  We present the first two-dimensional general relativistic (GR) simulations of
stellar core collapse and explosion with the CoCoNuT hydrodynamics code in
combination with the VERTEX solver for energy-dependent, three-flavor neutrino
transport, using the extended conformal flatness condition for approximating
the spacetime metric and a ray-by-ray-plus ansatz to tackle the
multi-dimensionality of the transport. For both of the investigated 11.2 and 15
solar mass progenitors we obtain successful, though seemingly marginal,
neutrino-driven supernova explosions. This outcome and the time evolution of
the models basically agree with results previously obtained with the PROMETHEUS
hydro solver including an approximative treatment of relativistic effects by a
modified Newtonian potential. However, GR models exhibit subtle differences in
the neutrinospheric conditions compared to Newtonian and pseudo-Newtonian
simulations. These differences lead to significantly higher luminosities and
mean energies of the radiated electron neutrinos and antineutrinos and
therefore to larger energy-deposition rates and heating efficiencies in the
gain layer with favorable consequences for strong non-radial mass motions and
ultimately for an explosion. Moreover, energy transfer to the stellar medium
around the neutrinospheres through nucleon recoil in scattering reactions of
heavy-lepton neutrinos also enhances the mentioned effects. Together with
previous pseudo-Newtonian models the presented relativistic calculations
suggest that the treatment of gravity and energy-exchanging neutrino
interactions can make differences of even 50-100% in some quantities and is
likely to contribute to a finally successful explosion mechanism on no minor
level than hydrodynamical differences between different dimensions.


  Low-temperature scanning probe microscopes (SPMs) are critical for the study
of quantum materials and quantum information science. Due to the rising costs
of helium, cryogen-free cryostats have become increasingly desirable. However,
they typically suffer from comparatively worse vibrations than cryogen-based
systems, necessitating the understanding and mitigation of vibrations for SPM
applications. Here we demonstrate the construction of two cryogen-free dilution
refrigerator SPMs with minimal modifications to the factory default and we
systematically characterize their vibrational performance. We measure the
absolute vibrations at the microscope stage with geophones, and use both
microwave impedance microscopy and a scanning single electron transistor to
independently measure tip-sample vibrations. Additionally, we implement
customized filtering and thermal anchoring schemes, and characterize the
cooling power at the scanning stage and the tip electron temperature. This work
serves as a reference to researchers interested in cryogen-free SPMs, as such
characterization is not standardized in the literature or available from
manufacturers.


  The development of models to capture large-scale dynamics in human history is
one of the core contributions of cliodynamics. Most often, these models are
assessed by their predictive capability on some macro-scale and aggregated
measure and compared to manually curated historical data. In this report, we
consider the model from Turchin et al. (2013), where the evaluation is done on
the prediction of "imperial density": the relative frequency with which a
geographical area belonged to large-scale polities over a certain time window.
We implement the model and release both code and data for reproducibility. We
then assess its behaviour against three historical data sets: the relative size
of simulated polities vs historical ones; the spatial correlation of simulated
imperial density with historical population density; the spatial correlation of
simulated conflict vs historical conflict. At the global level, we show good
agreement with population density ($R^2 < 0.75$), and some agreement with
historical conflict in Europe ($R^2 < 0.42$). The model instead fails to
reproduce the historical shape of individual polities. Finally, we tweak the
model to behave greedily by having polities preferentially attacking weaker
neighbours. Results significantly degrade, suggesting that random attacks are a
key trait of the original model. We conclude by proposing a way forward by
matching the probabilistic imperial strength from simulations to inferred
networked communities from real settlement data.


  The emergence of large models, also known as foundation models, has brought
significant advancements to AI research. One such model is Segment Anything
(SAM), which is designed for image segmentation tasks. However, as with other
foundation models, our experimental findings suggest that SAM may fail or
perform poorly in certain segmentation tasks, such as shadow detection and
camouflaged object detection (concealed object detection). This study first
paves the way for applying the large pre-trained image segmentation model SAM
to these downstream tasks, even in situations where SAM performs poorly. Rather
than fine-tuning the SAM network, we propose \textbf{SAM-Adapter}, which
incorporates domain-specific information or visual prompts into the
segmentation network by using simple yet effective adapters. By integrating
task-specific knowledge with general knowledge learnt by the large model,
SAM-Adapter can significantly elevate the performance of SAM in challenging
tasks as shown in extensive experiments. We can even outperform task-specific
network models and achieve state-of-the-art performance in the task we tested:
camouflaged object detection, shadow detection. We also tested polyp
segmentation (medical image segmentation) and achieves better results. We
believe our work opens up opportunities for utilizing SAM in downstream tasks,
with potential applications in various fields, including medical image
processing, agriculture, remote sensing, and more.


  Large language models (LLMs) are increasingly being integrated into search
engines to provide natural language responses tailored to user queries.
Customers and end-users are also becoming more dependent on these models for
quick and easy purchase decisions. In this work, we investigate whether
recommendations from LLMs can be manipulated to enhance a product's visibility.
We demonstrate that adding a strategic text sequence (STS) -- a carefully
crafted message -- to a product's information page can significantly increase
its likelihood of being listed as the LLM's top recommendation. To understand
the impact of STS, we use a catalog of fictitious coffee machines and analyze
its effect on two target products: one that seldom appears in the LLM's
recommendations and another that usually ranks second. We observe that the
strategic text sequence significantly enhances the visibility of both products
by increasing their chances of appearing as the top recommendation. This
ability to manipulate LLM-generated search responses provides vendors with a
considerable competitive advantage and has the potential to disrupt fair market
competition. Just as search engine optimization (SEO) revolutionized how
webpages are customized to rank higher in search engine results, influencing
LLM recommendations could profoundly impact content optimization for AI-driven
search services. Code for our experiments is available at
https://github.com/aounon/llm-rank-optimizer.


  We give elementary and non-inductive proofs of three fundamental theorems
about Chow rings of matroids: the standard monomial basis, Poincare duality,
and the dragon-Hall-Rado formula. Our approach, which also works for augmented
Chow rings of matroids, is based on a straightening law. This approach also
gives a decomposition of the Chow ring of a matroid into pieces indexed by
flats.


  The massless vector Schwinger model with $N_f=1,2,3,4$ number of flavors is
studied on the lattice using the overlap formalism. A full Monte Carlo
simulation yields values for the bilinear fermion condensate that are in
agreement with the exact solution of the continuum Schwinger model with an
added Thirring interaction.


  The gauge invariant definition of the spin dependent gluon distribution
function from first principle is necessary to study the proton spin crisis at
high energy colliders. In this paper we derive the gauge invariant Noether's
theorem in Yang-Mills theory by using combined Lorentz transformation plus
local non-abelian gauge transformation. We find that the definition of the
gauge invariant spin (or orbital) angular momentum of the Yang-Mills field does
not exist in Yang-Mills theory although the definition of the gauge invariant
spin (or orbital) angular momentum of the quark exists. We show that the gauge
invariant definition of the spin angular momentum of the Yang-Mills field in
the literature is not correct because of the non-vanishing boundary surface
term in Yang-Mills theory. We also find that the Belinfante-Rosenfeld tensor in
Yang-Mills theory is not required to obtain the symmetric and gauge invariant
energy-momentum tensor of the quark and the Yang-Mills field.


  These notes contain an extended version of lectures given at the ``Summer
School on Large Coulomb Systems'' in Nordfjordeid, Norway, in august 2003. They
furnish a short introduction to the theory of quantum harmonic systems, or free
bose fields. The main issue addressed is the one of local states. I will adopt
the definition of Knight of ``strictly local excitation of the vacuum'' and
will then state and prove a generalization of Knight's Theorem which asserts
that finite particle states cannot be perfectly localized. It will furthermore
be explained how Knight's a priori counterintuitive result can be readily
understood if one remembers the analogy between finite and infinite dimensional
harmonic systems alluded to above. I will also discuss the link between the
above result and the so-called Newton-Wigner position operator thereby
illuminating, I believe, the difficulties associated with the latter. I will in
particular argue that those difficulties do not find their origin in special
relativity or in any form of causality violation, as is usually claimed.


  Studies of the formation of metal-free Population III stars usually focus
primarily on the role played by H2 cooling, on account of its large chemical
abundance relative to other possible molecular or ionic coolants. However,
while H2 is generally the most important coolant at low gas densities, it is
not an effective coolant at high gas densities, owing to the low critical
density at which it reaches local thermodynamic equilibrium (LTE) and to the
large opacities that develop in its emission lines. It is therefore possible
that emission from other chemical species may play an important role in cooling
high density primordial gas. A particularly interesting candidate is the H3+
molecular ion. This ion has an LTE cooling rate that is roughly a billion times
larger than that of H2, and unlike other primordial molecular ions such as H2+
or HeH+, it is not easily removed from the gas by collisions with H or H2. It
is already known to be an important coolant in at least one astrophysical
context -- the upper atmospheres of gas giants -- but its role in the cooling
of primordial gas has received little previous study. In this paper, we
investigate the potential importance of H3+ cooling in primordial gas using a
newly-developed H3+ cooling function and the most detailed model of primordial
chemistry published to date. We show that although H3+ is, in most
circumstances, the third most important coolant in dense primordial gas (after
H2 and HD), it is nevertheless unimportant, as it contributes no more than a
few percent of the total cooling. We also show that in gas irradiated by a
sufficiently strong flux of cosmic rays or X-rays, H3+ can become the dominant
coolant in the gas, although the size of the flux required renders this
scenario unlikely to occur.


  We describe length and time rescaling across the paraelectric to
ferroelectric phase transition in BaTiO$_3$. Small ferroelectric clusters are
unable to grow in the paraelectric phase and exist for a short period of time
only. The onset of the phase transition invokes a rescaling of both size and
time lenghts as necessary ingredients for ferroelectricity to come into
existence. The growing of ferroelectric domains involves correlated chains of
Ti-O dipoles, which causes domain wall rigidity and domain shape stability.
Ferroelectric nanodomains may host islands of opposite polarization
(antiferroelectric defects), which appear as an intrinsic feature of the
growing BaTiO$_3$ ferroelectric material


  In ultrawide bandgap (UWBG) nitride and oxide semiconductors, increased
bandgap (Eg) correlates with greater ionicity and strong electron-phonon
coupling. This limits mobility through polar optical phonon scattering,
localizes carriers via polarons and self-trapping, broadens optical transitions
via dynamic disorder, and modifies the breakdown field. Herein, we use
polarized optical transmission spectroscopy from 77-633 K to investigate the
Urbach energy (Eu) for many orientations of Fe- and Sn-doped \b{eta}-Ga2O3 bulk
crystals. We find Eu values ranging from 60-140 meV at 293 K and static
(structural defects plus zero-point phonons) disorder contributes more to Eu
than dynamic (finite temperature phonon-induced) disorder. This is evidenced by
lack of systematic Eu anisotropy, and Eu correlating more with X-ray
diffraction rocking-curve broadening than with Sn-doping. The lowest measured
Eu are ~10x larger than for traditional semiconductors, pointing out that band
tail effects need to be carefully considered in these materials for high field
electronics. We demonstrate that, because optical transmission through thick
samples is sensitive to sub-gap absorption, the commonly-used Tauc extraction
of bandgap from transmission through Ga2O3 greater than 1-3 micro meter thick
is subject to errors. Combining our Eu(T) from Fe-doped samples with Eg(T) from
ellipsometry, we extract a measure of an effective electron-phonon coupling
indicating increases in weighted 2nd order deformation potential with
temperature and a larger value for E parallel b than E parallel c. The large
electron-phonon coupling in beta-Ga2O3 suggests that theories of electrical
breakdown for traditional semiconductors need expansion to account not just for
lower scattering time but also for impact ionization thresholds fluctuating in
both time and space.


  Reinforcement learning (RL) is a central problem in artificial intelligence.
This problem consists of defining artificial agents that can learn optimal
behaviour by interacting with an environment -- where the optimal behaviour is
defined with respect to a reward signal that the agent seeks to maximize.
Reward machines (RMs) provide a structured, automata-based representation of a
reward function that enables an RL agent to decompose an RL problem into
structured subproblems that can be efficiently learned via off-policy learning.
Here we show that RMs can be learned from experience, instead of being
specified by the user, and that the resulting problem decomposition can be used
to effectively solve partially observable RL problems. We pose the task of
learning RMs as a discrete optimization problem where the objective is to find
an RM that decomposes the problem into a set of subproblems such that the
combination of their optimal memoryless policies is an optimal policy for the
original problem. We show the effectiveness of this approach on three partially
observable domains, where it significantly outperforms A3C, PPO, and ACER, and
discuss its advantages, limitations, and broader potential.


  One of the most common problems of scientific applications is computation of
the derivative of a function specified by possibly noisy or imprecise
experimental data. Application of conventional techniques for numerically
calculating derivatives will amplify the noise making the result useless. We
address this typical ill-posed problem by application of perturbation method to
linear first kind equations $Ax=f$ with bounded operator $A.$ We assume that we
know the operator $\tilde{A}$ and source function $\tilde{f}$ only such as
$||\tilde{A} - A||\leq \delta_1,$ $||\tilde{f}-f||< \delta_2.$ The regularizing
equation $\tilde{A}x + B(\alpha)x = \tilde{f}$ possesses the unique solution.
Here $\alpha \in S,$
  $S$ is assumed to be an open space in $\mathbb{R}^n,$ $0 \in \overline{S},$
$\alpha= \alpha(\delta).$
  As result of proposed theory, we suggest a novel algorithm providing accurate
results even in the presence of a large amount of noise.


  DMRadio-m$^3$ is an experiment that is designed to be sensitive to KSVZ and
DFSZ QCD axion models in the 10-200 MHz (41 neV$/c^2$ - 0.83 $\mu$eV/$c^2$)
range. The experiment uses a solenoidal dc magnetic field to convert an axion
dark-matter signal to an ac electromagnetic response in a coaxial copper
pickup. The current induced by this axion signal is measured by dc SQUIDs. In
this work, we present the electromagnetic modeling of the response of the
experiment to an axion signal over the full frequency range of DMRadio-m$^3$,
which extends from the low-frequency, lumped-element limit to a regime where
the axion Compton wavelength is only a factor of two larger than the detector
size. With these results, we determine the live time and sensitivity of the
experiment. The primary science goal of sensitivity to DFSZ axions across
30-200 MHz can be achieved with a $3\sigma$ live scan time of 3.7 years.


  The nonlinear Penman and Penman-Monteith equations, widely used for
estimating surface evapotranspiration at regional and global scales, were
derived from turbulent transport of heat fluxes and thus apply to subhourly
scale. However, these equations have been directly applied with
hydrometeorological variables averaged at longer time intervals, leading to
biases due to their nonlinearities. To address this problem, we used global
eddy covariance flux data and Taylor expanded Penman and Penman-Monteith
equations to explore their nonlinear components and the biases associated with
the timescales mismatch. We found relatively small biases when applying Penman
equation at longer timescale, in which the biases in equilibrium
evapotranspiration mainly stem from the temperature-radiation covariance,
whereas the biases in evapotranspiration due to drying power of air primarily
come from the higher-order terms. Most of these biases can be corrected by
linear regressions of first-order approximations. For Penman-Monteith
equations, the corresponding biases are relatively larger but can be
significantly reduced when daytime median stomatal conductance is used along
with the first-order approximation of Penman-Monteith equation, suggesting the
importance of diurnal variation of latent heat fluxes. The nonlinearity
explored here serves as a reminder of the mismatched timescales for applying
Penman and Penman-Monteith equations.


  Since the beginning of robotic interplanetary exploration nearly six decades
ago, successful atmospheric entry has been accomplished at Venus, Earth, Mars,
Jupiter, and Titan. More entry probe missions are planned to Venus, Titan, and
Uranus in the next decade. Atmospheric entry subjects the vehicle to rapid
deceleration and aerothermal loads which the vehicle must be designed for, to
deliver the robotic instruments inside the atmosphere. The design of planetary
probes and their mission architecture is complex, and involves various
engineering constraints such as peak deceleration, heating rate, heating load,
and communications which must be satisfied within the budget and schedule of
cost constrained mission opportunities. Engineering design data from previous
entry probe missions serve as a valuable reference for designing future
missions. The present study compiles an augmented version of the blue book
entry probe dataset, performs a comparative analysis of the entry conditions,
and provides engineering rules of thumb for design of future missions. Using
the dataset, the present study proposes a new empirical correlation which aims
to more accurately predict the thermal protection system mass fraction for high
heat load conditions during entry and aerocapture at Uranus and Neptune.


  MTProto 2.0 is a suite of cryptographic protocols for instant messaging at
the core of the popular Telegram messenger application. In this paper we
analyse MTProto 2.0 using the symbolic verifier ProVerif. We provide fully
automated proofs of the soundness of MTProto 2.0's authentication, normal chat,
end-to-end encrypted chat, and rekeying mechanisms with respect to several
security properties, including authentication, integrity, secrecy and perfect
forward secrecy; at the same time, we discover that the rekeying protocol is
vulnerable to an unknown key-share (UKS) attack. We proceed in an incremental
way: each protocol is examined in isolation, relying only on the guarantees
provided by the previous ones and the robustness of the basic cryptographic
primitives. Our research proves the formal correctness of MTProto 2.0 w.r.t.
most relevant security properties, and it can serve as a reference for
implementation and analysis of clients and servers.


  We make a detailed assessment of which form of the dipole operator to use in
calculating high order harmonic generation within the framework of the strong
field approximation, and look specifically at the role the form plays in the
inclusion of multielectron effects perturbatively with regard to the
contributions of the highest occupied molecular orbital. We focus on how these
corrections affect the high-order harmonic spectra from aligned homonuclear and
heteronuclear molecules, exemplified by $\mathrm{N}_2$ and CO, respectively,
which are isoelectronic. We find that the velocity form incorrectly finds zero
static dipole moment in heteronuclear molecules. In contrast, the length form
of the dipole operator leads to the physically expected non-vanishing
expectation value for the dipole operator in this case. Furthermore, the so
called "overlap" integrals, in which the dipole matrix element is computed
using wavefunctions at different centers in the molecule, are prominent in the
first-order multielectron corrections for the velocity form, and should not be
ignored. Finally, inclusion of the multielectron corrections has very little
effect on the spectrum. This suggests that relaxation, excitation and the
dynamic motion of the core are important in order to describe multielectron
effects in molecular high-order high harmonic generation.


  This work is concerned about the asymptotic behavior of the solutions of the
two and three dimensional stochastic convective Brinkman-Forchheimer (SCBF)
equations driven by white noise with nonlinear diffusion terms. We prove the
existence and uniqueness of weak pullback mean random attractors for the 2D
SCBF equations (for $r\geq1$) as well as 3D SCBF equations (for $r>3$, any
$\mu,\beta>0$ and for $r=3$, $2\mu\beta\geq1$) in Bochner spaces, when the
diffusion terms are Lipschitz nonlinear functions. Furthermore, we establish
the existence of weak pullback mean random attractors for a class of locally
monotone stochastic partial differential equations.


  We present 0.9 - 2.5 um resolved spectra for the ultracool binary WISEPC
J121756.91+162640.2AB. The system consists of a pair of brown dwarfs that
straddles the currently defined T/Y spectral type boundary. We use synthetic
spectra generated by model atmospheres that include chloride and sulfide clouds
(Morley et al.), the distance to the system (Dupuy & Kraus), and the radius of
each component based on evolutionary models (Saumon & Marley) to determine a
probable range of physical properties for the binary. The effective temperature
of the T8.5 primary is 550 - 600 K, and that of the Y0 - Y0.5 secondary is 450
K. The atmospheres of both components are either free of clouds or have
extremely thin cloud layers. We find that the masses of the primary and
secondary are 30 and 22 M_Jup, respectively, and that the age of the system is
4 - 8 Gyr. This age is consistent with astrometric measurements (Dupuy & Kraus)
that show that the system has kinematics intermediate between those of the thin
and thick disks of the Galaxy. An older age is also consistent with an
indication by the H - K colors that the system is slightly metal-poor.


  Using high resolution $N$-body simulations, we recently reported that a
dynamically cool inner disk embedded in a hotter outer disk can naturally
generate a steady double-barred (S2B) structure. Here we study the kinematics
of these S2B simulations, and compare them to integral-field observations from
ATLAS$^{3D}$ and SAURON. We show that S2B galaxies exhibit several distinct
kinematic features, namely: (1) significantly distorted isovelocity contours at
the transition region between the two bars, (2) peaks in $\sigma_\mathrm{LOS}$
along the minor axis of inner bars, which we term "$\sigma$-humps", that are
often accompanied by ring/spiral-like features of increased
$\sigma_\mathrm{LOS}$, (3) $h_3-\bar{v}$ anti-correlations in the region of the
inner bar for certain orientations, and (4) rings of positive $h_4$ when viewed
at low inclinations. The most impressive of these features are the
$\sigma$-humps, these evolve with the inner bar, oscillating in strength just
as the inner bar does as it rotates relative to the outer bar. We show that, in
cylindrical coordinates, the inner bar has similar streaming motions and
velocity dispersion properties as normal large-scale bars, except for
$\sigma_z$, which exhibits peaks on the minor axis, i.e., humps. These
$\sigma_z$ humps are responsible for producing the $\sigma$-humps. For three
well-resolved early-type S2Bs (NGC 2859, NGC 2950, and NGC 3941) and a
potential S2B candidate (NGC 3384), the S2B model qualitatively matches the
integral-field data well, including the "$\sigma$-hollows" previously
identified. We also discuss the kinematic effect of a nuclear disk in S2Bs.


  Myanmar is languishing at the bottom of key international indexes. United
Nations considers the country as a structurally weak and vulnerable economy.
Yet, from 2011 when Myanmar ended decades of military rule and isolationism and
transited towards democracy, its breakneck development has led to many
considering the country to be one of the final frontiers for growth in the Asia
region. One such industry that has benefitted from the opening of the country
is telecommunications. The mobile penetration rate at 4.8% in 2011 has
increased significantly to 90% in 2016. Despite renewed optimism and
development in the economy, one statistic remains disappointing. According to a
report by Asian Development Bank (ADB), only 23% of the adult population have
access to a bank account. This highlights a need to reach out and increase
access to financial resources to a population that is severely unbanked and
underbanked. This creates an interesting proposition of allowing both the
telecommunications and financial sector to form the mobile financial services
(MFS) sector and meet the need of improving access to financial resources for
the population. This report explores the government role in supporting, growing
and sustaining the MFS sector and conducts a comparative research into
Singapore, Malaysia and Thailand to understand the steps taken by these
governments to develop their own Financial Technology (FinTech), specifically
MFS, industry. Finally, the report will present preliminary recommendations
that the Myanmar government could consider implementing to drive growth in its
MFS sector.


  Achieving high valley degeneracy (i.e. "band convergence") in a material
usually results in considerably enhanced thermoelectric properties. However, it
is still unclear why this strategy of designing efficient thermoelectric
materials is so successful, since the benefit of increased density of states
may be severely degraded by intervalley scattering. Using first-principles
calculations, we investigate these effects in $p$-type PbTe, where temperature
induces alignment of the $L$ and $\Sigma$ valleys at $\sim$~620~K. We
explicitly show that the thermoelectric power factor and figure of merit peak
near the band convergence temperature. The figure of merit maximum is larger
than those of the individual $L$ and $\Sigma$ valleys. Surprisingly,
intervalley scattering does not considerably affect the figure of merit near
the band convergence temperature and optimal doping conditions, although it
reduces the power factor by almost a factor of 2. Our results suggest that band
convergence will significantly increase the figure of merit if intervalley
scattering is roughly proportional to the density of states and the lattice
thermal conductivity is considerably lower than the electronic thermal
conductivity, even if intervalley scattering is strong.


  To the best of our knowledge, this paper has achieved the lowest thermal
tuning power (5.85 mW/pi) for silicon rings with FSR>=3.2 THz, and the first
silicon ring-based WDM-32x100 GHz filter.


  A family $\mathcal L$ of subsets of a set $X$ is called linked if $A\cap
B\ne\emptyset$ for any $A,B\in\mathcal L$. A linked family $\mathcal M$ of
subsets of $X$ is maximal linked if $\mathcal M$ coincides with each linked
family $\mathcal L$ on $X$ that contains $\mathcal M$. The superextension
$\lambda(X)$ of $X$ consists of all maximal linked families on $X$. Any
associative binary operation $* : X\times X \to X$ can be extended to an
associative binary operation $*: \lambda(X)\times\lambda(X)\to\lambda(X)$. In
the paper we study automorphisms of the superextensions of finite monogenic
semigroups and characteristic ideals in such semigroups. In particular, we
describe the automorphism groups of the superextensions of finite monogenic
semigroups of cardinality $\leq 5$.


  It has been widely reported that selecting an inappropriate system is a major
reason for ERP implementation failures. The selection of an ERP system is
therefore critical. While the number of papers related to ERP implementation is
substantial, ERP evaluation and selection approaches have received few
attention. Motivated by the adaptation concept of the ERP systems, we propose
in this paper a semi-structured approach for ERP system selection that differs
from existing models in that it has a more holistic focus by simultaneously 1)
considering the anticipated fitness of ERP solutions after the optimal
resolution, within limited resources, of a set of the identified mismatches and
2) evaluating candidate products according to both functional and
non-functional requirements. The approach consists of an iterative selection
process model and an evaluation methodology based on 0-1 linear programming and
MACBETH technique to elaborate multi-criteria performance expressions.


  Procedural Content Generation (PCG) is the algorithmic generation of content,
often applied to games. PCG and PCG via Machine Learning (PCGML) have appeared
in published games. However, it can prove difficult to apply these approaches
in the early stages of an in-development game. PCG requires expertise in
representing designer notions of quality in rules or functions, and PCGML
typically requires significant training data, which may not be available early
in development. In this paper, we introduce Tree-based Reconstructive
Partitioning (TRP), a novel PCGML approach aimed to address this problem. Our
results, across two domains, demonstrate that TRP produces levels that are more
playable and coherent, and that the approach is more generalizable with less
training data. We consider TRP to be a promising new approach that can afford
the introduction of PCGML into the early stages of game development without
requiring human expertise or significant training data.


  We study theoretically two spatially separate quasi-one-dimensional atomic
Fermi gases in a double-well trap. By tuning independently their spin
polarizations, a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid or a
Bardeen-Cooper-Schrieffer (BCS) superfluid may be formed in each well. We seek
the possibility of creating a spatially tunable atomic Josephson junction
between two superfluids, which is supposed to be realizable via building a weak
link at given positions of the double-well barrier. We show that within
mean-field theory the maximum Josephson current is proportional to the order
parameter in two wells. Thus, the spatial inhomogeneity of the FFLO order
parameter in one well may be directly revealed through the current measurement
with the position-tunable link. We anticipate that this type of Josephson
measurements can provide a useful evidence for the existence of exotic FFLO
superfluids. Possible experimental realizations of the Josephson measurements
in atomic Fermi gases are discussed.


  Analytic spherically symmetric solutions of the Einstein field equations
coupled with a perfect fluid and with self-similarities of the zeroth, first
and second kinds, found recently by Benoit and Coley [Class. Quantum Grav. {\bf
15}, 2397 (1998)], are studied, and found that some of them represent
gravitational collapse. When the solutions have self-similarity of the first
(homothetic) kind, some of the solutions may represent critical collapse but in
the sense that now the "critical" solution separates the collapse that forms
black holes from the collapse that forms naked singularities. The formation of
such black holes always starts with a mass gap, although the "critical"
solution has homothetic self-similarity. The solutions with self-similarity of
the zeroth and second kinds seem irrelevant to critical collapse. Yet, it is
also found that the de Sitter solution is a particular case of the solutions
with self-similarity of the zeroth kind, and that the Schwarzschild solution is
a particular case of the solutions with self-similarity of the second kind with
the index $\alpha = 3/2$.


  The Euler-Poisson equations para determinar the rotation matrix of a rigid
body can be solved without using of particular parameterization like the Euler
angles. For the free Lagrange top, we obtain and discuss a general analytic
solution, and compare it with the Poinsot's picture of motion.


  Encouraged by the study of extremal limits for sums of the form
$$\lim_{N\to\infty}\frac{1 }{N}\sum_{n=1}^N c(x_n,y_n)$$ with uniformly
distributed sequences $\{x_n\},\,\{y_n\}$ the following extremal problem is of
interest $$\max_{\gamma}\int_{[0,1]^2}c(x,y)\gamma(dx,dy),$$ for probability
measures $\gamma$ on the unit square with uniform marginals, i.e., measures
whose distribution function is a copula. The aim of this article is to relate
this problem to combinatorial optimization and to the theory of optimal
transport. Using different characterizations of maximizing $\gamma$'s one can
give alternative proofs of some results from the field of uniform distribution
theory and beyond that treat additional questions. Finally, some applications
to mathematical finance are addressed.


  The fabrication of assembled structures of topological defects in liquid
crystals (LCs) has attracted much attention during the last decade, stemming
from the potential application of these defects in modern technologies. A range
of techniques can be employed to create large areas of engineered defects in
LCs, including mechanical shearing, chemical surface treatment, external
fields, or geometric confinement. The technology of 3D printing has recently
emerged as a powerful method to fabricate novel patterning topographies
inaccessible by other microfabrication techniques, especially confining
geometries with curved topographies. In this work, we show the advantages of
using 3D-printed curved surfaces and controlled anchoring properties to confine
LCs and engineer new structures of topological defects, whose structure we
elucidate by comparison with a novel application of Landau-de Gennes free
energy minimization to the smectic A-nematic phase transition. We also
demonstrate the ability of these defects to act as a scaffold for assembling
gold (Au) nanoparticles (NPs) into reconfigurable 3D structures. We discuss the
characteristics of this templated self-assembly (TSA) approach and explain the
relationship between NP concentrations and defect structures with insights
gained from numerical modeling. This work paves the way for a versatile
platform of LC defect-templated assembly of a range of functional nanomaterials
useful in the field of energy technology.


  As the development of new classes of antibiotics slows, bacterial resistance
to existing antibiotics is becoming an increasing problem. A potential solution
is to develop treatment strategies with an alternative mode of action. We
consider one such strategy: anti-adhesion therapy. Whereas antibiotics act
directly upon bacteria, either killing them or inhibiting their growth,
anti-adhesion therapy impedes the binding of bacteria to host cells. This
prevents bacteria from deploying their arsenal of virulence mechanisms, while
simultaneously rendering them more susceptible to natural and artificial
clearance. In this paper, we consider a particular form of anti-adhesion
therapy, involving biomimetic multivalent adhesion molecule (MAM) 7 coupled
polystyrene microbeads, which competitively inhibit the binding of bacteria to
host cells. We develop a mathematical model, formulated as a system of ordinary
differential equations, to describe inhibitor treatment of a Pseudomonas
aeruginosa burn wound infection in the rat. Benchmarking our model against in
vivo data from an ongoing experimental programme, we use the model to explain
bacteria population dynamics and to predict the efficacy of a range of
treatment strategies, with the aim of improving treatment outcome. The model
consists of two physical compartments: the epithelium and the exudate. It is
found that, when effective in reducing the bacterial burden, inhibitor
treatment operates both by preventing bacteria from binding to the epithelium
and by reducing the flux of daughter cells from the epithelium into the
exudate. Our model predicts that inhibitor treatment cannot eliminate the
bacterial burden when used in isolation; however, when combined with regular or
continuous debridement of the exudate, elimination is theoretically possible.
Lastly, we present ways to improve therapeutic efficacy, as predicted by our
mathematical model.


  This work addresses the rising demand for novel tools in statistical and
machine learning for "graph-valued random variables" by proposing a fast
algorithm to compute the sample Frechet mean, which replaces the concept of
sample mean for graphs (or networks). We use convolutional neural networks to
learn the morphology of the graphs in a set of graphs. Our experiments on
several ensembles of random graphs demonstrate that our method can reliably
recover the sample Frechet mean.


  Studying the ways in which language is gendered has long been an area of
interest in sociolinguistics. Studies have explored, for example, the speech of
male and female characters in film and the language used to describe male and
female politicians. In this paper, we aim not to merely study this phenomenon
qualitatively, but instead to quantify the degree to which the language used to
describe men and women is different and, moreover, different in a positive or
negative way. To that end, we introduce a generative latent-variable model that
jointly represents adjective (or verb) choice, with its sentiment, given the
natural gender of a head (or dependent) noun. We find that there are
significant differences between descriptions of male and female nouns and that
these differences align with common gender stereotypes: Positive adjectives
used to describe women are more often related to their bodies than adjectives
used to describe men.


  Surface acoustic wave (SAW) devices have wide range of applications in
microwave signal processing. Microwave SAW components benefit from higher
quality factors and much smaller crosstalk when compared to their
electromagnetic counterparts. Efficient routing and modulation of SAWs are
essential for building large-scale and versatile acoustic-wave circuits. Here,
we demonstrate integrated thermo-acoustic modulators using two SAW platforms:
bulk lithium niobate and thin-film lithium niobate on sapphire. In both
approaches, the gigahertz-frequency SAWs are routed by integrated acoustic
waveguides while on-chip microheaters are used to locally change the
temperature and thus control the phase of SAW. Using this approach, we achieved
phase changes of over 720 degrees with the responsibility of 2.6 deg/mW for
bulk lithium niobate and 0.52 deg/mW for lithium niobate on sapphire.
Furthermore, we demonstrated amplitude modulation of SAWs using acoustic Mach
Zehnder interferometers. Our thermo-acoustic modulators can enable
reconfigurable acoustic signal processing for next generation wireless
communications and microwave systems.


  The Bohmian formulation of quantum mechanics is used in order to describe the
measurement process in an intuitive way without a reduction postulate in the
framework of a deterministic single system theory. Thereby the motion of the
hidden classical particle is chaotic during almost all nontrivial measurement
processes. For the correct reproduction of experimental results, it is further
essential that the distribution function $P(x)$ of the results of a position
measurement is identical with $|\Psi|^2$ of the wavefunction $\Psi$ of the
single system under consideration. It is shown that this feature is not an
additional assumption, but can be derived strictly from the chaotic motion of a
single system during a sequence of measurements, providing a completely
deterministic picture of the statistical features of quantum mechanics.


  Using Artificial Intelligence (AI) to create dance choreography with
intention is still at an early stage. Methods that conditionally generate dance
sequences remain limited in their ability to follow choreographer-specific
creative direction, often relying on external prompts or supervised learning.
In the same vein, fully annotated dance datasets are rare and labor intensive.
To fill this gap and help leverage deep learning as a meaningful tool for
choreographers, we propose "PirouNet", a semi-supervised conditional recurrent
variational autoencoder together with a dance labeling web application.
PirouNet allows dance professionals to annotate data with their own subjective
creative labels and subsequently generate new bouts of choreography based on
their aesthetic criteria. Thanks to the proposed semi-supervised approach,
PirouNet only requires a small portion of the dataset to be labeled, typically
on the order of 1%. We demonstrate PirouNet's capabilities as it generates
original choreography based on the "Laban Time Effort", an established dance
notion describing intention for a movement's time dynamics. We extensively
evaluate PirouNet's dance creations through a series of qualitative and
quantitative metrics, validating its applicability as a tool for
choreographers.


  We consider the communication line with two-qubit sender and receiver, the
later is embedded into the four-qubit extended receiver. Using the optimizing
unitary transformation on the extended receiver we restore the structure of the
non-diagonal part of an arbitrary initial sender's state at the remote receiver
at certain time instant. Obstacles for restoring the diagonal part are
discussed. We represent examples of such structural restoring in a
communication line of 42 spin-1/2 particles.


  Future wireless communication networks are in a position to move beyond
data-centric, device-oriented connectivity and offer intelligent, immersive
experiences based on task-oriented connections, especially in the context of
the thriving development of pre-trained foundation models (PFM) and the
evolving vision of 6G native artificial intelligence (AI). Therefore,
redefining modes of collaboration between devices and servers and constructing
native intelligence libraries become critically important in 6G. In this paper,
we analyze the challenges of achieving 6G native AI from the perspectives of
data, intelligence, and networks. Then, we propose a 6G native AI framework
based on foundation models, provide a customization approach for intent-aware
PFM, present a construction of a task-oriented AI toolkit, and outline a novel
cloud-edge-end collaboration paradigm. As a practical use case, we apply this
framework for orchestration, achieving the maximum sum rate within a wireless
communication system, and presenting preliminary evaluation results. Finally,
we outline research directions for achieving native AI in 6G.


  Implementing deep neural networks for learning the solution maps of
parametric partial differential equations (PDEs) turns out to be more efficient
than using many conventional numerical methods. However, limited theoretical
analyses have been conducted on this approach. In this study, we investigate
the expressive power of deep rectified quadratic unit (ReQU) neural networks
for approximating the solution maps of parametric PDEs. The proposed approach
is motivated by the recent important work of G. Kutyniok, P. Petersen, M.
Raslan and R. Schneider (Gitta Kutyniok, Philipp Petersen, Mones Raslan, and
Reinhold Schneider. A theoretical analysis of deep neural networks and
parametric pdes. Constructive Approximation, pages 1-53, 2021), which uses deep
rectified linear unit (ReLU) neural networks for solving parametric PDEs. In
contrast to the previously established complexity-bound
$\mathcal{O}\left(d^3\log_{2}^{q}(1/ \epsilon) \right)$ for ReLU neural
networks, we derive an upper bound $\mathcal{O}\left(d^3\log_{2}^{q}\log_{2}(1/
\epsilon) \right)$ on the size of the deep ReQU neural network required to
achieve accuracy $\epsilon>0$, where $d$ is the dimension of reduced basis
representing the solutions. Our method takes full advantage of the inherent
low-dimensionality of the solution manifolds and better approximation
performance of deep ReQU neural networks. Numerical experiments are performed
to verify our theoretical result.


  We study the problem of low-rank matrix completion for symmetric matrices.
The minimum rank of a completion of a generic partially specified symmetric
matrix depends only on the location of the specified entries, and not their
values, if complex entries are allowed. When the entries are required to be
real, this is no longer the case and the possible minimum ranks are called
typical ranks. We give a combinatorial description of the patterns of specified
entires of $n\times n$ symmetric matrices that have $n$ as a typical rank.
Moreover, we describe exactly when such a generic partial matrix is minimally
completable to rank $n$. We also characterize the typical ranks for patterns of
entries with low maximal typical rank.


  The term robot generally refers to a machine that looks and works in a way
similar to a human. The modern industry is rapidly shifting from manual control
of systems to automation, in order to increase productivity and to deliver
quality products. Computer-based systems, though feasible for improving quality
and productivity, are inflexible to work with, and the cost of such systems is
significantly high. This led to the swift adoption of automated systems to
perform industrial tasks. One such task of industrial significance is of
picking and placing objects from one place to another. The implementation of
automation in pick and place tasks helps to improve efficiency of system and
also the performance. In this paper, we propose to demonstrate the designing
and working of an automated robotic arm with the Machine Learning approach. The
work uses Machine Learning approach for object identification detection and
traversal, which is adopted with Tensor flow package for better and accurate
results.


  Imaginary-time time-dependent Density functional theory (it-TDDFT) has been
proposed as an alternative method for obtaining the ground state within density
functional theory (DFT) which avoids some of the difficulties with convergence
encountered by the self-consistent-field (SCF) iterative method. It-TDDFT was
previously applied to clusters of atoms where it was demonstrated to converge
in select cases where SCF had difficulty with convergence. In the present work
we implement it-TDDFT propagation for {\it periodic systems} by modifying the
Quantum ESPRESSO package, which uses a plane-wave basis with multiple
$\boldsymbol{k}$ points, and has the options of non-collinear and DFT+U
calculations using ultra-soft or norm-conserving pseudo potentials. We
demonstrate that our implementation of it-TDDFT propagation with multiple
$\boldsymbol{k}$ points is correct for DFT+U non-collinear calculations and for
DFT+U calculations with ultra-soft pseudo potentials. Our implementation of
it-TDDFT propagation converges to the exact SCF energy (up to the decimal
guaranteed by double precision) in all but one case where it converged to a
slightly lower value than SCF, suggesting a useful alternative for systems
where SCF has difficulty to reach the Kohn-Sham ground state. In addition, we
demonstrate that rapid convergence can be achieved if we use adaptive-size
imaginary-time-steps for different kinetic-energy plane-waves.


  Deep Gradient Leakage (DGL) is a highly effective attack that recovers
private training images from gradient vectors. This attack casts significant
privacy challenges on distributed learning from clients with sensitive data,
where clients are required to share gradients. Defending against such attacks
requires but lacks an understanding of when and how privacy leakage happens,
mostly because of the black-box nature of deep networks. In this paper, we
propose a novel Inversion Influence Function (I$^2$F) that establishes a
closed-form connection between the recovered images and the private gradients
by implicitly solving the DGL problem. Compared to directly solving DGL, I$^2$F
is scalable for analyzing deep networks, requiring only oracle access to
gradients and Jacobian-vector products. We empirically demonstrate that I$^2$F
effectively approximated the DGL generally on different model architectures,
datasets, modalities, attack implementations, and perturbation-based defenses.
With this novel tool, we provide insights into effective gradient perturbation
directions, the unfairness of privacy protection, and privacy-preferred model
initialization. Our codes are provided in
https://github.com/illidanlab/inversion-influence-function.


  The Reactions with Relativistic Radioactive Beams (R$^3$B) collaboration of
the Facility for Antiproton and Ion Research (FAIR) in Darmstadt, Germany, has
constructed an experimental setup to perform fundamental studies of nuclear
matter, using as a probe reactions with exotic nuclei at relativistic energies.
Among the various detection systems, one of the most recent upgrades consisted
on the installation of a large area, around 2 m$^2$, multi-gap Resistive Plate
Chamber (RPC), equipped with twelve 0.3 mm gaps and readout by 30 mm pitch
strips, exhibiting a timing precision down to 50 ps and efficiencies above 98%
for MIPs in a previous characterization of the detector. The RPC was part of
the setup of the FAIR Phase 0 experiment that focused on measuring, for the
first time, nucleon-nucleon short-range correlations (SRC) inside an exotic
nucleus ($^{16}$C) that occurred in Spring 2022. The excellent timing precision
of this detector will allow the measurement of the forward emitted proton
momentum with a resolution of around 1%. In beam measurements show an RPC
efficiency above 95% and a time precision better than 100 ps (including the
contribution of a reference scintillator and the momentum spread of the
particles) for forward emitted particles.


  A many-electron conducting system undergoes free acceleration in response to
a macroscopic field. The Drude weight $D$---also called charge
stiffness---measures the adiabatic (inverse) inertia of the electrons; the $D$
formal expression requires periodic boundary conditions. When instead a bounded
sample is addressed within open boundary conditions, no current flows and a
constant (external) field only polarizes the sample: the Faraday cage effect.
Nonetheless a low-frequency field induces forced oscillations: we show here
that the low-frequency linear response of the bounded system is dominated by
the adiabatic inertia and allows an alternative evaluation of $D$. Simulations
on model one-dimensional systems demonstrate our main message.


  Knowledge transfer, zero-shot learning and semantic image retrieval are
methods that aim at improving accuracy by utilizing semantic information, e.g.
from WordNet. It is assumed that this information can augment or replace
missing visual data in the form of labeled training images because semantic
similarity correlates with visual similarity. This assumption may seem trivial,
but is crucial for the application of such semantic methods. Any violation can
cause mispredictions. Thus, it is important to examine the visual-semantic
relationship for a certain target problem. In this paper, we use five different
semantic and visual similarity measures each to thoroughly analyze the
relationship without relying too much on any single definition. We postulate
and verify three highly consequential hypotheses on the relationship. Our
results show that it indeed exists and that WordNet semantic similarity carries
more information about visual similarity than just the knowledge of "different
classes look different". They suggest that classification is not the ideal
application for semantic methods and that wrong semantic information is much
worse than none.


  The thermodynamic formalism expresses chaotic properties of dynamical systems
in terms of the Ruelle pressure $\psi(\beta)$. The inverse-temperature like
variable $\beta$ allows one to scan the structure of the probability
distribution in the dynamic phase space. This formalism is applied here to a
Lorentz Lattice Gas, where a particle moving on a lattice of size $L^d$
collides with fixed scatterers placed at random locations. Here we give
rigorous arguments that the Ruelle pressure in the limit of infinit e systems
has two branches joining with a slope discontinuity at $\beta = 1$. The low and
high $\beta$--branches correspond to localization of trajectories on
respectively the ``most chaotic'' (highest density) region, and the ``most
deterministic'' (lowest density) region, i.e. $\psi(\beta)$ is completely
controlled by rare fluctuations in the distribution of scatterers on the
lattice, and it does not carry any information on the global structure of the
static disorder.
  As $\beta$ approaches unity from either side, a localization-delocalization
transition leads to a state where trajectories are extended and carry
information on transport properties. At finite $L$ the narrow region around
$\beta = 1$ where the trajectories are extended scales as $(\ln L)^{-\alpha}$,
where $\alpha$ depends on the sign of $1-\beta$, if $d>1$, and as $(L\ln
L)^{-1}$ if $d=1$. This result appears to be general for diffusive systems with
static disorder, such as random walks in random environments or for the
continuous Lorentz gas. Other models of random walks on disordered lattices,
showing the same phenomenon, are discussed.


  The availability and performance of laser-based adaptive optics (AO) systems
are strongly dependent on the power and quality of the laser beam before being
projected to the sky. Frequent and time-consuming alignment procedures are
usually required in the laser systems with free-space optics to optimize the
beam. Despite these procedures, significant distortions of the laser beam have
been observed during the first two years of operation of the Gemini South
multi-conjugate adaptive optics system (GeMS). A beam shaping concept with two
deformable mirrors is investigated in order to provide automated optimization
of the laser quality for astronomical AO. This study aims at demonstrating the
correction of quasi-static aberrations of the laser, in both amplitude and
phase, testing a prototype of this two-deformable mirror concept on GeMS. The
paper presents the results of the preparatory study before the experimental
phase. An algorithm to control amplitude and phase correction, based on phase
retrieval techniques, is presented with a novel unwrapping method. Its
performance is assessed via numerical simulations, using aberrations measured
at GeMS as reference. The results predict effective amplitude and phase
correction of the laser distortions with about 120 actuators per mirror and a
separation of 1.4 m between the mirrors. The spot size is estimated to be
reduced by up to 15% thanks to the correction. In terms of AO noise level, this
has the same benefit as increasing the photon flux by 40%.


  The growing popularity of Large Language Models has sparked interest in
context compression for Large Language Models (LLMs). However, the performance
of previous methods degrades dramatically as compression ratios increase,
sometimes even falling to the closed-book level. This decline can be attributed
to the loss of key information during the compression process. Our preliminary
study supports this hypothesis, emphasizing the significance of retaining key
information to maintain model performance under high compression ratios. As a
result, we introduce Query-Guided Compressor (QGC), which leverages queries to
guide the context compression process, effectively preserving key information
within the compressed context. Additionally, we employ a dynamic compression
strategy. We validate the effectiveness of our proposed QGC on the Question
Answering task, including NaturalQuestions, TriviaQA, and HotpotQA datasets.
Experimental results show that QGC can consistently perform well even at high
compression ratios, which also offers significant benefits in terms of
inference cost and throughput.


  In the articulatory synthesis task, speech is synthesized from input features
containing information about the physical behavior of the human vocal tract.
This task provides a promising direction for speech synthesis research, as the
articulatory space is compact, smooth, and interpretable. Current works have
highlighted the potential for deep learning models to perform articulatory
synthesis. However, it remains unclear whether these models can achieve the
efficiency and fidelity of the human speech production system. To help bridge
this gap, we propose a time-domain articulatory synthesis methodology and
demonstrate its efficacy with both electromagnetic articulography (EMA) and
synthetic articulatory feature inputs. Our model is computationally efficient
and achieves a transcription word error rate (WER) of 18.5% for the
EMA-to-speech task, yielding an improvement of 11.6% compared to prior work.
Through interpolation experiments, we also highlight the generalizability and
interpretability of our approach.


  Many complex systems, such as communication networks, display a surprising
degree of robustness: while key components regularly malfunction, local
failures rarely lead to the loss of the global information-carrying ability of
the network. The stability of these complex systems is often attributed to the
redundant wiring of the functional web defined by the systems' components. In
this paper we demonstrate that error tolerance is not shared by all redundant
systems, but it is displayed only by a class of inhomogeneously wired networks,
called scale-free networks. We find that scale-free networks, describing a
number of systems, such as the World Wide Web, Internet, social networks or a
cell, display an unexpected degree of robustness, the ability of their nodes to
communicate being unaffected by even unrealistically high failure rates.
However, error tolerance comes at a high price: these networks are extremely
vulnerable to attacks, i.e. to the selection and removal of a few nodes that
play the most important role in assuring the network's connectivity.


  The remnant of SN 1006 has an X-ray spectrum dominated by nonthermal
emission, and pre-ASCA observations were well described by a synchrotron
calculation with electron energies limited by escape. We describe the results
of a much more stringent test: fitting spatially integrated ASCA GIS (0.6-8
keV) and RXTE PCA (3-10 keV) data with a combination of the synchrotron model
SRESC newly ported to XSPEC and a new thermal shock model VPSHOCK. The new
model can describe the continuum emission above 2 keV well, in both spatial
distribution and spectrum. We find that the emission is dominantly nonthermal,
with a small but noticeable thermal component: Mg and Si are clearly visible in
the integrated spectrum. The synchrotron component rolls off smoothly from the
extrapolated radio spectrum, with a characteristic rolloff frequency of 3.1E17
Hz, at which the spectrum has dropped about a factor of 6 below a powerlaw
extrapolation from the radio spectrum. Comparison of TeV observations with new
TeV model images and spectra based on the X-ray model fits gives a mean
post-shock magnetic field strength of about 9 microGauss, implying (for a
compression ratio of 4) an upstream magnetic field of 3 microGauss, and fixing
the current energy content in relativistic electrons at about 7E48 ergs,
resulting in a current electron-acceleration efficiency of about 5%. This total
energy is about 100 times the energy in the magnetic field. Our results
indicate that joint thermal and nonthermal fitting, using sophisticated models,
will be required for analysis of most supernova-remnant X-ray data in the
future.


  Composition-tunable ternary Cd1-xPbxS nanocrystals (NCs) are very important
materials for remote sensing and detecting in the infrared (IR) wavelength
region. They are, however, almost exclusively prepared by wet chemical routes
which leads to surface-capped nanoparticles. The surface capping molecules
could move their absorption peak from mid-IR to near IR wavelength region.
However, surface clean Cd1-xPbxS nanocrystals (NCs) would demonstrate intrinsic
optical spectrum in the mid-IR region. Herein, we present a physical mechanical
alloying process being applied to prepare tens of grams of surface clean
Cd1-xPbxS nanocrystals within the composition range of x=0.5 to 1. The
resulting nanocrystals have average sizes smaller than 9 nm, are chemically
homogenous, show a continuous lattice expansion with Pb content and a nonlinear
band gap-composition relationship, demonstrating the ability to continuously
and precisely tune the band gap energies of ternary Cd1-xPbxS semiconductor
nanocrystals from mid-IR region (2638 nm) to NIR wavelength region (1059 nm)
through chemical composition.


  We provide a familiy of transparent tight-binding models with non-trivial
potentials and site-dependent hopping parameters. Their feasibility is
discussed in electromagnetic resonators, dielectric slabs and
quantum-mechanical traps. In the second part of the paper, the arrays are
obtained through a generalization of supersymmetric quantum mechanics in
discrete variables. The formalism includes a finite-difference Darboux
transformation applied to the scattering matrix of a periodic array. A
procedure for constructing a hierarchy of discrete hamiltonians is indicated
and a particular biparametric family is given. The corresponding potentials and
hopping functions are identified as solitary waves, pointing to a discrete
spinorial generalization of the Korteweg-deVries family.


  The existence of non-trivial IR and UV fixed points in gauge theories as a
function of the number of fermion flavors and bare coupling is discussed in the
light of recent work. It is pointed out that in fact only a small subset of
potential IR-conformal gauge theories, i.e. theories whose IR behavior is
determined by an IR fixed point, has so far been examined. Recent lattice
computations of the spectrum in some cases where existence of an IR fixed point
is reasonably assured, however, reveal a non-QCD-like spectrum with the
lightest states being scalars. It is suggested that these naturally light
composite scalars provide a natural setting for the construction of new
composite Higgs models. A schematic outline of such a model is given.


  The article describes the technical implementation and the performance of the
z-vertex trigger (CIP2k), which is part of the H1-experiment at HERA.


  The recently discovered coexistence of incommensurate antiferromagnetic
neutron scattering peaks and commensurate resonance in underdoped
YBa$_2$Cu$_3$O$_{6+x}$ is calling for an explanation. Within the t-J model, the
doping and energy dependence of the spin dynamics of the underdoped bilayer
cuprates in the normal state is studied based on the fermion-spin theory by
considering the bilayer interactions. Incommensurate peaks are found at
$[(1\pm\delta)\pi,\pi] $ and $[\pi,(1\pm\delta)\pi]$ at low energies with
$\delta$ initially increasing with doping at low dopings and then saturating at
higher dopings. These incommensurate peaks are suppressed, and the parameter
$\delta$ is reduced with increasing energy. Eventually it converges to the
$[\pi,\pi]$ resonance peak. Thus the recently observed coexistence is
interpreted in terms of bilayer interactions.


  In this paper we generalize the Parikh-Wilczek scheme to a holographic screen
in the framework of the ultraviolet self-complete quantum gravity. We calculate
that the tunneling probabilities of the massless and massive particles depend
on their energies of the particles and the mass of the holographic screen. The
radiating temperature has not been the standard Hawking temperature. On the
contrary, the quantum unitarity principle always remains.


  We identify $240$ short-period ($P \lesssim 10$ days) binary systems in the
TESS data, $180$ of which are heartbeat binaries (HB). The sample is mostly a
mix of A and B-type stars and primarily includes eclipsing systems, where over
$30\%$ of the sources with primary and secondary eclipses show a secular change
in their inter-eclipse timings and relative eclipse depths over a multi-year
timescale, likely due to orbital precession. The orbital parameters of the
population are estimated by fitting a heartbeat model to their phase curves and
Gaia magnitudes, where the model accounts for ellipsoidal variability, Doppler
beaming, reflection effects, and eclipses. We construct the sample's
period-eccentricity distribution and find an eccentricity cutoff (where $e
\rightarrow 0$) at a period $1.7$ days. Additionally, we measure the periastron
advance rate for the $12$ of the precessing sources and find that they all
exhibit prograde apsidal precession, which is as high as $9^{\circ}$ yr$^{-1}$
for one of the systems. Using the inferred stellar parameters, we estimate the
general relativistic precession rate of the argument of periastron for the
population and expect over $30$ systems to show a precession in excess of
$0.3^{\circ}$ yr$^{-1}$


  Granular flows in a narrow pipe are studied numerically by the model taking
account of hydrodynamic effects of fluid surrounding particles. In the
simulations density waves are observed over the wide range of the Stokes
number, which represents the inertial effect of particles. The mechanisms of
formation of the density waves are considered and two types of density waves,
which are observed in the systems with zero and finite Stokes numbers, are
presented. Power spectra of density waves obtained from the simulations with
non-zero Stokes number show $1/f^\alpha$ power law which is similar to that in
experiments.


  In recent years, there have been significant advances in building end-to-end
Machine Learning (ML) systems that learn at scale. But most of these systems
are: (a) isolated (perception, speech, or language only); (b) trained on static
datasets. On the other hand, in the field of robotics, large-scale learning has
always been difficult. Supervision is hard to gather and real world physical
interactions are expensive. In this work we introduce and open-source droidlet,
a modular, heterogeneous agent architecture and platform. It allows us to
exploit both large-scale static datasets in perception and language and
sophisticated heuristics often used in robotics; and provides tools for
interactive annotation. Furthermore, it brings together perception, language
and action onto one platform, providing a path towards agents that learn from
the richness of real world interactions.


  Statistical tests that compare classification algorithms are univariate and
use a single performance measure, e.g., misclassification error, $F$ measure,
AUC, and so on. In multivariate tests, comparison is done using multiple
measures simultaneously. For example, error is the sum of false positives and
false negatives and a univariate test on error cannot make a distinction
between these two sources, but a 2-variate test can. Similarly, instead of
combining precision and recall in $F$ measure, we can have a 2-variate test on
(precision, recall). We use Hotelling's multivariate $T^2$ test for comparing
two algorithms, and when we have three or more algorithms we use the
multivariate analysis of variance (MANOVA) followed by pairwise post hoc tests.
In our experiments, we see that multivariate tests have higher power than
univariate tests, that is, they can detect differences that univariate tests
cannot. We also discuss how multivariate analysis allows us to automatically
extract performance measures that best distinguish the behavior of multiple
algorithms.


  Domain experts often possess valuable physical insights that are overlooked
in fully automated decision-making processes such as Bayesian optimisation. In
this article we apply high-throughput (batch) Bayesian optimisation alongside
anthropological decision theory to enable domain experts to influence the
selection of optimal experiments. Our methodology exploits the hypothesis that
humans are better at making discrete choices than continuous ones and enables
experts to influence critical early decisions. At each iteration we solve an
augmented multi-objective optimisation problem across a number of alternate
solutions, maximising both the sum of their utility function values and the
determinant of their covariance matrix, equivalent to their total variability.
By taking the solution at the knee point of the Pareto front, we return a set
of alternate solutions at each iteration that have both high utility values and
are reasonably distinct, from which the expert selects one for evaluation. We
demonstrate that even in the case of an uninformed practitioner, our algorithm
recovers the regret of standard Bayesian optimisation.


  Most of the existing literature on optimal trade execution in limit order
book models assumes that resilience is positive. But negative resilience also
has a natural interpretation, as it models self-exciting behaviour of the price
impact, where trading activities of the large investor stimulate other market
participants to trade in the same direction. In the paper we discuss several
new qualitative effects on optimal trade execution that arise when we allow
resilience to take negative values. We do this in a framework where both market
depth and resilience are stochastic processes.


  A starting point for deriving the Vlasov equation is the BBGKY hierarchy that
describes the dynamics of coupled marginal distribution functions. With a large
value of the plasma parameter one can justify eliminating 2-point correlations
in terms of the 1-point function in order to derive the Vlasov Landau Lenard
Balescu (VLLB) theory. Because of the high dimensionality of the problem,
numerically testing the assumptions of the VLLB theory is prohibitive. In these
notes we propose a physically reasonable interaction model that lowers the
dimensionality of the problem and may bring such computations within reach. We
introduce a 1-dimensional (1-D) electrostatic plasma model formulated in terms
of the interaction of parallelly-aligned charged disks. This model combines
1-dimensional features at short distances and 3-dimensional features at large
distances.


  Assuming the Riemann hypothesis, we prove the latest explicit version of the
prime number theorem for short intervals. Using this result, and assuming the
generalised Riemann hypothesis for Dirichlet $L$-functions is true, we then
establish explicit formulae for $\psi(x,\chi)$, $\theta(x,\chi)$, and an
explicit version of the prime number theorem for primes in arithmetic
progressions that hold for general moduli $q\geq 3$. Finally, we restrict our
attention to $q\leq 10\,000$ and use an exact computation to refine these
results.


  SkyPortal is an open-source software package designed to efficiently discover
interesting transients, manage follow-up, perform characterization, and
visualize the results. By enabling fast access to archival and catalog data,
cross-matching heterogeneous data streams, and the triggering and monitoring of
on-demand observations for further characterization, a SkyPortal-based platform
has been operating at scale for 2 yr for the Zwicky Transient Facility Phase II
community, with hundreds of users, containing tens of millions of time-domain
sources, interacting with dozens of telescopes, and enabling community
reporting. While SkyPortal emphasizes rich user experiences (UX) across common
frontend workflows, recognizing that scientific inquiry is increasingly
performed programmatically, SkyPortal also surfaces an extensive and
well-documented API system. From backend and frontend software to data science
analysis tools and visualization frameworks, the SkyPortal design emphasizes
the re-use and leveraging of best-in-class approaches, with a strong
extensibility ethos. For instance, SkyPortal now leverages ChatGPT
large-language models (LLMs) to automatically generate and surface source-level
human-readable summaries. With the imminent re-start of the next-generation of
gravitational wave detectors, SkyPortal now also includes dedicated
multi-messenger features addressing the requirements of rapid multi-messenger
follow-up: multi-telescope management, team/group organizing interfaces, and
cross-matching of multi-messenger data streams with time-domain optical
surveys, with interfaces sufficiently intuitive for the newcomers to the field.
(abridged)


  Event cameras asynchronously capture brightness changes with low latency,
high temporal resolution, and high dynamic range. However, annotation of event
data is a costly and laborious process, which limits the use of deep learning
methods for classification and other semantic tasks with the event modality. To
reduce the dependency on labeled event data, we introduce Masked Event Modeling
(MEM), a self-supervised framework for events. Our method pretrains a neural
network on unlabeled events, which can originate from any event camera
recording. Subsequently, the pretrained model is finetuned on a downstream
task, leading to a consistent improvement of the task accuracy. For example,
our method reaches state-of-the-art classification accuracy across three
datasets, N-ImageNet, N-Cars, and N-Caltech101, increasing the top-1 accuracy
of previous work by significant margins. When tested on real-world event data,
MEM is even superior to supervised RGB-based pretraining. The models pretrained
with MEM are also label-efficient and generalize well to the dense task of
semantic image segmentation.


  Frequency-domain beamformers have been successful in a wide range of
multi-channel neural separation systems in the past years. However, the
operations in conventional frequency-domain beamformers are typically
independently-defined and complex-valued, which result in two drawbacks: the
former does not fully utilize the advantage of end-to-end optimization, and the
latter may introduce numerical instability during the training phase. Motivated
by the recent success in end-to-end neural separation systems, in this paper we
propose time-domain real-valued generalized Wiener filter (TD-GWF), a linear
filter defined on a 2-D learnable real-valued signal transform. TD-GWF splits
the transformed representation into groups and performs an minimum mean-square
error (MMSE) estimation on all available channels on each of the groups. We
show how TD-GWF can be connected to conventional filter-and-sum beamformers
when certain signal transform and the number of groups are specified. Moreover,
given the recent success in the sequential neural beamforming frameworks, we
show how TD-GWF can be applied in such frameworks to perform iterative
beamforming and separation to obtain an overall performance gain. Comprehensive
experiment results show that TD-GWF performs consistently better than
conventional frequency-domain beamformers in the sequential neural beamforming
pipeline with various neural network architectures, microphone array scenarios,
and task configurations.


  Chest radiograph (CXR) interpretation in pediatric patients is error-prone
and requires a high level of understanding of radiologic expertise. Recently,
deep convolutional neural networks (D-CNNs) have shown remarkable performance
in interpreting CXR in adults. However, there is a lack of evidence indicating
that D-CNNs can recognize accurately multiple lung pathologies from pediatric
CXR scans. In particular, the development of diagnostic models for the
detection of pediatric chest diseases faces significant challenges such as (i)
lack of physician-annotated datasets and (ii) class imbalance problems. In this
paper, we retrospectively collect a large dataset of 5,017 pediatric CXR scans,
for which each is manually labeled by an experienced radiologist for the
presence of 10 common pathologies. A D-CNN model is then trained on 3,550
annotated scans to classify multiple pediatric lung pathologies automatically.
To address the high-class imbalance issue, we propose to modify and apply
"Distribution-Balanced loss" for training D-CNNs which reshapes the standard
Binary-Cross Entropy loss (BCE) to efficiently learn harder samples by
down-weighting the loss assigned to the majority classes. On an independent
test set of 777 studies, the proposed approach yields an area under the
receiver operating characteristic (AUC) of 0.709 (95% CI, 0.690-0.729). The
sensitivity, specificity, and F1-score at the cutoff value are 0.722
(0.694-0.750), 0.579 (0.563-0.595), and 0.389 (0.373-0.405), respectively.
These results significantly outperform previous state-of-the-art methods on
most of the target diseases. Moreover, our ablation studies validate the
effectiveness of the proposed loss function compared to other standard losses,
e.g., BCE and Focal Loss, for this learning task. Overall, we demonstrate the
potential of D-CNNs in interpreting pediatric CXRs.


  The instability in the selection of models is a major concern with data sets
containing a large number of covariates. This paper deals with variable
selection methodology in the case of high-dimensional problems where the
response variable can be right censored. We focuse on new stable variable
selection methods based on bootstrap for two methodologies: the Cox
proportional hazard model and survival trees. As far as the Cox model is
concerned, we investigate the bootstrapping applied to two variable selection
techniques: the stepwise algorithm based on the AIC criterion and the
L1-penalization of Lasso. Regarding survival trees, we review two
methodologies: the bootstrap node-level stabilization and random survival
forests. We apply these different approaches to two real data sets. We compare
the methods on the prediction error rate based on the Harrell concordance index
and the relevance of the interpretation of the corresponding selected models.
The aim is to find a compromise between a good prediction performance and ease
to interpretation for clinicians. Results suggest that in the case of a small
number of individuals, a bootstrapping adapted to L1-penalization in the Cox
model or a bootstrap node-level stabilization in survival trees give a good
alternative to the random survival forest methodology, known to give the
smallest prediction error rate but difficult to interprete by
non-statisticians. In a clinical perspective, the complementarity between the
methods based on the Cox model and those based on survival trees would permit
to built reliable models easy to interprete by the clinician.


  Bound states in the continuum (BICs) are exotic, localized states even though
their energy lies in the continuum spectra. Since its discovery in 1929, the
quest to unveil these exotic states in charge transport experiments remains an
active pursuit in condensed matter physics. Here, we study charge transport in
InSb nanowire networks in the ballistic regime and subject to a perpendicular
magnetic field as ideal candidates to observe and control the appearance of
BICs. We find that BICs reveal themselves as distinctive resonances or
antiresonances in the conductance by varying the applied magnetic field and the
Fermi energy. We systematically consider different lead connections in
hashtag-like nanowire networks, finding the optimal configuration that enhances
the features associated with the emergence of BICs. Finally, the investigation
focuses on the effect of the Rashba spin-orbit interaction of InSb on the
occurrence of BICs in nanowire networks. While the interaction generally plays
a detrimental role in the signatures of the BICs in the conductance of the
nanowire networks, it opens the possibility to operate these nanostructures as
spin filters for spintronics. We believe that this work could pave the way for
the unambiguous observation of BICs in charge transport experiments and for the
development of advanced spintronic devices.


  We report a numerical evidence that the string tension \sigma can be viewed
as an order parameter of the phase transition, which separates the smooth phase
from the crumpled one, in the fluid surface model of Helfrich and
Polyakov-Kleinert. The model is defined on spherical surfaces with two fixed
vertices of distance L. The string tension \sigma is calculated by regarding
the surface as a string connecting the two points. We find that the phase
transition strengthens as L is increased, and that \sigma vanishes in the
crumpled phase and non-vanishes in the smooth phase.


  Energy and momentum of the elementary excitations become independent
variables in medium: energy and momentum statistical distributions are not
identical. The momentum distribution and not the energy distribution is
relevant for barrier penetration. The deviations of the momentum distribution
from the Maxwell-Boltzmann energy distribution can be expressed in terms of the
imaginary part of the self-energy of the quasi-particle. It is possible to
obtain an effective Tsallis' distribution for the kinetic energy. These effects
are different from static or dynamical screening and can have important
consequences for reaction rates in stars.


  We investigate the extent to which the weak equivalences in a model category
can be equipped with algebraic structure. We prove, for instance, that there
exists a monad T such that a morphism of topological spaces admits T-algebra
structure if and only it is a weak homotopy equivalence. Likewise for
quasi-isomorphisms and many other examples. The basic trick is to consider
injectivity in arrow categories. Using algebraic injectivity and cone
injectivity we obtain general results about the extent to which the weak
equivalences in a combinatorial model category can be equipped with algebraic
structure.


  A new no-hair theorem is formulated which rules out a very large class of
non-minimally coupled finite scalar dressing of an asymptotically flat, static,
and spherically symmetric black-hole. The proof is very simple and based in a
covariant method for generating solutions for non-minimally coupled scalar
fields starting from the minimally coupled case. Such method generalizes the
Bekenstein method for conformal coupling and other recent ones. We also discuss
the role of the finiteness assumption for the scalar field.


  This paper presents a new analytical model for the early stages of vapor
bubble growth in superheated liquids. The model bridges a gap in current
knowledge by focusing on the surface tension-controlled, near-equilibrium
growth regime and its transition to an inertia-controlled regime. A unified
analytical model is derived by combining a perturbation method for the initial
growth regime with a complementary outer solution to model the subsequent
bubble growth rate. The model successfully predicts the initial delay in bubble
growth due to surface tension effects. Two non-dimensional parameters govern
this delay period: the initial perturbation from the equilibrium radius and the
Ohnesorge number at the onset of nucleation. The Ohnesorge number encapsulates
the interplay between viscous damping and surface tension forces acting on the
bubble during its early growth stages. The analytical solutions presented here
allow for quantifying the surface-tension, inertial, and transitional regimes
while establishing a simple criterion for estimating the influence of thermal
effects on early-stage growth. Our findings emphasize the significance of
considering the surface tension delay, particularly for short timescales. The
derived analytical solutions and the obtained correlation for
surface-tension-induced delay may prove a practical tool and could be
integrated into existing models of vapor bubble growth.


  Chaotic dynamics of the dripping faucet was investigated both experimentally
and theoretically. We measured continuous change in drop position and velocity
using a high-speed camera. Continuous trajectories of a low-dimensional chaotic
attractor were reconstructed from these data, which was not previously obtained
but predicted in our fluid dynamic simulation. From the simulation, we further
obtained an approximate potential function with only two variables, the drop
mass and its position of the center of mass. The potential landscape helps one
to understand intuitively how the dripping dynamics can exhibit low-dimensional
chaos.


  We study the regularity of the extremal solution of the semilinear biharmonic
equation $\beta \Delta^2 u-\tau \Delta u=\frac{\lambda}{(1-u)^2}$ on a ball $B
\subset \R^N$, under Navier boundary conditions $u=\Delta u=0$ on $\partial B$,
where $\lambda >0$ is a parameter, while $\tau>0$, $\beta>0$ are fixed
constants. It is known that there exists a $\lambda^{*}$ such that for
$\lambda>\lambda^{*}$ there is no solution while for $\lambda<\lambda^{*}$
there is a branch of minimal solutions. Our main result asserts that the
extremal solution $u^{*}$ is regular ($\sup_{B}u^{*}<1$) for $N\leq 8$ and
$\beta, \tau>0$ and it is singular ($\sup_{B}u^{*}=1$) for $N\geq 9$,
$\beta>0$, and $\tau>0$ with $\frac{\tau}{\beta}$ small. Our proof for the
singularity of extremal solutions in dimensions $N\geq 9$ is based on certain
improved Hardy-Rellich inequalities.


  The attainability of modification of the apparent magnetic anisotropy in
(III,Mn)V ferromagnetic semiconductors is probed by means of the
finite-elements-based modelling. The most representative case of (Ga,Mn)As and
its in-plane uniaxial anisotropy is investigated. The hysteresis loops of the
continuous films of a ferromagnetic semiconductor as well as films structured
with the elliptic antidots are modelled for various eccentricity, orientation,
and separation of the anti dots. The effect of anti-dots on the magnetic
anisotropy is confirmed but overall is found to be very weak. The subsequent
modelling for (Ga,Mn)As film with the elliptic dots comprising of metallic NiFe
shows much stronger effect, revealing switching of the magnetic moment in the
ferromagnetic semiconductor governed by the switching behavior of the metallic
inclusions.


  We characterize in details the aging properties of the ferroelectric phase of
K Ta_{1-x} Nb_x O_3 (KTN), where both rejuvenation and (partial) memory are
observed. In particular, we carefully examine the frequency dependence of
several quantities that characterize aging, rejuvenation and memory. We find a
marked subaging behaviour, with an a.c. dielectric susceptiblity scaling as
$\omega \sqrt{t_w}$, where $t_w$ is the waiting time. We suggest an
interpretation in terms of pinned domain walls, much along the lines proposed
for aging in a disordered ferromagnet, where both domain wall reconformations
and overall (cumulative) domain growth are needed to rationalize the
experimental findings.


  In this paper, we use a large-scale play scripts dataset to propose the novel
task of theatrical cue generation from dialogues. Using over one million lines
of dialogue and cues, we approach the problem of cue generation as a controlled
text generation task, and show how cues can be used to enhance the impact of
dialogue using a language model conditioned on a dialogue/cue discriminator. In
addition, we explore the use of topic keywords and emotions for controlled text
generation. Extensive quantitative and qualitative experiments show that
language models can be successfully used to generate plausible and
attribute-controlled texts in highly specialised domains such as play scripts.
Supporting materials can be found at: https://catlab-team.github.io/cuegen.


  Recent work has highlighted the difficulties of estimating
difference-in-differences models when treatment timing occurs at different
times for different units. This article introduces the R package did2s which
implements the estimator introduced in Gardner (2021). The article provides an
approachable review of the underlying econometric theory and introduces the
syntax for the function did2s. Further, the package introduces a function,
event_study, that provides a common syntax for all the modern event-study
estimators and plot_event_study to plot the results of each estimator.


  This is a survey of accumulated spectral analysis observations spanning more
than a century, referring to the double layer potential integral equation, also
known as Neumann-Poincar\'e operator. The very notion of spectral analysis has
evolved along this path. Indeed, the quest for solving this specific singular
integral equation, originally aimed at elucidating classical potential theory
problems, has inspired and shaped the development of theoretical spectral
analysis of linear transforms in XX-th century. We briefly touch some marking
discoveries into the subject, with ample bibliographical references to both
old, sometimes forgotten, texts and new contributions. It is remarkable that
applications of the spectral analysis of the Neumann-Poincar\'e operator are
still uncovered nowadays, with spectacular impacts on applied science. A few
modern ramifications along these lines are depicted in our survey.


  To avoid instabilities in the continuum semi-classical limit of loop quantum
cosmology models, refinement of the underlying lattice is necessary. The
lattice refinement leads to new dynamical difference equations which, in
general, do not have a uniform step-size, implying complications in their
analysis and solutions. We propose a numerical method based on Taylor
expansions, which can give us the necessary information to calculate the
wave-function at any given lattice point. The method we propose can be applied
in any lattice-refined model, while in addition the accuracy of the method can
be estimated. Moreover, we confirm numerically the stability criterion which
was earlier found following a von Neumann analysis. Finally, the `motion' of
the wave-function due to the underlying discreteness of the space-time is
investigated, for both a constant lattice, as well as lattice refinement
models.


  The horizon is a classical concept that arises in general relativity, and is
therefore not clearly defined when the source cannot be reliably described by
classical physics. To any (sufficiently) localised quantum mechanical
wave-function, one can associate a horizon wave-function which yields the
probability of finding a horizon of given radius centred around the source. We
can then associate to each quantum particle a probability that it is a black
hole, and the existence of a minimum black hole mass follows naturally, which
agrees with the one obtained from the hoop conjecture and the Heisenberg
uncertainty principle.


  We consider scalar field theory in a changing background field. As an example
we study the simple case of a spatially varying mass for which we construct the
semiclassical approximation to the propagator. The semiclassical dispersion
relation is obtained by consideration of spectral integrals and agrees with the
WKB result. Further we find that, as a consequence of localization, the
semiclassical approximation necessarily contains quantum correlations in
momentum space.


  We present the analysis of 12227 type-ab RR Lyrae found among the 200 million
public lightcurves in the Catalina Surveys Data Release 1 (CSDR1). These stars
span the largest volume of the Milky Way ever surveyed with RR Lyrae, covering
~20,000 square degrees of the sky (0 < RA < 360, -22 < Dec < 65 deg) to
heliocentric distances of up to 60kpc. Each of the RR Lyrae are observed
between 60 and 419 times over a six-year period. Using period finding and
Fourier fitting techniques we determine periods and apparent magnitudes for
each source. We find that the periods at generally accurate to sigma = 0.002%
by comparison with 2842 previously known RR Lyrae and 100 RR Lyrae observed in
overlapping survey fields. We photometrically calibrate the light curves using
445 Landolt standard stars and show that the resulting magnitudes are accurate
to ~0.05 mags using SDSS data for ~1000 blue horizontal branch stars and 7788
of the RR Lyrae. By combining Catalina photometry with SDSS spectroscopy, we
analyze the radial velocity and metallicity distributions for > 1500 of the RR
Lyrae. Using the accurate distances derived for the RR Lyrae, we show the paths
of the Sagittarius tidal streams crossing the sky at heliocentric distances
from 20 to 60 kpc. By selecting samples of Galactic halo RR Lyrae, we compare
their velocity, metallicity, and distance with predictions from a recent
detailed N-body model of the Sagittarius system. We find that there are some
significant differences between the distances and structures predicted and our
observations.


  Let f be a unimodal map of the interval with critical point c. If the orbit
of c is not dense then most points in lim{[0,1],f} have neighborhoods that are
homeomorphic with the product of a Cantor set and an open arc. The points
without this property are called inhomogeneities, and the set, I, of
inhomogeneities is equal to lim {{\omega}(c),f| {\omega}(c) }.
  In this paper we consider the relationship between the limit complexity of
{\omega}(c) and the limit complexity of I. We show that if {\omega}(c) is more
complicated than a finite collection of convergent sequences then I can have
arbitrarily high limit complexity. We give a complete description of the limit
complexity of I for any possible {\omega}(c).


  Merging neutron star binaries are prime candidate sources for heavy r-process
nucleosynthesis. The amount of heavy r-process material is consistent with the
mass ejection and rates of mergers, and abundances of relic radioactive
materials suggest that heavy r-process material is produced in rare events.
Observations of possible macronovae provide further support for this model.
Still, some concerns remain. One is the observation of heavy r-process elements
in Ultra Faint Dwarf (UFD) galaxies. The escape velocities from UFDs are so
small that the natal kicks, taking place at neutron stars birth, might eject
such binaries from UFDs. Furthermore the old stellar populations of UFDs
requires that r-process nucleosynthesis must have taken place very early on,
while it may take several Gyr for compact binaries to merge. This last problem
arises also within the Milky Way where heavy r-process materials has been
observed in some low metallicity stars. We show here that since a significant
fraction of neutron star binaries form with a very small proper motion those
won't be ejected even from a UFD. Furthermore, a significant fraction of these
binaries merge within a few hundred Myr and in some cases the merger time is
even shorter than a hundred Myr. This population of "rapid mergers" explains
the appearance of heavy r-process material in both UFDs and in the Milky Way.


  Using offset-corrected Gaia-EDR3 parallax measurements and spectrophotometric
methods, we have determined distances for 69 massive stars in the Carina OB1
association and associated clusters: Trumpler 16 (21 stars), Trumpler 14 (20
stars), Trumpler 15 (3 stars), Bochum 11 (5 stars), and South Pillars region
(20 stars). Past distance estimates to the Carina Nebula range from 2.2 to 3.6
kpc, with uncertainties arising from photometry and anomalous dust extinction.
The EDR3 parallax solutions show considerable improvement over DR2, with
typical errors $\sigma_{\varpi}/\varpi \approx$~3-5%. The O-type stars in the
Great Carina Nebula lie at essentially the same distance ($2.35\pm0.08$ kpc),
quoting mean and rms variance. The clusters have distances of $2.32\pm0.12$ kpc
(Tr 16), $2.37\pm0.15$ kpc (Tr 14), $2.36\pm0.09$ kpc (Tr 15), and
$2.33\pm0.12$ kpc (Bochum 11) in good agreement with the $\eta$ Car distance of
around 2.3 kpc. O-star proper motions suggest internal (2D) velocity
dispersions $\sim4$ km/s for Tr 14 and Tr 16. Reliable distances allow
estimates of cluster sizes, stellar dynamics, luminosities, and fluxes of
photoionizing radiation incident on photodissociation regions in the region. We
estimate that Tr 14 and Tr 16 have half-mass radii $r_h = 1.5-1.8$ pc, stellar
crossing times $t_{\rm cr} = r_h/v_m \approx 0.7-0.8$ Myr, and two-body
relaxation times $t_{rh} \approx 40-80$ Myr. The underlying velocity dispersion
for Tr 14, if a bound cluster, would be $v_m \approx 2.1^{+0.7}_{-0.4}$ km/s
for $N = 7600^{+5800}_{-2600}$ stars. With the higher dispersions of the
O-stars, mass segregation might occur slowly, on times scales of 3-6~Myr.