  The availability of handy multi-modal (i.e., RGB-D) sensors has brought about
a surge of face anti-spoofing research. However, the current multi-modal face
presentation attack detection (PAD) has two defects: (1) The framework based on
multi-modal fusion requires providing modalities consistent with the training
input, which seriously limits the deployment scenario. (2) The performance of
ConvNet-based model on high fidelity datasets is increasingly limited. In this
work, we present a pure transformer-based framework, dubbed the Flexible Modal
Vision Transformer (FM-ViT), for face anti-spoofing to flexibly target any
single-modal (i.e., RGB) attack scenarios with the help of available
multi-modal data. Specifically, FM-ViT retains a specific branch for each
modality to capture different modal information and introduces the Cross-Modal
Transformer Block (CMTB), which consists of two cascaded attentions named
Multi-headed Mutual-Attention (MMA) and Fusion-Attention (MFA) to guide each
modal branch to mine potential features from informative patch tokens, and to
learn modality-agnostic liveness features by enriching the modal information of
own CLS token, respectively. Experiments demonstrate that the single model
trained based on FM-ViT can not only flexibly evaluate different modal samples,
but also outperforms existing single-modal frameworks by a large margin, and
approaches the multi-modal frameworks introduced with smaller FLOPs and model
parameters.


  Experiments as IceCube or Super-Kamiokande have been successful in detecting
highly energetic neutrinos in the. Neutrinos in the ultra-low energy range
($\mathcal{E}<1.0~\rm{eV}$) have been theoretically predicted but their
observation remain elusive, and no concrete experimental scheme has been
proposed for that job. Here, we propose a novel scheme based on graphene
plasmonic metamaterials to designed to detect ultra-low energetic neutrinos. We
claim that slow neutrino fluxes, interacting with solid-state plasmas, can
generate an instability due to the weak neutrino-plasmon interaction, which is
reminiscent of the beam-plasma instability taking place in astrophysics and
laboratory plasmas. We make use of the semi-classical limit of the weak
interaction to describe the coupling between the neutrinos and electrons in
graphene. To render the scheme practical, we investigate the neutrino-plasma
instability produced in a graphene metamaterial, composed by a periodic
stacking of graphene layers. Our findings reveal that the controlled excitation
of plasma waves in such graphene metamaterial allows for the detection of
neutrinos in the energy range $\sim 1.0~\rm{\mu eV}-100~\rm{meV}$, and fluxes
in the range $10^{4}-10^{10} \rm{cm^{-2} s^{-1}}$.


  We derive a total set of MHD equations in SM describing evolution of a dense
plasma with neutrinos. First this is done for a hot pair plasma consisting of
electrons and positrons, neutrinos and antineutrinos of all flavors in an
isotropic medium like the early universe plasma at the lepton stage. Then we
find how axial vector currents violating parity in SM contribute to MHD for a
slightly polarized (anisotropic) plasma where a new mechanism for the
amplification of mean magnetic fields arises due to the collective
neutrino-plasma interactions instead of assumed asymmetry of fluid velocity
vortices leading to the same effect of $\alpha^2$-dynamo.


  This paper reviews the development status of GRAPE (the Gamma-Ray Polarimeter
Experiment), a hard X-ray Compton Polarimeter. The purpose of GRAPE is to
measure the polarization of hard X-rays in the 50-300 keV energy range. We are
particularly interested in X-rays that are emitted from solar flares and
gamma-ray bursts (GRBs), although GRAPE could also be employed in the study of
other astrophysical sources. Accurately measuring the polarization of the
emitted radiation will lead to a better understating of both emission
mechanisms and source geometries. The GRAPE design consists of an array of
plastic scintillators surrounding a central high-Z crystal scintillator. The
azimuthal distribution of photon scatters from the plastic array into the
central calorimeter provides a measure of the polarization fraction and
polarization angle of the incident radiation. The design of the detector
provides sensitivity over a large field-of-view (>pi steradian). The design
facilitates the fabrication of large area arrays with minimal deadspace. This
paper presents the latest design concept and the most recent results from
laboratory tests of a GRAPE science model.


  Deep Video Quality Assessment (VQA) methods have shown impressive
high-performance capabilities. Notably, no-reference (NR) VQA methods play a
vital role in situations where obtaining reference videos is restricted or not
feasible. Nevertheless, as more streaming videos are being created in
ultra-high definition (e.g., 4K) to enrich viewers' experiences, the current
deep VQA methods face unacceptable computational costs. Furthermore, the
resizing, cropping, and local sampling techniques employed in these methods can
compromise the details and content of original 4K videos, thereby negatively
impacting quality assessment. In this paper, we propose a highly efficient and
novel NR 4K VQA technology. Specifically, first, a novel data sampling and
training strategy is proposed to tackle the problem of excessive resolution.
This strategy allows the VQA Swin Transformer-based model to effectively train
and make inferences using the full data of 4K videos on standard consumer-grade
GPUs without compromising content or details. Second, a weighting and scoring
scheme is developed to mimic the human subjective perception mode, which is
achieved by considering the distinct impact of each sub-region within a 4K
frame on the overall perception. Third, we incorporate the frequency domain
information of video frames to better capture the details that affect video
quality, consequently further improving the model's generalizability. To our
knowledge, this is the first technology for the NR 4K VQA task. Thorough
empirical studies demonstrate it not only significantly outperforms existing
methods on a specialized 4K VQA dataset but also achieves state-of-the-art
performance across multiple open-source NR video quality datasets.


  This paper presents an intertemporal bimodal network to analyze the evolution
of the semantic content of a scientific field within the framework of topic
modeling, namely using the Latent Dirichlet Allocation (LDA). The main
contribution is the conceptualization of the topic dynamics and its
formalization and codification into an algorithm. To benchmark the
effectiveness of this approach, we propose three indexes which track the
transformation of topics over time, their rate of birth and death, and the
novelty of their content. Applying the LDA, we test the algorithm both on a
controlled experiment and on a corpus of several thousands of scientific papers
over a period of more than 100 years which account for the history of the
economic thought.


  This paper constructs an analytic form for a triaxial potential that
describes the dynamics of a wide variety of astrophysical systems, including
the inner portions of dark matter halos, the central regions of galactic
bulges, and young embedded star clusters. Specifically, this potential results
from a density profile of the form $\rho (m) \propto m^{-1}$, where the radial
coordinate is generalized to triaxial form so that $m^2 = x^2/a^2 + y^2/b^2 +
z^2/c^2 $. Using the resulting analytic form of the potential, and the
corresponding force laws, we construct orbit solutions and show that a robust
orbit instability exists in these systems. For orbits initially confined to any
of the three principal planes, the motion in the perpendicular direction can be
unstable. We discuss the range of parameter space for which these orbits are
unstable, find the growth rates and saturation levels of the instability, and
develop a set of analytic model equations that elucidate the essential physics
of the instability mechanism. This orbit instability has a large number of
astrophysical implications and applications, including understanding the
formation of dark matter halos, the structure of galactic bulges, the survival
of tidal streams, and the early evolution of embedded star clusters.


  We prove an equivariant Lefschetz formula for elliptic complexes over a
compact manifold carrying the action of a compact Lie group of isometries via
heat equation methods.


  A sound synthesis model for woodwind instruments is developed using modal
decomposition of the input impedance, accounting for viscothermal losses as
well as localized nonlinear losses at the end of the resonator. To extend the
definition of the input impedance to the nonlinear domain, the method
incorporates a dependence on the RMS acoustic velocity at a geometric
discontinuity. The poles and residues resulting from the modal decomposition
are then fitted with respect to this velocity. Thus, the pressure-flow relation
defined by the resonator is completed by new equations which account for the
dependence with the RMS velocity at the end of the tube. The ability of the
model to reproduce the bifurcation diagram of a reed instrument was confirmed
in a previous article from the authors [1]. The present work focuses on the
influence of localized nonlinear losses on the acoustic pressure signal.
Results are discussed with the observations of [2].


  The paper investigates the milli-arcsecond scale structure of the present-day
mass-loss of the post-Red Supergiant IRC+10420. We use three telescopes of the
VLT Interferometer in combination with the AMBER near-infrared beam combiner to
measure spectrally dispersed correlated fluxes in the K-band around the Br
gamma transition. The resulting visibilities are compared to the predicted
visibilities of emission structures with various simple models in order to
infer the size of the observed emission region. The Br gamma line is resolved
by VLTI+AMBER on all three baselines, with the maximum projected baseline
extending 69 meter and a P.A. ranging between 10 and 30 degrees. A differential
phase between line and continuum is detected on the longest baseline. The Br
gamma emission region is found to have a diameter of 3.3 milli-arcseconds
(FWHM), when compared to a Gaussian intensity distribution. A uniform disk and
a ring-like intensity distribution do not fit the line visibilities. Comparing
the AMBER equivalent width of Br gamma with measurements from various epochs,
we find that the stellar photosphere contributes about 60% of the total
continuum light at 2.2 micron. The remaining 40% continuum emission is found on
scales larger than the 66mas AMBER field of view. Using simple arguments, and
assuming optically thick line emission, we find that the line emitting region
is elongated. We briefly discuss the possibilities whether such a structure is
due to a bi-polar flow or a circumstellar disk. (Abridged).


  Let $A$ be an abelian scheme over a smooth affine complex variety $S$,
$\varOmega_A$ the $\sO_S$-module of $1$-forms of the first kind on $A$,
$\sD_S\varOmega_A$ the $\sD_S$-module spanned by $\varOmega_A$ in the first
algebraic De Rham cohomology module, and $\theta_\partial: \varOmega_A \to
\sD_S\varOmega_A/\varOmega_A$ the Kodaira-Spencer map attached to a tangent
vector field $\partial$ on $S$. We compare the rank of
$\sD_S\varOmega_A/\varOmega_A$ to the maximal rank of $\theta_\partial$ when
$\partial$ varies: we show that both ranks do not change when one passes to the
"modular case", \ie when one replaces $S$ by the smallest weakly special
subvariety of $\sA_g$ containing the image of $S$ (assuming, as one may up to
isogeny, that $A/S$ is principally polarized), we then analyse the "modular
case" and deduce, for instance, that {\it for any abelian pencil of relative
dimension $g$ with Zariski-dense monodromy in $Sp_{2g}$}, {\it the derivative
with respect to a parameter of a non zero abelian integral of the first kind is
never of the first kind}.


  Nonconfining Schwinger Model [AR] is studied with a one parameter class of
kinetic energy like regularization. It may be thought of as a generalization
over the regularization considered in [AR]. Phasespace structure has been
determined in this new situation. The mass of the gauge boson acquires a
generalized expression with the bare coupling constant and the parameters
involved in the regularization. Deconfinement scenario has become transparent
at the quark-antiquark potential level.


  The paper deals with the approximate solution of integro-differential
equations of Prandtl's type. Quadrature methods involving ``optimal'' Lagrange
interpolation processes are proposed and conditions under which they are stable
and convergent in suitable weighted spaces of continuous functions are proved.
  The efficiency of the method has been tested by some numerical experiments,
some of them including comparisons with other numerical procedures. In
particular, as an application, we have implemented the method for solving
Prandtl's equation governing the circulation air flow along the contour of a
plane wing profile, in the case of elliptic or rectangular wing-shape.


  In this paper we introduce the notion of weak operator and the theory of
Yetter-Drinfeld modules over a weak braided Hopf algebra with invertible
antipode in a strict monoidal category. We prove that the class of such objects
constitutes a non strict monoidal category. It is also shown that this category
is not trivial, that is to say that it admits objects generated by the adjoint
action (coaction) associated to the weak braided Hopf algebra.


  An enhancement of vortex-motion damping in thin Pb/In superconducting films
is obtained through coupling to an adjacent two-dimensional electron gas formed
in a modulation-doped GaAs/AlGaAs heterostructure. This effect is observed by
monitoring the power dissipation at the superconductor in the vortex state
while increasing the density of the electron gas using a gate voltage.
Quantitative agreement is found with calculations based on a viscous model of
vortex damping which considers generation of eddy currents in the electron gas
by moving flux lines. In the regime of filamentary and channel vortex flow,
eddy-current damping leads to striking dissipation breakdown due to stopping of
entire vortex channels.


  We show that any coboundary Lie bialgebra can be quantized. For this, we
prove that: (a) Etingof-Kazhdan quantization functors are compatible with Lie
bialgebra twists, and (b) if such a quantization functor corresponds to an even
associator, then it is also compatible with the operation of taking
coopposites. We also use the relation between the Etingof-Kazhdan construction
of quantization functors and the alternative approach to this problem, which
was established in a previous work.


  We study the evolution of the cross-correlation between voids and the mass
density field - i.e. of void profiles. We show that approaches based on the
spherical model alone miss an important contribution to the evolution on large
scales of most interest to cosmology: they fail to capture the well-known fact
that the large-scale bias factor of conserved tracers evolves. We also show
that the operations of evolution and averaging do not commute, but this
difference is only significant within about two effective radii. We show how to
include a term which accounts for the evolution of bias, which is directly
related to the fact that voids move. The void motions are approximately
independent of void size, so they are more significant for smaller voids that
are typically more numerous. This term also contributes to void-matter pairwise
velocities: including it is necessary for modeling the typical outflow speeds
around voids. It is, therefore, important for void redshift space distortions.
Finally, we show that the excursion set peaks/troughs approach provides a
useful, but not perfect framework for describing void profiles and their
evolution.


  A fermion node is subset of fermionic configurations for which a real wave
function vanishes due to the antisymmetry and the node divides the
configurations space into compact nodal cells (domains). We analyze the
properties of fermion nodes of fermionic ground state wave functions for a
number of systems. For several models we demonstrate that noninteracting
spin-polarized fermions in dimension two and higher have closed-shell ground
state wave functions with the minimal two nodal cells for any system size and
we formulate a theorem which sumarizes this result. The models include periodic
fermion gas, fermions on the surface of a sphere, fermions in a box. We prove
the same property for atomic states with up to 3d half-filled shells. Under
rather general assumptions we then derive that the same is true for unpolarized
systems with arbitrarily weak interactions using Bardeen-Cooper-Schrieffer
(BCS) variational wave function. We further show that pair correlations
included in the BCS wave function enable singlet pairs of particles to wind
around the periodic box without crossing the node pointing towards the
relationship of nodes to transport and many-body phases such as
superconductivity. Finally, we point out that the arguments extend also to
fermionic temperature dependent/imaginary-time density matrices. The results
reveal fundamental properties of fermion nodal structures and provide new
insights for accurate constructions of wave functions and density matrices in
quantum and path integral Monte Carlo methods.


  DBSCAN is a classical density-based clustering procedure with tremendous
practical relevance. However, DBSCAN implicitly needs to compute the empirical
density for each sample point, leading to a quadratic worst-case time
complexity, which is too slow on large datasets. We propose DBSCAN++, a simple
modification of DBSCAN which only requires computing the densities for a chosen
subset of points. We show empirically that, compared to traditional DBSCAN,
DBSCAN++ can provide not only competitive performance but also added robustness
in the bandwidth hyperparameter while taking a fraction of the runtime. We also
present statistical consistency guarantees showing the trade-off between
computational cost and estimation rates. Surprisingly, up to a certain point,
we can enjoy the same estimation rates while lowering computational cost,
showing that DBSCAN++ is a sub-quadratic algorithm that attains minimax optimal
rates for level-set estimation, a quality that may be of independent interest.


  In the last decade, a variety of high-precision experiments have searched for
miniscule violations of Lorentz symmetry. These searches are largely motivated
by the possibility of uncovering experimental signatures from a fundamental
unified theory. Experimental results are reported in the framework called the
Standard-Model Extension (SME), which describes general Lorentz violation for
each particle species in terms of its coefficients for Lorentz violation.
Recently, the role of gravitational experiments in probing the SME has been
explored in the literature. In this talk, I will summarize theoretical and
experimental aspects of these works. I will also discuss recent lunar laser
ranging and atom interferometer experiments, which place stringent constraints
on gravity coefficients for Lorentz violation.


  We propose a generalization of the isometry transformations to the geometric
context of the field theories with spin where the local frames are explicitly
involved. We define the external symmetry transformations as isometries
combined with suitable tetrad gauge transformations and we show that these form
a group which is locally isomorphic with the isometry one. We point out that
the symmetry transformations that leave invariant the equations of the fields
with spin have generators with specific spin terms which represent new physical
observables. The examples we present are the generators of the central symmetry
and those of the maximal symmetries of the de Sitter and anti-de Sitter
spacetimes derived in different tetrad gauge fixings.
  Pacs: 04.20.Cv, 04.62.+v, 11.30.-j


  Recently observed spectrum of $P_c$ states exhibits a strong link to
$\Sigma_c \bar{D}^{(*)}$ thresholds. In spite of successful molecular
interpretations, we still push forward to wonder whether there exist finer
structures. Utilizing the effecitve lagrangians respecting heavy quark symmetry
and chiral symmetry, as well as instantaneous Bethe-Salpeter equations, we
investigate the $\Sigma_c \bar{D}^{(*)}$ interactions and three $P_c$ states.
We confirm that $P_c(4312)$ and $P_c(4440)$ are good candidates of $\Sigma_c
\bar{D}$ and $\Sigma_c \bar{D}^{*}$ molecules with spin-$\frac12$,
respectively. Unlike other molecular calculations, our results indicate
$P_c(4457)$ signal might be a mixture of spin-$\frac32$ and spin-$\frac12$
$\Sigma_c \bar{D}^{*}$ molecules, where the latter one appears to be an
excitation of $P_c(4440)$. Therefore we conclude that, confronting three LHCb
$P_c$ signals, there may exist not three, but four molecular states.


  The current and the shot noise in a graphene sheet were analyzed in the
ballistic regime for arbitrary voltage drops between leads and the sheet in the
limit of infinite aspect ratio of the sheet width to its length, when
quantization of transversal wave vectors is not essential. The cases of
coherent and incoherent ballistic transport were compared. At high voltages the
difference with coherent transport is not essential. But at low voltages
conductance and Fano-factor dependences for incoherent transport become
non-monotonous so that the conductance has a minimum and the Fano factor has a
maximum at non-zero voltage bias.


  A single unicast index coding problem (SUICP) is called symmetric neighboring
and consecutive (SNC) side-information problem if it has $K$ messages and $K$
receivers, the $k$th receiver $R_{k}$ wanting the $k$th message $x_{k}$ and
having the side-information $D$ messages immediately after $x_k$ and $U$
($D\geq U$) messages immediately before $x_k$. Maleki, Cadambe and Jafar
obtained the capacity of this SUICP(SNC) and proposed $(U+1)$-dimensional
optimal length vector linear index codes by using Vandermonde matrices.
However, for a $b$-dimensional vector linear index code, the transmitter needs
to wait for $b$ realizations of each message and hence the latency introduced
at the transmitter is proportional to $b$. For any given single unicast index
coding problem (SUICP) with the side-information graph $G$, MAIS($G$) is used
to give a lowerbound on the broadcast rate of the ICP. In this paper, we derive
MAIS($G$) of SUICP(SNC) with side-information graph $G$. We construct scalar
linear index codes for SUICP(SNC) with length $\left \lceil \frac{K}{U+1}
\right \rceil - \left \lfloor \frac{D-U}{U+1} \right \rfloor$. We derive the
minrank($G$) of SUICP(SNC) with side-information graph $G$ and show that the
constructed scalar linear index codes are of optimal length for SUICP(SNC) with
some combinations of $K,D$ and $U$. For SUICP(SNC) with arbitrary $K,D$ and
$U$, we show that the length of constructed scalar linear index codes are
atmost two index code symbols per message symbol more than the broadcast rate.
The given results for SUICP(SNC) are of practical importance due to its
relation with topological interference management problem in wireless
communication networks.


  Quantized networks use less computational and memory resources and are
suitable for deployment on edge devices. While quantization-aware training QAT
is the well-studied approach to quantize the networks at low precision, most
research focuses on over-parameterized networks for classification with limited
studies on popular and edge device friendly single-shot object detection and
semantic segmentation methods like YOLO. Moreover, majority of QAT methods rely
on Straight-through Estimator (STE) approximation which suffers from an
oscillation phenomenon resulting in sub-optimal network quantization. In this
paper, we show that it is difficult to achieve extremely low precision (4-bit
and lower) for efficient YOLO models even with SOTA QAT methods due to
oscillation issue and existing methods to overcome this problem are not
effective on these models. To mitigate the effect of oscillation, we first
propose Exponentially Moving Average (EMA) based update to the QAT model.
Further, we propose a simple QAT correction method, namely QC, that takes only
a single epoch of training after standard QAT procedure to correct the error
induced by oscillating weights and activations resulting in a more accurate
quantized model. With extensive evaluation on COCO dataset using various YOLO5
and YOLO7 variants, we show that our correction method improves quantized YOLO
networks consistently on both object detection and segmentation tasks at
low-precision (4-bit and 3-bit).


  How can we explore the unknown properties of high-dimensional sensitive
relational data while preserving privacy? We study how to construct an
explorable privacy-preserving materialized view under differential privacy. No
existing state-of-the-art methods simultaneously satisfy the following
essential properties in data exploration: workload independence, analytical
reliability (i.e., providing error bound for each search query), applicability
to high-dimensional data, and space efficiency. To solve the above issues, we
propose HDPView, which creates a differentially private materialized view by
well-designed recursive bisected partitioning on an original data cube, i.e.,
count tensor. Our method searches for block partitioning to minimize the error
for the counting query, in addition to randomizing the convergence, by choosing
the effective cutting points in a differentially private way, resulting in a
less noisy and compact view. Furthermore, we ensure formal privacy guarantee
and analytical reliability by providing the error bound for arbitrary counting
queries on the materialized views. HDPView has the following desirable
properties: (a) Workload independence, (b) Analytical reliability, (c) Noise
resistance on high-dimensional data, (d) Space efficiency. To demonstrate the
above properties and the suitability for data exploration, we conduct extensive
experiments with eight types of range counting queries on eight real datasets.
HDPView outperforms the state-of-the-art methods in these evaluations.


  We report results on a lattice calculation of the heavy-light meson decay
constant employing the non-relativistic QCD approach for heavy quark and Wilson
action for light quark. Simulations are carried out at $\beta=6.0$ on a
$16^3\times 48$ lattice. Signal to noise ratio for the ground state is
significantly improved compared to simulations in the static approximation,
enabling us to extract the decay constant reliably. We compute the heavy-light
decay constant for several values of heavy quark mass and estimate the
magnitude of the deviation from the heavy mass scaling law $f_{P} \sqrt{m_{P}}
= const$. For the $B$ meson we find $f_{B} = 171\pm 22^{+19}_{-45}$ MeV, while
an extrapolation to the static limit yields $f_{B}^{static}$ = $297\pm
36^{+15}_{-30}$ MeV.


  The fraction of high-redshift sources which are multiply-imaged by
intervening galaxies is strongly dependent on the cosmological constant, and so
can be a useful probe of the cosmological model. However its power is limited
by various systematic (and random) uncertainties in the calculation of lensing
probabilities, one of the most important of which is the dynamical
normalisation of elliptical galaxies. Assuming ellipticals' mass distributions
can be modelled as isothermal spheres, the mass normalisation depends on: the
velocity anisotropy; the luminosity density; the core radius; and the area over
which the velocity dispersion is measured. The differences in the lensing
probability and optical depth produced by using the correct normalisation can
be comparable to the differences between even the most extreme cosmological
models. The existing data is not sufficient to determine the correct
normalisation with enough certainty to allow lensing statistics to be used to
their full potential. However, as the correct lensing probability is almost
certainly higher than is usually assumed, upper bounds on the cosmological
constant are not weakened by these possibilities.


  We extend our previous analysis of the decays B_{d,s} -> mu^+ mu^- in the
Minimal Supersymmetric Standard Model (MSSM) to include gluino and neutralino
contributions. We provide analytic formulae, valid at large values of
tan(beta), for the scalar and pseudoscalar Wilson coefficients arising from
neutral Higgs boson exchange diagrams with gluinos and neutralinos. Together
with the remaining contributions (W^{+/-}, H^{+/-}, charginos), and assuming
the Cabibbo-Kobayashi-Maskawa (CKM) matrix to be the only source of flavour
violation, we assess their implications for the branching fractions Br(B_{d,s}
-> mu^+ mu^-). Of particular interest is the quantity R = Br(B_d -> mu^+
mu^-)/Br(B_s -> mu^+ mu^-), since (i) the theoretical errors cancel to a large
extent, and (ii) it offers a theoretically clean way of extracting the ratio
|V_{td}/V_{ts}| in the Standard Model (SM), which predicts R_SM ~
|V_{td}/V_{ts}|^2 ~ O(10^{-2}). Exploring three different scenarios of modified
minimal flavour violation, we find that part of the MSSM parameter space can
accommodate large Br(B_{d,s} -> mu^+ mu^-) branching fractions, while being
consistent with various experimental constraints. More importantly, we show
that the ratio R can be as large as O(1), while the individual branching
fractions may be amenable to detection by ongoing experiments. We conclude that
within the MSSM with large tan(beta) the decay rates of B_{d} -> mu^+ mu^- and
B_{s} -> mu^+ mu^- can be of comparable size even in the case where flavour
violation is due solely to the CKM matrix.


  We study $\mathcal{N}=2$ superconformal field theory and define the R-matrix
which acts as an intertwining operator between different realizations of
$\mathcal{N}=2$ $W-$algebras of type $A$. Using this R-matrix we define $RLL$
algebra and relate it to current realization of affine Yangian of
$\hat{\mathfrak{gl}}(1|1)$.


  Automating pavement maintenance suggestions is challenging,especially for
actionable recommendations such as patching location,depth and priority.It is
common practice among State agencies to manually inspect road segments of
interest and decide maintenance requirements based on the pavement condition
index (PCI).However,standalone PCI only evaluates the pavement surface
condition and coupled with the variability in human perception of pavement
distress,limits the accuracy and quality of current pavement maintenance
practices.Here,a need for multi-sensor data integrated with standardized
pavement distress condition ratings is required.This study explores the
possibility of estimating the appropriate pavement patching strategy
(i.e.,patching location,depth,and quantity) by integrating pavement structural
and surface condition assessment with pavement specific ratings of
distress.Especially,it combines pavement structural condition assessment
parameter;falling weight deflectometer deflections along with surface condition
assessment parameters;international roughness index,and cracking density for a
better representation of overall pavement distress condition.Then,a pavement
specific threshold-based patching suggestion algorithm is implemented to
evaluate the pavement overall distress condition into a priority-based patching
suggestion.The novelty in the use of pavement specific thresholds is placed on
its data-driven ability to determine threshold values from current road
condition measurements using a reliability concept validated by the theoretical
pavement condition rating,pavement structural number.A web-based patching
manager tool (PMT) was implemented to automate the patching suggestion
procedure and visualize the results.Validated with road surface images obtained
from three-dimensional laser sensors,PMT could successfully capture localized
distresses in existing pavements.


  Multi-focus image fusion (MFF) is a popular technique to generate an
all-in-focus image, where all objects in the scene are sharp. However, existing
methods pay little attention to defocus spread effects of the real-world
multi-focus images. Consequently, most of the methods perform badly in the
areas near focus map boundaries. According to the idea that each local region
in the fused image should be similar to the sharpest one among source images,
this paper presents an optimization-based approach to reduce defocus spread
effects. Firstly, a new MFF assessmentmetric is presented by combining the
principle of structure similarity and detected focus maps. Then, MFF problem is
cast into maximizing this metric. The optimization is solved by gradient
ascent. Experiments conducted on the real-world dataset verify superiority of
the proposed model. The codes are available at
https://github.com/xsxjtu/MFF-SSIM.


  Exploiting the full computational power of always deeper hierarchical
multiprocessor machines requires a very careful distribution of threads and
data among the underlying non-uniform architecture. The emergence of multi-core
chips and NUMA machines makes it important to minimize the number of remote
memory accesses, to favor cache affinities, and to guarantee fast completion of
synchronization steps. By using the BubbleSched platform as a threading backend
for the GOMP OpenMP compiler, we are able to easily transpose affinities of
thread teams into scheduling hints using abstractions called bubbles. We then
propose a scheduling strategy suited to nested OpenMP parallelism. The
resulting preliminary performance evaluations show an important improvement of
the speedup on a typical NAS OpenMP benchmark application.


  In this paper, we prove the global well-posedness for the 3D rotating
Navier-Stokes equations in the critical functional framework. Especially, this
result allows to construct global solutions for a class of highly oscillating
initial data.


  Using the post-Gaussian trial functions, we calculate the variational
solutions to the quantum-mechanical anharmonic oscillator. We evaluate not only
the ground state but also some excited energies, and compare them with
numerical results.


  We show how certain properties of the Anderson model on a tree are related to
the solutions of a non-linear integral equation. Whether the wave function is
extended or localized, for example, corresponds to whether or not the equation
has a complex solution. We show how the equation can be solved in a weak
disorder expansion. We find that, for small disorder strength $\lambda$, there
is an energy $E_c(\lambda )$ above which the density of states and the
conducting properties vanish to all orders in perturbation theory. We compute
perturbatively the position of the line $E_c(\lambda )$ which begins, in the
limit of zero disorder, at the band edge of the pure system. Inside the band of
the pure system the density of states and conducting properties can be computed
perturbatively. This expansion breaks down near $E_c(\lambda )$ because of
small denominators. We show how it can be resummed by choosing the appropriate
scaling of the energy. For energies greater than $E_c(\lambda )$ we show that
non-perturbative effects contribute to the density of states but have been
unable tell whether they also contribute to the conducting properties.


  Industrial manufacturing has developed during the last decades from a
labor-intensive manual control of machines to a fully-connected automated
process. The next big leap is known as industry 4.0, or smart manufacturing.
With industry 4.0 comes increased integration between IT systems and the
factory floor from the customer order system to final delivery of the product.
One benefit of this integration is mass production of individually customized
products. However, this has proven challenging to implement into existing
factories, considering that their lifetime can be up to 30 years. The single
most important parameter to measure in a factory is the operating hours of each
machine. Operating hours can be affected by machine maintenance as well as
re-configuration for different products. For older machines without
connectivity, the operating state is typically indicated by signal lights of
green, yellow and red colours. Accordingly, the goal is to develop a solution
which can measure the operational state using the input from a video camera
capturing a factory floor. Using methods commonly employed for traffic light
recognition in autonomous cars, a system with an accuracy of over 99% in the
specified conditions is presented. It is believed that if more diverse video
data becomes available, a system with high reliability that generalizes well
could be developed using a similar methodology.


  We have developed a low temperature, high resolution magnetic force
microscope (MFM) using a quartz tuning fork that can operate in a magnetic
field. A tuning fork with a spring constant of 1300 N/m mounted with a
commercial MFM cantilever tip was used. We have obtained high resolution images
of the stray magnetic fields exerted from grains with a spatial resolution of
15 nm and force resolution of 2 pN at 4.2 K. Tuning fork based magnetic force
microscopes have the potential to be used at millikelvin temperatures due to
their low power dissipation and high force sensitivity.


  A design is said to be $f$-pyramidal when it has an automorphism group which
fixes $f$ points and acts sharply transitively on all the others. The problem
of establishing the set of values of $v$ for which there exists an
$f$-pyramidal Steiner triple system of order $v$ has been deeply investigated
in the case $f=1$ but it remains open for a special class of values of $v$. The
same problem for the next possible $f$, which is $f=3$, is here completely
solved: there exists a $3$-pyramidal Steiner triple system of order $v$ if and
only if $v\equiv7,9,15$ (mod $24$) or $v\equiv 3, 19$ (mod 48).


  Using numerical simulations, we show that two coupled qubits can amplify a
weak signal about hundredfold. This can be achieved if the two qubits are
biased simultaneously by this weak signal and a strong pump signal, both of
which having frequencies close to the inter-level transitions in the system.
The weak signal strongly affects the spectrum generated by the strong pumping
drive by producing and controlling mixed harmonics with amplitudes of the order
of the main harmonic of the strong drive. We show that the amplification is
robust with respect to noise, with an intensity of the order of the weak
signal. When deviating from the optimal regime (corresponding to strong qubit
coupling and a weak-signal frequency equal to the inter-level transition
frequency) the proposed amplifier becomes less efficient, but it can still
considerably enhance a weak signal (by several tens). We therefore propose to
use coupled qubits as a combined parametric amplifier and frequency shifter.


  This paper is in continuation of our previous work on the structural,
electrical and magnetic properties of Ru doped La(0.67)Ca(0.33)MnO(3) compounds
(Ref.: L.Seetha Lakshmi et.al, J. Magn. Magn. Mater. 257, 195 (2003)). Here we
report the results of magnetotransport measurements on
La(0.67)Ca(0.33)Mn(1-x)Ru(x)O(3) (0<x< 0.1) compounds in the light of proposed
magnetic phase separation.


  Magnetic fields of a large intensity can be generated in peripheral
high-energy heavy-ion collisions. Although their intensity drops fast and,
moreover, it is not clear whether these fields last long enough to induce a
magnetization during the quark-gluon plasma phase, most of the models and
simulations predict a significant intensity that lasts up to proper times of
order 1 fm after the beginning of the reaction, which is a typical time for the
hydrodynamical phase to start. This interval of time is referred to as the
pre-equilibrium stage. The evolution of the reaction during pre-equilibrium is
thus likely to be influenced by these fields. In this work we adopt a strong
field approximation to study the effects of the magnetic field-induced
anisotropy on the gluon pressure. We include this anisotropy within the
description obtained by means of Effective Kinetic Theory and explore the
consequences to reach isotropization at proper times of order 1 fm. We show
that when including the magnetic field effects, isotropization is achieved
faster.


  Social Network Analysis is the use of Network and Graph Theory to study
social phenomena, which was found to be highly relevant in areas like
Criminology. This chapter provides an overview of key methods and tools that
may be used for the analysis of criminal networks, which are presented in a
real-world case study. Starting from available juridical acts, we have
extracted data on the interactions among suspects within two Sicilian Mafia
clans, obtaining two weighted undirected graphs. Then, we have investigated the
roles of these weights on the criminal network's properties, focusing on two
key features: weight distribution and shortest path length. We also present an
experiment that aims to construct an artificial network that mirrors criminal
behaviours. To this end, we have conducted a comparative degree distribution
analysis between the real criminal networks, using some of the most popular
artificial network models: Watts-Strogatz, Erd\H{o}s-R\'{e}nyi, and
Barab\'{a}si-Albert, with some topology variations. This chapter will be a
valuable tool for researchers who wish to employ social network analysis within
their own area of interest.


  We present various types of reduced models including five vibrational modes
and three electronic states for the pyrazine molecule in order to investigate
the lifetime of electronic coherence in a rigid and neutral system. Using an
ultrafast optical pumping in the ground state (1 1 A g ), we prepare a coherent
superposition of two bright excited states, 1 1 B 2u and 1 1 B 1u , and reveal
the effect of the nuclear motion on the preservation of the electronic
coherence induced by the laser pulse. More specifically, two aspects are
considered: the anharmonicity of the potential energy surfaces and the
dependence of the transition dipole moments (TDMs) with respect to the nuclear
coordinates. To this end, we define an ideal model by making three
approximations: (i) only the five totally symmetric modes move, (ii) which
correspond to uncoupled harmonic oscillators, and (iii) the TDMs from the
ground electronic state to the two bright states are constant (Franck-Condon
approximation). We then lift the second and third approximations by
considering, first, the effect of anharmonicity, second, the effect of
coordinate-dependence of the TDMs (first-order Herzberg- Teller contribution),
third, both. Our detailed numerical study with quantum dynamics confirms
long-term revivals of the electronic coherence even for the most realistic
model.


  Highly supercritical accretion discs are probable sources of dense optically
thick axisymmetric winds. We introduce a new approach based on diffusion
approximation radiative transfer in a funnel geometry and obtain an analytical
solution for the energy density distribution inside the wind assuming that all
the mass, momentum and energy are injected well inside the spherization radius.
This allows to derive the spectrum of emergent emission for various inclination
angles. We show that self-irradiation effects play an important role altering
the temperature of the outcoming radiation by about 20% and the apparent X-ray
luminosity by a factor of 2-3. The model has been successfully applied to two
ULXs. The basic properties of the high ionization HII-regions found around some
ULXs are also easily reproduced in our assumptions.


  We give a new, constructive uniqueness theorem for tensor decomposition. It
applies to order 3 tensors of format $n \times n \times p$ and can prove
uniqueness of decomposition for generic tensors up to rank $r=4n/3$ as soon as
$p \geq 4$. One major advantage over Kruskal's uniqueness theorem is that our
theorem has an algorithmic proof, and the resulting algorithm is efficient.
Like the uniqueness theorem, it applies in the range $n \leq r \leq 4n/3$. As a
result, we obtain the first efficient algorithm for overcomplete decomposition
of generic tensors of order 3.
  For instance, prior to this work it was not known how to efficiently
decompose generic tensors of format $n \times n \times n$ and rank $r=1.01n$
(or rank $r \leq (1+\epsilon) n$, for some constant $\epsilon >0$). Efficient
overcomplete decomposition of generic tensors of format $n \times n \times 3$
remains an open problem.
  Our results are based on the method of commuting extensions pioneered by
Strassen for the proof of his $3n/2$ lower bound on tensor rank and border
rank. In particular, we rely on an algorithm for the computation of commuting
extensions recently proposed in a companion paper, and on the classical
diagonalization-based "Jennrich algorithm" for undercomplete tensor
decomposition.


  The representation for infinite sum of higher twists (HT) tower in DIS
implied by analyticity of virtual Compton amplitude is suggested. Its simplest
realization allows to describe the Bjorken sum rule at all momentum transfers.
It is stressed that TMDs accommodate the infinite tower of HT similar to
non-local vacuum condensates for the case of vacuum matrix element. The D-term
in hadronic GPDs bears some similarity to vacuum cosmological constant. The
negative sign of D-term may be understood as a similarity between inflation and
annihilation via the graviton exchange.


  TMIC is an App Inventor extension for the deployment of ML models for image
classification developed with Google Teachable Machine in educational settings.
Google Teachable Machine, is an intuitive visual tool that provides
workflow-oriented support for the development of ML models for image
classification. Aiming at the usage of models developed with Google Teachable
Machine, the extension TMIC enables the deployment of the trained models
exported as TensorFlow.js to Google Cloud as part of App Inventor, one of the
most popular block-based programming environments for teaching computing in
K-12. The extension was created with the App Inventor extension framework based
on the extension PIC and is available under the BSD 3 license. It can be used
for teaching ML in K-12, in introductory courses in higher education or by
anyone interested in creating intelligent apps with image classification. The
extension TMIC is being developed by the initiative Computa\c{c}\~ao na Escola
of the Department of Informatics and Statistics at the Federal University of
Santa Catarina/Brazil as part of a research effort aiming at introducing AI
education in K-12.


  We prove the genericity of the shadowing and periodic shadowing properties
for both conservative and dissipative homeomorphisms on a compact connected
manifold. Our proof is valid for topological manifolds and still holds in the
dissipative case. As a consequence of this result, we establish the genericity
of the specification property, the average shadowing property and the
asymptotic average shadowing property in the conservative case.


  We present a full list of all representations of the special linear group
$\mathrm{SL}_n$ over the complex numbers with complete intersection invariant
ring, completing the classification of Shmelkin. For this task, we combine
three techniques. Firstly, the graph method for invariants of $\mathrm{SL}_n$
developed by the author to compute invariants, covariants and explicit forms of
syzygies. Secondly, a new algorithm for finding a monomial order such that a
certain basis of an ideal is a Gr\"obner basis with respect to this order,
inbetween usual Gr\"obner basis computation and computation of the Gr\"obner
fan. Lastly, a modification of an algorithm by Xin for MacMahon partition
analysis to compute Hilbert series.


  Through history, the human being tried to relay its daily tasks to other
creatures, which was the main reason behind the rise of civilizations. It
started with deploying animals to automate tasks in the field of
agriculture(bulls), transportation (e.g. horses and donkeys), and even
communication (pigeons). Millenniums after, come the Golden age with
"Al-jazari" and other Muslim inventors, which were the pioneers of automation,
this has given birth to industrial revolution in Europe, centuries after. At
the end of the nineteenth century, a new era was to begin, the computational
era, the most advanced technological and scientific development that is driving
the mankind and the reason behind all the evolutions of science; such as
medicine, communication, education, and physics. At this edge of technology
engineers and scientists are trying to model a machine that behaves the same as
they do, which pushed us to think about designing and implementing "Things
that-Thinks", then artificial intelligence was. In this work we will cover each
of the major discoveries and studies in the field of machine cognition, which
are the "Elementary Perceiver and Memorizer"(EPAM) and "The General Problem
Solver"(GPS). The First one focus mainly on implementing the human-verbal
learning behavior, while the second one tries to model an architecture that is
able to solve problems generally (e.g. theorem proving, chess playing, and
arithmetic). We will cover the major goals and the main ideas of each model, as
well as comparing their strengths and weaknesses, and finally giving their
fields of applications. And Finally, we will suggest a real life implementation
of a cognitive machine.


  The IceCube experiment discovered PeV-energy neutrinos originating beyond our
Galaxy with an energy flux that is comparable to that of TeV-energy gamma rays
and EeV-energy cosmic rays. Neutrinos provide the only unobstructed view of the
cosmic accelerators that power the highest energy radiation reaching us from
the universe. We will review the rationale for building kilometer-scale
neutrino detectors that led to the IceCube project, which transformed a cubic
kilometer of deep transparent natural Antarctic ice into a neutrino telescope
of such a scale. We will summarize the results from the first decade of
operations: the status of the observations of cosmic neutrinos and of their
first identified source, the supermassive black hole TXS 0506+056.
Subsequently, we will introduce the phenomenology associated with cosmic
accelerators in some detail. Besides the search for the sources of Galactic and
extragalactic cosmic rays, the scientific missions of IceCube and similar
instruments under construction in the Mediterranean Sea and Lake Baikal include
the observation of Galactic supernova explosions, the search for dark matter,
and the study of neutrinos themselves. This review resulted from notes created
for summer school lectures and should be accessible to nonexperts.


  Entanglement is one of the pillars of quantum mechanics and quantum
information processing, and as a result the quantumness of nonentangled states
has typically been overlooked and unrecognized. We give a robust definition for
the classicality versus quantumness of a single multipartite quantum state, a
set of states, and a protocol using quantum states. We show a variety of
nonentangled (separable) states that exhibit interesting quantum properties,
and we explore the ``zoo'' of separable states; several interesting subclasses
are defined based on their diagonalizing bases, and their non-classical
behavior is investigated.


  The porous PLA foams potential for tissue engineering usage are prepared by a
modified solvent casting/particulate leaching method with different
crystallinity. Since in typical method the porogens are solved in the solution
and flow with the polymers during the casting and the crystallinity behavior of
PLA chains in the limited space cannot be tracked, in this work the processing
is modified by diffusing the PLA solution into a steady salt stack. With a
thermal treatment before leaching while maintaining the stable structure of the
porogens stack, the crystallinity of porous foams is made possible to control.
The characterizations indicate the crystallization of porous foams is in a
manner of lower crystallibility than the bulk materials. Pores and caves of
around 250{\mu}m size are obtained in samples with different crystallinity. The
macro-structures are not much impaired by the crystallization nevertheless the
morphological effect of the heating process is still obvious.


  Analytic expressions for the correlation length temperature dependences are
given for antiferromagnetic spin-1/2 Heisenberg ladders using a finite-size
non-linear sigma-model approach. These calculations rely on identifying three
successive crossover regimes as a function of temperature. In each of these
regimes, precise and controlled approximations are formulated. The analytical
results are found to be in excellent agreement with Monte Carlo simulations for
the Heisenberg Hamiltonian.


  Given a graph G, the graph associahedron is a simple convex polytope whose
face poset is based on the connected subgraphs of G. With the additional
assignment of a color palette, we define the colorful graph associahedron, show
it to be a collection of simple abstract polytopes, and explore its properties.


  We introduce a pressure robust Finite Element Method for the linearized
Magnetohydrodynamics equations in three space dimensions, which is provably
quasi-robust also in the presence of high fluid and magnetic Reynolds numbers.
The proposed scheme uses a non-conforming BDM approach with suitable DG terms
for the fluid part, combined with an $H^1$-conforming choice for the magnetic
fluxes. The method introduces also a specific CIP-type stabilization associated
to the coupling terms. Finally, the theoretical result are further validated by
numerical experiments.


  Communication networks are vulnerable to natural disasters, such as
earthquakes or floods, as well as to physical attacks, such as an
Electromagnetic Pulse (EMP) attack. Such real-world events happen at specific
geographical locations and disrupt specific parts of the network. Therefore,
the geographical layout of the network determines the impact of such events on
the network's physical topology in terms of capacity, connectivity, and flow.
  Recent works focused on assessing the vulnerability of a deterministic
network to such events. In this work, we focus on assessing the vulnerability
of (geographical) random networks to such disasters. We consider stochastic
graph models in which nodes and links are probabilistically distributed on a
plane, and model the disaster event as a circular cut that destroys any node or
link within or intersecting the circle.
  We develop algorithms for assessing the damage of both targeted and
non-targeted (random) attacks and determining which attack locations have the
expected most disruptive impact on the network. Then, we provide experimental
results for assessing the impact of circular disasters to communications
networks in the USA, where the network's geographical layout was modeled
probabilistically, relying on demographic information only. Our results
demonstrates the applicability of our algorithms to real-world scenarios.
  Our algorithms allows to examine how valuable is public information about the
network's geographical area (e.g., demography, topography, economy) to an
attacker's destruction assessment capabilities in the case the network's
physical topology is hidden or examine the affect of hiding the actual physical
location of the fibers on the attack strategy. Thereby, our schemes can be used
as a tool for policy makers and engineers to design more robust networks and
identifying locations which require additional protection efforts.


  21 cm cosmology, the statistical observation of the high redshift universe
using the hyperfine transition of neutral hydrogen, has the potential to
revolutionize our understanding of cosmology and the astrophysical processes
that underlie the formation of the first stars, galaxies, and black holes
during the "Cosmic Dawn." By making tomographic maps with low frequency radio
interferometers, we can study the evolution of the 21 cm signal with time and
spatial scale and use it to understand the density, temperature, and ionization
evolution of the intergalactic medium over this dramatic period in the history
of the universe.
  For my Ph.D. thesis, I explore a number of advancements toward detecting and
characterizing the 21 cm signal from the Cosmic Dawn, especially during its
final stage, the epoch of reionization. In seven different previously published
papers, I explore new techniques for the statistical analysis of
interferometric measurements, apply them to data from current generation
telescopes like the Murchison Widefield Array, and look forward to what we
might measure with the next generation of 21 cm observatories. I focus in
particular on estimating the power spectrum of 21 cm brightness temperature
fluctuations in the presence enormous astrophysical foregrounds and how those
measurements may constrain the physics of the Cosmic Dawn.
  Thesis Supervisor: Max Tegmark


  Spin ordering and its effect on low energy quasiparticles in a p-wave
superconducting liquid are investigated. We show that there is a new 2D p-wave
superconducting liquid where the ground state is rotation invariant. In quantum
spin disordered liquids, the low energy quasiparticles are bound states of the
bare Bogolubov- De Gennes (${\em BdeG}$) quasiparticles and zero energy
skyrmions, which are charge neutral bosons at the low energy limit. Further
more, spin collective excitations are fractionalized ones carrying a half spin
and obeying fermionic statistics. In thermally spin disordered limits, the
quasi-particles are bound states of bare ${\em BdeG}$ quasi-particles. The
latter situation can be realized in some layered p-wave superconductors where
the spin-orbit coupling is weak.


  Elastic geodesic grids (EGG) are lightweight structures that can be easily
deployed to approximate designer provided free-form surfaces. In the initial
configuration the grids are perfectly flat, during deployment, though,
curvature is induced to the structure, as grid elements bend and twist. Their
layout is found geometrically, it is based on networks of geodesic curves on
free-form design-surfaces. Generating a layout with this approach encodes an
elasto-kinematic mechanism to the grid that creates the curved shape during
deployment. In the final state the grid can be fixed to supports and serve for
all kinds of purposes like free-form sub-structures, paneling, sun and rain
protectors, pavilions, etc. However, so far these structures have only been
investigated using small-scale desktop models. We investigate the scalability
of such structures, presenting a medium sized model. It was designed by an
architecture student without expert knowledge on elastic structures or
differential geometry, just using the elastic geodesic grids design-pipeline.
We further present a fabrication-process for EGG-models. They can be built
quickly and with a small budget.


  We show that a minimal triangulation of the associahedron (Stasheff polytope)
of dimension n is made of (n+1)^{n-1} simplices. We construct a natural
bijection with the set of parking functions from a new interpretation of
parking functions in terms of shuffles.


  The generalized recurrence plot is a modern tool for quantification of
complex spatial patterns. Its application spans the analysis of trabecular bone
structures, Turing patterns, turbulent spatial plankton patterns, and fractals.
Determinism is a central measure in this framework quantifying the level of
regularity of spatial structures. We show by basic examples of fully regular
patterns of different symmetries that this measure underestimates the
orderliness of circular patterns resulting from rotational symmetries. We
overcome this crucial problem by checking additional structural elements of the
generalized recurrence plot which is demonstrated with the examples.
Furthermore, we show the potential of the extended quantity of determinism
applying it to more irregular circular patterns which are generated by the
complex Ginzburg-Landau-equation and which can be often observed in real
spatially extended dynamical systems. So, we are able to reconstruct the main
separations of the system's parameter space analyzing single snapshots of the
real part only, in contrast to the use of the original quantity. This ability
of the proposed method promises also an improved description of other systems
with complicated spatio-temporal dynamics typically occurring in fluid
dynamics, climatology, biology, ecology, social sciences, etc.


  Magnitude homology is an $\mathbf{R}^+$-graded homology theory of metric
spaces that captures information on the complexity of geodesics. Here we
address the question: when are two metric spaces magnitude homology equivalent,
in the sense that there exist back-and-forth maps inducing mutually inverse
maps in homology? We give a concrete geometric necessary and sufficient
condition in the case of closed Euclidean sets. Along the way, we introduce the
convex-geometric concepts of inner boundary and core, and prove a strengthening
for closed convex sets of the classical theorem of Carath\'eodory.


  This paper presents a novel method for extracting acoustic features that
characterise the background environment in audio recordings. These features are
based on the output of an alignment that fits multiple parallel
background--based Constrained Maximum Likelihood Linear Regression
transformations asynchronously to the input audio signal. With this setup, the
resulting features can track changes in the audio background like appearance
and disappearance of music, applause or laughter, independently of the speakers
in the foreground of the audio. The ability to provide this type of acoustic
description in audiovisual data has many potential applications, including
automatic classification of broadcast archives or improving automatic
transcription and subtitling. In this paper, the performance of these features
in a genre identification task in a set of 332 BBC shows is explored. The
proposed background--tracking features outperform short--term Perceptual Linear
Prediction features in this task using Gaussian Mixture Model classifiers (62%
vs 72% accuracy). The use of more complex classifiers, Hidden Markov Models and
Support Vector Machines, increases the performance of the system with the novel
background--tracking features to 79% and 81% in accuracy respectively.


  The autodependogram is a graphical device recently proposed in the literature
to analyze autodependencies. It is defined computing the classical Pearson
chi-square statistics of independence at various lags in order to point out the
presence lag-depedencies. This paper proposes an improvement of this diagram
obtained by substituting the chi-square statistics with an estimator of the
Kulback-Leibler divergence between the bivariate density of two delayed
variables and the product of their marginal distributions. A simulation study,
on well-established time series models, shows that this new autodependogram is
more powerful than the previous one. An application to financial data is also
shown.


  We propose a quantum memory for a single-photon wave packet in a
superposition of two different colors, i.e., two different frequency
components, using the electromagnetically induced transparency technique in a
double-{\Lambda} system. We examine a specific configuration in which the two
frequency components are able to exchange energy through a four-wave mixing
process as they propagate, so the state of the incident photon is recovered
periodically at certain positions in the medium. We investigate the propagation
dynamics as a function of the relative phase between the coupling beams and the
input single-photon frequency components. Moreover, by considering
time-dependent coupling beams, we numerically simulate the storage and
retrieval of a two-frequency-component single-photon qubit.


  We study the dynamics near a 1+1 dimensional intersection of two orthogonal
stacks of fivebranes in type IIB string theory, using an open string
description valid at weak coupling, and a closed string description valid at
strong coupling. The weak coupling description suggests that this system is
invariant under eight supercharges with a particular chirality in 1+1
dimensions, and its spectrum contains chiral fermions localized at the
intersection. The closed string description leads to a rather different picture
-- a three dimensional Poincare invariant theory with a gap and sixteen
supercharges. We show that this dramatic change in the behavior of the system
is partly due to anomaly inflow. Taking it into account leads to a coherent
picture, both when the fivebranes in each stack are coincident and when they
are separated.


  We prove that any link in $S^3$ whose Khovanov homology is the same as that
of a Hopf link must be isotopic to that Hopf link. This holds for both reduced
and unreduced Khovanov homology, and with coefficients in either $\mathbb{Z}$
or $\mathbb{Z}/2\mathbb{Z}$.


  Despite significant progress in the field, it is still challenging to create
personalized visual representations that align closely with the desires and
preferences of individual users. This process requires users to articulate
their ideas in words that are both comprehensible to the models and accurately
capture their vision, posing difficulties for many users. In this paper, we
tackle this challenge by leveraging historical user interactions with the
system to enhance user prompts. We propose a novel approach that involves
rewriting user prompts based on a newly collected large-scale text-to-image
dataset with over 300k prompts from 3115 users. Our rewriting model enhances
the expressiveness and alignment of user prompts with their intended visual
outputs. Experimental results demonstrate the superiority of our methods over
baseline approaches, as evidenced in our new offline evaluation method and
online tests. Our code and dataset are available at
https://github.com/zzjchen/Tailored-Visions.


  We study the convergence rate of a hierarchy of upper bounds for polynomial
optimization problems, proposed by Lasserre [SIAM J. Optim. 21(3) (2011), pp.
864-885], and a related hierarchy by De Klerk, Hess and Laurent [SIAM J. Optim.
27(1), (2017) pp. 347-367]. For polynomial optimization over the hypercube, we
show a refined convergence analysis for the first hierarchy. We also show lower
bounds on the convergence rate for both hierarchies on a class of examples.
These lower bounds match the upper bounds and thus establish the true rate of
convergence on these examples. Interestingly, these convergence rates are
determined by the distribution of extremal zeroes of certain families of
orthogonal polynomials.


  The concept of network slicing is considered as a key part in the development
of 5G. Network slicing is the means to logically isolate network capabilities
in order to make each slice responsible for specific network requirement. In
the same light, the micro-operator concept has emerged for local deployment of
5G for vertical specific service delivery. Even though microoperator networks
are expected to be deployed using 5G, most research on network slicing has been
directed towards the description on the traditional (MNO) networks with little
emphasis on slicing in local 5G networks deployed by different stakeholders. In
order to achieve slicing in a micro-operator network, it is of vital importance
to understand the different deployment scenarios that can exist and how slicing
can be realized for each of these deployments. In this paper, the microoperator
networks described include closed, open and mixed network, and for each of
these network, different deployment scenarios are established. The paper
further proposes approaches for the configuration of Network Slice Instances
(NSIs) using the Network Slice Subnet Instances (NSSIs) and other Network
Functions (NFs) in a micro-operator network while considering the different
deployments. The results highlight the possible deployment scenarios that can
be established in a micro-operator network and how network slicing can be
efficiently realized for the various local deployments.


  The first measurement of diffractive processes in deep inelastic scattering
at the HERA collider is analysed in terms of a "soft" pomeron exchange model.
The partonic structure of the pomeron which emerges in this picture is
determined using the QCD parton model. The important role of the gluonic
component in the partonic interpretation of the data is particularly
emphasized.


  The Problem of Time in Quantum Gravity is analyzed from a classical
presymplectic perspective. In the first part of the paper the Three Space
Approach to General Relativity is introduced via the Barbour-Foster-\'O
Murchadha action and the dynamics corresponding to a theory of relativistic
gravity where spacetime is not an a priori requirement. We also look into the
nature and physical interpretation of the constraints in this theory and
compare them with those of Standard ADM General Relativity. We then study the
presymplectic phase space of three space general relativity and discuss briefly
the notion of observables and perennials of the system. We then move on to
re-deriving the ephemeris lapse identification, and then discuss the notion of
re-foliation invariance and its resolution in the conformal theory. Further, we
study a new perspective of three space general relativity involving a
Hamiltonian reduction of the phase space and subsequently, we discuss the path
integral quantization of the same.


  Ubiquitous information access becomes more and more important nowadays and
research is aimed at making it adapted to users. Our work consists in applying
machine learning techniques in order to bring a solution to some of the
problems concerning the acceptance of the system by users. To achieve this, we
propose a fundamental shift in terms of how we model the learning of
recommender system: inspired by models of human reasoning developed in robotic,
we combine reinforcement learning and case-base reasoning to define a
recommendation process that uses these two approaches for generating
recommendations on different context dimensions (social, temporal, geographic).
We describe an implementation of the recommender system based on this
framework. We also present preliminary results from experiments with the system
and show how our approach increases the recommendation quality.


  In the context of the imaginary-time formalism for a scalar thermal field
theory, it is shown that the result of performing the sums over Matsubara
frequencies associated with loop Feynman diagrams can be written, for some
classes of diagrams, in terms of the action of a simple linear operator on the
corresponding energy integrals of the Euclidean theory at T=0. In its simplest
form the referred operator depends only on the number of internal propagators
of the graph.
  More precisely, it is shown explicitly that this \emph{thermal operator
representation} holds for two generic classes of diagrams, namely, the
two-vertex diagram with an arbitrary number of internal propagators, and the
one-loop diagram with an arbitrary number of vertices.
  The validity of the thermal operator representation for diagrams of more
complicated topologies remains an open problem. Its correctness is shown to be
equivalent to the correctness of some diagrammatic rules proposed a few years
ago.


  In Location-Based Services(LBS), user behavior naturally has a strong
dependence on the spatiotemporal information, i.e., in different geographical
locations and at different times, user click behavior will change
significantly. Appropriate spatiotemporal enhancement modeling of user click
behavior and large-scale sparse attributes is key to building an LBS model.
Although most of existing methods have been proved to be effective, they are
difficult to apply to takeaway scenarios due to insufficient modeling of
spatiotemporal information. In this paper, we address this challenge by seeking
to explicitly model the timing and locations of interactions and proposing a
Spatiotemporal-Enhanced Network, namely StEN. In particular, StEN applies a
Spatiotemporal Profile Activation module to capture common spatiotemporal
preference through attribute features. A Spatiotemporal Preference Activation
is further applied to model the personalized spatiotemporal preference embodied
by behaviors in detail. Moreover, a Spatiotemporal-aware Target Attention
mechanism is adopted to generate different parameters for target attention at
different locations and times, thereby improving the personalized
spatiotemporal awareness of the model.Comprehensive experiments are conducted
on three large-scale industrial datasets, and the results demonstrate the
state-of-the-art performance of our methods. In addition, we have also released
an industrial dataset for takeaway industry to make up for the lack of public
datasets in this community.


  We report X-ray imaging - spectroscopy of the jet of M87 at sub arc second
resolution with the Chandra X-ray Observatory. The galaxy nucleus and all the
knots seen at radio and optical wavelengths, as far from the nucleus as knot C,
are detected in the X-ray observations. There is a strong trend for the ratio
of X-ray to radio, or optical, flux to decline with increasing distance from
the nucleus. At least three knots are displaced from their radio/optical
counterparts, being tens of pc closer to the nucleus at X-ray than at radio or
optical wavelengths. The X-ray spectra of the nucleus and knots are well
described by power laws absorbed by cold gas, with only the unresolved nucleus
exhibiting intrinsic absorption. In view of the similar spectra of the nucleus
and jet knots, and the high X-ray flux of the knots closest to the nucleus, we
suggest that the X-ray emission coincident with the nucleus may actually
originate from the pc - or sub-pc - scale jet rather than the accretion disk.
  Arguments are given that the X-ray emission process is unlikely to be inverse
Compton scattering. Instead, we favor synchrotron radiation. Plotted as
$\nu$S$_{\rm \nu}$, the spectra of the knots generally peak in or just above
the optical - near infrared band. However, the overall spectra of at least
three knots cannot be described by simple models in which the spectral index
monotonically increases with frequency, as would result from synchrotron losses
or a high energy cut-off to the injected electron spectrum. Instead, these
spectra must turn down just above the optical band and then flatten in the
X-ray band. (Abstract truncated)


  We study the linearized Vlasov equations and the linearized
Vlasov-Fokker-Planck equations in the weakly collisional limit in a uniform
magnetic field. In both cases, we consider periodic confinement and Maxwellian
(or close to Maxwellian) backgrounds. In the collisionless case, for modes
transverse to the magnetic field, we provide a precise decomposition into a
countably infinite family of standing waves for each spatial mode. These are
known as Bernstein modes in the physics literature, though the decomposition is
not an obvious consequence of any existing arguments that we are aware of. We
show that other modes undergo Landau damping. In the presence of collisions
with collision frequency $\nu \ll 1$, we show that these modes undergo
uniform-in-$\nu$ Landau damping and enhanced collisional relaxation at the
time-scale $O(\nu^{-1/3})$. The modes transverse to the field are uniformly
stable and exponentially thermalize on the time-scale $O(\nu^{-1})$. Most of
the results are proved using Laplace transform analysis of the associated
Volterra equations, whereas a simple case of Yan Guo's energy method for
hypocoercivity of collision operators is applied for stability in the
collisional case.


  In this paper, we examine and analyze the challenges associated with
developing and introducing language technologies to low-resource language
communities. While doing so, we bring to light the successes and failures of
past work in this area, challenges being faced in doing so, and what they have
achieved. Throughout this paper, we take a problem-facing approach and describe
essential factors which the success of such technologies hinges upon. We
present the various aspects in a manner which clarify and lay out the different
tasks involved, which can aid organizations looking to make an impact in this
area. We take the example of Gondi, an extremely-low resource Indian language,
to reinforce and complement our discussion.


  We explore a systematic approach to studying the dynamics of evolving
networks at a coarse-grained, system level. We emphasize the importance of
finding good observables (network properties) in terms of which coarse grained
models can be developed. We illustrate our approach through a particular social
network model: the "rise and fall" of a networked society [1]: we implement our
low-dimensional description computationally using the equation-free approach
and show how it can be used to (a) accelerate simulations and (b) extract
system-level stability/bifurcation information from the detailed dynamic model.
We discuss other system-level tasks that can be enabled through such a
computer-assisted coarse graining approach.


  We demonstrate enhanced light extraction for monochrome top-emitting organic
light-emitting diodes (OLEDs). The enhancement by a factor of 1.2 compared to a
reference sample is caused by the use of a hole transport layer (HTL) material
possessing a low refractive index (1.52). The low refractive index reduces the
in-plane wave vector of the surface plasmon polariton (SPP) excited at the
interface between the bottom opaque metallic electrode (anode) and the HTL. The
shift of the SPP dispersion relation decreases the power dissipated into lost
evanescent excitations and thus increases the outcoupling efficiency, although
the SPP remains constant in intensity. The proposed method is suitable for
emitter materials owning isotropic orientation of the transition dipole moments
as well as anisotropic, preferentially horizontal orientation, resulting in
comparable enhancement factors. Furthermore, for sufficiently low refractive
indices of the HTL material, the SPP can be modeled as a propagating plane wave
within other organic materials in the optical microcavity. Thus, by applying
further extraction methods, such as micro lenses or Bragg gratings, it would
become feasible to obtain even higher enhancements of the light extraction.


  In this study, we fabricated hybrid white organic light-emitting diodes
(WOLEDs) based on triplet harvesting with simple structure. All the hole
transporting material and host in emitting layer (EML) of devices were utilized
with same material by using
N,N'-di-1-naphthalenyl-N,N'-diphenyl-[1,1':4',1":4",1"'-quaterphenyl]-4,4"'-diamine
(4P-NPD) which were known to be blue fluorescent material. Simple hybrid WOLEDs
were fabricated three color with blue fluorescent and green, red phosphorescent
materials. We was investigated the effect of triplet harvesting (TH) by exciton
generation zone on simple hybrid WOLEDs. Characteristic of simple hybrid WOLEDs
were dominant hole mobility, therefore exciton generation zone was expected in
EML. Additionally, we was optimization thickness of hole transporting layer and
electron transporting layer was fabricated a simple hybrid WOLEDs. Simple
hybrid WOLED exhibits maximum luminous efficiency of 29.3 cd/A and maximum
external quantum efficiency of 11.2%. Commission Internationale de l'Eclairage
(International Commission on Illumination) coordinates of (0.45, 0.43) at about
10,000 cd/m^2.


  Modeling and analysis of soft errors in electronic circuits has traditionally
been done using computer simulations. Computer simulations cannot guarantee
correctness of analysis because they utilize approximate real number
representations and pseudo random numbers in the analysis and thus are not well
suited for analyzing safety-critical applications. In this paper, we present a
higher-order logic theorem proving based method for modeling and analysis of
soft errors in electronic circuits. Our developed infrastructure includes
formalized continuous random variable pairs, their Cumulative Distribution
Function (CDF) properties and independent standard uniform and Gaussian random
variables. We illustrate the usefulness of our approach by modeling and
analyzing soft errors in commonly used dynamic random access memory sense
amplifier circuits.


  We describe laboratory-grown snow crystals that exhibit a triangular,
plate-like morphology, and we show that the occurrence of these crystals is
much more frequent than one would expect from random growth perturbations of
the more-typical hexagonal forms. We then describe an aerodynamic model that
explains the formation of these crystals. A single growth perturbation on one
facet of a hexagonal plate leads to air flow around the crystal that promotes
the growth of alternating facets. Aerodynamic effects thus produce a weak
growth instability that can cause hexagonal plates to develop into triangular
plates. This mechanism solves a very old puzzle, as observers have been
documenting the unexplained appearance of triangular snow crystals in nature
for nearly two centuries.


  We propose a mechanism explaining the generation of localized magnetic
moments in charge-density-wave compounds. Our model Hamiltonian describes an
Anderson impurity placed in a host material exhibiting the charge-density wave.
There is a region of the model's parameter space, where even weak Coulomb
repulsion on the impurity site is able to localize the magnetic moment on the
impurity. The phase diagram of a single impurity at T=0 is mapped. To establish
the connection with experiment thermodynamic properties of a random impurity
ensemble is studied. Magnetic susceptibility of the ensemble diverges at low
temperature; heat capacity as a function of the magnetic field demonstrates
pronounced low field peak. Both features are consistent with experiments on
orthorhombic TaS3 and blue bronze.


  We theoretically demonstrate that screw dislocation (SD), a 1D topological
defect widely present in semiconductors, exhibits ubiquitously a new form of
spin-orbit coupling (SOC) effect. Differing from the widely known conventional
2D Rashba-Dresselhaus (RD) SOC effect that typically exists at
surfaces/interfaces, the deep-level nature of SD-SOC states in semiconductors
readily makes it an ideal SOC. Remarkably, the spin texture of 1D SD-SOC,
pertaining to the inherent symmetry of SD, exhibits a significantly higher
degree of spin coherency than the 2D RD-SOC. Moreover, the 1D SD-SOC can be
tuned by ionicity in compound semiconductors to ideally suppress spin
relaxation, as demonstrated by comparative first-principles calculations of SDs
in Si/Ge, GaAs, and SiC. Our findings therefore open a new door to manipulating
spin transport in semiconductors by taking advantage of an otherwise
detrimental topological defect.


  As an extension of Gabor signal processing, the covariant Weyl-Heisenberg
integral quantization is implemented to transform functions on the
eight-dimensional phase space $\left(x,k\right)$ into Hilbertian operators. The
$x=\left(x^{\mu}\right)$'s are space-time variables and the
$k=\left(k^{\mu}\right)$'s are As an extension of Gabor signal processing, the
covariant Weyl-Heisenberg integral quantization is implemented to transform
functions on the eight-dimensional phase space $\left(x,k\right)$ into
Hilbertian operators. The $x=\left(x^{\mu}\right)$'s are space-time variables
and the $k=\left(k^{\mu}\right)$'s are their conjugate wave vector-frequency
variables. The procedure is first applied to the variables $\left(x,k\right)$
and produces canonically conjugate essentially self-adjoint operators. It is
next applied to the metric field $g_{\mu\nu}(x)$ of general relativity and
yields regularised semi-classical phase space portraits
$\check{g}_{\mu\nu}(x)$. The latter give rise to modified tensor energy
density. Examples are given with the uniformly accelerated reference system and
the Schwarzschild metric. Interesting probabilistic aspects are discussed.


  The classical problem of phase retrieval arises in various signal acquisition
systems. Due to the ill-posed nature of the problem, the solution requires
assumptions on the structure of the signal. In the last several years, sparsity
and support-based priors have been leveraged successfully to solve this
problem. In this work, we propose replacing the sparsity/support priors with
generative priors and propose two algorithms to solve the phase retrieval
problem. Our proposed algorithms combine the ideas from AltMin approach for
non-convex sparse phase retrieval and projected gradient descent approach for
solving linear inverse problems using generative priors. We empirically show
that the performance of our method with projected gradient descent is superior
to the existing approach for solving phase retrieval under generative priors.
We support our method with an analysis of sample complexity with Gaussian
measurements.


  We study the optical conductivity of the one-band Hubbard model in the N\'eel
state at half filling at T=0 using the dynamical mean-field theory. For small
values of the Coulomb parameter clear signatures of a Slater insulator expected
from a weak-coupling theory are found, while the strongly correlated system can
be well described in terms of a Mott-Heisenberg picture. However, in contrast
to the paramagnet, we do not find any evidence for a transition between these
two limiting cases but rather a smooth crossover as a function of the Coulomb
interaction.


  We present a numerical method for studying the normal modes of accretion
flows around black holes. In this first paper, we focus on two-dimensional,
viscous, hydrodynamic disks, for which the linear modes have been calculated
analytically in previous investigations. We use pseudo-spectral methods and low
storage Runge-Kutta methods to solve the continuity equation, the Navier-Stokes
equation, and the energy equation. We devise a number of test problems to
verify the implementation. These tests demonstrate the ability of spectral
methods to handle accurately advection problems and to reproduce correctly the
stability criteria for differentially rotating hydrodynamic flows. They also
show that our implementation is able to handle sound wave correctly with
non-reflective boundary conditions, to recover the standard solution for a
viscous spreading ring, and produce correctly the Shakura-Sunyaev steady disk
solution. Finally, we have applied our algorithm to the problem of a
non-axisymmetric viscous spreading ring and verify that such configuration is
unstable to non-antisymmetric perturbations.


  Empirical risk minimization (ERM) is ubiquitous in machine learning and
underlies most supervised learning methods. While there has been a large body
of work on algorithms for various ERM problems, the exact computational
complexity of ERM is still not understood. We address this issue for multiple
popular ERM problems including kernel SVMs, kernel ridge regression, and
training the final layer of a neural network. In particular, we give
conditional hardness results for these problems based on complexity-theoretic
assumptions such as the Strong Exponential Time Hypothesis. Under these
assumptions, we show that there are no algorithms that solve the aforementioned
ERM problems to high accuracy in sub-quadratic time. We also give similar
hardness results for computing the gradient of the empirical loss, which is the
main computational burden in many non-convex learning tasks.


  The dynamics of GRB jets during the afterglow phase have an important effect
on the interpretation of their observations and for inferring key physical
parameters such as their true energy and event rate. Semi-analytic models
generally predict a fast lateral expansion, where the jet opening angle
asymptotically grows exponentially with its radius. Numerical simulations,
however, show a much more modest lateral expansion, where the jet retains
memory of its initial opening angle for a very long time, and the flow remains
non-spherical until it becomes sub-relativistic, and only then gradually
approaches spherical symmetry. Here we suggest a new analytic model based on a
new physically derived recipe for the lateral expansion. We also generalize the
model by relaxing the common approximations of ultra-relativistic motion and a
narrow jet opening angle. We find that the new analytic model fits much better
the results of numerical simulations, mainly because it remains valid also in
the mildly relativistic, quasi spherical regime. This model shows that for
modest initial jet half-opening angles, \theta_0, the outflow is not
sufficiently ultra-relativistic when its Lorentz factor reaches \Gamma =
1/\theta_0 and therefore the sideways expansion is rather slow, showing no
rapid, exponential phase. On the other hand, we find that jets with an
extremely narrow initial half-opening angle, of about \theta_0 << 10^{-1.5} or
so, which are still sufficiently ultra-relativistic at \Gamma = 1/\theta_0, do
show a phase of rapid, exponential lateral expansion. However, even such jets
that expand sideways exponentially are still not spherical when they become
sub-relativistic.


  The integrated Sachs-Wolfe (ISW) effect is an important implication for dark
energy. In this paper, we have calculated the power spectrum of the ISW effect
in the time varying vacuum cosmological model, where the model parameter
$\beta=4.407$ is obtained by the observational constraint of the growth rate.
It's found that the source of the ISW effect is not only affected by the
different evolutions of the Hubble function $H(a)$ and the dimensionless matter
density $\Omega_m(a)$, but also by the different growth function $D_+(a)$, all
of which are changed due to the presence of matter production term in the time
varying vacuum model. However, the difference of the ISW effect in
$\Lambda(t)\textmd{CDM}$ model and $\Lambda \textmd{CDM}$ model is lessened to
a certain extent due to the integration from the time of last scattering to the
present. It's implied that the observations of the galaxies with high redshift
are required to distinguish the two models.


  In this paper we investigate a model (based on the idea of the outflow
dynamics), in which only conformity and anticonformity can lead to the opinion
change. We show that for low level of aniconformity the consensus is still
reachable but spontaneous reorientations between two types of consensus ('all
say yes' or 'all say now') appear.


  Digital archives contribute to Big data. Combining social network analysis,
coincidence analysis, data reduction, and visual analytics leads to better
characterize topics over time, publishers' main themes and best authors of all
times, according to the British newspaper The Guardian and from the 3 million
records of the British National Bibliography.


  Audenaert and Datta recently introduced a two-parameter family of relative
R\'{e}nyi entropies, known as the $\alpha$-$z$-relative R\'{e}nyi entropies.
The definition of the $\alpha$-$z$-relative R\'{e}nyi entropy unifies all
previously proposed definitions of the quantum R\'{e}nyi divergence of order
$\alpha$ under a common framework. Here we will prove that the
$\alpha$-$z$-relative R\'{e}nyi entropies are a proper generalization of the
quantum relative entropy by computing the limit of the $\alpha$-$z$ divergence
as $\alpha$ approaches one and $z$ is an arbitrary function of $\alpha$. We
also show that certain operationally relevant families of R\'enyi divergences
are differentiable at $\alpha = 1$. Finally, our analysis reveals that the
derivative at $\alpha = 1$ evaluates to half the relative entropy variance, a
quantity that has attained operational significance in second-order quantum
hypothesis testing.


  (Abridged) In this work, we study the 2.8x2.6 deg2 region in the emblematic
Rosette Nebula, centred at the young cluster NGC 2244, with the aim of
constructing the most reliable candidate member list to date, determining
various structural and kinematic parameters, and learning about the past and
the future of the region. Starting from a catalogue containing optical to
mid-infrared photometry, as well as positions and proper motions from Gaia
EDR3, we apply the Probabilistic Random Forest algorithm and derive membership
probability for each source. Based on the list of almost 3000 probable members,
of which about a third are concentrated within the radius of 20' from the
centre of NGC 2244, we identify various clustered sources and stellar
concentrations, and estimate the average distance of 1489+-37 pc (entire
region), 1440+-32 pc (NGC 2244) and 1525+-36 pc (NGC 2237). The masses,
extinction, and ages are derived by SED fitting, and the internal dynamic is
assessed via proper motions relative to the mean proper motion of NGC 2244. NGC
2244 is showing a clear expansion pattern, with an expansion velocity that
increases with radius. Its IMF is well represented by two power laws
(dN/dM\propto M^{-\alpha}), with slopes \alpha = 1.05+-0.02 for the mass range
0.2 - 1.5 MSun, and \alpha = 2.3+-0.3 for the mass range 1.5 - 20 MSun, in
agreement with other star forming regions. The mean age of the region is ~2
Myr. We find evidence for the difference in ages between NGC 2244 and the
region associated with the molecular cloud, which appears slightly younger. The
velocity dispersion of NGC 2244 is well above the virial velocity dispersion
derived from the total mass (1000+-70 MSun) and half-mass radius (3.4+-0.2 pc).
From the comparison to other clusters and to numerical simulations, we conclude
that NGC 2244 may be unbound, and possibly even formed in a super-virial state.


  Artificial Neural Network computation relies on intensive vector-matrix
multiplications. Recently, the emerging nonvolatile memory (NVM) crossbar array
showed a feasibility of implementing such operations with high energy
efficiency, thus there are many works on efficiently utilizing emerging NVM
crossbar array as analog vector-matrix multiplier. However, its nonlinear I-V
characteristics restrain critical design parameters, such as the read voltage
and weight range, resulting in substantial accuracy loss. In this paper,
instead of optimizing hardware parameters to a given neural network, we propose
a methodology of reconstructing a neural network itself optimized to resistive
memory crossbar arrays. To verify the validity of the proposed method, we
simulated various neural network with MNIST and CIFAR-10 dataset using two
different specific Resistive Random Access Memory (RRAM) model. Simulation
results show that our proposed neural network produces significantly higher
inference accuracies than conventional neural network when the synapse devices
have nonlinear I-V characteristics.


  A numerical study of the nonlinear Schr\"odinger (NLS) equation subject to
homogeneous Dirichlet, Neumann and Robin boundary conditions in the finite line
is presented. The results are compared with both the exact analytical ones for
the initial-value problem (IVP) of the NLS equation and the numerical ones for
periodic boundary conditions. It is shown that initial solutions obtained by
truncating the exact N-soliton solution of the IVP of the NLS equation into a
finite interval develop solitary waves that behave as solitons, even after
collisions with the boundaries. For periodic and homogeneous Dirichlet and
Neumann boundary conditions, it is observed that the interaction between
solitons and boundaries is equivalent to the collision between solitons in IVP
or quarterplane problems. It is shown that for homogeneous Robin boundary
conditions, boundary layers that trap and delay the soliton are formed at the
boundaries. Phase diagrams for the soliton amplitude at the boundary points and
for the soliton's maximum amplitude show a recurrent phenomenon, and are
similar to those of the cubic Duffing equation. It is also shown that the phase
diagrams are strong functions of the parameter that defines the Robin boundary
conditions. A method of images, similar to the one used in potential theory, is
developed for the NLS equation in the quarterplane with homogeneous Dirichlet
and Neumann boundary conditions at the finite boundary.


  Over short time intervals planetary ephemerides have been traditionally
represented in analytical form as finite sums of periodic terms or sums of
Poisson terms that are periodic terms with polynomial amplitudes. Nevertheless,
this representation is not well adapted for the evolution of the planetary
orbits in the solar system over million of years as they present drifts in
their main frequencies, due to the chaotic nature of their dynamics. The aim of
the present paper is to develop a numerical algorithm for slowly diffusing
solutions of a perturbed integrable Hamiltonian system that will apply to the
representation of the chaotic planetary motions with varying frequencies. By
simple analytical considerations, we first argue that it is possible to recover
exactly a single varying frequency. Then, a function basis involving
time-dependent fundamental frequencies is formulated in a semi-analytical way.
Finally, starting from a numerical solution, a recursive algorithm is used to
numerically decompose the solution on the significant elements of the function
basis. Simple examples show that this algorithm can be used to give compact
representations of different types of slowly diffusing solutions. As a test
example, we show how this algorithm can be successfully applied to obtain a
very compact approximation of the La2004 solution of the orbital motion of the
Earth over 40 Myr ([-35Myr,5Myr]). This example has been chosen as this
solution is widely used for the reconstruction of the climates of the past.


  We calculate the characteristics of interband HgTe-CdHgTe quantum-well
infrared photodetectors (QWIPs). Due to a small probability of the electron
capture into the QWs, the interband HgTe-CdHgTe QWIPs can exhibit very high
photoconductive gain. Our analysis demonstrates significant potential
advantages of these devices compared to the conventional CdHgTe photodetectors
and the A$_3$B$_5$ heterostructures.