  Topic of this work are comets, small and elusive objects that may hold great
secrets about the origin of the Solar System and life on Earth, being among the
most primitive objects. The method of investigation addressed in this work is
the visible and infrared spectrophotometry by imaging spectrometers, designed
for the observation of remote planetary atmospheres and surfaces, capable to
acquire hyperspectral data with high spatial and spectral resolution. The
context under which this mission moves its steps is described in the first
chapter. In the second chapter the performances of the VIRTS instrument,
onboard Rosetta spacecraft, are analyzed in detail. In particular the modeling
of the signal to noise ratio is the main argument of this chapter. The third
chapter shows simulations of possible spectra of the comet's nucleus, which are
useful for both a comparison with real spectra, and for a planning of the
observations. Hapke's radiative transfer model is used to invert acquired data
to infer physical properties. The fourth chapter introduces a method for
spectral modeling. It includes the information on the instrumental noise,
permitting the analysis of the goodness of the models, and an estimation of the
error of the retrieved parameters. The fifth chapter presents the spectral
analysis of Tempel 1 and Hartley 2 whose data are coming from Deep Impact space
mission and its extended investigation. The sixth chapter shows the photometric
analysis of Lutetia asteroid, which was encountered by Rosetta during its
cruise phase. This work have paved the way to the analysis of the final target
of Rosetta: comet 67P/Churyumov-Gerasimenko. The tools presented are currently
used by the VIRTIS Team to produce works on the comet, that are recommended to
the reader. Since a complete analysis on the comet is outside the scope of this
work, just preliminary results are shown here.


  We report measurements of electric potentials at the surface of a spherical
container of liquid sodium in which a magnetized inner core is differentially
rotating. The azimuthal angular velocities inferred from these potentials
reveal a strong super-rotation of the liquid sodium in the equatorial region,
for small differential rotation. Super-rotation was observed in numerical
simulations by Dormy et al. [1]. We find that the latitudinal variation of the
electric potentials in our experiments differs markedly from the predictions of
a similar numerical model, suggesting that some of the assumptions used in the
model - steadiness, equatorial symmetry, and linear treatment for the evolution
of both the magnetic and velocity fields - are violated in the experiments. In
addition, radial velocity measurements, using ultrasonic Doppler velocimetry,
provide evidence of oscillatory motion near the outer sphere at low latitude:
it is viewed as the signature of an instability of the super-rotating region.


  In this paper we formulate structure from motion as a learning problem. We
train a convolutional network end-to-end to compute depth and camera motion
from successive, unconstrained image pairs. The architecture is composed of
multiple stacked encoder-decoder networks, the core part being an iterative
network that is able to improve its own predictions. The network estimates not
only depth and motion, but additionally surface normals, optical flow between
the images and confidence of the matching. A crucial component of the approach
is a training loss based on spatial relative differences. Compared to
traditional two-frame structure from motion methods, results are more accurate
and more robust. In contrast to the popular depth-from-single-image networks,
DeMoN learns the concept of matching and, thus, better generalizes to
structures not seen during training.


  In sonic models of special relativity, the fact that the sonic medium
violates (ordinary) Lorentz symmetry is apparent to observers external to the
sonic medium but not to a class of observers existing within the medium itself.
We show that the situation is symmetric: internal observers will judge physics
in the external laboratory to violate their own sonic Lorentz symmetries. We
therefore treat all observers on an equal footing such that each is able to
retain a commitment to their own Lorentz symmetries. We then generalize beyond
the case of subsystem-environment decompositions to situations in which there
exist multiple phonon fields, all obeying Lorentz symmetries but with different
invariant speeds. In such cases, we argue that all observers have freedom to
choose which field is symmetry preserving, and so -- in a certain precise sense
-- which other fields are perceived as having an 'ether.' This choice is
influenced -- but not determined -- by a desire for simplicity in the
description of physical laws. Sending information faster than sound serves as a
model of tachyonic signalling to a distant receiver. Immutable causality of the
laboratory setup when perceived externally to a sonic medium manifests
internally through the confinement of the tachyons to an apparent ether (with a
rest frame), which we call a 'tachyonic medium,' thereby preventing tachyonic
exchange from emulating the scenario of a round-trip signal travelling into an
observer's past causal cone. The assignment of sonic-Lorentz-violating effects
to fields that obey 'photonic' Lorentz symmetries thus ensures that causality
associated with the 'sonic' Lorentz symmetries is preserved.


  A multilayered particle is illuminated by plane acoustic or electromagnetic
waves of one or several frequencies. We consider the inverse scattering problem
for the identification of the layers and of the refraction coefficients of the
scatterer in a non-Born region of scattering. Local deterministic and global
probabilistic minimization methods are studied. A special Reduction Procedure
is introduced to reduce the dimensionality of the minimization space. Deep's
and the Multilevel
  Single-Linkage methods for global minimization are used for the solution of
the inverse problem. Their performance is analyzed for various multilayer
configurations.


  We propose a parallel introduction to Galilean and Einsteinian relativity
based on the causal structure and inertial motions. Galilean and Poincare
transformations, as objects secondary to the geometrical structure, are left
aside.


  We study integrable and conformal boundary conditions for ^sl(2) Z_k
parafermions on a cylinder. These conformal field theories are realized as the
continuum scaling limit of critical A-D-E lattice models with negative spectral
parameter. The conformal boundary conditions labelled by (a,m) in (G, Z_{2k})
are identified with associated integrable lattice boundary conditions labelled
by (r,a) in (A_{g-2},G) where g is the Coxeter number of the A-D-E graph G. We
obtain analytically the boundary free energies, present general expressions for
the parafermion cylinder partition functions and confirm these results by
numerical calculations.


  Bialynicki-Birula and Charzynski argued that a gravitational wave emitted
during the merger of a black hole binary may be approximated by a circularly
polarized wave
  which may in turn trap particles [1]. In this paper we consider particle
motion in a class of gravitational waves which includes, besides circularly
polarized periodic waves (CPP) [2], also the one proposed by Lukash [3] to
study anisotropic cosmological models. Both waves have a 7-parameter conformal
symmetry which contains, in addition to the generic 5-parameter (broken)
Carroll group, also a 6th isometry. The Lukash spacetime can be transformed by
a conformal rescaling of time to a perturbed CPP problem. Bounded geodesics,
found both analytically and numerically, arise when the Lukash wave is of
Bianchi type VI. Their symmetries can also be derived from the Lukash-CPP
relation. Particle trapping is discussed.


  Ground-state cooling of mechanical resonators is a prerequisite for the
observation of various quantum effects in optomechanical systems and thus has
always been a crucial task in quantum optomechanics. In this paper, we study
how to realize ground-state cooling of the mechanical mode in a Fano-mirror
optomechanical setup, which allows for enhanced effective optomechanical
interaction but typically works in the (deeply) unresolved-sideband regime. We
reveal that for such a two-sided cavity geometry with very different decay
rates at the two cavity mirrors when using an appropriate single-sided coherent
feedback, it is possible to cool the mechanical mode down to its ground state
within a broad range of parameters. This is possible even if the total optical
loss is more than seven orders of magnitude larger than the mechanical
frequency and the feedback efficiency is relatively low. Importantly, we show
that a more standard two-sided feedback scheme is not appropriate to cooperate
with a Fano-mirror system.


  In this work we investigate the interatomic correlation moments in
two-dimensional model of a weakly anharmonic crystal (i.e., not very high
temperatures) with hexagonal lattice, using the Correlative Method of
Unsymmetrized Self-Consistent Field (CUSF). The numerical results are obtained
(and compared) by using the Morse and Lenard-Jones potentials.


  We present a method for classifying conformal field theories based on Coulomb
gases (bosonic free-field construction). Given a particular geometric
configuration of the screening charges, we give necessary conditions for the
existence of degenerate representations and for the closure of the
vertex-operator algebra. The resulting classification contains, but is more
general than, the standard one based on classical Lie algebras. We then apply
the method to the Coulomb gas theory for the two-flavoured loop model of
Jacobsen and Kondev. The purpose of the study is to clarify the relation
between Coulomb gas models and conformal field theories with extended
symmetries.


  We begin by considering the expectations of the creators of VisiCalc, the
first spreadsheet. The emphasis is on the nature of the spreadsheet grid. The
grid is taken as a presentational method for showing a solution to a Sudoku
puzzle. We consider methods or approaches for the solution. We look at the
relationship between this model and academic papers on the methods for
describing and categorising end-user models generally. We consider whether the
type of model described here should be categorised separately. The complexity
of the model is reviewed in the context of commendations to minimise overly
sophisticated presentational constructs and formulae.


  Superflares on the solar type stars observed by \textit{Kepler} demonstrate
the contrast in the optical continuum of the order 0.1--1 per cent. The
mechanism of formation of this radiation is not firmly established. We consider
a model where the stellar atmosphere is irradiated by the soft X rays emitted
from the flaring loop filled with the hot plasma. This radiation heats a large
area beneath the loop. Subsequent cooling due to {\sc h$^{-}$} and hydrogen
free-bound emission can contribute to the observed enhanced continuum. We solve
the equations of radiative transfer, statistical equilibrium, ionization
balance and radiative equilibrium in the model atmosphere illuminated by the
soft X rays, compute the temperature and the electron density in the atmosphere
and find the emergent radiation. We found that a flare loop of the length
$\sim10^{10}$~cm and plasma density $10^{12}$~cm$^{-3}$ at the temperature $T =
20$ MK can provide the contrast in the \textit{Kepler} bandpass of 0.1 and 0.8
per cent if the heated region covers $\sim$~1 and 10 per cent of the visible
stellar surface respectively. The required emission measure is of the order
$10^{55}$~cm$^{-3}$.


  Twisted bilayer graphene (TBG) is a recently discovered two-dimensional
superlattice structure which exhibits strongly-correlated quantum many-body
physics, including strange metallic behavior and unconventional
superconductivity. Most of TBG exotic properties are connected to the emergence
of a pair of isolated and topological flat electronic bands at the so-called
magic angle, $\theta \approx 1.05^{\circ}$, which are nevertheless very
fragile. In this work, we show that, by employing chiral optical cavities, the
topological flat bands can be stabilized away from the magic angle in an
interval of approximately $0.8^{\circ}<\theta<1.3^{\circ}$. As highlighted by a
simplified theoretical model, time reversal symmetry breaking (TRSB), induced
by the chiral nature of the cavity, plays a fundamental role in flattening the
isolated bands and gapping out the rest of the spectrum. Additionally, TRSB
suppresses the Berry curvature and induces a topological phase transition, with
a gap closing at the $\Gamma$ point, towards a band structure with two isolated
flat bands with Chern number equal to $0$. The efficiency of the cavity is
discussed as a function of the twisting angle, the light-matter coupling and
the optical cavity characteristic frequency. Our results demonstrate the
possibility of engineering flat bands in TBG using optical devices, extending
the onset of strongly-correlated topological electronic phases in moir\'e
superlattices to a wider range in the twisting angle.


  In biodiversity and ecosystem functioning (BEF) research, the Loreau-Hector
(LH) statistical scheme is widely-used to partition the effect of biodiversity
on ecosystem properties into a "complementarity effect" and a "selection
effect". This selection effect was originally considered analogous to the
selection term in the Price equation from evolutionary biology. However, a key
paper published over thirteen years ago challenged this interpretation by
devising a new tripartite partitioning scheme that purportedly quantified the
role of selection in biodiversity experiments more accurately. This tripartite
method, as well as its recent spatiotemporal extension, were both developed as
an attempt to apply the Price equation in a BEF context. Here, we demonstrate
that the derivation of this tripartite method, as well as its spatiotemporal
extension, involve a set of incoherent and nonsensical mathematical arguments
driven largely by na\"ive visual analogies with the original Price equation,
that result in neither partitioning scheme quantifying any real property in the
natural world. Furthermore, we show that Loreau and Hector's original selection
effect always represented a true analog of the original Price selection term,
making the tripartite partitioning scheme a nonsensical solution to a
non-existent problem [...]


  Pronouns are frequently omitted in pro-drop languages, such as Chinese,
generally leading to significant challenges with respect to the production of
complete translations. To date, very little attention has been paid to the
dropped pronoun (DP) problem within neural machine translation (NMT). In this
work, we propose a novel reconstruction-based approach to alleviating DP
translation problems for NMT models. Firstly, DPs within all source sentences
are automatically annotated with parallel information extracted from the
bilingual training corpus. Next, the annotated source sentence is reconstructed
from hidden representations in the NMT model. With auxiliary training
objectives, in terms of reconstruction scores, the parameters associated with
the NMT model are guided to produce enhanced hidden representations that are
encouraged as much as possible to embed annotated DP information. Experimental
results on both Chinese-English and Japanese-English dialogue translation tasks
show that the proposed approach significantly and consistently improves
translation performance over a strong NMT baseline, which is directly built on
the training data annotated with DPs.


  Scalar-induced Gravitational Waves (SIGWs) represent a particular class of
primordial signals which are sourced at second-order in perturbation theory
whenever a scalar fluctuation of the metric is present. They form a guaranteed
Stochastic Gravitational Wave Background (SGWB) that, depending on the
amplification of primordial scalar fluctuations, can be detected by GW
detectors. The amplitude and the frequency shape of the scalar-induced SGWB can
be influenced by the statistical properties of the scalar density
perturbations. In this work we study the intuitive physics behind SIGWs and we
analyze the imprints of local non-Gaussianity of the primordial curvature
perturbation on the GW spectrum. We consider all the relevant non-Gaussian
contributions up to fifth-order in the scalar seeds without any hierarchy, and
we derive the related GW energy density $\Omega_{\rm GW}(f)$. We perform a
Fisher matrix analysis to understand to which accuracy non-Gaussianity can be
constrained with the LISA detector, which will be sensitive in the milli-Hertz
frequency band. We find that LISA, neglecting the impact of astrophysical
foregrounds, will be able to measure the amplitude, the width and the peak of
the spectrum with an accuracy up to $\mathcal{O}(10^{-4})$, while
non-Gaussianity can be measured up to $\mathcal{O}(10^{-3})$. Finally, we
discuss the implications of our non-Gaussianity expansion on the fraction of
Primordial Black Holes.


  We present the first full demonstration of unambiguous state discrimination
between non-orthogonal quantum states. Using a novel free space interferometer
we have realised the optimum quantum measurement scheme for two non-orthogonal
states of light, known as the Ivanovic-Dieks-Peres (IDP) measurement. We have
for the first time gained access to all three possible outcomes of this
measurement. All aspects of this generalised measurement scheme, including its
superiority over a standard von Neumann measurement, have been demonstrated
within 1.5% of the IDP predictions.


  We consider the motion of ballistic electrons within a superlattice miniband
under the influence of an alternating electric field. We show that the
interaction of electrons with the self-consistent electromagnetic field
generated by the electron current may lead to the transition from regular to
chaotic dynamics. We estimate the conditions for the experimental observation
of this deterministic chaos and discuss the similarities of the superlattice
system with the other condensed matter and quantum optical systems.


  We study the production of spin-one mesons in high-energy heavy-ion
collisions with peripheral kinematics in the framework of QED. The cross
sections of the production of a single vector meson and of two different ones
are presented. The explicit dependence on the virtuality of the intermediate
vector meson is obtained within a quark model. The effect of reggeization of
the intermediate vector meson state in the case of the production of two vector
mesons is taken into account.


  The detection of delayed X-ray, optical and radio emission, "afterglow",
associated with $\gamma$-ray bursts (GRBs) is consistent with fireball models,
where the emission are produced by relativistic expanding blast wave, driven by
expanding fireball at cosmogical distances. The emission mechanisms of GRB
afterglow have been discussed by many authors and synchrotron radiation is
believed to be the main mechanism. The observations show that the optical light
curves of two observed gamma-ray bursts, GRB970228 and GRB GRB970508, can be
described by a simple power law, which seems to support the synchrotron
radiation explanation. However, here we shall show that under some
circumstances, the inverse Compton scattering (ICS) may play an important role
in emission spectrum and this may influence the temporal properties of GRB
afterglow. We expect that the light curves of GRB afterglow may consist of
multi-components, which depends on the fireball parameters.


  In their paper [arXiv:1403.4299v1], Frenkel and Warren claim that the Gibbs
temperature does not characterize thermal equilibrium correctly. We point out
the main logical errors in their argument.


  We focus on the problem of estimating human hand-tremor frequency from input
RGB video data. Estimating tremors from video is important for non-invasive
monitoring, analyzing and diagnosing patients suffering from motor-disorders
such as Parkinson's disease. We consider two approaches for hand-tremor
frequency estimation: (a) a Lagrangian approach where we detect the hand at
every frame in the video, and estimate the tremor frequency along the
trajectory; and (b) an Eulerian approach where we first localize the hand, we
subsequently remove the large motion along the movement trajectory of the hand,
and we use the video information over time encoded as intensity values or phase
information to estimate the tremor frequency.
  We estimate hand tremors on a new human tremor dataset, TIM-Tremor,
containing static tasks as well as a multitude of more dynamic tasks, involving
larger motion of the hands. The dataset has 55 tremor patient recordings
together with: associated ground truth accelerometer data from the most
affected hand, RGB video data, and aligned depth data.


  We revisit the calculation of one-loop corrections to the partition functions
of a string ending on a circular or straight line in type IIB string theory on
$AdS_3\times S^3 \times T^4$ supported by a mixture of 3-form fluxes depending
on a parameter $q$ (with $q=0$ being R-R and $q=1$ pure NS-NS cases).
Correcting earlier results in the literature, we find that the partition
function depends on $q$ only through rescaled tension $T= T_0/(1-q^2)$.


  Decoherence effects associated to the damping of a tunneling two-level system
are shown to dominate the tunneling probability at short times in strong
coupling regimes in the context of a soluble model. A general decomposition of
tunneling rates in dissipative and unitary parts is implemented. Master
equation treatments fail to describe the model system correctly when more than
a single relaxation time is involved.


  The framework of Simulation-to-real learning, i.e, learning policies in
simulation and transferring those policies to the real world is one of the most
promising approaches towards data-efficient learning in robotics. However, due
to the inevitable reality gap between the simulation and the real world, a
policy learned in the simulation may not always generate a safe behaviour on
the real robot. As a result, during adaptation of the policy in the real world,
the robot may damage itself or cause harm to its surroundings. In this work, we
introduce a novel learning algorithm called SafeAPT that leverages a diverse
repertoire of policies evolved in the simulation and transfers the most
promising safe policy to the real robot through episodic interaction. To
achieve this, SafeAPT iteratively learns a probabilistic reward model as well
as a safety model using real-world observations combined with simulated
experiences as priors. Then, it performs Bayesian optimization on the
repertoire with the reward model while maintaining the specified safety
constraint using the safety model. SafeAPT allows a robot to adapt to a wide
range of goals safely with the same repertoire of policies evolved in the
simulation. We compare SafeAPT with several baselines, both in simulated and
real robotic experiments and show that SafeAPT finds high-performance policies
within a few minutes in the real world while minimizing safety violations
during the interactions.


  Parkinson's disease (PD) is a slowly progressive, debilitating
neurodegenerative disease which causes motor symptoms including gait
dysfunction. Motor fluctuations are alterations between periods with a positive
response to levodopa therapy ("on") and periods marked by re-emergency of PD
symptoms ("off") as the response to medication wears off. These fluctuations
often affect gait speed and they increase in their disabling impact as PD
progresses. To improve the effectiveness of current indoor localisation
methods, a transformer-based approach utilising dual modalities which provide
complementary views of movement, Received Signal Strength Indicator (RSSI) and
accelerometer data from wearable devices, is proposed. A sub-objective aims to
evaluate whether indoor localisation, including its in-home gait speed features
(i.e. the time taken to walk between rooms), could be used to evaluate motor
fluctuations by detecting whether the person with PD is taking levodopa
medications or withholding them. To properly evaluate our proposed method, we
use a free-living dataset where the movements and mobility are greatly varied
and unstructured as expected in real-world conditions. 24 participants lived in
pairs (consisting of one person with PD, one control) for five days in a smart
home with various sensors. Our evaluation on the resulting dataset demonstrates
that our proposed network outperforms other methods for indoor localisation.
The sub-objective evaluation shows that precise room-level localisation
predictions, transformed into in-home gait speed features, produce accurate
predictions on whether the PD participant is taking or withholding their
medications.


  Thousands of exoplanets have been discovered and the search for life outside
Earth is at the forefront of astrophysical research. The planets we observe
show a mind-blowing diversity that current theories strive to explain as part
of the quest to assess the chances of finding life outside the Earth.


  The main linacs of the ILC consist of nine-cell cavities based on the TESLA
design. In order to facilitate reaching higher gradients we have re-designed
the cavity shape. This leads to a reduction, comparable to several current
designs, in both the ratio of the surface electric field to the accelerating
field (Es/Ea) and the magnetic field to the accelerating field (Bs/Ea). The
bandwidth of the accelerating mode is also optimized. This new shape, which we
refer to as the New Low Surface Field (NLSF) design, bears comparison with the
Ichiro, Re-entrant and LSF designs.


  In contact-rich tasks, setting the stiffness of the control system is a
critical factor in its performance. Although the setting range can be extended
by making the stiffness matrix asymmetric, its stability has not been proven.
This study focuses on the stability of compliance control in a robot arm that
deals with an asymmetric stiffness matrix. It discusses the convergence
stability of the admittance control. The paper explains how to derive an
asymmetric stiffness matrix and how to incorporate it into the admittance
model. The authors also present simulation and experimental results that
demonstrate the effectiveness of their proposed method.


  The electronic structure of carbon shells of carbon encapsulated iron
nanoparticles carbon encapsulated Fe@C has been studied by X-ray resonant
emission and X-ray absorption spectroscopy. The recorded spectra have been
compared to the density functional calculations of the electronic structure of
graphene. It has been shown that an Fe@C carbon shell can be represented in the
form of several graphene layers with Stone-Wales defects. The dispersion of
energy bands of Fe@C has been examined using the measured C Ka resonant X-ray
emission spectra.


  We fit the most updated broadband spectral energy distribution from radio to
X-rays for NGC 4258 with a coupled accretion-jet model that surrounding a Kerr
black hole (BH), where both the jet and the warped H_2O maser disk are assumed
to be triggered by a spinning BH through Blandford-Znajek mechanism and
Bardeen-Petterson effect respectively. The accretion flow consists with an
inner radiatively inefficient accretion flow (RIAF) and an outer truncated
standard thin disk, where the transition radius R_tr~3*10^3Rg for NGC 4258
based on the width and variability of its narrow Fe K$\alpha$ line. The hybrid
jet formation model, as a variant of Blandford-Znajek model, is used to model
the jet power. Therefore, we can estimate the accretion rate and BH spin
through the two observed quantities--X-ray emission and jet power, where the
observed jet power is estimated from the low-frequency radio emission. Through
this method, we find that the BH of NGC 4258 should be mildly spinning with
dimensionless spin parameter a_*=0.7\pm0.2. The outer thin disk mainly radiates
at near infrared waveband and the jet contributes predominantly at radio
waveband. Using above estimated BH spin and the inferred accretion rate at the
region of the maser disk based on the physical existence of the H_2 O maser, we
find that the warp radius is ~8.6*10^4 R_g if it is driven by the
Bardeen-Petterson effect, which is consistent with the observational result
very well.


  It has been shown that self-assembled chains of active colloidal particles
can present sustained oscillations. These oscillations are possible because of
the effective diffusiophoretic forces that mediate the interactions of colloids
do not respect the action--reaction principle and hence, a Hopf bifurcation is
possible even for overdamped dynamics. Anchoring the particles in one extreme
breaks the head-tail symmetry and the oscillation is transformed into a
traveling wave pattern and thus the chain behaves like a beating cilium. The
net force on the anchor, estimated using the resistive force theory, vanishes
before the bifurcation and thereafter grows linearly with the bifurcation
parameter. If the mobilities of the particles on one extreme are reduced to
mimic an elongated cargo, the traveling wave generates a net velocity on the
chain that now behaves like a moving flagellum. The average velocity again
grows linearly with the bifurcation parameter. Our results demonstrate that
simplified systems, consisting only of a few particles with non-reciprocal
interaction and head-tail asymmetry show beating motion and self-propulsion.
Both properties are present in many non-equilibrium models thus making our
results a general feature of active matter.


  Three-dimensional (3D) gapped topological phases with fractional excitations
are divided into two subclasses: one has topological order with point-like and
loop-like excitations fully mobile in the 3D space, and the other has fracton
order with point-like excitations constrained in lower-dimensional subspaces.
These exotic phases are often studied by exactly solvable Hamiltonians made of
commuting projectors, which, however, are not capable of describing those
exhibiting surface states with gapless chiral dispersion. Here we introduce a
systematic way, based on cellular construction recently proposed for 3D
topological phases, to construct another type of exactly solvable models in
terms of coupled quantum wires with given inputs of cellular structure,
two-dimensional Abelian topological order, and their gapped interfaces. We show
that our models can describe both 3D topological and fracton orders (and even
their hybrid) and study their universal properties such as quasiparticle
statistics and topological ground-state degeneracy. We also apply this
construction to two-dimensional coupled-wire models with ordinary topological
orders and translation-symmetry-enriched topological orders. Our results pave
the way for effective quantum field theory descriptions or microscopic model
realizations of fracton orders with chiral gapless surface states.


  Parental allele-specific expression of imprinted genes is mediated by
imprinting control regions (ICRs) that are constitutively marked by DNA
methylation imprints on the maternal or paternal allele. Mono-allelic DNA
methylation is strictly required for the process of imprinting and has to be
faithfully maintained during the entire lifespan. While the regulation of DNA
methylation itself is well understood, the mechanisms whereby the opposite
allele remains unmethylated are unclear. Here, we show that in the mouse, at
maternally methylated ICRs, the paternal allele, which is constitutively
associated with H3K4me2/3, is marked by default by H3K27me3 when these ICRs are
transcriptionally inactive, leading to the formation of a bivalent chromatin
signature. Our data suggest that at ICRs, chromatin bivalency has a protective
role by ensuring that DNA on the paternal allele remains unmethylated and
protected against spurious and unscheduled gene expression. Moreover , they
provide the proof of concept that, beside pluripotent cells, chromatin
bivalency is the default state of transcriptionally inactive CpG island
promoters , regardless of the developmental stage, thereby contributing to
protect cell identity.


  We solve a technical problem related to adeles on an algebraic surface. Given
a finite set of natural numbers up to two, one associates an adelic group. We
show that this operation commutes with taking intersections if the surface is
defined over an uncountable field and we provide a counterexample otherwise.


  Neutrinos drive core-collapse supernovae, launch outflows from neutron star
merger accretion disks, and set the ratio of protons to neutrons in ejecta from
both systems that generate heavy elements in the universe. Neutrinos of
different flavors interact with matter differently, and much recent work has
suggested that fast flavor instabilities are likely ubiquitous in both systems,
but the final flavor content after the instability saturates has not been well
understood. In this work we present particle-in-cell calculations which follow
the evolution of all flavors of neutrinos and antineutrinos through saturation
and kinematic decoherence. We conduct one-dimensional three-flavor simulations
of neutrino quantum kinetics to demonstrate the outcome of this instability in
a few example cases. We demonstrate the growth of both axially symmetric and
asymmetric modes whose wavelength and growth rate match predictions from linear
stability analysis. Finally, we vary the number density, flux magnitude, and
flux direction of the neutrinos and antineutrinos and demonstrate that these
factors modify both the growth rate and post-saturation neutrino flavor
abundances. Weak electron lepton number (ELN) crossings in these simulations
produce both slow growth of the instability and little difference between the
flavor abundances in the initial and final states. In all of these calculations
the same number of neutrinos and antineutrinos change flavor, making the least
abundant between them the limiting factor for post-saturation flavor change.
Many more simulations and multi-dimensional simulations are needed to fully
probe the parameter space of the initial conditions.


  In this article we consider an open conjecture about coherently labelling a
polyhedron in three dimensions. We exhibit all the forty eight possible
coherent labellings of a tetrahedron. We also exhibit that some simplicial
polyhedra like bipyramids, Kleetopes, gyroelongated bipyramids are coherently
labellable. Also we prove that pyramids over $n$-gons for $n\geq 4$, which are
not simplicial polyhedra, are coherently labellable. We prove that among
platonic solids, the cube and the dodecahedron are not coherently labellable,
even though, the tetrahedron, the octahedron and the icosahedron are coherently
labellable. Unlike the case of a tetrahedron, in general for a polyhedron, we
show that a coherent labelling need not induce a coherent labelling at a
vertex. We prove the main conjecture in the affirmative for a certain class of
polyhedra which are constructible from tetrahedra through certain types of edge
and face vanishing tetrahedron attachments. As a consequence we conclude that a
cube cannot be obtained from only these type of tetrahedron attachments. We
also give an obstruction criterion for a polyhedron to be not coherently
labellable and consequentially show that any polyhedron obtained from a pyramid
with its apex chopped off is not coherently labellable. Finally with the
suggestion of the affirmative results we prove the main theorem that any
simplicial polyhedron is coherently labellable.


  In this paper we focus our attention on a particle that follows a
unidirectional quantum walk, an alternative version of the nowadays widespread
discrete-time quantum walk on a line. Here the walker at each time step can
either remain in place or move in a fixed direction, e.g., rightward or upward.
While both formulations are essentially equivalent, the present approach leads
to consider Discrete Fourier Transforms, which eventually results in obtaining
explicit expressions for the wave functions in terms of finite sums, and allows
the use of efficient algorithms based on the Fast Fourier Transform. The wave
functions here obtained govern the probability of finding the particle at any
given location, but determine as well the exit-time probability of the walker
from a fixed interval, which is also analyzed.


  In this paper, we study the zero-error capacity of channels with memory,
which are represented by graphs. We provide a method to construct code for any
graph with one edge, thereby determining a lower bound on its zero-error
capacity. Moreover, this code can achieve zero-error capacity when the symbols
in a vertex with degree one are the same. We further apply our method to the
one-edge graphs representing the binary channels with two memories. There are
28 possible graphs, which can be organized into 11 categories based on their
symmetries. The code constructed by our method is proved to achieve the
zero-error capacity for all these graphs except for the two graphs in Case 11.


  Recent developments in QCD phenomenology have spurred on several improved
approaches to Monte Carlo event generation, relative to the post--LEP state of
the art. In this brief review, the emphasis is placed on approaches for 1)
consistently merging fixed--order matrix element calculations with parton
showers, 2) improving the parton shower algorithms themselves, and 3) improving
the description of the underlying event in hadron collisions.


  We compute completely the BRST--antibracket cohomology on local functionals
in two-dimensional Weyl invariant gravity for given classical field content
(two dimensional metric and scalar matter fields) and gauge symmetries (two
dimensional diffeomorphisms and local Weyl transformations). This covers the
determination of all classical actions, of all their rigid symmetries, of all
background charges and of all candidate gauge anomalies. In particular we show
that the antifield dependence can be entirely removed from the anomalies and
that, if the target space has isometries, the condition for the absence of
matter field dependent Weyl anomalies is more general than the familiar
`dilaton equations'.


  This paper develops a new communication strategy, ergodic interference
alignment, for the K-user interference channel with time-varying fading. At any
particular time, each receiver will see a superposition of the transmitted
signals plus noise. The standard approach to such a scenario results in each
transmitter-receiver pair achieving a rate proportional to 1/K its
interference-free ergodic capacity. However, given two well-chosen time
indices, the channel coefficients from interfering users can be made to exactly
cancel. By adding up these two observations, each receiver can obtain its
desired signal without any interference. If the channel gains have independent,
uniform phases, this technique allows each user to achieve at least 1/2 its
interference-free ergodic capacity at any signal-to-noise ratio. Prior
interference alignment techniques were only able to attain this performance as
the signal-to-noise ratio tended to infinity. Extensions are given for the case
where each receiver wants a message from more than one transmitter as well as
the "X channel" case (with two receivers) where each transmitter has an
independent message for each receiver. Finally, it is shown how to generalize
this strategy beyond Gaussian channel models. For a class of finite field
interference channels, this approach yields the ergodic capacity region.


  This paper introduces a local-to-unity/small sigma process for a stationary
time series with strong persistence and non-negligible long run risk. This
process represents the stationary long run component in an unobserved short-
and long-run components model involving different time scales. More
specifically, the short run component evolves in the calendar time and the long
run component evolves in an ultra long time scale. We develop the methods of
estimation and long run prediction for the univariate and multivariate
Structural VAR (SVAR) models with unobserved components and reveal the
impossibility to consistently estimate some of the long run parameters. The
approach is illustrated by a Monte-Carlo study and an application to
macroeconomic data.


  Few-shot node classification is tasked to provide accurate predictions for
nodes from novel classes with only few representative labeled nodes. This
problem has drawn tremendous attention for its projection to prevailing
real-world applications, such as product categorization for newly added
commodity categories on an E-commerce platform with scarce records or diagnoses
for rare diseases on a patient similarity graph. To tackle such challenging
label scarcity issues in the non-Euclidean graph domain, meta-learning has
become a successful and predominant paradigm. More recently, inspired by the
development of graph self-supervised learning, transferring pretrained node
embeddings for few-shot node classification could be a promising alternative to
meta-learning but remains unexposed. In this work, we empirically demonstrate
the potential of an alternative framework, \textit{Transductive Linear
Probing}, that transfers pretrained node embeddings, which are learned from
graph contrastive learning methods. We further extend the setting of few-shot
node classification from standard fully supervised to a more realistic
self-supervised setting, where meta-learning methods cannot be easily deployed
due to the shortage of supervision from training classes. Surprisingly, even
without any ground-truth labels, transductive linear probing with
self-supervised graph contrastive pretraining can outperform the
state-of-the-art fully supervised meta-learning based methods under the same
protocol. We hope this work can shed new light on few-shot node classification
problems and foster future research on learning from scarcely labeled instances
on graphs.


  The white-rot fungus, Physisporinus vitreus, degrades the membranes of
bordered pits in tracheids and consequently increases the permeability of wood,
which is a process that can be used by the wood industry to improve the uptake
of wood preservatives and environmentally benign wood modification substances
to enhance the use and sustainability of native conifer wood species. To
understand and apply this process requires an understanding of how a complex
system (fungus-wood) interacts under defined conditions. We present a
three-dimensional fungal growth model (FGM) of the hyphal growth of P. vitreus
in the heartwood of Norway spruce. The model considers hyphae and nutrients as
discrete structures and links the microscopic interactions between fungus and
wood (e.g. degradation rate and degree of opening of pits) with macroscopic
system properties, such penetration depth of the fungus, biomass and
distribution of destroyed pits in early- and latewood. Simulations were
compared with experimental data. The growth of P. vitreus is characterized by a
stepwise capture of the substrate and the effect of this on wood according to
different model parameters is discussed.


  In this article, we study zigzag graphene nanoribbons with edges
reconstructed with Stone-Wales defects, by means of an empirical
(first-neighbor) tight-binding method, with parameters determined by ab-initio
calculations of very narrow ribbons. We explore the characteristics of the
electronic band structure with a focus on the nature of edge states. Edge
reconstruction allows the appearance of a new type of edge states. They are
dispersive, with non-zero amplitudes in both sub-lattices; furthermore, the
amplitudes have two components that decrease with different decay lengths with
the distance from the edge; at the Dirac points one of these lengths diverges,
whereas the other remains finite, of the order of the lattice parameter. We
trace this curious effect to the doubling of the unit cell along the edge,
brought about by the edge reconstruction. In the presence of a magnetic field,
the zero-energy Landau level is no longer degenerate with edge states as in the
case of pristine zigzag ribbon.


  We present mathematical models, computational algorithms and software, which
can be used for prediction of results of prosthetic treatment. More interest
issue is biomechanics of the periodontal complex because any prosthesis is
accompanied by a risk of overloading the supporting elements. Such risk can be
avoided by the proper load distribution and prediction of stresses that occur
during the use of dentures. We developed the mathematical model of the
periodontal complex and its software implementation. This model is based on
linear elasticity theory and allows to calculate the stress and strain fields
in periodontal ligament and jawbone. The input parameters for the developed
model can be divided into two groups. The first group of parameters describes
the mechanical properties of periodontal ligament, teeth and jawbone (for
example, elasticity of periodontal ligament etc.). The second group
characterized the geometric properties of objects: the size of the teeth, their
spatial coordinates, the size of periodontal ligament etc. The mechanical
properties are the same for almost all, but the input of geometrical data is
complicated because of their individual characteristics. In this connection, we
develop algorithms and software for processing of images obtained by computed
tomography (CT) scanner and for constructing individual digital model of the
tooth-periodontal ligament-jawbone system of the patient. Integration of models
and algorithms described allows to carry out biomechanical analysis on
three-dimensional digital model and to select prosthesis design.


  Explicit decomposition modeling, which involves breaking down complex tasks
into more straightforward and often more interpretable sub-tasks, has long been
a central theme in developing robust and interpretable NLU systems. However,
despite the many datasets and resources built as part of this effort, the
majority have small-scale annotations and limited scope, which is insufficient
to solve general decomposition tasks. In this paper, we look at large-scale
intermediate pre-training of decomposition-based transformers using distant
supervision from comparable texts, particularly large-scale parallel news. We
show that with such intermediate pre-training, developing robust
decomposition-based models for a diverse range of tasks becomes more feasible.
For example, on semantic parsing, our model, DecompT5, improves 20% to 30% on
two datasets, Overnight and TORQUE, over the baseline language model. We
further use DecompT5 to build a novel decomposition-based QA system named
DecompEntail, improving over state-of-the-art models, including GPT-3, on both
HotpotQA and StrategyQA by 8% and 4%, respectively.


  An ab-initio calculation of the 4He(e,e') inelastic longitudinal response
function R_L is presented. Realistic two- and three-body forces are used. The
four-body continuum dynamics is treated rigorously with the help of the Lorentz
integral transform. The three-nucleon force reduces the quasi-elastic peak
height by about 10% for momentum transfers q between 300 and 500 MeV/c.
Experimental data are well described, but not sufficiently precise to resolve
this effect. The reduction due to the three-nucleon force increases
significantly at lower q reaching up to about 40% at q=100 MeV/c. However, at
such q values data are missing.


  We address challenges of active learning under scarce informational resources
in non-stationary environments. In real-world settings, data labeled and
integrated into a predictive model may become invalid over time. However, the
data can become informative again with switches in context and such changes may
indicate unmodeled cyclic or other temporal dynamics. We explore principles for
discarding, caching, and recalling labeled data points in active learning based
on computations of value of information. We review key concepts and study the
value of the methods via investigations of predictive performance and costs of
acquiring data for simulated and real-world data sets.


  We propose, implement, and evaluate a method to estimate the daily number of
new symptomatic COVID-19 infections, at the level of individual U.S. counties,
by deconvolving daily reported COVID-19 case counts using an estimated
symptom-onset-to-case-report delay distribution. Importantly, we focus on
estimating infections in real-time (rather than retrospectively), which poses
numerous challenges. To address these, we develop new methodology for both the
distribution estimation and deconvolution steps, and we employ a sensor fusion
layer (which fuses together predictions from models that are trained to track
infections based on auxiliary surveillance streams) in order to improve
accuracy and stability.


  We obtain a complete description of closed ideals of the algebra
$\mathcal{D}\cap \mathrm{lip}_\alpha},$ $0<\alpha\leq{1/2},$ where
$\mathcal{D}$ is the Dirichlet space and $\mathrm{lip}_\alpha}$ is the algebra
of analytic functions satisfying the Lipschitz condition of order $\alpha.$


  We perform an optimal-observable analysis of the final charged-lepton/b-quark
momentum distributions in gamma+gamma -> t+tbar -> lX/bX for various beam
polarizations in order to study possible anomalous t-tbar-gamma, tbW and
gamma-gamma-H couplings, which could be generated by SU(2)xU(1) gauge-invariant
dimension-6 effective operators. We find optimal beam polarizations that will
minimize the uncertainty in determination of those non-standard couplings. We
also compare e+ebar and gamma+gamma colliders from the viewpoint of the
anomalous-top-quark-coupling determination.


  Qualitative probabilistic networks have been introduced as qualitative
abstractions of Bayesian belief networks. One of the major drawbacks of these
qualitative networks is their coarse level of detail, which may lead to
unresolved trade-offs during inference. We present an enhanced formalism for
qualitative networks with a finer level of detail. An enhanced qualitative
probabilistic network differs from a regular qualitative network in that it
distinguishes between strong and weak influences. Enhanced qualitative
probabilistic networks are purely qualitative in nature, as regular qualitative
networks are, yet allow for efficiently resolving trade-offs during inference.


  To detect brown dwarfs in the dark galactic halo through gravitational
lensing, experiments follow the luminosity of millions of stars to observe a
few lensing events par year. The luminosity of a star too faint to be
continuously followed can be temporarily increased above the detection limit by
a lensing. The detection of these invisible stars would increase the number of
events by a factor 2 to 7, and moreover their presence would confirm the
lensing interpretation of events due to continuously monitored stars.


  PSR B1259-63/LS 2883 is a very high energy (VHE; E > 100 GeV) gamma-ray
emitting binary consisting of a 48 ms pulsar orbiting around a Be star with a
period of 3.4 years. The Be star features a circumstellar disk which is
inclined with respect to the orbit in such a way that the pulsar crosses it
twice every orbit. The circumstellar disk provides an additional field of
target photons which may contribute to inverse Compton scattering and
gamma-gamma absorption, leaving a characteristic imprint in the observed
spectrum and light curve of the high energy emission. We study the signatures
of Compton-supported, VHE gamma-ray induced pair cascades in the circumstellar
disc of the Be star and their possible contribution to the GeV flux. We also
study a possible impact of the gamma-gamma absorption in the disk on the
observed TeV light curve. We show that the cumulative absorption of VHE
gamma-rays in stellar and disk photon fields can explain the modulation of the
flux at the periastron passage.


  A wide variety of methods have been developed to enable lifelong learning in
conventional deep neural networks. However, to succeed, these methods require a
`batch' of samples to be available and visited multiple times during training.
While this works well in a static setting, these methods continue to suffer in
a more realistic situation where data arrives in \emph{online streaming
manner}. We empirically demonstrate that the performance of current approaches
degrades if the input is obtained as a stream of data with the following
restrictions: $(i)$ each instance comes one at a time and can be seen only
once, and $(ii)$ the input data violates the i.i.d assumption, i.e., there can
be a class-based correlation. We propose a novel approach (CIOSL) for the
class-incremental learning in an \emph{online streaming setting} to address
these challenges. The proposed approach leverages implicit and explicit dual
weight regularization and experience replay. The implicit regularization is
leveraged via the knowledge distillation, while the explicit regularization
incorporates a novel approach for parameter regularization by learning the
joint distribution of the buffer replay and the current sample. Also, we
propose an efficient online memory replay and replacement buffer strategy that
significantly boosts the model's performance. Extensive experiments and
ablation on challenging datasets show the efficacy of the proposed method.


  Differentially Private Stochastic Gradient Descent (DP-SGD) and its variants
have been proposed to ensure rigorous privacy for fine-tuning large-scale
pre-trained language models. However, they rely heavily on the Gaussian
mechanism, which may overly perturb the gradients and degrade the accuracy,
especially in stronger privacy regimes (e.g., the privacy budget $\epsilon <
3$). To address such limitations, we propose a novel Language Model-based
Optimal Differential Privacy (LMO-DP) mechanism, which takes the first step to
enable the tight composition of accurately fine-tuning (large) language models
with a sub-optimal DP mechanism, even in strong privacy regimes (e.g., $0.1\leq
\epsilon<3$). Furthermore, we propose a novel offline optimal noise search
method to efficiently derive the sub-optimal DP that significantly reduces the
noise magnitude. For instance, fine-tuning RoBERTa-large (with 300M parameters)
on the SST-2 dataset can achieve an accuracy of 92.20% (given $\epsilon=0.3$,
$\delta=10^{-10}$) by drastically outperforming the Gaussian mechanism (e.g.,
$\sim 50\%$ for small $\epsilon$ and $\delta$). We also draw similar findings
on the text generation tasks on GPT-2. Finally, to our best knowledge, LMO-DP
is also the first solution to accurately fine-tune Llama-2 with strong
differential privacy guarantees. The code will be released soon and available
upon request.


  Recently, a type of multi-resolution methods in community detection was
introduced, which can adjust the resolution of modularity by modifying the
modularity function with tunable resolution parameters, such as those proposed
by Arenas, Fernandez and Gomez and by Reichardt and Bornholdt. In this paper,
we show that these methods still have the intrinsic limitation-large
communities may have been split before small communities become visible-because
it is at the cost of the community stability that the enhancement of the
modularity resolution is obtained. The theoretical results indicated that the
limitation depends on the degree of interconnectedness of small communities and
the difference between the sizes of small communities and of large communities,
while independent of the size of the whole network. These findings have been
confirmed in several example networks, where communities even are
full-completed sub-graphs.


  We consider a two-dimensional homogeneous ensemble of cold bosonic atoms
loaded inside two optical cavities and pumped by a far-detuned external laser
field. We examine the conditions for these atoms to self-organize into
triangular and honeycomb lattices as a result of superradiance. By collectively
scattering the pump photons, the atoms feed the initially empty cavity modes.
As a result, the superposition of the pump and cavity fields creates a
space-periodic light-shift external potential and atoms self-organize into the
potential wells of this optical lattice. Depending on the phase of the cavity
fields with respect to the pump laser, these minima can either form a
triangular or a hexagonal lattice. By numerically solving the dynamical
equations of the coupled atom-cavity system, we have shown that the two stable
atomic structures at long times are the triangular lattice and the honeycomb
lattice with equally-populated sites. We have also studied how to drive atoms
from one lattice structure to another by dynamically changing the phase of the
cavity fields with respect to the pump laser.


  Solid-state elastic-wave phonons are a promising platform for a wide range of
quantum information applications. An outstanding challenge and enabling
capability in harnessing phonons for quantum information processing is
achieving strong nonlinear interactions between them. To this end, we propose a
general architecture using piezoelectric-semiconductor heterostructures
consisting of a piezoelectric acoustic material hosting phonon modes in direct
proximity to a two-dimensional electron gas (2DEG). Each phonon in the
piezoelectric material carries an electric field, which extends into the 2DEG.
The fields induce polarization of 2DEG electrons, which in turn interact with
other piezoelectric phononic electric fields. The net result is coupling
between the various phonon modes. We derive, from first principles, the
nonlinear phononic susceptibility of the system. We show that many nonlinear
processes are strongly favored at high electron mobility, motivating the use of
the 2DEG to mediate the nonlinearities. We derive in detail the first, second,
and third-order susceptibilities and calculate them for the case of a lithium
niobate surface acoustic wave interacting with a GaAs-AlGaAs heterostructure
2DEG. We show that, for this system, the strong third-order nonlinearity could
enable single-phonon Kerr shift in an acoustic cavity that exceeds realistic
cavity linewidths, potentially leading to a new class of acoustic qubit. We
further show that the strong second-order nonlinearity could be used to produce
a high-gain, traveling-wave parametric amplifier to amplify--and ultimately
detect--the outputs of the acoustic cavity qubits. Assuming favorable losses in
such a system, these capabilities, combined with the ability to efficiently
transduce phonons from microwave electromagnetic fields in transmission lines,
thus hold promise for creating all-acoustic quantum information processors.


  We derive source integrals for multipole moments that describe the behavior
of static and axially symmetric spacetimes close to spatial infinity. We assume
that the matter distribution is isolated. We outline also some applications of
these source integrals of the asymptotic multipole moments.


  Machine learning and computer vision techniques have grown rapidly in recent
years due to their automation, suitability, and ability to generate astounding
results. Hence, in this paper, we survey the key studies that are published
between 2014 and 2022, showcasing the different machine learning algorithms
researchers have used to segment the liver, hepatic tumors, and
hepatic-vasculature structures. We divide the surveyed studies based on the
tissue of interest (hepatic-parenchyma, hepatic-tumors, or hepatic-vessels),
highlighting the studies that tackle more than one task simultaneously.
Additionally, the machine learning algorithms are classified as either
supervised or unsupervised, and they are further partitioned if the amount of
work that falls under a certain scheme is significant. Moreover, different
datasets and challenges found in literature and websites containing masks of
the aforementioned tissues are thoroughly discussed, highlighting the
organizers' original contributions and those of other researchers. Also, the
metrics used excessively in literature are mentioned in our review, stressing
their relevance to the task at hand. Finally, critical challenges and future
directions are emphasized for innovative researchers to tackle, exposing gaps
that need addressing, such as the scarcity of many studies on the vessels'
segmentation challenge and why their absence needs to be dealt with sooner than
later.


  The main goal of this paper is to investigate one of the important
astrophysical systems, namely Thick accretion disks, in the background of the
spherically symmetric solution in Born-Infeld teleparallel gravity to examine
observable predictions of the theory in the vicinity of black holes. Thus, the
properties of the non-self-gravitating equilibrium surfaces characterising the
Thick accretion disks model are studied. In addition, we find an observational
bound on the parameter of the model as $\lambda\gtrsim 140$. We show this
analytical accretion disk model for different values of $\lambda$ and compare
the result with the corresponding Schwarzschild solution in the general theory
of relativity.


  In the paper `Automorphic functions for a Whitehead-complement group', [Osaka
J Math 43 (2006) 63-77] Matsumoto, Nishi and Yoshida constructed automorphic
functions on real 3-dimensional hyperbolic space for a Kleinian group called
the Whitehead-link-complement group. For a Kleinian group (of the first kind),
no automorphic function/form has been studied before. In this note, their
motivation is presented with a historical background.


  The Generalized Uncertainty Principle (GUP) has emerged in numerous attempts
to a theory of quantum gravity and predicts the existence of a minimum length
in Nature. In this work, we consider two cosmological models arising from
Friedmann equations modified by the GUP (in its linear and quadratic
formulations) and compare them with observational data. Our aim is to derive
constraints on the GUP parameter and discuss the viability and physical
implications of such models. We find for the parameter in the quadratic
formulation the constraint $\alpha^{2}_{Q}<10^{59}$ (tighter than most of those
obtained in an astrophysical context) while the linear formulation does not
appear compatible with present cosmological data. Our analysis highlights the
powerful role of high-precision cosmological probes in the realm of quantum
gravity phenomenology.


  We study the time dependent transitions of quantum forced harmonic oscillator
(QFHO) in noncommutative $\mathds{R}^{1,1}$ perturbatively to linear order in
the noncommutativity $\theta$. We show that the Poisson distribution gets
modified, and that the vacuum state evolves into a "squeezed" state rather than
a coherent state. The time evolutions of uncertainties in position and momentum
in vacuum are also studied and imply interesting consequences for modeling
nonlinear phenomena in quantum optics.


  We define and construct a quantum Grothendieck ring for a certain monoidal
subcategory of the category $\mathcal{O}$ of representations of the quantum
loop algebra introduced by Hernandez-Jimbo. We use the cluster algebra
structure of the Grothendieck ring of this category to define the quantum
Grothendieck ring as a quantum cluster algebra. When the underlying simple Lie
algebra is of type $A$, we prove that this quantum Grothendieck ring contains
the quantum Grothendieck ring of the category of finite-dimensional
representations of the associated quantum affine algebra. In type $A_1$, we
identify remarkable relations in this quantum Grothendieck ring.


  Colossal negative magnetoresistance \Delta \rho (T,B) observed in
La(0.6)Y(0.1)Ca(0.3)MnO(3) at B=1T shows a nearly perfect symmetry around
T_0=160K suggesting a universal field-induced transport mechanism in this
material. Attributing this symmetry to strong magnetic fluctuations (triggered
by the Y substitution and further enhanced by magnetic field, both above and
below the field-dependent Curie temperature T_C(B)=T_0), the data are
interpreted in terms of the nonthermal spin hopping and magnetization M
dependent charge carrier localization scenario leading to \Delta \rho (T,B)=
-\rho_s(1-exp(-\gamma M^2)) with M(T,B)=CB/|T-T_C|^n. The separate fits through
all the data points above and below T_C yield C^{+}\simeq C^{-} and n^{+}\simeq
n^{-}\simeq 1. The obtained results corroborate the importance of fluctuation
effects in this material recently found (cond-mat/9812219) to dominate its
magneto-thermopower behavior far beyond T_C.


  It is well-known that the Sobolev spaces $W^{k,p}(\mathbb R^d)$ are vector
lattices with respect to the pointwise almost everywhere order if $k \in
\{0,1\}$, but not if $k \ge 2$. In this note, we consider negative $k$ and show
that the span of the positive cone in $W^{k,p}(\mathbb R^d)$ is a vector
lattice in this case.
  We also prove a related abstract result: if $(T(t))_{t \in [0,\infty)}$ is a
positive $C_0$-semigroup on a Banach lattice $X$ with order continuous norm,
then the span of the cone $X_{-1,+}$ in the extrapolation space $X_{-1}$ is a
vector lattice. This complements results obtained by B\'atkai, Jacob,
Wintermayr, and Voigt in the context of perturbation theory and provides
additional context for the theory of infinite-dimensional positive systems.


  Although deep neural network (DNN)-based speech enhancement (SE) methods
outperform the previous non-DNN-based ones, they often degrade the perceptual
quality of generated outputs. To tackle this problem, we introduce a DNN-based
generative refiner, Diffiner, aiming to improve perceptual speech quality
pre-processed by an SE method. We train a diffusion-based generative model by
utilizing a dataset consisting of clean speech only. Then, our refiner
effectively mixes clean parts newly generated via denoising diffusion
restoration into the degraded and distorted parts caused by a preceding SE
method, resulting in refined speech. Once our refiner is trained on a set of
clean speech, it can be applied to various SE methods without additional
training specialized for each SE module. Therefore, our refiner can be a
versatile post-processing module w.r.t. SE methods and has high potential in
terms of modularity. Experimental results show that our method improved
perceptual speech quality regardless of the preceding SE methods used.


  In this article, we propose algorithms to address two critical transportation
system problems: the Generalized Real-Time Line Planning Problem (GRLPP) and
the Generalized Budgeted Multi-Visit Team Orienteering Problem (GBMTOP). The
GRLPP aims to optimize high-capacity line plans for multimodal transportation
networks to enhance connectivity between passengers and lines. The GBMTOP
focuses on finding optimal routes for a team of heterogeneous vehicles within
budget constraints to maximize the reward collected. We present two randomized
approximation algorithms for the generalized budgeted multi-assignment problem
(GBMAP), which arises when items need to be assigned to bins subject to
capacity constraints, budget constraints, and other feasibility constraints.
Each item can be assigned to at most a specified number of bins, and the goal
is to maximize the total reward. GBMAP serves as the foundation for solving
GRLPP and GBMTOP. In addition to these two algorithms, our contributions
include the application of our framework to GRLPP and GBMTOP, along with
corresponding models, numerical experiments, and improvements on prior work.


  A large body of previous machine learning methods for ultrasound-based
prostate cancer detection classify small regions of interest (ROIs) of
ultrasound signals that lie within a larger needle trace corresponding to a
prostate tissue biopsy (called biopsy core). These ROI-scale models suffer from
weak labeling as histopathology results available for biopsy cores only
approximate the distribution of cancer in the ROIs. ROI-scale models do not
take advantage of contextual information that are normally considered by
pathologists, i.e. they do not consider information about surrounding tissue
and larger-scale trends when identifying cancer. We aim to improve cancer
detection by taking a multi-scale, i.e. ROI-scale and biopsy core-scale,
approach. Methods: Our multi-scale approach combines (i) an "ROI-scale" model
trained using self-supervised learning to extract features from small ROIs and
(ii) a "core-scale" transformer model that processes a collection of extracted
features from multiple ROIs in the needle trace region to predict the tissue
type of the corresponding core. Attention maps, as a byproduct, allow us to
localize cancer at the ROI scale. We analyze this method using a dataset of
micro-ultrasound acquired from 578 patients who underwent prostate biopsy, and
compare our model to baseline models and other large-scale studies in the
literature. Results and Conclusions: Our model shows consistent and substantial
performance improvements compared to ROI-scale-only models. It achieves 80.3%
AUROC, a statistically significant improvement over ROI-scale classification.
We also compare our method to large studies on prostate cancer detection, using
other imaging modalities. Our code is publicly available at
www.github.com/med-i-lab/TRUSFormer


  While the relationship of time and space is an established topic in
traditional centralised complexity theory, this is not the case in distributed
computing. We aim to remedy this by studying the time and space complexity of
algorithms in a weak message-passing model of distributed computing. While a
constant number of communication rounds implies a constant number of states
visited during the execution, the other direction is not clear at all. We
consider several graph families and show that indeed, there exist non-trivial
graph problems that are solvable by constant-space algorithms but that require
a non-constant running time. This provides us with a new complexity class for
distributed computing and raises interesting questions about the existence of
further combinations of time and space complexity.


  The transfer learning of a neural network is one of its most outstanding
aspects and has given supervised learning with neural networks a prominent
place in data science. Here we explore this feature in the context of strongly
interacting many-body systems. Through case studies, we test the potential of
this deep learning technique to detect phases and their transitions in
frustrated spin systems, using fully-connected and convolutional neural
networks. In addition, we explore a recently-introduced technique, which is at
the middle point of supervised and unsupervised learning. It consists in
evaluating the performance of a neural network that has been deliberately
"confused" during its training. To properly demonstrate the capability of the
"confusion" and transfer learning techniques, we apply them to a paradigmatic
model of frustrated magnetism in two dimensions, to determine its phase diagram
and compare it with high-performance Monte Carlo simulations.


  A collection of $N$-diffusing interacting particles where each particle
belongs to one of $K$ different populations is considered. Evolution equation
for a particle from population $k$ depends on the $K$ empirical measures of
particle states corresponding to the various populations and the form of this
dependence may change from one population to another. In addition, the drift
coefficients in the particle evolution equations may depend on a factor that is
common to all particles and which is described through the solution of a
stochastic differential equation coupled, through the empirical measures, with
the $N$-particle dynamics. We are interested in the asymptotic behavior as
$N\to \infty$. Although the full system is not exchangeable, particles in the
same population have an exchangeable distribution. Using this structure, one
can prove using standard techniques a law of large numbers result and a
propagation of chaos property. In the current work we study fluctuations about
the law of large number limit. For the case where the common factor is absent
the limit is given in terms of a Gaussian field whereas in the presence of a
common factor it is characterized through a mixture of Gaussian distributions.
We also obtain, as a corollary, new fluctuation results for disjoint
sub-families of single type particle systems, i.e. when $K=1$. Finally, we
establish limit theorems for multi-type statistics of such weakly interacting
particles, given in terms of multiple Wiener integrals.


  A dimer model is a quiver with faces embedded into a disk. A consistent dimer
model gives rise to a strand diagram, and hence to a positroid. The
Gorenstein-projective module category over the completed boundary algebra of a
dimer model was shown by Pressland to categorify a cluster structure on the
corresponding positroid variety. Outside of the Grassmannian case, boundary
algebras of dimer models are not well understood. We give an explicit
description of the boundary algebra of a consistent dimer model as a quiver
with relations calculated only from the data of the decorated permutation or,
equivalently, Grassmann necklace of its positroid.


  We discuss a general theory of Lorentzian Kac--Moody algebras which should be
a hyperbolic analogy of the classical theories of finite-dimensional
semi-simple and affine Kac-Moody algebras. First examples of Lorentzian
Kac-Moody algebras were found by Borcherds. We consider general finiteness
results about the set of Lorentzian Kac--Moody algebras and the problem of
their classification. As an example, we give classification of Lorentzian
Kac--Moody algebras of the rank three with the symmetry group which is an
extended paramodular group. Perhaps, this is the first example when a large
class of Lorentzian Kac--Moody algebras was classified. This paper is closely
related with our papers math.AG/9810001, math.AG/0010329


  We propose a new scalable algorithm for holistic linear regression building
on Bertsimas & King (2016). Specifically, we develop new theory to model
significance and multicollinearity as lazy constraints rather than checking the
conditions iteratively. The resulting algorithm scales with the number of
samples $n$ in the 10,000s, compared to the low 100s in the previous framework.
Computational results on real and synthetic datasets show it greatly improves
from previous algorithms in accuracy, false detection rate, computational time
and scalability.


  Let $(X,B)$ be a pair, and let $f \colon X \rightarrow S$ be a contraction
with $-(K_X + B)$ nef over $S$. A conjecture, known as the Shokurov-Koll\'{a}r
connectedness principle, predicts that $f^{-1} (s) \cap \mathrm{Nklt}(X,B)$ has
at most two connected components, where $s \in S$ is an arbitrary schematic
point and $\mathrm{Nklt}(X,B)$ denotes the non-klt locus of $(X,B)$. In this
work, we prove this conjecture, characterizing those cases in which
$\mathrm{Nklt}(X,B)$ fails to be connected, and we extend these same results
also to the category of generalized pairs. Finally, we apply these results and
the techniques to the study of the dual complex for generalized log Calabi-Yau
pairs, generalizing results of Koll\'{a}r-Xu and Nakamura.


  We report results from ultrafast two-color optical pump-probe spectroscopy on
bulk $\beta$-Ga$_2$O$_3$. A two-photon absorption scheme is used to photoexcite
carriers with the pump pulse and free-carrier absorption of the probe pulse is
used to record the subsequent dynamics of the photoexcited carriers. Our
results are consistent with carrier recombination via defect-assisted
processes. We also observe transient polarization-selective optical absorption
of the probe pulse by defect states under nonequilibrium conditions. A rate
equation model for electron and hole capture by defects is proposed and used to
explain the data. Whereas the rate constants for electron capture by defects
are found to be temperature-independent, they are measured to be strongly
temperature-dependent for hole capture and point to a lattice
deformation/relaxation process accompanying hole capture. Our results shed
light on the mechanisms and rates associated with carrier capture by defects in
$\beta$-Ga$_2$O$_3$.


  A code is said to be two-weight if the non-zero codewords have only two
different a weight w1 and w2. Two-weight codes are closely related to strongly
regular graphs. In this paper. It is shown that a consta-cyclic code of
composite length can be put in the quasi-twisted form. Based on this
transformation, a new construction method of quasi-twisted (QT) two-weight
codes is presented. A large amount of QT two-weight codes are found, and some
new codes are also constructed.


  We analyzed radio and X-ray observations of GRS 1915+105, between May 1995
and June 2006, focusing on the times characterized by radio flares and cycles
of hard dips-soft spikes in the X-ray lightcurve. Assuming these flares to be
discrete ejections, we applied a plasmon model to the radio data, with good
agreement with the lightcurves. We fitted a total of 687 radio flares with a
standard model of a plasmon. We found that the distribution of width is
t_0=1160 s with an rms deviation of 360 s, while that of the amplitude is
S_{max}=59 mJy with an rms deviation of 28 mJy. The distribution of width is
thus rather peaked, while that of the amplitude not.
  Regarding radio and X-ray links, this study confirms previous observations on
smaller datasets, namely that X-ray cycles of hard dips-soft spikes are always
followed by radio flares. A strong correlation is found between the length of
X-ray "dips" in the X-ray lightcurves, and the amplitude and fluence of the
subsequent radio oscillations. A model of an exponential rise of the form L_{15
GHz}(Delta t) = L_{max} (1-exp(-(Delta t - Delta t_{min})/tau) is in good
agreement with the observations, with the maximum fluence L_{max} of the order
70 Jy.s, and the characteristic time tau of the order 200-500 s. We discuss
possible physical interpretations of this correlation, regarding the nature of
the ejected material, and the physical process responsible for the ejection.


  We consider a general monotone regression estimation where we allow for
independent and dependent regressors. We propose a modification of the
classical isotonic least squares estimator and establish its rate of
convergence for the integrated $L_1$-loss function. The methodology captures
the shape of the data without assuming additivity or a parametric form for the
regression function. Furthermore, the degree of smoothing is chosen
automatically and no auxiliary tuning is required for the theoretical analysis.
Some simulations and two real data illustrations complement the study of the
proposed estimator.


  We report on the analysis of archival ASCA, ROSAT and BeppoSAX data of PSR
B1055-52, PSR B0656+14 and Geminga, performed in order to investigate the
reality of the putative ~10-20 arcmin wide X-ray pulsar-wind nebulae recently
proposed to exist around these pulsars.
  In all these cases, the ROSAT and/or BeppoSAX data show that the diffuse and
clumpy X-ray nebulae found by ASCA can be resolved in the contribution of
unidentified point sources, unlikely related to the pulsars.


  We discuss a framework for constructing large subsets of $\mathbb{R}^n$ and
$K^n$ for non-archimedean local fields $K$. This framework is applied to obtain
new estimates for the Hausdorff dimension of angle-avoiding sets and to provide
a counterexample to a limiting version of the Capset problem.


  The confinement scenario in N=2 supersymmetric gauge theory at the monopole
point is reviewed. Basic features of this U(1) confinement are contrasted with
those we expect in QCD. In particular, extra states in the hadron spectrum and
non-linear Regge trajectories are discussed. Then another confinement scenario
arising on Higgs branches of the theory with fundamental matter is also
reviewed. Peculiar properties of the Abrikosov-Nielsen-Olesen string on the
Higgs branch lead to a new confining regime with the logarithmic suppression of
the linear rising potential. Motivations for a search for tensionless strings
are proposed.


  A eutactic star on an integral lattice is called extremal if it induces a
holomorphic Jacobi form of lattice index and singular weight via the theta
block. The famous Macdonald identities imply that root systems are extremal as
eutactic stars. In this paper we prove that every extremal eutactic star arises
as a root system. This answers a question posed by Skoruppa.


  Extensive numerical simulations were performed to investigate all stages of
modulation instability development from the initial pulse of pico-second
duration in photonic crystal fiber: quasi-solitons and dispersive waves
formation, their interaction stage and the further propagation. Comparison
between 4 different NLS-like systems was made: the classical NLS equation, NLS
system plus higher dispersion terms, NLS plus higher dispersion and
self-steepening and also fully generalized NLS equation with Raman scattering
taken into account. For the latter case a mechanism of energy transfer from
smaller quasi-solitons to the bigger ones is proposed to explain the dramatical
increase of rogue waves appearance frequency in comparison to the systems when
the Raman scattering is not taken into account.


  Developing and maintaining life requires a lot of computation. This is done
by gene regulatory networks. But we have little understanding of how this
computation is organized. I show that there is a direct correspondence between
the structural and functional building blocks of regulatory networks, which I
call regulatory motifs. I derive a simple bound on the range of function that
these motifs can perform, in terms of the local network structure. I prove that
this range is a small fraction of all possible functions, which severely
constrains global network behavior. Part of this restriction is due to
redundancy in the function that regulatory motifs can achieve - there are many
ways to perform the same task. Regulatory motifs help us understanding how
genetic computation is organized and what it can achieve.


  We report on the observation of optical activity of quantum wells resulting
in the conversion of the light polarization state controlled by the light
propagation direction. The polarization conversion is detected in reflection
measurements. We show that a pure $s$-polarized light incident on a quantum
well is reflected as an elliptically polarized wave. The signal is drastically
enhanced in the vicinity of the light-hole exciton resonance. We show that the
polarization conversion is caused by the spin-orbit splitting of the light hole
states and the birefringence of the studied structure. The bulk inversion
asymmetry constant $\beta_{h} \approx 0.14$ eV\AA, is determined for the ground
light hole subband in a 10 nm ZnSe/ZnMgSSe quantum well.


  We present optical luminosity functions (LFs) of galaxies in the $^{0.1}g$,
$^{0.1}r$, and $^{0.1}i$ bands, calculated using data in $\sim 40$ $deg^{2}$
sky area of LAMOST Complete Spectroscopic Survey of Pointing Area (LaCoSSPAr)
in Southern Galactic Cap. Redshifts for galaxies brighter $r = 18.1$ were
obtained mainly with LAMOST. In each band, LFs derived using both parametric
and non-parametric maximum likelihood methods agree well with each other. In
the $^{0.1}r$ band, our fitting parameters of the Schechter function are
$\phi_{*}=(1.65\pm0.36)\times10^{-2}h^{3}Mpc^{-3}$, $M_{*}=-20.69\pm0.06$ mag,
and $\alpha=-1.12\pm0.08$, in agreements with previous studies. Separate LFs
are also derived for emission line galaxies and absorption line galaxies,
respectively. The LFs of absorption line galaxies show a dip at $^{0.1}r \sim
18.5$ and can be well fitted by a double-Gaussian function, suggesting a
bi-modality in passive galaxies.


  In high performance domains like image processing, physics simulation or
machine learning, program performance is critical. Programmers called
performance engineers are responsible for the challenging task of optimising
programs. Two major challenges prevent modern compilers targeting heterogeneous
architectures from reliably automating optimisation. First, domain-specific
compilers such as Halide for image processing and TVM for machine learning are
difficult to extend with the new optimisations required by new algorithms and
hardware. Second, automatic optimisation is often unable to achieve the
required performance, and performance engineers often fall back to painstaking
manual optimisation.
  This thesis shows the potential of the Shine compiler to achieve
domain-extensibility, controllable automation, and generate high performance
code. Domain-extensibility facilitates adapting compilers to new algorithms and
hardware. Controllable automation enables performance engineers to gradually
take control of the optimisation process.
  The first research contribution is to add 3 code generation features to
Shine, namely: synchronisation barrier insertion, kernel execution, and storage
folding. The second research contribution is to demonstrate how extensibility
and controllability are exploited to optimise a standard image processing
pipeline for corner detection. The final research contribution is to introduce
sketch-guided equality saturation, a semi-automated technique that allows
performance engineers to guide program rewriting by specifying rewrite goals as
sketches: program patterns that leave details unspecified.


  With plasma shielding effects of the Debye-H\"uckel model, we investigate the
relativistic photoionization processes of H, Nb$^{40+}$ and Pb$^{81+}$ plasmas
in the H-isoelectronic series. The shielded nuclear potential of Yukawa-type
experienced by the electron is parameterized by Debye-length $D$. To account
for relativistic effects non- perturbatively, we solve the Dirac equation for
the bound as well as continuum wavefunctions. Contributions from multipole
fields are calculated for high incident photon energies, while the angular
distribution and spin polarization parameters of photoelectrons are provided in
the electric-dipole approximation. Our results of photoionization cross
sections for the H plasma agree with other available theoretical calculations.
The interplay between the relativistic and plasma shielding effects on the
photoionization parameters is also studied. \keywords{Photoionization,
Multipole effect, Debye plasma, Hydrogen atom, Hydrogen-like ions


  We investigate the long-range phase coherence of homogeneous and trapped Bose
gases as a function of the geometry of the trap, the temperature, and the
mean-field interactions in the weakly interacting limit. We explicitly take
into account the (quasi)condensate depletion due to quantum and thermal
fluctuations, i.e., we include the effects of both phase and density
fluctuations. In particular, we determine the phase diagram of the gas by
calculating the off-diagonal one-particle density matrix and discuss the
various crossovers that occur in this phase diagram and the feasibility of
their experimental observation in trapped Bose gases.


  The CALICE collaboration has constructed highly granular electromagnetic and
hadronic calorimeter prototypes to evaluate technologies for the use in
detector systems at a future Linear Collider. The hadron calorimeter uses small
scintillator cells individually read out with silicon photomultipliers. The
system with 7608 channels has been successfully operated in beam tests at DESY,
CERN and Fermilab since 2006, and represents the first large scale tests of
these devices in high energy physics experiments. The unprecedented granularity
of the detector provides detailed information of the properties of hadronic
showers, which helps to constrain hadronic shower models through comparisons
with model calculations. Results on longitudinal and lateral shower profiles,
compared to a variety of hadronic shower models, first results with a software
compensation technique for the energy resolution and an outlook on the next
generation detector prototype are presented.


  We consider the information fiber optical channel modeled by the nonlinear
Schrodinger equation with additive Gaussian noise. Using path-integral approach
and perturbation theory for the small dimensionless parameter of the second
dispersion, we calculate the conditional probability density functional in the
leading and next-to-leading order in the dimensionless second dispersion
parameter associated with the input signal bandwidth. Taking into account
specific filtering of the output signal by the output signal receiver, we
calculate the mutual information in the leading and next-to-leading order in
the dispersion parameter and in the leading order in the parameter
signal-to-noise ratio (SNR). Further, we find the explicit expression for the
mutual information in case of the modified Gaussian input signal distribution
taking into account the limited frequency bandwidth of the input signal.


  This paper proposes an integrated architecture for Thrust Vector Control
(TVC) and state estimation for low-cost small-scale launchers, naturally
unstable, and propelled by a solid motor. The architecture is based on a
non-linear, six-degrees-of-freedom model for the generic
thrust-vector-controlled launcher dynamics and kinematics, deduced and
implemented in a realistic simulation environment. For estimation and control
design purposes, a linearized version of the model is proposed. Single-nozzle
TVC actuation is adopted, allowing for pitch and yaw control, with the control
law being derived from the Linear Quadratic Regulator (LQR) with additional
integral action (LQI). The control system is implemented through gain
scheduling. Full state estimation is performed resorting to complementary
kinematic filters, closely related to linear Kalman fitering theory. The
architecture, composed by the navigation and control systems, is tested in
simulation environment, demonstrating satisfactory attitude tracking
performance and robustness to both external disturbances and model
uncertainties.


  We refine Lagrange's four-square theorem in new ways by imposing some
restrictions involving powers of two (including $1$). For example, we show that
each $n=1,2,3,\ldots$ can be written as $x^2+y^2+z^2+w^2$ $(x,y,z,w\in\mathbb
N=\{0,1,2,\ldots\})$ with $|x+y-z|\in\{4^k:\ k\in\mathbb N\}$ (or
$|2x-y|\in\{4^k:\ k\in\mathbb N\}$, or $x+y-z\in\{\pm 8^k:\ k\in\mathbb
N\}\cup\{0\}\subseteq\{t^3:\ t\in\mathbb Z\}$), and that we can write any
positive integer as $x^2+y^2+z^2+w^2$ $(x,y,z,w\in\mathbb Z)$ with $x+y+2z$ (or
$x+2y+2z$) a power of four. We also prove that any $n\in\mathbb N$ can be
written as $x^2+y^2+z^2+2w^2$ $(x,y,z,w\in\mathbb Z)$ with $x+y+z+w$ a square
(or a cube). In addition, we pose some open conjectures for further research;
for example, we conjecture that any integer $n>1$ can be written as
$a^2+b^2+3^c+5^d$ with $a,b,c,d\in\mathbb N$.


  Contemporary machine learning applications often involve classification tasks
with many classes. Despite their extensive use, a precise understanding of the
statistical properties and behavior of classification algorithms is still
missing, especially in modern regimes where the number of classes is rather
large. In this paper, we take a step in this direction by providing the first
asymptotically precise analysis of linear multiclass classification. Our
theoretical analysis allows us to precisely characterize how the test error
varies over different training algorithms, data distributions, problem
dimensions as well as number of classes, inter/intra class correlations and
class priors. Specifically, our analysis reveals that the classification
accuracy is highly distribution-dependent with different algorithms achieving
optimal performance for different data distributions and/or training/features
sizes. Unlike linear regression/binary classification, the test error in
multiclass classification relies on intricate functions of the trained model
(e.g., correlation between some of the trained weights) whose asymptotic
behavior is difficult to characterize. This challenge is already present in
simple classifiers, such as those minimizing a square loss. Our novel
theoretical techniques allow us to overcome some of these challenges. The
insights gained may pave the way for a precise understanding of other
classification algorithms beyond those studied in this paper.


  We study the collision of a highly energetic light closed string off a stack
of Dp-branes at (sub)string-scale impact parameters and in a regime justifying
a perturbative treatment. Unlike at larger impact parameters - where elastic
scattering and/or tidal excitations dominate - here absorption of the closed
string by the brane system, with the associated excitation of open strings
living on it, becomes important. As a first step, we study this phenomenon at
the disk level, in which the energetic closed string turns into a single heavy
open string at rest whose particularly simple properties are described.


  We investigate the effects of massive black hole growth on the structural
evolution of dwarf galaxies within the Romulus25 cosmological hydrodynamical
simulation. We study a sample of 228 central, isolated dwarf galaxies with
stellar masses $M_{star} < 10^{10} M_\odot$ and a central BH. We find that the
local $M_{BH} - M_{star}$ relation exhibits a high degree of scatter below
$M_{star} < 10^{10} M_\odot$, which we use to classify BHs as overmassive or
undermassive relative to their host $M_{star}$. Overmassive BHs grow through a
mixture of BH mergers and relatively high average accretion rates, while
undermassive BHs grow slowly through accretion. We find that isolated dwarf
galaxies that host overmassive BHs also follow different evolutionary tracks
relative to their undermassive BH counterparts, building up their stars and
dark matter earlier and experiencing star formation suppression starting around
$z=2$. By $z=0.05$, overmassive BH hosts above $M_{star} > 10^{9} M_\odot$ are
more likely to exhibit lower central stellar mass density, lower HI gas
content, and lower star formation rates than their undermassive BH
counterparts. Our results suggest that overmassive BHs in isolated galaxies
above $M_{star} > 10^{9} M_\odot$ are capable of driving feedback, in many
cases suppressing and even quenching star formation by late times.


  Item representation learning (IRL) plays an essential role in recommender
systems, especially for sequential recommendation. Traditional sequential
recommendation models usually utilize ID embeddings to represent items, which
are not shared across different domains and lack the transferable ability.
Recent studies use pre-trained language models (PLM) for item text embeddings
(text-based IRL) that are universally applicable across domains. However, the
existing text-based IRL is unaware of the important collaborative filtering
(CF) information. In this paper, we propose CoWPiRec, an approach of
Collaborative Word-based Pre-trained item representation for Recommendation. To
effectively incorporate CF information into text-based IRL, we convert the
item-level interaction data to a word graph containing word-level
collaborations. Subsequently, we design a novel pre-training task to align the
word-level semantic- and CF-related item representation. Extensive experimental
results on multiple public datasets demonstrate that compared to
state-of-the-art transferable sequential recommenders, CoWPiRec achieves
significantly better performances in both fine-tuning and zero-shot settings
for cross-scenario recommendation and effectively alleviates the cold-start
issue. The code is available at: https://github.com/ysh-1998/CoWPiRec.


  A local order parameter which is important in the analysis of phase
transitions in frustrated combinatorial problems is the probability that a node
is frozen in a particular state. There is a percolative transition when an
infinite connected cluster of these frozen nodes emerges. In this contribution,
we develop theories based on this percolation process and discuss its relation
to conventional connectivity percolation and its generalisation to
k-connectivity percolation. The emergence of frozen order may also be
considered to be a form of constraint percolation (CP) which enables us to draw
analogies with rigidity percolation and its associated matching problems. We
show that very simple CP processes on Bethe lattices lead to the replica
symmetric equations for KSAT, coloring and the Viana-Bray model.


  Nonreciprocity, i.e. inequivalence in amplitudes and frequencies of spin
waves propagating in opposite directions, is a key property underlying
functionality in prospective magnonic devices. Here we demonstrate
experimentally and theoretically a simple approach to induce frequency
nonreciprocity in a magnetostatically coupled ferromagnetic bilayer structure
with a nonmagnetic spacer by its geometrical asymmetry. Using Brillouin light
scattering, we show the formation of two collective spin wave modes in
Fe$_{81}$Ga$_{19}$/Cu/Fe$_{81}$Ga$_{19}$ structure with different thicknesses
of ferromagnetic layers. Experimental reconstruction and theoretical modeling
of the dispersions of acoustic and optical collective spin wave modes reveal
that both possess nonreciprocity reaching several percent at the wavenumber of
$22~\cdot~10^4$ rad cm$^{-1}$. The analysis demonstrates that the shift of the
amplitudes of counter-propagating coupled modes towards either of the layers is
responsible for the nonreciprocity because of the pronounced dependence of spin
wave frequency on the layers thickness. The proposed approach enables the
design of multilayered ferromagnetic structures with a given spin wave
dispersion for magnonic logic gates.


  A cross-bifix-free set of words is a set in which no prefix of any length of
any word is the suffix of any other word in the set. A construction of
cross-bifix-free sets has recently been proposed by Chee {\it et al.} in 2013
within a constant factor of optimality. We propose a \emph{trace partitioned}
Gray code for these cross-bifix-free sets and a CAT algorithm generating it.


  Asteroseismology can make a substantial contribution to our understanding of
the formation history and evolution of our Galaxy by providing precisely
determined stellar properties for thousands of stars in different regions of
the Milky Way. We present here the different sets of observables used in
determining asteroseismic stellar properties, the typical level of precision
obtained, the current status of results for ages of dwarfs and giants and the
improvements than can be expected in the near future in the context of Galactic
archaeology.