  Interactions play a key role in understanding objects and scenes, for both
virtual and real world agents. We introduce a new general representation for
proximal interactions among physical objects that is agnostic to the type of
objects or interaction involved. The representation is based on tracking
particles on one of the participating objects and then observing them with
sensors appropriately placed in the interaction volume or on the interaction
surfaces. We show how to factorize these interaction descriptors and project
them into a particular participating object so as to obtain a new functional
descriptor for that object, its interaction landscape, capturing its observed
use in a spatio-temporal framework. Interaction landscapes are independent of
the particular interaction and capture subtle dynamic effects in how objects
move and behave when in functional use. Our method relates objects based on
their function, establishes correspondences between shapes based on functional
key points and regions, and retrieves peer and partner objects with respect to
an interaction.


  In an early paper, He and Tang [Biometrika 100 (2013) 254-260] introduced and
studied a new class of designs, strong orthogonal arrays, for computer
experiments, and characterized such arrays through generalized orthogonal
arrays. The current paper presents a simple characterization for strong
orthogonal arrays of strength three. Besides being simple, this new
characterization through a notion of semi-embeddability is more direct and
penetrating in terms of revealing the structure of strong orthogonal arrays.
Some other results on strong orthogonal arrays of strength three are also
obtained along the way, and in particular, two $\operatorname
{SOA}(54,5,27,3)$'s are constructed.


  There are two abelian groups which can naturally be associated to an additive
category A: the split Grothendieck group of A and the triangulated Grothendieck
group of the homotopy category of (bounded) complexes in A. We prove that these
groups are isomorphic. Along the way, we deduce that the `Euler characteristic'
of a complex in A is invariant under homotopy equivalence.


  This paper is a significant part of a general project aimed to classify all
irreducible representations of finite quasi-simple groups over an algebraically
closed field, in which the image of at least one element is represented by an
almost cyclic matrix. (A square matrix $M$ is called almost cyclic if it is
similar to a block-diagonal matrix with two blocks, such that one block is
scalar and another block is a matrix whose minimum and characteristic
polynomials coincide. Reflections and transvections are examples of almost
cyclic matrices.
  The paper focuses on the Weil representations of finite classical groups, as
there is strong evidence that these representations play a key role in the
general picture.


  This paper gathers results obtained with a software written in Java. For
exceptional minuscule, quasi-minuscule, cominuscule or adjoint homogeneous
spaces, the Schubert cells are expressed as polynomials in the generators of
the quantum cohomology algebra.


  We discuss rare meson decays $K^ + \to \pi ^ - \ell ^ + \ell '^ + $ and $D^ +
\to K^ - \ell ^ + \ell '^ +$ ($\ell, \ell'=e, \mu$) in a supersymmetric
extension of the Standard Model with R-parity violation. Estimates of the
branching ratios for these decays are presented.


  In this work we develop tools that enable the study of non-adiabatic effects
with variational and diffusion Monte Carlo methods. We introduce a highly
accurate wave function ansatz for electron-ion systems that can involve a
combination of both fixed and quantum ions. We explicitly calculate the ground
state energies of H$_{2}$, LiH, H$_{2}$O and FHF$^{-}$ using fixed-node quantum
Monte Carlo with wave function nodes that explicitly depend on the ion
positions. The obtained energies implicitly include the effects arising from
quantum nuclei and electron-nucleus coupling. We compare our results to the
best theoretical and experimental results available and find excellent
agreement.


  We extend the relative entropy identity to the class of hyperbolic-parabolic
systems whose hyperbolic part is symmetrizable. The resulting identity, in the
general theory, is useful to provide stability of viscous solutions and yields
a convergence result in the zero-viscosity limit to smooth solutions in an
$L^p$ framework. Also it provides measure valued weak versus strong uniqueness
theorems for the hyperbolic problem. The relative entropy identity is also
developed for the system of gas dynamics for viscous and heat conducting gases,
and for the system of thermoviscoelasticity with viscosity and heat-conduction.
Existing differences in applying the relative entropy method between the
general hyperbolic-parabolic theory and the examples are underlined.


  In this paper, we introduce new properties of the relative interior calculus
for nearly convex sets, functions, and set-valued mappings. These properties
are important for the development of duality theory in optimization. Then we
investigate optimal value functions defined by nearly convex functions and
nearly convex set-valued mappings, and derive the near convexity of the optimal
value function under a qualification condition. We also develop formulas for
subgradients and Fenchel conjugates of this class of functions, and explore
their applications to duality theory.


  Martin Kneser proved the following addition theorem for every abelian group
$G$. If $A,B \subseteq G$ are finite and nonempty, then $|A+B| \ge |A+K| +
|B+K| - |K|$ where $K = \{g \in G \mid g+A+B = A+B \}$. Here we give a short
proof of this based on a simple intersection union argument.


  We propose theoretically a generalized memristive system based on controlled
spin polarizations in the giant magnetoresistive material using a feedback loop
with the classical Hall Effect. The dynamics can exhibit a memristive pinched
hysteretic loop that possesses the self-crossing knot not located at the
origin. Additionally, one can also observe a single-looped orbit in the device.
We also provide a sufficient condition for the stability based on an estimation
of the Floquet exponent. The analysis shows that the non-origin-crossing
dynamics is generally permitted in a class of passive memory systems that are
not subject to Ohm's Law. We further develop the prevailing homogeneous
definition to a broadened concept of generalized heterogeneous memristive
systems, permitting no self-crossing knot at the origin, and ultimately to the
compound memory electronic systems.


  A substantial body of phenomenological and theoretical work over the last few
years strengthens the possibility that the vacuum energy density (VED) of the
universe is dynamical, and in particular that it adopts the `running vacuum
model' (RVM) form, in which the VED evolves mildly as $\delta \rho_{\rm
vac}(H)\sim \nu_{\rm eff} m_{\rm Pl}^2{\cal O}\left(H^2\right)$, where $H$ is
the Hubble rate and $\nu_{\rm eff}$ is a (small) free parameter. This dynamical
scenario is grounded on recent studies of quantum field theory (QFT) in curved
spacetime and also on string theory. It turns out that what we call the
`cosmological constant', $\Lambda$, is no longer a rigid parameter but the
nearly sustained value of $8\pi G(H)\rho_{\rm vac}(H)$ around (any) given epoch
$H(t)$, where $G(H)$ is the gravitational coupling, which can also be very
mildly running (logarithmically). Of particular interest is the possibility
suggested in past works that such a running may help to cure the cosmological
tensions afflicting the $\Lambda$CDM. In the current study, we reanalyze it in
full and we find it becomes further buttressed. Using the modern cosmological
data, namely a compilation of the latest $SNIa+BAO+$H(z)$+LSS+CMB$
observations, we probe to which extent the RVM provides a quality fit better
than the concordance $\Lambda$CDM model, paying particular emphasis on its
impact on the $\sigma_8$ and $H_0$ tensions. We utilize the Einstein-Boltzmann
system solver $CLASS$ and the Monte Carlo sampler $MontePython$ for the
statistical analysis, as well as the statistical $DIC$ criterion to compare the
running vacuum against the rigid vacuum ($\nu_{\rm eff} = 0$). We show that
with a tiny amount of vacuum dynamics ($|\nu_{\rm eff}|\ll 1$) the global fit
can improve significantly with respect to the $\Lambda$CDM and the mentioned
tensions may subside to inconspicuous levels.


  We present new quantitative classification methods for emission-line
galaxies, which are specially designed to be used in deep galaxy redshift
surveys. A good segregation between starbursts and active galactic nuclei, i.e.
Seyferts 2s and LINERs, is obtained from diagnostic diagrams involving the [O
II]\lambda 3727 \AA, [Ne III]\lambda3869 \AA, H\beta and [O III]\lambda5007 \AA
relative intensities or the [O II]\lambda 3727 \AA and H\beta equivalent
widths. Furthermore, the colour index of the continuum underlying [O II]\lambda
3727 \AA and H\beta provides an additional separation parameter between the two
types of emission-line galaxies. We have applied the equivalent widths method
to the 0 < z \leq 0.3 emission-line galaxies of the Canada-France Redshift
Survey. Our results are in very good agreement with those obtained using the
standard diagnostic diagrams including all the strong optical emission-line
intensity ratios.


  Hole propagator of spin 1/2 Calogero-Sutherland model is derived using
Uglov's method, which maps the exact eigenfunctions of the model, called
Yangian Gelfand-Zetlin basis, to a limit of Macdonald polynomials (gl_2-Jack
polynomials). To apply this mapping method to the calculation of 1-particle
Green's function, we confirm that the sum of the field annihilation operator on
Yangian Gelfand-Zetlin basis is transformed to the field annihilation operator
on gl_2-Jack polynomials by the mapping. The resultant expression for hole
propagator for finite-size system is written in terms of renormalized momenta
and spin of quasi-holes and the expression in the thermodynamic limit coincides
with the earlier result derived by another method. We also discuss the
singularity of the spectral function for a specific coupling parameter where
the hole propagator of spin Calogero-Sutherland model becomes equivalent to
dynamical colour correlation function of SU(3) Haldane-Shastry model.


  Widespread sharing of long, identical-by-descent (IBD) genetic segments is a
hallmark of populations that have experienced recent genetic drift. Detection
of these IBD segments has recently become feasible, enabling a wide range of
applications from phasing and imputation to demographic inference. Here, we
study the distribution of IBD sharing in the Wright-Fisher model. Specifically,
using coalescent theory, we calculate the variance of the total sharing between
random pairs of individuals. We then investigate the cohort-averaged sharing:
the average total sharing between one individual and the rest of the cohort. We
find that for large cohorts, the cohort-averaged sharing is distributed
approximately normally. Surprisingly, the variance of this distribution does
not vanish even for large cohorts, implying the existence of "hyper-sharing"
individuals. The presence of such individuals has consequences for the design
of sequencing studies, since, if they are selected for whole-genome sequencing,
a larger fraction of the cohort can be subsequently imputed. We calculate the
expected gain in power of imputation by IBD, and subsequently, in power to
detect an association, when individuals are either randomly selected or
specifically chosen to be the hyper-sharing individuals. Using our framework,
we also compute the variance of an estimator of the population size that is
based on the mean IBD sharing and the variance in the sharing between inbred
siblings. Finally, we study IBD sharing in an admixture pulse model, and show
that in the Ashkenazi Jewish population the admixture fraction is correlated
with the cohort-averaged sharing.


  We review the theoretical description of the role of quantum geometry in
superfluidity and superconductivity of multiband systems, with focus on flat
bands where quantum geometry is wholly responsible for supercurrents. This
review differs from previous ones in that it is based on the most recent
understanding of the theory: the dependence of the self-consistent order
parameter on the supercurrent is properly taken into account, and the
superfluid weight in a flat band becomes proportional to the minimal quantum
metric. We provide a recap of basic quantum geometric quantities and the
concept of superfluid density. The geometric contribution of superconductivity
is introduced via considering the two-body problem. The superfluid weight of a
multiband system is derived within mean-field theory, leading to a topological
bound of flat band superconductivity. The physical interpretation of the flat
band supercurrent in terms of Wannier function overlaps is discussed.


  In this paper, we look to address the problem of estimating the dynamic
direction of arrival (DOA) of a narrowband signal impinging on a sensor array
from the far field. The initial estimate is made using a Bayesian compressive
sensing (BCS) framework and then tracked using a Bayesian compressed sensing
Kalman filter (BCSKF). The BCS framework splits the angular region into N
potential DOAs and enforces a belief that only a few of the DOAs will have a
non-zero valued signal present. A BCSKF can then be used to track the change in
the DOA using the same framework. There can be an issue when the DOA approaches
the endfire of the array. In this angular region current methods can struggle
to accurately estimate and track changes in the DOAs. To tackle this problem,
we propose changing the traditional sparse belief associated with BCS to a
belief that the estimated signals will match the predicted signals given a
known DOA change. This is done by modelling the difference between the expected
sparse received signals and the estimated sparse received signals as a Gaussian
distribution. Example test scenarios are provided and comparisons made with the
traditional BCS based estimation method. They show that an improvement in
estimation accuracy is possible without a significant increase in computational
complexity.


  This paper is intended as a sequel to a paper arXiv:0803.2636 written by four
of the coauthors here. In the paper, they proved a stronger form of the
Erd\H{o}s-Mirksy conjecture which states that there are infinitely many
positive integers $x$ such that $d(x)=d(x+1)$ where $d(x)$ denotes the number
of divisors of $x$. This conjecture was first proven by Heath-Brown in 1984,
but the method did not reveal the nature of the set of values $d(x)$ for such
$x$. In particular, one could not conclude that there was any particular value
$A$ for which $d(x)=d(x+1)=A$ infinitely often. In the previous paper
arXiv:0803.2636, the authors showed that there are infinitely many positive
integers $x$ such that both $x$ and $x+1$ have exponent pattern $\{2,1,1,1\}$,
so $d(x)=d(x+1)=24$. Similar results were known for certain shifts $n$, i.e.,
$x$ and $x+n$ have the same fixed exponent pattern infinitely often. This was
done for shifts $n$ which are either even or not divisible by the product of a
pair of twin primes. The goal of this paper is to give simple proofs of results
on exponent patterns for an arbitrary shift $n$.


  Voice-controlled smart speaker devices have gained a foothold in many modern
households. Their prevalence combined with their intrusion into core private
spheres of life has motivated research on security and privacy intrusions,
especially those performed by third-party applications used on such devices. In
this work, we take a closer look at such third-party applications from a less
pessimistic angle: we consider their potential to provide personalized and
secure capabilities and investigate measures to authenticate users (``PIN'',
``Voice authentication'', ``Notification'', and presence of ``Nearby
devices''). To this end, we asked 100 participants to evaluate 15 application
categories and 51 apps with a wide range of functions. The central questions we
explored focused on: users' preferences for security and personalization for
different categories of apps; the preferred security and personalization
measures for different apps; and the preferred frequency of the respective
measure.
  After an initial pilot study, we focused primarily on 7 categories of apps
for which security and personalization are reported to be important; those
include the three crucial categories finance, bills, and shopping. We found
that ``Voice authentication'', while not currently employed by the apps we
studied, is a highly popular measure to achieve security and personalization.
Many participants were open to exploring combinations of security measures to
increase the protection of highly relevant apps. Here, the combination of
``PIN'' and ``Voice authentication'' was clearly the most desired one. This
finding indicates systems that seamlessly combine ``Voice authentication'' with
other measures might be a good candidate for future work.


  In recent paper 5, it is shown that the upper decay rate of global solution
of compressible Navier-Stokes(CNS) equations converging to constant equilibrium
state $(1, 0)$ in $H^1-$norm is $(1+t)^{\frac34(\frac{2}{p}-1)}$ when the
initial data is large and belongs to $H^2(\mathbb{R}^3) \cap L^p(\mathbb{R}^3)
(p\in[1,2))$. Thus, the first result in this paper is devoted to showing that
the upper decay rate of the first order spatial derivative converging to zero
in $H^1-$norm is $(1+t)^{-\frac32(\frac1p-\frac12)-\frac12}$. For the case of
$p=1$, the lower bound of decay rate for the global solution of CNS equations
converging to constant equilibrium state $(1, 0)$ in $L^2-$norm is
$(1+t)^{-\frac{3}{4}}$ if the initial data satisfies some low frequency
assumption additionally. In other words, the optimal decay rate for the global
solution of CNS equations converging to constant equilibrium state in
$L^2-$norm is $(1+t)^{-\frac{3}{4}}$ although the associated initial data is
large.


  The framework of the Covariant Canonical Gauge theory of Gravity (CCGG) is
described in detail. CCGG emerges naturally in the Palatini formulation, where
the vierbein and the spin connection are independent fields. Neither torsion
nor non-metricity are excluded. The manifestly covariant gauge process is based
on canonical transformations in the De Donder-Weyl Hamiltonian formalism,
starting from a small number of basic postulates. Thereby, the original system
of matter fields in flat spacetime, represented by non-degenerate Hamiltonian
densities, is amended by spacetime fields. The coupling of matter and spacetime
fields leaves the action integral of the combined system invariant under active
local Lorentz transformations and passive diffeomorphisms, aka Principle of
General Relativity. We consider the Klein-Gordon, Maxwell-Proca, and Dirac
fields and derive the corresponding equations of motion. Albeit the coupling of
the given matter fields to the gauge fields are unambiguously determined by
CCGG, the dynamics of the free gauge fields must be postulated based on
physical reasoning. Our choice allows to derive Poisson-like equations of
motion also for curvature and torsion. The latter is proven to be totally
anti-symmetric. The affine connection is a function of the spin connection and
vierbein fields. Requesting the spin connection to be anti-symmetric gives
naturally metric compatibility. The canonical equations combine to an extension
of the Einstein-Hilbert action with a quadratic Riemann-Cartan concomitant that
endows spacetime with inertia. Moreover, a non-degenerate, quadratic version of
the free Dirac Lagrangian is deployed. When coupled to gravity, the Dirac
equation is endowed with an emergent mass parameter, a curvature-dependent mass
correction, and novel interactions between particle spin and spacetime torsion.


  We develop tools to study the problem of containment of symbolic powers
$I^{(m)}$ in powers $I^r$ for a homogeneous ideal $I$ in a polynomial ring
$k[{\bf P}^N]$ in $N+1$ variables over an algebraically closed field $k$. We
obtain results on the structure of the set of pairs $(r,m)$ such that
$I^{(m)}\subseteq I^r$. As corollaries, we show that $I^2$ contains $I^{(3)}$
whenever $S$ is a finite generic set of points in ${\bf P}^2$ (thereby giving a
partial answer to a question of Huneke), and we show that the containment
theorems of Ein-Lazarsfeld-Smith and Hochster-Huneke are optimal for every
fixed dimension and codimension.


  We present a novel method for the search of high energy extraterrestrial
neutrinos in extended regions. The method is based on the study of the spatial
correlations between the events recorded by neutrino telescopes. Extended
regions radiating neutrinos may exist in the Galaxy due to the hierarchical
clustering of massive stars, the progenitors of all the Galactic accelerators
known so far. The neutrino emission associated to such extended regions might
be faint and complex due to both the escape of cosmic rays and the intricate
distribution of gas in the environment of the accelerators. We have simulated
extended neutrino emission over an area of 10deg x 10deg, where the intensity
fluctuations across the region are modelled as a Gaussian random field with a
given correlation structure. We tested our proposed method over realizations of
this intensity field plus a uniform random field representative of the spatial
distribution of the atmospheric neutrino background. Our results indicate that
the method proposed here can detect significant event patterns that would be
missed by standard search methods, mostly focused in the detection of
individual hot spots.


  We study compact K\"ahler threefolds X with infinite fundamental group whose
universal cover can be compactified. Combining techniques from $L^2$ -theory,
Campana's geometric orbifolds and the minimal model program we show that this
condition imposes strong restrictions on the geometry of X. In particular we
prove that if a projective threefold with infinite fundamental group has a
quasi-projective universal cover, the latter is then isomorphic to the product
of an affine space with a simply connected manifold.


  We introduce a flexible family of fairness regularizers for (linear and
logistic) regression problems. These regularizers all enjoy convexity,
permitting fast optimization, and they span the rang from notions of group
fairness to strong individual fairness. By varying the weight on the fairness
regularizer, we can compute the efficient frontier of the accuracy-fairness
trade-off on any given dataset, and we measure the severity of this trade-off
via a numerical quantity we call the Price of Fairness (PoF). The centerpiece
of our results is an extensive comparative study of the PoF across six
different datasets in which fairness is a primary consideration.


  In recent years, neural networks have continued to flourish, achieving high
efficiency in detecting relevant objects in photos or simply recognizing
(classifying) these objects - mainly using CNN networks. Current solutions,
however, are far from ideal, because it often turns out that network can be
effectively confused with even natural images examples. I suspect that the
classification of an object is strongly influenced by the background pixels on
which the object is located. In my work, I analyze the above problem using for
this purpose saliency maps created by the LICNN network. They are designed to
suppress the neurons surrounding the examined object and, consequently, reduce
the contribution of background pixels to the classifier predictions. My
experiments on the natural and adversarial images datasets show that, indeed,
there is a visible correlation between the background and the wrong-classified
foreground object. This behavior of the network is not supported by human
experience, because, for example, we do not confuse the yellow school bus with
the snow plow just because it is on the snowy background.


  In recent years, there have been significant efforts on mitigating unethical
demographic biases in machine learning methods. However, very little is done
for kernel methods. In this paper, we propose a new fair kernel regression
method via fair feature embedding (FKR-F$^2$E) in kernel space. Motivated by
prior works on feature selection in kernel space and feature processing for
fair machine learning, we propose to learn fair feature embedding functions
that minimize demographic discrepancy of feature distributions in kernel space.
Compared to the state-of-the-art fair kernel regression method and several
baseline methods, we show FKR-F$^2$E achieves significantly lower prediction
disparity across three real-world data sets.


  Janus oscillators have been recently introduced as a remarkably simple phase
oscillator model that exhibits non-trivial dynamical patterns -- such as
chimeras, explosive transitions, and asymmetry-induced synchronization -- that
once were only observed in specifically tailored models. Here we study
ensembles of Janus oscillators coupled on large homogeneous and heterogeneous
networks. By virtue of the Ott-Antonsen reduction scheme, we find that the rich
dynamics of Janus oscillators persists in the thermodynamic limit of random
regular, Erd\H{o}s-R\'enyi and scale-free random networks. We uncover for all
these networks the coexistence between partially synchronized state and a
multitude of states displaying global oscillations. Furthermore, abrupt
transitions of the global and local order parameters are observed for all
topologies considered. Interestingly, only for scale-free networks, it is found
that states displaying global oscillations vanish in the thermodynamic limit.


  Responding to user data deletion requests, removing noisy examples, or
deleting corrupted training data are just a few reasons for wanting to delete
instances from a machine learning (ML) model. However, efficiently removing
this data from an ML model is generally difficult. In this paper, we introduce
data removal-enabled (DaRE) forests, a variant of random forests that enables
the removal of training data with minimal retraining. Model updates for each
DaRE tree in the forest are exact, meaning that removing instances from a DaRE
model yields exactly the same model as retraining from scratch on updated data.
  DaRE trees use randomness and caching to make data deletion efficient. The
upper levels of DaRE trees use random nodes, which choose split attributes and
thresholds uniformly at random. These nodes rarely require updates because they
only minimally depend on the data. At the lower levels, splits are chosen to
greedily optimize a split criterion such as Gini index or mutual information.
DaRE trees cache statistics at each node and training data at each leaf, so
that only the necessary subtrees are updated as data is removed. For numerical
attributes, greedy nodes optimize over a random subset of thresholds, so that
they can maintain statistics while approximating the optimal threshold. By
adjusting the number of thresholds considered for greedy nodes, and the number
of random nodes, DaRE trees can trade off between more accurate predictions and
more efficient updates.
  In experiments on 13 real-world datasets and one synthetic dataset, we find
DaRE forests delete data orders of magnitude faster than retraining from
scratch while sacrificing little to no predictive power.


  Polyak proved that all oriented versions of Reidemeister moves for knot and
link diagrams can be generated by a set of just four oriented Reidemeister
moves, and that no fewer than four oriented Reidemeister moves generate them
all. We refer to a set containing four oriented Reidemeister moves that
collectively generate all of the other oriented Reidemeister moves as a minimal
generating set. Polyak also proved that a certain set containing two
Reidemeister moves of type 1, one move of type 2, and one move of type 3 form a
minimal generating set for all oriented Reidemeister moves. We expand upon
Polyak's work by providing an additional eleven minimal, 4-element, generating
sets of oriented Reidemeister moves, and we prove that these twelve sets
represent all possible minimal generating sets of oriented Reidemeister moves.
We also consider the Reidemeister-type moves that relate oriented spatial
trivalent graph diagrams with trivalent vertices that are sources and sinks and
prove that a minimal generating set of oriented Reidemeister-type moves for
spatial trivalent graph diagrams contains ten moves.


  We construct a new family of analytic models of black hole accretion disks in
dynamical equilibria. Our construction is based on assuming distributions of
angular momentum and entropy. For a particular choice of the distribution of
angular momentum, we calculate the shapes of equipressure surfaces. The
equipressure surfaces we find are similar to those in thick, slim and thin
disks, and to those in ADAFs.


  We study finite-temperature properties of the Kondo effect in a carbon
nanotube (CNT) quantum dot using the Wilson numerical renormalization group
(NRG). In the absence of magnetic fields, four degenerate energy levels of the
CNT consisting of spin and orbital degrees of freedom give rise to the SU(4)
Kondo effect. We revisit the universal scaling behavior of the SU(4)
conductance for quarter- and half-filling in a wide temperature range. We find
that the filling dependence of the universal scaling behavior at low
temperatures $T$ can be explained clearly with an extended Fermi-liquid theory.
This theory clarifies that a $T^{2}$ coefficient of conductance becomes zero at
quarter-filling whereas the coefficient at half-filling is finite. We also
study a field-induced crossover from the SU(4) to SU(2) Kondo state observed at
the half-filled CNT dot. The crossover is caused by the matching of the spin
and orbital Zeeman splittings, which lock two levels among the four at the
Fermi level even in magnetic fields $B$. We find that the conductance shows the
SU($4$) scaling behavior at $\mu_{B}B<k_{B}T_{K}^{\mathrm{SU(4)}}$ and it
exhibits the SU($2$) universality at $\mu_{B}B\gg k_{B}T_{K}^{\mathrm{SU(4)}}$,
where $T_{K}^{\mathrm{SU(4)}}$ is the SU($4$) Kondo temperature. To clarify how
the excited states evolve along the SU(4) to SU(2) crossover, we also calculate
the spectral function. The results show that the Kondo resonance width of the
two states locked at the Fermi level becomes sharper with increasing fields.
The spectral peaks of the other two levels moving away from the Fermi level
merge with atomic limit peaks for $\mu_{B}B \gtrsim
k_{B}T_{K}^{\mathrm{SU(4)}}$.


  We investigate ways in which an algorithm can improve its expected
performance by fine-tuning itself automatically with respect to an unknown
input distribution D. We assume here that D is of product type. More precisely,
suppose that we need to process a sequence I_1, I_2, ... of inputs I = (x_1,
x_2, ..., x_n) of some fixed length n, where each x_i is drawn independently
from some arbitrary, unknown distribution D_i. The goal is to design an
algorithm for these inputs so that eventually the expected running time will be
optimal for the input distribution D = D_1 * D_2 * ... * D_n.
  We give such self-improving algorithms for two problems: (i) sorting a
sequence of numbers and (ii) computing the Delaunay triangulation of a planar
point set. Both algorithms achieve optimal expected limiting complexity. The
algorithms begin with a training phase during which they collect information
about the input distribution, followed by a stationary regime in which the
algorithms settle to their optimized incarnations.


  State-of-the-art slot filling models for goal-oriented human/machine
conversational language understanding systems rely on deep learning methods.
While multi-task training of such models alleviates the need for large
in-domain annotated datasets, bootstrapping a semantic parsing model for a new
domain using only the semantic frame, such as the back-end API or knowledge
graph schema, is still one of the holy grail tasks of language understanding
for dialogue systems. This paper proposes a deep learning based approach that
can utilize only the slot description in context without the need for any
labeled or unlabeled in-domain examples, to quickly bootstrap a new domain. The
main idea of this paper is to leverage the encoding of the slot names and
descriptions within a multi-task deep learned slot filling model, to implicitly
align slots across domains. The proposed approach is promising for solving the
domain scaling problem and eliminating the need for any manually annotated data
or explicit schema alignment. Furthermore, our experiments on multiple domains
show that this approach results in significantly better slot-filling
performance when compared to using only in-domain data, especially in the low
data regime.


  We synthesized a series of Nb$_{2}$Pd$_{1-x}$Ru$_{x}$S$_{5}$ polycrystalline
samples by a solid-state reaction method and systematically investigated the
Ru-doping effect on superconductivity by transport and magnetic measurements.
It is found that superconductivity is enhanced with Ru doping and is quite
robust upon disorder. Hall coefficient measurements indicate that the charge
transport is dominated by hole-type charge carriers similar to the case of Ir
doping, suggesting multi-band superconductivity. Upon Ru or Ir doping, \emph
H$_{c2}$/$\emph T_c$ exhibits a significant enhancement, exceeding the Pauli
paramagnetic limit value by a factor of approximately 4. A comparison of $T_c$
and the upper critical field ($H_{c2}$) amongst the different doping elements
on Pd site, reveals a significant role of spin--orbit coupling.


  We construct examples of finitely generated groups L that have non-trivial
actions on $\mathbb{R}$-trees but which cannot act, without fixing a vertex, on
any simplicial tree. Moreover, any finitely presented group mapping onto L does
have a fixed point-free action on some simplicial tree.


  The presence and distribution of water on the Moon are fundamental to our
understanding of the Earth-Moon system. Despite extensive research and remote
detection, the origin and chemical form of lunar water (H2O) have remained
elusive. In this study, we present the discovery of a hydrated mineral,
(NH4)MgCl3*6H2O, in lunar soil samples returned by the Chang'e-5 mission,
containing approximately 41 wt% H2O. The mineral's structure and composition
closely resemble novograblenovite, a terrestrial fumarole mineral formed
through the reaction of hot basalt with water-rich volcanic gases, and
carnallite, an earth evaporite mineral. We rule out terrestrial contamination
or rocket exhaust as the origin of this hydrate, based on its chemical and
isotopic compositions and formation conditions. The presence of ammonium
indicates a more complex lunar degassing history and highlights its potential
as a resource for lunar habitation. Our findings also suggest that water
molecules can persist in sunlit areas of the Moon as hydrated salt, providing
crucial constraints to the fugacity of water and ammonia vapor in lunar
volcanic gases.


  We study the short-range nucleon-nucleon interaction in a chiral constituent
quark model by diagonalizing a Hamiltonian comprising a linear confinement and
a Goldstone boson exchange interaction between quarks. The six-quark harmonic
oscillator basis contains up to two excitation quanta. We show that the highly
dominant configuration is $\mid s^4p^2[42]_O [51]_{FS}>$ due to its specific
flavour-spin symmetry. Using the Born-Oppenheimer approximation we find a
strong effective repulsion at zero separation between nucleons in both $^3S_1$
and $^1S_0$ channels. The symmetry structure of the highly dominant
configuration implies the existence of a node in the S-wave relative motion
wave function at short distances. The amplitude of the oscillation of the wave
function at short range will be however strongly suppressed. We discuss the
mechanism leading to the effective short-range repulsion within the chiral
constituent quark model as compared to that related with the one-gluon exchange
interaction.


  In two previous papers we constructed new families of completely regular
codes by concatenation methods. Here we determine cases in which the new codes
are completely transitive. For these cases we also find the automorphism groups
of such codes. For the remaining cases, we show that the codes are not
completely transitive assuming an upper bound on the order of the monomial
automorphism groups, according to computational results.


  Unitarity of the global evolution is an extremely stringent condition on
finite state models in discrete spacetime. Quantum cellular automata, in
particular, are tightly constrained. In previous work we proved a simple No-go
Theorem which precludes nontrivial homogeneous evolution for linear quantum
cellular automata. Here we carefully define general quantum cellular automata
in order to investigate the possibility that there be nontrivial homogeneous
unitary evolution when the local rule is nonlinear. Since the unitary global
transition amplitudes are constructed from the product of local transition
amplitudes, infinite lattices require different treatment than periodic ones.
We prove Unitarity Theorems for both cases, expressing the equivalence in $1+1$
dimensions of global unitarity and certain sets of constraints on the local
rule, and then show that these constraints can be solved to give a variety of
multiparameter families of nonlinear quantum cellular automata. The Unitarity
Theorems, together with a Surjectivity Theorem for the infinite case, also
imply that unitarity is decidable for one dimensional cellular automata.


  The properties of the uniform Bose gas is studied within the optimized
variational perturbation theory (Gaussian approximation) in a self-consistent
way. It is shown that the atomic BEC with a repulsive interaction becomes
unstable when the gas parameter gamma=rho a^3 exceeds a critical value
gamma_{crit} ~ 0.01. The quantum corrections beyond the Bogoliubov-Popov
approximation to the energy density, chemical potential and pressure in powers
of gamma expansions are presented.


  We show that the maximum number of pairwise intersecting positive homothets
of a $d$-dimensional centrally symmetric convex body, none of which contains
the center of another in its interior, is at most $3^{d+1}$. Also, we improve
upper bounds for cardinalities of $k$-distance sets in Minkowski spaces.


  Given a finite point set $X$ in the plane, the degree of a pair $\{x,y\}
\subset X$ is the number of empty triangles $t=conv\{x,y,z\}$, where empty
means $t\cap X=\{x,y,z\}$. Define $deg X$ as the maximal degree of a pair in
$X$. Our main result is that if $X$ is a random sample of $n$ independent and
uniform points from a fixed convex body, then $deg X \ge cn/\ln n$ in
expectation.


  Financial markets populated by human traders often exhibit "market impact",
where the traders' quote-prices move in the direction of anticipated change,
before any transaction has taken place, as an immediate reaction to the arrival
of a large (i.e., "block") buy or sell order in the market: e.g., traders in
the market know that a block buy order will push the price up, and so they
immediately adjust their quote-prices upwards. Most major financial markets now
involve many "robot traders", autonomous adaptive software agents, rather than
humans. This paper explores how to give such trader-agents a reliable
anticipatory sensitivity to block orders, such that markets populated entirely
by robot traders also show market-impact effects. In a 2019 publication Church
& Cliff presented initial results from a simple deterministic robot trader,
ISHV, which exhibits this market impact effect via monitoring a metric of
imbalance between supply and demand in the market. The novel contributions of
our paper are: (a) we critique the methods used by Church & Cliff, revealing
them to be weak, and argue that a more robust measure of imbalance is required;
(b) we argue for the use of multi-level order-flow imbalance (MLOFI: Xu et al.,
2019) as a better basis for imbalance-sensitive robot trader-agents; and (c) we
demonstrate the use of the more robust MLOFI measure in extending ISHV, and
also the well-known AA and ZIP trading-agent algorithms (which have both been
previously shown to consistently outperform human traders). We demonstrate that
the new imbalance-sensitive trader-agents introduced here do exhibit market
impact effects, and hence are better-suited to operating in markets where
impact is a factor of concern or interest, but do not suffer the weaknesses of
the methods used by Church & Cliff. The source-code for our work reported here
is freely available on GitHub.


  We have mapped the central region of NGC 4945 in the $J=2\to1$ transition of
$^{12}$CO, $^{13}$CO, and C$^{18}$O, as well as the continuum at 1.3 mm, at an
angular resolution of $5\farc \times 3\farc$ with the Submillimeter Array. The
relative proximity of NGC 4945 (distance of only 3.8 Mpc) permits a detailed
study of the circumnuclear molecular gas and dust in a galaxy exhibiting both
an AGN (classified as a Seyfert 2) and a circumnuclear starburst in an inclined
ring with radius $\sim$2\farcs5 ($\sim$50 pc). We find that all three molecular
lines trace an inclined rotating disk with major axis aligned with that of the
starburst ring and large-scale galactic disk, and which exhibits solid-body
rotation within a radius of $\sim$5\farc ($\sim$95 pc). We infer an inclination
for the nuclear disk of $62^{\circ} \pm 2^{\circ}$, somewhat smaller than the
inclination of the large-scale galactic disk of $\sim$$78^{\circ}$. The
continuum emission at 1.3 mm also extends beyond the starburst ring, and is
dominated by thermal emission from dust. If it traces the same dust emitting in
the far-infrared, then the bulk of this dust must be heated by star-formation
activity rather than the AGN. We discover a kinematically-decoupled component
at the center of the disk with a radius smaller than $1\farcs4$ (27 pc), but
which spans approximately the same range of velocities as the surrounding disk.
This component has a higher density than its surroundings, and is a promising
candidate for the circumnuclear molecular torus invoked by AGN unification
models.


  Quark and gluon helicity flip generalized parton distributions (GPDs) encode
the information on the nucleon structure in the transversity sector. In order
to build a theoretically consistent phenomenological parametrization for these
hadronic matrix element within the framework of the dual parametrization of
GPDs (or with the equivalent approach of the SO(3) partial waves (PW) expansion
with the Mellin-Barnes integral techniques) we establish the set of
combinations of parton helicity flip GPDs suitable for the expansion in the
cross channel SO(3) PWs.


  In this article, we propose a simple rule that generates scale-free networks
with very large clustering coefficient and very small average distance. These
networks are called {\bf Random Apollonian Networks}(RAN) as they can be
considered as a variation of Apollonian networks. We obtain the analytic
results of power-law exponent $\gamma =3$ and clustering coefficient
$C={46/3}-36\texttt{ln}{3/2}\approx 0.74$, which agree very well with the
simulation results. We prove that the increasing tendency of average distance
of RAN is a little slower than the logarithm of the number of nodes in RAN.
Since most real-life networks are both scale-free and small-world networks, RAN
may perform well in mimicking the reality. The RAN possess hierarchical
structure as $C(k)\sim k^{-1}$ that in accord with the observations of many
real-life networks. In addition, we prove that RAN are maximal planar networks,
which are of particular practicability for layout of printed circuits and so
on. The percolation and epidemic spreading process are also studies and the
comparison between RAN and Barab\'{a}si-Albert(BA) as well as Newman-Watts(NW)
networks are shown. We find that, when the network order $N$(the total number
of nodes) is relatively small(as $N\sim 10^4$), the performance of RAN under
intentional attack is not sensitive to $N$, while that of BA networks is much
affected by $N$. And the diseases spread slower in RAN than BA networks during
the outbreaks, indicating that the large clustering coefficient may slower the
spreading velocity especially in the outbreaks.


  This is a first of a series of two papers. Our motive is to tackle the
question raised in B\"ohm's "The Gray Monoidal Product of Double Categories"
from Applied Categorical Structures: which would be an alternative notion to
intercategories of Grandis and Par\'e, so that monoids in B\"ohm's monoidal
category $Dbl$ of strict double categories and double pseudo functors be an
example of it? Before addressing this question we observe that although
bicategories embed into pseudo double categories, this embedding is not
monoidal, with the usual notion of a monoidal pseudo double category. We then
prove that monoidal bicategories embed into the mentioned monoids of B\"ohm. In
order to fit B\"ohm's monoid into an intercategory-type object, we start by
upgrading the category $Dbl$ to a 2-category and end up rather with a
tricategory $\DblPs$. We propose an alternative definition of intercategories
as internal categories in this tricategory, enabling $Dbl$ to be an example of
this gadget. The formal definition of a category internal to the (type of a)
tricategory (of) $\DblPs$, as well as another important example of these in the
literature, we leave for a subsequent paper.


  A spectral Favard theorem for bounded banded lower Hessenberg matrices that
admit a positive bidiagonal factorization is found. The large knowledge on the
spectral and factorization properties of oscillatory matrices leads to this
spectral Favard theorem in terms of sequences of multiple orthogonal
polynomials of types I and II with respect to a set of positive
Lebesgue-Stieltjes~measures. Also a multiple Gauss quadrature is proven and
corresponding degrees of precision are found.
  This spectral Favard theorem is applied to Markov chains with
$(p+2)$-diagonal transition matrices, i.e. beyond birth and death, that admit a
positive stochastic bidiagonal factorization. In the finite case, the
Karlin-McGregor spectral representation is given. It is shown that the Markov
chains are recurrent and explicit expressions in terms of the orthogonal
polynomials for the stationary distributions are given. Similar results are
obtained for the countable infinite Markov chain. Now the Markov chain is not
necessarily recurrent, and it is characterized in terms of the first measure.
Ergodicity of the Markov chain is discussed in terms of the existence of a mass
at $1$, which is an eigenvalue corresponding to the right and left
eigenvectors.


  It was known that for non-Hermitian topological systems due to the
non-Hermitian skin effect, the bulk-edge correspondence is broken down. In this
paper, by using one-dimensional Su-SchriefferHeeger model and two-dimensional
(deformed) Qi-Wu-Zhang model as examples, we focus on a special type of
non-Hermitian topological system without non-Hermitian skin effect-topological
systems under non-Hermitian similarity transformation. In these non-Hermitian
systems, the defective edge states and the breakdown of bulk-edge
correspondence are discovered. To characterize the topological properties, we
introduce a new type of inversion symmetry-protected topological
invariant-total Z2 topological invariant. In topological phases, defective edge
states appear. With the help of the effective edge Hamiltonian, we find that
the defective edge states are protected by (generalized) chiral symmetry and
thus the (singular) defective edge states are unstable against the perturbation
breaking the chiral symmetry. In addition, the results are generalized to
nonHermitian topological insulators with inversion symmetry in higher
dimensions. This work could help people to understand the defective edge states
and the breakdown of bulk-edge correspondence for non-Hermitian topological
systems.


  We study symplectic Laplacians on compact symplectic manifolds with boundary.
These Laplacians are associated with symplectic cohomologies of differential
forms and can be of fourth-order. We introduce several natural boundary
conditions on differential forms and use them to establish Hodge theory by
proving various form decomposition and also isomorphisms between the symplectic
cohomologies and the spaces of harmonic fields. These novel boundary conditions
can be applied in certain cases to study relative symplectic cohomologies and
Lefschetz maps between relative de Rham cohomologies. As an application, our
results are used to solve boundary value problems of differential forms.


  We propose a mixed integer programming (MIP) model and iterative algorithms
based on topological orders to solve optimization problems with acyclic
constraints on a directed graph. The proposed MIP model has a significantly
lower number of constraints compared to popular MIP models based on cycle
elimination constraints and triangular inequalities. The proposed iterative
algorithms use gradient descent and iterative reordering approaches,
respectively, for searching topological orders. A computational experiment is
presented for the Gaussian Bayesian network learning problem, an optimization
problem minimizing the sum of squared errors of regression models with L1
penalty over a feature network with application of gene network inference in
bioinformatics.


  In this paper, we give various identities for the weighted average of the
product of generalized Anderson-Apostol sums with weights concerning completely
multiplicative function, completely additive function, logarithms, the Gamma
function, Bernoulli polynomials and binomial coefficients respectively. Our
results generalize many known results.


  Braneworld effective action is constructed by two different methods based
respectively on the Dirichlet and Neumann boundary value problems. The
equivalence of these methods is shown due to nontrivial duality relations
between special boundary operators of these two problems. Previously known
braneworld action algorithms in two-brane Randall-Sundrum model are generalized
to curved branes with deSitter and Anti-deSitter geometries.


  We study the effects of the gapless color-flavor locked (gCFL) phase on the
equation of state of strongly interacting matter in the range of baryonic
chemical potential involved in a compact star. We analyze the possibility of a
phase transition from hadronic matter to gCFL quark matter and we discuss, for
different values of the strange quark mass and diquark coupling strength, the
existence of a gCFL phase in quark or hybrid stars. The mass-radius relation
and the structure of compact stars containing the gCFL phase are shown and the
physical relevance of this superconducting phase inside a stellar object is
also discussed.


  Field-level inference provides a means to optimally extract information from
upcoming cosmological surveys, but requires efficient sampling of a
high-dimensional parameter space. This work applies Microcanonical Langevin
Monte Carlo (MCLMC) to sample the initial conditions of the Universe, as well
as the cosmological parameters $\sigma_8$ and $\Omega_m$, from simulations of
cosmic structure. MCLMC is shown to be over an order of magnitude more
efficient than traditional Hamiltonian Monte Carlo (HMC) for a $\sim 2.6 \times
10^5$ dimensional problem. Moreover, the efficiency of MCLMC compared to HMC
greatly increases as the dimensionality increases, suggesting gains of many
orders of magnitude for the dimensionalities required by upcoming cosmological
surveys.


  Undistorted monolayer graphene has energy bands which cross at protected
Dirac points. It elastically deforms and much research has assumed the Dirac
description persists, now in a curved space and coupled to a gauge field
related to lattice strain. We show this is incorrect by using a real space
gradient expansion to study how the Dirac equation derives from the tight
binding model. Generic spatially varying hopping functions give rise to large
magnetic fields which spoil the truncation in derivatives. In the perturbative
regime, the only consistent truncation to Dirac is one with nontrivial gauge
field but in flat space. One can instead fine tune the magnetic field to be
small, and we derive the resulting differential condition that the hopping
functions must satisfy to yield a consistent truncation to Dirac in curved
space. We consider whether mechanical effects might impose this fine tuning,
but find this is not the case for a simple elastic membrane model.


  In order to successfully perform manipulation tasks in new environments, such
as grasping, robots must be proficient in segmenting unseen objects from the
background and/or other objects. Previous works perform unseen object instance
segmentation (UOIS) by training deep neural networks on large-scale data to
learn RGB/RGB-D feature embeddings, where cluttered environments often result
in inaccurate segmentations. We build upon these methods and introduce a novel
approach to correct inaccurate segmentation, such as under-segmentation, of
static image-based UOIS masks by using robot interaction and a designed body
frame-invariant feature. We demonstrate that the relative linear and rotational
velocities of frames randomly attached to rigid bodies due to robot
interactions can be used to identify objects and accumulate corrected
object-level segmentation masks. By introducing motion to regions of
segmentation uncertainty, we are able to drastically improve segmentation
accuracy in an uncertainty-driven manner with minimal, non-disruptive
interactions (ca. 2-3 per scene). We demonstrate the effectiveness of our
proposed interactive perception pipeline in accurately segmenting cluttered
scenes by achieving an average object segmentation accuracy rate of 80.7%, an
increase of 28.2% when compared with other state-of-the-art UOIS methods.


  We study the ground state of the Gross Pitaveskii energy in a strip, with a
phase imprinting condition, motivated by recent experiments on matter waves
solitons. We prove that when the width of the strip is small, the ground state
is a one dimensional soliton. On the other hand, when the width is large, the
ground state is a solitonic vortex. We provide an explicit expression for the
limiting phase of the solitonic vortex as the size of the strip is large: it
has the same behaviour as the soliton in the infinite direction and decays
exponentially due to the geometry of the strip, instead of algebraically as
vortices in the whole space.


  Over n-dimensional manifolds, I classify ternary differential operators
acting on the spaces of weighted densities and invariant with respect to the
Lie algebra of vector fields. For n=1, some of these operators can be expressed
in terms of the de Rham exterior differential, the Poisson bracket, the Grozman
operator and the Feigin-Fuchs anti-symmetric operators; four of the operators
are new, up to dualizations and permutations. For n>1, I list multidimensional
conformal tranvectors, i.e.,operators acting on the spaces of weighted
densities and invariant with respect to o(p+1,q+1), where p+q=n. Except for the
scalar operator, these conformally invariant operators are not invariant with
respect to the whole Lie algebra of vector fields.


  Device-to-Device (D2D) communication as a promising technology in 5G cellular
networks provides the communication of the users in the vicinity and thereby
decreases end-to-end delay and power consumption. In addition to the
aforementioned advantages, it also supports the high-speed data transmission
services such as content delivery. In this paper, we consider the D2D multicast
communications opportunity in the D2D-cellular hybrid network, in which that
one transmitter targets multiple receivers at the same time. We provide the
analysis for the proposed system by using tools from stochastic geometry, to
calculate the cache hitting probability of the receivers as well as the energy
consumption of the hybrid network aiming to seek the optimal number of caching
contents in the D2D multicast opportunities.


  Langevin simulation provides an effective way to study collisional effects in
beams by reducing the six-dimensional Fokker-Planck equation to a group of
stochastic ordinary differential equations. These resulting equations usually
have multiplicative noise since the diffusion coefficients in these equations
are functions of position and time. Conventional algorithms, e.g. Euler and
Heun, give only first order convergence of moments in a finite time interval.
In this paper, a stochastic leap-frog algorithm for the numerical integration
of Langevin stochastic differential equations with multiplicative noise is
proposed and tested. The algorithm has a second-order convergence of moments in
a finite time interval and requires the sampling of only one uniformly
distributed random variable per time step. As an example, we apply the new
algorithm to the study of a mechanical oscillator with multiplicative noise.


  Let u = {u(t, x), t $\in$ [0, T ], x $\in$ R d } be the solution to the
linear stochastic heat equation driven by a fractional noise in time with
correlated spatial structure. We study various path properties of the process u
with respect to the time and space variable, respectively. In particular, we
derive their exact uniform and local moduli of continuity and Chung-type laws
of the iterated logarithm.


  We generate experimentally spin-wave envelope dark solitons from rectangular
high-frequency dark input pulses with externally introduced phase shifts in
yttrium-iron garnet magnetic fims. We observe the generation of both odd and
even numbers of magnetic dark solitons when the external phase shift varies.
The experimental results are in a good qualitative agreement with the theory of
the dark-soliton generation in magnetic films developed earlier [Phys. Rev.
Lett. 82, 2583 (1999)].


  We present different regularizations and numerical methods for the nonlinear
Schr\"odinger equation with singular nonlinearity (sNLSE) including the
regularized Lie-Trotter time-splitting (LTTS) methods and regularized
Lawson-type exponential integrator (LTEI) methods. Due to the blowup of the
singular nonlinearity, i.e., $f(\rho)=\rho^{\alpha}$ with a fixed exponent
$\alpha<0$ goes to infinity when $\rho \to 0^+$ ($\rho = |\psi|^2$ represents
the density with $\psi$ being the complex-valued wave function or order
parameter), there are significant difficulties in designing accurate and
efficient numerical schemes to solve the sNLSE. In order to suppress the
round-off error and avoid blowup near $\rho = 0^+$, two types of
regularizations for the sNLSE are proposed with a small regularization
parameter $0 < \eps \ll 1$. One is based on the local energy regularization
(LER) for the sNLSE via regularizing the energy density $F(\rho) =
\frac{1}{\alpha+1}\rho^{\alpha+1}$ locally near $\rho = 0^+$ with a polynomial
approximation and then obtaining a local energy regularized nonlinear
Schr\"odinger equation via energy variation. The other one is the global
nonlinearity regularization which directly regularizes the singular
nonlinearity $f(\rho)=\rho^{\alpha}$ to avoid blowup near $\rho = 0^+$. For the
regularized models, we apply the first-order Lie-Trotter time-splitting method
and Lawson-type exponential integrator method for temporal discretization and
combine with the Fourier pseudospectral method in space to numerically solve
them. Numerical examples are provided to show the convergence of the
regularized models to the sNLSE and they suggest that the local energy
regularization performs better than directly regularizing the singular
nonlinearity globally.


  The [O III] 5007 Angstrom line is typically the brightest line in planetary
nebula (PN) spectra. Observations show that the brightest [O III] 5007 Angstrom
PN in a galaxy -- the planetary nebula luminosity function (PNLF) bright-end
cutoff -- is surprisingly independent of galaxy type. To understand the origin
of this puzzling uniformity, we simulate PNe with a range of cloud and star
parameters using the photoionization code CLOUDY. We find that the peak [O III]
5007 Angstrom luminosity depends weakly on both the central stellar effective
temperature at high temperature and on the total PN ejecta mass; however, the
peak [O III] 5007 Angstrom luminosity depends strongly on the central stellar
luminosity and the PN dust-to-gas mass ratio. We explain these scalings
physically. They imply that a higher dust-to-gas mass ratio at higher central
stellar luminosity can help explain a constant bright-end cutoff in the PNLF
across galaxy types. This prediction is testable with a survey of galactic PNe.
The surviving remnants of double white dwarf mergers should also produce
photoionized nebulae analogous to PNe. These may be preferentially present at
the high luminosity end of the [O III] PLNF and could explain the existence of
PNe in early-type galaxies that are more luminous in [O III] than expected from
single-star evolutionary models. The presence of white dwarf mergers in both
young and old stellar populations could contribute to the uniformity of the [O
III] PNLF across galaxy types; such nebulae would lack the hydrogen lines
otherwise characteristic of PNe.


  We review the result of SUSY parameter fits based on frequentist analyses of
experimental constraints from electroweak precision data, (g-2)_mu, B-physics
and cosmological data. We investigate the parameters of the constrained MSSM
(CMSSM) with universal soft supersymmetry-breaking mass parameters, and a model
with common non-universal Higgs mass parameters in the superpotential (NUHM1).
Shown are the results for the SUSY and Higgs spectrum of the models. Many
sparticle masses are highly correlated in both the CMSSM and NUHM1, and parts
of the regions preferred at the 68% C.L. are accessible to early LHC running.
The best-fit points could be tested even with 1/fb at sqrt[s] = 7 Tev.


  Ponzi schemes, a form of scam, have been discovered in Ethereum smart
contracts in recent years, causing massive financial losses. Existing detection
methods primarily focus on rule-based approaches and machine learning
techniques that utilize static information as features. However, these methods
have significant limitations. Rule-based approaches rely on pre-defined rules
with limited capabilities and domain knowledge dependency. Using static
information like opcodes for machine learning fails to effectively characterize
Ponzi contracts, resulting in poor reliability and interpretability. Moreover,
relying on static information like transactions for machine learning requires a
certain number of transactions to achieve detection, which limits the
scalability of detection and hinders the identification of 0-day Ponzi schemes.
  In this paper, we propose PonziGuard, an efficient Ponzi scheme detection
approach based on contract runtime behavior. Inspired by the observation that a
contract's runtime behavior is more effective in disguising Ponzi contracts
from the innocent contracts, PonziGuard establishes a comprehensive graph
representation called contract runtime behavior graph (CRBG), to accurately
depict the behavior of Ponzi contracts. Furthermore, it formulates the
detection process as a graph classification task on CRBG, enhancing its overall
effectiveness. The experiment results show that PonziGuard surpasses the
current state-of-the-art approaches in the ground-truth dataset. We applied
PonziGuard to Ethereum Mainnet and demonstrated its effectiveness in real-world
scenarios. Using PonziGuard, we identified 805 Ponzi contracts on Ethereum
Mainnet, which have resulted in an estimated economic loss of 281,700 Ether or
approximately $500 million USD. We also found 0-day Ponzi schemes in the
recently deployed 10,000 smart contracts.


  We studied the electronic structure of a layered antiferromagnetic metal,
EuSnP, in the paramagnetic and in the antiferromagnetic phase using angle
resolved photoemission spectroscopy (ARPES) alongside density functional theory
(DFT) based first principles calculations. The temperature dependence of the
magnetic susceptibility measurements exhibits an antiferromagnetic transition
at a Neel temperature of 21 K. Employing high resolution ARPES, the valence
band structure was measured at several temperatures above and below the Neel
temperature, which produced identical spectra independent of temperature.
Through analysis of the ARPES results presented here, we attribute the
temperature independent spectra to the weak coupling of the Sn, and P
conduction electrons with Eu 4f states.


  A model-potential approach to calculating positron-molecule binding energies
and annihilation rates is developed. Unlike existing ab initio calculations,
which have mostly been applied to strongly polar molecules, the present
methodology can be applied to both strongly polar and weakly polar or nonpolar
systems. The electrostatic potential of the molecule is calculated at the
Hartree-Fock level, and a model potential that describes short-range
correlations and long-range polarization of the electron cloud by the positron
is then added. The Schrodinger equation for a positron moving in this effective
potential is solved to obtain the binding energy. The model potential contains
a single adjustable parameter for each type of atom present in the molecule.
The wave function of the positron bound state may be used to compute the rate
of electron-positron annihilation from the bound state. As a first application,
we investigate positron binding and annihilation for the hydrogen cyanide (HCN)
molecule. Results for the binding energy are found to be in accord with
existing calculations, and we predict the rate of annihilation from the bound
state to be $\Gamma=0.1$--$0.2 \times 10^9~\text{s}^{-1}$.


  Let $S(\rho)$ be the von Neumann entropy of a density matrix $\rho$. Weak
monotonicity asserts that $S(\rho_{AB}) - S(\rho_A) + S(\rho_{BC}) -
S(\rho_C)\geq 0$ for any tripartite density matrix $\rho_{ABC}$, a fact that is
equivalent to the strong subadditivity of entropy. We prove an operator
inequality, which, upon taking an expectation value with respect to the state
$\rho_{ABC}$, reduces to the weak monotonicity inequality. Generalizations of
this inequality to the one involving two independent density matrices, as well
as their R\'enyi-generalizations, are also presented.


  We investigate the generation of quantum operations for one-qubit systems
under classical noise with 1/f^\alpha power spectrum, where 2>\alpha > 0. We
present an efficient way to approximate the noise with a discrete multi-state
Markovian fluctuator. With this method, the average temporal evolution of the
qubit density matrix under 1/f^\alpha noise can be feasibly determined from
recently derived deterministic master equations. We obtain qubit operations
such as quantum memory and the NOT}gate to high fidelity by a gradient based
optimization algorithm. For the NOT gate, the computed fidelities are
qualitatively similar to those obtained earlier for random telegraph noise. In
the case of quantum memory however, we observe a nonmonotonic dependency of the
fidelity on the operation time, yielding a natural access rate of the memory.


  We establish the degrees of freedom of the two-user X-channel with delayed
channel knowledge at transmitters (i.e., delayed CSIT), assuming linear coding
strategies at the transmitters. We derive a new upper bound and characterize
the linear degrees of freedom of this network to be 6/5. The converse builds
upon our development of a general lemma that shows that, if two distributed
transmitters employ linear strategies, the ratio of the dimensions of received
linear subspaces at the two receivers cannot exceed 3/2, due to delayed CSIT.
As a byproduct, we also apply this general lemma to the three-user interference
channel with delayed CSIT, thereby deriving a new upper bound of 9/7 on its
linear degrees of freedom. This is the first bound that captures the impact of
delayed CSIT on the degrees of freedom of this network, under the assumption of
linear encoding strategies.


  The negative results in the search for Kaluza-Klein graviton modes at the
LHC, when confronted with the discovery of the Higgs, has been construed to
have severely limited the efficacy of the Randall-Sundrum model as an
explanation of the hierarchy problem. We show, though, that the presence of
multiple warping offers a natural resolution of this conundrum through
modifications in both the graviton spectrum and their couplings to the Standard
Model fields.


  We present an efficient and robust protocol for quantum-enhanced sensing
using a single-spin qubit in the topological waveguide system. Our method
relies on the topological-paired bound states, which are localized near the
spin and can be effectively regarded as a two-level system. Through the lens of
Bayesian inference theory, we show the sensitivity can reach the Heisenberg
limit across a large field range. Inheriting from the topological robustness of
the waveguide, our sensing protocol is robust against local perturbations. The
advantages of our protocol are multifold as it allows for sensing various
parameters and uses a product initial state, which can be easily prepared in
experiments. We expect this approach would pave the way towards robust
topological quantum sensors based on near term quantum platforms such as
topological photonics and Rydberg arrays.


  The role of electron-electron interactions on two-dimensional Dirac fermions
remains enigmatic. Using a combination of nonperturbative numerical and
analytical techniques that incorporate both the contact and long-range parts of
the Coulomb interaction, we identify the two previously discussed regimes: a
Gross-Neveu transition to a strongly correlated Mott insulator, and a
semi-metallic state with a logarithmically diverging Fermi velocity accurately
described by the random phase approximation. Most interestingly, experimental
realizations of Dirac fermions span the crossover between these two regimes
providing the physical mechanism that masks this velocity divergence. We
explain several long-standing mysteries including why the observed Fermi
velocity in graphene is consistently about 20 percent larger than the best
values calculated using ab initio and why graphene on different substrates show
different behavior.


  We study the asymptotic behavior of the Lyapunov exponent in a meromorphic
family of random products of matrices in SL(2, C), as the parameter converges
to a pole. We show that the blow-up of the Lyapunov exponent is governed by a
quantity which can be interpreted as the non-Archimedean Lyapunov exponent of
the family. We also describe the limit of the corresponding family of
stationary measures on P 1 (C).


  Human action recognition aims at classifying the category of human action
from a segment of a video. Recently, people have dived into designing GCN-based
models to extract features from skeletons for performing this task, because
skeleton representations are much more efficient and robust than other
modalities such as RGB frames. However, when employing the skeleton data, some
important clues like related items are also discarded. It results in some
ambiguous actions that are hard to be distinguished and tend to be
misclassified. To alleviate this problem, we propose an auxiliary feature
refinement head (FR Head), which consists of spatial-temporal decoupling and
contrastive feature refinement, to obtain discriminative representations of
skeletons. Ambiguous samples are dynamically discovered and calibrated in the
feature space. Furthermore, FR Head could be imposed on different stages of
GCNs to build a multi-level refinement for stronger supervision. Extensive
experiments are conducted on NTU RGB+D, NTU RGB+D 120, and NW-UCLA datasets.
Our proposed models obtain competitive results from state-of-the-art methods
and can help to discriminate those ambiguous samples. Codes are available at
https://github.com/zhysora/FR-Head.


  Geriatric depression is a common mental health condition affecting majority
of older adults in the US. As per Attention Restoration Theory (ART),
participation in outdoor activities is known to reduce depression and provide
restorative benefits. However, many older adults, who suffer from depression,
especially those who receive care in organizational settings, have less access
to sensory experiences of the outdoor natural environment. This is often due to
their physical or cognitive limitations and from lack of organizational
resources to support outdoor activities. To address this, we plan to study how
technology can bring the restorative benefits of outdoors to the indoor
environments through augmented spatial natural soundscapes. Thus, we propose an
interview and observation-based study at an assisted living facility to
evaluate how augmented soundscapes substitute for outdoor restorative, social,
and experiential benefits. We aim to integrate these findings into a minimally
intrusive and intuitive design of an interactive augmented soundscape, for
indoor organizational care settings.


  Grid-interactive power converters are normally synchronized to the grid using
phase-locked loops (PLLs). The performance of the PLLs is affected by the
non-ideal conditions in the sensed grid voltage such as harmonics, frequency
deviations and dc offsets in single-phase systems. In this paper, a
single-phase PLL is presented to mitigate the effects of these non-idealities.
This PLL is based on the popular second order generalized integrator (SOGI)
structure. The SOGI structure is modified to eliminate of the effects of input
dc offsets. The resulting SOGI structure has a high-pass filtering property.
Hence, this PLL is termed as high-pass generalized integrator based PLL
(HGI-PLL). It has fixed parameters which reduces the implementation complexity
and aids in the implementation in low-end digital controllers. The HGI-PLL is
shown to have least resource utilization among the SOGI based PLLs with dc
cancelling capability. Systematic design methods are evolved leading to the
design that limits the unit vector THD to within 1% for given non-ideal input
conditions in terms of frequency deviation and harmonic distortion. The
proposed designs achieve the fastest transient response. The performance of
this PLL has been verified experimentally. The results are found to agree with
the theoretical prediction.


  Fish exhibit impressive locomotive performance and agility in complex
underwater environments, using their undulating tails and pectoral fins for
propulsion and maneuverability. Replicating these abilities in robotic fish is
challenging; existing designs focus on either fast swimming or directional
control at limited speeds, mainly within a confined environment. To address
these limitations, we designed Snapp, an integrated robotic fish capable of
swimming in open water with high speeds and full 3-dimensional maneuverability.
A novel cyclic-differential method is layered on the mechanism. It integrates
propulsion and yaw-steering for fast course corrections. Two independent
pectoral fins provide pitch and roll control. We evaluated Snapp in open water
environments. We demonstrated significant improvements in speed and
maneuverability, achieving swimming speeds of 1.5 m/s (1.7 Body Lengths per
second) and performing complex maneuvers, such as a figure-8 and S-shape
trajectory. Instantaneous yaw changes of 15$^{\circ}$ in 0.4 s, a minimum turn
radius of 0.85 m, and maximum pitch and roll rates of 3.5 rad/s and 1 rad/s,
respectively, were recorded. Our results suggest that Snapp's swimming
capabilities have excellent practical prospects for open seas and contribute
significantly to developing agile robotic fishes.


  Controlling magnetic anisotropy (MA) is important in a variety of
applications including magnetic memories, spintronic sensors, and
skyrmion-based data distribution. The perovskite manganite family provides a
fertile playground for complex, intricate, and potentially useful
structure-magnetism relations. Here we report on the MA that emerges in 10% Ru
substituted $La_{0.7}Sr_{0.3}MnO_{3}$ (Ru-LSMO) films for which strong
perpendicular magnetization and anisotropic in-plane magnetization are found.
These moderately compressively strained films possess a rich microstructure,
consisting of coherently strained phase which evolves into a one dimensional
(1D) periodically-modulated structure above a critical thickness. We illustrate
how 10% Ru substitution plays a crucial role behind the observed MA, and how
the structural distortion and 1D periodic structural modulation produce the
anisotropic in-plane magnetization. We highlight the practical significance of
the observed MA, which could pave the way towards the realization of
cutting-edge oxide-based room temperature spintronic memory devices.


  Unsupervised models can provide supplementary soft constraints to help
classify new, "target" data since similar instances in the target set are more
likely to share the same class label. Such models can also help detect possible
differences between training and target distributions, which is useful in
applications where concept drift may take place, as in transfer learning
settings. This paper describes a general optimization framework that takes as
input class membership estimates from existing classifiers learnt on previously
encountered "source" data, as well as a similarity matrix from a cluster
ensemble operating solely on the target data to be classified, and yields a
consensus labeling of the target data. This framework admits a wide range of
loss functions and classification/clustering methods. It exploits properties of
Bregman divergences in conjunction with Legendre duality to yield a principled
and scalable approach. A variety of experiments show that the proposed
framework can yield results substantially superior to those provided by popular
transductive learning techniques or by naively applying classifiers learnt on
the original task to the target data.


  Dinaburg and Sinai recently proposed a quasi-linear model of the
Navier-Stokes equations. Their model assumes that nonlocal interactions in
Fourier space are dominant, contrary to the Kolmogorov turbulence phenomenology
where local interactions prevail. Their equation corresponds to the linear
evolution of small scales on a background field with uniform gradient, but the
latter is defined as the linear superposition of all the small scale gradients
at the origin. This is not self-consistent.


  In the formulation of his celebrated Formality conjecture, M. Kontsevich
introduced a universal version of the deformation theory for the Schouten
algebra of polyvector fields on affine manifolds. This universal deformation
complex takes the form of a differential graded Lie algebra of graphs, denoted
$\mathsf{fGC}_2$, together with an injective morphism towards the
Chevalley-Eilenberg complex associated with the Schouten algebra. The latter
morphism is given by explicit local formulas making implicit use of the
supergeometric interpretation of the Schouten algebra as the algebra of
functions on a graded symplectic manifold of degree $1$. The ambition of the
present work is to generalise Kontsevich's construction to graded symplectic
manifolds of arbitrary degree $n\geq1$. The corresponding graph model is given
by the full Kontsevich graph complex $\mathsf{fGC}_d$ where $d=n+1$ stands for
the dimension of the associated AKSZ type $\sigma$-model. This generalisation
is instrumental to classify universal structures on graded symplectic
manifolds. In particular, the zeroth cohomology of the full graph complex
$\mathsf{fGC}_{d}$ is shown to act via $\mathsf{Lie}_\infty$-automorphisms on
the algebra of functions on graded symplectic manifolds of degree $n$. This
generalises the known action of the Grothendieck-Teichm\"{u}ller algebra
$\mathfrak{grt}_1\simeq H^0(\mathsf{fGC}_2)$ on the space of polyvector fields.
This extended action can in turn be used to generate new universal deformations
of Hamiltonian functions, generalising Kontsevich flows on the space of Poisson
manifolds to differential graded manifolds of higher degrees. As an application
of the general formalism, universal deformations of Courant algebroids via
trivalent graphs are presented.


  The multipole expansion technique is applied to one of the largest magnetic
molecules, Fe30. The molecule's dipole, toroid and quadrupole magnetic moments
are equal to zero (in the absence of magnetic field) so the multipole expansion
starts from the octopole moment. Probably the Fe30 molecule is the most
symmetrical magnetic body synthesized so far. The magnetization process is
considered theoretically in different geometries. Some components of the
octopole moment experience a jump while the magnetization rises linearly up to
its saturation value. An elementary octopole moment consisting of four magnetic
dipoles is proposed as a hint for designing of an experiment for measurement of
octopole magnetic moment components.


  We report on the growth and properties of high quality bicolor oxide
superlattices, composed of two perovskites out of BaTiO3, CaTiO3, and SrTiO3.
The artificially grown superlattices are structurally unique and have a
macroscopically homogeneous phase, which is not feasible to recreate in bulk
form. By artificial structuring, it is found that the polarization of such
superlattices can be highly increased as compared to pseudo-binary ceramics
with the same overall composition. Such strong enhancement in superlattice is
attributed to newly-developed ionic motions of A-site cations at the
hetero-interfaces due to the interfacial coupling of electrostatic and elastic
interactions, which cannot be found in single phase materials.


  Deep reinforcement learning is prone to overfitting, and traditional
benchmarks such as Atari 2600 benchmark can exacerbate this problem. The
Obstacle Tower Challenge addresses this by using randomized environments and
separate seeds for training, validation, and test runs. This paper examines
various improvements and best practices to the PPO algorithm using the Obstacle
Tower Challenge to empirically study their impact with regards to
generalization. Our experiments show that the combination provides
state-of-the-art performance on the Obstacle Tower Challenge.


  The main topic of this paper is to show that in the 3-dimensional Minkowski
spacetime, the torsion of a null curve is equal to the Schwarzian derivative of
a certain function appearing in a description of the curve. As applications, we
obtain descriptions of the slant helices, and null curves for which the torsion
is of the form $\tau=-2\lambda s$, $s$ being the pseudo-arc parameter and
$\lambda=\mathop{\rm constant}\not=0$.


  The classical approach to measure the expressive power of deep neural
networks with piecewise linear activations is based on counting their maximum
number of linear regions. This complexity measure is quite relevant to
understand general properties of the expressivity of neural networks such as
the benefit of depth over width. Nevertheless, it appears limited when it comes
to comparing the expressivity of different network architectures. This lack
becomes particularly prominent when considering permutation-invariant networks,
due to the symmetrical redundancy among the linear regions. To tackle this, we
propose a refined definition of piecewise linear function complexity: instead
of counting the number of linear regions directly, we first introduce an
equivalence relation among the linear functions composing a piecewise linear
function and then count those linear functions relative to that equivalence
relation. Our new complexity measure can clearly distinguish between the two
aforementioned models, is consistent with the classical measure, and increases
exponentially with depth.


  We introduce a new concept of quasi-Yang-Baxter algebras. The quantum
quasi-Yang-Baxter algebras being simple but non-trivial deformations of
ordinary algebras of monodromy matrices realize a new type of quantum dynamical
symmetries and find an unexpected and remarkable applications in quantum
inverse scattering method (QISM). We show that applying to quasi-Yang-Baxter
algebras the standard procedure of QISM one obtains new wide classes of quantum
models which, being integrable (i.e. having enough number of commuting
integrals of motion) are only quasi-exactly solvable (i.e. admit an algebraic
Bethe ansatz solution for arbitrarily large but limited parts of the spectrum).
These quasi-exactly solvable models naturally arise as deformations of known
exactly solvable ones. A general theory of such deformations is proposed. The
correspondence ``Yangian --- quasi-Yangian'' and ``$XXX$ spin models ---
quasi-$XXX$ spin models'' is discussed in detail. We also construct the
classical conterparts of quasi-Yang-Baxter algebras and show that they
naturally lead to new classes of classical integrable models. We conjecture
that these models are quasi-exactly solvable in the sense of classical inverse
scattering method, i.e. admit only partial construction of action-angle
variables.


  Multi-photon and coherent states of light are formulated in terms of a
reducible representation of canonical commutation relations. Standard
properties of such states are recovered as certain limiting cases. The new
formalism leads to field operators and not operator-valued distributions. The
example of radiation fields produced by a classical current shows an automatic
regularization of the infrared divergence.


  In addition to being suitable for laser cooling and trapping in a
magneto-optical trap (MOT) using a relatively broad ($\sim$5 MHz) transition,
the molecule YO possesses a narrow-line transition. This forbidden transition
between the $X^{2}\Sigma$ and $A'^{2}\Delta_{3/2}$ states has linewidth
$\sim$2$\pi\times$160 kHz. After cooling in a MOT on the $X^{2}\Sigma$ to
$A^{2}\Pi_{1/2}$ (orange) transition, the narrow (red) transition can be used
to further cool the sample, requiring only minimal additions to the first stage
system. The narrow line cooling stage will bring the temperature from $\sim$1
mK to $\sim$10 $\mu$K, significantly advancing the frontier on direct cooling
achievable for molecules.


  It has been recently demonstrated that it is possible to construct
isochronous cosmologies, extending to general relativity a result valid for
non-relativistic Hamiltonian systems. In this paper we review these findings
and we discuss the Newtonian limit of these isochronous spacetimes, showing
that it reproduces the analogous findings in the context of non-relativistic
dynamics.


  MHD kink instability can trigger the fragmentation of a twisted magnetic flux
tube into small-scale current sheets that dissipate as aperiodic impulsive
heating events. This instability propagates as an avalanche to nearby flux
tubes and leads to a nanoflare storm. Our previous work was devoted to related
3D MHD numerical modeling with a stratified and realistic atmosphere. This work
addresses predictions for the EUV imaging spectroscopy of such structure and
evolution of a loop, with an average temperature of 2.5 MK in the solar corona.
We set a particular focus on the forthcoming MUSE mission. From the output of
the numerical simulations, we synthesized the intensities, Doppler shifts, and
non-thermal line broadening in 3 EUV spectral lines in the MUSE passbands: Fe
IX 171A, Fe XV 284 A, and Fe XIX 108 A, at 1 MK, 2 MK, and 10 MK, respectively,
according to the MUSE expected pixel size, temporal resolution, and temperature
response functions. We provide maps showing different view angles and realistic
spectra. Finally, we discuss the relevant evolutionary processes from the
perspective of possible observations. We find that the MUSE observations might
be able to detect the fine structure determined by tube fragmentation. In
particular, the Fe IX line is mostly emitted at the loop footpoints, where we
track the motions that drive the magnetic stressing and detect the upward
motion of evaporating plasma from the chromosphere. In Fe XV, we see the bulk
of the loop with increasing intensity. The Fe XIX line is very faint within the
chosen simulation parameters; thus, any transient brightening around the loop
apex may possibly be emphasized by the folding of sheet-like structure. In
conclusion, we show that coronal loop observations with MUSE can pinpoint some
crucial features of MHD-modeled ignition processes, such as the related
dynamics, helping to identify the heating processes.


  We report a combined experimental and theoretical investigation of the
layered antimonide PrMnSbO which is isostructural to the parent phase of the
iron pnictide superconductors. We find linear resistivity near room temperature
and Fermi liquid-like T^{2} behaviour below 150 K. Neutron powder diffraction
shows that unfrustrated C-type Mn magnetic order develops below \sim 230 K,
followed by a spin-flop coupled to induced Pr order. At T \sim 35 K, we find a
tetragonal to orthorhombic (T-O) transition. First principles calculations show
that the large magnetic moments observed in this metallic compound are of local
origin. Our results are thus inconsistent with either the itinerant or
frustrated models proposed for symmetry breaking in the iron pnictides. We show
that PrMnSbO is instead a rare example of a metal where structural distortions
are driven by f-electron degrees of freedom.


  We introduce a generative adversarial network (GAN) model to simulate the
3-dimensional Lagrangian motion of particles trapped in the recirculation zone
of a buoyancy-opposed flame. The GAN model comprises a stochastic recurrent
neural network, serving as a generator, and a convoluted neural network,
serving as a discriminator. Adversarial training was performed to the point
where the best-trained discriminator failed to distinguish the ground truth
from the trajectory produced by the best-trained generator. The model
performance was then benchmarked against a statistical analysis performed on
both the simulated trajectories and the ground truth, with regard to the
accuracy and generalization criteria.


  Empirical processes for stationary, causal sequences are considered. We
establish empirical central limit theorems for classes of indicators of left
half lines, absolutely continuous functions and piecewise differentiable
functions. Sample path properties of empirical distribution functions are also
discussed. The results are applied to linear processes and Markov chains.


  The general covariance of the Dirac equation is exploited in order to explore
the curvature effects appearing in the electronic properties of graphene. Two
physical situations are then considered: the weak curvature regime, with
$\left|R\right|<1/L^2$, and the strong curvature regime, with $1/L^2\ll
\left|R\right|<1/d^2$, where $R$ is the scalar curvature, $L$ is a typical size
of a sample of graphene and $d$ is a typical size of a local domain where the
curvature is pronounced. In the first scenario, we found that the curvature
transforms the conical nature of the dispersion relation due to a shift in the
momentum space of the Dirac cone. In the second scenario, the curvature in the
local domain affects the charge carriers in such a manner that bound states
emerge; these states are declared to be pseudo-Landau states because of the
analogy with the well known Landau problem; here the curvature emulates the
role of the magnetic field. Seeking more tangible curvature effects we
calculate e.g. the electronic internal energy and heat capacity of graphene in
the small curvature regime and give an expresssion for the ground state energy
in the strong curvature regime.


  We give alternative definitions of the boundary relative extremal function
and show that Edwards' theorem does not hold in open sets.


  Muon spin rotation measurements of the temperature dependence of the Knight
shift in single crystals of U_{0.965}Th_{0.035}Be_{13} have been used to study
the static spin susceptibility below the transition temperatures T_{c1} and
T_{c2}. While an abrupt reduction of the susceptibility with decreasing
temperature is observed below T_{c1}, the susceptibility does not change below
T_{c2} and remains at a value below the normal-state susceptibility. In the
normal state we find an anomalous anisotropic temperature dependence of the
transferred hyperfine coupling between the muon spin and the U 5f-electrons.


  The interaction of a plane gravitational wave with test masses can be
described in the proper detector frame, using Fermi coordinates, in terms of a
gravitoelectric and a gravitomagnetic field. We use this approach to calculate
the displacements produced by gravitational waves up to second order in the
distance parameter and, in doing so, we emphasize the relevance of the
gravitomagnetic contribution related to gravitational induction. In addition,
we show how this approach can be generalized to calculate displacements up to
arbitrary order.


  Let $G$ be a Lie group, and let $(M,\omega)$ be a symplectic manifold. If $G$
admits a Hamiltonian action on $(M,\omega)$ with momentum map $\mu$, then $M$,
the zero-level set of $\mu$, the orbit space, and the corresponding symplectic
quotient all have induced stratifications. We push this setting into the
language of differential spaces, and as a consequence we find that the
stratifications are intrinsic to the ring of smooth functions on each space.


  It is commonly believed that Bayesian optimization (BO) algorithms are highly
efficient for optimizing numerically costly functions. However, BO is not often
compared to widely different alternatives, and is mostly tested on narrow sets
of problems (multimodal, low-dimensional functions), which makes it difficult
to assess where (or if) they actually achieve state-of-the-art performance.
Moreover, several aspects in the design of these algorithms vary across
implementations without a clear recommendation emerging from current practices,
and many of these design choices are not substantiated by authoritative test
campaigns. This article reports a large investigation about the effects on the
performance of (Gaussian process based) BO of common and less common design
choices. The experiments are carried out with the established COCO (COmparing
Continuous Optimizers) software. It is found that a small initial budget, a
quadratic trend, high-quality optimization of the acquisition criterion bring
consistent progress. Using the GP mean as an occasional acquisition contributes
to a negligible additional improvement. Warping degrades performance. The
Mat\'ern 5/2 kernel is a good default but it may be surpassed by the
exponential kernel on irregular functions. Overall, the best EGO variants are
competitive or improve over state-of-the-art algorithms in dimensions less or
equal to 5 for multimodal functions. The code developed for this study makes
the new version (v2.1.1) of the R package DiceOptim available on CRAN. The
structure of the experiments by function groups allows to define priorities for
future research on Bayesian optimization.


  This Letter presents a search for heavy charged long-lived particles produced
in proton-proton collisions at $\sqrt{s} = 13$ TeV at the LHC using a data
sample corresponding to an integrated luminosity of 36.1 fb$^{-1}$ collected by
the ATLAS experiment in 2015 and 2016. These particles are expected to travel
with a velocity significantly below the speed of light, and therefore have a
specific ionisation higher than any high-momentum Standard Model particle of
unit charge. The pixel subsystem of the ATLAS detector is used in this search
to measure the ionisation energy loss of all reconstructed charged particles
which traverse the pixel detector. Results are interpreted assuming the pair
production of $R$-hadrons as composite colourless states of a long-lived gluino
and Standard Model partons. No significant deviation from Standard Model
background expectations is observed, and lifetime-dependent upper limits on
$R$-hadron production cross-sections and gluino masses are set, assuming the
gluino always decays in two quarks and a stable neutralino. $R$-hadrons with
lifetimes above 1.0 ns are excluded at the 95% confidence level, with lower
limits on the gluino mass ranging between 1290 GeV and 2060 GeV. In the case of
stable $R$-hadrons, the lower limit on the gluino mass at the 95% confidence
level is 1890 GeV.


  This paper develops a deep-learning framework to synthesize a ground-level
view of a location given an overhead image. We propose a novel conditional
generative adversarial network (cGAN) in which the trained generator generates
realistic looking and representative ground-level images using overhead imagery
as auxiliary information. The generator is an encoder-decoder network which
allows us to compare low- and high-level features as well as their
concatenation for encoding the overhead imagery. We also demonstrate how our
framework can be used to perform land cover classification by modifying the
trained cGAN to extract features from overhead imagery. This is interesting
because, although we are using this modified cGAN as a feature extractor for
overhead imagery, it incorporates knowledge of how locations look from the
ground.


  We have studied the ordering of a two dimensional charge stabilised colloidal
system in the presence of a stationary one dimensionally modulated laser field
formed by the superposition of two modulations with wavevectors $q_0 \tau$ and
$q_0/\tau$, where $q_0$ is the wavevector corresponding to the first peak of
the direct correlation function of the unperturbed liquid, and $\tau$ is the
golden mean. In the framework of the Landau-Alexander-McTague theory we find
that a decagonal quasicrystalline phase is stabler than the liquid or the
triangular lattice in certain regions of the phase diagram. Our study also
shows a reentrant melting phenomena for larger laser field strengths. We find
that the transition from the modulated liquid to the quasicrystalline phase is
continuous in contrast to a first order transition from the modulated liquid to
the triangular crystalline phase.


  We present a somewhat new proof to the $C^{2,\alpha}$-aprori estimate for the
uniform elliptic Monge-Ampere equations, in both the real and complex settings.
Our estimates do not need to differentiate the equation, and only depends on
the $C^{\alpha^{\prime}}-$norm of the right hand side of the equation,
$0<\alpha<\alpha^{\prime}$.