  The unpolarized and polarized Beam Char\-ge Asymmetries (BCAs) of the
$\vv{e}^{\pm}p \to e^{\pm}p \gamma$ process off unpolarized hydrogen are
discussed. The measurement of BCAs with the CLAS12 spectrometer at the Thomas
Jefferson National Accelerator Facility, using polarized positron and electron
beams at 10.6 GeV is investigated. This experimental configuration allows to
measure azimuthal and $t$-dependences of the unpolarized and polarized BCAs
over a large $(x_B,Q^2)$ phase space, providing a direct access to the real
part of the Compton Form Factor (CFF) ${\mathcal H}$. Additionally, these
measurements confront the Bethe-Heitler dominance hypothesis and eventual
effects beyond leading twist. The impact of potential positron beam data on the
determination of CFFs is also investigated within a local fitting approach of
experimental observables. Positron data are shown to strongly reduce
correlations between CFFs and consequently improve significantly the
determination of $\Re {\rm e} [\mathcal{H}]$.


  In this note we discuss a characteristic collider signature of models of
gauge mediated supersymmetry breaking in which the selectron and smuon are
mass-degenerate co-NLSP. In these models, all processes involving superpartners
give rise to two NLSP selectrons or smuons, each of which subsequently decays
to a nearly massless LSP gravitino and an electron or a muon. In a large region
of the parameter space, the NLSPs travel macroscopic distances, of the order
0.1-1000 mm, before they decay. Hence, these models give rise to collider
signatures involving charged tracks that end at vertices, which are inside the
detector volume but displaced with respect to the original collision point,
from which an electron or a muon is emitted. In order to probe this class of
models we propose a search for disappearing charged tracks in association with
displaced electrons or muons.


  We determine the invariants, with arbitrary determinant twists, of the
parabolic subgroups of the finite general linear group GL_n(q) acting on the
tensor product of the symmetric algebra and the exterior algebra of the natural
GL_n(q)-module V. In addition, we obtain the graded multiplicity of the
Steinberg module of GL_n(q) in the tensor product of the symmetric algebra and
the exterior algebra of V, twisted by an arbitrary determinant power.


  We have used three different techniques for permeability prediction from
porosity data in well PX12 at El Lago de Maracaibo. One of these techniques is
statistical and is based in Fuzzy Logic. Another has been developed by H. Pape
et al, based in Fractal Theory and the Kozeny-Carman equations, and the other
one is an empirical model obtained in 1949 by Tixier. We have used 100% of the
permeability-porosity data to obtain the predictor equations in each case. We
have found bet- ter results with the statistical approach. The results obtained
from the fractal model and the Tixier equations are similar in this case. We
have also taken randomly 25% of the data to obtain the pre- dictor equations.
In this case the best results are those obtained with fractal theory.


  We show H\"older continuity for the integrated density of states of a
quasi-periodic Jacobi operator with analytic coefficients, in the regime of
positive Lyapunov exponent and with a strong Diophantine condition on the
frequency. In particular, when the coefficients are trigonometric polynomials
we express the H\"older exponent in terms of the degrees of the coefficients.


  Radio emission in the direction of galaxy clusters is due to the individual
emission of AGNs, and to the diffuse non-thermal emission of the intracluster
medium (ICM). The population of AGNs in clusters is correlated to the overall
halo properties, and likely impacts their evolutions. In order to better
understand this connection (which will also leads to constraints on the
non-thermal ICMemission for lower mass systems), we are conducting a
statistical analysis of the radio emission in the direction of a large number
of X-ray clusters. By means of their stacked radio emission, we are
investigating the radio luminosities in clusters of galaxies with respect to
their mass, with the goal to better understand their link to and their imprint
on the intra-cluster gas physics.


  XPath is a language for addressing parts of an XML document. We give an
abstract interpretation of XPath expressions in terms of relations on document
node types. Node-set-related XPath language constructs are mapped
straightforwardly onto basic, well-understood and easily computable relational
operations. Hence our interpretation gives both extremely concise type-level
denotational semantics and a practical analysis tool for the node-set fragment
of the XPath 1.0 language. This method is part of the TPath implementation of
XPath.
  XSL-T is a pure functional language for transforming XML documents. For the
most common case, the transformation into an XML document, type checking of the
transformation code is unfeasible in general, but strongly required in
practice. It turned out that the relational approach of TPath can be carried
over to check all fragments of the result language, which are contained
verbatim in the transformation code. This leads to a technique called
"Fragmented Validation" and is part of the txsl implementation of XSL-T.


  Continuous tuning of the frequency of laser light is the cornerstone for a
plethora of applications in basic science as well as in the industrial
environment. They range from the hunt for gravitational waves, the realization
of optical clocks over health and environmental monitoring to distance
measurements. So far, it is difficult to combine a wide tuning range (> 100
GHz) with sub-microsecond tuning times, intrinsic tuning linearity and
coherence lengths beyond 10 m. We show that electro-optically driven adiabatic
frequency converters using high Q microresonators made of lithium niobate are
able to transfer arbitrary voltage signals into frequency chirps on time scales
far below 1 {\mu}s. The temporal variation of the frequency nicely agrees with
the one of the voltage applied. Superimposing the converted light with the
unconverted one, we derived from the beat signal that 200-ns-long linear
frequency chirps deviate less than 1 % from perfectness without any additional
measures. The Coefficient of Determination is R2 > 0.999. The coherence length
of the emitted light is of the order of 100 m. In order to prove these
findings, we apply linear frequency sweeps for FMCW LiDAR for distances between
0.5 and 10 m without any signs of nonlinearity. Combined with the demonstrated
ns tuning, with the potential to tune the eigenfrequency of
lithiumniobate-based resonators by several 100 GHz, our results show that
electro-optically driven adiabatic frequency converters can be used in
applications that require ultrafast and flexible continuous frequency tuning
with intrinsic linearity and large coherence length.


  We report the synthesis and structural study of mixed oxides in the Ln2ScNbO7
series. New phases with Ln = Pr, Eu, Gd and Dy are obtained. All crystallize in
the cubic pyrochlore structure type, space group F-d3m, with no Sc-Nb ordering
on the B-site. The structures are determined by Rietveld refinement. The
evolution of cell parameters, interatomic distances and angles as a function of
lanthanide cation size is discussed. Magnetic measurements show the absence of
ordering down to 2 K, in agreement with the presence of strong geometric
frustration in the lanthanide sublattice. The europium phase shows a peculiar
magnetic behaviour; its magnetic susceptibility becomes constant below ca 50 K.
This feature confirms the behaviour observed previously on Eu2Ti2O7 and is
ascribed to crystal field effects.


  I review recent and less recent work on globular cluster systems in
early-type galaxies. Explaining their properties and possible assembly
scenarios, touches on a variety of astrophysical topics from cluster formation
itself to galaxy formation and evolution and even details of observational
techniques. The spectacular cluster systems of central galaxies in galaxy
clusters may owe their richness to a plethora of less spectacular galaxies and
their star formation processes. It seems that dwarf galaxies occupy a
particularly important role.


  Denote by $G$ the group of interval exchange transformations (IETs) on the
unit interval. Let $G_{per}\subset G$ be the subgroup generated by torsion
elements in $G$ (periodic IETs), and let $G_{rot}\subset G$ be the subset of
2-IETs (rotations).
  The elements of the subgroup $G_1=< G_{per},G_{rot}>\subset G$ (generated by
the sets $G_{per}$ and $G_{rot}$) are characterized constructively in terms of
their Sah-Arnoux-Fathi (SAF) invariant. The characterization implies that a
non-rotation type 3-IET lies in $G_1$ if and only if the lengths of its
exchanged intervals are linearly dependent over $\Q$. In particular,
$G_1\subsetneq G$.
  The main tools used in the paper are the SAF invariant and a recent result by
Y. Vorobets that $G_{per}$ coincides with the commutator subgroup of $G$.


  We construct a nonlinear sigma (NL$\sigma$) model description of 2+1d spin
systems, by coupling together antiferromagnetic spin chains via interchain
exchange terms. Our mapping incorporates methods developed recently by
ourselves and by Senthil and Fisher, which aim at describing competition
between antiferromagnetic and valence-bond-solid orders in quantum magnets. The
resulting 2+1d $O$(4) NL$\sigma$ model contains a topological $\theta$-term
whose vacuum angle $\theta$ varies continuously with $\delta$, the
bond-alternation strength of the interchain interaction. This implies that the
$\theta$-vacua structure for this NL$\sigma$ model can be explored by tuning
$\delta$ in a suitable 2d spin system, which is strongly reminiscent of the
situation for 1+1 AF spin chains with bond-alternation.


  We investigate representations of *-algebras associated with posets.
Unitarizable representations of the corresponding (bound) quivers (which are
polystable representations for some appropriately chosen slope function) give
rise to representations of these algebras. Considering posets which correspond
to unbound quivers this leads to an ADE-classification which describes the
unitarization behaviour of their representations. Considering posets which
correspond to bound quivers, it is possible to construct unitarizable
representations starting with polystable representations of related unbound
quivers which can be glued together with a suitable direct sum of simple
representations. Finally, we estimate the number of complex parameters
parametrizing irreducible unitary non-equivalent representations of the
corresponding algebras.


  The simulation of spin models close to critical points of continuous phase
transitions is heavily impeded by the occurrence of critical slowing down. A
number of cluster algorithms, usually based on the Fortuin-Kasteleyn
representation of the Potts model, and suitable generalizations for
continuous-spin models have been used to increase simulation efficiency. The
first algorithm making use of this representation, suggested by Sweeny in 1983,
has not found widespread adoption due to problems in its implementation.
However, it has been recently shown that it is indeed more efficient in
reducing critical slowing down than the more well-known algorithm due to
Swendsen and Wang. Here, we present an efficient implementation of Sweeny's
approach for the random-cluster model using recent algorithmic advances in
dynamic connectivity algorithms.


  The Precision Medicine Initiative states that treatments for a patient should
take into account not only the patient's disease, but his/her specific genetic
variation as well. The vast biomedical literature holds the potential for
physicians to identify effective treatment options for a cancer patient.
However, the complexity and ambiguity of medical terms can result in vocabulary
mismatch between the physician's query and the literature. The physician's
search intent (finding treatments instead of other types of studies) is
difficult to explicitly formulate in a query. Therefore, simple ad hot
retrieval approach will suffer from low recall and precision. In this paper, we
propose a new retrieval system that helps physicians identify effective
treatments in precision medicine. Given a cancer patient with a specific
disease, genetic variation, and demographic information, the system aims to
identify biomedical publications that report effective treatments. We approach
this goal from two directions. First, we expand the original disease and gene
terms using biomedical knowledge bases to improve recall of the initial
retrieval. We then improve precision by promoting treatment-related
publications to the top using a machine learning reranker trained on 2017 Text
Retrieval Conference Precision Medicine (PM) track corpus. Batch evaluation
results on 2018 PM track corpus show that the proposed approach effectively
improves both recall and precision, achieving performance comparable to the top
entries on the leaderboard of 2018 PM track.


  Events which meet certain criteria from star tracker images onboard the Juno
spacecraft have been proposed to be due to interplanetary dust particle impacts
on its solar arrays. These events have been suggested to be caused by particles
with diameters larger than 10 micrometers. Here, we compare the reported event
rates to expected dust impact rates using dynamical meteoroid models for the
four most abundant meteoroid/dust populations in the inner solar system. We
find that the dust impact rates predicted by dynamical meteoroid models are not
compatible with either the Juno observations in terms of the number of star
tracker events per day, or with the variations of dust flux on Juno's solar
panels with time and position in the solar system. For example, the rate of
star tracker events on Juno's anti-sunward surfaces is the largest during a
period during which Juno is expected to experience the peak impact fluxes on
the opposite, sunward hemisphere. We also investigate the hypothesis of dust
leaving the Martian Hill sphere originating either from the surface of Mars
itself or from one of its moons. We do not find such a hypothetical source to
be able to reproduce the star tracker event rate variations observed by Juno.
We conclude that the star tracker events observed by Juno are unlikely to be
the result of instantaneous impacts from the Zodiacal Cloud.


  We investigate the fundamental limits of reliable communication over
multi-view channels, in which the channel output is comprised of a large number
of independent noisy views of a transmitted symbol. We consider first the
setting of multi-view discrete memoryless channels and then extend our results
to general multi-view channels (using multi-letter formulas). We argue that the
channel capacity and dispersion of such multi-view channels converge
exponentially fast in the number of views to the entropy and varentropy of the
input distribution, respectively. We identify the exact rate of convergence as
the smallest Chernoff information between two conditional distributions of the
output, conditioned on unequal inputs. For the special case of the deletion
channel, we compute upper bounds on this Chernoff information. Finally, we
present a new channel model we term the Poisson approximation channel -- of
possible independent interest -- whose capacity closely approximates the
capacity of the multi-view binary symmetric channel for any fixed number of
views.


  We give a direct microscopic derivation of the F-theory background that
corresponds to four D7 branes of type I' theory by taking into account the
D-instanton contributions to the emission of the axio-dilaton field in the
directions transverse to the D7's. The couplings of the axio-dilaton to the
D-instanton moduli modify its classical source terms which are shown to be
proportional to the elements of the D7 brane chiral ring. Solving the bulk
field equations with the non-perturbatively corrected sources yields the full
F-theory background. This solution represents the gravitational dual of the
four-dimensional theory living on a probe D3 brane of type I', namely of the
N=2, Sp(1) SYM theory with Nf=4. Our results provide an explicit microscopic
derivation of the non-perturbative gravitational dual of this theory. They also
explain the recent observation that the exact coupling for this theory can be
entirely reconstructed from its perturbative part plus the knowledge of the
chiral ring on the D7 branes supporting its flavor degrees of freedom.


  We revisit the slow-bond (SB) problem of the one-dimensional (1D) totally
asymmetric simple exclusion process (TASEP) with modified hopping rates. In the
original SB problem, it turns out that a local defect is always relevant to the
system as jamming, so that phase separation occurs in the 1D TASEP. However,
crossover scaling behaviors are also observed as finite-size effects. In order
to check if the SB can be irrelevant to the system with particle interaction,
we employ the condensation concept in the zero-range process. The hopping rate
in the modified TASEP depends on the interaction parameter and the distance up
to the nearest particle in the moving direction, besides the SB factor. In
particular, we focus on the interplay of jamming and condensation in the
current-density relation of 1D driven flow. Based on mean-field calculations,
we present the fundamental diagram and the phase diagram of the modified SB
problem, which are numerically checked. Finally, we discuss how the
condensation of holes suppresses the jamming of particles and vice versa, where
the partially-condensed phase is the most interesting, compared to that in the
original SB problem.


  We present a general analysis of gauge invariant, exact and metric
independent forms which can be constructed using higher rank field-strength
tensors. The integrals of these forms over the corresponding space-time
coordinates provides new topological Lagrangians. With these Lagrangians one
can define gauge field theories which generalize the Chern-Simons quantum field
theory. We also present explicit expressions for the potential gauge anomalies
associated with the tensor gauge fields and classify all possible anomalies
that can appear in lower dimensions. Of special interest are those which can be
constructed in four, six, eight and ten dimensions.


  Multi-Sensor Fusion (MSF) based perception systems have been the foundation
in supporting many industrial applications and domains, such as self-driving
cars, robotic arms, and unmanned aerial vehicles. Over the past few years, the
fast progress in data-driven artificial intelligence (AI) has brought a
fast-increasing trend to empower MSF systems by deep learning techniques to
further improve performance, especially on intelligent systems and their
perception systems. Although quite a few AI-enabled MSF perception systems and
techniques have been proposed, up to the present, limited benchmarks that focus
on MSF perception are publicly available. Given that many intelligent systems
such as self-driving cars are operated in safety-critical contexts where
perception systems play an important role, there comes an urgent need for a
more in-depth understanding of the performance and reliability of these MSF
systems. To bridge this gap, we initiate an early step in this direction and
construct a public benchmark of AI-enabled MSF-based perception systems
including three commonly adopted tasks (i.e., object detection, object
tracking, and depth completion). Based on this, to comprehensively understand
MSF systems' robustness and reliability, we design 14 common and realistic
corruption patterns to synthesize large-scale corrupted datasets. We further
perform a systematic evaluation of these systems through our large-scale
evaluation. Our results reveal the vulnerability of the current AI-enabled MSF
perception systems, calling for researchers and practitioners to take
robustness and reliability into account when designing AI-enabled MSF.


  It is well known that non-Hermitian systems can be extremely sensitive to
boundary conditions owing to non-Hermitian skin effect (NHSE). Analogously, we
investigate two boundary-sensitive $U(1)$ symmetric Lindbladians: one carries
current in the steady state, and the other does not. The numerical results
indicate significant change of the Liouvillian spectrum, eigenmodes and
relaxation time for both Lindbladians when the boundary conditions are altered.
This phenomenon is found to be triggered by the Liouvillian skin effect (LSE),
specifically the localization of eigenmodes, which stems from the NHSE of the
non-Hermitian effective Hamiltonian. In addition, these two Lindbladians
manifest different LSE, ultimately resulting in distinct relaxation behaviors.


  The VLTI/GENIE configuration will operate using at least 4 of the VLTI
telescopes (and possibly with one or more of the AT telescopes in the future if
adaptive optics become available on them). GENIE effectively can be thought of
as a 'smart' coronagraph, enabling high dynamic range imaging to be achieved at
moderate spatial resolution, with high rejection of the emission of a central
bright point source. However, but this bright source rejection may only provide
a rather moderate image quality (due to the few baselines and transfer function
on the sky). Operated in this way, only limited image reconstruction is
possible since classical radio and millimeter wavelength interferometry
techniques are not directly applicable to the outputs of optical
interferometers because the absolute phases are generally not measured.
However, measurements of visibility and closure phase could lead to situations
where image reconstruction becomes possible. This paper addresses the issue of
whether there are areas outside of the exoplanet search where it might be able
to make a useful impact on astronomy.


  We revisit and generalize inequalities for the summatory function of the sum
of digits in a given integer base. We prove that several known results can be
deduced from a theorem in a 2023 paper by Mohanty, Greenbury, Sarkany,
Narayanan, Dingle, Ahnert, and Louis, whose primary scope is the maximum
mutational robustness in genotype-phenotype maps.


  The evolution of $N$ spin-$1/2$ system with all-range Ising-type interaction
is considered. For this system we study the entanglement of one spin with the
rest spins. It is shown that the entanglement depends on the amount of spins
and the initial state. Also the geometry of manifold which contains entangled
states is obtained. Finally we find the dependence of entanglement on the
scalar curvature of manifold and examine it for different number of spins in
the system.


  An idealized storm scenario is examined in which a wind-generated inertial
wave interacts with a turbulent baroclinic quasi-geostrophic flow. The flow is
initialized by spinning up a Eady model with a realistic stratification
profile. The storm is modeled as an initial value problem for a mixed-layer
confined, horizontally-uniform inertial oscillation. The primordial inertial
oscillation then evolves under the effects of advection, refraction, dispersion
and dissipation. Waves feedback onto the flow by modifying its potential
vorticity. In the first few days, refraction dominates and wave energy is
attracted (repelled) by regions of negative (positive) vorticity. Wave energy
is subsequently drained down anticyclonic pipes. This drainage halts as wave
energy encounters weakening vorticity. After a week or two, wave energy
accumulates at the bottom of negative vorticity features, i.e. along
filamentary structures at shallow depths and in larger anticyclones at greater
depths. Wave feedback tends to weaken vortices and thus slow down wave
penetration. This effect, however, is found to be weak even for vigorous
storms.


  Unsupervised learning has been a long-standing goal of machine learning and
is especially important for medical image analysis, where the learning can
compensate for the scarcity of labeled datasets. A promising subclass of
unsupervised learning is self-supervised learning, which aims to learn salient
features using the raw input as the learning signal. In this paper, we use a
contrastive self-supervised learning method called SimCLR that achieved
state-of-the-art results on natural-scene images and apply this method to
digital histopathology by collecting and pretraining on 57 histopathology
datasets without any labels. We find that combining multiple multi-organ
datasets with different types of staining and resolution properties improves
the quality of the learned features. Furthermore, we find using more images for
pretraining leads to a better performance in multiple downstream tasks. Linear
classifiers trained on top of the learned features show that networks
pretrained on digital histopathology datasets perform better than ImageNet
pretrained networks, boosting task performances by more than 28% in F1 scores
on average. These findings may also be useful when applying newer contrastive
techniques to histopathology data. Pretrained PyTorch models are made publicly
available at https://github.com/ozanciga/self-supervised-histopathology.


  We discuss a geometrical method to define a preferred reference frame for
precessing binary systems and the gravitational waves they emit. This
minimal-rotation frame is aligned with the angular-momentum axis and fixes the
rotation about that axis up to a constant angle, resulting in an essentially
invariant frame. Gravitational waveforms decomposed in this frame are similarly
invariant under rotations of the inertial frame and exhibit relatively smoothly
varying phase. By contrast, earlier prescriptions for radiation-aligned frames
induce extraneous features in the gravitational-wave phase which depend on the
orientation of the inertial frame, leading to fluctuations in the frequency
that may compound to many gravitational-wave cycles. We explore a simplified
description of post-Newtonian approximations for precessing systems using the
minimal-rotation frame, and describe the construction of analytical/numerical
hybrid waveforms for such systems.


  In this manuscript, we study the problem of robust synchronization in
networks of diffusively time-delayed coupled nonlinear systems. In particular,
we prove that, under some mild conditions on the input-output dynamics of the
systems and the network topology, there always exists a unimodal region in the
parameter space (coupling strength versus time-delay), such that if they belong
to this region, the systems synchronize. Moreover, we show how this unimodal
region scales with the network topology, which, in turn, provides useful
insights on how to design the network topology to maximize robustness against
time-delays. The results are illustrated by extensive simulation experiments of
time-delayed coupled Hindmarsh-Rose neural chaotic oscillators.


  Binary star systems represent a significant proportion of the Galactic
stellar population, with X-ray binaries being an important subset of these for
high energy astrophysics. Although hundreds of X-ray binaries are detected in
the Milky Way and beyond, only 12 of these systems are listed in the 4FGL-DR2,
the latest Fermi-LAT point source catalogue. With such a small number
detectable by Fermi-LAT, much is still unknown about the mechanisms by which
these systems emit $\gamma$-rays. We present the method and current status of
our large-scale survey of the X-ray binary population using over 12 years of
Fermi-LAT data, and current catalogues and background models.


  Word embeddings are fixed-length, dense and distributed word representations
that are used in natural language processing (NLP) applications. There are
basically two types of word embedding models which are non-contextual (static)
models and contextual models. The former method generates a single embedding
for a word regardless of its context, while the latter method produces distinct
embeddings for a word based on the specific contexts in which it appears. There
are plenty of works that compare contextual and non-contextual embedding models
within their respective groups in different languages. However, the number of
studies that compare the models in these two groups with each other is very few
and there is no such study in Turkish. This process necessitates converting
contextual embeddings into static embeddings. In this paper, we compare and
evaluate the performance of several contextual and non-contextual models in
both intrinsic and extrinsic evaluation settings for Turkish. We make a
fine-grained comparison by analyzing the syntactic and semantic capabilities of
the models separately. The results of the analyses provide insights about the
suitability of different embedding models in different types of NLP tasks. We
also build a Turkish word embedding repository comprising the embedding models
used in this work, which may serve as a valuable resource for researchers and
practitioners in the field of Turkish NLP. We make the word embeddings,
scripts, and evaluation datasets publicly available.


  Enabling robots to perform complex dynamic tasks such as picking up an object
in one sweeping motion or pushing off a wall to quickly turn a corner is a
challenging problem. The dynamic interactions implicit in these tasks are
critical towards the successful execution of such tasks. Graph neural networks
(GNNs) provide a principled way of learning the dynamics of interactive systems
but can suffer from scaling issues as the number of interactions increases.
Furthermore, the problem of using learned GNN-based models for optimal control
is insufficiently explored. In this work, we present a method for efficiently
learning the dynamics of interacting systems by simultaneously learning a
dynamic graph structure and a stable and locally linear forward model of the
system. The dynamic graph structure encodes evolving contact modes along a
trajectory by making probabilistic predictions over the edges of the graph.
Additionally, we introduce a temporal dependence in the learned graph structure
which allows us to incorporate contact measurement updates during execution
thus enabling more accurate forward predictions. The learned stable and locally
linear dynamics enable the use of optimal control algorithms such as iLQR for
long-horizon planning and control for complex interactive tasks. Through
experiments in simulation and in the real world, we evaluate the performance of
our method by using the learned interaction dynamics for control and
demonstrate generalization to more objects and interactions not seen during
training. We introduce a control scheme that takes advantage of contact
measurement updates and hence is robust to prediction inaccuracies during
execution.


  We consider the $Y$-systems satisfied by the $A_1^{(1)}$, $A_2^{(1)}$,
$A_2^{(2)}$ vertex and loop models at roots of unity with twisted boundary
conditions on the cylinder. The vertex models are the 6-, 15- and
Izergin-Korepin 19-vertex models respectively. The corresponding loop models
are the dense, fully packed and dilute Temperley-Lieb loop models respectively.
For all three models, our focus is on roots of unity values of $e^{i\lambda}$
with the crossing parameter $\lambda$ corresponding to the principal and dual
series of these models. Converting the known functional equations to nonlinear
integral equations in the form of Thermodynamic Bethe Ansatz (TBA) equations,
we solve the $Y$-systems for the finite-size $\frac 1N$ corrections to the
groundstate eigenvalue following the methods of Kl\"umper and Pearce. The
resulting expressions for $c-24\Delta$, where $c$ is the central charge and
$\Delta$ is the conformal weight associated with the groundstate, are
simplified using various dilogarithm identities. Our analytic results are in
agreement with previous results obtained by different methods and are new for
the dual series of the $A_2^{(1)}$ model.


  In this paper we provide two new semantics for proofs in the constructive
modal logics CK and CD. The first semantics is given by extending the syntax of
combinatorial proofs for propositional intuitionistic logic, in which proofs
are factorised in a linear fragment (arena net) and a parallel
weakening-contraction fragment (skew fibration). In particular we provide an
encoding of modal formulas by means of directed graphs (modal arenas), and an
encoding of linear proofs as modal arenas equipped with vertex partitions
satisfying topological criteria. The second semantics is given by means of
winning innocent strategies of a two-player game over modal arenas. This is
given by extending the Heijltjes-Hughes-Stra{\ss}burger correspondence between
intuitionistic combinatorial proofs and winning innocent strategies in a
Hyland-Ong arena. Using our first result, we provide a characterisation of
winning strategies for games on a modal arena corresponding to proofs with
modalities.


  In this note we are dealing with the problem of existence and asymptotic
behavior of solutions for the non-resonant singularly perturbed linear Neumann
boundary value problem \begin{eqnarray*} \epsilon y"+ky=f(t),\quad k>0,\quad
0<\epsilon<<1,\quad t\in\langle a,b\rangle \end{eqnarray*} \begin{equation*}
y'(a)=0,\quad y'(b)=0. \end{equation*} Our approach is based on the analysis of
an integral equation equivalent to this problem.


  High-resolution images offer more information about scenes that can improve
model accuracy. However, the dominant model architecture in computer vision,
the vision transformer (ViT), cannot effectively leverage larger images without
finetuning -- ViTs poorly extrapolate to more patches at test time, although
transformers offer sequence length flexibility. We attribute this shortcoming
to the current patch position encoding methods, which create a distribution
shift when extrapolating.
  We propose a drop-in replacement for the position encoding of plain ViTs that
restricts attention heads to fixed fields of view, pointed in different
directions, using 2D attention masks. Our novel method, called LookHere,
provides translation-equivariance, ensures attention head diversity, and limits
the distribution shift that attention heads face when extrapolating. We
demonstrate that LookHere improves performance on classification (avg. 1.6%),
against adversarial attack (avg. 5.4%), and decreases calibration error (avg.
1.5%) -- on ImageNet without extrapolation. With extrapolation, LookHere
outperforms the current SoTA position encoding method, 2D-RoPE, by 21.7% on
ImageNet when trained at $224^2$ px and tested at $1024^2$ px. Additionally, we
release a high-resolution test set to improve the evaluation of high-resolution
image classifiers, called ImageNet-HR.


  More than ever COVID-19 is putting pressure on health systems all around the
world, especially in Brazil. In this study we propose an analytical approach
based on statistics and machine learning that uses lab exam data coming from
patients to predict whether patients are going to require special care
(hospitalisation in regular or special-care units). We also predict the number
of days the patients will stay under such care. The two-step procedure
developed uses Bayesian Optimisation to select the best model among several
candidates leads us to final models that achieve 0.94 area under ROC curve
performance for the first target and 1.87 root mean squared error for the
second target (which is a 77% improvement over the mean baseline), making our
model ready to be deployed as a decision system that could be available for
everyone interested. The analytical approach can be used in other diseases and
can help the planning hospital capacity.


  An explicit pionic component of the nucleon may be identified by measuring
polarized $\Delta^{++}$ fragments produced in deep-inelastic scattering off
polarized protons. The pion-exchange model predicts highly correlated
polarizations of the $\Delta^{++}$ and target proton, in marked contrast with
the competing diquark fragmentation process.


  We have measured trigonometric parallaxes for four water masers associated
with distant massive young stars in the inner regions of the Galaxy using the
VLBA as part of the BeSSeL Survey. G026.50$+$0.28. is located at the near end
of the Galactic bar, perhaps at the origin of the Norma spiral arm.
G020.77$-$0.05 is in the Galactic Center region and is likely associated with a
far-side extension of the Scutum arm. G019.60$-$0.23 and G020.08$-$0.13 are
likely associated and lie well past the Galactic Center. These sources appear
to be in the Sagittarius spiral arm, but an association with the Perseus arm
cannot be ruled out.


  We report on the properties of nuclear regions in the Toomre Sequence of
merging galaxies, based on imaging data gathered with the Hubble Space
Telescope WFPC2 camera. We have imaged the 11 systems in the proposed
evolutionary merger sequence in the F555W and F814W broad-band filters, and in
H-alpha+[NII] narrow-band filters. The broad-band morphology of the nuclear
regions varies from non-nucleated starburst clumps through dust-covered nuclei
to a nucleated morphology. There is no unambiguous trend in the morphology with
merger stage. The emission-line morphology is extended beyond the nucleus in
most cases, but centrally concentrated (within 1 kpc) emission-line gas can be
seen in the four latest-stage merger systems. We have quantified the intrinsic
luminosity densities and colors within the inner 100 pc and 1 kpc of each
identified nucleus. We find little evidence for a clear trend in nuclear
properties along the merger sequence, other than a suggestive rise in the
nuclear luminosity density in the most evolved members of the sequence. The
lack of clear trends in nuclear properties is likely due both to the effects of
obscuration and geometry, as well as the physical variety of galaxies included
in the Toomre Sequence.


  The spinal cord is frequently affected by atrophy and/or lesions in multiple
sclerosis (MS) patients. Segmentation of the spinal cord and lesions from MRI
data provides measures of damage, which are key criteria for the diagnosis,
prognosis, and longitudinal monitoring in MS. Automating this operation
eliminates inter-rater variability and increases the efficiency of
large-throughput analysis pipelines. Robust and reliable segmentation across
multi-site spinal cord data is challenging because of the large variability
related to acquisition parameters and image artifacts. The goal of this study
was to develop a fully-automatic framework, robust to variability in both image
parameters and clinical condition, for segmentation of the spinal cord and
intramedullary MS lesions from conventional MRI data. Scans of 1,042 subjects
(459 healthy controls, 471 MS patients, and 112 with other spinal pathologies)
were included in this multi-site study (n=30). Data spanned three contrasts
(T1-, T2-, and T2*-weighted) for a total of 1,943 volumes. The proposed cord
and lesion automatic segmentation approach is based on a sequence of two
Convolutional Neural Networks (CNNs). To deal with the very small proportion of
spinal cord and/or lesion voxels compared to the rest of the volume, a first
CNN with 2D dilated convolutions detects the spinal cord centerline, followed
by a second CNN with 3D convolutions that segments the spinal cord and/or
lesions. When compared against manual segmentation, our CNN-based approach
showed a median Dice of 95% vs. 88% for PropSeg, a state-of-the-art spinal cord
segmentation method. Regarding lesion segmentation on MS data, our framework
provided a Dice of 60%, a relative volume difference of -15%, and a lesion-wise
detection sensitivity and precision of 83% and 77%, respectively. The proposed
framework is open-source and readily available in the Spinal Cord Toolbox.


  There is a gap in scientific information systems development concerning
modern software engineering and scientific computing. Historically, software
engineering methodologies have been perceived as an unwanted accidental
complexity to computational scientists in their scientific systems development.
More recent trends, like the end of Moore's law and the subsequent
diversification of hardware platforms, combined with the increasing
multidisciplinarity of science itself have exacerbated the problem because
self-taught "end user developers" are not familiar with the disciplines needed
to tackle this increased complexity. On a more positive note, agile programming
methods have approached software development practices to the way scientific
software is produced. In this work, we present the experience of a multi-year
industry research project where agile methods, microservices and DevOps were
applied. Our goal is to validate the hypothesis that the use of microservices
would allow computational scientists to work in the more minimalistic
prototype-oriented way that they prefer while the software engineering team
would handle the integration. Hence, scientific multidisciplinary systems would
gain in a twofold way: (i) Subject Matter Experts(SME) use their preferable
tools to develop the specific scientific part of the system; (ii) software
engineers provide the high quality software code for the system delivery.


  In digital pathology, the multiple instance learning (MIL) strategy is widely
used in the weakly supervised histopathology whole slide image (WSI)
classification task where giga-pixel WSIs are only labeled at the slide level.
However, existing attention-based MIL approaches often overlook contextual
information and intrinsic spatial relationships between neighboring tissue
tiles, while graph-based MIL frameworks have limited power to recognize the
long-range dependencies. In this paper, we introduce the integrative
graph-transformer framework that simultaneously captures the context-aware
relational features and global WSI representations through a novel Graph
Transformer Integration (GTI) block. Specifically, each GTI block consists of a
Graph Convolutional Network (GCN) layer modeling neighboring relations at the
local instance level and an efficient global attention model capturing
comprehensive global information from extensive feature embeddings. Extensive
experiments on three publicly available WSI datasets: TCGA-NSCLC, TCGA-RCC and
BRIGHT, demonstrate the superiority of our approach over current
state-of-the-art MIL methods, achieving an improvement of 1.0% to 2.6% in
accuracy and 0.7%-1.6% in AUROC.


  We review the assumptions and the logic underlying the derivation of DLCQ
Matrix models. In particular we try to clarify what remains valid at finite
$N$, the role of the non-renormalization theorems and higher order terms in the
supergravity expansion. The relation to Maldacena's conjecture is also
discussed. In particular the compactification of the Matrix model on $T_3$ is
compared to the $AdS_5\times S_5$ ${\cal N}=4$ super Yang-Mills duality, and
the different role of the branes in the two cases is pointed out.


  We present a theoretical study of the influence of the nuclear ferromagnetism
on superconductivity in the presence of the electron-nuclear spin interaction.
It is demonstrated that in some metals, e.g. Rh, W, the BCS condensate imbedded
in a matrix of ferromagneticaly ordered nuclear spins should manifest the FFLO
(Fulde-Ferel-Larkin-Ovchinniov) state. We outline that the optimal experimental
conditions for observation of FFLO could be achieved by creation, via adiabatic
nuclear demagnetization, of the negative nuclear spin temperatures. In this
case the nuclear polarization points in the opposite to the external magnetic
field direction and the electromagnetic part of the nuclear spin magnetization
compensates the external magnetic field, while the exchange part creates the
nonhomogeneous superconducting order parameter.


  With the continuous development of science and technology, the intelligent
development of community system becomes a trend. Meanwhile, smart mobile
devices and cloud computing technology are increasingly used in intelligent
information systems; however, smart mobile devices such as smartphone and smart
pad, also known as thin clients, limited by either their capacities (CPU,
memory or battery) or their network resources, do not always meet users'
satisfaction in using mobile services. Mobile cloud computing, in which
resource-rich virtual machines of smart mobile device are provided to a
customer as a service, can be terrific solution for expanding the limitation of
real smart mobile device, but the resources utilization rate is low and the
information cannot be shared easily. To address the problems above, this paper
proposes an information system for intelligent community, which is composed of
thin clients, wide band network and cloud computing servers. On one hand, the
thin clients with the characteristics of energy efficiency, high robustness and
high computing capacity can efficiently avoid the problems encountered in the
PC architecture and mobile devices. On the other hand, the cloud computing
servers in the proposed information system solve the problems of resource
sharing barriers. Finally, the system is built in real environments to evaluate
the performance. We deploy the proposed system in a community with more than
2000 residents, and it is demonstrated that the proposed system is robust and
efficient.


  Emergent model spectra of neutron star atmospheres are widely used to fit the
observed soft X-ray spectra of different types of isolated neutron stars. We
investigate the effect of Compton scattering on the emergent spectra of hot
(T_eff > 10^6 K) isolated neutron stars with weak magnetic fields. In order to
compute model atmospheres in hydrostatic and radiative equilibrium we solve the
radiation transfer equation with the Kompaneets operator. We calculate a set of
models with effective temperatures in the range 1 - 5 * 10^6 K, with two values
of surface gravity (log g = 13.9 and 14.3) and different chemical compositions.
Radiation spectra computed with Compton scattering are softer than those
computed without Compton scattering at high energies (E > 5 keV) for light
elements (H or He) model atmospheres. The Compton effect is more significant in
H model atmospheres and models with low surface gravity. The emergent spectra
of the hottest (T_eff > 3 * 10^6 K) model atmospheres can be described by
diluted blackbody spectra with hardness factors ~ 1.6 - 1.9. Compton scattering
is less important in models with solar abundance of heavy elements.


  Reconfigurable intelligent surfaces (RISs) is a novel communication
technology that has been recognized and recently presented as a candidate for
beyond fifth generation wireless communication technology. In this paper, we
propose a priority aware user traffic dependent grouping based multihop routing
scheme for a RIS-assisted millimeter wave (mmWave) device-to-device (D2D)
communication network with spatially correlated channels. Specifically, the
proposed scheme exploits the priority of the users (based on their respective
delay constrained applications) and the aspect of spatial correlation in the
narrowly spaced reflecting elements of the RISs. In this context, we establish
a multihop connection for information transfer from one of the users to its
desired receiver based on the other users in the neighbourhood, their
respective traffic characteristics, and the already deployed RISs in the
surroundings. Moreover, we also take into account the impact of considering
practical discrete phase shifts at the RIS patches instead of its ideal
continuous counterpart. Furthermore, we claim as well as demonstrate that the
existing classic least remaining distance (LRD)-based approach is not always
the optimal solution. Finally, numerical results demonstrate the advantages of
the proposed strategy and that it significantly outperforms the existing
benchmark schemes in terms of system performance metrics such as data
throughput, energy consumption, as well as energy efficiency.


  The presence/absence of a Berry phase depends on the topology of the manifold
of dynamical Jahn-Teller potential minima. We describe in detail the relation
between these topological properties and the way the lowest two adiabatic
potential surfaces get locally degenerate. We illustrate our arguments through
spherical generalizations of the linear T x h and H x h cases, relevant for the
physics of fullerene ions. Our analysis allows us to classify all the spherical
Jahn-Teller systems with respect to the Berry phase. Its absence can, but does
not necessarily, lead to a nondegenerate ground state.


  With the emergence of Internet-of-Things (IoT) and ever-increasing demand for
the newly connected devices, there is a need for more effective storage and
processing paradigms to cope with the data generated from these devices. In
this study, we have discussed different paradigms for data processing and
storage including Cloud, Fog, and Edge computing models and their suitability
in integrating with the IoT. Moreover, a detailed discussion on low latency and
massive connectivity requirements of future cellular networks in accordance
with machine-type communication (MTC) is also presented. Furthermore, the need
to bring IoT devices to Internet connectivity and a standardized protocol stack
to regulate the data transmission between these devices is also addressed while
keeping in view the resource constraint nature of IoT devices.


  We present the long-term monitoring of the High Mass X-ray Binary GX 301-2
performed with the SuperAGILE instrument on-board the AGILE mission. The source
was monitored in the 20-60 keV energy band during the first year of the mission
from 2007 July 17 to 2008 August 31, covering about one whole orbital period
and three more pre-periastron passages for a total net observation time of
about 3.7 Ms. The SuperAGILE dataset represents one of the most continuous and
complete monitoring at hard X-ray energies of the 41.5 day long binary period
available to date. The source behavior was characterized at all orbital phases
in terms of hard X-ray flux, spectral hardness, spin period history, pulsed
fraction and pulse shape profile. We also complemented the SuperAGILE
observations with the soft X-ray data of the RossiXTE/ASM. Our analysis shows a
clear orbital modulation of the spectral hardness, with peaks in correspondence
with the pre-periastron flare and near phase 0.25. The hardness peaks we found
could be related with the wind-plus-stream accretion model proposed in order to
explain the orbital light curve modulation of GX 301-2. Timing analysis of the
pulsar spin period shows that the secular trend of the about 680 s pulse period
is consistent with the previous observations, although there is evidence of a
slight decrease in the spin-down rate. The analysis of the hard X-ray pulsed
emission also showed a variable pulse shape profile as a function of the
orbital phase, with substructures detected near the passage at the periastron,
and a clear modulation of the pulsed fraction, which appears in turn strongly
anti-correlated with the source intensity.


  While metastability enhanced water-oxidation activity was experimentally
reported, the reason behind this effect is still unclear. We determine here,
using density functional theory calculations, oxygen evolution reaction
overpotentials for a variety of defective (001) surfaces of three different
perovskite materials. For all three, we find a large range of overpotentials
for different reaction sites including also overpotentials at the top of the
activity volcano. Assuming that these sites dominate the apparent catalytic
activity, this implies that a large number of geometrically different reaction
sites, as they occur when a catalyst is operated at the border of its stability
conditions, can lead to a strong enhancement of the apparent activity. This
also implies that a pre-treatment of the catalyst creating a variety of
different reactive sites could lead to superior catalytic activities for
thermodynamically stable materials.


  The CMS experiment will collect data from the proton-proton collisions
delivered by the Large Hadron Collider (LHC) at a centre-of-mass energy up to
14 TeV. The CMS trigger system is designed to cope with unprecedented
luminosities and LHC bunch-crossing rates up to 40 MHz. The unique CMS trigger
architecture only employs two trigger levels. The Level-1 trigger is
implemented using custom electronics, while the High Level Trigger (HLT) is
based on software algorithms running on a large cluster of commercial
processors, the Event Filter Farm. We present the major functionalities of the
CMS High Level Trigger system as of the starting of LHC beams operations in
September 2008. The validation of the HLT system in the online environment with
Monte Carlo simulated data and its commissioning during cosmic rays data taking
campaigns are discussed in detail. We conclude with the description of the HLT
operations with the first circulating LHC beams before the incident occurred
the 19th September 2008.


  We show that if $A\subset \{1,\ldots,N\}$ contains no non-trivial three-term
arithmetic progressions then $\lvert A\rvert \ll N/(\log N)^{1+c}$ for some
absolute constant $c>0$. In particular, this proves the first non-trivial case
of a conjecture of Erd\H{o}s on arithmetic progressions.


  We discuss three modes of oscillation of accretion disks around rotating
magnetized neutron stars which may explain the separations of the kilo-Hertz
quasi periodic oscillations (QPO) seen in low mass X-ray binaries. The
existence of these compressible, non-barotropic magnetohydrodynamic (MHD) modes
requires that there be a maximum in the angular velocity $\Omega_\phi(r)$ of
the accreting material larger than the angular velocity of the star $\Omega_*$,
and that the fluid is in approximately circular motion near this maximum rather
than moving rapidly towards the star or out of the disk plane into funnel
flows. Our MHD simulations show this type of flow and $\Omega_\phi(r)$ profile.
The first mode is a Rossby wave instability (RWI) mode which is radially
trapped in the vicinity of the maximum of a key function $g(r){\cal F}(r)$ at
$r_{R}$. The real part of the angular frequency of the mode is
$\omega_r=m\Omega_\phi(r_{R})$, where $m=1,2...$ is the azimuthal mode number.
The second mode, is a mode driven by the rotating, non-axisymmetric component
of the star's magnetic field. It has an angular frequency equal to the star's
angular rotation rate $\Omega_*$. This mode is strongly excited near the radius
of the Lindblad resonance which is slightly outside of $r_R$. The third mode
arises naturally from the interaction of flow perturbation with the rotating
non-axisymmetric component of the star's magnetic field. It has an angular
frequency $\Omega_*/2$. We suggest that the first mode with $m=1$ is associated
with the upper QPO frequency, $\nu_u$; that the nonlinear interaction of the
first and second modes gives the lower QPO frequency, $\nu_\ell =\nu_u-\nu_*$;
and that the nonlinear interaction of the first and third modes gives the lower
QPO frequency $\nu_\ell=\nu_u-\nu_*/2$, where $\nu_*=\Omega_*/2\pi$.


  We study the generic behavior of the method of successive approximations for
set-valued mappings in separable Banach spaces. We consider the case of
nonexpansive mappings with convex and compact point images and show that for
the typical such mapping and typical points of its domain the sequence of
successive approximations is unique and converges to a fixed point of the
mapping.


  We study magnetism in magnetically doped quantum dots as a function of
confining potential, particle numbers, temperature, and strength of Coulomb
interactions. We explore possibility of tailoring magnetism by controlling the
electron-electron Coulomb interaction, without changing the number of
particles. The interplay of strong Coulomb interactions and quantum confinement
leads to enhanced inhomogeneous magnetization which persist at higher
temperatures than in the non-interacting case. The temperature of the onset of
magnetization can be controlled by changing the number of particles as well as
by modifying the quantum confinement and the strength of Coulomb interactions.
We predict a series of electronic spin transitions which arise from the
competition between the many-body gap and magnetic thermal fluctuations.


  The equation of state of cold supra-nuclear-density matter, such as in
neutron stars, is an open question in astrophysics. A promising method for
constraining the neutron star equation of state is modelling pulse profiles of
thermonuclear X-ray burst oscillations from hotspots on accreting neutron
stars. The pulse profiles, constructed using spherical and oblate neutron star
models, are comparable to what would be observed by a next-generation X-ray
timing instrument like ASTROSAT, NICER, or LOFT. In this paper, we showcase the
use of an evolutionary optimization algorithm to fit pulse profiles to
determine the best-fit masses and radii. By fitting synthetic data, we assess
how well the optimization algorithm can recover the input parameters. Multiple
Poisson realizations of the synthetic pulse profiles, constructed with 1.6
million counts and no background, were fitted with the Ferret algorithm to
analyze both statistical and degeneracy-related uncertainty, and to explore how
the goodness-of-fit depends on the input parameters. For the regions of
parameter space sampled by our tests, the best-determined parameter is the
projected velocity of the spot along the observer's line-of-sight, with an
accuracy of $\le3$% compared to the true value and with $\le5$\% statistical
uncertainty. The next best-determined are the mass and radius; for a neutron
star with a spin frequency of 600\,Hz, the best-fit mass and radius are
accurate to $\le5$%, with respective uncertainties of $\le7$% and $\le10$%. The
accuracy and precision depend on the observer inclination and spot co-latitude,
with values of $\sim1$ % achievable in mass and radius if both the inclination
and co-latitude are > 60 degrees.


  Graph construction from a given set of edges is a data-intensive operator
that appears in social network analysis, ontology enabled databases, and, other
analytics processing. The operator represents an edge list to compressed sparse
row (CSR) representation (or sometimes in adjacency list, or as clustered
B-Tree storage). In this work, we show how to scale CSR construction to massive
scale on SSD-enabled supercomputers such as Gordon using pipelined processing.
We develop several abstraction and operations for external memory and parallel
edge list and integer array processing that are utilized towards building a
scalable algorithm for creating CSR representation.
  Our experiments demonstrate that this scheme is four to six times faster than
currently available implementation. Moreover, our scheme can handle up to 8
billion edges (128GB) by using external memory as compared to prior schemes
where performance degrades considerably for edge list size 26 million and
beyond.


  As an emerging business phenomenon especially in China, instant messaging
(IM) based social commerce is growing increasingly popular, attracting hundreds
of millions of users and is becoming one important way where people make
everyday purchases. Such platforms embed shopping experiences within IM apps,
e.g., WeChat, WhatsApp, where real-world friends post and recommend products
from the platforms in IM group chats and quite often form lasting
recommending/buying relationships. How and why do users engage in IM based
social commerce? Do such platforms create novel experiences that are distinct
from prior commerce? And do these platforms bring changes to user social lives
and relationships? To shed light on these questions, we launched a qualitative
study where we carried out semi-structured interviews on 12 instant messaging
based social commerce users in China. We showed that IM based social commerce:
1) enables more reachable, cost-reducing, and immersive user shopping
experience, 2) shapes user decision-making process in shopping through
pre-existing social relationship, mutual trust, shared identity, and community
norm, and 3) creates novel social interactions, which can contribute to new tie
formation while maintaining existing social relationships. We demonstrate that
all these unique aspects link closely to the characteristics of IM platforms,
as well as the coupling of user social and economic lives under such business
model. Our study provides important research and design implications for social
commerce, and decentralized, trusted socio-technical systems in general.


  Postulated by Pauli to explain the electronic structure of atoms and
molecules, the exclusion principle establishes an upper bound of 1 for the
fermionic natural occupation numbers $\{n_i\}$. A recent analysis of the pure
$N$-representability problem provides a wide set of inequalities for the
$\{n_i\}$, leading to constraints on these numbers. This has a strong potential
impact on reduced density matrix functional theory as we know it. In this work
we continue our study the nature of these inequalities for some atomic and
molecular systems. The results indicate that (quasi)saturation of some of them
leads to selection rules for the dominant configurations in configuration
interaction expansions, in favorable cases providing means for significantly
reducing their computational requirements.


  Learning to solve precision-based manipulation tasks from visual feedback
using Reinforcement Learning (RL) could drastically reduce the engineering
efforts required by traditional robot systems. However, performing fine-grained
motor control from visual inputs alone is challenging, especially with a static
third-person camera as often used in previous work. We propose a setting for
robotic manipulation in which the agent receives visual feedback from both a
third-person camera and an egocentric camera mounted on the robot's wrist.
While the third-person camera is static, the egocentric camera enables the
robot to actively control its vision to aid in precise manipulation. To fuse
visual information from both cameras effectively, we additionally propose to
use Transformers with a cross-view attention mechanism that models spatial
attention from one view to another (and vice-versa), and use the learned
features as input to an RL policy. Our method improves learning over strong
single-view and multi-view baselines, and successfully transfers to a set of
challenging manipulation tasks on a real robot with uncalibrated cameras, no
access to state information, and a high degree of task variability. In a hammer
manipulation task, our method succeeds in 75% of trials versus 38% and 13% for
multi-view and single-view baselines, respectively.


  For a given bi-continuous semigroup T on a Banach space X we define its
adjoint on an appropriate closed subspace X^o of the norm dual X'. Under some
abstract conditions this adjoint semigroup is again bi-continuous with respect
to the weak topology (X^o,X). An application is the following: For K a Polish
space we consider operator semigroups on the space C(K) of bounded, continuous
functions (endowed with the compact-open topology) and on the space M(K) of
bounded Baire measures (endowed with the weak*-topology). We show that
bi-continuous semigroups on M(K) are precisely those that are adjoints of a
bi-continuous semigroups on C(K). We also prove that the class of bi-continuous
semigroups on C(K) with respect to the compact-open topology coincides with the
class of equicontinuous semigroups with respect to the strict topology. In
general, if K is not Polish space this is not the case.


  We propose a new mechanism to generate the electroweak scale within the
framework of QCD, which is extended to include conformally invariant scalar
degrees of freedom belonging to a larger irreducible representation of
$SU(3)_c$. The electroweak symmetry breaking is triggered dynamically via the
Higgs portal by the condensation of the colored scalar field around 1 TeV. The
mass of the colored boson is restricted to be 350 GeV $\lesssim m_S\lesssim $ 3
TeV, with the upper bound obtained from perturbative renormalization group
evolution. This implies that the colored boson can be produced at LHC. If the
colored boson is electrically charged, the branching fraction of the Higgs
decaying into two photons can slightly increase, and moreover, it can be
produced at future linear colliders. Our idea of non-perturbative EW scale
generation can serve as a new starting point for more realistic model building
in solving the hierarchy problem.


  Recent conjectures of the c-theorem in four and higher dimensions have
suggested that the coefficient of the Euler characteristic in the trace anomaly
could measure the degrees of freedom in field theory and decrease along the
renormalization-group flow. We compute this quantity for free massless scalar,
fermion and antisymmetric tensor fields in any dimension, and analyse its
dependence on spin and space-time dimension. In the limit of large number of
dimensions, where the theories become semiclassical, we find that this quantity
does not approach the classical number of field components, but is enhanced for
spinful particles. This seemingly strange behaviour is found to be consistent
with known renormalization-group patterns and a specific c-theorem conjecture.


  We consider the Schr{\"o}dinger operator --$\Delta$ + V on the Euclidean
space with potential in the Lorentz space L^{n/2,1} and we find necessary and
sufficient conditions for zero to be a resonance or an eigenvalue. We consider
functions with gradient in L^2 and that verify the equation (--$\Delta$ +
V)$\psi$ = 0, namely the kernel of (--$\Delta$ + V) in the homogeneous Sobolev
space of order one. We prove that a function in this set is either in a weak
Lebesgue space or in L^2 , in the latter case we have a zero eigenfunction. The
set of eigenfunctions is the hyperplane of functions that are orthogonal to V,
furthermore we show that under some classic orthogonality conditions a zero
eigenfunction belongs to the weak Lebesgue space of order one or to L^1. We
study dimensions n $\ge$ 3 and in dimension three we generalize a result proved
by Beceanu.


  We describe algorithms for computing various functors for algebraic
D-modules, i.e. systems of linear partial differential equations with
polynomial coefficients. We will give algorithms for restriction, tensor
product, localization, and local cohomology groups for all degrees.


  Final state medium-induced gluon radiation in ultradense nuclear matter is
examined and shown to favor large angle emission when compared to vacuum
bremsstrahlung due to the suppression of collinear gluons. Perturbative
expression for the contribution of its hadronic fragments to the back-to-back
particle correlations is derived. It is found that in the limit of large jet
energy loss gluon radiation determines the yield and angular distribution of |
Delta phi | > Pi/2 di-hadrons to transverse momenta pT2 of the associated
particles. Clear transition from enhancement to suppression of the away-side
hadron correlations is established at moderate pT2 and its experimentally
accessible features are predicted versus the trigger particle momentum pT1.


  Multi-hop QA with annotated supporting facts, which is the task of reading
comprehension (RC) considering the interpretability of the answer, has been
extensively studied. In this study, we define an interpretable reading
comprehension (IRC) model as a pipeline model with the capability of predicting
unanswerable queries. The IRC model justifies the answer prediction by
establishing consistency between the predicted supporting facts and the actual
rationale for interpretability. The IRC model detects unanswerable questions,
instead of outputting the answer forcibly based on the insufficient
information, to ensure the reliability of the answer. We also propose an
end-to-end training method for the pipeline RC model. To evaluate the
interpretability and the reliability, we conducted the experiments considering
unanswerability in a multi-hop question for a given passage. We show that our
end-to-end trainable pipeline model outperformed a non-interpretable model on
our modified HotpotQA dataset. Experimental results also show that the IRC
model achieves comparable results to the previous non-interpretable models in
spite of the trade-off between prediction performance and interpretability.


  Kinetic Riemann simulations have been completed to explore particle heating
during guide field reconnection in the low-$\beta$ environment of the inner
heliosphere and the solar corona. The reconnection exhaust is bounded by two
rotational discontinuities (RD) and two slow shocks (SS) form within the
exhaust as in magnetohydrodynamic (MHD) models. At the RDs, ions are
accelerated by the magnetic field tension to drive the reconnection outflow as
well as flows in the out-of-plane direction. The out-of-plane flows stream
toward the midplane and meet to drive the SSs. The SSs differ greatly from
those in the MHD model. The turbulence at the shock fronts and both upstream
and downstream is weak so the shocks are laminar and produce little
dissipation. Downstream of the SSs the counterstreaming ion beams lead to
higher density, which leads to a positive potential between the SSs that acts
to confine the downstream electrons to maintain charge neutrality. The
potential accelerates electrons from upstream of the SSs to downstream region
and traps a small fraction but only modestly increases the downstream electron
temperature above the upstream value. In the low-$\beta$ limit the released
magnetic energy is split between bulk flow and ion heating with little energy
going to electrons. That the model does not produce strong electron heating nor
an energetic electron component suggests that other mechanisms, such as
multiple x-line reconnection, are required to explain energetic electron
production in large flares. The model can be tested with the expected data from
the Parker Solar Probe.


  We give ground-state representation for the fractional Laplacian with
Dirichlet condition on the half-line


  A key promise of machine learning is the ability to assist users with
personal tasks. Because the personal context required to make accurate
predictions is often sensitive, we require systems that protect privacy. A gold
standard privacy-preserving system will satisfy perfect secrecy, meaning that
interactions with the system provably reveal no private information. However,
privacy and quality appear to be in tension in existing systems for personal
tasks. Neural models typically require copious amounts of training to perform
well, while individual users typically hold a limited scale of data, so
federated learning (FL) systems propose to learn from the aggregate data of
multiple users. FL does not provide perfect secrecy, but rather practitioners
apply statistical notions of privacy -- i.e., the probability of learning
private information about a user should be reasonably low. The strength of the
privacy guarantee is governed by privacy parameters. Numerous privacy attacks
have been demonstrated on FL systems and it can be challenging to reason about
the appropriate privacy parameters for a privacy-sensitive use case. Therefore
our work proposes a simple baseline for FL, which both provides the stronger
perfect secrecy guarantee and does not require setting any privacy parameters.
We initiate the study of when and where an emerging tool in ML -- the
in-context learning abilities of recent pretrained models -- can be an
effective baseline alongside FL. We find in-context learning is competitive
with strong FL baselines on 6 of 7 popular benchmarks from the privacy
literature and a real-world case study, which is disjoint from the pretraining
data. We release our code here: https://github.com/simran-arora/focus


  We show that a simple rate-and-state theory accounts for most features of
both time-independent and time-dependent plasticity in a spatially
inhomogeneous situation, specifically, a circular hole in a large stressed
plate. Those features include linear viscoelastic flow at small applied
stresses, strain hardening at larger stresses, and a dynamic transition to
viscoplasticity at a yield stress. In the static limit, this theory predicts
the existence of a plastic zone near the hole for some but not all ranges of
parameters. The rate-and-state theory also predicts dynamic failure modes that
we believe may be relevant to fracture mechanics.


  We present an integrable Hamiltonian which describes the sinh-Gordon model on
the half line coupled to a non-linear oscillator at the boundary. We explain
how we apply Sklyanin's formalism to a dynamical reflection matrix to obtain
this model. This method can be applied to couple other integrable field
theories to dynamical systems at the boundary. We also show how to find the
dynamical solution of the quantum reflection equation corresponding to our
particular example.


  Critical infrastructure systems - for which high reliability and availability
are paramount - must operate securely. Attack trees (ATs) are hierarchical
diagrams that offer a flexible modelling language used to assess how systems
can be attacked. ATs are widely employed both in industry and academia but - in
spite of their popularity - little work has been done to give practitioners
instruments to formulate queries on ATs in an understandable yet powerful way.
In this paper we fill this gap by presenting ATM, a logic to express
quantitative security properties on ATs. ATM allows for the specification of
properties involved with security metrics that include "cost", "probability"
and "skill" and permits the formulation of insightful what-if scenarios. To
showcase its potential, we apply ATM to the case study of a CubeSAT, presenting
three different ways in which an attacker can compromise its availability. We
showcase property specification on the corresponding attack tree and we present
theory and algorithms - based on binary decision diagrams - to check properties
and compute metrics of ATM-formulae.


  After the recent discovery of a Higgs-like boson particle at the CERN
LHC-collider, it becomes more necessary than ever to prepare ourselves for
identifying its standard or non-standard nature. The Electroweak parameter
Delta r relating the values of the gauge boson masses [MW,MZ] and the Fermi
constant [G_F] is the traditional observable encoding high precision
information of the electroweak physics at the quantum level. In this work we
present a complete quantitative study of Delta r in the framework of the
general (unconstrained) Two-Higgs-Doublet Model (2HDM). First of all we report
on a systematic analysis of Delta r at the full one loop level in the general
2HDM, which to our knowledge was missing in the literature. Thereby we extract
a theoretical prediction for the mass of the W-boson in this model, taking MZ,
\alpha_{em} and G_F as experimental inputs. We find typical corrections leading
to mass shifts $\delta MW \sim 20-40 MeV$ which help to improve the agreement
with the experimentally measured value, in a degree no less significant than in
the MSSM case. In the second part of our study we extend our calculation beyond
the mere one-loop order. We devise an effective Lagrangian approach that
captures the dominant higher order quantum effects on delta rho (viz. that part
of Delta r describing the breaking of the approximate SU(2) custodial symmetry)
in the limit of large Higgs boson self-interactions. This limit constitutes a
telltale property of the general 2HDM which is unmatched by e.g. the MSSM. Our
conclusion is that the Electroweak precision program to be conducted at the
LHC, and maybe at a future linear collider, can nicely complement the direct
searches. Should these distinctive loop effects be eventually found they would
signal a smoking gun hinting at non-standard Higgs physics.


  Four types of global error for initial value problems are considered in a
common framework. They include classical forward error analysis and shadowing
error analysis together with extensions of both to rescaling of time. To
determine the amplification of the local error that bounds the global error we
present a linear analysis similar in spirit to condition number estimation for
linear systems of equations. We combine these ideas with techniques for
dimension reduction of differential equations via a boundary value formulation
of numerical inertial manifold reduction. These global error concepts are
exercised to illustrate their utility on the Lorenz equations and inertial
manifold reductions of the Kuramoto-Sivashinsky equation.


  In this paper we show a a proof by explicit bijections of the famous
Kirkman-Cayley formula for the number of dissections of a convex polygon. Our
starting point is the bijective correspondence between the set of nested sets
made by \(k\) subsets of \(\{1,2,...,n\}\) with cardinality \(\geq 2\) and the
set of partitions of \(\{1,2,...,n+k-1\}\) into \(k\) parts with cardinality
\(\geq 2\).


  The dynamical breaking of chiral symmetry in QCD is caused by nonperturbative
interactions on a scale rho ~ 0.3 fm, much smaller than the hadronic size R ~ 1
fm. These short-distance interactions influence the intrinsic transverse
momentum distributions of partons and their correlations at a low normalization
point. We study this phenomenon in an effective description of low-energy
dynamics based on chiral constituent quark degrees of freedom, which refers to
the large-N_c limit of QCD. The nucleon is obtained as a system of constituent
quarks and antiquarks moving in a self-consistent classical chiral field
(chiral quark-soliton model). The calculated distributions of constituent
quarks/antiquarks are matched with QCD partons at the scale rho^{-2}. The p_T
distribution of valence quarks is localized at p_T^2 ~ R^{-2} and roughly of
Gaussian shape. The sea quark distribution exhibits a would-be power-like tail
~1/p_T^2 extending up to the chiral symmetry-breaking scale. Such behavior is
seen in the flavor-singlet unpolarized and nonsinglet polarized sea. The
high-momentum tails are the result of short-range correlations between sea
quarks in the nucleon's light-cone wave function, analogous to NN correlations
in nuclei. The nucleon wave function contains correlated pairs of transverse
size rho << R with sigma- and pi-like quantum numbers, whose internal wave
functions become identical at p_T^2 ~ rho^{-2} (restoration of chiral
symmetry). These features are model-independent and represent an effect of
dynamical chiral symmetry breaking on the nucleon's partonic structure. Our
results have numerous implications for the P_T distributions of particles
produced in hard scattering processes. The nonperturbative parton correlations
predicted here could be observed in particle correlations between the current
and target fragmentation regions of DIS.


  We propose a novel class of count time series models alternative to the
classic Galton-Watson process with immigration (GWI) and Bernoulli offspring. A
new offspring mechanism is developed and its properties are explored. This
novel mechanism, called geometric thinning operator, is used to define a class
of modified GWI (MGWI) processes, which induces a certain non-linearity to the
models. We show that this non-linearity can produce better results in terms of
prediction when compared to the linear case commonly considered in the
literature. We explore both stationary and non-stationary versions of our MGWI
processes. Inference on the model parameters is addressed and the finite-sample
behavior of the estimators investigated through Monte Carlo simulations. Two
real data sets are analyzed to illustrate the stationary and non-stationary
cases and the gain of the non-linearity induced for our method over the
existing linear methods. A generalization of the geometric thinning operator
and an associated MGWI process are also proposed and motivated for dealing with
zero-inflated or zero-deflated count time series data.


  We study long-time spin diffusion of harmonically trapped lattice fermions in
one dimension. Combining thermodynamic Bethe ansatz approach and local density
approximation, we calculate spin current and spin diffusion coefficient driven
by the population imbalance. We find spin current is driven by susceptibility
effects rather than typical diffusion where magnetization would transport from
regions of high magnetization to low. As expected, spin transport is zero
through insulating regions and are only present in the metallic regions. In the
weak coupling limit, the local spin diffusion coefficient shows maxima at all
the insulating regions. Further, we estimate damping rate of diffusion modes in
the weak coupling limit within the lower metallic portion of the cloud. The
predicted spin current pattern can be probed via currently available
experimental techniques.


  A simply implemented activation function with even cubic nonlinearity is
introduced that increases the accuracy of neural networks without substantial
additional computational resources. This is partially enabled through an
apparent tradeoff between convergence and accuracy. The activation function
generalizes the standard RELU function by introducing additional degrees of
freedom through optimizable parameters that enable the degree of nonlinearity
to be adjusted. The associated accuracy enhancement is quantified in the
context of the MNIST digit data set through a comparison with standard
techniques.


  In this paper, we consider the impact of time delay by media on the control
of the disease. We set up a class of SISM epidemic model with the time delay
and the cumulative density of awareness caused by media. The sufficient
condition of global asymptotic stability of disease-free equilibrium is
approved. We get the global stability of the epidemic equilibrium and the
existence conditions of Hopf bifurcation. Numerical simulations are presented
to illustrate the analytical results. Finally, we analyze the influence of
parameters on the control of infectious disease by combining the data of H1N1.
By shortening the time of media lag, increasing transmission rate of media and
the implementation rate of the media project, the spread of disease will be
controlled effectively.


  Considering a generalised action for Einstein Maxwell theory in four
dimensions coupled to scalar and pseudo-scalar fields, the thermodynamic
properties of asymptotically flat black holes solutions in such a background
are investigated. Bekenstein-Hawking area-entropy law is verified for these
class of black holes. From the property of specific heat, it is shown that such
black holes can be stable for certain choice of the parameters like charge,
mass and the scalar vacuum expectation value. The possibility of a black hole
phase transition is discussed in this context.


  We consider content caching between a service provider and multiple
cache-enabled users, using the recently proposed modified coded caching scheme
(MCCS) that provides an improved delivery strategy for random user requests. We
develop the optimal cache placement solution for the MCCS with arbitrary cache
size by formulating the cache placement as an optimization problem to minimize
the average rate during the delivery phase under random user requests. Through
reformulation, we show that the problem is a linear programming problem. By
exploring the properties in the caching constraints, we obtain the optimal
cache placement solution in closed-form. We verify that the existing cache
placement scheme obtained at specific cache sizes is a special case of our
solution. Numerical studies show how the caching gain changes as the user
population increases, as a result of different cache placement patterns.


  After reviewing some basic relevant properties of stationary stochastic
processes (SSP), we discuss the properties of the so-called Harrison-Zeldovich
like spectra of mass density perturbations. These correlations are a
fundamental feature of all current standard cosmological models. Examining them
in real space we note they imply a "sub-poissonian" normalised variance in
spheres $\sigma_M^2(R) \sim R^{-4} \ln R$. In particular this latter behaviour
is at the limit of the most rapid decay ($\sim R^{-4}$) of this quantity
possible for any stochastic distribution (continuous or discrete). In a simple
classification of all SSP into three categories, we highlight with the name
``super-homogeneous'' the properties of the class to which models like this,
with $P(0)=0$, belong. In statistical physics language they are well described
as lattice or glass-like. We illustrate their properties through two simple
examples: (i) the ``shuffled'' lattice and the One Component Plasma at thermal
equilibrium.


  IceCube DeepCore, the existing low-energy extension of the IceCube Neutrino
Observatory, was designed to lower the neutrino detection energy threshold to
the GeV range. A new extension, called the IceCube Upgrade, will consist of
seven additional strings installed within the DeepCore fiducial volume. The new
modules will have spacings of about 20 m horizontally and 3 m vertically,
compared to about 40-70 m horizontally and 7 m vertically in DeepCore. It will
be deployed in the polar season of 2025/26. This additional hardware features
new types of optical modules with multi-PMT configurations, as well as
calibration devices. This upgrade will more than triple the number of PMT
channels with respect to current IceCube, and will significantly enhance its
capabilities in the GeV energy range. However, the increased channel count also
poses new computational challenges for the event simulation, selection, and
reconstruction. In this contribution we present updated oscillation
sensitivities based on the latest advancements in simulation, event selection,
and reconstruction techniques.


  Long-term prediction of multivariate time series is still an important but
challenging problem. The key to solve this problem is to capture the spatial
correlations at the same time, the spatio-temporal relationships at different
times and the long-term dependence of the temporal relationships between
different series. Attention-based recurrent neural networks (RNN) can
effectively represent the dynamic spatio-temporal relationships between
exogenous series and target series, but it only performs well in one-step time
prediction and short-term time prediction. In this paper, inspired by human
attention mechanism including the dual-stage two-phase (DSTP) model and the
influence mechanism of target information and non-target information, we
propose DSTP-based RNN (DSTP-RNN) and DSTP-RNN-2 respectively for long-term
time series prediction. Specifically, we first propose the DSTP-based structure
to enhance the spatial correlations between exogenous series. The first phase
produces violent but decentralized response weight, while the second phase
leads to stationary and concentrated response weight. Secondly, we employ
multiple attentions on target series to boost the long-term dependence.
Finally, we study the performance of deep spatial attention mechanism and
provide experiment and interpretation. Our methods outperform nine baseline
methods on four datasets in the fields of energy, finance, environment and
medicine, respectively.


  Variational formulations of time-dependent PDEs in space and time yield
$(d+1)$-dimensional problems to be solved numerically. This increases the
number of unknowns as well as the storage amount. On the other hand, this
approach enables adaptivity in space and time as well as model reduction w.r.t.
both type of variables. In this paper, we show that matrix oriented techniques
can significantly reduce the computational timings for solving the arising
linear systems outperforming both time-stepping schemes and other solvers.


  TextCNN, the convolutional neural network for text, is a useful deep learning
algorithm for sentence classification tasks such as sentiment analysis and
question classification. However, neural networks have long been known as black
boxes because interpreting them is a challenging task. Researchers have
developed several tools to understand a CNN for image classification by deep
visualization, but research about deep TextCNNs is still insufficient. In this
paper, we are trying to understand what a TextCNN learns on two classical NLP
datasets. Our work focuses on functions of different convolutional kernels and
correlations between convolutional kernels.


  We study the effects of a small density of holes, delta, on a square lattice
antiferromagnet undergoing a continuous transition from a Neel state to a
valence bond solid at a deconfined quantum critical point. We argue that at
non-zero delta, it is likely that the critical point broadens into a non-Fermi
liquid `holon metal' phase with fractionalized excitations. The holon metal
phase is flanked on both sides by Fermi liquid states with Fermi surfaces
enclosing the usual Luttinger area. However the electronic quasiparticles carry
distinct quantum numbers in the two Fermi liquid phases, and consequently the
limit of the ratio A_F/delta, as delta tends to zero (where A_F is the area of
a hole pocket) has a factor of 2 discontinuity across the quantum critical
point of the insulator. We demonstrate that the electronic spectrum at this
transition is described by the `boundary' critical theory of an impurity
coupled to a 2+1 dimensional conformal field theory. We compute the finite
temperature quantum-critical electronic spectra and show that they resemble
"Fermi arc" spectra seen in recent photoemission experiments on the pseudogap
phase of the cuprates.


  Quantum devices for sensing and computing applications require coherent
quantum systems which can be manipulated in a fast and robust way. Such quantum
control is typically achieved using external electric or magnetic fields which
drive the system's orbital or spin degrees of freedom. However, most of these
approaches require complex and unwieldy antenna or gate structures, and with
few exceptions are limited to the regime of weak driving. Here, we present a
novel approach to strongly and coherently drive a single electron spin in the
solid state using internal strain fields in an integrated quantum device.
Specifically, we study individual Nitrogen-Vacancy (NV) spins embedded in
diamond mechanical oscillators and exploit the intrinsic strain coupling
between spin and oscillator to strongly drive the spins. As hallmarks of the
strong driving regime, we directly observe the energy spectrum of the emerging
phonon-dressed states and employ our strong, continuous driving for enhancement
of the NV spin coherence time. Our results constitute a first step towards
strain-driven, integrated quantum devices and open new perspectives to
investigate unexplored regimes of strongly driven multi-level systems and to
study exotic spin dynamics in hybrid spin-oscillator devices.


  In this paper a novel method called Extended Two-Dimensional PCA (E2DPCA) is
proposed which is an extension to the original 2DPCA. We state that the
covariance matrix of 2DPCA is equivalent to the average of the main diagonal of
the covariance matrix of PCA. This implies that 2DPCA eliminates some
covariance information that can be useful for recognition. E2DPCA instead of
just using the main diagonal considers a radius of r diagonals around it and
expands the averaging so as to include the covariance information within those
diagonals. The parameter r unifies PCA and 2DPCA. r = 1 produces the covariance
of 2DPCA, r = n that of PCA. Hence, by controlling r it is possible to control
the trade-offs between recognition accuracy and energy compression (fewer
coefficients), and between training and recognition complexity. Experiments on
ORL face database show improvement in both recognition accuracy and recognition
time over the original 2DPCA.


  We present 36 new mid-eclipse times obtained between 2017 and 2023 using the
T100 telescope in Turkey, extending the time span of the $O-C$ diagram to 25
years. Once again, these new observations show significant deviations from
previous published models that were able to explain the observed variations of
the binary period. We investigate two plausible explanations for this
variability: the LTT effect due to the presence of one or two invisible
low-mass (planetary) companion(s) in distant circumbinary orbits; other
mechanisms, like e.g. the Applegate mechanism, associated with the magnetic
cycles of the M-dwarf component of the WD+dM binary. Through MCMC analyzes, we
demonstrate that the observed $O-C$ variability can be explained by the
presence of a planet with a minimum mass of $\sim9.5 M_J$. This circumbinary
planet orbits around the binary system with a period of about 19.5 years,
maintaining a stable orbit for a timeline of 10 Myr. By adding a weak LTT
signal from a secondary hypothetical planet we achieve statistically better
results. However, the orbits of the bodies in a two-planet system remain stable
only for a small range of the parameter space. The energy required to power the
Applegate and other Applegate-like mechanisms is too high to explain the period
variations observed. Thus, on the one hand there is substantial evidence
supporting the existence of a planet in the NN Ser system, but on the other
hand there are also compelling indications that cast doubt on the existence of
a second hypothetical planet.


  We consider dynamical scales in magnetized GRB outflows, using the solutions
to the Riemann problem of expanding arbitrarily magnetized outflows (Lyutikov
2010). For high ejecta magnetization, the behavior of the forward shock closely
resembles the so-called thick shell regime of the hydrodynamical expansion. The
exception is at small radii, where the motion of the forward shock is
determined by the dynamics of subsonic relativistic outflows. The behaviors of
the reverse shock is different in fluid and magnetized cases: in the latter
case, even for medium magnetization, sigma ~ 1, the reverse shock forms at
fairly large distances, and may never form in a wind-type external density
profile.


  We investigate both free energy and complexity of the spherical bipartite
spin glass model. We first prove a variational formula in high temperature for
the limiting free energy based on the well-known Crisanti-Sommers
representation of the mixed p-spin spherical model. Next, we show that the mean
number of local minima at low levels of energy is exponentially large in the
size of the system and we derive a bound on the location of the ground state
energy.


  We take the novel perspective to view data not as a probability distribution
but rather as a current. Primarily studied in the field of geometric measure
theory, $k$-currents are continuous linear functionals acting on compactly
supported smooth differential forms and can be understood as a generalized
notion of oriented $k$-dimensional manifold. By moving from distributions
(which are $0$-currents) to $k$-currents, we can explicitly orient the data by
attaching a $k$-dimensional tangent plane to each sample point. Based on the
flat metric which is a fundamental distance between currents, we derive
FlatGAN, a formulation in the spirit of generative adversarial networks but
generalized to $k$-currents. In our theoretical contribution we prove that the
flat metric between a parametrized current and a reference current is Lipschitz
continuous in the parameters. In experiments, we show that the proposed shift
to $k>0$ leads to interpretable and disentangled latent representations which
behave equivariantly to the specified oriented tangent planes.


  In this paper, we investigate the geometry of the moduli space of curves by
using the curvature properties of direct image sheaves of vector bundles. We
show that the moduli space $(M_g, \omega_{WP})$ of curves with genus $g>1$ has
dual-Nakano negative and semi-Nakano-negative curvature, and in particular, it
has non-positive Riemannain curvature operator and also non-positive complex
sectional curvature. As applications, we prove that any submanifold in $M_g$
which is totally geodesic in $A_g$ with finite volume must be a ball quotient.


  It is congruous with the quantum nature of the world to view the space-time
geometry as an emergent structure that shows classical features only at some
observational level. One can thus conceive the space-time manifold as a purely
theoretical arena, where quantum states are defined, with the additional
freedom of changing coordinates like any other symmetry. Observables, including
positions and distances, should then be described by suitable operators acting
on such quantum states. In principle, the top-down (canonical) quantisation of
Einstein-Hilbert gravity falls right into this picture, but is notoriously very
involved. The complication stems from allowing all the classical canonical
variables that appear in the (presumably) fundamental action to become quantum
observables acting on the "superspace" of all metrics, regardless of whether
they play any role in the description of a specific physical system. On can
instead revisit the more humble "minisuperspace" approach and choose the
gravitational observables not simply by imposing some symmetry, but motivated
by their proven relevance in the (classical) description of a given system. In
particular, this review focuses on compact, spherically symmetric, quantum
mechanical sources, in order to determine the probability they are black holes
rather than regular particles. The gravitational radius is therefore lifted to
the status of a quantum mechanical operator acting on the "horizon
wave-function", the latter being determined by the quantum state of the source.
This formalism is then applied to several sources with a mass around the
fundamental scale, which are viewed as natural candidates of quantum black
holes.