  This paper is concerned with the stability of shares in a cryptocurrency
where the new coins are issued according to the Proof of Stake protocol. We
identify large, medium and small investors under various rewarding schemes, and
show that the limiting behaviors of these investors are different -- for large
investors their shares are stable, while for medium to small investors their
shares may be volatile or even shrink to zero. For instance, with a geometric
reward there is chaotic centralization, where all the shares will eventually
concentrate on one investor in a random manner. This leads to the phase
transition phenomenon, and the thresholds for stability are characterized. In
response to the increasing activities in blockchain networks, we also propose
and analyze a dynamical population model for the PoS protocol, which allows the
number of investors to grow over the time. Numerical experiments are provided
to corroborate our theory.


  Motivated by recent experiments [Vera-Marun et al., arXiv:1109.5969], we
formulate a non-linear theory of spin transport in quantum coherent conductors.
We show how a mesoscopic constriction with energy-dependent transmission can
convert a spin current injected by a spin accumulation into an electric signal,
relying neither on magnetic nor exchange fields. When the transmission through
the constriction is spin-independent, the spin-charge coupling is non-linear,
with an electric signal that is quadratic in the accumulation. We estimate that
gated mesoscopic constrictions have a sensitivity that allows to detect
accumulations much smaller than a percent of the Fermi energy.


  Motivated by an application in Magnetic Particle Imaging, we study bivariate
Lagrange interpolation at the node points of Lissajous curves. The resulting
theory is a generalization of the polynomial interpolation theory developed for
a node set known as Padua points. With appropriately defined polynomial spaces,
we will show that the node points of non-degenerate Lissajous curves allow
unique interpolation and can be used for quadrature rules in the bivariate
setting. An explicit formula for the Lagrange polynomials allows to compute the
interpolating polynomial with a simple algorithmic scheme. Compared to the
already established schemes of the Padua and Xu points, the numerical results
for the proposed scheme show similar approximation errors and a similar growth
of the Lebesgue constant.


  We present new global fits of the cMSSM, including LHC 1/fb integrated
luminosity SUSY exclusion limits, recent LHC 5/fb constraints on the mass of
the Higgs boson and XENON100 direct detection data. Our analysis fully takes
into account astrophysical and hadronic uncertainties that enter the analysis
when translating direct detection limits into constraints on the cMSSM
parameter space. We provide results for both a Bayesian and a Frequentist
statistical analysis. We find that LHC 2011 constraints in combination with
XENON100 data can rule out a significant portion of the cMSSM parameter space.
Our results further emphasise the complementarity of collider experiments and
direct detection searches in constraining extensions of Standard Model physics.
The LHC 2011 exclusion limit strongly impacts on low-mass regions of cMSSM
parameter space, such as the stau co-annihilation region, while direct
detection data can rule out regions of high SUSY masses, such as the
Focus-Point region, which is unreachable for the LHC in the near future. We
show that, in addition to XENON100 data, the experimental constraint on the
anomalous magnetic moment of the muon plays a dominant role in disfavouring
large scalar and gaugino masses. We find that, should the LHC 2011 excess
hinting towards a Higgs boson at 126 GeV be confirmed, currently favoured
regions of the cMSSM parameter space will be robustly ruled out from both a
Bayesian and a profile likelihood statistical perspective.


  In this article we show that the complex Burgers and the Kundu--Eckhaus
equations are related by a Miura transformation. We use this relation to
discretize the Kundu--Eckhaus equation.


  Observational learning often involves congestion: an agent gets lower payoff
from an action when more predecessors have taken that action. This preference
to act differently from previous agents may paradoxically increase all but one
agent's probability of matching the actions of the predecessors. The reason is
that when previous agents conform to their predecessors despite the preference
to differ, their actions become more informative. The desire to match
predecessors' actions may reduce herding by a similar reasoning.


  For autonomous vehicles (AVs) to behave appropriately on roads populated by
human-driven vehicles, they must be able to reason about the uncertain
intentions and decisions of other drivers from rich perceptual information.
Towards these capabilities, we present a probabilistic forecasting model of
future interactions between a variable number of agents. We perform both
standard forecasting and the novel task of conditional forecasting, which
reasons about how all agents will likely respond to the goal of a controlled
agent (here, the AV). We train models on real and simulated data to forecast
vehicle trajectories given past positions and LIDAR. Our evaluation shows that
our model is substantially more accurate in multi-agent driving scenarios
compared to existing state-of-the-art. Beyond its general ability to perform
conditional forecasting queries, we show that our model's predictions of all
agents improve when conditioned on knowledge of the AV's goal, further
illustrating its capability to model agent interactions.


  We expand the ergodic theory developed by Furstenberg and Hochman on
dynamical systems that are obtained from magnifications of measures. We prove
that any fractal distribution in the sense of Hochman is generated by a
uniformly scaling measure, which provides a converse to a regularity theorem on
the structure of distributions generated by the scenery flow. We further show
that the collection of fractal distributions is closed under the weak topology
and, moreover, is a Poulsen simplex, that is, extremal points are dense. We
apply these to show that a Baire generic measure is as far as possible from
being uniformly scaling: at almost all points, it has all fractal distributions
as tangent distributions.


  We investigate a class of 1/2-BPS bubbling geometries associated to
orientifolds of type IIB string theory and thereby to excited states of the
SO(N)/Sp(N) N=4 supersymmetric Yang-Mills theory. The geometries are in
correspondence with free fermions moving in a harmonic oscillator potential on
the half-line. Branes wrapped on torsion cycles of these geometries are
identified in the fermi fluid description. Besides being of intrinsic interest,
these solutions may also occur as local geometries in flux compactifications
where orientifold planes are present to ensure global charge cancellation. We
comment on the extension of this procedure to M-theory orientifolds.


  The maximum mass of a neutron star is generally determined by the equation of
state of the star material. In this study, we take into account dark matter
particles, assumed to behave like fermions with a free parameter to account for
the interaction strength among the particles, as a possible constituent of
neutron stars. We find dark matter inside the star would soften the equation of
state more strongly than that of hyperons, and reduce largely the maximum mass
of the star. However, the neutron star maximum mass is sensitive to the
particle mass of dark matter, and a very high neutron star mass larger than 2
times solar mass could be achieved when the particle mass is small enough. Such
kind of dark-matter- admixed neutron stars could explain the recent measurement
of the Shapiro delay in the radio pulsar PSR J1614-2230, which yielded a
neutron star mass of 2 times solar mass that may be hardly reached when
hyperons are considered only, as in the case of the microscopic Brueckner
theory. Furthermore, in this particular case, we point out that the dark matter
around a neutron star should also contribute to the mass measurement due to its
pure gravitational effect. However, our numerically calculation illustrates
that such contribution could be safely ignored because of the usual diluted
dark matter environment assumed. We conclude that a very high mass measurement
of about 2 times solar mass requires a really stiff equation of state in
neutron stars, and find a strong upper limit (<= 0.64 GeV) for the particle
mass of non-self- annihilating dark matter based on the present model.


  Programming-by-Examples (PBE) aims to generate an algorithm from input-output
examples. Such systems are practically and theoretically important: from an
end-user perspective, they are deployed to millions of people, and from an AI
perspective, PBE corresponds to a very general form of few-shot inductive
inference. Given the success of Large Language Models (LLMs) in code-generation
tasks, we investigate here the extent to which LLMs can be said to have
`solved' PBE. We experiment on classic domains such as lists and strings, and
an uncommon graphics programming domain not well represented in typical
pretraining data. We find that pretrained models are not effective at PBE, but
that they can be fine-tuned for much higher performance, provided the test
problems are in-distribution. We analyze empirically what causes these models
to succeed and fail, and take steps toward understanding how to achieve better
out-of-distribution generalization. Collectively these results suggest that
LLMs make strong progress toward solving the typical suite of PBE tasks,
potentially increasing the flexibility and applicability of PBE systems, while
also identifying ways in which LLMs still fall short.


  We establish an exact asymptotic formula for the square variation of certain
partial sum processes. Let $\{X_{i}\}$ be a sequence of independent,
identically distributed mean zero random variables with finite variance
$\sigma$ and satisfying a moment condition $\mathbb{E}[|X_{i}|^{2+\delta} ] <
\infty$ for some $\delta > 0$. If we let $\mathcal{P}_{N}$ denote the set of
all possible partitions of the interval $[N]$ into subintervals, then we have
that $\max_{\pi \in \mathcal{P}_{N}} \sum_{I \in \pi} | \sum_{i\in I} X_{i}|^2
\sim 2 \sigma^2N \ln \ln(N)$ holds almost surely. This can be viewed as a
variational strengthening of the law of the iterated logarithm and refines
results of J. Qian on partial sum and empirical processes. When $\delta = 0$,
we obtain a weaker `in probability' version of the result.


  Grasping occluded objects in cluttered environments is an essential component
in complex robotic manipulation tasks. In this paper, we introduce an
AffordanCE-driven Next-Best-View planning policy (ACE-NBV) that tries to find a
feasible grasp for target object via continuously observing scenes from new
viewpoints. This policy is motivated by the observation that the grasp
affordances of an occluded object can be better-measured under the view when
the view-direction are the same as the grasp view. Specifically, our method
leverages the paradigm of novel view imagery to predict the grasps affordances
under previously unobserved view, and select next observation view based on the
highest imagined grasp quality of the target object. The experimental results
in simulation and on a real robot demonstrate the effectiveness of the proposed
affordance-driven next-best-view planning policy. Project page:
https://sszxc.net/ace-nbv/.


  Recent electroweak precision measurements from e+e- and pbarp colliders are
presented. Some emphasis is placed on the recent developments in the heavy
flavor sector. The measurements are compared to predictions from the Standard
Model of electroweak interactions. All results are found to be consistent with
the Standard Model. The indirect constraint on the top quark mass from all
measurements is in excellent agreement with the direct Mt measurements. Using
the world's electroweak data in conjunction with the current measurement of the
top quark mass, the constraints on the Higgs mass are discussed.


  Cloud computing has penetrated the Information Technology industry deep
enough to influence major companies to adopt it into their mainstream business.
A strong thrust on the use of virtualization technology to realize
Infrastructure-as-a-Service (IaaS) has led enterprises to leverage
subscription-oriented computing capabilities of public Clouds for hosting their
application services. In parallel, research in academia has been investigating
transversal aspects such as security, software frameworks, quality of service,
and standardization. We believe that the complete realization of the Cloud
computing vision will lead to the introduction of a virtual market where Cloud
brokers, on behalf of end users, are in charge of selecting and composing the
services advertised by different Cloud vendors. In order to make this happen,
existing solutions and technologies have to be redesigned and extended from a
market-oriented perspective and integrated together, giving rise to what we
term Market-Oriented Cloud Computing.
  In this paper, we will assess the current status of Cloud computing by
providing a reference model, discuss the challenges that researchers and IT
practitioners are facing and will encounter in the near future, and present the
approach for solving them from the perspective of the Cloudbus toolkit, which
comprises of a set of technologies geared towards the realization of Market
Oriented Cloud Computing vision. We provide experimental results demonstrating
market-oriented resource provisioning and brokering within a Cloud and across
multiple distributed resources. We also include an application illustrating the
hosting of ECG analysis as SaaS on Amazon IaaS (EC2 and S3) services.


  We present a human-in-the-loop dashboard tailored to diagnosing potential
spurious features that NLI models rely on for predictions. The dashboard
enables users to generate diverse and challenging examples by drawing
inspiration from GPT-3 suggestions. Additionally, users can receive feedback
from a trained NLI model on how challenging the newly created example is and
make refinements based on the feedback. Through our investigation, we discover
several categories of spurious correlations that impact the reasoning of NLI
models, which we group into three categories: Semantic Relevance, Logical
Fallacies, and Bias. Based on our findings, we identify and describe various
research opportunities, including diversifying training data and assessing NLI
models' robustness by creating adversarial test suites.


  Introduction: Real-world data generated from clinical practice can be used to
analyze the real-world evidence (RWE) of COVID-19 pharmacotherapy and validate
the results of randomized clinical trials (RCTs). Machine learning (ML) methods
are being used in RWE and are promising tools for precision-medicine. In this
study, ML methods are applied to study the efficacy of therapies on COVID-19
hospital admissions in the Valencian Region in Spain. Methods: 5244 and 1312
COVID-19 hospital admissions - dated between January 2020 and January 2021 from
10 health departments, were used respectively for training and validation of
separate treatment-effect models (TE-ML) for remdesivir, corticosteroids,
tocilizumab, lopinavir-ritonavir, azithromycin and
chloroquine/hydroxychloroquine. 2390 admissions from 2 additional health
departments were reserved as an independent test to analyze retrospectively the
survival benefits of therapies in the population selected by the TE-ML models
using cox-proportional hazard models. TE-ML models were adjusted using
treatment propensity scores to control for pre-treatment confounding variables
associated to outcome and further evaluated for futility. ML architecture was
based on boosted decision-trees. Results: In the populations identified by the
TE-ML models, only Remdesivir and Tocilizumab were significantly associated
with an increase in survival time, with hazard ratios of 0.41 (P = 0.04) and
0.21 (P = 0.001), respectively. No survival benefits from chloroquine
derivatives, lopinavir-ritonavir and azithromycin were demonstrated. Tools to
explain the predictions of TE-ML models are explored at patient-level as
potential tools for personalized decision making and precision medicine.
Conclusion: ML methods are suitable tools toward RWE analysis of COVID-19
pharmacotherapies. Results obtained reproduce published results on RWE and
validate the results from RCTs.


  Massive data centers housing thousands of computing nodes have become
commonplace in enterprise computing, and the power consumption of such data
centers is growing at an unprecedented rate. Adding to the problem is the
inability of the servers to exhibit energy proportionality, i.e., provide
energy-efficient execution under all levels of utilization, which diminishes
the overall energy efficiency of the data center. It is imperative that we
realize effective strategies to control the power consumption of the server and
improve the energy efficiency of data centers. With the advent of Intel Sandy
Bridge processors, we have the ability to specify a limit on power consumption
during runtime, which creates opportunities to design new power-management
techniques for enterprise workloads and make the systems that they run on more
energy-proportional.
  In this paper, we investigate whether it is possible to achieve energy
proportionality for enterprise-class server workloads, namely SPECpower_ssj2008
and SPECweb2009 benchmarks, by using Intel's Running Average Power Limit (RAPL)
interfaces. First, we analyze the average power consumption of the full system
as well as the subsystems and describe the energy proportionality of these
components. We then characterize the instantaneous power profile of these
benchmarks within different subsystems using the on-chip energy meters exposed
via the RAPL interfaces. Finally, we present the effects of power limiting on
the energy proportionality, performance, power and energy efficiency of
enterprise-class server workloads. Our observations and results shed light on
the efficacy of the RAPL interfaces and provide guidance for designing
power-management techniques for enterprise-class workloads.


  We review the main recent progresses in non-commutative space-time
phenomenology in underground experiments. A popular model of non-commutative
space-time is $\theta$-Poincar\'e model, based on the Groenewold-Moyal plane
algebra. This model predicts a violation of the Spin-statistic theorem, in turn
implying an energy and angular dependent violation of the Pauli Exclusion
principle. Pauli Exclusion Principle Violating transitions in nuclear and
atomic systems can be tested with very high accuracy in underground laboratory
experiments such as DAMA/LIBRA and VIP(2). In this paper we derive that the
$\theta$-Poincar\'e model can be already ruled-out until the Planck scale, from
nuclear transitions tests by DAMA/LIBRA experiment.


  The spectrum of any star viewed through a sufficient quantity of diffuse
interstellar material reveals a number of absorption features collectively
called diffuse interstellar bands (DIBs). The first DIBs were reported 90 years
ago, and currently well over 500 are known. None of them has been convincingly
identified with any specific element or molecule, although recent studies
suggest that the DIB carriers are polyatomic molecules containing carbon. Most
of the DIBs currently known are at visible and very near-infrared wavelengths,
with only two previously known at wavelengths beyond one micron (10,000
Angstroms), the longer of which is at 1.318 microns. Here we report the
discovery of thirteen diffuse interstellar bands in the 1.5-1.8 micron interval
on high extinction sightlines toward stars in the Galactic centre. We argue
that they originate almost entirely in the Galactic Centre region, a
considerably warmer and harsher environment than where DIBs have been observed
previously. The relative strengths of these DIBs toward the Galactic Centre and
the Cygnus OB2 diffuse cloud are consistent with their strengths scaling mainly
with extinction by diffuse material.


  Evidence for Higgs boson decay to a pair of muons is presented. This result
combines searches in four exclusive categories targeting the production of the
Higgs boson via gluon fusion, via vector boson fusion, in association with a
vector boson, and in association with a top quark-antiquark pair. The analysis
is performed using proton-proton collision data at $\sqrt{s} =$ 13 TeV,
corresponding to an integrated luminosity of 137 fb$^{-1}$, recorded by the CMS
experiment at the CERN LHC. An excess of events over the background expectation
is observed in data with a significance of 3.0 standard deviations, where the
expectation for the standard model (SM) Higgs boson with mass of 125.38 GeV is
2.5. The combination of this result with that from data recorded at $\sqrt{s}
=$ 7 and 8 TeV, corresponding to integrated luminosities of 5.1 and 19.7
fb$^{-1}$, respectively, increases both the expected and observed significances
by 1%. The measured signal strength, relative to the SM prediction, is 1.19
$^{+0.40}_{-0.39}$ (stat) $^{+0.15}_{-0.14}$ (syst). This result constitutes
the first evidence for the decay of the Higgs boson to second generation
fermions and is the most precise measurement of the Higgs boson coupling to
muons reported to date.


  Video object detection is challenging in the presence of appearance
deterioration in certain video frames. Therefore, it is a natural choice to
aggregate temporal information from other frames of the same video into the
current frame. However, RoI Align, as one of the most core procedures of video
detectors, still remains extracting features from a single-frame feature map
for proposals, making the extracted RoI features lack temporal information from
videos. In this work, considering the features of the same object instance are
highly similar among frames in a video, a novel Temporal RoI Align operator is
proposed to extract features from other frames feature maps for current frame
proposals by utilizing feature similarity. The proposed Temporal RoI Align
operator can extract temporal information from the entire video for proposals.
We integrate it into single-frame video detectors and other state-of-the-art
video detectors, and conduct quantitative experiments to demonstrate that the
proposed Temporal RoI Align operator can consistently and significantly boost
the performance. Besides, the proposed Temporal RoI Align can also be applied
into video instance segmentation. Codes are available at
https://github.com/open-mmlab/mmtracking


  Most neutrino mass theories contain non-standard interactions (NSI) of
neutrinos which can be either non-universal (NU) or flavor-changing (FC). We
study the impact of such interactions on the determination of neutrino mixing
parameters at a neutrino factory using the so-called ``golden channels''
\pnu{e}\to\pnu{\mu} for the measurement of \theta_{13}. We show that a certain
combination of FC interactions in neutrino source and earth matter can give
exactly the same signal as oscillations arising due to \theta_{13}. This
implies that information about \theta_{13} can only be obtained if bounds on
NSI are available. Taking into account the existing bounds on FC interactions,
this leads to a drastic loss in sensitivity in \theta_{13}, at least two orders
of magnitude. A near detector at a neutrino factory offers the possibility to
obtain stringent bounds on some NSI parameters. Such near site detector
constitutes an essential ingredient of a neutrino factory and a necessary step
towards the determination of \theta_{13} and subsequent study of leptonic CP
violation.


  Face covering, commonly known as facemask, is considered to be one of the
most effective Personal Protective Equipments (PPEs) to reduce transmissions of
pathogens through respiratory droplets - both large drops and liquid aerosol
particles. Face masks, not only inhibit the expulsion of such respiratory
droplets from the user, but also protects the user from inhaling pathogen-laden
potentially harmful droplets or their dried nuclei. While the efficacies of
various dry face masks have been explored in the recent past, a comprehensive
investigation of a wet mask is lacking. Yet, users wear masks for a long period
of time and during this period, owing to respiratory droplets released through
multiple respiratory events, the mask matrix becomes wet. We, herein, present
an experimental study on the dynamics of sequential impacts of droplets on
masks to understand how wetness affects possible penetration and secondary
atomization of the impacted droplet. Two different types of masks, hydrophobic
and hydrophilic, were used in this study to evaluate the underlying physical
mechanism that controls the penetration in each of them.


  The aim of this paper is to investigate the distribution of a continuous
polymer in the presence of an attractive finitely supported potential. The most
intricate behavior can be observed if we simultaneously and independently vary
two parameters: the temperature, which approaches the critical value, and the
length of the polymer chain, which tends to infinity. We describe how the
typical size of the polymer depends on the two parameters.


  In this addendum to our paper entitled "W^+- H^-+ Associated Production at
the Large Hadron Collider" [Phys. Rev. D 59, 015009 (1999)], we list analytic
results for the helicity amplitudes of the partonic subprocess gg -> W^-H^+
induced by virtual quarks.


  The approximate cloaking is investigated for time-harmonic Maxwell's
equations via the approach of transformation optics. The problem is reduced to
certain boundary effect estimates due to an inhomogeneous electromagnetic
inclusion with an asymptotically small support but an arbitrary content
enclosed by a thin high-conducting layer. Sharp estimates are established in
terms of the asymptotic parameter, which are independent of the material
tensors of the small electromagnetic inclusion. The result implies that the
`blow-up-a-small-region' construction via the transformation optics approach
yields a near-cloak for the electromagnetic waves. A novelty lies in the fact
that the geometry of the cloaking construction of this work can be very
general. Moreover, by incorporating the conducting layer developed in the
present paper right between the cloaked region and the cloaking region,
arbitrary electromagnetic contents can be nearly cloaked. Our mathematical
technique extends the general one developed in [30] for nearly cloaking scalar
optics. In order to investigate the approximate electromagnetic cloaking for
general geometries with arbitrary cloaked contents, new techniques and analysis
tools must be developed for this more challenging vector optics case.


  Tunable metasurfaces are ultra-thin, artificial electromagnetic components
that provide engineered and externally adjustable functionalities. The
programmable metasurface, the HyperSurFace, concept consists in integrating
controllers within the metasurface that interact locally and communicate
globally to obtain a given electromagnetic behaviour. Here, we address the
design constraints introduced by both functions accommodated by the
programmable metasurface, i.e., the desired metasurface operation and the unit
cells wireless communication enabling such programmable functionality. The
design process for meeting both sets of specifications is thoroughly discussed.
Two scenarios for wireless intercell communication are proposed. The first
exploits the metasurface layer itself, while the second employs a dedicated
communication layer beneath the metasurface backplane. Complexity and
performance trade-offs are highlighted.


  It is well-known that Resolution proofs can be efficiently simulated by
Sherali-Adams (SA) proofs. We show, however, that any such simulation needs to
exploit huge coefficients: Resolution cannot be efficiently simulated by SA
when the coefficients are written in unary. We also show that Reversible
Resolution (a variant of MaxSAT Resolution) cannot be efficiently simulated by
Nullstellensatz (NS).
  These results have consequences for total NP search problems. First, we
characterise the classes PPADS, PPAD, SOPL by unary-SA, unary-NS, and
Reversible Resolution, respectively. Second, we show that, relative to an
oracle, PLS $\not\subseteq$ PPP, SOPL $\not\subseteq$ PPA, and EOPL
$\not\subseteq$ UEOPL. In particular, together with prior work, this gives a
complete picture of the black-box relationships between all classical TFNP
classes introduced in the 1990s.


  The error estimates and convergence rate of a two-level MacCormack rapid
solver method for solving a two-dimensional incompressible Navier-Stokes
equations are analyzed. This represents a continuation of the work on the
stability analysis of the method. The theoretical result suggests that the
rapid solver method is both convergent and second order accurate with respect
to time step $\Delta t.$ A wide set of numerical evidences confirm this
theoretical analysis.


  We analyzed a sample of high and low surface brightness (HSB and LSB) disc
galaxies and elliptical galaxies to investigate the correlation between the
circular velocity (Vc) and the central velocity dispersion (sigma). We better
defined the previous Vc-sigma correlation for HSB and elliptical galaxies,
especially at the lower end of the sigma values. Elliptical galaxies with Vc
based on dynamical models or directly derived from the HI rotation curves
follow the same relation as the HSB galaxies in the V-sigma plane. On the
contrary, the LSB galaxies follow a different relation, since most of them show
either higher Vc (or lower sigma) with respect to the HSB galaxies. This argues
against the relevance of baryon collapse in the radial density profile of the
dark matter haloes of LSB galaxies. Moreover, if the Vc-sigma relation is
equivalent to one between the mass of the dark matter halo and that of the
supermassive black hole, these results suggest that the LSB galaxies host a
supermassive black hole with a smaller mass compared to HSB galaxies of equal
dark matter halo. On the other hand, if the fundamental correlation of SMBH
mass is with the halo Vc, then LSBs should have larger black hole masses for
given bulge sigma.


  Providing authoritative information tailored to a student's specific doubt is
a hurdle in this era where search engines return an overwhelming number of
article links. Large Language Models such as GPTs fail to provide answers to
questions that were derived from sensitive confidential information. This
information which is specific to some organisations is not available to LLMs
due to privacy constraints. This is where knowledge-augmented retrieval
techniques become particularly useful. The proposed platform is designed to
cater to the needs of learners from divergent fields. Today, the most common
format of learning is video and books, which our proposed platform allows
learners to interact and ask questions. This increases learners' focus time
exponentially by restricting access to pertinent content and, at the same time
allowing personalized access and freedom to gain in-depth knowledge.
Instructor's roles and responsibilities are significantly simplified allowing
them to train a larger audience. To preserve privacy, instructors can grant
course access to specific individuals, enabling personalized conversation on
the provided content. This work includes an extensive spectrum of software
development and product management skills, which also circumscribe knowledge of
cloud computing for running Large Language Models and maintaining the
application. For Frontend development, which is responsible for user
interaction and user experience, Streamlit and React framework have been
utilized. To improve security and privacy, the server is routed to a domain
with an SSL certificate, and all the API key/s are stored securely on an AWS
EC2 instance, to enhance user experience, web connectivity to an Android
Studio-based mobile app has been established, and in-process to publish the app
on play store, thus addressing all major software engineering disciplines


  Born-Infeld AdS black hole exhibits a reentrant phase transition for certain
values of the Born-Infeld parameter $b$. This behaviour is an additional
feature compared to the van der Waals like phase transition observed in charged
AdS black holes. Therefore, it is worth observing the underlying microscopic
origin of this reentrant phase transition. Depending on the value of the
parameter $b$, the black hole system has four different cases: no phase
transition, a reentrant phase transition with two scenarios, or a van der
Waals-like (standard) phase transition. In this article, by employing a novel
Ruppeiner geometry method in the parameter space of temperature and volume, we
investigate the microstructure of Born-Infeld AdS black hole via the phase
transition study, which includes standard and reentrant phase transition. We
find that the microstructures of the black hole that lead to standard and
reentrant phase transitions are distinct in nature. The standard phase
transition is characterised by the typical RN-AdS microstructure. In this case,
the small black hole phase has a dominant repulsive interaction for the low
temperature case. Interestingly, during the reentrant phase transition,
displayed by the system in a range of pressures for specific $b$ values, the
dominant attractive nature of interaction in the microstructure is preserved.
Our results suggest that in the reentrant phase transition case, the
intermediate black holes behave like a bosonic gas, and in the standard phase
transition case the small black holes behave like a quantum anyon gas. In both
cases, the large black hole phase displays an interaction similar to the
bosonic gas. The critical phenomenon is observed from the curvature scalar,
including the signature of the reentrant phase transition.


  We show that the Hankel determinants of a generalized Catalan sequence
satisfy the equations of the elliptic sequence. As a consequence, the
coordinates of the multiples of an arbitrary point on the elliptic curve are
expressed by the Hankel determinants.


  We present the detailed quantum electrodynamical description of
Vavilov-Cherenkov radiation emitted by a relativistic twisted electron in the
transparent medium. Simple expressions for the spectral and spectral-angular
distributions as well as for the polarization properties of the emitted
radiation are obtained. Unlike the plane-wave case, the twisted electron
produces radiation within the annular angular region, with enhancement towards
its boundaries. Additionally, the emitted photons can have linear polarization
not only in the scattering plane but also in the orthogonal direction. We find
that the Vavilov-Cherenkov radiation emitted by an electron in a superposition
of two vortex states exhibits a strong azimuthal asymmetry. Thus, the
Vavilov-Cherenkov radiation offers itself as a convenient diagnostic tool of
such electrons and complements the traditional microscopic imaging.


  The status of the Monte Carlo programs for the simulation of the tau-lepton
production and decay in high energy accelerator experiments is reviewed. In
particular, the status of the following packages is discussed: (i) TAUOLA for
tau-lepton decay and PHOTOS for radiative corrections in decays, (ii) MC-TESTER
for universal tests of the Monte Carlo programs describing particle decays,
(iii) KORALB, KORALZ, KKMC packages for tau-pair production in e+e- collisions,
and (iv) universal interface of TAUOLA for the decay of tau-leptons produced by
``any'' generator.


  We present a new catalog of $9318$ Ly$\alpha$ emitter (LAE) candidates at $z
= 2.2$, $3.3$, $4.9$, $5.7$, $6.6$, and $7.0$ that are photometrically selected
by the SILVERRUSH program with a machine learning technique from large area (up
to $25.0$ deg$^2$) imaging data with six narrowband filters taken by the Subaru
Strategic Program with Hyper Suprime-Cam (HSC SSP) and a Subaru intensive
program, Cosmic HydrOgen Reionization Unveiled with Subaru (CHORUS). We
construct a convolutional neural network that distinguishes between real LAEs
and contaminants with a completeness of $94$% and a contamination rate of $1$%,
enabling us to efficiently remove contaminants from the photometrically
selected LAE candidates. We confirm that our LAE catalogs include $177$ LAEs
that have been spectroscopically identified in our SILVERRUSH programs and
previous studies, ensuring the validity of our machine learning selection. In
addition, we find that the object-matching rates between our LAE catalogs and
our previous results are $\simeq 80$-$100$% at bright NB magnitudes of
$\lesssim 24$ mag. We also confirm that the surface number densities of our LAE
candidates are consistent with previous results. Our LAE catalogs will be made
public on our project webpage.


  We propose a novel method for approximate inference in Bayesian networks
(BNs). The idea is to sample data from a BN, learn a latent tree model (LTM)
from the data offline, and when online, make inference with the LTM instead of
the original BN. Because LTMs are tree-structured, inference takes linear time.
In the meantime, they can represent complex relationship among leaf nodes and
hence the approximation accuracy is often good. Empirical evidence shows that
our method can achieve good approximation accuracy at low online computational
cost.


  A repulsive gravitational effect of general relativity (without cosmological
term), which was pointed out by Hilbert many years ago, could play a decisive
role in the explanation of the observational data concerning the accelerated
expansion of the universe.


  We study the problem of maximizing the geometric mean of $d$ low-degree
non-negative forms on the real or complex sphere in $n$ variables. We show that
this highly non-convex problem is NP-hard even when the forms are quadratic and
is equivalent to optimizing a homogeneous polynomial of degree $O(d)$ on the
sphere. The standard Sum-of-Squares based convex relaxation for this polynomial
optimization problem requires solving a semidefinite program (SDP) of size
$n^{O(d)}$, with multiplicative approximation guarantees of
$\Omega(\frac{1}{n})$. We exploit the compact representation of this polynomial
to introduce a SDP relaxation of size polynomial in $n$ and $d$, and prove that
it achieves a constant factor multiplicative approximation when maximizing the
geometric mean of non-negative quadratic forms. We also show that this analysis
is asymptotically tight, with a sequence of instances where the gap between the
relaxation and true optimum approaches this constant factor as $d \rightarrow
\infty$. Next we propose a series of intermediate relaxations of increasing
complexity that interpolate to the full Sum-of-Squares relaxation, as well as a
rounding algorithm that finds an approximate solution from the solution of any
intermediate relaxation. Finally we show that this approach can be generalized
for relaxations of products of non-negative forms of any degree.


  Spin and transverse momentum dependent parton distributions - Generalized
Parton Distributions (GPDs) - are at the interface between the QCD structure of
the hadrons and observable quantities. The GPDs are linear superpositions
within helicity amplitudes. The amplitudes are probed in high energy
leptoproduction processes through angular dependent cross sections and
polarization asymmetries. Phenomenological extraction of the amplitudes and the
distributions is a challenging task. We present observables that connect
particularly with the chiral odd quark-nucleon helicity amplitudes for Deeply
Virtual $\pi^0$ Production.


  Economic growth in Western Europe, Eastern Europe, Asia, countries of the
former USSR, Africa and Latin America were analysed. It is demonstrated that
the fundamental postulate of the Unified Growth Theory about the existence of
the three regimes of growth (Malthusian regime, post-Malthusian regime and
sustained-growth regime) is contradicted by data. These regimes did not exist.
In particular, there was no escape from the Malthusian trap because there was
no trap. Economic growth in all these regions was not stagnant but hyperbolic.
Unified Growth Theory is fundamentally incorrect. However, this theory is also
dangerously misleading because it claims a transition from the endless epoch of
stagnation to the new era of sustained economic growth, the interpretation
creating the sense of security and a promise of prosperity. The data show that
the opposite is true. Economic growth in the past was sustained and secure.
Now, it is supported by the increasing ecological deficit. The long-term
sustained and secure economic growth has yet to be created. It did not happen
automatically, as suggested incorrectly by the Unified Growth Theory.


  Every weighted tree corresponds naturally to a cooperative game that we call
a "tree game"; it assigns to each subset of leaves the sum of the weights of
the minimal subtree spanned by those leaves. In the context of phylogenetic
trees, the leaves are species and this assignment captures the diversity
present in the coalition of species considered. We consider the Shapley value
of tree games and suggest a biological interpretation. We determine the linear
transformation M that shows the dependence of the Shapley value on the edge
weights of the tree, and we also compute a null space basis of M. Both depend
on the "split counts" of the tree. Finally, we characterize the Shapley value
on tree games by four axioms, a counterpart to Shapley's original theorem on
the larger class of cooperative games.


  We present high-resolution (0.3") Very Large Array (VLA) imaging of the
molecular gas in the host galaxy of the high redshift quasar PSS J2322+1944
(z=4.12). These observations confirm that the molecular gas (CO) in the host
galaxy of this quasar is lensed into a full Einstein ring, and reveal the
internal dynamics of the molecular gas in this system. The ring has a diameter
of ~1.5", and thus is sampled over ~20 resolution elements by our observations.
Through a model-based lens inversion, we recover the velocity gradient of the
molecular reservoir in the quasar host galaxy of PSS J2322+1944. The Einstein
ring lens configuration enables us to zoom in on the emission and to resolve
scales down to ~1 kpc. From the model-reconstructed source, we find that the
molecular gas is distributed on a scale of 5 kpc, and has a total mass of
M(H2)=1.7 x 10^10 M_sun. A basic estimate of the dynamical mass gives M_dyn =
4.4 x 10^10 (sin i)^-2 M_sun, that is, only ~2.5 times the molecular gas mass,
and ~30 times the black hole mass (assuming that the dynamical structure is
highly inclined). The lens configuration also allows us to tie the optical
emission to the molecular gas emission, which suggests that the active galactic
nucleus (AGN) does reside within, but not close to the center of the molecular
reservoir. Together with the (at least partially) disturbed structure of the
CO, this suggests that the system is interacting. Such an interaction, possibly
caused by a major `wet' merger, may be responsible for both feeding the quasar
and fueling the massive starburst of 680 M_sun/yr in this system, in agreement
with recently suggested scenarios of quasar activity and galaxy assembly in the
early universe.


  Paper examines the validity and soundness of the standard equation derived to
find the amount of energy stored inside an elastic material when it is
stretched. The paper also tries to include the parameters that where neglected
while deriving the so-called standard equation and thus by trying to solve the
anomalies associated with it. The paper suggests a new equation that can solve
the problems.


  The infinite upper triangular Pascal matrix is $T = [\binom{j}{i}]$ for
$0\leq i,j$. It is easy to see that any leading principle square submatrix is
triangular with determinant $1$, hence invertible. In this paper, we
investigate the invertibility of arbitrary square submatrices $T_{r,c}$
comprised of rows $r=[r_0,\ldots,r_m]$ and columns $c=[c_0,\ldots,c_m]$ of $T$.
We show that $T_{r,c}$ is invertible iff $r \leq c$ (i.e., $r_i \leq c_i$ for
$i=0, \ldots, m$), or equivalently, iff all diagonal entries are nonzero. To
prove this result we establish a connection between the invertibility of these
submatrices and polynomial interpolation. In particular, we apply the theory of
Birkhoff interpolation and \polya{} systems.


  We study the symmetry resolved entanglement entropies in one-dimensional
systems with boundaries. We provide some general results for conformal
invariant theories and then move to a semi-infinite chain of free fermions. We
consider both an interval starting from the boundary and away from it. We
derive exact formulas for the charged and symmetry resolved entropies based on
theorems and conjectures about the spectra of Toeplitz+Hankel matrices. En
route to characterise the interval away from the boundary, we prove a general
relation between the eigenvalues of Toeplitz+Hankel matrices and block Toeplitz
ones. An important aspect is that the saddle-point approximation from charged
to symmetry resolved entropies introduces algebraic corrections to the scaling
that are much more severe than in systems without boundaries.


  Biological data in digital form has become a, if not the, driving force
behind innovations in biology, medicine, and the environment. No study and no
model would be complete without access to digital data (including text)
collected by others and available in public repositories. With this ascent in
the fundamental importance of data for reproducible scientific progress has
come a troubling paradox.


  Designing a web-application from a specification involves a series of
well-planned and well executed steps leading to the final product. This often
involves critical changes in design while testing the application, which itself
is slow and cumbersome. Traditional approaches either fully automate the
web-application development process, or let developers write everything from
scratch. Our approach is based on a middle-ground, with precise control on the
workflow and usage of a set of custom-made software tools to automate a
significant part of code generation.


  Levitation of optical scatterers provides a new mean to develop free-space
volumetric displays. The principle is to illuminate a levitating particle
displaced at high velocity in three dimensions (3D) to create images based on
persistence of vision (POV). Light scattered by the particle can be observed
all around the volumetric display and therefore provides a true 3D image that
does not rely on interference effects and remains insensitive to the angle of
observation. The challenge is to control with a high accuracy and at high speed
the trajectory of the particle in three dimensions. Systems that use light to
generate free-space images either in plasma or with a bead are strictly
dependent of the scanning method used. Mechanical systems are required to scan
the particles in the volume which weakens the time dynamics. Here we use
electrically driven planar Paul traps (PPTs) to control the trajectory of
electrically charged particles. A single gold particle colloid is manipulated
in three dimensions through AC and DC electrical voltages applied to a PPT.
Electric voltages can be modulated at high frequencies (150 kHz) and allow for
a high speed displacement of particles without moving any other system
component. The optical scattering of the particle in levitation yields
free-space images that are imaged with conventional optics. The trajectory of
the particle is entirely encoded in the electric voltage and driven through
stationary planar electrodes. We show in this paper, the proof-of-concept for
the generation of 3D free space graphics with a single electrically scanned
particle.


  The timing properties of the 4.45 s pulsar in the Be X-ray binary system GRO
J1750-27 are examined using hard X-ray data from INTEGRAL and Swift during a
Type II outburst observed during 2008. The orbital parameters of the system are
measured and agree well with those found during the last known outburst of the
system in 1995. Correcting the effects of the doppler shifting of the period,
due to the orbital motion of the pulsar, leads to the detection of an intrinsic
spin-up that is well described by a simple model including Pdot and Pdotdot
terms of -7.5E-10 ss^-1 and 1E-16 ss^-2 respectively. The model is then used to
compare the time-resolved variation of the X-ray flux and intrinsic spin-up
against the accretion torque model of Ghosh & Lamb (1979); this finds that GRO
J1750-27 is likely located 12-22 kpc distant and that the surface magnetic
field of the neutron star is ~2E12 G. The shape of the pulse and the pulsed
fraction shows different behaviour above and below 20 keV indicating that the
observed pulsations are the convolution of many complex components.


  Despite their widespread success in various domains, Transformer networks
have yet to perform well across datasets in the domain of 3D atomistic graphs
such as molecules even when 3D-related inductive biases like translational
invariance and rotational equivariance are considered. In this paper, we
demonstrate that Transformers can generalize well to 3D atomistic graphs and
present Equiformer, a graph neural network leveraging the strength of
Transformer architectures and incorporating SE(3)/E(3)-equivariant features
based on irreducible representations (irreps). First, we propose a simple and
effective architecture by only replacing original operations in Transformers
with their equivariant counterparts and including tensor products. Using
equivariant operations enables encoding equivariant information in channels of
irreps features without complicating graph structures. With minimal
modifications to Transformers, this architecture has already achieved strong
empirical results. Second, we propose a novel attention mechanism called
equivariant graph attention, which improves upon typical attention in
Transformers through replacing dot product attention with multi-layer
perceptron attention and including non-linear message passing. With these two
innovations, Equiformer achieves competitive results to previous models on QM9,
MD17 and OC20 datasets.


  We investigate the Aharonov-Bohm (AB) effect for the double quantum dots in
the Kondo regime using the slave-boson mean-field approximation. In contrast to
the non-interacting case, where the AB oscillation generally has the period of
4$\pi$ when the two-subring structure is formed via the interdot tunneling
$t_c$, we find that the AB oscillation has the period of 2$\pi$ in the Kondo
regime. Such effects appear for the double quantum dots close to the T-shaped
geometry even in the charge-fluctuation regime. These results follow from the
fact that the Kondo resonance is always fixed to the Fermi level irrespective
of the detailed structure of the bare dot-levels.


  We estimate the sensitivity of the upcoming CTA gamma-ray telescope to DM
annihilation at the Galactic centre, improving on previous analyses in a number
of significant ways. First, we perform a detailed analyses of all backgrounds,
including diffuse astrophysical emission for the first time in a study of this
type. Second, we present a statistical framework for including systematic
errors and estimate the consequent degradation in sensitivity. These errors may
come from e.g. event reconstruction, Monte Carlo determination of the effective
area or uncertainty in atmospheric conditions. Third, we show that performing
the analysis on a set of suitably optimised regions of interest makes it
possible to partially compensate for the degradation in sensitivity caused by
systematics and diffuse emission. To probe dark matter with the canonical
thermal annihilation cross-section, CTA systematics like non-uniform variations
in acceptance over a single field of view must be kept below the 0.3% level,
unless the dark matter density rises more steeply in the centre of the Galaxy
than predicted by a typical Navarro-Frenk-White or Einasto profile. For a
contracted $r^{-1.3}$ profile, and systematics at the 1% level, CTA can probe
annihilation to $b\bar{b}$ at the canonical thermal level for dark matter
masses between 100 GeV and 10 TeV.


  In Diophantine approximation, Vaaler's theorem was an important partial
result towards the Duffin--Schaeffer conjecture, which was open for almost
eighty years before it was recently proven by Koukoulopoulos and Maynard. A
version of this result was previously proven to also hold in imaginary
quadratic fields: in this paper, we establish a version of Vaaler's theorem in
general number fields.


  We present FUSE H Lyman series spectroscopy of the hot white dwarf companion
to the 4th magnitude A1III star Beta Crateris, which shows that is has an
unusually low mass, 0.43Msun, and has almost certainly evolved through binary
interaction. This system could be a long-sought remnant of Algol-type
evolution, although radial velocity measurements appear to show that the pair
are not close. Instead, micro-variations in Beta Crt's proper motion as
measured by Hipparcos suggests that the period could be as high as 10 years.
However, a low mass white dwarf in a system with a period >3 years is difficult
to explain by conventional models for binary evolution. We speculate on
alternative models for the evolution of this system which involve an eccentric
binary or multiple components.


  We investigate the near infrared evolution of brightest cluster galaxies
(BCGs) from a sample of rich galaxy clusters since z=1. By employing an X-ray
selection of Lx>1e44 erg s-1 we limit environmental effects by selecting BCGs
in comparably high density regions. We find a positive relationship between
X-ray and near-infrared luminosity for BCGs in clusters with Lx>5e44 erg s-1.
Applying a correction for this relation we reduce the scatter in the BCG
absolute magnitude by a factor of 30%. The near-infrared J-K colour evolution
demonstrates that the stellar population in BCGs has been in place since at
least z=2 and that we expect a shorter period of star formation than that
predicted by current hierarchical merger models. We also confirm that there is
a relationship between `blue' J-K colour and the presence of BCG emission lines
associated with star formation in cooling flows.


  A measure $\mu$ on $\mathbb{R}^d$ is called reflectionless for the $s$-Riesz
transform if the singular integral $R^s\mu(x)=\int
\frac{y-x}{|y-x|^{s+1}}\,d\mu(y)$ is constant on the support of $\mu$ in some
weak sense and, moreover, the operator defined by $R^s_\mu(f)=R^s(f\,\mu)$ is
bounded in $L^2(\mu)$. In this paper we show that the only reflectionless
measure for the $s$-Riesz transform is the zero measure when $0<s<1$.


  We report the results of a search for the decay $B^0 \to X(3872)(\to J/\psi
\pi^+ \pi^-) \gamma$. The analysis is performed on a data sample corresponding
to an integrated luminosity of $711\,{\rm fb}^{-1}$ and containing $772 \times
10^6 B\bar{B}$ pairs, collected with the Belle detector at the KEKB
asymmetric-energy $e^+ e^-$ collider running at the $\Upsilon(4S)$ resonance
energy. We find no evidence for a signal and place an upper limit of
$\mathcal{B}(B^0 \to X(3872)\gamma)\times \mathcal{B}(X(3872) \to J/\psi \pi^+
\pi^-) < 5.1 \times 10^{-7}$ at 90% confidence level.


  We review some recent results for elastic electron deuteron scattering
(deuteron form factors) and photodisintegration of the deuteron, with emphasis
on the recent high energy data from Jefferson Laboratory (JLab).


  Let $\mathcal R$ be a $\Sigma^1_1$ binary relation and call a set $\mathcal
R$-discrete iff no two distinct of its elements are $\mathcal R$-related. We
show that in the extension of $\mathbf{L}$ by iterated Sacks forcing, there is
a $\Delta^1_2$ maximal $\mathcal R$-discrete set, and thus the existence of
such sets is compatible with the negation of the continuum hypothesis. As an
application we find a $\Pi^1_1$ maximal orthogonal family of Borel probability
measures in said extension. The basis of this is a new Ramsey theoretic result.


  For a one-dimensional dissipative system with position depending coefficient,
two constant of motion are deduce. These constants of motion bring about two
Hamiltonians to describe the dynamics of same classical system. However, their
quantization describe the dynamics of two completely different quantum systems.


  In this paper, we propose a more refined video segment based Mobile Edge
Computing (MEC) enhanced cache update strategy, which takes into account the
client's playback status and transmission state, MEC cache capacity and the
popularity of each segment, to improve the quality of experience (QoE) of
clients and the use ratio of MEC cache. In each cache update period, the
segments which cannot bring significant QoE improvement will be deleted and
meanwhile more suitable representations of the segments will be cahed instead.
First, we divide the MEC cache space into three parts based on segment
popularity and segment importance level. In addition, the size of different
cache parts can be transformed to each other to further exploit the MEC cache
space. For different parts, the corresponding deleted strategy and caching
strategy are formulated, where the deleted strategy combines the requested
times of segment and transmission capability of clients, and the caching
strategy utilizes the playback state of clients to calculate the caching
priority. Furthermore, we formulate the cache update problem to maximize the
utility function of clients subject to the constraint of MEC cache size and
transmission capacity. The brand and branch method is emplyed to obatain the
optimal solution. Simulation results show that our proposed algorithm can
improve system throughput and hit ratio of video segment, and at the same time
decrease playback frozen time and system backhaul traffic compared with other
existing algorithms.


  We introduce UFO, an innovative UI-Focused agent to fulfill user requests
tailored to applications on Windows OS, harnessing the capabilities of
GPT-Vision. UFO employs a dual-agent framework to meticulously observe and
analyze the graphical user interface (GUI) and control information of Windows
applications. This enables the agent to seamlessly navigate and operate within
individual applications and across them to fulfill user requests, even when
spanning multiple applications. The framework incorporates a control
interaction module, facilitating action grounding without human intervention
and enabling fully automated execution. Consequently, UFO transforms arduous
and time-consuming processes into simple tasks achievable solely through
natural language commands. We conducted testing of UFO across 9 popular Windows
applications, encompassing a variety of scenarios reflective of users' daily
usage. The results, derived from both quantitative metrics and real-case
studies, underscore the superior effectiveness of UFO in fulfilling user
requests. To the best of our knowledge, UFO stands as the first UI agent
specifically tailored for task completion within the Windows OS environment.
The open-source code for UFO is available on https://github.com/microsoft/UFO.


  Dataset is the key of deep learning in Autism disease research. However, due
to the few quantity and heterogeneity of samples in current dataset, for
example ABIDE (Autism Brain Imaging Data Exchange), the recognition research is
not effective enough. Previous studies mostly focused on optimizing feature
selection methods and data reinforcement to improve accuracy. This paper is
based on the latter technique, which learns the edge distribution of real brain
network through GraphRNN, and generates the synthetic data which has incentive
effect on the discriminant model. The experimental results show that the
combination of original and synthetic data greatly improves the discrimination
of the neural network. For instance, the most significant effect is the
50-layer ResNet, and the best generation model is GraphRNN, which improves the
accuracy by 32.51% compared with the model reference experiment without
generation data reinforcement. Because the generated data comes from the
learned edge connection distribution of Autism patients and typical controls
functional connectivity, but it has better effect than the original data, which
has constructive significance for further understanding of disease mechanism
and development.


  We study in some detail the structure of the projective quadric Q' obtained
by taking the quotient of the isotropic cone in a standard pseudo-Hermitian
space H_{p,q} with respect to the positive real numbers R^+ and, further, by
taking the quotient Q'/U(1). The case of signature (1,1) serves as an
illustration. Q'/U(1) is studied as a compactification of RxH_{p-1,q-1}.


  In this letter we study adiabatic and isocurvature perturbations in the frame
of inflation with multiple sound speeds involved. We suggest this scenario can
be realized by a number of generalized scalar fields with arbitrary kinetic
forms. These scalars have their own sound speeds respectively, so the
propagations of field fluctuations are individual. Specifically, we study a
model constructed by two DBI type actions. We find that the critical length
scale for the freezing of perturbations corresponds to the maximum sound
horizon. Moreover, if the mass term of one field is much lighter than that of
the other, the entropy perturbation could be quite large and so may give rise
to a growth outside sound horizon. At cubic order, we find that the
non-Gaussianity of local type is possibly large when entropy perturbations are
able to convert into curvature perturbations. We also calculate the
non-Gaussianity of equilateral type approximately.


  We point out that conservation of information implies that remnants produced
at the end of black hole evaporation should radiate in the low-frequency
spectrum. We model this emission and derive properties of the diffuse radiation
emitted by an otherwise dark population of such objects. We show that for early
universe black holes the frequency and energy density of this radiation, which
are in principle measurable, suffice to estimate the remnant density.


  We study the optical absorption of arrays of quantum dots and antidots in a
perpendicular homogeneous magnetic field. The electronic system is described
quantum mechanically using a Hartree approximation for the mutual Coulomb
interaction of the electrons. The evolution of the absorption is traced from
the homogeneous to the strongly modulated case identifying the ensuing
collective modes, the magnetoplasmons, and their correlations with inherent
length scales of the system.


  We prove that any surjective self-morphism with $\delta_f > 1$ on a
potentially dense smooth projective surface defined over a number field $K$ has
densely many $L$-rational points for a finite extension $L/K$.


  Injuries to the knee joint are very common for long-distance and frequent
runners, an issue which is often attributed to fatigue. We address the problem
of fatigue detection from biomechanical data from different sources, consisting
of lower extremity joint angles and ground reaction forces from running
athletes with the goal of better understanding the impact of fatigue on the
biomechanics of runners in general and on an individual level. This is done by
sequentially testing for change in a datastream using a simple martingale test
statistic. Time-uniform probabilistic martingale bounds are provided which are
used as thresholds for the test statistic. Sharp bounds can be developed by a
hybrid of a piece-wise linear- and a law of iterated logarithm- bound over all
time regimes, where the probability of an early detection is controlled in a
uniform way. If the underlying distribution of the data gradually changes over
the course of a run, then a timely upcrossing of the martingale over these
bounds is expected. The methods are developed for a setting when change sets in
gradually in an incoming stream of data. Parameter selection for the bounds are
based on simulations and methodological comparison is done with respect to
existing advances. The algorithms presented here can be easily adapted to an
online change-detection setting. Finally, we provide a detailed data analysis
based on extensive measurements of several athletes and benchmark the fatigue
detection results with the runners' individual feedback over the course of the
data collection. Qualitative conclusions on the biomechanical profiles of the
athletes can be made based on the shape of the martingale trajectories even in
the absence of an upcrossing of the threshold.


  This paper introduces BI-Directional DEliberation Reasoning (BIDDER), a novel
reasoning approach to enhance the decision rationality of language models.
Traditional reasoning methods typically rely on historical information and
employ uni-directional (left-to-right) reasoning strategy. This lack of
bi-directional deliberation reasoning results in limited awareness of potential
future outcomes and insufficient integration of historical context, leading to
suboptimal decisions. BIDDER addresses this gap by incorporating principles of
rational decision-making, specifically managing uncertainty and predicting
expected utility. Our approach involves three key processes: Inferring hidden
states to represent uncertain information in the decision-making process from
historical data; Using these hidden states to predict future potential states
and potential outcomes; Integrating historical information (past contexts) and
long-term outcomes (future contexts) to inform reasoning. By leveraging
bi-directional reasoning, BIDDER ensures thorough exploration of both past and
future contexts, leading to more informed and rational decisions. We tested
BIDDER's effectiveness in two well-defined scenarios: Poker (Limit Texas
Hold'em) and Negotiation. Our experiments demonstrate that BIDDER significantly
improves the decision-making capabilities of LLMs and LLM agents.


  We prove the Lipman-Zariski conjecture for complex surface singularities with
$p_g - g - b \le 2$. Here $p_g$ is the geometric genus, $g$ is the sum of the
genera of the exceptional curves and $b$ is the first Betti number of the dual
graph. This improves on a previous result of the second author. As an
application, we show that a compact complex surface with locally free tangent
sheaf is smooth as soon as it admits two generically linearly independent
twisted vector fields and its canonical sheaf has at most two global sections.


  BACKGROUND: Some but not all prior studies have shown that women receiving a
primary prophylactic implantable cardioverter defibrillator (ICD) have a lower
risk of death and appropriate shocks than men.
  PURPOSE: To evaluate the effect of gender on the risk of appropriate shock,
all-cause mortality and inappropriate shock in contemporary studies of patients
receiving a primary prophylactic ICD.
  DATA SOURCE: PubMed, LIVIVO, Cochrane CENTRAL between 2010 and 2016.
  STUDY SELECTION: Studies providing at least 1 gender-specific risk estimate
for the outcomes of interest.
  DATA EXTRACTION: Abstracts were screened independently for potentially
eligible studies for inclusion. Thereby each abstract was reviewed by at least
two authors.
  DATA SYNTHESIS: Out of 680 abstracts retained by our search strategy, 20
studies including 46'657 patients had gender-specific information on at least
one of the relevant endpoints. Mean age across the individual studies varied
between 58 and 69 years. The proportion of women enrolled ranged from 10% to
30%. Across 6 available studies, women had a significantly lower risk of first
appropriate shock compared with men (pooled multivariable adjusted hazard ratio
0.62 (95% CI [0.44; 0.88]). Across 14 studies reporting multivariable adjusted
gender-specific hazard ratio estimates for all-cause mortality, women had a
lower risk of death than men (pooled hazard ratio 0.75 (95% CI [0.66; 0.86]).
There was no statistically significant difference for the incidence of first
inappropriate shocks (3 studies, pooled hazard ratio 0.99 (95% CI [0.56;
1.73]).
  CONCLUSION: In this large contemporary meta-analysis, women had a
significantly lower risk of appropriate shocks and death than men, but a
similar risk of inappropriate shocks. These data may help to select patients
who benefit from primary prophylactic ICD implantation.


  This paper introduces the XOR-OR-AND normal form (XNF) for logical formulas.
It is a generalization of the well-known Conjunctive Normal Form (CNF) where
literals are replaced by XORs of literals. As a first theoretic result, we show
that every formula is equisatisfiable to a formula in 2-XNF, i.e., a formula in
XNF where each disjunction involves at most two XORs of literals. Subsequently,
we present an algorithm which converts Boolean polynomials efficiently from
their Algebraic Normal Form (ANF) to formulas in 2-XNF. Experiments with the
cipher ASCON-128 show that cryptographic problems, which by design are based
strongly on XOR-operations, can be represented using far fewer variables and
clauses in 2-XNF than in CNF. In order to take advantage of this compact
representation, new SAT solvers based on input formulas in 2-XNF need to be
designed. By taking inspiration from graph-based 2-CNF SAT solving, we devise a
new DPLL-based SAT solver for formulas in 2-XNF. Among others, we present
advanced pre- and in-processing techniques. Finally, we give timings for random
2-XNF instances and instances related to key recovery attacks on round reduced
ASCON-128, where our solver outperforms state-of-the-art alternative solving
approaches.


  We describe the essential algebra, $\widehat{kB_T}(G)$, of the Burnside biset
functor shifted by a group $T$, at a group $G$, in two cases. First, when $G$
and $T$ are both finite abelian groups and $k$ is a field of characteristic
$0$. In this case, $\widehat{kB_T}(G)$ is isomorphic to a quotient of the
shifted star algebra, which is defined in terms of the subgroups of $G\times
G\times T$. The second case is when $G$ and $T$ are any finite groups
satisfying $(|G|, |T|)=1$ and $k$ is a commutative unitary ring. In this case,
$\widehat{kB_T}(G)$ is isomorphic to a semidirect product of $Out(G)$ and
$kB^{Z(G)}(T)$, the monomial Burnside ring of $T$ with coefficients in $Z(G)$.
  The aim of the article is to consider the natural set of generators of
$\widehat{kB_T}(G)$ coming from the transitive elements in $kB_T(G\times G)$
and explore some cases in which it is possible to give a basis for
$\widehat{kB_T}(G)$ in this set.


  Probabilistic techniques are central to data analysis, but different
approaches can be difficult to apply, combine, and compare. This paper
introduces composable generative population models (CGPMs), a computational
abstraction that extends directed graphical models and can be used to describe
and compose a broad class of probabilistic data analysis techniques. Examples
include hierarchical Bayesian models, multivariate kernel methods,
discriminative machine learning, clustering algorithms, dimensionality
reduction, and arbitrary probabilistic programs. We also demonstrate the
integration of CGPMs into BayesDB, a probabilistic programming platform that
can express data analysis tasks using a modeling language and a structured
query language. The practical value is illustrated in two ways. First, CGPMs
are used in an analysis that identifies satellite data records which probably
violate Kepler's Third Law, by composing causal probabilistic programs with
non-parametric Bayes in under 50 lines of probabilistic code. Second, for
several representative data analysis tasks, we report on lines of code and
accuracy measurements of various CGPMs, plus comparisons with standard baseline
solutions from Python and MATLAB libraries.


  For ultrashort pulses having different states of polarization, the
experienced time delay when passing through small apertures is different. In
the case of a small slit (or a circular aperture), we report a significantly
stronger dispersion for the TE (or azimuthal) mode as compared to that for the
TM (or radial) mode, creating a noticeable time delay between the two
orthogonal polarization states, even for very thin apertures. The birefringent
effect of small apertures is caused by waveguide mode dispersion. In essence,
the propagation constant of the excited modes varies with wavelength
differently for othogonal polarization states: it increases with the incoming
wavelength for TE (or azimuthal) and remains constant for TM (or radial) mode.
A fundamental understanding of this phenomenon helps to explain, for example,
the use of small apertures as wave plates. Furthermore, this effect can be
exploited by tailoring the width and thickness of the aperture to obtain the
desired pulse-shape and delay.


  We present simulation details and results for the light hadron spectrum in N
f = 2 + 1 lattice QCD with the nonperturbatively O(a)-improved Wilson quark
action and the Iwasaki gauge action. Simulations are carried out at a lattice
spacing of 0.09 fm on a (2.9fm)^3 box using the PACS-CS computer. We employ the
Luscher's domain-decomposed HMC algorithm with several improvements to reduce
the degenerate up-down quark mass toward the physical value. So far the
resulting pseudoscalar meson mass is ranging from 702MeV down to 156MeV. We
discuss on the stability and the efficiency of the algorithm. The light harden
spectrum extrapolated at the physical point is compared with the experimental
values. We also present the values of the quark masses and the pseudoscalar
meson decay constants.


  We identify velocity channel map intensities as a new way to trace magnetic
fields in turbulent media. This work makes use of both of the modern theory of
MHD turbulence predicting that the magnetic eddies are aligned with the local
direction of magnetic field, and also the theory of the spectral line
Position-Position-Velocity (PPV) statistics describing how the velocity and
density fluctuations are mapped into the PPV space. In particular, we use the
fact that, the fluctuations of intensity of thin channel maps are mostly
affected by the turbulent velocity, while the thick maps are dominated by
density variations. We study how contributions of the fundamental MHD modes
affect the Velocity Channel Gradients (VChGs) and demonstrate that the VChGs
arising from Alfven and slow modes are aligned perpendicular to the local
direction of magnetic field, while the VChGs produced by the fast mode are
aligned parallel to the magnetic field. The dominance of the Alfven and slow
modes in the interstellar media will therefore allow a reliable magnetic field
tracing using the VChGs. We explore ways of identifying self-gravitating
regions that do not require polarimetric information. In addition, we also
introduce a new measure termed "Reduced Velocity Centroids" (RVCGs) and compare
its abilities with the VChGs. We employed both measures to the GALFA 21cm data
and successfully compared thus magnetic field directions with the {\it PLANCK}
polarization. The applications of the suggested techniques include both tracing
magnetic field in diffuse interstellar media and star forming regions, as well
as removing the galactic foreground in the framework of cosmological
polarization studies.


  Multispectral photometric stereo(MPS) aims at recovering the surface normal
of a scene from a single-shot multispectral image captured under multispectral
illuminations. Existing MPS methods adopt the Lambertian reflectance model to
make the problem tractable, but it greatly limits their application to
real-world surfaces. In this paper, we propose a deep neural network named
NeuralMPS to solve the MPS problem under general non-Lambertian spectral
reflectances. Specifically, we present a spectral reflectance
decomposition(SRD) model to disentangle the spectral reflectance into geometric
components and spectral components. With this decomposition, we show that the
MPS problem for surfaces with a uniform material is equivalent to the
conventional photometric stereo(CPS) with unknown light intensities. In this
way, NeuralMPS reduces the difficulty of the non-Lambertian MPS problem by
leveraging the well-studied non-Lambertian CPS methods. Experiments on both
synthetic and real-world scenes demonstrate the effectiveness of our method.


  For any knot, the following are equivalent. (1) The infinite cyclic cover has
uncountably many finite covers; (2) there exists a finite-image representation
of the knot group for which the twisted Alexander polynomial vanishes; (3) the
knot group admits a finite-image representation such that the image of the
fundamental group of an incompressible Seifert surface is a proper subgroup of
the image of the commutator subgroup of the knot group.


  Let $\mathcal{R}$ be an open Riemann surface. In this paper we prove that
every continuous function $M \to \mathbb{R}^n$, $n\ge 3$, defined on a
divergent Jordan arc $M \subset \mathcal{R}$ can be approximated in the
Carleman sense by conformal minimal immersions; thus providing a new
generalization of Carleman's theorem. In fact, we prove that this result
remains true for null curves and many other classes of directed holomorphic
immersions for which the directing variety satisfies a certain flexibility
property. Furthermore, the constructed immersions may be chosen to be complete
or proper under natural assumptions on the variety and the continuous map.
  As a consequence we give an approximate solution to a Plateau problem for
divergent Jordan curves in the Euclidean spaces.


  Quasi-two-dimensional transport is investigated in a system consisting of one
ferromagnetic layer placed between two insulating layers. Using the mechanism
of skew-scattering to describe the Extraordinary Hall Effect (EHE) and
calculating the conductivity tensor, we compare the quasi- two-dimensional Hall
resistance with the resistance of a massive sample. In this study a new
mechanism of EHE (geometric mechanism of EHE) due to non-ideal interfaces and
volume defects is also proposed.


  Following the Gallavotti's conjecture, Stationary states of Navier-Stokes
fluids are proposed to be described equivalently by alternative equations
besides the NS equation itself. We propose a model system symmetric under
time-reversal based on the Navier-Stokes equations constrained to keep the
Enstrophy constant. It is demonstrated through high-resolved numerical
experiments that the reversible model evolves to a stationary state which
reproduces quite accurately all statistical observables relevant for the
physics of turbulence extracted by direct numerical simulations at different
Reynolds numbers. The possibility of using reversible models to mimic
turbulence dynamics is of practical importance for coarse-grained version of
Navier-Stokes equations, as used in Large-eddy simulations. Furthermore, the
reversible model appears mathematically simpler, since enstrophy is bounded to
be constant for every Reynolds. Finally, the theoretically interest in the
context of statistical mechanics is briefly discussed.


  We study the Emptiness Formation Probability (EFP) for the spin 1/2 XXZ spin
chain. EFP P(n) detects a formation of ferromagnetic string of the length n in
the ground state. It is expected that EFP decays in a Gaussian way for large
strings P(n) ~ n^{-gamma} C^{-n^2}. Here, we propose the explicit expressions
for the rate of Gaussian decay C as well as for the exponent gamma. In order to
confirm the validity of our formulas, we employed an ab initio simulation
technique of the density-matrix renormalization group to simulate XXZ spin
chain of sufficient length. Furthermore, we performed Monte-Carlo integration
of the Jimbo-Miwa multiple integral for P(n). Those numerical results for P(n)
support our formulas fairly definitely.


  The anomalies in five-dimensional orbifold theories are examined in a generic
type of non-factorizable geometries. In spite of complicated fermion
wavefunctions, the shape of anomaly is found to be identical to that of flat
theories. In particular it is split evenly on the orbifold fixed points. This
result also follows from the arguments on the AdS/CFT correspondence and an
anomaly cancellation mechanism. The cancellation with Chern-Simons term works
if the four-dimensional effective theory is free from chiral anomalies. We also
discuss the Fayet-Iliopoulos (FI) term in warped supersymmetric theories.
Unlike the gauge anomaly, FI divergences reside not only on the orbifold fixed
points but also in the whole five-dimensional bulk. The effect of the FI term
is to generate supersymmetric masses for charged hypermultiplets, which are no
longer constant but have metric factor dependence. We calculate the spectrum
and wavefunctions of Kaluza-Klein modes in the presence of the FI term and
discuss phenomenological implications to quark-lepton masses and large scale
hierarchies.


  This paper from 2000 is a presentation of a status qu{\ae}stionis at that
tiime, to wit of the problem of the interpretability logic of {\em all}\/
reasonable arithmetical theories. We present both the arithmetical side and the
modal side of the question.


  We provide a holographic interpretation of a class of three-dimensional
wormhole spacetimes. These spacetimes have multiple asymptotic regions which
are separated from each other by horizons. Each such region is isometric to the
BTZ black hole and there is non-trivial spacetime topology hidden behind the
horizons. We show that application of the real-time gauge/gravity duality
results in a complete holographic description of these spacetimes with the dual
state capturing the non-trivial topology behind the horizons. We also show that
these spacetimes are in correspondence with trivalent graphs and provide an
explicit metric description with all physical parameters appearing in the
metric.


  We investigate the combined effects of anisotropy and a magnetic field in
strongly interacting gauge theories by the gauge/gravity correspondence. Our
main motivation is the quark-gluon plasma produced in off-central heavy-ion
collisions which exhibits large anisotropy in pressure gradients as well as
large external magnetic fields. We explore two different configurations, with
the anisotropy either parallel or perpendicular to the magnetic field, focusing
on the competition and interplay between the two. A detailed study of the RG
flow in the ground state reveals a rich structure where depending on which of
the two, anisotropy or magnetic field, is stronger, intermediate geometries
with approximate AdS$_4\times \mathbb{R}$ and AdS$_3\times \mathbb{R}^2$
factors arise. This competition is also manifest in the phase structure at
finite temperature, specifically in the dependence of the chiral transition
temperature on anisotropy and magnetic field, from which we infer the presence
of inverse magnetic and anisotropic catalyses of the chiral condensate.
Finally, we consider other salient observables in the theory, including the
quark-antiquark potential, shear viscosity, entanglement entropy and the
butterfly velocity. We demonstrate that they serve as good probes of the
theory, in particular, distinguishing between the effects of the magnetic field
and anisotropy in the ground and plasma states. We also find that the butterfly
velocity, which codifies how fast information propagates in the plasma,
exhibits a rich structure as a function of temperature, anisotropy and magnetic
field, exceeding the conformal value in certain regimes.


  In this work, we show the flux tubes of the quark-antiquark and quark-quark
at finite temperature for SU(3) Lattice QCD. The chromomagnetic and
chromoelectric fields are calculated above and below the phase transition.


  Intrinsic aberrations are those which occur due to the finite length of the
desired field configuration. They are often loosely ascribed to the fringing
field. This is misleading as it implies that the effects can be minimized by
shaping the fields. In fact, there is an irreducible component related to the
broken symmetry. It is present even in the hard-edge limit, and moreover, the
other (soft-edge) effects can be simply ascribed to the intrinsic aberration
spread over a finite length.
  We rederive the aberration formulas for quadrupoles using a Hamiltonian
formalism. This allows for an easy comparison of electrostatic and magnetic
quadrupoles. For different combinations of large and small emittances in the
two transverse planes, it is found that in some situations electrostatic
quadrupoles have lower aberrations, while in others, magnetic quadrupoles are
better. As well, we discuss the ways in which existing transport codes handle
quadrupole fringe fields. Pitfalls are pointed out and improvements proposed.


  The Hales-Jewett theorem asserts that for every r and every k there exists n
such that every r-colouring of the n-dimensional grid {1,...,k}^n contains a
combinatorial line. This result is a generalization of van der Waerden's
theorem, and it is one of the fundamental results of Ramsey theory. The theorem
of van der Waerden has a famous density version, conjectured by Erdos and Turan
in 1936, proved by Szemeredi in 1975, and given a different proof by
Furstenberg in 1977. The Hales-Jewett theorem has a density version as well,
proved by Furstenberg and Katznelson in 1991 by means of a significant
extension of the ergodic techniques that had been pioneered by Furstenberg in
his proof of Szemeredi's theorem. In this paper, we give the first elementary
proof of the theorem of Furstenberg and Katznelson, and the first to provide a
quantitative bound on how large n needs to be. In particular, we show that a
subset of {1,2,3}^n of density delta contains a combinatorial line if n is at
least a tower of 2's of height O(1/delta^3). Our proof is reasonably simple:
indeed, it gives what is arguably the simplest known proof of Szemeredi's
theorem.


  Saturation affects a significant rate of images recorded by the Atmospheric
Imaging Assembly on the Solar Dynamics Observatory. This paper describes a
computational method and a technological pipeline for the de-saturation of such
images, based on several mathematical ingredients like Expectation
Maximization, image correlation and interpolation. An analysis of the
computational properties and demands of the pipeline, together with an
assessment of its reliability are performed against a set of data recorded from
the Feburary 25 2014 flaring event.


  Bottomonium production is a powerful tool to investigate hadron collisions
and the properties of the medium created in heavy-ion collisions. According to
the color-screening model, these mesons give important information about the
deconfined medium called Quark-Gluon Plasma (QGP) produced in ultrarelativistic
heavy-ion collisions. Cold nuclear matter (CNM) effects can modify the
bottomonium production even in absence of deconfined matter: the study of
proton-nucleus collisions is therefore essential to disentangle these effects
from the hot ones. Last but not least, measurement in pp collisions serve as
crucial test of different QCD models of quarkonium hadroproduction and provide
the reference for the study in nucleus-nucleus collisions.
  In ALICE, bottomonium is measured at forward rapidity ($2.5 < y < 4$) down to
zero transverse momentum, exploiting the dimuon decay channel. The latest
results in pp, Pb-Pb and p-Pb collisions are discussed and compared to
theoretical calculations.


  We investigate transport properties of gate-all-around Si nanowires using
non-equilibrium Green's function technique. By taking into account of the
ionized impurity scattering we calculate Green's functions self-consistently
and examine the effects of ionized impurity scattering on electron densities
and currents. For nano-scale Si wires, it is found that, due to the impurity
scattering, the local density of state profiles loose it's interference
oscillations as well as is broaden and shifted. In addition, the impurity
scattering gives rise to a different transconductance as functions of
temperature and impurity scattering strength when compared with the
transconductance without impurity scattering.


  For most deep learning algorithms training is notoriously time consuming.
Since most of the computation in training neural networks is typically spent on
floating point multiplications, we investigate an approach to training that
eliminates the need for most of these. Our method consists of two parts: First
we stochastically binarize weights to convert multiplications involved in
computing hidden states to sign changes. Second, while back-propagating error
derivatives, in addition to binarizing the weights, we quantize the
representations at each layer to convert the remaining multiplications into
binary shifts. Experimental results across 3 popular datasets (MNIST, CIFAR10,
SVHN) show that this approach not only does not hurt classification performance
but can result in even better performance than standard stochastic gradient
descent training, paving the way to fast, hardware-friendly training of neural
networks.


  A kernelization for a parameterized decision problem $\mathcal{Q}$ is a
polynomial-time preprocessing algorithm that reduces any parameterized instance
$(x,k)$ into an instance $(x',k')$ whose size is bounded by a function of $k$
alone and which has the same yes/no answer for $\mathcal{Q}$. Such
preprocessing algorithms cannot exist in the context of counting problems, when
the answer to be preserved is the number of solutions, since this number can be
arbitrarily large compared to $k$. However, we show that for counting minimum
feedback vertex sets of size at most $k$, and for counting minimum dominating
sets of size at most $k$ in a planar graph, there is a polynomial-time
algorithm that either outputs the answer or reduces to an instance $(G',k')$ of
size polynomial in $k$ with the same number of minimum solutions. This shows
that a meaningful theory of kernelization for counting problems is possible and
opens the door for future developments. Our algorithms exploit that if the
number of solutions exceeds $2^{\mathsf{poly}(k)}$, the size of the input is
exponential in terms of $k$ so that the running time of a parameterized
counting algorithm can be bounded by $\mathsf{poly}(n)$. Otherwise, we can use
gadgets that slightly increase $k$ to represent choices among $2^{O(k)}$
options by only $\mathsf{poly}(k)$ vertices.


  Dynamic topic models track the evolution of topics in sequential documents,
which have derived various applications like trend analysis and opinion mining.
However, existing models suffer from repetitive topic and unassociated topic
issues, failing to reveal the evolution and hindering further applications. To
address these issues, we break the tradition of simply chaining topics in
existing work and propose a novel neural \modelfullname. We introduce a new
evolution-tracking contrastive learning method that builds the similarity
relations among dynamic topics. This not only tracks topic evolution but also
maintains topic diversity, mitigating the repetitive topic issue. To avoid
unassociated topics, we further present an unassociated word exclusion method
that consistently excludes unassociated words from discovered topics. Extensive
experiments demonstrate our model significantly outperforms state-of-the-art
baselines, tracking topic evolution with high-quality topics, showing better
performance on downstream tasks, and remaining robust to the hyperparameter for
evolution intensities. Our code is available at https://github.com/bobxwu/CFDTM .


  As a continuation of our previous works studying the holographic principle in
the plane-wave limit, we discuss the 3-point correlation functions of BMN
operators with bosonic excitations when impurities are not conserved. We show
that our proposal for a holographic mapping between the conformal OPE
coefficients of super Yang-Mills theory and the 3-point vertex of the
holographic string field theory is valid to the leading order in the large
$\mu$ limit. Our results provide for the first time a direct holographic
relation for the 3-point correlators of BMN operators including impurity
non-preserving processes.


  We present a comprehensive analysis of approximately $15$ years ($2006-2021$)
of X-ray observations of UGC~6728, a low-mass bare AGN, for the first time. Our
study encompasses both spectral and temporal aspects of this source. The
spectral properties of this source are studied using various phenomenological
and physical models. We conclude that (a) the observed variability in X-ray
luminosity is not attributed to the Hydrogen column density ($N_H$) as UGC~6728
exhibits a bare nucleus, implying a negligible $N_H$ contribution along the
line of sight, and (b) the spectral slope in the X-ray band demonstrates a
systematic variation over time, indicating a transition from a relatively hard
state to a comparatively soft state. We propose that the underlying accretion
dynamics around the central object account for this behavior. By performing
X-ray spectral fitting, we estimate the mass of the central supermassive black
hole (SMBH) in UGC~6728 to be $M_{BH}=(7.13\pm1.23)\times10^5$ M$_\odot$ with
spin $a=0.97^{+0.20}_{-0.27}$ and inclination angle $i=49.5\pm14.5$ degree.
Based on our spectral and temporal analysis, we suggest that UGC~6728 lacks a
prominent Compton hump or exhibits a very subtle hump that remains undetectable
in our analysis. Furthermore, the high-energy X-ray photons in this source are
likely to originate from the low-energy X-ray photons through inverse Compton
scattering in a Compton cloud, highlighting a connection between the emission
in two energy ranges. We notice a strong soft excess component in the initial
part of our observations, which later reduced substantially. This variation of
soft excess is explained in view of accretion dynamics.


  A central goal of meta-learning is to find a learning rule that enables fast
adaptation across a set of tasks, by learning the appropriate inductive bias
for that set. Most meta-learning algorithms try to find a \textit{global}
learning rule that encodes this inductive bias. However, a global learning rule
represented by a fixed-size representation is prone to meta-underfitting or
-overfitting since the right representational power for a task set is difficult
to choose a priori. Even when chosen correctly, we show that global, fixed-size
representations often fail when confronted with certain types of
out-of-distribution tasks, even when the same inductive bias is appropriate. To
address these problems, we propose a novel nonparametric meta-learning
algorithm that utilizes a meta-trained local learning rule, building on recent
ideas in attention-based and functional gradient-based meta-learning. In
several meta-regression problems, we show improved meta-generalization results
using our local, nonparametric approach and achieve state-of-the-art results in
the robotics benchmark, Omnipush.


  AI algorithms used in the public sector, e.g., for allocating social benefits
or predicting fraud, often involve multiple public and private stakeholders at
various phases of the algorithm's life-cycle. Communication issues between
these diverse stakeholders can lead to misinterpretation and misuse of
algorithms. We investigate the communication processes for AI fairness-related
decisions by conducting interviews with practitioners working on algorithmic
systems in the public sector. By applying qualitative coding analysis, we
identify key elements of communication processes that underlie fairness-related
human decisions. We analyze the division of roles, tasks, skills, and
challenges perceived by stakeholders. We formalize the underlying communication
issues within a conceptual framework that i. represents the communication
patterns ii. outlines missing elements, such as actors who miss skills for
their tasks. The framework is used for describing and analyzing key
organizational issues for fairness-related decisions. Three general patterns
emerge from the analysis: 1. Policy-makers, civil servants, and domain experts
are less involved compared to developers throughout a system's life-cycle. This
leads to developers taking on extra roles such as advisor, while they
potentially miss the required skills and guidance from domain experts. 2.
End-users and policy-makers often lack the technical skills to interpret a
system's limitations, and rely on developer roles for making decisions
concerning fairness issues. 3. Citizens are structurally absent throughout a
system's life-cycle, which may lead to decisions that do not include relevant
considerations from impacted stakeholders.


  We study the spin-mixing dynamics of a one-dimensional strongly repulsive
Fermi gas under harmonic confinement. By employing a mapping onto an
inhomogeneous isotropic Heisenberg model and the symmetries under particle
exchange, we follow the dynamics till very long times. Starting from an initial
spin-separated state, we observe superdiffusion, spin-dipolar large amplitude
oscillations and thermalization. We report a universal scaling of the
oscillations with particle number N^1/4, implying a slow-down of the motion and
the decrease of the zero-temperature spin drag coefficient as the particle
number grows.


  Chalcogenides (Q = S, Se, Te), one of the most important family of materials
in solid-state chemistry, differ from oxides by their ability to form
covalently-bonded (Qn)2- oligomers. Each chalcogen atom within such entity
fulfills the octet rule by sharing electrons with other chalcogen atoms but
some antibonding levels are vacant. This makes these oligomers particularly
suited for redox reactions in solid state, namely towards elemental metals with
a low redox potential that may be oxidized. We recently used this strategy to
design, at low temperature and in an orientated manner, materials with 2D
infinite layers through the topochemical insertion of copper into preformed
precursors containing (S2)2- and/or (Se2)2- dimers (i.e. La2O2S2, Ba2F2S2 and
LaSe2). Herein we extend the validity of the concept to the redox activity of
(S2)2- and (S3)2- oligomers towards 3d transition metal elements (Cu, Ni, Fe)
and highlight the strong relationship between the structures of the precursors,
BaS2 and BaS3, and the products, BaCu2S2, BaCu4S3, BaNiS2 and BaFe2S3. Clearly,
beyond the natural interest for the chemical reactivity of oligomers to
generate compounds, this soft chemistry route may conduct to the rational
conception of materials with a predicted crystal structure.