  A deep neural network (DNN) based power control method is proposed, which
aims at solving the non-convex optimization problem of maximizing the sum rate
of a multi-user interference channel. Towards this end, we first present PCNet,
which is a multi-layer fully connected neural network that is specifically
designed for the power control problem. PCNet takes the channel coefficients as
input and outputs the transmit power of all users. A key challenge in training
a DNN for the power control problem is the lack of ground truth, i.e., the
optimal power allocation is unknown. To address this issue, PCNet leverages the
unsupervised learning strategy and directly maximizes the sum rate in the
training phase. Observing that a single PCNet does not globally outperform the
existing solutions, we further propose ePCNet, a network ensemble with multiple
PCNets trained independently. Simulation results show that for the standard
symmetric multi-user Gaussian interference channel, ePCNet can outperform all
state-of-the-art power control methods by 1.2%-4.6% under a variety of system
configurations. Furthermore, the performance improvement of ePCNet comes with a
reduced computational complexity.


  An elementary combinatorial Tanner graph construction for a family of
near-regular low density parity check codes achieving high girth is presented.
The construction allows flexibility in the choice of design parameters like
rate, average degree, girth and block length of the code and yields an
asymptotic family. The complexity of constructing codes in the family grows
only quadratically with the block length.


  We report the discovery of an extremely luminous galaxy lying at a redshift
of z=5.74, SSA22-HCM1. The object was found in narrowband imaging of the SSA22
field using a 105 Angstrom bandpass filter centered at 8185 Angstroms during
the course of the Hawaii narrowband survey using LRIS on the 10 m Keck II
Telescope, and was identified by the equivalent width of the emission
W_lambda(observed)=175 Angstroms, flux = 1.7 x 10^{-17} erg cm^{-2} s^{-1}).
Comparison with broadband colors shows the presence of an extremely strong
break (> 4.2 at the 2 sigma level) between the Z band above the line, where the
AB magnitude is 25.5, and the R band below, where the object is no longer
visible at a 2 sigma upper limit of 27.1 (AB mags). These properties are only
consistent with this object's being a high-z Ly alpha emitter. A 10,800 s
spectrum obtained with LRIS yields a redshift of 5.74. The object is similar in
its continuum shape, line properties, and observed equivalent width to the
z=5.60 galaxy, HDF 4-473.0, as recently described by Weymann et al. (1998), but
is 2-3 times more luminous in the line and in the red continuum. For H_0 = 65
km s^{-1} Mpc^{-1} and q_0 = (0.02, 0.5) we would require star formation rates
of around (40, 7) solar masses per year to produce the UV continuum in the
absence of extinction.


  Sunspot number series are composed from observations of hundreds of different
observers that requires careful normalization of the observers to the standard
conditions. Here we present a new normalized series of the number of sunspot
groups for the period 1749-1996. The reconstruction is based on the active day
fraction (ADF) method, which is slightly updated with respect to the previous
works, and a revised database of sunspot group observations. Stability of some
key solar observers has been evaluated against the composite series. The Royal
Greenwich Observatory dataset appears fairly stable since the 1890s but is
about 10% too low before that. A declining trend of 10-15% in the quality of
Wolfer's observation is found between the 1880s and 1920s, suggesting that
using him as the reference observer may lead to additional uncertainties. Wolf
(small telescope) appears fairly stable between the 1860s and 1890s, without
any obvious trend. The new reconstruction reflects the centennial variability
of solar activity as evaluated using the singular spectrum analysis method. It
depicts a highly significant feature of the Modern grand maximum of solar
activity in the second half of the 20th century, being a factor 1.33-1.77
higher than during the 18-19th centuries. The new series of the sunspot group
numbers with monthly and annual resolution, available also in the electronic
format, is provided forming a basis for new studies of the solar variability
and solar dynamo for the last 250 years.


  Shared Memory is a mechanism that allows several processes to communicate
with each other by accessing -- writing or reading -- a set of variables that
they have in common. A Consistency Model defines how each process observes the
state of the Memory, according to the accesses performed by it and by the rest
of the processes in the system. Therefore, it determines what value a read
returns when a given process issues it. This implies that there must be an
agreement among all, or among processes in different subsets, on the order in
which all or a subset of the accesses happened. It is clear that a higher
quantity of accesses or proceses taking part in the agreement makes it possibly
harder or slower to be achieved. This is the main reason for which a number of
Consistency Models for Shared Memory have been introduced. This paper is a
handy summary of [2] and [3] where consistency models (Sequential, Causal,
PRAM, Cache, Processors, Slow), including synchronized ones (Weak, Release,
Entry), were formally defined. This provides a better understanding of those
models and a way to reason and compare them through a concise notation. There
are many papers on this subject in the literature such as [11] with which this
work shares some concepts.


  There is a growing interest in the use of video sensor networks in
surveillance applications in order to detect intruders with low cost. The
essential concern of such networks is whether or not a specified target can
pass or intrude the monitored region without being detected. This concern forms
a serious challenge to wireless video sensor networks of weak computation and
battery power.
  In this paper, our aim is to prolong the whole network lifetime while
fulfilling the surveillance application needs. We present a novel scheduling
algorithm where only a subset of video nodes contribute significantly to detect
intruders and prevent malicious attacker to predict the behavior of the network
prior to intrusion. Our approach is chaos-based, where every node based on its
last detection, a hash value and some pseudo-random numbers easily computes a
decision function to go to sleep or active mode. We validate the efficiency of
our approach through theoretical analysis and demonstrate the benefits of our
scheduling algorithm by simulations. Results show that in addition of being
able to increase the whole network lifetime and to present comparable results
against random attacks (low stealth time), our scheme is also able to withstand
malicious attacks due to its fully unpredictable behavior.


  Existing document filtering systems learn user profiles based on user
relevance feedback on documents. In some cases, users may have prior knowledge
about what features are important. For example, a Spanish speaker may only want
news written in Spanish, and thus a relevant document should contain the
feature "Language: Spanish"; a researcher focusing on HIV knows an article with
the medical subject "Subject: AIDS" is very likely to be relevant to him/her.
  Semi-structured documents with rich metadata are increasingly prevalent on
the Internet. Motivated by the well-adopted faceted search interface in
e-commerce, we study the exploitation of user prior knowledge on faceted
features for semi-structured document filtering. We envision two faceted
feedback mechanisms, and propose a novel user profile learning algorithm that
can incorporate user feedback on features. To evaluate the proposed work, we
use two data sets from the TREC filtering track, and conduct a user study on
Amazon Mechanical Turk. Our experiment results show that user feedback on
faceted features is useful for filtering. The proposed user profile learning
algorithm can effectively learn from user feedback on both documents and
features, and performs better than several existing methods.


  Imaging polarimetry is an important tool for the study of cosmic magnetic
fields. In our Galaxy, polarization levels of a few up to $\sim$10\% are
measured in the submillimeter dust emission from molecular clouds and in the
synchrotron emission from supernova remnants. Only few techniques exist to
image the distribution of polarization angles, as a means of tracing the
plane-of-sky projection of the magnetic field orientation. At submillimeter
wavelengths, polarization is either measured as the differential total power of
polarization-sensitive bolometer elements, or by modulating the polarization of
the signal. Bolometer arrays such as LABOCA at the APEX telescope are used to
observe the continuum emission from fields as large as $\sim0\fdg2$ in
diameter. %Here we present the results from the commissioning of PolKa, a
polarimeter for Here we present PolKa, a polarimeter for LABOCA with a
reflection-type waveplate of at least 90\% efficiency. The modulation
efficiency depends mainly on the sampling and on the angular velocity of the
waveplate. For the data analysis the concept of generalized synchronous
demodulation is introduced. The instrumental polarization towards a point
source is at the level of $\sim0.1$\%, increasing to a few percent at the
$-10$db contour of the main beam. A method to correct for its effect in
observations of extended sources is presented. Our map of the polarized
synchrotron emission from the Crab nebula is in agreement with structures
observed at radio and optical wavelengths. The linear polarization measured in
OMC1 agrees with results from previous studies, while the high sensitivity of
LABOCA enables us to also map the polarized emission of the Orion Bar, a
prototypical photon-dominated region.


  Let $n$ be a positive integer and $H$ a Hilbert space. The description of the
general form of bijective maps on the set of $n$-dimensional subspaces of $H$
preserving the maximal principal angle has been obtained recently. This is a
generalization of Wigner's unitary-antiunitary theorem. In this paper we will
obtain another extension of Wigner's theorem in which the maximal principal
angle is replaced by the minimal one. Moreover, in this case we do not need the
bijectivity assumption.


  We analyze a spatially homogeneous SU(2) Yang-Mills-Higgs system both in
classical and quantum mechanics. By using the Toda criterion of the Gaussian
curvature we find a classical chaos-order transition as a function of the Higgs
vacuum, the Yang-Mills coupling constant and the energy of the system. Then, we
study the nearest-neighbour spacing distribution of the energy levels, which
shows a Wigner-Poisson transition by increasing the value of the Higgs field in
the vacuum. This transition is a clear quantum signature of the classical
chaos-order transition of the system.


  The wave equation on network is defined by $\partial_{tt}u=\Delta_{G}u+g(u)$,
where $u\in\mathbb{R}^{n}$ and the graph Laplacian $\Delta_{G}$ is an operator
on functions on $n$ vertices. We suppose that $g:\mathbb{R}^{n}\rightarrow
\mathbb{R}^{n}$ is an odd continuous function that satisfies $g(0)=g^{\prime
}(0)=0$ and the Nagumo condition. Assuming that the graph is invariant by a
subgroup of permutations $\Gamma$, using a $\Gamma$-equivariant topological
invariant we prove the existence of multiple non-constant $p$-periodic
solutions characterized by their symmetries.


  We consider Glauber dynamics for the Ising model on the complete graph on $n$
vertices, known as the Curie-Weiss model. It is well-known that the mixing-time
in the high temperature regime ($\beta < 1$) has order $n\log n$, whereas the
mixing-time in the case $\beta > 1$ is exponential in $n$. Recently, Levin,
Luczak and Peres proved that for any fixed $\beta < 1$ there is cutoff at time
$[2(1-\beta)]^{-1} n\log n$ with a window of order $n$, whereas the mixing-time
at the critical temperature $\beta=1$ is $\Theta(n^{3/2})$. It is natural to
ask how the mixing-time transitions from $\Theta(n\log n)$ to $\Theta(n^{3/2})$
and finally to $\exp(\Theta(n))$. That is, how does the mixing-time behave when
$\beta=\beta(n)$ is allowed to tend to 1 as $n\to\infty$.
  In this work, we obtain a complete characterization of the mixing-time of the
dynamics as a function of the temperature, as it approaches its critical point
$\beta_c=1$. In particular, we find a scaling window of order $1/\sqrt{n}$
around the critical temperature. In the high temperature regime, $\beta = 1 -
\delta$ for some $0 < \delta < 1$ so that $\delta^2 n \to\infty$ with $n$, the
mixing-time has order $(n/\delta)\log(\delta^2 n)$, and exhibits cutoff with
constant 1/2 and window size $n/\delta$. In the critical window, $\beta = 1\pm
\delta$ where $\delta^2 n$ is O(1), there is no cutoff, and the mixing-time has
order $n^{3/2}$. At low temperature, $\beta = 1 + \delta$ for $\delta > 0$ with
$\delta^2 n \to\infty$ and $\delta=o(1)$, there is no cutoff, and the mixing
time has order $(n/\delta)\exp(({3/4}+o(1))\delta^2 n)$.


  In the half-space $\mathbb{R}^d \times \mathbb{R}_+$, we consider the
Hermite-Schr\"odinger equation $i\partial u/\partial t = - \Delta u + |x|^2 u$,
with given boundary values on $\mathbb{R}^d$.
  We prove a formula that links the solution of this problem to that of the
classical Schr\"odinger equation. It shows that mixed norm estimates for the
Hermite-Schr\"odinger equation can be obtained immediately from those known in
the classical case. In one space dimension, we deduce sharp pointwise
convergence results at the boundary, by means of this link.


  Traditionally, results given by the direct numerical simulation (DNS) of
Navier-Stokes equations are widely regarded as reliable benchmark solutions of
turbulence, as long as grid spacing is fine enough (i.e. less than the minimum
Kolmogorov scale) and time-step is small enough, say, satisfying the
Courant-Friedrichs-Lewy condition. Is this really true? In this paper a
two-dimensional sustained turbulent Kolmogorov flow is investigated numerically
by the two numerical methods with detailed comparisons: one is the traditional
`direct numerical simulation' (DNS), the other is the `clean numerical
simulation' (CNS). The results given by DNS are a kind of mixture of the false
numerical noise and the true physical solution, which however are mostly at the
same order of magnitude due to the butterfly-effect of chaos. On the contrary,
the false numerical noise of the results given by CNS is much smaller than the
true physical solution of turbulence in a long enough interval of time so that
a CNS result is very close to the true physical solution and thus can be used
as a benchmark solution. It is found that numerical noise as a kind of
artificial tiny disturbances can lead to huge deviations at large scale on the
two-dimensional Kolmogorov turbulence, not only quantitatively (even in
statistics) but also qualitatively (such as symmetry of flow). Thus, fine
enough spatial grid spacing with small enough time-step alone cannot guarantee
the validity of the DNS: it is only a necessary condition but not sufficient.
This finding might challenge some assumptions in investigation of turbulence.
So, DNS results of a few sustained turbulent flows might have huge deviations
on both of small and large scales from the true solution of Navier-Stokes
equations even in statistics. Hopefully, CNS as a new tool to investigate
turbulent flows more accurately than DNS could bring us some new discoveries.


  This article is a continuation of a previous article which concerned the
splitting problem for subspaces of superspaces. We begin with a general account
of projective superspaces. Subsequently, we specialise to subvarieties of
`positive' projective superspaces. Our main result is: positive, projective
superspaces are `normal', in a sense we define. Then, among others, our main
application is: smooth, non-reduced, superspace quadric hypersurfaces are
non-split.


  We present the analysis of ASCA archival data from the Galactic source W51.
The ASCA spectra show that the soft (kT<= 2.5 keV) X-rays are of thermal origin
and are compatible with W51C being a single, isothermal (kT~0.3 keV) supernova
remnant at the far-side of the Sagittarius arm. The ASCA images reveal hard
(kT>=2.5 keV) X-ray sources which were not seen in previous X-ray observations.
Some of these sources are coincident with massive star-forming regions and the
spectra are used to derive X-ray parameters. By comparing the X-ray absorbing
column density with atomic hydrogen column density, we infer the location of
star-forming regions relative to molecular clouds. There are unidentified hard
X-ray sources superposed on the supernova remnant and we discuss the
possibility of their association.


  Numerous magnetic hot stars exhibit gyrosynchrotron radio emission. The
source electrons were previously thought to be accelerated to relativistic
velocities in the current sheet formed in the middle magnetosphere by the wind
opening magnetic field lines. However, a lack of dependence of radio luminosity
on the wind power, and a strong dependence on rotation, has recently challenged
this paradigm. We have collected all radio measurements of magnetic early-type
stars available in the literature. When constraints on the magnetic field
and/or the rotational period are not available, we have determined these using
previously unpublished spectropolarimetric and photometric data. The result is
the largest sample of magnetic stars with radio observations that has yet been
analyzed: 131 stars with rotational and magnetic constraints, of which 50 are
radio-bright. We confirm an obvious dependence of gyrosynchrotron radiation on
rotation, and furthermore find that accounting for rotation neatly separates
stars with and without detected radio emission. There is a close correlation
between H$\alpha$ emission strength and radio luminosity. These factors suggest
that radio emission may be explained by the same mechanism responsible for
H$\alpha$ emission from centrifugal magnetospheres, i.e. centrifugal breakout
(CBO), however, whereas the H$\alpha$-emitting magnetosphere probes the cool
plasma before breakout, radio emission is a consequence of electrons
accelerated in centrifugally-driven magnetic reconnection.


  The categorical compositional distributional model of natural language
provides a conceptually motivated procedure to compute the meaning of
sentences, given grammatical structure and the meanings of its words. This
approach has outperformed other models in mainstream empirical language
processing tasks. However, until recently it has lacked the crucial feature of
lexical entailment -- as do other distributional models of meaning.
  In this paper we solve the problem of entailment for categorical
compositional distributional semantics. Taking advantage of the abstract
categorical framework allows us to vary our choice of model. This enables the
introduction of a notion of entailment, exploiting ideas from the categorical
semantics of partial knowledge in quantum computation.
  The new model of language uses density matrices, on which we introduce a
novel robust graded order capturing the entailment strength between concepts.
This graded measure emerges from a general framework for approximate
entailment, induced by any commutative monoid. Quantum logic embeds in our
graded order.
  Our main theorem shows that entailment strength lifts compositionally to the
sentence level, giving a lower bound on sentence entailment. We describe the
essential properties of graded entailment such as continuity, and provide a
procedure for calculating entailment strength.


  We consider discrete-time one-dimensional random dynamical systems with
bounded noise, which generate an associated set-valued dynamical system. We
provide necessary and sufficient conditions for a discontinuous bifurcation of
a minimal invariant set of the set-valued dynamical system in terms of the
derivatives of the so-called extremal maps. We propose an algorithm for
reconstructing the derivatives of the extremal maps from a time series that is
generated by iterations of the original random dynamical system. We demonstrate
that the derivative reconstructed for different parameters can be used as an
early-warning signal to detect an upcoming bifurcation, and apply the algorithm
to the bifurcation analysis of the stochastic return map of the Koper model,
which is a three-dimensional multiple time scale ordinary differential equation
used as prototypical model for the formation of mixed-mode oscillation
patterns. We apply our algorithm to data generated by this map to detect an
upcoming transition.


  We define two transformations from term rewriting systems (TRSs) to
context-sensitive TRSs in such a way that termination of the target system
implies outermost termination of the original system. In the transformation
based on 'context extension', each outermost rewrite step is modeled by exactly
one step in the transformed system. This transformation turns out to be
complete for the class of left-linear TRSs. The second transformation is called
`dynamic labeling' and results in smaller sized context-sensitive TRSs. Here
each modeled step is adjoined with a small number of auxiliary steps. As a
result state-of-the-art termination methods for context-sensitive rewriting
become available for proving termination of outermost rewriting. Both
transformations have been implemented in Jambox, making it the most successful
tool in the category of outermost rewriting of the last edition of the annual
termination competition.


  Contributions of primordial gravitational waves to the large-angular-scale
anisotropies of the cosmic microwave background radiation in multidimensional
cosmological models (Kaluza-Klein models) are studied. We derive limits on free
parameters of the models using results of the COBE experiment and other
astrophysical data. It is shown that in principle there is a room for
Kaluza-Klein models as possible candidates for the description of the Early
Universe. However, the obtained limits are very restrictive. Assuming that the
anisotropies are mostly due to gravitational waves, none of the concrete
models, analyzed in the article, satisfy them. On the other hand, if the
contribution of gravitational waves is very small then a string inspired model
is not ruled out.


  The objective of clusterability evaluation is to check whether a clustering
structure exists within the data set. As a crucial yet often-overlooked issue
in cluster analysis, it is essential to conduct such a test before applying any
clustering algorithm. If a data set is unclusterable, any subsequent clustering
analysis would not yield valid results. Despite its importance, the majority of
existing studies focus on numerical data, leaving the clusterability evaluation
issue for categorical data as an open problem. Here we present TestCat, a
testing-based approach to assess the clusterability of categorical data in
terms of an analytical $p$-value. The key idea underlying TestCat is that
clusterable categorical data possess many strongly correlated attribute pairs
and hence the sum of chi-squared statistics of all attribute pairs is employed
as the test statistic for $p$-value calculation. We apply our method to a set
of benchmark categorical data sets, showing that TestCat outperforms those
solutions based on existing clusterability evaluation methods for numeric data.
To the best of our knowledge, our work provides the first way to effectively
recognize the clusterability of categorical data in a statistically sound
manner.


  A local photo-response of an asymmetric quantum Hall system in tilted
magnetic field is demonstrated to be a complicate non-monotonic function of
macroscopic distances to the sample edges. A local photo-response in the dark
has been observed caused by illumination of the sample arias remote on a
macroscopic distances. These macroscopic-range correlatons indicate the
presence of a macroscopic ordering of electrons in the system.


  We construct the Neumann Green function and establish scale invariant
regularity estimates for solutions to the Neumann problem for the elliptic
operator $Lu=-{\rm div}({\bf A} \nabla u+ \boldsymbol{b}u)+ \boldsymbol{c}
\cdot \nabla u+du$ in a Lipschitz domain $\Omega$. We assume that ${\bf A}$ is
elliptic and bounded, that the lower order coefficients belong to scale
invariant Lebesgue spaces, and that either $d\geq{\rm div}\boldsymbol{b}$ in
$\Omega$ and $\boldsymbol{b}\cdot\nu\geq 0$ on $\partial\Omega$ in the sense of
distributions, or the analogous condition for $\boldsymbol{c}$ holds. We
develop the $L^2$ theory, construct the Neumann Green function and show
estimates in the respective optimal spaces, and show local and global pointwise
estimates for solutions. The main novelty is that our estimates are scale
invariant, since our constants depend on the lower order coefficients only via
their norms, and on the Lipschitz domain only via its Lipschitz character.
Moreover, our pointwise estimates are shown in the optimal scale invariant
setting for the inhomogeneous terms and the Neumann data.


  We have conducted a deep survey (r.m.s noise 17 microJy) with the Very Large
Array (VLA) at 1.4 GHz, with a resolution of 6 arcsec, of a 1 square degree
region included in the VIRMOS VLT Deep Survey. In the same field we already
have multiband photometry down to I(AB)=25, and spectroscopic observations will
be obtained during the VIRMOS VLT survey. The homogeneous sensitivity over the
whole field has allowed to derive a complete sample of 1054 radio sources (5
sigma limit). We give a detailed description of the data reduction and of the
analysis of the radio observations, with particular care to the effects of
clean bias and bandwidth smearing, and of the methods used to obtain the
catalogue of radio sources. To estimate the effect of the resolution bias on
our observations we have modelled the effective angular-size distribution of
the sources in our sample and we have used this distribution to simulate a
sample of radio sources. Finally we present the radio count distribution down
to 0.08 mJy derived from the catalogue. Our counts are in good agreement with
the best fit derived from earlier surveys, and are about 50 % higher than the
counts in the HDF. The radio count distribution clearly shows, with extremely
good statistics, the change in the slope for the sub-mJy radio sources.


  We evaluate the relic density of the lightest neutralino, the lightest
supersymmetric particle, in the Minimal Supersymmetric extension of the
Standard Model (MSSM). For the first time, we include all coannihilation
processes between neutralinos and charginos for any neutralino mass and
composition. We use the most sophisticated routines for integrating the cross
sections and the Boltzmann equation. We properly treat (sub)threshold and
resonant annihilations. We also include one-loop corrections to neutralino
masses. We find that coannihilation processes are important not only for light
higgsino-like neutralinos, as pointed out before, but also for heavy higgsinos
and for mixed and gaugino-like neutralinos. Indeed, coannihilations should be
included whenever $|\mu| \lsim 2 |M_1|$, independently of the neutralino
composition. When $|\mu| \sim |M_1|$, coannihilations can increase or decrease
the relic density in and out of the cosmologically interesting region. We find
that there is still a window of light higgsino-like neutralinos that are viable
dark matter candidates and that coannihilations shift the cosmological upper
bound on the neutralino mass from 3 to 7 TeV.


  This work is concerned with practical stabilization of nonlinear systems by
means of inf-convolution-based sample-and-hold control. It is a fairly general
stabilization technique based on a generic non-smooth control Lyapunov function
(CLF) and robust to actuator uncertainty, measurement noise, etc. The
stabilization technique itself involves computation of descent directions of
the CLF. It turns out that non-exact realization of this computation leads not
just to a quantitative, but also qualitative obstruction in the sense that the
result of the computation might fail to be a descent direction altogether and
there is also no straightforward way to relate it to a descent direction.
Disturbance, primarily measurement noise, complicate the described issue even
more. This work suggests a modified inf-convolution-based control that is
robust w. r. t. system and measurement noise, as well as computational
uncertainty. The assumptions on the CLF are mild, as, e. g., any piece-wise
smooth function, which often results from a numerical LF/CLF construction,
satisfies them. A computational study with a three-wheel robot with dynamical
steering and throttle under various tolerances w. r. t. computational
uncertainty demonstrates the relevance of the addressed issue and the necessity
of modifying the used stabilization technique. Similar analyses may be extended
to other methods which involve optimization, such as Dini aiming or steepest
descent.


  We investigate the roles of chiral three-nucleon force (3NF) in
nucleon-nucleus elastic scattering, using the standard framework based on the
Brueckner-Hartree-Fock method for nuclear matter and the $g$-matrix folding
model for the nucleon-nucleus scattering. In nuclear matter, chiral 3NF at NNLO
level (mainly the 2$\pi$-exchange diagram) makes the single particle potential
less attractive for the singlet-even channel and more absorptive for the
triplet channels. The single-particle potential calculated from chiral
two-nucleon force (2NF) at N$^{3}$LO level is found to be close to that from
Bonn-B 2NF. The Melbourne $g$-matrix interaction is a practical effective
interaction constructed by localizing the $g$-matrices calculated from Bonn-B
2NF. We then introduce the chiral-3NF effects to the local Melbourne $g$-matrix
interaction. For nucleon-nucleus elastic scattering on various targets at 65
MeV, chiral 3NF makes the folding potential less attractive and more
absorptive. The novel property for the imaginary part is originated in the
enhancement of tensor correlations due to chiral 3NF. The two effects are small
for differential cross sections and vector analyzing powers at the forward and
middle angles where the experimental data are available. If backward
measurements are done, the data will reveal the effects of chiral 3NF.


  Pancharatnam's geometric phase is associated with the phase of a
complex-valued weak value arising in a certain type of weak measurement in pre-
and post-selected quantum ensembles. This makes it possible to test the
nontransitive nature of the relative phase in quantum mechanics, in the weak
measurement scenario.


  Causal discovery from observational data holds great promise, but existing
methods rely on strong assumptions about the underlying causal structure, often
requiring full observability of all relevant variables. We tackle these
challenges by leveraging the score function $\nabla \log p(X)$ of observed
variables for causal discovery and propose the following contributions. First,
we generalize the existing results of identifiability with the score to
additive noise models with minimal requirements on the causal mechanisms.
Second, we establish conditions for inferring causal relations from the score
even in the presence of hidden variables; this result is two-faced: we
demonstrate the score's potential as an alternative to conditional independence
tests to infer the equivalence class of causal graphs with hidden variables,
and we provide the necessary conditions for identifying direct causes in latent
variable models. Building on these insights, we propose a flexible algorithm
for causal discovery across linear, nonlinear, and latent variable models,
which we empirically validate.


  Coronary angiography remains the gold standard for diagnosis of coronary
artery disease, the most common cause of death worldwide. While this procedure
is performed more than 2 million times annually, there remain few methods for
fast and accurate automated measurement of disease and localization of coronary
anatomy. Here, we present our solution to the Automatic Region-based Coronary
Artery Disease diagnostics using X-ray angiography images (ARCADE) challenge
held at MICCAI 2023. For the artery segmentation task, our three-stage approach
combines preprocessing and feature selection by classical computer vision to
enhance vessel contrast, followed by an ensemble model based on YOLOv8 to
propose possible vessel candidates by generating a vessel map. A final
segmentation is based on a logic-based approach to reconstruct the coronary
tree in a graph-based sorting method. Our entry to the ARCADE challenge placed
3rd overall. Using the official metric for evaluation, we achieved an F1 score
of 0.422 and 0.4289 on the validation and hold-out sets respectively.


  It is a classical important problem of differential topology by Thom; for a
homology class of a compact manifold, can we realize this by a closed
submanifold with no boundary? This is true if the degree of the class is
smaller or equal to the half of the dimension of the outer manifold under the
condition that the coefficient ring is Z_2. If the degree of the class is
smaller or equal to 6 or equal to k-2 or k-1 under the condition that the
coefficient ring is the integer ring where k is the dimension of the manifold,
then this is also true. As a specific study, for 4-dimensional closed
manifolds, the topologies (genera) of closed and connected surfaces realizing
given 2nd homology classes have been actively studied, for example.
  In the present paper, we consider the following similar problem; can we
realize a homology class of a compact manifold by a homology class of an
explicit closed manifold embedded in the (interior of the) given compact
manifold? This problem is considered as a variant of previous problems. We
present an affirmative answer via important theory in the singularity theory of
differentiable maps: lifting a given smooth map to an embedding or obtaining an
embedding such that the composition of this with the canonical projection is
the given map. Presenting this application of lifting smooth maps and related
fundamental propositions is also a main purpose of the present paper.


  In this note we apply some theoretical predictions that arise in the mean
field framework for a large class of infinite range models to structural
glasses and we present a first comparison of these predictions with numerical
results.


  To understand an emergent spacetime is to understand the emergence of
locality. Entanglement entropy is a powerful diagnostic of locality, because
locality leads to a large amount of short distance entanglement. Two
dimensional string theory is among the very simplest instances of an emergent
spatial dimension. We compute the entanglement entropy in the large $N$ matrix
quantum mechanics dual to two dimensional string theory, in the semiclassical
limit of weak string coupling. We isolate a logarithmically large, but finite,
contribution that corresponds to the short distance entanglement of the tachyon
field in the emergent spacetime. From the spacetime point of view, the
entanglement is regulated by a nonperturbative `graininess' of space.


  A money-based model for the power law distribution (PLD) of wealth in an
economically interacting population is introduced. The basic feature of our
model is concentrating on the capital movements and avoiding the complexity of
micro behaviors of individuals. It is proposed as an extension of the Equiluz
and Zimmermann's (EZ) model for crowding and information transmission in
financial markets. Still, we must emphasize that in EZ model the PLD without
exponential correction is obtained only for a particular parameter, while our
pattern will give it within a wide range. The Zipf exponent depends on the
parameters in a nontrivial way and is exactly calculated in this paper.


  Standard epidemiological models for COVID-19 employ variants of compartment
(SIR) models at local scales, implicitly assuming spatially uniform local
mixing. Here, we examine the effect of employing more geographically detailed
diffusion models based on known spatial features of interpersonal networks,
most particularly the presence of a long-tailed but monotone decline in the
probability of interaction with distance, on disease diffusion. Based on
simulations of unrestricted COVID-19 diffusion in 19 U.S cities, we conclude
that heterogeneity in population distribution can have large impacts on local
pandemic timing and severity, even when aggregate behavior at larger scales
mirrors a classic SIR-like pattern. Impacts observed include severe local
outbreaks with long lag time relative to the aggregate infection curve, and the
presence of numerous areas whose disease trajectories correlate poorly with
those of neighboring areas. A simple catchment model for hospital demand
illustrates potential implications for health care utilization, with
substantial disparities in the timing and extremity of impacts even without
distancing interventions. Likewise, analysis of social exposure to others who
are morbid or deceased shows considerable variation in how the epidemic can
appear to individuals on the ground, potentially affecting risk assessment and
compliance with mitigation measures. These results demonstrate the potential
for spatial network structure to generate highly non-uniform diffusion behavior
even at the scale of cities, and suggest the importance of incorporating such
structure when designing models to inform healthcare planning, predict
community outcomes, or identify potential disparities.


  Twisted double bilayer graphene (tDBG) comprises two Bernal-stacked bilayer
graphene sheets with a twist between them. Gate voltages applied to top and
back gates of a tDBG device tune both the flatness and topology of the
electronic bands, enabling an unusual level of experimental control. Broken
spin/valley symmetry metallic states have been observed in tDBG devices with
twist angles $\sim $ 1.2-1.3$^\circ$, but the topologies and order parameters
of these states have remained unclear. We report the observation of an
anomalous Hall effect in the correlated metal state of tDBG, with hysteresis
loops spanning 100s of mT in out-of-plane magnetic field ($B_{\perp}$) that
demonstrate spontaneously broken time-reversal symmetry. The $B_{\perp}$
hysteresis persists for in-plane fields up to several Tesla, suggesting valley
(orbital) ferromagnetism. At the same time, the resistivity is strongly
affected by even mT-scale values of in-plane magnetic field, pointing to
spin-valley coupling or to a direct orbital coupling between in-plane field and
the valley degree of freedom.


  Some key notions of line geometry are recalled, along with their application
to mechanics. It is then shown that most of the basic structures that one
introduces in the pre-metric formulation of electromagnetism can be interpreted
directly in terms of corresponding concepts in line geometry. The results are
summarized in a table.


  In this article, the conversion of color RGB images to grayscale is covered
by characterizing the mathematical operators used to project 3 color channels
to a single one. Based on the fact that most operators assign each of the
$256^3$ colors a single gray level, ranging from 0 to 255, they are clustering
algorithms that distribute the color population into 256 clusters of increasing
brightness. To visualize the way operators work the sizes of the clusters and
the average brightness of each cluster are plotted. The equalization mode (EQ)
introduced in this work focuses on cluster sizes, while the brightness mapping
(BM) mode describes the CIE L* luminance distribution per cluster. Three
classes of EQ modes and two classes of BM modes were found in linear operators,
defining a 6-class taxonomy. The theoretical/methodological framework
introduced was applied in a case study considering the equal-weights uniform
operator, the NTSC standard operator, and an operator chosen as ideal to
lighten the faces of black people to improve facial recognition in current
biased classifiers. It was found that most current metrics used to assess the
quality of color-to-gray conversions better assess one of the two BM mode
classes, but the ideal operator chosen by a human team belongs to the other
class. Therefore, this cautions against using these general metrics for
specific purpose color-to-gray conversions. It should be noted that eventual
applications of this framework to non-linear operators can give rise to new
classes of EQ and BM modes. The main contribution of this article is to provide
a tool to better understand color to gray converters in general, even those
based on machine learning, within the current trend of better explainability of
models.


  Let (\Omega,\mu) be a finite measure space, X a Banach space, and let 1\le
p<\infty. The aim of this paper is to give an elementary proof of the
Diaz--Mayoral theorem that a subset V of L^p(\mu;X) is relatively compact if
and only if it is uniformly p-integrable, uniformly tight, and scalarly
relatively compact.


  We present a model of inflation based on the interaction between a
homogeneous and isotropic configuration of a U(1) gauge field and fermionic
charge density $\mathcal{J}_{0}$. The regulated fermionic charge density is
generated from a Bunch-Davies vacuum state using the methods of Koksma and
Prokopec \cite{Koksma:2009tc}, and is found to redshift as $1/a(\eta)$. The
time-like component of gauge field is sourced by the fermionic charge leading
to a growth in the gauge field $A(\eta)_{0}\sim a(\eta)$. As a result inflation
is dominated by the energy density contained in the gauge field and fermionic
charge interaction, $A_{0}\, \mathcal{J}^{0}$, which remains constant during
inflation. We also provide a mechanism to generate a net lepton asymmetry. The
coupling of a pseudo scalar to the Chern-Simons term converts the gauge field
fluctuations into lepton number and all three Sahkarov conditions are satisfied
during inflation. Finally, the rapid oscillation of the pseudo scalar field
near its minimum thermalizes the gauge field and ends inflation. We provide the
necessary initial condition on the gauge field and fermionic charge to
simultaneously generate enough e-folds and baryon asymmetry index.


  The collective behaviour of stochastic multi-agents swarms driven by Gaussian
and non-Gaussian environments is analytically discussed in a mean-field
approach. We first exogenously implement long range mutual interactions rules
with strengths that are modulated by the real-time distance separating each
agent with the swarm barycentre. Depending on the form of this barycentric
modulation, a transition between drastically collective behaviours can be
unveiled. A behavioural bifurcation threshold due to the tradeoff between the
desynchronisation effects of the stochastic environment and the synchronising
interactions is analytically calculated. For strong enough interactions, the
emergence of a swarm soliton propagating wave is observable. Alternatively,
weaker interactions cannot overcome the environmental noise and evanescent
diffusive waves result. In a second and complementary approach, we show the the
emergent solitons can alternatively be interpreted as being the optimal
equilibrium of mean-field games (MFG) models with ad-hoc running cost functions
which are here exactly determined. The MFG's equilibria resulting from the
optimisation of individual utility functions are solitons that are therefore
endogenously generated. Hence for the classes of models here proposed, an
explicit correspondence between exogenous and endogenous interaction rules
ultimately producing similar collective effects can be explicitly constructed.
For both Gaussian and non-Gaussian environments our exact results unveil new
classes of exactly solvable mean-field games dynamics.


  We consider the prototypical "piston pump" operating on a ring, where a
circulating current is induced by means of an AC driving. This can be regarded
as a generalized Fermi-Ulam model, incorporating a finite-height moving wall
(piston) and non trivial topology (ring). The amount of particles transported
per cycle is determined by a layered structure of phase-space. Each layer is
characterized by a different drift velocity. We discuss the differences
compared with the adiabatic and Boltzmann pictures, and highlight the
significance of the "diabatic" contribution that might lead to a
counter-stirring effect.


  The large cross section for t-tbar production at the LHC and at any future
hadron collider provides a high-statistics and relatively clean environment for
a study of W boson properties: after tagging on a leptonic decay of one of the
Ws and the two b-jets, an additional W still remains in the event. We study the
prospect of making the first exclusive hadronic decay of a fundamental boson of
the standard model, using the decay modes W to pi gamma and W to pi pi pi, and
other related decays. By using strong isolation criteria, which we impose by
searching for jets with a single particle constituent, we show that the three
particle hadronic W decays have potential to be measured at the LHC. The
possibility of measuring an involved spectrum of decay products could
considerably expand our knowledge of how the W decays, and experimental
techniques acquired in making these measurements would be useful for
application to future measurements of exclusive hadronic Higgs boson decays.


  Moderators of online communities often employ comment deletion as a tool. We
ask here whether, beyond the positive effects of shielding a community from
undesirable content, does comment removal actually cause the behavior of the
comment's author to improve? We examine this question in a particularly
well-moderated community, the ChangeMyView subreddit.
  The standard analytic approach of interrupted time-series analysis
unfortunately cannot answer this question of causality because it fails to
distinguish the effect of having made a non-compliant comment from the effect
of being subjected to moderator removal of that comment. We therefore leverage
a "delayed feedback" approach based on the observation that some users may
remain active between the time when they posted the non-compliant comment and
the time when that comment is deleted. Applying this approach to such users, we
reveal the causal role of comment deletion in reducing immediate noncompliance
rates, although we do not find evidence of it having a causal role in inducing
other behavior improvements. Our work thus empirically demonstrates both the
promise and some potential limits of content removal as a positive moderation
strategy, and points to future directions for identifying causal effects from
observational data.


  The branching fractions and the decay amplitudes of B -> J/psi K^* decays are
measured in a 29.4/fb data sample collected with the Belle detector at the KEKB
electron-positron collider. The decay amplitudes of helicity states of the
J/psi K^* system are determined from the full angular distribution of the final
state particles in the transversity basis. The branching fractions are measured
to be (1.29\pm0.05\pm0.13) \times 10^{-3} for neutral mesons and
(1.28\pm0.07\pm0.14) \times 10^{-3} for charged mesons. The measured
longitudinal and transverse (perpendicular to the transversity plane)
amplitudes are |A_0|^2 = 0.62\pm0.02\pm0.03 and |A_{\perp}|^2 =
0.19\pm0.02\pm0.03, respectively. The value of |A_{\perp}|^2 shows that the CP
even component dominates in the B^0 \to J/\psi K^{*0}(K_S\pi^0) decay.


  Persistent key value stores are an important component of many distributed
data serving solutions with innovations targeted at taking advantage of growing
flash speeds. Unfortunately their performance is hampered by the need to
maintain and replicate a write ahead log to guarantee availability in the face
of machine and storage failures. Cyclone is a replicated log plug-in for key
value stores that systematically addresses various sources of this bottleneck.
It uses a small amount of non-volatile memory directly addressable by the CPU -
such as in the form of NVDIMMs or Intel 3DXPoint - to remove block oriented IO
devices such as SSDs from the critical path for appending to the log. This
enables it to address network overheads using an implementation of the RAFT
consensus protocol that is designed around a userspace network stack to relieve
the CPU of the burden of data copies. Finally, it provides a way to efficiently
map the commutativity in key-value store APIs to the parallelism available in
commodity NICs. Cyclone is able to replicate millions of small updates per
second using only commodity 10 gigabit ethernet adapters. As a practical
application, we use it to improve the performance (and availability) of
RocksDB, a popular persistent key value store by an order of magnitude when
compared to its own write ahead log without replication.


  We present the first calculation of the $x$-dependence of the isovector
transversity generalized parton distributions (GPDs) for the proton within
lattice QCD. We compute the matrix elements with non-local operators containing
a Wilson line. The calculation implements the Breit symmetric frame. The proton
momenta are chosen as $0.83,\,1.25,\,1.67$ GeV, and the values of the momentum
transfer squared are $0.69,\,1.02$ GeV$^2$. These combinations include cases
with zero and nonzero skewness. The calculation is performed using one ensemble
of two degenerate-mass light, a strange and a charm quark of maximally twisted
mass fermions with a clover term. The lattice results are renormalized
non-perturbatively and finally matched to the light-cone GPDs using one-loop
perturbation theory within the framework of large momentum effective theory.
The final GPDs are given in the $\overline{\rm MS}$ scheme at a scale of 2 GeV.
In addition to the individual GPDs, we form the combination of the transversity
GPDs that is related to the transverse spin structure of the proton. Finally,
we extract the lowest two moments of GPDs and draw a number of important
qualitative conclusions.


  The electronic properties and optical excitations are investigated in the
geometry- and field-modulated bilayer graphene systems, respectively, by using
the tight-binding model and Kubo formula. The stacking symmetry of bilayer
graphene can be manipulated by varying the width and position of domain wall
(DW) within two normally stacked graphene. All the layer-dependent atomic
interactions are taken into consideration under external fields. The modulation
of stacking configuration gives rise to significant effects of zone folding on
energy subbands, subenvelope wave functions, density of states, and optical
absorption spectra. This study clearly illustrates the diverse 1D phenomena in
the energy band structure and absorption spectra; the DW- and $V_z$-created
dramatic variations are comprehensively explored under accurate calculations
and delicate analysis. Concise physical pictures are proposed to give further
insight into the quasi-1D behaviors.


  We introduce and investigate the stochastic dynamics of the density of local
extrema (minima and maxima) of non-equilibrium surface fluctuations. We give a
number of exact, analytic results for interface fluctuations described by
linear Langevin equations, and for on-lattice, solid-on-solid surface growth
models. We show that in spite of the non-universal character of the quantities
studied, their behavior against the variation of the microscopic length scales
can present generic features, characteristic to the macroscopic observables of
the system. The quantities investigated here present us with tools that give an
entirely un-orthodox approach to the dynamics of surface morphologies: a
statistical analysis from the short wavelength end of the Fourier decomposition
spectrum. In addition to surface growth applications, our results can be used
to solve the asymptotic scalability problem of massively parallel algorithms
for discrete event simulations, which are extensively used in Monte-Carlo type
simulations on parallel architectures.


  In isolated nonlinear optical waveguide arrays with bounded energy spectrum,
simultaneous conservation of energy and power of the optical modes enables
study of coupled thermal and particle transport in the negative temperature
regime. Here, based on exact numerical simulation and rationale from Landauer
formalism, we predict generic violation of the Wiedemann-Franz law in such
systems. This is rooted in the spectral decoupling of thermal and power current
of optical modes, and their different temperature dependence. Our work extends
the study of coupled thermal and particle transport into unprecedented regimes,
not reachable in natural condensed matter and atomic gas systems.


  We discuss the dependence of running couplings on the choice of
regularization method in a general softly-broken N=1 supersymmetric theory.
Regularization by dimensional reduction respects supersymmetry, but standard
dimensional regularization does not. We find expressions for the differences
between running couplings in the modified minimal subtraction schemes of these
two regularization methods, to one loop order. We also find the two-loop
renormalization group equations for gaugino masses in both schemes, and discuss
the application of these results to the Minimal Supersymmetric Standard Model.


  We study D-branes in SU(2) WZW model by means of the boundary state
techniques. We realize the ``fuzzy sphere'' configuration of multiple D0-branes
as the boundary state with the insertion of suitable Wilson line. By making use
of the path-integral representation we show that this boundary state preserves
the appropriate boundary conditions and leads to the Cardy state describing a
spherical D2-brane under the semi-classical approximation. This result directly
implies that the spherical D2-brane in SU(2) WZW model can be well described as
the bound state of D0-branes.
  After presenting the supersymmetric extension, we also investigate the BPS
and the non-BPS configurations of D-branes in the NS5 background. We
demonstrate that the non-BPS configurations are actually unstable, since they
always possess the open string tachyons. We further notice that the stable BPS
bound state constructed by the tachyon condensation is naturally interpreted as
the brane configuration of fuzzy sphere.


  We present a theory of frequency-dependent counting statistics of electron
transport through nanostructures within the framework of Markovian quantum
master equations. Our method allows the calculation of finite-frequency current
cumulants of arbitrary order, as we explicitly show for the second- and
third-order cumulants. Our formulae generalize previous zero-frequency
expressions in the literature and can be viewed as an extension of MacDonald's
formula beyond shot noise. When combined with an appropriate treatment of
tunneling, using, e.g. Liouvillian perturbation theory in Laplace space, our
method can deal with arbitrary bias voltages and frequencies, as we illustrate
with the paradigmatic example of transport through a single resonant level
model. We discuss various interesting limits, including the recovery of the
fluctuation-dissipation theorem near linear response, as well as some drawbacks
inherent of the Markovian description arising from the neglect of quantum
fluctuations.


  We consider a nonlocal parabolic equation describing the dynamics of a
population structured by a spatial position and a phenotypic trait, submitted
to dispersion , mutations and growth. The growth term may be of the Fisher-KPP
type but may also be subject to an Allee effect which can be weak (non-KPP
monostable nonlinearity, possibly degenerate) or strong (bistable
nonlinearity). The type of growth depends on the value of a variable $\theta$ :
the Allee threshold, which is considered here as an evolutionary trait. After
proving the well-posedness of the Cauchy problem, we study the long time
behavior of the solutions. Due to the richness of the model and the interplay
between the various phenomena and the nonlocality of the growth term, the
outcomes (extinction vs. persistence) are various and in sharp contrast with
earlier results of the existing literature on local reaction-diffusion
equations.


  In his recently discovered handwritten notes on "An alternate way to handle
electrodynamics" dated on 1963, Richard P. Feynman speculated with the idea of
getting the inhomogeneous Maxwell's equations for the electric and magnetic
fields from the wave equation for the vector potential. With the aim of
implementing this pedagogically interesting idea, we develop in this paper the
approach of introducing the scalar and vector potentials before the electric
and magnetic fields. We consider the charge conservation expressed through the
continuity equation as a basic axiom and make a heuristic handle of this
equation to obtain the retarded scalar and vector potentials, whose wave
equations yield the homogeneous and inhomogeneous Maxwell's equations. We also
show how this axiomatic-heuristic procedure to obtain Maxwell's equations can
be formulated covariantly in the Minkowski spacetime.


  Recently there has been progress on the calculation of three-point functions
with two "heavy" operators via semiclassical methods. We extend this analysis
to the case of the Lunin-Maldacena background, and examine the suggested
procedure for several simple string solutions. By making use of AdS/CFT
duality, we derive the relevant correlation functions of operators belonging to
the dual N=1 superconformal gauge theory, and recover an important relation
connecting the dimensions of "heavy" states and the structure constants.


  In 2014, Reeder and Yu constructed epipelagic representations of a reductive
$p$-adic group $G$ from stable functions on shallowest Moy-Prasad quotients. In
this paper, we extend these methods when $G$ is split. In particular, we
classify all complex-valued characters vanshing on a slightly deeper Moy-Prasad
subgroup and show that, while sufficient, a naive extension of Reeder-Yu's
stability condition is not necessary for constructing supercuspidal
representations.


  Jech proved that every partially ordered set can be embedded into the
cardinals of some model of $ZF$. We extend this result to show that every
partially ordered set can be embedded into the cardinals of some model of
$ZF+DC_{<\kappa}$ for any regular $\kappa$. We use this theorem to show that
for all $\kappa$, the assumption of $DC_\kappa$ does not entail that there are
no decreasing chains of cardinals. We also show how to extend the result to and
embed into the cardinals a proper class which is definable over the ground
model. We use this extension to give a large cardinals-free proof of
independence of the weak choice principle known as $WISC$.


  We propose to generalize Bekenstein model for the time variation of the fine
structure "constant" $\alpha_{em}$ to QCD strong coupling constant $\alpha_S$.
We find that, except for a ``fine tuned'' choice of the free parameters, the
extension can not be performed trivially without being in conflict with
experimental constraints and this rules out $\alpha_S$ variability. This is due
largely to the huge numerical value of the QCD vacuum gluon condensate when
compared to the matter density of the universe.


  Corrections to scaling in the 3D Ising model are studied based on Monte Carlo
(MC) simulation results for very large lattices with linear lattice sizes up to
L=3456. Our estimated values of the correction-to-scaling exponent omega tend
to decrease below the usually accepted value about 0.83 when the smallest
lattice sizes are discarded from the fits. This behavior apparently confirms
some of the known estimates of the Monte Carlo renormalization group (MCRG)
method, i.e., omega about 0.7 and omega = 0.75(5). We discuss the possibilities
that omega is either really smaller than usually expected or these values of
omega describe some transient behavior. We propose refining MCRG simulations
and analysis to resolve this issue. In distinction from omega, our actual MC
estimations of the critical exponents eta and nu provide stable values
eta=0.03632(13) and nu=0.63017(31), which well agree with those of the
conformal bootstrap method, i.e., eta=0.0362978(20) and nu=0.6299709(40).


  We study Gutzwiller-correlated wave functions as variational ground states
for the two-impurity Anderson model (TIAM) at particle-hole symmetry as a
function of the impurity separation ${\bf R}$. Our variational state is
obtained by applying the Gutzwiller many-particle correlator to a
single-particle product state. We determine the optimal single-particle product
state fully variationally from an effective non-interacting TIAM that contains
a direct electron transfer between the impurities as variational degree of
freedom. For a large Hubbard interaction $U$ between the electrons on the
impurities, the impurity spins experience a Heisenberg coupling proportional to
$V^2/U$ where $V$ parameterizes the strength of the on-site hybridization. For
small Hubbard interactions we observe weakly coupled impurities. In general,
for a three-dimensional simple cubic lattice we find discontinuous quantum
phase transitions that separate weakly interacting impurities for small
interactions from singlet pairs for large interactions.


  Incorporating dynamic contact networks and delayed awareness into a contagion
model with memory, we study the spreading patterns of infectious diseases in
connected populations. It is found that the spread of an infectious disease is
not only related to the past exposures of an individual to the infected but
also to the time scales of risk perception reflected in the social network
adaptation. The epidemic threshold $p_{c}$ is found to decrease with the rise
of the time scale parameter s and the memory length T, they satisfy the
equation $p_{c} =\frac{1}{T}+ \frac{\omega T}{<k>a^s(1-e^{-\omega T^2/a^s})}$.
Both the lifetime of the epidemic and the topological property of the evolved
network are considered. The standard deviation $\sigma_{d}$ of the degree
distribution increases with the rise of the absorbing time $t_{c}$, a power-law
relation $\sigma_{d}=mt_{c}^\gamma$ is found.


  Suppose that a countably $n$-rectifiable set $\Gamma_0$ is the support of a
multiplicity-one stationary varifold in $\mathbb{R}^{n+1}$ with a point
admitting a flat tangent plane $T$ of density $Q \geq 2$. We prove that, under
a suitable assumption on the decay rate of the blow-ups of $\Gamma_0$ towards
$T$, there exists a non-constant Brakke flow starting with $\Gamma_0$. This
shows non-uniqueness of Brakke flow under these conditions, and suggests that
the stability of a stationary varifold with respect to mean curvature flow may
be used to exclude the presence of flat singularities.


  Single-file transport, which corresponds to the diffusion of particles that
cannot overtake each other in narrow channels, is an important topic in
out-of-equilibrium statistical physics. Various microscopic models of
single-file systems have been considered, such as the simple exclusion process,
which has reached the status of a paradigmatic model. Several different models
of single-file diffusion have been shown to be related by a duality relation,
which holds either microscopically or only in the hydrodynamic limit of large
time and large distances. Here, we show that, within the framework of
fluctuating hydrodynamics, these relations are not specific to these models and
that, in the hydrodynamic limit, every single-file system can be mapped onto a
dual single-file system, which we characterise. This general duality relation
allows us to obtain new results for different models, by exploiting the
solutions that are available for their dual model.


  For extremely large telescopes, adaptive optics will be required to correct
the Earth's turbulent atmosphere. The performance of tomographic adaptive
optics is strongly dependent on the vertical distribution (profile) of this
turbulence. An important way in which this manifests is the tomographic error,
arising from imperfect measurement and reconstruction of the turbulent phase at
altitude. Conventionally, a small number of reference profiles are used to
obtain this error in simulation however these profiles are not constructed to
be representative in terms of tomographic error. It is therefore unknown
whether these simulations are providing realistic performance estimates. Here,
we employ analytical adaptive optics simulation that drastically reduces
computation times to compute tomographic error for 10 691 measurements of the
turbulence profile gathered by the Stereo-SCIDAR instrument at ESO Paranal. We
assess for the first time the impact of the profile on tomographic error in a
statistical manner. We find, in agreement with previous work, that the
tomographic error is most directly linked with the distribution of turbulence
into discrete, stratified layers. Reference profiles are found to provide
mostly higher tomographic error than expected, which we attribute to the fact
that these profiles are primarily composed of averages of many measurements
resulting in unrealistic, continuous distributions of turbulence. We propose
that a representative profile should be defined with respect to a particular
system, and that as such simulations with a large statistical sample of
profiles must be an important step in the design process.


  The reported work points at developing a practical approach for power
transmission planners to secure power networks from potential deliberate
attacks. We study the interaction between a system planner (defender) and a
rational attacker who threatens the operation of the power grid. In addition to
the commonly used hardening strategy for protecting the network, a new sort of
resource is introduced under the deception concept. Feint and deception are
acknowledged as effective tools for misleading the attacker in strategic
planning. To this end, the defender deception is mathematically formulated by
releasing misinformation about his plan in the shared cognition-based model. To
reduce the risk of damage in case of deception failure, preemptive-goal
programming is utilized to prioritize the hardening strategy for the vital
components. Furthermore, the value of posturing is introduced which is the
benefits that the deception brings to the system. The problems are formulated
as tri-level mixed-integer linear programming and solved by the
constraint-and-column generation method. Comprehensive simulation studies
performed on WSCC 9-bus and IEEE 118-bus systems indicate how the defender will
save significant cost from protecting his network with posturing rather than
hardening and the proposed approach is a promising development to ensure the
secure operation of power networks.


  All orientation preserving isometries of the hyperbolic three-space are
studied, and the probability density of conjugate pair separations for each
isometry is presented. The study is relevant for the cosmic crystallography,
and is the theoretical counterpart of the mean histograms arising from computer
simulations of the isometries.


  When used in quantum state estimation, projections onto mutually unbiased
bases have the ability to maximize information extraction per measurement and
to minimize redundancy. We present the first experimental demonstration of
quantum state tomography of two-qubit polarization states to take advantage of
mutually unbiased bases. We demonstrate improved state estimation as compared
to standard measurement strategies and discuss how this can be understood from
the structure of the measurements we use. We experimentally compared our method
to the standard state estimation method for three different states and observe
that the infidelity was up to 1.84+/-0.06 times lower using our technique than
it was using standard state estimation methods.


  Let G be the group A_4 or Z_2xZ_2. We compute the integral of \lambda_g on
the Hurwitz locus H_G\subset M_g of curves admitting a degree 4 cover of P^1
having monodromy group G. We compute the generating functions for these
integrals and write them as a trigonometric expression summed over the positive
roots of the E_6 and D_4 root systems respectively. As an application, we prove
the Crepant Resolution Conjecture for the orbifolds [C^3/A_4] and
[C^3/(Z_2xZ_2)].


  We prove that the integrated density of states (IDS) associated to a random
Schroedinger operator is locally uniformly Hoelder continuous as a function of
the disorder parameter lambda. In particular, we obtain convergence of the IDS,
as lambda tends to 0, to the IDS for the unperturbed operator at all energies
for which the IDS for the unperturbed operator is continuous in energy.


  We study the thermodynamics associated to topological black hole solutions of
AdS gravity coupled to nonlinear electrodynamics (Born-Infeld) in any
dimension, using a background-independent regularization prescription for the
Euclidean action given by boundary terms which explicitly depend on the
extrinsic curvature (Kounterterms series). A finite action principle leads to
the correct definition of thermodynamic variables as Noether charges, which
satisfy a Smarr-like relation. In particular, for the odd-dimensional case, a
consistent thermodynamic description is achieved if the internal energy of the
system includes the vacuum energy for AdS spacetime.


  Long non-coding RNA, microRNA, and messenger RNA enable key regulations of
various biological processes through a variety of diverse interaction
mechanisms. Identifying the interactions and cross-talk between these
heterogeneous RNA classes is essential in order to uncover the functional role
of individual RNA transcripts, especially for unannotated and newly-discovered
RNA sequences with no known interactions. Recently, sequence-based deep
learning and network embedding methods are becoming promising approaches that
can either predict RNA-RNA interactions from a sequence or infer missing
interactions from patterns that may exist in the network topology. However, the
majority of these methods have several limitations, eg, the inability to
perform inductive predictions, to distinguish the directionality of
interactions, or to integrate various sequence, interaction, and annotation
biological datasets. We proposed a novel deep learning-based framework,
rna2rna, which learns from RNA sequences to produce a low-dimensional embedding
that preserves the proximities in both the interactions topology and the
functional affinity topology. In this proposed embedding space, we have
designated a two-part" source and target contexts" to capture the targeting and
receptive fields of each RNA transcript, while encapsulating the heterogenous
cross-talk interactions between lncRNAs and miRNAs. From experimental results,
our method exhibits superior performance in AUPR rates compared to state-of-art
approaches at predicting missing interactions in different RNA-RNA interaction
databases and was shown to accurately perform link predictions to novel RNA
sequences not seen at training time, even without any prior information.
Additional results suggest that our proposed framework can capture a manifold
for heterogeneous RNA sequences to discover novel functional annotations.


  Recent observations have shown that circumstellar and circumbinary discs in
young stellar binaries are often misaligned with respect to the binary orbital
plane. We analyze the tidal truncation of such misaligned discs due to torques
applied to the disc at the Lindblad resonances from the tidal forcings of the
binary. We consider eccentric binaries with arbitrary binary-disc inclination
angles. We determine the dependence of the tidal forcing strengths on the
binary parameters and show that they are complicated non-monotonic functions of
eccentricity and inclination. We adopt a truncation criterion determined by the
balance between resonant torque and viscous torque, and use it to calculate the
outer radii of circumstellar discs and the inner radii of circumbinary discs.
Misaligned circumstellar discs have systematically larger outer radii than
aligned discs, and are likely to fill their Roche lobes if inclined by more
than $45^\circ - 90^\circ$, depending on the binary mass ratio and disc
viscosity parameter. Misaligned circumbinary discs generally have smaller inner
radii than aligned discs, but the details depend sensitively on the binary and
disc parameters.


  I review the ways that have been proposed to measure the quark transversity
distribution in the nucleon. I then explain a proposal, developed by Xuemin
Jin, Jian Tang and myself, to measure transversity through the final state
interaction between two mesons ($\pi\pi$, $K \bar K$, or $\pi K$) produced in
the current fragmentation region in deep inelastic scattering on a transversely
polarized nucleon.


  We prove a characterization result in the spirit of the Kinderlehrer-Pedregal
Theorem for Young measures generated by gradients of Sobolev maps satisfying
the orientation-preserving constraint, that is the pointwise Jacobian is
positive almost everywhere. The argument to construct the appropriate
generating sequences from such Young measures is based on a variant of convex
integration in conjunction with an explicit lamination construction in matrix
space. Our generating sequence is bounded in $L^p$ for $p$ less than the space
dimension, a regime in which the pointwise Jacobian loses some of its important
properties. On the other hand, for $p$ larger than, or equal to, the space
dimension the situation necessarily becomes rigid and a construction as
presented here cannot succeed. Applications to relaxation of integral
functionals, the theory of semiconvex hulls, and approximation of weakly
orientation-preserving maps by strictly orientation-preserving ones in Sobolev
spaces are given.


  The aim of the paper is to analyze the expressive power of the square
operator of Lukasiewicz logic: $\ast x=x\odot x$, where $\odot$ is the strong
Lukasiewicz conjunction. In particular, we aim at understanding and
characterizing those cases in which the square operator is enough to construct
a finite MV-chain from a finite totally ordered set endowed with an involutive
negation. The first of our main results shows that, indeed, the whole structure
of MV-chain can be reconstructed from the involution and the Lukasiewicz square
if and only if the obtained structure has only trivial subalgebras and,
equivalently, if and only if the cardinality of the starting chain is of the
form $n+1$ where $n$ belongs to a class of prime numbers that we fully
characterize. Secondly, we axiomatize the algebraizable matrix logic whose
semantics is given by the variety generated by a finite totally ordered set
endowed with an involutive negation and Lukasiewicz's square operator. Finally,
we propose an alternative way to account for Lukasiewicz square operator on
involutive G\"odel chains. In this setting, we show that such an operator can
be captured by a rather intuitive set of equations.


  Historical palm-leaf manuscript and early paper documents from Indian
subcontinent form an important part of the world's literary and cultural
heritage. Despite their importance, large-scale annotated Indic manuscript
image datasets do not exist. To address this deficiency, we introduce
Indiscapes, the first ever dataset with multi-regional layout annotations for
historical Indic manuscripts. To address the challenge of large diversity in
scripts and presence of dense, irregular layout elements (e.g. text lines,
pictures, multiple documents per image), we adapt a Fully Convolutional Deep
Neural Network architecture for fully automatic, instance-level spatial layout
parsing of manuscript images. We demonstrate the effectiveness of proposed
architecture on images from the Indiscapes dataset. For annotation flexibility
and keeping the non-technical nature of domain experts in mind, we also
contribute a custom, web-based GUI annotation tool and a dashboard-style
analytics portal. Overall, our contributions set the stage for enabling
downstream applications such as OCR and word-spotting in historical Indic
manuscripts at scale.


  Continued fraction expansions and Hankel determinants of automatic sequences
are extensively studied during the last two decades. These studies found
applications in number theory in evaluating irrationality exponents. The
present paper is motivated by the converse problem: to study continued
fractions of which the elements form an automatic sequence. We consider two
such continued fractions defined by the Thue-Morse and period-doubling
sequences respectively, and prove that they are congruent to algebraic series
in $\mathbb{Z}[[x]]$ modulo $4$. Consequently, the sequences of the
coefficients of the power series expansions of the two continued fractions
modulo $4$ are $2$-automatic. Our approach is to first guess the explicit
formulas of certain subsequences of $(P_n(x))$ and $(Q_n(x))$, where
$P_n(x)/Q_n(x)$ is the canonical representation of the truncated continued
fractions, then prove these formulas by an intricate induction involving eight
subsequences while exploiting the relations between these subsequences.


  We show that the perfect matching problem in general graphs is in Quasi-NC.
That is, we give a deterministic parallel algorithm which runs in $O(\log^3 n)$
time on $n^{O(\log^2 n)}$ processors. The result is obtained by a
derandomization of the Isolation Lemma for perfect matchings, which was
introduced in the classic paper by Mulmuley, Vazirani and Vazirani [1987] to
obtain a Randomized NC algorithm.
  Our proof extends the framework of Fenner, Gurjar and Thierauf [2016], who
proved the analogous result in the special case of bipartite graphs. Compared
to that setting, several new ingredients are needed due to the significantly
more complex structure of perfect matchings in general graphs. In particular,
our proof heavily relies on the laminar structure of the faces of the perfect
matching polytope.


  We investigate deconstruction of five dimensional supersymmetric abelian
gauge theories compactified on $S_1/Z_2$, with various sets of bulk and matter
multiplets. The problem of anomalies, chirality and stability in the
deconstructed theories is discussed. We find that for most of the 5d brane/bulk
matter assignments there exists the deconstructed version. There are, however,
some exceptions.


  We propose a methodology to measure the mechanical properties of membranes
from their fluctuations and apply this to optical microscopy measurements of
giant unilamellar vesicles of lipids. We analyze the effect of the projection
of thermal shape undulations across the focal depth of the microscope. We
derive an analytical expression for the mode spectrum that varies with the
focal depth and accounts for the projection of fluctuations onto the equatorial
plane. A comparison of our model with existing approaches, that use only the
apparent equatorial fluctuations without averaging out of this plane, reveals a
significant and systematic reduction in the inferred value of the bending
rigidity. Our results are in full agreement with the values measured through
X-ray scattering and other micromechanical manipulation techniques, resolving a
long standing discrepancy with these other experimental methods.


  Graph neural networks (GNNs) based methods have achieved impressive
performance on node clustering task. However, they are designed on the
homophilic assumption of graph and clustering on heterophilic graph is
overlooked. Due to the lack of labels, it is impossible to first identify a
graph as homophilic or heterophilic before a suitable GNN model can be found.
Hence, clustering on real-world graph with various levels of homophily poses a
new challenge to the graph research community. To fill this gap, we propose a
novel graph clustering method, which contains three key components: graph
reconstruction, a mixed filter, and dual graph clustering network. To be
graph-agnostic, we empirically construct two graphs which are high homophily
and heterophily from each data. The mixed filter based on the new graphs
extracts both low-frequency and high-frequency information. To reduce the
adverse coupling between node attribute and topological structure, we
separately map them into two subspaces in dual graph clustering network.
Extensive experiments on 11 benchmark graphs demonstrate our promising
performance. In particular, our method dominates others on heterophilic graphs.


  To every semigroup presentation $\mathcal{P}= \langle \Sigma \mid \mathcal{R}
\rangle$ and every baseword $w \in \Sigma^+$ can be associated a diagram group
$D(\mathcal{P},w)$, defined as the fundamental group of the so-called Squier
complex $S(\mathcal{P},w)$. Roughly speaking, $D(\mathcal{P},w)$ encodes the
lack of asphericity of $\mathcal{P}$. Examples of diagram groups include
Thompson's group $F$, the lamplighter group $\mathbb{Z} \wr \mathbb{Z}$, the
pure planar braid groups, and various right-angled Artin groups. This survey
aims at summarising what is known about the family of diagram groups.


  The packing number of a graph $G$ is the maximum number of closed
neighborhoods of vertices in $G$ with pairwise empty intersections. Similarly,
the open packing number of $G$ is the maximum number of open neighborhoods in
$G$ with pairwise empty intersections. We consider the packing and open packing
numbers on graph products. In particular we give a complete solution with
respect to some properties of factors in the case of lexicographic and rooted
products. For Cartesian, strong and direct products, we present several lower
and upper bounds on these parameters.


  We consider new performance measures for vibrational systems based on the
$H_2$ norm of linear time invariant systems. New measures will be used as an
optimization criterion for the optimal damping of vibrational systems. We
consider both theoretical and concrete cases in order to show how new measures
stack up against the standard measures. The quality and advantages of new
measures as well as the behaviour of optimal damping positions and
corresponding damping viscosities are illustrated in numerical experiments.


  Homotopy Type Theory may be seen as an internal language for the
$\infty$-category of weak $\infty$-groupoids which in particular models the
univalence axiom. Voevodsky proposes this language for weak $\infty$-groupoids
as a new foundation for mathematics called the Univalent Foundations of
Mathematics. It includes the sets as weak $\infty$-groupoids with contractible
connected components, and thereby it includes (much of) the traditional set
theoretical foundations as a special case. We thus wonder whether those
`discrete' groupoids do in fact form a (predicative) topos. More generally,
homotopy type theory is conjectured to be the internal language of `elementary'
$\infty$-toposes. We prove that sets in homotopy type theory form a $\Pi
W$-pretopos. This is similar to the fact that the $0$-truncation of an
$\infty$-topos is a topos. We show that both a subobject classifier and a
$0$-object classifier are available for the type theoretical universe of sets.
However, both of these are large and moreover, the $0$-object classifier for
sets is a function between $1$-types (i.e. groupoids) rather than between sets.
Assuming an impredicative propositional resizing rule we may render the
subobject classifier small and then we actually obtain a topos of sets.


  The prototypical $\alpha\to\omega$ phase transition in zirconium is an ideal
test-bed for our understanding of polymorphism under extreme loading
conditions. After half a century of study, a consensus had emerged that the
transition is realized via one of two distinct displacive mechanisms, depending
on the nature of the compression path. However, recent dynamic-compression
experiments equipped with in situ diffraction diagnostics performed in the past
few years have revealed new transition mechanisms, demonstrating that our
understanding of the underlying atomistic dynamics and transition kinetics is
in fact far from complete. We present classical molecular dynamics simulations
of the $\alpha\to\omega$ phase transition in single-crystal zirconium
shock-compressed along the [0001] axis using a machine-learning-class
potential. The transition is predicted to proceed primarily via a modified
version of the two-stage Usikov-Zilberstein mechanism, whereby the
high-pressure $\omega$-phase heterogeneously nucleates at boundaries between
grains of an intermediate $\beta$-phase. We further observe the fomentation of
atomistic disorder at the junctions between $\beta$ grains, leading to the
formation of highly defective interstitial material between the $\omega$
grains. We directly compare synthetic x-ray diffraction patterns generated from
our simulations with those obtained using femtosecond diffraction in recent
dynamic-compression experiments, and show that the simulations produce the same
unique, anisotropic diffuse scattering signal unlike any previously seen from
an elemental metal. Our simulations suggest that the diffuse signal arises from
a combination of thermal diffuse scattering, nanoparticle-like scattering from
residual kinetically stabilized $\alpha$ and $\beta$ grains, and scattering
from interstitial defective structures.


  LangXAI is a framework that integrates Explainable Artificial Intelligence
(XAI) with advanced vision models to generate textual explanations for visual
recognition tasks. Despite XAI advancements, an understanding gap persists for
end-users with limited domain knowledge in artificial intelligence and computer
vision. LangXAI addresses this by furnishing text-based explanations for
classification, object detection, and semantic segmentation model outputs to
end-users. Preliminary results demonstrate LangXAI's enhanced plausibility,
with high BERTScore across tasks, fostering a more transparent and reliable AI
framework on vision tasks for end-users.


  We introduce a modified divergence law for the energy-momentum tensor in the
theory of unimodular relativity. Consequently, an additional equation for the
measure field follows from the divergence of the field equations. The equations
of motion are derived and the weak-field, low-velocity limit is investigated.
It is found that the gravitational acceleration acquires a term that is
proportional to the gradient of the mass density. We show that this term can
provide the additional acceleration observed on astrophysical scales without
the need for dark matter.


  Modern high-energy particle accelerators and Free-Electron Lasers incorporate
large quantities of sensitive RF and microwave frequency devices distributed
over kilometer distances. Such devices require extreme stable phase and time
synchronization by means of high frequency signal distributed along the
accelerator facility. Coaxial cables are commonly used to distribute the
reference signal over the large machine to synchronize electronic systems and
they are the main source of undesirable phase drifts in the synchronization
system. Signal phase drifts in cables are mainly caused by temperature and
humidity variations and their values usually exceed required phase
synchronization accuracy by more than order of magnitude. There are several
approaches to reduce signal phase drifts in coaxial cables. This paper
describes the realization of active phase stabilization system based on
interference phenomenon. A phase-locked signal from the transmitter is
reflected at the end of a coaxial cable link. Directional couplers placed along
the cable pick up the forward and reflected signals and interfere them to
cancel out the cable phase drifts. Distributed hardware including
interferometer controller/transmitter and receiver modules were built to
demonstrate system concept and performance. Link input and output devices used
FPGA I/O boards with Ethernet interface to control system operation.
Specialized firmware and software was developed to calibrate and control the
system. This paper describes the concept of interferometer link, designed
hardware, basic control algorithms and performance evaluation results. The link
prototype was built to distribute 1.3 GHz signal through a coaxial cable.
Measured phase drift suppression factor value exceeded level of 100.


  The bus system is a critical component of sustainable urban transportation.
However, due to the significant uncertainties in passenger demand and traffic
conditions, bus operation is unstable in nature and bus bunching has become a
common phenomenon that undermines the reliability and efficiency of bus
services. Despite recent advances in multi-agent reinforcement learning (MARL)
on traffic control, little research has focused on bus fleet control due to the
tricky asynchronous characteristic -- control actions only happen when a bus
arrives at a bus stop and thus agents do not act simultaneously. In this study,
we formulate route-level bus fleet control as an asynchronous multi-agent
reinforcement learning (ASMR) problem and extend the classical actor-critic
architecture to handle the asynchronous issue. Specifically, we design a novel
critic network to effectively approximate the marginal contribution for other
agents, in which graph attention neural network is used to conduct inductive
learning for policy evaluation. The critic structure also helps the ego agent
optimize its policy more efficiently. We evaluate the proposed framework on
real-world bus services and actual passenger demand derived from smart card
data. Our results show that the proposed model outperforms both traditional
headway-based control methods and existing MARL methods.


  Mild cognitive impairment (MCI) leading to dementia results in a
constellation of psychiatric disorders including depression, mood disorders,
schizophrenia and others. With increasing age, mild cognitive impairment leads
to increased disability-adjusted life-years and healthcare burden. A huge
number of drug trials for the treatment of MCI associated with Alzheimer's
disease have undergone failure leading to the development of drugs that could
avert the progression of the disease. However, some novel non-drug-based
therapies like ultrasound ablation of amyloid plaques have influenced
researchers to explore the non-pharmacological modalities for the treatment of
mild cognitive impairment.
  To compensate for neurodegenerative loss resulting in coexisting psychiatric
disorders, neurofeedback therapy has also been proven to improve behavioural
outcomes by inducing neuroplasticity. The aim of the current review is to
highlight the pathophysiological aspects of mild cognitive impairment leading
to dementia that could be addressed with no pharmacological interventions and
to understand the mechanisms behind the effects of these interventions.


  Multi-soliton form factors in sine-Gordon theory from the bootstrap are
compared to finite volume matrix elements computed using the truncated
conformal space approach. We find convincing agreement, and resolve most of the
issues raised in a previous work.


  The Fiber Optical Cable and Connector System, FOCCoS, for the Prime Focus
Spectrograph, PFS, is responsible for transporting light from the Subaru
Telescope focal plane to a set of four spectrographs. Each spectrograph will be
fed by a convex curved slit with 616 optical fibers organized in a linear
arrangement. The slit frontal surface is covered with a special dark composite,
made with refractory oxide, which is able to sustain its properties with
minimum quantities of abrasives during the polishing process; this stability is
obtained This stability is obtained by the detachment of the refractory oxide
nanoparticles, which then gently reinforce gently the polishing process and
increase its the efficiency. The surface roughness measured in several samples
after high performance polishing was about 0.01 microns. Furthermore, the time
for obtaining a polished surface with this quality is about 10 times less than
the time required for polishing a brass, glass or ceramic surface of the same
size. In this paper, we describe the procedure developed for high quality
polishing of this type of slit. The cylindrical polishing described here, uses
cylindrical concave metal bases on which glass paper is based. The polishing
process consists to use grid sequences of 30 microns, 12 microns, 9 microns, 5
microns, 3 microns, 1 micron and, finally, a colloidal silica on a chemical
cloth. To obtain the maximum throughput, the surface of the fibers should be
polished in such a way that they are optically flat and free from scratches.
The optical fibers are inspected with a microscope at all stages of the
polishing process to ensure high quality. The efficiency of the process may be
improved by using a cylindrical concave composite base as a substrate suitable
for diamond liquid solutions. Despite this process being completely by hand,
the final result shows a very high quality.


  When are two germs of analytic systems conjugate or orbitally equivalent
under an analytic change of coordinates in the neighborhood of a singular
point? A way to answer is to use normal forms. But there are large classes of
dynamical systems for which the change of coordinates to a normal form
diverges. In this paper we discuss the case of singularities for which the
normalizing transformation is $k$-summable, thus allowing to provide moduli
spaces. We explain the common geometric features of these singularities, and
show that the study of their unfoldings allows understanding both the
singularities themselves, and the geometric obstructions to convergence of the
normalizing transformations. We also present some moduli spaces for generic
$k$-parameter families unfolding such singularities.


  Current-day genomes bear the mark of the evolutionary processes. One of the
strongest indications is the sequence homology among families of proteins that
perform similar biological functions in different species. The number of
proteins in a family can grow over time as genetic information is duplicated
through evolution. We explore how evolution directs the size distribution of
these families. Theoretical predictions for family sizes are obtained from two
models, one in which individual genes duplicate and a second in which the
entire genome duplicates. Predictions from these models are compared with the
family size distributions for several organisms whose complete genome sequence
is known. We find that protein family size distributions in nature follow a
power-law distribution. Comparing these results to the model systems, we
conclude that genome duplication is the dominant mechanism leading to increased
genetic material in the species considered.


  A One-Dimensional (1D) Reduced-Order Model (ROM) has been developed for a 3D
Rayleigh-B\'enard convection system in the turbulent regime with Rayleigh
number $\mathrm{Ra}=10^6$. The state vector of the 1D ROM is horizontally
averaged temperature. Using the Green's Function (GRF) method, which involves
applying many localized, weak forcings to the system one at a time and
calculating the responses using long-time averaged Direct Numerical Simulations
(DNS), the system's Linear Response Function (LRF) has been computed. Another
matrix, called the Eddy Flux Matrix (EFM), that relates changes in the
divergence of vertical eddy heat fluxes to changes in the state vector, has
also been calculated. Using various tests, it is shown that the LRF and EFM can
accurately predict the time-mean responses of temperature and eddy heat flux to
external forcings, and that the LRF can well predict the forcing needed to
change the mean flow in a specified way (inverse problem). The non-normality of
the LRF is discussed and its eigen/singular vectors are compared with the
leading Proper Orthogonal Decomposition (POD) modes of the DNS data.
Furthermore, it is shown that if the LRF and EFM are simply scaled by the
square-root of Rayleigh number, they perform equally well for flows at other
$\mathrm{Ra}$, at least in the investigated range of $ 5 \times 10^5 \le
\mathrm{Ra} \le 1.25 \times 10^6$. The GRF method can be applied to develop 1D
or 3D ROMs for any turbulent flow, and the calculated LRF and EFM can help with
better analyzing and controlling the nonlinear system.


  The development of machine learning in particular and artificial intelligent
in general has been strongly conditioned by the lack of an appropriate
interface layer between deduction, abduction and induction. In this work we
extend traditional algebraic specification methods in this direction. Here we
assume that such interface for AI emerges from an adequate Neural-Symbolic
integration. This integration is made for universe of discourse described on a
Topos governed by a many-valued {\L}ukasiewicz logic. Sentences are integrated
in a symbolic knowledge base describing the problem domain, codified using a
graphic-based language, wherein every logic connective is defined by a neuron
in an artificial network. This allows the integration of first-order formulas
into a network architecture as background knowledge, and simplifies symbolic
rule extraction from trained networks. For the train of such neural networks we
changed the Levenderg-Marquardt algorithm, restricting the knowledge
dissemination in the network structure using soft crystallization. This
procedure reduces neural network plasticity without drastically damaging the
learning performance, allowing the emergence of symbolic patterns. This makes
the descriptive power of produced neural networks similar to the descriptive
power of {\L}ukasiewicz logic language, reducing the information lost on
translation between symbolic and connectionist structures. We tested this
method on the extraction of knowledge from specified structures. For it, we
present the notion of fuzzy state automata, and we use automata behaviour to
infer its structure. We use this type of automata on the generation of models
for relations specified as symbolic background knowledge.