  Localization of a robotic system within a previously mapped environment is
important for reducing estimation drift and for reusing previously built maps.
Existing techniques for geometry-based localization have focused on the
description of local surface geometry, usually using pointclouds as the
underlying representation. We propose a system for geometry-based localization
that extracts features directly from an implicit surface representation: the
Signed Distance Function (SDF). The SDF varies continuously through space,
which allows the proposed system to extract and utilize features describing
both surfaces and free-space. Through evaluations on public datasets, we
demonstrate the flexibility of this approach, and show an increase in
localization performance over state-of-the-art handcrafted surfaces-only
descriptors. We achieve an average improvement of ~12% on an RGB-D dataset and
~18% on a LiDAR-based dataset. Finally, we demonstrate our system for
localizing a LiDAR-equipped MAV within a previously built map of a search and
rescue training ground.


  Loop closure detection, the task of identifying locations revisited by a
robot in a sequence of odometry and perceptual observations, is typically
formulated as a combination of two subtasks: (1) bag-of-words image retrieval
and (2) post-verification using RANSAC geometric verification. The main
contribution of this study is the proposal of a novel post-verification
framework that achieves good precision recall trade-off in loop closure
detection. This study is motivated by the fact that not all loop closure
hypotheses are equally plausible (e.g., owing to mutual consistency between
loop closure constraints) and that if we have evidence that one hypothesis is
more plausible than the others, then it should be verified more frequently. We
demonstrate that the problem of loop closure detection can be viewed as an
instance of a multi-model hypothesize-and-verify framework and build guided
sampling strategies on the framework where loop closures proposed using image
retrieval are verified in a planned order (rather than in a conventional
uniform order) to operate in a constant time. Experimental results using a
stereo SLAM system confirm that the proposed strategy, the use of loop closure
constraints and robot trajectory hypotheses as a guide, achieves promising
results despite the fact that there exists a significant number of false
positive constraints and hypotheses.


  The first N-body simulation of interacting galaxies, even producing spiral
arms, was performed by Erik Holmberg in Lund (1941), not with a numerical
computer, but by his arrangement of movable light-bulbs and photocells to
measure the luminosity at each bulb and thereby estimate the gravitational
force. A decade later, and with the arrival of the first programable computers,
computations of galactic dynamics were performed, which were later transferred
into a N-body simulation movie. I present here the background details for this
work with a description of the important elements to note in the movie which
may be retrieved at http://ttt.astro.su.se/~po .


  We give a solution of the Inverse Scattering Problem for integrable systems
with a finite number degrees of freedom, admitting a Lax representation with
spectral parameter on a Riemann surface. While conventional approaches deal
with the systems with $GL(n)$ symmetry, we focus on the problems arising in the
case of symmetry with respect to a semi-simple group. Our main results apply to
Hitchin systems of the types $B_n$, $C_n$, $D_n$.


  We study the existence of singular separable solutions to a class of
quasilinear equations with reaction term. In the 2-dim case, we use a dynamical
system approach to construct our solutions.


  We prove the existence of an algorithm $A$ for computing 2-d or 3-d convex
hulls that is optimal for every point set in the following sense: for every
sequence $\sigma$ of $n$ points and for every algorithm $A'$ in a certain class
$\mathcal{A}$, the running time of $A$ on input $\sigma$ is at most a constant
factor times the maximum running time of $A'$ on the worst possible permutation
of $\sigma$ for $A'$. We establish a stronger property: for every sequence
$\sigma$ of points and every algorithm $A'$, the running time of $A$ on
$\sigma$ is at most a constant factor times the average running time of $A'$
over all permutations of $\sigma$. We call algorithms satisfying these
properties instance-optimal in the order-oblivious and random-order setting.
Such instance-optimal algorithms simultaneously subsume output-sensitive
algorithms and distribution-dependent average-case algorithms, and all
algorithms that do not take advantage of the order of the input or that assume
the input is given in a random order. The class $\mathcal{A}$ under
consideration consists of all algorithms in a decision tree model where the
tests involve only multilinear functions with a constant number of arguments.
To establish an instance-specific lower bound, we deviate from traditional
Ben-Or-style proofs and adopt a new adversary argument. For 2-d convex hulls,
we prove that a version of the well known algorithm by Kirkpatrick and Seidel
(1986) or Chan, Snoeyink, and Yap (1995) already attains this lower bound. For
3-d convex hulls, we propose a new algorithm. We further obtain
instance-optimal results for a few other standard problems in computational
geometry. Our framework also reveals connection to distribution-sensitive data
structures and yields new results as a byproduct, for example, on on-line
orthogonal range searching in 2-d and on-line halfspace range reporting in 2-d
and 3-d.


  Transverse momentum dependent parton distributions (TMDPDFs) which appear in
factorized cross sections involve infinite Wilson lines with edges on or close
to the light-cone. Since these TMDPDFs are not directly calculable with a
Euclidean path integral in lattice QCD, we study the construction of
quasi-TMDPDFs with finite-length spacelike Wilson lines that are amenable to
such calculations. We define an infrared consistency test to determine which
quasi-TMDPDF definitions are related to the TMDPDF, by carrying out a one-loop
study of infrared logarithms of transverse position $b_T\sim \Lambda_{\rm
QCD}^{-1}$, which must agree between them. This agreement is a necessary
condition for the two quantities to be related by perturbative matching.
TMDPDFs necessarily involve combining a hadron matrix element, which nominally
depends on a single light-cone direction, with soft matrix elements that
necessarily depend on two light-cone directions. We show at one loop that the
simplest definitions of the quasi hadron matrix element, the quasi soft matrix
element, and the resulting quasi-TMDPDF all fail the infrared consistency test.
Ratios of impact parameter quasi-TMDPDFs still provide nontrivial information
about the TMDPDFs, and are more robust since the soft matrix elements cancel.
We show at one loop that such quasi ratios can be matched to ratios of the
corresponding TMDPDFs. We also introduce a modified "bent" quasi soft matrix
element which yields a quasi-TMDPDF that passes the consistency test with the
TMDPDF at one loop, and discuss potential issues at higher orders.


  We give a complete and unified description -- under some stability
assumptions -- of the functional scaling limits associated with some persistent
random walks for which the recurrent or transient type is studied in [1]. As a
result, we highlight a phase transition phenomenon with respect to the memory.
It turns out that the limit process is either Markovian or not according to --
to put it in a nutshell -- the rate of decrease of the distribution tails
corresponding to the persistent times. In the memoryless situation, the limits
are classical strictly stable L{\'e}vy processes of infinite variations.
However, we point out that the description of the critical Cauchy case fills
some lacuna even in the closely related context of Directionally Reinforced
Random Walks (DRRWs) for which it has not been considered yet. Besides, we need
to introduced some relevant generalized drift -- extended the classical one --
in order to study the critical case but also the situation when the limit is no
longer Markovian. It appears to be in full generality a drift in mean for the
Persistent Random Walk (PRW). The limit processes keeping some memory -- given
by some variable length Markov chain -- of the underlying PRW are called
arcsine Lamperti anomalous diffusions due to their marginal distribution which
are computed explicitly here. To this end, we make the connection with the
governing equations for L{\'e}vy walks, the occupation times of skew Bessel
processes and a more general class modelled on Lamperti processes. We also
stress that we clarify some misunderstanding regarding this marginal
distribution in the framework of DRRWs. Finally, we stress that the latter
situation is more flexible -- as in the first paper -- in the sense that the
results can be easily generalized to a wider class of PRWs without renewal
pattern.


  Integrated optical interconnect is believed to be one of the main
technologies to replace electrical wires. Optical Network-on-Chip (ONoC) has
attracted more attentions nowadays. Benes topology is a good choice for ONoC
for its rearrangeable non-blocking character, multistage feature and easy
scalability. Routing algorithm plays an important role in determining the
performance of ONoC. But traditional routing algorithms for Benes network are
not suitable for ONoC communication, we developed a new distributed routing
algorithm for Benes ONoC in this paper. Our algorithm selected the routing path
dynamically according to network condition and enables more path choices for
the message traveling in the network. We used OPNET to evaluate the performance
of our routing algorithm and also compared it with a well-known bit-controlled
routing algorithm. ETE delay and throughput were showed under different packet
length and network sizes. Simulation results show that our routing algorithm
can provide better performance for ONoC.


  Current object-centric learning models such as the popular SlotAttention
architecture allow for unsupervised visual scene decomposition. Our novel
MusicSlots method adapts SlotAttention to the audio domain, to achieve
unsupervised music decomposition. Since concepts of opacity and occlusion in
vision have no auditory analogues, the softmax normalization of alpha masks in
the decoders of visual object-centric models is not well-suited for decomposing
audio objects. MusicSlots overcomes this problem. We introduce a
spectrogram-based multi-object music dataset tailored to evaluate
object-centric learning on western tonal music. MusicSlots achieves good
performance on unsupervised note discovery and outperforms several established
baselines on supervised note property prediction tasks.


  A functional of the solution of the Kadomtsev-Petviashvili II equation maps
multi-soliton solutions onto systems of vertices - structures that are
localized around soliton junctions. A solution with one junction is mapped onto
a single vertex, which emulates a free, spatially extended, particle. In
solutions with several junctions, each junction is mapped onto a vertex. Moving
in the x-y plane, the vertices collide, coalesce upon collision, and then split
up. When well separated, they emulate free particles. Multi-soliton solutions,
whose structure does not change under space-time inversion as for infinite
times, are mapped onto vertex systems that undergo elastic collisions.
Solutions, whose structure does change, are mapped onto systems that undergo
inelastic collisions. The inelastic vertex collisions generated from the
infinite family of (M,1) solutions (M external solitons, (M-2) Y-shaped soliton
junctions, M greater than 3) play a unique role: The only definition of vertex
mass consistent with momentum conservation in these collisions is the spatial
integral of the vertex profile. This definition ensures, in addition, that, in
these collisions, the total mass and kinetic energy due to the motion in the
y-direction are conserved. In general, the kinetic energy due to the motion in
the x-direction is not conserved in these collisions.


  Bayes [Philos. Trans. R. Soc. Lond. 53 (1763) 370--418; 54 296--325]
introduced the observed likelihood function to statistical inference and
provided a weight function to calibrate the parameter; he also introduced a
confidence distribution on the parameter space but did not provide present
justifications. Of course the names likelihood and confidence did not appear
until much later: Fisher [Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng.
Sci. 222 (1922) 309--368] for likelihood and Neyman [Philos. Trans. R. Soc.
Lond. Ser. A Math. Phys. Eng. Sci. 237 (1937) 333--380] for confidence. Lindley
[J. Roy. Statist. Soc. Ser. B 20 (1958) 102--107] showed that the Bayes and the
confidence results were different when the model was not location. This paper
examines the occurrence of true statements from the Bayes approach and from the
confidence approach, and shows that the proportion of true statements in the
Bayes case depends critically on the presence of linearity in the model; and
with departure from this linearity the Bayes approach can be a poor
approximation and be seriously misleading. Bayesian integration of weighted
likelihood thus provides a first-order linear approximation to confidence, but
without linearity can give substantially incorrect results.


  In this work, we study the fractional power series solutions around regular
singular point x=0 of conformable fractional Bessel differential equation and
fractional Bessel functions. Then, we compare fractional solutions with
ordinary solutions. In addition, we present certain property of fractional
Bessel functions.


  Physical layer security (PLS) technology based on the fixed-position antenna
(FPA) has {attracted widespread attention}. Due to the fixed feature of the
antennas, current FPA-based PLS schemes cannot fully utilize the spatial degree
of freedom, and thus a weaken secure gain in the desired/undesired direction
may exist. Different from the concept of FPA, mobile antenna (MA) is a novel
technology that {reconfigures} the wireless channels and enhances the
corresponding capacity through the flexible movement of antennas on a minor
scale. MA-empowered PLS enjoys huge potential and deserves further
investigation. In this paper, we, for the first time, investigate the secrecy
performance of MA-enabled PLS system where a MA-based Alice transmits the
confidential information to multiple single-antenna Bobs, in the presence of
the single-antenna eavesdropper (Eve) {in the absence} of perfect channel state
information (CSI). For the purpose of the secrecy rate maximization of the
worst Bob, we jointly design the transmit beamforming and antenna positions at
the Alice, subject to the minimum moving distance of the antenna, uncertainty
CSI of Eve, and maximum transmit power. Furthermore, the projected gradient
ascent (PGA), alternating optimization (AO), and simulated annealing (SA) {are}
adopted to solve the non-convex characteristics of the problem of the secrecy
rate maximization. Simulation results demonstrate the effectiveness and
correctness of the proposed method. In particular, MA-enabled PLS scheme can
significantly enhance the secrecy rate compared to the conventional FPA-based
ones for different settings of key system parameters.


  By offering sophisticated services and centralizing a huge volume of personal
data, modern smartphones changed the way we socialize, entertain and work. To
this aim, they rely upon complex hardware/software frameworks leading to a
number of vulnerabilities, attacks and hazards to profile individuals or gather
sensitive information. However, the majority of works evaluating the security
degree of smartphones neglects steganography, which can be mainly used to: i)
exfiltrate confidential data via camouflage methods, and ii) conceal valuable
or personal information into innocent looking carriers.
  Therefore, this paper surveys the state of the art of steganographic
techniques for smartphones, with emphasis on methods developed over the period
2005 to the second quarter of 2014. The different approaches are grouped
according to the portion of the device used to hide information, leading to
three different covert channels, i.e., local, object and network. Also, it
reviews the relevant approaches used to detect and mitigate steganographic
attacks or threats. Lastly, it showcases the most popular software applications
to embed secret data into carriers, as well as possible future directions.


  We propose a function-learning methodology with a control-theoretical
foundation. We parametrise the approximating function as the solution to a
control system on a reproducing-kernel Hilbert space, and propose several
methods to find the set of controls which bring the initial function as close
as possible to the target function. At first, we derive the expression for the
gradient of the cost function with respect to the controls that parametrise the
difference equations. This allows us to find the optimal controls by means of
gradient descent. In addition, we show how to compute derivatives of the
approximating functions with respect to the controls and describe two
optimisation methods relying on linear approximations of the approximating
functions. We show how the assumptions we make lead to results which are
coherent with Pontryagin's maximum principle. We test the optimisation methods
on two toy examples and on two higher-dimensional real-world problems, showing
that the approaches succeed in learning from real data and are versatile enough
to tackle learning tasks of different nature.


  In this paper, we present a theoretical description to the quantum coherence
and decoherence phenomena of energy transfer in photosynthesis observed in a
recent experiment [see Science 316, 1462 (2007)]. As a successive two-color
laser pulses with selected frequencies cast on a sample of the photosynthetic
purple bacterium Rb. sphaeroides two resonant excitations of electrons in
chromophores can be generated. However, this effective two-level subsystem will
interact with its protein environment and decoherence is inevitable. We
describe this subsystem coupled with its environment as a dynamical spin-boson
model. The non-Markovian decoherence dynamics is described using a
quasi-adiabatic propagator path integral (QUAPI) approach. With the
photon-induced effective time-dependent level splitting energy and level flip
coupling coefficient between the two excited states and the environment-induced
non-Markovian decoherence dynamics, our theoretical result is in good agreement
with the experimental data.


  This paper continues on the work of the B-Matrix approach in hebbian learning
proposed by Dr. Kak. It reports the results on methods of improving the memory
retrieval capacity of the hebbian neural network which implements the B-Matrix
approach. Previously, the approach to retrieving the memories from the network
was to clamp all the individual neurons separately and verify the integrity of
these memories. Here we present a network with the capability to identify the
"active sites" in the network during the training phase and use these "active
sites" to generate the memories retrieved from these neurons. Three methods are
proposed for obtaining the update order of the network from the proximity
matrix when multiple neurons are to be clamped. We then present a comparison
between the new methods to the classical case and also among the methods
themselves.


  We generalize the concepts of Internal Time Superoperator, its associated non
unitary similarity transformations and Liapounov variables, to quantum systems
with diagonal singularity, and we give a constructive proof of the existence of
these superoperators for systems with purely diagonal Hamiltonian having
uniform absolutely continuous spectrum on the interval from zero to infinity.


  The presented paper is a review of papers on the microcosm physics
geometrization in the last twenty years. These papers develop a new direction
of the microcosm physics. It is so-called geometric paradigm, which is
alternative to the quantum paradigm, which is conventionally used now. The
hypothesis on discreteness of the space-time geometry appears to be more
fundamental, than the hypothesis on quantum nature of microcosm. Discrete
space-time geometry admits one to describe quantum effects as pure geometric
effects. Mathematical technique of the microcosm physics geometrization
(geometric paradigm) is based on the physical geometry, which is described
completely by the world function. Equations, describing motion of particles in
the microcosm, are algebraic (not differential) equations. They are written in
a coordinateless form in terms of world function. The geometric paradigm
appeared as a result of overcoming of inconsistency of the conventional
elementary particle theory. In the suggested skeleton conception the state of
an elementary particle is described by its skeleton (several space-time
points). The skeleton contains all information on the particle properties
(mass, charge, spin, etc.). The skeleton conception is a monistic construction,
where elementary particle motion is described in terms of skeleton and world
function and only in these terms. The skeleton conception can be constructed
only on the basis of the physical geometry. Unfortunately, most mathematicians
do not accept the physical geometries, because these geometries are
nonaxiomatizable. It is a repetition of the case, when mathematicians did not
accept the non-Euclidean geometries of Lobachevsky-Bolyai. As a result this
review is a review of papers of one author.


  This paper presents a model-free reinforcement learning (RL) algorithm to
solve the risk-averse optimal control (RAOC) problem for discrete-time
nonlinear systems. While successful RL algorithms have been presented to learn
optimal control solutions under epistemic uncertainties (i.e., lack of
knowledge of system dynamics), they do so by optimizing the expected utility of
outcomes, which ignores the variance of cost under aleatory uncertainties
(i.e., randomness). Performance-critical systems, however, must not only
optimize the expected performance, but also reduce its variance to avoid
performance fluctuation during RL's course of operation. To solve the RAOC
problem, this paper presents the following three variants of RL algorithms and
analyze their advantages and preferences for different situations/systems: 1) a
one-shot static convex program -based RL, 2) an iterative value iteration (VI)
algorithm that solves a linear programming (LP) optimization at each iteration,
and 3) an iterative policy iteration (PI) algorithm that solves a convex
optimization at each iteration and guarantees the stability of the consecutive
control policies. Convergence of the exact optimization problems, which are
infinite-dimensional in all three cases, to the optimal risk-averse value
function is shown. To turn these optimization problems into standard
optimization problems with finite decision variables and constraints, function
approximation for value estimations as well as constraint sampling are
leveraged. Data-driven implementations of these algorithms are provided based
on Q-function which enables learning the optimal value without any knowledge of
the system dynamics. The performance of the approximated solutions is also
verified through a weighted sup-norm bound and the Lyapunov bound. A simulation
example is provided to verify the effectiveness of the presented approach.


  We show that the M\"{o}bius function is orthogonal to the Thue-Morse sequence
$t(n)$ taken along the Piatetski-Shapiro numbers $\lfloor n^c \rfloor$ for any
$1 < c < 2$. Previously this property was established for the subsequence along
the squares $t(n^2)$. These are both examples of M\"{o}bius orthogonal
sequences with maximum entropy.


  In this paper, a relation between shadow price and the Lagrangian multiplier
for nonsmooth problem is explored. It is shown that the Lagrangian Multiplier
is the upper bound of shadow price for convex optimization and a class of
Lipschtzian optimizations. This work can be used in shadow pricing for
nonsmooth situation. The several nonsmooth functions involved in this class of
Lipschtzian optimizations is listed. Finally, an application to electricity
pricing is discussed.


  An isobaric yield ratio difference (IBD) method is proposed to study the
ratio of the difference between the chemical potential of neutron and proton to
temperature ($\Delta\mu/T$) in heavy-ion collisions. The $\Delta\mu/T$
determined by the IBD method (IB-$\Delta\mu/T$) is compared to the results of
the isoscaling method (IS-$\Delta\mu/T$), which uses the isotopic or the
isotonic yield ratio. Similar distributions of the IB- and IS-$\Delta\mu/T$ are
found in the measured 140$A$ MeV $^{40,48}$Ca + $^{9}$Be and the $^{58,64}$Ni +
$^{9}$Be reactions. The IB- and IS-$\Delta\mu/T$ both have a distribution with
a plateau in the small mass fragments plus an increasing part in the fragments
of relatively larger mass. The IB- and IS-$\Delta\mu/T$ plateaus show
dependence on the $n/p$ ratio of the projectile. It is suggested that the
height of the plateau is decided by the difference between the neutron density
($\rho_n$) and the proton density ($\rho_p$) distributions of the projectiles,
and the width shows the overlapping volume of the projectiles in which $\rho_n$
and $\rho_p$ change very little. The difference between the IB- and
IS-$\Delta\mu/T$ is explained by the isoscaling parameters being constrained by
the many isotopes and isotones, while the IBD method only uses the yields of
two isobars. It is suggested that the IB-$\Delta\mu/T$ is more reasonable than
the IS-$\Delta\mu/T$, especially when the isotopic or isotonic ratio disobeys
the isoscaling. As to the question whether the $\Delta\mu/T$ depends on the
density or the temperature, the density dependence is preferred since the low
density can result in low temperature in the peripheral reactions.


  We present here a preliminary report and commentary of recently processed
observations of Ha emission towards the Magellanic Bridge. These data have been
analysed in an attempt to quantify the extent to which the stellar population
is capable of reshaping the local ISM. We find that the Ha emission regions are
small, weak and sparsely distributed, consistent with a relatively quiescent
and inactive ISM where radiative and collisional ionisation is inefficient and
sporadic. This suggests that energetic processes at the small scale (i.e. ~tens
of pc) do not dominate the energy balance within the ISM of the Bridge, which
therefore hosts a pristine turbulent structure, otherwise inaccessible within
our own Galaxy. We find Ha emission that is well correlated with detected
12CO(1-0) line emission (a proxy for molecular hydrogen), as well as other
easily identified ring-like HI features.


  V471 Tauri, an eclipsing system consisting of a hot DA white dwarf (WD) and a
dK2 companion in a 12.5-hour orbit, is the prototype of the pre-cataclysmic
binaries. The late-type component is magnetically active, due to its being
constrained to rotate synchronously with the short orbital period. During a
program of UV spectroscopy of V471 Tau, carried out with the Goddard High
Resolution Spectrograph (GHRS) onboard the Hubble Space Telescope, we
serendipitously detected two episodes in which transient absorptions in the Si
III 1206 A resonance line appeared suddenly, on a timescale of <2 min. The
observations were taken in a narrow spectral region around Ly-alpha, and were
all obtained near the two quadratures of the binary orbit, i.e., at maximum
projected separation (~3.3 Rsun) of the WD and K star.
  We suggest that these transient features arise when coronal mass ejections
(CME's) from the K2 dwarf pass across the line of sight to the WD. Estimates of
the velocities, densities, and masses of the events in V471 Tau are generally
consistent with the properties of solar CME's. Given our detection of 2 events
during 6.8 hr of GHRS observing, along with a consideration of the restricted
range of latitudes and longitudes on the K star's surface that can give rise to
trajectories passing in front of the WD as seen from Earth, we estimate that
the active V471 Tau dK star emits some 100-500 CME's per day, as compared to
1-3 per day for the Sun. The K dwarf's mass-loss rate associated with CME's is
at least (5-25) x 10^{-14} Msun/yr, but it may well be orders of magnitude
higher if most of the silicon is in ionization states other than Si III.


  PURPOSE: Deep learning methods for classifying prostate cancer (PCa) in
ultrasound images typically employ convolutional networks (CNNs) to detect
cancer in small regions of interest (ROI) along a needle trace region. However,
this approach suffers from weak labelling, since the ground-truth
histopathology labels do not describe the properties of individual ROIs.
Recently, multi-scale approaches have sought to mitigate this issue by
combining the context awareness of transformers with a CNN feature extractor to
detect cancer from multiple ROIs using multiple-instance learning (MIL). In
this work, we present a detailed study of several image transformer
architectures for both ROI-scale and multi-scale classification, and a
comparison of the performance of CNNs and transformers for ultrasound-based
prostate cancer classification. We also design a novel multi-objective learning
strategy that combines both ROI and core predictions to further mitigate label
noise. METHODS: We evaluate 3 image transformers on ROI-scale cancer
classification, then use the strongest model to tune a multi-scale classifier
with MIL. We train our MIL models using our novel multi-objective learning
strategy and compare our results to existing baselines. RESULTS: We find that
for both ROI-scale and multi-scale PCa detection, image transformer backbones
lag behind their CNN counterparts. This deficit in performance is even more
noticeable for larger models. When using multi-objective learning, we can
improve performance of MIL, with a 77.9% AUROC, a sensitivity of 75.9%, and a
specificity of 66.3%. CONCLUSION: Convolutional networks are better suited for
modelling sparse datasets of prostate ultrasounds, producing more robust
features than transformers in PCa detection. Multi-scale methods remain the
best architecture for this task, with multi-objective learning presenting an
effective way to improve performance.


  The role of incoherent tunneling in the diffusion of light atoms on surfaces
is investigated. With this purpose, a Chudley-Elliot master equation
constrained to nearest neighbors is considered within the Grabert-Weiss
approach to quantum diffusion in periodic lattices. This model is applied to
recent measurements of atomic H and D on Pt(111), rendering friction
coefficients that are in the range of those available in the literature for
other species of adsorbates. A simple extension of the model has also been
considered to evaluate the relationship between coverage and tunneling, and
therefore the feasibility of the approach. An increase of the tunneling rate
has been observed as the surface coverage decreases.


  A simple method to canonically quantize noncommutative field theories is
proposed. As a result, the elementary excitations of a (2n+1)-dimensional
scalar field theory are shown to be bilocal objects living in an
(n+1)-dimensional space-time. Feynman rules for their scattering are derived
canonically. They agree, upon suitable redefinitions, with the rules obtained
via star-product methods. The IR/UV connection is interpreted within this
framework.


  Normalizing flows have emerged as an important family of deep neural networks
for modelling complex probability distributions. In this note, we revisit their
coupling and autoregressive transformation layers as probabilistic graphical
models and show that they reduce to Bayesian networks with a pre-defined
topology and a learnable density at each node. From this new perspective, we
provide three results. First, we show that stacking multiple transformations in
a normalizing flow relaxes independence assumptions and entangles the model
distribution. Second, we show that a fundamental leap of capacity emerges when
the depth of affine flows exceeds 3 transformation layers. Third, we prove the
non-universality of the affine normalizing flow, regardless of its depth.


  We describe how to efficiently construct the quantum chemical Hamiltonian
operator in matrix product form. We present its implementation as a density
matrix renormalization group (DMRG) algorithm for quantum chemical applications
in a purely matrix product based framework. Existing implementations of DMRG
for quantum chemistry are based on the traditional formulation of the method,
which was developed from a viewpoint of Hilbert space decimation and attained a
higher performance compared to straightforward implementations of matrix
product based DMRG. The latter variationally optimizes a class of ansatz states
known as matrix product states (MPS), where operators are correspondingly
represented as matrix product operators (MPO). The MPO construction scheme
presented here eliminates the previous performance disadvantages while
retaining the additional flexibility provided by a matrix product approach; for
example, the specification of expectation values becomes an input parameter. In
this way, MPOs for different symmetries - abelian and non-abelian - and
different relativistic and non-relativistic models may be solved by an
otherwise unmodified program.


  It is presumed that thermal fluctuations present during inflationary epoch
can make inflaton scalar field to interact with other fields resulting in the
existence of a thermal component during the inflationary period. The presence
of this thermal component assists structure formation and reduces reheating
dependence as in the contemporary inflationary paradigm. This is known as warm
inflation. In 1990 J . D. Barrow \cite{25} considered a scenario of inflation
with matter field having a phenomenological equation of state of the type
$p+\rho=\gamma\rho^{\lambda},~\gamma\neq 0$ and $\lambda$ constant. He called
such inflationary scenarios as "graduated inflation". In this work we
reconsider the above equation of state in a scenario of warm inflation. Our aim
would be to investigate and understand whether such matter can also act as a
viable candidate for warm inflation.


  Quantum state tomography often operates in the highly idealised scenario of
assuming perfect measurements. The errors implied by such an approach are
entwined with other imperfections relating to the information processing
protocol or application of interest. We consider the problem of retrodicting
the quantum state of a system, existing prior to the application of random but
known phase errors, allowing those errors to be separated and removed. The
continuously random nature of the errors implies that there is only one click
per measurement outcome -- a feature having a drastically adverse effect on
data-processing times. We provide a thorough analysis of coarse-graining under
various reconstruction algorithms, finding dramatic increases in speed for only
modest sacrifices in fidelity.


  Model selection is basically a process of finding the best model from the
subset of models in which the explanatory variables are effective on the
response variable. The log likelihood function for the lack of fit term and a
specified penalty term are used as two parts in a model selection criteria. In
this paper, we derive a new tool for the model selection in robust regression.
We introduce a new definition of relative entropy based on objective functions.
Due to the analytical simplicity, we use Huber's objective function $\rho_H$
and propose our specified penalty term $C_0^{\rho_H}$ to derive new Information
Complexity Criterion ($RICOMP_{C_0^{\rho_H}}$) as a robust model selection
tool. Additionally, by using the properties of $C_0^{\rho_H}$, we propose a new
value of tuning parameter called $k_{C_0}$ for the Huber's $\rho_H$. If a
contamination to normal distribution exists, $RICOMP_{C_0^{\rho_H}}$ chooses
the true model better than the rival ones. Monte Carlo Simulation studies are
carried out to show the utility both of $k_{C_0}$ and $RICOMP_{C_0^{\rho_H}}$.
A real data example is also given.


  Federated learning is an emerging distributed machine learning framework for
privacy preservation. However, models trained in federated learning usually
have worse performance than those trained in the standard centralized learning
mode, especially when the training data are not independent and identically
distributed (Non-IID) on the local devices. In this survey, we pro-vide a
detailed analysis of the influence of Non-IID data on both parametric and
non-parametric machine learning models in both horizontal and vertical
federated learning. In addition, cur-rent research work on handling challenges
of Non-IID data in federated learning are reviewed, and both advantages and
disadvantages of these approaches are discussed. Finally, we suggest several
future research directions before concluding the paper.


  Recent advances in photonic optimization have enabled calculation of
performance bounds for a wide range of electromagnetic objectives, albeit
restricted to single-material systems. Motivated by growing theoretical
interest and fabrication advances, we present a framework to bound the
performance of photonic heterostructures and apply it to investigate maximum
absorption characteristics of multilayer films and compact, free-form
multi-material scatterers. Limits predict trends seen in topology-optimized
geometries -- often coming within factors of two of specific designs -- and may
be exploited in conjunction with inverse designs to predict when
heterostructures are expected to outperform their optimal single-material
counterparts.


  We prove that the ring $\Aff{\R}{M}$ of all polynomials defined on a real
algebraic variety $M\subset\R^n$ is dense in the Hilbert space
$L^2(M,e^{-|x|^2}\de\mu)$, where $\de\mu$ denotes the volume form of $M$ and
$\de\nu=e^{-|x|^2}\de\mu$ the Gaussian measure on $M$.


  In contrast with Mercer kernel-based approaches as used e.g., in Kernel
Principal Component Analysis (KPCA), it was previously shown that Singular
Value Decomposition (SVD) inherently relates to asymmetric kernels and
Asymmetric Kernel Singular Value Decomposition (KSVD) has been proposed.
However, the existing formulation to KSVD cannot work with infinite-dimensional
feature mappings, the variational objective can be unbounded, and needs further
numerical evaluation and exploration towards machine learning. In this work, i)
we introduce a new asymmetric learning paradigm based on coupled covariance
eigenproblem (CCE) through covariance operators, allowing infinite-dimensional
feature maps. The solution to CCE is ultimately obtained from the SVD of the
induced asymmetric kernel matrix, providing links to KSVD. ii) Starting from
the integral equations corresponding to a pair of coupled adjoint
eigenfunctions, we formalize the asymmetric Nystr\"om method through a finite
sample approximation to speed up training. iii) We provide the first empirical
evaluations verifying the practical utility and benefits of KSVD and compare
with methods resorting to symmetrization or linear SVD across multiple tasks.


  We present results from the first large parameter study of neutron star
mergers using fully general relativistic simulations with finite-temperature
microphysical equations of state and neutrino cooling. We consider equal and
unequal-mass binaries drawn from the galactic population and simulate each
binary with three different equations of state. Our focus is on the emission of
energy and angular momentum in gravitational waves in the postmerger phase. We
find that the emitted gravitational-wave energy in the first
$\sim$$10\,\mathrm{ms}$ of the life of the resulting hypermassive neutron star
(HMNS) is about twice the energy emitted over the entire inspiral history of
the binary. The total radiated energy per binary mass is comparable to or
larger than that of nonspinning black hole inspiral-mergers. About $0.8-2.5\%$
of the binary mass-energy is emitted at kHz frequencies in the early HMNS
evolution. We find a clear dependence of the postmerger GW emission on binary
configuration and equation of state and show that it can be encoded as a broad
function of the binary tidal coupling constant $\kappa^T_2$. Our results also
demonstrate that the dimensionless spin of black holes resulting from
subsequent HMNS collapse are limited to $\lesssim0.7-0.8$. This may
significantly impact the neutrino pair annihilation mechanism for powering
short gamma-ray bursts (sGRB).


  A new type of algebras that represent a generalization of both quantum groups
and braided groups is defined. These algebras are given by a pair of solutions
of the Yang--Baxter equation that satisfy some additional conditions. Several
examples are presented.


  The dynamical coupling between the solar chromospheric plasma and magnetic
field is investigated by numerically solving a fully self-consistent,
two-dimensional initial-value problem for the nonlinear collisional MHD
equations including electric resistivity, thermal conduction, and, in some
cases, gas-dynamic viscosity. The processes in the contact zone between two
horizontal magnetic fields of opposite polarities are considered. The plasma is
assumed to be initially motionless and having a temperature of 50,000 K uniform
throughout the plasma volume; the characteristic magnetic field corresponds to
a plasma $\beta\gtrsim 1$. In a physical-time interval of 17~seconds typically
covered by a computational run, the plasma temperature gradually increases by a
factor of two to three. Against this background, an impulsive (in 0.1 seconds
or less) increase in the current-aligned plasma velocity occurs at the site of
the current-layer thinning (sausage-type deformation, or $m=0$ pinch
instability). Such a "velocity burst" can be interpreted physically as an event
of suprathemal-proton generation. Further development of the sausage
instability results in an increase in the kinetic temperature of the protons to
high values, even to those observed in flares. The form of our system of MHD
equations indicates that such increases are a property of the exact solution of
the system at an appropriate choice of the parameters. Magnetic reconnection
does not manifest itself in this solution: it would generate flows forbidden by
the chosen geometry. Therefore, the pinch-sausage effect can act as an
energiser of the upper chromosphere and be an alternative to the
magnetic-reconnection process as the producer of flares.


  An exact method is suggested to treat the nonlinear self-interactions (NLSI)
in the relativistic Hartree-Fock (RHF) approach for nuclear systems. We
consider here the NLSI constructed from the relativistic scalar nucleon
densities and including products of six and eight fermion fields. This type of
NLSI corresponds to the zero range limit of the standard cubic and quartic
self-interactions of the scalar field. The method to treat the NLSI uses the
Fierz transformation, which enables one to express the exchange (Fock)
components in terms of the direct (Hartree) ones. The method is applied to
nuclear matter and finite nuclei. It is shown that, in the RHF formalism, the
NLSI, which are explicitly isovector-independent, generate scalar, vector and
tensor nucleon self-energies strongly density-dependent. This strong isovector
structure of the self-energies is due to the exchange terms of the RHF method.
Calculations are carried out with a parametrization containing five free
parameters. The model allows a description of both types of systems compatible
with experimental data.


  The averaging principle is established for the slow component and the fast
component being two dimensional stochastic Navier-Stokes equations and
stochastic reaction-diffusion equations, respectively. The classical
Khasminskii approach based on time discretization is used for the proof of the
slow component strong convergence to the solution of the corresponding averaged
equation under some suitable conditions. Meanwhile, some powerful techniques
are used to overcome the difficulties caused by the nonlinear term and to
release the regularity of the initial value.


  This paper targets interactive object-level editing (e.g., deletion,
recoloring, transformation, composition) in dynamic scenes. Recently, some
methods aiming for flexible editing static scenes represented by neural
radiance field (NeRF) have shown impressive synthesis quality, while similar
capabilities in time-variant dynamic scenes remain limited. To solve this
problem, we propose 4D-Editor, an interactive semantic-driven editing
framework, allowing editing multiple objects in a dynamic NeRF with user
strokes on a single frame. We propose an extension to the original dynamic NeRF
by incorporating a hybrid semantic feature distillation to maintain
spatial-temporal consistency after editing. In addition, we design Recursive
Selection Refinement that significantly boosts object segmentation accuracy
within a dynamic NeRF to aid the editing process. Moreover, we develop
Multi-view Reprojection Inpainting to fill holes caused by incomplete scene
capture after editing. Extensive experiments and editing examples on real-world
demonstrate that 4D-Editor achieves photo-realistic editing on dynamic NeRFs.
Project page: https://patrickddj.github.io/4D-Editor


  The availability of satellite communication systems is extremely limited by
atmospheric impairments, such as rain (for radio frequencies) and cloud
coverage (for optical frequencies). A solution to this problem is the site
diversity technique, where a network of geographically distributed ground
stations (GSs) can ensure, with high probability, that at least one GS is
available for connection to the satellite at each time period. However, the
installation of redundant GSs induces unnecessary additional costs for the
network operator. In this context, we study an optimization problem that
minimizes the number of required GSs, subject to availability constraints.
First, the problem is transformed into a binary-integer-linear-programming
(BILP) problem, which is proven to be NP-hard. Subsequently, we design a
branch-and-bound (B&B) algorithm, with global-optimization guarantee, based on
the linear-programming (LP) relaxation and a greedy method as well. Finally,
numerical results show that the proposed algorithm significantly outperforms
state-of-the-art methods, and has low complexity in the average case.


  Our ability to calculate rates of biochemical processes using molecular
dynamics simulations is severely limited by the fact that the time scales for
reactions, or changes in conformational state, scale exponentially with the
relevant free-energy barriers. In this work, we improve upon a recently
proposed rate estimator that allows us to predict transition times with
molecular dynamics simulations biased to rapidly explore one or several
collective variables. This approach relies on the idea that not all bias goes
into promoting transitions, and along with the rate, it estimates a concomitant
scale factor for the bias termed the collective variable biasing efficiency
$\gamma$. First, we demonstrate mathematically that our new formulation allows
us to derive the commonly used Infrequent Metadynamics (iMetaD) estimator when
using a perfect collective variable, $\gamma=1$. After testing it on a model
potential, we then study the unfolding behavior of a previously well
characterized coarse-grained protein, which is sufficiently complex that we can
choose many different collective variables to bias, but which is sufficiently
simple that we are able to compute the unbiased rate dire ctly. For this
system, we demonstrate that our new Exponential Average Time-Dependent Rate
(EATR) estimator converges to the true rate more rapidly as a function of bias
deposition time than does the previous iMetaD approach, even for bias
deposition times that are short. We also show that the $\gamma$ parameter can
serve as a good metric for assessing the quality of the biasing coordinate.
Finally, we demonstrate that the approach works when combining multiple
less-than-optimal bias coordinates.


  Social media studies often collect data retrospectively to analyze public
opinion. Social media data may decay over time and such decay may prevent the
collection of the complete dataset. As a result, the collected dataset may
differ from the complete dataset and the study may suffer from data persistence
bias. Past research suggests that the datasets collected retrospectively are
largely representative of the original dataset in terms of textual content.
However, no study analyzed the impact of data persistence bias on social media
studies such as those focusing on controversial topics. In this study, we
analyze the data persistence and the bias it introduces on the datasets of
three types: controversial topics, trending topics, and framing of issues. We
report which topics are more likely to suffer from data persistence among these
datasets. We quantify the data persistence bias using the change in political
orientation, the presence of potentially harmful content and topics as
measures. We found that controversial datasets are more likely to suffer from
data persistence and they lean towards the political left upon recollection.
The turnout of the data that contain potentially harmful content is
significantly lower on non-controversial datasets. Overall, we found that the
topics promoted by right-aligned users are more likely to suffer from data
persistence. Account suspensions are the primary factor contributing to data
removals, if not the only one. Our results emphasize the importance of
accounting for the data persistence bias by collecting the data in real time
when the dataset employed is vulnerable to data persistence bias.


  The $\nu_e-^{56}$Fe cross section is evaluated in the projected quasiparticle
random phase approximation (PQRPA). This model solves the puzzle observed in
RPA for nuclei with mass around $^{12}$C, because it is the only RPA model that
treats the Pauli principle correctly. The cross sections as a function of the
incident neutrino energy are compared with recent theoretical calculations of
similar models. The average cross section weighted with the flux spectrum
yields a good agreement with the experimental data. The expected number of
events in the detection of supernova neutrinos is calculated for the LVD
detector leading to an upper limit for the electron neutrino energy of
particular importance in this experiment


  We formalize eight different notions of isomorphism among (unital) graph
C*-algebras, and initiate the study of which of these notions may be described
geometrically as generated by moves. We propose a list of seven types of moves
that we conjecture has the property that the collection of moves respecting one
of six notions of isomorphism indeed generate that notion, in the sense that
two graphs are equivalent in that sense if and only if one may transform one
into another using only these kinds of moves.
  We carefully establish invariance properties of each move on our list, and
prove a collection of generation results supporting our conjecture with an
emphasis on the gauge simple case. In two of the six cases, we may prove the
conjecture in full generality, and in two we can show it for all graphs
defining gauge simple C*-algebras. In the two remaining cases we can show the
conjecture for all graphs defining gauge simple C*-algebras provided that they
are either finite or have at most one vertex allowing a path back to itself.


  The Real Extended Bialas-Bzdak (ReBB) model study is extended to the 8 TeV
$pp$ TOTEM elastic differential cross section data. The analysis shows that the
ReBB model describes the $pp$ and $p\bar{p}$ differential cross section data in
the limited $0.37 \leq -t \leq 1.2$ GeV$^2$ and $1.96 \leq \sqrt{s} \leq 8$ TeV
kinematic region, in a statistically acceptable manner. In this kinematic
region a greater than 30 $\sigma$ model-dependent Odderon signal is observed by
comparing the $pp$ and ReBB extrapolated $p\bar{p}$ differential cross
sections. Thus, in practical terms, within the framework of the ReBB model,
Odderon exchange is not a probability, but a certainty.


  We introduce a fragment of second-order unification, referred to as
\emph{Second-Order Ground Unification (SOGU)}, with the following properties:
(i) only one second-order variable is allowed, and (ii) first-order variables
do not occur. We study an equational variant of SOGU where the signature
contains \textit{associative} binary function symbols (ASOGU) and show that
Hilbert's 10$^{th}$ problem is reducible to ASOGU unifiability, thus proving
undecidability. Our reduction provides a new lower bound for the undecidability
of second-order unification, as previous results required first-order variable
occurrences, multiple second-order variables, and/or equational theories
involving \textit{length-reducing} rewrite systems. Furthermore, our reduction
holds even in the case when associativity of the binary function symbol is
restricted to \emph{power associative}, i.e. f(f(x,x),x)= f(x,f(x,x)), as our
construction requires a single constant.


  Boson stars are gravitationally bound objects that arise in ultralight dark
matter models and form in the centers of galactic halos or axion miniclusters.
We systematically study the excitations of a boson star, taking into account
the mixing between positive and negative frequencies introduced by gravity. We
show that the spectrum contains zero-energy modes in the monopole and dipole
sectors resulting from spontaneous symmetry breaking by the boson star
background. We analyze the general properties of the eigenmodes and derive
their orthogonality and completeness conditions which have non-standard form
due to the positive-negative frequency mixing. The eigenvalue problem is solved
numerically for the first few energy levels in different multipole sectors and
the results are compared to the solutions of the Schr\"odinger equation in
fixed boson star gravitational potential. The two solutions differ
significantly for the lowest modes, but get close for higher levels. We further
confirm the normal mode spectrum in 3D wave simulations where we inject
perturbations with different multipoles. As an application of the normal mode
solutions, we compute the matrix element entering the evaporation rate of a
boson star immersed in a hot axion gas. The computation combines the use of
exact wavefunctions for the low-lying bound states and of the Schr\"odinger
approximation for the high-energy excitations.


  It is unclear if existing interpretations of deep neural network models
respond effectively to the needs of users. This paper summarizes the common
forms of explanations (such as feature attribution, decision rules, or probes)
used in over 200 recent papers about natural language processing (NLP), and
compares them against user questions collected in the XAI Question Bank. We
found that although users are interested in explanations for the road not taken
-- namely, why the model chose one result and not a well-defined, seemly
similar legitimate counterpart -- most model interpretations cannot answer
these questions.


  Let $L_n$ be the length of the longest common subsequence of two independent
i.i.d. sequences of Bernoulli variables of length $n$. We prove that the order
of the standard deviation of $L_n$ is $\sqrt{n}$, provided the parameter of the
Bernoulli variables is small enough. This validates Waterman's conjecture in
this situation [Philos. Trans. R. Soc. Lond. Ser. B 344 (1994) 383--390]. The
order conjectured by Chvatal and Sankoff [J. Appl. Probab. 12 (1975) 306--315],
however, is different.


  2-point topological charge correlation functions of several types of
geometric singularity in gaussian random fields are calculated explicitly,
using a general scheme: zeros of $n$-dimensional random vectors, signed by the
sign of their jacobian determinant; critical points (gradient zeros) of real
scalars in two dimensions signed by the hessian; and umbilic points of real
scalars in two dimensions, signed by their index. The functions in each case
depend on the underlying spatial correlation function of the field. These
topological charge correlation functions are found to obey the first
Stillinger-Lovett sum rule for ionic fluids.


  We study the strong gravitational lensing on the equatorial plane of a
quasi-Kerr compact object with arbitrary quadrupole moments which can be used
to model the super-massive central object of the galaxy. We find that, when the
quadrupolar correction parameter $\xi$ takes the positive (negative) value, the
photon-sphere radius $r_{ps}$, the minimum impact parameter $u_{ps}$, the
coefficient $\bar{b}$, the relative magnitudes $r_m$ and the angular position
of the relativistic images $\theta_{\infty}$ are larger (smaller) than the
results obtained in the Kerr black hole, but the coefficient $\bar{a}$, the
deflection angle $\alpha(\theta)$ and the angular separation $s$ are smaller
(larger) than that in the Kerr black hole. These features may offer a way to
probe special properties for some rotating compact objects by the astronomical
instruments in the future.


  We study baryogenesis through lepton number violation in left-right symmetric
models. In these models the lepton number and CP violating interactions of the
triplet higgs scalars can give rise to lepton number asymmetry through
non-equilibrium decays of the $SU(2)_L$ triplet higgs and the right handed
neutrinos. This in turn generates baryon asymmetry during the electroweak
anomalous processes.


  Composite Higgs models are only now starting to be probed at the Large Hadron
Collider by Higgs searches. We point out that new resonances, abundant in these
models, can mediate new production mechanisms for the composite Higgs. The new
channels involve the exchange of a massive color octet and single production of
new fermion resonances with subsequent decays into the Higgs and a Standard
Model quark. The sizable cross section and very distinctive kinematics allow
for a very clean extraction of the signal over the background with high
statistical significance. Heavy gluon masses up to 2.8 TeV can be probed with
data collected during 2012 and up to 5 TeV after the energy upgrade to
$\sqrt{s}=14$ TeV.


  The memory subsystem has always been a bottleneck in performance as well as
significant power contributor in memory intensive applications. Many
researchers have presented multi-layered memory hierarchies as a means to
design energy and performance efficient systems. However, most of the previous
work do not explore trade-offs systematically. We fill this gap by proposing a
formalized technique that takes into consideration data reuse, limited lifetime
of the arrays of an application and application specific prefetching
opportunities, and performs a thorough trade-off exploration for different
memory layer sizes. This technique has been implemented on a prototype tool,
which was tested successfully using nine real-life applications of industrial
relevance. Following this approach we have able to reduce execution time up to
60%, and energy consumption up to 70%.


  Considering the mass splittings of three active neutrinos, we investigate how
the nature of dark energy affects the cosmological constraints on the total
neutrino mass $\sum m_\nu$ using the latest cosmological observations. In this
paper, some typical dark energy models, including $\Lambda$CDM, $w$CDM, CPL,
and HDE models, are discussed. In the analysis, we also consider the effects
from the neutrino mass hierarchies, i.e., the degenerate hierarchy (DH), the
normal hierarchy (NH), and the inverted hierarchy (IH). We employ the current
cosmological observations to do the analysis, including the Planck 2018
temperature and polarization power spectra, the baryon acoustic oscillations
(BAO), the type Ia supernovae (SNe), and the Hubble constant $H_0$ measurement.
In the $\Lambda$CDM+$\sum m_\nu$ model, we obtain the upper limits of the
neutrino mass $\sum m_\nu < 0.123$ eV (DH), $\sum m_\nu < 0.156$ eV (NH), and
$\sum m_\nu < 0.185$ eV (IH) at the $95\%$ C.L., using the Planck+BAO+SNe data
combination. For the $w$CDM+$\sum m_\nu$ model and the CPL+$\sum m_\nu$ model,
larger upper limits of $\sum m_\nu$ are obtained compared to those of the
$\Lambda$CDM+$\sum m_\nu$ model. The most stringent constraint on the neutrino
mass, $\sum m_\nu<0.080$ eV (DH), is derived in the HDE+$\sum m_\nu$ model. In
addition, we find that the inclusion of the local measurement of the Hubble
constant in the data combination leads to tighter constraints on the total
neutrino mass in all these dark energy models.


  We report results of an HST "snapshot" survey aimed at finding resolved
binary companions of the central stars of Galactic planetary nebulae (PNe).
Using WF/PC and WFPC2, we searched the fields of 113 PNe for stars whose close
proximity to the central star suggests a physical association. We find 10
binary nuclei that are very likely to be physically associated, and another six
that are possible binary associations. By correcting for interstellar
extinction and placing the central stars' companions on the main sequence, we
derive distances to the objects, and thereby significantly increase the number
of PNe with reliable distances.
  Comparison of our derived distances with those obtained from various
statistical methods shows that all of the latter have systematically
overestimated the distances, by factors ranging up to a factor of two or more.
We show that this error is most likely due to the fact that the properties of
our PNe with binary nuclei are systematically different from those of PNe used
heretofore to calibrate statistical methods. Specifically, our PNe tend to have
lower surface brightnesses at the same physical radius than the traditional
calibration objects. This difference may arise from a selection effect: the PNe
in our survey are typically nearby, old nebulae, whereas most of the objects
that calibrate statistical techniques are low-latitude,
high-surface-brightness, and more distant nebulae. As a result, the statistical
methods that seem to work well with samples of distant PNe, e.g., those in the
Galactic bulge or external galaxies, may not be applicable to the more diverse
population of local PNe.


  It was recently suggested that in a class of supersymmetric SO(10) models
with Higgs multiplets in 10, and a single $126+\bar{126}$ representations, if
the $\bar{126}$ contributes both to the right handed neutrino masses as well as
to the charged fermion masses, one can have a complete prediction of the
neutrino masses and mixings. It turns out that if one chooses only one 10,
there are no regions in the parameter space where one can have a large
$\nu_{\mu}-\nu_{\tau}$ mixing angle necessary to solve the atmospheric neutrino
deficit while at the same time solving the solar neutrino puzzle via the $\nu_e
\leftrightarrow \nu_{\mu}$ oscillation. We show that this problem can be solved
in a particular class of SO(10) models with a pair of 10 multiplets if we
include the additional left-handed triplet contribution to the light neutrino
mass matrix. This model cannot reproduce the mass and mixing parameters
required to explain the LSND observations neither does it have have a neutrino
hot dark matter.


  A 3-dimensional non-commutative oscillator with no mass term but with a
certain momentum-dependent potential admits a conserved Runge-Lenz vector,
derived from the dual description in momentum space. The latter corresponds to
a Dirac monopole with a fine-tuned inverse-square plus Newtonian potential,
introduced by McIntosh, Cisneros, and by Zwanziger some time ago. The
trajectories are (arcs of) ellipses, which, in the commutative limit, reduce to
the circular hodographs of the Kepler problem. The dynamical symmetry allows
for an algebraic determination of the bound-state spectrum and actually extends
to the conformal algebra o(4,2).


  Neural programming involves training neural networks to learn programs,
mathematics, or logic from data. Previous works have failed to achieve good
generalization performance, especially on problems and programs with high
complexity or on large domains. This is because they mostly rely either on
black-box function evaluations that do not capture the structure of the
program, or on detailed execution traces that are expensive to obtain, and
hence the training data has poor coverage of the domain under consideration. We
present a novel framework that utilizes black-box function evaluations, in
conjunction with symbolic expressions that define relationships between the
given functions. We employ tree LSTMs to incorporate the structure of the
symbolic expression trees. We use tree encoding for numbers present in function
evaluation data, based on their decimal representation. We present an
evaluation benchmark for this task to demonstrate our proposed model combines
symbolic reasoning and function evaluation in a fruitful manner, obtaining high
accuracies in our experiments. Our framework generalizes significantly better
to expressions of higher depth and is able to fill partial equations with valid
completions.


  The recent experimental realization of spin-orbit (SO) coupling for ultracold
bosons and fermions opens an exciting avenue for engineering quantum matter
that may be challenging to realize in solid state materials such as SO coupled
spin-1 fermions. While one-dimensional SO coupling for spin-1 bosons has been
experimentally realized, the generation of two-dimensional (2D) SO coupling and
its topological properties are largely unexplored. Here we propose an
experimental scheme for realizing a 2D Dresselhaus-type SO coupling in a square
lattice for spin-1 Fermi gases. Because of the extended spin degree of freedom,
many interesting topological phases could exist without relying on lattice
point group symmetries that are crucial in solid state materials. These exotic
phases include triply-degenerate points, quadratic band touching, a large Chern
number ($C=5$) superfluid with 5 Majorana modes, triple-Weyl fermions, etc. Our
scheme can be generalized to larger spins and provides a new route for
engineering topological quantum matter by utilizing large spin degrees of
freedom, instead of specific lattice symmetries.


  Recently, the result obtained from `Stardust' mission suggests that the
overall ratio of compact to aggregate particles is 65:35 (or 13:7) for Comet
81P/Wild 2 (Burchell et al. 2008). In the present work, we propose a model
which considers cometary dust as a mixture of compact and aggregate particles,
with composition of silicate and organic. We consider compact particles as
spheroidal particles and aggregates as BCCA and BAM2 aggregate with some size
distribution. For modeling Comet 1P/ Halley, the power-law size distribution
n(a)= a^{-2.6}, for both compact and aggregate particles is taken. We take a
mixture of BAM2 and BCCA aggregates with a lower and upper cutoff size around
0.20$\mu m$ and 1$\mu m$. We also take a mixture of prolate, spherical and
oblate compact particles with axial ratio (E) from 0.8 to 1.2 where a lower and
upper cutoff size around 0.1$\mu m$ and 10$\mu m$ are taken. Using T-matrix
code, the average simulated polarization curves are generated which can best
fit the observed polarization data at the four wavelengths $\lambda$ =
0.365$\mu m$, 0.485$\mu m$, 0.670$\mu m$ and 0.684$\mu m$. The suitable mixing
percentage of aggregates emerging out from the present modeling corresponds to
50% BAM2 and 50% BCCA particles and silicate to organic mixing percentage
corresponds to 78% silicate and 22% organic in terms of volume. The present
model successfully reproduces the observed polarization data, especially the
negative branch, more effectively as compared to other work done in the past.
It is found that among the aggregates, the BAM2 aggregate plays a major role,
in deciding the cross-over angle and depth of negative polarization branch.


  In this paper we connect Calder\'on and Zygmund's notion of $L^p$\-
-differentiability with some recent characterizations of Sobolev spaces via the
asymptotics of non-local functionals due to Bourgain, Brezis, and Mironescu. We
show how the results of the former can be generalized to the setting of the
latter, while the latter results can be strengthened in the spirit of the
former. As a consequence of these results we give several new characterizations
of Sobolev spaces, a novel condition for whether a function of bounded
variation is in the Sobolev space $W^{1,1}$, and complete the proof of a
characterization of the Sobolev spaces claimed in the paper "Characterization
of Sobolev and BV spaces".


  We report a consequence of the orbital angular momentum (OAM) of a beam to
its group velocity. We calculate the group velocity $v_g$ of Laguerre-Gauss
beam ($\emph{LG}$) with $\ell$ and at $p=0$. The $v_g$ reduction of $\emph{LG}$
beam even in free space is observed to have dependence on both orbital or
winding number $\ell$ and the beam's divergence $\theta_0$. We found that light
possessing higher $\ell$ travels relatively slower than that with lower $\ell$
values. This suggests that light of different OAM separate in the temporal
domain along propagation and it is an added effect to the dispersion due to
field confinement. Our results are useful for treating information embedded in
light with OAM from astronomical sources and/or data transmission in free
space.


  Cyanogen (NCCN) is the simplest member of the dicyanopolyynes group, and has
been proposed as a major source of the CN radical observed in cometary
atmospheres. Although not detected through its rotational spectrum in the cold
interstellar medium, this very stable species is supposed to be very abundant.
The chemistry of cyanogen in the cold interstellar medium can be investigated
through its metastable isomer, CNCN (isocyanogen). Its formation may provide a
clue on the widely abundant CN radical observed in cometary atmospheres. We
performed an unbiased spectral survey of the L1544 proto-typical prestellar
core, using the IRAM-30m and have analysed, for this paper, the nitrogen
chemistry that leads to the formation of isocyanogen. We report on the first
detection of CNCN, NCCNH+, C3N, CH3CN, C2H3CN, and H2CN in L1544. We built a
detailed chemical network for NCCN/CNCN/HC2N2+ involving all the nitrogen
bearing species detected (CN, HCN, HNC, C3N, CNCN, CH3CN, CH2CN, HCCNC, HC3N,
HNC3, H2CN, C2H3CN, HCNH+, HC3NH+) and the upper limits on C4N, C2N. The main
cyanogen production pathways considered in the network are the CN + HNC and N +
C3N reactions. The comparison between the observations of the nitrogen bearing
species and the predictions from the chemical modelling shows a very good
agreement, taking into account the new chemical network. The expected cyanogen
abundance is greater than the isocyanogen abundance by a factor of 100.
Although cyanogen cannot be detected through its rotational spectrum, the
chemical modelling predicts that it should be abundant in the gas phase and
hence might be traced through the detection of isocyanogen. It is however
expected to have a very low abundance on the grain surfaces compared to HCN.


  A general description of weak and strong tunneling fixed points is developed
in the chiral-Luttinger-liquid model of quantum Hall edge states. Tunneling
fixed points are a subset of `termination' fixed points, which describe
boundary conditions on a multicomponent edge. The requirement of unitary time
evolution at the boundary gives a nontrivial consistency condition for possible
low-energy boundary conditions. The effect of interactions and random hopping
on fixed points is studied through a perturbative RG approach which generalizes
the Giamarchi-Schulz RG for disordered Luttinger liquids to broken left-right
symmetry and multiple modes. The allowed termination points of a multicomponent
edge are classified by a B-matrix with rational matrix elements. We apply our
approach to a number of examples, such as tunneling between a quantum Hall edge
and a superconductor and tunneling between two quantum Hall edges in the
presence of interactions. Interactions are shown to induce a continuous
renormalization of effective tunneling charge for the integrable case of
tunneling between two Laughlin states. The correlation functions of
electronlike operators across a junction are found from the B matrix using a
simple image-charge description, along with the induced lattice of boundary
operators. Many of the results obtained are also relevant to ordinary Luttinger
liquids.


  Hydrophobic hydration plays a crucial role in self-assembly processes over
multiple length-scales, but the extrapolation of molecular-scale models to
larger length-scale hydration phenomena is sometimes not warranted.
Scaled-particle theories are based upon an interpolative view of that issue. We
revisit the scaled-particle theory proposed thirty years ago by Stillinger,
adopt a practical generalization, and consider the implications for hydrophobic
hydration in light of our current understanding. The generalization is based
upon identifying a molecular length, implicit in previous applications of
scaled-particle models, that provides an effective radius for joining
microscopic and macroscopic descriptions. We demonstrate that the generalized
theory correctly reproduces many of the anomalous thermodynamic properties of
hydrophobic hydration for molecularly sized solutes, including solubility
minima and entropy convergence, successfully interpolates between the
microscopic and macroscopic extremes, and provides new insights into the
underlying molecular mechanisms. The results are discussed in terms of
length-scales associated with component phenomena; in particular we first
discuss the micro-macroscopic joining radius identified by the theory, then we
discuss in turn the Tolman length that leads to an analogous length describing
curvature corrections of a surface area model of hydrophobic hydration free
energies, and the length-scales on which entropy convergence of hydration free
energies are expected.


  Entanglement distillation transforms weakly entangled noisy states into
highly entangled states, a primitive to be used in quantum repeater schemes and
other protocols designed for quantum communication and key distribution. In
this work, we present a comprehensive framework for continuous-variable
entanglement distillation schemes that convert noisy non-Gaussian states into
Gaussian ones in many iterations of the protocol. Instances of these protocols
include (a) the recursive-Gaussifier protocol, (b) the temporally-reordered
recursive-Gaussifier protocol, and (c) the pumping-Gaussifier protocol. The
flexibility of these protocols give rise to several beneficial trade-offs
related to success probabilities or memory requirements, which that can be
adjusted to reflect experimental demands. Despite these protocols involving
measurements, we relate the convergence in this protocols to new instances of
non-commutative central limit theorems, in a formalism that we lay out in great
detail. Implications of the findings for quantum repeater schemes are
discussed.


  Matchgates are an especially multiflorous class of two-qubit nearest
neighbour quantum gates, defined by a set of algebraic constraints. They occur
for example in the theory of perfect matchings of graphs, non-interacting
fermions, and one-dimensional spin chains. We show that the computational power
of circuits of matchgates is equivalent to that of space-bounded quantum
computation with unitary gates, with space restricted to being logarithmic in
the width of the matchgate circuit. In particular, for the conventional setting
of polynomial-sized (logarithmic-space generated) families of matchgate
circuits, known to be classically simulatable, we characterise their power as
coinciding with polynomial-time and logarithmic-space bounded universal unitary
quantum computation.


  For a given class $\mathcal{F}$ of closed sets of a measured metric space
$(E,d,\mu)$, we want to find the smallest element $B$ of the class
$\mathcal{F}$ such that $\mu(B)\geq 1-\alpha$, for a given $0<\alpha<1$. This
set $B$ \textit{localizes the mass} of $\mu$. Replacing the measure $\mu$ by
the empirical measure $\mu_n$ gives an empirical smallest set $B_n$. The
article introduces a formal definition of small sets (and their size) and study
the convergence of the sets $B_n$ to $B$ and of their size.


  A photonic-crystal slab can support bound states in the continuum (BICs)
which have infinite lifetimes but embedded into the continuous spectrum of
optical modes in free space. The formation of BICs requires a total internal
reflection (TIR) condition at both interfaces between the slab and free space.
Here, we show that the TIR of Bloch waves can be directly obtained based on the
generalized Fresnel equations proposed. If each of these Bloch waves picks up a
phase with integer multiples of 2pi for traveling a round trip, light can be
perfectly guided in the slab, namely, forming a BIC. A BIC solver with low
computational complexity and fast convergence speed is developed, which can
also work efficiently at high frequencies beyond the diffraction limit where
multiple radiation channels exist. Two examples of multi-channel BICs are
shown, and their topological nature in momentum space is also revealed. Both
can be attributed to the coincidence of the topological charges of far-field
radiations from different radiation channels. The concept of the generalized
TIR and the TIR-based BIC solver developed offer highly effective approaches
for explorations of BICs which could have many potential applications in
guided-wave optics and enhanced light-matter interactions.


  In this paper we have demonstrated the double Q^2-rescaling model (DQ^2RM) of
parton distribution functions of nucleon bounded in nucleus. With different
x-region of l-A deep inelastic scattering process we take different approach:
in high x-region (0.1\le x\le 0.7) we use the distorted QCD vacuum model which
resulted from topologically multi -connected domain vacuum structure of
nucleus; in low x-region (10^{-4}\le x\le10^{-3}) we adopt the Glauber
(Mueller) multi- scattering formula for gluon coherently rescattering in
nucleus. From these two approach we justified the rescaling parton distribution
functions in bound nucleon are in agreement well with those we got from DQ^2RM,
thus the validity for this phenomenologically model are demonstrated.


  Variational inference has become one of the most widely used methods in
latent variable modeling. In its basic form, variational inference employs a
fully factorized variational distribution and minimizes its KL divergence to
the posterior. As the minimization can only be carried out approximately, this
approximation induces a bias. In this paper, we revisit perturbation theory as
a powerful way of improving the variational approximation. Perturbation theory
relies on a form of Taylor expansion of the log marginal likelihood, vaguely in
terms of the log ratio of the true posterior and its variational approximation.
While first order terms give the classical variational bound, higher-order
terms yield corrections that tighten it. However, traditional perturbation
theory does not provide a lower bound, making it inapt for stochastic
optimization. In this paper, we present a similar yet alternative way of
deriving corrections to the ELBO that resemble perturbation theory, but that
result in a valid bound. We show in experiments on Gaussian Processes and
Variational Autoencoders that the new bounds are more mass covering, and that
the resulting posterior covariances are closer to the true posterior and lead
to higher likelihoods on held-out data.


  We perform a-priori validation tests of subgrid-scale (SGS) models for the
turbulent transport of momentum, energy and passive scalars. To this end, we
conduct two sets of high-resolution hydrodynamical simulations with a
Lagrangian code: an isothermal turbulent box with rms Mach number of 0.3, 2 and
8, and the classical wind tunnel where a cold cloud traveling through a hot
medium gradually dissolves due to fluid instabilities. Two SGS models are
examined: the eddy diffusivity (ED) model wildly adopted in astrophysical
simulations and the "gradient model" due to Clark et al. (1979). We find that
both models predict the magnitude of the SGS terms equally well (correlation
coefficient > 0.8). However, the gradient model provides excellent predictions
on the orientation and shape of the SGS terms while the ED model predicts
poorly on both, indicating that isotropic diffusion is a poor approximation of
the instantaneous turbulent transport. The best-fit coefficient of the gradient
model is in the range of [0.16, 0.21] for the momentum transport, and the
turbulent Schmidt number and Prandtl number are both close to unity, in the
range of [0.92, 1.15].


  We examine the convergence properties of the 2-nucleon Effective Range
Expansion as used in Effective Theories (ET-ERE's) for 3-nucleon calculations.
We accomplish this by accounting for the 2-body dynamics with a simple rank-1
separable 2-body potential where the finite range effects can be incorporated
systematically in both the 2- and 3-body problems. We make our initial
comparisons in the simple context of the $^3S_1$ 2-nucleon channel and the
$^4S_{3/2}$ 3-nucleon channel. We find that convergence problems for some of
the 3-nucleon scattering amplitudes using the ET-ERE can be traced to its poor
account of finite range effects that soften the momentum dependence of the
deuteron propagator in the Faddeev kernel. In contrast, our simple separable
potential with dipole form factors works very well in all cases considered.


  Four groups (even-even, even-odd, odd-even and odd-odd) of heavy and
super-heavy nuclei are of interest for the synthesis of the isotopes with
$Z=119, 120$. We report calculations of $\alpha$~decay half-lives using four
models: AKRA (Akrawy); ASAF (Analytical Super-Asymmetric Fission); UNIV
(Universal Formula), and semFIS (Semi-empirical formula based on Fission
Theory). We compare the experimental $Q_\alpha$ values either with AME16 atomic
mass evaluation (whenever available) and with the theoretical model WS4, able
to give masses of not yet measured nuclides. For $^{92,94}$Sr cluster
radioactivity of $^{300,302}$120 we predict a branching ratio relative to
$\alpha$~decay of -0.10 and 0.49, respectively, meaning that it is worth trying
to detect such kind of decay modes in competition with $\alpha$~decay.


  The purpose of this paper is to study motivic aspects of the Hitchin system
for $\mathrm{GL}_n$. Our results include the following. (a) We prove the
motivic decomposition conjecture of Corti-Hanamura for the Hitchin system; in
particular, the decomposition theorem associated with the Hitchin system is
induced by algebraic cycles. This yields an unconditional construction of the
motivic perverse filtration for the Hitchin system, which lifts the
cohomological/sheaf-theoretic perverse filtration. (b) We prove that the
inverse of the relative Hard Lefschetz symmetry is induced by a relative
algebraic correspondence, confirming the relative Lefschetz standard conjecture
for the Hitchin system. (c) We show a strong perversity bound for the
normalized Chern classes of a universal bundle with respect to the motivic
perverse filtration; this specializes to the sheaf-theoretic result obtained
earlier by Maulik-Shen. (d) We prove a $\chi$-independence result for the
relative Chow motives associated with Hitchin systems.
  Our methods combine Fourier transforms for compactified Jacobian fibrations
associated with integral locally planar curves, nearby and vanishing cycle
techniques, and a Springer-theoretic interpretation of parabolic Hitchin moduli
spaces.


  Reserve systems are used to accommodate multiple essential or
underrepresented groups in allocating indivisible scarce resources by creating
categories that prioritize their respective beneficiaries. Some applications
include the optimal allocation of vaccines, or assignment of minority students
to elite colleges in India. An allocation is called smart if it optimizes the
number of units distributed. Previous literature mostly assumed baseline
priorities, which impose significant interdependencies between the priority
ordering of different categories. It also assumes either everybody is eligible
for receiving a unit from any category, or only the beneficiaries are eligible.
The comprehensive Threshold Model we propose allows independent priority
orderings among categories and arbitrary beneficiary and eligibility
thresholds, enabling policymakers to avoid comparing incomparables in
affirmative action systems. We present a new smart reserve system that
optimizes two objectives simultaneously to allocate scarce resources. Our Smart
Pipeline Matching Mechanism achieves all desirable properties in the most
general domain possible. Our results apply to any resource allocation market,
but we focus our attention on the vaccine allocation problem.


  We study the partition function of the compactified 5D U(1) gauge theory (in
the Omega-background) with a single adjoint hypermultiplet, calculated using
the refined topological vertex. We show that this partition function is an
example a periodic Schur process and is a refinement of the generating function
of cylindric plane partitions. The size of the cylinder is given by the mass of
adjoint hypermultiplet and the parameters of the Omega-background. We also show
that this partition function can be written as a trace of operators which are
generalizations of vertex operators studied by Carlsson and Okounkov. In the
last part of the paper we describe a way to obtain (q,t) identities using the
refined topological vertex.


  We propose a new approach to the problem of optimizing autoencoders for lossy
image compression. New media formats, changing hardware technology, as well as
diverse requirements and content types create a need for compression algorithms
which are more flexible than existing codecs. Autoencoders have the potential
to address this need, but are difficult to optimize directly due to the
inherent non-differentiabilty of the compression loss. We here show that
minimal changes to the loss are sufficient to train deep autoencoders
competitive with JPEG 2000 and outperforming recently proposed approaches based
on RNNs. Our network is furthermore computationally efficient thanks to a
sub-pixel architecture, which makes it suitable for high-resolution images.
This is in contrast to previous work on autoencoders for compression using
coarser approximations, shallower architectures, computationally expensive
methods, or focusing on small images.


  The branching fractions from the excited state $6P_{1/2}$ of singly charged
barium ion has been measured with a precision $0.05%$ in an ion trap
experiment. This measurement along with the known value of the upper state
life-time allowed the determination of the dipole matrix elements for the
transitions $P-S$ and $P-D$ to below one percent level. Therefore, for the
first time it is now possible to compare the many body calculations of these
matrix elements at level which is of significance to any parity
non-conservation experiment on barium ion. Moreover, these dipole matrix
elements are the most significant contributors to the parity violating matrix
element between the $S-D$ transition, contributing upto $90%$ to the total. Our
results on the dipole matrix elements are $3.306\pm0.014$ and $3.036\pm0.016$
for the $S-P$ and $P-D$ transitions respectively.


  The fine-grained uncertainty relation can be used to discriminate among
classical, quantum and super-quantum correlations based on their strength of
nonlocality, as has been shown for bipartite and tripartite systems with
unbiased measurement settings. Here we consider the situation when two and
three parties, respectively, choose settings with bias for playing certain
non-local games. We show analytically that while the fine-grained uncertainty
principle is still able to distinguish classical, quantum and super-quantum
correlations for biased settings corresponding to certain ranges of the biasing
parameters, the above-mentioned discrimination is not manifested for all
biasing.


  We present results of meson and baryon spectroscopy using the Chirally
Improved Dirac operator on lattices of size 16**3 x 32 with two mass-degenerate
light sea quarks. Three ensembles with pion masses of 322(5), 470(4) and 525(7)
MeV and lattice spacings close to 0.15 fm are investigated. Results on ground
and excited states for several channels are given, including spin two mesons
and hadrons with strange valence quarks. The analysis of the states is done
with the variational method, including two kinds of Gaussian sources and
derivative sources. We obtain several ground states fairly precisely and find
radial excitations in various channels. Excited baryon results seem to suffer
from finite size effects, in particular at small pion masses. We discuss the
possible appearance of scattering states in various channels, considering
masses and eigenvectors. Partially quenched results in the scalar channel
suggest the presence of a 2-particle state, however, in most channels we cannot
identify them. Where available, we compare our results to results of quenched
simulations using the same action.


  This paper investigates the stability properties and performance of
super-twisting sliding-mode control loops subject to periodic perturbations.
Although there exist conditions on the control gains that guarantee finite-time
stability of the closed-loop system, such conditions are often too restrictive
from a practical standpoint, especially in relation to actuator limitations and
induced chatter. Using regularisation and averaging theory, it is proven that
under milder conditions for the control gains, the trajectories of the
periodically perturbed closed-loop system converge to a stable limit cycle of
the same period containing the origin. Additionally, guidelines for selecting
the controller gains are provided based on bounds of the closed-loop system
states. Finally, the theoretical findings are validated through simulations.


  We consider the $\mathbb{Z}_2$ toric code, surface code and Floquet code
defined on a non-orientable surface, which can be considered as families of
codes extending Shor's 9-qubit code. We investigate the fault-tolerant logical
gates of the $\mathbb{Z}_2$ toric code in this setup, which corresponds to
$e\leftrightarrow m$ exchanging symmetry of the underlying $\mathbb{Z}_2$ gauge
theory. We find that non-orientable geometry provides a new way the emergent
symmetry acts on the code space, and discover the new realization of the
fault-tolerant Hadamard gate of 2d $\mathbb{Z}_2$ toric code on a surface with
a single cross-cap, dubbed a non-orientable toric code. This Hadamard gate can
be realized by a constant-depth local unitary circuit modulo non-locality
caused by a cross-cap. Via folding, the non-orientable surface code can be
turned into a bilayer local quantum code, where the folded cross-cap is
equivalent to a bi-layer twist terminated on a gapped boundary and the logical
Hadamard only contains local gates with intra-layer couplings. We further
obtain the complete logical Clifford gate set for a stack of non-orientable
surface codes. We then construct the honeycomb Floquet code in the presence of
a single cross-cap, and find that the period of the sequential Pauli
measurements acts as a $HZ$ logical gate on the single logical qubit, where the
cross-cap enriches the dynamics compared with the orientable case. We find that
the dynamics of the honeycomb Floquet code is precisely described by a
condensation operator of the $\mathbb{Z}_2$ gauge theory, and illustrate the
exotic dynamics of our code in terms of a condensation operator supported at a
non-orientable surface.


  Interaction design for Augmented Reality (AR) is gaining increasing attention
from both academia and industry. This survey discusses 260 articles (68.8% of
articles published between 2015 - 2019) to review the field of human
interaction in connected cities with emphasis on augmented reality-driven
interaction. We provide an overview of Human-City Interaction and related
technological approaches, followed by a review of the latest trends of
information visualization, constrained interfaces, and embodied interaction for
AR headsets. We highlight under-explored issues in interface design and input
techniques that warrant further research, and conjecture that AR with
complementary Conversational User Interfaces (CUIs) is a key enabler for
ubiquitous interaction with immersive systems in smart cities. Our work helps
researchers understand the current potential and future needs of AR in
Human-City Interaction.


  Let $(\mathcal{E},D(\mathcal{E}))$ be a quasi-regular semi-Dirichlet form and
$(X_t)_{t\geq0}$ be the associated Markov process. For $u\in
D(\mathcal{E})_{loc}$, denote $A_t^{[u]}:=\tilde{u}(X_{t})-\tilde{u}(X_{0})$
and $F^{[u]}_t:=\sum_{0<s\leq t}(\tilde u(X_{s})-\tilde u(X_{s-}))1_{\{|\tilde
u(X_{s})-\tilde u(X_{s-})|>1\}}$, where $\tilde{u}$ is a quasi-continuous
version of $u$. We show that there exist a unique locally square integrable
martingale additive functional $Y^{[u]}$ and a unique continuous local additive
functional $Z^{[u]}$ of zero quadratic variation such that
$$A_t^{[u]}=Y_t^{[u]}+Z_t^{[u]}+F_t^{[u]}.$$ Further, we define the stochastic
integral $\int_0^t\tilde v(X_{s-})dA_s^{[u]}$ for $v\in D(\mathcal{E})_{loc}$
and derive the related It\^{o}'s formula.


  Non-Fermi liquid behavior is shown to occur in two-dimensional metals which
are close to a charge ordering transition driven by the Coulomb repulsion. A
linear temperature dependence of the scattering rate together with an increase
of the electron effective mass occur above T*, a temperature scale much smaller
than the Fermi temperature. It is shown that the anomalous temperature
dependence of the optical conductivity of the quasi-two-dimensional organic
metal alpha-(BEDT-TTF)2MHg(SCN)4, with M=NH4 and Rb, above T*=50-100 K, agrees
qualitatively with our predictions for the electronic properties of nearly
charge ordered two-dimensional metals.


  A proposal to improve routing security---Route Origin Authorization
(ROA)---has been standardized. A ROA specifies which network is allowed to
announce a set of Internet destinations. While some networks now specify ROAs,
little is known about whether other networks check routes they receive against
these ROAs, a process known as Route Origin Validation (ROV). Which networks
blindly accept invalid routes? Which reject them outright? Which de-preference
them if alternatives exist?
  Recent analysis attempts to use uncontrolled experiments to characterize ROV
adoption by comparing valid routes and invalid routes. However, we argue that
gaining a solid understanding of ROV adoption is impossible using currently
available data sets and techniques. Our measurements suggest that, although
some ISPs are not observed using invalid routes in uncontrolled experiments,
they are actually using different routes for (non-security) traffic engineering
purposes, without performing ROV. We conclude with a description of a
controlled, verifiable methodology for measuring ROV and present three ASes
that do implement ROV, confirmed by operators.


  We investigate the adaptation and performance of modularity-based algorithms,
designed in the scope of complex networks, to analyze the mesoscopic structure
of correlation matrices. Using a multi-resolution analysis we are able to
describe the structure of the data in terms of clusters at different
topological levels. We demonstrate the applicability of our findings in two
different scenarios: to analyze the neural connectivity of the nematode {\em
Caenorhabditis elegans}, and to automatically classify a typical benchmark of
unsupervised clustering, the Iris data set, with considerable success.


  Recently D. Vollick [Phys. Rev. D68, 063510 (2003)] has shown that the
inclusion of the 1/R curvature terms in the gravitational action and the use of
the Palatini formalism offer an alternative explanation for cosmological
acceleration. In this work we show not only that this model of Vollick does not
have a good Newtonian limit, but also that any f(R) theory with a pole of order
n in R=0 and its second derivative respect to R evaluated at Ro is not zero,
where Ro is the scalar curvature of background, does not have a good Newtonian
limit.


  While many aspects of general relativity have been tested, and general
principles of quantum dynamics demand its quantization, there is no direct
evidence for that. It has been argued that development of detectors sensitive
to individual gravitons is unlikely, and perhaps impossible. We argue here,
however, that measurement of polarization of the Cosmic Microwave Background
due to a long wavelength stochastic background of gravitational waves from
Inflation in the Early Universe would firmly establish the quantization of
gravity.


  The valley splitting (VS) of a silicon quantum dot plays an important role
for the performance and scalability of silicon spin qubits. In this work we
investigate the VS of a SiGe/Si/SiGe heterostructure as a function of the size
and location of the silicon quantum dot. We use the effective mass approach to
describe a realistic system, which takes into account concentration
fluctuations at the Si/SiGe interfaces and also the interface roughness. We
predict that the size of the quantum dot is an important parameter for the
enhancement of the VS and it can also induce a transition between the
disorder-dominated to deterministic-enhanced regimes. Analyzing how the VS
changes when we move the quantum dot in a specific direction, we obtain that
the size of the quantum dot can be used to reduce the variability of the VS,
which is relevant for charge/spin shuttling.