  The challenge of the Reengineering Case is to extract a state machine model
out of the abstract syntax graph of a Java program. The extracted state machine
offers a reduced view on the full program graph and thus helps to understand
the program regarding the question of interest. We tackle this task employing
the general purpose graph rewrite system GrGen.NET (www.grgen.net).


  Solvable vertex models in two dimensions are of importance in conformal field
theory, phase
  transitions and integrable models.
  We consider here the $D_n$ spin vertex models, for $n$ which is odd.
  The models involve also the anti--spinor representation. We describe here the
Boltzmann weights
  for these representations using crossing symmetry from the previously known
spinor representations.
  For calculation reasons we limit ourself to the $n=3$ and $n=5$ cases, which
are described
  explicitly.


  We develop an approach to parametrize cosmological perturbations beyond
linear order for general dark energy and modified gravity models characterized
by a single scalar degree of freedom. We derive the full nonlinear action,
focusing on Horndeski theories. In the quasi-static, non-relativistic limit,
there are a total of six independent relevant operators, three of which start
at nonlinear order. The new nonlinear couplings modify, beyond linear order,
the generalized Poisson equation relating the Newtonian potential to the matter
density contrast. We derive this equation up to cubic order in perturbations
and, in a companion article, we apply it to compute the one-loop matter power
spectrum. Within this approach, we also discuss the Vainshtein regime around
spherical sources and the relation between the Vainshtein scale and the
nonlinear scale for structure formation.


  A modified generally covariant Yang-Mills action, which depends on the
complex structure of spacetime and not its metric, is proved to be
renormalizable. This proof makes this Lagrangian model the unique known
generally covariant four dimensional model to be renormalizable without higher
order derivatives. The first order one-loop diagrams are computed in an
appropriate gauge condition and they are found to be finite.


  We propose a new numerical method to compute quasi-equilibrium sequences of
general relativistic irrotational binary neutron star systems. It is a good
approximation to assume that (1) the binary star system is irrotational, i.e.
the vorticity of the flow field inside component stars vanishes everywhere
(irrotational flow), and (2) the binary star system is in quasi-equilibrium,
for an inspiraling binary neutron star system just before the coalescence as a
result of gravitational wave emission. We can introduce the velocity potential
for such an irrotational flow field, which satisfies an elliptic partial
differential equation (PDE) with a Neumann type boundary condition at the
stellar surface. For a treatment of general relativistic gravity, we use the
Wilson--Mathews formulation, which assumes conformal flatness for spatial
components of metric. In this formulation, the basic equations are expressed by
a system of elliptic PDEs. We have developed a method to solve these PDEs with
appropriate boundary conditions. The method is based on the established
prescription for computing equilibrium states of rapidly rotating axisymmetric
neutron stars or Newtonian binary systems. We have checked the reliability of
our new code by comparing our results with those of other computations
available. We have also performed several convergence tests. By using this
code, we have obtained quasi-equilibrium sequences of irrotational binary star
systems with strong gravity as models for final states of real evolution of
binary neutron star systems just before coalescence. Analysis of our
quasi-equilibrium sequences of binary star systems shows that the systems may
not suffer from dynamical instability of the orbital motion and that the
maximum density does not increase as the binary separation decreases.


  It was suggested on several occasions by Deligne, Drinfeld and Kontsevich
that all the moduli spaces arising in the classical problems of deformation
theory should be extended to natural "derived" moduli spaces which are always
smooth in an appropriate sense and whose tangent spaces involve the entire
cohomology of the sheaf of infinitesimal automorphisms, not just H^1. In this
note we give an algebraic construction of such an extension for the simplest
class of moduli spaces, namely for moduli of local systems (representations of
the fundamental group).


  The mechanical vulnerability of the Nb3Sn-coated cavities is identified as
one of the significant technical hurdles toward deploying them in practical
accelerator applications in the not-so-distant future. It is crucial to
characterize the material's mechanical properties in ways to address such
vulnerability. Nanoindentation is a widely used technique for measuring the
mechanical properties of thin films that involves indenting the film with a
small diamond tip and measuring the force-displacement response to calculate
the film's elastic modulus, hardness, and other mechanical properties. The
nanoindentation analysis was performed on multiple vapor-diffused Nb3Sn samples
coated at Jefferson Lab and Fermilab coating facilities for the first time.
This contribution will discuss the first results obtained from the
nanoindentation of Nb3Sn-coated Nb samples prepared via the Sn vapor diffusion
technique.


  We present results of a study to quantify the effects of dust on the derived
photometric parameters of disk and bulges obtained from bulge-disk
decomposition: scale-length, effective radius, Sersic index, disk axis-ratio,
and bulge-to-disk ratio. The dust induced changes in these parameters were
obtained by fitting simulated images of composite systems (containing a disk
and a bulge) produced using radiative transfer calculations. The simulations
were fitted with the GALFIT 3.0.2 data analysis algorithm. Fits were done with
both a combination of an exponential plus a variable-index Sersic function as
well as with a combination of two variable-index Sersic functions. We find that
dust is biasing the derived exponential scale-length of decomposed disks
towards smaller values than would be otherwise derived if the galaxy were to
have no bulge. Similarly, the derived bulge-to-disk ratio is biased towards
smaller values. However, the derived axis-ratio of the disk is not changed in
the decomposition process. The derived effective radius of decomposed disks of
systems having exponential bulges is found to be less affected by dust when
fits are done with two variable-index Sersic functions. For the same type of
fits dust is found to bias the value of the derived effective radius of
decomposed disks towards lower values for systems having de Vaucouleurs bulges.
All corrections derived in this paper are made available in electronic form.


  We show by a counter example the failure of rational dilation on the
tetrablock, a polynomially convex and non-convex domain in $\mathbb C^3$,
defined as $$ \mathbb E = \{ (x_1,x_2,x_3)\in\mathbb C^3\,:\,
1-zx_1-wx_2+zwx_3\neq 0 \textup{ whenever } |z|\leq 1, |w|\leq 1 \}. $$ A
commuting triple of operators $(T_1,T_2,T_3)$ for which the closed tetrablock
$\overline{\mathbb E}$ is a spectral set, is called an $\mathbb E$-contraction.
For an $\mathbb E$-contraction $(T_1,T_2,T_3)$, the two operator equations $$
T_1-T_2^*T_3=D_{T_3}X_1D_{T_3} \textup{ and } T_2-T_1^*T_3= D_{T_3}X_2D_{T_3},
\quad D_{T_3}=(I-T_3^*T_3)^{\frac{1}{2}},$$ have unique solutions $A_1,A_2$ on
$\mathcal D_{T_3}=\overline{Ran} D_{T_3}$ and they are called the fundamental
operators of $(T_1,T_2,T_3)$. For a particular class of $\mathbb
E$-contractions, we prove it necessary for the existence of rational dilation
that the corresponding fundamental operators $A_1,A_2$ satisfy the conditions
\begin{equation}\label{abstract} A_1A_2=A_2A_1 \textup{ and }
A_1^*A_1-A_1A_1^*=A_2^*A_2-A_2A_2^*. \end{equation} Then we construct an
$\mathbb E$-contraction from that particular class which fails to satisfy
(\ref{abstract}). We produce a concrete functional model for pure $\mathbb
E$-isometries, a class of $E$-contractions analogous to the pure isometries in
one variable. The fundamental operators play the main role in this model.


  We present analysis of high-resolution spectra of a sample of stars in the
globular cluster M5 (NGC 5904). The sample includes stars from the red giant
branch (seven stars), the red horizontal branch (two stars), and the asymptotic
giant branch (eight stars), with effective temperatures ranging from 4000 K to
6100 K. Spectra were obtained with the HIRES spectrometer on the Keck I
telescope, with a wavelength coverage from 3700 to 7950 angstroms for the HB
and AGB sample, and 5300 to 7600 angstroms for the majority of the RGB sample.
We find offsets of some abundance ratios between the AGB and the RGB branches.
However, these discrepancies appear to be due to analysis effects, and indicate
that caution must be exerted when directly comparing abundance ratios between
different evolutionary branches. We find the expected signatures of pollution
from material enriched in the products of the hot hydrogen burning cycles such
as the CNO, Ne-Na, and Mg-Al cycles, but no significant differences within
these signatures among the three stellar evolutionary branches especially when
considering the analysis offsets. We are also able to measure an assortment of
neutron-capture element abundances, from Sr to Th, in the cluster. We find that
the neutron-capture signature for all stars is the same, and shows a
predominately r-process origin. However, we also see evidence of a small but
consistent extra s-process signature that is not tied to the light-element
variations, pointing to a pre-enrichment of this material in the protocluster
gas.


  Photonic integrated circuits (PICs) are enabling major breakthroughs in a
number of areas, including quantum computing, neuromorphic processors, wearable
devices, and more. Nevertheless, existing PIC measurement methods lack the
spectral precision, speed, and sensitivity required for refining current
applications and exploring new frontiers such as point-of-care or wearable
biosensors. Here, we present the Sweeping Optical Frequency Mixing Method
(SOHO), surpassing traditional PIC measurement methods with real-time
operation, 30 dB higher sensitivity, and over 100 times better spectral
resolution. Leveraging the frequency mixing process with a sweeping laser and
custom control software, SOHO excels in simplicity, eliminating the need for
advanced optical components and additional calibration procedures. We showcase
its superior performance on ultrahigh-quality factor (Q) fiber-loop resonators
(Q = 46M) as well as microresonators realized on a new optical waveguide
platform. An experimental spectral resolution of 19.1 femtometers is
demonstrated using an 85-meter-long unbalanced fiber Mach Zehnder
Interferometer, constrained by noise resulting from the extended fiber length,
while the theoretical resolution is calculated to be 6.2 femtometers, limited
by the linewidth of the reference laser. With its excellent performance
metrics, SOHO has the potential to become a vital measurement tool in
photonics, excelling in high-speed and high-resolution measurements of weak
optical signals.


  Certain Petrov-Galerkin schemes are inherently stable formulations of
variational problems on a given mesh. This stability is primarily obtained by
computing an optimal test basis for a given approximation space. Furthermore,
these Petrov-Galerkin schemes are equipped with a robust a posteriori error
estimate which makes them an ideal candidate for mesh adaptation. One could
extend these Petrov-Galerkin schemes not only to have optimal test spaces but
also optimal approximation spaces with respect to current estimates of the
solution. These extensions are the main focus of this article. In this article,
we provide a methodology to drive mesh adaptation to produce optimal meshes for
resolving solution features and output functionals which we demonstrate through
numerical experiments.


  Non-Fermi liquid (NFL) behavior in the normal state of the heavy-fermion
superconductor UBe13 is studied by means of low-temperature measurements of the
specific heat, C, and electrical resistivity, \rho, on a high-quality single
crystal in magnetic fields up to 15.5 T. At B=0, unconventional
superconductivity forms at Tc=0.9 K out of an incoherent state, characterized
by a large and strongly temperature dependent \rho(T). In the magnetic field
interval 4 T \leq B \leq 10 T, \rho(T) follows a T^3/2 behavior for Tc(B)\leq T
\leq 1 K, while \rho is proportional to T at higher temperatures. Corresponding
Non-Fermi liquid behavior is observed in C/T as well and hints at a nearby
antiferromagnetic (AF) quantum critical point (QCP) covered by the
superconducting state. We speculate that the suppression of short-range AF
correlations observed by thermal expansion and specific heat measurements below
T_L \simeq 0.7 K (B=0) yields a field-induced QCP, T_L \to 0, at B=4.5 T.


  We present a large-scale galaxy structure Cl J021734-0513 at z~0.65
discovered in the UKIDSS UDS field, made of ~20 galaxy groups and clusters,
spreading over 10 Mpc. We report on a VLT/VIMOS spectroscopic follow-up program
that, combined with past spectroscopy, allowed us to confirm four galaxy
clusters (M200 ~ 10^14 Msol) and a dozen associated groups and star-forming
galaxy overdensities. Two additional filamentary structures at z ~ 0.62 and z ~
0.69 and foreground and background clusters at 0.6 < z < 0.7 were also
confirmed along the line-of-sight. The structure subcomponents are at different
formation stages. The clusters have a core dominated by passive galaxies and an
established red sequence. The remaining structures are a mix of star-forming
galaxy overdensities and forming groups. The presence of quiescent galaxies in
the core of the latter shows that `preprocessing' has already happened before
the groups fall into their more massive neighbours. Our spectroscopy allows us
to derive spectral index measurements e.g. emission/absorption line equivalent
widths, strength of the 4000A break, valuable to investigate the star formation
history of structure members. Based on these line measurements, we select a
population of `poststarburst' galaxies. These galaxies are preferentially found
within the virial radius of clusters, supporting a scenario in which their
recent quenching could be prompted by gas stripping by the dense intracluster
medium. We derive stellar age estimates using MCMC-based spectral fitting for
quiescent galaxies and find a correlation between ages and colours/stellar
masses which favours a top-down formation scenario of the red sequence. A
catalogue of ~650 redshifts in UDS will be released alongside the paper.


  We present an empirical assessment of the use of broadband optical colours as
age indicators for unresolved extragalactic clusters and investigate stochastic
sampling effects on integrated colours. We use the integrated properties of
Galactic open clusters as models for unresolved extragalactic clusters. The
population synthesis code Starburst99 (Leitherer et al. 1999) and four optical
colours were used to estimate how well we can recover the ages of 62
well-studied Galactic open clusters with published ages. We provide a method
for estimating the ages of unresolved clusters and for reliably determining the
uncertainties in the age estimates. Our results support earlier conclusions
based on comparisons to synthetic clusters, namely the (U-B) colour is critical
to the estimation of the ages of star forming regions. We compare the observed
optical colours with those obtained from Starburst99 using the published ages
and get good agreement. The scatter in the (B-V)_observed-(B-V)_model is larger
for lower luminosity clusters, perhaps due to stochastic effects.


  We study nonparametric maximum likelihood estimation for two classes of
multivariate distributions that imply strong forms of positive dependence;
namely log-supermodular (MTP$_2$) distributions and log-$L^\#$-concave (LLC)
distributions. In both cases we also assume log-concavity in order to ensure
boundedness of the likelihood function. Given $n$ independent and identically
distributed random vectors in $\mathbb R^d$ from one of our distributions, the
maximum likelihood estimator (MLE) exists a.s. and is unique a.e. with
probability one when $n\geq 3$. This holds independently of the ambient
dimension $d$. We conjecture that the MLE is always the exponential of a tent
function. We prove this result for samples in $\{0,1\}^d$ or in $\mathbb{R}^2$
under MTP$_2$, and for samples in $\mathbb{Q}^d$ under LLC. Finally, we provide
a conditional gradient algorithm for computing the maximum likelihood estimate.


  We argue that in the small x processes, in the black disc QCD regime (BDR) a
very forward parton propagating through the nuclear matter should loose a
significant and increasing with energy and atomic number fraction of its
initial energy as a result of dominance of inelastic interactions, causality
and energy-momentum conservation. We evaluate these energy losses and find them
to lead to the significant suppression of the forward jet production in the
central NA collisions at collider energies with a moderate suppression of
recoiling jet at central rapidities. We confront our expectations with the
recent RHIC data of the STAR collaboration on the probability, $P$, for
emission of at least one fast hadron at a central rapidity in association with
production of a very forward high $p_t$ neutral pion in $pp$ and $dAu$
collisions. We calculate the A-dependence of $P$, and find that the data imply
a strong suppression of leading pion production at central impact parameters.
We also conclude that production of recoil jets in the hard subprocess is not
suppressed providing further evidence for the dominance of peripheral
collisions. Both features of the data are consistent with the onset of BDR. We
suggest new phenomena and new observables to investigate BDR at RHIC and LHC.


  Neural networks have recently been employed as material discretizations
within adjoint optimization frameworks for inverse problems and topology
optimization. While advantageous regularization effects and better optima have
been found for some inverse problems, the benefit for topology optimization has
been limited -- where the focus of investigations has been the compliance
problem. We demonstrate how neural network material discretizations can, under
certain conditions, find better local optima in more challenging optimization
problems, where we here specifically consider acoustic topology optimization.
The chances of identifying a better optimum can significantly be improved by
running multiple partial optimizations with different neural network
initializations. Furthermore, we show that the neural network material
discretization's advantage comes from the interplay with the Adam optimizer and
emphasize its current limitations when competing with constrained and
higher-order optimization techniques. At the moment, this discretization has
only been shown to be beneficial for unconstrained first-order optimization.


  Here we investigate the birational geometry of projective varieties of
arbitrary dimension having defective higher secant varieties. We apply the
classical tool of tangential projections and we determine natural conditions
for uniruledness, rational connectivity, and rationality.


  It is advisable to avoid and, even better, demystify such grandiose terms as
"infinity" or "singularity" in the description of the cosmos. Its proliferation
does not positively contribute to the understanding of key concepts that are
essential for an updated account of its origin and evolutionary history. It
will be here argued that, as a matter of fact, there are no infinities in
physics, in the real world: all that appears, in any given formulation of
nature by means of mathematical equations, actually arises from extrapolations,
which are made beyond the bounds of validity of the equations themselves. Such
a crucial point is rather well known, but too often forgotten, and is discussed
in this paper with several examples; namely, the famous Big Bang singularity
and others, which appeared before in classical mechanics and electrodynamics,
and notably in the quantization of field theories. A brief description of the
Universe's history and evolution follows. Special emphasis is put on what is
presently known, from detailed observations of the cosmos and, complementarily,
from advanced experiments of very high-energy physics. To conclude, a future
perspective on how this knowledge might soon improve is given.


  The standard paradigm in Neural Architecture Search (NAS) is to search for a
fully deterministic architecture with specific operations and connections. In
this work, we instead propose to search for the optimal operation distribution,
thus providing a stochastic and approximate solution, which can be used to
sample architectures of arbitrary length. We propose and show, that given an
architectural cell, its performance largely depends on the ratio of used
operations, rather than any specific connection pattern in typical search
spaces; that is, small changes in the ordering of the operations are often
irrelevant. This intuition is orthogonal to any specific search strategy and
can be applied to a diverse set of NAS algorithms. Through extensive validation
on 4 data-sets and 4 NAS techniques (Bayesian optimisation, differentiable
search, local search and random search), we show that the operation
distribution (1) holds enough discriminating power to reliably identify a
solution and (2) is significantly easier to optimise than traditional
encodings, leading to large speed-ups at little to no cost in performance.
Indeed, this simple intuition significantly reduces the cost of current
approaches and potentially enable NAS to be used in a broader range of
applications.


  In this paper, we study biharmonic hypersurfaces in a product of an Einstein
space and a real line. We prove that a biharmonic hypersurface with constant
mean curvature in such a product is either minimal or a vertical cylinder
generalizing a result of \cite{OW} and \cite{FOR}. We derived the biharmonic
equation for hypersurfaces in $S^m\times \mathbb{R}$ and $H^m\times \mathbb{R}$
in terms of the angle function of the hypersurface, and use it to obtain some
classifications of biharmonic hypersurfaces in such spaces. These include
classifications of biharmonic hypersurfaces which are totally umbilical or
semi-parallel for $m\ge 3$, and some classifications of biharmonic surfaces in
$S^2\times \mathbb{R}$ and $H^2\times \mathbb{R}$ which are constant angle or
belong to certain classes of rotation surfaces.


  Extensive research on social media usage during emergencies has shown its
value to provide life-saving information, if a mechanism is in place to filter
and prioritize messages. Existing ranking systems can provide a baseline for
selecting which updates or alerts to push to emergency responders. However,
prior research has not investigated in depth how many and how often should
these updates be generated, considering a given bound on the workload for a
user due to the limited budget of attention in this stressful work environment.
This paper presents a novel problem and a model to quantify the relationship
between the performance metrics of ranking systems (e.g., recall, NDCG) and the
bounds on the user workload. We then synthesize an alert-based ranking system
that enforces these bounds to avoid overwhelming end-users. We propose a Pareto
optimal algorithm for ranking selection that adaptively determines the
preference of top-k ranking and user workload over time. We demonstrate the
applicability of this approach for Emergency Operation Centers (EOCs) by
performing an evaluation based on real world data from six crisis events. We
analyze the trade-off between recall and workload recommendation across
periodic and realtime settings. Our experiments demonstrate that the proposed
ranking selection approach can improve the efficiency of monitoring social
media requests while optimizing the need for user attention.


  Dynamical simulations are a fundamental tool for studying the secular
evolution of disc galaxies. Even at their maximum resolution, they still follow
a limited number of particles and typically resolve scales of the order of a
few tens of parsecs. Generally, the spatial resolution is defined by (some
multiple of) the softening length, whose value is set as a compromise between
the desired resolution and the need for limiting small-scale noise. Several
works have studied the question whether a softening scale fixed in space and
time provides a good enough modelling of an astrophysical system. Here we
address this question within the context of dynamical simulations and disc
instabilities. We first follow the evolution of a galaxy-like object in
isolation and then set up a simulation of an idealised merger event. Alongside
a run using the standard fixed-softening approach, we performed simulations
where the softening lengths were let to vary from particle to particle
according to the evolution of the local density field in space and time. Even
though during the most violent phases of the merging the fixed-softening
simulation tends to underestimate the resulting matter densities, as far as the
evolution of the disc component is concerned we found no significant
differences among the runs. We conclude that using an appropriate fixed
softening scale is a safe approach to the problem of modelling an N-body,
non-cosmological disc galaxy system.


  Overranging or overscanning increases the dose delivered to patients
undergoing helical Computed Tomography examinations. In order to reduce it,
nowadays most of the multidetector tomographs close the X-ray beam aperture at
the scan extremes. This technical innovation, usually referred to as dynamic or
adaptive collimation, also influences the overranging assessment methods. In
particular, the film free approach proposed in previous studies is not suitable
for these modern tomographs. The present study aims to introduce a new method
of estimating overranging with real time dosimetry, even suitable for
tomographs equipped with adaptive collimation. The approach proposed is very
easy to implement and time saving because only a pencil chamber is required. It
is also equivalent in precision and in accuracy to the film based one,
considered an absolute benchmark.


  Krylov subspace methods for approximating a matrix function $f(A)$ times a
vector $v$ are analyzed in this paper. For the Arnoldi approximation to
$e^{-\tau A}v$, two reliable a posteriori error estimates are derived from the
new bounds and generalized error expansion we establish. One of them is similar
to the residual norm of an approximate solution of the linear system, and the
other one is determined critically by the first term of the error expansion of
the Arnoldi approximation to $e^{-\tau A}v$ due to Saad. We prove that each of
the two estimates is reliable to measure the true error norm, and the second
one theoretically justifies an empirical claim by Saad. In the paper, by
introducing certain functions $\phi_k(z)$ defined recursively by the given
function $f(z)$ for certain nodes, we obtain the error expansion of the
Krylov-like approximation for $f(z)$ sufficiently smooth, which generalizes
Saad's result on the Arnoldi approximation to $e^{-\tau A}v$. Similarly, it is
shown that the first term of the generalized error expansion can be used as a
reliable a posteriori estimate for the Krylov-like approximation to some other
matrix functions times $v$. Numerical examples are reported to demonstrate the
effectiveness of the a posteriori error estimates for the Krylov-like
approximations to $e^{-\tau A}v$, $\cos(A)v$ and $\sin(A)v$.


  After the first nine years of INTEGRAL operational life, the discovery of new
sources and source types, a large fraction of which are highly transient or
highly absorbed, is certainly one of the most compelling results and legacies
of INTEGRAL. Frequent monitoring of the Galactic Plane in AO8 and AO9 campaigns
allowed us to detect transient sources, both known and new, confirming that the
gamma-ray sky is dominated by the extreme variability of different classes of
objects. Regular scans of the Galactic Plane by INTEGRAL provide the most
sensitive hard X-ray wide survey to date of our Galaxy, with flux limits of the
order of 0.3 mCrab for an exposure time of ~2Ms. Many transient sources have
been detected on a wide range of time scales (~hours to months) and identified
by triggered followup observations, mainly by Swift/XRT and optical/infrared
telescopes. These discoveries are very important to characterize the X-ray
binary population in our Galaxy, that is necessary input for evolution studies.
The transient source monitoring is crucial to sample a variety of physical
conditions corresponding to a large span in luminosity. The long exposure times
available allow us to define the spectral and timing properties of the known
sources and the global properties of each object class.


  As information filtering services, recommender systems have extremely
enriched our daily life by providing personalized suggestions and facilitating
people in decision-making, which makes them vital and indispensable to human
society in the information era. However, as people become more dependent on
them, recent studies show that recommender systems potentially own
unintentional impacts on society and individuals because of their unfairness
(e.g., gender discrimination in job recommendations). To develop trustworthy
services, it is crucial to devise fairness-aware recommender systems that can
mitigate these bias issues. In this survey, we summarise existing methodologies
and practices of fairness in recommender systems. Firstly, we present concepts
of fairness in different recommendation scenarios, comprehensively categorize
current advances, and introduce typical methods to promote fairness in
different stages of recommender systems. Next, after introducing datasets and
evaluation metrics applied to assess the fairness of recommender systems, we
will delve into the significant influence that fairness-aware recommender
systems exert on real-world industrial applications. Subsequently, we highlight
the connection between fairness and other principles of trustworthy recommender
systems, aiming to consider trustworthiness principles holistically while
advocating for fairness. Finally, we summarize this review, spotlighting
promising opportunities in comprehending concepts, frameworks, the balance
between accuracy and fairness, and the ties with trustworthiness, with the
ultimate goal of fostering the development of fairness-aware recommender
systems.


  Comparing with traditional text-to-speech (TTS) systems, conversational TTS
systems are required to synthesize speeches with proper speaking style
confirming to the conversational context. However, state-of-the-art context
modeling methods in conversational TTS only model the textual information in
context with a recurrent neural network (RNN). Such methods have limited
ability in modeling the inter-speaker influence in conversations, and also
neglect the speaking styles and the intra-speaker inertia inside each speaker.
Inspired by DialogueGCN and its superiority in modeling such conversational
influences than RNN based approaches, we propose a graph-based multi-modal
context modeling method and adopt it to conversational TTS to enhance the
speaking styles of synthesized speeches. Both the textual and speaking style
information in the context are extracted and processed by DialogueGCN to model
the inter- and intra-speaker influence in conversations. The outputs of
DialogueGCN are then summarized by attention mechanism, and converted to the
enhanced speaking style for current utterance. An English conversation corpus
is collected and annotated for our research and released to public. Experiment
results on this corpus demonstrate the effectiveness of our proposed approach,
which outperforms the state-of-the-art context modeling method in
conversational TTS in both MOS and ABX preference rate.


  We study a node-wise monotone barrier coupling law, motivated by the synaptic
coupling of neural central pattern generators. It is illustrated that this
coupling imitates the desirable properties of neural central pattern
generators. In particular, the coupling law 1) allows us to assign multiple
central patterns on the circle and 2) allows for rapid switching between
different patterns via simple `kicks'. In the end, we achieve full control by
partitioning the state space by utilizing a barrier effect and assigning a
unique steady-state behavior to each element of the resulting partition. We
analyze the global behavior and study the viability of the design.


  New visible and K-band polarization measurements on stars surrounding
molecular clouds in Orion A and stars in the BN vicinity are presented. Our
results confirm that magnetic fields located inside the Orion A molecular
clouds and in their close neighborhood are spatially connected. On and around
the BN object, we measured the angular offsets between the K-band polarization
data and available submm data. We find high values of the polarization degree,
P_{K}, and of the optical depth, \tau_{K}, close to an angular offset position
of 90^{\circ} whereas lower values of P_{K} and \tau_{K} are observed for
smaller angular offsets. We interpret these results as evidence for the
presence of various magnetic field components toward lines of sight in the
vicinity of BN. On a larger scale, we measured the distribution of angular
offsets between available H-band polarization data and the same submm data set.
Here we find an increase of <P_{H}> with angular offset which we interpret as a
rotation of the magnetic field by \lesssim 60^{\circ}. This trend generalizes
previous results on small scale toward and around lines of sight to BN and is
consistent with a twist of the magnetic field on a larger scale towards OMC-1.
A comparison of our results with several other studies suggests that a
two-component magnetic field, maybe helical, could be wrapping the OMC-1
filament.


  Let $\mathcal{X}$ be a (projective, geometrically irreducible, nonsingular)
algebraic curve of genus $g \ge 2$ defined over an algebraically closed field
$\mathbb{K}$ of odd characteristic $p\ge 0$, and let $\rm{Aut}(\mathcal{X})$ be
the group of all automorphisms of $\mathcal{X}$ which fix $\mathbb{K}$
element-wise. For any a subgroup $G$ of $\rm{Aut}(\mathcal{X})$ whose order is
a power of an odd prime $d$ other than $p$, the bound proven by Zomorrodian for
Riemann surfaces is $|G|\leq 9(g-1)$ where the extremal case can only be
obtained for $d=3$. We prove Zomorrodian's result for any $\mathbb{K}$. The
essential part of our paper is devoted to extremal $3$-Zomorrodian curves
$\mathcal{X}$. Two cases are distinguished according as the quotient curve
$\mathcal{X}/Z$ for a central subgroup $Z$ of $\rm{Aut}(\mathcal{X})$ of order
$3$ is either elliptic, or not. For elliptic type extremal $3$-Zomorrodian
curves $\mathcal{X}$, we completely determine the two possibilities for the
abstract structure of $G$ using deeper results on finite $3$-groups. We also
show infinite families of extremal $3$-Zomorrodian curves for both types,
elliptic or non-elliptic. Our paper does not adapt methods from the theory of
Riemann surfaces, nevertheless it sheds a new light on the connection between
Riemann surfaces and their automorphism groups.


  We study the distribution of products of conjugacy classes in finite simple
groups, obtaining various effective uniformity results, which give rise to an
approximation to a conjecture of Thompson. Our results, combined with work of
Gowers and Viola, also lead to the solution of recent conjectures they posed on
interleaved products and related complexity lower bounds, extending their work
on the groups SL$(2,q)$ to all (nonabelian) finite simple groups. In particular
it follows that, if $G$ is a finite simple group, and $A, B \subseteq G^t$ for
$t \ge 2$ are subsets of fixed positive densities, then, as $a = (a_1, \ldots ,
a_t) \in A$ and $b = (b_1, \ldots , b_t) \in B$ are chosen uniformly, the
interleaved product $a \bullet b := a_1b_1 \cdots a_tb_t$ is almost uniform on
$G$ (with quantitative estimates) with respect to the $\ell_{\infty}$-norm. It
also follows that the communication complexity of an old decision problem
related to interleaved products of $a, b \in G^t$ is at least $\Omega(t \log
|G|)$ when $G$ is a finite simple group of Lie type of bounded rank, and at
least $\Omega(t \log \log |G|)$ when $G$ is any finite simple group. Both these
bounds are best possible.


  Clear influence of particle size, surfactants and dispersion medium on
surface plasmon resonance (SPR) features of Ag nanoparticles (NPs), synthesized
in thermal decomposition method, in the broad range of ultraviolet (UV)
radiation, critical for many potential applications such as a photocatalyst,
UV-sensor and detector, has been demonstrated here. It involves adsorbate
coverage, interparticle distance or agglomeration, surface charge density and
solvent refractive index ({\mu}). NP agglomeration and surface charge density
in solvents of varying {\mu} have been studied systematically through
zeta-potential ({\zeta}) and hydrodynamic diameter (HD) using dynamic light
scattering (DLS). The main SPR feature found at 316 nm in 31.5 nm NPs shifts to
320 nm in 15.1 nm NPs. The peak at 320 nm in air shifts to 259, 261 and 277 nm
in polar solvent methanol, deionized water and ethanol, respectively and to
255, 275 and 282 nm in non-polar solvent n-hexane, benzene and toluene,
respectively. In general, the decrease in particle size and increase in {\mu}
of solvents show red-shift. Curiously, a number of peaks up to seven in these
solvents that are attributed to charge-transfer mechanism and change in
inter-particle interaction of the NPs turning from a single peak of SPR in air
has been observed for the first time. A model for re-adjustment of Fermi level
(E_F) of Ag NP and the highest occupied molecular orbital (HOMO) and lowest
unoccupied molecular orbital (LUMO) to explain them has also been used.
Moreover, the Drude model for shift in the position of SPR in these NPs is only
applicable in non-polar solvents, not in polar solvents. Such novel features
will be potential candidates for various applications.


  Interpretable AI tools are often motivated by the goal of understanding model
behavior in out-of-distribution (OOD) contexts. Despite the attention this area
of study receives, there are comparatively few cases where these tools have
identified previously unknown bugs in models. We argue that this is due, in
part, to a common feature of many interpretability methods: they analyze model
behavior by using a particular dataset. This only allows for the study of the
model in the context of features that the user can sample in advance. To
address this, a growing body of research involves interpreting models using
\emph{feature synthesis} methods that do not depend on a dataset.
  In this paper, we benchmark the usefulness of interpretability tools on
debugging tasks. Our key insight is that we can implant human-interpretable
trojans into models and then evaluate these tools based on whether they can
help humans discover them. This is analogous to finding OOD bugs, except the
ground truth is known, allowing us to know when an interpretation is correct.
We make four contributions. (1) We propose trojan discovery as an evaluation
task for interpretability tools and introduce a benchmark with 12 trojans of 3
different types. (2) We demonstrate the difficulty of this benchmark with a
preliminary evaluation of 16 state-of-the-art feature attribution/saliency
tools. Even under ideal conditions, given direct access to data with the trojan
trigger, these methods still often fail to identify bugs. (3) We evaluate 7
feature-synthesis methods on our benchmark. (4) We introduce and evaluate 2 new
variants of the best-performing method from the previous evaluation. A website
for this paper and its code is at
https://benchmarking-interpretability.csail.mit.edu/


  Larger language models, such as GPT-3, have shown to be excellent in many
tasks. However, we demonstrate that out-of-ordinary questions can throw the
model off guard. This work focuses on finding answers to negated complementary
questions in commonsense scenarios. We illustrate how such questions adversely
affect the model responses. We propose a model-agnostic methodology to improve
the performance in negated complementary scenarios. Our method outperforms
few-shot generation from GPT-3 (by more than 11 points) and, more importantly,
highlights the significance of studying the response of large language models
in negated complementary questions. The code, data, and experiments are
available under: https://github.com/navidre/negated_complementary_commonsense.


  This paper is about metric data structures in high-dimensional or
non-Euclidean space that permit cached sufficient statistics accelerations of
learning algorithms.
  It has recently been shown that for less than about 10 dimensions, decorating
kd-trees with additional "cached sufficient statistics" such as first and
second moments and contingency tables can provide satisfying acceleration for a
very wide range of statistical learning tasks such as kernel regression,
locally weighted regression, k-means clustering, mixture modeling and Bayes Net
learning.
  In this paper, we begin by defining the anchors hierarchy - a fast data
structure and algorithm for localizing data based only on a
triangle-inequality-obeying distance metric. We show how this, in its own
right, gives a fast and effective clustering of data. But more importantly we
show how it can produce a well-balanced structure similar to a Ball-Tree
(Omohundro, 1991) or a kind of metric tree (Uhlmann, 1991; Ciaccia, Patella, &
Zezula, 1997) in a way that is neither "top-down" nor "bottom-up" but instead
"middle-out". We then show how this structure, decorated with cached sufficient
statistics, allows a wide variety of statistical learning algorithms to be
accelerated even in thousands of dimensions.


  Large-scale analysis of pedestrian infrastructures, particularly sidewalks,
is critical to human-centric urban planning and design. Benefiting from the
rich data set of planimetric features and high-resolution orthoimages provided
through the New York City Open Data portal, we train a computer vision model to
detect sidewalks, roads, and buildings from remote-sensing imagery and achieve
83% mIoU over held-out test set. We apply shape analysis techniques to study
different attributes of the extracted sidewalks. More specifically, we do a
tile-wise analysis of the width, angle, and curvature of sidewalks, which aside
from their general impacts on walkability and accessibility of urban areas, are
known to have significant roles in the mobility of wheelchair users. The
preliminary results are promising, glimpsing the potential of the proposed
approach to be adopted in different cities, enabling researchers and
practitioners to have a more vivid picture of the pedestrian realm.


  Weyl semimetals are a class of topological materials that exhibit a bulk Hall
effect due to time-reversal symmetry breaking. We show that for the idealized
semi-infinite case, the Casimir force between two identical Weyl semimetals is
repulsive at short range and attractive at long range. Considering plates of
finite thickness, we can reduce the size of the long-range attraction even
making it repulsive for all distances when thin enough. In the thin-film limit,
we study the appearance of an attractive Casimir force at shorter distances due
to the longitudinal conductivity. Magnetic field, thickness, and chemical
potential provide tunable nobs for this effect, controlling the Casimir force:
whether it is attractive or repulsive, the magnitude of the effect, and the
positions and existence of a trap and antitrap.


  Fibre ropes with the latest technology have emerged as an appealing
alternative to steel ropes for offshore industries due to their lightweight and
high tensile strength. At the same time, frequent inspection of these ropes is
essential to ensure the proper functioning and safety of the entire system. The
development of deep learning (DL) models in condition monitoring (CM)
applications offers a simpler and more effective approach for defect detection
in synthetic fibre ropes (SFRs). The present paper investigates the performance
of Detectron2, a state-of-the-art library for defect detection and instance
segmentation. Detectron2 with Mask R-CNN architecture is used for segmenting
defects in SFRs. Mask R-CNN with various backbone configurations has been
trained and tested on an experimentally obtained dataset comprising 1,803
high-dimensional images containing seven damage classes (placking high,
placking medium, placking low, compression, core out, chafing, and normal
respectively) for SFRs. By leveraging the capabilities of Detectron2, this
study aims to develop an automated and efficient method for detecting defects
in SFRs, enhancing the inspection process, and ensuring the safety of the fibre
ropes.


  We show that a baryon asymmetry can be generated by dissipative effects
during warm inflation via a supersymmetric two-stage mechanism, where the
inflaton is coupled to heavy mediator fields that then decay into light species
through B- and CP-violating interactions. In contrast with thermal GUT
baryogenesis models, the temperature during inflation is always below the heavy
mass threshold, simultaneously suppressing thermal and quantum corrections to
the inflaton potential and the production of dangerous GUT relics. This
naturally gives a small baryon asymmetry close to the observed value, although
parametrically larger values may be diluted after inflation along with any
gravitino overabundance. Furthermore, this process yields baryon isocurvature
perturbations within the range of future experiments, making this an attractive
and testable model of GUT baryogenesis.


  This paper considers dyadic-exchange networks in which individual agents
autonomously form coalitions of size two and agree on how to split a
transferable utility. Valid results for this game include stable (if agents
have no unilateral incentive to deviate), balanced (if matched agents obtain
similar benefits from collaborating), or Nash (both stable and balanced)
outcomes. We design provably-correct continuous-time algorithms to find each of
these classes of outcomes in a distributed way. Our algorithmic design to find
Nash bargaining solutions builds on the other two algorithms by having the
dynamics for finding stable outcomes feeding into the one for finding balanced
ones. Our technical approach to establish convergence and robustness combines
notions and tools from optimization, graph theory, nonsmooth analysis, and
Lyapunov stability theory and provides a useful framework for further
extensions. We illustrate our results in a wireless communication scenario
where single-antenna devices have the possibility of working as 2-antenna
virtual devices to improve channel capacity.


  The first observations of the recently completed Wisconsin H-Alpha Mapper
(WHAM) facility include a study of emission lines from high velocity clouds in
the M, A, and C complexes, with most of the observations on the M I cloud. We
present results including clear detections of H-alpha emission from all three
complexes with intensities ranging from 0.06 R to 0.20 R. In every observed
direction where there is significant high velocity H I gas seen in the 21 cm
line we have found associated ionized hydrogen emitting the H-alpha line. The
velocities of the H-alpha and 21 cm emission are well correlated in every case
except one, but the intensities are not correlated. There is some evidence that
the ionized gas producing the H-alpha emission envelopes the 21 cm emitting
neutral gas but the H-alpha "halo", if present, is not large. If the H-alpha
emission arises from the photoionization of the H I clouds, then the implied
Lyman continuum flux F_{LC} at the location of the clouds ranges from 1.3 to
4.2 x 10^5 photons cm^{-2} s^{-1}. If, on the other hand, the ionization is due
to a shock arising from the collision of the high-velocity gas with an ambient
medium in the halo, then the density of the pre-shocked gas can be constrained.
We have also detected the [S II] 6716 angstrom line from the M I cloud and have
evidence that the [S II] to H-alpha ratio varies with location on the cloud.


  We have performed 3D isothermal MHD simulation of a magnetic rotating massive
star with a non-zero dipole obliquity and predicted the radio/sub-mm observable
lightcurves and continuum spectra for a frequency range compatible with ALMA.
From these results we also compare the model input mass-loss to that calculated
from the synthetic thermal emission. Spherical and cylindrical symmetry is
broken due to the obliquity of the stellar magnetic dipole resulting in an
inclination and phase dependence of both the spectral flux and inferred
mass-loss rate, providing testable predictions of variability for oblique
rotator. Both quantities vary by factors between 2 and 3 over a full rotational
period of the star, demonstrating that the role of rotation as critical in
understanding the emission. This illustrates the divergence from a symmetric
wind, resulting in a two armed spiral structure indicative of a oblique
magnetic rotator. We show that a constant spectral index, $\alpha$, model
agrees well with our numerical prediction for a spherical wind for
$\nu~<~10^{3} \ \mathrm{GHz}$, however it is unable to capture the behavior of
emission at $\nu~>~10^{3} \ \mathrm{GHz}$. As such we caution the use of such
constant $\alpha$ models for predicting emission from non-spherical winds such
as those which form around magnetic massive stars.


  Here we extend the concept of blind client-server quantum computation, in
which a client with limited quantum power controls the execution of a quantum
computation on a powerful server, without revealing any details of the
computation. Our extension is to introduce a three-node setting in which an
oracular quantum computation can be executed blindly. In this Blind Oracular
Quantum Computation (BOQC), the oracle (Oscar) is another node, with limited
power, who acts in cooperation with the client (Alice) to supply quantum
information to the server so that the oracle part of the quantum computation
can also be executed blindly. We develop tests of this protocol using two- and
three-qubit versions of the exact Grover algorithm (i.e., with database sizes
$4\leq N\leq 8$), obtaining optimal implementations of these algorithms within
a gate array scheme and the blinded cluster-state scheme. We discuss the
feasibility of executing these protocols in state-of-the-art three-node
experiments using NV-diamond electronic and nuclear qubits.


  IPHASXJ194359.5+170901 is a new high-excitation planetary nebula with
remarkable characteristics. It consists of a knotty ring expanding at a speed
of 28 km/s, and a fast collimated outflow in the form of faint lobes and caps
along the direction perpendicular to the ring. The expansion speed of the polar
caps is 100 km/s, and their kinematical age is twice as large as the age of the
ring. Time-resolved photometry of the central star of IPHASXJ194359.5+170901
reveals a sinusoidal modulation with a period of 1.16 days. This is interpreted
as evidence for binarity of the central star, the brightness variations being
related to the orbital motion of an irradiated companion. This is supported by
the spectrum of the central star in the visible range, which appears to be
dominated by emission from the irradiated zone, consisting of a warm (6000-7000
K) continuum, narrow C III, C IV, and N III emission lines, and broader lines
from a flat H I Balmer sequence in emission. IPHASXJ194359.5+170901 helps to
clarify the role of (close) binaries in the formation and shaping of planetary
nebulae. The output of the common-envelope evolution of the system is a
strongly flattened circumstellar mass deposition, a feature that seems to be
distinctive of this kind of binary system. Also, IPHASXJ194359.5+170901 is
among the first post-CE PNe for which the existence of a high-velocity polar
outflow has been demonstrated. Its kinematical age might indicate that the
polar outflow is formed before the common-envelope phase. This points to mass
transfer onto the secondary as the origin, but alternative explanations are
also considered.


  In this note, we consider a Lie group G acting on a manifold M. We prove that
the category of bundles with connection on the differential quotient stack is
equivalent to the category of G-equivariant bundles on M with G-invariant
connection.


  We study the cascading traffic jamming on a two-dimensional random geometric
graph using the Motter and Lai model. The traffic jam is caused by a localized
attack incapacitating circular region or a line of a certain size, as well as a
dispersed attack on an equal number of randomly selected nodes. We investigate
if there is a critical size of the attack above which the network becomes
completely jammed due to cascading jamming, and how this critical size depends
on the average degree $\langle k\rangle$ of the graph, on the number of nodes
$N$ in the system, and the tolerance parameter $\alpha$ of the Motter and Lai
model.


  We consider the monomial weight $|x_1|^{A_1}...|x_n|^{A_n}$ in $\mathbb R^n$,
where $A_i\geq0$ is a real number for each $i=1,...,n$, and establish Sobolev,
isoperimetric, Morrey, and Trudinger inequalities involving this weight. They
are the analogue of the classical ones with the Lebesgue measure $dx$ replaced
by $|x_1|^{A_1}...|x_n|^{A_n}dx$, and they contain the best or critical
exponent (which depends on $A_1$, ..., $A_n$). More importantly, for the
Sobolev and isoperimetric inequalities, we obtain the best constant and
extremal functions.
  When $A_i$ are nonnegative \textit{integers}, these inequalities are exactly
the classical ones in the Euclidean space $\mathbb R^D$ (with no weight) when
written for axially symmetric functions and domains in $\mathbb R^D=\mathbb
R^{A_1+1}\times...\times\mathbb R^{A_n+1}$.


  Real-life statistical samples are often plagued by selection bias, which
complicates drawing conclusions about the general population. When learning
causal relationships between the variables is of interest, the sample may be
assumed to be from a distribution in a causal Bayesian network (BN) model under
selection. Understanding the constraints in the model under selection is the
first step towards recovering causal structure in the original model. The
conditional-independence (CI) constraints in a BN model under selection have
been already characterised; there exist, however, additional, non-CI
constraints in such models. In this work, some initial results are provided
that simplify the characterisation problem. In addition, an algorithm is
designed for identifying compelled ancestors (definite causes) from a completed
partially directed acyclic graph (CPDAG). Finally, a non-CI, non-factorisation
constraint in a BN model under selection is computed for the first time.


  We propose a theoretical framework to compute, rapidly and accurately, the
signal-to-noise ratio at the output of spatial-division multiplexing (SDM)
linear MIMO equalizers with arbitrary numbers of spatial modes and filter taps
and demonstrate three orders of magnitude of speed-up compared to Monte Carlo
simulations.


  Motivated by understanding the limiting case of a certain systolic inequality
we study compact Riemannian manifolds having all harmonic 1-forms of constant
length. We give complete characterizations as far as K\"ahler and hyperbolic
geometries are concerned. In the second part of the paper, we give algebraic
and topological obstructions to the existence of a geometrically 2-formal
K\"ahler metric, at the level of the second cohomology group. A strong
interaction with almost K\"ahler geometry is to be noted. In complex dimension
3, we list all the possible values of the second Betti number of a
geometrically 2-formal K\"ahler metric.


  We model power grids transporting electricity generated by intermittent
renewable sources as complex networks, where line failures can emerge
indirectly by noisy power input at the nodes. By combining concepts from
statistical physics and the physics of power flows, and taking weather
correlations into account, we rank line failures according to their likelihood
and establish the most likely way such failures occur and propagate. Our
insights are mathematically rigorous in a small-noise limit and are validated
with data from the German transmission grid.


  In this paper, the Pazy's Fixed Point Theorems of monotone
$\alpha-$nonexpansive mapping $T$ are proved in a uniformly convex Banach space
$E$ with the partial order "$\leq$". That is, we obtain that the fixed point
set of $T$ with respect to the partial order "$\leq$" is nonempty whenever the
Picard iteration $\{T^nx_0\}$ is bounded for some initial point $x_0$ with
$x_0\leq Tx_0$ or $Tx_0\leq x_0$. When restricting the demain of $T$ to the
cone $P$, a monotone $\alpha-$nonexpansive mapping $T$ has at least a fixed
point if and only if the Picard iteration $\{T^n0\}$ is bounbed. Furthermore,
with the help of the properties of the normal cone $P$, the weakly and strongly
convergent theorems of the Picard iteration $\{T^nx_0\}$ are showed for finding
a fixed point of $T$ with respect to the partial order "$\leq$" in uniformly
convex ordered Banach space.


  We show that the insecurity claim of the AlphaEta cryptosystem made by C. Ahn
and K. Birnbaum in Phys. Lett. A 370 (2007) 131-135 under heterodyne attack is
based on invalid extrapolations of Shannon's random cipher analysis and on an
invalid statistical independence assumption. We show, both for standard ciphers
and AlphaEta, that expressions of the kind given by Ahn and Birnbaum can at
best be interpreted as security lower bounds.


  We study three fundamental topics in the representation theory of
disconnected algebraic groups whose identity component is reductive: (i) the
classification of irreducible representations; (ii) the existence and
properties of Weyl and dual Weyl modules; and (iii) the decomposition map
relating representations in characteristic $0$ and those in characteristic $p$
(for groups defined over discrete valuation rings). For each of these topics,
we obtain natural generalizations of the well-known results for connected
reductive groups.


  Korner and Marton established the capacity region for the 2-receiver
broadcast channel with degraded message sets. Recent results and conjectures
suggest that a straightforward extension of the Korner-Marton region to more
than 2 receivers is optimal. This paper shows that this is not the case. We
establish the capacity region for a class of 3-receiver broadcast channels with
2 degraded message sets and show that it can be strictly larger than the
straightforward extension of the Korner-Marton region. The key new idea is
indirect decoding, whereby a receiver who cannot directly decode a cloud
center, finds it indirectly by decoding satellite codewords. This idea is then
used to establish new inner and outer bounds on the capacity region of the
general 3-receiver broadcast channel with 2 and 3 degraded message sets. We
show that these bounds are tight for some nontrivial cases. The results suggest
that the capacity of the 3-receiver broadcast channel with degraded message
sets is as at least as hard to find as the capacity of the general 2-receiver
broadcast channel with common and private message.


  We present a photometrical and morphological study of the properties of low
redshift (z < 0.5) quasars based on a large and homogeneous dataset of objects
derived from the Sloan Digital Sky Survey (DR7). This study over number by a
factor about 5 any other previous study of QSO host galaxies at low redshift
undertaken either on ground or on space surveys. We used about 400 quasars that
were imaged in the SDSS Stripe82 that is up to 2 mag deeper than standard Sloan
images. For these quasars we undertake a study of the host galaxies and of
their environments. In this paper we report the results for the quasar hosts.
We are able to detect the host galaxy for more than 3/4 of the whole dataset
and characterise the properties of their hosts. We found that QSO hosts are
dominated by luminous galaxies of absolute magnitude M*-3 < M(R) < M*. For the
unresolved objects we computed a upper limit to the host luminosity. For each
well resolved quasar we are also able to characterise the morphology of the
host galaxy that turn out to be more complex than what found in previous
studies. QSO are hosted in a variety of galaxies from pure ellipticals to
complex/composite morphologies that combine spheroids, disk, lens and halo. The
black hole mass of the quasar, estimated from the spectral properties of the
nuclei, are poorly correlated with the total luminosity of the host galaxy.
However, taking into account only the bulge component we found a significant
correlation between the BH mass and the bulge luminosity of the host.


  We present our analysis of the three HII-buried-AGN: SDSS J091053+333008,
SDSS J121837+091324, and SDSS J153002-020415, by studying their optical spectra
extracted from SDSS. The location in the BPT diagnostic diagrams of the three
galaxies indicates that the narrow emission lines are mainly exited from HII
regions. However, after the removal of the host galaxy's stellar emission, the
emission lines display the typical feature of Narrow-line Seyfert 1-like. All
of the three objects have large Eddington ratio, small black hole mass, and low
star formation rate. We propose that the three galaxies are at the transit
stage from the starburst-dominated phase to AGN-dominated phase.


  The advent of moderately high-resolution X-ray spectroscopy with Chandra and
XMM promised to usher in a new age in the study of neutron stars: we thought we
would study neutron stars like stars, with resolved absorption spectra
revealing their surface chemical composition and physical conditions (e.g.
surface gravity, pressure, temperature). Nature, however, did not cooperate in
this endeavor, as observations of neutron stars have not revealed verified
atomic absorption lines yet. In the near future, advancements in
transition-edge sensors (TES) technology will allow for
electron-volt-resolution spectroscopy combined with nanoseconds-precision
timing. Combining these detectors with collector optics will also us to study
neutron stars in much greater detail by achieving high-energy resolution with
much larger collecting areas to uncover even weak spectral features over a wide
range of the photon energies. Perhaps we will finally be able to study neutron
stars like stars.


  Relative variations in the number of sunspots and sunspot groups in activity
cycles have been analyzed based on data from the Kislovodsk Mountain
Astronomical Station and international indices. The following regularities have
been established: (1) The relative fraction of small sunspots decreases
linearly and that of large sunspots increase with increasing activity cycle
amplitude. (2) The variation in the average number of sunspots in one group has
a trend, and this number decreased from 12 in cycle 19 to 7.5 in cycle 24. (3)
The ratio of the sunspot index (Ri) to the sunspot group number index (Ggr)
varies with a period of about 100 years. (4) An analysis of the sunspot group
number index (Ggr) from 1610 indicates that the Gnevyshev-Ohl rule reverses at
the minimums of secular activity cycles. (5) The ratio of the total sunspot
area to the umbra area shows a long-term variation with a period about eight
cycles and minimum in cycles 16-17. (6) It has been indicated that the magnetic
field intensity and sunspot area in the current cycle are related to the
amplitude of the next activity cycle.


  In order to assess the potential of future microwave anisotropy space
experiments for detecting clusters by their Sunyaev-Zeldovich (SZ) thermal
effect, we have simulated maps of the large scale distribution of their Compton
parameter $y$ and of the temperature anisotropy $\Delta T/T$ induced by their
proper motion. Our model is based on a predicted distribution of clusters per
unit redshift and flux density using a Press-Schecter approach. These maps were
used to create simulated microwave sky by adding them to the microwave
contributions of the emissions of our Galaxy and the primary Cosmic Microwave
Background (CMB) anisotropies. In order to simulate measurements representative
of what current technology should achieve, ``observations'' were performed
according to the instrumental characteristics of the COBRAS/SAMBA space
mission. We then analyzed the resulting $y$ and $\Delta T/T$ maps which now
include both the primary anisotropies and those superimposed due to cluster
motions.


  This is a Bourbaki report on the work of Y. Andr\'e on the direct summand
conjecture, and subsequent developments by Andr\'e and Bhatt on big
Cohen-Macaulay algebras.


  The PIC model relies on two building blocks. The first stems from the
capability of computers to handle only up to $\sim10^{10}$ particles, while
real plasmas contain from $10^4$ to $10^{20}$ particles per Debye sphere: a
coarse-graining step must be used, whereby of the order of $p\sim10^{10}$ real
particles are represented by a single computer superparticle. The second is
field storage on a grid with its subsequent finite superparticle size. We
introduce the notion of coarse-graining dependent quantities, i.e. physical
quantities depending on the number $p$. They all derive from the plasma
parameter $\Lambda$, which we show to be proportional to $1/p$.
  We explore three examples: the rapid collision- and fluctuation-induced
thermalization of plasmas with different temperatures, that scale with the
number of superparticles per grid cell and are a factor $p\sim10^{10}$ faster
than in real plasmas; the high level of electrostatic fluctuations in a thermal
plasma, with corrections due to the finite superparticle sizes; and the
blurring of the linear spectrum of the filamentation instability, where the
fastest growing modes do not dominate the total energy because of a high level
of fluctuations.
  We stress that the enhanced collisions and correlations of PIC plasmas must
be kept negligible toward kinetic physics.


  I present a model addressing coherently the naturalness problem of the
electroweak scale and the observed pattern of deviations from the Standard
Model in semi-leptonic decays of $B$ mesons. The Higgs and the two scalar
leptoquarks responsible for the $B$-physics anomalies, $S_1 = ({\bf \bar 3},
{\bf 1}, 1/3)$ and $S_3 = ({\bf \bar 3}, {\bf 3}, 1/3)$, arise as pseudo
Nambu-Goldstone bosons of a new strongly coupled sector at the multi-TeV scale.
I focus on an explicit realization of such a dynamics in terms of a new
strongly coupled gauge interaction and extra vectorlike fermions charged under
it. The model presents a very rich phenomenology, ranging from flavour
observables, Higgs and electroweak precision measurements, and direct searches
of new states at the LHC.


  In this work we prove a Baum-Bott type residue theorem for flags of
holomorphic foliations. We prove some relations between the residues of the
flag and the residues of their correspondent foliations. We define the Nash
residue for flags and we give a partial answer to the Baum-Bott type
rationality conjecture in this context .


  Using the ultrafast pump-probe transient absorption spectroscopy, the
femtosecond-resolved plasmon-exciton interaction of graphene-Ag nanowire
hybrids is experimentally investigated, in the VIS-NIR region. The plasmonic
lifetime of Ag nanowire is about 150 femtosecond (fs). For a single layer of
graphene, the fast dynamic process at 275 fs is due to the excitation of
graphene excitons, and the slow process at 1.4 picosecond (ps) is due to the
plasmonic hot electron interaction with phonons of graphene. For the
graphene-Ag nanowire hybrids, the time scale of the plasmon-induced hot
electron transferring to graphene is 534 fs, and the metal plasmon enhanced
graphene plasmon is about 3.2 ps in the VIS region. The graphene-Ag nanowire
hybrids can be used for plasmon-driven chemical reactions. This
graphene-mediated surface-enhanced Raman scattering substrate significantly
increases the probability and efficiency of surface catalytic reactions
co-driven by graphene-Ag nanowire hybridization, in comparison with reactions
individually driven by monolayer graphene or single Ag nanowire. This implies
that the graphene-Ag nanowire hybrids can not only lead to a significant
accumulation of high-density hot electrons, but also significantly increase the
plasmon-to-electron conversion efficiency, due to strong plasmon-exciton
coupling.


  Spatial correlation characteristics of the anomalous density matrix $\kappa$
in a slab of nuclear matter with the Paris and Argonne v18 forces are
calculated. A detailed comparison with predictions of the effective Gogny force
is made. It is found that the two realistic forces lead to very close results
which are qualitatively similar to those for the Gogny force. At the same time,
the magnitude of $\kappa$ for realistic forces is essentially smaller than the
one for the Gogny force. The correlation characteristics are practically
independent of the magnitude of $\kappa$ and turn out to be quite close for the
three kinds of the force. In particular, all of them predict a small value of
the local correlation length at the surface of the slab and a big one, inside.
These results are in agreement with those obtained recently by Pillet at al.
for finite nuclei with the Gogny force.


  We show that under certain conditions, closed string tachyon condensation
produces a topology changing transition from black strings to Kaluza-Klein
"bubbles of nothing." This can occur when the curvature at the horizon is much
smaller than the string scale, so the black string is far from the
correspondence point when it would make a transition to an excited fundamental
string. This provides a dramatic new endpoint to Hawking evaporation. A similar
transition occurs for black p-branes, and can be viewed as a nonextremal
version of a geometric transition. Applications to AdS black holes and the AdS
soliton are also discussed.


  We apply a method recently derived based on the extended Hubbard Hamiltonian
and the BCS approach to obtain the superconducting critical temperature
dependence with carrier density for the HgBaCuO compounds. We show that this
procedure can be used to study pressure effect with the assumption that
pressure changes the supercondutor gap. The results reproduce well the
experimental data for the whole doping regime and the high and low pressure
dependence.


  It appears that having our own brane to somehow interact with other branes
could give rise to quite an interesting system and that that interaction could
lead to some observable effects. We consider the question of whether or not
these signatures of interaction between the branes can be observed. To answer
this question, we investigate the effect induced by the inflaton in the WMAP7
data using the warm inflationary model. In this model, slow-roll and
perturbation parameters are given in terms of the inflaton thermal
distribution. We show that this distribution depends on the orbital radius of
the brane motion under the interaction potential of other branes in extra
dimensions. Thus, an enhancement in the brane inflation can be a signature of
an orbital motion in extra dimensions and consequently, some signals of other
branes can be detected by observational data. According to experimental data,
the N = 50 case leads to ns = 0:96, where N and ns are the number of e-folds
and the spectral index, respectively. This standard case may be found in the
range 0:01 < R(Tensor-scalar) < 0:22, where R(Tensor-scalar) is the
tensor-scalar ratio. We find that at this point, the radial distance between
our brane and another brane is R = 1/(1:5GeV ) in intermediate, and R =
1/(0:02225GeV ) in logamediate inflation.


  For many random constraint satisfaction problems such as random
satisfiability or random graph or hypergraph coloring, the best current
estimates of the threshold for the existence of solutions are based on the
first and the second moment method. However, in most cases these techniques do
not yield matching upper and lower bounds. Sophisticated but non-rigorous
arguments from statistical mechanics have ascribed this discrepancy to the
existence of a phase transition called condensation that occurs shortly before
the actual threshold for the existence of solutions and that affects the
combinatorial nature of the problem (Krzakala, Montanari, Ricci-Tersenghi,
Semerjian, Zdeborova: PNAS 2007). In this paper we prove for the first time
that a condensation transition exists in a natural random CSP, namely in random
hypergraph 2-coloring. Perhaps surprisingly, we find that the second moment
method breaks down strictly \emph{before} the condensation transition. Our
proof also yields slightly improved bounds on the threshold for random
hypergraph 2-colorability. We expect that our techniques can be extended to
other, related problems such as random k-SAT or random graph k-coloring.


  As the key to realizing aBCIs, EEG emotion recognition has been widely
studied by many researchers. Previous methods have performed well for
intra-subject EEG emotion recognition. However, the style mismatch between
source domain (training data) and target domain (test data) EEG samples caused
by huge inter-domain differences is still a critical problem for EEG emotion
recognition. To solve the problem of cross-dataset EEG emotion recognition, in
this paper, we propose an EEG-based Emotion Style Transfer Network (E2STN) to
obtain EEG representations that contain the content information of source
domain and the style information of target domain, which is called stylized
emotional EEG representations. The representations are helpful for
cross-dataset discriminative prediction. Concretely, E2STN consists of three
modules, i.e., transfer module, transfer evaluation module, and discriminative
prediction module. The transfer module encodes the domain-specific information
of source and target domains and then re-constructs the source domain's
emotional pattern and the target domain's statistical characteristics into the
new stylized EEG representations. In this process, the transfer evaluation
module is adopted to constrain the generated representations that can more
precisely fuse two kinds of complementary information from source and target
domains and avoid distorting. Finally, the generated stylized EEG
representations are fed into the discriminative prediction module for final
classification. Extensive experiments show that the E2STN can achieve the
state-of-the-art performance on cross-dataset EEG emotion recognition tasks.


  Combining empirical risk minimization with capacity control is a classical
strategy in machine learning when trying to control the generalization gap and
avoid overfitting, as the model class capacity gets larger. Yet, in modern deep
learning practice, very large over-parameterized models (e.g. neural networks)
are optimized to fit perfectly the training data and still obtain great
generalization performance. Past the interpolation point, increasing model
complexity seems to actually lower the test error.
  In this tutorial, we explain the concept of double descent and its
mechanisms. The first section sets the classical statistical learning framework
and introduces the double descent phenomenon. By looking at a number of
examples, section 2 introduces inductive biases that appear to have a key role
in double descent by selecting, among the multiple interpolating solutions, a
smooth empirical risk minimizer. Finally, section 3 explores the double descent
with two linear models, and gives other points of view from recent related
works.


  Large numbers of muons will be produced at facilities developed to probe
lepton flavor violating process $\mu\to e\gamma$. We show that by constructing
a suitable asymmetry, radiative muon decay $\mu\to e \gamma\nu_\mu\bar{\nu}_e$
can also be used to test the $WW\gamma$ vertex at such facilities. The process
has two missing neutrinos in the final state and on integrating their momenta,
the partial differential decay rate shows no radiation-amplitude-zero. We
establish, however, that an easily separable part of the normalized
differential decay rate, odd under the exchange of photon and electron
energies, does have a zero in the case of standard model (SM). This "new type
of zero" has hitherto not been studied in literature. A suitably constructed
asymmetry using this fact, enables a sensitive probe for the $WW\gamma$ vertex
beyond the SM. With a simplistic analysis, we find that the $C$ and $P$
conserving dimension four $WW\gamma$ vertex can be probed at ${\cal
O}(10^{-2})$ with satisfactory significance level.


  We review X-ray studies of the highest redshift (z > 4) quasars, focusing on
recent advances enabled largely by the capabilities of Chandra and XMM-Newton.
Included are discussions of basic X-ray population studies, X-ray spectroscopy,
high-redshift AGN in X-ray surveys, and future prospects.


  Superdeduction is a method specially designed to ease the use of first-order
theories in predicate logic. The theory is used to enrich the deduction system
with new deduction rules in a systematic, correct and complete way.
  A proof-term language and a cut-elimination reduction already exist for
superdeduction, both based on Christian Urban's work on classical sequent
calculus. However the computational content of Christian Urban's calculus is
not directly related to the (lambda-calculus based) Curry-Howard
correspondence. In contrast the Lambda bar mu mu tilde calculus is a
lambda-calculus for classical sequent calculus.
  This short paper is a first step towards a further exploration of the
computational content of superdeduction proofs, for we extend the Lambda bar mu
mu tilde calculus in order to obtain a proofterm langage together with a
cut-elimination reduction for superdeduction. We also prove strong
normalisation for this extension of the Lambda bar mu mu tilde calculus.


  A discussion of the history of scientific computing for Radio Astronomy in
the Cavendish Laboratory of the University of Cambridge in the decades after
the Second World War. This covers the development of the aperture synthesis
technique for Radio Astronomy and how that required using the new computing
technology developed by the University's Mathematical Laboratory: the EDSAC,
EDSAC 2 and TITAN computers. It looks at the scientific advances made by the
Radio Astronomy group, particularly the assembling of evidence which
contradicted the Steady State Hypothesis. It also examines the software
advances that allowed bigger telescopes to be built: the Fast Fourier Transform
(FFT) and the degridding algorithm. Throughout, the contribution of women is
uncovered, from the diagrams they drew for scientific publications, through
programming and operating computers, to writing scientific papers.


  The recent description of the cooling through the glass transition in terms
of irreversible structural Eshelby rearrangements with a single average fictive
temperature is extended to a distribution of fictive temperatures around the
average one. The extension has only little influence on the cooling scans, but
turns out to be necessary to understand the heating back to equilibrium.


  In this paper, we analyse singular values of a large $p\times n$ data matrix
$\mathbf{X}_n= (\mathbf{x}_{n1},\ldots,\mathbf{x}_{nn})$ where the column
$\mathbf{x}_{nj}$'s are independent $p$-dimensional vectors, possibly with
different distributions. Such data matrices are common in high-dimensional
statistics.
  Under a key assumption that the covariance matrices
$\mathbf{\Sigma}_{nj}=\text{Cov}(\mathbf{x}_{nj})$ can be asymptotically
simultaneously diagonalizable, and appropriate convergence of their spectra, we
establish a limiting distribution for the singular values of $\mathbf{X}_n$
when both dimension $p$ and $n$ grow to infinity in a comparable magnitude.
  The matrix model goes beyond and includes many existing works on different
types of sample covariance matrices, including the weighted sample covariance
matrix, the Gram matrix model and the sample covariance matrix of linear times
series models. Furthermore, we develop two applications of our general
approach.
  First, we obtain the existence and uniqueness of a new limiting spectral
distribution of realized covariance matrices for a multi-dimensional diffusion
process with anisotropic time-varying co-volatility processes.
  Secondly, we derive the limiting spectral distribution for singular values of
the data matrix for a recent matrix-valued auto-regressive model.
  Finally, for a generalized finite mixture model, the limiting spectral
distribution for singular values of the data matrix is obtained.


  This work deals with the construction of networks of topological defects in
models described by a single complex scalar field. We take advantage of the
deformation procedure recently used to describe kinklike defects in order to
build networks of topological defects, which appear from complex field models
with potentials that engender a finite number of isolated minima, both in the
case where the minima present discrete symmetry, and in the non symmetric case.
We show that the presence of symmetry guide us to the construction of regular
networks, while the non symmetric case gives rise to irregular networks which
spread throughout the complex field space. We also discuss bifurcation, a
phenomenon that appear in the non symmetric case, but is washed out by the
deformation procedure used in the present work.


  For each integer \(n\ge 1\), denote by \(T_{n}\) the map \(x\mapsto nx\mod
1\) from the circle group \(\T=\mathbb{R}/\mathbb{Z}\) into itself. Let $p,q\ge
2$ be two multiplicatively independent integers. Using Baire Category
arguments, we show that generically a \(T_{p}\)-invariant probability measure
$\mu$ on \(\mathbb{T}T\) with no atom has some large Fourier coefficients along
the sequence $(q^n)_{n\ge 0}$. In particular, \((T_{q^{n}}\mu )_{n\ge 0}\) does
not converges weak-star to the normalised Lebesgue measure on $\mathbb{T}$.
This disproves a conjecture of Furstenberg and complements previous results of
Johnson and Rudolph. In the spirit of previous work by Meiri and
Lindenstrauss-Meiri-Peres, we study generalisations of our main result to
certain classes of sequences \((c_n)_{n\ge 0}\) other than the sequences
\((q^{n})_{n\ge 0}\), and also investigate the multidimensional setting.


  We present an improved parallel algorithm for the enumeration of fixed
benzenoids B_h containing h hexagonal cells. We can thus extend the enumeration
of B_h from the previous best h=35 up to h=50. Analysis of the associated
generating function confirms to a very high degree of certainty that $B_h \sim
A \kappa^h /h$ and we estimate that the growth constant $\kappa =
5.161930154(8)$ and the amplitude $A=0.2808499(1)$.


  Gravitational waves are propagating undulations in the spacetime fabric,
which interact very weakly with their environment. In cosmology,
gravitational-wave distortions are produced by most of the inflationary
scenarios and their anticipated detection should open a new window to the early
universe. Motivated by the relative lack of studies on the potential
implications of gravitational radiation for the large-scale structure of the
universe, we consider its coupling to density perturbations during the
post-recombination era. We do so by assuming an Einstein-de Sitter background
cosmology and by employing a second-order perturbation study. At this
perturbative level and on superhorizon scales, we find that gravitational
radiation adds a distinct and faster growing mode to the standard linear
solution for the density contrast. Given the expected weakness of cosmological
gravitational waves, however, the effect of the new mode is currently
subdominant and it could start becoming noticeable only in the far future.
Nevertheless, this still raises the intriguing possibility that the late-time
evolution of large-scale density perturbations may be dictated by the
long-range (the Weyl), rather than the local (the Ricci) component of the
gravitational field.


  We report the first detection of c-C3H2 in a circumstellar disk. The c-C3H2
J=6-5 line (217.882 GHz) is detected and imaged through Atacama Large
Millimeter Array (ALMA) Science Verification observations toward the disk
around the Herbig Ae star HD 163296 at 0.8" resolution. The emission is
consistent with that arising from a Keplerian rotating disk. Two additional
c-C3H2 transitions are also tentatively detected, bolstering the identification
of this species, but with insufficient signal-to-noise ratio to constrain the
spatial distribution. Using a previously developed model for the physical
structure of this disk, we fit a radial power-law distribution model to the
c-C3H2 6-5 emission and find that c-C3H2 is present in a ring structure from an
inner radius of about 30 AU to an outer radius of about 165 AU. The column
density is estimated to be 1e12-1e13 cm-2. The clear detection and intriguing
ring structure suggest that c-C3H2 has the potential to become a useful probe
of radiation penetration in disks.


  Organ at risk (OAR) segmentation is a critical process in radiotherapy
treatment planning such as head and neck tumors. Nevertheless, in clinical
practice, radiation oncologists predominantly perform OAR segmentations
manually on CT scans. This manual process is highly time-consuming and
expensive, limiting the number of patients who can receive timely radiotherapy.
Additionally, CT scans offer lower soft-tissue contrast compared to MRI.
Despite MRI providing superior soft-tissue visualization, its time-consuming
nature makes it infeasible for real-time treatment planning. To address these
challenges, we propose a method called SegReg, which utilizes Elastic Symmetric
Normalization for registering MRI to perform OAR segmentation. SegReg
outperforms the CT-only baseline by 16.78% in mDSC and 18.77% in mIoU, showing
that it effectively combines the geometric accuracy of CT with the superior
soft-tissue contrast of MRI, making accurate automated OAR segmentation for
clinical practice become possible. See project website
https://steve-zeyu-zhang.github.io/SegReg


  Retrosynthesis is one of the fundamental problems in organic chemistry. The
task is to identify reactants that can be used to synthesize a specified
product molecule. Recently, computer-aided retrosynthesis is finding renewed
interest from both chemistry and computer science communities. Most existing
approaches rely on template-based models that define subgraph matching rules,
but whether or not a chemical reaction can proceed is not defined by hard
decision rules. In this work, we propose a new approach to this task using the
Conditional Graph Logic Network, a conditional graphical model built upon graph
neural networks that learns when rules from reaction templates should be
applied, implicitly considering whether the resulting reaction would be both
chemically feasible and strategic. We also propose an efficient hierarchical
sampling to alleviate the computation cost. While achieving a significant
improvement of $8.1\%$ over current state-of-the-art methods on the benchmark
dataset, our model also offers interpretations for the prediction.


  The (independent) chromatic vertex stability ($\ivs(G)$) $\vs(G)$ is the
minimum size of (independent) set $S\subseteq V(G)$ such that
$\chi(G-S)=\chi(G)-1$. In this paper we construct infinitely many graphs $G$
with $\Delta(G)=4$, $\chi(G)=3$, $\ivs(G)=3$ and $\vs(G)=2$, which gives a
partial negative answer to a problem posed in \cite{ABKM}.


  In 1993, Mermin (Rev. Mod. Phys. 65, 803--815) gave lucid and strikingly
simple proofs of the Bell-Kochen-Specker (BKS) theorem in Hilbert spaces of
dimensions four and eight by making use of what has since been referred to as
the Mermin(-Peres) "magic square" and the Mermin pentagram, respectively. The
former is a $3 \times 3$ array of nine observables commuting pairwise in each
row and column and arranged so that their product properties contradict those
of the assigned eigenvalues. The latter is a set of ten observables arranged in
five groups of four lying along five edges of the pentagram and characterized
by similar contradiction. An interesting one-to-one correspondence between the
operators of the Mermin-Peres square and the points of the projective line over
the product ring ${\rm GF}(2) \otimes \rm{GF}(2)$ is established. Under this
mapping, the concept "mutually commuting" translates into "mutually distant"
and the distinguishing character of the third column's observables has its
counterpart in the distinguished properties of the coordinates of the
corresponding points, whose entries are both either zero-divisors, or units.
The ten operators of the Mermin pentagram answer to a specific subset of points
of the line over GF(2)[$x$]/$<x^{3} - x>$. The situation here is, however, more
intricate as there are two different configurations that seem to serve equally
well our purpose. The first one comprises the three distinguished points of the
(sub)line over GF(2), their three "Jacobson" counterparts and the four points
whose both coordinates are zero-divisors; the other features the neighbourhood
of the point ($1, 0$) (or, equivalently, that of ($0, 1$)). Some other ring
lines that might be relevant for BKS proofs in higher dimensions are also
mentioned.


  Inspired by macroscale vehicles, many molecular machines have been
synthesized yet. Due to the importance of atomic manipulation at the surface,
nanocars are of particular interest. Nanocar wheels play a crucial role in
their motion. One of the popular candidate for using as a nanocar wheel is C60
molecule. In addition, the investigation of nanocar motion on two dimensional
substrates is important due to formation of ripples on surface. Therefore, in
this work we study the motion of C60 on graphene and boron nitride monolayer
substrates at 300 K. The simulations are conducted by the means of molecular
dynamics method. The trajectory of motion shows more displacement range when
fullerene is moving on the graphene surface and as a result, it has a greater
diffusion coefficient in this case. It has been showed that C60 motion on
graphene and boron nitride obey a same super-diffusion regime at 300 K with
different anomaly parameters.


  To probe the effects of hydrogel particle additives on the water-accessible
pore structure of sandy soils, we introduce a custom pressure plate method in
which the volume of water expelled from a wet granular packing is measured as a
function of applied pressure. Using a capillary bundle model, we show that the
differential change in retained water per pressure increment is directly
related to the cumulative cross-sectional area distribution $f(r)$ of the
water-accessible pores with radii less than $r$. This is validated by
measurements of water expelled from a model sandy soil composed of 2 mm
diameter glass beads. In particular, the expelled water is found to depend
dramatically on sample height and that analysis using the capillary bundle
model gives the same pore size distribution for all samples. The distribution
is found to be approximately log-normal, and the total cross-sectional area
fraction of the accessible pore space is found to be $f_0=0.34$. We then report
on how the pore distribution and total water-accessible area fraction are
affected by superabsorbent hydrogel particle additives, uniformly mixed into a
fixed-height sample at varying concentrations. Under both fixed volume and free
swelling conditions, the total area fraction of water-accessible pore space in
a packing decreases exponentially as the gel concentration increases. The size
distribution of the pores is significantly modified by the swollen hydrogel
particles, such that large pores are clogged while small pores are formed.


  We consider an ergodic Schr\"odinger operator with magnetic field within the
non-interacting particle approximation. Justifying the linear response theory,
a rigorous derivation of a Kubo formula for the electric conductivity tensor
within this context can be found in a recent work of Bouclet, Germinet, Klein
and Schenker. If the Fermi level falls into a region of localization, the
well-known Kubo-Streda formula for the quantum Hall conductivity at zero
temperature is recovered. In this review we go along the lines of but make a
more systematic use of noncommutative Lp-spaces, leading to a somewhat more
transparent proof.


  The rapid increase in data traffic demand has overloaded existing cellular
networks. Planned upgrades in the communication architecture (e.g. LTE), while
helpful, are not expected to suffice to keep up with demand. As a result,
extensive densification through small cells, caching content closer to or even
at the device, and device-to-device (D2D) communications are seen as necessary
components for future heterogeneous cellular networks to withstand the data
crunch. Nevertheless, these options imply new CAPEX and OPEX costs, extensive
backhaul support, contract plan incentives for D2D, and a number of interesting
tradeoffs arise for the operator. In this paper, we propose an analytical model
to explore how much local storage and communication through "edge" nodes could
help offload traffic in various heterogeneous network (HetNet) setups and
levels of user tolerance to delays. We then use this model to optimize the
storage allocation and access mode of different contents as a tradeoff between
user satisfaction and cost to the operator. Finally, we validate our findings
through realistic simulations and show that considerable amounts of traffic can
be offloaded even under moderate densification levels.


  Cadmium arsenide (Cd3As2) - a time-honored and widely explored material in
solid-state physics - has recently attracted considerable attention. This was
triggered by a theoretical prediction concerning the presence of 3D
symmetry-protected massless Dirac electrons, which could turn Cd3As2 into a 3D
analogue of graphene. Subsequent extended experimental studies have provided us
with compelling experimental evidence of conical bands in this system, and
revealed a number of interesting properties and phenomena. At the same time,
some of the material properties remain the subject of vast discussions despite
recent intensive experimental and theoretical efforts, which may hinder the
progress in understanding and applications of this appealing material. In this
review, we focus on the basic material parameters and properties of Cd3As2, in
particular those which are directly related to the conical features in the
electronic band structure of this material. The outcome of experimental
investigations, performed on Cd3As2 using various spectroscopic and transport
techniques within the past sixty years, is compared with theoretical studies.
These theoretical works gave us not only simplified effective models, but more
recently, also the electronic band structure calculated numerically using ab
initio methods.


  In this paper, we first incorporate the weak interaction into the theory of
General Nonlocality by finding a appropriate metric for it. Accordingly, we
suggest the theoretical frame of General Nonlocality as the candidate theory of
unifying three microscope interactions in low energy limit. In this unifying
scenario, the essential role of photon field is stressed.


  Characterizing the reputation of an evaluator is particularly significant for
consumer to obtain useful information from online rating systems. Furthermore,
to overcome the difficulties with spam attacks on the rating system and to get
the reliable on reputation of evaluators is an important topic in the research.
We have noticed that most of the existing evaluator reputation evaluation
methods only rely on the evaluator's rating information and abnormal behavior
to establish a reputation system, which miss the systematic aspects of the
rating systems including the structure of the evaluator-object bipartite
network and the effects of nonlinear effects. This study we propose an improved
reputation evaluation method by combining the structure of the evaluator-object
bipartite network with rating information and introducing penalty and reward
factors. This novel method has been empirically analyzed on a large-scale
artificial data set and two real data sets. The results show that the proposed
method is more accurate and robust in the presence of spam attacks. This fresh
idea contributes a new way for building reputation evaluation models in sparse
bipartite rating network.


  We analyze the collective light scattering by cold atoms in free space of a
pump laser beam possessing orbital angular momentum. We derive a set of coupled
equations for the atomic motion in which the vacuum-mode field is adiabatically
eliminated. The resulting equations describe collective recoil as due to either
transfer of linear momentum or orbital angular momentum. For a transverse
annular atomic distribution the initial equilibrium with uniform atomic phases
and no scattered field, is unstable. The atoms are set in rotation and bunched
in phase at different harmonics depending on the pump azimuthal index l and on
the ring radius.


  In this paper the problems of deriving a taxonomy from a text and
concept-oriented text segmentation are approached. Formal Concept Analysis
(FCA) method is applied to solve both of these linguistic problems. The
proposed segmentation method offers a conceptual view for text segmentation,
using a context-driven clustering of sentences. The Concept-oriented Clustering
Segmentation algorithm (COCS) is based on k-means linear clustering of the
sentences. Experimental results obtained using COCS algorithm are presented.


  We write down an explicit formula for the $+$ version of the Heegaard Floer
homology (as an absolutely graded vector space over an arbitrary field) of the
results of Dehn surgery on a knot $K$ in $S^3$ in terms of homological data
derived from $CFK^{\infty}(K)$. This allows us to prove some results about Dehn
surgery on knots in $S^3$. In particular, we show that for a fixed manifold
there are only finitely many alternating knots that can produce it by surgery.
This is an improvement on a recent result by Lackenby and Purcell. We also
derive a lower bound on the genus of knots depending on the manifold they give
by surgery. Some new restrictions on Seifert fibred surgery are also presented.