  The purpose of this paper is to develop a self-optimized association
algorithm based on PGRL (Policy Gradient Reinforcement Learning), which is both
scalable, stable and robust. The term robust means that performance degradation
in the learning phase should be forbidden or limited to predefined thresholds.
The algorithm is model-free (as opposed to Value Iteration) and robust (as
opposed to Q-Learning). The association problem is modeled as a Markov Decision
Process (MDP). The policy space is parameterized. The parameterized family of
policies is then used as expert knowledge for the PGRL. The PGRL converges
towards a local optimum and the average cost decreases monotonically during the
learning process. The properties of the solution make it a good candidate for
practical implementation. Furthermore, the robustness property allows to use
the PGRL algorithm in an "always-on" learning mode.


  We presents results of joint modeling of the probability distribution
function (PDF) and the one-dimensional power spectrum (PS) of the Lya forest
flux decrement. The sensitivity of these statistical measures to the shape and
amplitude of the linear matter power spectrum is investigated using two
variants of the LCDM cosmology. In the first model, the linear power spectrum
has a scale-invariant spectral index, whereas in the second, it has a negative
running index (RSI). We generate mock catalogs of QSO spectra, and compare
their statistical properties to those of the observations at z=3. We perform a
joint fit of the power spectrum and PDF. A scale-invariant model with
\sigma_8=0.9 matches well the data if the mean IGM temperature is T\leq 15000K.
For higher temperature, it tends to overestimate the flux power spectrum over
scales k < 0.01s/km. The discrepancy is less severe when the PS alone is
fitted. However, models matching the PS alone do not yield a good fit to the
PDF. A joint analysis of the flux PS and PDF tightens the constraints on the
model parameters and reduces systematic biases. The RSI model is consistent
with the observed PS and PDF only if the temperature is T\geq 20000K. The best
fit models reproduce the slope and normalisation of the column density
distribution, irrespective of the shape and amplitude of the linear power
spectrum. They are also consistent with the observed line-width distribution
given the large uncertainties. Our joint analysis suggests that \sigma_8 is
likely to be in the range 0.7 - 0.9 for a temperature 10000K<T<20000K and a
reasonable reionization history.


  We extend the results of the 2019 paper by the third and fourth author
globally in time. More precisely, we prove uniform in $N$ estimates for the
solutions $\phi$, $\Lambda$ and $\Gamma$ of a coupled system of
Hartree-Fock-Bogoliubov type with interaction potential $V_N(x-y)=N^{3
\beta}v(N^{\beta}(x-y))$ with $\beta<1$. The potential satisfies some technical
conditions, but is not small. The initial conditions have finite energy and the
"pair correlation" part satisfies a smallness condition, but are otherwise
general functions in suitable Sobolev spaces, and the expected correlations in
$\Lambda$ develop dynamically in time. The estimates are expected to improve
the Fock space bounds from the 2021 paper of the first and fifth author. This
will be addressed in a different paper.


  A pertinent question in cavity optomechanics is whether reaching the regime
of large single-photon cooperativity, where the single-photon coupling rate
exceeds the geometric mean of the cavity and mechanical decay rates, can enable
any new phenomena. We show that in some multimode optomechanical systems, the
single-photon cooperativity can indeed be a figure of merit. We first study a
system with one cavity mode and two mechanical oscillators which combines the
concepts of levitated optomechanics and coherent scattering with standard
dispersive optomechanics. Later, we study a more complicated setup comprising
three cavity modes which does not rely on levitated optomechanics and only
features dispersive optomechanical interactions with direct cavity driving.
These systems can effectively realize the degenerate or the nondegenerate
parametric oscillator models known from quantum optics, but in the unusual
finite-size regime for the fundamental mode(s) when the single-photon
cooperativity is large. We show that the response of these systems to a
coherent optical probe can be highly nonlinear in probe power even for average
photon occupation numbers below unity. The nonlinear optomechanical interaction
has the peculiar consequence that the probe drive will effectively
amplitude-squeeze itself. For large single-photon cooperativity, this occurs
for small occupation numbers, which enables observation of nonclassical
antibunching of the transmitted probe photons due to a destructive interference
effect. Finally, we show that as the probe power is increased even further, the
system enters a critical regime characterized by intrinsically nonlinear
dynamics and non-Gaussian states.


  We use AStroLens, a newly developed gravitational lens-modeling code that
relies only on geometric and photometric information of cluster galaxies as
input, to map the strong-lensing regions and estimate the lensing strength of
96 galaxy clusters at $z=0.5$-$0.9$. All clusters were identified during the
extended Massive Cluster Survey (eMACS) based on their X-ray flux and optical
appearance. Building on the well tested assumption that the distribution of
both luminous and dark matter in galaxy clusters is approximately traced by the
distribution of light, i.e., that light traces mass, AStroLens uses three
global parameters to automatically model the deflection from
strong-gravitational lensing for all galaxy clusters in this diverse sample. We
test the robustness of our code by comparing AStroLens estimates derived solely
from shallow optical images in two passbands with the results of in-depth
lens-modeling efforts for two well studied eMACS clusters and find good
agreement, both with respect to the size and the shape of the strong-lensing
regime delineated by the respective critical lines. Our study finds 31 eMACS
clusters with effective Einstein radii ($\theta_{E}$) in excess of 20" and
eight with $\theta_{E} >$ 30", thereby underlining the value of X-ray selection
for the discovery of powerful cluster lenses that complement giants like
MACSJ0717 at ever-increasing redshift. As a first installment toward the public
release of the eMACS sample, we list physical properties of the ten calibration
clusters as well as of the ten most powerful eMACS cluster lenses, according to
AStroLens.


  We investigate the Hasse principle for complete intersections cut out by a
quadric and cubic hypersurface defined over the rational numbers.


  Let $S \subset \mathbb{P}^g$ be a smooth $K3$ surface of degree $2g-2$, $g
\geq 3$. We classify all the cases for which
$h^0(\mathcal{N}_{S/\mathbb{P}^g}(-2)) \neq 0$ and the cases for which
$h^0(\mathcal{N}_{S/\mathbb{P}^g}(-2)) <
h^0(\mathcal{N}_{C/\mathbb{P}^{g-1}}(-2))$ for $C \subset \mathbb{P}^{g-1}$ a
general canonical curve section of $S$.


  Strong variability is a common characteristic of the prompt emission of
gamma-ray bursts (GRB). This observed variability is widely attributed to an
intermittency of the central engine, through formation of strong internal
shocks in the GRB-emitting jet expelled by the engine. In this paper we study
numerically the propagation of hydrodynamic jets, injected periodically by a
variable engine, through the envelope of a collapsed star. By post-processing
the output of 3D numerical simulations, we compute the net radiative efficiency
of the outflow. We find that all intermittent jets are subject to heavy baryon
contamination that inhibits the emission at and above the photosphere well
below detection limits. This is in contrast to continuous jets that, as shown
recently, produce a highly variable gamma-ray photospheric emission with high
efficiency, owing to the interaction of the jet with the stellar envelope. Our
results challenge the variable engine model for hydrodynamic jets, and may
impose constraints on the duty cycle of GRB engines. If such systems exist in
nature, they are not expected to produce bright gamma-ray emission, but should
appear as X-ray, optical and radio transients that resemble a delayed GRB
afterglow signal.


  The generation of exponential flavor hierarchies from extra-dimensional
wavefunction overlaps is re-examined. We find, surprisingly, that coexistence
of anarchic fermion mass matrices with such hierarchies is intrinsic and
natural to this setting. The salient features of charged fermion and neutrino
masses and mixings can thereby be captured within a single framework. Both
Dirac and Majorana neutrinos can be realized. The minimal phenomenological
consequences are discussed, including the need for a fundamental scale far
above the weak scale to adequately suppress flavor-changing neutral currents.
Two broad scenarios for stabilizing this electroweak hierarchy are studied,
warped compactification and supersymmetry. In warped compactifications and
"Flavorful Supersymmetry," where non-trivial flavor structure appears in the
new TeV physics, Dirac neutrinos are strongly favored over Majorana by lepton
flavor violation tests. We argue that this is part of a more general result for
flavor-sensitive TeV-scale physics. Our scenario strongly suggests that the
supersymmetric flavor problem is not solved locally in the extra dimension, but
rather at or below the compactification scale. In the supersymmetric Dirac
case, we discuss how the appearance of light right-handed sneutrinos
considerably alters the physics of dark matter.


  The method using the propagation of acoustic body waves within the stress
modified areas around a vertical borehole has been applied to the granitic
formation penetrated by the SAFOD Pilot hole near the San Andreas Fault trace.
This method allows us investigating the horizontal in situ stresses. Only P
waves supplied useful and surprising information. A depth of 1270 m separates
an upper region of uniform thickness of stress modified areas, possibly
corresponding to a shear domain, and a lower region where there are
simultaneously two values of the thicknesses of the stress modified areas
(particularly between 1500 and 1600 m of depth) possibly corresponding to a
compressive and a shear domain. In order to integrate the contradictory effects
of the simultaneity of shear and compressive domains at some depths, as well as
the presence of three shear zones at particular depths, we propose that the San
Andreas Fault could be bayonet-shaped instead of planar. Other recent available
information in the literature about this fault, such as the presence of a fault
zone of low shear wave velocity, stress rotation measured with depth, and the
large angles of the frictional coefficients, can be logically explained by this
kind of fault geometry.


  Surface plasmons in graphene may provide an attractive alternative to
noble-metal plasmons due to their tighter confinement, peculiar dispersion, and
longer propagation distance. We present theoretical studies of the nonlinear
difference frequency generation of terahertz surface plasmon modes supported by
two-dimensional layers of massless Dirac electrons, which includes graphene and
surface states in topological insulators. Our results demonstrate strong
enhancement of the DFG efficiency near the plasmon resonance and the
feasibility of phase-matched nonlinear generation of plasmons over a broad
range of frequencies.


  We use spectra and maps of the $J=1-0$ and $J=2-1$ DCO$^{+}$, DCN, DNC, $\rm
N_2D^+$ lines and $1_{11}-1_{01}$ ortho- and para-NH$_{2}$D lines, obtained
with the IRAM-30m telescope, as well as observations of their hydrogenated
isotopologues to study deuteration processes in five high-mass star-forming
regions. The temperature was estimated from CH$_3$CCH lines, also observed with
the IRAM-30m telescope, and from NH$_3$ lines, observed with the 100-m radio
telescope in Effelsberg, as well as using the integrated intensity ratios of
the $J=1-0$ H$^{13}$CN and HN$^{13}$C lines and their main isotopologues.
Applying a non-LTE radiative transfer model with RADEX, the gas density and the
molecular column densities were estimated. D/H ratios are $0.001-0.05$ for
DCO$^{+}$, $0.001-0.02$ for DCN, $0.001-0.05$ for DNC and $0.02-0.4$ for
NH$_{2}$D. The D/H ratios decrease with increasing temperature in the range of
$\rm 20-40 \,K$ and slightly vary at densities $n(\rm H_2) \sim 10^4-10^6\,
cm^{-3}$. The deuterium fraction of $\rm N_2H^{+}$ is $0.008-0.1$ at
temperatures in the range of $\rm 20-25\, K$ and at a density of $\sim 10^5\,
\rm cm^{-3}$. We also estimate relative abundances and find $ \sim
10^{-11}-10^{-9}$ for DCO$^{+}$ and DNC, $ \sim 10^{-11}-10^{-10}$ for $\rm
N_2D^+$ and $ \sim 10^{-10}-10^{-8}$ for NH$_{2}$D. The relative abundances of
these species decrease with increasing temperature. However, the DCN/H$_2$
ratio is almost constant ($\sim 10^{-10}$). The observational results agree
with the predictions of chemical models (although in some cases there are
significant differences).


  Approximate analytical energy formulas for N-body relativistic Hamiltonians
with one- and two-body interactions are obtained within the framework of the
auxiliary field method. This method has already been proved to be a powerful
technique in the case of two-body problems. A general procedure is given and
applied to various Hamiltonians of interest, in atomic and hadronic physics in
particular. A test of formulas is performed for baryons described as a
three-quark system.


  Interaction-free measurements introduced by Elitzur and Vaidman [Found. Phys.
23, 987 (1993)] allow finding infinitely fragile objects without destroying
them. Paradoxical features of these and related measurements are discussed. The
resolution of the paradoxes in the framework of the Many-Worlds Interpretation
is proposed.


  Low-light scenes are prevalent in real-world applications (e.g. autonomous
driving and surveillance at night). Recently, multi-object tracking in various
practical use cases have received much attention, but multi-object tracking in
dark scenes is rarely considered. In this paper, we focus on multi-object
tracking in dark scenes. To address the lack of datasets, we first build a
Low-light Multi-Object Tracking (LMOT) dataset. LMOT provides well-aligned
low-light video pairs captured by our dual-camera system, and high-quality
multi-object tracking annotations for all videos. Then, we propose a low-light
multi-object tracking method, termed as LTrack. We introduce the adaptive
low-pass downsample module to enhance low-frequency components of images
outside the sensor noises. The degradation suppression learning strategy
enables the model to learn invariant information under noise disturbance and
image quality degradation. These components improve the robustness of
multi-object tracking in dark scenes. We conducted a comprehensive analysis of
our LMOT dataset and proposed LTrack. Experimental results demonstrate the
superiority of the proposed method and its competitiveness in real night
low-light scenes. Dataset and Code: https: //github.com/ying-fu/LMOT


  Web accessibility is actually the most important aspect for providing access
to information and interaction for people with disabilities. However, it seems
that the ability of users with disabilities to navigate over the Web is not
dependent on the graphical complexity, but on the markup used to create the
structure of the website. Consequently, it is necessary to design some software
assistants to help all users to mark themselves in space during a navigation
session. In this paper, we propose an assistant for browsing on the Internet to
allow user to get one s bearings within Web navigation. We describe our
approach which puts at the disposal of the user a visited site map, thus giving
an explicit representation of virtual space. Different levels of visualization
are implemented in order to make the map more visible and less overloaded.


  We consider a canonical $S^1$ action on $S^3$ which is defined by
$(\rho,(z_1,z_2))\mapsto (z_1\rho^p,z_2\rho^q)$ for $\rho\in S^1$ and
$(z_1,z_2)\in S^3\subset {\mathbb C}^2$. We consider a link consisting of
finite orbits of this action, which some of the orbits are reversely oriented.
Such a link appears as a link of a certain type of mixed polynomials. We study
the space of such links and show smooth degeneration relations.


  We introduce a class of partial differential equations on metric graphs
associated with mixed evolution: on some edges we consider diffusion processes,
on other ones transport phenomena. This yields a system of equations with
possibly nonlocal couplings at the boundary. We provide sufficient conditions
for these to be governed by a contractive semigroup on a Hilbert space
naturally associated with the system. We show that our setting is also adequate
to discuss specific systems of diffusion equations with boundary delays.


  We calculate static and spherically symmetric solutions for the Rastall
modification of gravity to describe Neutron Stars (NS). The key feature of the
Rastall gravity is the non-conservation of the energy-momentum tensor
proportionally to the space-time curvature. Using realistic equations of state
for the NS interior we place a conservative bound on the non-GR behaviour of
the Rastall theory which should be $\lesssim 1\%$ level. This work presents the
more stringent constraints on the deviations of GR caused by the Rastall
proposal.


  [ABRIDGED] Since the discovery of the first transiting extrasolar planet,
transit timing has been recognized as a powerful method to discover and
characterize additional planets in these systems. However, the gravitational
influence of additional planets is not the only expected source of transit
timing variations. In this work, we derive the expected detection frequency of
stellar companions of hot-jupiter transiting planets host-stars, detectable by
means of transit timing analysis. Since roughly half of the stars in the solar
neighborhood belong to binary or multiple stellar systems, the same fraction of
binary systems may be expected to be present among transiting planet-host
stars, unless planet formation is significantly influenced by the presence of a
stellar companion. Transit searches are less affected by the selection biases
against long-period binaries that plague radial velocity surveys. If the
frequency of binaries among hot-jupiter planets host stars is the same as
determined in the solar neighborhood, after 5 years since the discovery of a
sample of transiting planets 1.0%+/-0.2% of them have a probability >99% to
present transit timing variations >50 sec induced by stellar binarity, and
2.8%+/-0.3% after 10 years, if the planetary and binary orbits are coplanar.
Considering the case of random inclinations the probabilities are 0.6%+/-0.1%
and 1.7%+/-0.2% after 5 and 10 years respectively. Our estimates can be
considered conservative lower limits, since we have taken into account only
binaries with periods P>5x10^3 days (a>=6 AU). Our simulations indicate that
transit timing variations due to the light travel time effect allow discovery
of stellar companions up to maximum separations equal to a\sim36 AU after 5
years since the discovery of the planet (a\sim75 AU after 10 years).


  We establish pointwise estimates for the ground states of some classes of
posi- tivity preserving operators. The considered operators are negatively
perturbed (by measures) strongly local Dirichlet operators. These estimates
will be written in terms of the Green's kernel of the considered operators,
whose existence will be proved. In many circumstances our estimates are even
sharp so that they recover known results about the subject. The results will
deserve to obtain large time heat kernel estimates for the related operators.


  The temperature of an atmosphere decreases with increasing altitude, unless a
shortwave absorber exists that causes a temperature inversion. Ozone plays this
role in the Earth`s atmosphere. In the atmospheres of highly irradiated
exoplanets, shortwave absorbers are predicted to be titanium oxide (TiO) and
vanadium oxide (VO). Detections of TiO and VO have been claimed using both low
and high spectral resolution observations, but later observations have failed
to confirm these claims or overturned them. Here we report the unambiguous
detection of TiO in the ultra-hot Jupiter WASP-189b using high-resolution
transmission spectroscopy. This detection is based on applying the
cross-correlation technique to many spectral lines of TiO from 460 to 690 nm.
Moreover, we report detections of metals, including neutral and singly ionised
iron and titanium, as well as chromium, magnesium, vanadium and manganese (Fe,
Fe+, Ti, Ti+, Cr, Mg, V, Mn). The line positions of the detected species
differ, which we interpret as a consequence of spatial gradients in their
chemical abundances, such that they exist in different regions or dynamical
regimes. This is direct observational evidence for the three-dimensional
thermo-chemical stratification of an exoplanet atmosphere derived from
high-resolution ground-based spectroscopy.


  This paper explores recommender systems in social networks which leverage
information such as item rating, intra-item similarities, and trust graph. We
demonstrate that item-rating information is more influential than other
information types in a collaborative filtering approach. The trust graph-based
approaches were found to be more robust to network adversarial attacks due to
hard-to-manipulate trust structures. Intra-item information, although
sub-optimal in isolation, enhances the consistency of predictions and lower-end
performance when fused with other information forms. Additionally, the Weighted
Average framework is introduced, enabling the construction of recommendation
systems around any user-to-user similarity metric.


  Silicon-based micro-electromechanical systems (MEMS) can be fabricated using
bulk and surface micromachining technology. A micro mirror designed as an
oscillatory MEMS constitutes a prominent example. Typically, in order to
minimize energy consumption, the micro mirror is designed to have high quality
factors. In addition, a phase-locked loop guarantees resonant actuation despite
the occurrence of frequency shifts. In these cases, the oscillation amplitude
of the micro mirror is expected to scale linearly with the actuation input
power. Here, however, we report on an experimental observation which clearly
shows an amplitude depletion that is not in accordance with any linear
behaviour. As a consequence, the actuation forces needed to reach the desired
oscillation amplitude are by multiples higher than expected. We are able to
explain the experimental observations accurately by introducing a single
degree-of-freedom model including an amplitude-dependent nonlinear damping
term. Remarkably, we find that the nonlinear damping shows a clear gas pressure
dependency. We investigate the concepts and compare our findings on two
different micro mirror design layouts.


  We present a comprehensive study on how to distinguish the properties of
heavy dijet resonances at hadron colliders. A variety of spins, chiral
couplings, charges, and QCD color representations are considered.
Distinguishing the different color representations is particularly difficult at
hadron colliders. To determine the QCD color structure, we consider a third jet
radiated in a resonant dijet event. We show that the relative rates of
three-jet versus two-jet processes are sensitive to the color representation of
the resonance. We also show analytically that the antennae radiation pattern of
soft radiation depends on the color structure of dijet events and develops an
observable that is sensitive to the antennae patterns. Finally, we exploit a
Convolutional Neural Network with Machine Learning techniques to differentiate
the radiation patterns from different colored resonances and find encouraging
results to discriminate them. We demonstrate our results numerically at a 14
TeV LHC, and the methodology presented here should be applicable to other
future hadron colliders.


  We present simple new approximate formulas, for both scalar and spinor QED,
for the number of particles produced from vacuum by a time dependent electric
field, incorporating the interference effects that arise from an arbitrary
number of distinct semiclassical turning points. Such interference effects are
important when the temporal profile of the laser pulse has subcycle structure.
We show how the resulting semiclassical intuition may be used to guide the
design of temporal profiles that enhance the momentum spectrum due to
interference effects. The result is easy to implement and generally applicable
to time-dependent tunneling problems, such as appear in many other contexts in
particle and nuclear physics, condensed matter physics, atomic physics,
chemical physics, and gravitational physics.


  We consider the growth of clusters in disordered media at zero temperature,
as exemplified by supercritical generalized percolation and by the random field
Ising model. We show that the morphology of such clusters and of their surfaces
can be of different types: They can be standard compact clusters with rough or
smooth surfaces, but there exists also a completely different "spongy" phase.
Clusters in the spongy phase are `compact' as far as the size-mass relation M ~
R^D is concerned (with D the space dimension), but have an outer surface (or
`hull') whose fractal dimension is also D and which is indeed dense in the
interior of the entire cluster. This behavior is found in all dimensions D >=
3. Slightly supercritical clusters can be of either type in $D=3$, while they
are always spongy in D >= 4. Possible consequences for the applicability of KPZ
(Kardar-Parisi-Zhang) scaling to interfaces in media with frozen randomness are
studied in detail.


  Back-to-Back Correlations (BBC) of particle-antiparticle pairs are predicted
to appear if hot and dense hadronic matter is formed in high energy
nucleus-nucleus collisions. The BBC correlations are related to in-medium
mass-modification and squeezing of the quanta involved. The formalisms are
analogous in the bosonic (bBBC) and in the fermionic (fBBC) cases. Both the
bBBC and the fBBC are positive and unlimited correlations of similar strength.
For testing the survival and the intensity of the effect in a more realistic
situation, we study the back-to-back correlations for mass-modification
occurring in a finite sized, thermalized medium. For illustration, we consider
a non-relativistically expanding fireball with finite emission time. We show
that the BBC signal indeed survives the expansion and flow effects, with
sufficient magnitude to be observed at RHIC.


  We present a handlebody construction of small symplectic caps, and hence of
small closed symplectic 4-manifolds. We use this to construct handlebody
descriptions of symplectic embeddings of rational homology balls in
$\mathbb{C}\mathrm{P}^2$, and thereby provide the first examples of (infinitely
many) symplectic handlebody decompositions of a closed symplectic 4-manifold.
Our constructions provide a new topological interpretation of almost toric
fibrations of $\mathbb{C}\mathrm{P}^2$ in terms of symplectic handlebody
decompositions.


  We study solutions to nonlinear hyperbolic systems with fully nonlinear
relaxation terms in the limit of, both, infinitely stiff relaxation and
arbitrary late time. In this limit, the dynamics is governed by effective
systems of parabolic type, with possibly degenerate and/or fully nonlinear
diffusion terms. For this class of problems, we develop here an
implicit-explicit method based on Runge-Kutta discretization in time, and we
use this method in order to investigate several examples of interest in
compressible fluid dynamics. Importantly, we impose here a realistic stability
condition on the time-step and we demonstrate that solutions in the
hyperbolic-to-parabolic regime can be computed numerically with high robustness
and accuracy, even in presence of fully nonlinear relaxation terms.


  A modification of the canonical quantization procedure for systems with
time-dependent second-class constraints is discussed and applied to the
quantization of the relativistic particle in a plane wave. The time dependence
of constraints appears in the problem in two ways. The Lagrangian depends on
time explicitly by origin, and a special time-dependent gauge is used. Two
possible approaches to the quantization are demonstrated in this case. One is
to solve directly a system of operator equations, proposed by Tyutin and one of
the authors (Gitman) as a generalization of Dirac canonical quantization in
nonstationary case, and another to find first a canonical transformation, which
makes it possible to discribe the dynamics in the physical sactor by means of
some effective Hamiltonian. Quantum mechanics constructed in both cases proves
to be equivalent to Klein-Gordon theory of the relativistic particle in a plane
wave. The general conditions of unitarity of the dynamics in the physical
sector are discussed.


  This article presents a general solution to the problem of computational
complexity. First, it gives a historical introduction to the problem since the
revival of the foundational problems of mathematics at the end of the 19th
century. Second, building on the theory of functional relations in mathematics,
it provides a theoretical framework where we can rigorously distinguish two
pairs of concepts: Between solving a problem and verifying the solution to a
problem. Between a deterministic and a non-deterministic model of computation.
Third, it presents the theory of computational complexity and the difficulties
in solving the P versus NP problem. Finally, it gives a complete proof that a
certain decision problem in NP has an algorithmic exponential lower bound thus
establishing firmly that P is different from NP. The proof presents a new way
of approaching the subject: neither by entering into the unmanageable
difficulties of proving this type of lower bound for the known NP-complete
problems nor by entering into the difficulties regarding the properties of the
many complexity classes established since the mid-1970s.


  We numerically simulate ensembles of SU(2) Yang-Mills dimeron solutions with
a statistical weight determined by the classical action and perform a
comprehensive analysis of their properties. In particular, we examine the
extent to which these ensembles capture topological and confinement properties
of the Yang-Mills vacuum. This further allows us to test the classic picture of
meron-induced quark confinement as triggered by dimeron dissociation. At small
bare couplings, spacial, topological-charge and color correlations among the
dimerons generate a short-range order which screens topological charges. With
increasing coupling this order weakens rapidly, however, in part because the
dimerons gradually dissociate into their meron constituents. Monitoring
confinement properties by evaluating Wilson-loop expectation values, we find
the growing disorder due to these progressively liberated merons to generate a
finite and (with the coupling) increasing string tension. The short-distance
behavior of the static quark-antiquark potential, on the other hand, is
dominated by small, "instanton-like" dimerons. String tension, action density
and topological susceptibility of the dimeron ensembles in the physical
coupling region turn out to be of the order of standard values. Hence the above
results demonstrate without reliance on weak-coupling or low-density
approximations that the dissociating dimeron component in the Yang-Mills vacuum
can indeed produce a meron-populated confining phase. The density of
coexisting, hardly dissociated and thus instanton-like dimerons seems to remain
large enough, on the other hand, to reproduce much of the additional
phenomenology successfully accounted for by non-confining instanton vacuum
models. Hence dimeron ensembles should provide an efficient basis for a rather
complete description of the Yang-Mills vacuum.


  Using a cross-correlation method, we study the X-ray halo of Cyg X-3. Two
components of dust distributions are needed to explain the time lags derived by
the cross-correlation method. Assuming the distance as 1.7 kpc for Cygnus OB2
association (a richest OB association in the local Galaxy) and another uniform
dust distribution, we get a distance of $7.2^{+0.3}_{-0.5}$ kpc (68$%$
confidence level) for Cyg X-3. When using the distance estimation of Cygnus OB2
as 1.38 kpc or 1.82 kpc, the inferred distance for Cyg X-3 is
$3.4^{+0.2}_{-0.2}$ kpc or $9.3^{+0.6}_{-0.4}$ kpc respectively. The distance
estimation uncertainty of Cyg X-3 is mainly related to the distance of the
Cygnus OB2, which may be improved in the future with high precision astrometric
measurements. The advantage of this method is that the result depends weakly on
the photon energy, dust grain radius, scattering cross-section and so on.


  The width $k$ of a directed acyclic graph (DAG) $G = (V, E)$ equals the
largest number of pairwise non-reachable vertices. Computing the width dates
back to Dilworth's and Fulkerson's results in the 1950s, and is doable in
quadratic time in the worst case. Since $k$ can be small in practical
applications, research has also studied algorithms whose complexity is
parameterized on $k$. Despite these efforts, it is still open whether there
exists a linear-time $O(f(k)(|V| + |E|))$ parameterized algorithm computing the
width. We answer this question affirmatively by presenting an $O(k^24^k|V| +
k2^k|E|)$ time algorithm, based on a new notion of frontier antichains. As we
process the vertices in a topological order, all frontier antichains can be
maintained with the help of several combinatorial properties, paying only
$f(k)$ along the way. The fact that the width can be computed by a single
$f(k)$-sweep of the DAG is a new surprising insight into this classical
problem. Our algorithm also allows deciding whether the DAG has width at most
$w$ in time $O(f(\min(w,k))(|V|+|E|))$.


  Hyperspectral image analysis has become an important topic widely researched
by the remote sensing community. Classification and segmentation of such
imagery help understand the underlying materials within a scanned scene, since
hyperspectral images convey a detailed information captured in a number of
spectral bands. Although deep learning has established the state of the art in
the field, it still remains challenging to train well-generalizing models due
to the lack of ground-truth data. In this letter, we tackle this problem and
propose an end-to-end approach to segment hyperspectral images in a fully
unsupervised way. We introduce a new deep architecture which couples 3D
convolutional autoencoders with clustering. Our multi-faceted experimental
study---performed over benchmark and real-life data---revealed that our
approach delivers high-quality segmentation without any prior class labels.


  Let $X$ be a compact connected Riemann surface of genus $g$, with $g\geq 2$,
and ${\cal M}_{\xi}$ a smooth moduli space of fixed determinant semistable
vector bundles of rank $n$, with $n\geq 2$, over $X$. Take a smooth
anticanonical divisor $D$ on ${\cal M}_{\xi}$. So $D$ is a Calabi-Yau variety.
We compute the number of moduli of $D$, namely $\dim H^1(D, T_D)$, to be $3g-4
+ \dim H^0({\cal M}_{\xi}, K^{-1}_{{\cal M}_{\xi}})$. Denote by $\cal N$ the
moduli space of all such pairs $(X',D')$, namely $D'$ is a smooth anticanonical
divisor on a smooth moduli space of semistable vector bundles over the Riemann
surface $X'$. It turns out that the Kodaira-Spencer map from the tangent space
to $\cal N$, at the point represented by the pair $(X,D)$, to $H^1(D, T_D)$ is
an isomorphism. This is proved under the assumption that if $g =2$, then $n\neq
2,3$, and if $g=3$, then $n\neq 2$.


  We present the complete physical picture for the evolution of a high-energy
jet propagating through a weakly-coupled quark-gluon plasma (QGP) by analytical
and numerical investigation of thermalization of the soft components of the
jet. Our results support the following physical picture: the leading particle
emits a significant number of mini-jets which promptly evolve via multiple
branching and thus degrade into a myriad of soft gluons, with energies of the
order of the medium temperature $T$. Via elastic collisions with the medium
constituents, these soft gluons relax to local thermal equilibrium with the
plasma over a time scale which is considerably shorter than the typical
lifetime of the mini-jet. The thermalized gluons form a tail which lags behind
the hard components of the jet. Together with the background QGP, they behave
hydrodynamically.


  Relative Lempel-Ziv (RLZ) parsing is a dictionary compression method in which
a string $S$ is compressed relative to a second string $R$ (called the
reference) by parsing $S$ into a sequence of substrings that occur in $R$. RLZ
is particularly effective at compressing sets of strings that have a high
degree of similarity to the reference string, such as a set of genomes of
individuals from the same species. With the now cheap cost of DNA sequencing,
such data sets have become extremely abundant and are rapidly growing. In this
paper, instead of using a single reference string for the entire collection, we
investigate the use of different reference strings for subsets of the
collection, with the aim of improving compression. In particular, we form a
rooted tree (or hierarchy) on the strings and then compressed each string using
RLZ with parent as reference, storing only the root of the tree in plain text.
To decompress, we traverse the tree in BFS order starting at the root,
decompressing children with respect to their parent. We show that this approach
leads to a twofold improvement in compression on bacterial genome data sets,
with negligible effect on decompression time compared to the standard single
reference approach. We show that an effective hierarchy for a given set of
strings can be constructed by computing the optimal arborescence of a completed
weighted digraph of the strings, with weights as the number of phrases in the
RLZ parsing of the source and destination vertices. We further show that
instead of computing the complete graph, a sparse graph derived using locality
sensitive hashing can significantly reduce the cost of computing a good
hierarchy, without adversely effecting compression performance.


  This is the contribution representing Parallel Session A3, on Modified
Gravity, in the Proceedings of the GR 20 Conference (July 2013, Warszawa,
Poland). It consists of three invited chapters, selected by the Session Chair
(P.H.) to represent the broad spectrum of topics discussed in the Session,
which ranged from theoretical and phenomenological, to experimental,
observational and numerical aspects of gravity. The three chapters are
"Einstein-Aether Theory: Thermodynamics of Universal Horizons" by Arif Mohd,
"The Curious Case of Conformal Anomalies in Horava-Lifshitz Gravity" by Charles
M. Melby-Thompson, and "Detectability of Scalar Gravitational-Wave Bursts with
LIGO and Virgo" by Peter Shawhan.


  Gaussian networks are fundamental objects in network information theory. Here
many senders and receivers are connected by physically motivated Gaussian
channels while auxiliary Gaussian components, such as Gaussian relays, are
entailed. Whilst the theoretical backbone of classical Gaussian networks is
well established, the quantum analogue is yet immature. Here, we theoretically
tackle composable security of arbitrary Gaussian quantum networks (quantum
networks), with generally untrusted nodes, in the finite-size regime. We put
forward a general methodology for parameter estimation, which is only based on
the data shared by the remote end-users. Taking a chain of identical quantum
links as an example, we further demonstrate our study. Additionally, we find
that the key rate of a quantum amplifier-assisted chain can ideally beat the
fundamental repeaterless limit with practical block sizes. However, this
objective is practically questioned leading the way to new network/chain
designs.


  TikTok is a popular new social media, where users express themselves through
short video clips. A common form of interaction on the platform is
participating in "challenges", which are songs and dances for users to iterate
upon. Challenge contagion can be measured through replication reach, i.e.,
users uploading videos of their participation in the challenges. The uniqueness
of the TikTok platform where both challenge content and user preferences are
evolving requires the combination of challenge and user representation. This
paper investigates social contagion of TikTok challenges through predicting a
user's participation. We propose a novel deep learning model, deepChallenger,
to learn and combine latent user and challenge representations from past videos
to perform this user-challenge prediction task. We collect a dataset of over
7,000 videos from 12 trending challenges on the ForYouPage, the app's landing
page, and over 10,000 videos from 1303 users. Extensive experiments are
conducted and the results show that our proposed deepChallenger (F1=0.494)
outperforms baselines (F1=0.188) in the prediction task.


  Let $alb_X: X \rightarrow A$ be the Albanese map of a smooth projective
variety and $f: X \rightarrow Y$ the fibration from the Stein factorization of
$alb_X$. For a positive integer $m$, if $f$ and $m$ satisfy the assumptions
AS(1,2), then the translates through the origin of all components of
cohomological locus $V^0(\omega_X^m, alb_X)$ generates $I^*Pic^0(S)$ where $I:
X \rightarrow S$ denotes the Iitaka fibration. This result applies to studying
pluricanonical maps. We also considered the problem about whether a fibration
is isotrivial and isogenous to a product.


  Digital holography enables us to reconstruct objects in three-dimensional
space from holograms captured by an imaging device. For the reconstruction, we
need to know the depth position of the recoded object in advance. In this
study, we propose depth prediction using convolutional neural network
(CNN)-based regression. In the previous researches, the depth of an object was
estimated through reconstructed images at different depth positions from a
hologram using a certain metric that indicates the most focused depth position;
however, such a depth search is time-consuming. The CNN of the proposed method
can directly predict the depth position with millimeter precision from
holograms.


  Previous studies of haze formation in the atmosphere of the Early Earth have
focused on N$_{2}$/CO$_{2}$/CH$_{4}$ atmospheres. Here, we experimentally
investigate the effect of O$_{2}$ on the formation and composition of aerosols
to improve our understanding of haze formation on the Neoproterozoic Earth. We
obtained in situ size, particle density, and composition measurements of
aerosol particles produced from N$_{2}$/CO$_{2}$/CH$_{4}$/O$_{2}$ gas mixtures
subjected to FUV radiation (115-400 nm) for a range of initial
CO$_{2}$/CH$_{4}$/O$_{2}$ mixing ratios (O$_{2}$ ranging from 2 ppm to 0.2\%).
At the lowest O$_{2}$ concentration (2 ppm), the addition increased particle
production for all but one gas mixture. At higher oxygen concentrations (20 ppm
and greater) particles are still produced, but the addition of O$_{2}$
decreases the production rate. Both the particle size and number density
decrease with increasing O$_{2}$, indicating that O$_{2}$ affects particle
nucleation and growth. The particle density increases with increasing O$_{2}$.
The addition of CO$_{2}$ and O$_{2}$ not only increases the amount of oxygen in
the aerosol, but it also increases the degree of nitrogen incorporation. In
particular, the addition of O$_{2}$ results in the formation of nitrate bearing
molecules. The fact that the presence of oxygen bearing molecules increases the
efficiency of nitrogen fixation has implications for the role of haze as a
source of molecules required for the origin and evolution of life. The
composition changes also likely affect the absorption and scattering behavior
of these particles but optical properties measurements are required to fully
understand the implications for the effect on the planetary radiative energy
balance and climate.


  This work examines how head-mounted AR can be used to build an interactive
sonic landscape to engage with a public sculpture. We describe a sonic artwork,
"Listening To Listening", that has been designed to accompany a real-world
sculpture with two prototype interaction schemes. Our artwork is created for
the HoloLens platform so that users can have an individual experience in a
mixed reality context. Personal head-mounted AR systems have recently become
available and practical for integration into public art projects, however
research into sonic sculpture works has yet to account for the affordances of
current portable and mainstream AR systems. In this work, we take advantage of
the HoloLens' spatial awareness to build sonic spaces that have a precise
spatial relationship to a given sculpture and where the sculpture itself is
modelled in the augmented scene as an "invisible hologram". We describe the
artistic rationale for our artwork, the design of the two interaction schemes,
and the technical and usability feedback that we have obtained from
demonstrations during iterative development.


  We study certificates in static data structures. In the cell-probe model,
certificates are the cell probes which can uniquely identify the answer to the
query. As a natural notion of nondeterministic cell probes, lower bounds for
certificates in data structures immediately imply deterministic cell-probe
lower bounds. In spite of this extra power brought by nondeterminism, we prove
that two widely used tools for cell-probe lower bounds: richness lemma of
Miltersen et al. and direct-sum richness lemma of Patrascu and Thorup, both
hold for certificates in data structures with even better parameters. Applying
these lemmas and adopting existing reductions, we obtain certificate lower
bounds for a variety of static data structure problems. These certificate lower
bounds are at least as good as the highest known cell-probe lower bounds for
the respective problems. In particular, for approximate near neighbor (ANN)
problem in Hamming distance, our lower bound improves the state of the art.
When the space is strictly linear, our lower bound for ANN in d-dimensional
Hamming space becomes t=Omega(d), which along with the recent breakthrough for
polynomial evaluation of Larsen, are the only two t=Omega(d) lower bounds ever
proved for any problems in the cell-probe model.


  We examine the BRS cohomology of chiral matter in $N=1$, $D=4$ supersymmetry
to determine a general form of composite superfield operators which can suffer
from supersymmetry anomalies. Composite superfield operators $\Y_{(a,b)}$ are
products of the elementary chiral superfields $S$ and $\ov S$ and the
derivative operators $D_\a$, $\ov D_{\dot \b}$ and $\pa_{\a \dot \b}$. Such
superfields $\Y_{(a,b)}$ can be chosen to have `$a$' symmetrized undotted
indices $\a_i$ and `$b$' symmetrized dotted indices $\dot \b_j$. The result
derived here is that each composite superfield $\Y_{(a,b)}$ is subject to
potential supersymmetry anomalies if $a-b$ is an odd number, which means that
$\Y_{(a,b)}$ is a fermionic superfield.


  We prove a uniqueness result for asymptotically conical (AC) gradient
shrinking solitons for the Laplacian flow of closed G_2-structures: If two
gradient shrinking solitons to Laplacian flow are asymptotic to the same closed
G_2-cone, then their G_2-structures are equivalent, and in particular, the two
solitons are isometric. The proof extends Kotschwar and Wang's argument for
uniqueness of AC gradient shrinking Ricci solitons. We additionally show that
the symmetries of the G_2-structure of an AC shrinker end are inherited from
its asymptotic cone; under a mild assumption on the fundamental group, the
symmetries of the asymptotic cone extend to global symmetries.


  We prove Chern class equalities for abelian families with a holomorphic
normal projective connection.


  Large Language Models (LLMs) have seen an impressive wave of advances
recently, with models now excelling in a variety of tasks, such as mathematical
reasoning and program synthesis. However, their potential to effectively use
tools via API calls remains unfulfilled. This is a challenging task even for
today's state-of-the-art LLMs such as GPT-4, largely due to their inability to
generate accurate input arguments and their tendency to hallucinate the wrong
usage of an API call. We release Gorilla, a finetuned LLaMA-based model that
surpasses the performance of GPT-4 on writing API calls. When combined with a
document retriever, Gorilla demonstrates a strong capability to adapt to
test-time document changes, enabling flexible user updates or version changes.
It also substantially mitigates the issue of hallucination, commonly
encountered when prompting LLMs directly. To evaluate the model's ability, we
introduce APIBench, a comprehensive dataset consisting of HuggingFace,
TorchHub, and TensorHub APIs. The successful integration of the retrieval
system with Gorilla demonstrates the potential for LLMs to use tools more
accurately, keep up with frequently updated documentation, and consequently
increase the reliability and applicability of their outputs. Gorilla's code,
model, data, and demo are available at https://gorilla.cs.berkeley.edu


  The supernova (SN) neutronization phase produces mainly electron ($\nu_e$)
neutrinos, the oscillations of which must take place within a few
mean-free-paths of their resonance surface located nearby their neutrinosphere.
The state-of-the-art on the SN dynamics suggests that a significant part of
these $\nu_e$ can convert into right-handed neutrinos in virtue of the
interaction of the electrons and the protons flowing with the SN outgoing
plasma, whenever the Dirac neutrino magnetic moment be of strength $\mu_\nu <
10^{-11} \mu_{\rm B}$, with $\mu_{\rm B}$ being the Bohr magneton. In the
supernova envelope, part of these neutrinos can flip back to the left-handed
flavors due to the interaction of the neutrino magnetic moment with the
magnetic field in the SN expanding plasma (Kuznetsov & Mikheev 2007; Kuznetsov,
Mikheev & Okrugin 2008), a region where the field strength is currently
accepted to be $B \gtrsim 10^{13}$ ~G. This type of $\nu$ oscillations were
shown to generate powerful gravitational wave (GW) bursts (Mosquera Cuesta
2000, Mosquera Cuesta 2002, Mosquera Cuesta & Fiuza 2004, Loveridge 2004). If
such double spin-flip mechanism does run into action inside the SN core, then
the release of both the oscillation-produced $\nu_\mu$s, $\nu_\tau$s and the GW
pulse generated by the coherent $\nu$ spin-flips provides a unique emission
offset $\Delta T^{emission}_{\rm GW} \leftrightarrow \nu = 0$ for measuring the
$\nu$ travel time to Earth. As massive $\nu$s get noticeably delayed on its
journey to Earth with respect to the Einstein GW they generated during the
reconversion transient, then the accurate measurement of this time-of-flight
delay by SNEWS + LIGO, VIRGO, BBO, DECIGO, etc., might readily assess the
absolute $\nu$ mass spectrum.


  With the recent advancements in Artificial Intelligence (AI), various
organizations and individuals started debating about the progress of AI as a
blessing or a curse for the future of the society. This paper conducts an
investigation on how the public perceives the progress of AI by utilizing the
data shared on Twitter. Specifically, this paper performs a comparative
analysis on the understanding of users from two categories -- general
AI-Tweeters (AIT) and the expert AI-Tweeters (EAIT) who share posts about AI on
Twitter. Our analysis revealed that users from both the categories express
distinct emotions and interests towards AI. Users from both the categories
regard AI as positive and are optimistic about the progress of AI but the
experts are more negative than the general AI-Tweeters. Characterization of
users manifested that `London' is the popular location of users from where they
tweet about AI. Tweets posted by AIT are highly retweeted than posts made by
EAIT that reveals greater diffusion of information from AIT.


  This work establishes rigorous, novel and widely applicable stability
guarantees and transferability bounds for graph convolutional networks --
without reference to any underlying limit object or statistical distribution.
Crucially, utilized graph-shift operators (GSOs) are not necessarily assumed to
be normal, allowing for the treatment of networks on both undirected- and for
the first time also directed graphs. Stability to node-level perturbations is
related to an 'adequate (spectral) covering' property of the filters in each
layer. Stability to edge-level perturbations is related to Lipschitz constants
and newly introduced semi-norms of filters. Results on stability to topological
perturbations are obtained through recently developed mathematical-physics
based tools. As an important and novel example, it is showcased that graph
convolutional networks are stable under graph-coarse-graining procedures
(replacing strongly-connected sub-graphs by single nodes) precisely if the GSO
is the graph Laplacian and filters are regular at infinity. These new
theoretical results are supported by corresponding numerical investigations.


  This work presents a novel method to generate secret keys shared between a
legitimate node pair (Alice and Bob) to safeguard the communication between
them from an unauthorized node (Eve). To this end, we exploit the {\it
reciprocal carrier frequency offset} (CFO) between the legitimate node pair to
extract common randomness out of it to generate shared secret keys. The
proposed key generation algorithm involves standard steps: the legitimate nodes
exchange binary phase-shift keying (BPSK) signals to perform blind CFO
estimation on the received signals, and do equi-probable quantization of the
noisy CFO estimates followed by information reconciliation--to distil a shared
secret key. Furthermore, guided by the Allan deviation curve, we distinguish
between the two frequency-stability regimes---when the randomly time-varying
CFO process i) has memory, ii) is memoryless; thereafter, we compute the key
generation rate for both regimes. Simulation results show that the key
disagreement rate decreases exponentially with increase in the signal to noise
ratio of the link between Alice and Bob. Additionally, the decipher probability
of Eve decreases as soon as either of the two links observed by the Eve becomes
more degraded compared to the link between Alice and Bob.


  Einsteinian cubic gravity (ECG) is the most general theory up to cubic order
in curvature, which have the same graviton spectrum as the Einstein theory. In
this paper, we investigate the geodesic motions of timelike particles around
the four dimensional asymptotically flat black holes in ECG, and discuss their
potential applications when connecting them with recent observational results.
We first explore the effects of the cubic couplings on the marginally bound
orbits (MBO), innermost stable circular orbits (ISCO) and on the periodic
orbits around the Einsteinian cubic black hole. We find that comparing to
Schwarzschild black hole in general relativity, the cubic coupling enhances the
energy as well as the angular momentum for all the bound orbits of the
particles. Then, we derive the relativistic periastron precessions of the
particles and give a preliminary bound on the cubic coupling employing the
observational result of the S2 star' precession in SgrA*. Finally, after
calculating the periodic orbits' configurations, we preliminarily evaluate the
gravitational waveform radiated from several periodic orbits in one complete
period of a test object which orbits a supermassive Einsteinian cubic black
hole. Our studies could be helpful for us to better understand the
gravitational structure of the theory with high curvatures.


  We introduce a Monte--Carlo simulation approach to thermodynamic Bethe ansatz
(TBA). We exemplify the method on one particle integrable models, which include
a free boson and a free fermions systems along with the scaling Lee--Yang model
(SLYM). It is confirmed that the central charges and energies are correct to a
very good precision, typically 0.1% or so. The advantage of the method is that
it enables the calculation of all the dimensions and even the particular
partition function.


  A finite group is said to be weakly separable if every algebraic isomorphism
between two $S$-rings over this group is induced by a combinatorial
isomorphism. In the paper we prove that every abelian weakly separable group
belongs to one of several explicitly given families only.


  We present a new catalog of photometric and spectroscopic data on M31
globular clusters. The catalog includes new optical and near-infrared
photometry for a substantial fraction of the 435 clusters and cluster
candidates. We use these data to determine the reddening and intrinsic colors
of individual clusters, and find that the extinction laws in the Galaxy and M31
are not significantly different. There are significant (up to 0.2mag in V-K)
offsets between the clusters' intrinsic colors and simple stellar population
colors predicted by population synthesis models; we suggest that these are due
to systematic errors in the models. The distributions of M31 clusters'
metallicities and metallicity-sensitive colors are bimodal, with peaks at
[Fe/H] ~ -1.4 and -0.6. The distribution of V-I is often bimodal in elliptical
galaxies' globular cluster systems, but is not sensitive enough to metallicity
to show bimodality in M31 and Galactic cluster systems. The radial distribution
and kinematics of the two M31 metallicity groups imply that they are analogs of
the Galactic `halo' and `disk/bulge' cluster systems. The globular clusters in
M31 have a small radial metallicity gradient, suggesting that some dissipation
occurred during the GCS formation. The lack of correlation between cluster
luminosity and metallicity in M31 GCs shows that self-enrichment is not
important in GC formation.


  We report new heat capacity measurements on single crystal Ce$_2$Zr$_2$O$_7$
down to $\sim$ 0.1 K in a magnetic field along the $[1,\bar{1}, 0]$ direction.
These new measurements show that the broad hump in the zero-field heat capacity
moves higher in temperature with increasing field strength and is split into
two humps by the $[1,\bar{1}, 0]$ field at $\sim$ 2 T. These separate features
are due to the decomposition of the pyrochlore lattice into effectively
decoupled chains for fields in this direction: one set of chains
($\alpha$-chains) is polarized by the field while the other ($\beta$-chains)
remains free. Our theoretical modelling suggests that the $\beta$-chains are
close to a critical state, with nearly-gapless excitations. We also report new
elastic and inelastic neutron scattering measurements on single crystal
Ce$_2$Zr$_2$O$_7$ in $[1, \bar{1}, 0]$ and $[0, 0, 1]$ magnetic fields at
temperatures down to 0.03 K. The elastic scattering behaves consistently with
the formation of independent chains for a $[1, \bar{1}, 0]$ field, while the
$[0, 0, 1]$ field produces a single field-induced magnetic Bragg peak at $(0,
2, 0)$ and equivalent wavevectors, indicating a polarized spin ice for fields
above $\sim$ 3 T. For both $[1, \bar{1}, 0]$ and $[0, 0, 1]$ fields, our
inelastic neutron scattering results show an approximately-dispersionless
continuum of scattering that increases in both energy and intensity with
increasing field strength. By modelling the complete set of experimental data
using numerical linked cluster and semiclassical molecular dynamics
calculations, we demonstrate the dominantly multipolar nature of the exchange
interactions in Ce$_2$Zr$_2$O$_7$ and the smallness of the parameter $\theta$
which controls the mixing between dipolar and octupolar degrees of freedom.
These results support previous estimates of the microscopic exchange
parameters.


  25% of people who received a liver transplant will go on to develop diabetes
within the next 5 years. These thousands of individuals are at 2-fold higher
risk of cardiovascular events, graft loss, infections, as well as lower
long-term survival. This is partly due to the medication used during and/or
after transplant that significantly impacts metabolic balance. To assess which
medication best suits the patient's condition, clinicians need an accurate
estimate of diabetes risk. Both patient's historical data and observations at
the current visit are informative in predicting whether the patient will
develop diabetes within the following year. In this work we compared a variety
of time-to-event prediction models as well as classifiers predicting the
likelihood of the event within a year from the current checkup. We are
particularly interested in comparing two types of models: 1) standard
time-to-event predictors where the historical measurements are merely
concatenated, 2) incorporating Deep Markov Model to first obtain
low-dimensional embedding of historical data and then using this embedding as
an additional input into the model. We compared a variety of algorithms
including standard and regularized Cox proportional-hazards model (CPH), mixed
effect random forests, survival-forests and Weibull Time-To-Event Recurrent
Neural Network (WTTE-RNN). The results show that although all methods'
performances varied from year to year and there was no clear winner across all
the time points, regularized CPH model that used 1 to 3 years of historical
visits data on average achieved a high, clinically relevant Concordance Index
of .863. We thus recommend this model for further prospective clinical
validation and hopefully, an eventual use in the clinic to improve clinicians'
ability to personalize post-operative care and reduce the incidence of
new-onset diabetes post liver transplant.


  New experimental data on inclusive spectra of identified particles produced
in pp collisions at the RHIC are used to test z-scaling. Energy and
multiplicity independence of the scaling function is established. The RHIC data
confirm z-scaling observed at U70, ISR, SpS and Tevatron energies. The obtained
results are of interest to search for new physics phenomena of particle
production in high transverse momentum and high multiplicity region at RHIC,
Tevatron and LHC.


  High-field charge transport in semiconductors is of fundamental interest and
practical importance. While the \textit{ab initio} treatment of low-field
transport is well-developed, the treatment of high-field transport is much less
so, particularly for multi-phonon processes that are reported to be relevant in
GaAs. Here, we report a calculation of the high-field transport properties and
current power spectral density (PSD) of hot electrons in GaAs from first
principles including on-shell two-phonon (2ph) scattering. The on-shell 2ph
scattering rates are found to qualitatively alter the high-field distribution
function by increasing both the momentum and energy relaxation rates as well as
contributing markedly to intervalley scattering. This finding reconciles a
long-standing discrepancy regarding the strength of intervalley scattering in
GaAs as inferred from transport and optical studies. The characteristic
non-monotonic trend of PSD with electric field is not predicted at this level
of theory. Our work shows how \textit{ab initio} calculations of high-field
transport and noise may be used as a stringent test of the electron-phonon
interaction in semiconductors.


  We present the refinement of the crystal structure of charge-ordered LuFe2O4,
based on single-crystal x-ray diffraction data. The arrangement of the
different Fe-valence states, determined with bond-valence-sum analysis,
corresponds to a stacking of charged Fe bilayers, in contrast to the polar
bilayers previously suggested. This arrangement is supported by an analysis of
x-ray magnetic circular dichroism spectra, which also evidences a strong
charge-spin coupling. The non-polar bilayers are inconsistent with charge order
based ferroelectricity.


  Almost all modern hardware, from phone SoCs to high-end servers with
accelerators, contain memory translation and protection hardware like IOMMUs,
firewalls, and lookup tables which make it impossible to reason about, and
enforce protection and isolation based solely on the processor's MMUs. This has
led to numerous bugs and security vulnerabilities in today's system software.
  In this paper we regain the ability to reason about and enforce access
control using the proven concept of a reference monitor mediating accesses to
memory resources. We present a fine-grained, realistic memory protection model
that makes this traditional concept applicable today, and bring system software
in line with the complexity of modern, heterogeneous hardware.
  Our design is applicable to any operating system, regardless of architecture.
We show that it not only enforces the integrity properties of a system, but
does so with no inherent performance overhead and it is even amenable to
automation through code generation from trusted hardware specifications.


  CCD UBVRI photometry is presented for type IIn SN 2005kd. The maximum
luminosity exceeded Mv=-19.8, and SN remained brighter than -18 mag for about
400 days. While overall photometric evolution is quite similar to SN 1997cy, SN
2005kd shows a plateau at phases between 119 and 311 days past explosion, which
is a unique feature for SN IIn.


  We investigate the use of a non-parametric independence measure, the
Hilbert-Schmidt Independence Criterion (HSIC), as a loss-function for learning
robust regression and classification models. This loss-function encourages
learning models where the distribution of the residuals between the label and
the model prediction is statistically independent of the distribution of the
instances themselves. This loss-function was first proposed by Mooij et al.
(2009) in the context of learning causal graphs. We adapt it to the task of
learning for unsupervised covariate shift: learning on a source domain without
access to any instances or labels from the unknown target domain, but with the
assumption that $p(y|x)$ (the conditional probability of labels given
instances) remains the same in the target domain. We show that the proposed
loss is expected to give rise to models that generalize well on a class of
target domains characterised by the complexity of their description within a
reproducing kernel Hilbert space. Experiments on unsupervised covariate shift
tasks demonstrate that models learned with the proposed loss-function
outperform models learned with standard loss functions, achieving
state-of-the-art results on a challenging cell-microscopy unsupervised
covariate shift task.


  We study asset price bubbles in market models with proportional transaction
costs $\lambda\in (0,1)$ and finite time horizon $T$ in the setting of [49]. By
following [28], we define the fundamental value $F$ of a risky asset $S$ as the
price of a super-replicating portfolio for a position terminating in one unit
of the asset and zero cash. We then obtain a dual representation for the
fundamental value by using the super-replication theorem of [50]. We say that
an asset price has a bubble if its fundamental value differs from the ask-price
$(1+\lambda)S$. We investigate the impact of transaction costs on asset price
bubbles and show that our model intrinsically includes the birth of a bubble.


  We consider the Landau-Lifshitz equation for the spin torque oscillator - a
uniaxial ferromagnet in an external magnetic field with polarised spin current
driven through it. In the absence of the Gilbert damping, the equation turns
out to be PT-symmetric. We interpret the PT-symmetry as a balance between gain
and loss - and identify the gaining and losing modes. In the vicinity of the
bifurcation point of a uniform static state of magnetisation, the PT-symmetric
Landau-Lifshitz equation with a small dissipative perturbation reduces to a
nonlinear Schr\"odinger equation with a quadratic nonlinearity. The analysis of
the Schr\"odinger dynamics demonstrates that the spin torque oscillator
supports stable magnetic solitons. The PT near-symmetry is crucial for the
soliton stability: the addition of a finite dissipative term to the
Landau-Lifshitz equation destabilises all solitons that we have found.


  In this work we examine the effect of phase-space noncommutativity on some
typically quantum properties such as quantum beating, quantum information, and
decoherence. To exemplify these issues we consider the two-dimensional
noncommutative quantum harmonic oscillator whose components behavior we monitor
in time. This procedure allows us to determine how the noncommutative
parameters are related to the missing information quantified by the linear
quantum entropy and by the mutual information between the relevant Hilbert
space coordinates. Particular questions concerning the thermodynamic limit of
some relevant properties are also discussed in order to evidence the effects of
noncommutativity. Finally, through an analogy with the Zeeman effect, we
identify how some aspects of the axial symmetry of the problem suggest the
possibility of decoupling the noncommutative quantum perturbations from
unperturbed commutative well-known solutions.


  Neutral macroevolutionary models, such as the Yule model, give rise to a
probability distribution on the set of discrete rooted binary trees over a
given leaf set. Such models can provide a signal as to the approximate location
of the root when only the unrooted phylogenetic tree is known, and this signal
becomes relatively more significant as the number of leaves grows. In this
short note, we show that among models that treat all taxa equally, and are
sampling consistent (i.e. the distribution on trees is not affected by taxa yet
to be included), all such models, except one, convey some information as to the
location of the ancestral root in an unrooted tree.


  We identify the largest known lensed images of a single spiral galaxy, lying
close to the centre of the distant cluster MACS J1149.5+2223 ($z=0.544$). These
images cover a total area of $\simeq 150 \Box\arcsec$ and are magnified $\simeq
200$ times. Unusually, there is very little image distortion implying the
central mass distribution is almost uniform over a wide area ($r\simeq200 kpc$)
with a surface density equal to the critical density for lensing, corresponding
to maximal lens magnification. Many fainter multiply-lensed galaxies are also
uncovered by our model, outlining a very large tangential critical curve, of
radius $r\simeq 170 kpc$, posing a potential challenge for the standard
LCDM-Cosmology. Because of the uniform central mass distribution a particularly
clean measurement of the mass of the brightest cluster galaxy is possible here,
for which we infer stars contribute most of the mass within a limiting radius
of $\simeq 30 kpc$, with a mass-to-light ratio of $M/L_{B}\simeq
4.5(M/L)_{\odot}$. This cluster with its uniform and central mass distribution
acts analogously to a regular magnifying glass, converging light without
distorting the images, resulting in the most powerful lens yet discovered for
accessing the faint high-$z$ Universe.


  We present a study at next-to-leading-order (NLO) of the process $pp \to
W^\pm Z \to \ell \nu_l \ell'^+ \ell'^-$, where $\ell,\ell' =e, \mu$, at the
Large Hadron Collider. We include the full NLO QCD corrections and the NLO
electroweak (EW) corrections in the double-pole approximation. We define eight
fiducial polarization coefficients directly constructed from the
polar-azimuthal angular distribution of the decay leptons. These coefficients
depend strongly on the kinematical cuts on the transverse momentum or rapidity
of the individual leptons. Similarly, fiducial polarization fractions are also
defined and they can be directly related to the fiducial coefficients. We
perform a detailed analysis of the NLO QCD+EW fiducial polarization observables
including theoretical uncertainties stemming from the scale variation and
parton distribution function uncertainties, using the fiducial phase space
defined by the ATLAS and CMS experiments. We provide results in the helicity
coordinate system and in the Collins-Soper coordinate system, at a
center-of-mass energy of 13 TeV. The EW corrections are found to be important
in two of the angular coefficients related to the $Z$ boson, irrespective of
the kinematical cuts or the coordinate system. Meanwhile, those EW corrections
are very small for the $W^\pm$ bosons.


  We perform a detailed renormalization group analysis to study a
(2+1)-dimensional quantum field theory that is composed of two interacting
scalar bosons, which represent the order parameters for two continuous phase
transitions. This sort of field theory can describe the competition and
coexistence between distinct long-range orders, and therefore plays a vital
role in statistical physics and condensed matter physics. We first derive and
solve the renormalization group equations of all the relevant physical
parameters, and then show that the system does not have any stable fixed point
in the lowest energy limit. Interestingly, this conclusion holds in both the
ordered and disordered phases, and also at the quantum critical point.
Therefore, the originally continuous transitions are unavoidably turned to
first-order due to ordering competition. Moreover, we examine the impacts of
massless Goldstone boson generated by continuous symmetry breaking on ordering
competition, and briefly discuss the physical implications of our results.


  Choreographies are global descriptions of communication structures, inspired
by the "Alice and Bob" notation of security protocols. They have been
successfully employed in the design and implementation of distributed systems.
However, there is still limited evidence of the applicability of choreographies
in the real-world setting of distributed programming, where communication
actions may fail. In this work, we propose the first choreography model that
allows for communication failures and the programming of user-defined code to
deal with such failures. We validate our model by implementing common
strategies for handling communication failures in a robust way, which in turn
can be used as a library by choreographies that assume reliable communication.
We equip our model with a typing discipline that can statically verify
reliability properties, in particular at-most-once and exactly-once delivery.
We demonstrate the applicability of our model by defining a
semantics-preserving compilation procedure towards a process calculus equipped
with unreliable I/O actions.


  We study the photoionization of argon atoms close to the 3s$^2$3p$^6$
$\rightarrow$ 3s$^1$3p$^6$4p $\leftrightarrow$ 3s$^2$3p$^5$ $\varepsilon \ell$,
$\ell$=s,d Fano window resonance. An interferometric technique using an
attosecond pulse train, i.e. a frequency comb in the extreme ultraviolet range,
and a weak infrared probe field allows us to study both amplitude and phase of
the photoionization probability amplitude as a function of photon energy. A
theoretical calculation of the ionization process accounting for several
continuum channels and bandwidth effects reproduces well the experimental
observations and shows that the phase variation of the resonant two-photon
amplitude depends on the interaction between the channels involved in the
autoionization process.


  Even before the experimental discovery of spin- and charge-stripe order in
La$_{2-x-y}$Nd$_y$Sr$_x$CuO$_4$ and La$_{2-x}$Ba$_x$CuO$_4$ at x = 1/8, stripe
formation was predicted from theoretical considerations. Nevertheless, a
consistent description of the complex coexistence of stripe order with
superconductivity has remained a challenge. Here we introduce a Hartree-Fock
decoupling scheme which unifies previous approaches and allows for a detailed
analysis of the competition between antiferromagnetism and superconductivity in
real and momentum space. We identify two distinct parameter regimes, where
spin-stripe order coexists with either one- or two-dimensional
superconductivity; experiments on different striped cuprates are either
compatible with the former or the latter regime. We argue that the cuprates at
x = 1/8 fall into an intermediate coupling regime with a crossover to
long-range phase coherence between individual superconducting stripes.


  Single image super-resolution (SISR) aims to reconstruct high-resolution (HR)
images from the given low-resolution (LR) ones, which is an ill-posed problem
because one LR image corresponds to multiple HR images. Recently,
learning-based SISR methods have greatly outperformed traditional ones, while
suffering from over-smoothing, mode collapse or large model footprint issues
for PSNR-oriented, GAN-driven and flow-based methods respectively. To solve
these problems, we propose a novel single image super-resolution diffusion
probabilistic model (SRDiff), which is the first diffusion-based model for
SISR. SRDiff is optimized with a variant of the variational bound on the data
likelihood and can provide diverse and realistic SR predictions by gradually
transforming the Gaussian noise into a super-resolution (SR) image conditioned
on an LR input through a Markov chain. In addition, we introduce residual
prediction to the whole framework to speed up convergence. Our extensive
experiments on facial and general benchmarks (CelebA and DIV2K datasets) show
that 1) SRDiff can generate diverse SR results in rich details with
state-of-the-art performance, given only one LR input; 2) SRDiff is easy to
train with a small footprint; and 3) SRDiff can perform flexible image
manipulation including latent space interpolation and content fusion.


  The recently developed self consistent {\it ab initio} lattice dynamical
method (SCAILD) has been applied to the high temperature bcc phase of La and Th
which are dynamically unstable at low temperatures. The bcc phase of these
metals is found to be stabilized by phonon-phonon interactions. The calculated
high temperature phonon frequencies for La are found to be in good agreement
with the corresponding experimental data.


  Machine translation is evolving quite rapidly in terms of quality. Nowadays,
we have several machine translation systems available in the web, which provide
reasonable translations. However, these systems are not perfect, and their
quality may decrease in some specific domains. This paper examines the effects
of different training methods when it comes to Polish - English Statistical
Machine Translation system used for the medical data. Numerous elements of the
EMEA parallel text corpora and not related OPUS Open Subtitles project were
used as the ground for creation of phrase tables and different language models
including the development, tuning and testing of these translation systems. The
BLEU, NIST, METEOR, and TER metrics have been used in order to evaluate the
results of various systems. Our experiments deal with the systems that include
POS tagging, factored phrase models, hierarchical models, syntactic taggers,
and other alignment methods. We also executed a deep analysis of Polish data as
preparatory work before automatized data processing such as true casing or
punctuation normalization phase. Normalized metrics was used to compare
results. Scores lower than 15% mean that Machine Translation engine is unable
to provide satisfying quality, scores greater than 30% mean that translations
should be understandable without problems and scores over 50 reflect adequate
translations. The average results of Polish to English translations scores for
BLEU, NIST, METEOR, and TER were relatively high and ranged from 70,58 to
82,72. The lowest score was 64,38. The average results ranges for English to
Polish translations were little lower (67,58 - 78,97). The real-life
implementations of presented high quality Machine Translation Systems are
anticipated in general medical practice and telemedicine.


  We consider the observational aspects of the value of dark energy density
from quantum vacuum fluctuations based initially on the Gurzadyan-Xue model. We
reduce the Djorgovski-Gurzadyan integral equation to a differential equation
for the co-moving horizon and then, by means of the obtained explicit form for
the luminosity distance, we construct the Hubble diagram for two classes of
observational samples. For supernova and gamma-ray burst data we show that this
approach provides viable predictions for distances up to $z \simeq 9$,
quantitatively at least as good as those provided by the lambda cold dark
matter ($\Lambda$CDM) model. The Hubble parameter dependence $H(z)$ of the two
models also reveals mutual crossing at $z=0.4018$, the interpretation of which
is less evident.


  In this note we explore a fully unsupervised deep-learning framework for
simulating non-linear structural equation models from observational training
data. The main contribution of this note is an architecture for applying
moment-matching loss functions to the edges of a causal Bayesian graph,
resulting in a generative conditional-moment-matching graph-neural-network.
This framework thus enables automated sampling of latent space conditional
probability distributions for various graphical interventions, and is capable
of generating out-of-sample interventional probabilities that are often
faithful to the ground truth distributions well beyond the range contained in
the training set. These methods could in principle be used in conjunction with
any existing autoencoder that produces a latent space representation containing
causal graph structures.


  We study learners (computable devices) inferring formal languages, a setting
referred to as language learning in the limit or inductive inference. In
particular, we require the learners we investigate to be witness-based, that
is, to justify each of their mind changes. Besides being a natural requirement
for a learning task, this restriction deserves special attention as it is a
specialization of various important learning paradigms. In particular, with the
help of witness-based learning, explanatory learners are shown to be equally
powerful under these seemingly incomparable paradigms. Nonetheless, until now,
witness-based learners have only been studied sparsely.
  In this work, we conduct a thorough study of these learners both when
requiring syntactic and semantic convergence and obtain normal forms thereof.
In the former setting, we extend known results such that they include
witness-based learning and generalize these to hold for a variety of learners.
Transitioning to behaviourally correct learning, we also provide normal forms
for semantically witness-based learners. Most notably, we show that set-driven
globally semantically witness-based learners are equally powerful as their
Gold-style semantically conservative counterpart. Such results are key to
understanding the, yet undiscovered, mutual relation between various important
learning paradigms when learning behaviourally correctly.


  Based on the photometric data from the Spitzer/SAGE survey and with red
giants as the extinction tracers, the mid-infrared (MIR) extinction laws in the
Large Magellanic Cloud (LMC) are derived for the first time in the form of
A_\lambda/A_Ks, the extinction in the four IRAC bands (i.e., [3.6], [4.5],
[5.8] and [8.0]um) relative to the 2MASS Ks band at 2.16um. We obtain the
near-infrared (NIR) extinction coefficient to be E(J-H)/E(H-Ks)=1.29\pm0.04 and
E(J-Ks)/E(H-Ks)=1.94\pm0.04. The wavelength dependence of the MIR extinction
A_\lambda/A_Ks in the LMC varies from one sightline to another. The overall
mean MIR extinction is A_[3.6]/A_Ks=0.72\pm0.03, A_[4.5]/A_Ks=0.94\pm0.03,
A_[5.8]/A_Ks=0.58\pm0.04, and A_[8.0]/A_Ks=0.62\pm0.05. Except for the
extinction in the IRAC [4.5] band which may be contaminated by the 4.6um CO gas
absorption of red giants (which are used to trace the LMC extinction), the
extinction in the other three IRAC bands show a flat curve, close to the Milky
Way Rv = 5.5 model extinction curve (where Rv is the optical total-to-selective
extinction ratio). The possible systematic bias caused by the correlated
uncertainties of Ks-\lambda and J-Ks is explored in terms of Monte-Carlo
simulations. It is found that this could lead to an overestimation of
A_lambda/A_Ks in the MIR.


  This paper, along with E592 and E636, seems to consider the binomial
expansion (1+z)^n in the case where z is complex. Euler even gives the sums of
divergent series. The paper is translated from Euler's Latin original into
German.


  In this paper, we revisit McLaughlin's inverse problem, which consists in the
recovery of the fourth-order differential operator from the eigenvalues and two
sequences of weight numbers. We for the first time prove the uniqueness for
solution of this problem. Moreover, we obtain the interpretation of
McLaughlin's problem in the framework of the general inverse problem theory by
Yurko for differential operators of arbitrary orders. An advantage of our
approach is that it requires neither smoothness of the coefficients nor
self-adjointness of the operator. In addition, we establish the connection
between McLaughlin's problem and Barcilon's three-spectra inverse problem.


  A semi-empirical acoustic model for self-noise was adapted to predict the
sound radiated from an axial fan featuring rotating controlled diffusion blades
(RCDB). Experimental data for wake velocity, mass flow rate across the fan, and
fan rotational speed were obtained. These experimental data along with typical
characteristics of turbulent boundary layers were used to predict the noise of
the axial fan. Hot-wire wake measurements were made in the near region
downstream of the fan plane. The fan noise was measured upstream of the fan.
The experimentally obtained self-noise was then compared to the predictions
made by the semi-empirical acoustic model. Goody's and Rozenberg's models for
surface pressure spectra were used in the semi-empirical acoustic model.
Rozenberg's model offered a more accurate prediction in the final fan noise
spectra. The predictions were in reasonable agreement with experimental data,
and the model was found to be a useful tool to reasonably estimate acoustic
emissions of a fan with limited information about the velocity field in the fan
wake. Different operating conditions and blade configurations were examined.
For a given dimensionless operating condition, the self-noise was obtained for
different rotational speeds, and the effect of the fan speed on the propagated
noise was evaluated. The acoustic scaling function was experimentally obtained
as a function of normalized frequency and dimensionless operating condition and
it was found to be quite frequency dependent despite it is often assumed as a
constant value.


  Let C be an algebraic curve of genus g. Consider extensions E of a vector
bundle F'' of rank n'' by a vector bundle F' of rank n'. The following
statement was conjectured by Lange: If 0<n'deg F''-n''degF'\le n'n''(g-1), then
there exist extensions like this with E stable. We prove this result for the
generic curve when F' is a line bundle. Our method uses a degeneration argument
to a reducible curve.


  For a vector bundle V over a curve X of rank n and for each integer r in the
range 1 \le r \le n-1, the Segre invariant s_r is defined by generalizing the
minimal self-intersection number of the sections on a ruled surface. In this
paper we generalize Lange and Narasimhan's results on rank 2 bundles which
related the invariant s_1 to the secant varieties of the curve inside certain
extension spaces. For any n and r, we find a way to get information on the
invariant s_r from the secant varieties of certain subvariety of a scroll over
X. Using this geometric picture, we obtain a new proof of the Hirschowitz bound
on s_r.


  Out-of-time-ordered correlators (OTOCs) are of crucial importance for
studying a wide variety of fundamental phenomena in quantum physics, ranging
from information scrambling to quantum chaos and many-body localization.
However, apart from a few special cases, they are notoriously difficult to
compute even numerically due to the exponential complexity of generic quantum
many-body systems. In this paper, we introduce a machine learning approach to
OTOCs based on the restricted-Boltzmann-machine architecture, which features
wide applicability and could work for arbitrary-dimensional systems with
massive entanglement. We show, through a concrete example involving a
two-dimensional transverse field Ising model, that our method is capable of
computing early-time OTOCs with respect to random pure quantum states or
infinite-temperature thermal ensembles. Our results showcase the great
potential for machine learning techniques in computing OTOCs, which open up
numerous directions for future studies related to similar physical quantities.


  The article revisits a result of Antonio Lei, David Loeffler, and Sarah Livia
Zerbes concerning the structure of the image by the Iwasawa regulator map of
the Iwasawa module associated with a semi-stable $p$-adic representation on an
unramified finite extension of $Q_p$ and give a direct proof based on the
results of "Repr\'esentations $p$-adiques et normes universelles: I. le cas
cristallin" in the crystalline case and of "Th\'eorie d'Iwasawa des
repr\'esentations $p$-adiques semi-stables" in the semi-stable case.


  Large pre-trained neural networks such as BERT have had great recent success
in NLP, motivating a growing body of research investigating what aspects of
language they are able to learn from unlabeled data. Most recent analysis has
focused on model outputs (e.g., language model surprisal) or internal vector
representations (e.g., probing classifiers). Complementary to these works, we
propose methods for analyzing the attention mechanisms of pre-trained models
and apply them to BERT. BERT's attention heads exhibit patterns such as
attending to delimiter tokens, specific positional offsets, or broadly
attending over the whole sentence, with heads in the same layer often
exhibiting similar behaviors. We further show that certain attention heads
correspond well to linguistic notions of syntax and coreference. For example,
we find heads that attend to the direct objects of verbs, determiners of nouns,
objects of prepositions, and coreferent mentions with remarkably high accuracy.
Lastly, we propose an attention-based probing classifier and use it to further
demonstrate that substantial syntactic information is captured in BERT's
attention.


  We studied the spherical collapse model in the flat $\Lambda$CDM cosmology
and provided exact and analytical formulaes for the calculation of the two
important parameters in the application of Press-Schechter theory, the critical
density contrast and the ratio of cluster/background densities at the
virialization point in terms of a media variable which can be solved precisely
by numerical methods.


  This study presents a systematic machine learning approach for creating
efficient hybrid models and discovering sorption uptake models in non-linear
advection-diffusion-sorption systems. It demonstrates an effective method to
train these complex systems using gradient based optimizers, adjoint
sensitivity analysis, and JIT-compiled vector Jacobian products, combined with
spatial discretization and adaptive integrators. Sparse and symbolic regression
were employed to identify missing functions in the artificial neural network.
The robustness of the proposed method was tested on an in-silico data set of
noisy breakthrough curve observations of fixed-bed adsorption, resulting in a
well-fitted hybrid model. The study successfully reconstructed sorption uptake
kinetics using sparse and symbolic regression, and accurately predicted
breakthrough curves using identified polynomials, highlighting the potential of
the proposed framework for discovering sorption kinetic law structures.


  We develop a method to control the group delay of electromagnetic waves
continuously using a doubly resonant metasurface. The method is based on the
dependences of i) the group velocity in a medium featuring two resonance lines
on the resonance linewidths and ii) the resonance linewidth of a metasurface
composed of split-ring resonators on an incidence angle of electromagnetic
wave. To verify this method for group-delay control, we design a terahertz
metasurface composed of two split-ring resonators with different resonance
frequencies and numerically analyze the transmission characteristic of the
metasurface. Double resonance lines are observed for oblique incidence and the
resonance transmission dips become deeper and broader with increasing the
incidence angle. The group delay at around the center frequency of the double
resonance lines is found to vary in the range about from 0s to 20 times the
period of the incident wave with the incidence angle. In contrast with a
previously reported method for variable control of group delay using
electromagnetically-induced-transparency-like metamaterials, a high
transmittance is achieved for a small group delay condition.


  We examine the role of small-scale granulation in helping to drive
supergranulation and even larger scales of convection. The granulation is
modeled as localized cooling events introduced at the upper boundary of a 3-D
simulation of compressible convection in a rotating spherical shell segment.
With a sufficient number of stochastic cooling events compared to uniform
cooling, we find that supergranular scales are realized, along with a
differential rotation that becomes increasingly solar-like.


  In 1988 S. Mori, D. Morrison, and I. Morrison gave a computer-based
conjectural classification of four-dimensional cyclic quotient singularities of
prime index. It was partially proven in 1990 by G. Sankaran. In 1991 Jim
Lawrence basically proved this and much more, been unaware of algebro-geometric
meaning of what he did. In this short note I just bring this all together to
prove that all n-dimensional toric singularities with log-discrepancy greater
than (or equal to) $\epsilon$ form finitely many "series".


  We present a relativistic density functional approach to color
superconducting quark matter that mimics quark confinement by a fast growth of
the quasiparticle selfenergy in the confining region. The approach is shown to
be equivalent to a chiral model of quark matter with medium dependent
couplings. While the (pseudo)scalar sector of the model is fitted to the vacuum
phenomenology of quantum chromodynamics, the strength of interaction in the
vector and diquark channels is varied in order to provide the best agreement
with the observational constraints on the mass-radius relation and tidal
deformability of neutron stars modelled with our approach. In order to recover
the conformal behavior of quark matter at asymptotically high densities we
introduce a medium dependence of the vector and diquark couplings motivated by
the nonperturbative gluon exchange. Our analysis signals that the onset of
deconfinement to color superconducting quark matter is likely to occur in
neutron stars with masses below 1.0 $M_\odot$.


  The usual formulations of quantum field theory in Minkowski spacetime make
crucial use of features--such as Poincare invariance and the existence of a
preferred vacuum state--that are very special to Minkowski spacetime. In order
to generalize the formulation of quantum field theory to arbitrary globally
hyperbolic curved spacetimes, it is essential that the theory be formulated in
an entirely local and covariant manner, without assuming the presence of a
preferred state. We propose a new framework for quantum field theory, in which
the existence of an Operator Product Expansion (OPE) is elevated to a
fundamental status, and, in essence, all of the properties of the quantum field
theory are determined by its OPE. We provide general axioms for the OPE
coefficients of a quantum field theory. These include a local and covariance
assumption (implying that the quantum field theory is locally and covariantly
constructed from the spacetime metric), a microlocal spectrum condition, an
"associativity" condition, and the requirement that the coefficient of the
identity in the OPE of the product of a field with its adjoint have positive
scaling degree. We prove curved spacetime versions of the spin-statistics
theorem and the PCT theorem. Some potentially significant further implications
of our new viewpoint on quantum field theory are discussed.


  We consider an elliptic Kolmogorov equation $\lambda u - Ku = f$ in a
separable Hilbert space $H$. The Kolmogorov operator $K$ is associated to an
infinite dimensional convex gradient system: $dX = (AX - DU(X))dt + dW (t)$,
where $A $ is a self--adjoint operator in $H$ and $U$ is a convex lower
semicontinuous function. Under mild assumptions we prove that for $\lambda >0$
and $f\in L^2(H,\nu)$ the weak solution $u$ belongs to the Sobolev space
$W^{2,2}(H,\nu)$, where $\nu$ is the log-concave probability measure of the
system. Moreover maximal estimates on the gradient of $u$ are proved. The
maximal regularity results are used in the study of perturbed non gradient
systems, for which we prove that there exists an invariant measure. The general
results are applied to Kolmogorov equations associated to reaction--diffusion
and Cahn--Hilliard stochastic PDE's.


  Cells with the same genome can exist in different phenotypes. and can change
between distinct phenotypes when subject to specific stimuli and
microenvironments. Some examples include cell differentiation during
development, reprogramming for induced pluripotent stem cells and
transdifferentiation, cancer metastasis and fibrosis development. The
regulation and dynamics of cell phenotypic conversion is a fundamental problem
in biology, and has a long history of being studied within the formalism of
dynamical systems. A main challenge for mechanism-driven modeling studies is
acquiring sufficient amount of quantitative information for constraining model
parameters. Advances in quantitative approaches, especially high throughput
single-cell techniques, have accelerated the emergence of a new direction for
reconstructing the governing dynamical equations of a cellular system from
quantitative single-cell data, beyond the dominant statistical approaches. Here
I review a selected number of recent studies using live- and fixed-cell data
and provide my perspective on future development.