  We show that, among all smooth one-dimensional maps conjugated to an N-ary
shift (a Bernoulli shift of N symbols), Chebyshev maps are distinguished in the
sense that they have least higher-order correlations. We generalise our
consideration and study a family of shifted Chebyshev maps, presenting analytic
results for two-point and higher-order correlation functions. We also review
results for the eigenvalues and eigenfunctions of the Perron-Frobenius operator
of N-th order Chebyshev maps and their shifted generalisations. The spectrum is
degenerate for odd N. Finally, we consider coupled map lattices (CMLs) of
shifted Chebyshev maps and numerically investigate zeros of the temporal and
spatial nearest-neighbour correlations, which are of interest in chaotically
quantized field theories.


  A spin-qubit transformation protocol is proposed for an electron in a
mesoscopic quantum ring with tunable Rashba interaction controlled by the
external electric field. The dynamics of an electron driven around the ring by
a series of Landau-Zenner-like transitions between a finite number of local
voltage gates is determined analytically. General single-qubit transformations
are demonstrated to be feasible in a dynamical basis of localized pseudo-spin
states. It is also demonstrated that by the use of suitable protocols based on
changes of the Rashba interaction full Bloch sphere can be covered. The
challenges of a possible realization of the proposed system in semiconductor
heterostructures are discussed.


  The Hohenberg-Kohn theorem and Kohn-Sham procedure are extended to
functionals of the localized intrinsic density of a self-bound system such as a
nucleus. After defining the intrinsic-density functional, we modify the usual
Kohn-Sham procedure slightly to evaluate the mean-field approximation to the
functional, and carefully describe the construction of the leading corrections
for a system of fermions in one dimension with a spin-degeneracy equal to the
number of particles N. Despite the fact that the corrections are complicated
and nonlocal, we are able to construct a local Skyrme-like intrinsic-density
functional that, while different from the exact functional, shares with it a
minimum value equal to the exact ground-state energy at the exact ground-state
intrinsic density, to next-to-leading order in 1/N. We briefly discuss
implications for real Skyrme functionals.


  We have studied thermoelectric effect of a Kane-Mele
normal-insulator-superconductor (KMNIS) junction at ultra-low temperatures
using a modified version of the well-known Blonder-Tinkham-Klapwijk (BTK)
theory. Since both the (electronic) charge and thermal current due to the
carriers are sensitive to the strengths of the spin-orbit coupling (SOC)
present in the Kane-Mele model, a tunability of this junction device with
regard to its thermoelectric properties can be experimentally achieved by
certain techniques that are used to manipulate the values of the spin-orbit
couplings. We have computed the Seebeck coefficient, the Figure of Merit, the
thermoelectric cooling, the coefficient of performance of the KMNIS junction as
a self-cooling device and investigated the role of the Rashba SOC (RSOC) and
intrinsic SOC (ISOC) parameters therein. Our results on the thermoelectric
cooling indicate practical realizability and usefulness for efficient cooling
detectors, sensors, and quantum devices and hence could be crucial to
experimental success of the thermoelectric applications of such junction
devices. Further we have briefly touched upon the condition that distinguishes
transmission through a topological insulator from an ordinary one.


  In this article we study quotients of deformations of simple singularities,
and attempt to characterize them in terms of subsystems of simple root systems.
The quotient of a semiuniversal deformation of a simple singularity of
inhomogeneous type $B_r$ ($r \geq 2$), $C_r$ ($r \geq 3$), $F_4$ or $G_2$ by
the natural symmetry of the associated Dynkin diagram is a deformation of a
simple singularity of homogeneous type $X = D_s$, $E_6$ or $E_7$, but not
semiuniversal anymore. Therefore not all subdiagrams of $X$ appear as singular
configurations of the fibers of the deformation. We propose a conjecture for
the types of singular configurations in terms of sub-root systems of a root
system of type $X$. The conjecture is then proved for the types $B_2$, $B_3$,
$C_3$, $F_4$ and $G_2$.


  This article discusses the techniques used to select online promising events
at high energy and high luminosity colliders. After a brief introduction,
explaining some general aspects of triggering, the more specific implementation
options for well established machines like the Tevatron and Large Hadron
Collider are presented. An outlook on what difficulties need to be met is given
when designing trigger systems at the Super Large Hadron Collider, or at the
International Linear Collider


  It is well known that textual data on the internet and other digital
platforms contain significant levels of bias and stereotypes. Although many
such texts contain stereotypes and biases that inherently exist in natural
language for reasons that are not necessarily malicious, there are crucial
reasons to mitigate these biases. For one, these texts are being used as
training corpus to train language models for salient applications like
cv-screening, search engines, and chatbots; such applications are turning out
to produce discriminatory results. Also, several research findings have
concluded that biased texts have significant effects on the target demographic
groups. For instance, masculine-worded job advertisements tend to be less
appealing to female applicants.
  In this paper, we present a text style transfer model that can be used to
automatically debias textual data. Our style transfer model improves on the
limitations of many existing style transfer techniques such as loss of content
information. Our model solves such issues by combining latent content encoding
with explicit keyword replacement. We will show that this technique produces
better content preservation whilst maintaining good style transfer accuracy.


  Slender marine structures such as deep-water riser systems are continuously
exposed to currents leading to vortex-induced vibrations (VIV) of the
structure. This may result in amplified drag loads and fast accumulation of
fatigue damage. Consequently, accurate prediction of VIV responses is of great
importance for the safe design and operation of marine risers. Model tests with
elastic pipes have shown that VIV responses are influenced by many structural
and hydrodynamic parameters, which have not been fully modelled in present
frequency domain VIV prediction tools. Traditionally, predictions have been
computed using a single set of hydrodynamic parameters, often leading to
inconsistent prediction accuracy when compared with observed field measurements
and experimental data. Hence, it is necessary to implement a high safety factor
of 10 - 20 in the riser design, which increases development cost and adds extra
constraints in the field operation. One way to compensate for the
simplifications in the mathematical prediction model is to apply adaptive
parameters to describe different riser responses. The objective of this work is
to demonstrate a new method to improve the prediction consistency and accuracy
by applying adaptive hydrodynamic parameters. In the present work, a four-step
approach has been proposed: First, the measured VIV response will be analysed
to identify key parameters to represent the response characteristics. These
parameters will be grouped using data clustering algorithms. Secondly, optimal
hydrodynamic parameters will be identified for each data group by optimisation
against measured data. Thirdly, the VIV response using the obtained parameters
will be calculated and the prediction accuracy evaluated. The correct
hydrodynamic parameters to be used for new cases can be obtained from the
clustering. This concept has been demonstrated with examples from experimental
data.


  In this study, we perform a numerical analysis of the instability of a
ligament in shear flow and investigate the effects of air-liquid shear on the
growth rate of the ligament interface, breakup time, and droplet diameter
formed by the breakup. The ligament is stretched in the flow direction by the
shearing of airflow. Furthermore, as the influence of the shear flow increases,
the ligament becomes deformed into a liquid sheet, and a perforation forms at
the center of the liquid sheet. The liquid sheet breaks up due to the growth of
the perforation and contracts under the influence of surface tension, forming
two ligaments with diameters smaller than that of the original ligament. The
shearing of the airflow causes the original ligament to elongate, and the
cross-section of the ligament becomes elliptical, which increases instability.
As a result, the growth rate of the ligament exceeds the theoretical value, and
increases with increasing wavenumber of the initial disturbance. Therefore, the
diameter of the formed droplets in shear flow decreases due to the increase in
the wavenumber that governs the breakup of the ligament, and because the growth
rate increases, the breakup time for the ligament decreases. As the velocity
difference of the shear flow increases, constrictions of the ligament form
earlier and the diameter of the satellite droplet increases. As the diameter of
the satellite droplet increases and that of the main droplet decreases, the
dispersion of the droplet diameter decreases, making the diameter uniform.


  In an instance of the weighted Nash Social Welfare problem, we are given a
set of $m$ indivisible items, $\mathscr{G}$, and $n$ agents, $\mathscr{A}$,
where each agent $i \in \mathscr{A}$ has a valuation $v_{ij}\geq 0$ for each
item $j\in \mathscr{G}$. In addition, every agent $i$ has a non-negative weight
$w_i$ such that the weights collectively sum up to $1$. The goal is to find an
assignment $\sigma:\mathscr{G}\rightarrow \mathscr{A}$ that maximizes
$\prod_{i\in \mathscr{A}} \left(\sum_{j\in \sigma^{-1}(i)}
v_{ij}\right)^{w_i}$, the product of the weighted valuations of the players.
When all the weights equal $\frac1n$, the problem reduces to the classical Nash
Social Welfare problem, which has recently received much attention. In this
work, we present a $5\cdot\exp\left(2\cdot D_{\text{KL}}(\mathbf{w}\, ||\,
\frac{\vec{\mathbf{1}}}{n})\right) = 5\cdot\exp\left(2\log{n} + 2\sum_{i=1}^n
w_i \log{w_i}\right)$-approximation algorithm for the weighted Nash Social
Welfare problem, where $D_{\text{KL}}(\mathbf{w}\, ||\,
\frac{\vec{\mathbf{1}}}{n})$ denotes the KL-divergence between the distribution
induced by $\mathbf{w}$ and the uniform distribution on $[n]$.
  We show a novel connection between the convex programming relaxations for the
unweighted variant of Nash Social Welfare presented in \cite{cole2017convex,
anari2017nash}, and generalize the programs to two different mathematical
programs for the weighted case. The first program is convex and is necessary
for computational efficiency, while the second program is a non-convex
relaxation that can be rounded efficiently. The approximation factor derives
from the difference in the objective values of the convex and non-convex
relaxation.


  We propose a series of quantum algorithms for computing a wide range of
quantum entropies and distances, including the von Neumann entropy, quantum
R\'{e}nyi entropy, trace distance, and fidelity. The proposed algorithms
significantly outperform the prior best (and even quantum) ones in the low-rank
case, some of which achieve exponential speedups. In particular, for
$N$-dimensional quantum states of rank $r$, our proposed quantum algorithms for
computing the von Neumann entropy, trace distance and fidelity within additive
error $\varepsilon$ have time complexity of $\tilde O(r/\varepsilon^2)$,
$\tilde O(r^5/\varepsilon^6)$ and $\tilde O(r^{6.5}/\varepsilon^{7.5})$,
respectively. By contrast, prior quantum algorithms for the von Neumann entropy
and trace distance usually have time complexity $\Omega(N)$, and the prior best
one for fidelity has time complexity $\tilde O(r^{12.5}/\varepsilon^{13.5})$.
  The key idea of our quantum algorithms is to extend block-encoding from
unitary operators in previous work to quantum states (i.e., density operators).
It is realized by developing several convenient techniques to manipulate
quantum states and extract information from them. The advantage of our
techniques over the existing methods is that no restrictions on density
operators are required; in sharp contrast, the previous methods usually require
a lower bound on the minimal non-zero eigenvalue of density operators.


  My ten-week Massive Open Online Course "Statistical Mechanics: Algorithms and
Computations", in early 2014, focused on subjects such as Monte Carlo sampling,
molecular dynamics, transition phases in hard-sphere liquids, simulated
annealing, classical spin models, quantum Monte Carlo algorithms, and
Bose-Einstein condensation, etc. It familiarized a huge international crowd of
students with cutting-edge subjects in computational physics.
  Here, I present the topics of the course, its basic design ideas, its scope
and challenges, and compare it with earlier attempts in online teaching.


  Many models of inflation predict oscillatory features in the bispectrum of
primordial fluctuations. Since it has been shown that primordial
non-Gaussianity can lead to a scale-dependent halo bias, we investigate the
effect of oscillations in the three-point function on the clustering of
dark-matter halos. Interestingly, we find that features in the inflaton
potential such as oscillations or sharp steps get imprinted in the mass
dependence of the non-Gaussian halo bias. In this paper, we focus on models
displaying a sharp feature in the inflaton potential as well as Resonant
non-Gaussianity. In both cases, we find a strong scale dependence for the
non-Gaussian halo bias with a slope similar to that of the local model. In the
resonant case, we find that the non-Gaussian bias oscillates with halo mass, a
novel feature that is unique to this type of models. In the case of a sharp
feature in the inflaton potential, we find that the clustering of halos is
enhanced at the mass scale corresponding to the Fourier mode that exited the
horizon when the inflaton was crossing the feature in the potential. Both of
these are new effects that open the possibility of characterizing the
inflationary potential with large-scale-structure surveys. We briefly discuss
the prospects for detecting these non-Gaussian effects.


  Most prior approaches to offline reinforcement learning (RL) utilize
\textit{behavior regularization}, typically augmenting existing off-policy
actor critic algorithms with a penalty measuring divergence between the policy
and the offline data. However, these approaches lack guaranteed performance
improvement over the behavior policy. In this work, we start from the
performance difference between the learned policy and the behavior policy, we
derive a new policy learning objective that can be used in the offline setting,
which corresponds to the advantage function value of the behavior policy,
multiplying by a state-marginal density ratio. We propose a practical way to
compute the density ratio and demonstrate its equivalence to a state-dependent
behavior regularization. Unlike state-independent regularization used in prior
approaches, this \textit{soft} regularization allows more freedom of policy
deviation at high confidence states, leading to better performance and
stability. We thus term our resulting algorithm Soft Behavior-regularized Actor
Critic (SBAC). Our experimental results show that SBAC matches or outperforms
the state-of-the-art on a set of continuous control locomotion and manipulation
tasks.


  We develop a theory of graph C*-algebras using path groupoids and inverse
semigroups. Row finiteness is not assumed so that the theory applies to graphs
for which there are vertices emitting a countably infinite set of edges. We
show that the path groupoid is amenable, and give a groupoid proof of a recent
theorem of Szymanski characterizing when a graph C*-algebra is simple.


  X-ray lines of helium-like calcium (\ion{Ca}{19}) between 3.17~\AA\ and
3.21~\AA\ and associated \ion{Ca}{18} dielectronic satellites have previously
been observed in solar flare spectra, and their excitation mechanisms are well
established. Dielectronic satellites of lower ionization stages
(\ion{Ca}{17}~--~\ion{Ca}{15}) are not as well characterized. Several spectra
during a large solar flare in 2001 by the DIOGENESS X-ray spectrometer on the
{\em CORONAS-F}\/ spacecraft show the \ion{Ca}{17} and \ion{Ca}{16} satellites
as well as lines of ionized argon (\ion{Ar}{17}, \ion{Ar}{16}) including
dielectronic satellites. The DIOGENESS spectra are compared with spectra from a
synthesis code developed here based on an isothermal assumption with various
atomic sources including dielectronic satellite data from the Cowan
Hartree--Fock code. Best-fit comparisons are made by varying the temperature as
the code's input (Ar/Ca abundance ratio fixed at 0.33); close agreement is
achieved although with adjustments to some ion fractions. The derived
temperature is close to that derived from the two {\em GOES}\/ X-ray channels,
$T_{\rm GOES}$. Some lines are identified for the first time. Similar spectra
from the {\em P78-1}\/ spacecraft and the Alcator C-Mod tokamak have also been
analyzed and similar agreement obtained. The importance of blends of calcium
and argon lines is emphasized, affecting line ratios used for temperature
diagnostics. This analysis will be applied to the {\em Solar Maximum Mission}\/
Bent Crystal Spectrometer archive and to X-ray spectra expected from the ChemiX
instrument on the Sun-orbiting {\em Interhelioprobe}\/ spacecraft, while the
relevance to X-ray spectra from non-solar sources is indicated.


  We present an inflationary scenario based on a phenomenologically viable
model with direct gauge mediation of low-scale supersymmetry breaking.
Inflation can occur in the supersymmetry-breaking hidden sector. Although the
reheating temperature from the inflaton decay is so high that the gravitino
problem seems to be severe, late time entropy production from the decay of the
pseudomoduli field associated with the supersymmetry breaking can dilute
gravitinos sufficiently. We show that gravitinos are also produced from the
pseudomoduli decay and there is a model parameter space where gravitinos can be
the dark matter in the present universe.


  Bessel beams generated via axicons are widely used for various applications
like optical tweezers or laser microfabrication of transparent materials. The
specific intensity profile having high aspect ratio of beam width and length in
turn generates high aspect ratio void that resembles a needle. In contrast to
commonly generated Bessel beam that has a fixed axial intensity distribution.
We present a novel method to engineer an optical needle that can have an
arbitrary axial intensity distribution via superposition of different cone
angle Bessel beams. We analytically describe spatial spectra of an optical
needle having arbitrary axial intensity distribution. We also demonstrate a
superposition of independent optical needles and analyze the physical
limitations to observe well separated optical needles as they are influence by
mutual interference of the individual beams. In order to verify our theoretical
and numerical results we generate controllable spatial arrays of individual
beams with various numbers and spatial separations by altering a spectrum of
incoming laser beam via spatial light modulator. Lastly, we numerically examine
distortions caused by propagation through planar air-dielectric interface and
show compensation method by appropriately modifying spectral masks.


  In high dimensional quantum communication networks, quantum frequency
convertor (QFC) is indispensable as an interface in the frequency domain. For
example, many QFCs have been built to link atomic memories and fiber channels.
However, almost all of QFCs work in a two-dimensional space. It is still a
pivotal challenge to construct a high-quality QFC for some complex quantum
states, e.g., a high dimensional single-photon state that refers to a qudit.
Here, we firstly propose a high-dimensional QFC for an orbital angular momentum
qudit via sum frequency conversion with a flat top beam pump. As a
proof-of-principle demonstration, we realize quantum frequency conversions for
a qudit from infrared to visible range. Based on the qudit quantum state
tomography, the fidelities of converted state are 98.29(95.02)\%,
97.42(91.74)\%, and 86.75(67.04)\% for a qudit without (with) dark counts in
2,3, and 5 dimensions, respectively. The demonstration is very promising for
constructing a high capacity quantum communication network.


  We investigate the possibility that the energetic Type II supernova
OGLE-2014-SN-073 is powered by a fallback accretion following the failed
explosion of a massive star. Taking massive hydrogen-rich supernova progenitor
models, we estimate the fallback accretion rate and calculate the light curve
evolution of supernovae powered by the fallback accretion. We find that such
fallback accretion powered models can reproduce the overall observational
properties of OGLE-2014-SN-073. It may imply that some failed supernovae could
be observed as energetic supernovae like OGLE-2014-SN-073 instead of faint
supernovae as previously proposed.


  A convolutional encoder is said to be catastrophic if it maps an information
sequence of infinite weight into a code sequence of finite weight. As a
consequence of this mapping, a finite number of channel errors may cause an
infinite number of information bit errors when decoding. This situation should
be avoided. A catastrophic condition to determine if a time-invariant
convolutional encoder is catastrophic or not is stated in \cite{Massey:LSC}.
Palazzo developed this condition for periodically time-varying convolutional
encoders in \cite{Palazzo:Analysis}. Since Palazzo's condition is based on the
state transition table of the constituent encoders, its complexity increases
exponentially with the number of memory elements in the encoders. A novel
catastrophic condition making use of time-varying equivalent convolutional
encoders is presented in this letter. A technique to convert a catastrophic
periodically time-varying convolutional encoder into a non-catastrophic one can
also be developed based on these encoders. Since they do not involve the state
transitions of the convolutional encoder, the time complexity of these methods
grows linearly with the encoder memory.


  Networks or graphs are widely used across the sciences to represent
relationships of many kinds. igraph (https://igraph.org) is a general-purpose
software library for graph construction, analysis, and visualisation, combining
fast and robust performance with a low entry barrier. igraph pairs a fast core
written in C with beginner-friendly interfaces in Python, R, and Mathematica.
Over the last two decades, igraph has expanded substantially. It now scales to
billions of edges, supports Mathematica and interactive plotting, integrates
with Jupyter notebooks and other network libraries, includes new graph layouts
and community detection algorithms, and has streamlined the documentation with
examples and Spanish translations. Modern testing features such as continuous
integration, address sanitizers, stricter typing, and memory-managed vectors
have also increased robustness. Hundreds of bug reports have been fixed and a
community forum has been opened to connect users and developers. Specific
effort has been made to broaden use and community participation by women,
non-binary people, and other demographic groups typically underrepresented in
open source software.


  We study scrambling of the Hartree-Fock single-particle levels and wave
functions as electrons are added to an almost isolated diffusive or chaotic
quantum dot with electron-electron interactions. We use the generic framework
of the induced two-body ensembles where the randomness of the two-body
interaction matrix elements is induced by the randomness of the eigenfunctions
of the chaotic or diffusive single-particle Hamiltonian. After an appropriate
scaling of the number of added electrons, the scrambling of both the HF levels
and wave functions is described by a universal function each. These functions
can be derived from a parametric random matrix process of the Brownian-motion
type. An exception to this universality occurs when an empty level just gets
filled, in which case scrambling is delayed by one electron. An explanation of
these results is given in terms of a generalized Koopmans' approach.


  We study the axisymmetric, time-dependent hydrodynamics of rotating flows
that are under the influence of supermassive black hole gravity and radiation
from an accretion disk surrounding the black hole. This work is an extension of
the earlier work presented by Proga, where nonrotating flows were studied.
Here, we consider effects of rotation, a position-dependent radiation
temperature, density at large radii, and uniform X-ray background radiation. As
in the non-rotating case, the rotating flow settles into a configuration with
two components (1) an equatorial inflow and (2) a bipolar inflow/outflow with
the outflow leaving the system along the pole. However, with rotation the flow
does not always reach a steady state. In addition, rotation reduces the outflow
collimation and the outward flux of mass and kinetic energy. Moreover rotation
increases the outward flux of the thermal energy and can lead to fragmentation
and time-variability of the outflow. We also show that a position-dependent
radiation temperature can significantly change the flow solution. In
particular, the inflow in the equatorial region can be replaced by a thermally
driven outflow. Generally, as it have been discussed and shown in the past, we
find that self-consistently determined preheating/cooling from the quasar
radiation can significantly reduce the rate at which the central BH is fed with
matter. However, our results emphasize also a little appreciated feature.
Namely, quasar radiation drives a non-spherical, multi-temperature and very
dynamic flow. These effects become dominant for luminosities in excess of 0.01
of the Eddington luminosity.


  We study the anomalous Hall effect in a disordered Weyl semimetal. While the
intrinsic contribution is expressed solely in terms of Berry curvature, the
extrinsic contribution is given by a combination of the skew scattering and
side jump terms. For the model of small size impurities, we are able to express
the skew scattering contribution in terms of scattering phase shifts. We
identify the regime in which the skew scattering contribution dominates the
side-jump contribution: the impurities are either strong or resonant, and at
dilute concentration. In this regime, the Hall resistivity $\rho_{xy}$ is
expressed in terms of two scattering phases, analogous to the s-wave scattering
phase in a non-topological metal. We compute the dependence of $\rho_{xy}$ on
the chemical potential, and show that $\rho_{xy}$ scales with temperature as
$T^2$ in low temperatures and as $T^{3/2}$ in the high temperature limit.


  We present a search for lepton-flavor-violating tau decays into three leptons
(electrons or muons) using 782 fb^-1 of data collected with the Belle detector
at the KEKB asymmetric-energy e+e- collider. No evidence for these decays is
observed and we set 90% confidence level upper limits on the branching
fractions between 1.5 x 10^-8 and 2.7 x 10^-8.


  We investigate FASER@LHC perspectives in searches for light ($0.1-5$ GeV)
sgoldstinos in models with low energy ($10-10^4$ TeV) supersymmetry breaking.
We consider flavor conserving and flavor violating couplings of sgoldstinos to
Standard Model fermions and find the both options to be testable at FASER. Even
the first FASER run allows one to probe interesting patches in the model
parameter space, while the second run, FASER-II, with significantly larger
detector fiducial volume, gives a possibility to thoroughly explore a wide
class of supersymmetric extensions of particle physics complementary to those
probed at LHC with ATLAS and CMS detectors.


  We discuss exploration for isotropic gravitational wave backgrounds around 1
mHz by correlation analysis, targeting both parity odd and even polarization
modes. Even though the space interferometer LISA alone cannot probe the two
modes due to cancellations, the outlook is being changed drastically by the
strong development of other space detectors such as Taiji. In fact, a
heliocentric interferometer network holds a preferable geometrical symmetry
{illuminated by a virtual sphere off-center from the Sun}. By utilizing an
internal symmetry of data streams, we can optimally decompose the odd and even
parity modes at correlation analysis. By simultaneously using LISA and Taiji
for 10 years, our sensitivity to the two modes could reach $\sim 10^{-12}$ in
terms of the normalized energy density.


  The aim of this article is twofold. First, we shall review and analyse the
Neo-Kantian justification for the application of probabilistic concepts in
physics that was defended by Hans Reichenbach early in his career, notably in
his dissertation of 1916. At first sight this Kantian approach seems to
contrast sharply with Reichenbach's later logical positivist, frequentist
viewpoint. But, and this is our second goal, we shall attempt to show that
there is an underlying continuity in Reichenbach's thought: typical features of
his early Kantian conceptions can still be recognized in his later work.


  Lead-halide perovskites enjoy a number of remarkable optoelectronic
properties. To explain their origin, it is necessary to study how
electromagnetic fields interact with these systems. We address this problem
here by studying two classical quantities: Faraday rotation and the complex
refractive index in a paradigmatic perovskite CH$_3$NH$_3$PbBr$_3$ in a broad
wavelength range. We find that the minimal coupling of electromagnetic fields
to the k$\cdot$p Hamiltonian is insufficient to describe the observed data even
on the qualitative level. To amend this, we demonstrate that there exists a
relevant atomic-level coupling between electromagnetic fields and the spin
degree of freedom. This spin-electric coupling allows for quantitative
description of a number of previous as well as present experimental data. In
particular, we use it here to show that the Faraday effect in lead-halide
perovskites is dominated by the Zeeman splitting of the energy levels, and has
a substantial beyond-Becquerel contribution. Finally, we present general
symmetry-based phenomenological arguments that in the low-energy limit our
effective model includes all basis coupling terms to the electromagnetic field
in the linear order.


  In this paper, we report the results from the analysis of a numerical model
used for the design of a magnetic linear actuator with applications to
fin-based locomotion. Most of the current robotic fish generate bending motion
using rotary motors which implies at least one mechanical conversion of the
motion. We seek a solution that directly bends the fin and, at the same time,
is able to exploit the magneto-mechanical properties of the fin material. This
strong fin-actuator coupling blends the actuator and the body of the robot,
allowing cross optimization of the system's elements.
  We study a simplified model of an elastic element, a spring-mass system
representing a flexible fin, subjected to nonlinear forcing, emulating magnetic
interaction. The dynamics of the system is studied under unforced and periodic
forcing conditions. The analysis is focused on the limit cycles present in the
system, which allows the periodic bending of the fin and the generation of
thrust. The frequency, maximum amplitude and center of the periodic orbits
(offset of the bending) depend directly on the stiffness of the fin and the
intensity of the forcing; we use this dependency to sketch a simple parameter
controller. Although the model is strongly simplified, it provides means to
estimate first values of the parameters for this kind of actuator and it is
useful to evaluate the feasibility of minimal actuation control of such
systems.


  We prove that non-coisotropic branes in the Poisson-Sigma model are allowed
at the quantum level. When the brane is defined by second-class constraints,
the perturbative quantization of the model yields the Kontsevich's star product
associated to the Dirac bracket on the brane. We also discuss the quantization
when both first and second-class constraints are present.


  Stochastic thermodynamics is a developing theory for systems out of thermal
equilibrium. It allows to formulate a wealth of nontrivial relations among
thermodynamic quantities such as heat dissipation, excess work, and entropy
production in generic nonequilibrium stochastic processes. A key quantity for
the derivation of these relations is the propagator - the probability to
observe a transition from one point in phase space to another after a given
time. Here, applying stochastic Taylor expansions, we devise a formal expansion
procedure for the propagator of overdamped Langevin dynamics. The three leading
orders are obtained explicitly. The technique resolves the shortcomings of the
current mathematical machinery for the calculation of the propagator. For the
evaluation of the first two displacement cumulants, the leading order Gaussian
propagator is sufficient. However, some functionals of the propagator, such as
the entropy production, which we refer to as "first derivatives of the
trajectory", need to be evaluated to a previously-unrecognized higher order.
The method presented here can be extended to arbitrarily higher orders in order
to accurately compute any other functional of the propagator.


  Hot flow anomalies (HFAs) are studied using observations of the FGM
magnetometer and the CIS plasma detector aboard the four Cluster spacecraft.
Previously we studied several specific features of tangential discontinuities
on the basis of Cluster measurements in February-April 2003 and discovered a
new condition for forming HFAs that is the solar wind speed is higher than the
average. However during the whole spring season of 2003, the solar wind speed
was higher than average. In this study we analyse HFAs detected in 2007, the
year of solar cycle minimum. Our earlier result was confirmed: the higher solar
wind speed is a real condition for HFA formation; furthermore this constraint
is independent of Schwartz et al. s condition for HFA formation.


  Early-type dwarf galaxies are the most common type of galaxies observed in
the Universe. The origin of this kind of systems is still not well understood.
The aim of this paper is to investigate whether the different locations of
dwarf galaxies with respect to ellipticals in the face-on view of the
fundamental plane could be due to the transformation of bright disc galaxies in
low-mass systems by harassment. We have run high-resolution N-body numerical
simulations to test the tidal stripping scenario of the dE galaxies. The
present simulations modelled several individual tidal stripping events on
initial disc-like galaxy models with different bulge-to-disc mass ratios. Tidal
stripping is a very efficient mechanism for removing stars and dark matter
particles from galaxies. The particles of the disc and halo components were
easily stripped, while the bulge not. Thus, the scale length of the discs were
40-50% shorter than the initial ones. Prograde tidal interactions create tidal
features like stable bars in the discs of the galaxies. After several tidal
interactions the galaxy remnants looks like a dwarf spheroidal system.
Simulated galaxies with initial large B/D ratios are closer to the face-on view
of the fundamental plane defined by bright E and bulges of early-type galaxies.
Nevertheless, galaxies with initial small B/D ratio are located, after four
fast tidal encounters, at the position of dE galaxies in the face-on view of
the fundamental plane. We conclude that fast galaxy-galaxy interactions are
efficient mechanisms for transforming bright galaxies in dwarf ones. Indeed,
the different location observed between Es and dEs in the face-on view of the
fundamental plane can be explained by the formation of dwarf galaxies by
harassment of late-type bright ones.


  Spam phone calls have been rapidly growing from nuisance to an increasingly
effective scam delivery tool. To counter this increasingly successful attack
vector, a number of commercial smartphone apps that promise to block spam phone
calls have appeared on app stores, and are now used by hundreds of thousands or
even millions of users. However, following a business model similar to some
online social network services, these apps often collect call records or other
potentially sensitive information from users' phones with little or no formal
privacy guarantees.
  In this paper, we study whether it is possible to build a practical
collaborative phone blacklisting system that makes use of local differential
privacy (LDP) mechanisms to provide clear privacy guarantees. We analyze the
challenges and trade-offs related to using LDP, evaluate our LDP-based system
on real-world user-reported call records collected by the FTC, and show that it
is possible to learn a phone blacklist using a reasonable overall privacy
budget and at the same time preserve users' privacy while maintaining utility
for the learned blacklist.


  We analyse the implications of the fact that there are two claims for a dual
to \N=4 superconformal SU(N) Yang-Mills theory (SCYM), the Maldacena conjecture
and the theorem of Rehren. While the Maldacena dual is conjectured to be a
non-perturbative string theory for large string coupling $g_s$ and small $N$,
the Rehren dual is an ordinary quantum field theory on $AdS_5$ for all values
of the parameters. We argue that as a result, if we accept the Maldacena
conjecture, one of the following statements must be true: 1) SCYM does not
satisfy the axioms of algebraic quantum field theory for finite $N$ because its
observables do not obey the causal structure of conformal Minkowski space;. 2)
String theory on $AdS_5 \times S^5$ is not a quantum theory of gravity in 10
dimensions because it is dual to an ordinary quantum field theory on $AdS_5$
whose causal structure remains fixed for all values of its couplings; or 3)
there is no consistent quantisation of string theory on $AdS_5 \times S^5$ for
finite string scale $l_s$ and $g_s$.
  In evaluating the evidence for each of these conclusions we point out that
many of the tests of the Maldacena conjecture can be explained by a weaker form
of an $AdS/CFT$ correspondence.


  Let P be the right-angled dodecahedron or 120-cell in hyperbolic space, and
let W be the group generated by reflections across codimension-one faces of P.
We prove that if Gamma is a torsion-free subgroup of minimal index in W, then
the corresponding hyperbolic manifold H^n/Gamma is determined up to
homeomorphism by Gamma (modulo symmetries of P).


  It is shown how the theory of the fields can be constructed in a consistent
way in quantized spaces. All constructions are connected with unitary
irreducible representations of real forms of six dimensional rotation algebras
O(1,5), O(2,4), O(3,3) or equivalent real forms of four-dimensional unitary
algebras SU^*(4),SU(2,2),SL(4). The most surprising fact is that that all
operations in the construction of such field theories are connected with
compact manifolds. The gauge invariant theory in quantized space is proposed.


  We present the abundances of magnesium (Mg) and silicon (Si) for 314 dwarf
stars with spectral types in the interval K7.0-M5.5 (Teff range ~4200-3050 K)
observed with the CARMENES high-resolution spectrograph at the 3.5 m telescope
at the Calar Alto Observatory. Our analysis employs the BT-Settl model
atmospheres, the radiative transfer code Turbospectrum, and a state-of-the-art
selection of atomic and molecular data. These Mg and Si abundances are critical
for understanding both the chemical evolution and assembly of the Milky Way and
the formation and composition of rocky planets. Our chemical abundances show a
line-to-line scatter at the level of 0.1 dex for all studied spectral types.
The typical error bar of our chemical abundance measurements is +- 0.11 dex
(Mg) and +- 0.16 dex (Si) for all spectral types based on the comparison of the
results obtained for stellar components of multiple systems. The derived
abundances are consistent with the galactic evolution trends and observed
chemical abundance distribution of earlier FGK-type stars in the solar
neighbourhood. Besides, our analysis provides compatible abundances for stars
in multiple systems. In addition, we studied the abundances of different
galactic stellar populations. In this paper, we also explore the relation of
the Mg and Si abundances of stars with and without known planets.


  We establish empirical quantile process CLTs based on $n$ independent copies
of a stochastic process $\{X_t: t \in E\}$ that are uniform in $t \in E$ and
quantile levels $\alpha \in I$, where $I$ is a closed sub-interval of $(0,1)$.
Typically $E=[0,T]$, or a finite product of such intervals. Also included are
CLT's for the empirical process based on $\{I_{X_t \le y} - \rm {Pr}(X_t \le
y): t \in E, y \in R \}$ that are uniform in $t \in E, y \in R$. The process
$\{X_t: t \in E\}$ may be chosen from a broad collection of Gaussian processes,
compound Poisson processes, stationary independent increment stable processes,
and martingales.


  We present simulation studies in preparation for analyzing
$\tau^-\to\pi^-\pi^+\pi^-\nu_\tau$ in data from the Belle experiment at the KEK
$\mathrm{e}^+\mathrm{e}^-$ collider. Analyzing this decay can shed light on the
$\mathrm{a}_1(1260)$ and $\mathrm{a}_1(1420)$ resonances and yield results that
improve measurement of the $\tau$ electric and magnetic dipole moments. We show
that we can achieve a higher signal efficiency than previous analyses of the
same decay. We also demonstrate that neural networks can model our complicated
six-dimensional background distributions and that quasi-model-independent
partial-wave analysis can extract resonance masses, widths, and production
amplitudes and phases.


  Spatiotemporal correlations of the two-dimensional spring-block
(Burridge-Knopoff) models of earthquakes with the long-range inter-block
interactions are extensively studied by means of numerical computer
simulations. The long-range interaction derived from an elasticd theory, which
takes account of the effect of the elastic body adjacent to the fault plane,
falls off with distance r as 1/r^3. Comparison is made with the properties of
the corresponding short-range models studied earlier. Seismic spatiotemporal
correlations of the long-range models generally tend to be weaker than those of
the short-range models. The magnitude distribution exhibits a ``near-critical''
behavior, i.e., a power-law-like behavior close to the Gutenberg-Richter law,
for a wide parameter range with its B-value, B\simeq 0.55, insensitive to the
model parameters, in sharp contrast to that of the 2D short-range model and
those of the 1D short-range and long-range models where such a
``near-critical'' behavior is realized only by fine-tuning the model
parameters. In contrast to the short-range case, the mean stress-drop at a
seismic event of the long-range model is nearly independent of its magnitude,
consistently with the observation. Large events often accompany foreshocks
together with a doughnut-like quiescence as their precursors, while they hardly
accompany aftershocks with almost negligible seismic correlations observed
after the mainshock.


  We formulate a geometric measurement theory of dynamical classical systems
possessing both continuous and discrete degrees of freedom. The approach is
covariant with respect to choices of clocks and canonically incorporates
laboratories. The latter are embedded symplectic submanifolds of an
odd-dimensional symplectic structure. When suitably defined, symplectic
geometry in odd dimensions is exactly the structure needed for covariance. A
fundamentally probabilistic viewpoint allows classical supergeometries to
describe discrete dynamics. We solve the problem of how to construct
probabilistic measures on supermanifolds given a (possibly odd dimensional)
supersymplectic structure. This relies on a superanalog of the Hodge star for
differential forms and a description of probabilities by convex cones. We also
show how stochastic processes such as Markov chains can be described by
supergeometry.


  Due to the expectedly higher density of mobile devices and exhaust of radio
resources, the fifth generation (5G) mobile networks introduce small cell
concept in the radio access technologies, so-called Small Cell Networks (SCNs),
to improve radio spectrum utilization. However, this increases the chance of
handover due to smaller coverage of a micro base station, i.e., home eNodeB
(HeNB) in 5G. Subsequently, the latency will increase as the costs of
authenticated key exchange protocol, which ensures entity authentication and
communication confidentiality for secure handover, also increase totally. Thus,
this work presents a secure region-based handover scheme (ReHand) with user
anonymity and fast revocation for SCNs in 5G. ReHand greatly reduces the
communication costs when UEs roam between small cells within the region of a
macro base station, i.e., eNB in 5G, and the computation costs due to the
employment of symmetry-based cryptographic operations. Compared to the three
elaborated related works, ReHand dramatically reduces the costs from 82.92% to
99.99%. Nevertheless, this work demonstrates the security of ReHand by
theoretically formal proofs.


  We investigate quasi-Newton methods for minimizing a strictly convex
quadratic function which is subject to errors in the evaluation of the
gradients. The methods all give identical behavior in exact arithmetic,
generating minimizers of Krylov subspaces of increasing dimensions, thereby
having finite termination. A BFGS quasi-Newton method is empirically known to
behave very well on a quadratic problem subject to small errors. We also
investigate large-error scenarios, in which the expected behavior is not so
clear. In particular, we are interested in the behavior of quasi-Newton
matrices that differ from the identity by a low-rank matrix, such as a
memoryless BFGS method. Our numerical results indicate that for large errors, a
memory-less quasi-Newton method often outperforms a BFGS method. We also
consider a more advanced model for generating search directions, based on
solving a chance-constrained optimization problem. Our results indicate that
such a model often gives a slight advantage in final accuracy, although the
computational cost is significantly higher.


  In this paper, we construct eight infinite families of ternary linear codes
associated with double cosets with respect to certain maximal parabolic
subgroup of the special orthogonal group $SO^{-}(2n,q)$. Here ${q}$ is a power
of three. Then we obtain four infinite families of recursive formulas for power
moments of Kloosterman sums with square arguments and four infinite families of
recursive formulas for even power moments of those in terms of the frequencies
of weights in the codes. This is done via Pless power moment identity and by
utilizing the explicit expressions of exponential sums over those double cosets
related to the evaluations of $"$Gauss sums" for the orthogonal groups
$O^{-}(2n,q)$.


  The quantum circuit model is the most commonly used model for implementing
quantum computers and quantum neural networks whose essential tasks are to
realize certain unitary operations. Here we propose an alternative approach; we
use a simple discrete-time quantum walk (DTQW) on a cycle graph to model an
arbitrary unitary operation $U(N)$ without the need to decompose it into a
sequence of gates of smaller sizes. Our model is essentially a quantum neural
network based on DTQW. Firstly, it is universal as we show that any unitary
operation $U(N)$ can be realized via an appropriate choice of coin operators.
Secondly, our DTQW-based neural network can be updated efficiently via a
learning algorithm, i.e., a modified stochastic gradient descent algorithm
adapted to our network. By training this network, one can promisingly find
approximations to arbitrary desired unitary operations. With an additional
measurement on the output, the DTQW-based neural network can also implement
general measurements described by positive-operator-valued measures (POVMs). We
show its capacity in implementing arbitrary 2-outcome POVM measurements via
numeric simulation. We further demonstrate that the network can be simplified
and can overcome device noises during the training so that it becomes more
friendly for laboratory implementations. Our work shows the capability of the
DTQW-based neural network in quantum computation and its potential in
laboratory implementations.


  Considering different self-adjoint realisations of positively projected
massless Coulomb-Dirac operators we find out, under which conditions any
negative perturbation, however small, leads to emergence of negative spectrum.
We also prove some weighted Lieb-Thirring estimates for negative eigenvalues of
such operators. In the process we find explicit spectral representations for
all self-adjoint realisations of massless Coulomb-Dirac operators on the
half-line.


  Optical singularities manifesting at the center of vector vortex beams are
unstable, since their topological charge is higher than the lowest value
permitted by Maxwell's equations. Inspired by conceptually similar phenomena
occurring in the polarization pattern characterizing the skylight, we show how
perturbations that break the symmetry of radially symmetric vector beams lead
to the formation of a pair of fundamental and stable singularities, i.e. points
of circular polarization. We prepare a superposition of a radial (or azimuthal)
vector beam and a uniformly linearly polarized Gaussian beam; by varying the
amplitudes of the two fields, we control the formation of pairs of these
singular points and their spatial separation. We complete this study by
applying the same analysis to vector vortex beams with higher topological
charges, and by investigating the features that arise when increasing the
intensity of the Gaussian term. Our results can find application in the context
of singularimetry, where weak fields are measured by considering them as
perturbation of unstable optical beams.


  It is well-known that the solution of the classical linear wave equation with
compactly supported initial condition and vanishing initial velocity is also
compactly supported in a set depending on time : the support of the solution at
time t is causally related to that of the initially given condition. Reed and
Simon have shown that for a real-valued Klein-Gordon equation with (nonlinear)
right-hand side $- \lambda u^3$, causality still holds. We show the same
property for a one-dimensional Klein-Gordon problem but with transmission and
with a more general repulsive nonlinear right-hand side $F$. We also prove the
global existence of a solution using the repulsiveness of $F$. In the
particular case $F(u) = - \lambda u^3$, the problem is a physical model for a
quantum particle submitted to self-interaction and to a potential step.


  Likelihood is a standard estimate for outlier detection. The specific role of
the normalization constraint is to ensure that the out-of-distribution (OOD)
regime has a small likelihood when samples are learned using maximum
likelihood. Because autoencoders do not possess such a process of
normalization, they often fail to recognize outliers even when they are
obviously OOD. We propose the Normalized Autoencoder (NAE), a normalized
probabilistic model constructed from an autoencoder. The probability density of
NAE is defined using the reconstruction error of an autoencoder, which is
differently defined in the conventional energy-based model. In our model,
normalization is enforced by suppressing the reconstruction of negative
samples, significantly improving the outlier detection performance. Our
experimental results confirm the efficacy of NAE, both in detecting outliers
and in generating in-distribution samples.


  Fracton phases of matter constitute an interesting point of contact between
condensed matter and high-energy physics. The limited mobility property of
fracton quasiparticles finds applications in many different contexts, including
quantum information, spin liquids, elasticity, hydrodynamics, gravity and
holography. In this paper we adopt a field theoretical approach to investigate
the three dimensional action of a rank-2 symmetric tensor field invariant under
the covariant fracton symmetry. The theory appears as a non-topological higher
rank generalization of the ordinary Chern-Simons model, depending only on the
traceless part of the tensor gauge field. After defining a field strength, a
rank-2 traceless ``electric'' field and a ``magnetic'' vector field are
identified, in analogy with the standard Chern-Simons ones. Once matter is
introduced, a Hall-like behaviour with fractonic features emerges. In
particular, our model shows a Hall-like dipole current, together with a
vectorial ``flux-attachment'' relation for dipoles. This gives a possible
starting point for a fracton - vortex duality. A gauge-fixing term is then
introduced, from which propagators are computed and the counting of the degrees
of freedom is performed. Finally, the energy-momentum tensor is shown to be
conserved and the integrated energy density is proved to be zero, which reminds
the topological nature of the standard Chern-Simons model.


  Using the formulation for N=2 conformal supergravity in SU(2) superspace, we
define super-Weyl (or superconformal) anomalies and construct two types of
nonlocal effective actions that generate these anomalies. We also present the
local Wess-Zumino action for spontaneously broken N=2 superconformal symmetry,
with the Goldstone supermultiplet identified with a reduced chiral superfield
containing the dilaton and the axion among its components.


  The automated generation of music playlists can be naturally regarded as a
sequential task, where a recommender system suggests a stream of songs that
constitute a listening session. In order to predict the next song in a
playlist, some of the playlist models proposed so far consider the current and
previous songs in the playlist (i.e., the song context) and possibly the order
of the songs in the playlist. We investigate the impact of the song context and
the song order on next-song recommendations by conducting dedicated off-line
experiments on two datasets of hand-curated music playlists. Firstly, we
compare three playlist models, each able to consider a different song context
length: a popularity-based model, a song-based Collaborative Filtering (CF)
model and a Recurrent-Neural-Network-based model (RNN). We also consider a
model that predicts next songs at random as a reference. Secondly, we challenge
the RNN model (the only model from the first experiment able to consider the
song order) by manipulating the order of songs within playlists. Our results
indicate that the song context has a positive impact on the quality of
next-song recommendations, even though this effect can be masked by the bias
towards very popular songs. Furthermore, in our experiments the song order does
not appear as a crucial variable to predict better next-song recommendations.


  The top quark pairs produced at a polarized muon collider are in a (nearly)
pure spin configuration. This result holds for all center-of-mass energies, and
is insensitive to the next-to-leading order QCD radiative corrections. The
decay products of a polarized top quark show strong angular correlations. We
describe an interesting interference effect between the left-handed and
longitudinally polarized W bosons in top quark decay. This effect is easily
observable in the angular distribution of the charged lepton with respect to
the beam axis.


  Recently several minimum free energy (MFE) folding algorithms for predicting
the joint structure of two interacting RNA molecules have been proposed. Their
folding targets are interaction structures, that can be represented as diagrams
with two backbones drawn horizontally on top of each other such that (1)
intramolecular and intermolecular bonds are noncrossing and (2) there is no
"zig-zag" configuration. This paper studies joint structures with arc-length at
least four in which both, interior and exterior stack-lengths are at least two
(no isolated arcs). The key idea in this paper is to consider a new type of
shape, based on which joint structures can be derived via symbolic enumeration.
Our results imply simple asymptotic formulas for the number of joint structures
with surprisingly small exponential growth rates. They are of interest in the
context of designing prediction algorithms for RNA-RNA interactions.


  Boron subphthalocyanine chloride is an electron donor material used in small
molecule organic photovoltaics with an unusually large molecular dipole moment.
Using first-principles calculations, we investigate enhancing the electronic
and optical properties of boron subphthalocyanine chloride, by substituting the
boron and chlorine atoms with other trivalent and halogen atoms in order to
modify the molecular dipole moment. Gas phase molecular structures and
properties are predicted with hybrid functionals. Using positions and
orientations of the known compounds as the starting coordinates for these
molecules, stable crystalline structures are derived following a procedure that
involves perturbation and accurate total energy minimization. Electronic
structure and photonic properties of the predicted crystals are computed using
the GW method and the Bethe-Salpeter equation, respectively. Finally, a simple
transport model is use to demonstrate the importance of molecular dipole
moments on device performance.


  We give sufficient conditions on a labeled direct graph to determine whether
the Tanaka prolongation of its associated Lie algebra is infinite-dimensional.
In the case that all directed edges are labeled differently, the corresponding
graph Lie algebra is of infinite type if and only if the graph has a vertex of
degree one.


  Deep learning algorithms, often critiqued for their 'black box' nature,
traditionally fall short in providing the necessary transparency for trusted
clinical use. This challenge is particularly evident when such models are
deployed in local hospitals, encountering out-of-domain distributions due to
varying imaging techniques and patient-specific pathologies. Yet, this
limitation offers a unique avenue for continual learning. The
Uncertainty-Guided Annotation (UGA) framework introduces a human-in-the-loop
approach, enabling AI to convey its uncertainties to clinicians, effectively
acting as an automated quality control mechanism. UGA eases this interaction by
quantifying uncertainty at the pixel level, thereby revealing the model's
limitations and opening the door for clinician-guided corrections. We evaluated
UGA on the Camelyon dataset for lymph node metastasis segmentation which
revealed that UGA improved the Dice coefficient (DC), from 0.66 to 0.76 by
adding 5 patches, and further to 0.84 with 10 patches. To foster broader
application and community contribution, we have made our code accessible at


  It is proved that certain types of modular cusp forms generate irreducible
automorphic representation of the underlying algebraic group. Analogous
archimedean and non-archimedean local statements are also given.


  We provide a numerical algorithm for the model characterizing anomalous
diffusion in expanding media, which is derived in [F. Le Vot, E. Abad, and S.
B. Yuste, Phys. Rev. E {\bf96} (2017) 032117]. The Sobolev regularity for the
equation is first established. Then we use the finite element method to
discretize the Laplace operator and present error estimate of the spatial
semi-discrete scheme based on the regularity of the solution; the backward
Euler convolution quadrature is developed to approximate Riemann-Liouville
fractional derivative and error estimates for the fully discrete scheme are
established by using the continuity of solution. Finally, the numerical
experiments verify the effectiveness of the algorithm.


  The internal rotation of low mass stars all along their evolution is of
primary interest when studying their rotational dynamics, internal mixing and
magnetic fields generation. In this context, helio- and asteroseismology probe
angular velocity gradients deep within solar type stars. Still the rotation of
the close center of such stars on the main sequence is hardly detectable and
the dynamical interactions of the radiative core with the surface convective
envelope is not well understood. Among them, the influence of the differential
rotation profile sustained by convection and applied as a boundary condition to
the radiation zone may be very important leading to the formation of
tachoclines. In the solar convective region, the equator is rotating faster
than the pole while numerical simulations predict either a solar or an
anti-solar rotation in other low mass stars envelopes depending on their
convective Rossby number. In this work, we therefore build for the first time
2D steady hydrodynamical models of low mass stars radiation zone providing a
full 2D description of their dynamics and studying the influence of a general
shear boundary condition accounting for a solar or an anti-solar differential
rotation in the convective envelope. We compute coherently differential
rotation and the associated meridional circulation using the Boussinesq
approximation.


  In "Square partitions and Catalan numbers" (arXiv0912.4983), Bennett et al.
presented a recursive algorithm to create a family of partitions from one or
several partitions. They were mainly interested in the cases when we begin with
a single square partition or with several partitions with only one part. The
cardinalities of those families of partitions are the Catalan and ballot
numbers, respectively. In this paper we present a closed description for those
families. We also present bijections between those sets of partitions and sets
of trees and forests enumerated by the Catalan an ballot numbers.


  Although deep learning has enabled a huge leap forward in image inpainting,
current methods are often unable to synthesize realistic high-frequency
details. In this paper, we propose applying super-resolution to coarsely
reconstructed outputs, refining them at high resolution, and then downscaling
the output to the original resolution. By introducing high-resolution images to
the refinement network, our framework is able to reconstruct finer details that
are usually smoothed out due to spectral bias - the tendency of neural networks
to reconstruct low frequencies better than high frequencies. To assist training
the refinement network on large upscaled holes, we propose a progressive
learning technique in which the size of the missing regions increases as
training progresses. Our zoom-in, refine and zoom-out strategy, combined with
high-resolution supervision and progressive learning, constitutes a
framework-agnostic approach for enhancing high-frequency details that can be
applied to any CNN-based inpainting method. We provide qualitative and
quantitative evaluations along with an ablation analysis to show the
effectiveness of our approach. This seemingly simple, yet powerful approach,
outperforms state-of-the-art inpainting methods. Our code is available in
https://github.com/google/zoom-to-inpaint


  Industrial Fog computing deploys various industrial services, such as
automatic monitoring/control and imminent failure detection, at the Fog Nodes
(FNs) to improve the performance of industrial systems. Much effort has been
made in the literature on the design of fog network architecture and
computation offloading. This paper studies an equally important but much less
investigated problem of service hosting where FNs are adaptively configured to
host services for Sensor Nodes (SNs), thereby enabling corresponding tasks to
be executed by the FNs. The problem of service hosting emerges because of the
limited computational and storage resources at FNs, which limit the number of
different types of services that can be hosted by an FN at the same time.
Considering the variability of service demand in both temporal and spatial
dimensions, when, where, and which services to host have to be judiciously
decided to maximize the utility of the Fog computing network. Our proposed Fog
configuration strategies are tailored to battery-powered FNs. The limited
battery capacity of FNs creates a long-term energy budget constraint that
significantly complicates the Fog configuration problem as it introduces
temporal coupling of decision making across the timeline. To address all these
challenges, we propose an online distributed algorithm, called Adaptive Fog
Configuration (AFC), based on Lyapunov optimization and parallel Gibbs
sampling. AFC jointly optimizes service hosting and task admission decisions,
requiring only currently available system information while guaranteeing
close-to-optimal performance compared to an oracle algorithm with full future
information.


  RGB-Thermal salient object detection (SOD) combines two spectra to segment
visually conspicuous regions in images. Most existing methods use boundary maps
to learn the sharp boundary. These methods ignore the interactions between
isolated boundary pixels and other confident pixels, leading to sub-optimal
performance. To address this problem,we propose a position-aware relation
learning network (PRLNet) for RGB-T SOD based on swin transformer. PRLNet
explores the distance and direction relationships between pixels to strengthen
intra-class compactness and inter-class separation, generating salient object
masks with clear boundaries and homogeneous regions. Specifically, we develop a
novel signed distance map auxiliary module (SDMAM) to improve encoder feature
representation, which takes into account the distance relation of different
pixels in boundary neighborhoods. Then, we design a feature refinement approach
with directional field (FRDF), which rectifies features of boundary
neighborhood by exploiting the features inside salient objects. FRDF utilizes
the directional information between object pixels to effectively enhance the
intra-class compactness of salient regions. In addition, we constitute a pure
transformer encoder-decoder network to enhance multispectral feature
representation for RGB-T SOD. Finally, we conduct quantitative and qualitative
experiments on three public benchmark datasets.The results demonstrate that our
proposed method outperforms the state-of-the-art methods.


  Variational quantum circuits (VQCs) have become a powerful tool for
implementing Quantum Neural Networks (QNNs), addressing a wide range of complex
problems. Well-trained VQCs serve as valuable intellectual assets hosted on
cloud-based Noisy Intermediate Scale Quantum (NISQ) computers, making them
susceptible to malicious VQC stealing attacks. However, traditional model
extraction techniques designed for classical machine learning models encounter
challenges when applied to NISQ computers due to significant noise in current
devices. In this paper, we introduce QuantumLeak, an effective and accurate QNN
model extraction technique from cloud-based NISQ machines. Compared to existing
classical model stealing techniques, QuantumLeak improves local VQC accuracy by
4.99\%$\sim$7.35\% across diverse datasets and VQC architectures.


  Any positive integer $n$ other than 10 with abundancy index 9/5 must be a
square with at least 6 distinct prime factors, the smallest being 5. Further,
at least one of the prime factors must be congruent to 1 modulo 3 and appear
with an exponent congruent to 2 modulo 6 in the prime power factorization of
$n$.


  We study a fundamental class of regression models called the second order
linear model (SLM). The SLM extends the linear model to high order functional
space and has attracted considerable research interest recently. Yet how to
efficiently learn the SLM under full generality using nonconvex solver still
remains an open question due to several fundamental limitations of the
conventional gradient descent learning framework. In this study, we try to
attack this problem from a gradient-free approach which we call the
moment-estimation-sequence (MES) method. We show that the conventional gradient
descent heuristic is biased by the skewness of the distribution therefore is no
longer the best practice of learning the SLM. Based on the MES framework, we
design a nonconvex alternating iteration process to train a $d$-dimension
rank-$k$ SLM within $O(kd)$ memory and one-pass of the dataset. The proposed
method converges globally and linearly, achieves $\epsilon$ recovery error
after retrieving $O[k^{2}d\cdot\mathrm{polylog}(kd/\epsilon)]$ samples.
Furthermore, our theoretical analysis reveals that not all SLMs can be learned
on every sub-gaussian distribution. When the instances are sampled from a
so-called $\tau$-MIP distribution, the SLM can be learned by $O(p/\tau^{2})$
samples where $p$ and $\tau$ are positive constants depending on the skewness
and kurtosis of the distribution. For non-MIP distribution, an addition
diagonal-free oracle is necessary and sufficient to guarantee the learnability
of the SLM. Numerical simulations verify the sharpness of our bounds on the
sampling complexity and the linear convergence rate of our algorithm.


  Quantum autoencoder (QAE) compresses a bipartite quantum state into its
subsystem by a self-checking mechanism. How to characterize the lost
information in this process is essential to understand the compression
mechanism of<EMAIL_ADDRESS>Here we investigate how to decrease the lost information in
QAE for any input mixed state. We theoretically show that the lost information
is the quantum mutual information between the remaining subsystem and the
ignorant one, and the encoding unitary transformation is designed to minimize
this mutual information. Further more, we show that the optimized unitary
transformation can be decomposed as the product of a permutation unitary
transformation and a disentanglement unitary transformation, and the
permutation unitary transformation can be searched by a regular Young tableau
algorithm. Finally we numerically identify that our compression scheme
outperforms the quantum variational circuit based<EMAIL_ADDRESS>


  Knowledge distillation (KD) is a popular method to train efficient networks
("student") with the help of high-capacity networks ("teacher"). Traditional
methods use the teacher's soft logits as extra supervision to train the student
network. In this paper, we argue that it is more advantageous to make the
student mimic the teacher's features in the penultimate layer. Not only the
student can directly learn more effective information from the teacher feature,
feature mimicking can also be applied for teachers trained without a softmax
layer. Experiments show that it can achieve higher accuracy than traditional
KD. To further facilitate feature mimicking, we decompose a feature vector into
the magnitude and the direction. We argue that the teacher should give more
freedom to the student feature's magnitude, and let the student pay more
attention on mimicking the feature direction. To meet this requirement, we
propose a loss term based on locality-sensitive hashing (LSH). With the help of
this new loss, our method indeed mimics feature directions more accurately,
relaxes constraints on feature magnitudes, and achieves state-of-the-art
distillation accuracy. We provide theoretical analyses of how LSH facilitates
feature direction mimicking, and further extend feature mimicking to
multi-label recognition and object detection.


  We consider compactly supported perturbations of periodic Sturm-Liouville
equations. In this context, one can use the Floquet solutions of the periodic
background to define scattering coefficients. We prove that if the reflection
coefficient is identically zero, then the operators corresponding to the
periodic and perturbed equations, respectively, are unitarily equivalent. In
some appendices, we also provide the proofs of several basic estimates, e.g.
bounds and asymptotics for the relevant m-functions.


  The route towards manipulation of the optoelectronic properties of matter
beyond the current limits of electronics starts from a comprehensive study of
the ultrafast dynamics triggered by interaction with light. Among them, a
fundamental role is played by charge photoinjection, a complex process that
stems from the interplay of many different physical phenomena, which cannot be
easily disentangled. Single- and multi-photon absorption, diabatic tunnelling,
intra-band motion, and field-driven band dressing, all concur in determining
the overall excited electron population, dictating the electro-optical
properties of a material. Here we investigate ultrafast photoinjection in a
prototypical semiconductor (monocrystalline germanium) by using attosecond
transient reflection spectroscopy. The precise pump-field characterization
ensured by a simultaneous attosecond streaking experiment, in tandem with a
comprehensive theoretical approach, allowed us to disentangle the different
physical phenomena unfolding at different positions in the reciprocal space and
at different timing within the envelope of the pump pulse. Moreover, we found
that intra-band phenomena hinder charge injection, in contrast to what was
previously observed for resonant, direct band-gap semiconductors. Therefore,
besides other known parameters as the central wavelength and peak intensity,
our results indicate that the pulse temporal envelope and the local band
structure probed by intra-band effects are of key importance to achieve an
optimal control over the ultrafast carrier injection process and tailor the
complex optical and electronic properties of a semiconductor on the few- to
sub-femtosecond time scale.


  This white paper was submitted to the US Astronomy and Astrophysics Decadal
Survey (Astro2020) and defines the science questions to be answered in the next
decade in the field of Ultra-High Energy Cosmic-Rays. Following a review of the
recent experimental and theoretical advances in the field, the paper outlines
strategies and requirements desirable for the design of future experiments.


  A Regret Minimizing Set (RMS) is a useful concept in which a smaller subset
of a database is selected while mostly preserving the best scores along every
possible utility function. In this paper, we study the $k$-Regret Minimizing
Sets ($k$-RMS) and Average Regret Minimizing Sets (ARMS) problems. $k$-RMS
selects $r$ records from a database such that the maximum regret ratio between
the $k$-th best score in the database and the best score in the selected
records for any possible utility function is minimized. Meanwhile, ARMS
minimizes the average of this ratio within a distribution of utility functions.
Particularly, we study approximation algorithms for $k$-RMS and ARMS from the
perspective of approximating the happiness ratio, which is equivalent to one
minus the regret ratio.
  In this paper, we show that the problem of approximating the happiness of a
$k$-RMS within any finite factor is NP-Hard when the dimensionality of the
database is unconstrained and extend the result to an inapproximability proof
for the regret. We then provide approximation algorithms for approximating the
happiness of ARMS with better approximation ratios and time complexities than
known algorithms for approximating the regret. We further provide dataset
reduction schemes which can be used to reduce the runtime of existing heuristic
based algorithms, as well as to derive polynomial-time approximation schemes
for $k$-RMS when dimensionality is fixed. Finally, we provide experimental
validation.


  We explore the vertical light distribution as a function of galactocentric
radius in the edge-on (i=88) Sd `superthin' galaxy UGC7321. UGC7321 is a
low-luminosity spiral (M_B,i=-17.0) with a diffuse, low surface brightness
stellar disk and no discernible bulge component. Within 0.25' (725 pc) of the
disk center the global luminosity profile of UGC7321 can be reasonably
characterized by an exponential function with a scale height h_z=2.9" (140 pc)
in H and h_z=3.1" (150 pc) in R, making this among the thinnest galaxy disks
know. Near the disk center we derive a ratio of disk scale length to global
disk scale height h_r/h_z=14 in both H and R; near the edge of the disk,
h_r/h_z=10. At intermediate galactocentric radii (0.25'<r<1.5'), the disk of
UGC7321 becomes less peaked than an exponential near the galactic plane. At
these radii the vertical luminosity profiles can be well reproduced by a linear
combination of two isothermal disk components of differing scale heights. These
fits, together with the strong disk color gradients by Matthews, Gallagher, &
van Driel (1999), suggest that UGC7321 has multiple disk subcomponents
comprised of stellar populations with different ages and velocity dispersions.
Thus even examples of the thinnest pure disk galaxies exhibit complex structure
and signatures of dynamical heating.


  The large scale properties of spatiotemporal chaos in the 2d
Kuramoto-Sivashinsky equation are studied using an explicit coarse graining
scheme. A set of intermediate equations are obtained. They describe
interactions between the small scale (e.g., cellular) structures and the
hydrodynamic degrees of freedom. Possible forms of the effective large scale
hydrodynamics are constructed and examined. Although a number of different
universality classes are allowed by symmetry, numerical results support the
simplest scenario, that being the KPZ universality class.


  Image steganography is the art of hiding secret message in grayscale or color
images. Easy detection of secret message for any state-of-art image
steganography can break the stego system. To prevent the breakdown of the stego
system data is embedded in the selected area of an image which reduces the
probability of detection. Most of the existing adaptive image steganography
techniques achieve low embedding capacity. In this paper a high capacity
Predictive Edge Adaptive image steganography technique is proposed where
selective area of cover image is predicted using Modified Median Edge Detector
(MMED) predictor to embed the binary payload (data). The cover image used to
embed the payload is a grayscale image. Experimental results show that the
proposed scheme achieves better embedding capacity with minimum level of
distortion and higher level of security. The proposed scheme is compared with
the existing image steganography schemes. Results show that the proposed scheme
achieves better embedding rate with lower level of distortion.


  We analyze representative ill-posed scenarios of tomographic PIV with a focus
on conditions for unique volume reconstruction. Based on sparse random seedings
of a region of interest with small particles, the corresponding systems of
linear projection equations are probabilistically analyzed in order to
determine (i) the ability of unique reconstruction in terms of the imaging
geometry and the critical sparsity parameter, and (ii) sharpness of the
transition to non-unique reconstruction with ghost particles when choosing the
sparsity parameter improperly. The sparsity parameter directly relates to the
seeding density used for PIV in experimental fluids dynamics that is chosen
empirically to date. Our results provide a basic mathematical characterization
of the PIV volume reconstruction problem that is an essential prerequisite for
any algorithm used to actually compute the reconstruction. Moreover, we connect
the sparse volume function reconstruction problem from few tomographic
projections to major developments in compressed sensing.


  A Conway semiring is a semiring $S$ equipped with a unary operation $^*:S \to
S$, always called 'star', satisfying the sum star and product star identities.
It is known that these identities imply a Kleene type theorem. Some
computationally important semirings, such as $N$ or $N^{\rat}\llangle \Sigma^*
\rrangle$ of rational power series of words on $\Sigma$ with coefficients in
$N$, cannot have a total star operation satisfying the Conway identities. We
introduce here partial Conway semirings, which are semirings $S$ which have a
star operation defined only on an ideal of $S$; when the arguments are
appropriate, the operation satisfies the above identities. We develop the
general theory of partial Conway semirings and prove a Kleene theorem for this
generalization.


  I propose an orthogonalization procedure preserving the grading of the
initial graded set of linearly independent vectors. In particular, this
procedure is applicable for orthonormalization of any countable set of
polynomials in several (finitely many) indeterminates.


  We examine the switching dynamics of a stochastic population subjected to a
deterministically time-varying environment. Our approach is demonstrated in the
realm of ecology on a problem of population establishment. Here, by assuming a
constant immigration pressure along with a strong Allee effect, at the
deterministic level one obtains a critical population size beyond which the
system experiences establishment. Notably the latter has been shown to be
strongly influenced by the interplay between demographic and environmental
noise. We consider two prototypical examples for environmental variations: a
temporary environmental change, and a periodically-varying environment. By
employing a semi-classical approximation we compute, within exponential
accuracy, the change in the establishment probability and mean establishment
time of the population, due to the environmental variability. Our analytical
results are verified by using a modified Gillespie algorithm which accounts for
explicitly time-dependent reaction rates. Finally, our theoretical approach can
also be useful in studying switching dynamics in gene regulatory networks under
extrinsic variations.


  The operational formulations of quantum theory are drastically time oriented.
However, to the best of our knowledge, microscopic physics is time-symmetric.
We address this tension by showing that the asymmetry of the operational
formulations does not reflect a fundamental time-orientation of physics.
Instead, it stems from built-in assumptions about the $users$ of the theory. In
particular, these formalisms are designed for predicting the future based on
information about the past, and the main mathematical objects contain implicit
assumption about the past, but not about the future. The main asymmetry in
quantum theory is the difference between knowns and unknowns.


  We report a search for radio continuum emission from the gamma-ray pulsar
Geminga. We have used the VLA to image the location of the optical counterpart
of Geminga at 74 and 326 MHz. We detect no radio counterpart. We derive upper
limits to the pulse-averaged flux density of Geminga, taking diffractive
scintillation into account. We find that diffractive scintillation is probably
quenched at 74 MHz and does not influence our upper limit, S < 56 mJy
(2\sigma), but that a 95% confidence level at 326 MHz is S < 5 mJy. Owing to
uncertainties on the other low-frequency detections and the possibility of
intrinsic variability or extrinsic variability (refractive interstellar
scintillation) or both, our non-detections are nominally consistent with these
previous detections.


  Risk parity, also known as equal risk contribution, has recently gained
increasing attention as a portfolio allocation method. However, solving
portfolio weights must resort to numerical methods as the analytic solution is
not available. This study improves two existing iterative methods: the cyclical
coordinate descent (CCD) and Newton methods. We enhance the CCD method by
simplifying the formulation using a correlation matrix and imposing an
additional rescaling step. We also suggest an improved initial guess inspired
by the CCD method for the Newton method. Numerical experiments show that the
improved CCD method performs the best and is approximately three times faster
than the original CCD method, saving more than 40% of the iterations.


  In this paper, we investigate the two-weight Hardy inequalities on metric
measure space possessing polar decompositions for the case $p=1$ and $1 \leq q
<\infty.$ This result complements the Hardy inequalities obtained in \cite{RV}
in the case $1< p\le q<\infty.$ The case $p=1$ requires a different argument
and does not follow as the limit of known inequalities for $p>1.$ As a
byproduct, we also obtain the best constant in the established inequality. We
give examples obtaining new weighted Hardy inequalities on homogeneous Lie
groups, on hyperbolic spaces and on Cartan-Hadamard manifolds for the case
$p=1$ and $1\le q<\infty.$


  As automation advances in manufacturing, the demand for precise and
sophisticated defect detection technologies grows. Existing vision models for
defect recognition methods are insufficient for handling the complexities and
variations of defects in contemporary manufacturing settings. These models
especially struggle in scenarios involving limited or imbalanced defect data.
In this work, we introduce MemoryMamba, a novel memory-augmented state space
model (SSM), designed to overcome the limitations of existing defect
recognition models. MemoryMamba integrates the state space model with the
memory augmentation mechanism, enabling the system to maintain and retrieve
essential defect-specific information in training. Its architecture is designed
to capture dependencies and intricate defect characteristics, which are crucial
for effective defect detection. In the experiments, MemoryMamba was evaluated
across four industrial datasets with diverse defect types and complexities. The
model consistently outperformed other methods, demonstrating its capability to
adapt to various defect recognition scenarios.


  The use of metal van der Waals contacts and the implicit reduction in
Fermi-level pinning in contacted semiconductors has led to remarkable device
optimizations. For example, using graphene as an electrical contact allows for
tunable Schottky barriers in transistors and barristors. In this study, we
present a double Schottky barrier model and apply it to barrier tunable all van
der Waals transistors. In a molybdenum disulfide (MoS$_2$) transistor with
graphene and few-layer graphene contacts, we find that the model can be applied
to extract Schottky barrier heights that agree with the Schottky-Mott rule from
simple two-terminal current-voltage measurements at room temperature.
Furthermore, we show tunability of the Schottky barrier \textit{in-situ} using
a regional contact gate. Our results show that a basic back-to-back diode
model, applied to two terminal measurements, can capture the diode properties
of all-van-der-Waals transistors relatively well.


  The term Clifford group was introduced in 1998 by D. Gottesmann in his
investigation of quantum error-correcting codes. The simplest Clifford group in
multiqubit quantum computation is generated by a restricted set of unitary
Clifford gates - the Hadamard, $\pi/4$-phase and controlled-X gates. Because of
this restriction the Clifford model of quantum computation can be efficiently
simulated on a classical computer (the Gottesmann-Knill theorem). However, this
fact does not diminish the importance of the Clifford model, since it may serve
as a suitable starting point for a full-fledged quantum computation.
  In the general case of a single or composite quantum system with
finite-dimensional Hilbert space the finite Weyl-Heisenberg group of unitary
operators defines the quantum kinematics and the states of the quantum
register. Then the corresponding Clifford group is defined as the group of
unitary operators leaving the Weyl-Heisenberg group invariant. The aim of this
contribution is to show that our comprehensive results on symmetries of the
Pauli gradings of quantum operator algebras -- covering any single as well as
composite finite quantum systems -- directly correspond to Clifford groups
defined as quotients with respect to $\U(1)$.


  New moderate-resolution mid-infrared spectroscopy at 10 micron of 27 infrared
galaxies is presented. The galaxies have been chosen from three 60 micron
selected and one 12 micron selected complete flux-limited catalogs of galaxies;
17 of these sources have L_IR(8--1000 micron) >= 5 times 10^11 L_sun. A
high-resolution spectrum of the source Arp 299B1 is also presented. Combining
these new results with previously published results, a nearly complete 60
micron selected flux limited subsample, with L_IR(8--1000 micron) >= 1.6 times
10^11 L_sun of 25 galaxies is defined. Within this subsample, it is found that
the dominant power source of infrared galaxies in the luminosity range 1.6
times 10^11 < L_IR(8--1000 micron) < 10^{12} L_sun is massive star formation
based on the clear presence of the 11.3 micron aromatic hydrocarbon emission
feature in the majority of the spectra. Three of the five ultraluminous
infrared galaxies (L_IR(8--1000 micron) >= 10^12 L_sun) within this subsample
show evidence that an active galactic nucleus provides an energetically
important power source based on the detection of silicate absorption in their
mid-infrared spectra. The physical basis of a possible anti-correlation between
the 11.3 micron feature equivalent width and infrared light to molecular gas
mass ratios is discussed.


  We show how the notion of the transcendence degree of a zero-cycle on a
smooth projective variety X is related to the structure of the motive M(X).
This can be of particular interest in the context of Bloch's conjecture,
especially for Godeaux surfaces, when the surface is given as a finite quotient
of a suitable quintic in P^3.


  Poorly managed postoperative acute pain can have long-lasting negative
impacts and pose a major healthcare issue. There is limited investigation to
understand and address the unique needs of patients experiencing acute pain. In
this paper, we tackle this gap through an interview study with 14 patients who
recently underwent postoperative acute pain to understand their challenges in
pain self-management and their need for supportive tools. Our analysis
identified various factors associated with the major aspects of acute pain
self-management. Together, our findings indicated that tools for supporting
these patients need to carefully consider information and support delivery to
adapt to rapid changes in pain experiences, offer personalized and dynamic
assistance that adapts to individual situations in context, and monitor emotion
when promoting motivation. Overall, our work provided valuable knowledge to
address the less-investigated but highly-needed problem of designing technology
for the self-management of acute pain and similar health conditions.


  For an overdetermined system $\mathsf{A}\mathsf{x} \approx \mathsf{b}$ with
$\mathsf{A}$ and $\mathsf{b}$ given, the least-square (LS) formulation $\min_x
\, \|\mathsf{A}\mathsf{x}-\mathsf{b}\|_2$ is often used to find an acceptable
solution $\mathsf{x}$. The cost of solving this problem depends on the
dimensions of $\mathsf{A}$, which are large in many practical instances. This
cost can be reduced by the use of random sketching, in which we choose a matrix
$\mathsf{S}$ with fewer rows than $\mathsf{A}$ and $\mathsf{b}$, and solve the
sketched LS problem $\min_x \, \|\mathsf{S}(\mathsf{A}
\mathsf{x}-\mathsf{b})\|_2$ to obtain an approximate solution to the original
LS problem. Significant theoretical and practical progress has been made in the
last decade in designing the appropriate structure and distribution for the
sketching matrix $\mathsf{S}$. When $\mathsf{A}$ and $\mathsf{b}$ arise from
discretizations of a PDE-based inverse problem, tensor structure is often
present in $\mathsf{A}$ and $\mathsf{b}$. For reasons of practical efficiency,
$\mathsf{S}$ should be designed to have a structure consistent with that of
$\mathsf{A}$. Can we claim similar approximation properties for the solution of
the sketched LS problem with structured $\mathsf{S}$ as for fully-random
$\mathsf{S}$? We give estimates that relate the quality of the solution of the
sketched LS problem to the size of the structured sketching matrices, for two
different structures. Our results are among the first known for random
sketching matrices whose structure is suitable for use in PDE inverse problems.


  Assuming the holographic principle, the gravitational force can be formulated
thermodynamically as an entropic force, but the mechanism by which the
attraction between two masses occurs is not clear. The physical basis for the
holographic principle is also unknown. My primary assumption is that empty
space consists of discrete countable units that have on the order of one bit of
entropy per cubic Planck unit. The basic idea here is simply that rather than
matter just occupying empty space, the presence of matter excludes discrete
units of space that have entropy. I argue that this volume exclusion of empty
space leads to an attractive gravitational force and to the holographic
principle.


  We present simultaneous multiwavelength observations of the 4.66 ms redback
pulsar PSR J1048+2339. We performed phase-resolved spectroscopy with the Very
Large Telescope (VLT) searching for signatures of a residual accretion disk or
intra-binary shock emission, constraining the companion radial velocity
semi-amplitude ($K_2$), and estimating the neutron star mass ($M_{\rm NS}$).
Using the FORS2-VLT intermediate-resolution spectra, we measured a companion
velocity of $291 < K_2 < 348$ km s$^{-1}$ and a binary mass ratio of $0.209 < q
< 0.250$. Combining our results for $K_2$ and $q$, we constrained the mass of
the neutron star and the companion to $(1.0 < M_{\rm NS} < 1.6){\rm
sin}^{-3}i\,M_{\odot}$ and $(0.24 < M_2 < 0.33){\rm sin}^{-3}i\,M_{\odot}$,
respectively, where $i$ is the system inclination. The Doppler map of the
H$\alpha$ emission line exhibits a spot feature at the expected position of the
companion star and an extended bright spot close to the inner Lagrangian point.
We interpret this extended emission as the effect of an intra-binary shock
originating from the interaction between the pulsar relativistic wind and the
matter leaving the companion star. The mass loss from the secondary star could
be either due to Roche-lobe overflow or to the ablation of its outer layer by
the energetic pulsar wind. Contrastingly, we find no evidence for an accretion
disk. We report on the results of the SRT and the LOFAR simultaneous radio
observations at three different frequencies (150 MHz, 336 MHz, and 1400 MHz).
No pulsed radio signal is found in our search. This is probably due to both
scintillation and the presence of material expelled from the system which can
cause the absorption of the radio signal at low frequencies. Finally, we report
on an attempt to search for optical pulsations using IFI+Iqueye mounted at the
1.2 m Galileo telescope at the Asiago Observatory.


  We study cosmological solutions in nonlocal teleparallel gravity or $f(T)$
theory, where $T$ is the torsion scalar in teleparallel gravity. This is a
natural extenstion of the usual teleparallel gravity with nonlocal terms. In
this work the phase space portrait proposed to describe the dynamics of an
arbitrary flat, homogeneous cosmological background with a number of matter
contents, both in early and late time epochs. The aim was to convert the system
of the equations of the motion to a first order autonomous dynamical system and
to find fixed points and attractors using numerical codes. For this purpose,
firstly we derive effective forms of cosmological field equations describing
the whole cosmic evolution history in a homogeneous and isotropic cosmological
background and construct the autonomous system of the first order dynamical
equations. In addition, we investigate the local stability in the dynamical
systems called "the stable/unstable manifold" by introducing a specific form of
the interaction between matter, dark energy, radiation and a scalar field.
Furthermore, we explore the exact solutions of the cosmological equations in
the case of de Sitter spacetime. In particular, we examine the role of an
auxiliary function called "gauge" $\eta$ in the formation of such cosmological
solutions and show whether the de Sitter solutions can exist or not. Moreover,
we study the stability issue of the de Sitter solutions both in vacuum and
non-vacuum spacetimes. It is demonstrated that for nonlocal $f(T)$ gravity, the
stable de Sitter solutions can be produced even in vacuum spacetime.


  Two types of stable, highly localized Faraday's resonant standing waves with
multiple crests and troughs are observed in the alcoholic solution partly
filled in a Hele-Shaw cell vertically oscillated with a single frequency. These
oscillons have never been reported. Systematical experiments are performed to
investigate the properties of these ocsillons. Especially, some experiments are
performed, for the first time, to indicate the high localization of the
oscillons, which suggest that these oscillons may be regarded as a combination
of the two elementary oscillons discovered by Rajchenbach et al. (Physical
Review Letters, 107, 2011), for instance, (2,3) = (1,1) + (1,2), where ($m,n$)
denotes oscillon with m crests and n troughs. So, our experiments also reveal
an interesting, elegant "arithmetic" of these oscillons.


  Boolean functions have very nice applications in cryptography and coding
theory, which have led to a lot of research focusing on their applications. The
objective of this paper is to construct binary linear codes with few weights
from the defining set, which is defined by some special Boolean functions and
some additional restrictions. First, we provide two general constructions of
binary linear codes with three or four weights from Boolean functions with at
most three Walsh transform values and determine the parameters of their dual
codes. Then many classes of binary linear codes with explicit weight
enumerators are obtained. Some binary linear codes and their duals obtained are
optimal or almost optimal. The binary linear codes obtained in this paper may
have a special interest in secret sharing schemes, association schemes,
strongly regular graphs.


  We prove that the concentration effects arising from weakly-* convergent
sequences of gradients of maps of bounded variation have gradient structure.
This is in stark contrast with the corresponding oscillation phenomena.