  In this study, we thoroughly investigate the covariant and $B$-field gauge
invariant odd-parity NS-NS couplings at order $\alpha'^3$, while considering
the removal of field redefinitions, Bianchi identities, and total derivative
freedoms. Our comprehensive analysis reveals the existence of 477 independent
couplings. To establish a specific basis, we construct it in such a way that
none of the couplings contain terms involving structures such as $R$,
$R_{\mu\nu}$, $\nabla_\mu H^{\mu\alpha\beta}$, $\nabla_\mu\nabla^\mu\Phi$, or
terms with more than two derivatives, except for one term that possesses three
derivatives on $H$. Interestingly, the mentioned coupling with the
four-derivative on the $B$-field is rendered zero by the sphere-level
three-point S-matrix element.
  Furthermore, we demonstrate that the remaining 476 parameters in type II
superstring theory are fixed to zero by imposing the requirement that the
circular reduction of the couplings remains invariant under $O(1,1,\MZ)$
T-duality transformations. This result is consistent with our expectations and
highlights the crucial role played by the $O(1,1,\MZ)$ symmetry in constraining
the parameter space of the classical effective actions in string theory.


  In general relativity, for fluids with a linear equation of state (EoS) or
scalar fields, the high isotropy of the universe requires special initial
conditions, and singularities are anisotropic in general. In the brane world
scenario anisotropy at the singularity is suppressed by an effective quadratic
equation of state. There is no reason why the effective EoS of matter should be
linear at the highest energies, and a non-linear EoS may describe dark energy
or unified dark matter (Paper I, astro-ph/0512224). In view of this, here we
study the effects of a quadratic EoS in homogenous and inhomogeneous
cosmological models in general relativity, in order to understand if in this
context the quadratic EoS can isotropize the universe at early times. With
respect to Paper I, here we use the simplified EoS P=alpha rho + rho^2/rho_c,
which still allows for an effective cosmological constant and phantom behavior,
and is general enough to analyze the dynamics at high energies. We first study
anisotropic Bianchi I and V models, focusing on singularities. Using dynamical
systems methods, we find the fixed points of the system and study their
stability. We find that models with standard non-phantom behavior are in
general asymptotic in the past to an isotropic fixed point IS, i.e. in these
models even an arbitrarily large anisotropy is suppressed in the past: the
singularity is matter dominated. Using covariant and gauge invariant variables,
we then study linear perturbations about the homogenous and isotropic spatially
flat models with a quadratic EoS. We find that, in the large scale limit, all
perturbations decay asymptotically in the past, indicating that the isotropic
fixed point IS is the general asymptotic past attractor for non phantom
inhomogeneous models with a quadratic EoS. (Abridged)


  Inspired by recent use of polarimetry to study the Cosmic Microwave
Background and extragalatic supernovae, a foray into the statistical properties
of Stokes parameters expressed in spherical coordinates is began, allowing
circular polarization and linear polarization to be treated in a unified
manner. The use of spherical coordinates is quite necessary as it permits a
Stokes polarization state to be expressed in terms of the customary
polarization angles and degree of polarization usually needed for human
interpretation. As shall be demonstrated, circular and linear polarization are
not statistically independent quantities but intertwined in a way that is
especially important, for instance, at low signal-to-noise. New distributions,
classical estimators, and marginalizations are presented for this
"three-dimensional" polarization problem including a generalization of the Rice
distribution. The paper concludes with discussion regarding the potential
pitfalls of a lower dimensional analysis.


  Reference-model-assisted deep reinforcement learning (DRL) for inverter-based
Volt-Var Control (IB-VVC) in active distribution networks is proposed. We
investigate that a large action space increases the learning difficulties of
DRL and degrades the optimization performance in the process of generating data
and training neural networks. To reduce the action space of DRL, we design a
reference-model-assisted DRL approach. We introduce definitions of the
reference model, reference-model-based optimization, and reference actions. The
reference-model-assisted DRL learns the residual actions between the reference
actions and optimal actions, rather than learning the optimal actions directly.
Since the residual actions are considerably smaller than the optimal actions
for a reference model, we can design a smaller action space for the
reference-model-assisted DRL. It reduces the learning difficulties of DRL and
optimises the performance of the reference-model-assisted DRL approach. It is
noteworthy that the reference-model-assisted DRL approach is compatible with
any policy gradient DRL algorithms for continuous action problems. This work
takes the soft actor-critic algorithm as an example and designs a
reference-model-assisted soft actor-critic algorithm. Simulations show that 1)
large action space degrades the performance of DRL in the whole training stage,
and 2) reference-model-assisted DRL requires fewer iteration times and returns
a better optimization performance.


  The article introduces efficient quantum state tomography schemes for qutrits
and entangled qubits subject to pure decoherence. We implement the dynamic
state reconstruction method for open systems sent through phase-damping
channels which was proposed in: Open Syst. Inf. Dyn. 23, 1650019 (2016). In the
current article we prove that two distinct observables measured at four
different time instants suffice to reconstruct the initial density matrix of a
qutrit with evolution given by a phase-damping channel. Furthermore, we
generalize the approach in order to determine the optimal criteria for quantum
tomography of entangled qubits. Finally, we prove two universal theorems
concerning the minimal number of distinct observables required for quantum
tomography of qudits. We believe that dynamic state reconstruction schemes
bring significant advancement and novelty to quantum tomography since they
allow to reduce the number of distinct measurements required to solve the
problem, which is important from the experimental point of view.


  Let $s \geq 3$ be a natural number, let $\psi(x)$ be a polynomial with real
coefficients and degree $d \geq 2$, and let $A$ be some large, non-empty,
finite subset of real numbers. We use $E_{s,2}(A)$ to denote the number of
solutions to the system of equations \[ \sum_{i=1}^{s} (\psi(x_i) -
\psi(x_{i+s}) )= \sum_{i=1}^{s} ( x_i - x_{i+s} ) = 0, \] where $x_i \in A$ for
each $1 \leq i \leq 2s$. Our main result shows that \[ E_{s,2}(A) \ll_{d,s}
|A|^{2s -3 + \eta_{s}}, \] where $\eta_3 = 1/2$, and $\eta_{s} = (1/4-
1/7246)\cdot 2^{-s + 4}$ when $s \geq 4$. The only other previously known
result of this flavour is due to Bourgain and Demeter, who showed that when
$\psi(x) = x^2$ and $s=3$, we have \[E_{3,2}(A) \ll_{\epsilon} |A|^{3 + 1/2 +
\epsilon},\] for each $\epsilon > 0$. Thus our main result improves upon the
above estimate, while also generalising it for larger values of $s$ and more
wide-ranging choices of $\psi(x)$.
  The novelty of our estimates is that they only depend on $d$, $s$ and $|A|$,
and are independent of the diameter of $A$. Thus when $A$ is a sparse set, our
results are stronger than the corresponding bounds that are provided by methods
such as decoupling and efficient congruencing. Consequently, our strategy
differs from these two lines of approach, and we employ techniques from
incidence geometry, arithmetic combinatorics and analytic number theory.
Amongst other applications, our estimates lead to stronger discrete restriction
estimates for sparse sequences.


  We use a version of the instant-form relativistic quantum mechanics of
composite systems to obtain the gravitational form factors of the pion in a
common approach to its electroweak and gravitational properties. In the
preceding work [arXiv:2010.11640] we formulated the mathematical background,
presented the principal scheme of calculation and testified the obtained
qualitative results to satisfy the general constraints given by the principles
of the theory of hadron structure. In the present work we give the detailed
calculation of the gravitational form factors in large range of momentum
transfer, their static limits and the slopes at zero value, the mean-square
mass and mechanical radii of the pion. Now we take into account the
qravitational structure of the constituent quarks. We show that the results are
almost insensitive to the type of the model two-quark wave function in a close
analogy to the case of the pion electromagnetic form factor. We present a
correct calculation of the form factor $D$ and corresponding matrix element of
the energy-momentum tensor, going beyond the scope of the modified impulse
approximation. Most of the parameters that we use for the calculation had been
fixed even earlier in our works on the pion electromagnetic form factors. The
only free parameter is the $D$-term of the constituent quark, which we fix by
fitting the result for the slope at zero of the normalized to pion $D$-term
form factor $D$ of pion, to a choosen experimental value.


  Size can widely affect the surface chemical activities (SCAs) of
nanomaterials in chemisorption, catalysis, surface effects, etc., but the
underlying electronic nature has long remained mysterious. We report a general
electronic principle that drives the origin of size-dependent SCAs by combining
experimental probing and theoretical modeling. Using the chemisorption of H2O2
on TiO2 as a model reaction, we experimentally reveal that the central
electronic process of surface chemical interactions lies in the competitive
redistribution of surface atomic orbitals from energy band states into surface
coordination bonds. By defining orbital potential, a site-dependent intrinsic
electronic property that determines surface activities, we further establish a
mathematical model to uncover the physical nature of how structural factors
correlate to SCAs, particularly the roles of size. We discover that the
electronic nature of size effect lies in its inverse correlation to orbital
potential and amplification effect on other structural factors like defects and
coordination numbers.


  We demonstrate super-resolution imaging of single rare-earth emitting
centers, namely, trivalent cerium, in yttrium aluminum garnet (YAG) crystals by
means of stimulated emission depletion (STED) microscopy. The achieved
all-optical resolution is $\approx$ 80nm. Similar results were obtained on H3
color centers in diamond with resolution of $\approx$ 60nm. In both cases, STED
resolution is improving slower than the inverse square-root of the depletion
beam intensity. This is caused by excited state absorption (ESA) and
interaction of the emitter with non-fluorescing crystal defects in its near
surrounding.


  We propose Poisson integrators for the numerical integration of separable
Poisson systems. We analyze three situations in which the Poisson systems are
separated in three ways and the Poisson integrators can be constructed by using
the splitting method. Numerical results show that the Poisson integrators
outperform the higher order non-Poisson integrators in phase orbit tracking,
long-term energy conservation and efficiency.


  The analysis of vast amounts of data constitutes a major challenge in modern
high energy physics experiments. Machine learning (ML) methods, typically
trained on simulated data, are often employed to facilitate this task. Several
choices need to be made by the user when training the ML algorithm. In addition
to deciding which ML algorithm to use and choosing suitable observables as
inputs, users typically need to choose among a plethora of algorithm-specific
parameters. We refer to parameters that need to be chosen by the user as
hyperparameters. These are to be distinguished from parameters that the ML
algorithm learns autonomously during the training, without intervention by the
user. The choice of hyperparameters is conventionally done manually by the user
and often has a significant impact on the performance of the ML algorithm. In
this paper, we explore two evolutionary algorithms: particle swarm optimization
(PSO) and genetic algorithm (GA), for the purposes of performing the choice of
optimal hyperparameter values in an autonomous manner. Both of these algorithms
will be tested on different datasets and compared to alternative methods.


  The Galactic diffuse soft gamma-ray (30-800 keV) emission has been measured
from the Galactic Center by the HIREGS balloon-borne germanium spectrometer to
determine the spectral characteristics and origin of the emission. The
resulting Galactic diffuse continuum is found to agree well with a single
power-law (plus positronium) over the entire energy range, consistent with RXTE
and COMPTEL/CGRO observations at lower and higher energies, respectively. We
find no evidence of spectral steepening below 200 keV, as has been reported in
previous observations. The spatial distribution along the Galactic ridge is
found to be nearly flat, with upper limits set on the longitudinal gradient,
and with no evidence of an edge in the observed region. The soft gamma-ray
diffuse spectrum is well modeled by inverse Compton scattering of interstellar
radiation off of cosmic-ray electrons, minimizing the need to invoke
inefficient nonthermal bremsstrahlung emission. The resulting power requirement
is well within that provided by Galactic supernovae. We speculate that the
measured spectrum provides the first direct constraints on the cosmic-ray
electron spectrum below 300 MeV.


  In this paper, a multiscale virtual particle based elastic network model
(MVP-ENM) is proposed for biomolecular normal mode analysis. The multiscale
virtual particle model is proposed for the discretization of biomolecular
density data in different scales. Essentially, the model works as the
coarse-graining of the biomolecular structure, so that a delicate balance
between biomolecular geometric representation and computational cost can be
achieved. To form "connections" between these multiscale virtual particles, a
new harmonic potential function, which considers the influence from both mass
distributions and distance relations, is adopted between any two virtual
particles. Unlike the previous ENMs that use a constant spring constant, a
particle-dependent spring parameter is used in MVP-ENM. Two independent models,
i.e., multiscale virtual particle based Gaussian network model (MVP-GNM) and
multiscale virtual particle based anisotropic network model (MVP-ANM), are
proposed. Even with a rather coarse grid and a low resolution, the MVP-GNM is
able to predict the Debye-Waller factors (B-factors) with considerable good
accuracy. Similar properties have also been observed in MVP-ANM. More
importantly, in B-factor predictions, the mismatch between the predicted
results and experimental ones is predominantly from higher fluctuation regions.
Further, it is found that MVP-ANM can deliver a very consistent low-frequency
eigenmodes in various scales. This demonstrates the great potential of MVP-ANM
in the deformation analysis of low resolution data. With the multiscale
rigidity function, the MVP-ENM can be applied to biomolecular data represented
in density distribution and atomic coordinates. Further, the great advantage of
my MVP-ENM model in computational cost has been demonstrated by using two
poliovirus virus structures. Finally, the paper ends with a conclusion.


  Implicit discourse relation recognition is a crucial component for automatic
discourselevel analysis and nature language understanding. Previous studies
exploit discriminative models that are built on either powerful manual features
or deep discourse representations. In this paper, instead, we explore
generative models and propose a variational neural discourse relation
recognizer. We refer to this model as VarNDRR. VarNDRR establishes a directed
probabilistic model with a latent continuous variable that generates both a
discourse and the relation between the two arguments of the discourse. In order
to perform efficient inference and learning, we introduce neural discourse
relation models to approximate the prior and posterior distributions of the
latent variable, and employ these approximated distributions to optimize a
reparameterized variational lower bound. This allows VarNDRR to be trained with
standard stochastic gradient methods. Experiments on the benchmark data set
show that VarNDRR can achieve comparable results against stateof- the-art
baselines without using any manual features.


  By considering pseudodistributive laws in which the involved pseudomonads are
presented in no-iteration form, we deduce a number of alternative presentations
of pseudodistributive laws including a 'decagon' form, a pseudoalgebra form,
and a no-iteration form. As an application, we show that five coherence axioms
suffice in the usual monoidal definition of a pseudodistributive law.


  Regression evaluation has been performed for decades. Some metrics have been
identified to be robust against shifting and scaling of the data but
considering the different distributions of data is much more difficult to
address (imbalance problem) even though it largely impacts the comparability
between evaluations on different datasets. In classification, it has been
stated repeatedly that performance metrics like the F-Measure and Accuracy are
highly dependent on the class distribution and that comparisons between
different datasets with different distributions are impossible. We show that
the same problem exists in regression. The distribution of odometry parameters
in robotic applications can for example largely vary between different
recording sessions. Here, we need regression algorithms that either perform
equally well for all function values, or that focus on certain boundary regions
like high speed. This has to be reflected in the evaluation metric. We propose
the modification of established regression metrics by weighting with the
inverse distribution of function values $Y$ or the samples $X$ using an
automatically tuned Gaussian kernel density estimator. We show on synthetic and
robotic data in reproducible experiments that classical metrics behave wrongly,
whereas our new metrics are less sensitive to changing distributions,
especially when correcting by the marginal distribution in $X$. Our new
evaluation concept enables the comparison of results between different datasets
with different distributions. Furthermore, it can reveal overfitting of a
regression algorithm to overrepresented target values. As an outcome,
non-overfitting regression algorithms will be more likely chosen due to our
corrected metrics.


  Understanding the mechanisms through which neural networks extract statistics
from input-label pairs through feature learning is one of the most important
unsolved problems in supervised learning. Prior works demonstrated that the
gram matrices of the weights (the neural feature matrices, NFM) and the average
gradient outer products (AGOP) become correlated during training, in a
statement known as the neural feature ansatz (NFA). Through the NFA, the
authors introduce mapping with the AGOP as a general mechanism for neural
feature learning. However, these works do not provide a theoretical explanation
for this correlation or its origins. In this work, we further clarify the
nature of this correlation, and explain its emergence. We show that this
correlation is equivalent to alignment between the left singular structure of
the weight matrices and the newly defined pre-activation tangent features at
each layer. We further establish that the alignment is driven by the
interaction of weight changes induced by SGD with the pre-activation features,
and analyze the resulting dynamics analytically at early times in terms of
simple statistics of the inputs and labels. Finally, motivated by the
observation that the NFA is driven by this centered correlation, we introduce a
simple optimization rule that dramatically increases the NFA correlations at
any given layer and improves the quality of features learned.


  In this paper we study the sub-Finsler geometry as a time-optimal control
problem. In particular, we consider non-smooth and non-strictly convex
sub-Finsler structures associated with the Heisenberg, Grushin, and Martinet
distributions. Motivated by problems in geometric group theory, we characterize
extremal curves, discuss their optimality, and calculate the metric spheres,
proving their Euclidean rectifiability.


  We consider a decentralized online convex optimization problem in a network
of agents, where each agent controls only a coordinate (or a part) of the
global decision vector. For such a problem, we propose two decentralized
variants (ODA-C and ODA-PS) of Nesterov's primal-dual algorithm with dual
averaging. In ODA-C, to mitigate the disagreements on the primal-vector
updates, the agents implement a generalization of the local
information-exchange dynamics recently proposed by Li and Marden over a static
undirected graph. In ODA-PS, the agents implement the broadcast-based push-sum
dynamics over a time-varying sequence of uniformly connected digraphs. We show
that the regret bounds in both cases have sublinear growth of $O(\sqrt{T})$,
with the time horizon $T$, when the stepsize is of the form $1/\sqrt{t}$ and
the objective functions are Lipschitz-continuous convex functions with
Lipschitz gradients. We also implement the proposed algorithms on a sensor
network to complement our theoretical analysis.


  Solidity smart contracts are programs that manage up to 2^160 users on a
blockchain. Verifying a smart contract relative to all users is intractable due
to state explosion. Existing solutions either restrict the number of users to
under-approximate behaviour, or rely on manual proofs. In this paper, we
present local bundles that reduce contracts with arbitrarily many users to
sequential programs with a few representative users. Each representative user
abstracts concrete users that are locally symmetric to each other relative to
the contract and the property. Our abstraction is semi-automated. The
representatives depend on communication patterns, and are computed via static
analysis. A summary for the behaviour of each representative is provided
manually, but a default summary is often sufficient. Once obtained, a local
bundle is amenable to sequential static analysis. We show that local bundles
are relatively complete for parameterized safety verification, under moderate
assumptions. We implement local bundle abstraction in SmartACE, and show
order-of-magnitude speedups compared to a state-of-the-art verifier.


  This paper analyses the world web of mergers and acquisitions (M&As) using a
complex network approach. We use data of M&As to build a temporal sequence of
binary and weighted-directed networks for the period 1995-2010 and 224
countries (nodes) connected according to their M&As flows (links). We study
different geographical and temporal aspects of the international M&A network
(IMAN), building sequences of filtered sub-networks whose links belong to
specific intervals of distance or time. Given that M&As and trade are
complementary ways of reaching foreign markets, we perform our analysis using
statistics employed for the study of the international trade network (ITN),
highlighting the similarities and differences between the ITN and the IMAN. In
contrast to the ITN, the IMAN is a low density network characterized by a
persistent giant component with many external nodes and low reciprocity.
Clustering patterns are very heterogeneous and dynamic. High-income economies
are the main acquirers and are characterized by high connectivity, implying
that most countries are targets of a few acquirers. Like in the ITN,
geographical distance strongly impacts the structure of the IMAN: link-weights
and node degrees have a non-linear relation with distance, and an assortative
pattern is present at short distances.


  Label noise in medical image classification datasets significantly hampers
the training of supervised deep learning methods, undermining their
generalizability. The test performance of a model tends to decrease as the
label noise rate increases. Over recent years, several methods have been
proposed to mitigate the impact of label noise in medical image classification
and enhance the robustness of the model. Predominantly, these works have
employed CNN-based architectures as the backbone of their classifiers for
feature extraction. However, in recent years, Vision Transformer (ViT)-based
backbones have replaced CNNs, demonstrating improved performance and a greater
ability to learn more generalizable features, especially when the dataset is
large. Nevertheless, no prior work has rigorously investigated how
transformer-based backbones handle the impact of label noise in medical image
classification. In this paper, we investigate the architectural robustness of
ViT against label noise and compare it to that of CNNs. We use two medical
image classification datasets -- COVID-DU-Ex, and NCT-CRC-HE-100K -- both
corrupted by injecting label noise at various rates. Additionally, we show that
pretraining is crucial for ensuring ViT's improved robustness against label
noise in supervised training.


  In this paper, we present an explicit cyclic minimal $A_\infty$ model for the
category of matrix factorizations $\MF(W)$ of an isolated hypersurface
singularity. The key observation is to use Kontsevich's deformation
quantization technique. Pushing this idea further, we use the Tsygan formality
map to obtain a comparison theorem that the categorical Variation of
Semi-infinite Hodge Structure of $\MF(W)$ is isomorphic to Saito's original
geometric construction in primitive form theory. An immediate corollary of this
comparison result is that the analogue of Caldararu's conjecture holds for the
category $\MF(W)$.


  Given a graph where every node has certain attributes associated with it and
some nodes have labels associated with them, Collective Classification (CC) is
the task of assigning labels to every unlabeled node using information from the
node as well as its neighbors. It is often the case that a node is not only
influenced by its immediate neighbors but also by higher order neighbors,
multiple hops away. Recent state-of-the-art models for CC learn end-to-end
differentiable variations of Weisfeiler-Lehman (WL) kernels to aggregate
multi-hop neighborhood information. In this work, we propose a Higher Order
Propagation Framework, HOPF, which provides an iterative inference mechanism
for these powerful differentiable kernels. Such a combination of classical
iterative inference mechanism with recent differentiable kernels allows the
framework to learn graph convolutional filters that simultaneously exploit the
attribute and label information available in the neighborhood. Further, these
iterative differentiable kernels can scale to larger hops beyond the memory
limitations of existing differentiable kernels. We also show that existing WL
kernel-based models suffer from the problem of Node Information Morphing where
the information of the node is morphed or overwhelmed by the information of its
neighbors when considering multiple hops. To address this, we propose a
specific instantiation of HOPF, called the NIP models, which preserves the node
information at every propagation step. The iterative formulation of NIP models
further helps in incorporating distant hop information concisely as summaries
of the inferred labels. We do an extensive evaluation across 11 datasets from
different domains. We show that existing CC models do not provide consistent
performance across datasets, while the proposed NIP model with iterative
inference is more robust.


  We rewrite the 1+1 Causal Dynamical Triangulations model as a spin system and
thus provide a new method of solution of the model.


  The paper considers the problem of planning a set of non-conflict
trajectories for the coalition of intelligent agents (mobile robots). Two
divergent approaches, e.g. centralized and decentralized, are surveyed and
analyzed. Decentralized planner - MAPP is described and applied to the task of
finding trajectories for dozens UAVs performing nap-of-the-earth flight in
urban environments. Results of the experimental studies provide an opportunity
to claim that MAPP is a highly efficient planner for solving considered types
of tasks.


  This paper focuses on the uncertainty estimation for white matter lesions
(WML) segmentation in magnetic resonance imaging (MRI). On one side,
voxel-scale segmentation errors cause the erroneous delineation of the lesions;
on the other side, lesion-scale detection errors lead to wrong lesion counts.
Both of these factors are clinically relevant for the assessment of multiple
sclerosis patients. This work aims to compare the ability of different voxel-
and lesion-scale uncertainty measures to capture errors related to segmentation
and lesion detection, respectively. Our main contributions are (i) proposing
new measures of lesion-scale uncertainty that do not utilise voxel-scale
uncertainties; (ii) extending an error retention curves analysis framework for
evaluation of lesion-scale uncertainty measures. Our results obtained on the
multi-center testing set of 58 patients demonstrate that the proposed
lesion-scale measure achieves the best performance among the analysed measures.
All code implementations are provided at
https://github.com/NataliiaMolch/MS_WML_uncs


  We propose a new search strategy for higgsinos. Assuming associated
production of higgsino-like pairs with a $W$ or $Z$ boson, we search in the
missing energy plus hadronically-tagged vector boson channel. We place
sensitivity limits for (HL-)LHC searches assuming
$\mathcal{O}({1\mathrm{-}3.5}~\mathrm{GeV})$ mass differences between the
lightest neutral and charged states. We point out that using the
$E_T^\mathrm{miss}$ distribution significantly increases the sensitivity of
this search. We find the higgsinos up to 110 (210) GeV can be excluded with
$139~(300)~\mathrm{fb}^{-1}$ data. The full data of the HL-LHC will exclude
(discover) the higgsinos up to 520 (280) GeV.


  A numerical description of an algebraic subvariety of projective space is
given by a general linear section, called a witness set. For a subvariety of a
product of projective spaces (a multiprojective variety), the corresponding
numerical description is given by a witness collection, whose structure is more
involved. We build on recent work to develop a toolkit for the numerical
manipulation of multiprojective varieties that operates on witness collections,
and use this toolkit in an algorithm for numerical irreducible decomposition of
multiprojective varieties. The toolkit and decomposition algorithm are
illustrated throughout in a series of examples.


  In this paper, we propose a complex short pulse equation of both focusing and
defocusing types, which governs the propagation of ultra-short pulses in
nonlinear optical fibers. It can be viewed as an analogue of the nonlinear
Schr\"odinger (NLS) equation in the ultra-short pulse regime. Furthermore, we
construct the multi-dark soliton solution for the defocusing complex short
pulse equation through the Darboux transformation and reciprocal (hodograph)
transformation. One- and two-dark soliton solutions are given explicitly, whose
properties and dynamics are analyzed and illustrated.


  An accurate seizure prediction system enables early warnings before seizure
onset of epileptic patients. It is extremely important for drug-refractory
patients. Conventional seizure prediction works usually rely on features
extracted from Electroencephalography (EEG) recordings and classification
algorithms such as regression or support vector machine (SVM) to locate the
short time before seizure onset. However, such methods cannot achieve
high-accuracy prediction due to information loss of the hand-crafted features
and the limited classification ability of regression and SVM algorithms. We
propose an end-to-end deep learning solution using a convolutional neural
network (CNN) in this paper. One and two dimensional kernels are adopted in the
early- and late-stage convolution and max-pooling layers, respectively. The
proposed CNN model is evaluated on Kaggle intracranial and CHB-MIT scalp EEG
datasets. Overall sensitivity, false prediction rate, and area under receiver
operating characteristic curve reaches 93.5%, 0.063/h, 0.981 and 98.8%,
0.074/h, 0.988 on two datasets respectively. Comparison with state-of-the-art
works indicates that the proposed model achieves exceeding prediction
performance.


  We investigate the Japanese personal income distribution in the high income
range over the 112 years 1887-1998, and that in the middle income range over
the 44 years 1955-98. It is observed that the distribution pattern of the
lognormal with power law tail is the universal structure. However the indexes
specifying the distribution differ from year to year. One of the index
characterizing the distribution is the mean value of the lognormal
distribution; the mean income in the middle income range. It is found that this
value correlates linearly with the Gross Domestic Product (GDP). To clarify the
temporal change of the equality or inequality of the distribution, we analyze
Pareto and Gibrat indexes, which characterize the distribution in the high
income range and that in the middle income range respectively. It is found for
some years that there is no correlation between the high income and the middle
income. It is also shown that the mean value of Pareto index equals to 2, and
the change of this index is effected by the change of the asset price. From
these analysis we derive four constraints that must be satisfied by
mathematical models.


  Decentralized learning empowers wireless network devices to collaboratively
train a machine learning (ML) model relying solely on device-to-device (D2D)
communication. It is known that the convergence speed of decentralized
optimization algorithms severely depends on the degree of the network
connectivity, with denser network topologies leading to shorter convergence
time. Consequently, the local connectivity of real world mesh networks, due to
the limited communication range of its wireless nodes, undermines the
efficiency of decentralized learning protocols, rendering them potentially
impracticable. In this work we investigate the role of an unmanned aerial
vehicle (UAV), used as flying relay, in facilitating decentralized learning
procedures in such challenging conditions. We propose an optimized UAV
trajectory, that is defined as a sequence of waypoints that the UAV visits
sequentially in order to transfer intelligence across sparsely connected group
of users. We then provide a series of experiments highlighting the essential
role of UAVs in the context of decentralized learning over mesh networks.


  We determine the set of connected components of closed affine Deligne-Lusztig
varieties for hyperspecial maximal parahoric subgroups of unramified connected
reductive groups. This extends the work by Viehmann for split reductive groups,
and the work by Chen-Kisin-Viehmann on minuscule affine Deligne-Lusztig
varieties.


  We treat baryons as bound states of scalar or axialvector diquarks and a
constituent quark which interact through quark exchange. This description
results as an approximation to the relativistic Faddeev equation for three
quarks which yields an effective Bethe-Salpeter equation. Octet and decuplet
masses and fully four-dimensional wave functions have been computed for two
cases: assuming an essentially pointlike diquark on the one hand, and a diquark
with internal structure on the other hand. Whereas the differences in the mass
spectrum are fairly small, the nucleon electromagnetic form factors are greatly
improved assuming a diquark with structure. First calculations to the
pion-nucleon form factor also suggest improvements.


  In this paper, we present a comprehensive architecture for confidential
computing, which we show to be general purpose and quite efficient. It executes
the application as is, without any added burden or discipline requirements from
the application developers. Furthermore, it does not require the trust of
system software at the computing server and does not impose any added burden on
the communication subsystem. The proposed Encrypted Data Processing (EDAP)
architecture accomplishes confidentiality, authenticity, and freshness of the
key-based cryptographic data protection by adopting data encryption with a
multi-level key protection scheme. It guarantees that the user data is visible
only in non-privileged mode to a designated program trusted by the data owner
on a designated hardware, thus protecting the data from an untrusted hardware,
hypervisor, OS, or other users' applications. The cryptographic keys and
protocols used for achieving these confidential computing requirements are
described in a use case example. Encrypting and decrypting data in an
EDAP-enabled processor can lead to performance degradation as it adds cycle
time to the overall execution. However, our simulation result shows that the
slowdown is only 6% on average across a collection of commercial workloads when
the data encryption engine is placed between the L1 and L2 cache. We
demonstrate that the EDAP architecture is valuable and practicable in the
modern cloud environment for confidential computing. EDAP delivers a zero trust
model of computing where the user software does not trust system software and
vice versa.


  The nearby brown dwarf LP 944-20 has been monitored for radial velocity
variability at optical and near-infrared wavelengths using the VLT/UVES and the
Keck/NIRSPEC spectrographs, respectively. The UVES radial velocity data
obtained over 14 nights spanning a baseline of 841 days shows significant
variability with an amplitude of 3.5 km s$^{-1}$. The periodogram analysis of
the UVES data indicates a possible period between 2.5 hours and 3.7 hours,
which is likely due to the rotation of the brown dwarf. However, the NIRSPEC
data obtained over 6 nights shows an rms dispersion of only 0.36 km s$^{-1}$
and do not follow the periodic trend. These results indicate that the
variability seen with UVES is likely to be due to rotationally modulated
inhomogeneous surface features. We suggest that future planet searches around
very low-mass stars and brown dwarfs using radial velocities will be better
conducted in the near-infrared than in the optical.


  Gaia DR3 opens a new era of all-sky spectral analysis of stellar populations
thanks to the nearly 5.6 million stars observed by the RVS and parametrised by
the GSP-spec module. The all-sky Gaia chemical cartography allows a powerful
and precise chemo-dynamical view of the Milky Way with unprecedented spatial
coverage and statistical robustness. First, it reveals the strong vertical
symmetry of the Galaxy and the flared structure of the disc. Second, the
observed kinematic disturbances of the disc -- seen as phase space correlations
-- and kinematic or orbital substructures are associated with chemical patterns
that favour stars with enhanced metallicities and lower [alpha/Fe] abundance
ratios compared to the median values in the radial distributions. This is
detected both for young objects that trace the spiral arms and older
populations. Several alpha, iron-peak elements and at least one heavy element
trace the thin and thick disc properties in the solar cylinder. Third, young
disc stars show a recent chemical impoverishment in several elements. Fourth,
the largest chemo-dynamical sample of open clusters analysed so far shows a
steepening of the radial metallicity gradient with age, which is also observed
in the young field population. Finally, the Gaia chemical data have the
required coverage and precision to unveil galaxy accretion debris and heated
disc stars on halo orbits through their [alpha/Fe] ratio, and to allow the
study of the chemo-dynamical properties of globular clusters. Gaia DR3
chemo-dynamical diagnostics open new horizons before the era of ground-based
wide-field spectroscopic surveys. They unveil a complex Milky Way that is the
outcome of an eventful evolution, shaping it to the present day (abridged).


  We report the detection of 6.2um polycyclic aromatic hydrocarbon (PAH) and
rest-frame 4-7um continuum emission in the z=4.055 submillimeter galaxy GN20,
using the Infrared Spectrograph (IRS) on board the Spitzer Space Telescope.
This represents the first detection of PAH emission at z>4. The strength of the
PAH emission feature is consistent with a very high star formation rate of
~1600Msun/yr. We find that this intense starburst powers at least ~1/3 of the
faint underlying 6um continuum emission, with an additional, significant (and
perhaps dominant) contribution due to a power-law-like hot dust source, which
we interpret to likely be a faint, dust-obscured active galactic nucleus (AGN).
The inferred 6um AGN continuum luminosity is consistent with a sensitive upper
limit on the hard X-ray emission as measured by the Chandra X-Ray Observatory
if the previously undetected AGN is Compton-thick. This is in agreement with
the finding at optical/infrared wavelengths that the galaxy and its nucleus are
heavily dust-obscured. Despite the strong power-law component enhancing the
mid-infrared continuum emission, the intense starburst associated with the
photon-dominated regions that give rise to the PAH emission appears to dominate
the total energy output in the infrared. GN20 is one of the most luminous
starburst galaxies known at any redshift, embedded in a rich protocluster of
star-forming galaxies. This investigation provides an improved understanding of
the energy sources that power such exceptional systems, which represent the
extreme end of massive galaxy formation at early cosmic times.


  Geroch's theorem about the splitting of globally hyperbolic spacetimes is a
central result in global Lorentzian Geometry. Nevertheless, this result was
obtained at a topological level, and the possibility to obtain a metric (or, at
least, smooth) version has been controversial since its publication in 1970. In
fact, this problem has remained open until a definitive proof, recently
provided by the authors. Our purpose is to summarize the history of the
problem, explain the smooth and metric splitting results (including
smoothability of time functions in stably causal spacetimes), and sketch the
ideas of the solution.


  Writers, poets, singers usually do not create their compositions in just one
breath. Text is revisited, adjusted, modified, rephrased, even multiple times,
in order to better convey meanings, emotions and feelings that the author wants
to express. Amongst the noble written arts, Poetry is probably the one that
needs to be elaborated the most, since the composition has to formally respect
predefined meter and rhyming schemes. In this paper, we propose a framework to
generate poems that are repeatedly revisited and corrected, as humans do, in
order to improve their overall quality. We frame the problem of revising poems
in the context of Reinforcement Learning and, in particular, using Proximal
Policy Optimization. Our model generates poems from scratch and it learns to
progressively adjust the generated text in order to match a target criterion.
We evaluate this approach in the case of matching a rhyming scheme, without
having any information on which words are responsible of creating rhymes and on
how to coherently alter the poem words. The proposed framework is general and,
with an appropriate reward shaping, it can be applied to other text generation
problems.


  This note is an extended version of the contribution to the CERN Council Open
Symposium on European Strategy for Particle Physics. It discusses an
experimental programme to explore the QCD confinement phenomena at CERN with a
new electron-proton and electron-nucleus collider using the existing SPS beams
(optionally also the future SPL and PS proton and ions beams) and the polarised
electron beam in the range of 5 to 20 GeV from a newly built Energy Recovery
Linac.


  Very high energy cosmic rays are typically studied by measuring extensive air
showers formed by secondary particles produced in collisions with air nuclei.
The indirect character of the measurement makes the physics interpretation of
cosmic ray data strongly dependent on simulations of multiparticle production
in showers. In April 2002 about 50 physicists met in Karlsruhe to discuss
various aspects of hadronic multiparticle production with the aim of
intensifying the interaction between high energy physics and cosmic ray groups.
Current and upcoming possibilities at accelerators for measuring features of
hadronic interactions of relevance to air showers were the focus of the
workshop. This article is a review of the discussions and conclusions.


  One of the critical issues in bibliometric research assessments is the time
required to achieve maturity in citations. Citation counts can be considered a
reliable proxy of the real impact of a work only if they are observed after
sufficient time has passed from publication date. In the present work the
authors investigate the effect of varying the time of citation observation on
accuracy of productivity rankings for research institutions. Research
productivity measures are calculated for all Italian universities active in the
hard sciences in the 2001-2003 period, by individual field and discipline, with
the time of the citation observation varying from 2004 to 2008. The objective
is to support policy-makers in choosing a citation window that optimizes the
tradeoff between accuracy of rankings and timeliness of the exercise.


  An a posteriori error estimator based on an equilibrated flux reconstruction
is proposed for defeaturing problems in the context of finite element
discretizations. Defeaturing consists in the simplification of a geometry by
removing features that are considered not relevant for the approximation of the
solution of a given PDE. In this work, the focus is on Poisson equation with
Neumann boundary conditions on the feature boundary. The estimator accounts
both for the so-called defeaturing error and for the numerical error committed
by approximating the solution on the defeatured domain. Unlike other estimators
that were previously proposed for defeaturing problems, the use of the
equilibrated flux reconstruction allows to obtain a sharp bound for the
numerical component of the error. Furthermore, it does not require the
evaluation of the normal trace of the numerical flux on the feature boundary:
this makes the estimator well-suited for finite element discretizations, in
which the normal trace of the numerical flux is typically discontinuous across
elements. The reliability of the estimator is proven and verified on several
numerical examples. Its capability to identify the most relevant features is
also shown, in anticipation of a future application to an adaptive strategy.


  Intelligent terminals often produce a large number of data packets of small
lengths. For these packets, it is inefficient to follow the conventional medium
access control (MAC) protocols because they lead to poor utilization of service
resources. We propose a novel multiple access scheme that targets massive
multiple-input multiple-output (MIMO) systems based on compressive sensing
(CS). We employ block precoding in the time domain to enable the simultaneous
transmissions of many users, which could be even more than the number of
receive antennas at the base station. We develop a block-sparse system model
and adopt the block orthogonal matching pursuit (BOMP) algorithm to recover the
transmitted signals. Conditions for data recovery guarantees are identified and
numerical results demonstrate that our scheme is efficient for uplink small
packet transmission.


  We obtain finite parts (as well as $\epsilon$-pole parts) of massive
three-loop vacuum diagrams with three-point and/or four-point interaction
vertices by reducing them to tetrahedron diagrams with both massive and
massless lines, whose finite parts were given analytically in a recent paper by
Broadhurst. In the procedure of reduction, the method of integration-by-parts
recurrence relations is employed. We use our result to compute the $\bar{\rm
MS}$ effective potential of the massive $\phi^4$ theory.


  The task of determining item similarity is a crucial one in a recommender
system. This constitutes the base upon which the recommender system will work
to determine which items are more likely to be enjoyed by a user, resulting in
more user engagement. In this paper we tackle the problem of determining song
similarity based solely on song metadata (such as the performer, and song
title) and on tags contributed by users. We evaluate our approach under a
series of different machine learning algorithms. We conclude that tf-idf
achieves better results than Word2Vec to model the dataset to feature vectors.
We also conclude that k-NN models have better performance than SVMs and Linear
Regression for this problem.


  We consider a new MacDowell-Mansouri R^2-type of supergravity theory, an
extension of conformal supergravity, based on the superalgebra Osp(1|8).
Invariance under local symmetries with negative Weyl weight is achieved by
imposing chirality-duality and double-duality constraints on curvatures, along
with the usual constraint of vanishing supertorsion. An analysis of the
remaining gauge symmetries shows that those with vanishing Weyl weight are
invariances of the action at the linearized level. For the symmetries with
positive Weyl weight we find that invariance of the action would require
further modifications of the transformation rules. This conclusion is supported
by a kinematical analysis of the closure of the gauge algebra.


  A general Landauer-B\"uttiker-type current formula is derived, which can be
applied to the ferromagnet (F)/Normal metal (N)/superconductor (S), F/N/N,
N/N/S and N/N/N systems in the presence of various kinds of interactions in the
central region.


  For capillary driven flow the interface curvature is essential in the
modelling of surface tension via the imposition of the Young--Laplace jump
condition. We show that traditional geometric volume of fluid (VOF) methods,
that are based on a piecewise linear approximation of the interface, do not
lead to an interface curvature which is convergent under mesh refinement in
time-dependent problems. Instead, we propose to use a piecewise parabolic
approximation of the interface, resulting in a class of piecewise parabolic
interface calculation (PPIC) methods. In particular, we introduce the parabolic
LVIRA and MOF methods, PLVIRA and PMOF, respectively. We show that a Lagrangian
remapping method is sufficiently accurate for the advection of such a parabolic
interface. It is numerically demonstrated that the newly proposed PPIC methods
result in an increase of reconstruction accuracy by one order, convergence of
the interface curvature in time-dependent advection problems and Weber number
independent convergence of a droplet translation problem, where the advection
method is coupled to a two-phase Navier--Stokes solver. The PLVIRA method is
applied to the simulation of a 2D rising bubble, which shows good agreement to
a reference solution.


  Plant-pollinator associations are often seen as purely mutualistic, while in
reality they can be more complex. Indeed they may also display a diverse array
of antagonistic interactions, such as competition and victim--exploiter
interactions. In some cases mutualistic and antagonistic interactions are
carried-out by the same species but at different life-stages. As a consequence,
population structure affects the balance of inter-specific associations, a
topic that is receiving increased attention. In this paper, we developed a
model that captures the basic features of the interaction between a flowering
plant and an insect with a larval stage that feeds on the plant's vegetative
tissues (e.g. leaves) and an adult pollinator stage. Our model is able to
display a rich set of dynamics, the most remarkable of which involves
victim--exploiter oscillations that allow plants to attain abundances above
their carrying capacities, and the periodic alternation between states
dominated by mutualism or antagonism. Our study indicates that changes in the
insect's life cycle can modify the balance between mutualism and antagonism,
causing important qualitative changes in the interaction dynamics. These
changes in the life cycle could be caused by a variety of external drivers,
such as temperature, plant nutrients, pesticides and changes in the diet of
adult pollinators.
  Abstract Keywords: mutualism, pollination, herbivory, insects,
stage-structure, oscillations


  The simplest spin-orbital model can host a nematic spin-orbital liquid state
on the triangular lattice. We provide clear evidence that the ground state of
the SU(4) Kugel-Khomskii model on the triangular lattice can be well described
by a "single" Gutzwiller projected wave function with an emergent parton Fermi
surface, despite it exhibits strong finite-size effect in quasi-one-dimensional
cylinders. The finite-size effect can be resolved by the fact that the parton
Fermi surface consists of open orbits in the reciprocal space. Thereby, a
stripy liquid state is expected in the two-dimensional limit, which preserves
the SU(4) symmetry while breaks the translational symmetry by doubling the unit
cell along one of the lattice vector directions. It is indicative that these
stripes are critical and the central charge is $c=3$, in agreement with the
SU(4)$_1$ Wess-Zumino-Witten conformal field theory. All these results are
consistent with the Lieb-Schultz-Mattis-Oshikawa-Hastings theorem.


  We introduce Dynamic SOS as a framework for describing semantics of
programming languages that include dynamic software upgrades, for upgrading
software code during run-time. Dynamic SOS (DSOS) is built on top of the
Modular SOS of P. Mosses, with an underlying category theory formalization. The
idea of Dynamic SOS is to bring out the essential differences between dynamic
upgrade constructs and program execution constructs. The important feature of
Modular SOS (MSOS) that we exploit in DSOS is the sharp separation of the
program execution code from the additional (data) structures needed at
run-time. In DSOS we aim to achieve the same modularity and decoupling for
dynamic software upgrades. This is partly motivated by the long term goal of
having machine-checkable proofs for general results like type safety.
  We exemplify Dynamic SOS on two languages supporting dynamic software
upgrades, namely the C-like Proteus, which supports updating of variables,
functions, records, or types at specific program points, and Creol, which
supports dynamic class upgrades in the setting of concurrent objects. Existing
type analyses for software upgrades can be done on top of DSOS too, as we
illustrate for Proteus.
  As a side result we define of a general encapsulating construction on Modular
SOS useful in situations where a form of encapsulation of the execution is
needed. We use encapsulation in the Creol setting of concurrent object-oriented
programming with active objects and asynchronous method calls.


  Adsorption of carbon, nitrogen, and oxygen on the (111) surface of
delta-Plutonium has been studied within the framework of density functional
theory using the full-potential linear augmented plane wave plus local basis
(FP-LAPW+lo) method. All adatoms prefer to bind at the higher coordinated
hollow sites, with the chemisorption energies for C, N, and O being 6.539 eV,
6.714 eV, and 8.2 eV respectively. The work function and the surface Pu
magnetic moments respectively increased and decreased in all cases upon
chemisorption. The partial charges inside the muffin tins spheres, difference
charge density distributions, and the local density of states have been used to
analyze the Pu-adatom bond interactions.


  We investigate the interaction of many wind turbines in a wind farm with a
focus on their electrical power production. The operational data of two
offshore wind farms with a ten minute and a ten second time resolution,
respectively, are analyzed. For the correlations of the active power between
turbines over the entire wind farms, we find a dominant collective behavior. We
manage to subtract the collective behavior and find a significant dependence of
the correlation structure on the spatial structure of the wind farms. We
further show a connection between the observed correlation structures and the
prevailing wind direction. We attribute the differences between the two wind
farms to the differences in the turbine spacing within the two wind farms.


  A prominent signature of Majorana bound states is the exotic Josephson
effects they produce, the classic example being a fractional Josephson current
with 4\pi periodicity in the phase difference across the junction. Recent work
established that topological insulator edges support a novel `magneto-Josephson
effect', whereby a dissipationless current exhibits 4\pi-periodic dependence
also on the relative orientation of the Zeeman fields in the two banks of the
junction. Here, we explore the magneto-Josephson effect in junctions based on
spin-orbit coupled quantum wires. In contrast to the topological insulator
case, the periodicities of the magneto-Josephson effect no longer follow from
an exact superconductor-magnetism duality of the Hamiltonian. We employ
numerical calculations as well as analytical arguments to identify the domain
configurations that display exotic Josephson physics for quantum-wire
junctions, and elucidate the characteristic differences with the corresponding
setups for topological insulators edges. To provide guidance to experiments, we
also estimate the magnitude of the magneto-Josephson effects in realistic
parameter regimes, and compare the Majorana-related contribution to the
coexisting 2\pi-periodic effects emerging from non-Majorana states.


  We give an essentially self-contained proof of Guth's recent endpoint
multilinear Kakeya theorem which avoids the use of somewhat sophisticated
algebraic topology, and which instead appeals to the Borsuk-Ulam theorem.


  Large Language Models have become the de facto approach to
sequence-to-sequence text generation tasks, but for specialized tasks/domains,
a pretrained LLM lacks specific capabilities to produce accurate or
well-formatted responses. Supervised fine-tuning specializes a LLM by training
it on dataset of example prompts with target responses, but real-world data
tends to be noisy. While many fine-tuning algorithms exist, here we consider a
\emph{data-centric AI} perspective on LLM fine-tuning, studying how to
\emph{systematically} curate the training dataset to improve the LLM produced
via \emph{any} fine-tuning algorithm.
  We introduce an automated data curation pipeline CLEAR (Confidence-based LLM
Evaluation And Rectification) for instruction tuning datasets, that can be used
with any LLM and fine-tuning procedure. CLEAR estimates which training data is
low-quality and either filters or corrects it. Automatically identifying which
data to filter or correct is done via LLM-derived confidence estimates, to
ensure only confident modifications to the dataset. Unlike existing data
curation techniques, CLEAR is a comprehensive framework that can improve a
dataset (and trained model outputs) without additional fine-tuning
computations. We don't assume access to a stronger LLM than the model being
fine-tuned (e.g.\ relying on GPT-4 when fine-tuning GPT-3.5), to see whether
CLEAR can meaningfully improve the capabilities of any LLM. Experiments reveal
that CLEAR consistently improves the performance of fine-tuned models across
many datasets and models (like GPT-3.5 and Llama2).


  Evidence is presented to suggest that, in three dimensions, spherical
6-designs with N points exist for N=24, 26, >= 28; 7-designs for N=24, 30, 32,
34, >= 36; 8-designs for N=36, 40, 42, >= 44; 9-designs for N=48, 50, 52, >=
54; 10-designs for N=60, 62, >= 64; 11-designs for N=70, 72, >= 74; and
12-designs for N=84, >= 86. The existence of some of these designs is
established analytically, while others are given by very accurate numerical
coordinates. The 24-point 7-design was first found by McLaren in 1963, and --
although not identified as such by McLaren -- consists of the vertices of an
"improved" snub cube, obtained from Archimedes' regular snub cube (which is
only a 3-design) by slightly shrinking each square face and expanding each
triangular face. 5-designs with 23 and 25 points are presented which, taken
together with earlier work of Reznick, show that 5-designs exist for N=12, 16,
18, 20, >= 22. It is conjectured, albeit with decreasing confidence for t >= 9,
that these lists of t-designs are complete and that no others exist. One of the
constructions gives a sequence of putative spherical t-designs with N= 12m
points (m >= 2) where N = t^2/2 (1+o(1)) as t -> infinity.


  Recent breakthroughs in large language models (LLMs) have centered around a
handful of data-rich languages. What does it take to broaden access to
breakthroughs beyond first-class citizen languages? Our work introduces Aya, a
massively multilingual generative language model that follows instructions in
101 languages of which over 50% are considered as lower-resourced. Aya
outperforms mT0 and BLOOMZ on the majority of tasks while covering double the
number of languages. We introduce extensive new evaluation suites that broaden
the state-of-art for multilingual eval across 99 languages -- including
discriminative and generative tasks, human evaluation, and simulated win rates
that cover both held-out tasks and in-distribution performance. Furthermore, we
conduct detailed investigations on the optimal finetuning mixture composition,
data pruning, as well as the toxicity, bias, and safety of our models. We
open-source our instruction datasets and our model at
https://hf.co/CohereForAI/aya-101


  Fekete, Jord\'an and Kaszanitzky [4] characterised the graphs which can be
realised as 2-dimensional, infinitesimally rigid, bar-joint frameworks in which
two given vertices are coincident. We formulate a conjecture which would extend
their characterisation to an arbitrary set T of vertices and verify our
conjecture when |T| = 3.


  By deriving a generalized Harper's equation, we investigate the effects of
temperature $T$ and hole doping $\d$ on antiferromagnetically correlated
electrons under the influence of an applied magnetic field. We obtain a phase
diagram in a $T$-$\d$ plane for staggered magnetization under the external
field. We find that away from half filling the maximum values of staggered
magnetization occur with rapid convergence to a finite temperature constant
near half filling. We discover the reentrant behavior of the staggered
magnetization in the presence of the magnetic field.


  A theoretical framework for emission originating from rapidly rotating oblate
compact objects is described in detail. By using a Hamilton-Jacobi formalism,
we show how the special relativistic rotational effects such as aberration of
angles, Doppler boosting, and time dilatation naturally emerge from the general
relativistic treatment of rotating compact objects. We use the
Butterworth-Ipser metric expanded up to the second order in rotation and hence
include effects of light bending, frame-dragging, and quadrupole deviations to
our geodesic calculations. We also give detailed descriptions of the numerical
algorithms used and provide an open source implementation of the numerical
framework called bender. As an application, we study spectral line profiles
(i.e., smearing kernels) from rapidly rotating oblate neutron stars. We find
that in this metric description the second order quadrupole effects are not
strong enough to produce narrow observable features in the spectral energy
distribution for almost any physically realistic parameter combination, and
hence, actually detecting them is unlikely. The full width at tenth-maximum and
full width at half-maximum of the rotation smearing kernels are also reported
for all viewing angles. These can be then used to quantitatively estimate the
effects of rotational smearing on the observed spectra. We also calculate
accurate pulse profiles and observer skymaps of emission from hot spots on
rapidly rotating accreting millisecond pulsars. These allow us to quantify the
strength of the pulse fractions one expects to observe from typical fast
spinning millisecond pulsars.


  We consider the focusing mass-critical NLS $iu_t + \Delta u = - |u|^{4/d} u$
in high dimensions $d \geq 4$, with initial data $u(0) = u_0$ having finite
mass $M(u_0) = \int_{\R^d} |u_0(x)|^2 dx < \infty$. It is well known that this
problem admits unique (but not global) strong solutions in the Strichartz class
$C^0_{t,\loc} L^2_x \cap L^2_{t,\loc} L^{2d/(d-2)}_x$, and also admits global
(but not unique) weak solutions in $L^\infty_t L^2_x$. In this paper we
introduce an intermediate class of solution, which we call a
\emph{semi-Strichartz class solution}, for which one does have global existence
and uniqueness in dimensions $d \geq 4$. In dimensions $d \geq 5$ and assuming
spherical symmetry, we also show the equivalence of the Strichartz class and
the strong solution class (and also of the semi-Strichartz class and the
semi-strong solution class), thus establishing ``unconditional'' uniqueness
results in the strong and semi-strong classes. With these assumptions we also
characterise these solutions in terms of the continuity properties of the mass
function $t \mapsto M(u(t))$.


  We consider distinction of representations in the context of $p$-adic Galois
symmetric spaces. We provide new sufficient conditions for distinction of
parabolically induced representations in terms of similar conditions on the
inducing data and deduce a characterization for distinction of representations
parabolically induced from cuspidal. We explicate the results further for
classical groups and give several applications, in particular, concerning the
preservation of distinction via Langlands functoriality. We relate our results
with a conjecture of Dipendra Prasad.


  We construct a randomized vector quantizer which has a smaller maximum error
compared to all known lattice quantizers with the same entropy for dimensions
5, 6, ..., 48, and also has a smaller mean squared error compared to known
lattice quantizers with the same entropy for dimensions 35, ..., 48, in the
high resolution limit. Moreover, our randomized quantizer has a desirable
property that the quantization error is always uniform over the ball and
independent of the input. Our construction is based on applying rejection
sampling on universal quantization, which allows us to shape the error
distribution to be any continuous distribution, not only uniform distributions
over basic cells of a lattice as in conventional dithered quantization. We also
characterize the high SNR limit of one-shot channel simulation for any additive
noise channel under a mild assumption (e.g., the AWGN channel), up to an
additive constant of 1.45 bits.


  The phenomenon of frustration, which gives rise to many fascinating
phenomena, is conventionally associated with the topology of non-bipartite
lattices, where nearest-neighbor (nn) interactions and global connectivity
compete in the lowering of energy. The issue of rattling atoms in spacious
lattice sites is a separate occurrence that can also lead to a high density of
low energy states (unusual low temperature thermodynamics) and to practical
applications such as in improved thermoelectric materials. In this letter we
address a unique situation where both phenomena arise: a four-fold single-site
instability leads to rattling of cations on a diamond structure sublattice
where nn interactions frustrate simple ordering of the displacements. The
system deals with this coupling of rattling+frustration by commensurate
ordering. Such a disorder-order transition may account for the second phase
transition seen in KOs2O6 within the superconducting state, and the unusual
low-energy dynamics and associated electron-phonon coupling can account for the
qualitative differences in physical properties of KOs2O6 compared to RbOs2O6
and CsOs2O6, all of which have essentially identical average crystal and
electronic structures.


  N--body + hydrodynamical simulations of formation and evolution of galaxy
groups in a LambdaCDM cosmology have been performed. The properties of the
galaxy populations in 12 groups are here discussed, with focus on the
colour-magnitude relation in both normal and fossil groups.


  Quantum Toda lattice may solved by means of the Representation Theory of
semisimple Lie groups, or alternatively by using the technique of the Quantum
Inverse Scattering Method. A comparison of the two approaches, which is the
purpose of the present review article, sheds a new light on Representation
Theory and leads to a number of challenging questions.


  This work presents conclusive observations about the long lasting topic of
eumelanins' electronic vs. ionic conduction, allowing to access unprecedented
conductivity of this mammal pigment. Key strengths of the study include, the
easy eumelanin thin film fabrication protocol based on solvent free and high
vacuum annealing technology; the first achievement of eumelanin conductivity up
to 10^2 S/cm, an exceptional increase of over nine order of magnitude with
respect to commonly recorded values; decisive demonstration of the electronic
nature of charge transport in eumelanins. Overall these elements provide the
reversal of the long lasting paradigm attributing a key role to water in
eumelanin electrical conductivity, opening - thanks to the conductivity level
achieved - to a completely new perspective for the eumelanin exploitation in
organic electronics and bioelectronics.


  We present the third edition of the Sloan Digital Sky Survey (SDSS) Quasar
Catalog. The catalog consists of the 46,420 objects in the SDSS Third Data
Release that have luminosities larger than M_i = -22 (in a cosmology with H_0 =
70 km/s/Mpc, Omega_M = 0.3, and Omega_Lambda = 0.7), have at least one emission
line with FWHM larger than 1000 km/s or are unambiguously broad absorption line
quasars, are fainter than i = 15.0, and have highly reliable redshifts. The
area covered by the catalog is 4188 sq. deg. The quasar redshifts range from
0.08 to 5.41, with a median value of 1.47; the high-redshift sample includes
520 quasars at redshifts greater than four, of which 17 are at redshifts
greater than five. For each object the catalog presents positions accurate to
better than 0.2 arcsec. rms per coordinate, five-band (ugriz) CCD-based
photometry with typical accuracy of 0.03 mag, and information on the morphology
and selection method. The catalog also contains radio, near-infrared, and X-ray
emission properties of the quasars, when available, from other large-area
surveys. The calibrated digital spectra cover the wavelength region 3800--9200A
at a spectral resolution about 2000; the spectra can be retrieved from the
public database using the information provided in the catalog. A total of
44,221 objects in the catalog were discovered by the SDSS; 28,400 of the SDSS
discoveries are reported here for the first time.


  We report analytic results on quantum capacitance (C$_{q}$) measurements and
their optical tuning in dual-gated device with potassium-doped multi-layered
black phosphorous (BP) as the channel material. The two-dimensional (2D)
layered BP is highly anisotropic with a semi-Dirac dispersion marked by linear
and quadratic contributions. The C$_{q}$ calculations mirror this asymmetric
arrangement. A further increase to the asymmetry and consequently C$_{q}$ is
predicted by photon-dressing the BP dispersion. To achieve this and tune
C$_{q}$ in a field-effect transistor (FET), we suggest a configuration wherein
a pair of electrostatic (top) and optical (back) gates clamp a BP channel. The
back gate shines an optical pulse to rearrange the dispersion of the 2D BP.
Analytic calculations are done with Floquet Hamiltonians in the off-resonant
regime. The value of such C$_{q}$ calculations, in addition, to its role in
adjusting the current drive of an FET is discussed in context of
metal-insulator and topological phase transitions and enhancements to the
thermoelectric figure of merit.


  Smart Close-out Netting aims to standardise and automate specific operational
aspects of the legal and regulatory processes of close-out netting for
prudentially regulated financial institutions. This article provides a review,
analysis and perspective of these operational processes, their benefits for
prudentially regulated trading institutions, their current inefficiencies, and
the extent to which they are amenable to standardisation and automation. The
main concepts of Smart Close-out Netting are introduced, including the use of a
controlled natural language in legal opinions and the use of a data-driven
framework during netting determination.


  In this paper, the concept of the {\it broken diagonal pair} in the
chess-like square board is used to define some well-structured block designs
whose incidence matrices can be considered as the parity-check matrices of some
high rate cycle codes with girth 12. The structure of the proposed parity-check
matrices significantly reduces the complexity of encoding and decoding.
Interestingly, the constructed regular cycle codes with row-weights $t$, $3\leq
t \leq 20$, $t\neq 7, 15, 16$, have the best lengths among the known regular
girth-12 cycle codes. In addition, the proposed cycle codes can be easily
extended to some high rate column weight-3 LDPC codes with girth 6. Simulation
results show that the constructed codes achieve excellent performances,
specially the constructed column weight 3 LDPC codes outperform LDPC codes
based on Steiner triple systems (STS).


  Learning from set-structured data, such as point clouds, has gained
significant attention from the machine learning community. Geometric deep
learning provides a blueprint for designing effective set neural networks that
preserve the permutation symmetry of set-structured data. Of our interest are
permutation invariant networks, which are composed of a permutation equivariant
backbone, permutation invariant global pooling, and regression/classification
head. While existing literature has focused on improving equivariant backbones,
the impact of the pooling layer is often overlooked. In this paper, we examine
the interplay between permutation equivariant backbones and permutation
invariant global pooling on three benchmark point cloud classification
datasets. Our findings reveal that: 1) complex pooling methods, such as
transport-based or attention-based poolings, can significantly boost the
performance of simple backbones, but the benefits diminish for more complex
backbones, 2) even complex backbones can benefit from pooling layers in low
data scenarios, 3) surprisingly, the choice of pooling layers can have a more
significant impact on the model's performance than adjusting the width and
depth of the backbone, and 4) pairwise combination of pooling layers can
significantly improve the performance of a fixed backbone. Our comprehensive
study provides insights for practitioners to design better permutation
invariant set neural networks. Our code is available at
https://github.com/mint-vu/backbone_vs_pooling.


  A well known result from functional analysis states that any compact operator
between Hilbert spaces admits a singular value decomposition (SVD). This
decomposition is a powerful tool that is the workhorse of many methods both in
mathematics and applied fields. A prominent application in recent years is the
approximation of high-dimensional functions in a low-rank format. This is based
on the fact that, under certain conditions, a tensor can be identified with a
compact operator and SVD applies to the latter. One key assumption for this
application is that the tensor product norm is not weaker than the injective
norm. This assumption is not fulfilled in Sobolev spaces, which are widely used
in the theory and numerics of partial differential equations. Our goal is the
analysis of the SVD in Sobolev spaces. This work consists of two parts. In this
manuscript (part I), we address low-rank approximations and minimal subspaces
in H1. We analyze the H1-error of the SVD performed in the ambient L2-space. In
part II, we will address variants of the SVD in norms stronger than the
L2-norm. We will provide a few numerical examples that support our theoretical
findings.


  We observe a large fraction of circular polarization in radio emission from
extensive air showers recorded during thunderstorms, much higher than in the
emission from air showers measured during fair-weather circumstances. We show
that the circular polarization of the air showers measured during thunderstorms
can be explained by the change in the direction of the transverse current as a
function of altitude induced by atmospheric electric fields. Thus by using the
full set of Stokes parameters for these events, we obtain a good
characterization of the electric fields in thunderclouds. We also measure a
large horizontal component of the electric fields in the two events that we
have analysed.


  Using quantum field-theoretic arguments, Witten has established a relation
between the Donaldson and Seiberg-Witten invariants of smooth four-manifolds.
In this survey article, we describe the program to prove this relation using a
moduli space of PU(2) = SO(3) monopoles as a cobordism between the Donaldson
moduli space of anti-self-dual SO(3) connections and moduli spaces of U(1)
monopoles. We provide an overview of some of our transversality and Uhlenbeck
compactness results for PU(2) monopoles, along with some of our calculations of
Donaldson invariants in terms of Seiberg-Witten invariants. We give a brief
outline of issues concerning the gluing theory, focussing on some of the
analytical difficulties that are particular to PU(2) monopoles, and its
application to the PU(2) monopole program to prove the relation between
Donaldson and Seiberg-Witten invariants.


  A typical bottleneck of model predictive control algorithms is the
computational burden in order to compute the receding horizon feedback law
which is predominantly determined by the length of the prediction horizon.
Based on a relaxed Lyapunov inequality we present techniques which allow us to
show stability and suboptimality estimates for a reduced prediction horizon. In
particular, the known structural properties of suboptimality estimates based on
a controllability condition are used to cut the gap between theoretic stability
results and numerical observations.


  We propose a new local-binary ghost imaging by using point-by-point method.
This method can compensate the degradation of imaging quality due to the loss
of information during binarization process. The numerical and experimental
results show that the target details can be reconstructed well by this method
when compared with traditional ghost imaging. By comparing the differences of
the speckle patterns from different binarization methods, we also give the
corresponding explanation. Our results may have the potential applications in
areas with high requirements for imaging details, such as target recognition.


  Disjoint-Set forests, consisting of Union-Find trees, are data structures
having a widespread practical application due to their efficiency. Despite them
being well-known, no exact structural characterization of these trees is known
(such a characterization exists for Union trees which are constructed without
using path compression) for the case assuming union-by-rank strategy for
merging. In this paper we provide such a characterization by means of a simple
push operation and show that the decision problem whether a given tree (along
with the rank info of its nodes) is a Union-Find tree is NP-complete,
complementing our earlier similar result for the union-by-size strategy.


  Fix a $C^\infty$ principal $G$--bundle $E^0_G$ on a compact connected Riemann
surface $X$, where $G$ is a connected complex reductive linear algebraic group.
We consider the gradient flow of the Yang--Mills--Higgs functional on the
cotangent bundle of the space of all smooth connections on $E^0_G$. We prove
that this flow preserves the subset of Higgs $G$--bundles, and, furthermore,
the flow emanating from any point of this subset has a limit. Given a Higgs
$G$--bundle, we identify the limit point of the integral curve passing through
it. These generalize the results of the second named author on Higgs vector
bundles.


  We present a relativistic and model-independent method to derive
structure-dependent electromagnetic finite-size effects. This is a systematic
procedure, particularly well-suited for automatization, which works at
arbitrarily high orders in the large-volume expansion. Structure-dependent
coefficients appear as zero-momentum derivatives of physical form factors which
can be obtained through experimental measurements or auxiliary lattice
calculations. As an application we derive the electromagnetic finite-size
effects on the pseudoscalar meson mass and leptonic decay amplitude, through
orders $\mathcal{O}(1/L^3)$ and $\mathcal{O}(1/L^2)$, respectively. The
structure dependence appears at this order through the meson charge radius and
the real radiative leptonic amplitude, which are known experimentally.


  We find that the structure constants 4-form of a metric 3-Lie algebra is the
sum of the volume forms of orthogonal 4-planes proving a conjecture in
math/0211170. In particular, there is no metric 3-Lie algebra associated to a
$\mathfrak{u}(N)$ Lie algebra for $N>2$. We examine the implication of this
result on the existence of a multiple M2-brane theory based on metric 3-Lie
algebras.


  We analyze the problem of calculating the solutions and the spectrum of a
string with arbitrary density and fixed ends. We build a perturbative scheme
which uses a basis of WKB-type functions and obtain explicit expressions for
the eigenvalues and eigenfunctions of the string. Using this approach we show
that it is possible to derive the asymptotic (high energy) behavior of the
string, obtaining explicit expressions for the first three coefficients (the
first two can also be obtained with the WKB method). Finally using an iterative
approach we also obtain analytical expressions for the low energy behavior of
the eigenvalues and eigenfunctions of a string with rapidly oscillating
density, recovering (in a simpler way) results in the literature.


  Deep inelastic structure functions for the nucleon are obtained in a
constituent quark model on the light cone. In the Bjorken limit the parton
model is derived. Structure functions from the hadronic tensor at the scale
$\mu \sim 0.25$ GeV are evolved from (0.6 GeV$)^{2}$ to $-q^{2}\sim 15$
GeV$^{2}$. The model incorporates the quark boosts, is designed to describe
form factors and structure functions, and to provide a link between the parton
and constituent quark models. The main effect of the spin force between quarks
is described in terms of smaller (and lighter) scalar $u-d$ quark pairs in the
nucleon. To account for the negative slope of $F^{n}_{2}(x)/F^{p}_{2}(x)$,
attraction between scalar $u-d$ quark pairs and incorporation of boosts are
required. The two-body spin force between quarks from color magnetism also
leads to a negative slope. The polarization asymmetry $A^{p}_{1}$ is in fair
agreement with the EMC data in the valence quark region. Revised
hep-ph/9401342, Phys. Rev. D.


  We consider online optimization problems with time-varying linear equality
constraints. In this framework, an agent makes sequential decisions using only
prior information. At every round, the agent suffers an environment-determined
loss and must satisfy time-varying constraints. Both the loss functions and the
constraints can be chosen adversarially. We propose the Online Projected
Equality-constrained Newton Method (OPEN-M) to tackle this family of problems.
We obtain sublinear dynamic regret and constraint violation bounds for OPEN-M
under mild conditions. Namely, smoothness of the loss function and boundedness
of the inverse Hessian at the optimum are required, but not convexity. Finally,
we show OPEN-M outperforms state-of-the-art online constrained optimization
algorithms in a numerical network flow application.


  We study (p)reheating in alpha-attractor T-models of inflation, taking into
account both scalar fields present in these models: the inflaton and the
spectator. The two-field model has a negative field-space curvature which, at
the end of inflation, may lead to geometrical destabilization of the spectator
for small values of alpha<~10^(-3). We perform the instability (Floquet)
analysis of the linear dynamics and a fully non-linear lattice computations
with our numerical code, which we specifically designed for a class of
two-field models with non-canonical kinetic terms. We find that the
perturbations of the spectator field are much more unstable than the
perturbations of the inflaton field, so the dynamics of the early stages of
preheating is dominated by the evolution of the spectator perturbations. As a
result, the transition from the inflationary era to radiation domination era is
practically instantaneous and much faster than previously found in an effective
theory including only the inflaton field.


  A comprehensive study of the generalized Lambert series
$\displaystyle\sum_{n=1}^{\infty}\frac{n^{N-2h}\exp{(-an^{N}x)}}{1-\exp{(-n^{N}x)}},
0<a\leq 1,\ x>0$, $N\in\mathbb{N}$ and $h\in\mathbb{Z}$, is undertaken. Two of
the general transformations of this series that we obtain here lead to
two-parameter generalizations of Ramanujan's famous formula for $\zeta(2m+1)$,
$m>0$ and the transformation formula for $\log\eta(z)$. Numerous important
special cases of our transformations are derived. An identity relating
$\zeta(2N+1), \zeta(4N+1),\cdots, \zeta(2Nm+1)$ is obtained for $N$ odd and
$m\in\mathbb{N}$. Certain transcendence results of Zudilin- and Rivoal-type are
obtained for odd zeta values and generalized Lambert series. A criterion for
transcendence of $\zeta(2m+1)$ and a Zudilin-type result on irrationality of
Euler's constant $\gamma$ are also given. New results analogous to those of
Ramanujan and Klusch for $N$ even, and a transcendence result involving
$\zeta\left(2m+1-\frac{1}{N}\right)$, are obtained.


  In this paper we initiate the study of the computational complexity of
learning linear temporal logic (LTL) formulas from examples. We construct
approximation algorithms for fragments of LTL and prove hardness results; in
particular we obtain tight bounds for approximation of the fragment containing
only the next operator and conjunctions, and prove NP-completeness results for
many fragments.


  Matrix multiplication is a fundamental building block for large scale
computations arising in various applications, including machine learning. There
has been significant recent interest in using coding to speed up distributed
matrix multiplication, that are robust to stragglers (i.e., machines that may
perform slower computations). In many scenarios, instead of exact computation,
approximate matrix multiplication, i.e., allowing for a tolerable error is also
sufficient. Such approximate schemes make use of randomization techniques to
speed up the computation process. In this paper, we initiate the study of
approximate coded matrix multiplication, and investigate the joint synergies
offered by randomization and coding. Specifically, we propose two coded
randomized sampling schemes that use (a) codes to achieve a desired recovery
threshold and (b) random sampling to obtain approximation of the matrix
multiplication. Tradeoffs between the recovery threshold and approximation
error obtained through random sampling are investigated for a class of coded
matrix multiplication schemes.


  In this paper we argue that monojet and monophoton searches can be a
sensitive test of very highly ionizing particles such as particles with charges
$\gtrsim 150e$ and more generally particles that do not reach the outer parts
of the detector. 8 TeV monojet data from the CMS experiment excludes such
objects with masses in the range $\lesssim 650~{\text{GeV}}$ and charges
$\gtrsim 100e$. This nicely complements searches for highly ionizing objects at
ALICE, ATLAS, CMS and LHCb. Expected improvements in these channels will extend
the sensitivity range to $m\lesssim 750~{\text{GeV}}$. This search strategy can
directly be generalized to other particles that strongly interact with the
detector material, such as e.g. magnetic monopoles.


  Previous neural machine translation models used some heuristic search
algorithms (e.g., beam search) in order to avoid solving the maximum a
posteriori problem over translation sentences at test time. In this paper, we
propose the Gumbel-Greedy Decoding which trains a generative network to predict
translation under a trained model. We solve such a problem using the
Gumbel-Softmax reparameterization, which makes our generative network
differentiable and trainable through standard stochastic gradient methods. We
empirically demonstrate that our proposed model is effective for generating
sequences of discrete words.


  This study explores two zero-training methods aimed at enhancing the
usability of brain-computer interfaces (BCIs) by eliminating the need for a
calibration session. We introduce a novel method rooted in the event-related
potential (ERP) domain, unsupervised mean maximization (UMM), to the fast
code-modulated visual evoked potential (c-VEP) stimulus protocol. We compare
UMM to the state-of-the-art c-VEP zero-training method that uses canonical
correlation analysis (CCA). The comparison includes instantaneous
classification and classification with cumulative learning from previously
classified trials for both CCA and UMM. Our study shows the effectiveness of
both methods in navigating the complexities of a c-VEP dataset, highlighting
their differences and distinct strengths. This research not only provides
insights into the practical implementation of calibration-free BCI methods but
also paves the way for further exploration and refinement. Ultimately, the
fusion of CCA and UMM holds promise for enhancing the accessibility and
usability of BCI systems across various application domains and a multitude of
stimulus protocols.


  Young T Tauri stars (TTS) are surrounded by an accretion disk, which over
time disperses due to photoevaporation, accretion, and possibly planet
formation. The accretion shock on the central star produces an UV/optical
veiling continuum, line emission, and X-ray signatures. As the accretion rate
decreases, the impact on the central star must change. In this article we study
MN Lup, a young star where no indications of a disk are seen in IR
observations. We present XMM-Newton and VLT/UVES observations, some of them
taken simultaneously. The X-ray data show that MN Lup is an active star with
L_X/L_bol close to the saturation limit. However, we find high densities (n_e >
3e10 /cm^3) in the X-ray grating spectrum. This can be well fitted using an
accretion shock model with an accretion rate of 2e-11 M_sun/yr. Despite the
simple Halpha line profile which has a broad component, but no absorption
signatures as typically seen on accreting TTS, we find rotational modulation in
Ca II K and in photospheric absorption lines. In the Halpha line we see a
prominence in absorption about 2R_* above the stellar surface - the first of
its kind on a TTS. MN Lup is also the only TTS where accretion is seen, but no
dust disk is detected that could fuel it. We suggest that MN Lup presents a
unique and short-lived state in the disk evolution. It may have lost its dust
disk only recently and is now accreting the remaining gas at a very low rate.


  We propose to apply the idea of analytical continuation in the complex domain
to the problem of geodesic completeness. We shall analyse rather in detail the
cases of analytical warped products of real lines, these ones in parallel with
their complex counterparts, and of Clifton-Pohl torus, to show that our
definition sheds a bit of new light on the behaviour of 'singularities' of
geodesics in space-time. We also show that some geodesics, which 'end' at
finite time in the classical sense, can be naturally continued besides their
ends. As a matter of fact, complex metrics naturally show a meromorphic
behaviour, or a degenerating one, so we shall study also this fact in detail.


  The collapse of Landau levels under an electric field perpendicular to the
magnetic field is one of the distinctive features of Dirac materials. So is the
coupling of lattice deformations to the electronic degrees of freedom in the
form of gauge fields which allows the formation of pseudo-Landau levels from
strain. We analyze the collapse of Landau levels induced by strain on realistic
Weyl semimetals hosting anisotropic, tilted Weyl cones in momentum space. We
perform first-principles calculations, to establish the conditions on the
external strain for the collapse of Landau levels in TaAs which can be
experimentally accessed.


  Trading algorithms that execute large orders are susceptible to exploitation
by order anticipation strategies. This paper studies the influence of order
anticipation strategies in a multi-investor model of optimal execution under
transient price impact. Existence and uniqueness of a Nash equilibrium is
established under the assumption that trading incurs quadratic transaction
costs. A closed-form representation of the Nash equilibrium is derived for
exponential decay kernels. With this representation, it is shown that while
order anticipation strategies raise the execution costs of a large order
significantly, they typically do not cause price overshooting in the sense of
Brunnermeier and Pedersen.


  Magnetic microrobots that swim through liquid media are of interest for
minimally invasive medical procedures, bioengineering, and manufacturing. Many
of the envisaged applications, such as micromanipulation and targeted cargo
delivery, necessitate the use and adequate control of multiple microrobots,
which will increase the velocity, robustness, and efficacy of a procedure.
While various methods involving heterogeneous geometries, magnetic properties,
and surface chemistries have been proposed to enhance independent control, the
main challenge has been that the motion between all microwsimmers remains
coupled through the global control signal of the magnetic field. Katsamba and
Lauga proposed transchiral microrobots, a theoretical design with magnetized
spirals of opposite handedness. The competition between the spirals can be
tuned to give an intrinsic nonlinearity that each device can function only
within a given band of frequencies. This allows individual microrobots to be
selectively controlled by varying the frequency of the rotating magnetic field.
Here we present the experimental realization and characterization of
transchiral micromotors composed of independently driven magnetic helices. We
show a swimming micromotor that yields negligible net motion until a critical
frequency is reached and a micromotor that changes its translation direction as
a function of the frequency of the rotating magnetic field. This work
demonstrates a crucial step towards completely decoupled and addressable
swimming magnetic microrobots.


  Generalized multifractality characterizes system size dependence of pure
scaling local observables at Anderson transitions in all ten symmetry classes
of disordered systems. Recently, the concept of generalized multifractality has
been extended to boundaries of critical disordered noninteracting systems. Here
we study the generalized boundary multifractality in the presence of
electron-electron interaction, focusing on the spin quantum Hall symmetry class
(class C). Employing the two-loop renormalization group analysis within
Finkel'stein nonlinear sigma model we compute the anomalous dimensions of the
pure scaling operators located at the boundary of the system. We find that
generalized boundary multifractal exponents are twice larger than their bulk
counterparts. Exact symmetry relations between generalized boundary
multifractal exponents in the case of noninteracting systems are explicitly
broken by the interaction.


  We present a realization of fracton-elasticity duality purely formulated in
terms of ordinary gauge fields, encompassing standard elasticity and
incommensurate crystals as those describing twisted bilayer graphene,
quasicrystals or more general moir\'e lattices. Our construction comprises a
description of all types of two-dimensional defects: disclinations,
dislocations, discompressions and point-like defects, and takes into account
body forces and impurities. The original form of the duality in terms of tensor
gauge fields is recovered after partial gauge fixing. We identify the coupling
of each type of defect to the dual gauge fields, and from gauge invariance we
derive generalized continuity equations for the defect currents and the
expected mobility restrictions of elasticity defects.


  The recent measurements of baryon acoustic oscillations (BAO) from the DESI
collaboration have presented an indication for dynamical dark energy, when
adopting the $(w_0,w_a)$ parametrization of the equation of state. The
associated posterior constraints imply a crossing of the phantom divide. The
latter, however, has profound theoretical implications because not all models
can do so without developing incurable instabilities. Simple quintessence
models of dark energy, for instance, would be ruled out if such a crossing is
confirmed. We perform a non-parametric reconstruction of the equation of state,
and confirm that crossing of the phantom divide is required by the DESI BAO
data. We then explore the theory space of Horndeski gravity employing a
reconstruction method based on the effective field theory of dark energy, and
show that for most of the models it is still difficult to safely cross the
divide. We identify non-minimal coupling to gravity as the key modification
which sustains a stable phantom crossing in the general Horndeski theory space
and fits DESI observations. Guided by these insights, we propose the
\textit{Thawing Gravity} model which has the same number of parameters as
$w_0w_a$CDM and naturally realizes non-minimal coupling when dark energy
becomes non-negligible. \textit{Thawing Gravity} improves the fit over
$\Lambda$CDM for DESI BAO, CMB as well as type Ia Supernovae.