  Previous active inference accounts of emotion translate fluctuations in free
energy to a sense of emotion, mainly focusing on valence. However, in affective
science, emotions are often represented as multi-dimensional. In this paper, we
propose to adopt a Circumplex Model of emotion by mapping emotions into a
two-dimensional spectrum of valence and arousal. We show how one can derive a
valence and arousal signal from an agent's expected free energy, relating
arousal to the entropy of posterior beliefs and valence to utility less
expected utility. Under this formulation, we simulate artificial agents engaged
in a search task. We show that the manipulation of priors and object presence
results in commonsense variability in emotional states.


  A new tecnique for the production of special shaped SPM tips is reported.
Noble metal coated tips are produced with flat and circular tip front. The
unusual truncated-cone tip shape is obtained by modifying commercial tips. The
diameter of the tip front flat area can be varied continuously in the range
0.05 - 1 micrometer.


  The origin of classical reality in our quantum world is a long-standing
mystery. Here, we examine a nitrogen vacancy center evolving naturally in the
presence of its environment to study quantum Darwinism - the proliferation of
information about preferred quantum states throughout the world via the
environment. This redundantly imprinted information accounts for the perception
of objective reality, as it is independently accessible by many without
perturbing the system of interest. To observe the emergence of redundant
information, we implement a novel dynamical decoupling scheme that enables the
measurement/control of several nuclear spins (the environment E) interacting
with a nitrogen vacancy (the system S). In addition to showing how to create
entangled SE states relevant to quantum metrology, we demonstrate that under
the decoherence of S, redundant information is imprinted onto E, giving rise to
classical objectivity - a consensus of the nuclear spins about the state of S.
This provides the first laboratory verification of the objective classical
world emerging from the underlying quantum substrate.


  The rare decay B -> K* (-> K pi) mu+ mu- is regarded as one of the crucial
channels for B physics as the polarization of the K* allows a precise angular
reconstruction resulting in many observables that offer new important tests of
the Standard Model and its extensions. These angular observables can be
expressed in terms of CP-conserving and CP-violating quantities which we study
in terms of the full form factors calculated from QCD sum rules on the
light-cone, including QCD factorization corrections. We investigate all
observables in the context of the Standard Model and various New Physics
models, in particular the Littlest Higgs model with T-parity and various MSSM
scenarios, identifying those observables with small to moderate dependence on
hadronic quantities and large impact of New Physics. One important result of
our studies is that new CP-violating phases will produce clean signals in
CP-violating asymmetries. We also identify a number of correlations between
various observables which will allow a clear distinction between different New
Physics scenarios.


  Usual analyses based on scans of the seesaw parameter-space can be biassed
since they do not cover in a fair way the complete parameter-space. More
precisely, we show that in the common "R-parametrization", many acceptable
R-matrices, compatible with the perturbativity of Yukawa couplings, are
normally disregarded from the beginning, which produces biasses in the results.
We give a straightforward procedure to scan the space of complex R-matrices in
a complete way, giving a very simple rule to incorporate the perturbativity
requirement as a condition for the entries of the R-matrix, something not
considered before. As a relevant application of this, we show that the extended
believe that BR(mu --> e, gamma) in supersymmetric seesaw models depends
strongly on the value of theta_13 is an "optical effect" produced by such
biassed scans, and does not hold after a careful analytical and numerical
study. When the complete scan is done, BR(mu --> e, gamma) gets very
insensitive to theta_13. Moreover, the values of the branching ratio are
typically larger than those quoted in the literature, due to the large number
of acceptable points in the parameter-space which were not considered before.
Including (unflavoured) leptogenesis does not introduce any further dependence
on theta_13, although decreases the typical value of BR(mu --> e, gamma).


  Determining the relative position and orientation of objects in an
environment is a fundamental building block for a wide range of robotics
applications. To accomplish this task efficiently in practical settings, a
method must be fast, use common sensors, and generalize easily to new objects
and environments. We present MSL-RAPTOR, a two-stage algorithm for tracking a
rigid body with a monocular camera. The image is first processed by an
efficient neural network-based front-end to detect new objects and track 2D
bounding boxes between frames. The class label and bounding box is passed to
the back-end that updates the object's pose using an unscented Kalman filter
(UKF). The measurement posterior is fed back to the 2D tracker to improve
robustness. The object's class is identified so a class-specific UKF can be
used if custom dynamics and constraints are known. Adapting to track the pose
of new classes only requires providing a trained 2D object detector or labeled
2D bounding box data, as well as the approximate size of the objects. The
performance of MSL-RAPTOR is first verified on the NOCS-REAL275 dataset,
achieving results comparable to RGB-D approaches despite not using depth
measurements. When tracking a flying drone from onboard another drone, it
outperforms the fastest comparable method in speed by a factor of 3, while
giving lower translation and rotation median errors by 66% and 23%
respectively.


  We use the Galaxy Evolution Explorer (GALEX) Medium and All-Sky-Imaging
Survey (MIS & AIS) data from the first public data release (GR1), matched to
the Sloan Digital Sky Survey (SDSS) DR3 catalog, to perform source
classification. The GALEX surveys provide photometry in far- and near-UV bands
and the SDSS in five optical bands (u,g,r,i,z). The GR1/DR3 overlapping areas
are 363[83]deg^2 for the GALEX AIS[MIS], for sources within the 0.5deg central
area of the GALEX fields. Our sample covers mostly |b|>30deg galactic
latitudes. We present statistical properties of the GALEX/SDSS matched sources
catalog, containing >2x10^6 objects detected in at least one UV band. We
classify the matched sources by comparing the seven-band photometry to model
colors constructed for different classes of astrophysical objects. For sources
with photometric errors <0.3 mag, the corresponding typical AB-magnitude limits
are m_FUV~21.5, m_NUV~22.5 for AIS, and m_FUV~24, m_NUV~24.5 for MIS. At AIS
depth, the number of Galactic and extragalactic objects are comparable, but the
latter predominate in the MIS. Based on our stellar models, we estimate the
GALEX surveys detect hot White Dwarfs throughout the Milky Way halo (down to a
radius of 0.04 R_sun at MIS depth), providing an unprecedented improvement in
the Galactic WD census. Their observed surface density is consistent with Milky
Way model predictions. We also select low-redshift QSO candidates, extending
the known QSO samples to lower magnitudes, and providing candidates for
detailed z~1 follow-up investigations. SDSS optical spectra available for a
large subsample confirm the classification for the photometrically selected
candidates with 97% purity for single hot stars, ~45%(AIS)/31%(MIS) for
binaries containing a hot star and a cooler companion, and about 85% for QSOs.


  Internet of Things (IoT) systems in general consist of a lot of devices with
massive connectivity. Those devices are usually constrained with limited energy
supply and can only operate at low power and low rate. In this paper, we
investigate a cellular-based IoT system combined with energy harvesting and
NOMA. We consider all base stations (BS) and IoT devices follow the Poisson
Point Process (PPP) distribution in a given area. The unit time slot is divided
into two phases, energy harvesting phase in downlink (DL) and data transmission
phase in uplink (uplink). That is, IoT devices will first harvest energy from
all BS transmissions and then use the harvested energy to do the NOMA
information transmission. We define an energy harvesting circle within which
all IoT devices can harvest enough energy for NOMA transmission. The design
objective is to maximize the total throughput in uplink within the circle by
varying the duration T of energy harvesting phase. In our work, we also
consider the inter-cell interference in the throughput calculation. The
analysis of Probability Mass Function (PMF) for IoT devices in the energy
harvesting circle is also compared with simulation results. It is shown that
the BS density needs to be carefully set so that the IoT devices in the energy
harvesting circle receive relatively smaller interference and energy circles
overlap only with a small probability. Our simulations show that there exists
an optimal T to achieve the maximum throughput. When the BSs are densely
deployed consequently the total throughput will decrease because of the
interference.


  We study the adjacency matrix of the Linial-Meshulam complex model, which is
a higher-dimensional generalization of the Erd\H{o}s-R\'enyi graph model.
Recently, Knowles and Rosenthal proved that the empirical spectral distribution
of the adjacency matrix is asymptotically given by Wigner's semicircle law in a
diluted regime. In this article, we prove a central limit theorem for the
linear eigenvalue statistics for test functions of polynomial growth that is of
class $C^{2}$ on a closed interval. The proof is based on higher-dimensional
combinatorial enumerations and concentration properties of random symmetric
matrices. Furthermore, when the test function is a polynomial function, we
obtain the explicit formula for the variance of the limiting Gaussian
distribution.


  We extend two of the methods previously introduced to find discrete
symmetries of differential equations to the case of difference and
differential-difference equations. As an example of the application of the
methods, we construct the discrete symmetries of the discrete Painlev\'e I
equation and of the Toda lattice equation.


  Our knowledge about the "cold" Universe often relies on molecular spectra. A
general property of such spectra is that the energy level populations are
rarely at local thermodynamic equilibrium. Solving the radiative transfer thus
requires the availability of collisional rate coefficients with the main
colliding partners over the temperature range 10-1000 K. These rate
coefficients are notoriously difficult to measure and expensive to compute. In
particular, very few reliable collisional data exist for collisions involving
reactive radicals or ions. Here we explore the use of a fast quantum
statistical method to determine molecular collisional excitation rate
coefficients. The method is benchmarked against accurate (but costly)
close-coupling calculations. For collisions proceeding through the formation of
a strongly-bound complex, the method is found to be highly satisfactory up to
room temperature. Its accuracy decreases with the potential well depth and with
increasing temperature, as expected. This new method opens the way to the
determination of accurate inelastic collisional data involving key reactive
species such as H3+, H2O+, and H3O+ for which exact quantum calculations are
currently not feasible.


  Differential Evolution (DE) proved to be one of the most successful
evolutionary algorithms for global optimization purposes in continuous
problems. The core operator in DE is mutation which can provide the algorithm
with both exploration and exploitation. In this article, a new notation for DE
is proposed which has a formula that can be utilized for generating and
extracting novel mutations and by applying this new notation, four novel
mutations are proposed. More importantly, by combining these novel trial vector
generation strategies and four other well-known ones, we proposed Generalized
Mutation Differential Evolution (GMDE) that takes advantage of two mutation
pools that have both explorative and exploitative strategies inside them.
Results and experimental analysis are performed on CEC2005 benchmarks and the
results stated that GMDE is surprisingly competitive and significantly improved
the performance of this algorithm. Finally, GMDE is also applied to parameters
optimization, modification and improvement of a feature selection method for
cancer classification purposes over gene expression microarray profiles.


  (On behalf of the JUNO Collaboration) The Jiangmen Underground Neutrino
Observatory (JUNO) is an underground 20 kton liquid scintillator detector being
built in the south of China and expected to start data taking in 2020. JUNO has
a physics programme focused on neutrino properties using electron
anti-neutrinos emitted from two near-by nuclear power plants. Its primary aim
is to determine the neutrino mass hierarchy from the ${{\bar{\nu}_e}}$
oscillation pattern. With an unprecedented relative energy resolution of 3$\%$
as target, JUNO will be able to do so with a statistical significance of 3-4
$\sigma$ within six years of running. It will also measure other oscillation
parameters to an accuracy better than 1$\%$. An ambitious experimental
programme is in place to develop and optimize the detector and the calibration
system, to maximize the light yield and minimize energy biases. JUNO will also
be in a good position to study neutrinos from the sun and the earth and from
supernova explosions, as well as provide a large acceptance for the search for
proton decay. JUNO's physics potential was described and the status of its
construction reviewed in my talk at the conference.


  The gravitational-wave and accretion driven evolution of the angular
velocity, core temperature, and (small) amplitude of an r-mode of neutron stars
in low mass X-ray binaries and similar systems is investigated. The conditions
required for evolution to a stable equilibrium state (with gravitational wave
flux proportional to average X-ray flux) are determined. In keeping with
conclusions derived from observations of neutron star cooling, the core
neutrons are taken to be normal while the core protons and hyperons and the
crust neutrons are taken to be singlet superfluids. The dominant sources of
damping are then hyperon bulk viscosity (if much of the core is at least 2--3
times nuclear density) and (e-e and n-n) shear (and possibly magnetic)
viscosity within the core--crust boundary layer. It is found that a stable
equilibrium state can be reached if the superfluid transition temperature of
the hyperons is sufficiently small ($\lesssim 2\times 10^9$ K), allowing the
gravitational radiation from Sco X-1 and several other neutron stars in
low-mass X-ray binaries to be potentially detectable by the second generation
LIGO (and VIRGO) arrays.


  In stochastic multistable systems driven by the gradient of a potential,
transitions between equilibria is possible because of noise. We study the
ability of linear delay feedback control to mitigate these transitions,
ensuring that the system stays near a desirable equilibrium. For small delays,
we show that the control term has two effects: i) a stabilizing effect by
deepening the potential well around the desirable equilibrium, and ii) a
destabilizing effect by intensifying the noise by a factor of
$(1-\tau\alpha)^{-1/2}$, where $\tau$ and $\alpha$ denote the delay and the
control gain, respectively. As a result, successful mitigation depends on the
competition between these two factors. We also derive analytical results that
elucidate the choice of the appropriate control gain and delay that ensure
successful mitigations. These results eliminate the need for any Monte Carlo
simulations of the stochastic differential equations, and therefore
significantly reduce the computational cost of determining the suitable control
parameters. We demonstrate the application of our results on two examples.


  The lifelong efforts of Paul A. M. Dirac were to construct localized quantum
systems in the Lorentz covariant world. In 1927, he noted that the time-energy
uncertainty should be included in the Lorentz-covariant picture. In 1945, he
attempted to construct a representation of the Lorentz group using a
normalizable Gaussian function localized both in the space and time variables.
In 1949, he introduced his instant form to exclude time-like oscillations. He
also introduced the light-cone coordinate system for Lorentz boosts. Also in
1949, he stated the Lie algebra of the inhomogeneous Lorentz group can serve as
the uncertainty relations in the Lorentz-covariant world. It is possible to
integrate these three papers to produce the harmonic oscillator wave function
which can be Lorentz-transformed. In addition, Dirac, in 1963, considered two
coupled oscillators to derive the Lie algebra for the generators of the
$O(3,\,2)$ de Sitter group, which has ten generators. It is proven possible to
contract this group to the inhomogeneous Lorentz group with ten generators,
which constitute the fundamental symmetry of quantum mechanics in Einstein's
Lorentz-covariant world.


  Multimodal demand forecasting aims at predicting product demand utilizing
visual, textual, and contextual information. This paper proposes a method for
multimodal product demand forecasting using convolutional, graph-based, and
transformer-based architectures. Traditional approaches to demand forecasting
rely on historical demand, product categories, and additional contextual
information such as seasonality and events. However, these approaches have
several shortcomings, such as the cold start problem making it difficult to
predict product demand until sufficient historical data is available for a
particular product, and their inability to properly deal with category
dynamics. By incorporating multimodal information, such as product images and
textual descriptions, our architecture aims to address the shortcomings of
traditional approaches and outperform them. The experiments conducted on a
large real-world dataset show that the proposed approach effectively predicts
demand for a wide range of products. The multimodal pipeline presented in this
work enhances the accuracy and reliability of the predictions, demonstrating
the potential of leveraging multimodal information in product demand
forecasting.


  Let G be a finite abelian group and F a field such that char(F) does not
divide |G|. Denote by FG the group algebra of G over F. A (semisimple) abelian
code is an ideal of FG. Two codes I and J of FG are G-equivalent if there
exists an automorphism of G whose linear extension to FG maps I onto J In this
paper we give a necessary and sufficient condition for minimal abelian codes to
be G-equivalent and show how to correct some results in the literature.


  There is overwhelming evidence on SARS-CoV-2 Airborne Transmission (AT) in
the ongoing COVID-19 outbreak. It is extraordinarily difficult, however, to
deduce a generalized framework to assess the relative airborne transmission
risk with respect to other modes. This is due to the complex biophysics
entailed in such phenomena. Since the SARS outbreak in 2002, Computational
Fluid Dynamics (CFD) has been one of the main tools scientists used to
investigate AT of respiratory viruses. Now, CFD simulations produce intuitive
and physically plausible colour-coded results that help scientists understand
SARS-CoV-2 airborne transmission patterns. In addition to validation
requirements, for any CFD model to be of epistemic value to the scientific
community; it must be reproducible. In 2020, more than 45 published studies
investigated SARS-CoV-2 airborne transmission in different scenarios using CFD.
Here, I systematically review the published CFD studies of COVID-19 and discuss
their reproducibility criteria with respect to the CFD modeling process. Using
a Weighted Scoring Model (WSM), I propose a novel reproducibility index for CFD
simulations of SARS-CoV-2 AT. The proposed index $(0 \leq R^{CFD}_j \leq 1)$
relies on three reproducibility criteria comprising 10 elements that represent
the possibility of a CFD study (j) to be reproduced. Frustratingly, only 3 of
23 studies (13%) achieved full reproducibility index $(R^{CFD}_j\geq 0.9)$
while the remaining 87% were found generally irreproducible $(R^{CFD}_j<0.9)$.
Without reproducible models, the scientific benefit of CFD simulations will
remain hindered, fragmented and limited. In conclusion, I call the scientific
community to apply more rigorous measures on reporting and publishing CFD
simulations in COVID-19 research.


  We analyze the question whether sliding window time averages applied to
stationary increment processes converge to a limit in probability. The question
centers on averages, correlations, and densities constructed via time averages
of the increment x(t,T)=x(t+T)-x(t)and the assumption is that the increment is
distributed independently of t. We show that the condition for applying
Tchebyshev's Theorem to time averages of functions of stationary increments is
strongly violated. We argue that, for both stationary and nonstationary
increments, Tchebyshev's Theorem provides the basis for constructing emsemble
averages and densities from a single, historic time series if, as in FX
markets, the series shows a definite statistical periodicity on the average.


  Thermoresponsive microgels are polymeric colloidal networks that can change
their size in response to a temperature variation. This peculiar feature is
driven by the nature of the solvent-polymer interactions, which triggers the
so-called volume phase transition from a swollen to a collapsed state above a
characteristic temperature. Recently, an advanced modelling protocol to
assemble realistic, disordered microgels has been shown to reproduce
experimental swelling behavior and form factors. In the original framework, the
solvent was taken into account in an implicit way, condensing solvent-polymer
interactions in an effective attraction between monomers. To go one step
further, in this work we perform simulations of realistic microgels in an
explicit solvent. We identify a suitable model which fully captures the main
features of the implicit model and further provides information on the solvent
uptake by the interior of the microgel network and on its role in the collapse
kinetics. These results pave the way for addressing problems where solvent
effects are dominant, such as the case of microgels at liquid-liquid
interfaces.


  We prove that $|\sum_{n \leq x} \mu(n) | \leq x/160\,383$ for all $x\geq 8.4
\times 10^9$ thus improving the record for this type of estimates which was
$|\sum_{n \leq x} \mu(n) | \leq x/4345$ for all $x\geq 2\,160\,535$ and was due
to Cohen, Dress and El Marraki. We also prove that $|\sum_{n \leq x} \mu(n) |
\leq x/180\,194$ for all $x\geq 10^{19}$.


  We report the epitaxial thin film synthesis of SrCu$_3$O$_4$ with infinitely
stacked Cu$_3$O$_4$ layers composed of edge-sharing CuO$_4$ square-planes,
using molecular beam epitaxy. Experimental and theoretical characterizations
showed that this material is a metastable phase that can exist by applying
tensile biaxial strain from the (001)-SrTiO$_3$ substrate. SrCu$_3$O$_4$ shows
an insulating electrical resistivity in accordance with the Cu$^{2+}$ valence
state revealed X-ray photoelectron spectroscopy. First-principles calculations
also indicated that the unoccupied $d_{3z^2-r^2}$ band becomes substantially
stabilized owing to the absence of apical anions, in contrast to
$A_2$Cu$_3$O$_4$Cl$_2$ ($A = $Sr, Ba) with an $A_2$Cl$_2$ block layer and
therefore a trans-CuO$_4$Cl$_2$ octahedron. These results suggest that
SrCu$_3$O$_4$ is a suitable parent material for electron-doped
superconductivity based on the Cu$_3$O$_4$ plane.


  We prove a duality principle for a special class of submanifolds in
pseudo-Euclidean spaces. This class of submanifolds with potential of normals
is introduced in this paper. We prove also, for example, that an arbitrary
Frobenius manifold can be realized as a certain flat submanifold of this very
natural class.


  It is shown that in the presence of anisotropic kinetic dissipation existence
of scale invariant power law spectrum of plasma turbulence is possible.
Obtained scale invariant spectrum is not associated with the constant flux of
any physical quantity. Application of the model to the high frequency part of
the solar wind turbulence is discussed.


  We develop the frozen Gaussian approximation (FGA) for the fractional
Schr\"odinger equation in the semi-classical regime, where the solution is
highly oscillatory when the scaled Planck constant $\varepsilon$ is small. This
method approximates the solution to the Schr\"odinger equation by an integral
representation based on asymptotic analysis and provides a highly efficient
computational method for high-frequency wave function evolution. In particular,
we revise the standard FGA formula to address the singularities arising in the
higher-order derivatives of coefficients of the associated Hamiltonian flow
that are second-order continuously differentiable or smooth in conventional FGA
analysis. We then establish its convergence to the true solution. Additionally,
we provide some numerical examples to verify the accuracy and convergence
behavior of the frozen Gaussian approximation method.


  Any network studied in the literature is inevitably just a sampled
representative of its real-world analogue. Additionally, network sampling is
lately often applied to large networks to allow for their faster and more
efficient analysis. Nevertheless, the changes in network structure introduced
by sampling are still far from understood. In this paper, we study the presence
of characteristic groups of nodes in sampled social and information networks.
We consider different network sampling techniques including random node and
link selection, network exploration and expansion. We first observe that the
structure of social networks reveals densely linked groups like communities,
while the structure of information networks is better described by modules of
structurally equivalent nodes. However, despite these notable differences, the
structure of sampled networks exhibits stronger characterization by
community-like groups than the original networks, irrespective of their type
and consistently across various sampling techniques. Hence, rich community
structure commonly observed in social and information networks is to some
extent merely an artifact of sampling.


  In this work, we propose a novel two-level discretization for solving
semilinear elliptic equations with random coefficients. Motivated by the
two-grid method for deterministic partial differential equations (PDEs)
introduced by Xu \cite{xu1994novel}, our two-level stochastic collocation
method utilizes a two-grid finite element discretization in the physical space
and a two-level collocation method in the random domain. In particular, we
solve semilinear equations on a coarse mesh $\mathcal{T}_H$ with a low level
stochastic collocation (corresponding to the polynomial space
$\mathcal{P}_{\boldsymbol{P}}$) and solve linearized equations on a fine mesh
$\mathcal{T}_h$ using high level stochastic collocation (corresponding to the
polynomial space $\mathcal{P}_{\boldsymbol{p}}$). We prove that the
approximated solution obtained from this method achieves the same order of
accuracy as that from solving the original semilinear problem directly by
stochastic collocation method with $\mathcal{T}_h$ and
$\mathcal{P}_{\boldsymbol{p}}$. The two-level method is computationally more
efficient than the standard stochastic collocation method for solving nonlinear
problems with random coefficients. Numerical experiments are provided to verify
the theoretical results.


  Heisenberg's uncertainty relation for measurement noise and disturbance
states that any position measurement with noise epsilon brings the momentum
disturbance not less than hbar/2epsilon. This relation holds only for
restricted class of measuring apparatuses. Here, Heisenberg's uncertainty
relation is generalized to a relation that holds for all the possible quantum
measurements, from which conditions are obtained for measuring apparatuses to
satisfy Heisenberg's relation. In particular, every apparatus with the noise
and the disturbance statistically independent from the measured object is
proven to satisfy Heisenberg's relation. For this purpose, all the possible
quantum measurements are characterized by naturally acceptable axioms. Then, a
mathematical notion of the distance between probability operator valued
measures and observables is introduced and the basic properties are explored.
Based on this notion, the measurement noise and disturbance are naturally
defined for any quantum measurements in a model independent formulation. Under
this formulation, various uncertainty relations are also derived for
apparatuses with independent noise, independent disturbance, unbiased noise,
and unbiased disturbance as well as noiseless apparatuses and nondisturbing
apparatuses. Two models of position measurements are discussed to show that
Heisenberg's relation can be violated even by approximately repeatable position
measurements.


  In recent years, visual SLAM has achieved great progress and development, but
in complex scenes, especially rotating scenes, the error of mapping will
increase significantly, and the slam system is easy to lose track. In this
article, we propose an InterpolationSLAM framework, which is a visual SLAM
framework based on ORB-SLAM2. InterpolationSLAM is robust in rotating scenes
for Monocular and RGB-D configurations. By detecting the rotation and
performing interpolation processing at the rotated position, pose of the system
can be estimated more accurately at the rotated position, thereby improving the
accuracy and robustness of the SLAM system in the rotating scenes. To the best
of our knowledge, it is the first work combining the interpolation network into
a Visual SLAM system to improve SLAM system robustness in rotating scenes. We
conduct experiments both on KITTI Monocular and TUM RGB-D datasets. The results
demonstrate that InterpolationSLAM outperforms the accuracy of standard Visual
SLAM baselines.


  In human relations individuals' gender and age play a key role in the
structures and dynamics of their social arrangements. In order to analyze the
gender preferences of individuals in interaction with others at different
stages of their lives we study a large mobile phone dataset. To do this we
consider four fundamental gender-related caller and callee combinations of
human interactions, namely male to male, male to female, female to male, and
female to female, which together with age, kinship, and different levels of
friendship give rise to a wide scope of human sociality. Here we analyse the
relative strength of these four types of interaction using a large dataset of
mobile phone communication records. Our analysis suggests strong age dependence
for an ego of one gender choosing to call an individual of either gender. We
observe a strong opposite sex bonding across most of their reproductive age.
However, older women show a strong tendency to connect to another female that
is one generation younger in a way that is suggestive of the
\emph{grandmothering effect}. We also find that the relative strength among the
four possible interactions depends on phone call duration. For calls of medium
and long duration, opposite gender interactions are significantly more probable
than same gender interactions during the reproductive years, suggesting
potential emotional exchange between spouses. By measuring the fraction of
calls to other generations we find that mothers tend to make calls more to
their daughters than to their sons, whereas fathers make calls more to their
sons than to their daughters. For younger people, most of their calls go to
same generation alters, while older people call the younger people more
frequently, which supports the suggestion that \emph{affection flows downward}.


  The e-commerce has started a new trend in natural language processing through
sentiment analysis of user-generated reviews. Different consumers have
different concerns about various aspects of a specific product or service.
Aspect category detection, as a subtask of aspect-based sentiment analysis,
tackles the problem of categorizing a given review sentence into a set of
pre-defined aspect categories. In recent years, deep learning approaches have
brought revolutionary advances in multiple branches of natural language
processing including sentiment analysis. In this paper, we propose a deep
neural network method based on attention mechanism to identify different aspect
categories of a given review sentence. Our model utilizes several attentions
with different topic contexts, enabling it to attend to different parts of a
review sentence based on different topics. Experimental results on two datasets
in the restaurant domain released by SemEval workshop demonstrates that our
approach outperforms existing methods on both datasets. Visualization of the
topic attention weights shows the effectiveness of our model in identifying
words related to different topics.


  In this correspondence our aim is to use some tight lower and upper bounds
for the differential quaternary phase shift keying transmission bit error rate
in order to deduce accurate approximations for the bit error rate by improving
the known results in the literature. The computation of our new approximate
expressions are significantly simpler than that of the exact expression.


  Planetary engulfment events can occur while host stars are on the main
sequence. The addition of rocky planetary material during engulfment will lead
to refractory abundance enhancements in the host star photosphere, but the
level of enrichment and its duration will depend on mixing processes that occur
within the stellar interior, such as convection, diffusion, and thermohaline
mixing. We examine engulfment signatures by modeling the evolution of
photospheric lithium abundances. Because lithium can be burned before or after
the engulfment event, it produces unique signatures that vary with time and
host star type. Using MESA stellar models, we quantify the strength and
duration of these signatures following the engulfment of a 1, 10, or 100
$M_{\oplus}$ planetary companion with bulk Earth composition, for
solar-metallicity host stars with masses ranging from 0.5$-$1.4 $M_{\odot}$. We
find that lithium is quickly depleted via burning in low-mass host stars
($\lesssim 0.7 \, M_\odot$) on a time scale of a few hundred Myrs, but
significant lithium enrichment signatures can last for Gyrs in G-type stars
($\sim \! 0.9 \, M_{\odot}$). For more massive stars (1.3$-$1.4 $M_{\odot}$),
engulfment can enhance internal mixing and diffusion processes, potentially
decreasing the surface lithium abundance. Our predicted signatures from
exoplanet engulfment are consistent with observed lithium-rich solar-type stars
and abundance enhancements in chemically inhomogeneous binary stars.


  During inflation quantum effects from massless, minimally coupled scalars and
gravitons can be strengthened so much that perturbation theory breaks down. To
follow the subsequent evolution one must employ a nonperturbative resummation.
Starobinski\u{\i} has developed such a technique for simple scalDuring
inflation quantum effects from massless, minimally coupled scalars and
gravitons can be strengthened so much that perturbation theory breaks down. To
follow the subsequent evolution one must employ a nonperturbative resummation.
Starobinski\u{\i} has developed such a technique for simple scalar theories. I
discuss recent progress in applying this technique to more complicated models.


  We present a study of the decay B- --> D0_(CP) K- and its charge conjugate,
where D0_(CP) is reconstructed in CP-even, CP-odd, and non-CP flavor
eigenstates, based on a sample of 232 million Y(4S) --> B Bbar decays collected
with the BABAR detector at the PEP-II e+e- storage ring. We measure the
partial-rate charge asymmetries A_CP+, A_CP- and the ratios R_CP+, R_CP- of the
B --> D0 K decay branching fractions as measured in CP+, CP-, and non-CP D0
decays: A_CP+ = 0.35 +/- 0.13 (stat) +/- 0.04 (syst) A_CP- = -0.06 +/- 0.13
(stat) +/- 0.04 (syst) R_CP+ = 0.90 +/- 0.12 (stat) +/- 0.04 (syst) R_CP- =
0.86 +/- 0.10 (stat) +/- 0.05 (syst)


  Supernova (SN) light echoes could be a powerful tool for determining
distances to galaxies geometrically, Sparks 1994. In this paper we present CCD
photometry of the environments of 64 historical supernovae, the first results
of a program designed to search for light echoes from these SNe. We commonly
find patches of optical emission at, or close to, the sites of the supernovae.
The color distribution of these patches is broad, and generally consistent with
stellar population colors, possibly with some reddening. However there are in
addition patches with both unusually red and unusually blue colors. We expect
light echoes to be blue, and while none of the objects are quite as blue in V-R
as the known light echo of SN1991T, there are features that are unusually blue
and we identify these as candidate light echoes for follow-on observations.


  In the probabilistic energy forecasting literature, emphasis is mainly placed
on deriving marginal predictive densities for which each random variable is
dealt with individually. Such marginals description is sufficient for power
systems related operational problems if and only if optimal decisions are to be
made for each lead-time and each location independently of each other. However,
many of these operational processes are temporally and spatially coupled, while
uncertainty in photovoltaic (PV) generation is strongly dependent in time and
in space. This issue is addressed here by analysing and capturing
spatio-temporal dependencies in PV generation. Multivariate predictive
distributions are modelled and space-time trajectories describing the potential
evolution of forecast errors through successive lead-times and locations are
generated. Discrimination ability of the relevant scoring rules on performance
assessment of space-time trajectories of PV generation is also studied.
Finally, the advantage of taking into account space-time correlations over
probabilistic and point forecasts is investigated. The empirical investigation
is based on the solar PV dataset of the Global Energy Forecasting Competition
(GEFCom) 2014.


  From the perspective of global warming, efficiency improvement of power grids
is a pressing issue. Power grids have many switching devices to control the
flow of electricity. Since there is a slight resistance in the wires and power
consumption is proportional to the square of the current, the value of power
loss on the wires changes depending on the combination of switch values that
change the supply path of the current. The total number of switch combinations
increases exponentially with the number of switches, and various algorithms
have been studied to find the optimal combination of switch values. We propose
a method to capture the switch combination problem in power grids as quadratic
unconstrained binary optimization (QUBO) and derive an evaluation function to
solve it using quantum annealing. The result is registered as a patent P6736787
at Japanese patent office.


  This paper consider solving a class of nonconvex-strongly-convex distributed
stochastic bilevel optimization (DSBO) problems with personalized inner-level
objectives. Most existing algorithms require computational loops for
hypergradient estimation, leading to computational inefficiency. Moreover, the
impact of data heterogeneity on convergence in bilevel problems is not
explicitly characterized yet. To address these issues, we propose LoPA, a
loopless personalized distributed algorithm that leverages a tracking mechanism
for iterative approximation of inner-level solutions and Hessian-inverse
matrices without relying on extra computation loops. Our theoretical analysis
explicitly characterizes the heterogeneity across nodes denoted by $b$, and
establishes a sublinear rate of ${{\mathcal{O}}}( {\frac{{1}}{{(1-\rho)^2K}} +
\frac{{b^{\frac{2}{3}} }}{{\left( {1 - \rho }
\right)^{\frac{2}{3}}K^{\frac{2}{3}} }} + \frac{{1}}{\sqrt{ K }} (
\sigma_{\rm{p}} + \frac{1}{\sqrt{m}}\sigma_{\rm{c}}) } )$ without the
boundedness of local hypergradients, where $\sigma_{\rm p}$ and $\sigma_{\rm
c}$ represent the gradient sampling variances associated with the inner- and
outer-level variables, respectively. We also develop a variant of LoPA based on
gradient tracking to eliminate the impact of data heterogeneity, yielding an
improved rate of ${{\mathcal{O}}}(\frac{{{1}}}{{ (1-\rho)^4K }} +
\frac{1}{{\sqrt{K}}}( \sigma_{\rm{p}} + \frac{1}{\sqrt{m}}\sigma_{\rm{c}} ) )$.
The computational complexity of LoPA is of ${{\mathcal{O}}}({\epsilon^{-2}})$
to an $\epsilon$-stationary point, matching the communication complexity due to
the loopless structure, which outperforms existing counterparts for DSBO.
Numerical experiments validate the effectiveness of the proposed algorithm.


  This paper presents an experiment based comparison of absolute threshold (AT)
and non-linear energy operator (NEO) spike detection algorithms in
Intra-cortical Brain Machine Interfaces (iBMIs). Results show an average
increase in decoding performance of approx. 5% in monkey A across 28 sessions
recorded over 6 days and approx. 2% in monkey B across 35 sessions recorded
over 8 days when using NEO over AT. To the best of our knowledge, this is the
first ever reported comparison of spike detection algorithms in an iBMI
experimental framework involving two monkeys. Based on the improvements
observed in an experimental setting backed by previously reported improvements
in simulation studies, we advocate switching from state of the art spike
detection technique - AT to NEO.


  Imaging methods used in modern neuroscience experiments are quickly producing
large amounts of data capable of providing increasing amounts of knowledge
about neuroanatomy and function. A great deal of information in these datasets
is relatively unexplored and untapped. One of the bottlenecks in knowledge
extraction is that often there is no feedback loop between the knowledge
produced (e.g., graph, density estimate, or other statistic) and the earlier
stages of the pipeline (e.g., acquisition). We thus advocate for the
development of sample-to-knowledge discovery pipelines that one can use to
optimize acquisition and processing steps with a particular end goal (i.e.,
piece of knowledge) in mind. We therefore propose that optimization takes place
not just within each processing stage but also between adjacent (and
non-adjacent) steps of the pipeline. Furthermore, we explore the existing
categories of knowledge representation and models to motivate the types of
experiments and analysis needed to achieve the ultimate goal. To illustrate
this approach, we provide an experimental paradigm to answer questions about
large-scale synaptic distributions through a multimodal approach combining
X-ray microtomography and electron microscopy.


  Motivated by a recently found class of AdS_7 solutions, we classify AdS_5
solutions in massive IIA, finding infinitely many new analytical examples. We
reduce the general problem to a set of PDEs, determining the local internal
metric, which is a fibration over a surface. Under a certain simplifying
assumption, we are then able to analytically solve the PDEs and give a complete
list of all solutions. Among these, one class is new and regular. These spaces
can be related to the AdS_7 solutions via a simple universal map for the
metric, dilaton and fluxes. The natural interpretation of this map is that the
dual CFT_6 and CFT_4 are related by twisted compactification on a Riemann
surface $\Sigma_g$. The ratio of their free energy coefficients is proportional
to the Euler characteristic of $\Sigma_g$. As a byproduct, we also find the
analytic expression for the AdS_7 solutions, which were previously known only
numerically. We determine the free energy for simple examples: it is a simple
cubic function of the flux integers.


  We analyze current fluctuations in mesoscopic coherent conductors in the
presence of electron-electron interactions. In a wide range of parameters we
obtain explicit universal dependencies of the current noise on temperature,
voltage and frequency. We demonstrate that Coulomb interaction decreases the
Nyquist noise. In this case the interaction correction to the noise spectrum is
governed by the combination $\sum_nT_n(T_n-1)$, where $T_n$ is the transmission
of the $n$-th conducting mode. The effect of electron-electron interactions on
the shot noise is more complicated. At sufficiently large voltages we recover
two different interaction corrections entering with opposite signs. The net
result is proportional to $\sum_nT_n(T_n-1)(1-2T_n)$, i.e. Coulomb interaction
decreases the shot noise at low transmissions and increases it at high
transmissions.


  This paper proposes a novel sensor fusion based on Unscented Kalman Filtering
for the online estimation of joint-torques of humanoid robots without
joint-torque sensors. At the feature level, the proposed approach considers
multimodal measurements (e.g. currents, accelerations, etc.) and non-directly
measurable effects, such as external contacts, thus leading to joint torques
readily usable in control architectures for human-robot interaction. The
proposed sensor fusion can also integrate distributed, non-collocated
force/torque sensors, thus being a flexible framework with respect to the
underlying robot sensor suit. To validate the approach, we show how the
proposed sensor fusion can be integrated into a twolevel torque control
architecture aiming at task-space torquecontrol. The performances of the
proposed approach are shown through extensive tests on the new humanoid robot
ergoCub, currently being developed at Istituto Italiano di Tecnologia. We also
compare our strategy with the existing state-of-theart approach based on the
recursive Newton-Euler algorithm. Results demonstrate that our method achieves
low root mean square errors in torque tracking, ranging from 0.05 Nm to 2.5 Nm,
even in the presence of external contacts.


  The task of image-based virtual try-on aims to transfer a target clothing
item onto the corresponding region of a person, which is commonly tackled by
fitting the item to the desired body part and fusing the warped item with the
person. While an increasing number of studies have been conducted, the
resolution of synthesized images is still limited to low (e.g., 256x192), which
acts as the critical limitation against satisfying online consumers. We argue
that the limitation stems from several challenges: as the resolution increases,
the artifacts in the misaligned areas between the warped clothes and the
desired clothing regions become noticeable in the final results; the
architectures used in existing methods have low performance in generating
high-quality body parts and maintaining the texture sharpness of the clothes.
To address the challenges, we propose a novel virtual try-on method called
VITON-HD that successfully synthesizes 1024x768 virtual try-on images.
Specifically, we first prepare the segmentation map to guide our virtual try-on
synthesis, and then roughly fit the target clothing item to a given person's
body. Next, we propose ALIgnment-Aware Segment (ALIAS) normalization and ALIAS
generator to handle the misaligned areas and preserve the details of 1024x768
inputs. Through rigorous comparison with existing methods, we demonstrate that
VITON-HD highly surpasses the baselines in terms of synthesized image quality
both qualitatively and quantitatively. Code is available at
https://github.com/shadow2496/VITON-HD.


  We give a status report on inclusive rare B decays, highlighting recent
developments and open problems. We focus on the decay modes $B \to X_{s,d}
\gamma$, $ B \to X_s \ell^+\ell^-$ and $B \to X_s \nu \bar \nu$ and on their
role in the search for new physics. Most of the inclusive rare B decays are
important modes of flavour physics due to the small hadronic uncertainties.
They can be regarded as laboratories to search for new physics. We collect the
experimental data already available from CLEO and the $B$ factories BABAR and
BELLE. We review the NLL and NNLL QCD calculations of the inclusive decay rates
that were recently completed, and discuss future prospects, especially the
issue of the charm mass scheme ambiguity. Finally, we analyse the
phenomenological impact of these decay modes, in particular on the CKM
phenomenology and on the indirect search for supersymmetry. We also briefly
discuss direct CP violation in inclusive rare B decays, as well as the rare
kaon decays $K^+\to \pi^+\nu\bar{\nu}$ and $K_L \to \pi^0 \nu \bar{\nu}$, which
offer complementary theoretically clean information.


  The proton spin puzzle has inspired a vast programme of experiments and
theoretical work challenging our understanding of QCD and its role in the
structure of hadrons.The proton's internal spin structure is connected to
chiral symmetry and, through gluon degrees of freedom in the flavour singlet
channel, to the physics of the $\eta'$ meson. Why do quarks contribute just
about one third of the proton's spin? Why are $\eta'$ mesons and their
interactions so sensitive to gluonic degrees of freedom? We review the status
of these topics and some key observables for forthcoming experiments.


  Deep generative models have been accelerating the inverse design process in
material and drug design. Unlike their counterpart property predictors in
typical molecular design frameworks, generative molecular design models have
seen fewer efforts on uncertainty quantification (UQ) due to computational
challenges in Bayesian inference posed by their large number of parameters. In
this work, we focus on the junction-tree variational autoencoder (JT-VAE), a
popular model for generative molecular design, and address this issue by
leveraging the low dimensional active subspace to capture the uncertainty in
the model parameters. Specifically, we approximate the posterior distribution
over the active subspace parameters to estimate the epistemic model uncertainty
in an extremely high dimensional parameter space. The proposed UQ scheme does
not require alteration of the model architecture, making it readily applicable
to any pre-trained model. Our experiments demonstrate the efficacy of the
AS-based UQ and its potential impact on molecular optimization by exploring the
model diversity under epistemic uncertainty.


  This paper is about the general truncated matrix-valued moment problem. Let
$\mathcal{H}_q$ denote the complex Hermitian $q\times q$-matrices, $q\in
\mathbb{N}$. Suppose that $(\mathcal{X},\mathfrak{X})$ is a measurable space
and $\mathcal{E}$ is a finite-dimensional vector space of measurable mappings
of $\mathcal{X}$ into $\mathcal{H}_q$. A linear functional $\Lambda$ on
$\mathcal{E}$ is called a moment functional if there exists a positive
$\mathcal{H}_q$-valued measure $\mu$ on $(\mathcal{X},\mathfrak{X})$ such that
$\Lambda(F)=\int_\mathcal{X} \langle F,\mathrm{d}\mu\rangle$ for $F\in
\mathcal{E}$.
  We prove a matricial version of the Richter-Tchakaloff theorem which states
that each moment functional on $\mathcal{E}$ has a finitely atomic representing
measure. It is shown that strictly positive linear functionals on $\mathcal{E}$
are moment functionals. For a moment functional $\Lambda$, we study the set of
atoms $\mathcal{W}(\Lambda)$ and the Carath\'eodory numbers
$\mathrm{Car}(\Lambda)$, $\mathrm{car}(\Lambda)$ and we define and investigate
the core set $\mathcal{V}(\Lambda)$. A main result of the paper is the equality
$\mathcal{W}(\Lambda)=\mathcal{V}(\Lambda)$.


  For practical automatic speaker verification (ASV) systems, replay attack
poses a true risk. By replaying a pre-recorded speech signal of the genuine
speaker, ASV systems tend to be easily fooled. An effective replay detection
method is therefore highly desirable. In this study, we investigate a major
difficulty in replay detection: the over-fitting problem caused by variability
factors in speech signal. An F-ratio probing tool is proposed and three
variability factors are investigated using this tool: speaker identity, speech
content and playback & recording device. The analysis shows that device is the
most influential factor that contributes the highest over-fitting risk. A
frequency warping approach is studied to alleviate the over-fitting problem, as
verified on the ASV-spoof 2017 database.


  The new notion of maturity-independent risk measures is introduced and
contrasted with the existing risk measurement concepts. It is shown, by means
of two examples, one set on a finite probability space and the other in a
diffusion framework, that, surprisingly, some of the widely utilized risk
measures cannot be used to build maturity-independent counterparts. We
construct a large class of maturity-independent risk measures and give
representative examples in both continuous- and discrete-time financial models.


  The electronic and optical properties of various polycyclic aromatic
hydrocarbons (PAHs) with lower symmetry, namely, benzo[ghi]perylene
(C$_{22}$H$_{12}$), benzo[a]coronene (C$_{28}$H$_{14}$), naphtho[2,3a]coronene
(C$_{32}$H$_{16}$), anthra[2,3a]coronene (C$_{36}$H$_{18}$), and
naphtho[8,1,2-abc]coronene (C$_{30}$H$_{14}$) were investigated. For the
purpose, we performed electron-correlated calculations using screened, and
standard parameters in the $\pi$-electron Pariser-Parr-Pople (PPP) Hamiltonian,
and the correlation effects were included, both for ground and excited states,
using the multi-reference singles-doubles configuration-interaction (MRSDCI)
methodology. PPP model Hamiltonian includes long-range Coulomb interactions,
which increase the accuracy of our calculations. The results of our
calculations predict that, with the increasing sizes of the coronene
derivatives, optical spectra are red shifted, and the optical gaps decrease. In
each spectrum, the first peak representing the optical gap is of moderate
intensity, while the more intense peaks appear at higher energies. Our computed
spectra are in good agreement with the available experimental data. For the
purpose of comparison, we also performed first-principles time-dependent
density-functional theory (TDDFT) calculations of the optical gaps of these
molecules using Gaussian basis functions, and found that they yielded values
lower than our CI results.


  The final orbital configuration of a planetary system is shaped by both its
early star-disk environment and late-stage gravitational interactions.
Assessing the relative importance of each of these factors is not
straightforward due to the observed diversity of planetary systems compounded
by observational biases. Our goal is to understand how a planetary system may
change when planetesimal accretion and planet migrations stop and secular
gravitational effects take over. Our approach starts with a novel
classification of planetary systems based on their orbital architecture,
validated using Approximate Bayesian Computation methods. We apply this scheme
to observed planetary systems and also to $\sim 400$ synthetic systems hosting
$\sim 5000$ planets, synthesized from a Monte Carlo planet population model.
Our classification scheme robustly yields four system classes according to
their planet masses and semi-major axes, for both observed and synthetic
systems. We then estimate the orbital distribution density of each of the
synthetic systems before and after dynamically evolving them for up to 1 Myr
with a gravitational+collisional $N$-body code. Using the Kullback-Leibler
divergence to statistically measure orbital configuration changes, we find that
$\lesssim 10 \%$ of synthetic planetary systems experience such changes. We
also find that this fraction belongs to a class of systems for which their
center of mass is very close to their host star. Although changes in the
orbital configuration of planetary systems may not very common, they are more
likely to happen in systems with close-in, massive planets, with F- and G-type
host-stars and stellar metallicities $\mathrm{[Fe/H]} > 0.2$.


  In this paper, we introduce the concept of the weighted (harmonic) chromatic
polynomials of graphs and discuss some of its properties. We also present the
notion of the weighted (harmonic) Tutte--Grothendieck polynomials of graphs and
give a generalization of the recipe theorem between the harmonic
Tutte--Grothendieck polynomials graphs and the harmonic Tutte polynomials of
matroids. Moreover, we give some constructions of the weighted (harmonic)
Tutte--Grothendieck invariants for graphs and the weighted (harmonic) Tutte
invariants for matroids. Finally, we give a remark on the categorification of
the harmonic chromatic polynomials of graphs and harmonic Tutte polynomials of
matroids.


  We present the first lattice QCD results of the second order fluctuations of
and correlations among net baryon number, electric charge and strangeness in
(2+1)-flavor lattice QCD in the presence of a background magnetic field with
physical pion mass $m_{\pi}=135$ MeV. To mimic the magnetic field strength
produced in the early stage of heavy-ion collision experiments we use 6
different values of the magnetic field strength up to $ \sim $10$m_{\pi}^2$. We
find that the correlations between baryon number and electric charge along the
transition line are substantially affected by magnetic fields in the current
$eB$ window, which could be useful for probing the existence of a magnetic
field in heavy-ion collision experiments.


  The prevalence of tree-like structures, encompassing hierarchical structures
and power law distributions, exists extensively in real-world applications,
including recommendation systems, ecosystems, financial networks, social
networks, etc. Recently, the exploitation of hyperbolic space for tree-likeness
modeling has garnered considerable attention owing to its exponential growth
volume. Compared to the flat Euclidean space, the curved hyperbolic space
provides a more amenable and embeddable room, especially for datasets
exhibiting implicit tree-like architectures. However, the intricate nature of
real-world tree-like data presents a considerable challenge, as it frequently
displays a heterogeneous composition of tree-like, flat, and circular regions.
The direct embedding of such heterogeneous structures into a homogeneous
embedding space (i.e., hyperbolic space) inevitably leads to heavy distortions.
To mitigate the aforementioned shortage, this study endeavors to explore the
curvature between discrete structure and continuous learning space, aiming at
encoding the message conveyed by the network topology in the learning process,
thereby improving tree-likeness modeling. To the end, a curvature-aware
hyperbolic graph convolutional neural network, \{kappa}HGCN, is proposed, which
utilizes the curvature to guide message passing and improve long-range
propagation. Extensive experiments on node classification and link prediction
tasks verify the superiority of the proposal as it consistently outperforms
various competitive models by a large margin.


  This paper deals with the fractional Caputo--Fabrizio derivative and some
basic properties related. A computation of this fractional derivative to power
functions is given in terms of Mittag--Lefler functions. The inverse operator
named the fractional Integral of Caputo--Fabrizio is also analyzed. The main
result consists in the proof of existence and uniqueness of a global solution
to a nonlinear fractional differential equation, which has been solved
previously for short times by Lozada and Nieto (Progr. Fract. Differ. Appl.,
1(2):87--92, 2015). The effects of memory as well as the convergence of the
obtained results when $\al \nearrow 1$ (and the classical first derivative is
recovered) are analyzed throughout the paper.


  The initial proposal for scalable optical quantum computing required single
photon sources, linear optical elements such as beamsplitters and
phaseshifters, and photon detection. Here we demonstrate a two qubit gate using
indistinguishable photons from a quantum dot in a pillar microcavity. As the
emitter, the optical circuitry, and the detectors are all semiconductor, this
is a promising approach towards creating a fully integrated device for scalable
quantum computing.


  We consider a large neutral molecule with total nuclear charge $Z$ in a model
with self-generated classical magnetic field and where the kinetic energy of
the electrons is treated relativistically. To ensure stability, we assume that
$Z \alpha < 2/\pi$, where $\alpha$ denotes the fine structure constant. We are
interested in the ground state energy in the simultaneous limit $Z \rightarrow
\infty$, $\alpha \rightarrow 0$ such that $\kappa=Z \alpha$ is fixed. The
leading term in the energy asymptotics is independent of $\kappa$, it is given
by the Thomas-Fermi energy of order $Z^{7/3}$ and it is unchanged by including
the self-generated magnetic field. We prove the first correction term to this
energy, the so-called Scott correction of the form $S(\alpha Z) Z^2$. The
current paper extends the result of \cite{SSS} on the Scott correction for
relativistic molecules to include a self-generated magnetic field. Furthermore,
we show that the corresponding Scott correction function $S$, first identified
in \cite{SSS}, is unchanged by including a magnetic field. We also prove new
Lieb-Thirring inequalities for the relativistic kinetic energy with magnetic
fields.


  We survey some recent developments on the problem of understanding
degenerations of Calabi-Yau manifolds equipped with their Ricci-flat Kahler
metrics, with an emphasis on the case when the metrics are volume collapsing.


  Fashion apparel companies require planning for the next season, a year in
advance for supply chain management. This study focuses on size selection
decision making for Levi Strauss. Currently, the region and planning group
level size grids are built and managed manually. The company suffers from the
workload it creates for sizing, merchant and planning teams. This research is
aiming to answer two research questions: "Which sizes should be available to
the planners under each size grid name for the next season(s)?" and "Which
sizes should be adopted for each planning group for the next season(s)?". We
approach to the problem with a classification model, which is one of the
popular models used in machine learning. With this research, a more automated
process was created by using machine learning techniques. A decrease in
workload of the teams in the company is expected after it is put into practice.
Unlike many studies in the state of art for fashion and apparel industry, this
study focuses on sizes where the stock keeping unit represents a product with a
certain size.


  The woylier package implements tour interpolation paths between frames using
Givens rotations. This provides an alternative to the geodesic interpolation
between planes currently available in the tourr package. Tours are used to
visualise high-dimensional data and models, to detect clustering, anomalies and
non-linear relationships. Frame-to-frame interpolation can be useful for
projection pursuit guided tours when the index is not rotationally invariant.
It also provides a way to specifically reach a given target frame. We
demonstrate the method for exploring non-linear relationships between currency
cross-rates.


  We report on the study of the non-trivial Berry phase in superconducting
multiterminal quantum dots biased at commensurate voltages. Starting with the
time-periodic Bogoliubov-de Gennes equations, we obtain a tight binding model
in the Floquet space, and we solve these equations in the semiclassical limit.
We observe that the parameter space defined by the contact transparencies and
quartet phase splits into two components with a non-trivial Berry phase. We use
the Bohr-Sommerfeld quantization to calculate the Berry phase. We find that if
the quantum dot level sits at zero energy, then the Berry phase takes the
values $\varphi_B=0$ or $\varphi_B=\pi$. We demonstrate that this non-trivial
Berry phase can be observed by tunneling spectroscopy in the Floquet spectra.
Consequently, the Floquet-Wannier-Stark ladder spectra of superconducting
multiterminal quantum dots are shifted by half-a-period if $\varphi_B=\pi$. Our
numerical calculations based on Keldysh Green's functions show that this Berry
phase spectral shift can be observed from the quantum dot tunneling density of
states.


  Determination of an exoplanet's mass is a key to understanding its basic
properties, including its potential for supporting life. To date, mass
constraints for exoplanets are predominantly based on radial velocity (RV)
measurements, which are not suited for planets with low masses, large
semi-major axes, or those orbiting faint or active stars. Here, we present a
method to extract an exoplanet's mass solely from its transmission spectrum. We
find good agreement between the mass retrieved for the hot Jupiter HD189733b
from transmission spectroscopy with that from RV measurements. Our method will
be able to retrieve the masses of Earth-sized and super-Earth planets using
data from future space telescopes that were initially designed for atmospheric
characterization.


  Real economies can be modeled as a sequential imperfect-information game with
many heterogeneous agents, such as consumers, firms, and governments. Dynamic
general equilibrium (DGE) models are often used for macroeconomic analysis in
this setting. However, finding general equilibria is challenging using existing
theoretical or computational methods, especially when using microfoundations to
model individual agents. Here, we show how to use deep multi-agent
reinforcement learning (MARL) to find $\epsilon$-meta-equilibria over agent
types in microfounded DGE models. Whereas standard MARL fails to learn
non-trivial solutions, our structured learning curricula enable stable
convergence to meaningful solutions. Conceptually, our approach is more
flexible and does not need unrealistic assumptions, e.g., continuous market
clearing, that are commonly used for analytical tractability. Furthermore, our
end-to-end GPU implementation enables fast real-time convergence with a large
number of RL economic agents. We showcase our approach in open and closed
real-business-cycle (RBC) models with 100 worker-consumers, 10 firms, and a
social planner who taxes and redistributes. We validate the learned solutions
are $\epsilon$-meta-equilibria through best-response analyses, show that they
align with economic intuitions, and show our approach can learn a spectrum of
qualitatively distinct $\epsilon$-meta-equilibria in open RBC models. As such,
we show that hardware-accelerated MARL is a promising framework for modeling
the complexity of economies based on microfoundations.


  The edge-degeneracy model is an exponential random graph model that uses the
graph degeneracy, a measure of the graph's connection density, and number of
edges in a graph as its sufficient statistics. We show this model is relatively
well-behaved by studying the statistical degeneracy of this model through the
geometry of the associated polytope.


  This paper describes universal lossless coding strategies for compressing
sources on countably infinite alphabets. Classes of memoryless sources defined
by an envelope condition on the marginal distribution provide benchmarks for
coding techniques originating from the theory of universal coding over finite
alphabets. We prove general upper-bounds on minimax regret and lower-bounds on
minimax redundancy for such source classes. The general upper bounds emphasize
the role of the Normalized Maximum Likelihood codes with respect to minimax
regret in the infinite alphabet context. Lower bounds are derived by tailoring
sharp bounds on the redundancy of Krichevsky-Trofimov coders for sources over
finite alphabets. Up to logarithmic (resp. constant) factors the bounds are
matching for source classes defined by algebraically declining (resp.
exponentially vanishing) envelopes. Effective and (almost) adaptive coding
techniques are described for the collection of source classes defined by
algebraically vanishing envelopes. Those results extend ourknowledge concerning
universal coding to contexts where the key tools from parametric inference


  We generalize several important results from the perturbation theory of
linear operators to the setting of semisimple orthogonal symmetric Lie
algebras. These Lie algebras provide a unifying framework for various notions
of matrix diagonalization, such as the eigenvalue decomposition of real
symmetric or complex Hermitian matrices, and the real or complex singular value
decomposition. Concretely, given a path of structured matrices with a certain
smoothness, we study what kind of smoothness one can obtain for the
corresponding diagonalization of the matrices.


  Let $R$ be a ring with unity. The graph $\Gamma(R)$ is a graph with vertices
as elements of $R$, where two distinct vertices $a$ and $b$ are adjacent if and
only if $Ra+Rb=R$. Let $\Gamma_2(R)$ is the subgraph of $\Gamma(R)$ induced by
the non-unit elements. H.R. Maimani et al. [H.R. Maimani et al., Comaximal
graph of commutative rings, J. Algebra $319$ $(2008)$ $1801$-$1808$] proved
that: ``If $R$ is a commutative ring with unity and the graph
$\Gamma_2(R)\backslash J(R)$ is $n$-partite, then the number of maximal ideals
of $R$ is at most $n$." The proof of this result is not correct. In this paper
we present a correct proof for this result. Also we generalize some results
given in the aforementioned paper for the non-commutative rings.


  We have calculated the charge gap and spin gap for the two-chain Hubbard
model as a function of the on-site Coulomb interaction and the interchain
hopping amplitude. We used the density matrix renormalization group method and
developed a method to calculate separately the gaps numerically for the
symmetric and antisymmetric modes with respect to the exchange of the chain
indices. We have found very different behaviors for the weak and strong
interaction cases. Our calculated phase diagram is compared to the one obtained
by Balents and Fisher using the weak coupling renormalization group technique.


  Millions of learners worldwide are now using intelligent tutoring systems
(ITSs). At their core, ITSs rely on machine learning algorithms to track each
user's changing performance level over time to provide personalized
instruction. Crucially, student performance models are trained using
interaction sequence data of previous learners to analyse data generated by
future learners. This induces a cold-start problem when a new course is
introduced for which no training data is available. Here, we consider transfer
learning techniques as a way to provide accurate performance predictions for
new courses by leveraging log data from existing courses. We study two
settings: (i) In the naive transfer setting, we propose course-agnostic
performance models that can be applied to any course. (ii) In the inductive
transfer setting, we tune pre-trained course-agnostic performance models to new
courses using small-scale target course data (e.g., collected during a pilot
study). We evaluate the proposed techniques using student interaction sequence
data from 5 different mathematics courses containing data from over 47,000
students in a real world large-scale ITS. The course-agnostic models that use
additional features provided by human domain experts (e.g, difficulty ratings
for questions in the new course) but no student interaction training data for
the new course, achieve prediction accuracy on par with standard BKT and PFA
models that use training data from thousands of students in the new course. In
the inductive setting our transfer learning approach yields more accurate
predictions than conventional performance models when only limited student
interaction training data (<100 students) is available to both.


  Recent approaches for dialogue act recognition have shown that context from
preceding utterances is important to classify the subsequent one. It was shown
that the performance improves rapidly when the context is taken into account.
We propose an utterance-level attention-based bidirectional recurrent neural
network (Utt-Att-BiRNN) model to analyze the importance of preceding utterances
to classify the current one. In our setup, the BiRNN is given the input set of
current and preceding utterances. Our model outperforms previous models that
use only preceding utterances as context on the used corpus. Another
contribution of the article is to discover the amount of information in each
utterance to classify the subsequent one and to show that context-based
learning not only improves the performance but also achieves higher confidence
in the classification. We use character- and word-level features to represent
the utterances. The results are presented for character and word feature
representations and as an ensemble model of both representations. We found that
when classifying short utterances, the closest preceding utterances contributes
to a higher degree.


  Chemical AI is chemically synthesized artificial intelligence that has the
ability of learning in addition to information processing. A research project
on chemical AI, called the Molecular Cybernetics Project, was launched in Japan
in 2021 with the goal of creating a molecular machine that can learn a type of
conditioned reflex through the process called classical conditioning. If the
project succeeds in developing such a molecular machine, the next step would be
to configure a network of such machines to realize more complex functions. With
this motivation, this paper develops a method for learning a desired function
in the network of nodes each of which can implement classical conditioning.
First, we present a model of classical conditioning, which is called here a
classical conditioning gate. We then propose a learning algorithm for the
network of classical conditioning gates.


  We calculate the entanglement-assisted classical capacity of symmetric and
asymmetric Pauli channels where two consecutive uses of the channels are
correlated. It is evident from our study that in the presence of memory, a
higher amount of classical information is transmitted over quantum channels if
there exists prior entanglement as compared to product and entangled state
coding.


  Markovian growth-fragmentation processes introduced by Bertoin model a system
of growing and splitting cells in which the size of a typical cell evolves as a
Markov process $X$ without positive jumps. We find that two
growth-fragmentation processes associated respectively with two processes $X$
and $Y$ (with different laws) may have the same distribution, if $(X,Y)$ is a
bifurcator, roughly speaking, which means that they coincide up to a
bifurcation time and then evolve independently. Using this criterion, we deduce
that the law of a self-similar growth-fragmentation is determined by a cumulant
function $\kappa$ and its index of self-similarity.


  QBism is a recently developed version of Quantum Bayesianism. QBists think
that the primitive concept of experience is the central subject of science.
QBism refuses the idea that the quantum state of a system is an objective
description of this system. It is a tool for assigning a subjective probability
to the agent's future experience. So quantum mechanics does not directly say
something about the "external world". A measurement (in the usual sense) is
just a special case of what QBism calls experience and this is any action done
by any agent on her external world. The result of the measurement is the
experience that the agent gets from her action on her personal world. For
Qbists, this way of seeing the measurement helps rejecting any non-local
influences. We will examine if these claims are robust and will show that a
certain number of issues needs to be clarified in order to get a coherent
picture. Depending on the way these necessary clarifications are made, the
global image given by Qbism can vary from pure instrumentalism to
interpretations making the observer play a radical role.


  In this work, we use the Belief Function Theory which extends the
probabilistic framework in order to provide uncertainty bounds to different
categories of crowd density estimators. Our method allows us to compare the
multi-scale performance of the estimators, and also to characterize their
reliability for crowd monitoring applications requiring varying degrees of
prudence.


  We prove that every solution of the Helmholtz equation within an equilateral
triangle, which obeys the Dirichlet conditions on the boundary, is a member of
one of four symmetry classes. We then show how solutions with different
symmetries, or different energies, can be generated from any given solution
using symmetry operators or a differential operator derived from symmetry
considerations. Our method also provides a novel way of generating the ground
state solution (that is, the solution with the lowest energy). Finally, we
establish a correspondence between solutions in the equilateral and (30,60, 90)
triangles.


  Oscillation modes with a mixed character, as observed in evolved low-mass
stars, are highly sensitive to the physical properties of the innermost
regions. Measuring their properties is therefore extremely important to probe
the core, but requires some care, due to the complexity of the mixed-mode
pattern. This work aims at providing a consistent description of the mixed-mode
pattern of low-mass stars, based on the asymptotic expansion. We also aim at
studying the variation of the gravity offset $\varepsilon_{g}$ with stellar
evolution. We revisit previous work about mixed modes in red giants and
empirically test how period spacings, rotational splittings, mixed-mode widths
and heights can be estimated in a consistent view, based on the properties of
the mode inertia ratios. From the asymptotic fit of the mixed-mode pattern of a
large set of red giants at various evolutionary stages, we derive unbiased and
precise asymptotic parameters. As the asymptotic expansion of gravity modes is
verified with a precision close to the frequency resolution for stars on the
red giant branch (10$^{-4}$ in relative values), we can derive accurate values
of the asymptotic parameters. We decipher the complex pattern in a rapidly
rotating star, and explain how asymmetrical splittings can be inferred, as well
as the stellar inclinations. This allows us to revisit the stellar inclinations
in two open clusters, NGC 6819 and NGC 6791: our results show that the stellar
inclinations in these clusters do not have privileged orientation in the sky.
The variation of the asymptotic gravity offset along with stellar evolution is
investigated in detail. We also derive generic properties that explain under
which conditions mixed modes can be observed.


  We will report on an ongoing effort towards calculating the N4LO perturbative
QCD corrections to the DIS total inclusive cross-section. We are developing a
method based on differential equations and series expansion in the inverse
Bjorken parameter. As a byproduct our calculation should also deliver analytic
or at least precise numerical approximations for the four-loop splitting
functions.


  Quantum mechanics is a successful theory that describes the behavior of
photons, electrons, and other atomic- and molecular-scale objects. However, it
is far from being well understood. In this paper, a new theory - knot physics
for entangled vortex-membranes is developed to explore the underline physics of
quantum mechanics. From point view of information, three dimensional quantum
Dirac model is developed to effectively describe the fluctuations of local
deformation of vortex-membranes: The elementary excitations are knots with
information unit; The physics quality to describe local deformation is knot
density that is defined by the density of zeros between two projected
vortex-membranes; The Biot-Savart equation for Kelvin waves becomes Schrodinger
equation for probability waves of knots; the classical functions for
perturbative Kelvin waves become wave functions for knots; The probability of
quantum mechanics comes from dynamic projection for inner observers owing to
"fast clock" effect; The angular frequency for leapfrogging motion plays the
role of the mass of knots; etc. This work would help people to understand the
mystery of quantum mechanics.


  We propose and analyze a space-time virtual element method for the
discretization of the heat equation in a space-time cylinder, based on a
standard Petrov-Galerkin formulation. Local discrete functions are solutions to
a heat equation problem with polynomial data. Global virtual element spaces are
nonconforming in space, so that the analysis and the design of the method are
independent of the spatial dimension. The information between time slabs is
transmitted by means of upwind terms involving polynomial projections of the
discrete functions. We prove well posedness and optimal error estimates for the
scheme, and validate them with several numerical tests.


  We consider the problem of direction finding using partly calibrated arrays,
a distributed subarray with position errors between subarrays. The key
challenge is to enhance angular resolution in the presence of position errors.
To achieve this goal, existing algorithms, such as subspace separation and
sparse recovery, have to rely on multiple snapshots, which increases the burden
of data transmission and the processing delay. Therefore, we aim to enhance
angular resolution using only a single snapshot. To this end, we exploit the
orthogonality of the signals of partly calibrated arrays. Particularly, we
transform the signal model into a special multiple-measurement model, show that
there is approximate orthogonality between the source signals in this model,
and then use blind source separation to exploit the orthogonality. Simulation
and experiment results both verify that our proposed algorithm achieves high
angular resolution as distributed arrays without position errors, inversely
proportional to the whole array aperture.


  Dynamical systems that are invariant under the action of a non-trivial
symmetry group can possess structurally stable heteroclinic cycles. In this
paper we study stability properties of a class of structurally stable
heteroclinic cycles in R^n which we call heteroclinic cycles of type Z. It is
well-known that a heteroclinic cycle that is not asymptotically stable can
attract nevertheless a positive measure set from its neighbourhood. We say that
an invariant set X is fragmentarily asymptotically stable, if for any delta>0
the measure of its local basin of attraction B_delta(X) is positive. A local
basin of attraction B_delta(X) is the set of such points that trajectories
starting there remain in the delta-neighbourhood of X for all t>0, and are
attracted by X as t\to\infty. Necessary and sufficient conditions for
fragmentary asymptotic stability are expressed in terms of eigenvalues and
eigenvectors of transition matrices. If all transverse eigenvalues of
linearisations near steady states involved in the cycle are negative, then
fragmentary asymptotic stability implies asymptotic stability. In the latter
case the condition for asymptotic stability is that the transition matrices
have an eigenvalue larger than one in absolute value. Finally, we discuss
bifurcations occurring when the conditions for asymptotic stability or for
fragmentary asymptotic stability are broken.


  In this paper, we classify Left-invariant Ricci collineations associated to
Yano connections on three-dimensional Lorentzian Lie groups.


  We present well-sampled $UBVRIJHK$ photometry of SN 2002fk starting 12 days
before maximum light through 122 days after peak brightness, along with a
series of 15 optical spectra from -4 to +95 days since maximum. Our
observations show the presence of C II lines in the early-time spectra of SN
2002fk, expanding at ~11,000 km s$^{-1}~$ and persisting until ~8 days past
maximum light with a velocity of $\sim$9,000 km s$^{-1}~$. SN 2002fk is
characterized by a small velocity gradient of $\dot v_{Si~II}=26$ km s$^{-1}$
day$^{-1}$, possibly caused by an off-center explosion with the ignition region
oriented towards the observer. The connection between viewing angle of an
off-center explosion and the presence of C II in the early time spectrum
suggests that the observation of C II could be also due to a viewing angle
effect. Adopting the Cepheid distance to NGC 1309 we provide the first $H_{0}$
value based on near-IR measurements of a Type Ia supernova between 63.0$\pm$
0.8 ($\pm$ 2.8 systematic) and 66.7$\pm$1.0 ($\pm$ 3.5 systematic) km/s/Mpc,
depending on the absolute magnitude/decline rate relationship adopted. It
appears that the near-IR yields somewhat lower (6-9 %) $H_0$ values than the
optical. It is essential to further examine this issue by (1) expanding the
sample of high-quality near-IR light curves of SNe in the Hubble flow, and (2)
increasing the number of nearby SNe with near-IR SN light curves and precise
Cepheid distances, which affords the promise to deliver a more precise
determination of $H_0$.


  We report the discovery of the new pulsar wind nebula (PWN) G141.2+5.0 in
data observed with the Dominion Radio Astrophysical Observatory's Synthesis
Telescope at 1420 MHz. The new PWN has a diameter of about 3.5', which
translates at a distance of 4.0 kpc to a spatial extent of about 4 pc. It
displays a radio spectral index of $\alpha\approx -0.7$, similar to the PWN
G76.9+1.1. G141.2+5.0 is highly polarized up to 40% with an average of 15% in
the 1420 MHz data. It is located in the centre of a small spherical HI bubble,
which is expanding at a velocity of 6 km/s. The bubble's systemic velocity is
-53 km/s and could be the result of the progenitor star's mass loss or the
shell-type SNR created by the same supernova explosion in a highly advanced
stage. The systemic velocity of the bubble shares the velocity of HI associated
with the Cygnus spiral arm, which is seen across the 2nd and 3rd quadrants and
an active star-forming arm immediately beyond the Perseus arm. A kinematical
distance of 4+/-0.5 kpc is found for G141.2+5.0, similar to the optical
distance of the Cygnus arm (3.8+/-1.1 kpc) and its kinematic HI distance
(4.4+/-0.6 kpc). G141.2+5.0 represents the first radio PWN discovered in 17
years and the first SNR discovered in the Cygnus spiral arm, which is in stark
contrast with the Perseus arm's overwhelming population of shell-type remnants.


  Scaling of various local observables with a system size at Anderson
transition criticality is characterized by a generalized multifractality. We
study the generalized multifractality in the spin quantum Hall symmetry class
(class C) in the presence of interaction. We employ Finkel'stein nonlinear
sigma model and construct the pure scaling derivativeless operators for class C
in the presence of interaction. Within the two-loop renormalization group
analysis we compute the anomalous dimensions of the pure scaling operators and
demonstrate that they are affected by the interaction. We find that the
interaction breaks exact symmetry relations between generalized multifractal
exponents known for a noninteracting problem.


  In this article we study higher preprojective algebras, showing that various
known results for ordinary preprojective algebras generalize to the higher
setting. We first show that the quiver of the higher preprojective algebra is
obtained by adding arrows to the quiver of the original algebra, and these
arrows can be read off from the last term of the bimodule resolution of the
original algebra. In the Koszul case we are able to obtain the new relations of
the higher preprojective algebra by differentiating a superpotential and we
show that when our original algebra is $d$-hereditary all the relations come
from the superpotential.
  We then construct projective resolutions of all simple modules for the higher
preprojective algebra of a $d$-hereditary algebra. This allows us to recover
various known homological properties of the higher preprojective algebras and
to obtain a large class of almost Koszul dual pairs of algebras. We also show
that when our original algebra is Koszul there is a natural map from the
quadratic dual of the higher preprojective algebra to a graded trivial
extension algebra.


  These lecture notes review current progress on the class of conformal
theories which may be studied by quantizing the conformal Toda dynamics. After
summarizing recent developments in undertanding the quantum group structure of
the Liouville theory, one recalls how classically, two-dimensional black holes
come out from the non-abelian Toda systems, and reviews the geometrical
interpretation of the classical $A_n$-Toda theories, just put forward, that
relates W-geometries with the external geometries of holomorphic surfaces in
complex projective spaces.


  Context. Two millisecond pulsars, PSR J1513$-$2550 and PSR J2017$-$1614, with
spin periods of about 2.1 and 2.3 ms were recently discovered in the radio and
$\gamma$-rays and classified as black widow pulsars in tight binary stellar
systems with orbital periods of about 4.3 and 2.3 h. Aims. Our goals are to
reveal fundamental parameters of both systems and their binary components using
multi-wavelength observations. Methods. We carried out the first time-series
multi-band optical photometry of the objects with the 2.1-metre telescope of
the Observatorio Astron\'omico Nacional San Pedro M\'artir, the 6.5-metre
\magel-1 telescope, and the 10.4-metre Gran Telescopio Canarias. To derive the
parameters of both systems, we fitted the obtained light curves with a model
assuming heating of the companion by the pulsar. We also analysed archival
X-ray data obtained with the XMM-Newton observatory. Results. For the first
time, we firmly identified J1513$-$2550 in the optical and both pulsars in
X-rays. The optical light curves of both systems have a single peak per orbital
period with peak-to-peak amplitude of $\gtrsim2$ magnitudes. The J2017$-$1614
light curves are symmetric, while J1513$-$2550 demonstrates strong asymmetry
whose nature remains unclear. Conclusions. We constrained the orbital
inclinations, pulsar masses, companion temperatures and masses, as well as the
distances to both systems. We also conclude that J2017$-$1614 may contain a
massive neutron star of 2.4$\pm$0.6 M$_{\odot}$. The X-ray spectra of both
sources can be fitted by power laws with parameters typical for black widow
systems.


  If $G_1,...,G_n$ are limit groups and $S\subset G_1\times...\times G_n$ is of
type $\FP_n(\mathbb Q)$ then $S$ contains a subgroup of finite index that is
itself a direct product of at most $n$ limit groups. This settles a question of
Sela.


  Unique affine extensions $H^{\aff}_2$, $H^{\aff}_3$ and $H^{\aff}_4$ are
determined for the noncrystallographic Coxeter groups $H_2$, $H_3$ and $H_4$.
They are used for the construction of new mathematical models for quasicrystal
fragments with 10-fold symmetry. The case of $H^{\aff}_2$ corresponding to
planar point sets is discussed in detail. In contrast to the cut-and-project
scheme we obtain by construction finite point sets, which grow with a model
specific growth parameter.


  Object detection is crucial for ensuring safe autonomous driving. However,
data-driven approaches face challenges when encountering minority or novel
objects in the 3D driving scene. In this paper, we propose VisLED, a
language-driven active learning framework for diverse open-set 3D Object
Detection. Our method leverages active learning techniques to query diverse and
informative data samples from an unlabeled pool, enhancing the model's ability
to detect underrepresented or novel objects. Specifically, we introduce the
Vision-Language Embedding Diversity Querying (VisLED-Querying) algorithm, which
operates in both open-world exploring and closed-world mining settings. In
open-world exploring, VisLED-Querying selects data points most novel relative
to existing data, while in closed-world mining, it mines novel instances of
known classes. We evaluate our approach on the nuScenes dataset and demonstrate
its efficiency compared to random sampling and entropy-querying methods. Our
results show that VisLED-Querying consistently outperforms random sampling and
offers competitive performance compared to entropy-querying despite the
latter's model-optimality, highlighting the potential of VisLED for improving
object detection in autonomous driving scenarios. We make our code publicly
available at https://github.com/Bjork-crypto/VisLED-Querying


  In this paper, we propose a deep learning based model for Acoustic Anomaly
Detection of Machines, the task for detecting abnormal machines by analysing
the machine sound. By conducting extensive experiments, we indicate that
multiple techniques of pseudo audios, audio segment, data augmentation,
Mahalanobis distance, and narrow frequency bands, which mainly focus on feature
engineering, are effective to enhance the system performance. Among the
evaluating techniques, the narrow frequency bands presents a significant
impact. Indeed, our proposed model, which focuses on the narrow frequency
bands, outperforms the DCASE baseline on the benchmark dataset of DCASE 2022
Task 2 Development set. The important role of the narrow frequency bands
indicated in this paper inspires the research community on the task of Acoustic
Anomaly Detection of Machines to further investigate and propose novel network
architectures focusing on the frequency bands.


  We investigate if feedback can increase the capacity of an energy harvesting
communication channel where a transmitter powered by an exogenous energy
arrival process and equipped with a finite battery communicates to a receiver
over a memoryless channel. For a simple special case where the energy arrival
process is deterministic and the channel is a BEC, we explicitly compute the
feed-forward and feedback capacities and show that feedback can strictly
increase the capacity of this channel. Building on this example, we also show
that feedback can increase the capacity when the energy arrivals are i.i.d.
known noncausally at the transmitter and the receiver.


  We construct a Hereditarily Indecomposable Banach space $\eqs_d$ with a
Schauder basis \seq{e}{n} on which there exist strictly singular non-compact
diagonal operators. Moreover, the space $\mc{L}_{\diag}(\eqs_d)$ of diagonal
operators with respect to the basis \seq{e}{n} contains an isomorphic copy of
$\ell_{\infty}(\N)$.


  A new two-pole approximation, which allows to describe the transition from an
insulating state to a metallic one at increase of bandwidth, and also the
observable in some compounds transition from a metalic state to an insulating
one with increasing temperature, is presented. The case of a paramagnetic
narrow-band material at half-filling is considered. Single-particle Green
function and energy spectrum of electron system are calculated. The expressions
for energy gap width and the concentration of polar states (holes or doublons)
are obtained. The conditions for metallic and insulating states are found.


  We study gravitational perturbations around the near horizon geometry of the
(near) extreme Kerr black hole. By considering a consistent truncation for the
metric fluctuations, we obtain a solution to the linearized Einstein equations.
The dynamics is governed by two master fields which, in the context of the
nAdS$_2$/nCFT$_1$ correspondence, are both irrelevant operators of conformal
dimension $\Delta=2$. These fields control the departure from extremality by
breaking the conformal symmetry of the near horizon region. One of the master
fields is tied to large diffeomorphisms of the near horizon, with its equations
of motion compatible with a Schwarzian effective action. The other field is
essential for a consistent description of the geometry away from the horizon.


  We characterize $A_\infty$-structures that are transfers over a chain
homotopy equivalence or a quasi-isomorphism, answering a question posed by D.
Sullivan. Along the way, we present an obstruction theory for weak
$A_\infty$-morphisms over an arbitrary commutative ring. We then generalize our
results to ${\mathcal P}_\infty$-structures over a field of characteristic
zero, for any quadratic Koszul operad ${\mathcal P}$.


  Direct calculation of the one-loop contributions to the energy density of
bosonic and supersymmetric phi-to-the-fourth kinks exhibits: (1) Local mode
regularization. Requiring the mode density in the kink and the trivial sectors
to be equal at each point in space yields the anomalous part of the energy
density. (2) Phase space factorization. A striking position-momentum
factorization for reflectionless potentials gives the non-anomalous energy
density a simple relation to that for the bound state. For the supersymmetric
kink, our expression for the energy density (both the anomalous and
non-anomalous parts) agrees with the published central charge density, whose
anomalous part we also compute directly by point-splitting regularization.
Finally we show that, for a scalar field with arbitrary scalar background
potential in one space dimension, point-splitting regularization implies local
mode regularization of the Casimir energy density.


  We present an analysis of the gamma-ray measurements by the Large Area
Telescope onboard the \textit{Fermi Gamma-ray Space Telescope} in the region of
the supernova remnant~(SNR) Monoceros Loop~(G205.5$+$0.5). The brightest
gamma-ray peak is spatially correlated with the Rosette Nebula, which is a
molecular cloud complex adjacent to the southeast edge of the SNR. After
subtraction of this emission by spatial modeling, the gamma-ray emission from
the SNR emerges, which is extended and fit by a Gaussian spatial template. The
gamma-ray spectra are significantly better reproduced by a curved shape than a
simple power law. The luminosities between 0.2--300~GeV are $\sim$~$4 \times
10^{34}$~erg~s$^{-1}$ for the SNR and $\sim$~$3 \times 10^{34}$~erg~s$^{-1}$
for the Rosette Nebula, respectively. We argue that the gamma rays likely
originate from the interactions of particles accelerated in the SNR. The decay
of neutral pions produced in nucleon-nucleon interactions of accelerated
hadrons with interstellar gas provides a reasonable explanation for the
gamma-ray emission of both the Rosette Nebula and the Monoceros SNR.