chiral symmetry breaking in QCD with emphasizing the
importance of the scale ambiguity. Previous calculation done so far naively
used one-loop MSbar coupling in the improved ladder SD equation without
examining the scale ambiguity. As a result, the calculated pion decay constant
f_\pi was less than a half of its experimental value f_\pi=92.4MeV once the QCD
scale is fixed from the high energy coupling \alpha_s(M_Z). In order to settle
the ambiguity in a proper manner, we adopt here in the present paper the
next-to-leading-order effective coupling instead of a naive use of the MSbar
coupling. The pion decay constant f_\pi is then calculated from high energy QCD
coupling strength \alpha_s(M_Z)=0.1172 \pm 0.0020. Within the
Higashijima-Miransky approximation, we obtain f_\pi=85--106MeV depending on the
value of \alpha_s(M_Z) which agrees well with the experimentally observed value
f_\pi=92.4MeV. The validity of the improved ladder SD equation is therefore
ascertained more firmly than considered before.


  Mining software repositories is a useful technique for researchers and
practitioners to see what software developers actually do when developing
software. Tools like Boa provide users with the ability to easily mine these
open-source software repositories at a very large scale, with datasets
containing hundreds of thousands of projects. The trade-off is that users must
use the provided infrastructure, query language, runtime, and datasets and this
might not fit all analysis needs. In this work, we present Boidae: a family of
Boa installations controlled and customized by users. Boidae uses automation
tools such as Ansible and Docker to facilitate the deployment of a customized
Boa installation. In particular, Boidae allows the creation of custom datasets
generated from any set of Git repositories, with helper scripts to aid in
finding and cloning repositories from GitHub and SourceForge. In this paper, we
briefly describe the architecture of Boidae and how researchers can utilize the
infrastructure to generate custom datasets. Boidae's scripts and all
infrastructure it builds upon are open-sourced. A video demonstration of
Boidae's installation and extension is available at https://go.unl.edu/boidae.