  Endometrial cancer is one of the most common tumors in the female
reproductive system and is the third most common gynecological malignancy that
causes death after ovarian and cervical cancer. Early diagnosis can
significantly improve the 5-year survival rate of patients. With the
development of artificial intelligence, computer-assisted diagnosis plays an
increasingly important role in improving the accuracy and objectivity of
diagnosis, as well as reducing the workload of doctors. However, the absence of
publicly available endometrial cancer image datasets restricts the application
of computer-assisted diagnostic techniques.In this paper, a publicly available
Endometrial Cancer PET/CT Image Dataset for Evaluation of Semantic Segmentation
and Detection of Hypermetabolic Regions (ECPC-IDS) are published. Specifically,
the segmentation section includes PET and CT images, with a total of 7159
images in multiple formats. In order to prove the effectiveness of segmentation
methods on ECPC-IDS, five classical deep learning semantic segmentation methods
are selected to test the image segmentation task. The object detection section
also includes PET and CT images, with a total of 3579 images and XML files with
annotation information. Six deep learning methods are selected for experiments
on the detection task.This study conduct extensive experiments using deep
learning-based semantic segmentation and object detection methods to
demonstrate the differences between various methods on ECPC-IDS. As far as we
know, this is the first publicly available dataset of endometrial cancer with a
large number of multiple images, including a large amount of information
required for image and target detection. ECPC-IDS can aid researchers in
exploring new algorithms to enhance computer-assisted technology, benefiting
both clinical doctors and patients greatly.


  We construct $s$-interleaved linearized Reed--Solomon (ILRS) codes and
variants and propose efficient decoding schemes that can correct errors beyond
the unique decoding radius in the sum-rank metric. The proposed
interpolation-based scheme for ILRS codes can be used as a list decoder or as a
probabilistic unique decoder that corrects errors of sum-rank up to
$t\leq\frac{s}{s+1}(n-k)$, where $s$ is the interleaving order, $n$ the length
and $k$ the dimension of the code. Upper bounds on the list size and the
decoding failure probability are given where the latter is based on a novel
Loidreau--Overbeck-like decoder for ILRS codes. We show how the proposed
decoding schemes can be used to decode errors beyond the unique decoding radius
in the skew metric by using an isometry between the sum-rank metric and the
skew metric.
  We generalize fast minimal approximant basis interpolation techniques to
obtain efficient decoding schemes for ILRS codes (and variants) with
subquadratic complexity in the code length.
  Up to our knowledge, the presented decoding schemes are the first being able
to correct errors beyond the unique decoding region in the sum-rank and skew
metric. The performance of the proposed decoding schemes and the tightness of
the upper bound on the decoding failure probability are validated via Monte
Carlo simulations.


  Effective recommendation systems rely on capturing user preferences, often
requiring incorporating numerous features such as universally unique
identifiers (UUIDs) of entities. However, the exceptionally high cardinality of
UUIDs poses a significant challenge in terms of model degradation and increased
model size due to sparsity. This paper presents two innovative techniques to
address the challenge of high cardinality in recommendation systems.
Specifically, we propose a bag-of-words approach, combined with layer sharing,
to substantially decrease the model size while improving performance. Our
techniques were evaluated through offline and online experiments on Uber use
cases, resulting in promising results demonstrating our approach's
effectiveness in optimizing recommendation systems and enhancing their overall
performance.


  We carry out non-rotating high-resolution calculations of the solar global
convection, which resolve convective scales of less than 10 Mm. To cope with
the low Mach number conditions in the lower convection zone, we use the reduced
speed of sound technique (RSST), which is simple to implement and requires only
local communication in the parallel computation. In addition, the RSST allows
us to expand the computational domain upward to about $0.99 R_{\odot}$ as it
can also handle compressible flows. Using this approach, we study the solar
convection zone on the global scale, including small-scale near-surface
convection. In particular, we investigate the influence of the top boundary
condition on the convective structure throughout the convection zone as well as
on small-scale dynamo action. Our main conclusions are: 1. The small-scale
downflows generated in the near-surface layer penetrate into deeper layers to
some extent and excite small-scale turbulence in the region $>0.9R_\odot$,
where $R_\odot$ is the solar radius. 2. In the deeper convection zone
($<0.9R_\odot$), the convection is not influenced by the location of the upper
boundary. 3. Using an LES approach, we can achieve small-scale dynamo action
and maintain a field of about $0.15-0.25 B_\mathrm{eq}$ throughout the
convection zone, where $B_\mathrm{eq}$ is the equipartition magnetic field to
the kinetic energy. 4. The overall dynamo efficiency varies significantly in
the convection zone as a consequence of the downward directed Poynting flux and
the depth variation of the intrinsic convective scales.


  The problem of heat and electricity pricing in combined heat and power
systems regarding the time scales of electricity and heat, as well as thermal
energy quality, is studied. Based on the asynchronous coordinated dispatch of
the combined heat and power system, an energy-grade double pricing mechanism is
proposed. Under the pricing mechanism, the resulting merchandise surplus of the
heat system operator at each heat dispatch interval can be decomposed into
interpretable parts and its revenue adequacy can be guaranteed for all heat
dispatch intervals. And the electric power system operator's resulting
merchandise surplus is composed of non-negative components at each electricity
dispatch interval, also ensuring its revenue adequacy. In addition, the effects
of different time scales and cogeneration are analyzed in different kinds of
combined heat and power units' pricing.


  Neutron stars are unique testbeds for exploring the physics of strongly
interacting matter in extreme regimes of density, temperature, and isospin that
are not accessible anywhere else in the universe. The nature of neutron star
matter can now be probed with gravitational-waves (GWs) from binary driven by
nonlinear gravity, where phenomena such as tidal effects lead to characteristic
matter-dependent GW signatures. We focus here on the dominant tidal GW imprints
that were most relevant for the event GW170817. We review the role of the tidal
deformability parameter, its definition, computation, and relation to the
equation of state. We briefly discuss the implications of GW170817,
representing the first-ever constraints on tidal deformability from GW data.
Finally, we outline opportunities and challenges for probing subatomic physics
with GWs, as the measurements will become more precise and will probe a
diversity of the binary neutron star population in the coming years.


  We discuss a method to construct observables protected against QCD
uncertainties based on the angular distribution of the exclusive Bd -> K(*0}(->
Kpi) l+ l- decay. We focus on the identification and the interpretation of all
the symmetries of the distribution. They constitute a key ingredient to
construct a set of so-called transverse observables. We work in the framework
of QCD factorization at NLO supplemented by an estimate of power-suppressed
Lambda/mb corrections. A discussion of the new physics properties of two of the
transverse asymmetries, AT^{(2)} and AT^{(5)}, is presented. A comparison
between the transverse asymmetry AT^{(2)} and the forward-backward asymmetry
shows that AT^{(2)} emerges as an improved version of it.


  Over the past years, Printed Mathematical Expression Recognition (PMER) has
progressed rapidly. However, due to the insufficient context information
captured by Convolutional Neural Networks, some mathematical symbols might be
incorrectly recognized or missed. To tackle this problem, in this paper, a Dual
Branch transformer-based Network (DBN) is proposed to learn both local and
global context information for accurate PMER. In our DBN, local and global
features are extracted simultaneously, and a Context Coupling Module (CCM) is
developed to complement the features between the global and local contexts. CCM
adopts an interactive manner so that the coupled context clues are highly
correlated to each expression symbol. Additionally, we design a Dynamic Soft
Target (DST) strategy to utilize the similarities among symbol categories for
reasonable label generation. Our experimental results have demonstrated that
DBN can accurately recognize mathematical expressions and has achieved
state-of-the-art performance.


  Investigating the role of disorder in superconductors is an essential part of
characterizing the fundamental superconducting properties as well as assessing
potential applications of the material. In most cases, the information
available on the defect matrix is poor, making such studies difficult, but the
situation can be improved by introducing defects in a controlled way, as
provided by neutron irradiation. In this work, we analyze the effects of
neutron irradiation on a Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ single crystal. We
mainly concentrate on the magnetic properties which were determined by
magnetometry. Introducing disorder by neutron irradiation leads to significant
effects on both the reversible and the irreversible magnetic properties, such
as the transition temperature, the upper critical field, the anisotropy, and
the critical current density. The results are discussed in detail by comparing
them with the properties in the unirradiated state.


  We apply degenerate many-body perturbation theory at high orders for the
ab-initio description of ground states and excitation spectra of open-shell
nuclei using soft realistic nucleon-nucleon interactions. We derive a recursive
formulation of standard degenerate many-body perturbation theory that enables
us to evaluate order-by-order perturbative energy and state corrections up to
the 30th order. We study 6,7-Li as test cases using a similarity
renormalization group (SRG) evolved nucleon-nucleon interaction from chiral
effective field theory. The simple perturbation series exhibits a strong, often
oscillatory divergence, as was observed previously for ground states of
closed-shell nuclei. Even for very soft interactions resulting from SRG
evolutions up to large flow parameter, i.e. low momentum scales, the
perturbation series still diverges. However, a resummation of the perturbation
series via Pad\'e approximants yields very stable and converged ground and
excited-state energies in very good agreement with exact no-core shell-model
calculations for the same model space.


  The resonance scattering of Ly$\alpha$ photons with neutral hydrogen atoms in
the intergalactic medium not only couples the spin temperature to the kinetic
temperature but also leads to a heating of the gas. We investigate the impact
of this heating on the average brightness temperature of the 21-cm signal from
the Cosmic Dawn in the context of the claimed detection by the EDGES low-band
experiment. We model the evolution of the global signal taking into account the
Ly$\alpha$ coupling and heating and a cooling which can be stronger than the
Hubble cooling. Using the claimed detection of a strong absorption signal at
$z\approx 17$ as a constraint, we find that a strong Ly$\alpha$ background is
ruled out. Instead the results favour a weak Ly$\alpha$ background combined
with an excess cooling mechanism which is substantially stronger than
previously considered. We also show that the cooling mechanism driven by the
interaction between millicharged baryons and dark matter particles no longer
provides a viable explanation for the EDGES result when Ly$\alpha$ heating is
taken into account.


  Empirical Colebrook equation from 1939 is still accepted as an informal
standard to calculate friction factor during the turbulent flow through pipes
from smooth with almost negligible relative roughness to the very rough inner
surface. The Colebrook equation contains flow friction factor in implicit
logarithmic form where it is, aside of itself, a function of the Reynolds
number Re and the relative roughness of inner pipe surface. To evaluate the
error introduced by many available explicit approximations to the Colebrook
equation, it is necessary to determinate value of the friction factor from the
Colebrook equation as accurate as possible. The most accurate way to achieve
that is using some kind of iterative methods. Usually classical approach also
known as simple fixed point method requires up to 8 iterations to achieve the
high level of accuracy, but does not require derivatives of the Colebrook
function as here presented accelerated Householder approach (3rd order, 2nd
order: Halley and Schroder method and 1st order: Newton-Raphson) which needs
only 3 to 7 iteration and three-point iterative methods which needs only 1 to 4
iteration to achieve the same high level of accuracy. Strategies how to find
derivatives of the Colebrook function in symbolic form, how to avoid use of the
derivatives (Secant method) and how to choose optimal starting point for the
iterative procedure are shown. Householder approach to the Colebrook equations
expressed through the Lambert W-function is also analyzed. One approximation to
the Colebrook equation based on the analysis from the paper with the error of
no more than 0.0617% is shown.


  We study the resurgence properties of the coefficients $C_n(\tau)$ appearing
in the asymptotic expansion of the incomplete gamma function within the
transition region. Our findings reveal that the asymptotic behaviour of
$C_n(\tau)$ as $n\to +\infty$ depends on the parity of $n$. Both
$C_{2n-1}(\tau)$ and $C_{2n}(\tau)$ exhibit behaviours characterised by a
leading term accompanied by an inverse factorial series, where the coefficients
are once again $C_{2k-1}(\tau)$ and $C_{2k}(\tau)$, respectively. Our
derivation employs elementary tools and relies on the known resurgence
properties of the asymptotic expansion of the gamma function and the uniform
asymptotic expansion of the incomplete gamma function. To the best of our
knowledge, prior to this paper, there has been no investigation in the existing
literature regarding the resurgence properties of asymptotic expansions in
transition regions.


  We refine the physical parameters of the transiting hot Jupiter planet XO-1b
and its stellar host XO-1 using HST NICMOS observations. XO-1b has a radius
Rp=1.21+/-0.03 RJup, and XO-1 has a radius Rs=0.94+/-0.02 RSun, where the
uncertainty in the mass of XO-1 dominates the uncertainty of Rp and Rs. There
are no significant differences in the XO-1 system properties between these
broad-band NIR observations and previous determinations based upon ground-based
optical observations. We measure two transit timings from these observations
with 9 s and 15 s precision. As a residual to a linear ephemeris model, there
is a 2.0 sigma timing difference between the two HST visits that are separated
by 3 transit events (11.8 days). These two transit timings and additional
timings from the literature are sufficient to rule out the presence of an Earth
mass planet orbiting in 2:1 mean motion resonance coplanar with XO-1b. We
identify and correct for poorly understood gain-like variations present in
NICMOS time series data. This correction reduces the effective noise in time
series photometry by a factor of two, for the case of XO-1.


  Pre-training strategies based on self-supervised learning (SSL) have proven
to be effective pretext tasks for many downstream tasks in computer vision. Due
to the significant disparity between medical and natural images, the
application of typical SSL is not straightforward in medical imaging.
Additionally, those pretext tasks often lack context, which is critical for
computer-aided clinical decision support. In this paper, we developed a
longitudinal masked auto-encoder (MAE) based on the well-known
Transformer-based MAE. In particular, we explored the importance of time-aware
position embedding as well as disease progression-aware masking. Taking into
account the time between examinations instead of just scheduling them offers
the benefit of capturing temporal changes and trends. The masking strategy, for
its part, evolves during follow-up to better capture pathological changes,
ensuring a more accurate assessment of disease progression. Using OPHDIAT, a
large follow-up screening dataset targeting diabetic retinopathy (DR), we
evaluated the pre-trained weights on a longitudinal task, which is to predict
the severity label of the next visit within 3 years based on the past time
series examinations. Our results demonstrated the relevancy of both time-aware
position embedding and masking strategies based on disease progression
knowledge. Compared to popular baseline models and standard longitudinal
Transformers, these simple yet effective extensions significantly enhance the
predictive ability of deep classification models.


  Large scale databases are available that contain homologous gene families
constructed from hundreds of complete genome sequences from across the three
domains of Life. Here we discuss approches of increasing complexity aimed at
extracting information on the pattern and process of gene family evolution from
such datasets. In particular, we consider models that invoke processes of gene
birth (duplication and transfer) and death (loss) to explain the evolution of
gene families. First, we review birth-and-death models of family size evolution
and their implications in light of the universal features of family size
distribution observed across different species and the three domains of life.
Subsequently, we proceed to recent developments on models capable of more
completely considering information in the sequences of homologous gene families
through the probabilistic reconciliation of the phylogenetic histories of
individual genes with the phylogenetic history of the genomes in which they
have resided. To illustrate the methods and results presented, we use data from
the HOGENOM database, demonstrating that the distribution of homologous gene
family sizes in the genomes of the Eukaryota, Archaea and Bacteria exhibit
remarkably similar shapes. We shown that these distributions are best described
by models of gene family size evolution where for individual genes the death
(loss) rate is larger than the birth (duplication and transfer) rate, but new
families are continually supplied to the genome by a process of origination.
Finally, we use probabilistic reconciliation methods to take into consideration
additional information from gene phylogenies, and find that, for prokaryotes,
the majority of birth events are the result of transfer.


  We study moduli spaces of (possibly non-nodal) curves (C,p_1,\ldots,p_n) of
arithmetic genus g with n smooth marked points, equipped with nonzero tangent
vectors, such that ${\mathcal O}_C(p_1+\ldots+p_n)$ is ample and $H^1({\mathcal
O}_C(a_1p_1+\ldots+a_np_n))=0$ for given weights ${\bf a}=(a_1,\ldots,a_n)$
such that $a_i\ge 0$ and $\sum a_i=g$. We show that each such moduli space
$\widetilde{{\mathcal U}}^{ns}_{g,n}({\bf a})$ is an affine scheme of finite
type, and the Krichever map identifies it with the quotient of an explicit
locally closed subscheme of the Sato Grassmannian by the free action of the
group of changes of formal parameters. We study the GIT quotients of
$\widetilde{{\mathcal U}}^{ns}_{g,n}({\bf a})$ by the natural torus action and
show that some of the corresponding stack quotients give modular
compactifications of ${\mathcal M}_{g,n}$ with projective coarse moduli spaces.
More generally, using similar techniques, we construct moduli spaces of curves
with chains of divisors supported at marked points, with prescribed number of
sections, which in the case n=1 corresponds to specifying the Weierstrass gap
sequence at the marked point.


  We first prove that the set of domino tilings of a fixed finite figure is a
distributive lattice, even in the case when the figure has holes. We then give
a geometrical interpretation of the order given by this lattice, using (not
necessarily local) transformations called {\em flips}.
  This study allows us to formulate an exhaustive generation algorithm and a
uniform random sampling algorithm.
  We finally extend these results to other types of tilings (calisson tilings,
tilings with bicolored Wang tiles).


  A pressure-induced simultaneous metal-insulator transition (MIT) and
structural-phase transformation in lithium hydride with about 1% volume
collapse has been predicted by means of the local density approximation (LDA)
in conjunction with an all-electron GW approximation method. The LDA wrongly
predicts that the MIT occurs before the structural phase transition. As a
byproduct, it is shown that only the use of the generalized-gradient
approximation together with the zero-point vibration produces an equilibrium
lattice parameter, bulk modulus, and an equation of state that are in excellent
agreement with experimental results.


  As both legged robots and embedded compute have become more capable,
researchers have started to focus on field deployment of these robots. Robust
autonomy in unstructured environments requires perception of the world around
the robot in order to avoid hazards. However, incorporating perception online
while maintaining agile motion is more challenging for legged robots than other
mobile robots due to the complex planners and controllers required to handle
the dynamics of locomotion. This report will compare three recent approaches
for perceptive locomotion and discuss the different ways in which vision can be
used to enable legged autonomy.


  The problem of spin precession in a time-dependent magnetic field is
considered in the adiabatic approximation where the field direction or the
angular velocity of its rotation is changing slowly. The precession angles are
given by integrals in a way similar to the semi-classical approximation for the
Schr\"{o}dinger equation.


  During fabrication and scanning-tunneling-microscope (STM) imaging of
dangling bonds (DBs) on a hydrogenated silicon surface, we consistently
observed halo-like features around isolated DBs for specific imaging
conditions. These surround individual or small groups of DBs, have abnormally
sharp edges, and cannot be explained by conventional STM theory. Here we
investigate the nature of these features by a comprehensive 3-dimensional model
of elastic and inelastic charge transfer in the vicinity of a DB. Our essential
finding is that non-equilibrium current through the localized electronic state
of a DB determines the charging state of the DB. This localized charge distorts
the electronic bands of the silicon sample, which in turn affects the STM
current in that vicinity causing the halo effect. The influence of various
imaging conditions and characteristics of the sample on STM images of DBs is
also investigated.


  Extracting Handwritten text is one of the most important components of
digitizing information and making it available for large scale setting.
Handwriting Optical Character Reader (OCR) is a research problem in computer
vision and natural language processing computing, and a lot of work has been
done for English, but unfortunately, very little work has been done for low
resourced languages such as Urdu. Urdu language script is very difficult
because of its cursive nature and change of shape of characters based on it's
relative position, therefore, a need arises to propose a model which can
understand complex features and generalize it for every kind of handwriting
style. In this work, we propose a transformer based Urdu Handwritten text
extraction model. As transformers have been very successful in Natural Language
Understanding task, we explore them further to understand complex Urdu
Handwriting.


  Qubit initialization is a critical task in quantum computation and
communication. Extensive efforts have been made to achieve this with high
speed, efficiency and scalability. However, previous approaches have either
been measurement-based and required fast feedback, suffered from crosstalk or
required sophisticated calibration. Here, we report a fast and high-fidelity
reset scheme, avoiding the issues above without any additional chip
architecture. By modulating the flux through a transmon qubit, we realize a
swap between the qubit and its readout resonator that suppresses the excited
state population to 0.08% $\pm$ 0.08% within 34 ns (284 ns if photon depletion
of the resonator is required). Furthermore, our approach (i) can achieve
effective second excited state depletion, (ii) has negligible effects on
neighbouring qubits, and (iii) offers a way to entangle the qubit with an
itinerant single photon, useful in quantum communication applications.


  Lusztig \cite{L5,L6} gave a parametrization for $\rm{Irr}(G^F)$, where $G$ is
a reductive algebraic group defined over $\mathbb{F}_q$, with Frobenius map
$F$. This parametrization is known as Lusztig's Jordan decomposition or Lusztig
correspondence. However, there is not a canonical choice of Lusztig
correspondence. In this paper, we consider classical groups. We pick a
canonical choice of Lusztig correspondence which is compatible with parabolic
induction and is compatible with theta correspondence. This result extends
Pan's result in \cite{P3}. As an application, we give a refinement of the
results of the finite Gan-Gross-Prasad problem in \cite{Wang1} and prove a
duality between Theta correspondence and finite Gan-Gross-Prasad problem, which
can be regarded as a finite field instance of relative Langlands duality of
Ben-Zvi-Sakellaridis-Venkatesh \cite{BZSV}.


  This paper is a brief review of the processes responsible for X-ray emission
from radio jets, lobes and hot spots. Possible photons in inverse Compton
scattering models include the radio synchrotron radiation itself (i.e.
synchrotron self-Compton [SSC] emission), the cosmic microwave background
(CMB), the galaxy starlight and radiation from the active nucleus. SSC emission
has been detected from a number of hot spots. Scattering of the CMB is expected
to dominate for jets (and possibly hot spots) undergoing bulk relativistic
motion close to the direction towards the observer. Scattering of infrared
radiation from the AGN should be observable from radio lobes, especially if
they are close to the active nucleus. Synchrotron radiation is detected in some
sources, most notably the jet of M87. I briefly discuss why different hot spots
emit X-rays by different emission mechanisms and the nature of the synchrotron
spectra.


  In continuation of the papers hep-th/0505012 and hep-th/0508101 we
investigate the consequences when $N$ open-string tachyons roll down
simultaneously. We demonstrate that the $N$-Tachyon system coupled to gravity
does indeed give rise to the assisted slow-roll inflation.


  Network coding achieves optimal throughput in multicast networks. However,
throughput optimality \emph{relies} on the network nodes or routers to code
\emph{correctly}. A Byzantine node may introduce junk packets in the network
(thus polluting downstream packets and causing the sinks to receive the wrong
data) or may choose coding coefficients in a way that significantly reduces the
throughput of the network.
  Most prior work focused on the problem of Byzantine nodes polluting packets.
However, even if a Byzantine node does not pollute packets, he can still affect
significantly the throughput of the network by not coding correctly. No
previous work attempted to verify if a certain node \emph{coded correctly using
random coefficients} over \emph{all} of the packets he was supposed to code
over.
  We provide two novel protocols (which we call PIP and Log-PIP) for detecting
whether a node coded correctly over all the packets received (i.e., according
to a random linear network coding algorithm). Our protocols enable any node in
the network to examine a packet received from another node by running a
"verification test". With our protocols, the worst an adversary can do and
still pass the packet verification test is in fact equivalent to random linear
network coding, which has been shown to be optimal in multicast networks. Our
protocols resist collusion among nodes and are applicable to a variety of
settings.
  Our topology simulations show that the throughput in the worst case for our
protocol is two to three times larger than the throughput in various
adversarial strategies allowed by prior work. We implemented our protocols in
C/C++ and Java, as well as incorporated them on the Android platform (Nexus
One). Our evaluation shows that our protocols impose modest overhead.


  Recent measurements of various charm-hadron ratios in $pp$, $p$-Pb and Pb-Pb
collisions at the LHC have posed challenges to the theoretical understanding of
heavy-quark hadronization. The $\Lambda_c/D^0$ ratio in $pp$ and $p$-Pb
collisions shows larger values than those found in $e^+e^-$ and $ep$ collisions
and predicted by Monte-Carlo event generators based on string fragmentation, at
both low and intermediate transverse momenta ($p_T$). In AA collisions, the
$D_s/D$ ratio is significantly enhanced over its values in $pp$, while the
$\Lambda_c/D^0$ data indicates a further enhancement at intermediate $p_T$.
Here, we report on our recent developments for a comprehensive description of
the charm hadrochemistry and transport in $pp$ and $AA$ collisions. For $pp$
collisions we find that the discrepancy between the $\Lambda_c/D^0$ data and
model predictions is much reduced by using a statistical hadronization model
augmented by a large set of "missing" states in the charm-baryon spectrum,
contributing to the $\Lambda_c$ via decay feeddown. For $AA$ collisions, we
develop a 4-momentum conserving resonance recombination model for charm-baryon
formation implemented via event-by-event simulations that account for
space-momentum correlations (SMCs) in transported charm- and thermal
light-quark distributions. The SMCs, together with the augmented charm-baryon
states, are found to play an important role in describing the baryon-to-meson
enhancement at intermediate momenta. We emphasize the importance of satisfying
the correct (relative) chemical equilibrium limit when computing the charm
hadrochemistry and its momentum dependence with coalescence models.


  We critique the hypothesis that the first stars were very massive stars (VMS;
M > 140 Msun). We review the two major lines of evidence for the existence of
VMS: (1) that the relative metal abundances of extremely metal-poor Galactic
halo stars show evidence of VMS enrichment, and (2) that the high
electron-scattering optical depth (tau_e) to the CMB found by WMAP requires VMS
for reionization in a concordance LambdaCDM cosmology. The supernova yield
patterns of VMS are incompatible with the Fe-peak and r-process abundances in
halo stars. Models including Type II supernovae and/or ``hypernovae'' from
metal-free progenitors with 8 - 40 Msun can better explain the observed trends.
With a simple metal-transport model, we estimate that halo enrichment curtails
metal-free star formation after ~10^8 yr at z ~ 20. Because the ionizing photon
efficiency of metal-free stars peaks at ~120 Msun and declines at higher mass,
an IMF with a lower bound at M ~ 10 - 20 Msun and no VMS can maximize the
ionizing photon budget and still be consistent with the nucleosynthetic
evidence. An IMF devoid of low-mass stars is justified independently by models
of the formation of primordial stars. Using a semi-analytic model for H I and
He II reionization, we find that such an IMF can reproduce tau_e = 0.10 - 0.14,
consistent with the range from WMAP. We conclude, on the basis of these
results, that VMS are not necessary to meet the existing constraints commonly
taken to motivate them.


  The stable marriage problem and its extensions have been extensively studied,
with much of the work in the literature assuming that agents fully know their
own preferences over alternatives. This assumption however is not always
practical (especially in large markets) and agents usually need to go through
some costly deliberation process in order to learn their preferences. In this
paper we assume that such deliberations are carried out via interviews, where
an interview involves a man and a woman, each of whom learns information about
the other as a consequence. If everybody interviews everyone else, then clearly
agents can fully learn their preferences. But interviews are costly, and we may
wish to minimize their use. It is often the case, especially in practical
settings, that due to correlation between agents' preferences, it is
unnecessary for all potential interviews to be carried out in order to obtain a
stable matching. Thus the problem is to find a good strategy for interviews to
be carried out in order to minimize their use, whilst leading to a stable
matching. One way to evaluate the performance of an interview strategy is to
compare it against a naive algorithm that conducts all interviews. We argue
however that a more meaningful comparison would be against an optimal offline
algorithm that has access to agents' preference orderings under complete
information. We show that, unless P=NP, no offline algorithm can compute the
optimal interview strategy in polynomial time. If we are additionally aiming
for a particular stable matching (perhaps one with certain desirable
properties), we provide restricted settings under which efficient optimal
offline algorithms exist.


  We present a relativistic generalization of the Wigner inequality for the
scalar and pseudoscalar particles decaying to two particles with spin (fermions
and photons.) We consider Wigner's inequality with the full spin
anticorrelation (with the non-relativistic analog) as well as the case with the
full spin correlation. The latter case may be obtained by a special choice of
the plane of measurement of the spin projections on the direction of
propagation of fermions. The possibility for relativistic testing of Bohr's
complementarity principle is shown.


  According to the leading models in modern finance, the presence of intraday
lead-lag relationships between financial assets is negligible in efficient
markets. With the advance of technology, however, markets have become more
sophisticated. To determine whether this has resulted in an improved market
efficiency, we investigate whether statistically significant lagged correlation
relationships exist in financial markets. We introduce a numerical method to
statistically validate links in correlation-based networks, and employ our
method to study lagged correlation networks of equity returns in financial
markets. Crucially, our statistical validation of lead-lag relationships
accounts for multiple hypothesis testing over all stock pairs. In an analysis
of intraday transaction data from the periods 2002--2003 and 2011--2012, we
find a striking growth in the networks as we increase the frequency with which
we sample returns. We compute how the number of validated links and the
magnitude of correlations change with increasing sampling frequency, and
compare the results between the two data sets. Finally, we compare topological
properties of the directed correlation-based networks from the two periods
using the in-degree and out-degree distributions and an analysis of three-node
motifs. Our analysis suggests a growth in both the efficiency and instability
of financial markets over the past decade.


  Using kinematics from Gaia and the large elemental abundance space of the
second data release of the GALAH survey, we identify two new members of the
Fimbulthul stellar stream, and chemically tag them to massive, multi-metallic
globular cluster $\omega$ Centauri. Recent analysis of the second data release
of Gaia had revealed the Fimbulthul stellar stream in the halo of the Milky
Way. It had been proposed that the stream is associated with the $\omega$
Centauri, but this proposition relied exclusively upon the kinematics and
metallicities of the stars to make the association. In this work, we find our
two new members of the stream to be metal-poor stars that are enhanced in
sodium and aluminium, typical of second population globular cluster stars, but
not otherwise seen in field stars. Furthermore, the stars share the s-process
abundance pattern seen in $\omega$ Centauri, which is rare in field stars.
Apart from one star within 1.5 deg of $\omega$ Centauri, we find no other stars
observed by GALAH spatially near $\omega$ Centauri or the Fimbulthul stream
that could be kinematically and chemically linked to the cluster. Chemically
tagging stars in the Fimbulthul stream to $\omega$ Centauri confirms the
earlier work, and further links this tidal feature in the Milky Way halo to
$\omega$ Centauri.


  We use multiband archival HST observations to measure the photometric and
structural parameters of the M81 globular cluster that hosts the Fast Radio
Burst FRB 20200120E. Our best-fitting King model has an effective radius $r_h =
3.06$ pc with a moderate King model concentration of $c = 53$, and an inferred
core radius of 0.81 pc. We revisit the exact astrometric location of the FRB
within the cluster, and find that FRB 20200120E is located 1.92 pc from the
center, but within the projected half-light radius. We estimate the relative
encounter rate of the FRB host, along with the corresponding rates of 210 other
globular clusters in M81, and compare these values with the encounter rates of
Galactic globular clusters. The FRB resides in a globular cluster with an
encounter rate that is moderately higher than the median stellar encounter rate
in our two comparison samples. While the estimated encounter rate of the FRB
host cluster (e.g., $\sim50\%$ of a cluster like 47 Tuc) is sufficient to allow
the possibility that the FRB formed dynamically, our results do not place
strong constraints on this scenario due to the limitations of the available HST
data and the possible systematic uncertainties and selection effects in the
comparison data.


  We present observations of CK Vul obtained with the Spitzer Space Telescope.
The infrared spectrum reveals a warm dust continuum with nebular, molecular
hydrogen and HCN lines superimposed, together with the "Unidentified Infrared"
(UIR) features. The nebular lines are consistent with emission by a low density
gas. We conclude that the Spitzer data, combined with other information, are
incompatible with CK Vul being a classical nova remnant in "hibernation" after
the event of 1670, a "Very Late Thermal Pulse", a "Luminous Red Variable" such
as V838 Mon, or a "Diffusion-induced nova". The true nature of CK Vul remains a
mystery.


  Sociologists associate the spatial variation of crime within an urban
setting, with the concept of collective efficacy. The collective efficacy of a
neighborhood is defined as social cohesion among neighbors combined with their
willingness to intervene on behalf of the common good. Sociologists measure
collective efficacy by conducting survey studies designed to measure
individuals' perception of their community. In this work, we employ the curated
data from a survey study (ground truth) and examine the effectiveness of
substituting costly survey questionnaires with proxies derived from social
media. We enrich a corpus of tweets mentioning a local venue with several
linguistic and topological features. We then propose a pairwise learning to
rank model with the goal of identifying a ranking of neighborhoods that is
similar to the ranking obtained from the ground truth collective efficacy
values. In our experiments, we find that our generated ranking of neighborhoods
achieves 0.77 Kendall tau-x ranking agreement with the ground truth ranking.
Overall, our results are up to 37% better than traditional baselines.


  Entanglement generation can be robust against noise in approaches that
deliberately incorporate dissipation into the system dynamics. The presence of
additional dissipation channels may, however, limit fidelity and speed of the
process. Here we show how quantum optimal control techniques can be used to
both speed up the entanglement generation and increase the fidelity in a
realistic setup, whilst respecting typical experimental limitations. For the
example of entangling two trapped ion qubits [Lin et al., Nature 504, 415
(2013)], we find an improved fidelity by simply optimizing the polarization of
the laser beams utilized in the experiment. More significantly, an alternate
combination of transitions between internal states of the ions, when combined
with optimized polarization, enables faster entanglement and decreases the
error by an order of magnitude.


  In this article we briefly review recent experimental and theoretical work on
quantum Hall effect in graphene, and argue that some of the quantum Hall states
exhibit spontaneous symmetry breaking that is driven by electron-electron
interaction. We will also discuss how to experimentally determine the actual
manner in which symmetry breaking occurs, and detect the collective charge and
neutral excitations associated with symmetry breaking. Other issues will also
be briefly mentioned.


  Traditionally, caregivers, whether formal or informal, have taken the
responsibility of providing assistance and care to patients with cognitive
decline. Usually, both the caregiver and the patient are subjected to financial
and emotional burdens, which impact the patient's life quality. To overcome
this issue, Ambient Assistive Living (AAL) technologies have been adopted to
replace the caregivers and complement patients' lack of intelligence.
Technologies such as Internet of Things (IoT) and Artificial Intelligence (AI)
have enabled intelligent ubiquitous learning for smart buildings to monitor the
cognitively declined occupants and provide in-home assistive services and
solutions. This paper aims to summarize and evaluate the intelligence
complements provided by smart buildings that can increase the cognitively
declined occupants' quality of life and autonomy. Through a systematic
literature review, the authors find that most of the existing contributions are
towards identifying the occupants' behavior, and thus, to determine
corresponding assistive services and solutions. Five key research gaps are
identified, including the lack of adequate adoption of technological
interventions to fully support the occupants' autonomy and independence. The
authors also propose a conceptual framework to highlight the research gaps in
smart building applications for cognitively declined occupants and to map the
future research directions.


  Data analysis plays an important role in the development of intelligent
energy networks (IENs). This article reviews and discusses the application of
data analysis methods for energy big data. The installation of smart energy
meters has provided a huge volume of data at different time resolutions,
suggesting data analysis is required for clustering, demand forecasting, energy
generation optimization, energy pricing, monitoring and diagnostics. The
currently adopted data analysis technologies for IENs include pattern
recognition, machine learning, data mining, statistics methods, etc. However,
existing methods for data analysis cannot fully meet the requirements for
processing the big data produced by the IENs and, therefore, more comprehensive
data analysis methods are needed to handle the increasing amount of data and to
mine more valuable information.


  Torsion is a non-Riemannian geometrical extension of general relativity that
allows including the spin of matter and the twisting of spacetime. Cosmological
models with torsion have been considered in the literature to solve problems of
either the very early (high redshift $z$) or the present-day Universe. This
paper focuses on distinguishable observational signatures of torsion that could
not be otherwise explained with a scalar field in pseudo-Riemannian geometry.
We show that when torsion is present, the cosmic duality relation between the
angular diameter distance, $D_{\mathrm A}$, and the luminosity distance,
$D_{\mathrm L}$, is broken. We show how the deviation described by the
parameter $\eta = D_{\mathrm L}/[ D_{\mathrm A}(1+z)^2] -1 $ is linked to
torsion and how different forms of torsion lead to special-case
parametrisations of $\eta$, including $\eta_0 z$, $\eta_0 z/(1+z)$, and $\eta_0
\ln (1+z)$. We also show that the effects of torsion could be visible in
low-redshift data, inducing biases in supernovae-based $H_0$ measurements. We
also show that torsion can impact the Clarkson-Bassett-Lu (CBL) function ${\cal
C}(z) = 1 + H^2 (D D'' - D'^2) + H H' D D'$, where $D$ is the transverse
comoving distance. If $D$ is inferred from the luminosity distance, then, in
general non-zero torsion models, ${\cal C}(z) \ne 0$. For pseudo-Riemannian
geometry, the Friedmann-Lemaitre-Robertson-Walker (FLRW) metric has ${\cal
C}(z) \equiv 0$; thus, measurement of the CBL function could provide another
diagnostic of torsion.


  In this survey paper we present recent results obtained by Khare,
Wintenberger and the author that have led to a proof of Serre's conjecture,
such as existence of compatible families, modular upper bounds for universal
deformation rings and existence of minimal lifts, prime switching and
modularity propagation, weight reduction (via existence of conjugates) and
(iterated) killing ramification.
  The main tools used in the proof of these results are modularity lifting
theorems a la Wiles and a result of potential modularity due to R. Taylor.


  The predictive functions that permit humans to infer their body state by
sensorimotor integration are critical to perform safe interaction in complex
environments. These functions are adaptive and robust to non-linear actuators
and noisy sensory information. This paper introduces a computational perceptual
model based on predictive processing that enables any multisensory robot to
learn, infer and update its body configuration when using arbitrary sensors
with Gaussian additive noise. The proposed method integrates different sources
of information (tactile, visual and proprioceptive) to drive the robot belief
to its current body configuration. The motivation is to enable robots with the
embodied perception needed for self-calibration and safe physical human-robot
interaction.
  We formulate body learning as obtaining the forward model that encodes the
sensor values depending on the body variables, and we solve it by Gaussian
process regression. We model body estimation as minimizing the discrepancy
between the robot body configuration belief and the observed posterior. We
minimize the variational free energy using the sensory prediction errors
(sensed vs expected).
  In order to evaluate the model we test it on a real multisensory robotic arm.
We show how different sensor modalities contributions, included as additive
errors, improve the refinement of the body estimation and how the system adapts
itself to provide the most plausible solution even when injecting strong
sensory visuo-tactile perturbations. We further analyse the reliability of the
model when different sensor modalities are disabled. This provides grounded
evidence about the correctness of the perceptual model and shows how the robot
estimates and adjusts its body configuration just by means of sensory
information.


  We provide a functional framework and a numerical algorithm to compute the
Bloch variety for Maxwell's equations when the electric permittivity is
frequency dependent. We incorporate the idea of a mixed formulation for
Maxwell's equations to obtain a quadratic eigenvalue for the wave-vector in
terms of the frequency. We reformulate this problem as a larger linear
eigenvalue problem and prove that this results in the need to compute
eigenvalues of a compact operator. Using finite elements, we provide
preliminary numerical examples of the scheme for both frequency independent and
frequency dependent permittivity.


  We address the existence of globally neutral neutron star configurations in
contrast with the traditional ones constructed by imposing local neutrality.
The equilibrium equations describing this system are the Einstein-Maxwell
equations which must be solved self-consistently with the general relativistic
Thomas-Fermi equation and $\beta$-equilibrium condition. To illustrate the
application of this novel approach we adopt the Baym, Bethe, and Pethick (1971)
strong interaction model of the baryonic matter in the core and of the
white-dwarf-like material of the crust. We illustrate the crucial role played
by the boundary conditions satisfied by the leptonic component of the matter at
the interface between the core and the crust. For every central density an
entire new family of equilibrium configurations exists for selected values of
the Fermi energy of the electrons at the surface of the core. Each such
configuration fulfills global charge neutrality and is characterized by a
non-trivial electrodynamical structure. The electric field extends over a thin
shell of thickness $\sim \hbar/(m_e c)$ between the core and the crust and
becomes largely overcritical in the limit of decreasing values of the crust
mass.


  The range to which the Laser Interferometer Gravitational-Wave Observatory
(LIGO) can observe astrophysical systems varies over time, limited by noise in
the instruments and their environments. Identifying and removing the sources of
noise that limit LIGO's range enables higher signal-to-noise observations and
increases the number of observations. The LIGO observatories are continuously
monitored by hundreds of thousands of auxiliary channels that may contain
information about these noise sources. This paper describes an algorithm that
uses linear regression, namely lasso (least absolute shrinkage and selection
operator) regression, to analyze all of these channels and identify a small
subset of them that can be used to reconstruct variations in LIGO's
astrophysical range. Exemplary results of the application of this method to
three different periods of LIGO Livingston data are presented, along with
computational performance and current limitations.


  The inflationary paradigm not only addresses early Universe puzzles but also
aligns well with the observational constraints, with slow-roll inflationary
models fitting best. Evaluating these model predictions requires considering
both slow-roll inflationary dynamics and the subsequent reheating epoch. This
involves the quantitative analysis that takes into account the effective
equation of state (EoS) and duration of reheating, connecting these with the
perturbations generated deep during the inflationary era. Given the
complexities involved, many approximations are often used for simplification.
However, as future observations are expected to improve the accuracy of these
observables significantly, this work takes a different approach. Instead of
relying on approximations, we consider the near-accurate solutions of
inflationary models and compare our results with the pre-existing ones. It
mainly incorporates two improvements: the first is the accurate dynamics of the
slow-roll evolution, and, thus, the end of inflation; and the second is the
higher-order slow-roll corrections to the perturbed observables. Our findings
indicate that, by implementing these corrections, the theoretical predictions
improve significantly. It also indicates that seemingly minor corrections can
have significant effects on the perturbed observables, and these refined
predictions can be compared with future observations to potentially rule out
models and help resolve the degeneracy problem of the inflationary paradigm.


  In his classical argument, Rao derives the Riemannian distance corresponding
to the Fisher metric using a mapping between the space of positive measures and
Euclidean space. He obtains the Hellinger distance on the full space of
measures and the Fisher distance on the subset of probability measures. In
order to highlight the interplay between Fisher theory and quantum information
theory, we extend this construction to the space of positive-definite Hermitian
matrices using Riemannian submersions and quotient manifolds. The analog of the
Hellinger distance turns out to be the Bures-Wasserstein (BW) distance, a
distance measure appearing in optimal transport, quantum information, and
optimisation theory. First we present an existing derivation of the Riemannian
metric and geodesics associated with this distance. Subsequently, we present a
novel derivation of the Riemannian distance and geodesics for this metric on
the subset of trace-one matrices, analogous to the Fisher distance for
probability measures.


  Observational studies of star formation reveal spatial distributions of Young
Stellar Objects (YSOs) that are `snapshots' of an ongoing star formation
process. Using methods from spatial statistics it is possible to test the
likelihood that a given distribution process could produce the observed
patterns of YSOs. The aim of this paper is to determine the usefulness of the
spatial statistics tests Diggle's G function (G), the `free-space' function
(F), Ripley's K and O-ring for application to astrophysical data. The spatial
statistics tests were applied to simulated data containing 2D Gaussian clusters
projected on random distributions of stars. The number of stars within the
Gaussian cluster and number of background stars were varied to determine the
tests' ability to reject complete spatial randomness (CSR) with changing
signal-to-noise. The best performing test was O-ring optimised with overlapping
logarithmic bins, closely followed by Ripley's K. The O-ring test is equivalent
to the 2-point correlation function. Both F and G (and the minimum spanning
tree, of which G is a subset) performed significantly less well, requiring a
cluster with a factor of two higher signal-to-noise in order to reject CSR
consistently. We demonstrate the tests on example astrophysical datasets drawn
from the Spitzer catalogue.


  We consider in this paper the Serre--Green--Naghdi equations with surface
tension. Smooth solutions of this system conserve an $H^1$-equivalent energy.
We prove the existence of global weak dissipative solutions for any relatively
small-energy initial data. We also prove that the Riemann invariants of the
solutions satisfy a one-sided Oleinik inequality.


  Shell-model states involving several pseudospin doublets and ``intruder''
levels in nuclei, are combined into larger multiplets. The corresponding
single-particle spectrum exhibits a supersymmetric pattern whose origin can be
traced to the relativistic pseudospin symmetry of a nuclear mean-field Dirac
Hamiltonian with scalar and vector potentials.


  We consider the general K\"ahler-Ricci flows which exist for all time. The
zeroth order control on the flow metric potential for various infinite time
singularities is the focus. The possible semi-amplness for numerically
effective classes serves as the main motivation.


  Let $\mathcal{M}$ be a Riemannian $n$-manifold with a metric such that the
manifold is Ahlfors-regular. We also assume either non-negative Ricci
curvature, or that the Ricci curvature is bounded from below together with a
bound on the gradient of the heat kernel. We characterize BMO-functions $u:
\mathcal{M} \to \mathbb{R}$ by a Carleson measure condition of their
$\sigma$-harmonic extension $U: \mathcal{M} \times (0,\infty) \to \mathbb{R}$.
We make crucial use of a $T(b)$ theorem proved by Hofmann, Mitrea, Mitrea, and
Morris.
  As an application we show that the famous theorem of
Coifman--Lions--Meyer--Semmes holds in this class of manifolds: Jacobians of
$W^{1,n}$-maps from $\mathcal{M}$ to $\mathbb{R}^n$ can be estimated against
BMO-functions, which now follows from the arguments for commutators recently
proposed by Lenzmann and the second-named author using only harmonic
extensions, integration by parts, and trace space characterizations.


  Machine learning approaches in drug discovery, as well as in other areas of
the chemical sciences, benefit from curated datasets of physical molecular
properties. However, there is a lack of sufficiently large data collections
that include first-principle quantum chemical information on bioactive
molecules, such as single-point electronic properties, quantum mechanical wave
functions and density-functional theory (DFT) matrices. The open-access QMugs
(Quantum-Mechanical Properties of Drug-like Molecules) dataset fills this void.
The QMugs collection comprises quantum mechanical properties of more than 665k
biologically and pharmacologically relevant molecules extracted from the ChEMBL
database, totaling $\sim$2M conformers. QMugs contains optimized molecular
geometries and thermodynamic data obtained via the semi-empirical method
GFN2-xTB. Atomic and molecular properties (e.g., partial charges, energies, and
rotational constants) are provided on both the GFN2-xTB and on the DFT
($\omega$B97X-D/def2-SVP) levels of theory. QMugs also comprises the respective
quantum mechanical wave functions, including DFT density and orbital matrices,
totaling over 7 terabytes of uncompressed data. This dataset is intended to
facilitate the development of models that learn from molecular data on
different levels of theory while also providing insight into the corresponding
relationships between molecular structure and biological activity.


  In this paper, we study the properties of weak approximation with
Brauer-Manin obstruction and the Hasse principle with Brauer-Manin obstruction
for surfaces with respect to field extensions of number fields. We assume a
conjecture of M. Stoll. For any nontrivial extension of number fields $L/K,$ we
construct two kinds of smooth, projective, and geometrically connected surfaces
defined over $K.$ For the surface of the first kind, it has a $K$-rational
point, and satisfies weak approximation with Brauer-Manin obstruction off
$\infty_K,$ while its base change by $L$ does not so off $\infty_L.$ For the
surface of the second kind, it is a counterexample to the Hasse principle
explained by the Brauer-Manin obstruction, while the failure of the Hasse
principle of its base change by $L$ cannot be so. We illustrate these
constructions with explicit unconditional examples.


  In millimeter wave (mmWave) communication systems, beamforming with large
antenna arrays is critical to overcome high path losses. Separating all-digital
beamforming into analog and digital stages can provide the large reduction in
power consumption and small loss in spectral efficiency needed for practical
implementations. Developing algorithms with this favorable tradeoff is
challenging due to the additional degrees of freedom in the analog stage and
its accompanying hardware constraints. In hybrid beamforming systems, for
example, channel estimation algorithms do not directly observe the channels,
face a high channel count, and operate at low SNR before transmit-receive beam
alignment. Since mmWave channels are sparse in time and beam domains, many
compressed sensing (CS) channel estimation algorithms have been developed that
randomly configure the analog beamformers, digital beamformers, and/or pilot
symbols. In this paper, we propose to design deterministic beamformers and
pilot symbols for open-loop channel estimation. We use CS approaches that rely
on low coherence for their recovery guarantees, and hence seek to minimize the
mutual coherence of the compressed sensing matrix. We also propose a precoder
column ordering to design the pilot symbols. Simulation results show that our
beamformer designs reduce channel estimation error over competing methods.


  In the first part of this paper we will work out a close and so far not yet
noticed correspondence between the swampland approach in quantum gravity and
geometric flow equations in general relativity, most notably the Ricci flow. We
conjecture that following the gradient flow towards a fixed point, which is at
infinite distance in the space of background metrics, is accompanied by an
infinite tower of states in quantum gravity. In case of the Ricci flow, this
conjecture is in accordance with the generalized distance and AdS distance
conjectures, which were recently discussed in the literature, but it should
also hold for more general background spaces. We argue that the entropy
functionals of gradient flows provide a useful definition of the generalized
distance in the space of background fields. In particular we give evidence that
for the Ricci flow the distance $\Delta$ can be defined in terms of the mean
scalar curvature of the manifold, $\Delta\sim\log \bar R$. For a more general
gradient flow, the distance functional also depends on the string coupling
constant.
  In the second part of the paper we will apply the generalized distance
conjecture to gravity theories with higher curvature interactions, like higher
derivative $R^2$ and $W^2$ terms. We will show that going to the weak coupling
limit of the higher derivative terms corresponds to the infinite distance limit
in metric space and hence this limit must be accompanied by an infinite tower
of light states. For the case of the $R^2$ or $W^2$ couplings, this limit
corresponds to the limit of a small cosmological constant or, respectively, to
a light additional spin-two field in gravity. In general we see that the limit
of small higher curvature couplings belongs to the swampland in quantum
gravity, just like the limit of a small $U(1)$ gauge coupling belongs to the
swampland as well.


  Understanding the statistical properties of a collection of individuals
subject to random displacements and birth-and-death events is key to several
applications in physics and life sciences, encompassing the diagnostic of
nuclear reactors and the analysis of epidemic patterns. Previous investigations
of the critical regime, where births and deaths balance on average, have shown
that highly non-Poissonian fluctuations might occur in the population, leading
to spontaneous spatial clustering, and eventually to a critical catastrophe,
where fluctuations can result in the extinction of the population. A milder
behaviour is observed when the population size is kept constant:
thefluctuations asymptotically level off and the critical catastrophe is
averted. In this paper, we shall extend these results by considering the
broader class of models with prompt and delayed birth-and-death events, which
mimic the presence of precursors in nuclear reactor physics or incubation
inepidemics. We shall consider models with and without population control
mechanisms. Analytical or semi-analytical results for the density, the
two-point correlation function and the mean-squared pair distance will be
derived and compared to Monte Carlo simulations, which will be used as a
reference.


  We present new criteria on the existence of fixed points that combine some
monotonicity assumptions with the classical fixed point index theory. As an
illustrative application, we use our theoretical results to prove the existence
of positive solutions for systems of nonlinear Hammerstein integral equations.
An example is also presented to show the applicability of our results.


  For a connected abelian Lie group T acting on a Poisson manifold (Y,{\pi}) by
Poisson isomorphisms, the T-leaves of {\pi} in Y are, by definition, the orbits
of the symplectic leaves of {\pi} under T, and the leaf stabilizer of a T-leaf
is the subspace of the Lie algebra of T that is everywhere tangent to all the
symplectic leaves in the T-leaf. In this paper, we first develop a general
theory on T-leaves and leaf stabilizers for a class of Poisson structures
defined by Lie bialgebra actions and quasitriangular r-matrices. We then apply
the general theory to four series of holomorphic Poisson structures on products
of flag varieties and related spaces of a complex semi-simple Lie group G. We
describe their T-leaf decompositions, where T is a maximal torus of G, in terms
of (open) extended Richardson varieties and extended double Bruhat cells
associated to conjugacy classes of G, and we compute their leaf stabilizers and
the dimension of the symplectic leaves in each T -leaf.


  We study the distributed Linear Quadratic Gaussian (LQG) control problem in
discrete-time and finite-horizon, where the controller depends linearly on the
history of the outputs and it is required to lie in a given subspace, e.g. to
possess a certain sparsity pattern. It is well-known that this problem can be
solved with convex programming within the Youla domain if and only if a
condition known as Quadratic Invariance (QI) holds. In this paper, we first
show that given QI sparsity constraints, one can directly descend the gradient
of the cost function within the domain of output-feedback controllers and
converge to a global optimum. Note that convergence is guaranteed despite
non-convexity of the cost function. Second, we characterize a class of Uniquely
Stationary (US) problems, for which first-order methods are guaranteed to
converge to a global optimum. We show that the class of US problems is strictly
larger than that of strongly QI problems and that it is not included in that of
QI problems. We refer to Figure 1 for details. Finally, we propose a tractable
test for the US property.


  We consider the spectral correlations of clean globally hyperbolic (chaotic)
quantum systems. Field theoretical methods are applied to compute quantum
corrections to the leading (`diagonal') contribution to the spectral form
factor. Far-reaching structural parallels, as well as a number of differences,
to recent semiclassical approaches to the problem are discussed.


  We review the recently found large-scale anomalies in the maps of temperature
anisotropies in the cosmic microwave background. These include alignments of
the largest modes of CMB anisotropy with each other and with geometry and
direction of motion of the Solar System, and the unusually low power at these
largest scales. We discuss these findings in relation to expectation from
standard inflationary cosmology, their statistical significance, the tools to
study them, and the various attempts to explain them.


  Transmission spectroscopy is a powerful technique for probing exoplanetary
atmospheres. A successful ground-based observational method uses a differential
technique based on high-dispersion spectroscopy, but that only preserves narrow
features in transmission spectra. Here we use the chromatic Rossiter-McLaughlin
(RM) effect to measure the Rayleigh-scattering slope in the transmission
spectrum of HD 189733b with the aim to show that it can be effectively used to
measure broadband transmission features. The amplitude of the RM effects
depends on the effective size of the planet, and in the case of an atmospheric
contribution therefore depends on the observed wavelength. We analysed archival
HARPS data of three transits of HD 189733b, covering a wavelength range of 400
to 700 nm. We measured the slope in the transmission spectrum of HD 189733b at
a $2.5\sigma$ significance. Assuming it is due to Rayleigh scattering and not
caused by stellar activity, it would correspond to an atmospheric temperature,
as set by the scale height, of $T = 2300 \pm 900 \mathrm{K}$, well in line with
previously obtained results. This shows that ground-based high-dispersion
spectral observations can be used to probe broad-band features in the
transmission spectra of extrasolar planets, by using the chromatic RM effect.
This method will be particularly interesting in conjunction with the new
echelle spectrograph ESPRESSO, which currently is under construction for ESOs
Very Large Telescope and will provide a gain in signal-to-noise ratio of about
a factor 4 compared to HARPS. This will be of great value because of the
limited and uncertain future of the Hubble Space Telescope and because the
future James Webb Space Telescope will not cover this wavelength regime.


  Renal transplantation emerges as the most effective solution for end-stage
renal disease. Occurring from complex causes, a substantial risk of transplant
chronic dysfunction persists and may lead to graft loss. Medical imaging plays
a substantial role in renal transplant monitoring in clinical practice.
However, graft supervision is multi-disciplinary, notably joining nephrology,
urology, and radiology, while identifying robust biomarkers from such
high-dimensional and complex data for prognosis is challenging. In this work,
taking inspiration from the recent success of Large Language Models (LLMs), we
propose MEDIMP -- Medical Images with clinical Prompts -- a model to learn
meaningful multi-modal representations of renal transplant Dynamic
Contrast-Enhanced Magnetic Resonance Imaging (DCE MRI) by incorporating
structural clinicobiological data after translating them into text prompts.
MEDIMP is based on contrastive learning from joint text-image paired embeddings
to perform this challenging task. Moreover, we propose a framework that
generates medical prompts using automatic textual data augmentations from LLMs.
Our goal is to learn meaningful manifolds of renal transplant DCE MRI,
interesting for the prognosis of the transplant or patient status (2, 3, and 4
years after the transplant), fully exploiting the limited available multi-modal
data most efficiently. Extensive experiments and comparisons with other renal
transplant representation learning methods with limited data prove the
effectiveness of MEDIMP in a relevant clinical setting, giving new directions
toward medical prompts. Our code is available at
https://github.com/leomlck/MEDIMP.


  As deep neural networks are growing in size and being increasingly deployed
to more resource-limited devices, there has been a recent surge of interest in
network pruning methods, which aim to remove less important weights or
activations of a given network. A common limitation of most existing pruning
techniques, is that they require pre-training of the network at least once
before pruning, and thus we can benefit from reduction in memory and
computation only at the inference time. However, reducing the training cost of
neural networks with rapid structural pruning may be beneficial either to
minimize monetary cost with cloud computing or to enable on-device learning on
a resource-limited device. Recently introduced random-weight pruning approaches
can eliminate the needs of pretraining, but they often obtain suboptimal
performance over conventional pruning techniques and also does not allow for
faster training since they perform unstructured pruning. To overcome their
limitations, we propose Set-based Task-Adaptive Meta Pruning (STAMP), which
task-adaptively prunes a network pretrained on a large reference dataset by
generating a pruning mask on it as a function of the target dataset. To ensure
maximum performance improvements on the target task, we meta-learn the mask
generator over different subsets of the reference dataset, such that it can
generalize well to any unseen datasets within a few gradient steps of training.
We validate STAMP against recent advanced pruning methods on benchmark
datasets, on which it not only obtains significantly improved compression rates
over the baselines at similar accuracy, but also orders of magnitude faster
training speed.


  Autonomous vehicles require accurate and reliable short-term trajectory
predictions for safe and efficient driving. While most commercial automated
vehicles currently use state machine-based algorithms for trajectory
forecasting, recent efforts have focused on end-to-end data-driven systems.
Often, the design of these models is limited by the availability of datasets,
which are typically restricted to generic scenarios. To address this
limitation, we have developed a synthetic dataset for short-term trajectory
prediction tasks using the CARLA simulator. This dataset is extensive and
incorporates what is considered complex scenarios - pedestrians crossing the
road, vehicles overtaking - and comprises 6000 perspective view images with
corresponding IMU and odometry information for each frame. Furthermore, an
end-to-end short-term trajectory prediction model using convolutional neural
networks (CNN) and long short-term memory (LSTM) networks has also been
developed. This model can handle corner cases, such as slowing down near zebra
crossings and stopping when pedestrians cross the road, without the need for
explicit encoding of the surrounding environment. In an effort to accelerate
this research and assist others, we are releasing our dataset and model to the
research community. Our datasets are publicly available on
https://github.com/sharmasushil/Navigating-Uncertainty-Trajectory-Prediction .


  We prove an infinite-dimensional generalization of Zenger's lemma that was
used in the proof of the fact that the convex hull of the point spectrum of a
linear operator is contained in its numerical range. Two relevant examples are
given, and possible application in the Arrow-Debreu model is also discussed.


  We present the algebraic Bethe Ansatz solution for the vertex model recently
proposed by Zhou as the classical analog of the Bariev interacting XY chains.
The relevant commutation rules between the creation fields contain the Hecke
symmetry pointed out recently by Hikami and Murakami. The eigenvalues of the
corresponding transfer matrix are explicitly given.


  We present a comprehensive analysis on connectivity and resilience of secure
sensor networks under the widely studied q-composite key predistribution
scheme. For network connectivity which ensures that any two sensors can find a
path in between for secure communication, we derive the conditions to guarantee
connectivity in consideration of (i) node-capture attacks, where the adversary
may capture a set of sensors and compromise keys in their memory; (ii) sensor
mobility, meaning that sensors can move around so that the network topology may
change over time; (iii) physical transmission constraints, under which two
sensors have to be within each other's transmission range for communication;
(iv) the boundary effect of network fields; and (v) link unreliability, meaning
that links are allowed to be unreliable. In contrast, many prior connectivity
analyses of secure sensor networks often ignore the above issues. For
resilience, although limited studies have presented formal analysis, it is
often assumed that the adversary captures a random set of sensors, whereas this
paper allows the adversary to capture an arbitrary set of sensors. We present
conditions to ensure unassailability and unsplittability in secure sensor
networks under the q-composite scheme. Unassailability ensures that an
adversary capturing any set consisting of a negligible fraction of sensors can
compromise only a negligible fraction of communication links although the
adversary may compromise communications between noncaptured nodes which happen
to use keys that are shared by captured nodes. Unsplittability means that when
a negligible fraction of sensors are captured, almost all of the remaining
nodes are still securely connected. Based on the results of connectivity,
unassailability and unsplittability, we provide useful guidelines for the
design of secure sensor networks.


  Numerous cutting-edge scientific technologies originate at the laboratory
scale, but transitioning them to practical industry applications is a
formidable challenge. Traditional pilot projects at intermediate scales are
costly and time-consuming. An alternative, the E-pilot, relies on high-fidelity
numerical simulations, but even these simulations can be computationally
prohibitive at larger scales. To overcome these limitations, we propose a
scalable, physics-constrained reduced order model (ROM) method. ROM identifies
critical physics modes from small-scale unit components, projecting governing
equations onto these modes to create a reduced model that retains essential
physics details. We also employ Discontinuous Galerkin Domain Decomposition
(DG-DD) to apply ROM to unit components and interfaces, enabling the
construction of large-scale global systems without data at such large scales.
This method is demonstrated on the Poisson and Stokes flow equations, showing
that it can solve equations about $15 - 40$ times faster with only $\sim$ $1\%$
relative error. Furthermore, ROM takes one order of magnitude less memory than
the full order model, enabling larger scale predictions at a given memory
limitation.


  The dynamics of innovation are nonlinear and complex: geographical,
technological, and economic selection environments can be expected to interact.
Can patents provide an analytical lens to this process in terms of different
attributes such as inventor addresses, classification codes, backward and
forward citations, etc.? Two recently developed patent maps with interactive
overlay techniques--Google Maps and maps based on citation relations among
International Patent Classifications (IPC)--are elaborated into dynamic
versions that allow for online animations and comparisons by using split
screens. Various forms of animation are explored. The recently developed
Cooperative Patent Classifications (CPC) of the U.S. Patent and Trade Office
(USPTO) and the European Patent Office (EPO) provide new options for a precise
delineation of samples in both USPTO data and the Worldwide Patent Statistics
Database (PatStat) of EPO. Among the "technologies for the mitigation of
climate change" (class Y02), we zoom in on nine material technologies for
photovoltaic cells; and focus on one of them (CuInSe2) as a lead case. The
longitudinal development of Rao-Stirling diversity in the IPC-based maps
provides a heuristics for studying technological generations during the period
under study (1975-2012). The sequencing of generations prevails in USPTO data
more than in PatStat data because PatStat aggregates patent information from
countries in different stages of technological development, whereas one can
expect USPTO patents to be competitive at the technological edge.


  We place new constraints on the primordial local non-Gaussianity parameter
f_NL using recent Cosmic Microwave Background anisotropy and galaxy clustering
data. We model the galaxy power spectrum according to the halo model,
accounting for a scale dependent bias correction proportional to f_NL/k^2. We
first constrain f_NL in a full 13 parameters analysis that includes 5
parameters of the halo model and 7 cosmological parameters. Using the WMAP7 CMB
data and the SDSS DR4 galaxy power spectrum, we find f_NL=171\pm+140 at 68%
C.L. and -69<f_NL<+492 at 95% C.L.. We discuss the degeneracies between f_NL
and other cosmological parameters. Including SN-Ia data and priors on H_0 from
Hubble Space Telescope observations we find a stronger bound: -35<f_NL<+479 at
95% C.L.. We also fit the more recent SDSS DR7 halo power spectrum data
finding, for a \Lambda-CDM+f_NL model, f_NL=-93\pm128 at 68% C.L. and
-327<f_{NL}<+177 at 95% C.L.. We finally forecast the constraints on f_NL from
future surveys as EUCLID and from CMB missions as Planck showing that their
combined analysis could detect f_NL\sim 5.


  Previous work in phonologically and phonetically grounded language generation
has mainly focused on domains such as puns and poetry. In this article, we
present new work on the generation of tongue-twisters - a form of language that
is required to be conditioned on a phoneme level to maximize sound overlap,
whilst maintaining semantic consistency with an input topic and still being
grammatically correct. We present TwisterLister, a pipeline for generating
phonologically informed tongue-twisters from Large Language Models (LLMs) that
we use to generate TwistList 2.0, the largest annotated dataset of
tongue-twisters to date, consisting of 17K+ examples from a combination of
human and LLM authors. Our generation pipeline involves the use of a
phonologically constrained vocabulary alongside LLM prompting to generate
novel, non-derivative tongue-twister examples. We additionally present the
results of automatic and human evaluation of smaller models trained on our
generated dataset to demonstrate the extent to which phonologically motivated
language types can be generated without explicit injection of phonological
knowledge. Additionally, we introduce a Phoneme-Aware Constrained Decoding
module (PACD) that can be integrated into any causal language model and
demonstrate that this method generates good quality tongue-twisters both with
and without fine-tuning the underlying language model. We also design and
implement a range of automatic metrics for the task of tongue-twister
generation that is phonologically motivated and captures the unique essence of
tongue-twisters based on Phonemic Edit Distance (PED).


  The goal of this research is to enable MCNP6 to produce high-energy light
fragments. These energetic light fragments may be emitted by our models through
three processes: Fermi breakup, preequilibrium, and coalescence. We explore the
emission of light fragments through each of these mechanisms and demonstrate an
improved agreement with experimental data achieved by extending precompound
models to include emission of fragments heavier than $^4$He.


  The multiplicity of an algebraic curve $C$ in the complex plane at a point
$p$ on that curve is defined as the number of points that occur at the
intersection of $C$ with a general complex line that passes close to the point
$p$. It is shown that $p$ is a singular point of the curve $C$ if and only if
this multiplicity is greater than or equal to 2, in this sense, such an integer
number can be considered as a measure of how singular can be a point of the
curve $C$. In these notes, we address the classical concept of multiplicity of
singular points of complex algebraic sets (not necessarily complex curves) and
we approach the nature of the multiplicity of singular points as a geometric
invariant from the perspective of the Multiplicity Conjecture (Zariski 1971).
More precisely, we bring a discussion on the recent results obtained jointly
with Lev Birbrair, Javier Fern\'andez de Bobadilla, L\^e Dung Trang and Mikhail
Verbitsky on the bi-Lipschitz invariance of the multiplicity.


  The ascent and descent of the Mittag-Leffler property were instrumental in
proving Zariski locality of the notion of an (infinite dimensional) vector
bundle by Raynaud and Gruson in \cite{RG}. More recently, relative
Mittag-Leffler modules were employed in the theory of (infinitely generated)
tilting modules and the associated quasi-coherent sheaves, \cite{AH},
\cite{HST}. Here, we study the ascent and descent along flat and faithfully
flat homomorphisms for relative versions of the Mittag-Leffler property. In
particular, we prove the Zariski locality of the notion of a locally
f-projective quasi-coherent sheaf for all schemes, and for each $n \geq 1$, of
the notion of an $n$-Drinfeld vector bundle for all locally noetherian schemes.


  We compute the Frobenius complexity for the determinantal ring of prime
characteristic $p$ obtained by modding out the $2 \times 2$ minors of an $m
\times n$ matrix of indeterminates, where $m > n \ge 2$. We also show that, as
$p \to \infty$, the Frobenius complexity approaches $m-1$.


  Lyman alpha emission presents a means of identifying very high redshift
galaxies, provided such objects can be reliably distinguished from foreground
emission-line galaxies. Here we report on a program of imaging and
spectroscopic studies being conducted with the Keck telescope, in concert with
additional efforts from the ground and with HST, to study such high-redshift
objects over the range from z=3 to 7. The first deep narrow-band imaging
studies with Keck are used to show that strong Lyman alpha emitters, such as
have been seen in high-redshift quasar fields at z>4.5, can be found in the
field populations. Based on studies of the HDF and the Hawaii Survey Fields
these are significant contributors to the star formation rates at these epochs.


  Given $f \in C_0(\mathbb{R}^n)$ and $\Lambda \subset \mathbb{R}^{2n}$ a
finite set we demonstrate the linear independence of the set of time-frequency
translates $\mathcal{G}(f, \Lambda) = \{\pi(\lambda)f\}_{\lambda\in \Lambda}$
when the time coordinates of points in $\Lambda$ are far apart relative to the
decay of $f.$ As a corollary, we prove that for any $f \in C_0(\mathbb{R}^n)$
and finite $\Lambda \subset \mathbb{R}^{2n}$ there exist infinitely many
dilations $D_r$ such that $\mathcal{G}(D_rf, \Lambda)$ is linearly independent.
Furthermore, we prove that $\mathcal{G}(f, \Lambda)$ is linearly independent
for functions like $f(t) = \frac{cos(t)}{|t|}$ which have a singularity and are
bounded away from any neighborhood of the singularity.


  The growth in online shopping and third party logistics has caused a revival
of interest in finding optimal solutions to the large scale in-transit freight
consolidation problem. Given the shipment date, size, origin, destination, and
due dates of multiple shipments distributed over space and time, the problem
requires determining when to consolidate some of these shipments into one
shipment at an intermediate consolidation point so as to minimize shipping
costs while satisfying the due date constraints. In this paper, we develop a
mixed-integer programming formulation for a multi-period freight consolidation
problem that involves multiple products, suppliers, and potential consolidation
points. Benders decomposition is then used to replace a large number of integer
freight-consolidation variables by a small number of continuous variables that
reduces the size of the problem without impacting optimality. Our results show
that Benders decomposition provides a significant scale-up in the performance
of the solver. We demonstrate our approach using a large-scale case with more
than 27.5 million variables and 9.2 million constraints.


  We propose a family of gradient reconstruction schemes based on the solution
of over-determined systems by orthogonal or oblique projections. In the case of
orthogonal projections, we retrieve familiar weighted least-squares gradients,
but we also propose new direction-weighted variants. On the other hand, using
oblique projections that employ cell face normal vectors we derive variations
of consistent Green-Gauss gradients, which we call Taylor-Gauss gradients. The
gradients are tested and compared on a variety of grids such as structured,
locally refined, randomly perturbed, unstructured, and with high aspect ratio.
The tests include quadrilateral and triangular grids, and employ both compact
and extended stencils, and observations are made about the best choice of
gradient and weighting scheme for each case. On high aspect ratio grids, it is
found that most gradients can exhibit a kind of numerical instability that may
be so severe as to make the gradient unusable. A theoretical analysis of the
instability reveals that it is triggered by roundoff errors in the calculation
of the cell centroids, but ultimately is due to truncation errors of the
gradient reconstruction scheme, rather than roundoff errors. Based on this
analysis, we provide guidelines on the range of weights that can be used safely
with least squares methods to avoid this instability.


  A systematic experimental study of inclusive pion double charge exchange in
4He has been undertaken. The reaction 4He(pi+,pi-)4p was observed at incident
energies 120, 150, 180, 240 and 270 MeV; the 4He(pi-,pi+)4n reaction was
observed at incident energies 180 and 240 MeV. At each incident energy, the
doubly differential cross section was measured at three to five outgoing pion
laboratory angles between 25 deg and 130 deg. At each angle, cross sections
were measured over the range of outgoing pion energies from 10 MeV up to the
kinematic limit for the reaction in which the final state consists of the
oppositely charged pion plus four free nucleons.
  The spectra of outgoing pions are strikingly different from those observed
for the inclusive double charge exchange reaction in heavier nuclei, but
resemble those observed in the (pi-,pi+) reaction in 3He. The forward-angle
spectra in the 3He and 4He reactions exhibit a prominent peak at high outgoing
pion energies. Interpretation of the peaks in 3He (4He) as a three-
(four-)nucleon resonance is ruled out by kinematic analysis. The results of a
calculation, wherein the double charge exchange reaction is assumed to proceed
as two sequential single charge exchange interactions, suggest that the
high-energy peak is naturally explained by this double scattering mechanism.
Non-static treatment of the pi-N interactions and the inclusion of nuclear
binding effects appear to be important in reproducing the shape of the energy
spectra at forward angles.


  We discuss the Equivalence Theorem (ET) in the BRST formalism. The existence
of a local inverse of the field transformation (at least as a formal power
expansion) suggests a formulation of the ET, which allows a nilpotent BRST
symmetry. This strategy cannot be implemented at the quantum level if the
inverse is non-local. In this case we propose an alternative formulation of the
ET, where, by using Faddeev-Popov fields, this difficulty is circumvented. We
study the quantum deformation of the associated ST identity, which turns out to
be anomaly free, and show that a selected set of Green functions, which in some
cases can be identified with the physical observables of the model, does not
depend on the choice of the transformation of the fields. In general the
transformation of the fields yields a non-renormalizable theory. When the
equivalence is established between a renormalizable and a non-renormalizable
theory, the ET provides a way to give a meaning to the last one by using the
resulting ST identity. In this case the Quantum Action Principle cannot be of
any help in the discussion of the ET. We assume and discuss the validity of a
Quasi Classical Action Principle, which turns out to be sufficient for the
present work. As an example we study the renormalizability and unitarity of
massive QED in Proca's gauge by starting from a linear Lorentz-covariant gauge.


  The large N spectrum of the quantum mechanical hamiltonian of two hermitean
matrices in a harmonic potential is studied in a framework where one of the
matrices is treated exactly and the other is treated as a creation operator
impurity in the background of the first matrix. For the free case, the complete
set of invariant eigenstates and corresponding energies are obtained. When
g_{YM}^2 interactions are added, it is shown that the full string tension
corrected spectrum of BMN loops is obtained.


  The formal analysis of security protocols is a challenging field, with
various approaches being studied nowadays. The famous Burrows-Abadi-Needham
Logic was the first logical system aiming to validate security protocols.
Combining ideas from previous approaches, in this paper we define a complete
system of dynamic epistemic logic for modeling security protocols. Our logic is
implemented, and few of its properties are verifyied, using the theorem prover
Lean.


  We study numerically the distributions of the length $L$ of the longest
increasing subsequence (LIS) for the two cases of random permutations and of
one-dimensional random walks. Using sophisticated large-deviation algorithms,
we are able to obtain very large parts of the distribution, especially also
covering probabilities smaller than $P(L) = 10^{-1000}$. This enables us to
verify for the length of the LIS of random permutations the analytically known
asymptotics of the rate function and even the whole Tracy-Widom distribution,
to which we observe a rather fast convergence in the larger than typical part.
For the length $L$ of LIS of random walks, where no analytical results are
known to us, we test a proposed scaling law and observe convergence of the
tails into a collapse for increasing system size. Further, we obtain estimates
for the leading order behavior of the rate functions of both tails.


  We study the dynamics of an oscillating, free-floating robot that generates
radially expanding gravity capillary waves at a fluid surface. In open water,
the device does not self-propel; near a rigid boundary, it can be attracted or
repelled. Visualization of the wave field dynamics reveals that when near a
boundary, a complex interference of generated and reflected waves induces a
wave amplitude fluctuation asymmetry. Attraction increases as wave frequency
increases or robot-boundary separation decreases. Theory on confined
gravity-capillary wave radiation dynamics developed by Hocking in the 1980s
captures the observed parameter dependence due to these "Hocking fields." The
flexibility of the robophysical system allows detailed characterization and
analysis of locally generated nonequilibrium fluctuation-induced forces [M.
Kardar and R. Golestanian, Rev. Mod. Phys. 71, 1233 (1999)].


  We study a simple model of algorithmic collusion in which Q-learning
algorithms repeatedly play a prisoner's dilemma and allow players to choose
different exploration policies. We characterize behavior of such algorithms
with asymmetric policies for extreme values and prove that any Nash equilibrium
features some cooperative behavior. We further investigate the dynamics for
general profiles of exploration policy by running extensive numerical
simulations which indicate symmetry of equilibria, and give insight for their
distribution.


  When observations are truncated, we are limited to an incomplete picture of
our dataset. Recent methods propose to use score matching for truncated density
estimation, where the access to the intractable normalising constant is not
required. We present a novel extension of truncated score matching to a
Riemannian manifold with boundary. Applications are presented for the von
Mises-Fisher and Kent distributions on a two dimensional sphere in
$\mathbb{R}^3$, as well as a real-world application of extreme storm
observations in the USA. In simulated data experiments, our score matching
estimator is able to approximate the true parameter values with a low
estimation error and shows improvements over a naive maximum likelihood
estimator.


  The equilibrium distributions of the different pasta geometries and their
linear sizes are calculated from the mean field Gibbs energy functional in
symmetric nuclear matter at finite temperature. The average sizes and shapes
coincide approximately with the ones predicted by a standard pasta calculation
in the coexisting phase approximation, but fluctuations are additionally
calculated and seen to increase with temperature and baryonic density. The
different pasta shapes are shown to coexist in a wide domain of density and
temperature, in qualitative agreement with the findings of large scale
molecular dynamics simulations, but with a much less expensive computational
cost.


  We use methods of harmonic analysis and group representation theory to study
the spectral properties of the abstract parabolic operator $\mathscr L =
-d/dt+A$ in homogeneous function spaces. We provide sufficient conditions for
invertibility of such operators in terms of the spectral properties of the
operator $A$ and the semigroup generated by $A$. We introduce a homogeneous
space of functions with absolutely summable spectrum and prove a generalization
of the Gearhart-Pr\"uss Theorem for such spaces. We use the results to prove
existence and uniqueness of solutions of a certain class of non-linear
equations.


  There is an urgent need for automated methods to assist accurate and
effective assessment of COVID-19. Radiology and nucleic acid test (NAT) are
complementary COVID-19 diagnosis methods. In this paper, we present an
end-to-end multitask learning (MTL) framework (COVID-MTL) that is capable of
automated and simultaneous detection (against both radiology and NAT) and
severity assessment of COVID-19. COVID-MTL learns different COVID-19 tasks in
parallel through our novel random-weighted loss function, which assigns
learning weights under Dirichlet distribution to prevent task dominance; our
new 3D real-time augmentation algorithm (Shift3D) introduces space variances
for 3D CNN components by shifting low-level feature representations of
volumetric inputs in three dimensions; thereby, the MTL framework is able to
accelerate convergence and improve joint learning performance compared to
single-task models. By only using chest CT scans, COVID-MTL was trained on 930
CT scans and tested on separate 399 cases. COVID-MTL achieved AUCs of 0.939 and
0.846, and accuracies of 90.23% and 79.20% for detection of COVID-19 against
radiology and NAT, respectively, which outperformed the state-of-the-art
models. Meanwhile, COVID-MTL yielded AUC of 0.800 $\pm$ 0.020 and 0.813 $\pm$
0.021 (with transfer learning) for classifying control/suspected, mild/regular,
and severe/critically-ill cases. To decipher the recognition mechanism, we also
identified high-throughput lung features that were significantly related (P <
0.001) to the positivity and severity of COVID-19.


  We study dark matter (DM) production in the mono-Z channel at the 13 TeV LHC
both in an effective field theory framework as well as in simplified models
with vector mediators, using a multivariate analysis. For DM-quark effective
operators with scalar, vector, and tensor couplings and DM mass of 100 GeV, the
5$\sigma$ reach in the DM interaction scale $\Lambda$ is around 2, 1, and 3
TeV, respectively, for 3 ab$^{-1}$ and assuming a 5\% systematic uncertainty on
the total background normalization. For simplified models with leptophobic
vector mediators, the 5$\sigma$ reach for the mass of the mediator is 1.7 TeV
also assuming a 5\% systematics and 3 ab$^{-1}$ of integrated luminosity. The
reach for the dark matter interaction scale obtained with the multivariate
analysis using a likelihood function discriminant is at least twice as high as
that obtained from a simple cut and count analysis, once systematics on the
background normalization larger than a few percent are taken into account.
Moreover, the reach is much more stable against degradation due these
systematic uncertainties.