  The evolution of economic and innovation systems at the national scale is
shaped by a complex dynamics, the footprint of which is the nested structure of
the activities in which different countries are competitive. Nestedness is a
persistent feature across multiple kinds (layers) of activities related to the
production of knowledge and goods: scientific research, technological
innovation, industrial production and trade. We observe that in the layers of
innovation and trade the competitiveness of countries correlates unambiguously
with their diversification, while the science layer displays some peculiar
feature. The evolution of scientific domains leads to an increasingly modular
structure, in which the most developed nations become less competitive in the
less advanced scientific domains, where they are replaced by the emerging
countries. This observation is in line with a capability-based view of the
evolution of economic systems, but with a slight twist. Indeed, while the
accumulation of specific know-how and skills is a fundamental step towards
development, resource constraints force countries to acquire competitiveness in
the more complex research fields at the price of losing ground in more basic,
albeit less visible (or more crowded), fields. This tendency towards a
relatively specialized basket of capabilities leads to a trade-off between the
need to diversify in order to evolve and the need to allocate resources
efficiently. Collaborative patterns among developed nations reduce the
necessity to be competitive in the less sophisticated fields, freeing resources
for the more complex domains.


  Multi-modal feature fusion as a core investigative component of RGBT tracking
emerges numerous fusion studies in recent years. However, existing RGBT
tracking methods widely adopt fixed fusion structures to integrate multi-modal
feature, which are hard to handle various challenges in dynamic scenarios. To
address this problem, this work presents a novel \emph{A}ttention-based
\emph{F}usion rou\emph{ter} called AFter, which optimizes the fusion structure
to adapt to the dynamic challenging scenarios, for robust RGBT tracking. In
particular, we design a fusion structure space based on the hierarchical
attention network, each attention-based fusion unit corresponding to a fusion
operation and a combination of these attention units corresponding to a fusion
structure. Through optimizing the combination of attention-based fusion units,
we can dynamically select the fusion structure to adapt to various challenging
scenarios. Unlike complex search of different structures in neural architecture
search algorithms, we develop a dynamic routing algorithm, which equips each
attention-based fusion unit with a router, to predict the combination weights
for efficient optimization of the fusion structure. Extensive experiments on
five mainstream RGBT tracking datasets demonstrate the superior performance of
the proposed AFter against state-of-the-art RGBT trackers. We release the code
in https://github.com/Alexadlu/AFter.


  The key innovation of our analytical method, CaRT, lies in establishing a new
hierarchical, distributed architecture to guarantee the safety and robustness
of a given learning-based motion planning policy. First, in a nominal setting,
the analytical form of our CaRT safety filter formally ensures safe maneuvers
of nonlinear multi-agent systems, optimally with minimal deviation from the
learning-based policy. Second, in off-nominal settings, the analytical form of
our CaRT robust filter optimally tracks the certified safe trajectory,
generated by the previous layer in the hierarchy, the CaRT safety filter. We
show using contraction theory that CaRT guarantees safety and the exponential
boundedness of the trajectory tracking error, even under the presence of
deterministic and stochastic disturbance. Also, the hierarchical nature of CaRT
enables enhancing its robustness for safety just by its superior tracking to
the certified safe trajectory, thereby making it suitable for off-nominal
scenarios with large disturbances. This is a major distinction from
conventional safety function-driven approaches, where the robustness originates
from the stability of a safe set, which could pull the system
over-conservatively to the interior of the safe set. Our log-barrier
formulation in CaRT allows for its distributed implementation in multi-agent
settings. We demonstrate the effectiveness of CaRT in several examples of
nonlinear motion planning and control problems, including optimal,
multi-spacecraft reconfiguration.


  We present the first X-ray spectropolarimetric results for Cygnus X-1 in its
soft state from a campaign of five IXPE observations conducted during 2023
May-June. Companion multiwavelength data during the campaign are likewise
shown. The 2-8 keV X-rays exhibit a net polarization degree PD=1.99%+/-0.13%
(68% confidence). The polarization signal is found to increase with energy
across IXPE's 2-8 keV bandpass. The polarized X-rays exhibit an
energy-independent polarization angle of PA=-25.7+/-1.8 deg. East of North (68%
confidence). This is consistent with being aligned to Cyg X-1's AU-scale
compact radio jet and its pc-scale radio lobes. In comparison to earlier
hard-state observations, the soft state exhibits a factor of 2 lower
polarization degree, but a similar trend with energy and a similar (also
energy-independent) position angle. When scaling by the natural unit of the
disk temperature, we find the appearance of a consistent trendline in the
polarization degree between soft and hard states. Our favored polarimetric
model indicates Cyg X-1's spin is likely high (a* above ~0.96). The substantial
X-ray polarization in Cyg X-1's soft state is most readily explained as
resulting from a large portion of X-rays emitted from the disk returning and
reflecting off the disk surface, generating a high polarization degree and a
polarization direction parallel to the black hole spin axis and radio jet. In
IXPE's bandpass, the polarization signal is dominated by the returning
reflection emission. This constitutes polarimetric evidence for strong
gravitational lensing of X-rays close to the black hole.


  Massive black holes are key ingredients of the assembly and evolution of
cosmic structures. Pulsar Timing Arrays (PTAs) currently provide the only means
to observe gravitational radiation from massive black hole binary systems with
masses >10^7 solar masses. The whole cosmic population produces a signal
consisting of two components: (i) a stochastic background resulting from the
incoherent superposition of radiation from the all the sources, and (ii) a
handful of individually resolvable signals that raise above the background
level and are produced by sources sufficiently close and/or massive.
Considering a wide range of massive black hole binary assembly scenarios, we
investigate both the level and shape of the background and the statistics of
resolvable sources. We predict a characteristic background amplitude in the
interval h_c(f = 10^-8 Hz)~5*10^-16 - 5*10^-15, within the detection range of
the complete Parkes PTA. We also quantify the capability of PTAs of measuring
the parameters of individual sources, focusing on monochromatic signals
produced by binaries in circular orbit. We investigate how the results depend
on the number and distribution of pulsars in the array, by computing the
variance-covariance matrix of the parameter measurements. For plausible Square
Kilometre Array (SKA) observations (100 pulsars uniformly distributed in the
sky), and assuming a coherent signal-to-noise ratio of 10, the sky position of
massive black hole binaries can be located within a ~40deg^2 error box, opening
promising prospects for detecting a putative electromagnetic counterpart to the
gravitational wave emission. The planned SKA, can plausibly observe these
unique systems, although the number of detections is likely to be small.
(Abridged)


  Swift response to the detection of endangered minors is an ongoing concern
for law enforcement. Many child-focused investigations hinge on digital
evidence discovery and analysis. Automated age estimation techniques are needed
to aid in these investigations to expedite this evidence discovery process, and
decrease investigator exposure to traumatic material. Automated techniques also
show promise in decreasing the overflowing backlog of evidence obtained from
increasing numbers of devices and online services. A lack of sufficient
training data combined with natural human variance has been long hindering
accurate automated age estimation -- especially for underage subjects. This
paper presented a comprehensive evaluation of the performance of two cloud age
estimation services (Amazon Web Service's Rekognition service and Microsoft
Azure's Face API) against a dataset of over 21,800 underage subjects. The
objective of this work is to evaluate the influence that certain human
biometric factors, facial expressions, and image quality (i.e. blur, noise,
exposure and resolution) have on the outcome of automated age estimation
services. A thorough evaluation allows us to identify the most influential
factors to be overcome in future age estimation systems.


  We construct spectral triples for compact metric spaces (X, d). This provides
us with a new metric d_s on X. We study its relation with the original metric
d. When X is a subshift space, or a discrete tiling space, and d satisfies
certain bounds we advocate that the property of d_s and d to be Lipschitz
equivalent is a characterization of high order. For episturmian subshifts, we
prove that d_s and d are Lipschitz equivalent if and only if the subshift is
repulsive (or power free). For Sturmian subshifts this is equivalent to linear
recurrence. For repetitive tilings we show that if their patches have
equi-distributed frequencies then the two metrics are Lipschitz equivalent.
Moreover, we study the zeta-function of the spectral triple and relate its
abscissa of convergence to the complexity exponent of the subshift or the
tiling. Finally, we derive Laplace operators from the spectral triples and
compare our construction with that of Pearson and Bellissard.


  We introduce the notion of a probabilistic measure which takes values in
hyperbolic numbers and which satisfies the system of axioms generalizing
directly Kolmogorov's system of axioms. We show that this new measure verifies
the usual properties of a probability; in particular, we treat the conditional
hyperbolic probability and we prove the hyperbolic analogues of the
multiplication theorem, of the law of total probability and of Bayes' theorem.
Our probability may take values which are zero--divisors and we discuss
carefully this peculiarity.


  The electromagnetic form factors $G_{\rm E}$ and $G_{\rm M}$ of the proton
and neutron in the timelike region are extracted in a study of the processes
$e^+ e^-\to \bar{p}p$ and $e^+ e^-\to \bar{n}n$. The reaction amplitude is
evaluated within the distorted wave Born approximation, with the interaction of
the antinucleon-nucleon ($\bar{N}N$) pair taken into account. The latter is
constructed within $SU(3)$ chiral effective field theory up to the
next-to-leading order. An excellent description of the $e^+ e^-\to \bar{N}N$
data in the energy region from the $\bar{N}N$ threshold up to center-of-mass
energies $E_{\rm cm}=2.2$~GeV is achieved. Results for the electromagnetic form
factors $G_{\rm E}, G_{\rm M}$, $G_{\rm E}/G_{\rm M}$, and the subtracted
effective form factors, $G_{\rm osc}$, are provided. These can be helpful for
further studies of the properties of the nucleons.


  An atomic routing game is a multiplayer game on a directed graph. Each player
in the game chooses a path -- a sequence of links that connect its origin node
to its destination node -- with the lowest cost, where the cost of each link is
a function of all players' choices. We develop a novel numerical method to
design the link cost function in atomic routing games such that the players'
choices at the Nash equilibrium minimize a given smooth performance function.
This method first approximates the nonsmooth Nash equilibrium conditions with
smooth ones, then iteratively improves the link cost function via implicit
differentiation. We demonstrate the application of this method to atomic
routing games that model noncooperative agents navigating in grid worlds.


  We recently developed SLM, a joint speech and language model, which fuses a
pretrained foundational speech model and a large language model (LLM), while
preserving the in-context learning capability intrinsic to the pretrained LLM.
In this paper, we apply SLM to speech dialog applications where the dialog
states are inferred directly from the audio signal.
  Task-oriented dialogs often contain domain-specific entities, i.e.,
restaurants, hotels, train stations, and city names, which are difficult to
recognize, however, critical for the downstream applications. Inspired by the
RAG (retrieval-augmented generation) paradigm, we propose a retrieval augmented
SLM (ReSLM) that overcomes this weakness. We first train a speech retriever to
retrieve text entities mentioned in the audio. The retrieved entities are then
added as text inputs to the underlying SLM to bias model predictions. We
evaluated ReSLM on speech MultiWoz task (DSTC-11 challenge), and found that
this retrieval augmentation boosts model performance, achieving joint goal
accuracy (38.6% vs 32.7%), slot error rate (20.6% vs 24.8%) and ASR word error
rate (5.5% vs 6.7%). While demonstrated on dialog state tracking, our approach
is broadly applicable to other speech tasks requiring contextual information or
domain-specific entities, such as contextual ASR with biasing capability.


  We discuss various proposals of separating a tensor field into pure-gauge and
gauge-invariant components. Such tensor field decomposition is intimately
related to the effort of identifying the real gravitational degrees of freedom
out of the metric tensor in Einstein's general relativity. We show that, as for
a vector field, the tensor field decomposition has exact correspondence to, and
can be derived from, the gauge-fixing approach. The complication for the tensor
field, however, is that there are infinitely many complete gauge conditions, in
contrast to the uniqueness of Coulomb gauge for a vector field. We make an
extensive exploration of these tensor gauge conditions and their corresponding
tensor field decompositions, regarding mathematical structures, equations of
motion, nonlinear properties; and show that apparently no single choice is
superior in all aspects.


  This paper introduces a methodology to analyze geometrically the
singularities of manipulators, of which legs apply both actuation forces and
constraint moments to their moving platform. Lower-mobility parallel
manipulators and parallel manipulators, of which some legs do not have any
spherical joint, are such manipulators. The geometric conditions associated
with the dependency of six Pl\"ucker vectors of finite lines or lines at
infinity constituting the rows of the inverse Jacobian matrix are formulated
using Grassmann-Cayley Algebra. Accordingly, the singularity conditions are
obtained in vector form. This study is illustrated with the singularity
analysis of four manipulators.


  An iterative scheme for solving ill-posed nonlinear equations with locally
$\sigma$-inverse monotone operators is studied in this paper. A stopping rule
of discrepancy type is proposed. The existence of $u_{n_\delta}$ satisfying the
proposed stopping rule is proved. The convergence of this element to the
minimal-norm solution is justified mathematically.


  We investigate the evolution of complexity and entanglement following a
quench in a one-dimensional topological system, namely the Su-Schrieffer-Heeger
model. We demonstrate that complexity can detect quantum phase transitions and
shows signatures of revivals; this observation provides a practical advantage
in information processing. We also show that the complexity saturates much
faster than the entanglement entropy in this system, and we provide a physical
argument for this. Finally, we demonstrate that complexity is a less sensitive
probe of topological order, compared with measures of entanglement.


  Wikidata is one of the most successful Semantic Web projects. Its underlying
Wikibase data model departs from RDF with the inclusion of several features
like qualifiers and references, built-in datatypes, etc. Those features are
serialized to RDF for content negotiation, RDF dumps and in the SPARQL
endpoint. Wikidata adopted the entity schemas namespace using the ShEx language
to describe and validate the RDF serialization of Wikidata entities. In this
paper we propose WShEx, a language inspired by ShEx that directly supports the
Wikibase data model and can be used to describe and validate Wikibase entities.
The paper presents a the abstract syntax and semantic of the WShEx language.


  Sentiment analysis (SA), is an approach of natural language processing (NLP)
for determining a text's emotional tone by analyzing subjective information
such as views, feelings, and attitudes toward specific topics, products,
services, events, or experiences. This study attempts to develop an advanced
deep learning (DL) model for SA to understand global audience emotions through
tweets in the context of the Olympic Games. The findings represent global
attitudes around the Olympics and contribute to advancing the SA models. We
have used NLP for tweet pre-processing and sophisticated DL models for arguing
with SA, this research enhances the reliability and accuracy of sentiment
classification. The study focuses on data selection, preprocessing,
visualization, feature extraction, and model building, featuring a baseline
Na\"ive Bayes (NB) model and three advanced DL models: Convolutional Neural
Network (CNN), Bidirectional Long Short-Term Memory (BiLSTM), and Bidirectional
Encoder Representations from Transformers (BERT). The results of the
experiments show that the BERT model can efficiently classify sentiments
related to the Olympics, achieving the highest accuracy of 99.23%.


  Trying to address the security challenges of a cloud-centric software
deployment paradigm, silicon and cloud vendors are introducing confidential
computing - an umbrella term aimed at providing hardware and software
mechanisms for protecting cloud workloads from the cloud provider and its
software stack. Today, Intel SGX, AMD SEV, Intel TDX, etc., provide a way to
shield cloud applications from the cloud provider through encryption of the
application's memory below the hardware boundary of the CPU, hence requiring
trust only in the CPU vendor. Unfortunately, existing hardware mechanisms do
not automatically enable the guarantee that a protected system was not tampered
with during configuration and boot time. Such a guarantee relies on a hardware
RoT, i.e., an integrity-protected location that can store measurements in a
trustworthy manner, extend them, and authenticate the measurement logs to the
user.
  In this work, we design and implement a virtual TPM that virtualizes the
hardware RoT without requiring trust in the cloud provider. To ensure the
security of a vTPM in a provider-controlled environment, we leverage unique
isolation properties of the SEV-SNP hardware that allows us to execute secure
services as part of the enclave environment protected from the cloud provider.
We further develop a novel approach to vTPM state management where the vTPM
state is not preserved across reboots. Specifically, we develop a stateless
ephemeral vTPM that supports remote attestation without any persistent state on
the host. This allows us to pair each confidential VM with a private instance
of a vTPM completely isolated from the provider-controlled environment and
other VMs. We built our prototype entirely on open-source components. Though
our work is AMD-specific, a similar approach could be used to build remote
attestation protocols on other trusted execution environments.


  The Neumann and Chaplygin systems on the sphere are simultaneously separable
in variables obtained from the standard elliptic coordinates by the proper
Backlund transformation. We also prove that after similar Backlund
transformations other curvilinear coordinates on the sphere and on the plane
become variables of separations for the system with quartic potential, for the
Henon-Heiles system and for the Kowalevski top. It allows us to say about some
analog of the hetero Backlund transformations relating different
Hamilton-Jacobi equations.


  We compute the cross section for the production of a high-mass photon pair in
association with two hadronic jets to next-to-leading order (NLO) in quantum
chromodynamics (QCD). Our results allow for the first time to reliably predict
the absolute normalisation of this process, and demonstrate that the shape of
important kinematical distributions is modified by higher-order effects. The
perturbative corrections will be an important ingredient to precision studies
of Higgs boson properties from its production in association with two jets.


  Background: Evaluation of the quality of research software is a challenging
and relevant issue, still not sufficiently addressed by the scientific
community.
  Methods: Our contribution begins by defining, precisely but widely enough,
the notions of research software and of its authors followed by a study of the
evaluation issues, as the basis for the proposition of a sound assessment
protocol: the CDUR procedure.
  Results: CDUR comprises four steps introduced as follows: Citation, to deal
with correct RS identification, Dissemination, to measure good dissemination
practices, Use, devoted to the evaluation of usability aspects, and Research,
to assess the impact of the scientific work.
  Conclusions: Some conclusions and recommendations are finally included. The
evaluation of research is the keystone to boost the evolution of the Open
Science policies and practices. It is as well our belief that research software
evaluation is a fundamental step to induce better research software practices
and, thus, a step towards more efficient science.


  Video frame interpolation (VFI) aims to generate predictive frames by warping
learnable motions from the bidirectional historical references. Most existing
works utilize spatio-temporal semantic information extractor to realize motion
estimation and interpolation modeling. However, they insufficiently consider
the real mechanistic rationality of generated middle motions. In this paper, we
reformulate VFI as a Joint Non-linear Motion Regression (JNMR) strategy to
model the complicated motions of inter-frame. Specifically, the motion
trajectory between the target frame and the multiple reference frames is
regressed by a temporal concatenation of multi-stage quadratic models. ConvLSTM
is adopted to construct this joint distribution of complete motions in temporal
dimension. Moreover, the feature learning network is designed to optimize for
the joint regression modeling. A coarse-to-fine synthesis enhancement module is
also conducted to learn visual dynamics at different resolutions through
repetitive regression and interpolation. Experimental results on VFI show that
the effectiveness and significant improvement of joint motion regression
compared with the state-of-the-art methods. The code is available at
https://github.com/ruhig6/JNMR.


  After observing WASP-12 in the second year of the primary mission, the
Transiting Exoplanet Survey Satellite (TESS) revisited the system in late 2021
during its extended mission. In this paper, we incorporate the new TESS
photometry into a reanalysis of the transits, secondary eclipses, and phase
curve. We also present a new $K_s$-band occultation observation of WASP-12b
obtained with the Palomar/Wide-field Infrared Camera instrument. The latest
TESS photometry spans three consecutive months, quadrupling the total length of
the TESS WASP-12 light curve and extending the overall time baseline by almost
two years. Based on the full set of available transit and occultation timings,
we find that the orbital period is shrinking at a rate of $-29.81 \pm 0.94$ ms
yr$^{-1}$. The additional data also increase the measurement precision of the
transit depth, orbital parameters, and phase-curve amplitudes. We obtain a
secondary eclipse depth of $466 \pm 35$ ppm, a $2\sigma$ upper limit on the
nightside brightness of 70 ppm, and a marginal $6\overset{\circ}{.}2 \pm
2\overset{\circ}{.}8$ eastward offset between the dayside hotspot and the
substellar point. The voluminous TESS dataset allows us to assess the level of
atmospheric variability on timescales of days, months, and years. We do not
detect any statistically significant modulations in the secondary eclipse depth
or day-night brightness contrast. Likewise, our measured $K_s$-band occultation
depth of $2810 \pm 390$ ppm is consistent with most $\sim$2.2 $\mu$m
observations in the literature.


  We estimate how well we will know the parameters of solar neutrino
oscillations after KamLAND and Borexino. The expected error on Delta m^2 is few
per-mille in the VO and QVO regions, few per-cent in the LMA region, and around
10% in the LOW region. The expected error on sin^2 2theta is around 5%. KamLAND
and Borexino will tell unambiguously which specific new measurement, dedicated
to pp solar neutrinos, is able to contribute to the determination of theta and
perhaps of Delta m^2. The present data suggest as more likely outcomes: no
measurement, or the total pp rate, or its day/night variation.


  We investigate the effect of radiation reaction on the motion of a wave
packet of a charged scalar particle linearly accelerated in quantum
electrodynamics. We give the details of the calculations for the case where the
particle is accelerated by a static potential that were outlined in Phys.Rev. D
70 (2004) 081701(R) and present similar results in the case of a time-dependent
but space-independent potential. In particular, we calculate the expectation
value of the position of the charged particle after the acceleration, to first
order in the fine structure constant in the $\hbar \to 0$ limit, and find that
the change in the expectation value of the position (the position shift) due to
radiation reaction agrees exactly with the result obtained using the
Lorentz-Dirac force in classical electrodynamics for both potentials. We also
point out that the one-loop correction to the potential may contribute to the
position change in this limit.


  This paper presents a clustering technique that reduces the susceptibility to
data noise by learning and clustering the data-distribution and then assigning
the data to the cluster of its distribution. In the process, it reduces the
impact of noise on clustering results. This method involves introducing a new
distance among distributions, namely the expectation distance (denoted, ED),
that goes beyond the state-of-art distribution distance of optimal mass
transport (denoted, $W_2$ for $2$-Wasserstein): The latter essentially depends
only on the marginal distributions while the former also employs the
information about the joint distributions. Using the ED, the paper extends the
classical $K$-means and $K$-medoids clustering to those over data-distributions
(rather than raw-data) and introduces $K$-medoids using $W_2$. The paper also
presents the closed-form expressions of the $W_2$ and ED distance measures. The
implementation results of the proposed ED and the $W_2$ distance measures to
cluster real-world weather data as well as stock data are also presented, which
involves efficiently extracting and using the underlying data distributions --
Gaussians for weather data versus lognormals for stock data. The results show
striking performance improvement over classical clustering of raw-data, with
higher accuracy realized for ED. Also, not only does the distribution-based
clustering offer higher accuracy, but it also lowers the computation time due
to reduced time-complexity.


  Direct detection of dark matter with directional sensitivity has the
potential to discriminate the dark matter velocity distribution. Especially, it
will be suitable to discriminate isotropic distribution from anisotropic one.
Analyzing data produced with Monte-Carlo simulation, required conditions for
the discrimination is estimated. If energy threshold of detector is optimized,
$O(10^3-10^4)$ event number is required to discriminate the anisotropy.


  Recent developments in cosmic strings are reviewed, with emphasis on
unresolved problems.


  We prove that various notions of supersolutions to the porous medium equation
are equivalent under suitable conditions. More spesifically, we consider weak
supersolutions, very weak supersolutions, and $m$-superporous functions defined
via a comparison principle. The proofs are based on comparison principles and a
Schwarz type alternating method, which are also interesting in their own right.
Along the way, we show that Perron solutions with merely continuous boundary
values are continuous up to the parabolic boundary of a sufficiently smooth
space-time cylinder.


  We explore properties of the class of B\'ekoll\'e-Bonami weights $B_\infty$
introduced by the authors in a previous work. Although B\'ekoll\'e-Bonami
weights are known to be ill-behaved because they do not satisfy a reverse
H\"older property, we prove than when restricting to a class of weights that
are "nearly constant on top halves", one recovers some of the classical
properties of Muckenhoupt weights. We also provide an application of this
result to the study of the spectra of certain integral operators.


  Let N be a prime and let A be a quotient of J_0(N) over Q associated to a
newform such that the special L-value of A (at s=1) is non-zero. Suppose that
the algebraic part of the special L-value of A is divisible by an odd prime q
such that q does not divide the numerator of (N-1)/12. Then the Birch and
Swinnerton-Dyer conjecture predicts that the q-adic valuations of the algebraic
part of the special L-value of A and of the order of the Shafarevich-Tate group
are both positive even numbers. Under a certain mod q non-vanishing hypothesis
on special L-values of twists of A, we show that the q-adic valuations of the
algebraic part of the special L-value of A and of the Birch and Swinnerton-Dyer
conjectural order of the Shafarevich-Tate group of A are both positive even
numbers. We also give a formula for the algebraic part of the special L-value
of A over quadratic imaginary fields K in terms of the free abelian group on
isomorphism classes of supersingular elliptic curves in characteristic N
(equivalently, over conjugacy classes of maximal orders in the definite
quaternion algebra over Q ramified at N and infinity) which shows that this
algebraic part is a perfect square up to powers of the prime two and of primes
dividing the discriminant of K. Finally, for an optimal elliptic curve E, we
give a formula for the special L-value of the twist E_D of E by a negative
fundamental discriminant -D, which shows that this special L-value is an
integer up to a power of 2, under some hypotheses. In view of the second part
of the Birch and Swinnerton-Dyer conjecture, this leads us to the surprising
conjecture that the square of the order of the torsion subgroup of E_D divides
the product of the order of the Shafarevich-Tate group of E_D and the orders of
the arithmetic component groups of E_D, under certain mild hypotheses.


  Just-infinite C*-algebras, i.e., infinite dimensional C*-algebras, whose
proper quotients are finite dimensional, were investigated in
[Grigorchuk-Musat-Rordam, 2016]. One particular example of a just-infinite
residually finite dimensional AF-algebras was constructed in that article. In
this paper we extend that construction by showing that each infinite
dimensional metrizable Choquet simplex is affinely homeomorphic to the trace
simplex of a just-infinite residually finite dimensional C*-algebras. The trace
simplex of any unital residually finite dimensional C*-algebra is hence
realized by a just-infinite one. We determine the trace simplex of the
particular residually finite dimensional AF-algebras constructed in the above
mentioned article, and we show that it has precisely one extremal trace of type
II_1.
  We give a complete description of the Bratteli diagrams corresponding to
residually finite dimensional AF-algebras. We show that a modification of any
such Bratteli diagram, similar to the modification that makes an arbitrary
Bratteli diagram simple, will yield a just-infinite residually finite
dimensional AF-algebra.


  The purpose of this research is to study the upper critical field (Hc2) of
two-band superconductors by two-band Ginzburg - Landau approach. The analytical
formula of Hc2 included anisotropy of order parameter and anisotropy of
effective-mass are found . The parameters of the upper critical field in
ab-plane and c-axis can be found by fitting to the experimental data . Finally,
we can find the ratio of upper critical field that temperature dependent in the
range of experimental result .


  The main result of this paper shows that the Castelnuovo-Mumford regularity
of the tangent cone of a local ring is effectively bounded by the dimension and
any extended degree. From this it follows that there are only a finite number
of Hilbert-Samuel functions of local rings with given dimension and extended
degree.


  We consider general, non-linear curvature perturbations on scales greater
than the Hubble horizon scale by invoking an expansion in spatial gradients,
the so-called gradient expansion. After reviewing the basic properties of the
gradient expansion, we derive the conservation law for non-linear curvature
perturbations for an isentropic fluid. We also define the gauge-invariant
curvature perturbation under a finite shift of time-slicing, and derive the
non-linear genralization of the $\delta N$ formalism. The results obtained are
straight-forward generalisations of those already proven in linear perturbation
theory, and the equations are simple, resembling closely the first-order
equations.


  Let $G$ be a bipartite graph with bipartition $(X,Y)$. Inspired by a
hypergraph problem, we seek an upper bound on the number of disjoint paths
needed to cover all the vertices of $X$. We conjecture that a Hall-type
sufficient condition holds based on the maximum value of
$|S|-|\mathsf\Lambda(S)|$, where $S\subseteq X$ and $\mathsf\Lambda(S)$ is the
set of all vertices in $Y$ with at least two neighbors in $S$. This condition
is also a necessary one for a hereditary version of the problem, where we
delete vertices from $X$ and try to cover the remaining vertices by disjoint
paths. The conjecture holds when $G$ is a forest, has maximum degree $3$, or is
regular with high girth, and we prove those results in this paper.


  Phenomenological rules that govern the collective behaviour of complex
physical systems are powerful tools because they can make concrete predictions
about their universality class based on generic considerations, such as
symmetries, conservation laws, and dimensionality. While in most cases such
considerations are manifestly ingrained in the constituents, novel
phenomenology can emerge when composite units associated with emergent
symmetries dominate the behaviour of the system. We study a generic class of
active matter systems with non-reciprocal interactions and demonstrate the
existence of true long-range polar order in two dimensions and above, both at
the linear level and by including all relevant nonlinearities in the
Renormalization Group sense. We achieve this by uncovering a mapping of our
scalar active mixture theory to the Toner-Tu theory of dry polar active matter
by employing a suitably defined polar order parameter. We then demonstrate that
the complete effective field theory -- which includes all the soft modes and
the relevant nonlinear terms -- belongs to the (Burgers-) Kardar-Parisi-Zhang
universality class. This classification allows us to prove the stability of the
emergent polar long-range order in scalar non-reciprocal mixtures in two
dimensions, and hence a conclusive violation of the Mermin-Wagner theorem.


  We investigate the relation between the topological entropy of pseudo-Anosov
maps on surfaces with punctures and the rank of the first homology of their
mapping tori. On the surface $S$ of genus $g$ with $n$ punctures, we show that
the entropy of a pseudo-Anosov map is bounded from above by
$\dfrac{(k+1)\log(k+3)}{|\chi(S)|}$ up to a constant multiple when the rank of
the first homology of the mapping torus is $k+1$ and $k, g, n$ satisfy a
certain assumption. This is a partial generalization of precedent works of Tsai
and Agol-Leininger-Margalit.


  Intermittent maps of Pomeau-Manneville type are well-studied in
one-dimension, and also in higher dimensions if the map happens to be Markov.
In general, the nonconformality of multidimensional intermittent maps
represents a challenge that up to now is only partially addressed. We show how
to prove sharp polynomial bounds on decay of correlations for a class of
multidimensional intermittent maps. In addition we show that the optimal
results on statistical limit laws for one-dimensional intermittent maps hold
also for the maps considered here. This includes the (functional) central limit
theorem and local limit theorem, Berry-Esseen estimates, large deviation
estimates, convergence to stable laws and L\'evy processes, and infinite
measure mixing.


  We perform hole burning with a low drift stabilized laser within the zero
phonon line of the 4f-5d transition in Ce$^{3+}$:Y$_2$SiO$_5$ at 2K. The
narrowest spectral holes appear for small applied magnetic fields and are
$6\pm4$ MHz wide (FWHM). This puts an upper bound on the homogeneous linewidth
of the transition to $3\pm2$ MHz, which is close to lifetime limited. The spin
level relaxation time is measured to $72\pm21$ ms with a magnetic field of 10
mT.
  A slow permanent hole burning mechanism is observed. If the excitation
frequency is not changed the fluorescence intensity is reduced by more than
50$\%$ after a couple of minutes of continuous excitation. The spectral hole
created by the permanent hole burning has a width in the tens of MHz range,
which indicates that a trapping mechanism occurs via the 5d-state.


  Using the WKB approximation we perform a linear stability analysis for a
rotational flow of a viscous and electrically conducting fluid in an external
azimuthal magnetic field that has an arbitrary radial profile B_{phi}(R). In
the inductionless approximation, we find the growth rate of the
three-dimensional perturbation in a closed form and demonstrate in particular
that it can be positive when the velocity profile is Keplerian and the magnetic
field profile is slightly shallower than R^{-1}.


  We present a detailed photometric and spectroscopic analysis of DD CMa, based
on published survey photometry and new spectroscopic data. We find an improved
orbital period of $P_\mathrm{o}= 2.0084530 \pm 0.0000006 ~\mathrm{d}$. Our
spectra reveal H$\beta$ and H$\alpha$ absorptions with weak emission shoulders
and we also find color excess in the WISE multiband photometry, interpreted as
signatures of circumstellar matter. We model the $V$-band orbital light curve
derived from the ASAS and ASAS-SN surveys, assuming a semidetached
configuration and using the mass ratio and temperature of the hotter star
derived from our spectroscopic analysis. Our model indicates that the system
consists of a B 2.5 dwarf and a B 9 giant of radii 3.2 and 3.7
$\mathrm{R_{\odot}}$, respectively, orbiting in a circular orbit of radius 6.75
$\mathrm{R_{\odot}}$. We also found $M_{\mathrm{c}} = 1.7 \pm 0.1
~\mathrm{M_{\odot}}$, $T_{\mathrm{c}} = 11350 \pm 100 ~\mathrm{K}$ and
$M_{\mathrm{h}} = 6.4 \pm 0.1 ~\mathrm{M_{\odot}}$, $T_{\mathrm{h}} = 20000 \pm
500 ~\mathrm{K}$, for the cooler and hotter star, respectively. We find broad
single emission peaks in H$\alpha$ and H$\beta$ after subtracting the synthetic
stellar spectra. Our results are consistent with mass exchange between the
stars, and suggest the existence of a stream of gas being accreted onto the
early B-type star.


  Anomaly detection plays a pivotal role in numerous real-world scenarios, such
as industrial automation and manufacturing intelligence. Recently, variational
inference-based anomaly analysis has attracted researchers' and developers'
attention. It aims to model the defect-free distribution so that anomalies can
be classified as out-of-distribution samples. Nevertheless, there are two
disturbing factors that need us to prioritize: (i) the simplistic prior latent
distribution inducing limited expressive capability; (ii) the strong
probability distance notion results in collapsed features. In this paper, we
propose a novel Patch-wise Wasserstein AutoEncoder (P-WAE) architecture to
alleviate those challenges. In particular, a patch-wise variational inference
model coupled with solving the jigsaw puzzle is designed, which is a simple yet
effective way to increase the expressiveness of the latent manifold. This makes
using the model on high-dimensional practical data possible. In addition, we
leverage a weaker measure, sliced-Wasserstein distance, to achieve the
equilibrium between the reconstruction fidelity and generalized
representations. Comprehensive experiments, conducted on the MVTec AD dataset,
demonstrate the superior performance of our proposed method.


  The morphology of planetary nebulae (PNe) provides an essential tool for
understanding their origin and evolution, as it reflects both the dynamics of
the gas ejected during the TP-AGB phase, and the central star energetics. Here
we study the morphology of 27 Magellanic Cloud planetary nebulae (MCPNe) and
present an analysis of their physical characteristics across morphological
classes. Similar studies have been successfully carried out for galactic PNe,
but were compromised by the uncertainty of individual PN distances. We present
our own HST/FOC images of 15 Magellanic Cloud PNe (MCPNe) acquired through a
narrow-band lambda 5007 [O III] filter. We use the Richardson-Lucy
deconvolution technique on these pre-COSTAR images to achieve post-COSTAR
quality. Three PNe imaged before and after COSTAR confirm the high reliability
of our deconvolution procedure. We derive morphological classes, dimensions,
and surface photometry for all these PNe. We have combined this sample with
HST/PC1 images of 15 MCPNe, three of which are in common with the FOC set,
acquired by Dopita et al. (1996), to obtain the largest MCPN sample ever
examined from the morphological viewpoint. By using the whole database,
supplemented with published data from the literature, we have analyzed the
properties of the MCPNe and compared them to a typical, complete galactic
sample. Morphology of the MCPNe is then correlated with PN density, chemistry,
and evolution.


  We find explicit bounds on the primary components and on the
Castelnuovo-Mumford regularity of powers of monomial ideals. We also analyze
the primary decompositions of Katzman's example.


  We use cosmological hydrodynamical galaxy formation simulations from the
NIHAO project to investigate the response of cold dark matter (CDM) haloes to
baryonic processes. Previous work has shown that the halo response is primarily
a function of the ratio between galaxy stellar mass and total virial mass, and
the density threshold above which gas is eligible to form stars, $n [{\rm
cm}^{-3}]$. At low $n$ all simulations in the literature agree that dwarf
galaxy haloes are cuspy, but at high $n\ge 100$ there is no consensus. We trace
halo contraction in dwarf galaxies with $n\ge 100$ reported in some previous
simulations to insufficient spatial resolution. Provided the adopted star
formation threshold is appropriate for the resolution of the simulation, we
show that the halo response is remarkably stable for $n\ge 5$, up to the
highest star formation threshold that we test, $n=500$. This free parameter can
be calibrated using the observed clustering of young stars. Simulations with
low thresholds $n\le 1$ predict clustering that is too weak, while simulations
with high star formation thresholds $n\ge 5$, are consistent with the observed
clustering. Finally, we test the CDM predictions against the circular
velocities of nearby dwarf galaxies. Low thresholds predict velocities that are
too high, while simulations with $n\sim 10$ provide a good match to the
observations. We thus conclude that the CDM model provides a good description
of the structure of galaxies on kpc scales provided the effects of baryons are
properly captured.


  This paper presents recent time-dependent measurements of neutral B meson
oscillations. Similar to the $K^0$--$\bar{K}^0$ system, there are two such
systems involving the b quark: $B_d^0$--$\bar{B}_d^0$ and
$B_s^0$--$\bar{B}_s^0$. Thus the physical states are respectively $K_{S}$ and
$K_{L}$, $(B_d)_S$ and $(B_d)_L$, and $(B_s)_S$ and $(B_s)_L$. The oscillation
between each pair of states can be used to determine their mass difference. The
present world average for the $(B_d)_S$--$(B_d)_L$ mass difference is $\Delta
m_d = 0.457\pm0.019 ps^{-1}$ (or $(3.01\pm0.13)\times 10^{-4}$ eV). Using
$f_{B_s}$ = 12\% (the fraction of $B_s$ produced in b events), the current
lower limit on the corresponding $\Delta m_s$ is 6.1 ps$^{-1}$ (or $4.0\times
10^{-3}$ eV).


  We explore the influence of heavy quarks on the deconfinement phase
transition in an effective model for gluons interacting with dynamical quarks
in color SU(3). With decreasing quark mass, the strength of the explicit
breaking of the Z(3) symmetry grows and the first-order transition ends in a
critical endpoint. The nature of the critical endpoint is examined by studying
the longitudinal and transverse fluctuations of the Polyakov loop, quantified
by the corresponding susceptibilities. The longitudinal susceptibility is
enhanced in the critical region, while the transverse susceptibility shows a
monotonic behavior across the transition point. We investigate the dependence
of the critical endpoint on the number of quark flavors at vanishing and finite
quark density. Finally we confront the model results with lattice calculations
and discuss a possible link between the hopping parameter and the quark mass.


  One-armed oscillation modes in the circumstellar discs of Be stars may
explain the cyclical variations in their emission lines. We show that a
three-dimensional effect, involving vertical motion and neglected in previous
treatments, profoundly influences the dynamics. Using a secular theory of
eccentric discs that reduces the problem to a second-order differential
equation, we show that confined prograde modes are obtained for all reasonable
disc temperatures and stellar rotation rates. We confirm these results using a
numerical analysis of the full set of linearized equations for
three-dimensional isothermal discs including viscous terms that couple the
horizontal motions at different altitudes. In order to make these modes grow,
viscous damping must be overcome by an excitation mechanism such as viscous
overstability.


  We calculate the thermal photon transverse momentum spectra and elliptic flow
in $\sqrt{s_{NN}} = 200$ GeV Au+Au collisions at RHIC and in $\sqrt{s_{NN}} =
2.76$ TeV Pb+Pb collisions at the LHC, using an ideal-hydrodynamical framework
which is constrained by the measured hadron spectra at RHIC and LHC. The
sensitivity of the results to the QCD-matter equation of state and to the
photon emission rates is studied, and the photon $v_2$ is discussed in the
light of the photonic $p_T$ spectrum measured by the PHENIX Collaboration. In
particular, we make a prediction for the thermal photon $p_T$ spectra and
elliptic flow for the current LHC Pb+Pb collisions.


  In this paper it is demonstrated that the scoring at each PGA Tour stroke
play event can be reasonably modeled as a Gaussian random variable. All 46
stroke play events in the 2007 season are analyzed. The distributions of scores
are favorably compared with a Gaussian distribution using the
Kolmogorov-Smirnov test. This observation suggests performance tracking on the
PGA tour should be done in terms of the z-score, calculated by subtracting the
mean from the raw score and dividing by the standard deviation. This
methodology measures performance relative to the field of competitors,
independent of the venue, and in terms of a statistic that has quantitative
meaning. Several examples of the use of this scoring methodology are provided,
including a calculation of the probability that Tiger Woods will break Byron
Nelson's record of eleven consecutive PGA Tour victories.


  We compute O(alpha_s) and O(alpha_s^n beta_0^{n-1}) (BLM) corrections to the
five structure functions relevant for b->q l nu decays and apply the results to
the moments of a few distributions of phenomenological importance. We present
compact analytic one-loop formulae for the structure functions, with proper
subtraction of the soft divergence.


  We analyze methanol excitation in the absence of external radiation and
consider LTE methods for probing interstellar gas. We show that rotation
diagrams correctly estimate the gas kinetic temperature only if they are built
from lines with the upper levels located in the same K-ladders, such as the
J_0-J_{-1}E lines at 157~GHz, the J_1-J_0E lines at 165~GHz or the J_2-J_1E
lines at 25~GHz. The gas density should be no less than 10^7~cm^{-3}. Rotation
diagrams built from lines with different K values of the upper levels (2_K-1_K
at 96~GHz, 3_K-2_K at 145~GHz, or 5_K-4_K at 241~GHz) significantly
underestimate the temperature but allow a density estimation. In addition, the
diagrams based on the 2_K-1_K lines make possible methanol column density
estimates within a factor of about 2--5. We suggest that rotation diagrams
should be used in the following manner. First, one should build two rotation
diagrams, one from the lines at 96, 145, or 241~GHz, and another from the lines
at 157, 165, or 25~GHz. The former diagram is used to estimate the gas density.
If the density is about 10^7~cm^{-3} or higher, the latter diagram reproduces
the temperature fairly well. If the density is around 10^6~cm^{-3}, the
temperature obtained from the latter diagram should be multiplied by a factor
of 1.5--2. If the density is about 10^5~cm^{-3} or lower, then the latter
diagram yields a temperature that is lower than the kinetic temperature by a
factor of three or larger and should be used only as a lower limit on the
kinetic temperature. Errors of methanol column density determined from the
integrated intensity of a single line may be larger than an order of magnitude
even when the gas temperature is well-known. However, if the J_0-(J-1)_0E
lines, as well as the J_1-(J-1)_1A^{+} or A^{-} lines are used, the relative
error of the column density proves to be no larger than several units.


  Chandra ACIS observations of PKS 0521-365 find that the X-ray emission of
this BL Lac object consists of emission from an unresolved core, a diffuse
halo, and a 2 arcsec jet feature coincident with the inner radio/optical jet. A
comparison with a new ATCA 8.6-GHz map also finds X-ray emission from the
bright hotspot south-east of the nucleus. The jet spectrum, from radio to
X-ray, is probably synchrotron emission from an electron population with a
broken power-law energy distribution, and resembles the spectra seen from the
jets of low-power (FR I) radio galaxies. The hotspot X-ray flux is consistent
with the expectations of synchrotron self-Compton emission from a plasma close
to equipartition, as seen in studies of high-power (FR II) radio galaxies.
While the angular structure of the halo is similar to that found by an analysis
of the ROSAT HRI image, its brightness is seen to be lower with Chandra, and
the halo is best interpreted as thermal emission from an atmosphere of similar
luminosity to the halos around FR I radio galaxies. The X-ray properties of PKS
0521-365 are consistent with it being a foreshortened, beamed, radio galaxy.


  Computer vision has become increasingly prevalent in solving real-world
problems across diverse domains, including smart agriculture, fishery, and
livestock management. These applications may not require processing many image
frames per second, leading practitioners to use single board computers (SBCs).
Although many lightweight networks have been developed for mobile/edge devices,
they primarily target smartphones with more powerful processors and not SBCs
with the low-end CPUs. This paper introduces a CNN-ViT hybrid network called
SBCFormer, which achieves high accuracy and fast computation on such low-end
CPUs. The hardware constraints of these CPUs make the Transformer's attention
mechanism preferable to convolution. However, using attention on low-end CPUs
presents a challenge: high-resolution internal feature maps demand excessive
computational resources, but reducing their resolution results in the loss of
local image details. SBCFormer introduces an architectural design to address
this issue. As a result, SBCFormer achieves the highest trade-off between
accuracy and speed on a Raspberry Pi 4 Model B with an ARM-Cortex A72 CPU. For
the first time, it achieves an ImageNet-1K top-1 accuracy of around 80% at a
speed of 1.0 frame/sec on the SBC. Code is available at
https://github.com/xyongLu/SBCFormer.


  We study closed dense collections of hard spheres that collide inelastically
with constant coefficient of normal restitution. We find inhomogeneous states
(IS) where the density profile is spatially non-uniform but constant in time.
The states are exact solutions of non-linear partial differential equations
that describe the coupled distributions of density and temperature when
inelastic losses of energy per collision are small. The derivation is performed
without modelling the equations' coefficients that are unknown in the dense
limit (such as the equation of state), using only their scaling form specific
for hard spheres. The IS is exact non-linear state of this many-body system. It
captures a fundamental property of inelastic collections of particles: the
possibility of preserving non-uniform temperature via the interplay of
inelastic cooling and heat conduction, generalizing previous results in the
dilute case. We perform numerical simulations to demonstrate that arbitrary
initial state evolves to the IS in the limit of long times where the container
has the geometry of the channel. The evolution is like gas-liquid transition.
The liquid condenses in a vanishing part of the total volume but takes most of
the mass of the system. However, the gaseous phase, which mass grows only
logarithmically with the system size, is relevant because its fast particles
carry most of the energy of the system. Remarkably, the system self-organizes
to dissipate no energy: the inelastic decay of energy is a power-law
$[1+t/t_c]^{-2}$ where $t_c$ diverges in the thermodynamic limit. This behavior
is caused by unusual spatial distribution of particles: on approach to one of
the container's walls the density grows inversely with the distance. We discuss
the relation of our results to the recently proposed finite-time singularity in
other container's geometries.


  Ever since Nikuradse's experiments on turbulent friction in 1933, there have
been theoretical attempts to describe his measurements by collapsing the data
into single-variable functions. However, this approach, which is common in
other areas of physics and in other fields, is limited by the lack of rigorous
quantitative methods to compare alternative data collapses. Here, we address
this limitation by using an unsupervised method to find analytic functions that
optimally describe each of the data collapses for the Nikuradse dataset. By
descaling these analytic functions, we show that a low dispersion of the scaled
data does not guarantee that a data collapse is a good description of the
original data. In fact, we find that, out of all the proposed data collapses,
the original one proposed by Prandtl and Nikuradse over 80 years ago provides
the best description of the data so far, and that it also agrees well with
recent experimental data, provided that some model parameters are allowed to
vary across experiments.


  In many research fields, the sizes of the existing datasets vary widely.
Hence, there is a need for machine learning techniques which are well-suited
for these different datasets. One possible technique is the self-organizing map
(SOM), a type of artificial neural network which is, so far, weakly represented
in the field of machine learning. The SOM's unique characteristic is the
neighborhood relationship of the output neurons. This relationship improves the
ability of generalization on small datasets. SOMs are mostly applied in
unsupervised learning and few studies focus on using SOMs as supervised
learning approach. Furthermore, no appropriate SOM package is available with
respect to machine learning standards and in the widely used programming
language Python. In this paper, we introduce the freely available Supervised
Self-organizing maps (SuSi) Python package which performs supervised regression
and classification. The implementation of SuSi is described with respect to the
underlying mathematics. Then, we present first evaluations of the SOM for
regression and classification datasets from two different domains of geospatial
image analysis. Despite the early stage of its development, the SuSi framework
performs well and is characterized by only small performance differences
between the training and the test datasets. A comparison of the SuSi framework
with existing Python and R packages demonstrates the importance of the SuSi
framework. In future work, the SuSi framework will be extended, optimized and
upgraded e.g. with tools to better understand and visualize the input data as
well as the handling of missing and incomplete data.


  Symmetric Monge-Kantorovich transport problems involving a cost function
given by a family of vector fields were used by Ghoussoub-Moameni to establish
polar decompositions of such vector fields into $m$-cyclically monotone maps
composed with measure preserving $m$-involutions ($m\geq 2$). In this note, we
relate these symmetric transport problems to the Brenier solutions of the Monge
and Monge-Kantorovich problem, as well as to the Gangbo-\'Swi\c{e}ch solutions
of their multi-marginal counterparts, both of which involving quadratic cost
functions.


  This paper introduces the CondorJ2 cluster management system. Traditionally,
cluster management systems such as Condor employ a process-oriented approach
with little or no use of modern database system technology. In contrast,
CondorJ2 employs a data-centric, 3-tier web-application architecture for all
system functions (e.g., job submission, monitoring and scheduling; node
configuration, monitoring and management, etc.) except for job execution.
Employing a data-oriented approach allows the core challenge (i.e., managing
and coordinating a large set of distributed computing resources) to be
transformed from a relatively low-level systems problem into a more abstract,
higher-level data management problem. Preliminary results suggest that
CondorJ2's use of standard 3-tier software represents a significant step
forward to the design and implementation of large clusters (1,000 to 10,000
nodes).


  These are some speculations on how Grothendieck's point of view and the idea
of complexity dynamics can come together in the problem of explaining the black
hole information paradox. They are neither complete, nor final, but can seem
like a new direction of research. If read as such they could prove useful to
some researchers. The basic idea is that entanglement alone cannot fully
account for the information extraction in black hole contexts. Complexity has
been proposed as an alternative but remains a vague concept. I employ
Grothendieck's point of view to expand the idea of entanglement entropy to a
categorical context in which the objects (states) and their maps are considered
together and the map space has additional topological and geometric structure
that intermingles with the object set of the category via Sieves, Sheafs, and
Toposes.


  Recent evidence for an excess of gamma rays in the GeV energy range about the
Galactic Center have refocused attention on models of dark matter in the low
mass regime ($m_\chi \lesssim m_Z/2$). Because this is an experimentally
well-trod energy range, it can be a challenge to develop simple models that
explain this excess, consistent with other experimental constraints. We
reconsider models where the dark matter couples to dark photon, which has a
weak kinetic mixing to the Standard Model photon, or scalars with a weak mixing
with the Higgs boson. We focus on the light ($\lesssim 1.5 GeV$) dark mediator
mass regime. Annihilations into the dark mediators can produce observable gamma
rays through decays to $\pi^0$, through radiative processes when decaying to
charged particles ($e^+e^-, \mu^+\mu^-,...$), and subsequent interactions of
high energy $e^+e^-$ with gas and light. However, these models have no signals
of $\bar p$ production, which is kinematically forbidden. We find that in these
models, the shape of resulting gamma-ray spectrum can provide a good fit to the
excess at Galactic Center. We discuss further constraints from AMS-02, and find
regions of compatibility.


  We propose a combinatorial model for the Schubert structure constants of the
complete flag manifold when one of the factors is Grassmannian.


  We present two novel approaches for the computation of the exact distribution
of a pattern in a long sequence. Both approaches take into account the sparse
structure of the problem and are two-part algorithms. The first approach relies
on a partial recursion after a fast computation of the second largest
eigenvalue of the transition matrix of a Markov chain embedding. The second
approach uses fast Taylor expansions of an exact bivariate rational
reconstruction of the distribution. We illustrate the interest of both
approaches on a simple toy-example and two biological applications: the
transcription factors of the Human Chromosome 5 and the PROSITE signatures of
functional motifs in proteins. On these example our methods demonstrate their
complementarity and their hability to extend the domain of feasibility for
exact computations in pattern problems to a new level.


  Over a field of characteristic two, we develop a theory of standard monomials
for polynomial rings modulo a Frobenius power of the maximal ideal generated by
all variables. As a result, we obtain a filtration by modular
GL_n-representations whose characters are given by particular truncated Schur
polynomials, thus proving a conjecture by Gao--Raicu--VandeBogert in the
characteristic two case.


  Older adults are using voice-based technologies in a variety of different
contexts and are uniquely positioned to benefit from smart speakers' handsfree,
voice-based interface. In order to better understand the ways in which older
adults engage with and learn how to use smart speakers, we conducted
qualitative, semi-structured interviews with four older adults who own smart
speakers. Emerging findings indicate that older adults benefit from smart
speakers as both an assistive and a social technology. Findings also suggest
that when older adults learn new technologies in a formal, communal environment
there is successful adoption.


  The avoidability, or unavoidability of patterns in words over finite
alphabets has been studied extensively. A word (pattern) over a finite set is
said to be unavoidable if, for all but finitely many words, there exists a
morphism mapping the pattern into every word. We present various
complexity-related properties of unavoidable words. For words that are
unavoidable, we provide an upper bound to the lengths of words that avoid them.
A natural subsequent question is how many unavoidable words there are. We show
that the fraction of words that are unavoidable drops exponentially fast in the
length of the word. This allows us to calculate an upper bound on the number of
unavoidable patterns for any given finite alphabet. Subsequently, we
investigate computational aspects of unavoidable words. In particular, we
exhibit concrete algorithms for determining whether a word is unavoidable. We
also prove results on the computational complexity of the problem of
determining whether a given word is unavoidable.


  The study aims to examine the spectral dynamics of the low-frequency,
optically thick gyrosynchrotron microwave emission in solar flares to determine
the characteristics of the emitting source. We present the high-resolution
spectra of a set of microwave bursts observed by the Expanded Owens Valley
Solar Array (EOVSA) during its commissioning phase in the $2.5-18$ GHz
frequency range with $1$ second time resolution. Out of the 12 events analyzed
in this study, nine bursts exhibit a direct decrease with time in the optically
thick spectral index $\alpha_l$, an indicator of source morphology.
Particularly, five bursts display "flat" spectrum ($\alpha_l\leq1.0$) compared
to that expected for a homogeneous/uniform source ($\alpha_l\approx2.9$). These
flat spectra at the low-frequencies (<$10$ GHz) can be defined as the emission
from a spatially inhomogeneous source with a large area and/or with multiple
emission components. In a subset of six events with partial cross-correlation
data, both the events with flat spectra show a source size of $\sim120$ arcsec
at $2.6-3$ GHz. Modeling based on inhomogeneity supports the conclusion that
multiple discrete sources can only reproduce a flat spectrum. We report that
these flat spectra appear predominantly in the decay phase and typically grow
flatter over the duration in most of the bursts, which indicates the increasing
inhomogeneity and complexity of the emitting volume as the flare progresses.
This large volume of flare emission filled with the trapped energetic particles
is often invisible in other wavelengths, like hard X-rays, presumably due to
the collisionless conditions in these regions of low ambient density and
magnetic field strength.


  Plasmon opens up the possibility to efficiently couple light and matter at
sub-wavelength scales. In general, the plasmon frequency is dependent of
carrier density. This dependency, however, renders fundamentally a weak plasmon
intensity at low frequency, especially for Dirac plasmon (DP) widely studied in
graphene. Here we demonstrate a new type of DP, excited by a Dirac
nodal-surface state, which exhibits an anomalously density-independent
frequency. Remarkably, we predict realization of anomalous DP (ADP) in 1D
topological electrides, such as Ba3CrN3 and Sr3CrN3, by first-principles
calculations. The ADPs in both systems have a density-independent frequency and
high intensity, and their frequency can be tuned from terahertz to mid-infrared
by changing the excitation direction. Furthermore, the intrinsic weak
electron-phonon coupling of anionic electrons in electrides affords an added
advantage of ultra-low phonon-assisted damping and hence a long lifetime of the
ADPs. Our work paves the way to developing novel plasmonic and optoelectronic
devices by combining topological physics with electride materials.


  This article is the first in a series of two in which we study the vanishing
cycles of curves in toric surfaces. We give a list of possible obstructions to
contract vanishing cycles within a given complete linear system. Using tropical
means, we show that any non-separating simple closed curve is a vanishing cycle
whenever none of the listed obstructions appears.


  Efficient multi-dimensional template placement is crucial in computationally
intensive matched-filtering searches for Gravitational Waves (GWs). Here, we
implement the Neighboring Cell Algorithm (NCA) to improve the detection volume
of an existing Compact Binary Coalescence (CBC) template bank. This algorithm
has already been successfully applied for a binary millisecond pulsar search in
data from the Fermi satellite. It repositions templates from over-dense regions
to under-dense regions and reduces the number of templates that would have been
required by a stochastic method to achieve the same detection volume. Our
method is readily generalizable to other CBC parameter spaces. Here we apply
this method to the aligned--single-spin neutron-star--black-hole binary
coalescence inspiral-merger-ringdown gravitational wave parameter space. We
show that the template nudging algorithm can attain the equivalent
effectualness of the stochastic method with 12% fewer templates.


  A phenomenological thermodynamic potential was constructed based on the
symmetry analysis and property characterization of bulk DyCo2. An eight-order
polynomial of Landau expansion was employed to describe the thermodynamic
behavior of DyCo2. Several properties were reproduced including ferromagnetic
transition temperature, magnetization curve, temperature dependence of
magnetization. The transition behavior was analyzed via the thermodynamic
potential. The Landau phenomenological thermodynamic model predicts the correct
metamagnetic transition near the Curie temperature.


  Let $F$ be a function in the Selberg class ${\mathcal S}$ and $a$ be a real
number not equal to 1/2. Consider the sum
$$\lambda_{F}(n,a)=\sum_{\rho}\left[1-\left(\frac{\rho-a}{\rho+a-1}\right)^{n}\right],$$
where $\rho$ runs over the non-trivial zeros of $F$. In this paper, we prove
that the Riemann hypothesis is equivalent to the positivity of the "modified Li
coefficient" $\lambda_{F}(n,a)$, for $n=1,2,..$ and $a<1/2$. Furthermore, we
give an explicit arithmetic and asymptotic formula of these coefficients.


  Highly-damped quasi-normal frequencies are very often of the form omega_n =
(offset) + i n (gap). We investigate the genericity of this phenomenon by
considering a model potential that is piecewise Eckart (piecewise
Poeschl-Teller), and developing an analytic "quantization condition" for the
highly-damped quasi-normal frequencies. We find that this omega_n = (offset) +
i n (gap) behaviour is generic but not universal, with the controlling feature
being whether or not the ratio of the rates of exponential falloff in the two
asymptotic directions is a rational number. These observations are of direct
relevance to any physical situation where highly-damped quasi-normal modes
(damped modes) are important --- in particular (but not limited to) to black
hole physics, both theoretical and observational.


  Starting from a point - like two - and three - particle interaction the
kinetic equation is derived. While the drift term of the kinetic equation turns
out to be determined by the known Skyrme mean field the collision integral
appears in two - and three - particle parts. The cross section results from the
same microscopic footing and is naturally density dependent due to the three -
particle force. By this way no hybrid model for drift and cross section is
needed for nuclear transport. Besides the mean field correlation energy the
resulting equation of state has also a two - and three - particle correlation
energy which are both calculated analytically for the ground state. These
energies contribute to the equation of state and lead to an occurrence of a
maximum at 3 times nuclear density in the total energy.


  The main goal of this work is to compare the results of three dynamical mass
estimators to the X-ray hydrostatic values, focussing on massive galaxy
clusters at intermediate redshifts $z\sim0.3$. We estimated dynamical masses
with the virial theorem, the Jeans equation, and the caustic method using
wide-field VIMOS spectroscopy. We investigated the role of colour selection and
the impact of substructures on the dynamical estimators. The Jeans and caustic
methods give consistent results, whereas the virial theorem leads to masses
$\sim15\%$ larger. The Jeans, caustic, and virial masses are respectively
$\sim20\%$, $\sim30\%$, and $\sim50\%$ larger than the hydrostatic values.
Large scatters of $\gtrsim50\%$ are mainly due to the two outliers RXCJ0014 and
RXCJ1347; excluding the latter increases the mass ratios by $\sim10\%$, giving
a fractional mass bias significant at $\gtrsim2\sigma$. We found a correlation
between the dynamical-to-hydrostatic mass ratio and two substructure
indicators, suggesting a bias in the dynamical measurements. The velocity
dispersions of blue galaxies are $\sim15\%$ ($\sim25\%$ after removing the
substructures) larger than that of the red-sequence galaxies; using the latter
leads to dynamical masses $\sim10\%-15\%$ smaller. Discarding the galaxies part
of substructures reduces the masses by $\sim15\%$; the effect is larger for the
more massive clusters, owing to a higher level of substructures. After the
substructure analysis, the dynamical masses are in perfect agreement with the
hydrostatic values and the scatters around the mean ratios are divided by
$\sim2$.


  We introduce the so far most efficient attack against the
Kirchhoff-law-Johnson-noise (KLJN) secure key exchange system. This attack
utilizes the lack of exact thermal equilibrium in practical applications and is
based on cable resistance losses and the fact that the Second Law of
Thermodynamics cannot provide full security when such losses are present. The
new attack does not challenge the unconditional security of the KLJN scheme,
but it puts more stringent demands on the security/privacy enhancing protocol
than for any earlier attack. In this paper we present a simple defense protocol
to fully eliminate this new attack by increasing the noise-temperature at the
side of the smaller resistance value over the noise-temperature at the at the
side with the greater resistance. It is shown that this simple protocol totally
removes Eve's information not only for the new attack but also for the old
Bergou-Scheuer-Yariv attack. The presently most efficient attacks against the
KLJN scheme are thereby completely nullified.


  These notes are based on the mini-course given in June 2004 in Cetraro,
Italy, in the frame of a C.I.M.E. school. Of course, they contain much more
material that I could present in the 6 hours course. The main goal is to give
an idea of the general variational and dynamical nature of nice and powerful
concepts and results mainly known in the narrow framework of Riemannian
Geometry. This concerns Jacobi fields, Morse's index formula, Levi Civita
connection, Riemannian curvature and related topics.
  I tried to make the presentation as light as possible: gave more details in
smooth regular situations and referred to the literature in more complicated
cases.


  Using our new 3-D relativistic electromagnetic particle (REMP) code
parallelized with MPI, we investigated long-term particle acceleration
associated with a relativistic electron-positron jet propagating in an
unmagnetized ambient electron-positron plasma. The simulations were performed
using a much longer simulation system than our previous simulations in order to
investigate the full nonlinear stage of the Weibel instability and its particle
acceleration mechanism. Cold jet electrons are thermalized and ambient
electrons are accelerated in the resulting shocks. Acceleration of ambient
electrons leads to a maximum ambient electron density three times larger than
the original value. Behind the bow shock in the jet shock strong
electromagnetic fields are generated. These fields may lead to time dependent
afterglow emission. We calculated radiation from electrons propagating in a
uniform parallel magnetic field to verify the technique. We also used the new
technique to calculate emission from electrons based on simulations with a
small system. We obtained spectra which are consistent with those generated
from electrons propagating in turbulent magnetic fields with red noise. This
turbulent magnetic field is similar to the magnetic field generated at an early
nonlinear stage of the Weibel instability. A fully developed shock within a
larger system generates a jitter/synchrotron spectrum.


  Scene text erasing seeks to erase text contents from scene images and current
state-of-the-art text erasing models are trained on large-scale synthetic data.
Although data synthetic engines can provide vast amounts of annotated training
samples, there are differences between synthetic and real-world data. In this
paper, we employ self-supervision for feature representation on unlabeled
real-world scene text images. A novel pretext task is designed to keep
consistent among text stroke masks of image variants. We design the Progressive
Erasing Network in order to remove residual texts. The scene text is erased
progressively by leveraging the intermediate generated results which provide
the foundation for subsequent higher quality results. Experiments show that our
method significantly improves the generalization of the text erasing task and
achieves state-of-the-art performance on public benchmarks.


  A correct high-energy asymptotic form of Faddeev type few-body integral
equations is found. Iterative series corresponding to these asymptotic
relations converge with a certain accuracy to a finite sum, which satisfies the
corresponding condition of unitarity.


  Energy losses of fast charged particles in randomly spatially inhomogeneous
stationary medium are considered. Analytical results for effective dielectric
permittivity are presented.


  In this paper, the motility model for the developed country, which United
State possesses the largest economy in the world and thus serves as an ideal
representation, is investigated. Early surveillance of the causes of death is
critical which can allow the preparation of preventive steps against critical
disease such as dengue fever. Studies reported that some search queries,
especially those diseases related terms on Google Trends are essential. To this
end, we include either main cause of death or the extended or the more general
terminologies from Google Trends to decode the mortality related terms using
the Wiener Cascade Model. Using time series and Wavelet scalogram of search
terms, the patterns of search queries are categorized into different levels of
periodicity. The results include the decoding trend, the features importance,
and the accuracy of the decoding patterns. Three scenarios regard predictors
include the use of all 19 features, the top ten most periodic predictors, or
the ten predictors with highest weighting. All search queries spans from
December 2013 - December 2018. The results show that search terms with both
higher weight and annual periodic pattern contribute more in forecasting the
word die; however, only predictors with higher weight are valuable to forecast
the word death.


  In this paper, we propose an eigenvalue analysis -- of system dynamics models
-- based on the Mutual Information measure, which in turn will be estimated via
the Kernel Density Estimation method. We postulate that the proposed approach
represents a novel and efficient multivariate eigenvalue sensitivity analysis.


  The isospin dependence of the saturation properties of asymmetric nuclear
matter, particularly the incompressibility $K_\infty (X) = K_\infty + K_\tau
X^2 + O(X^4)$ at saturation density is systematically studied using density
dependent M3Y interaction. The $K_\tau$ characterizes the isospin dependence of
the incompressibility at saturation density $\rho_0$. The approximate
expression $K_{asy} \approx K_{sym}-6L$ is often used for $K_\tau$ where $L$
and $K_{sym}$ represent, respectively, the slope and curvature parameters of
the symmetry energy at $\rho_0$. It can be expressed accurately as
$K_\tau=K_{sym}-6L-\frac{Q_0}{K_\infty}L$ where $Q_0$ is the third-order
derivative parameter of symmetric nuclear matter at $\rho_0$. The results of
this addendum to Phys. Rev. C 80, 011305(R) (2009) indicate that the $Q_0$
contribution to $K_\tau$ is not insignificant.


  We consider the setting of distributed empirical risk minimization where
multiple machines compute the gradients in parallel and a centralized server
updates the model parameters. In order to reduce the number of communications
required to reach a given accuracy, we propose a \emph{preconditioned}
accelerated gradient method where the preconditioning is done by solving a
local optimization problem over a subsampled dataset at the server. The
convergence rate of the method depends on the square root of the relative
condition number between the global and local loss functions. We estimate the
relative condition number for linear prediction models by studying
\emph{uniform} concentration of the Hessians over a bounded domain, which
allows us to derive improved convergence rates for existing preconditioned
gradient methods and our accelerated method. Experiments on real-world datasets
illustrate the benefits of acceleration in the ill-conditioned regime.


  Let $\Gamma$ be a Lipschitz curve on the complex plane $\mathbb{C}$ and
$\Omega_+$ is the domain above $\Gamma$, we define Hardy space $H^p(\Omega_+)$
as the set of holomorphic functions $F$ satisfying $\sup_{\tau>0}(\int_{\Gamma}
|F(\zeta+\mathrm{i}\tau)|^p |\,\mathrm{d}\zeta|)^{\frac1p}< \infty$. We mainly
focus on the case of $1<p<\infty$ in this paper, and prove that if $F(w)\in
H^p(\Omega_+)$, then $F(w)$ has non-tangential boundary limit $F(\zeta)$ a.e.
on $\Gamma$, and $F(w)$ is the Cauchy integral of $F(\zeta)$. We denote the
conformal mapping from $\mathbb{C}_+$ onto $\Omega_+$ as $\Phi$, and then prove
that, $ H^p(\Omega_+)$ is isomorphic to $H^p(\mathbb{C}_+)$, the classical
Hardy space on upper half plane, under the mapping $T\colon F\to
F(\Phi(z))\cdot (\Phi'(z))^\frac{1}{p}$, where $F\in H^p(\Omega_+)$.


  Using 448 million $\psi(2S)$ events, the spin-singlet $P$-wave charmonium
state $h_c$(1$^1P_1$) is studied via the $\psi(2S) \rightarrow \pi^0 h_c$ decay
followed by the $h_c \to \gamma \eta_c$ transition. The branching fractions are
measured to be $\mathcal{B}_{\rm Inc}(\psi(2S) \rightarrow \pi^0h_c) \times
\mathcal{B}_{\rm Tag}(h_c \rightarrow \gamma \eta_c) = (4.22 ^{+0.27}_{-0.26}
\pm 0.19) \times 10^{-4}$ , $\mathcal{B}_{\rm Inc}(\psi(2S) \rightarrow
\pi^0h_c) = (7.32 \pm 0.34 \pm 0.41) \times 10^{-4}$, and $\mathcal{B}_{\rm
Tag}(h_c \rightarrow \gamma \eta_c) = (57.66 ^{+3.62}_{-3.50} \pm 0.58)\%$,
where the uncertainties are statistical and systematic, respectively. The
$h_c$(1$^1P_1$) mass and width are determined to be $M = (3525.32 \pm 0.06 \pm
0.15)~\rm{MeV}/c^{\rm{2}}$ and ${\mathit \Gamma} = (0.78 ^{+0.27}_{-0.24} \pm
0.12)~\rm{MeV}$. Using the center of gravity mass of the three $\chi_{cJ}$(1$^3
P_J$) mesons ($M(\rm c.o.g.)$), the $1P$ hyperfine mass splitting is estimated
to be $\Delta_{\rm hyp} = M(h_c) - M(\rm c.o.g.) = (0.03 \pm 0.06 \pm 0.15) ~
\rm{MeV}/c^{\rm{2}}$, which is consistent with the expectation that the $1P$
hyperfine splitting is zero at the lowest-order.


  Positional games are a well-studied class of combinatorial game. In their
usual form, two players take turns to play moves in a set (`the board'), and
certain subsets are designated as `winning': the first person to occupy such a
set wins the game. For these games, it is well known that (with correct play)
the game cannot be a second-player win.
  In the avoidance (or mis\`{e}re) form, the first person to occupy such a set
\emph{loses} the game. Here it would be natural to expect that the game cannot
be a first-player win, at least if the game is transitive, meaning that all
points of the board look the same. Our main result is that, contrary to this
expectation, there are transitive games that are first-player wins, for all
board sizes which are not prime or a power of 2.
  Further, we show that such games can have additional properties such as
stronger transitivity conditions, fast winning times, and `small' winning sets.


  When light passes through a multimode fiber, two-dimensional random intensity
patterns are formed due to the complex interference within the fiber. The
extreme sensitivity of speckle patterns to the frequency of light paved the way
for high-resolution multimode fiber spectrometers. However, this approach
requires expensive IR cameras and impedes the integration of spectrometers
on-chip. In this study, we propose a single-pixel multimode fiber spectrometer
by exploiting wavefront shaping. The input light is structured with the help of
a spatial light modulator, and optimal phase masks, focusing light at the
distal end of the fiber, are stored for each wavelength. Variation of the
intensity in the focused region is recorded by scanning all wavelengths under
fixed optimal masks. Based on the intensity measurements, we show that an
arbitrary input spectrum having two wavelengths 20 pm apart from each other can
be reconstructed successfully (with a reconstruction error of ~3%) in the
near-infrared regime, corresponding to a resolving power of $ R \approx 10^5 $.
We also demonstrate the reconstruction of broadband continuous spectra for
various bandwidths. With the installation of a single-pixel detector, our
method provides low-budget and compact detection at an increased
single-to-noise ratio.


  Document management in the rental market is a critical process to ensure the
accuracy of financial transactions and regulatory compliance in the sector. In
Portugal, the challenges include the complexity of legislation, particularly
GDPR non-compliance, lack of transparency, and bureaucratic process
inefficiency. With this in mind, a solution based on Hyperledger Fabric, a
blockchain platform, is presented for the implementation of a document
management system for the rental process. This system oversees the rental
process, which consists of three phases: the application for a property by the
prospective tenant through the upload of necessary documents,
acceptance/rejection by the landlord of various received applications, and the
creation of a report by the system, which only the auditor can request and
view. The system smart contract records metadata associated with the documents
(hash, owner) and coordinates requests for file access by landlords to
prospective tenants. Thus, the system is responsible for creating immutable and
traceable records of the entire process. The underlying platform serves as the
foundation for conducting future audits. After the landlord verifies the files
and accepts the rental proposal, any authorised auditor can request a report
for a property by accessing the records through the final report, which
includes all events that occurred during the process.


  We discuss how hadronic bag models can be generalized in the framework of
fuzzy set theory to implement effects of a smooth and extended phase boundary.


  Six-loop massive scheme renormalization group functions of a d=3-dimensional
cubic model (J.M. Carmona, A. Pelissetto, and E. Vicari, Phys. Rev. B vol. 61,
15136 (2000)) are reconsidered by means of the pseudo-epsilon expansion. The
marginal order parameter components number N_c=2.862(5) as well as critical
exponents of the cubic model are obtained. Our estimate N_c<3 leads in
particular to the conclusion that all ferromagnetic cubic crystals with three
easy axis should undergo a first order phase transition.


  We extend to arbitrary rings a definition of the octonion special linear
group due to Baez. At the infinitesimal level we get a Lie ring, which we
describe over some large classes of rings, including all associative rings and
all algebras over a field. As a corollary we compute all the groups Baez
defined.


  Erwin Louis Hahn was one of the most innovative and influential physical
scientists in recent history, impacting generations of scientists through his
work in nuclear magnetic resonance (NMR), optics, and the intersection of these
two fields. Starting with his discovery of the spin echo, a phenomenon of
monumental significance and practical importance, Hahn launched a major
revolution in how we think about spin physics, with numerous implications to
follow in many other areas of science. Students of NMR and coherent optics
quickly discover that many of the key concepts and techniques in these fields
derive directly from his work.


  We propose a theoretical model of quark-gluon plasma (QGP) produced at the
Brookhaven National Laboratory (BNL) Relativistic Heavy Ion Collider (RHIC). In
this model, we hypothesize that the gas of quarks and gluons are confined
within the film of gravitons as a Bose-Einstein condensate (BEC) during the
production of QGP. The structure of this theoretical model of QGP explains why
QGP behaves in a liquid-like manner, resembling a perfect fluid rather than a
gas. Based on this theoretical model, we calculated the shear viscosity of QGP.
This is essentially the shear viscosity of the BEC film of gravitons. The
computational results obtained in this study appear to be consistent with
experimental findings.


  Reward allocation, also known as the credit assignment problem, has been an
important topic in economics, engineering, and machine learning. An important
concept in reward allocation is the core, which is the set of stable
allocations where no agent has the motivation to deviate from the grand
coalition. In previous works, computing the core requires either knowledge of
the reward function in deterministic games or the reward distribution in
stochastic games. However, this is unrealistic, as the reward function or
distribution is often only partially known and may be subject to uncertainty.
In this paper, we consider the core learning problem in stochastic cooperative
games, where the reward distribution is unknown. Our goal is to learn the
expected core, that is, the set of allocations that are stable in expectation,
given an oracle that returns a stochastic reward for an enquired coalition each
round. Within the class of strictly convex games, we present an algorithm named
\texttt{Common-Points-Picking} that returns a point in the expected core given
a polynomial number of samples, with high probability. To analyse the
algorithm, we develop a new extension of the separation hyperplane theorem for
multiple convex sets.


  We show that a smooth, small enough Cauchy datum launches a unique classical
solution of the relativistic Vlasov-Darwin (RVD) system globally in time. A
similar result is claimed in Comm. Math. Sci. 6, 749-764 (2008) following the
work in Int. Mat. Res. Not. 57191, 1-31 (2006). Our proof does not require
estimates derived from the conservation of the total energy, nor those
previously given on the transverse component of the electric field. These
estimates are crucial in the references cited above. Instead, we exploit the
formulation of the RVD system in terms of the generalized space and momentum
variables. By doing so, we produce a simple a-priori estimate on the transverse
component of the electric field. We widen the functional space required for the
Cauchy datum to extend the solution globally in time, and we improve decay
estimates given in Comm. Math. Sci. 6, 749-764 (2008) on the electromagnetic
field and its space derivatives. Our method extends the constructive proof
presented in "Collisionless kinetic equations from astrophysics: The
Vlasov-Poisson system. Handbook of Differential Equations: Evolutionary
Equations, Vol.3, Elsevier, 2007" to solve the Cauchy problem for the
Vlasov-Poisson system with a small initial datum.


  This paper aims at determining under which conditions the semi-discrete
optimal transport is twice differentiable with respect to the parameters of the
discrete measure and exhibits numerical applications. The discussion focuses on
minimal conditions on the background measure to ensure differentiability. We
provide numerical illustrations in stippling and blue noise problems.


  The Global Network of Optical Magnetometers for Exotic physics searches
(GNOME) conducts an experimental search for certain forms of dark matter based
on their spatiotemporal signatures imprinted on a global array of synchronized
atomic magnetometers. The experiment described here looks for a gradient
coupling of axion-like particles (ALPs) with proton spins as a signature of
locally dense dark matter objects such as domain walls. In this work,
stochastic optimization with machine learning is proposed for use in a search
for ALP domain walls based on GNOME data. The validity and reliability of this
method were verified using binary classification. The projected sensitivity of
this new analysis method for ALP domain-wall crossing events is presented.


  We have examined the impact of charged impurity scattering on charge carrier
transport in bilayer graphene (BLG) by deposition of potassium in ultra-high
vacuum at low temperature. Charged impurity scattering gives a conductivity
which is supra-linear in carrier density, with a magnitude similar to
single-layer graphene for the measured range of carrier densities of 2-4 x
10^12 cm^-2. Upon addition of charged impurities of concentration n_imp, the
minimum conductivity Sigma_min decreases proportional to n_imp^-1/2, while the
electron and hole puddle carrier density increases proportional to n_imp^1/2.
These results for the intentional deposition of potassium on BLG are in good
agreement with theoretical predictions for charged impurity scattering.
However, our results also suggest that charged impurity scattering alone cannot
explain the observed transport properties of pristine BLG on SiO2 before
potassium doping.


  We review several methods for determining the Kobayashi-Maskawa phase
$\gamma={\rm Arg} V^*_{ub}$ from rate and CP asymmetry measurements in hadronic
B decays. We focus on the processes $B\to DK, B_s\to D_s K$, and on charmless
decays to two light pseudoscalars and decays to a pair of a pseudoscalar and a
vector meson. Theoretical uncertainties underlying these methods are discussed.


  Let $K$ be an infinite field and $R=K[x_1,...,x_n]$ be the polynomial ring.
Let $V=V_1, ..., V_m$ be a collection of vector spaces of linear forms. Denote
by $A(V)$ the $K$-subalgebra of $R$ generated by the elements of the product
$V_1... V_m$. Our goal is to investigate the properties of the algebra $A(V)$
and the relations with two problems in algebraic combinatorics White's and
related conjectures on polymatroids and the study of integral posets.


  Galaxies which hosted many core-collapse supernovae (SN) explosions can be
used to study the conditions necessary for the formation of massive stars. NGC
2770 was dubbed a SN factory, because it hosted four core-collapse SNe in 20
years (three type Ib and one type IIn). Its star formation rate (SFR) was
reported not to be enhanced and therefore not compatible with such a high SN
rate. We aim at explaining the high SN rate of NGC 2770. We used archival HI
line data for NGC 2770 and reinterpret the Halpha and optical continuum data.
Even though the continuum-based SFR indicators do not yield high values, the
dust-corrected Halpha luminosity implies a high SFR, consistent with the high
SN rate. Such disparity between the SFR estimators is an indication of recently
enhanced star formation activity, because the continuum indicators trace long
timescale of the order of 100 Myr, unlike the line indicators, which trace
timescales of the order of 10 Myr. Hence, the unique feature of NGC 2770
compared to other galaxies is the fact that it is observed very recently after
the enhancement of the SFR. It also has high dust extinction, E(B-V) above 1
mag. We provide support for the hypothesis that the increased SFR in NGC 2770
is due to the interaction with its companion galaxies. We report an HI bridge
between NGC 2770 and its closest companion and the existence of a total of four
companions within 100 kpc (one identified for the first time). There are no
clear HI concentrations close to the positions of SNe in NGC 2770 such as those
detected for hosts of gamma-ray bursts (GRBs) and broad-lined SNe type Ic
(IcBL). This suggests that the progenitors of type Ib SNe are not born out of
recently accreted atomic gas, as was suggested for GRB and IcBL SN progenitors.


  We review the definition of bulk and boundary conformal field theory in a way
suited for logarithmic conformal field theory. The notion of a maximal bulk
theory which can be non-degenerately joined to a boundary theory is defined.
The purpose of this construction is to obtain the more complicated bulk
theories from simpler boundary theories. We then describe the algebraic
counterpart of the maximal bulk theory, namely the so-called full centre of an
algebra in an abelian braided monoidal category. Finally, we illustrate the
previous discussion in the example of the W(2,3)-model with central charge 0.


  Hardness of approximation (HA) -- the phenomenon that, assuming P $\neq$ NP,
one can easily compute an $\epsilon$-approximation to the solution of a
discrete computational problem for $\epsilon > \epsilon_0 > 0$, but for
$\epsilon < \epsilon_0$ it suddenly becomes intractable -- is a core phenomenon
in the foundations of computations that has transformed computer science. In
this paper we study the newly discovered phenomenon in the foundations of
computational mathematics: generalised hardness of approximation (GHA) -- which
in spirit is close to classical HA in computer science. However, GHA is
typically independent of the P vs. NP question in many cases. Thus, it requires
a new mathematical framework that we initiate in this paper. We demonstrate the
hitherto undiscovered phenomenon that GHA happens when using AI techniques in
order to train optimal neural networks (NNs). In particular, for any non-zero
underdetermined linear problem the following phase transition may occur: One
can prove the existence of optimal NNs for solving the problem but they can
only be computed to a certain accuracy $\epsilon_0 > 0$. Below the
approximation threshold $\epsilon_0$ -- not only does it become intractable to
compute the NN -- it becomes impossible regardless of computing power, and no
randomised algorithm can solve the problem with probability better than 1/2. In
other cases, despite the existence of a stable optimal NN, any attempts of
computing it below the approximation threshold $\epsilon_0$ will yield an
unstable NN. Our results use and extend the current mathematical framework of
the Solvability Complexity Index (SCI) hierarchy and facilitate a program for
detecting the GHA phenomenon throughout computational mathematics and AI.