  Take $G$ a locally compact second-countable group, and $H$ a subgroup of $G$.
Choose $\mu$ a probability measure on $G$, such that the group spanned by its
support is dense in $G$, and consider the Markov chain on the homogeneous space
$X=G/H$ with transition probability $P_x=\mu *\delta_x$ for $x\in X$. Under
some conditions on $G$, $H$, $\mu$, we know that this Markov chain is either
everywhere recurrent or everywhere transient. A natural question is whether
such a dichotomy is universally true. The goal of this paper is to show it is
not, even when $G$ is finitely generated, through the explicit construction of
a counter example. The methods used include the study of stable laws,
Gnedenko-Kolmogorov's local limit theorem for stable laws, and the study of the
time of first return to equilibrium.


  We present the results of a survey, the deepest to date, for HI emission at
21 cm and OH emission at 18 cm (lines at 1612, 1665, 1667 and 1720 MHz) in the
direction towards the Galactic globular clusters M 15, M 2, NGC 6934, NGC 7006
and Pal 13. The aim is to measure the amount of hydrogen in the intra-cluster
medium (ICM), and to find OH masers in the circumstellar envelopes of globular
cluster red giants. We present a tentative detection of 0.3 Msun of neutral
hydrogen in M 15 and possible detections of neutral hydrogen in M 2 and Pal 13.
We derive upper limits to the neutral hydrogen content of NGC 6934 and NGC
7006. No OH emission is detected. We also present deep HI data of the northern
tip of the Magellanic Stream behind Pal 13.


  We apply the 3-dimensional radiative transport code Wind3D to 3D hydrodynamic
models of Corotating Interaction Regions to fit the detailed variability of
Discrete Absorption Components observed in Si IV UV resonance lines of HD 64760
(B0.5 Ib). We discuss important effects of the hydrodynamic input parameters on
these large-scale equatorial wind structures that determine the detailed
morphology of the DACs computed with 3D transfer. The best fit model reveals
that the CIR in HD 64760 is produced by a source at the base of the wind that
lags behind the stellar surface rotation. The non-corotating coherent wind
structure is an extended density wave produced by a local increase of only 0.6
% in the smooth symmetric wind mass-loss rate.


  Understanding the evolution towards thermal equilibrium of an isolated
quantum system is at the foundation of statistical mechanics and a subject of
interest in such diverse areas as cold atom physics or the quantum mechanics of
black holes. Since a pure state can never evolve into a thermal density matrix,
the Eigenstate Thermalization Hypothesis (ETH) has been put forward by Deutsch
and Srednicki as a way to explain this apparent thermalization, similarly to
what the ergodic theorem does in classical mechanics. In this paper this
hypothesis is tested numerically. First, it is observed that thermalization
happens in a subspace of states (the Krylov subspace) with dimension much
smaller than that of the total Hilbert space. We check numerically the validity
of ETH in such a subspace, for a system of hard core bosons on a
two-dimensional lattice. We then discuss how well the eigenstates of the
Hamiltonian projected on the Krylov subspace represent the true eigenstates.
This discussion is aided by bringing the projected Hamiltonian to the
tridiagonal form and interpreting it as an Anderson localization problem for a
finite one-dimensional chain. We also consider thermalization of a subsystem
and argue that generation of a large entanglement entropy can lead to a thermal
density matrix for the subsystem well before the whole system thermalizes.
Finally, we comment on possible implications of ETH in quantum gravity.


  The $Q^2$ dependence of the ratios of nuclear structure functions $F_2^A$ is
studied by performing QCD evolution of nuclear parton distribution functions.
The log $Q^2$ slope of these ratios is very sensitive to the nuclear gluon
distribution function. Taking different parametrizations, we show that the NMC
data on the $Q^2$ dependence of $F_2^{\rm Sn}/F_2^{\rm C}$ rule out the case
where nuclear shadowing (suppression) of gluons at $x\sim 0.01$ is much larger
than the shadowing observed in the ratio $F_2^A/F_2^{\rm D}$. We also take into
account modifications to the DGLAP evolution by including gluon fusion terms
and see that the effect is small at present energies, and, in any case, a
strong gluon shadowing is not favored. The region studied ($x \sim 0.01$) is
the most relevant for RHIC multiplicities.


  Constituency parsing plays a fundamental role in advancing natural language
processing (NLP) tasks. However, training an automatic syntactic analysis
system for ancient languages solely relying on annotated parse data is a
formidable task due to the inherent challenges in building treebanks for such
languages. It demands extensive linguistic expertise, leading to a scarcity of
available resources. To overcome this hurdle, cross-lingual transfer techniques
which require minimal or even no annotated data for low-resource target
languages offer a promising solution. In this study, we focus on building a
constituency parser for $\mathbf{M}$iddle $\mathbf{H}$igh $\mathbf{G}$erman
($\mathbf{MHG}$) under realistic conditions, where no annotated MHG treebank is
available for training. In our approach, we leverage the linguistic continuity
and structural similarity between MHG and $\mathbf{M}$odern $\mathbf{G}$erman
($\mathbf{MG}$), along with the abundance of MG treebank resources.
Specifically, by employing the $\mathit{delexicalization}$ method, we train a
constituency parser on MG parse datasets and perform cross-lingual transfer to
MHG parsing. Our delexicalized constituency parser demonstrates remarkable
performance on the MHG test set, achieving an F1-score of 67.3%. It outperforms
the best zero-shot cross-lingual baseline by a margin of 28.6% points. These
encouraging results underscore the practicality and potential for automatic
syntactic analysis in other ancient languages that face similar challenges as
MHG.


  In this chapter, we describe our question answering system, which was the
winning system at the Human-Computer Question Answering (HCQA) Competition at
the Thirty-first Annual Conference on Neural Information Processing Systems
(NIPS). The competition requires participants to address a factoid question
answering task referred to as quiz bowl. To address this task, we use two novel
neural network models and combine these models with conventional information
retrieval models using a supervised machine learning model. Our system achieved
the best performance among the systems submitted in the competition and won a
match against six top human quiz experts by a wide margin.


  An updated analysis of New Physics violating Lepton Flavour Universality, by
using the Standard Model Effective Field Lagrangian with semileptonic dimension
six operators at $\Lambda = 1\,\mathrm{TeV}$ is presented. We perform a global
fit, by discussing the relevance of the mixing in the first generation. We use
for the first time in this context a Montecarlo analysis to extract the
confidence intervals and correlations between observables. Our results show
that machine learning, made jointly with the SHAP values, constitute a suitable
strategy to use in this kind of analysis.


  We develop a model that describes the gamma p -> K^+ pi Sigma reaction in the
Lambda(1405) region. The model consists of gauge invariant photo-production
mechanisms, and the chiral unitary model that gives the rescattering amplitudes
where Lambda(1405) is contained. The model also contains phenomenological
parameters, associated with short-range dynamics, to be used in fitting data.
We successfully fit recent CLAS data for the pi-Sigma invariant mass
distributions (line-shape) in the gamma p -> K^+ pi Sigma reaction for all the
charge states. We find that the higher mass pole for Lambda(1405) of the chiral
unitary model plays an important role in the reaction. We also find the
non-resonant background contribution is not negligible, and its sizable effect
shifts the Lambda(1405) peak position by several MeV. This work sets a starting
point for a fuller analysis in which line-shape as well as K^+ angular
distribution data are simultaneously analyzed for extracting Lambda(1405)
pole(s).


  Pinning down the total neutrino mass and the dark energy equation of state is
a key aim for upcoming galaxy surveys. Weak lensing is a unique probe of the
total matter distribution whose non-Gaussian statistics can be quantified by
the one-point probability distribution function (PDF) of the lensing
convergence. We calculate the convergence PDF on mildly non-linear scales from
first principles using large-deviation statistics, accounting for dark energy
and the total neutrino mass. For the first time, we comprehensively validate
the cosmology-dependence of the convergence PDF model against large suites of
simulated lensing maps, demonstrating its percent-level precision and accuracy.
We show that fast simulation codes can provide highly accurate covariance
matrices, which can be combined with the theoretical PDF model to perform
forecasts and eliminate the need for relying on expensive N-body simulations.
Our theoretical model allows us to perform the first forecast for the
convergence PDF that varies the full set of $\Lambda$CDM parameters. Our Fisher
forecasts establish that the constraining power of the convergence PDF compares
favourably to the two-point correlation function for a Euclid-like survey area
at a single source redshift. When combined with a CMB prior from Planck, the
PDF constrains both the neutrino mass $M_\nu$ and the dark energy equation of
state $w_0$ more strongly than the two-point correlation function.


  We discuss the application of the method of the gaugeless Hamiltonian
reduction to general relativity. This method is based on explicit resolving the
global part of the energy constraint and on identification of one of the metric
components with the evolution parameter of the equivalent unconstrained
(reduced) system. The Hamiltonian reduction reveals a possibility to unify
General Relativity and Standard Model of strong and electro-weak interactions
with the modulus of the Higgs field identified with the product of the
determinant of 3D metric and the Planck constant. We give the geometrical
foundation of the scalar field, derive and discuss experimental consequences of
this unified model: the cosmic Higgs vacuum, the Hoyle-Narlikar cosmology, a
$\sigma$-model version of Standard Model without Higgs particle excitations and
inflation.


  We use assembly maps to study $\mathbf{TC}(\mathbb{A}[G];p)$, the topological
cyclic homology at a prime $p$ of the group algebra of a discrete group $G$
with coefficients in a connective ring spectrum $\mathbb{A}$. For any finite
group, we prove that the assembly map for the family of cyclic subgroups is an
isomorphism on homotopy groups. For infinite groups, we establish
pro-isomorphism, (split) injectivity, and rational injectivity results, as well
as counterexamples to injectivity and surjectivity. In particular, for
hyperbolic groups and for virtually finitely generated abelian groups, we show
that the assembly map for the family of virtually cyclic subgroups is injective
but in general not surjective.


  Random matrix theory is used to assess the significance of weak correlations
and is well established for Gaussian statistics. However, many complex systems,
with stock markets as a prominent example, exhibit statistics with power-law
tails, that can be modelled with Levy stable distributions. We review
comprehensively the derivation of an analytical expression for the spectra of
covariance matrices approximated by free Levy stable random variables and
validate it by Monte Carlo simulation.


  Data dimensionality informs us about data complexity and sets limit on the
structure of successful signal processing pipelines. In this work we revisit
and improve the manifold-adaptive Farahmand-Szepesv\'ari-Audibert (FSA)
dimension estimator, making it one of the best nearest neighbor-based dimension
estimators available. We compute the probability density function of local FSA
estimates, if the local manifold density is uniform. Based on the probability
density function, we propose to use the median of local estimates as a basic
global measure of intrinsic dimensionality, and we demonstrate the advantages
of this asymptotically unbiased estimator over the previously proposed
statistics: the mode and the mean. Additionally, from the probability density
function, we derive the maximum likelihood formula for global intrinsic
dimensionality, if i.i.d. holds. We tackle edge and finite-sample effects with
an exponential correction formula, calibrated on hypercube datasets. We compare
the performance of the corrected-median-FSA estimator with kNN estimators:
maximum likelihood (ML, Levina-Bickel) and two implementations of DANCo (R and
matlab). We show that corrected-median-FSA estimator beats the ML estimator and
it is on equal footing with DANCo for standard synthetic benchmarks according
to mean percentage error and error rate metrics. With the median-FSA algorithm,
we reveal diverse changes in the neural dynamics while resting state and during
epileptic seizures. We identify brain areas with lower-dimensional dynamics
that are possible causal sources and candidates for being seizure onset zones.


  As language models (LMs) scale, they develop many novel behaviors, good and
bad, exacerbating the need to evaluate how they behave. Prior work creates
evaluations with crowdwork (which is time-consuming and expensive) or existing
data sources (which are not always available). Here, we automatically generate
evaluations with LMs. We explore approaches with varying amounts of human
effort, from instructing LMs to write yes/no questions to making complex
Winogender schemas with multiple stages of LM-based generation and filtering.
Crowdworkers rate the examples as highly relevant and agree with 90-100% of
labels, sometimes more so than corresponding human-written datasets. We
generate 154 datasets and discover new cases of inverse scaling where LMs get
worse with size. Larger LMs repeat back a dialog user's preferred answer
("sycophancy") and express greater desire to pursue concerning goals like
resource acquisition and goal preservation. We also find some of the first
examples of inverse scaling in RL from Human Feedback (RLHF), where more RLHF
makes LMs worse. For example, RLHF makes LMs express stronger political views
(on gun rights and immigration) and a greater desire to avoid shut down.
Overall, LM-written evaluations are high-quality and let us quickly discover
many novel LM behaviors.


  One method of constructing $(a^2+1, 2,a, 1)$-SEDFs (i.e., strong external
difference families) in $\mathbb{Z}_{a^2+1}$ makes use of $\alpha$-valuations
of complete bipartite graphs $K_{a,a}$. We explore this approach and we provide
a classification theorem which shows that all such $\alpha$-valuations can be
constructed recursively via a sequence of ``blow-up'' operations. We also
enumerate all $(a^2+1, 2,a, 1)$-SEDFs in $\mathbb{Z}_{a^2+1}$ for $a \leq 14$
and we show that all these SEDFs are equivalent to $\alpha$-valuations via
affine transformations. Whether this holds for all $a > 14$ as well is an
interesting open problem. We also study SEDFs in dihedral groups, where we show
that two known constructions are equivalent.


  For graphs $G$ and $H$, an $H$-coloring of $G$ is a map from the vertices of
$G$ to the vertices of $H$ that preserves edge adjacency. We consider the
following extremal enumerative question: for a given $H$, which connected
$n$-vertex graph with minimum degree $\delta$ maximizes the number of
$H$-colorings? We show that for non-regular $H$ and sufficiently large $n$, the
complete bipartite graph $K_{\delta,n-\delta}$ is the unique maximizer. As a
corollary, for non-regular $H$ and sufficiently large $n$ the graph $K_{k,n-k}$
is the unique $k$-connected graph that maximizes the number of $H$-colorings
among all $k$-connected graphs. Finally, we show that this conclusion does not
hold for all regular $H$ by exhibiting a connected $n$-vertex graph with
minimum degree $\delta$ which has more $K_{q}$-colorings (for sufficiently
large $q$ and $n$) than $K_{\delta,n-\delta}$.


  We are witnessing a heightened surge in remote privacy attacks on laptop
computers. These attacks often exploit malware to remotely gain access to
webcams and microphones in order to spy on the victim users. While webcam
attacks are somewhat defended with widely available commercial webcam privacy
covers, unfortunately, there are no adequate solutions to thwart the attacks on
mics despite recent industry efforts. As a first step towards defending against
such attacks on laptop mics, we propose TickTock, a novel mic on/off status
detection system. To achieve this, TickTock externally probes the
electromagnetic (EM) emanations that stem from the connectors and cables of the
laptop circuitry carrying mic clock signals. This is possible because the mic
clock signals are only input during the mic recording state, causing resulting
emanations. We design and implement a proof-of-concept system to demonstrate
TickTock's feasibility. Furthermore, we comprehensively evaluate TickTock on a
total of 30 popular laptops executing a variety of applications to successfully
detect mic status in 27 laptops. Of these, TickTock consistently identifies mic
recording with high true positive and negative rates.


  We use some classical estimates for polynomial roots to provide several
irreducibility criteria for pairs of polynomials with integer coefficients
whose resultant is a prime number, and for some of their linear combinations.
Similar results are then obtained for multivariate polynomials over an
arbitrary field, in a non-Archimedean setting.


  Sparse approximations using highly over-complete dictionaries is a
state-of-the-art tool for many imaging applications including denoising,
super-resolution, compressive sensing, light-field analysis, and object
recognition. Unfortunately, the applicability of such methods is severely
hampered by the computational burden of sparse approximation: these algorithms
are linear or super-linear in both the data dimensionality and size of the
dictionary. We propose a framework for learning the hierarchical structure of
over-complete dictionaries that enables fast computation of sparse
representations. Our method builds on tree-based strategies for nearest
neighbor matching, and presents domain-specific enhancements that are highly
efficient for the analysis of image patches. Contrary to most popular methods
for building spatial data structures, out methods rely on shallow, balanced
trees with relatively few layers. We show an extensive array of experiments on
several applications such as image denoising/superresolution, compressive
video/light-field sensing where we practically achieve 100-1000x speedup (with
a less than 1dB loss in accuracy).


  The ideals of the Lie algebras of unitriangular polynomial derivations are
classified. An isomorphism criterion is given for the Lie factor algebras of
the Lie algebras of unitriangular polynomial derivations.


  In this work, we analytically investigate a multi-component system for
describing phase separation and damage processes in solids. The model consists
of a parabolic diffusion equation of fourth order for the concentration coupled
with an elliptic system with material dependent coefficients for the strain
tensor and a doubly nonlinear differential inclusion for the damage function.
The main aim of this paper is to show existence of weak solutions for the
introduced model, where, in contrast to existing damage models in the
literature, different elastic properties of damaged and undamaged material are
regarded. To prove existence of weak solutions for the introduced model, we
start with an approximation system. Then, by passing to the limit, existence
results of weak solutions for the proposed model are obtained via suitable
variational techniques.


The authors are not satisfied about the analysis.


  This paper presents LE3D; a novel data drift detection framework for
preserving data integrity and confidentiality. LE3D is a generalisable platform
for evaluating novel drift detection mechanisms within the Internet of Things
(IoT) sensor deployments. Our framework operates in a distributed manner,
preserving data privacy while still being adaptable to new sensors with minimal
online reconfiguration. Our framework currently supports multiple drift
estimators for time-series IoT data and can easily be extended to accommodate
new data types and drift detection mechanisms. This demo will illustrate the
functionality of LE3D under a real-world-like scenario.


  In Ultra Relativistic Heavy-Ion Collisions (URHIC's) the light vector mesons
play a crucial role in the description of hadronic interactions in a
non-pertrubative QCD region. In this region efective hadron models use
composite hadrons and mesons as field carriers instead of quarks and gluons.
This theoretical review article tries to give a short way of understanding the
underlying theory that we have for the conversion of vector mesons into photons
together with the so-called Vector Dominance Model (VDM) and the
electromagnetic form factors.


  The aim of this paper is to present examples of Kahler holomorphically
pseudosymmetric metrics on the projective space CP^n.


  There has been significant interest in studying the asymptotics of certain
generalised moments, called the moments of moments, of characteristic
polynomials of random Haar-distributed unitary and symplectic matrices, as the
matrix size $N$ goes to infinity. These quantities depend on two parameters $k$
and $q$ and when both of them are positive integers it has been shown that
these moments are in fact polynomials in the matrix size $N$. In this paper we
classify the integer roots of these polynomials and moreover prove that the
polynomials themselves satisfy a certain symmetry property. This confirms some
predictions from the thesis of Bailey. The proof uses the Ehrhart-Macdonald
reciprocity for rational convex polytopes and certain bijections between
lattice points in some polytopes.


  Massive galaxies are expected to grow through different transformative
evolutionary phases where high-redshift starburst galaxies and quasars are
examples of such phases. The physical mechanisms driving these phases include
companion galaxy interactions, active galactic nuclei feedback, and magnetic
fields. Our aim is to characterize the physical properties and the environment
of the submillimeter galaxy AzTEC-3 at z = 5.3 and the lensed quasar BRI
0952-0115 at z = 4.4, to set a limit on the polarization properties, as well as
placing both in the broader context of galaxy evolution. We used full
polarization, sub-arcsecond-resolution, ALMA band-7 observations of both BRI
0952-0115 and AzTEC-3 and detect [CII] line emission towards both galaxies,
along with companions in each field. We present an updated gravitational
lensing model for BRI 0952-0115. We present infrared luminosities,
star-formation rates, and [CII] line to infrared luminosity ratios for each
source. The [CII] emission line profile for both BRI 0952-0115 and AzTEC-3
exhibit a broad, complex morphology, indicating the possible presence of
outflows. We present evidence of a 'gas bridge' between AzTEC-3 and a companion
source. Using a simple dynamical mass estimate for the sources, we suggest that
both systems are undergoing minor or major mergers. No polarization is detected
for the [CII], placing an upper limit below that of theoretical predictions.
Our results show that high-velocity wings are detected, indicating possible
signs of massive outflows; however, the presence of companion galaxies can
affect the final interpretation. Furthermore, the results provide additional
evidence in support of the hypothesis that massive galaxies form in overdense
regions, growing through interactions. Finally, strong, ordered magnetic fields
are unlikely to exist at the kiloparsec scale in the two studied sources.


  Human {\alpha}-synuclein (SNCA) is a 140-amino-acid protein belonging to the
three-member synuclein family. It has been extensively studied due to its
misfolding/aggregation in and genetic linkage to neurodegenerative diseases,
especially Parkinson's disease (PD). To better understand its biology, models
of SNCA toxicity have been developed in budding yeast over the past decade,
which have yielded insights into the protein's modes of action in specific
pathways and potential therapeutic targets. Given that the synuclein gene
family is not present in yeast, an extensive homology search was undertaken to
determine if any yeast protein may possess structural homology to SNCA and
whose native biology may shed more light on SNCA's pathomechanism in
eukaryotes. We identified Zeo1, a membrane-associated protein involved in the
cell wall integrity (CWI) pathway, as a candidate structural homolog. We show
that Zeo1 overexpression is toxic in yeast and, similar to SNCA, localizes to
lipid membranes. A number of biochemical similarities between Zeo1 and SNCA
also become apparent in light of this potential structural connection.
Moreover, the yeast PKC1 gene, a kinase acting as a downstream signaling hub in
the CWI pathway, rescues both SNCA- and Zeo1-induced toxicities. Using the same
homology search methods that identified Zeo1, we show that Pkc1 has a hybrid
structural similarity to PINK1 and PARIS, two mitochondrial PD-implicated
proteins not generally linked directly to synuclein-specific pathobiology.
Overall, this proof-of-concept study shows the potential utility of hitherto
uncharacterized cross-species structural homologs, identified using comparative
proteome-wide structure prediction algorithms, in shedding light on abstruse
connections among disease-relevant proteins.


  The multidimensional relativistic hydrodynamical code GENESIS has been used
to obtain first results of {\it 3D} simulations of relativistic jets. We have
studied the influence of a slight perturbation of the injection velocity field
on the morphodynamics of otherwise axisymmetric relativistic jets.


  An evolutionary process of the fast magnetic reconnection in ``free space''
which is free from any influence of outer circumstance has been studied
semi-analytically, and a self-similarly expanding solution has been obtained.
The semi-analytic solution is consistent with the results of our numerical
simulations performed in our previous paper (see Nitta et al. 2001). This
semi-analytic study confirms the existence of self-similar growth. On the other
hand, the numerical study by time dependent computer simulation clarifies the
stability of the self-similar growth with respect to any MHD mode. These
results confirm the stable self-similar evolution of the fast magnetic
reconnection system.


  Sabeth Verpoorte is professor at the University of Groningen. In this
contribution she describes the development of a microfluidic incubation system
for drug metabolism studies using a "top-down" precision-cut tissue slice
model. She also outlines a fundamental particle separation concept, which
relies on the generation of controlled bi-directional flow in microchannels
having variable cross-sectional dimensions, by opposing pressure-driven and
electrokinetic flows.


  This paper shows that decision trees constructed with Classification and
Regression Trees (CART) and C4.5 methodology are consistent for regression and
classification tasks, even when the number of predictor variables grows
sub-exponentially with the sample size, under natural 0-norm and 1-norm
sparsity constraints. The theory applies to a wide range of models, including
(ordinary or logistic) additive regression models with component functions that
are continuous, of bounded variation, or, more generally, Borel measurable.
Consistency holds for arbitrary joint distributions of the predictor variables,
thereby accommodating continuous, discrete, and/or dependent data. Finally, we
show that these qualitative properties of individual trees are inherited by
Breiman's random forests. A key step in the analysis is the establishment of an
oracle inequality, which allows for a precise characterization of the
goodness-of-fit and complexity tradeoff for a mis-specified model.


  Gradient descent yields zero training loss in polynomial time for deep neural
networks despite non-convex nature of the objective function. The behavior of
network in the infinite width limit trained by gradient descent can be
described by the Neural Tangent Kernel (NTK) introduced in
\cite{Jacot2018Neural}. In this paper, we study dynamics of the NTK for finite
width Deep Residual Network (ResNet) using the neural tangent hierarchy (NTH)
proposed in \cite{Huang2019Dynamics}. For a ResNet with smooth and Lipschitz
activation function, we reduce the requirement on the layer width $m$ with
respect to the number of training samples $n$ from quartic to cubic. Our
analysis suggests strongly that the particular skip-connection structure of
ResNet is the main reason for its triumph over fully-connected network.


  Nonequilibrium systems exchange the energy with an environment in the form of
work and heat. The work done on a system obeys the fluctuation theorem, while
the dissipated heat which differs from the work by the internal energy change
does not. We derive the modified fluctuation relation for the heat in the
overdamped Langevin system. It shows that mutual correlations among the work,
the heat, and the internal energy change are responsible for the different
fluctuation property of the work and the heat. The mutual correlation is
investigated in detail in a two-dimensional linear diffusion system. We develop
an analytic method which allows one to calculate the large deviation function
for the joint probability distributions. We find that the heat and the internal
energy change have a negative correlation, which explains the reason for the
breakdown of the fluctuation theorem for the heat.


  Magnetic skyrmion motion induced by an electric current has drawn much
interest because of its application potential in next-generation magnetic
memory devices. Recently, unidirectional skyrmion motion driven by an
oscillating magnetic field was also demonstrated on large (20 micrometer)
bubble domains with skyrmion topology. At smaller length scale which is more
relevant to high-density memory devices, we here show by numerical simulation
that a skyrmion of a few tens of nanometers could also be driven by
high-frequency field oscillations but with the motion direction different from
the tilted oscillating field direction. We found that high-frequency field for
small size skyrmions could excite skyrmion resonant modes and that a
combination of different modes would result in the final skyrmion motion with a
helical trajectory. Because this helical motion depends on the frequency of the
field, we can control both the speed and the direction of the skyrmion motion,
which is a distinguishable characteristic compared with other methods.


  Certain real parameters of a Hamiltonian, when continued to complex values,
can give rise to singular points called exceptional points ($EP$'s), where two
or more eigenvalues coincide and the complexified Hamiltonian becomes
non-diagonalizable. We show that for a generic $d$-dimensional topological
superconductor / superfluid with a chiral symmetry, one can find $EP$'s
associated with the chiral zero energy Majorana fermions bound to a topological
defect / edge. Exploiting the chiral symmetry, we propose a formula for
counting the number ($n$) of such chiral zero modes. We also establish the
connection of these solutions to the Majorana fermion wavefunctions in the
position space. The imaginary parts of these momenta are related to the
exponential decay of the wavefunctions localized at the defect / edge, and
hence their changes of signs at a topological phase transition point signal the
appearance or disappearance of chiral Majorana zero modes. Our analysis thus
explains why topological invariants like the winding number, defined for the
corresponding Hamiltonian in the momentum space for a defectless system with
periodic boundary conditions, capture the number of admissible Majorana fermion
solutions for the position space Hamiltonian with defect(s). Finally, we
conclude that $EP$'s cannot be associated with the Majorana fermion
wavefunctions for systems with no chiral symmetry, although one can use our
formula for counting $n$, using complex $k$ solutions where the determinant of
the corresponding BdG Hamiltonian vanishes.


  Retrieval and ranking models are the backbone of many applications such as
web search, open domain QA, or text-based recommender systems. The latency of
neural ranking models at query time is largely dependent on the architecture
and deliberate choices by their designers to trade-off effectiveness for higher
efficiency. This focus on low query latency of a rising number of efficient
ranking architectures make them feasible for production deployment. In machine
learning an increasingly common approach to close the effectiveness gap of more
efficient models is to apply knowledge distillation from a large teacher model
to a smaller student model. We find that different ranking architectures tend
to produce output scores in different magnitudes. Based on this finding, we
propose a cross-architecture training procedure with a margin focused loss
(Margin-MSE), that adapts knowledge distillation to the varying score output
distributions of different BERT and non-BERT passage ranking architectures. We
apply the teachable information as additional fine-grained labels to existing
training triples of the MSMARCO-Passage collection. We evaluate our procedure
of distilling knowledge from state-of-the-art concatenated BERT models to four
different efficient architectures (TK, ColBERT, PreTT, and a BERT CLS dot
product model). We show that across our evaluated architectures our Margin-MSE
knowledge distillation significantly improves re-ranking effectiveness without
compromising their efficiency. Additionally, we show our general distillation
method to improve nearest neighbor based index retrieval with the BERT dot
product model, offering competitive results with specialized and much more
costly training methods. To benefit the community, we publish the teacher-score
training files in a ready-to-use package.


  We perform classical molecular dynamics simulations to investigate the
enhancement of the mass sensitivity and resonant frequency of graphene
nanomechanical resonators that is achieved by driving them into the nonlinear
oscillation regime. The mass sensitivity as measured by the resonant frequency
shift is found to triple if the actuation energy is about 2.5 times the initial
kinetic energy of the nanoresonator. The mechanism underlying the enhanced mass
sensitivity is found to be the effective strain that is induced in the
nanoresonator due to the nonlinear oscillations, where we obtain an analytic
relationship between the induced effective strain and the actuation energy that
is applied to the graphene nanoresonator. An important implication of this work
is that there is no need for experimentalists to apply tensile strain to the
resonators before actuation in order to enhance the mass sensitivity. Instead,
enhanced mass sensitivity can be obtained by the far simpler technique of
actuating nonlinear oscillations of an existing graphene nanoresonator.


  We investigate chaotic scattering on an attractive step potential with a
quadrupolar deformation. The phase space features of the bound billiard are
studied by using the notion of symmetry lines to find periodic orbits. We show
that the scattering dynamics is intimately linked to structures in the bound
billiard (infinite potential wall) phase space. The existence of preferred
scattering directions is shown to be a consequence of large scale features of
the phase space such as the period-two orbits. Self-similarity in the
scattering functions is directly linked to unstable periodic orbits of the
bound phase space. The main observations and methodology are applicable to
concave billiards in general.


  We show that the Deep Underground Neutrino Experiment (DUNE), with
significant but feasible new efforts, has the potential to deliver
world-leading results in solar neutrinos. With a 100 kton-year exposure, DUNE
could detect $\gtrsim 10^5$ signal events above 5 MeV electron energy. Separate
precision measurements of neutrino-mixing parameters and the $^8$B flux could
be made using two detection channels ($\nu_e + \, ^{40}$Ar and
$\nu_{e,\mu,\tau} + e^-$) and the day-night effect ($> 10 \sigma$). New
particle physics may be revealed through the comparison of solar neutrinos
(with matter effects) and reactor neutrinos (without), which is discrepant by
$\sim 2 \sigma$ (and could become $5.6 \sigma$). New astrophysics may be
revealed through the most precise measurement of the $^8$B flux (to 2.5\%) and
the first detection of the {\it hep} flux (to 11\%). {\it DUNE is required:} No
other experiment, even proposed, has been shown capable of fully realizing
these discovery opportunities.


  Crowdsourcing is becoming an accepted method of software development for
different phases in the production lifecycle. Ideally, mass parallel production
through Crowdsourcing could be an option for rapid acquisition in software
engineering by leveraging infinite worker resource on the internet. It is
important to understand the patterns and strategies of decomposing and
uploading parallel tasks to maintain a stable worker supply as well as a
satisfactory task completion rate.
  This research report is an empirical analysis of the available tasks'
lifecycle patterns in crowdsourcing. Following the waterfall model in
Crowdsourced Software Development (CSD), this research identified four patterns
for the sequence of task arrival per project: 1) Prior Cycle, 2) Current Cycle,
3) Orbit Cycle, and 4) Fresh Cycle.


  The flicker-noise spectroscopy (FNS) approach is used to determine the
dynamic characteristics of neuromagnetic responses by analyzing the
magnetoencephalographic (MEG) signals recorded as the response of a group of
control human subjects and a patient with photosensitive epilepsy (PSE) to
equiluminant flickering stimuli of different color combinations. Parameters
characterizing the analyzed stochastic biomedical signals for different
frequency bands are identified. It is shown that the classification of the
parameters of analyzed MEG responses with respect to different frequency bands
makes it possible to separate the contribution of the chaotic component from
the overall complex dynamics of the signals. It is demonstrated that the
chaotic component can be adequately described by the anomalous diffusion
approximation in the case of control subjects. On the other hand, the chaotic
component for the patient is characterized by a large number of high-frequency
resonances. This implies that healthy organisms can suppress the perturbations
brought about by the flickering stimuli and reorganize themselves. The
organisms affected by photosensitive epilepsy no longer have this ability. This
result also gives a way to simulate the separate stages of the brain cortex
activity in vivo. The examples illustrating the use of the "FNS device" for
identifying even the slightest individual differences in the activity of human
brains using their responses to external standard stimuli show a unique
possibility to develop the "individual medicine" of the future.


  Few-shot object detection (FSOD) aims at learning a detector that can fast
adapt to previously unseen objects with scarce annotated examples, which is
challenging and demanding. Existing methods solve this problem by performing
subtasks of classification and localization utilizing a shared component (e.g.,
RoI head) in the detector, yet few of them take the distinct preferences of two
subtasks towards feature embedding into consideration. In this paper, we
carefully analyze the characteristics of FSOD, and present that a general
few-shot detector should consider the explicit decomposition of two subtasks,
as well as leveraging information from both of them to enhance feature
representations. To the end, we propose a simple yet effective Adaptive
Fully-Dual Network (AFD-Net). Specifically, we extend Faster R-CNN by
introducing Dual Query Encoder and Dual Attention Generator for separate
feature extraction, and Dual Aggregator for separate model reweighting.
Spontaneously, separate state estimation is achieved by the R-CNN detector.
Besides, for the acquisition of enhanced feature representations, we further
introduce Adaptive Fusion Mechanism to adaptively perform feature fusion in
different subtasks. Extensive experiments on PASCAL VOC and MS COCO in various
settings show that, our method achieves new state-of-the-art performance by a
large margin, demonstrating its effectiveness and generalization ability.


  Mutually unbiased bases (MUB) are an elusive discrete structure in Hilbert
spaces. Many (complete sets of) MUB are group covariant, but little is known
whether they can be sharply covariant in the sense that the generating groups
can have order equal to the total number of basis states, that is, $d(d+1)$ for
MUB in dimension $d$. Sharply covariant MUB, if they exist, would be most
appealing from both theoretical and practical point of view. Since stabilizer
MUB subsume almost all MUB that have ever been constructed, it is of
fundamental interest to single out those candidates that are sharply covariant.
We show that, quite surprisingly, only two stabilizer MUB are sharply
covariant, and the conclusion still holds even if antiunitary transformations
are taken into account. Our study provides valuable insight on the symmetry of
stabilizer MUB, which may have implications for a number of research topics in
quantum information and foundations. In addition, it exposes a sharp contrast
between MUB and another elusive discrete structure known as symmetric
informationally complete measurements (SICs), all known examples of which are
sharply covariant.


  We consider the quantum computational process as viewed by an insider
observer: this is equivalent to an isomorphism between the quantum computer and
a quantum space, namely the fuzzy sphere. The result is the formulation of a
reversible quantum measurement scheme, with no hidden information.


  We propose the use of bright matter-wave solitons formed from Bose-Einstein
condensates with attractive interactions to probe and study quantum reflection
from a solid surface at normal incidence. We demonstrate that the presence of
attractive interatomic interactions leads to a number of advantages for the
study of quantum reflection. The absence of dispersion as the soliton
propagates allows precise control of the velocity normal to the surface and for
much lower velocities to be achieved. Numerical modelling shows that the
robust, self-trapped nature of bright solitons leads to a clean reflection from
the surface, limiting the disruption of the density profile and permitting
accurate measurements of the reflection probability.


  Numerous applications all the way from biology and physics to economics
depend on the density of first crossings over a boundary. Motivated by the lack
of analytical tools for computing first-passage time densities (FPTDs) for
complex problems, we propose a new simple method based on the Independent
Interval Approximation (IIA). We generalise previous formulations of the IIA to
handle non-smooth processes, and derive a closed form expression for the FPTD
in Laplace and $z$-transform space for arbitrary boundary and starting points
in one dimension. We focus on Markov processes for which the IIA is exact. To
apply our equations, we calculate the FPTD in two cases: the Ornstein-Uhlenbeck
process and the discrete time Brownian walk. Our results are in good agreement
with Langevin dynamics simulations.


  Recent work has presented intriguing results examining the knowledge
contained in language models (LM) by having the LM fill in the blanks of
prompts such as "Obama is a _ by profession". These prompts are usually
manually created, and quite possibly sub-optimal; another prompt such as "Obama
worked as a _" may result in more accurately predicting the correct profession.
Because of this, given an inappropriate prompt, we might fail to retrieve facts
that the LM does know, and thus any given prompt only provides a lower bound
estimate of the knowledge contained in an LM. In this paper, we attempt to more
accurately estimate the knowledge contained in LMs by automatically discovering
better prompts to use in this querying process. Specifically, we propose
mining-based and paraphrasing-based methods to automatically generate
high-quality and diverse prompts, as well as ensemble methods to combine
answers from different prompts. Extensive experiments on the LAMA benchmark for
extracting relational knowledge from LMs demonstrate that our methods can
improve accuracy from 31.1% to 39.6%, providing a tighter lower bound on what
LMs know. We have released the code and the resulting LM Prompt And Query
Archive (LPAQA) at https://github.com/jzbjyb/LPAQA.


  Time series measurements in 2H-NbS$_2$ crystal had unravelled a drive induced
transition wherein the critical current (Ic) changes from a low to a high Ic
jammed vortex state, via a negative differential resistance (NDR) transition.
Here, using multiple current (I) - voltage (V) measurement cycles, we explore
the statistical nature of observing the NDR transition in the free-flux-flow
(FF) regime in a single crystal of 2H-NbS$_2$. The probability of observing the
NDR transition always remains finite for a vortex state created with either
fast or slow rate of magnetic field. The probability of observing the NDR
transition in the FF regime is found to systematically increase with magnetic
field (B) in weak collective pinning regime. In the strong pinning regime, the
said probability becomes B-independent. We show that the higher Ic state is
unique and cannot be accessed via any conventional route. While the I-V curves
do not distinguish between zero field cooled (ZFC) and field cooled (FC) modes
of preparing the vortex state, the probability for observing an NDR transition
has different B-dependences for the vortex matter prepared in the ZFC and FC
modes. We find that the NDR occurs in a high dissipation regime, where the flow
resistivity is well above the theoretical value expected in the FF regime. We
understand our results on the basis of a rapid drop in vortex viscosity at high
drives in 2H-NbS$_2$, which triggers a rapid increase in the vortex velocity
and reorganization in the moving vortex matter leading to a dynamical unstable
vortex flow. This dynamical instability leads to the NDR transition into a high
entropy vortex state with high Ic.


  Motivated by aggregation phenomena in gliding bacteria, we study collective
motion in a twodimensional model of active, self-propelled rods interacting
through volume exclusion. In simulations with individual particles, we find
that particle clustering is facilitated by a sufficiently large packing
fraction (eta) or length-to-width ratio (kappa). The transition to clustering
in simulations is well captured by a mean-field model for the cluster size
distribution, which predicts that the transition values kappa_c of the aspect
ratio for a fixed packing fraction is given by kappa_c = C/eta - 1 where C is a
constant.


  We present algorithms for topic modeling based on the geometry of
cross-document word-frequency patterns. This perspective gains significance
under the so called separability condition. This is a condition on existence of
novel-words that are unique to each topic. We present a suite of highly
efficient algorithms based on data-dependent and random projections of
word-frequency patterns to identify novel words and associated topics. We will
also discuss the statistical guarantees of the data-dependent projections
method based on two mild assumptions on the prior density of topic document
matrix. Our key insight here is that the maximum and minimum values of
cross-document frequency patterns projected along any direction are associated
with novel words. While our sample complexity bounds for topic recovery are
similar to the state-of-art, the computational complexity of our random
projection scheme scales linearly with the number of documents and the number
of words per document. We present several experiments on synthetic and
real-world datasets to demonstrate qualitative and quantitative merits of our
scheme.


  The charge topology of coherent-dissociation events is presented for $^{11}$C
and $^{12}$N nuclei of energy 1.2~\textit{A}~GeV per nucleon bombarding nuclear
track emulsions. This topology is compared with respective data for $^{7}$Be,
$^{8,10}$B, $^{9,10}$C and $^{14}$N nuclei.


  Putting a general, physically relevant upper bound on equilibration times in
closed quantum systems is a recently much pursued endeavor. In PRX, 7, 031027
(2017) Garc\'{\i}a-Pintos et al. suggest such a bound. We point out that the
general assumptions which allow for an actual estimation of this bound are
violated in cases in which Fermi's Golden Rule and related open quantum system
theories apply. To probe the range of applicability of Fermi's Golden Rule for
systems of the type addressed in the above work, we numerically solve the
corresponding Schr\"odinger equation for some finite spin systems comprising up
to 25 spins. These calculations shed light on the breakdown of standard quantum
master equations in the "superweak" coupling limit, which occurs for finite
sized baths.


  Statistical mechanics determines the abundance of different arrangements of
matter depending on cost-benefit balances. Its formalism and phenomenology
percolate throughout biological processes and set limits to effective
computation. Under specific conditions, self-replicating and computationally
complex patterns become favored, yielding life, cognition, and Darwinian
evolution. Neurons and neural circuits sit at a crossroads between statistical
mechanics, computation, and (through their role in cognition) natural
selection. Can we establish a {\em statistical physics} of neural circuits?
Such theory would tell what kinds of brains to expect under set energetic,
evolutionary, and computational conditions. With this big picture in mind, we
focus on the fate of duplicated neural circuits. We look at examples from
central nervous systems, with a stress on computational thresholds that might
prompt this redundancy. We also study a naive cost-benefit balance for
duplicated circuits implementing complex phenotypes. From this we derive {\em
phase diagrams} and (phase-like) transitions between single and duplicated
circuits, which constrain evolutionary paths to complex cognition. Back to the
big picture, similar phase diagrams and transitions might constrain I/O and
internal connectivity patterns of neural circuits at large. The formalism of
statistical mechanics seems a natural framework for thsi worthy line of
research.


  We focus here on the thermodynamic properties of adsorbates formed by
two-species $A+B \to \oslash$ reactions on a one-dimensional infinite lattice
with heterogeneous "catalytic" properties. In our model hard-core $A$ and $B$
particles undergo continuous exchanges with their reservoirs and react when
dissimilar species appear at neighboring lattice sites in presence of a
"catalyst." The latter is modeled by supposing either that randomly chosen
bonds in the lattice promote reactions (Model I) or that reactions are
activated by randomly chosen lattice sites (Model II). In the case of annealed
disorder in spatial distribution of a catalyst we calculate the pressure of the
adsorbate by solving three-site (Model I) or four-site (Model II) recursions
obeyed by the corresponding averaged grand-canonical partition functions. In
the case of quenched disorder, we use two complementary approaches to find
$\textit{exact}$ expressions for the pressure. The first approach is based on
direct combinatorial arguments. In the second approach, we frame the model in
terms of random matrices; the pressure is then represented as an averaged
logarithm of the trace of a product of random $3 \times 3$ matrices -- either
uncorrelated (Model I) or sequentially correlated (Model II).


  We recall results concerning one-dimensional classical and quantum systems
with ladder operators. We obtain the most general one-dimensional classical
systems respectively with a third and a fourth order ladder operators
satisfying polynomial Heisenberg algebras. These systems are written in terms
of the solutions of quartic and quintic equations. We use these results to
present two new families of superintegrable systems and examples of
trajectories that are deformed Lissajous's figures.


  In a composite model of leptons and quarks, composite particles with heavy
Majorana particles appear provided that the V-rishon is regarded as a Majorana
particle. In this paper, the decay mode of such "Majorana partners" is
isestigated. It is shown that the life time of Majorana partners are fairly
long. Our model suggests that a new mechanism of proton decay is possible,
where the X and Y bosons in GUTs are not necessary.


  We present stellar parameters and metallicities, obtained from a detailed
spectroscopic analysis, for a large sample of 98 stars known to be orbited by
planetary mass companions (almost all known targets), as well as for a
volume-limited sample of 41 stars not known to host any planet. For most of the
stars the stellar parameters are revised versions of the ones presented in our
previous works. However, we also present parameters for 18 stars with planets
not previously published, and a compilation of stellar parameters for the
remaining 4 planet-hosts for which we could not obtain a spectrum. A comparison
of our stellar parameters with values of Teff, log(g), and [Fe/H] available in
the literature shows a remarkable agreement. The derived [Fe/H] values are then
used to confirm the previously known result that planets are more prevalent
around metal-rich stars. Furthermore, we confirm that the frequency of planets
is a strongly rising function of the stellar metallicity, at least for stars
with [Fe/H]>0. While only about 3% of the solar metallicity stars in the
CORALIE planet search sample were found to be orbited by a planet, this number
increases to more than 25% for stars with [Fe/H] above +0.3. Curiously, our
results also suggest that these percentages might remain relatively constant
for values of [Fe/H] lower than about solar, increasing then linearly with the
mass fraction of heavy elements. These results are discussed in the context of
the theories of planetary formation.


  SXP 5.05 is a Be/X-ray binary with a neutron star companion located in the
Small Magellanic Cloud. It was first detected in 2013, and later that year, SXP
5.05 underwent a massive optical and X-ray outburst. This outburst dwarfs any
other optical event that has been observed for this system during the last 5
years. The large increase in optical brightness of the system implies an
increase in the size and density of the Be star's circumstellar disc. The X-ray
data show two occultations of the neutron star per orbit and is not consistent
with a neutron star passing behind the Be star, and hence the disc is
responsible for these occultations. In this paper, we model the outburst of
Be/neutron star binary SXP 5.05 as being due to a large increase in mass
ejection by the Be star. The neutron star passes directly through the growing
disc, and it is shown that the resulting obscuration can qualitatively explain
the observed X-ray behaviour of the system. We find the only way to reproduce
the timescales of the observed optical behaviour of the system is to increase
the mass ejection substantially for a short time (<2 orbits) and to decrease
the viscosity during the event. The general behaviour of the observed X-ray and
Ha line emission are also reproduced by the model. However, the inferred mass
ejection and viscosity needed to produce a sufficiently rapid increase of disc
size are both higher than suggested by previous works.


  Let \Gamma be a structure with a finite relational signature and a
first-order definition in (R;*,+) with parameters from R, that is, a relational
structure over the real numbers where all relations are semi-algebraic sets. In
this article, we study the computational complexity of constraint satisfaction
problem (CSP) for \Gamma: the problem to decide whether a given primitive
positive sentence is true in \Gamma. We focus on those structures \Gamma that
contain the relations \leq, {(x,y,z) | x+y=z} and {1}. Hence, all CSPs studied
in this article are at least as expressive as the feasibility problem for
linear programs. The central concept in our investigation is essential
convexity: a relation S is essentially convex if for all a,b\inS, there are
only finitely many points on the line segment between a and b that are not in
S. If \Gamma contains a relation S that is not essentially convex and this is
witnessed by rational points a,b, then we show that the CSP for \Gamma is
NP-hard. Furthermore, we characterize essentially convex relations in logical
terms. This different view may open up new ways for identifying tractable
classes of semi-algebraic CSPs. For instance, we show that if \Gamma is a
first-order expansion of (R;*,+), then the CSP for \Gamma can be solved in
polynomial time if and only if all relations in \Gamma are essentially convex
(unless P=NP).


  Sterile neutrinos can be produced through mixing with active neutrinos in the
hot and dense core of a core-collapse supernova (SN). The standard bounds on
the active-sterile mixing ($\sin^2 \theta$) from SN arise from SN1987A
energy-loss, requiring $E_{\text{loss}}<10^{52}~{\rm erg}$. In this letter, we
discuss a novel bound on sterile neutrino parameter space arising from the
energy deposition through its decays inside the SN envelope. Using the observed
underluminous SN IIP population, this energy deposition is constrained to be
below $\sim 10^{50}~{\rm erg}$. Focusing on sterile neutrino mixing only with
the tau neutrino, for heavy sterile masses $m_s$ in the range $100$-$500$ MeV,
we find stringent constraints on $\sin^2 \theta_\tau$ reaching two orders of
magnitude lower than those from the SN1987A energy-loss argument. Similar
bounds will also be applicable to sterile mixing only with muons ($\sin^2
\theta_\mu$).


  The measured rate of the 3^He A-B transition depends on the diameter of the
experimental cell. Theoretically, this can only be explained by a direct drag
on the interface exerted by the lateral walls, leading to a pressure
discontinuity across the interface. This has not been considered before, either
here or in similar circumstances. The general hydrodynamic theory that includes
the influence of finite geometries is presented.


  Recent work has demonstrated that the latent spaces of large language models
(LLMs) contain directions predictive of the truth of sentences. Multiple
methods recover such directions and build probes that are described as getting
at a model's "knowledge" or "beliefs". We investigate this phenomenon, looking
closely at the impact of context on the probes. Our experiments establish where
in the LLM the probe's predictions can be described as being conditional on the
preceding (related) sentences. Specifically, we quantify the responsiveness of
the probes to the presence of (negated) supporting and contradicting sentences,
and score the probes on their consistency. We also perform a causal
intervention experiment, investigating whether moving the representation of a
premise along these belief directions influences the position of the hypothesis
along that same direction. We find that the probes we test are generally
context sensitive, but that contexts which should not affect the truth often
still impact the probe outputs. Our experiments show that the type of errors
depend on the layer, the (type of) model, and the kind of data. Finally, our
results suggest that belief directions are (one of the) causal mediators in the
inference process that incorporates in-context information.


  We investigate the three-baryon system with charm +1 in a simple model.
  Charmed lambda $\Lambda_{c}$ is assumed to orbit an unperturbed deuteron in a
charmed lambda-deuteron potential based on a separable charmed lambda-nucleon
potential from chiral effective field theory techniques extrapolations of
lattice QCD data for the $\Lambda_{c}N$ $^{1}S_{0}$ and $^{3}S_{1}$ partial
waves.
  We have estimated the strength and the range of the $\Lambda_{c}$d potential.
  Also, the $\Lambda_{c}$ particle momentum distribution in
$_{\Lambda_{c}}^{3}H$ is presented and compared by $\Lambda$ particle in
$_{\Lambda}^{3}H$. It is found that there is no bound $_{\Lambda_{c}}^{3}H$
state by solving eigenvalue condition equation.


  We theoretically study the phase of the reflection amplitude of an electron
(massive Dirac fermion) at a lateral potential step in Bernal-stacked bilayer
graphene. The phase shows anomalous jump of $\pi$, as the electron incidence
angle (relative to the normal direction to the step) varies to pass $\pm
\pi/4$. The jump is attributed to the Berry phase associated with the
pseudospin-1/2 of the electron. This Berry-phase effect is robust against the
band gap opening due to the external electric gates generating the step. We
propose an interferometry setup in which collimated waves can be generated and
tuned. By using the setup, one can identify both the $\pi$ jump and the
collimation angle.


  The effectiveness of the hyperbolic relaxation method for solving the
Einstein constraint equations numerically is studied here on a variety of
compact orientable three-manifolds. Convergent numerical solutions are found
using this method on manifolds admitting negative Ricci scalar curvature
metrics, i.e. those from the $H^3$ and the $H^2\times S^1$ geometrization
classes. The method fails to produce solutions, however, on all the manifolds
examined here admitting non-negative Ricci scalar curvatures, i.e. those from
the $S^3$, $S^2\times S^1$, and the $E^3$ classes. This study also finds that
the accuracy of the convergent solutions produced by hyperbolic relaxation can
be increased significantly by performing fairly low-cost standard elliptic
solves using the hyperbolic relaxation solutions as initial guesses.


  The current paper is devoted to the study of existence, uniqueness and
Lifshitz tails of the integrated density of surface states (IDSS) for
Schr\"{o}dinger operators with alloy type random surface potentials. We prove
the existence and uniqueness of the IDSS for negative energies, which is
defined as the thermodynamic limit of the normalized eigenvalue counting
functions of localized operators on strips with sections being special cuboids.
Under the additional assumption that the single-site impurity potential decays
anisotropically, we also prove that the IDSS for negative energies exhibits
Lifshitz tails near the bottom of the almost sure spectrum in the following
three regimes: the quantum regime, the quantum-classical/classical-quantum
regime and the classical regime. We point out that the
quantum-classical/classical-quantum regime is new for random surface models.


  We generalize some fundamental results for noncompact Riemannian manfolds
without boundary, that only require completeness and no curvature assumptions,
to manifolds with boundary: let $M$ be a smooth Riemannian manifold with
boundary $\partial M$ and let $\hat{C}^\infty_c(M)$ denote the space of smooth
compactly supported cut-off functions with vanishing normal derivative, Neumann
cut-offs. We show, among other things, that under completeness:
  - $\hat{C}^\infty_c(M)$ is dense in $W^{1,p}(\mathring{M})$ for all $p\in
(1,\infty)$; this generalizes a classical result by Aubin [2] for $\partial
M=\emptyset$.
  - $M$ admits a sequence of first order cut-off functions in
$\hat{C}^\infty_c(M)$; for $\partial M=\emptyset$ this result can be traced
back to Gaffney [7].
  - the Laplace-Beltrami operator with domain of definition
$\hat{C}^\infty_c(M)$ is essentially self-adjoint; this is a generalization of
a classical result by Strichartz [20] for $\partial M=\emptyset$.


  Fast distributed algorithms that output a feasible solution for constraint
satisfaction problems, such as maximal independent sets, have been heavily
studied. There has been much less research on distributed sampling problems,
where one wants to sample from a distribution over all feasible solutions
(e.g., uniformly sampling a feasible solution). Recent work (Feng, Sun, Yin
PODC 2017; Fischer and Ghaffari DISC 2018; Feng, Hayes, and Yin arXiv 2018) has
shown that for some constraint satisfaction problems there are distributed
Markov chains that mix in $O(\log n)$ rounds in the classical LOCAL model of
distributed computation. However, these methods return samples from a
distribution close to the desired distribution, but with some small amount of
error. In this paper, we focus on the problem of exact distributed sampling.
Our main contribution is to show that these distributed Markov chains in tandem
with techniques from the sequential setting, namely coupling from the past and
bounding chains, can be used to design $O(\log n)$-round LOCAL model exact
sampling algorithms for a class of weighted local constraint satisfaction
problems. This general result leads to $O(\log n)$-round exact sampling
algorithms that use small messages (i.e., run in the CONGEST model) and
polynomial-time local computation for some important special cases, such as
sampling weighted independent sets (aka the hardcore model) and weighted
dominating sets.


  When a solid plate is withdrawn from a liquid bath, a receding contact line
is formed where solid, liquid, and gas meet. Above a critical speed $U_{cr}$, a
stationary contact line can no longer exist and the solid will eventually be
covered completely by a liquid film. Here we show that the bifurcation diagram
of this coating transition changes qualitatively, from discontinuous to
continuous, when decreasing the inclination angle of the plate. We show that
this effect is governed by the presence of capillary waves, illustrating that
the large scale flow strongly effects the maximum speed of dewetting.


  We study the formation and the subsequent dynamics of shock waves in
repulsive one-dimensional Bose gases during the free expansion of a density
hump. By building coherent Fermi states for interacting Bethe fermions, we
define a quantum fluctuating initial state expressed in terms of universal
quantities, namely the density and the Luttinger parameter. In the integrable
case, this fluctuating state is then evolved by generalized hydrodynamics (GHD)
and, differently from non-fluctuating initial states, it develops density
ripples on top of the hydrodynamic mean value. Our analysis gives a general
theory of quantum ripples and wave breaking in integrable and quasi-integrable
one-dimensional liquids and clarifies the role of the interaction strength. In
particular, for strongly/intermediately interacting bosons, we find quantum
ripples originating from low-energy modes at the Fermi surface interfering when
transported by GHD. In the low coupling limit, near the quasicondensate regime,
we find instead that density ripples have a semi-classical nature, and their
description requires information on the curvature of the Fermi surface.


  The boundary map in K-theory arising from the Wiener-Hopf extension of a
crossed product algebra with R is the Connes-Thom isomorphism. In this article
the Wiener Hopf extension is combined with the Heisenberg group algebra to
provide an elementary construction of a corresponding map on higher traces (and
cyclic cohomology). It then follows directly from a non-commutative Stokes
theorem that this map is dual w.r.t.Connes' pairing of cyclic cohomology with
K-theory. As an application, we prove equality of quantized bulk and edge
conductivities for the integer quantum Hall effect described by continuous
magnetic Schroedinger operators.


  We review the notions of (weak) Hermitian-Yang-Mills structure and
approximate Hermitian-Yang-Mills structure for Higgs bundles. Then, we
construct the Donaldson functional for Higgs bundles over compact K\"ahler
manifolds and we present some basic properties of it. In particular, we show
that its gradient flow can be written in terms of the mean curvature of the
Hitchin-Simpson connection. We also study some properties of the evolution
equation associated to that functional. Next, we study the problem of the
existence of approximate Hermitian-Yang-Mills structure and its relation with
the algebro-geometric notion of Mumford-Takemoto semistability and we show that
for a Higgs bundle over a compact Riemann surface, the notion of approximate
Hermitian-Yang- Mills structure is in fact the differential-geometric
counterpart of the notion of semistability. Finally, using Donaldson heat flow,
we show that the semistability of a Higgs bundle over a compact K\"ahler
manifold (of every dimension) implies the existence of an approximate
Hermitian-Yang-Mills structure. As a consequence of this we deduce that many
results about Higgs bundles written in terms of approximate
Hermitian-Yang-Mills structures can be translated in terms of semistability.


  This thesis focuses on the mathematical description and application of
nonlinear cavity optomechanical systems. The first part is concerned with
solving the dynamics of the standard nonlinear optomechanical Hamiltonian with
an additional time-dependent mechanical displacement and single-mode squeezing
term. The solution is based on identifying a Lie algebra that generates the
time-evolution of the system, which reduces the problem to considering a finite
set of coupled ordinary differential equations of real functions. The second
part applies the solutions of the extended optomechanical Hamiltonian to the
study of non-Gaussianity. We compute the non-Gaussian character of an
optomechanical state as a function of the parameters in the Hamiltonian, and
investigate the interplay between the non-Gaussianity, the strength of the
nonlinear coupling and the strength of the single-mode mechanical squeezing
term. We find that the strength and form of the nonlinear coupling strongly
impacts the non-Gaussianity, and that its relationship with the squeezing term
is highly complex. The third part concerns the use of nonlinear optomechanical
systems as quantum sensors. We derive a general expression of the quantum
Fisher information given the extended optomechanical Hamiltonian and
demonstrate its applicability through three concrete examples: estimating the
strength of a nonlinear light--matter coupling, the strength of a
time-modulated mechanical displacement, and the strength of a single-mode
mechanical squeezing parameter, all of which are modulated at resonance. In the
last Chapter of the thesis, we consider the estimation of a constant
gravitational acceleration with an optomechanical system. Our results suggest
that optomechanical systems could, in principle, be used as powerful quantum
sensors.


  We show that every geodesic metric space admitting an injective continuous
map into the plane as well as every planar graph has Nagata dimension at most
two, hence asymptotic dimension at most two. This relies on and answers a
question in a very recent work by Fujiwara and Papasoglu. We conclude that all
three-dimensional Hadamard manifolds have Nagata dimension three. As a
consequence, all such manifolds are absolute Lipschitz retracts.


  We consider the problem of identifying the CFT's that may be dual to pure
gravity in three dimensions with negative cosmological constant. The c-theorem
indicates that three-dimensional pure gravity is consistent only at certain
values of the coupling constant, and the relation to Chern-Simons gauge theory
hints that these may be the values at which the dual CFT can be holomorphically
factorized. If so, and one takes at face value the minimum mass of a BTZ black
hole, then the energy spectrum of three-dimensional gravity with negative
cosmological constant can be determined exactly. At the most negative possible
value of the cosmological constant, the dual CFT is very likely the monster
theory of Frenkel, Lepowsky, and Meurman. The monster theory may be the first
in a discrete series of CFT's that are dual to three-dimensional gravity. The
partition function of the second theory in the sequence can be determined on a
hyperelliptic Riemann surface of any genus. We also make a similar analysis of
supergravity.


  We address the construction of manifest U-duality invariant generalized
diffeomorphisms. The closure of the algebra requires an extension of the
tangent space to include a tensor hierarchy indicating the existence of an
underlying unifying structure, compatible with E_{11} and Borcherds algebras
constructions. We begin with four-dimensional gauged maximal supergravity, and
build a generalized Lie derivative that encodes all the gauge transformations
of the theory. A generalized frame is introduced, which accommodates for all
the degrees of freedom, including the tensor hierarchy. The generalized Lie
derivative defines generalized field-dependent fluxes containing all the
covariant quantities in the theory, and the closure conditions give rise to
their corresponding Bianchi Identities. We then move towards the construction
of a full generalized Lie derivative defined on an extended space, analyze the
closure conditions, and explore the connection with that of maximal gauged
supergravity via a generalized Scherk-Schwarz reduction, and with
11-dimensional supergravity.


  We show that a linear-time algorithm for computing Hong's bound for positive
roots of a univariate polynomial, described by K. Mehlhorn and S. Ray in an
article "Faster algorithms for computing Hong's bound on absolute
positiveness", is incorrect. We present a corrected version.


  We prove a fix point theorem for monoids of self-embeddings of trees. As a
corollary, we obtain a result by Laflamme, Pouzet and Sauer that a tree either
contains a subdivided binary tree as a subtree or has a vertex, and edge, an
end or two ends fixed by all its self-embeddings.


  Recent studies show that $D_{s0}^{\ast}(2317)$ and $D_{s1}(2460)$ contain
large molecular components. In this work, we employ the naive factorization
approach to calculate the production rates of $D_{s0}^{\ast}(2317)$ and
$D_{s1}(2460)$ as hadronic molecules in $B_{(s)}$ and $\Lambda_b(\Xi_b)$
decays, where their decay constants are estimated in the effective Lagrangian
approach. With the so-obtained decay constants $f_{D_{s0}^{\ast}(2317)}$ and
$f_{D_{s1}(2460)}$, we calculate the branching fractions of the $b$-meson
decays $B_{(s)}\to \bar{D}_{(s)}^{(*)}D_{s0}^*$ and $B_{(s)}\to
\bar{D}_{(s)}^{(*)}D_{s1}$ and the $b$-baryon decays $\Lambda_b(\Xi_{b}) \to
\Lambda_c(\Xi_{c}) D_{s0}^*$ and $\Lambda_b(\Xi_{b}) \to \Lambda_c(\Xi_c)
D_{s1}$. Our results show that the production rates of $D_{s0}^{\ast}(2317)$
and $D_{s1}(2460)$ in the $B_s$, $\Lambda_b$ and $\Xi_b$ decays are rather
large that future experiments could observe them. In particular, we demonstrate
that one can extract the decay constants of hadronic molecules via the triangle
mechanism because of the equivalence of the triangle mechanism to the tree
diagram established in calculating the decays $B \to
\bar{D}^{(*)}D_{s0}^{\ast}(2317)$ and $B \to \bar{D}^{(*)}D_{s1}(2460)$.


  The two- and three-body Coulomb explosion of carbonyl sulfide (OCS) by 790
nm, 50 fs laser pulses focussed to $\approx $ 10$^{16}$ Wcm$^{-2}$ has been
investigated by three-dimensional covariance mapping technique. For the first
time in a triatomic molecule, a single charge state, in this case the
trication, has been observed to dissociate into two distinct energy channels.
With the aid of a three dimensional visualization technique to reveal the
ionization hierarchy, evidence is presented for the existence of two sets of
ionization pathways resulting from these two initial states. While one group of
ions can be modeled using a Classical enhanced ionization model, the second
group, consisting of mainly asymmetric channels, can not. The results provide
clear evidence that an enhanced ionization approach must also be accompanied by
an appreciation of the effects of excited ionic states and multi-electronic
processes.


  We investigate heat engines whose working substance is made of two coupled
qubits performing a generalised Otto cycle by varying their applied magnetic
field or their interaction strength during the compression and expansion
strokes. During the heating and cooling strokes, the two qubits are coupled to
local and common environments that are not necessarily at equilibrium. We find
instances of quantum engines coupled to non equilibrium common environments
exhibiting non-trivial connections to quantum correlations as witnessed by a
monotonic dependence of the work produced on quantum discord and entanglement.


  Scholars have tried to explain how organizations can build agile teams by
only looking at one level of analysis. We argue in this short paper that
lessons can be learned from organizational science results explaining variance
on three different abstraction levels of organizations. We suggest agility
needs to be explained from organizational (macro), the team (meso), and
individual (micro) levels to provide useful and actionable guidelines to
practitioners. We are currently designing such studies and hope that they will
eventually result in validated measurements that can be used to prevent
companies from investing in the wrong areas when trying to move towards more
agility.


  We explore the possibility of inducing a topological insulator phase in a
honeycomb lattice lacking spin-orbit interaction using a metallic (or Fermi
gas) environment. The lattice and the metallic environment interact through a
density-density interaction without particle tunneling, and integrating out the
metallic environment produces a honeycomb sheet with in-plane oscillating
long-ranged interactions. We find the ground state of the interacting system in
a variational mean-field method and show that the Fermi wave vector, kF, of the
metal determines which phase occurs in the honeycomb lattice sheet. This is
analogous to the Ruderman-Kittel-Kasuya-Yosida (RKKY) mechanism in which the
metal's kF determines the interaction profile as a function of the distance.
Tuning kF and the interaction strength may lead to a variety of ordered phases,
including a topological insulator and anomalous quantum-hall states with
complex next-nearest-neighbor hopping, as in the Haldane and the Kane-Mele
model. We estimate the required range of parameters needed for the topological
state and find that the Fermi vector of the metallic gate should be of the
order of 3Pi/8a (with a being the graphene lattice constant). The net coupling
between the layers, which includes screening in the metal, should be of the
order of the honeycomb lattice bandwidth. This configuration should be most
easily realized in a cold-atoms setting with two interacting Fermionic species.


  Federated learning is inherently vulnerable to model poisoning attacks
because its decentralized nature allows attackers to participate with
compromised devices. In model poisoning attacks, the attacker reduces the
model's performance on targeted sub-tasks (e.g. classifying planes as birds) by
uploading "poisoned" updates. In this report we introduce \algoname{}, a novel
defense that uses global top-k update sparsification and device-level gradient
clipping to mitigate model poisoning attacks. We propose a theoretical
framework for analyzing the robustness of defenses against poisoning attacks,
and provide robustness and convergence analysis of our algorithm. To validate
its empirical efficacy we conduct an open-source evaluation at scale across
multiple benchmark datasets for computer vision and federated learning.


  We disprove the conjecture that distributional chaos of type 3 (briefly, DC3)
is iteration invariant and show that a slightly strengthened definition,
denoted by DC2$\frac{1}{2}$, is preserved under iteration, i.e. $f^n$ is
DC2$\frac{1}{2}$ if and only if $f$ is too. Unlike DC3, DC2$\frac{1}{2}$ is
also conjugacy invariant and implies Li-Yorke chaos. The definition of
DC2$\frac{1}{2}$ is the following: a pair $(x,y)$ is DC2$\frac{1}{2}$ iff
$\Phi_{(x,y)}(0)<\Phi^*_{(x,y)}(0)$, where $\Phi_{(x,y)}(\delta)$ (resp.
$\Phi^*_{(x,y)}(\delta)$) is lower (resp. upper) density of times $k$ when
$d(f^k(x),f^k(y))<\delta$ and both densities are defined at 0 as limits of
their values for $\delta\to 0^+$. Hence DC$2\frac{1}{2}$ shares similar
properties with DC1 and DC2 but unlike them, strict DC$2\frac{1}{2}$ systems
must have zero topological entropy.


  We consider the two-dimensional Gaussian Free Field on a box of side length
$N$, with Dirichlet boundary data, and prove the convergence of the law of the
recentered maximum of the field.


  Let ${\cal N}_{c_1,...,c_t}$ be the variety of polynilpotent groups of class
row $(c_1,...,c_t)$. In this paper, first, we show that a polynilpotent group
$G$ of class row $(c_1,...,c_t)$ has no any ${\cal
N}_{c_1,...,c_t,c_{t+1}}$-covering group if its Baer-invariant with respect to
the variety ${\cal N}_{c_1,...,c_t,c_{t+1}}$ is nontrivial. As an immediate
consequence, we can conclude that a solvable group $G$ of length $c$ with
nontrivial solvable multiplier, ${\cal S}_nM(G)$, has no ${\cal S}_n$-covering
group for all $n>c$, where ${\cal S}_n$ is the variety of solvable groups of
length at most $n$. Second, we prove that if $G$ is a polynilpotent group of
class row $(c_1,...,c_t,c_{t+1})$ such that ${\cal
N}_{c'_1,...,c'_t,c'_{t+1}}M(G)\neq 1$, where $c'_i\geq c_i$ for all $1\leq
i\leq t$ and $c'_{t+1}>c_{t+1}$, then $G$ has no any ${\cal
N}_{c'_1,...,c'_t,c'_{t+1}}$-covering group. This is a vast generalization of
the first author's result on nilpotent covering groups (Indian\ J.\ Pure\
Appl.\ Math.\ 29(7)\ 711-713,\ 1998).


  ALICE is devoted to the study of the properties of the Quark-Gluon Plasma
(QGP). This state of matter is created in ultra-relativistic heavy-ion
collisions at the LHC. Heavy quarks are considered effective probes of the QGP
since, due to their large masses, they are produced in hard scattering
processes and experience the full evolution of the hot and dense medium while
interacting with its constituents. The heavy-quark measurements provide
insights on processes like in-medium energy loss and hadronization.
Measurements in proton-proton collisions provide the baseline for interpreting
heavy-ion collision results and constitute an excellent test of pQCD
calculations. In addition, proton-nucleus collisions allow separating cold
nuclear matter effects from those due to the deconfined strongly interacting
matter created in heavy-ion collisions. In this contribution, an overview of
recent ALICE results for open heavy flavours, quarkonia, and heavy-flavour jets
is presented.


  In this paper we initiate the study of the class of cubic Kummer type towers
considered by Garcia, Stichtenoth and Thomas in 1997 by classifying the
asymptotically good ones in this class.


  First results of observations of the low mass X-ray binary Her X-1/HZ Her
performed by the INTEGRAL satellite in July-August 2005 are presented. A
significant part of one 35 day main-on state was covered. The cyclotron line in
the X-ray spectrum is well observed and its position and shape, as well as its
variability with time and phase of the 1.24 s pulsation are explored. X-ray
pulse profiles for different energy bands are studied throughout the
observation. The pulse period is found to vary on short time scales revealing a
dynamical spin-up/spin-down behavior. Results of simultaneous optical
observations of HZ Her are also discussed.


  This paper presents a model based adaptive monitoring method for the
estimation of flow tracers, with application to mapping, prediction and
observation of oil spills in the immediate aftermath of an incident. Autonomous
agents are guided to optimal sensing locations via the solution of a PDE
constrained optimisation problem, obtained using the adjoint method. The
proposed method employs a dynamic model of the combined ocean and oil dynamics,
with states that are updated in real-time using a Kalman filter that fuses
agent-based measurements with a reduced-order model of the ocean circulation
dynamics. In turn, the updated predictions from the fluid model are used to
identify and update the reduced order model, in a process of continuous
feedback. The proposed method exhibits a 30% oil presence mapping and
prediction improvement compared to standard industrial oil observation sensor
guidance and model use.


  Stimulus-evoked EEG data has a notoriously low signal-to-noise ratio and high
inter-subject variability. We propose a novel paradigm for the self-supervised
extraction of stimulus-related brain response data: a model is trained to
extract similar information between two time-aligned segments of EEG in
response to the same stimulus. The extracted information can subsequently be
used to obtain better results in downstream tasks that utilize the response to
the stimulus. We show the efficacy of our method for a downstream task of
decoding the speech envelope from auditory EEG. Our method outperforms other
state-of-the-art denoising techniques, improving reconstruction scores by 45\%.
Additionally, we show that in contrast to the baseline denoising techniques,
our method can be used with data of unseen subjects and stimuli without
retraining, improving decoding performance by 19\% and 34\% over raw EEG for
two holdout datasets. Finally, the last experiment reveals that the accuracies
obtained in the CLASH paradigm are significantly correlated with the percentile
of obtained reconstruction correlation on the null distribution. In general, we
showed that the proposed paradigm is suitable to train deep learning models to
extract stimulus information from EEG while being stimulus feature agnostic.


  In this paper, the main aim is to consider the Spanne-type boundedness of the
multiliinear fractional integral operator $\mathcal{I}_{\alpha,m}$ and
multiliinear fractional maximal operator $\mathcal{M}_{\alpha,m}$ in the
generalized Morrey spaces over some stratified Lie group $\mathbb{G}$.


  The nonequilibrium steady state of a granular fluid, driven by a random
external force, is demonstrated to exhibit long range correlations, which
behave as $\sim 1/r$ in three and $\sim \ln(L/r)$ in two dimensions. We
calculate the corresponding structure factors over the whole range of wave
numbers, and find good agreement with two-dimensional molecular dynamics
simulations. It is also shown by means of a mode coupling calculation, how the
mean field values for the steady state temperature and collision frequency, as
obtained from the Enskog-Boltzmann equation, are renormalized by long
wavelength hydrodynamic fluctuations.


  We study magnetic domain patterns in ferromagnetic thin films by numerical
simulations for a simple Ising-like model. Magnetic domain patterns after
quench demonstrate various types of patterns depending on the field sweep rate
and parameters of the model. How the domain patterns are formed is shown with
use of the number of domains, the domain area, and domain area distributions as
well as snapshots of domain patterns. Considering the proper time scale of the
system, we propose a criterion for the structure of domain patterns.


  This paper considers a scenario of pursuing a moving target that may switch
behaviors due to external factors in a dynamic environment by motion estimation
using visual sensors. First, we present an improved Visual Motion Observer with
switched Gaussian Process models for an extended class of target motion
profiles. We then propose a pursuit control law with an online method to
estimate the switching behavior of the target by the GP model uncertainty.
Next, we prove ultimate boundedness of the control and estimation errors for
the switch in target behavior with high probability. Finally, a Digital Twin
simulation demonstrates the effectiveness of the proposed switching estimation
and control law to prove applicability to real world scenarios.


  Steingrimsson has recently introduced a partition analogue of
Foata-Zeilberger's mak statistic for permutations and conjectured that its
generating function is equal to the classical q-Stirling numbers of second
kind. In this paper we prove a generalization of Steingrimsson's conjecture.


  In this paper we study the pricing of exchange options under a dynamic
described by stochastic correlation with random jumps. In particular, we
consider a Ornstein-Uhlenbeck covariance model with Levy Background Noise
Process driven by Inverse Gaussian subordinators. We use expansion in terms of
Taylor polynomials and cubic splines to approximately compute the price of the
derivative contract. Our findings show that this approach provides an efficient
way to compute the price when compared with a Monte Carlo method while
maintaining an equivalent degree of accuracy with the latter.


  Superconducting tips of YBa$_{2} $Cu$_{3}$O$_{7-x}$ were used to perform
point-contact Andreev reflection spectroscopy on half-metallic CrO$_{2}$ thin
films. At 4.2K, strong suppression of the d-wave Andreev reflection
characteristics was observed, consistent with the high spin polarization of
CrO$_{2}$. Our technique was validated by comparison with data taken on
non-magnetic Au films, and with data taken by superconducting Pb tips. The
point contacts were estimated to be $\lesssim$ 10nm in size, attesting to their
ballistic and microscopic nature. Our results demonstrate the feasibility of
using superconducting cuprate tips as spin-sensitive nanoprobes of
ferromagnets.


  We use the ASH code to model the convective dynamo of solar-type stars. Based
on a series of 15 3-D MHD simulations spanning 4 bins in rotation and mass, we
show what mechanisms are at work in these stellar dynamos with and without
magnetic cycles and how global stellar parameters affect the outcome. We also
derive scaling laws for the differential rotation and magnetic field based on
these simulations. We find a weaker trend between differential rotation and
stellar rotation rate, ($\Delta \Omega \sim (|\Omega|/\Omega_{\odot})^{0.46}$)
in the MHD solutions than in their HD counterpart
$(|\Omega|/\Omega_{\odot})^{0.66})$, yielding a better agreement with the
observational trends based on power laws. We find that for a fluid Rossby
number between $0.15 \lesssim Ro_f \lesssim 0.65$ the solutions possess long
magnetic cycle, if $Ro_f \lesssim 0.42$ a short cycle and if $Ro_f \gtrsim 1$
(anti-solar-like differential rotation) a statistically steady state. We show
that short-cycle dynamos follow the classical Parker-Yoshimura rule whereas the
long-cycle period ones do not. We further demonstrate that the Rossby number
dependency of the large-scale surface magnetic field in the simulation
($B_{L,surf} \sim Ro_{f}^{-1.26}$) agrees better with observations ($B_{V} \sim
Ro_{s}^{-1.4 \pm 0.1}$) and differs from dynamo scaling based on the global
magnetic energy ($B_{bulk} \sim Ro_{f}^{-0.5}$). We also show that up to few
percents of the stellar luminosity can be channelled into the star's magnetism,
hence providing a large energy reservoir for possible surface eruptive events.


  Niels Bohr proposed that the outcome of the measurement becomes objective and
real, and, hence, classical, when its results can be communicated by classical
means. In this work we revisit Bohr's postulate using modern tools from the
quantum information theory. We find a full confirmation of Bohr's idea: if a
measurement device is in a nonclassical state, the measurement results cannot
be communicated perfectly by classical means. In this case some part of
information in the measurement apparatus is lost in the process of
communication: the amount of this lost information turns out to be the quantum
discord. The information loss occurs even when the apparatus is not entangled
with the system of interest. The tools presented in this work allow to
generalize Bohr's postulate: we show that for pure system-apparatus states
quantum communication does not provide any advantage when measurement results
are communicated to more than one recipient. We further demonstrate the
superiority of quantum communication to two recipients on a mixed
system-apparatus state and show that this effect is fundamentally different
from quantum state cloning.


  The piezoelectric response is a measure of the sensitivity of a material's
polarization to stress or its strain to an applied field. Using in-operando
x-ray Bragg coherent diffraction imaging, we observe that topological vortices
are the source of a five-fold enhancement of the piezoelectric response near
the vortex core. The vortices form where several low symmetry ferroelectric
phases and phase boundaries coalesce. Unlike bulk ferroelectric solid solutions
in which a large piezoelectric response is associated with coexisting phases in
the proximity of the triple point, the largest responses for pure BaTiO3 at the
nanoscale are in spatial regions of extremely small spontaneous polarization at
vortex cores. The response decays inversely with polarization away from the
vortex, analogous to the behavior in bulk ceramics as the cation compositions
are varied away from the triple point. We use first-principles-based molecular
dynamics to augment our observations, and our results suggest that nanoscale
piezoelectric materials with large piezoelectric response can be designed
within a parameter space governed by vortex cores. Our findings have
implications for the development of next-generation nanoscale piezoelectric
materials.


  Priorities in exo-planet research are rapidly moving from finding planets to
characterizing their physical properties. Of key importance is their chemical
composition, which feeds back into our understanding of planet formation. For
the foreseeable future, far-ultraviolet spectroscopy of white dwarfs accreting
planetary debris remains the only way to directly and accurately measure the
bulk abundances of exo-planetary bodies. The exploitation of this method is
limited by the sensitivity of HST, and significant progress will require a
large-aperture space telescope with a high-throughput ultraviolet spectrograph.


  [Abridged] Context. The high-energy radiation from black-hole binaries may be
due to the reprocessing of a lamp located on the black hole axis, emitting
X-rays. The observed spectrum is made of 3 components: the direct spectrum; the
thermal bump; and the reflected spectrum made of the Compton hump and the
iron-line complex.
  Aims. We aim at computing accurately the complete reprocessed spectrum
(thermal bump + reflected) of black-hole binaries over the entire X-ray band.
We also determine the strength of the direct component. Our choice of
parameters is adapted to a source showing an important thermal component.
  Methods. We compute in full GR the illumination of a thin disk by a lamp
along the rotation axis. We use the ATM21 radiative transfer code to compute
the spectrum emitted along the disk. We ray trace this local spectrum to
determine the reprocessed spectrum as observed at infinity. We discuss the
dependence of the local and ray-traced spectra on the emission angle and spin.
  Results. We show the importance of the angle dependence of the total disk
specific intensity spectrum emitted by the illuminated atmosphere when the
thermal disk emission if fully taken into account. High spin implies high
temperature in the inner regions, so the emitted thermal disk spectrum covers
the iron-line complex. As a result we locally observe absorption lines produced
in the hot disk atmosphere. Absorption lines are narrow and disappear after ray
tracing the local spectrum.
  Conclusions. Our results mainly highlight the importance of considering the
angle dependence of the local spectrum when computing reprocessed spectra, as
was already found in a recent study. The main new result of our work is to show
the importance of computing the thermal bump of the spectrum, as this feature
can change considerably the observed iron-line complex.


  We conduct a local stability and Hopf bifurcation analysis for Compound TCP,
with small Drop-tail buffers, in three topologies. The first topology consists
of two sets of TCP flows having different round trip times, and feeding into a
core router. The second topology corresponds to two queues in tandem, and
consists of two distinct sets of TCP flows, regulated by a single edge router
and feeding into a core router. The third topology comprises of two distinct
sets of TCP flows, regulated by two separate edge routers, and feeding into a
common core router. For each of these cases, we conduct a detailed local
stability analysis and obtain conditions on the network and protocol parameters
to ensure stability. If these conditions get marginally violated, our analysis
shows that the underlying systems would lose local stability via a Hopf
bifurcation. After exhibiting a Hopf, a key concern is to determine the
asymptotic orbital stability of the bifurcating limit cycles. We present a
detailed analytical framework to address the stability of the limit cycles, and
the type of the Hopf bifurcation by invoking Poincare normal forms and the
center manifold theory. We conduct packet-level simulations to highlight the
existence and stability of the limit cycles in the queue size dynamics.


  We present the results of a search for heavy QCD axions performed by the
ArgoNeuT experiment at Fermilab. We search for heavy axions produced in the
NuMI neutrino beam target and absorber decaying into dimuon pairs, which can be
identified using the unique capabilities of ArgoNeuT and the MINOS near
detector. This decay channel is motivated by a broad class of heavy QCD axion
models that address the strong CP and axion quality problems with axion masses
above the dimuon threshold. We obtain new constraints at a 95\% confidence
level for heavy axions in the previously unexplored mass range between 0.2-0.9
GeV, for axion decay constants around tens of TeV.


  Monte Carlo data simulating phase transitions in Ising strips $D\times L,$
($D\llL) $ with periodic boundary conditions show that $T_{c}(D)=0$ for $D\leq
D^{\ast}\simeq 6$ and $0<T_{c}(D)<T_{c}(d=2)$ for $D>D^{\ast}.$ Regular scaling
of $ML^{\beta /\nu}$ vs $|T-T_{c}|L^{1/\nu}$ is obtained only for $%
D>D^{\ast}$and the Monte Carlo effective susceptibility critical exponent
$\gamma_{eff} (D)$ is shown to be well described by $\gamma (d)=\beta
(d)[\delta (d)-1]$ with $% d_{eff}(D)$ given by $d_{eff}(D)\simeq
1.5+({1/200})(D-6)$ and $\beta (d)=(\frac{3d%}{16}-{1/4}),$ $\delta
^{-1}(d)=(\frac{2d}{15}-{1/5})$, which can be understood as valid with
$d_{eff}(D)$.