  We present a new 3D lattice Boltzmann (LB) algorithm based on central moments
for the D3Q27 lattice using a cuboid grid, which is parameterized by two grid
aspect ratios that are related to the ratios of the particle speeds with
respect to that along a reference coordinate direction. The use of the cuboid
lattice grid enables the method to compute flows having different
characteristic length scales in different directions more efficiently. It is
constructed to simulate the Navier-Stokes equations consistently via
introducing counteracting corrections to the second order moment equilibria
obtained via a Chapman-Enskog analysis that eliminate the errors associated
with the grid anisotropy and the non-Galilean invariant terms. The
implementation is shown to be compact and modular, with an interpretation based
on special matrices, admitting ready extension of the standard algorithm for
the cubic lattice to the cuboid lattice via appropriate scaling of moments
based on grid aspect ratios before and after collision step and equilibria
corrections. The resulting formulation is general in that the same grid
corrections developed for the D3Q27 lattice for recovering the correct viscous
stress tensor is applicable for other lattice subsets, and a variety of
collision models, including those based on the relaxation of raw moments,
central moments and cumulants, as well as their special case involving the
distribution functions. The cuboid central moment LBM is validated against a
variety of benchmark flows, and when used in lieu of the corresponding raw
moment formulation for simulating shear flows, we show that it results in
significant improvements in numerical stability. Finally, we demonstrate that
our cuboid LB approach is efficient in simulating anisotropic shear flow
problems with significant savings in computational cost and memory storage when
compared to that based on the cubic lattice.


  To clarify how the electronic state of Sr1-xLaxRuO3 evolves with La doping,
we conducted photoemission (PES) experiments using soft x-rays. The spectral
shape of the Ru 4d derived peak near the Fermi level changes significantly with
increasing x. This variation indicates that a spectral weight transfer from the
coherent to incoherent component occurs due to an enhancement of the electron
correlation effect. Resonant PES experiments at the La 3d_{5/2} edge have
confirmed that there is no significant contribution of the La 5d state in the
energy range where the spectral weight transfer is observed. Using the
dependence of the photoelectron mean free path on the photon energy, we
subtracted the surface components from the PES spectra and confirmed that the
enhancement of the electron correlation effect with La doping is an intrinsic
bulk phenomenon. On the other hand, a large portion of the coherent component
remains at the Fermi level up to x = 0.5, reflecting that the Ru 4d state still
has itinerant characteristics. Moreover, we found that the PES spectra hardly
depend on the temperature and do not exhibit a discernible change with magnetic
ordering, suggesting that the temperature variation of the exchange splitting
does not follow the prediction of the Stoner theory. The presently obtained
experimental results indicate that the electron correlation effect plays an
important role in Sr1-xLaxRuO3 and that the Ru 4d electrons possess both local
and itinerant characteristics.


  A detailed elastic neutron scattering study of the structural and magnetic
phase transitions in single-crystal SrFe$_2$As$_2$ reveals that the
orthorhombic (O)-tetragonal (T) and the antiferromagnetic transitions coincide
at $T_\texttt{O}$ = $T_\texttt{N}$ = (201.5 $\pm$ 0.25) K. The observation of
coexisting O-T phases over a finite temperature range at the transition and the
sudden onset of the O distortion provide strong evidences that the structural
transition is first order. The simultaneous appearance and disappearance within
0.5 K upon cooling and within 0.25 K upon warming, respectively, indicate that
the magnetic and structural transitions are intimately coupled. We find that
the hysteresis in the transition temperature extends over a 1-2 K range. Based
on the observation of a remnant orthorhombic phase at temperatures higher than
\emph{T}$_\texttt{O}$, we suggest that the T-O transition may be an
order-disorder transition.


  We determine rotation periods for 127 stars in the ~115 Myr old Blanco 1 open
cluster using ~200 days of photometric monitoring with the Next Generation
Transit Survey (NGTS). These stars span F5-M3 spectral types (1.2 $\gtrsim M
\gtrsim$ 0.3 M$_{\odot}$) and increase the number of known rotation periods in
Blanco 1 by a factor of four. We determine rotation periods using three
methods: Gaussian process (GP) regression, generalised autocorrelation (G-ACF)
and Lomb-Scargle (LS) periodograms, and find that GPs and G-ACF are more
applicable to evolving spot modulation patterns. Between mid-F and mid-K
spectral types, single stars follow a well-defined rotation sequence from ~2 to
10 days, whereas stars in photometric multiple systems typically rotate faster.
This may suggest that the presence of a moderate-to-high mass ratio companion
inhibits angular momentum loss mechanisms during the early pre-main sequence,
and this signature has not been erased at ~100 Myr. The majority of mid-F to
mid-K stars display evolving modulation patterns, whereas most M stars show
stable modulation signals. This morphological change coincides with the shift
from a well-defined rotation sequence (mid-F to mid-K stars) to a broad
rotation period distribution (late-K and M stars). Finally, we compare our
rotation results for Blanco 1 to the similarly-aged Pleiades: the single star
populations in both clusters possess consistent rotation period distributions,
which suggests that the angular momentum evolution of stars follows a
well-defined pathway that is, at least for mid-F to mid-K stars, strongly
imprinted by ~100 Myr.


  Let $G$ be any simple and undirected graph. By a threshold assignment $\tau$
in $G$ we mean any function $\tau:V(G)\rightarrow \mathbb{N}$ such that
$\tau(v)\leq d_G(v)$ for any vertex $v$ of $G$. Given a graph $G$ with a
threshold assignment $\tau$, a subset of vertices $M$ is said to be a
$\tau$-monopoly if there exist at least $\tau(v)$ neighbors in $M$ for any
vertex $v \in V(G) \setminus M$. Similarly, a subset of vertices $D$ is said to
be a $\tau$-dynamic monopoly if starting with the set $D$ and iteratively
adding to the current set further vertices $u$ that have at least $\tau(u)$
neighbors in it, results in the entire vertex set $V(G)$. Denote by
$mon_{\tau}(G)$ (resp. $dyn_{\tau}(G)$) the smallest cardinality of a
$\tau$-monopoly (resp. $\tau$-dynamic monopoly) of the graph among all others.
In this paper we obtain some lower and upper bounds for these two parameters
with constant threshold assignments for Cartesian product graphs. Our bounds
improve the previous known bounds. We also determine the exact value of these
two parameters with fixed thresholds in some Cartesian graph products including
cycles and complete graphs.


  A mechanically bistable single-walled carbon nanotube can act as a
variable-shaped capacitor with a voltage-controlled transition between
collapsed and inflated states. This external control parameter provides a means
to tune the system so that collapsed and inflated states are degenerate, at
which point the tube's susceptibility to diverse external stimuli--
temperature, voltage, trapped atoms -- diverges following a universal curve,
yielding an exceptionally sensitive sensor or actuator that is characterized by
a vanishing energy scale. For example, the boundary between collapsed and
inflated states can shift hundreds of Angstroms in response to the presence or
absence of a single gas atom in the core of the tube. Several potential
nano-electromechanical devices can be based on this electrically tuned
crossover between near-degenerate collapsed and inflated configurations.


  We take the perspective of open quantum systems and examine from their
nonequilibrium dynamics the conditions when the physical quantities, their
relations and the laws of thermodynamics become well defined and viable for
quantum many body systems. We first describe how an open system nonequilibrium
dynamics (ONEq) approach is different from the closed combined system +
environment in a global thermal state (CGTs) setup. Only after the open system
equilibrates will it be amenable to conventional thermodynamics descriptions,
thus quantum thermodynamics (QTD) comes at the end rather than assumed in the
beginning. We see the open system approach having the advantage of dealing with
nonequilibrium processes as many experiments in the near future will call for.
Because it spells out the conditions of QTD's existence it can also aid us in
addressing the basic issues in quantum thermodynamics from first principles in
a systematic way. We then study one broad class of open quantum systems where
the full nonequilibrium dynamics can be solved exactly, that of the quantum
Brownian motion of $N$ strongly coupled harmonic oscillators, interacting
strongly with a scalar field environment. Here we focus on the internal energy,
heat capacity and the Third Law. We show for this class of physical models,
amongst other findings, the extensive property of the internal energy, the
positivity of the heat capacity and the validity of the Third Law from the
perspective of the behavior of the heat capacity toward zero temperature. These
conclusions obtained from exact solutions and quantitative analysis clearly
disprove claims of negative specific heat in such systems and dispel
allegations that in such systems the validity of the Third Law of
thermodynamics relies on quantum entanglement.


  AI for IT Operations (AIOps) is a powerful platform that Site Reliability
Engineers (SREs) use to automate and streamline operational workflows with
minimal human intervention. Automated log analysis is a critical task in AIOps
as it provides key insights for SREs to identify and address ongoing faults.
Tasks such as log format detection, log classification, and log parsing are key
components of automated log analysis. Most of these tasks require supervised
learning; however, there are multiple challenges due to limited labelled log
data and the diverse nature of log data. Large Language Models (LLMs) such as
BERT and GPT3 are trained using self-supervision on a vast amount of unlabeled
data. These models provide generalized representations that can be effectively
used for various downstream tasks with limited labelled data. Motivated by the
success of LLMs in specific domains like science and biology, this paper
introduces a LLM for log data which is trained on public and proprietary log
data. The results of our experiments demonstrate that the proposed LLM
outperforms existing models on multiple downstream tasks. In summary, AIOps
powered by LLMs offers an efficient and effective solution for automating log
analysis tasks and enabling SREs to focus on higher-level tasks. Our proposed
LLM, trained on public and proprietary log data, offers superior performance on
multiple downstream tasks, making it a valuable addition to the AIOps platform.


  We develop a theory of the nonlinear optical responses in superconducting
systems in the presence of a dc supercurrent. The optical transitions between
particle-hole pair bands across the superconducting gap are allowed in clean
superconductors as the inversion symmetry breaking by supercurrent. Vertex
correction is included in optical conductivity to maintain the $U(1)$ gauge
symmetry in the mean-field formalism, which contains the contributions from
collective modes. We show two pronounced current-dependent peaks in the
second-harmonic generalization $\sigma^{(2)}(2\omega,\omega,\omega)$ at the gap
edge $2\hbar\omega=2\Delta$ and $\hbar\omega=2\Delta$ and one in the
photocurrent effect $\sigma^{(2)}(0,\omega,-\omega)$ at $\hbar\omega=2\Delta$,
all of which diverge in the clean limit. We demonstrate this in the models of a
single-band superconductor with $s$-wave and $d$-wave pairings, and Dirac
fermion systems with $s$-wave pairing. Our theory predicts that the
current-induced peak in $\text{Im}[\sigma^{(2)}(\omega)]$ is proportional to
the square of the supercurrent density in the $s$-wave single-band model, with
the same order of magnitude as the recent experimental observation of
second-harmonic generation in NbN by Nakamura et al. [Phys. Rev. Lett. 125,
097004 (2020)]. Supercurrent induced nonlinear optical spectroscopy provides a
valuable toolbox to explore novel superconductors.


  We study the effects of the repulsive on-site interactions on the broadening
of the localized Wannier functions used for calculating the parameters to
describe ultracold atoms in optical lattices. For this, we replace the common
single-particle Wannier functions, which do not contain any information about
the interactions, by two-particle Wannier functions ("Twonniers") obtained from
an exact solution which takes the interactions into account. We then use these
interaction-dependent basis functions to calculate the Bose--Hubbard model
parameters, showing that they are substantially different both at low and high
lattice depths, from the ones calculated using single-particle Wannier
functions. Our results suggest that density effects are not negligible for many
parameter ranges and need to be taken into account in metrology experiments.


  The existence of the Hamiltonians of the renormalized point interactions in
two and three dimensional Riemannian manifolds and that of a relativistic
extension of this model in two dimensions are proven. Although it is much more
difficult, the proof of existence of the Hamiltonian for the renormalized
resolvent for the non-relativistic Lee model can still be given. To accomplish
these results directly from the resolvent formula, we employ some basic tools
from the semigroup theory.


  The excitation and propagation of electrostatic solitary waves(ESWs) are
observed in two-dimensional particle-in-cell simulations of ion beam
neutralization by electron injection by a filament. Electrons from the filament
are attracted by positive ions and bounce inside ion beam pulse. Bouncing back
and forth electron streams then starts to mix, creating the two-stream
instability. The instability saturates with the formation of ESWs. These ESWs
reach several centimeters in longitudinal size and are stable for a long time.
The excitation of large-amplitude ESWs reduces the degree of neutralization of
the ion beam pulse. In addition, the dissipation of ESWs causes heating of
neutralizing electrons and their escape from the ion beam, leading to further
reduction of neutralization degree.


  The fusion reaction of a halo nucleus 11Be on 208Pb is described by a
three-body direct reaction model. A time-dependent wave packet approach is
applied to a three-body reaction problem. The wave packet approach enables us
to obtain scattering solutions without considering the three-body scattering
boundary conditions. The time evolution of the wave packet also helps us to
obtain intuitive understanding of the reaction dynamics. The calculations
indicate a decrease of the fusion probability by the presence of the halo
neutron.


  We prove that if $(\varphi_n)_{n=0}^\infty, \; \varphi_0 \equiv 1, $ is a
basis in the space of entire functions of $d$ complex variables, $d\geq 1,$
then for every compact $K\subset \mathbb{C}^d$ there is a compact $K_1 \supset
K$ such that for every entire function $f= \sum_{n=0}^\infty f_n \varphi_n$ we
have $\sum_{n=0}^\infty |f_n|\, \sup_{K}|\varphi_n| \leq \sup_{K_1} |f|.$ A
similar assertion holds for bases in the space of global analytic functions on
a Stein manifold with the Liouville Property.


  We prove that there are no Shimura curves $X_0^D(N)$ of squarefree level and
of genus at least two admitting a smooth plane model.


  In this study, the creation of a database consisting of images obtained as a
result of deformation in the images recorded by these cameras by injecting
faults into the robot camera nodes and alternative uses of this database are
explained. The study is based on an existing camera fault injection software
that injects faults into the cameras of a working robot and collects the normal
and faulty images recorded during this injection. The database obtained in the
study is a source for the detection of anomalies that may occur in robotic
systems. Within the scope of this study, a database of 10000 images consisting
of 5000 normal and 5000 faulty images was created. Faulty images were obtained
by injecting seven different types of image faults, namely erosion, dilation,
opening, closing, gradient, motionblur and partialloss, at different times
while the robot was operating.


  One of the classical problems in group theory is determining the set of
positive integers $n$ such that every group of order $n$ has a particular
property $P$, such as cyclic or abelian. We first present the Sylow theorems
and the idea of solvable groups, both of which will be invaluable in our
analysis. We then gather various solutions to this problem for cyclic, abelian,
nilpotent, and supersolvable groups, as well as groups with ordered Sylow
towers.
  This work is an exposition of known results, but it is hoped that the reader
will find useful the presentation in a single account of the various tools that
have been used to solve this general problem. This article claims no
originality, but is meant as a synthesis of related knowledge and resources.


  To an orthogonal or unitary involution on a central simple algebra of degree
4, or to a symplectic involution on a central simple algebra of degree 8, we
associate a Pfister form that characterises the decomposability of the algebra
with involution. In this way we obtain a unified approach to known
decomposability criteria for several cases, and a new result for symplectic
involutions on degree $8$ algebras in characteristic 2.


  We study codes that are list-decodable under insertions and deletions.
Specifically, we consider the setting where a codeword over some finite
alphabet of size $q$ may suffer from $\delta$ fraction of adversarial deletions
and $\gamma$ fraction of adversarial insertions. A code is said to be
$L$-list-decodable if there is an (efficient) algorithm that, given a received
word, reports a list of $L$ codewords that include the original codeword.
  Using the concept of synchronization strings, introduced by the first two
authors [STOC 2017], we show some surprising results. We show that for every
$0\leq\delta<1$, every $0\leq\gamma<\infty$ and every $\epsilon>0$ there exist
efficient codes of rate $1-\delta-\epsilon$ and constant alphabet (so
$q=O_{\delta,\gamma,\epsilon}(1)$) and sub-logarithmic list sizes. We stress
that the fraction of insertions can be arbitrarily large and the rate is
independent of this parameter. Our result sheds light on the remarkable
asymmetry between the impact of insertions and deletions from the point of view
of error-correction: Whereas deletions cost in the rate of the code, insertion
costs are borne by the adversary and not the code!
  We also prove several tight bounds on the parameters of list-decodable insdel
codes. In particular, we show that the alphabet size of insdel codes needs to
be exponentially large in $\epsilon^{-1}$, where $\epsilon$ is the gap to
capacity above. Our result even applies to settings where the unique-decoding
capacity equals the list-decoding capacity and when it does so, it shows that
the alphabet size needs to be exponentially large in the gap to capacity. This
is sharp contrast to the Hamming error model where alphabet size polynomial in
$\epsilon^{-1}$ suffices for unique decoding and also shows that the
exponential dependence on the alphabet size in previous works that constructed
insdel codes is actually necessary!


  We provide a prescription to compute the gravitational multipole moments of
compact objects for asymptotically de Sitter spacetimes. Our prescription
builds upon a recent definition of the gravitational multipole moments in terms
of Noether charges associated to specific vector fields, within the residual
harmonic gauge, dubbed multipole symmetries. We first derive the multipole
symmetries for spacetimes which are asymptotically de Sitter; we also show that
these symmetry vector fields eliminate the non-propagating degrees of freedom
from the linearized gravitational wave equation in a suitable gauge. We then
apply our prescription to the Kerr-de Sitter black hole and compute its
multipole structure. Our result recovers the Geroch-Hansen moments of the Kerr
black hole in the limit of vanishing cosmological constant.


  We constrain the coupling between axionlike particles (ALPs) and photons,
measured with the superconducting resonant detection circuit of a cryogenic
Penning trap. By searching the noise spectrum of our fixed-frequency resonant
circuit for peaks caused by dark matter ALPs converting into photons in the
strong magnetic field of the Penning-trap magnet, we are able to constrain the
coupling of ALPs with masses around $2.7906-2.7914\,\textrm{neV/c}^2$ to
$g_{a\gamma}< 1 \times 10^{-11}\,\textrm{GeV}^{-1}$. This is more than one
order of magnitude lower than the best laboratory haloscope and approximately 5
times lower than the CERN axion solar telescope (CAST), setting limits in a
mass and coupling range which is not constrained by astrophysical observations.
Our approach can be extended to many other Penning-trap experiments and has the
potential to provide broad limits in the low ALP mass range.


  The goal of this paper is to understand the conditional law of a stochastic
process once it has been observed over an interval. To make this precise, we
introduce the notion of a continuous disintegration: a regular conditional
probability measure which varies continuously in the conditioned parameter. The
conditioning is infinite-dimensional in character, which leads us to consider
the general case of probability measures in Banach spaces. Our main result is
that for a certain quantity $M$ based on the covariance structure, the
finiteness of M is a necessary and sufficient condition for a Gaussian measure
to have a continuous disintegration. The condition is quite reasonable: for the
familiar case of stationary processes, M = 1.


  Majorana zero modes are localized quasiparticles that obey non-Abelian
exchange statistics. Braiding Majorana zero modes forms the basis of
topologically protected quantum operations which could in principle
significantly reduce qubit decoherence and gate control errors in the device
level. Therefore, searching for Majorana zero modes in various solid state
systems is a major topic in condensed matter physics and quantum computer
science. Since the first experimental signature observed in hybrid
superconductor-semiconductor nanowire devices, this field has witnessed a
dramatic expansion in material science, transport experiments and theory. While
making the first topological qubit based on these Majorana nanowires is
currently an on-going effort, several related important transport experiments
are still being pursued in the near term. These will not only serve as
intermediate steps but also show Majorana physics in a more fundamental aspect.
In this perspective, we summarize these key Majorana experiments and the
potential challenges.


  We answer a question raised by Lanier about the possibility of generating
$A_n$ and $S_n$ with two elements of order $k$, where $n \geqslant k \geqslant
3$. We show that this can always be done apart from some clear exceptions.


  Hydrodynamic flows in biological systems are often generated by active chiral
processes near or on surfaces. Important examples are beating cilia, force
generation in actomyosin networks, and motile bacteria interacting with
surfaces. Here we develop a coarse grained description of active chiral films
that captures generic features of flow and rotation patterns driven by chiral
motors. We discuss force and torque balances within the film and on the surface
and highlight the role of the intrinsic rotation field. We arrive at a two
dimensional effective theory and discuss our results in the context of ciliary
carpets and thin films of bacterial suspensions.


  The alignment of autonomous agents with human values is a pivotal challenge
when deploying these agents within physical environments, where safety is an
important concern. However, defining the agent's objective as a reward and/or
cost function is inherently complex and prone to human errors. In response to
this challenge, we present a novel approach that leverages one-class decision
trees to facilitate learning from expert demonstrations. These decision trees
provide a foundation for representing a set of constraints pertinent to the
given environment as a logical formula in disjunctive normal form. The learned
constraints are subsequently employed within an oracle constrained
reinforcement learning framework, enabling the acquisition of a safe policy. In
contrast to other methods, our approach offers an interpretable representation
of the constraints, a vital feature in safety-critical environments. To
validate the effectiveness of our proposed method, we conduct experiments in
synthetic benchmark domains and a realistic driving environment.


  Programming-by-example is the task of synthesizing a program that is
consistent with a set of user-provided input-output examples. As examples are
often an under-specification of one's intent, a good synthesizer must choose
the intended program from the many that are consistent with the given set of
examples. Prior work frames program synthesis as a cooperative game between a
listener (that synthesizes programs) and a speaker (a user choosing examples),
and shows that models of computational pragmatic inference are effective in
choosing the user intended programs. However, these models require
counterfactual reasoning over a large set of programs and examples, which is
infeasible in realistic program spaces. In this paper, we propose a novel way
to amortize this search with neural networks. We sample pairs of programs and
examples via self-play between listener and speaker models, and use pragmatic
inference to choose informative training examples from this sample.We then use
the informative dataset to train models to improve the synthesizer's ability to
disambiguate user-provided examples without human supervision. We validate our
method on the challenging task of synthesizing regular expressions from example
strings, and find that our method (1) outperforms models trained without
choosing pragmatic examples by 23% (a 51% relative increase) (2) matches the
performance of supervised learning on a dataset of pragmatic examples provided
by humans, despite using no human data in training.


  This text deals with multidimensional Borg-Levinson inverse theory. Its main
purpose is to establish that the Dirichlet eigenvalues and Neumann boundary
data of the Dirichlet Laplacian acting in a bounded domain of dimension 2 or
greater, uniquely determine the real-valued bounded potential. We first address
the case of incomplete spectral data, where finitely many boundary spectral
eigen-pairs remain unknown. Under suitable summability condition on the Neumann
data, we also consider the case where only the asymptotic behavior of the
eigenvalues is known. Finally, we use the multidimensional Borg-Levinson theory
for solving parabolic inverse coefficient problems.


  We develop a new method for studying sums of Kloosterman sums related to the
spectral exponential sum. As a corollary, we obtain a new proof of the estimate
of Soundararajan and Young for the error term in the prime geodesic theorem.


  We numerically study the Berezinskii-Kosterlitz-Thouless (BKT) transition of
a spin-1 spinor Bose gas under the quadratic Zeeman effect. A calculation of
the mass and spin superfluid densities shows that (i) the BKT transition occurs
only when vortices are classified by the integer group $\mathbb{Z}$, and
$\mathbb{Z}_2$ vortices do not contribute to the BKT transition, (ii) the two
BKT transition temperatures for mass and spin superfluid densities are
different for a positive quadratic Zeeman effect and equal for a negative
quadratic Zeeman effect, and (iii) the universal relation of the superfluid
densities at the BKT transition temperature is changed when multiple kinds of
vortices contribute to the transition. We have further found that (iv)
spin-singlet pairs in non-magnetic states show the
quasi-off-diagonal-long-range order at the different temperature lower than the
BKT transition temperature, giving the new universal relation of the superfluid
density.


  We find a new family of AdS_4 vacua in IIA string theory. The internal space
is topologically either the complex projective space CP^3 or the "flag
manifold" SU(3)/(U(1)xU(1)), but the metric is in general neither Einstein nor
Kaehler. All known moduli are stabilized by fluxes, without using quantum
effects or orientifold planes. The analysis is completely ten--dimensional and
does not rely on assumptions about Kaluza--Klein reduction.


  Graph neural networks (GNNs) have achieved state-of-the-art performance in
graph representation learning. Message passing neural networks, which learn
representations through recursively aggregating information from each node and
its neighbors, are among the most commonly-used GNNs. However, a wealth of
structural information of individual nodes and full graphs is often ignored in
such process, which restricts the expressive power of GNNs. Various graph data
augmentation methods that enable the message passing with richer structure
knowledge have been introduced as one main way to tackle this issue, but they
are often focused on individual structure features and difficult to scale up
with more structure features. In this work we propose a novel approach, namely
collective structure knowledge-augmented graph neural network (CoS-GNN), in
which a new message passing method is introduced to allow GNNs to harness a
diverse set of node- and graph-level structure features, together with original
node features/attributes, in augmented graphs. In doing so, our approach
largely improves the structural knowledge modeling of GNNs in both node and
graph levels, resulting in substantially improved graph representations. This
is justified by extensive empirical results where CoS-GNN outperforms
state-of-the-art models in various graph-level learning tasks, including graph
classification, anomaly detection, and out-of-distribution generalization.


  We provide a new bi-criteria $\tilde{O}(\log^2 k)$ competitive algorithm for
explainable $k$-means clustering. Explainable $k$-means was recently introduced
by Dasgupta, Frost, Moshkovitz, and Rashtchian (ICML 2020). It is described by
an easy to interpret and understand (threshold) decision tree or diagram. The
cost of the explainable $k$-means clustering equals to the sum of costs of its
clusters; and the cost of each cluster equals the sum of squared distances from
the points in the cluster to the center of that cluster. The best non
bi-criteria algorithm for explainable clustering $\tilde{O}(k)$ competitive,
and this bound is tight.
  Our randomized bi-criteria algorithm constructs a threshold decision tree
that partitions the data set into $(1+\delta)k$ clusters (where $\delta\in
(0,1)$ is a parameter of the algorithm). The cost of this clustering is at most
$\tilde{O}(1/ \delta \cdot \log^2 k)$ times the cost of the optimal
unconstrained $k$-means clustering. We show that this bound is almost optimal.


  Image captioning is a technology that produces text-based descriptions for an
image. Deep learning-based solutions built on top of feature recognition may
very well serve the purpose. But as with any other machine learning solution,
the user understanding in the process of caption generation is poor and the
model does not provide any explanation for its predictions and hence the
conventional methods are also referred to as Black-Box methods. Thus, an
approach where the model's predictions are trusted by the user is needed to
appreciate interoperability. Explainable AI is an approach where a conventional
method is approached in a way that the model or the algorithm's predictions can
be explainable and justifiable. Thus, this article tries to approach image
captioning using Explainable AI such that the resulting captions generated by
the model can be Explained and visualized. A newer architecture with a CNN
decoder and hierarchical attention concept has been used to increase speed and
accuracy of caption generation. Also, incorporating explainability to a model
makes it more trustable when used in an application. The model is trained and
evaluated using MSCOCO dataset and both quantitative and qualitative results
are presented in this article.


  It is well known that if $G$ is a countable amenable group and $G
\curvearrowright (Y, \nu)$ factors onto $G \curvearrowright (X, \mu)$, then the
entropy of the first action must be greater than or equal to the entropy of the
second action. In particular, if $G \curvearrowright (X, \mu)$ has infinite
entropy, then the action $G \curvearrowright (Y, \nu)$ does not admit any
finite generating partition. On the other hand, we prove that if $G$ is a
countable non-amenable group then there exists a finite integer $n$ with the
following property: for every probability-measure-preserving action $G
\curvearrowright (X, \mu)$ there is a $G$-invariant probability measure $\nu$
on $n^G$ such that $G \curvearrowright (n^G, \nu)$ factors onto $G
\curvearrowright (X, \mu)$. For many non-amenable groups, $n$ can be chosen to
be $4$ or smaller. We also obtain a similar result with respect to continuous
actions on compact spaces and continuous factor maps.


  Nitrogen is the fifth most abundant element in the Universe, yet the
gas-phase chemistry of N-bearing species remains poorly understood. Nitrogen
hydrides are key molecules of nitrogen chemistry. Their abundance ratios place
strong constraints on the production pathways and reaction rates of
nitrogen-bearing molecules. We observed the class 0 protostar IRAS16293-2422
with the heterodyne instrument HIFI, covering most of the frequency range from
0.48 to 1.78~THz at high spectral resolution. The hyperfine structure of the
amidogen radical o-NH2 is resolved and seen in absorption against the continuum
of the protostar. Several transitions of ammonia from 1.2 to 1.8~THz are also
seen in absorption. These lines trace the low-density envelope of the
protostar. Column densities and abundances are estimated for each hydride. We
find that NH:NH2:NH3=5:1:300. {Dark clouds chemical models predict steady-state
abundances of NH2 and NH3 in reasonable agreement with the present
observations, whilst that of NH is underpredicted by more than one order of
magnitude, even using updated kinetic rates. Additional modelling of the
nitrogen gas-phase chemistry in dark-cloud conditions is necessary before
having recourse to heterogen processes.


  First, second and third nearest neighbor mixing potentials for FePt alloys,
were calculated from first principles using a Connolly-Williams approach. Using
the mixing potentials obtained in this manner, the dependency of equilibrium
L1_0 ordering on temperature was studied for bulk and for a spherical
nanoparticle with 3.5nm diameter at equiatomic composition by use of Monte
Carlo simulation and the analytical ring approximation. The calculated
order-disorder temperature for bulk (1495-1514 K) was in relatively good
agreement (4% error) with the experimental value (1572K). For nanoparticles of
finite size, the (long range) order parameter changed continuously from unity
to zero with increasing temperature. Rather than a discontinuity indicative of
a phase transition we obtained an inflection point in the order as a function
of temperature. This inflection point occurred at a temperature below the bulk
phase transition temperature and which decreased as the particle size
decreased. Our calculations predict that 3.5nm diameter particles in
configurational equilibrium at 600 C (a typical annealing temperature for
promoting L1_0 ordering) have an L1_0 order parameter of 0.83 (compared to a
maximum possible value equal to unity). According to our investigations, the
experimental absence of (relatively) high L1_0 order in 3.5nm diameter
nanoparticles annealed at 600 C or below is primarily a problem of kinetics
rather than equilibrium


  Fueled by breakthrough technology developments, the biological, biomedical,
and behavioral sciences are now collecting more data than ever before. There is
a critical need for time- and cost-efficient strategies to analyze and
interpret these data to advance human health. The recent rise of machine
learning as a powerful technique to integrate multimodality, multifidelity
data, and reveal correlations between intertwined phenomena presents a special
opportunity in this regard. However, classical machine learning techniques
often ignore the fundamental laws of physics and result in ill-posed problems
or non-physical solutions. Multiscale modeling is a successful strategy to
integrate multiscale, multiphysics data and uncover mechanisms that explain the
emergence of function. However, multiscale modeling alone often fails to
efficiently combine large data sets from different sources and different levels
of resolution. We show how machine learning and multiscale modeling can
complement each other to create robust predictive models that integrate the
underlying physics to manage ill-posed problems and explore massive design
spaces. We critically review the current literature, highlight applications and
opportunities, address open questions, and discuss potential challenges and
limitations in four overarching topical areas: ordinary differential equations,
partial differential equations, data-driven approaches, and theory-driven
approaches. Towards these goals, we leverage expertise in applied mathematics,
computer science, computational biology, biophysics, biomechanics, engineering
mechanics, experimentation, and medicine. Our multidisciplinary perspective
suggests that integrating machine learning and multiscale modeling can provide
new insights into disease mechanisms, help identify new targets and treatment
strategies, and inform decision making for the benefit of human health.


  We ask whether neural networks can learn to use secret keys to protect
information from other neural networks. Specifically, we focus on ensuring
confidentiality properties in a multiagent system, and we specify those
properties in terms of an adversary. Thus, a system may consist of neural
networks named Alice and Bob, and we aim to limit what a third neural network
named Eve learns from eavesdropping on the communication between Alice and Bob.
We do not prescribe specific cryptographic algorithms to these neural networks;
instead, we train end-to-end, adversarially. We demonstrate that the neural
networks can learn how to perform forms of encryption and decryption, and also
how to apply these operations selectively in order to meet confidentiality
goals.


  The ground-state magnetic response of fullerene molecules with up to 36
vertices is calculated, when spins classical or with magnitude $s=\frac{1}{2}$
are located on their vertices and interact according to the nearest-neighbor
antiferromagnetic Heisenberg model. The frustrated topology, which originates
in the pentagons of the fullerenes and is enhanced by their close proximity,
leads to a significant number of classical magnetization and susceptibility
discontinuities, something not expected for a model lacking magnetic
anisotropy. This establishes the classical discontinuities as a generic feature
of fullerene molecules irrespective of their symmetry. The largest number of
discontinuities have the molecule with 26 sites, four of the magnetization and
two of the susceptibility, and an isomer with 34 sites, which has three each.
In addition, for several of the fullerenes the classical zero-field lowest
energy configuration has finite magnetization, which is unexpected for
antiferromagnetic interactions between an even number of spins and with each
spin having the same number of nearest-neighbors. The molecules come in
different symmetries and topologies and there are only a few patterns of
magnetic behavior that can be detected from such a small sample of relatively
small fullerenes. Contrary to the classical case, in the full quantum limit
$s=\frac{1}{2}$ there are no discontinuities for a subset of the molecules that
was considered. This leaves the icosahedral symmetry fullerenes as the only
ones known supporting ground-state magnetization discontinuities for
$s=\frac{1}{2}$. It is also found that a molecule with 34 sites has a
doubly-degenerate ground state when $s=\frac{1}{2}$.


  Free energy is energy that is available to do work. Maximizing the free
energy gain and the gain in work that can be extracted from a system is
important for a wide variety of physical and technological processes, from
energy harvesting processes such as photosynthesis to energy storage systems
such as fuels and batteries. This paper extends recent results from
non-equilibrium thermodynamics and quantum resource theory to derive
closed-form solutions for the maximum possible gain in free energy and
extractable work that can be obtained by varying the initial states of
classical and quantum stochastic processes. Simple formulae allow the
comparison the free energy increase for the optimal procedure with that for a
sub-optimal procedure. The problem of finding the optimal free-energy
harvesting procedure is shown to be convex and solvable via gradient descent.


  Let $R$ be a commutative Noetherian local ring of prime characteristic $p$
and $f:R\to R$ the Frobenius ring homomorphism. For $e\ge 1$ let $R^{(e)}$
denote the ring $R$ viewed as an $R$-module via $f^e$. Results of Peskine,
Szpiro, and Herzog state that for finitely generated modules $M$, $M$ has
finite projective dimension if and only if
$\operatorname{Tor}_i^R(R^{(e)},M)=0$ for all $i>0$ and all (equivalently,
infinitely many) $e\ge 1$. We prove this statement holds for arbitrary modules
using the theory of flat covers and minimal flat resolutions.


  We report results from a re-analysis of the BeppoSAX observation of Coma and
from the analysis of a second, yet unpublished observation of the same object.
  From our re-analysis of the first observation we find that the statistical
evidence for a hard tail is about 2 sigma. From the analysis of the second
observation which, thanks to the lower background and the longer exposure time,
is characterized by a larger signal to noise we find no evidence for a hard
tail. From the upper limit on the flux of the hard tail, using the standard
Inverse Compton formulae, we derive a lower limit for the magnetic of about
0.2-0.4 microGauss consistent with Faraday rotation measurements.


  Load frequency control (LFC) is widely employed in power systems to stabilize
frequency fluctuation and guarantee power quality. However, most existing LFC
methods rely on accurate power system modeling and usually ignore the nonlinear
characteristics of the system, limiting controllers' performance. To solve
these problems, this paper proposes a model-free LFC method for nonlinear power
systems based on deep deterministic policy gradient (DDPG) framework. The
proposed method establishes an emulator network to emulate power system
dynamics. After defining the action-value function, the emulator network is
applied for control actions evaluation instead of the critic network. Then the
actor network controller is effectively optimized by estimating the policy
gradient based on zeroth-order optimization (ZOO) and backpropagation
algorithm. Simulation results and corresponding comparisons demonstrate the
designed controller can generate appropriate control actions and has strong
adaptability for nonlinear power systems.


  The ubiquitous Variable-Byte encoding is one of the fastest compressed
representation for integer sequences. However, its compression ratio is usually
not competitive with other more sophisticated encoders, especially when the
integers to be compressed are small that is the typical case for inverted
indexes. This paper shows that the compression ratio of Variable-Byte can be
improved by 2x by adopting a partitioned representation of the inverted lists.
This makes Variable-Byte surprisingly competitive in space with the best
bit-aligned encoders, hence disproving the folklore belief that Variable-Byte
is space-inefficient for inverted index compression. Despite the significant
space savings, we show that our optimization almost comes for free, given that:
we introduce an optimal partitioning algorithm that does not affect indexing
time because of its linear-time complexity; we show that the query processing
speed of Variable-Byte is preserved, with an extensive experimental analysis
and comparison with several other state-of-the-art encoders.


  Shape Dynamics (SD) is a new theory of gravity that is based on fewer and
more fundamental first principles than General Relativity (GR). The most
important feature of SD is the replacement of GR's relativity of simultaneity
with a more tractable gauge symmetry, namely invariance under spatial conformal
transformations. This Tutorial contains both a quick introduction for readers
curious about SD and a detailed walk-through of the historical and conceptual
motivations for the theory, its logical development from first principles and
an in-depth description of its present status. The Tutorial is sufficiently
self-contained for an undergrad student with some basic background in GR and
Lagrangian/Hamiltonian mechanics. It is intended both as a reference text for
students approaching the subject and as a review for researchers interested in
the theory.


  This paper is a cursory study on how topological features are preserved
within the internal representations of neural network layers. Using techniques
from topological data analysis, namely persistent homology, the topological
features of a simple feedforward neural network's layer representations of a
modified torus with a Klein bottle-like twist were computed. The network
appeared to approximate homeomorphisms in early layers, before significantly
changing the topology of the data in deeper layers. The resulting noise
hampered the ability of persistent homology to compute these features, however
similar topological features seemed to persist longer in a network with a
bijective activation function.


  Epilepsy is a neurological disorder that affects normal neural activity.
These electrical activities can be recorded as signals containing information
about the brain known as Electroencephalography (EEG) signals. Analysis of the
EEG signals by individuals for epilepsy diagnosis is subjective and
time-consuming. So, an automatic classification system with high detection
accuracy is required to overcome possible errors. In this study, the discrete
wavelet transform has been applied to EEG signals. Then, entropy measures and
embedding parameters have been extracted. These features have been investigated
individually to find the most discriminating ones. The significance level of
each feature was evaluated by statistical analysis. Consequently, LDA and SVM
algorithms have been employed to categorize the EEG signals. The results have
indicated that the features of Embedding parameters, PermutationEntropy,
FuzzyEntropy, SampleEntropy, NormEntropy, SureEntropy, LogEntropy, and
ThresholdEntropy have the potential to discriminate epileptic patients from
healthy subjects significantly. Also, SVM classifier has achieved the highest
classification accuracy. In this study, we could find effective embedding-based
and entropy-based features as appropriate single measures for identifying
abnormal activities that can efficiently discriminate the EEG signals of
epileptics from healthy individuals. According to the results, they can be used
for automatic classification of epileptic EEG signals that are difficult to
examine visually.


  The ice-type model proposed by Linus Pauling to explain its entropy at low
temperatures is here approached in a didactic way. We first present a
theoretically estimated low-temperature entropy and compare it with numerical
results. Then, we consider the mapping between this model and the three-colour
problem, i.e.,colouring a regular graph with coordination equal to 4 (a
two-dimensional lattice) with three colours, for which we apply the
transfer-matrix method to calculate all allowed configurations for
two-dimensional square lattices of $N$ oxygen atoms ranging from 4 to 225.
Finally, from a linear regression of the transfer matrix results, we obtain an
estimate for the case $N\rightarrow \infty $ which is compared with the exact
solution by Lieb.


  Minimal triplet scalar extension of the Standard Model demanding custodial
symmetry gives rise to the extended Georgi-Machacek (eGM) model. We compute
one-loop corrections to all $2 \rightarrow 2$ bosonic scattering amplitudes in
the eGM model, and place next-to-leading order (NLO) unitarity bounds on the
quartic couplings. Additionally, we derive state-of-the-art constraints on the
quartic couplings demanding the stability of the scalar potential. We perform a
global fit of the eGM model to these theoretical bounds and to the latest Higgs
signal strength results from the LHC detectors. In addition to the custodial
symmetry, imposing a global $SU(2)_L\otimes SU(2)_R$ symmetry on the scalar
potential at the electroweak scale results in the well-known Georgi-Machacek
(GM) model. We assess the impact of the state-of-the-art theoretical
constraints on the fit to the Higgs signal strength data in the GM model, with
particular emphasis on the NLO unitarity bounds. We observe that the global fit
disfavors the region where $\kappa_V$ is greater than $1.05$ with a 95.4\%
confidence level. We obtain an upper limit on the absolute values of the
quartic couplings to be 1.9 (4.2) and see that the absolute mass differences
between the heavy Higgs bosons cannot exceed 400 GeV (380 GeV) in the GM (eGM)
model. Finally, we find that the maximal mass splitting within the members of
custodial symmetric multiplets is restricted to be smaller than 210 GeV in the
eGM model.


  Fake news on social media has become a hot topic of research as it negatively
impacts the discourse of real news in the public. Specifically, the ongoing
COVID-19 pandemic has seen a rise of inaccurate and misleading information due
to the surrounding controversies and unknown details at the beginning of the
pandemic. The FakeNews task at MediaEval 2020 tackles this problem by creating
a challenge to automatically detect tweets containing misinformation based on
text and structure from Twitter follower network. In this paper, we present a
simple approach that uses BERT embeddings and a shallow neural network for
classifying tweets using only text, and discuss our findings and limitations of
the approach in text-based misinformation detection.


  This paper proposes a new framework for constructing interval-valued state
estimators for discrete-time linear and switched linear systems. Our main
results are (i) the derivation of the tightest interval-valued estimator for
linear discrete-time systems; (ii) a systematic design method for
interval-valued state estimators; (iii) an application of the proposed
estimation framework to switched linear systems.


  The phase behavior of hydrocarbon fluids confined in porous media has been
reported to deviate significantly from that in the bulk environment due to the
existence of sub-10nm pores. Though experiments and simulations have measured
the bubble/dew points and sorption isotherms of hydrocarbons confined in both
natural and synthetic nanopores, the confinement effects in terms of the
strength of fluid-pore interactions tuned by surface wettability and chemistry
have received comparably less discussion. More importantly, the underlying
physics of confinement-induced phenomena remain obfuscated. In this work, we
studied the phase behavior and capillary condensation of n-hexane to understand
the effects of confinement at the molecular level. To systematically
investigate the pore effects, we constructed two types of wall confinements;
one is a structureless virtual wall described by the Steele potential and the
other one is an all-atom amorphous silica structure with surface modified by
hydroxyl groups. Our numerical results demonstrated the importance of
fluid-pore interaction, pore size, and pore morphology effects in mediating the
pressure-volume-temperature (PVT) properties of hydrocarbons. The most
remarkable finding of this work was that the saturation pressure predicted from
the van der Waals-type adsorption isothermal loop could be elevated or
suppressed relative to the bulk phase, as illustrated in the graphical
abstract. As the surface energy (i.e., fluid-pore interaction) decreased, the
isothermal vapor pressure increased, indicating a greater preference for the
fluid to exist in the vapor state. Sufficient reduction of the fluid-pore
interactions could even elevate the vapor pressure above that of the bulk
fluid.


  We present a highly parallelisable scheme for treating functional
Renormalisation Group equations which incorporates a quasi-particle-based
feedback on the flow and provides direct access to real-frequency self-energy
data. This allows to map out the boundaries of Fermi-liquid regimes and to
study the effect of quasi-particle degradation near Fermi liquid instabilities.
As a first application, selected results for the two-dimensional half-filled
perfectly nested Hubbard model are shown.


  The problem of mismatched decoding with an additive metric $q$ for a discrete
memoryless channel $W$ is addressed. The "product-space" improvement of the
random coding lower bound on the mismatch capacity, $C_q^{(\infty)}(W)$, was
introduced by Csisz\'ar and Narayan.
  We study two kinds of decoders. The {\it $\delta$-margin mismatched decoder}
outputs a message whose metric with the channel output exceeds that of all the
other codewords by at least $\delta$. The {\it $\tau$-threshold decoder}
outputs a single message whose metric with the channel output exceeds a
threshold $\tau$. Both decoders declare an error if they fail to find a message
that meets the requirement. It is assumed that $q$ is bounded.
  It is proved that $C_q^{(\infty)}(W)$ is equal to the mismatch capacity with
a constant margin decoder. We next consider sequences of $P$-constant
composition codebooks, whose empirical distribution of the codewords are at
least $o(n^{-1/2})$ close in the $L_1$ distance sense to $P$. Using the Central
Limit Theorem, it is shown that for such sequences of codebooks the supremum of
achievable rates with constant threshold decoding is upper bounded by the
supremum of the achievable rates with a constant margin decoder, and therefore
also by $C_q^{(\infty)}(W)$.
  Further, a soft converse is proved stating that if the average probability of
error of a sequence of codebooks converges to zero sufficiently fast, the rate
of the code sequence is upper bounded by $C_q^{(\infty)}(W)$. In particular, if
$q$ is a bounded rational metric, and the average probability of error
converges to zero faster than $O(n^{-1})$, then $R\leq C_q^{(\infty)}(W)$.
Finally, a max-min multi-letter upper bound on the mismatch capacity that bears
some resemblance to $C_q^{(\infty)}(W)$ is presented.


  In recent years, the concept of resilience has been introduced to the field
of engineering as it relates to disaster mitigation and management. However,
the built environment is only one element that supports community
functionality. Maintaining community functionality during and after a disaster,
defined as resilience, is influenced by multiple components. This report
summarizes the research activities of the first two years of an ongoing
collaboration between the Politecnico di Torino and the University of
California, Berkeley, in the field of disaster resilience. Chapter 1 focuses on
the economic dimension of disaster resilience with an application to the San
Francisco Bay Area; Chapter 2 analyzes the option of using base-isolation
systems to improve the resilience of hospitals and school buildings; Chapter 3
investigates the possibility to adopt discrete event simulation models and a
meta-model to measure the resilience of the emergency department of a hospital;
Chapter 4 applies the meta-model developed in Chapter 3 to the hospital network
in the San Francisco Bay Area, showing the potential of the model for design
purposes Chapter 5 uses a questionnaire combined with factorial analysis to
evaluate the resilience of a hospital; Chapter 6 applies the concept of
agent-based models to analyze the performance of socio-technical networks
during an emergency. Two applications are shown: a museum and a train station;
Chapter 7 defines restoration fragility functions as tools to measure
uncertainties in the restoration process; and Chapter 8 focuses on modeling
infrastructure interdependencies using temporal networks at different spatial
scales.


  The smallest Euler brick, discovered by Paul Halcke, has edges $(177, 44,
240) $ and face diagonals $(125, 267, 244 ) $, generated by the primitive
Pythagorean triple $ (3, 4, 5) $. Let $ (u,v,w) $ primitive Pythagorean triple,
Sounderson made a generalization parameterization of the edges
\begin{equation*} a = \vert u(4v^2 - w^2) \vert, \quad b = \vert v(4u^2 -
w^2)\vert, \quad c = \vert 4uvw \vert \end{equation*} give face diagonals
\begin{equation*} {\displaystyle d=w^{3},\quad e=u(4v^{2}+w^{2}),\quad
f=v(4u^{2}+w^{2})} \end{equation*} leads to an Euler brick. Finding other
formulas that generate these primitive bricks, other than formula above, or
making initial guesses that can be improved later, is the key to understanding
how they are generated.


  Scientific collaborations shape ideas as well as innovations and are both the
substrate for, and the outcome of, academic careers. Recent studies show that
gender inequality is still present in many scientific practices ranging from
hiring to peer-review processes and grant applications. In this work, we
investigate gender-specific differences in collaboration patterns of more than
one million computer scientists over the course of 47 years. We explore how
these patterns change over years and career ages and how they impact scientific
success. Our results highlight that successful male and female scientists
reveal the same collaboration patterns: compared to scientists in the same
career age, they tend to collaborate with more colleagues than other
scientists, seek innovations as brokers and establish longer-lasting and more
repetitive collaborations. However, women are on average less likely to adapt
the collaboration patterns that are related with success, more likely to embed
into ego networks devoid of structural holes, and they exhibit stronger gender
homophily as well as a consistently higher dropout rate than men in all career
ages.


  We study the generation of entangled states using a device constructed from
dipolar bosons confined to a triple-well potential. Dipolar bosons possess
controllable, long-range interactions. This property permits specific choices
to be made for the coupling parameters, such that the system is integrable.
Integrability assists in the analysis of the system via an effective
Hamiltonian constructed through a conserved operator. Through computations of
fidelity we establish that this approach, to study the time-evolution of the
entanglement for a class of non-entangled initial states, yields accurate
approximations given by analytic formulae.


  We construct a new graph on 120 vertices whose quantum and classical
independence numbers are different. At the same time, we construct an infinite
family of graphs whose quantum chromatic numbers are smaller than the classical
chromatic numbers. Furthermore, we discover the relation to Kochen-Specker sets
that characterizes quantum cocliques that are strictly bigger than classical
ones. Finally, we prove that for graphs with independence number is two,
quantum and classical independence numbers coincide.


  The expansion and upgrade of the global network of ground-based gravitational
wave detectors promises to improve our capacity to infer the sky-localization
of transient sources, enabling more effective multi-messenger follow-ups. At
the same time, the increase in the signal-to-noise ratio of detected events
allows for more precise estimates of the source parameters. This study aims to
assess the performance of advanced-era networks of ground-based detectors,
focusing on the Hanford, Livingston, Virgo, and KAGRA instruments. We use full
Bayesian parameter estimation procedures to predict the scientific potential of
a network. Assuming a fixed LIGO configuration, we find that the addition of
the Virgo detector is beneficial to the sky localization starting from a binary
neutron star horizon distance of 20 Mpc and improves significantly from 40 Mpc
onwards for both a single and double LIGO detector network, reducing the
inferred mean sky-area by up to 95%. Similarly, the KAGRA detector tightens the
constraints, starting from a sensitivity range of 10 Mpc. Looking at
highly-spinning binary black holes, we find significant improvements with
increasing sensitivity in constraining the intrinsic source parameters when
adding Virgo to the two LIGO detectors. Finally, we also examine the impact of
the low-frequency cut-off data on the signal-to-noise ratio. We find that
existing 20 Hz thresholds are sufficient and propose a metric to monitor this
to study detector performance. Our findings quantify how future enhancements in
detector sensitivity and network configurations will improve the localization
of gravitational wave sources and allow for more precise identification of
their intrinsic properties.


  We compare two distincts models of evaporative cooling of a magnetically
guided atomic beam: a continuous one, consisting in approximating the atomic
distribution function by a truncated equilibrium distribution, and a
discrete-step one, in which the evaporation process is described in terms of
successive steps consisting in a truncation of the distribution followed by
rethermalization. Calculations are performed for the semi-linear potential
relevant for experiments. We show that it is possible to map one model onto the
other, allowing us to infer, for the discrete-step model, the rethermalization
kinetics, which turns out to be strongly dependent upon the shape of the
confining potential.


  We develop a new technique for computing a class of four-point correlation
functions of heavy half-BPS operators in planar N=4 SYM theory which admit
factorization into a product of two octagon form factors with an arbitrary
bridge length. We show that the octagon can be expressed as the Fredholm
determinant of the integrable Bessel operator and demonstrate that this
representation is very efficient in finding the octagons both at weak and
strong coupling. At weak coupling, in the limit when the four half-BPS
operators become null separated in a sequential manner, the octagon obeys the
Toda lattice equations and can be found in a closed form. At strong coupling,
we exploit the strong Szego limit theorem to derive the leading asymptotic
behavior of the octagon and, then, apply the method of differential equations
to determine the remaining subleading terms of the strong coupling expansion to
any order in the inverse coupling. To achieve this goal, we generalize results
available in the literature for the asymptotic behavior of the determinant of
the Bessel operator. As a byproduct of our analysis, we formulate a
Szego-Akhiezer-Kac formula for the determinant of the Bessel operator with a
Fisher-Hartwig singularity and develop a systematic approach to account for
subleading power suppressed contributions.


  We present a detailed analysis of the heavy-to-light semileptonic decays of
the Lambda_b and Lambda_c baryons Lambda_b -> p l- bar(nu)_l and Lambda_c -> n
l+ nu_l in the covariant confined quark model. We calculate the invariant and
helicity amplitudes of the two processes which are then used to analyze their
angular decay distributions, their rates and asymmetry parameters.


  Nitrogen-vacancy centers in diamond are ideal platforms for quantum
simulation, which allows one to handle problems that are intractable
theoretically or experimentally. Here we propose a digital quantum simulation
scheme to simulate the quantum phase transition occurring in an ultrathin
topological insulator film placed in a parallel magnetic field [Zyuzin
\textit{et al.}, Phys. Rev. B \textbf{83}, 245428 (2011)]. The quantum
simulator employs high quality spin qubits achievable in nitrogen-vacancy
centers and can be realized with existing technology. The problem can be mapped
onto the Hamiltonian of two entangled qubits represented by the electron and
nuclear spins. The simulation uses the Trotter algorithm, with an operation
time of the order of 100 $\mu$s for each individual run.


  A proof of the Riemann's hypothesis (RH) about the non-trivial zeros of the
Riemann zeta-function is presented. It is based on the construction of an
infinite family of operators D^{(k,l)} in one dimension, and their respective
eigenfunctions \psi_s (t), parameterized by continuous real indexes k and l.
Orthogonality of the eigenfunctions is connected to the zeros of the Riemann
zeta-function. Due to the fundamental Gauss-Jacobi relation and the Riemann
fundamental relation Z (s') = Z (1-s'), one can show that there is a direct
concatenation among the following symmetries, t goes to 1/t, s goes to \beta -
s (\beta a real), and s' goes to 1 - s', which establishes a one-to-one
correspondence between the label s of one orthogonal state to a unique vacuum
state, and a zero s' of the \zeta. It is shown that the RH is a direct
consequence of these symmetries, by arguing in particular that an exclusion of
a continuum of the zeros of the Riemann zeta function results in the discrete
set of the zeros located at the points s_n = 1/2 + i \lambda_n in the complex
plane.


  Internet of Things (IoT) is the interconnection of heterogeneous smart
devices through the Internet with diverse application areas. The huge number of
smart devices and the complexity of networks has made it impossible to secure
the data and communication between devices. Various conventional security
controls are insufficient to prevent numerous attacks against these
information-rich devices. Along with enhancing existing approaches, a
peripheral defence, Intrusion Detection System (IDS), proved efficient in most
scenarios. However, conventional IDS approaches are unsuitable to mitigate
continuously emerging zero-day attacks. Intelligent mechanisms that can detect
unfamiliar intrusions seems a prospective solution. This article explores
popular attacks against IoT architecture and its relevant defence mechanisms to
identify an appropriate protective measure for different networking practices
and attack categories. Besides, a security framework for IoT architecture is
provided with a list of security enhancement techniques.


  In this paper we study the formation, evolution and disruption of
hierarchical systems in open clusters. With this purpose, N-body simulations of
star clusters containing an initial population of binaries have been carried
out using Aarseth's NBODY4 and NBODY5 codes. Stable triples may form from
strong interactions of two binaries in which the widest pair is disrupted. The
most frequent type of hierarchical systems found in the cluster models are
triples in which the outer star is single, but in some cases the outer body is
also a binary, giving a hierarchical quadruple. Many triple systems are
non-coplanar and the presence of even a very distant and small outer companion
may affect the orbital parameters of the inner binary, including a possible
mechanism of significant shrinkage if the binary experiences a weak tidal
dissipation. The main features of these systems are analyzed in order to derive
general properties which can be checked by observations. The formation of
exotic objects, such as blue stragglers and white dwarf binaries, inside
hierarchical triple systems is particularly interesting.


  We have demonstrated a recoil-free spectroscopy on the ${}^1S_0-{}^3P_1$
transition of strontium atoms confined in a one-dimensional optical lattice. By
investigating the wavelength and polarization dependence of the ac Stark shift
acting on the ${}^1S_0$ and ${}^3P_1(m_J=0)$ states, we determined the {\it
magic wavelength} where the Stark shifts for both states coincide. The
Lamb-Dicke confinement provided by this Stark-free optical lattice enabled the
measurement of the atomic spectrum free from Doppler as well as recoil shifts.


  We use first principles calculations to study the electronic properties of
rock salt rare earth monopnictides La$X$ ($X=$N, P, As, Sb, Bi). A new type of
topological band crossing termed `linked nodal rings' is found in LaN when the
small spin-orbital coupling (SOC) on nitrogen orbitals is neglected. Turning on
SOC gaps the nodal rings at all but two points, which remain gapless due to
$C_4$-symmetry and leads to a 3D Dirac semimetal. Interestingly, unlike LaN,
compounds with other elements in the pnictogen group are found to be
topological insulators (TIs), as a result of band reordering due to the
increased lattice constant as well as the enhanced SOC on the pnictogen atom.
These TI compounds exhibit multi-valley surface Dirac cones at three
$\bar{M}$-points on the $(111)$-surface.


  We consider the problem of determining all pairs (c_1, c_2) of Chern classes
of rank 2 bundles that are cokernel of a skew-symmetric matrix of linear forms
in 3 variables, having constant rank 2c_1 and size 2c_1+2. We completely solve
the problem in the "stable" range, i.e. for pairs with c_1^2-4c_2<0, proving
that the additional condition c_2\le {{c_1+1}\choose 2} is necessary and
sufficient. For c_1^2-4c_2\ge 0, we prove that there exist globally generated
bundles, some even defining an embedding of P^2 in a Grassmannian, that cannot
correspond to a matrix of the above type. This extends previous work on c_1\le
3.


  Following our previous work, which related generic features in the
sky-averaged (global) 21-cm signal to properties of the intergalactic medium,
we now investigate the prospects for constraining a simple galaxy formation
model with current and near-future experiments. Markov-Chain Monte Carlo fits
to our synthetic dataset, which includes a realistic galactic foreground, a
plausible model for the signal, and noise consistent with 100 hours of
integration by an ideal instrument, suggest that a simple four-parameter model
that links the production rate of Lyman-$\alpha$, Lyman-continuum, and X-ray
photons to the growth rate of dark matter halos can be well-constrained (to
$\sim 0.1$ dex in each dimension) so long as all three spectral features
expected to occur between $40 \lesssim \nu / \mathrm{MHz} \lesssim 120$ are
detected. Several important conclusions follow naturally from this basic
numerical result, namely that measurements of the global 21-cm signal can in
principle (i) identify the characteristic halo mass threshold for star
formation at all redshifts $z \gtrsim 15$, (ii) extend $z \lesssim 4$ upper
limits on the normalization of the X-ray luminosity star-formation rate
($L_X$-SFR) relation out to $z \sim 20$, and (iii) provide joint constraints on
stellar spectra and the escape fraction of ionizing radiation at $z \sim 12$.
Though our approach is general, the importance of a broad-band measurement
renders our findings most relevant to the proposed Dark Ages Radio Explorer,
which will have a clean view of the global 21-cm signal from $\sim 40-120$ MHz
from its vantage point above the radio-quiet, ionosphere-free lunar far-side.


  We expect the final theory of gravity to have more symmetries than we suspect
and our research points in this direction. To start with, standard general
coordinate invariance can be extended to complex holomorphic general coordinate
transformations. This is possible by introducing a non Riemannian Measure of
integration (NRMI) and where we avoid the non holomorphic standard
  $\sqrt{-g}$ measure of integration. Second, locally signed coordinate
transformations where the Jacobian changes sign locally but the Jacobian
approaches one asymptotically should be symmetries of Nature. This is unlike
globally signed transformations that produce a change of boundary conditions,
like in the cases of global parity and global time reversal, which are not
symmetries of Nature. The holomorphic extension can regularize the regions of
space time where the Jacobian changes sign. Consequences for Quantum Gravity
are discussed.


  Brown dwarf spectra are rich in information revealing of the chemical and
physical processes operating in their atmospheres. We apply a recently
developed atmospheric retrieval tool to an ensemble of late T-dwarf (600-800K)
near infrared spectra. With these spectra we are able to place direct
constraints the molecular abundances of H$_2$O, CH$_4$, CO, CO$_2$, NH$_3$,
H$_2$S, and Na+K, gravity, thermal structure (and effective temperature),
photometric radius, and cloud optical depths. We find that ammonia, water,
methane, and the alkali metals are present and well constrained in all 11
objects. From the abundance constraints we find no significant trend in the
water, methane, or ammonia abundances with temperature, but find a very strong
($>$25$\sigma$) increasing trend in the alkali metal abundances with effective
temperature, indicative of alkali rainout. We also find little evidence for
optically thick clouds. With the methane and water abundances, we derive the
intrinsic atmospheric metallicity and carbon-to-oxygen ratios. We find in our
sample, that metallicities are typically sub solar and carbon-to-oxygen ratios
are somewhat super solar, different than expectations from the local stellar
population. We also find that the retrieved vertical thermal profiles are
consistent with radiative equilibrium over the photospheric regions. Finally,
we find that our retrieved effective temperatures are lower than previous
inferences for some objects and that our radii are larger than expectations
from evolutionary models, possibly indicative of un-resolved binaries. This
investigation and methodology represents a paradigm in linking spectra to the
determination of the fundamental chemical and physical processes governing cool
brown dwarf atmospheres.


  Polytopes from subgraph statistics are important in applications and
conjectures and theorems in extremal graph theory can be stated as properties
of them. We have studied them with a view towards applications by inscribing
large explicit polytopes and semi-algebraic sets when the facet descriptions
are intractable. The semi-algebraic sets called curvy zonotopes are introduced
and studied using graph limits. From both volume calculations and algebraic
descriptions we find several interesting conjectures.


  It is well known that classical information can be cloned, but non-orthogonal
quantum states cannot be cloned, and non-commuting quantum states cannot be
broadcast. We conceive a scenario in which the object we want to broadcast is
the statistical distinguishability, as quantified by quantum Fisher
information, about a signal parameter encoded in quantum states. We show that
quantum Fisher information cannot be cloned, whilst it might be broadcast even
when the input states are non-commuting. This situation interpolates between
cloning of classical information and no-broadcasting of quantum information,
and indicates a hybrid way of information broadcasting which is of particular
significance from both practical and theoretical perspectives.


  Many software development organizations still lack support for obtaining
intellectual control over their software development processes and for
determining the performance of their processes and the quality of the produced
products. Systematic support for detecting and reacting to critical process and
product states in order to achieve planned goals is usually missing. One means
to institutionalize measurement on the basis of explicit models is the
development and establishment of a so-called Software Project Control Center
(SPCC) for systematic quality assurance and management support. An SPCC is
comparable to a control room, which is a well known term in the mechanical
production domain. One crucial task of an SPCC is the systematic visualization
of measurement data in order to provide context-, purpose-, and role-oriented
information for all stakeholders (e.g., project managers, quality assurance
managers, developers) during the execution of a software development project.
The article will present an overview of SPCC concepts, a concrete instantiation
that supports goal-oriented data visualization, as well as examples and
experiences from practical applications.


  It is shown that by defining the Debye mass through the relevant pole of the
static gluon propagator rather than the zero-momentum limit of the time-time
component of the gluon self-energy, a gauge-independent result for the
next-to-leading order correction can be derived upon resummation of
hard-thermal-loop contributions. The result turns out to be logarithmically
sensitive to the magnetic screening mass. [Talk given at the 3rd Workshop on
Thermal Field Theories and their Applications, August 15-27, 1993, Banff,
Alberta, Canada]


  The recent recomputation of the neutrino fluxes from nuclear reactors relaxes
the tension between the LSND and MiniBooNE anomalies and disappearance data
when interpreted in terms of sterile neutrino oscillations. The simplest
extension of the Standard Model with such fermion singlets is the addition of
right-handed sterile neutrinos with small Majorana masses. Even when
introducing three right-handed neutrinos, this scenario has less free
parameters than the 3+2 scenarios studied in the literature. This begs the
question whether the best fit regions obtained can be reproduced by this
simplest extension of the Standard Model. In order to address this question, we
devise an exact parametrization of Standard Model extensions with right-handed
neutrinos. Apart from the usual 3x3 neutrino mixing matrix and the 3 masses of
the lightest neutrinos, the extra degrees of freedom are encoded in another 3x3
unitary matrix and 3 additional mixing angles. The parametrization includes all
the correlations among masses and mixings and is valid beyond the usual seesaw
approximation. Through this parametrization we find that the best fit regions
for the LSND and MiniBooNE anomalies in a 3+2 scenario can indeed be reproduced
despite the smaller number of degrees of freedom.


  In this paper we raise the question whether every closed Riemannian manifold
has a spine of minimal area, and we answer it affirmatively in the surface
case. On constant curvature surfaces we introduce the spine systole, a
continuous real function on moduli space that measures the minimal length of a
spine in each surface. We show that the spine systole is a proper function and
has its global minima precisely on the extremal surfaces (those containing the
biggest possible discs).
  We also study minimal spines, which are critical points for the length
functional. We completely classify minimal spines on flat tori, proving that
the number of them is a proper function on moduli space. We also show that the
number of minimal spines of uniformly bounded length is finite on hyperbolic
surfaces.


  This letter complements a formation scenario of the progenitor of the
supernova iPTF13bvn proposed in Hirai (2017). Although the scenario was
successful in reproducing various observational features of the explosion and
pre-explosion photometry by assuming that the progenitor had a relatively large
black hole companion, it lacked an explanation for the origin of the black hole
itself. We now explore the possible evolutionary paths towards this binary with
a relatively large black hole companion. We found that the black hole was
probably produced by a very massive star that experienced common envelope
evolution. According to our MESA stellar models, the primary mass should have
been 70M to reproduce the required remnant mass and final separation. This
indicates that iPTF13bvn was likely a rare case and normal type Ib supernovae
originate from different paths.


  The Marinatto-Weber approach to quantum game is a straightforward way to
apply the power of quantum mechanics to classical game theory. In the simplest
case, the quantum scheme is that players manipulate their own qubits of a
two-qubit state either with the identity operator or the Pauli operator
$\sigma_{x}$. However, such a simplification of the scheme raises doubt as to
whether it could really reflect a quantum game. In this paper we put forward
examples which may constitute arguments against the present form of the
Marinatto-Weber scheme. Next, we modify the scheme to eliminate the undesirable
properties of the protocol by extending the players' strategy sets.


  Jet feedback from active galactic nuclei (AGN) is one of the most promising
mechanisms for suppressing cooling flows in cool-core clusters. However, the
composition of AGN jets and bubbles remains uncertain; they could be thermally
dominated, or dominated by cosmic-ray proton (CRp), cosmic-ray electron (CRe),
or magnetic energy. In this work, we investigate the evolution and feedback
effects of CRp and CRe dominated jets by conducting 3D magnetohydrodynamic
simulations of AGN jet-inflated bubbles in the intracluster medium using the
FLASH code. We present the evolution of their energies, dynamics and heating,
and model their expected cavity-power versus radio-luminosity relation ($P_{\rm
cav}-L_R$). We find that bubbles inflated by CRe dominated jets follow a very
similar dynamical evolution to CRp dominated bubbles even though CRe within
bubbles suffer significantly stronger synchrotron and inverse-Compton cooling.
This is because, as CRe lose their energy, the jet-inflated bubbles quickly
become thermally dominated within $\sim 30$ Myr. Their total energy stops
decreasing with CR energy and evolves similarly to CRp dominated bubbles. The
ability of CRe and CRp dominated bubbles to heat the intracluster medium is
also comparable; the cold gas formed via local thermal instabilities is well
suppressed in both cases. The CRp and CRe bubbles follow different evolutionary
trajectories on the $P_{\rm cav}-L_R$ plane, but the values are broadly
consistent with observed ranges for FRI sources. We also discuss observational
techniques that have potential for constraining the composition of AGN jets and
bubbles.


  The Bonabeau model of self-organized hierarchy formation is studied by using
a piecewise linear approximation to the sigmoid function. Simulations of the
piecewise-linear agent model show that there exist two-level and three-level
hierarchical solutions, and that each agent exhibits a transition from
non-ergodic to ergodic behaviors. Furthermore, by using a mean-field
approximation to the agent model, it is analytically shown that there are
asymmetric two-level solutions, even though the model equation is symmetric
(asymmetry is introduced only through the initial conditions), and that
linearly stable and unstable three-level solutions coexist. It is also shown
that some of these solutions emerge through supercritical-pitchfork-like
bifurcations in invariant subspaces. Existence and stability of the linear
hierarchy solution in the mean-field model are also presented.


  We extend to black branes (BB) in arbitrary dimensions the results of Ref.
[1] about hyperscaling violation and phase transition for scalar black
2-branes. We derive the analytic form of the (d+1)-dimensional scalar soliton
interpolating between a conformal invariant AdS vacuum in the infrared and a
scale covariant metric in the ultraviolet. We show that the thermodynamical
system undergoes a phase transition between Schwarzschild-AdS and a
scalar-dressed BB. We calculate the critical exponent and the hyperscaling
violation parameter in the two phases. We show that our scalar BB solutions
generically emerge as compactifications of p-brane solutions of supergravity
theories. We also derive the short distance form of the correlators for the
scalar operators corresponding to an UV exponential potential supporting our
black brane solution. We show that also for negative values of the hyperscaling
violation parameter these correlators have a short distance power-law behavior.


  We study the AC optical and hall conductivities of Dp/Dq-branes intersections
in the probe approximation and use sum-rules to study various associated
transport coefficients. We determine that the presence of massive fundamental
matter, as compared to massless fundamental matter described holographically by
a theory with no dimensional defects, reduces the plasma frequency. We further
show that this is not the case when the brane intersections include defects. We
discuss in detail how to implement correctly the regularization of retarded
Green's functions so that the dispersion relations are satisfied and the low
energy behaviour of the system is physically realistic.


  Enhancing properties and performances of aluminium alloys by a control of
their solidification is pivotal in automotive and aerospace industries. The
fundamental role of the structure-diffusion relationship is investigated for
Al-Mg-Si liquid alloys taken as a prototype of Al-6xxx. For this purpose, first
principles-based molecular dynamics simulations were performed for various Si
and Mg content for Al-rich compositions, including the binary alloy
counterparts. Results indicate that Mg and/or Si in alloys create a more
compact ordering around Al than in pure Al, lowering diffusion. Mg promotes
icosahedral short-range order, while Si displays a preference towards cubic
local ordering, impacting diffusion based on their respective content. It
suggests a mechanism whereby an increase in Mg content generally lowers the
diffusion of each species, whereas an increase in Si content enhances their
diffusion, providing insights for future alloy design.


  In $TmB_4$, localized electrons with a large magnetic moment interact with
metallic electrons in boron-derived bands. We examine the nature of $TmB_4$
using full-relativistic ab-initio density functional theory calculations,
approximate tight-binding Hamiltonian results, and the development of an
effective Kondo-Ising model for this system. Features of the Fermi surface
relating to the anisotropic conduction of charge are discussed. The observed
magnetic moment $\sim 6 \, \mu_B$ is argued to require a subtle crystal field
effect in metallic systems, involving a flipped sign of the effective charges
surrounding a Tm ion. The role of on-site quantum dynamics in the resulting
Kondo-Ising type "impurity" model are highlighted. From this model, elimination
of the conduction electrons will lead to spin-spin (RKKY-type) interaction of
Ising character required to understand the observed fractional magnetization
plateaus in $TmB_4$.


  We study the stability of patterns arising in rotating convection in weakly
anisotropic systems using a modified Swift-Hohenberg equation. The anisotropy,
either an endogenous characteristic of the system or induced by external
forcing, can stabilize periodic rolls in the K\"uppers-Lortz chaotic regime.
For the particular case of rotating convection with time-modulated rotation
where recently, in experiment, chiral patterns have been observed in otherwise
K\"uppers-Lortz-unstable regimes, we show how the underlying base-flow breaks
the isotropy, thereby affecting the linear growth-rate of convection rolls in
such a way as to stabilize spirals and targets. Throughout we compare
analytical results to numerical simulations of the Swift-Hohenberg equation.


  We investigate how individuals form expectations about population behavior
using statistical inference based on observations of their social relations.
Misperceptions about others' connectedness and behavior arise from sampling
bias stemming from the friendship paradox and uncertainty from small samples.
In a game where actions are strategic complements, we characterize the
equilibrium and analyze equilibrium behavior. We allow for agent sophistication
to account for the sampling bias and demonstrate how sophistication affects the
equilibrium. We show how population behavior depends on both sources of
misperceptions and illustrate when sampling uncertainty plays a critical role
compared to sampling bias.


  Deep generative models have recently emerged as a promising de novo drug
design method. In this respect, deep generative conditional variational
autoencoder (CVAE) models are a powerful approach for generating novel
molecules with desired drug-like properties. However, molecular graph-based
models with disentanglement and multivariate explicit latent conditioning have
not been fully elucidated. To address this, we proposed a molecular-graph
$\beta$-CVAE model for de novo drug design. Here, we empirically tuned the
value of disentanglement and assessed its ability to generate molecules with
optimised univariate- or-multivariate properties. In particular, we optimised
the octanol-water partition coefficient (ClogP), molar refractivity (CMR),
quantitative estimate of drug-likeness (QED), and synthetic accessibility score
(SAS). Results suggest that a lower $\beta$ value increases the uniqueness of
generated molecules (exploration). Univariate optimisation results showed our
model generated molecular property averages of ClogP = 41.07% $\pm$ 0.01% and
CMR 66.76% $\pm$ 0.01% by the Ghose filter. Multivariate property optimisation
results showed that our model generated an average of 30.07% $\pm$ 0.01%
molecules for both desired properties. Furthermore, our model improved the QED
and SAS (exploitation) of molecules generated. Together, these results suggest
that the $\beta$-CVAE could balance exploration and exploitation through
disentanglement and is a promising model for de novo drug design, thus
providing a basis for future studies.


  Multidimensional hypoelliptic diffusions arise naturally in different fields,
for example to model neuronal activity. Estimation in those models is complex
because of the degenerate structure of the diffusion coefficient. In this paper
we consider hypoelliptic diffusions, given as a solution of two-dimensional
stochastic differential equations (SDEs), with the discrete time observations
of both coordinates being available on an interval $T = n\Delta_n$, with
$\Delta_n$ the time step between the observations. The estimation is studied in
the asymptotic setting, with $T\to\infty$ as $\Delta_n\to 0$. We build a
consistent estimator of the drift and variance parameters with the help of a
discretized log-likelihood of the continuous process. We discuss the
difficulties generated by the hypoellipticity and provide a proof of the
consistency and the asymptotic normality of the estimator. We test our approach
numerically on the hypoelliptic FitzHugh-Nagumo model, which describes the
firing mechanism of a neuron.


  Deterministic one-way time-bounded multi-counter automata are studied with
respect to their ability to perform reversible computations, which means that
the automata are also backward deterministic and, thus, are able to uniquely
step the computation back and forth. We study the computational capacity of
such devices and obtain separation results between irreversible and reversible
k-counter automata for superpolynomial time. For exponential time we obtain
moreover an infinite and tight hierarchy with respect to the number of
counters. This hierarchy is shown with Kolmogorov complexity and
incompressibility arguments. In this way, on passing we can prove this
hierarchy also for ordinary counter automata. This improves the known hierarchy
for ordinary counter automata in the sense that here we consider a weaker
acceptance condition. Then, it turns out that k+1 reversible counters are not
better than k ordinary counters and vice versa. Finally, almost all usually
studied decidability questions turn out to be undecidable and not even
semidecidable for reversible multi-counter automata, if at least two counters
are provided.


  Unstructured Persona-oriented Dialogue Systems (UPDS) has been demonstrated
effective in generating persona consistent responses by utilizing predefined
natural language user persona descriptions (e.g., "I am a vegan"). However, the
predefined user persona descriptions are usually short and limited to only a
few descriptive words, which makes it hard to correlate them with the
dialogues. As a result, existing methods either fail to use the persona
description or use them improperly when generating persona consistent
responses. To address this, we propose a neural topical expansion framework,
namely Persona Exploration and Exploitation (PEE), which is able to extend the
predefined user persona description with semantically correlated content before
utilizing them to generate dialogue responses. PEE consists of two main
modules: persona exploration and persona exploitation. The former learns to
extend the predefined user persona description by mining and correlating with
existing dialogue corpus using a variational auto-encoder (VAE) based topic
model. The latter learns to generate persona consistent responses by utilizing
the predefined and extended user persona description. In order to make persona
exploitation learn to utilize user persona description more properly, we also
introduce two persona-oriented loss functions: Persona-oriented Matching
(P-Match) loss and Persona-oriented Bag-of-Words (P-BoWs) loss which
respectively supervise persona selection in encoder and decoder. Experimental
results show that our approach outperforms state-of-the-art baselines, in terms
of both automatic and human evaluations.


  We present ORB-SLAM2 a complete SLAM system for monocular, stereo and RGB-D
cameras, including map reuse, loop closing and relocalization capabilities. The
system works in real-time on standard CPUs in a wide variety of environments
from small hand-held indoors sequences, to drones flying in industrial
environments and cars driving around a city. Our back-end based on bundle
adjustment with monocular and stereo observations allows for accurate
trajectory estimation with metric scale. Our system includes a lightweight
localization mode that leverages visual odometry tracks for unmapped regions
and matches to map points that allow for zero-drift localization. The
evaluation on 29 popular public sequences shows that our method achieves
state-of-the-art accuracy, being in most cases the most accurate SLAM solution.
We publish the source code, not only for the benefit of the SLAM community, but
with the aim of being an out-of-the-box SLAM solution for researchers in other
fields.


  We study the magnetic field to density ($B-\rho$) relation in turbulent
molecular clouds with dynamically important magnetic fields using nonideal
three-dimensional magnetohydrodynamic simulations. Our simulations show that
there is a distinguishable break density $\rho_{\rm T}$ between the relatively
flat low density regime and a power-law regime at higher densities. We present
an analytic theory for $\rho_{\rm T}$ based on the interplay of the magnetic
field, turbulence, and gravity. The break density $\rho_{\rm T}$ scales with
the strength of the initial Alfv\'en Mach number $\mathcal{M}_{\rm A0}$ for
sub-Alfv\'enic ( $\mathcal{M}_{\rm A0}<1$) and trans-Alfv\'enic
($\mathcal{M}_{\rm A0} \sim 1$) clouds. We fit the variation of $\rho_{\rm T}$
for model clouds as a function of $\mathcal{M}_{\rm A0}$, set by different
values of initial sonic Mach number $\mathcal{M_{\rm 0}}$ and the initial ratio
of gas pressure to magnetic pressure $\beta_{\rm 0}$. This implies that
$\rho_{\rm T}$, which denotes the transition in mass-to-flux ratio from the
subcritical to supercritical regime, is set by the initial turbulent
compression of the molecular cloud.


  The experimental signatures for low energy supersymmetry breaking are
presented. The lightest standard model superpartner is unstable and decays to
its partner plus a Goldstino, $G$. For a supersymmetry breaking scale below a
few 1000 TeV this decay can take place within a detector, leading to very
distinctive signatures. If a neutralino is the lightest standard model
superpartner it decays by $\chi_1^0 \to \gamma + G$, and if kinematically
accessible by $\chi_1^0 \to (Z^0, h^0, H^0, A^0) + G$. These decays can give
rise to displaced vertices. Alternately, if a slepton is the lightest standard
model superpartner it decays by $\tilde{l} \to l + G$. This can be seen as a
greater than minimum ionizing charged particle track, possibly with a kink to a
minimum ionizing track.


  Nonlinear optical (NLO) effects have attracted great interest recently.
However, by far the computational studies on NLO use the independent particle
approximation and ignore many-body effects. Here we develop a generic Green's
function framework to calculate the NLO response functions, which can
incorporate various many-body interactions. We focus on the electron-phonon
coupling and reveal that phonon dressing can make significant impacts on
nonlinear photocurrent, such as the bulk photovoltaic (BPV) and bulk spin
photovoltaic (BSPV) currents. BPV/BSPV should be zero for centrosymmetric
crystals, but when phonons are driven out-of-equilibrium, by for example, a
temperature gradient $\nabla T$, the optical selections rules are altered and
phonon-pumped BPV/BSPV currents can be non-zero in nominally centrosymmetric
crystal. Moreover, we elucidate that such NLO responses under non-equilibrium
phonon dressing can be nonreciprocal, as the direction of the current does not
necessarily get reversed when the direction of the temperature gradient is
reversed.