  We prove a version of the quantum de Finetti theorem: permutation-invariant
quantum states are well approximated as a probabilistic mixture of multi-fold
product states. The approximation is measured by distinguishability under fully
one-way LOCC (local operations and classical communication) measurements. Our
result strengthens Brand\~{a}o and Harrow's de Finetti theorem where a kind of
partially one-way LOCC measurements was used for measuring the approximation,
with essentially the same error bound. As main applications, we show (i) a
quasipolynomial-time algorithm which detects multipartite entanglement with
amount larger than an arbitrarily small constant (measured with a variant of
the relative entropy of entanglement), and (ii) a proof that in quantum
Merlin-Arthur proof systems, polynomially many provers are not more powerful
than a single prover when the verifier is restricted to one-way LOCC
operations.


  The proton-air inelastic cross section value \sigmapairin=338$\pm$21({\it
stat})$\pm$19({\it syst})-28({\it syst}) mb at $\sqrt{s} \approx $ 2 TeV has
been measured by the EAS-TOP Extensive Air Shower experiment. The absorption
length of cosmic ray proton primaries cascades reaching the maximum development
at the observation level is obtained from the flux attenuation for different
zenith angles (i.e. atmospheric depths). The analysis, including the effects of
the heavier primaries contribution and systematic uncertainties, is described.
The experimental result is compared with different high energy interaction
models and the relationships with the {\it pp} ($\bar pp$) total cross section
measurements are discussed.


  A method for pricing and superhedging European options under proportional
transaction costs based on linear vector optimisation and geometric duality
developed by Lohne & Rudloff (2014) is compared to a special case of the
algorithms for American type derivatives due to Roux & Zastawniak (2014). An
equivalence between these two approaches is established by means of a general
result linking the support function of the upper image of a linear vector
optimisation problem with the lower image of the dual linear optimisation
problem.


  The presence of interlayer interactions in twisted bilayer graphene (TBG)
enhances several characteristics, including the optical and electrical
properties. We theoretically investigate the magic angle of TBG according to
the vanishing of Fermi velocity and find double magic angles in a series. The
thermal radiation from TBG can be tuned to the far infrared range by changing
twist angles. The peculiar radiation spectrum is out of atmospheric window,
which can be of great use in invisibility and keeping warm. The total radiation
of TBG is slightly more than twice of a single layer graphene.


  We give a purely complex geometric proof of the existence of the Bergman
kernel expansion. Our method provides a sharper estimate, and in the case that
the metrics are real analytic, we prove that the remainder decays faster than
any polynomial.


  We investigate random walks on a lattice with imperfect traps. In one
dimension, we perturbatively compute the survival probability by reducing the
problem to a particle diffusing on a closed ring containing just one single
trap. Numerical simulations reveal this solution, which is exact in the limit
of perfect traps, to be remarkably robust with respect to a significant
lowering of the trapping probability. We demonstrate that for randomly
distributed traps, the long-time asymptotics of our result recovers the known
stretched exponential decay. We also study an anisotropic three-dimensional
version of our model, where for sufficiently large transverse diffusion the
system is described by the mean-field kinetics. We discuss possible
applications of some of our findings to the decay of excitons in semiconducting
organic polymer materials, and emphasize the crucial influence of the spatial
trap distribution on the kinetics.


  In the companion paper [Ingebrigtsen et al., arXiv:1012.3447] an algorithm
was developed for tracing out a geodesic curve on the constant-potential-energy
hypersurface. Here simulations of this NVU dynamics are compared to results for
four other dynamics, both deterministic and stochastic. First, NVU dynamics is
compared to the standard energy-conserving Newtonian NVE dynamics by
simulations of the Kob-Andersen binary Lennard-Jones liquid, its WCA version
(i.e., with cut-off's at the pair potential minima), and the Gaussian
Lennard-Jones liquid. We find identical results for all quantities probed:
radial distribution functions, incoherent intermediate scattering functions,
and mean-square displacement as function of time. Arguments are then presented
for the equivalence of NVU and NVE dynamics in the thermodynamic limit; in
particular to leading order in 1/N these two dynamics give identical
time-autocorrelation functions. In the final section NVU dynamics is compared
to Monte Carlo dynamics, to a diffusive dynamics of small-step random walks on
the constant-potential-energy hypersurface, and to Nose-Hoover NVT dynamics. If
time is scaled for the two stochastic dynamics to make their single-particle
diffusion constants identical to those of NVE dynamics, the simulations show
that all five dynamics are equivalent at low temperatures except at short
times.


  We adopt up-to-date 7Li yields from asymptotic giant branch stars in order to
study the temporal evolution of this element in the solar neighbourhood.
Several lithium stellar sources are considered besides the AGBs: Type II
supernovae, novae, low-mass giants. Galactic cosmic ray nucleosynthesis is
taken into account as well. We conclude that AGB stars do not substantially
contribute to 7Li enrichment on a Galactic scale. Therefore, a significant 7Li
production from novae and low-mass stars is needed to explain the late, steep
rise of the 7Li abundance in disk stars and the meteoritic 7Li abundance.


  Context. The disc instability model (DIM) successfully explains why many
accreting compact binary systems exhibit outbursts, during which their
luminosity increases by orders of magnitude. The DIM correctly predicts which
systems should be transient and works regardless of whether the accretor is a
black hole, a neutron star or a white dwarf. However, it has been known for
some time that the outbursts of X-ray binaries (which contain neutron-star or
black-hole accretors) exhibit hysteresis in the X-ray hardness-intensity
diagram (HID). More recently, it has been shown that the outbursts of accreting
white dwarfs also show hysteresis, but in a diagram combining optical, EUV and
X-ray fluxes.
  Aims. We examine here the nature of the hysteresis observed in cataclysmic
variables and low-mass X-ray binaries.
  Methods. We use the Hameury et al. (1998) code for modelling dwarf nova
outbursts, and construct the hardness intensity diagram as predicted by the
disc instability model.
  Results. We show explicitly that the standard DIM - modified only to account
for disc truncation - can explain the hysteresis observed in accreting white
dwarfs, but cannot explain that observed in X-ray binaries.
  Conclusions. The spectral evidence for the existence of different accretion
regimes / components (disc, corona, jets, etc.) should be based only on
wavebands that are specific to the innermost parts of the discs, i.e. EUV and
X-rays, which is a difficult task because of interstellar absorption. The
existing data, however, indicate that an EUV/X-ray hysteresis is present in SS
Cyg.


  The propagation of ion-acoustic solitary waves (IASWs) in a magnetized,
collisionless degenerate plasma system for describing collective plasma
oscillations in dense quantum plasmas with relativistically degenerate
electrons, oppositely charged inertial ions, and positively charged immobile
heavy elements is investigated theoretically. The perturbations of the
magnetized quantum plasma are studied employing the reductive perturbation
technique to derive the Korteweg-de Vries (K-dV) and the modified K-dV (mK-dV)
equations that admits solitary wave solutions. Chandrasekhar limits are used to
investigate the degeneracy effects of interstellar compact objects through
equation of state for degenerate electrons in case of non-relativistic and
ultra-relativistic cases. The basic properties of small but finite-amplitude
IASWs are modified significantly by the combined effects of the degenerate
electron number density, pair ion number density, static heavy element number
density and magnetic field. It is found that the obliqueness affects both the
amplitude and width of the solitary waves, whereas the other parameters mainly
influence the width of the solitons. The results presented in this paper can be
useful for future investigations of astrophysical multi-ion plasmas.


  Let $g$ be a metric on the $2$-sphere $\mathbb{S}^2$ with positive Gaussian
curvature and $H$ be a positive constant. Under suitable conditions on $(g,
H)$, we construct smooth, asymptotically flat $3$-manifolds $M$ with
non-negative scalar curvature, with outer-minimizing boundary isometric to
$(\mathbb{S}^2, g)$ and having mean curvature $H$, such that near infinity $M$
is isometric to a spatial Schwarzschild manifold whose mass $m$ can be made
arbitrarily close to a constant multiple of the Hawking mass of
$(\mathbb{S}^2,g,H)$. Moreover, this constant multiplicative factor depends
only on $(g, H)$ and tends to $1$ as $H$ tends to $0$. The result provides a
new upper bound of the Bartnik mass associated to such boundary data.


  The Hamiltonian theory of a relativistic string is considered in a specific
reference frame in terms the diffeo-invariant variables. The evolution
parameter and energy invariant with respect to the time-coordinate
transformations are constructed, so that the dimension of the kinemetric group
of diffeomorphisms coincides with the dimension of a set of variables whose
velocities are removed by the Gauss-type constraints in accordance with the
second Noether theorem. This coincidence allows us to solve the energy
constraint, and fulfil Dirac's Hamiltonian reduction.


  Parton distributions in impact parameter space, which are obtained by Fourier
transforming GPDs, exhibit a significant deviation from axial symmetry when the
target and/or quark is transversely polarized. In combination with the final
state interactions, this transverse deformation provides a natural mechanism
for naive-T odd transverse single-spin asymmetries in semi-inclusive DIS. The
deformation can also be related to the transverse force acting on the active
quark in polarized DIS at higher twist.


  Model-free reinforcement learning is known to be memory and computation
efficient and more amendable to large scale problems. In this paper, two
model-free algorithms are introduced for learning infinite-horizon
average-reward Markov Decision Processes (MDPs). The first algorithm reduces
the problem to the discounted-reward version and achieves
$\mathcal{O}(T^{2/3})$ regret after $T$ steps, under the minimal assumption of
weakly communicating MDPs. To our knowledge, this is the first model-free
algorithm for general MDPs in this setting. The second algorithm makes use of
recent advances in adaptive algorithms for adversarial multi-armed bandits and
improves the regret to $\mathcal{O}(\sqrt{T})$, albeit with a stronger ergodic
assumption. This result significantly improves over the $\mathcal{O}(T^{3/4})$
regret achieved by the only existing model-free algorithm by Abbasi-Yadkori et
al. (2019a) for ergodic MDPs in the infinite-horizon average-reward setting.


  Variational quantum algorithms are ubiquitous in applications of noisy
intermediate-scale quantum computers. Due to the structure of conventional
parametrized quantum gates, the evaluated functions typically are finite
Fourier series of the input parameters. In this work, we use this fact to
derive new, general parameter-shift rules for single-parameter gates, and
provide closed-form expressions to apply them. These rules are then extended to
multi-parameter quantum gates by combining them with the stochastic
parameter-shift rule. We perform a systematic analysis of quantum resource
requirements for each rule, and show that a reduction in resources is possible
for higher-order derivatives. Using the example of the quantum approximate
optimization algorithm, we show that the generalized parameter-shift rule can
reduce the number of circuit evaluations significantly when computing
derivatives with respect to parameters that feed into many gates. Our approach
additionally reproduces reconstructions of the evaluated function up to a
chosen order, leading to known generalizations of the Rotosolve optimizer and
new extensions of the quantum analytic descent optimization algorithm.


  This paper compares three controllers for quasi-passive exoskeletons. The
Utility Maximizing Controller (UMC) uses intent estimation to recognize user
motions and decision theory to activate the support mechanism. The intent
estimation algorithm requires demonstrations for each motion to be recognized.
Depending on what motion is recognized, different control signals are sent to
the exoskeleton. The Extended UMC (E-UMC) adds a calibration step and a
velocity module to trigger the UMC. As a benchmark, and to compare the behavior
of the controllers irrespective of the hardware, a Passive Exoskeleton
Controller (PEC) is developed as well. The controllers were implemented on a
hip exoskeleton and evaluated in a user study consisting of two phases. First,
demonstrations of three motions were recorded: squat, stoop left and stoop
right. Afterwards, the controllers were evaluated. The E-UMC combines benefits
from the UMC and the PEC, confirming the need for the two extensions. The E-UMC
discriminates between the three motions and does not generate false positives
for previously unseen motions such as stair walking. The proposed methods can
also be applied to support other motions.


  Under the assignment of $a_0(1450)$ as the ground isovector scalar meson, the
strong decays of $a_0(1950)$ and $a_0(2020)$ are evaluated in the $^3P_0$
model. Our calculations suggest that $a_0(1950)$ and $a_0(2020)$ can be
regarded as the same resonance referring to $a_0(3^3P_0)$. The masses and
strong decays of $a_0(2^3P_0)$ and $a_0(4^3P_0)$ are also predicted, which can
be useful in the search for radially excited scalar mesons in the future.


  A physics package for a compact cold atomic clock is hereby presented. The
uniqueness of this package is its small dimensions that enable, for the first
time, implementation of a primary cold atomic clock in a standard package of 3U
height (=133mm). These dimensions are made possible by using an in-vacuum
Microwave (MW) Loop Gap Resonator (LGR) whose length and diameter can be
reduced from those of a typical resonator. Following our presentation of the
design, we analyze the homogeneity of the MW field amplitude and phase. We find
that the expected clock instability due to non-uniformity of the MW field is
$\sim1.5\cdot10^{-14}$/day. Adding other clock errors, we estimate the total
uncertainty of a cold atomic clock of this design will be around
$\sim2\cdot10^{-14}$/day which results in a time drift of a few
nanoseconds/day. Such a clock can serve as a primary-grade frequency reference,
and may replace the cesium beam atomic clock and the GPS-disciplined rubidium
atomic clocks.


  We present a fast and accurate algorithm to solve Poisson problems in complex
geometries, using regular Cartesian grids. We consider a variety of
configurations, including Poisson problems with interfaces across which the
solution is discontinuous (of the type arising in multi-fluid flows). The
algorithm is based on a combination of the Correction Function Method (CFM) and
Boundary Integral Methods (BIM). Interface and boundary conditions can be
treated in a fast and accurate manner using boundary integral equations, and
the associated BIM. Unfortunately, BIM can be costly when the solution is
needed everywhere in a grid, e.g. fluid flow problems. We use the CFM to
circumvent this issue. The solution from the BIM is used to rewrite the problem
as a series of Poisson problems in rectangular domains - which requires the BIM
solution at interfaces/boundaries only. These Poisson problems involve
discontinuities at interfaces, of the type that the CFM can handle. Hence we
use the CFM to solve them (to high order of accuracy) with finite differences
and a Fast Fourier Transform based fast Poisson solver. We present 2-D examples
of the algorithm applied to Poisson problems involving complex geometries,
including cases in which the solution is discontinuous. We show that the
algorithm produces solutions that converge with either 3rd or 4th order of
accuracy, depending on the type of boundary condition and solution
discontinuity.


  We theoretically show that intriguing features of coherent many-body physics
can be observed in electron transport through a quantum dot (QD). We first
derive a master equation based framework for electron transport in the
Coulomb-blockade regime which includes hyperfine (HF) interaction with the
nuclear spin ensemble in the QD. This general tool is then used to study the
leakage current through a single QD in a transport setting. We find that, for
an initially polarized nuclear system, the proposed setup leads to a strong
current peak, in close analogy with superradiant emission of photons from
atomic ensembles. This effect could be observed with realistic experimental
parameters and would provide clear evidence of coherent HF dynamics of nuclear
spin ensembles in QDs.


  With growing interest in the mid-infrared spectral region, dysprosium has
recently been revisited for efficient high-performance infrared source
development. Despite historically receiving less attention than other rare
earth ions, in recent years lasers utilizing the dysprosium ion as the laser
material have set record mid-infrared performance, including tunability from
2.8 to 3.4 um (in addition to 4.3 um lasing), continuous wave powers exceeding
10 W, greater than 73% slope efficiencies, and even ultrafast pulsed operation.
Herein, the unique energy level structure and spectroscopy of the dysprosium
ion are examined and the major developments that have led to this resurgence of
interest and subsequent record mid-infrared laser performance are surveyed.
Also mid-infrared applications of emerging dysprosium lasers are highlighted,
in addition to surveying the many opportunities that lie ahead.


  This paper was published in the special issue of the Journal of Inequalities
and Special Functions dedicated to Professor Ivan Dimovski's contributions to
different fields of mathematics: transmutation theory, special functions,
integral transforms, function theory etc.
  This short survey paper contains brief historical information, main known
facts and original author's results on the theory of the Buschman-Erd\'{e}lyi
transmutations and some of their applications. The operators of
Buschman-Erd\'{e}lyi type were first studied by E.T.~Copson, R.G.~Buschman and
A.~Erd\'{e}lyi as integral operators. In 1990's the author was first to prove
the transmutational nature of these operators and published papers with
detailed study of their properties. This class include as special cases such
famous objects as the Sonine-Poisson-Delsarte transmutations and the fractional
Riemann-Lioville integrals. In this paper, the Buschman-Erdelyi transmutations
are logically classified as operators of the first kind with special case of
zero order smoothness operators, second kind and third kind with special case
of unitary Sonine-Katrakhov and Poisson-Katrakhov transmutations. We study such
properties as transmutational conditions, factorizations, norm estimates,
connections with classical integral transforms. Applications are considered to
singular partial differential equations, embedding theorems with sharp
constants in Kipriyanov spaces, Euler-Poisson-Darboux equation including Copson
lemma, generalized translations, Dunkl operators, Radon transform, generalized
harmonics theory, Hardy operators, V.\,Katrakhov's results on
pseudodifferential operators and boundary-value problems of new kind for
equations with solutions of arbitrary growth at the isolated singularity for
elliptic partial differential equations.


  Modeling lepton-nucleus scattering with the accuracy required to extract
neutrino-oscillation parameters from long- and short-baseline experiments
necessitates retaining most quantum-mechanical effects. One such effect is the
interference between one- and two-body current operators in the transition
currents, which has been known to enhance the cross-sections, especially in
transverse kinematics. In this work, we incorporate such interference in the
spectral function formalism, which combines relativistic currents and
kinematics with an accurate description of the initial target state. Our
analysis of lepton-scattering off $^{12}$C demonstrates that interference
effects appreciably enhance the transverse electromagnetic response functions
and the flux-folded neutrino-nucleus cross section, in both cases, improving
the agreement with experimental data. We discuss the impact on the
neutrino-oscillation program and the determination of nucleon axial form
factors.


Recent experimental results on charmless rare b decays are reviewed.


  We develop an ultrawideband (UWB) inverse scattering technique for
reconstructing continuous random media based on Bayesian compressive sensing.
In addition to providing maximum a posteriori estimates of the unknown weights,
Bayesian inversion provides estimate of the confidence level of the solution,
as well as a systematic approach for optimizing subsequent measurement(s) to
maximize information gain. We impose sparsity priors directly on spatial
harmonics to exploit the spatial correlation exhibited by continuous media, and
solve for their posterior probability density functions efficiently using a
fast relevance vector machine. We linearize the problem using the first-order
Born approximation which enables us to combine, in a single inversion,
measurements from multiple transmitters and ultrawideband frequencies. We
extend the method to high-contrast media using the distorted-Born iterative
method. We apply time-reversal strategies to adaptively focus the inversion
effort onto subdomains of interest, and hence reduce the overall inversion
cost. The proposed techniques are illustrated in a number of canonical
scenarios including crosshole and borehole sensing.


  Recurrent Neural Networks (RNNs) have achieved remarkable performance on a
range of tasks. A key step to further empowering RNN-based approaches is
improving their explainability and interpretability. In this work we present
MEME: a model extraction approach capable of approximating RNNs with
interpretable models represented by human-understandable concepts and their
interactions. We demonstrate how MEME can be applied to two multivariate,
continuous data case studies: Room Occupation Prediction, and In-Hospital
Mortality Prediction. Using these case-studies, we show how our extracted
models can be used to interpret RNNs both locally and globally, by
approximating RNN decision-making via interpretable concept interactions.


  The main two families of real hypersurfaces in complex space forms are Hopf
and ruled. However, very little is known about real hypersurfaces in the
indefinite complex projective space $\cpn$. In a previous work, Kimura and the
second author introduced Hopf real hypersurfaces in $\cpn$. In this paper,
ruled real hypersurfaces in the indefinite complex projective space are
introduced, as those whose maximal holomorphic distribution is integrable, and
such that the leaves are totally geodesic holomorphic hyperplanes. A detailed
description of the shape operator is computed, obtaining two main different
families. A method of construction is exhibited, by gluing in a suitable way
totally geodesic holomorphic hyperplanes along a non-null curve. Next, the
classification of all minimal ruled real hypersurfaces is obtained, in terms of
three main families of curves, namely geodesics, totally real circles and a
third case which is not a Frenet curve, but can be explicitly computed. Four
examples of minimal ruled real hypersurfaces are described.


  The equaliser of a set of homomorphisms $S: F(a, b)\rightarrow F(\Delta)$ has
rank at most two if $S$ contains an injective map, and is not finitely
generated otherwise. This proves a strong form of Stallings' Equaliser
Conjecture for the free group of rank two.
  Results are also obtained for pairs of homomorphisms $g,
h:F(\Sigma)\rightarrow F(\Delta)$ when the images are inert in, or retracts of,
$F(\Delta)$.


  We extend our modeling of cooling of superfluid neutron stars by including
the production of muons in the core, in addition to neutrons, protons, and
electrons. The results are confronted with observations of middle-aged isolated
NSs. Muons have little effect on the hydrostatic structure of NSs, on the slow
cooling of low-mass NSs (RX J0822--43 and PSR 1055--52 in our model) and on the
rapid cooling of massive NSs. They affect, however, the moderately fast cooling
of medium-mass NSs (1E 1207--52, RX J0002+62, PSR 0656+14, Vela, and Geminga)
and shift appreciably the mass range of these NSs to lower masses, which is
important for correct interpretation of the observations. Moreover, the effects
of muons can accurately be reproduced by a simple renormalization of NS models
with no muons in the NS cores.


  In biological tissues, it is now well-understood that mechanical cues are a
powerful mechanism for pattern regulation. While much work has focused on
interactions between cells and external substrates, recent experiments suggest
that cell polarization and motility might be governed by the internal shear
stiffness of nearby tissue, deemed "plithotaxis". Meanwhile, other work has
demonstrated that there is a direct relationship between cell shapes and tissue
shear modulus in confluent tissues. Joining these two ideas, we develop a
hydrodynamic model that couples cell shape, and therefore tissue stiffness, to
cell motility and polarization. Using linear stability analysis and numerical
simulations, we find that tissue behavior can be tuned between largely
homogeneous states and patterned states such as asters, controlled by a
composite "morphotaxis" parameter that encapsulates the nature of the coupling
between shape and polarization. The control parameter is in principle
experimentally accessible, and depends both on whether a cell tends to move in
the direction of lower or higher shear modulus, and whether sinks or sources of
polarization tend to fluidize the system.


  Continuous formal deformations of the Poisson superbracket defined on
compactly supported smooth functions on R^2 taking values in a Grassmann
algebra with N generating elements are described up to an equivalence
transformation for N \ne 2.


  Electrical Resistivity Tomography (ERT) has been extensively used for imaging
the subsurface resistivity distribution and structure. Over the years, many
algorithms have been developed in order to solve the subsurface resistivity
distribution from the ERT measurements. In this paper a new method for
interpreting the ERT measurements is presented. Using supervised learning to
train a neural network, we are able to interpret the ERT measurement into a 2D
image of the underground resistivity up to depths of 50 meters while using a
simple Wenner-Schlumberger survey of 96 electrodes with 1 meter spacing. The
neural network is trained and tested using simulative data and it is shown to
have superior results over a well established inversion method.


  In super- or subradiance, a quantum superposition of excited atoms
collectively emits a photon much more or much less rapidly than an isolated
atom. Superradiant and subradiant lifetimes have been derived for finite
spheres of uniform media, either by simulating random samples or by expanding
in spherical harmonics and analyzing Bessel functions. We introduce a simple
regulator that applies to unbounded media, enabling trivial derivation and
analysis of lifetimes via elementary Fourier techniques. The regulator can be
interpreted as a correlation length for atomic positions; the regularized
system describes localized regions of enhanced radiative activity in otherwise
quiescent surroundings.


  Let $n$ be an integer such that the modular curve $X_0(n)$ is hyperelliptic
of genus $\ge2$ and such that the Jacobian of $X_0(n)$ has rank $0$ over
$\mathbb Q$. We determine all points of $X_0(n)$ defined over quadratic fields,
and we give a moduli interpretation of these points. As a consequence, we show
that up to $\overline{\mathbb Q}$-isomorphism, all but finitely many elliptic
curves with $n$-isogenies over quadratic fields are in fact $\mathbb Q$-curves,
and we list all exceptions. We also show that, again with finitely many
exceptions up to $\overline{\mathbb Q}$-isomorphism, every $\mathbb Q$-curve
$E$ over a quadratic field $K$ admitting an $n$-isogeny is $d$-isogenous, for
some $d\mid n$, to the twist of its Galois conjugate by some quadratic
extension $L$ of $K$; we determine $d$ and $L$ explicitly.


  Deformation in the lithosphere-asthenosphere system can be accommodated by
faulting and plastic flow. However, incorporating structural data in models of
distributed deformation still represents a challenge. Here, I present solutions
for the displacements and stress in a half-space caused by distributed
anelastic strain confined in a tetrahedral volume. These solutions form the
basis of curvilinear meshes that can adapt to realistic structural settings,
such as a mantle wedge corner, a spherical shell around a magma chamber, or an
aquifer. I provide computer programs to evaluate them in the cases of
anti-plane strain, in-plane strain, and three-dimensional deformation. These
tools may prove useful in the modeling of deformation data in tectonics,
volcanology, and hydrology.


  This paper provides a characterization of when two expansive matrices yield
the same anisotropic local Hardy and inhomogeneous Triebel-Lizorkin spaces. The
characterization is in terms of the coarse equivalence of certain quasi-norms
associated to the matrices. For nondiagonal matrices, these conditions are
strictly weaker than those classifying the coincidence of the corresponding
homogeneous function spaces. The obtained results complete the classification
of anisotropic Besov and Triebel-Lizorkin spaces associated to general
expansive matrices.


  Symmetric matrix-valued dynamical systems are an important class of systems
that can describe important processes such as covariance/second-order moment
processes, or processes on manifolds and Lie Groups. We address here the case
of processes that leave the cone of positive semidefinite matrices invariant,
thereby including covariance and second-order moment processes. Both the
continuous-time and the discrete-time cases are first considered. In the LTV
case, the obtained stability and stabilization conditions are expressed as
differential and difference Lyapunov conditions which are equivalent, in the
LTI case, to some spectral conditions for the generators of the processes.
Convex stabilization conditions are also obtained in both the continuous-time
and the discrete-time setting. It is proven that systems with constant delays
are stable provided that the systems with zero-delays are stable -- which
mirrors existing results for linear positive systems. The results are then
extended and unified into a impulsive formulation for which similar results are
obtained. The proposed framework is very general and can recover and/or extend
almost all the results on the literature of linear systems related to
(mean-square) exponential (uniform) stability. Several examples are discussed
to illustrate this claim by deriving stability conditions for stochastic
systems driven by Brownian motion and Poissonian jumps, Markov jump systems,
(stochastic) switched systems, (stochastic) impulsive systems, (stochastic)
sampled-data systems, and all their possible combinations.


  Robust Bayesian analysis has been mainly devoted to detecting and measuring
robustness to the prior distribution. Indeed, many contributions in the
literature aim to define suitable classes of priors which allow the computation
of variations of quantities of interest while the prior changes within those
classes. The literature has devoted much less attention to the robustness of
Bayesian methods to the likelihood function due to mathematical and
computational complexity, and because it is often arguably considered a more
objective choice compared to the prior. In this contribution, a new approach to
Bayesian local robustness to the likelihood function is proposed and extended
to robustness to the prior and to both. This approach is based on the notion of
distortion function introduced in the literature on risk theory, and then
successfully adopted to build suitable classes of priors for Bayesian global
robustness to the prior. The novel robustness measure is a local sensitivity
measure that turns out to be very tractable and easy to compute for certain
classes of distortion functions. Asymptotic properties are derived and
numerical experiments illustrate the theory and its applicability for modelling
purposes.


  We discuss chiral symmetry breaking critical points from the perspective of
PCAC, correlation length scaling and the chiral equation of state. A scaling
theory for the ratio $R_\pi$ of the pion to sigma masses is presented. The
Goldstone character of the pion and properties of the longitudinal and
transverse chiral susceptibilities determine the ratio $R_\pi$ which can be
used to locate critical points and measure critical indices such as $\delta$.
We show how PCAC and correlation length scaling determine the pion mass'
dependence on the chiral condensate and lead to a practical method to measure
the anomalous dimension $\eta$. These tools are proving useful in studies of
the chiral transition in lattice QED and the quark-gluon plasma transition in
lattice QCD.


  In this manuscript we prove that if two cuspidal plane curves have equivalent
braid monodromy factorizations, then they are smoothly isotopic in the plane.
As a consequence of this and the Chisini conjecture, we obtain that if two
discriminant curves (or branch curves in other terminology) of generic
projections (to the plane) of surfaces of general type imbedded in a projective
space by means of a multiple canonical class have equivalent braid monodromy
factorizations, then the surfaces are diffeomorphic (if we consider them as
real 4-folds).


  A measurement of the cross section for production of single, isolated photons
is reported for transverse energies in the range of 10-125 GeV, for two regions
of pseudorapidity, |\eta|<0.9 and 1.6<|\eta|<2.5. The data represent 12.9 pb-1
of integrated luminosity accumulated in p-pbar collisions at sqrt{s} = 1.8 TeV
and recorded with the D0 detector at the Fermilab Tevatron Collider.


  Digital archives are the preferred means for open access to research data.
They play essential roles in knowledge infrastructures - robust networks of
people, artifacts, and institutions - but little is known about how they
mediate information exchange between stakeholders. We open the "black box" of
data archives by studying DANS, the Data Archiving and Networked Services
institute of The Netherlands, which manages 50+ years of data from the social
sciences, humanities, and other domains. Our interviews, weblogs, ethnography,
and document analyses reveal that a few large contributors provide a steady
flow of content, but most are academic researchers who submit datasets
infrequently and often restrict access to their files. Consumers are a diverse
group that overlaps minimally with contributors. Archivists devote about half
their time to aiding contributors with curation processes and half to assisting
consumers. Given the diversity and infrequency of usage, human assistance in
curation and search remains essential. DANS' knowledge infrastructure
encompasses public and private stakeholders who contribute, consume, harvest,
and serve their data - many of whom did not exist at the time the DANS
collections originated - reinforcing the need for continuous investment in
digital data archives as their communities, technologies, and services evolve.


  Magnetic null points can develop near the ergosphere boundary of a rotating
black hole by the combined effects of strong gravitational field and the
frame-dragging mechanism. The induced electric component does not vanish an
efficient process of particle acceleration can occur. Furthermore, the effect
of imposed (weak) magnetic field can trigger an onset of chaos. The model
set-up appears to be relevant for low-accretion-rate nuclei of some galaxies
which exhibit episodic accretion events (such as the Milky Way's supermassive
black hole) embedded in a large-scale magnetic field of external origin. We
review our recent results and we give additional context for future work with
the focus on the role of gravito-magnetic effects caused by rotation of the
black hole. While the test motion is strictly regular in the classical black
hole space-time, with and without effects of rotation or electric charge,
gravitational perturbations and imposed external electromagnetic fields may
lead to chaos.


  In this paper, we introduce a novel fusion method that can enhance object
detection performance by fusing decisions from two different types of computer
vision tasks: object detection and image classification. In the proposed work,
the class label of an image obtained from image classification is viewed as
prior knowledge about existence or non-existence of certain objects. The prior
knowledge is then fused with the decisions of object detection to improve
detection accuracy by mitigating false positives of an object detector that are
strongly contradicted with the prior knowledge. A recently introduced novel
fusion approach called dynamic belief fusion (DBF) is used to fuse the detector
output with the classification prior. Experimental results show that the
detection performance of all the detection algorithms used in the proposed work
is improved on benchmark datasets via the proposed fusion framework.


  Recently, a new measurement of the auto- and cross-correlation angular power
spectrum (APS) of the isotropic gamma-ray background was performed, based on 81
months of data of the Fermi Large-Area Telescope (LAT). Here, we fit, for the
first time, the new APS data with a model describing the emission of unresolved
blazars. These sources are expected to dominate the anisotropy signal. The
model we employ in our analysis reproduces well the blazars resolved by Fermi
LAT. When considering the APS obtained by masking the sources in the 3FGL
catalogue, we find that unresolved blazars under-produce the measured APS below
$\sim$1 GeV. Contrary to past results, this suggests the presence of a new
contribution to the low-energy APS, with a significance of, at least,
5$\sigma$. The excess can be ascribed to a new class of faint gamma-ray
emitters. If we consider the APS obtained by masking the sources in the 2FGL
catalogue, there is no under-production of the APS below 1 GeV, but the new
source class is still preferred over the blazars-only scenario (with a
significance larger than 10$\sigma$). The properties of the new source class
and the level of anisotropies induced in the isotropic gamma-ray background are
the same, independent of the APS data used. In particular, the new gamma-ray
emitters must have a soft energy spectrum, with a spectral index ranging,
approximately, from 2.7 to 3.2. This complicates their interpretation in terms
of known sources, since, normally, star-forming and radio galaxies are observed
with a harder spectrum. The new source class identified here is also expected
to contribute significantly to the intensity of the isotropic gamma-ray
background.


  We present a statistical method to derive the mass functions of open clusters
using sky survey data such as the 2 Micron All Sky Survey and the Guide Star
Catalogue. We have used this method to derive the mass functions in the
stellar/substellar regime of three young, nearby open clusters, namely IC 348,
Sigma-Orionis and Pleiades. The mass function in the low mass range (M < 0.5
solar mass) is appreciably flatter than the stellar Salpeter function for all
three open clusters. The contribution of objects below 0.5 solar mass to the
total mass of the cluster is ~40% and the contribution of objects below 0.08
solar mass to the total is ~4%.


  Relatively simple algebraic relations are presented corresponding to Pachner
moves 3 -> 3 and 2 <-> 4, thus providing two thirds of the foundation for a
four-dimensional topological quantum field theory. These relations are written
in terms of Grassmann anticommuting variables and Berezin integral.


  While our natural intuition suggests us that we live in 3D space evolving in
time, modern physics presents fundamentally different picture: 4D spacetime,
Einstein's block universe, in which we travel in thermodynamically emphasized
direction: arrow of time. Arguments for such nonintuitive and nonlocal living
in kind of "4D jello" come among others from: Lagrangian mechanics we use from
QFT to GR saying that history between fixed past and future situation is the
one optimizing action, special relativity saying that different velocity
observers have different own time directions, general relativity deforming
shape of the entire spacetime up to switching time and space below the black
hole event horizon, or the CPT theorem concluding fundamental symmetry between
past and future for example in the Feynman-Stueckelberg interpretation of
antiparticles as propagating back in time.
  Accepting this nonintuitive living in 4D spacetime: with present moment being
in equilibrium between past and future - minimizing tension as action of
Lagrangian, leads to crucial surprising differences from intuitive "evolving
3D" picture - allowing to conclude Bell inequalities, violated by the real
physics. Specifically, particle in spacetime becomes own trajectory: 1D
submanifold of 4D, making that statistical physics should consider ensembles
like Boltzmann distribution among entire paths (like in Ising model), what
leads to quantum behavior as we know from Feynman's Euclidean path integrals or
similar Maximal Entropy Random Walk (MERW).


  We show that a contribution to the total curvature perturbation may be due to
the presence of flat directions in supersymmetric models. It is generated at
the first os- cillation of the flat direction condensate when the latter
relaxes to the minimum of its potential after the end of inflation. We also
point out that, if the contribution to the total curvature perturbation from
supersymmetric flat direction is the dominant one, then a significant level of
non-Gaussianity in the cosmological perturbation is also naturally expected.


  Recent data on inclusive B decays into charmonium states taken by the CLEO
collaboration suggest that a sizeable fraction of the nonleptonic decays may
consist of the $J/\psi \Lambda \overline p$ three body final state,
corresponding to a distinct enhancement in the inclusive $J/\psi$ momentum
distribution. The kinematical boundary of this structure corresponds to the
case where the $J/\psi$ recoils nearly monoenergetically in the B rest system
against a partner having mass of $\simeq$ 2 GeV. This may allow the observation
of a $\Lambda-\overline p $ bound state near or just below threshold; i.e.,
strange baryonium, even if the production rate is small.
  Using a phase space approach to the B meson decay, we study the $J/\psi$
momentum distribution and the effect of baryonium formation. We also discuss
the possible observation of pentaquarks and hadronically-bound $J/\psi$ by the
observation of monoenergetic baryons in these decays.


  We present the results of a set of high-resolution simulations of the merging
process of two white dwarfs. In order to do so, we use an up-to-date Smoothed
Particle Hydrodynamics code which incorporates very detailed input physics and
an improved treatment of the artificial viscosity. Our simulations have been
done using a large number of particles (4x10^5) and cover the full range of
masses and chemical compositions of the coalescing white dwarfs. We also
compare the time evolution of the system during the first phases of the
coalescence with that obtained using a simplified treatment of mass transfer,
we discuss in detail the characteristics of the final configuration, we assess
the possible observational signatures of the merger, like the associated
gravitational waveforms and the fallback X-ray flares, and we study the
long-term evolution of the coalescence.


  Given a set of points in the plane, we show that the $\theta$-graph with 5
cones is a geometric spanner with spanning ratio at most $\sqrt{50 + 22
\sqrt{5}} \approx 9.960$. This is the first constant upper bound on the
spanning ratio of this graph. The upper bound uses a constructive argument that
gives a (possibly self-intersecting) path between any two vertices, of length
at most $\sqrt{50 + 22 \sqrt{5}}$ times the Euclidean distance between the
vertices. We also give a lower bound on the spanning ratio of
$\frac{1}{2}(11\sqrt{5} -17) \approx 3.798$.


  Supergiant Fast X-ray transients are a subclass of high mass X-ray binaries
displaying a peculiar and still poorly understood extreme variability in the
X-ray domain. These sources undergo short sporadic outbursts (LX ~ 10^36 -
10^37 erg/s), lasting few ks at the most, and spend a large fraction of their
time in an intermediate luminosity state at about LX ~ 10^33 - 10^34 erg/s. The
sporadic and hardly predictable outbursts of supergiant fast X-ray transients
were so far best discovered by large field of view (FOV) coded-mask
instruments; their lower luminosity states require, instead, higher sensitivity
focusing instruments to be studied in sufficient details. In this contribution,
we provide a summary of the current knowledge on Supergiant Fast X-ray
Transients and explore the contribution that the new space mission concept
LOFT, the Large Observatory For X-ray Timing, will be able to provide in the
field of research of these objects.


  The unparalleled photometric data obtained by NASA's Kepler space telescope
led to an improved understanding of red giant stars and binary stars.
Seismology allows us to constrain the properties of red giants. In addition to
eclipsing binaries, eccentric non-eclipsing binaries, exhibiting ellipsoidal
modulations, have been detected with Kepler. We aim to study the properties of
eccentric binary systems containing a red giant star and derive the parameters
of the primary giant component. We apply asteroseismic techniques to determine
masses and radii of the primary component of each system. For a selected
target, light and radial velocity curve modelling techniques are applied to
extract the parameters of the system. The effects of stellar on the binary
system are studied. The paper presents the asteroseismic analysis of 18
pulsating red giants in eccentric binary systems, for which masses and radii
were constrained. The orbital periods of these systems range from 20 to
440days. From radial velocity measurements we find eccentricities between e=0.2
to 0.76. As a case study we present a detailed analysis of KIC5006817. From
seismology we constrain the rotational period of the envelope to be at least
165 d, roughly twice the orbital period. The stellar core rotates 13 times
faster than the surface. From the spectrum and radial velocities we expect that
the Doppler beaming signal should have a maximum amplitude of 300ppm in the
light curve. Through binary modelling, we determine the mass of the secondary
component to be 0.29$\pm$0.03\,$M_\odot$. For KIC5006817 we exclude
pseudo-synchronous rotation of the red giant with the orbit. The comparison of
the results from seismology and modelling of the light curve shows a possible
alignment of the rotational and orbital axis at the 2$\sigma$ level. Red giant
eccentric systems could be progenitors of cataclysmic variables and hot
subdwarf B stars.


  We address the interactions between optical solitons in the system with
longitudinally varying nonlocality degree and nonlinearity strength. We
consider a physical model describing light propagation in nematic liquid
crystals featuring a strongly nonlocal nonlinear response. We reveal that the
variation of the nonlocality and nonlinearity along the propagation direction
can substantially enhance or weaken the interaction between out-of-phase
solitons. This phenomenon manifests itself as a slowdown or acceleration of the
soliton collision dynamics in one-dimensional geometries or of the soliton
spiraling rate in bulk media. Therefore, one finds that by engineering the
nonlocality and nonlinearity variation rate one can control the output soliton
location.


  The notion of relatedness loci in the parabolic slices Per_1(e^{2\pi i p/q})
in moduli space of quadratic rational maps is introduced. They are counterparts
of the disconnectedness or escape locus in the slice of quadratic polynomials.
A model for these loci is presented, and a strategy of proof of the
faithfulness of the model is given.


  e^+e^- annihilation data recorded by the JADE detector at PETRA were used to
measure the C-parameter for the first time at sqrt{s}= 35 and 44 GeV. The
distributions were compared to a resummed QCD calculation which recently became
available for this observable. % In addition, we applied extended resummed
calculations to the heavy and wide jet broadening variables, B_T and B_W, which
now include a proper treatment of the quark recoil against multi-gluon emission
with single-logarithmic accuracy. % We further investigated power corrections
to the mean values of the observables mentioned above. In this study, we
considered all available e^+e^- data between sqrt{s}= 35 and 172 GeV.


  We present measurements of two-particle differential number correlation
functions $R_{2}$ and transverse momentum correlation functions $P_{2}$,
obtained from p-Pb collisions at 5.02 TeV and Pb-Pb collisions at 2.76 TeV. The
results are obtained using charged particles in the pseudorapidity range
$|\eta| <$ 1.0, and transverse momentum range $0.2 < p_{\rm T} < 2.0$ GeV/$c$
as a function of pair separation in pseudorapidity, $|\Delta\eta|$, azimuthal
angle, $\Delta\varphi$, and for several charged-particle multiplicity classes.
Measurements are carried out for like-sign and unlike-sign charged-particle
pairs separately and combined to obtain charge-independent and charge-dependent
correlation functions. We study the evolution of the width of the near-side
peak of these correlation functions with collision centrality. Additionally, we
study Fourier decompositions of the correlators in $\Delta\varphi$ as a
function of the pair separation $|\Delta\eta|$. Significant differences in the
dependence of their harmonic coefficients on multiplicity classes are found.
These differences can be exploited, in theoretical models, to obtain further
insight into charged-particle production and transport in heavy-ion collisions.
Moreover, an upper limit of non-flow contributions to flow coefficients $v_{n}$
measured in Pb-Pb collisions based on the relative strength of Fourier
coefficients measured in p-Pb interactions is estimated.


  A physical interpretation of translation-invariant polarons and bipolarons is
presented, some results of their existence are discussed. Consideration is
given to the problem of quantization in the vicinity of the classical solution
in the quantum field theory. The lowest variational estimate is obtained for
the bipolaron energy E(\eta) with E(0)=-0,440636\alpha^2, where \alpha is a
constant of electron-phonon coupling, \eta is a parameter of ion binding.


  Using an integral definition to calculate the relativistic multipole moments
(RMM), and the ensuing generalized relativistic Gauss theorem, we prove that
the evaluation of that volume integral in Erez-Rosen coordinates, leads to a
specific link between the RMM and the source of the exterior space--time,
provided we have a global static axisymmetric metric in that coordinate system
for any Weyl exterior field. This result allows to establish a relationship
between the RMM and certain volume integral expressions involving the material
content of the source from its energy-momentum tensor as well as the interior
metric. In particular the relativistic quadrupole moment for the Erez-Rosen
space-time is obtained.


  Large Language Models (LLMs) have become a pivotal research area, potentially
making beneficial contributions in fields like healthcare where they can
streamline automated billing and decision support. However, the frequent use of
specialized coded languages like ICD-10, which are regularly updated and
deviate from natural language formats, presents potential challenges for LLMs
in creating accurate and meaningful latent representations. This raises
concerns among healthcare professionals about potential inaccuracies or
``hallucinations" that could result in the direct impact of a patient.
Therefore, this study evaluates whether large language models (LLMs) are aware
of medical code ontologies and can accurately generate names from these codes.
We assess the capabilities and limitations of both general and
biomedical-specific generative models, such as GPT, LLaMA-2, and Meditron,
focusing on their proficiency with domain-specific terminologies. While the
results indicate that LLMs struggle with coded language, we offer insights on
how to adapt these models to reason more effectively.


  In the article, we will report on the recovery of a Melloni's optical bench
built at the end of 1800 by the "macchinista" Filippo Caliri in the "belle
\'epoque" of Palermo. A scientific instrument of particular historical and
didactic interest belonging to the collection of Liceo Classico Statale
"Umberto I" of Palermo. In the article, we will discuss the technical aspects
of the interventions carried out.
  In questo articolo discuteremo del recupero di uno strumento scientifico di
particolare interesse storico-didattico appartenente alla Collezione del Liceo
Classico Statale "Umberto I" di Palermo: un raro banco ottico del Melloni
costruito alla fine del 1800 nella Palermo della "belle \'epoque" dal
"macchinista" Filippo Caliri. Nell'articolo discuteremo gli aspetti tecnici
degli interventi conservativi effettuati.


  Unsupervised domain adaptation (UDA) aims to transfer knowledge from a
related but different well-labeled source domain to a new unlabeled target
domain. Most existing UDA methods require access to the source data, and thus
are not applicable when the data are confidential and not shareable due to
privacy concerns. This paper aims to tackle a realistic setting with only a
classification model available trained over, instead of accessing to, the
source data. To effectively utilize the source model for adaptation, we propose
a novel approach called Source HypOthesis Transfer (SHOT), which learns the
feature extraction module for the target domain by fitting the target data
features to the frozen source classification module (representing
classification hypothesis). Specifically, SHOT exploits both information
maximization and self-supervised learning for the feature extraction module
learning to ensure the target features are implicitly aligned with the features
of unseen source data via the same hypothesis. Furthermore, we propose a new
labeling transfer strategy, which separates the target data into two splits
based on the confidence of predictions (labeling information), and then employ
semi-supervised learning to improve the accuracy of less-confident predictions
in the target domain. We denote labeling transfer as SHOT++ if the predictions
are obtained by SHOT. Extensive experiments on both digit classification and
object recognition tasks show that SHOT and SHOT++ achieve results surpassing
or comparable to the state-of-the-arts, demonstrating the effectiveness of our
approaches for various visual domain adaptation problems. Code is available at
\url{https://github.com/tim-learn/SHOT-plus}.


  We investigate superconductor/insulator/ferromagnet/superconductor (SIFS)
tunnel Josephson junctions in the dirty limit, using the quasiclassical theory.
We consider the case of a strong tunnel barrier such that the left S layer and
the right FS bilayer are decoupled. We calculate quantitatively the density of
states (DOS) in the FS bilayer for arbitrary length of the ferromagnetic layer,
using a self-consistent numerical method. We compare these results with a known
analytical DOS approximation, which is valid when the ferromagnetic layer is
long enough. Finally we calculate quantitatively the current-voltage
characteristics of a SIFS junction.


  A recent paper by Boughammoura (2023) describes the back-propagation
algorithm in terms of an alternative formulation called the F-adjoint method.
In particular, by the F-adjoint algorithm the computation of the loss gradient,
with respect to each weight within the network, is straightforward and can
simply be done. In this work, we develop and investigate this theoretical
framework to improve some supervised learning algorithm for feed-forward neural
network. Our main result is that by introducing some neural dynamical model
combined by the gradient descent algorithm, we derived an equilibrium F-adjoint
process which yields to some local learning rule for deep feed-forward networks
setting. Experimental results on MNIST and Fashion-MNIST datasets, demonstrate
that the proposed approach provide a significant improvements on the standard
back-propagation training procedure.


  We investigate the optimal reinsurance problem when the loss process exhibits
jump clustering features and the insurance company has restricted information
about the loss process. We maximize expected exponential utility of terminal
wealth and show that an optimal solution exists. By exploiting both the
Kushner-Stratonovich and Zakai approaches, we provide the equation governing
the dynamics of the (infinite-dimensional) filter and characterize the solution
of the stochastic optimization problem in terms of a BSDE, for which we prove
existence and uniqueness of solution. After discussing the optimal strategy for
a general reinsurance premium, we provide more explicit results in some
relevant cases.


  In this paper, we show the relation between the thermodynamic geometry of a
four-dimensional Reissner-Nordstrom-AdS (RN-AdS) black hole and non-local
observables in boundary field theory. Instead of introducing the critical point
associating with the black hole charge to nondimensionalize the thermodynamics
parameters, we use the cosmological constant to rescale these variables, so
that a universal specific equation of state of the black hole is obtained.
Further, the correspondence between thermodynamic properties of the black hole
and the oscillating behaviors of the non-local observables has been studied
numerically. Our results indicate that the study of the dual field theory will
reveal to us the thermodynamic geometry of the AdS black hole.


  After providing a general formulation of Fermion flows within the context of
Hudson-Parthasarathy quantum stochastic calculus, we consider the problem of
determining the noise coefficients of the Hamiltonian associated with a Fermion
flow so as to minimize a naturally associated quadratic performance functional.
This extends to Fermion flows results of the authors previously obtained for
Boson flows .


  In this article, we propose a new type of square matrix associated with an
undirected graph by trading off the naturally imbedded symmetry in them. The
proposed matrix is defined using the neighbourhood sets of the vertices. It is
called as neighbourhood matrix and it is denoted by $ \mathcal{NM}(G)$ as this
proposed matrix also exhibits a bijection between the product of the two graph
matrices, namely the adjacency matrix and the graph Laplacian. This matrix can
also be obtained by looking at every vertex and the subgraph with vertices from
the first two levels in the level decomposition from that vertex. The two
levels in the level decomposition of the graph give us more information about
the neighbour of a vertex along with the neighbour of neighbour of a vertex.
This insight is required and is found useful in studying the impact of
broadcasting on social networks, in particular, and complex networks, in
general. We establish several interesting properties of the $ \mathcal{NM}(G)
$. In addition, we also show how to reconstruct a graph $G$, given a $
\mathcal{NM} (G)$. The proposed matrix is also found to solve many graph
theoretic problems using less time complexity in comparison to the existing
algorithms.


  In this paper, we are interested in the few-shot learning problem. In
particular, we focus on a challenging scenario where the number of categories
is large and the number of examples per novel category is very limited, e.g. 1,
2, or 3. Motivated by the close relationship between the parameters and the
activations in a neural network associated with the same category, we propose a
novel method that can adapt a pre-trained neural network to novel categories by
directly predicting the parameters from the activations. Zero training is
required in adaptation to novel categories, and fast inference is realized by a
single forward pass. We evaluate our method by doing few-shot image recognition
on the ImageNet dataset, which achieves the state-of-the-art classification
accuracy on novel categories by a significant margin while keeping comparable
performance on the large-scale categories. We also test our method on the
MiniImageNet dataset and it strongly outperforms the previous state-of-the-art
methods.


  Voice activity detection is an essential pre-processing component for
speech-related tasks such as automatic speech recognition (ASR). Traditional
supervised VAD systems obtain frame-level labels from an ASR pipeline by using,
e.g., a Hidden Markov model. These ASR models are commonly trained on clean and
fully transcribed data, limiting VAD systems to be trained on clean or
synthetically noised datasets. Therefore, a major challenge for supervised VAD
systems is their generalization towards noisy, real-world data. This work
proposes a data-driven teacher-student approach for VAD, which utilizes vast
and unconstrained audio data for training. Unlike previous approaches, only
weak labels during teacher training are required, enabling the utilization of
any real-world, potentially noisy dataset. Our approach firstly trains a
teacher model on a source dataset (Audioset) using clip-level supervision.
After training, the teacher provides frame-level guidance to a student model on
an unlabeled, target dataset. A multitude of student models trained on mid- to
large-sized datasets are investigated (Audioset, Voxceleb, NIST SRE). Our
approach is then respectively evaluated on clean, artificially noised, and
real-world data. We observe significant performance gains in artificially
noised and real-world scenarios. Lastly, we compare our approach against other
unsupervised and supervised VAD methods, demonstrating our method's
superiority.


  Practical machine learning applications involving time series data, such as
firewall log analysis to proactively detect anomalous behavior, are concerned
with real time analysis of streaming data. Consequently, we need to update the
ML models as the statistical characteristics of such data may shift frequently
with time. One alternative explored in the literature is to retrain models with
updated data whenever the models accuracy is observed to degrade. However,
these methods rely on near real time availability of ground truth, which is
rarely fulfilled. Further, in applications with seasonal data, temporal concept
drift is confounded by seasonal variation. In this work, we propose an approach
called Unsupervised Temporal Drift Detector or UTDD to flexibly account for
seasonal variation, efficiently detect temporal concept drift in time series
data in the absence of ground truth, and subsequently adapt our ML models to
concept drift for better generalization.


  The SPectrogram Analysis and Cataloguing Environment (SPACE) tool is an
interactive python tool designed to label radio emission features of interest
in a time-frequency map (called 'dynamic spectrum'). The program uses
Matplotlib's Polygon Selector widget to allow a user to select and edit an
undefined number of vertices on top of the dynamic spectrum before closing the
shape (polygon). Multiple polygons may be drawn on any spectrum, and the
feature name along with the coordinates for each polygon vertex are saved into
a '.json' file as per the 'Time-Frequency Catalogue' (TFCat) format along with
other data such as the feature id, observer name, and data units. This paper
describes the first official stable release (version 2.0) of the tool.


  In this paper, we develop a robust non-parametric realized integrated beta
estimator using high-frequency financial data contaminated by microstructure
noises, which is robust to the stylized features, such as the time-varying beta
and the dependence structure of microstructure noises. With this robust
realized integrated beta estimator, we investigate dynamic structures of
integrated betas and find an auto-regressive--moving-average (ARMA) structure.
To model this dynamic structure, we utilize the ARMA model for daily integrated
market betas. We call this the dynamic realized beta (DR Beta). We further
introduce a high-frequency data generating process by filling the gap between
the high-frequency-based non-parametric estimator and low-frequency dynamic
structure. Then, we propose a quasi-likelihood procedure for estimating the
model parameters with the robust realized integrated beta estimator as the
proxy. We also establish asymptotic theorems for the proposed estimator and
conduct a simulation study to check the performance of finite samples of the
estimator. The empirical study with the S&P 500 index and the top 50 large
trading volume stocks from the S&P 500 illustrates that the proposed DR Beta
model with the robust realized beta estimator effectively accounts for dynamics
in the market beta of individual stocks and better predicts future market
betas.


  Video post-processing methods can improve the quality of compressed videos at
the decoder side. Most of the existing methods need to train corresponding
models for compressed videos with different quantization parameters to improve
the quality of compressed videos. However, in most cases, the quantization
parameters of the decoded video are unknown. This makes existing methods have
their limitations in improving video quality. To tackle this problem, this work
proposes a diffusion model based post-processing method for compressed videos.
The proposed method first estimates the feature vectors of the compressed video
and then uses the estimated feature vectors as the prior information for the
quality enhancement model to adaptively enhance the quality of compressed video
with different quantization parameters. Experimental results show that the
quality enhancement results of our proposed method on mixed datasets are
superior to existing methods.


  Let k be a field not of characteristic two and L be a set of almost all
rational primes invertible in k. Suppose we have a variety X/k and strictly
compatible system {M_ell -> X : ell in L} of constructible F_ell-sheaves. If
the system is orthogonally or symplectically self-dual, then the geometric
monodromy group of M_ell is a subgroup of a corresponding isometry group G_ell
over F_ell, and we say it has big monodromy if it contains the derived subgroup
DG_ell=[G_ell,G_ell]. We prove a theorem which gives sufficient conditions for
M_ell to have big monodromy. We apply the theorem to explicit systems arising
from the middle cohomology of families of hyperelliptic curves and elliptic
surfaces to show that the monodromy is uniformly big as we vary ell and the
system.


  AST/RO is a 1.7m diameter submillimeter-wave telescope at the geographic
South Pole. A key AST/RO project is the mapping of C I and CO J=4-3 and J=7-6
emission from the inner Milky Way (Martin et al. 2003). These data are released
for general use.


  In this work we study the high-energy Higgs boson phenomenology associated to
the non-metricity scale $\Lambda_Q$ at the LHC. Non-metricity is present in
more generic non-Riemannian geometries describing gravity beyond General
Relativity and exhibits nice features in astronomy and cosmology, and it can be
analysed perturbatively. Using effective field theory tools, we calculate the
new physics contributions to the one-loop $H\to\gamma\gamma$ and $gg\to H$
processes and, together with previous bounds from Compton scattering, we obtain
relevant constraints and correlations in the model's parameter space. This can
help us take a step further, and no longer associate gravitational effects
uniquely to astronomical phenomena, and to start analysing these effects by
means of high energy experiments. In turn, this could also help us get a better
grasp at quantum phenomena associated to gravity.


  In this letter, we propose a new symbol detection method for
faster-than-Nyquist signaling (FTNS) systems. Based on frame theory, we
formulate a symbol detection problem as a under-determined linear equation on a
finite set. The problem is reformulated as a sum-of-absolute-values (SOAV)
optimization that can be efficiently solved by the fast iterative shrinkage
thresholding algorithm (FISTA). The proximity operator for the convex
optimization is derived analytically. Simulation results are given to show that
the proposed method can successfully detect symbols in faster-than-Nyquist
signaling systems and has lower complexity in terms of computation time.


  We survey applications of pretrained foundation models in robotics.
Traditional deep learning models in robotics are trained on small datasets
tailored for specific tasks, which limits their adaptability across diverse
applications. In contrast, foundation models pretrained on internet-scale data
appear to have superior generalization capabilities, and in some instances
display an emergent ability to find zero-shot solutions to problems that are
not present in the training data. Foundation models may hold the potential to
enhance various components of the robot autonomy stack, from perception to
decision-making and control. For example, large language models can generate
code or provide common sense reasoning, while vision-language models enable
open-vocabulary visual recognition. However, significant open research
challenges remain, particularly around the scarcity of robot-relevant training
data, safety guarantees and uncertainty quantification, and real-time
execution. In this survey, we study recent papers that have used or built
foundation models to solve robotics problems. We explore how foundation models
contribute to improving robot capabilities in the domains of perception,
decision-making, and control. We discuss the challenges hindering the adoption
of foundation models in robot autonomy and provide opportunities and potential
pathways for future advancements. The GitHub project corresponding to this
paper (Preliminary release. We are committed to further enhancing and updating
this work to ensure its quality and relevance) can be found here:
https://github.com/robotics-survey/Awesome-Robotics-Foundation-Models


  In this article, we consider joint returns to zero of $n$ Bessel processes
($n\geq 2$): our main goal is to estimate the probability that they avoid
having joint returns to zero for a long time. More precisely, considering $n$
independent Bessel processes $(X_t^{(i)})_{1\leq i \leq n}$ of dimension
$\delta \in (0,1)$, we are interested in the first joint return to zero of any
two of them: \[ H_n := \inf\big\{ t>0, \exists 1\leq i <j \leq n \text{ such
that } X_t^{(i)} = X_t^{(j)} =0 \big\} \,. \] We prove the existence of a
persistence exponent $\theta_n$ such that $\mathbb{P}(H_n>t) =
t^{-\theta_n+o(1)}$ as $t\to\infty$, and we provide some non-trivial bounds on
$\theta_n$. In particular, when $n=3$, we show that $2(1-\delta)\leq \theta_3
\leq 2 (1-\delta) + f(\delta)$ for some (explicit) function $f(\delta)$ with
$\sup_{[0,1]} f(\delta) \approx 0.079$.


  Using new ultradeep Spitzer/IRAC photometry from the IRAC Ultradeep Field
program (IUDF), we investigate the stellar populations of a sample of 63
Y-dropout galaxy candidates at z~8, only 650Myr after the Big Bang. The sources
are selected from HST/ACS+WFC3/IR data over the Hubble Ultra Deep Field (HUDF),
two HUDF parallel fields, and wide area data over the CANDELS/GOODS-South. The
new Spitzer/IRAC data increase the coverage at 3.6 micron and 4.5 micron to
~120h over the HUDF reaching depths of ~28 (AB,1 sigma). The improved depth and
inclusion of brighter candidates result in direct >3 sigma IRAC detections of
20/63 sources, of which 11/63 are detected at > 5 sigma. The average
[3.6]-[4.5] colors of IRAC detected galaxies at z~8 are markedly redder than
those at z~7, observed only 130Myr later. The simplest explanation is that we
witness strong rest-frame optical emission lines (in particular
[OIII]4959,5007+Hbeta) moving through the IRAC bandpasses with redshift.
Assuming that the average rest-frame spectrum is the same at both z~7 and z~8
we estimate a rest-frame equivalent width of W([OIII]4959,5007+Hbeta) = 670
(+260,-170) Angstrom contributing 0.56 (+0.16,-0.11) mag to the 4.5 micron
filter at z~8. The corresponding W(Halpha) = 430 (+160,-110) Angstrom implies
an average specific star formation rate of sSFR = 11 (+11,-5) Gyr^-1 and a
stellar population age of 100 (+100,-50) Myr. Correcting the spectral energy
distribution for the contribution of emission lines lowers the average best-fit
stellar masses and mass-to-light ratios by x3, decreasing the integrated
stellar mass density to rho*(z=8,MUV<-18)=0.6 (+0.4,-0.3) x 10^6 Msun Mpc^-3.


  In this paper, we give an affirmative answer to a conjecture in the Minimal
Model Program. We prove that log $Q$-Fano varieties of dim $n$ are rationally
connected. We also study the behavior of the canonical bundles under projective
morphisms.


  Reinforcement learning methods typically use Deep Neural Networks to
approximate the value functions and policies underlying a Markov Decision
Process. Unfortunately, DNN-based RL suffers from a lack of explainability of
the resulting policy. In this paper, we instead approximate the policy and
value functions using an optimization problem, taking the form of Quadratic
Programs (QPs). We propose simple tools to promote structures in the QP,
pushing it to resemble a linear MPC scheme. A generic unstructured QP offers
high flexibility for learning, while a QP having the structure of an MPC scheme
promotes the explainability of the resulting policy, additionally provides ways
for its analysis. The tools we propose allow for continuously adjusting the
trade-off between the former and the latter during learning. We illustrate the
workings of our proposed method with the resulting structure using a point-mass
task.


  We investigate the problem of training neural networks from incomplete images
without replacing missing values. For this purpose, we first represent an image
as a graph, in which missing pixels are entirely ignored. The graph image
representation is processed using a spatial graph convolutional network (SGCN)
-- a type of graph convolutional networks, which is a proper generalization of
classical CNNs operating on images. On one hand, our approach avoids the
problem of missing data imputation while, on the other hand, there is a natural
correspondence between CNNs and SGCN. Experiments confirm that our approach
performs better than analogical CNNs with the imputation of missing values on
typical classification and reconstruction tasks.


  Multichannel processing is widely used for speech enhancement but several
limitations appear when trying to deploy these solutions to the real-world.
Distributed sensor arrays that consider several devices with a few microphones
is a viable alternative that allows for exploiting the multiple devices
equipped with microphones that we are using in our everyday life. In this
context, we propose to extend the distributed adaptive node-specific signal
estimation approach to a neural networks framework. At each node, a local
filtering is performed to send one signal to the other nodes where a mask is
estimated by a neural network in order to compute a global multi-channel Wiener
filter. In an array of two nodes, we show that this additional signal can be
efficiently taken into account to predict the masks and leads to better speech
enhancement performances than when the mask estimation relies only on the local
signals.


  In this paper we prove that for toric varieties the uniform K-stability is
the necessary condition for the existence of extremal metrics.


  In this paper we study a long-standing conjecture of Huneke and Wiegand which
is concerned with the torsion submodule of certain tensor products of modules
over one-dimensional local domains. We utilize Hochster's theta invariant and
show that the conjecture is true for two periodic modules. We also make use of
a result of Orlov and formulate a new condition which, if true over
hypersurface rings, forces the conjecture of Huneke and Wiegand to be true over
complete intersection rings of arbitrary codimension. Along the way we
investigate the interaction between the vanishing of Tate (co)homology and
torsion in tensor products of modules, and obtain new results that are of
independent interest.


  The bulk photovoltaic effect is an example of a non-linear optical response
that leads to a DC current that is relevant for photo-voltaic applications. In
this work, we theoretically study this effect in the presence of
electron-phonon interactions. Using the response function formalism we find
that the non-linear optical response, in general, contains three operator
correlation functions, one of which is not ordered in time. This latter
correlator cannot be computed from equilibrium field theory. Using a
semiclassical approach instead, we show that the bulk photovoltaic effect can
be attributed to the dipole moment of the generated excitons. We then confirm
the validity of the semiclassical result (which agrees with the non-interacting
result) for non-linear DC response from a quantum master equation approach.
From this formalism we find that, in contrast to usual linear response, the
scattering rate has a strong implicit effect on the non-linear DC response.
Most interestingly, the semiclassical treatment shows that the non-linear DC
response for spatially inhomogeneous excitation profiles is strongly non-local
and must involve the aforementioned out-of-time-ordered correlators that cannot
be computed by equilibrium field theory.


  Metal/oxide support perimeter sites are known to provide unique properties
because the nearby metal changes the local environment on the support surface.
In particular, the electron scavenger effect reduces the energy necessary for
surface anion desorption, thereby contributes to activation of the (reverse)
Mars-van Krevelen mechanism. This study investigated the possibility of such
activation in hydrides, carbides, nitrides, and sulfides. The work functions
(WFs) of known hydrides, carbides, nitrides, oxides, and sulfides with group 3,
4, or 5 cations (Sc, Y, La, Ti, Zr, Hf, V, Nb, and Ta) were calculated. The WFs
of most hydrides, carbides, and nitrides are smaller than the WF of Ag,
implying that the electron scavenger effect may occur when late transition
metal nanoparticles are adsorbed on the surface. The WF of oxides and sulfides
decrease when reduced. The surface anion vacancy formation energy correlates
well with the bulk formation energy in carbides and nitrides, while almost no
correlation is found in hydrides because of the small range of surface hydrogen
vacancy formation energy values. The electron scavenger effect is explicitly
observed in nanorods adsorbed on TiH2 and Ti2O3; the surface vacancy formation
energy decreases at anion sites near the nanorod, and charge transfer to the
nanorod happens when an anion is removed at such sites. Activation of hydrides,
carbides, and nitrides by nanorod adsorption and screening support materials
through WF calculation are expected to open up a new category of supported
catalysts.


  Editable 3D-aware generation, which supports user-interacted editing, has
witnessed rapid development recently. However, existing editable 3D GANs either
fail to achieve high-accuracy local editing or suffer from huge computational
costs. We propose AttriHuman-3D, an editable 3D human generation model, which
address the aforementioned problems with attribute decomposition and indexing.
The core idea of the proposed model is to generate all attributes (e.g. human
body, hair, clothes and so on) in an overall attribute space with six feature
planes, which are then decomposed and manipulated with different attribute
indexes. To precisely extract features of different attributes from the
generated feature planes, we propose a novel attribute indexing method as well
as an orthogonal projection regularization to enhance the disentanglement. We
also introduce a hyper-latent training strategy and an attribute-specific
sampling strategy to avoid style entanglement and misleading punishment from
the discriminator. Our method allows users to interactively edit selected
attributes in the generated 3D human avatars while keeping others fixed. Both
qualitative and quantitative experiments demonstrate that our model provides a
strong disentanglement between different attributes, allows fine-grained image
editing and generates high-quality 3D human avatars.


  We evaluate the problem of galaxy formation in the landscape approach to
phenomenology of the axion sector. With other parameters of standard LambdaCDM
cosmology held fixed, the density of cold dark matter is bounded below relative
to the density of baryonic matter by the requirement that structure should form
before the era of cosmological constant domination of the universe. Galaxies
comparable to the Milky Way can only form if the ratio also satisfies an upper
bound. The resulting constraint on the density of dark matter is too loose to
select a low axion decay constant or small initial displacement angle on
anthropic grounds.


  We propose a machine-learning-based technique to determine the number density
of radio sources as a function of their flux density, for use in
next-generation radio surveys. The method uses a convolutional neural network
trained on simulations of the radio sky to predict the number of sources in
several flux bins. To train the network, we adopt a supervised approach wherein
we simulate training data stemming from a large domain of possible number count
models going down to fluxes a factor of 100 below the threshold for source
detection. We test the model reconstruction capabilities as well as benchmark
the expected uncertainties in the model predictions, observing good performance
for fluxes down to a factor of ten below the threshold. This work demonstrates
that the capabilities of simple deep learning models for radio astronomy can be
useful tools for future surveys.


  Inelastic electron transfer being regarded as one of the potential mechanisms
to explain the odorant recognition in the atomic-scale processes is still a
matter of intense debate. Here, we propose multiphonon processes of electrons
transfer using the Markvart model and calculate their lifetimes with values of
key parameters widely adopted in olfactory systems. We find that these
multiphonon processes are as quickly as the single phonon process, which
suggest that contributions from different phonon modes of odorant molecule for
electrons transfer in olfaction should be included. Meanwhile, temperature
dependence of electron transfer could be analyzed effectively based on the
reorganization energy is expanded into the linewidth of multiphonon processes.
Our theoretical results not only enrich the knowledge of the mechanism of the
olfaction recognition, but also provide insights for quantum processes in the
biological system.


  We utilize machine learning models which are based on recurrent neural
networks to optimize dynamical decoupling (DD) sequences. DD is a relatively
simple technique for suppressing the errors in quantum memory for certain noise
models. In numerical simulations, we show that with minimum use of prior
knowledge and starting from random sequences, the models are able to improve
over time and eventually output DD-sequences with performance better than that
of the well known DD-families. Furthermore, our algorithm is easy to implement
in experiments to find solutions tailored to the specific hardware, as it
treats the figure of merit as a black box.


  Recent magnetoconductance measurements performed on magnetic topological
insulator candidates have revealed butterfly-shaped hysteresis. This hysteresis
has been attributed to the formation of gapless chiral domain-wall bound states
during a magnetic field sweep. We treat this phenomenon theoretically,
providing a link between microscopic magnetization dynamics and butterfly
hysteresis in magnetoconductance. Further, we illustrate how a spatially
resolved conductance measurement can probe the most striking feature of the
domain-wall bound states: their chirality. This work establishes a regime where
a definitive link between butterfly hysteresis in longitudinal
magneto-conductance and domain-wall bound states can be made. This analysis
provides an important tool for the identification of magnetic topological
insulators.


  The notion of Online State Complexity, introduced by Karp in 1967, quantifies
the amount of states required to solve a given problem using an online
algorithm, which is represented by a deterministic machine scanning the input
from left to right in one pass. In this paper, we extend the setting to
alternating machines as introduced by Chandra, Kozen and Stockmeyer in 1976:
such machines run independent passes scanning the input from left to right and
gather their answers through boolean combinations. We devise a lower bound
technique relying on boundedly generated lattices of languages, and give two
applications of this technique. The first is a hierarchy theorem , stating that
the polynomial hierarchy of alternating online state complexity is infinite,
and the second is a linear lower bound on the alternating online state
complexity of the prime numbers written in binary. This second result
strengthens a result of Hartmanis and Shank from 1968, which implies an
exponentially worse lower bound for the same model.


  We study a two-band Hubbard model using the dynamical mean-field theory
combined with the exact diagonalization method. At the electron density $n=2$,
a transition from a band-insulator to a correlated semimetal occurs when the
on-site Coulomb interaction $U$ is varied for a fixed value of the
charge-transfer energy $\Delta$. At low temperature, the correlated semimetal
shows ferromagnetism or superconductivity. With increasing doping $|n-2|$, the
ferromagnetic transition temperature rapidly decreases and finally becomes zero
at a critical value of $n$. The second-order phase transition occurs at high
temperature, while a phase separation of ferromagnetic and paramagnetic states
takes place at low temperature. The superconducting transition temperature
gradually decreases and finally becomes zero near $n=1$ ($n=3$) where the
system is Mott insulator which shows antiferromagnetism at low temperature.


  The number of peaks of a random permutation is known to be asymptotically
normal. We give a new proof of this and prove a central limit theorem for the
distribution of peaks in a fixed conjugacy class of the symmetric group. Our
technique is to apply ``analytic combinatorics'' to study a complicated but
exact generating function for peaks in a given conjugacy class.


  The second quantum revolution has been producing groundbreaking scientific
and technological outputs since the early 2000s; however, the scientific
literature on the impact of this revolution on the industry, specifically on
start-ups, is limited. In this paper, we present a landscaping study with a
gathered dataset of 441 companies from 42 countries that we identify as quantum
start-ups, meaning that they mainly focus on quantum technologies (QT) as their
primary priority business. We answer the following questions: (1) What are the
temporal and geographical distributions of the quantum start-ups? (2) How can
we categorize them, and how are these categories populated? (3) Are there any
patterns that we can derive from empirical data on trends? We found that more
than 92% of these companies have been founded within the last 10 years, and
more than 50% of them are located in the US, the UK, and Canada. We categorized
the QT start-ups into six fields: (i) complementary technologies, (ii) quantum
computing (hardware), (iii) quantum computing
(software/application/simulation), (iv) quantum cryptography/communication, (v)
quantum sensing and metrology, and (vi) supporting companies, and analyzed the
population of each field both for countries, and temporally. Finally, we argue
that low levels of quantum start-up activity in a country might be an indicator
of a national initiative to be adopted afterwards, which later sees both an
increase in the number of start-ups, and a diversification of activity in
different QT fields.


  Topological insulators are unique devices supporting unidirectional edge
states at their interfaces. Due to topological protection, such edge states
persist in the presence of disorder and do not experience backscattering upon
interaction with defects. We show that despite the topological protection and
the fact that such states at the opposite edges of a ribbon carry opposite
currents, there exists a physical mechanism allowing to resonantly couple
topological excitations propagating at opposite edges. Such mechanism uses weak
periodic temporal modulations of the system parameters and does not affect the
internal symmetry and topology of the system. We study this mechanism in
truncated honeycomb arrays of microcavity pillars, where topological insulation
is possible for polaritons under the combined action of spin-orbit coupling and
Zeeman splitting in the external magnetic field. The temporal modulation of the
potential leads to a periodic switching between topological states with the
same Bloch momentum, but located at the opposite edges. The switching rate is
found to increase for narrower ribbon structures and for larger modulation
depth, though it is changing nonmonotonically with the Bloch momentum of the
input edge state. Our results provide a promising realization of a coupling
device based on topologically protected states. The proposed scheme can be used
in other topological photonic and condensed matter systems, including Floquet
insulators and graphene.


  A polymorphic analysis is an analysis whose input and output contain
parameters which serve as placeholders for information that is unknown before
analysis but provided after analysis. In this paper, we present a polymorphic
groundness analysis that infers parameterised groundness descriptions of the
variables of interest at a program point. The polymorphic groundness analysis
is designed by replacing two primitive operators used in a monomorphic
groundness analysis and is shown to be as precise as the monomorphic groundness
analysis for any possible values for mode parameters. Experimental results of a
prototype implementation of the polymorphic groundness analysis are given.


  We investigate deformations of a skew group algebra that arise from a finite
group acting on a polynomial ring. When the characteristic of the underlying
field divides the order of the group, a new type of deformation emerges that
does not occur in characteristic zero. This analogue of Lusztig's graded affine
Hecke algebra for positive characteristic can not be forged from the template
of symplectic reflection and related algebras as originally crafted by
Drinfeld. By contrast, we show that in characteristic zero, for arbitrary
finite groups, a Lusztig-type deformation is always isomorphic to a
Drinfeld-type deformation. We fit all these deformations into a general theory,
connecting Poincar\'e-Birkhoff-Witt deformations and Hochschild cohomology when
working over fields of arbitrary characteristic. We make this connection by way
of a double complex adapted from Guccione, Guccione, and Valqui, formed from
the Koszul resolution of a polynomial ring and the bar resolution of a group
algebra.


  Using quiver gauge theories in (1+2)-dimensions, we give brane realizations
of a class of Quantum Hall Solitons (QHS) embedded in Type IIA superstring on
the ALE spaces with exotic singularities. These systems are obtained by
considering two sets of wrapped D4-branes on 2-spheres. The space-time on which
the QHS live is identified with the world-volume of D4-branes wrapped on a
collection of intersecting 2-spheres arranged as extended Dynkin diagrams of
Kac-Moody Lie algebras. The magnetic source is given by an extra orthogonal
D4-brane wrapping a generic 2-cycle in the ALE spaces. It is shown as well that
data on the representations of Kac-Moody Lie algebras fix the filling factor of
the QHS. In case of finite Dynkin diagrams, we recover results on QHS with
integer and fractional filling factors known in the literature. In case of
hyperbolic bilayer models, we obtain amongst others filling factors describing
holes in the graphene.


  We give a comprehensive survey of the theory of finite dimensional Lie
algebras over an algebraically closed field of characteristic p>0 and announce
that for p>3 the classification of finite dimensional simple Lie algebras is
complete. Any such Lie algebra is up to isomorphism either classical (i.e.
comes from characteristic 0) or a filtered Lie algebra of Cartan type or a
Melikian algebra of characteristic 5.


  We study the electronic transport through a double quantum dot molecule
attached to leads, and examine the transition from a configuration in series to
a symmetrical parallel geometry. We find that a progressive reduction of the
tunneling through the antibonding state takes place as a result of the
destructive quantum interference between the different pathways through the
molecule. The Fano resonance narrows down, disappearing entirely when the
configuration is totally symmetric, so that only the bonding state participates
of the transmission. In this limit the antibonding state becomes completely
localized.


  The notions of Hom-coring, Hom-entwining structure and associated entwined
Hom-module are introduced. A theorem regarding base ring extension of a
Hom-coring is proven and then is used to acquire the Hom-version of Sweedler
coring. Motivated by the work of T. Brzezinski, a Hom-coring associated to an
entwining Hom-structure is constructed and an identification of entwined
Hom-modules with Hom-comodules of this Hom-coring is shown. The dual algebra of
this Hom-coring is proven to be a $\psi$-twisted convolution algebra. By a
construction, it is shown that a Hom-Doi-Koppinen datum comes from a
Hom-entwining structure and that the Doi-Koppinen Hom-Hopf modules are the same
as the associated entwined Hom-modules. A similar construction regarding an
alternative Hom-Doi-Koppinen datum is also given. A collection of Hom-Hopf-type
modules are gathered as special examples of Hom-entwining structures and
corresponding entwined Hom-modules, and structures of all relevant Hom-corings
are also considered.


  There is solid theoretical and observational motivation behind the idea of
scale-invariance as a fundamental symmetry of Nature. We consider a recently
proposed classically scale-invariant inflationary model, quadratic in curvature
and featuring a scalar field non-minimally coupled to gravity. We go beyond
earlier analytical studies, which showed that the model predicts inflationary
observables in qualitative agreement with data, by solving the full two-field
dynamics of the system -- this allows us to corroborate previous analytical
findings and set robust constraints on the model's parameters using the latest
Cosmic Microwave Background (CMB) data from Planck and BICEP/Keck. We
demonstrate that scale-invariance constrains the two-field trajectory such that
the effective dynamics are that of a single field, resulting in vanishing
entropy perturbations and protecting the model from destabilization effects. We
derive tight upper limits on the non-minimal coupling strength, excluding
conformal coupling at high significance. By explicitly sampling over them, we
demonstrate an overall insensitivity to initial conditions. We argue that the
model \textit{predicts} a minimal level of primordial tensor modes set by $r
\gtrsim 0.003$, well within the reach of next-generation CMB experiments. These
will therefore provide a litmus test of scale-invariant inflation, and we
comment on the possibility of distinguishing the model from Starobinsky and
$\alpha$-attractor inflation. Overall, we argue that scale-invariant inflation
is in excellent health, and possesses features which make it an interesting
benchmark for tests of inflation from future CMB data.