  Within the framework of Landau-Ginzburg-Devonshire (LGD) phenomenological
theory we consider the possibility to control properties of paraelectric
antiferromagnets via biquadratic rotomagnetic coupling with and without
external magnetic and electric field application. We use EuTiO3 as a prototype
with relatively well-known material parameters. Surprisingly strong influence
of this coupling practically on all the properties without external fields was
obtained in the temperature region with coexistence of antiferromagnetic and
antiferrodistorted phases i.e. in multiferroic state. In particular, the
observed Neel temperature TN (5.5 K) was shown to be defined by rotomagnetic
coupling, while without this coupling TN appeared to be much higher (26 K). For
small or high enough rotomagnetic coupling constant value the antiferromagnetic
phase transition order appeared to be the second or the first order
respectively. The essential influence of rotomagnetic coupling on the form and
value of magnetic and dielectric permittivity was also forecasted. The
rotomagnetic coupling along with rotoelectric one opens the additional way to
control the form of the phase diagrams by application of external magnetic or
electric field. The critical value of the electric field (for antiferromagnetic
to ferromagnetic phase transition) appeared essentially smaller than the one
calculated without rotomagnetic coupling that can be important for
applications.


  We present a theoretical study of an ensemble of X-like 4-level atoms placed
in an optical cavity driven by a linearly polarized field. We show that the
self-rotation (SR) process leads to polarization switching (PS). Below the PS
threshold, both the mean field mode and the orthogonal vacuum mode are
squeezed. We provide a simple analysis of the phenomena responsible for the
squeezing and trace the origin of vacuum squeezing not to SR, but to crossed
Kerr effect induced by the mean field. Last, we show that this vacuum squeezing
can be interpreted as polarization squeezing.


  A class of septuple-atomic-layer two-dimensional (2D) materials, MA$_2$Z$_4$,
is sought as an alternative to 2D hexagonal transition metal dichalcogenides in
the field of valleytronics and spintronics. In these materials, the structural
symmetry can be varied by changing the stacking of its three parts in the
monolayer. We show that in Janus monolayer WSiGeZ$_4$ (Z=N, P, As), the Berry
curvature and Rashba effect are enhanced by modifying the stacking orders.
Intrinsic electric field and composition of the d orbitals play a dominant role
in determining these properties. The vertical field lifts the spin degeneracy
along in-plane direction, inducing the Rashba effect around $\Gamma$ point. The
in-plane orbitals under the influence of in-plane electric field contribute to
the Zeeman splitting of bands at K/K' points. Berry curvature is strengthened
by up to 300% compared to its ground state through symmetry control, along with
a significant increment in the Rashba coefficient. Moreover, monolayer
WSiGeP$_4$ and WSiGeAs$_4$ have multiple valleys, implying another
valley-dimension. We construct a symmetry adapted k.p Hamiltonian for the
valleys and investigate the effect of strain and electric field on the band
structure. The interesting spin-valley physics in monolayer WSiGeZ$_4$ suggests
their exceptional potential for spintronics and valleytronics applications.


  This work presents a method for designing the weighting parameter required by
Wiener-based binaural noise reduction methods. This parameter establishes the
desired tradeoff between noise reduction and binaural cue preservation in
hearing aid applications. The proposed strategy was specially derived for the
preservation of interaural level difference, interaural time difference and
interaural coherence binaural cues. It is defined as a function of the average
input noise power at the microphones, providing robustness against the
influence of joint changes in noise and speech power (Lombard effect), as well
as to signal to noise ratio (SNR) variations. A theoretical framework, based on
the mathematical definition of the homogeneity degree, is presented and applied
to a generic augmented Wiener-based cost function. The theoretical insights
obtained are supported bycomputational simulations and psychoacoustic
experiments using the multichannel Wiener filter with interaural transfer
function preservation technique (MWF-ITF), as a case study. Statistical
analysis indicates that the proposed dynamic structure for the weighting
parameter and the design method of its fixed part provide significant
robustness against changes in the original binaural cues of both speech and
residual noise, at the cost of a small decrease in the noise reduction
performance, as compared to the use of a purely fixed weighting parameter.


  In this note we discuss the gravimagnetization of the ${\cal N}=2$ SYM vacuum
in the $\Omega$-background. It is argued that the Seiberg-Witten prepotential
is related to the vacuum density of the angular momentum in the Euclidean $R^4$
space. The possible role of the dyonic instantons as the microscopic angular
momentum carriers which could yield the spontaneous vacuum gravimagnetization
is conjectured. We interpret the dyonic instanton as a kind of the Euclidean
bounce in $R^4$ similar to one responsible for the Schwinger pair creation. The
induced angular momentum in $R^4$ is also briefly considered in the dual
Liouville formulation of $SU(2)$ theory via AGT relation.


  Starting from an informal requirements description of a toy production cell
used in an intra-project competition in 1994, we give a formal specification
that is as close as possible to requirements. We use the deductive program
synthesis approach by Manna and Waldinger (1980) to obtain a verified TTL-like
circuitery to control the cell. The formal specification also covers mechanical
aspects and thus allows to reason not only about software issues but also about
issues of mechanical engineering. Besides an approach confined to first order
predicate logic with explicit, continuous time, an attempt is presented to
employ application specific user-defined logical operators to get a more
concise specification as well as proof.


  In this paper we present randomization methods to enhance the accuracy of the
central limit theorem (CLT) based inferences about the population mean $\mu$.
We introduce a broad class of randomized versions of the Student $t$-statistic,
the classical pivot for $\mu$, that continue to possess the pivotal property
for $\mu$ and their skewness can be made arbitrarily small, for each fixed
sample size $n$. Consequently, these randomized pivots admit CLTs with smaller
errors. The randomization framework in this paper also provides an explicit
relation between the precision of the CLTs for the randomized pivots and the
volume of their associated confidence regions for the mean for both univariate
and multivariate data. This property allows regulating the trade-off between
the accuracy and the volume of the randomized confidence regions discussed in
this paper.


  We consider the complexity of finding weighted homomorphisms from
intersection graphs of curves (string graphs) with $n$ vertices to a fixed
graph $H$. We provide a complete dichotomy for the problem: if $H$ has no two
vertices sharing two common neighbors, then the problem can be solved in time
$2^{O(n^{2/3} \log n)}$, otherwise there is no algorithm working in time
$2^{o(n)}$, even in intersection graphs of segments, unless the ETH fails. This
generalizes several known results concerning the complexity of computatational
problems in geometric intersection graphs. Then we consider two variants of
graph homomorphism problem, called locally injective homomorphism and locally
bijective homomorphism, where we require the homomorphism to be injective or
bijective on the neighborhood of each vertex. We show that for each target
graph $H$, both problems can always be solved in time $2^{O(\sqrt{n} \log n)}$
in string graphs. For the locally surjecive homomorphism, defined in an
analogous way, the situation seems more complicated. We show the dichotomy
theorem for simple connected graphs $H$ with maximum degree 2. If $H$ is
isomorphic to $P_3$ or $C_4$, then the existence of a locally surjective
homomorphism from a string graph with $n$ vertices to $H$ can be decided in
time $2^{O(n^{2/3} \log^{3/2} n)}$, otherwise the problem cannot be solved in
time $2^{o(n)}$, unless the ETH fails. As a byproduct, we obtain several
results concerning the complexity of variants of homomorphism problem in
$P_t$-free graphs. In particular, we obtain the dichotomy theorem for weighted
homomorphism, analogous to the one for string graphs.


  In 1980, Ajtai, Komlos and Szemer{\'e}di defined "groupie": Let $G=(V,E)$ be
a simple graph, $|V|=n$, $|E|=e$. For a vertex $v\in V$, let $r(v)$ denote the
sum of the degrees of the vertices adjacent to $v$. We say $v\in V$ is a {\it
groupie}, if $\frac{r(v)}{\deg(v)}\geq\frac{e}{n}.$ In this paper, we prove
that in random graph $B(n,p)$, $0<p<1$, the proportion of groupies converges in
probability towards $\Phi(1)\approx0.8413$ as $n$ approaches infinity, where
$\Phi(x)$ is the distribution function of standard normal distribution N(0,1).
We also discuss the asymptotic behavior of the proportion of groupies in
complete bipartite graph $B(n_1,n_2,p)$.


  We have investigated the proof of the $H$ theorem within a manifestly
covariant approach by considering the relativistic statistical theory developed
in [G. Kaniadakis, Phy. Rev. E {\bf 66}, 056125, 2002; {\it ibid.} {\bf 72},
036108, 2005]. As it happens in the nonrelativistic limit, the molecular chaos
hypothesis is slightly extended within the Kaniadakis formalism. It is shown
that the collisional equilibrium states (null entropy source term) are
described by a $\kappa$ power law generalization of the exponential Juttner
distribution, e.g., $f(x,p)\propto (\sqrt{1+
\kappa^2\theta^2}+\kappa\theta)^{1/\kappa}\equiv\exp_\kappa\theta$, with
$\theta=\alpha(x)+\beta_\mu p^\mu$, where $\alpha(x)$ is a scalar, $\beta_\mu$
is a four-vector, and $p^\mu$ is the four-momentum. As a simple example, we
calculate the relativistic $\kappa$ power law for a dilute charged gas under
the action of an electromagnetic field $F^{\mu\nu}$. All standard results are
readly recovered in the particular limit $\kappa\to 0$.


  In predictive process analytics, current and historical process data in event
logs is used to predict the future, e.g., to predict the next activity or how
long a process will still require to complete. Recurrent neural networks (RNN)
and its subclasses have been demonstrated to be well suited for creating
prediction models. Thus far, event attributes have not been fully utilized in
these models. The biggest challenge in exploiting them in prediction models is
the potentially large amount of event attributes and attribute values. We
present a novel clustering technique that allows for trade-offs between
prediction accuracy and the time needed for model training and prediction. As
an additional finding, we also find that this clustering method combined with
having raw event attribute values in some cases provides even better prediction
accuracy at the cost of additional time required for training and prediction.


  We discuss the long-term evolution of the broad double-peaked H alpha profile
of the LINER/Seyfert 1 nucleus of NGC 1097. Besides the previously known
variation of the relative intensities of the blue and red peaks, the profile
has recently shown an increasing separation between the two peaks, at the same
time as the integrated flux has decreased. We successfully model these
variations using a precessing asymmetric accretion disk with a varying
emissivity law. We interpret the emissivity variation as due to the fact that
the source of ionization is getting dimmer, causing the region of maximum
emission to drift inwards (and thus to regions of higher velocities). In
addition, in the last 3 yrs of observations, the central wavelength of the
double-peaked line has shifted to bluer wavelengths, which may be due to a wind
from the disk. It is the first time that such evolution is observed so clearly,
giving additional support for an accretion disk as the origin of the
double-peaked profile in NGC 1097.


  Tensor function representation theory is an essential topic in both
theoretical and applied mechanics. For the elasticity tensor, Olive, Kolev and
Auffray (2017) proposed a minimal integrity basis of 297 isotropic invariants,
which is also a functional basis. Inspired by Smith's and Zheng's works, we use
a novel method in this article to seek a functional basis of the elasticity
tensor, that contains less number of isotropic invariants. We achieve this goal
by constructing 22 intermediate tensors consisting of 11 second order
symmetrical tensors and 11 scalars via the irreducible decomposition of the
elasticity tensor. Based on such intermediate tensors, we further generate 429
isotropic invariants which form a functional basis of the elasticity tensor.
After eliminating all the invariants that are zeros or polynomials in the
others, we finally obtain a functional basis of 251 isotropic invariants for
the elasticity tensor.


  Graphs are used to represent a plethora of phenomena, from the Web and social
networks, to biological pathways, to semantic knowledge bases. Arguably the
most interesting and important questions one can ask about graphs have to do
with their evolution. Which Web pages are showing an increasing popularity
trend? How does influence propagate in social networks? How does knowledge
evolve?
  This paper proposes a logical model of an evolving graph called a TGraph,
which captures evolution of graph topology and of its vertex and edge
attributes. We present a compositional temporal graph algebra TGA, and show a
reduction of TGA to temporal relational algebra with graph-specific primitives.
We formally study the properties of TGA, and also show that it is sufficient to
concisely express a wide range of common use cases. We describe an
implementation of our model and algebra in Portal, built on top of Apache Spark
/ GraphX. We conduct extensive experiments on real datasets, and show that
Portal scales.


  Recent work is reviewed which suggests that certain universal quantities,
defined for all Calabi-Yau manifolds, exhibit a specific behavior which is not
present for general K\"ahler manifolds. The variables in question, natural from
a mathematical perspective, are of physical importance because they determine
aspects of the low-energy string physics in four dimensions, such as Yukawa
couplings and threshold corrections. It is shown that these quantities,
evaluated on the complete class of Calabi-Yau hypersurfaces in weighted
projective 4-space, exhibit scaling behavior with respect to a new scaling
variable. (To appear in Mirror Symmetry II.)


  A speaker cluster-based speaker adaptive training (SAT) method under deep
neural network-hidden Markov model (DNN-HMM) framework is presented in this
paper. During training, speakers that are acoustically adjacent to each other
are hierarchically clustered using an i-vector based distance metric. DNNs with
speaker dependent layers are then adaptively trained for each cluster of
speakers. Before decoding starts, an unseen speaker in test set is matched to
the closest speaker cluster through comparing i-vector based distances. The
previously trained DNN of the matched speaker cluster is used for decoding
utterances of the test speaker. The performance of the proposed method on a
large vocabulary spontaneous speech recognition task is evaluated on a training
set of with 1500 hours of speech, and a test set of 24 speakers with 1774
utterances. Comparing to a speaker independent DNN with a baseline word error
rate of 11.6%, a relative 6.8% reduction in word error rate is observed from
the proposed method.


  We have carried out numerical simulation based on the equations of radiation
magnetohydrodynamics to study the interaction of solar granules and small-scale
magnetic fields in photospheric regions with various magnetic fluxes. Four
sequences of 2D time-dependent models were calculated for photospheric regions
with average vertical magnetic fluxes of 0, 10, 20, and 30 mT. The models
exhibit no substantial variations in their temperature structure with varying
average field strength, while the density and gas pressure profiles display
gross changes. The solar granulation brightness field also varies substantially
with magnetic flux. The contribution of the small-scale component to the
intensity power spectrum increases with average field strength, whereas the
large-scale component (of about a granule size) contributes less, the total rms
intensity fluctuations being approximately the same. Thus the observed decrease
in rms intensity fluctuations with growing average magnetic flux can be
interpreted as smoothing of the small-scale component in the power spectrum by
the modulation transfer function of the telescope.


  We discuss the existence of knot solitons (Hopfions) in a
Skryme-Faddeev-Niemi-type model on the target space $SU(3)/U(1)^2$, which can
be viewed as an effective theory of both the $SU(3)$ Yang-Mills theory and the
$SU(3)$ anti-ferromagnetic Heisenberg model. We derive the knot solitons with
two different types of ansatz: the first is a trivial embedding configuration
of $SU(2)$ into $SU(3)$, and the second is a non-embedding configuration that
can be generated through the B\"{a}cklund transformation. The resulting
Euler-Lagrange equations for both ansatz reduce exactly to those of the $CP^1$
Skyrme-Faddeev-Niemi model. We also examine some quantum aspects of the
solutions using the collective coordinate zero-mode quantization method.


  The search for a physical model which explains the observed recent
acceleration of the universe is a compelling task of modern fundamental
cosmology. Recently Fernandes \textit{et al.} presented low redshift
observational constraints on a scale invariant model by Maeder.
Phenomenologically this can be interpreted as a bimetric theory with a
time-dependent cosmological constant. It was shown that a matter density
$\Omega_m\sim0.3$ is a poor fit to the data, and the best-fit model would
require a fluid with a much smaller density and a significantly positive
equation of state parameter. This model is a particular case of an earlier and
broader class of models by Canuto \textit{et al.}, which we study here.
Specifically, we consider it in two distinct scenarios: as a genuine
alternative to $\Lambda$CDM (i.e., without any cosmological constant) and as a
parametric extension thereof (where both a cosmological constant and the new
mechanism can coexist, and the relative contributions of both are determined by
the data). We find that the first scenario can in principle fit the
low-redshift data (but a good fit would require values of model parameters,
such as the matter equation of state, in conflict with other data), while in
the second one the deviation from $\Lambda$CDM is constrained to be small.


  We present Human and Geometric Importance SLAM (HGI-SLAM), a novel approach
to loop closure using salient and geometric features. Loop closure is a key
element of SLAM, with many established methods for this problem. However,
current methods are narrow, using either geometric or salient based features.
We merge their successes into a model that outperforms both types of methods
alone. Our method utilizes inexpensive monocular cameras and does not depend on
depth sensors nor Lidar. HGI-SLAM utilizes geometric and salient features,
processes them into descriptors, and optimizes them for a bag of words
algorithm. By using a concurrent thread and combing our loop closure detection
with ORB-SLAM2, our system is a complete SLAM framework. We present extensive
evaluations of HGI loop detection and HGI-SLAM on the KITTI and EuRoC datasets.
We also provide a qualitative analysis of our features. Our method runs in real
time, and is robust to large viewpoint changes while staying accurate in
organic environments. HGI-SLAM is an end-to-end SLAM system that only requires
monocular vision and is comparable in performance to state-of-the-art SLAM
methods.


  Heat-Assisted Magnetic Recording (HAMR) has promise to allow for data writing
in hard disks of beyond 1 Tb/in2 areal density, by temporarily heating the area
of a single datum to its Curie temperature while simultaneously applying a
magnetic field from a conventional electromagnet. However, the metallic optical
antenna or near-field transducer (NFT) used to apply the nano-scale heating to
the media may self-heat by several hundreds of degrees. With the NFT reaching
such extreme temperatures, demonstrations of HAMR technology observe write-head
lifetimes that are orders of magnitude less than that required for commercial
product. Hence, thermal reliability of the NFT is of upmost importance. In this
paper, we first derive fundamental limits on the self-heating of the NFT to
drive design choices for low temperature operation. Next, we employ Inverse
Electromagnetic Design software, which provides deterministic gradient-based
optimization of electromagnetic structures with thousands of degrees of freedom
using the adjoint method. The Inverse Design software solves for unintuitive
solutions to Maxwells equations, and we present computationally generated
structures for HAMR write-heads that offer a 40 percent or 170 C reduction in
NFT self-heating compared to typical industry designs.


  We study the exponential map of group of volume-preserving diffeomorphisms on
closed orientable surfaces via the vorticity formulation of the incompressible
Euler equation. We present an alternative, fluid dynamical proof of the theorem
of Ebin--Misio\l{}ek--Preston: the exponential is a nonlinear Fredholm mapping
of index zero. We extend Shnirelman's rigidity result for the exponential map
from 2-dimensional flat torus to arbitrary orientable closed surfaces. That is,
we prove that the exponential map is Fredholm quasiregular.


  We develop a statistical estimator to infer the redshift probability
distribution of a photometric sample of galaxies from its angular
cross-correlation in redshift bins with an overlapping spectroscopic sample.
This estimator is a minimum variance weighted quadratic function of the data: a
quadratic estimator. This extends and modifies the methodology presented by
McQuinn & White (2013). The derived source redshift distribution is degenerate
with the source galaxy bias, which must be constrained via additional
assumptions. We apply this estimator to constrain source galaxy redshift
distributions in the Kilo-Degree imaging survey through cross-correlation with
the spectroscopic 2-degree Field Lensing Survey, presenting results first as a
binned step-wise distribution in the range z < 0.8, and then building a
continuous distribution using a Gaussian process model. We demonstrate the
robustness of our methodology using mock catalogues constructed from N-body
simulations, and comparisons with other techniques for inferring the redshift
distribution.


  The Simons Observatory will map the temperature and polarization over half of
the sky, at millimeter wavelengths in six spectral bands from the Atacama
Desert in Chile. These data will provide new insights into the genesis,
content, and history of our Universe; the astrophysics of galaxies and galaxy
clusters; objects in our solar system; and time-varying astrophysical
phenomena. This ambitious new instrument suite, initially comprising three 0.5
m small-aperture telescopes and one 6 m large aperture telescope, is designed
using a common combination of new technologies and new implementations to
realize an observatory significantly more capable than the previous generation.
In this paper, we present the pre-deployment performance of the first
mid-frequency "optics tube" which will be fielded on the large aperture
telescope with sensitivity to the 90 and 150 GHz spectral bands. This optics
tube contains lenses, filters, detectors, and readout components, all of which
operate at cryogenic temperatures. It is one of seven that form the core of the
large aperture telescope receiver in its initial deployment. We describe this
optics tube, including details of comprehensive testing methods, new techniques
for beam and passband characterization, and its measured performance. The
performance metrics include beams, optical efficiency, passbands, and forecasts
for the on-sky performance of the system. We forecast a sensitivity that
exceeds the requirements of the large aperture telescope with greater than 30%
margin in each spectral band, and predict that the instrument will realize
diffraction-limited performance and the expected detector passbands.


  Recommender Systems are tools that improve how users find relevant
information in web systems, so they do not face too much information. In order
to generate better recommendations, the context of information should be used
in the recommendation process. Context-Aware Recommender Systems were created,
accomplishing state-of-the-art results and improving traditional recommender
systems. There are many approaches to build recommender systems, and two of the
most prominent advances in area have been the use of Embeddings to represent
the data in the recommender system, and the use of Deep Learning architectures
to generate the recommendations to the user. A systematic review adopts a
formal and systematic method to perform a bibliographic review, and it is used
to identify and evaluate all the research in certain area of study, by
analyzing the relevant research published. A systematic review was conducted to
understand how the Deep Learning and Embeddings techniques are being applied to
improve Context-Aware Recommender Systems. We summarized the architectures that
are used to create those and the domains that they are used.


  We find the Seiberg-Witten geometry for four dimensional N=2 supersymmetric
E_6 gauge theories with massless fundamental hypermultiplets, by geometrically
embedding them in type II string theories compactified on Calabi-Yau
threefolds. The resulting geometry completely agrees with that of recent works,
which are based on the technique of N=1 confining phase superpotentials. We
also derive the Seiberg-Witten geometry for E_7 gauge theories with massive
fundamental hypermultiplets.


  A Verbal Autopsy is the record of an interview about the circumstances of an
uncertified death. In developing countries, if a death occurs away from health
facilities, a field-worker interviews a relative of the deceased about the
circumstances of the death; this Verbal Autopsy can be reviewed off-site. We
report on a comparative study of the processes involved in Text Classification
applied to classifying Cause of Death: feature value representation; machine
learning classification algorithms; and feature reduction strategies in order
to identify the suitable approaches applicable to the classification of Verbal
Autopsy text. We demonstrate that normalised term frequency and the standard
TFiDF achieve comparable performance across a number of classifiers. The
results also show Support Vector Machine is superior to other classification
algorithms employed in this research. Finally, we demonstrate the effectiveness
of employing a "locally-semi-supervised" feature reduction strategy in order to
increase performance accuracy.


  This work investigates hot quark matter under the thermodynamic conditions
characteristic of a binary neutron star (BNS) merger remnants. We use the
density-dependent quark mass model (DDQM) to access the microscopic nuclear
equation of state (EoS). The strange quark matter (SQM) is studied at finite
temperature and entropy in the presence of electrons and muons and their
neutrinos to simulate the BNS merger conditions. We observe that as the entropy
of the SQM increases, the merger remnant becomes more massive, and increases in
size whereas the neutrino population also increases. In the fixed temperature
case, on the other hand, we observe that the entropy spreads from the surface
towards the center of the remnant. We determine the particle distribution in
the remnants' core, the remnant's structure, the temperature profile, sound
velocity, and the polytropic index and discuss their effects. The strange quark
(SQ) remnants satisfy the $2\,{\rm M_\odot}$ mass constraint associated with
neutron stars (NS).


  In Vehicle-to-Everything networks that involve multi-hop communication, the
Road Side Units (RSUs) typically aim to collect location information from the
participating vehicles to provide security and network diagnostics features.
While the vehicles commonly use the Global Positioning System (GPS) for
navigation, they may refrain from sharing their precise GPS coordinates with
the RSUs due to privacy concerns. Therefore, to jointly address the high
localization requirements by the RSUs as well as the vehicles' privacy, we
present a novel spatial-provenance framework wherein each vehicle uses Bloom
filters to embed their partial location information when forwarding the
packets. In this framework, the RSUs and the vehicles agree upon fragmenting
the coverage area into several smaller regions so that the vehicles can embed
the identity of their regions through Bloom filters. Given the probabilistic
nature of Bloom filters, we derive an analytical expression on the error-rates
in provenance recovery and then pose an optimization problem to choose the
underlying parameters. With the help of extensive simulation results, we show
that our method offers near-optimal Bloom filter parameters in learning spatial
provenance. Some interesting trade-offs between the communication-overhead,
spatial privacy of the vehicles and the error rates in provenance recovery are
also discussed.


  We study a scheme to implement an asymptotic unitary 3-design. The scheme
implements a random Pauli once followed by the implementation of a random
transvection Clifford by using state twirling. Thus the scheme is implemented
in the form of a quantum channel. We show that when this scheme is implemented
$k$ times, then, in the $k \rightarrow \infty$ limit, the overall scheme
implements a unitary $3$-design. This is proved by studying the
eigendecomposition of the scheme: the $+1$ eigenspace of the scheme coincides
with that of an exact unitary $3$-design, and the remaining eigenvalues are
bounded by a constant. Using this we prove that the scheme has to be
implemented approximately $\mathcal{O}(m + \log 1/\epsilon)$ times to obtain an
$\epsilon$-approximate unitary $3$-design, where $m$ is the number of qubits,
and $\epsilon$ is the diamond-norm distance of the exact unitary $3$-design.
Also, the scheme implements an asymptotic unitary $2$-design with the following
convergence rate: it has to be sampled $\mathcal{O}(\log 1/\epsilon)$ times to
be an $\epsilon$-approximate unitary $2$-design. Since transvection Cliffords
are a conjugacy class of the Clifford group, the eigenspaces of the scheme's
quantum channel coincide with the irreducible invariant subspaces of the
adjoint representation of the Clifford group. Some of the subrepresentations we
obtain are the same as were obtained in J. Math. Phys. 59, 072201 (2018),
whereas the remaining are new invariant subspaces. Thus we obtain a partial
decomposition of the adjoint representation for $3$ copies for the Clifford
group. Thus, aside from providing a scheme for the implementation of unitary
$3$-design, this work is of interest for studying representation theory of the
Clifford group, and the potential applications of this topic. The paper ends
with open questions regarding the scheme and representation theory of the
Clifford group.


  We consider protocols where users communicate with multiple servers to
perform a computation on the users' data. An adversary exerts semi-honest
control over many of the parties but its view is differentially private with
respect to honest users. Prior work described protocols that required multiple
rounds of interaction or offered privacy against a computationally bounded
adversary. Our work presents limitations of non-interactive protocols that
offer privacy against unbounded adversaries. We show these protocols demand
exponentially more samples for some learning and estimation tasks than
centrally private counterparts. This means performing as well as the central
model requires interactivity or computational differential privacy, or both.


  The KELT project was originally designed as a small-aperture, wide-field
photometric survey that would be optimally sensitive to planets transiting
bright (V~8-10) stars. This magnitude range corresponded to the gap between the
faint magnitude limit where radial velocity surveys were complete, and the
bright magnitude limit for transiting planet hosts routinely found by dedicated
ground-based transit surveys. Malmquist bias and other factors have also led
the KELT survey to focus on discovering planets transiting relatively hot host
stars as well. To date, the survey has discovered 22 transiting hot Jupiters,
including some of the brightest transiting planet host stars known to date.
Over half of these planets transit rapidly-rotating stars with Teff > 6250 K,
which had been largely eschewed by both radial velocity and transit surveys,
due to the challenge of obtaining precision radial velocities for such stars.
The KELT survey has developed a protocol and specialized software for
confirming transiting planets around stars rotating as rapidly as ~200 km/s.
This chapter reviews KELT planet discoveries, describes their scientific value,
and also briefly discusses the non-exoplanet science produced by the KELT
project, especially long-timescale phenomena and preparations for the TESS
mission.


  Pre-main sequence (PMS) stars of mass $\gtrsim0.35\,{\rm M}_\odot$ transition
from hosting fully convective interiors to configurations with a radiative core
and outer convective envelope during their gravitational contraction. This
stellar structure change influences the external magnetic field topology and,
as we demonstrate herein, affects the coronal X-ray emission as a stellar
analog of the solar tachocline develops. We have combined archival X-ray,
spectroscopic, and photometric data for $\sim$1000 PMS stars from five of the
best studied star forming regions; the ONC, NGC 2264, IC 348, NGC 2362, and NGC
6530. Using a modern, PMS calibrated, spectral type-to-effective temperature
and intrinsic colour scale, we deredden the photometry using colours
appropriate for each spectral type, and determine the stellar mass, age, and
internal structure consistently for the entire sample. We find that PMS stars
on Henyey tracks have, on average, lower fractional X-ray luminosities ($L_{\rm
X}/L_\ast$) than those on Hayashi tracks, where this effect is driven by
changes in $L_{\rm X}$. X-ray emission decays faster with age for higher mass
PMS stars. There is a strong correlation between $L_\ast$ and $L_{\rm X}$ for
Hayashi track stars but no correlation for Henyey track stars. There is no
correlation between $L_{\rm X}$ and radiative core mass or radius. However, the
longer stars have spent with radiative cores, the less X-ray luminous they
become. The decay of coronal X-ray emission from young early K to late G-type
PMS stars, the progenitors of main sequence A-type stars, is consistent with
the dearth of X-ray detections of the latter.


  Soft limits of massless S-matrix are known to reflect symmetries of the
theory. In particular for theories with Goldstone bosons, the double-soft limit
of scalars reveals the coset structure of the vacuum manifold. In this letter,
we propose that such universal double-soft behavior is not only true for
scalars, but also for spin-1/2 particles in four dimensions and fermions in
three dimensions. We first consider Akulov-Volkov theory, and demonstrate the
double soft-limit of goldstinos yields the supersymmetry algebra. More
surprisingly we also find amplitudes in 3<N<=8 supergravity theories in four
dimensions as well as N=16 supergravity in three dimensions behave universally
in the double-soft-fermion limit, analogue to the scalar ones. The validity of
the new soft theorems at loop level is also studied. The results for
supergravity are beyond what is implied by SUSY Ward identities, and may impose
non-trivial constraints on the possible counter terms for supergravity
theories.


  Quantum emitters in hexagonal boron nitride (hBN) are promising building
blocks for the realization of integrated quantum photonic systems. However,
their spectral inhomogeneity currently limits their potential applications.
Here, we apply tensile strain to quantum emitters embedded in few-layer hBN
films and realize both red and blue spectral shifts with tuning magnitudes up
to 65 meV, a record for any two-dimensional quantum source. We demonstrate
reversible tuning of the emission and related photophysical properties. We also
observe rotation of the optical dipole in response to strain, suggesting the
presence of a second excited state. We derive a theoretical model to describe
strain-based tuning in hBN, and the rotation of the optical dipole. Our work
demonstrates the immense potential for strain tuning of quantum emitters in
layered materials to enable their employment in scalable quantum photonic
networks.


  In this paper, we prove a conjecture of Wei Zhang on comparison of certain
local spherical characters from which we draw some consequences for the
Ichino-Ikeda conjecture for unitary groups.


  Large Language Models (LLMs) have acquired ubiquitous attention for their
performances across diverse domains. Our study here searches through LLMs'
cognitive abilities and confidence dynamics. We dive deep into understanding
the alignment between their self-assessed confidence and actual performance. We
exploit these models with diverse sets of questionnaires and real-world
scenarios and extract how LLMs exhibit confidence in their responses. Our
findings reveal intriguing instances where models demonstrate high confidence
even when they answer incorrectly. This is reminiscent of the Dunning-Kruger
effect observed in human psychology. In contrast, there are cases where models
exhibit low confidence with correct answers revealing potential underestimation
biases. Our results underscore the need for a deeper understanding of their
cognitive processes. By examining the nuances of LLMs' self-assessment
mechanism, this investigation provides noteworthy revelations that serve to
advance the functionalities and broaden the potential applications of these
formidable language models.


  Recent measurements in the charm sector are reviewed, concentrating on
results which are sensitive to New Physics effects. The scope of the
presentation includes D0-D0bar mixing searches, a CPT / Lorentz invariance
study, and a range of searches for rare and forbidden decays. Results from the
BaBar, Belle, CDF, CLEO, and FOCUS collaborations are presented, including an
important first observation.


  We analyze a random walk strategy on undirected regular networks involving
power matrix functions of the type $L^{\frac{\alpha}{2}}$ where $L$ indicates a
`simple' Laplacian matrix. We refer such walks to as `Fractional Random Walks'
with admissible interval $0<\alpha \leq 2$. We deduce for the Fractional Random
Walk probability generating functions (network Green's functions). From these
analytical results we establish a generalization of Polya's recurrence theorem
for Fractional Random Walks on $d$-dimensional infinite lattices: The
Fractional Random Walk is transient for dimensions $d > \alpha$ (recurrent for
$d\leq\alpha$) of the lattice. As a consequence for $0<\alpha< 1$ the
Fractional Random Walk is transient for all lattice dimensions $d=1,2,..$ and
in the range $1\leq\alpha < 2$ for dimensions $d\geq 2$. Finally, for
$\alpha=2$ Polya's classical recurrence theorem is recovered, namely the walk
is transient only for lattice dimensions $d\geq 3$. The generalization of
Polya's recurrence theorem remains valid for the class of random walks with
L\'evy flight asymptotics for long-range steps. We also analyze for the
Fractional Random Walk mean first passage probabilities, mean first passage
times, and global mean first passage times (Kemeny constant). For the infinite
1D lattice (infinite ring) we obtain for the transient regime $0<\alpha<1$
closed form expressions for the fractional lattice Green's function matrix
containing the escape and ever passage probabilities. The ever passage
probabilities fulfill Riesz potential power law decay asymptotic behavior for
nodes far from the departure node. The non-locality of the Fractional Random
Walk is generated by the non-diagonality of the fractional Laplacian matrix
with L\'evy type heavy tailed inverse power law decay for the probability of
long-range moves.


  Gromov-Wasserstein (GW) is a powerful tool to compare probability measures
whose supports are in different metric spaces. GW suffers however from a
computational drawback since it requires to solve a complex non-convex
quadratic program. We consider in this work a specific family of cost metrics,
namely \textit{tree metrics} for a space of supports of each probability
measure, and aim for developing efficient and scalable discrepancies between
the probability measures. By leveraging a tree structure, we propose to align
\textit{flows} from a root to each support instead of pair-wise tree metrics of
supports, i.e., flows from a support to another, in GW. Consequently, we
propose a novel discrepancy, named Flow-based Alignment (\FlowAlign), by
matching the flows of the probability measures. We show that \FlowAlign~shares
a similar structure as a univariate optimal transport distance. Therefore,
\FlowAlign~is fast for computation and scalable for large-scale applications.
By further exploring tree structures, we propose a variant of \FlowAlign, named
Depth-based Alignment (\DepthAlign), by aligning the flows hierarchically along
each depth level of the tree structures. Theoretically, we prove that both
\FlowAlign~and \DepthAlign~are pseudo-distances. Moreover, we also derive
tree-sliced variants, computed by averaging the corresponding \FlowAlign~/
\DepthAlign~using random tree metrics, built adaptively in spaces of supports.
Empirically, we test our proposed discrepancies against other baselines on some
benchmark tasks.


  In this paper, we build a new test of rational expectations based on the
marginal distributions of realizations and subjective beliefs. This test is
widely applicable, including in the common situation where realizations and
beliefs are observed in two different datasets that cannot be matched. We show
that whether one can rationalize rational expectations is equivalent to the
distribution of realizations being a mean-preserving spread of the distribution
of beliefs. The null hypothesis can then be rewritten as a system of many
moment inequality and equality constraints, for which tests have been recently
developed in the literature. The test is robust to measurement errors under
some restrictions and can be extended to account for aggregate shocks. Finally,
we apply our methodology to test for rational expectations about future
earnings. While individuals tend to be right on average about their future
earnings, our test strongly rejects rational expectations.


  Axions are hypothetical particles that may explain the observed dark matter
(DM) density and the non-observation of a neutron electric dipole moment. An
increasing number of axion laboratory searches are underway worldwide, but
these efforts are made difficult by the fact that the axion mass is largely
unconstrained. If the axion is generated after inflation there is a unique mass
that gives rise to the observed DM abundance; due to nonlinearities and
topological defects known as strings, computing this mass accurately has been a
challenge for four decades. Recent works, making use of large static lattice
simulations, have led to largely disparate predictions for the axion mass,
spanning the range from 25 microelectronvolts to over 500 microelectronvolts.
In this work we show that adaptive mesh refinement (AMR) simulations are better
suited for axion cosmology than the previously-used static lattice simulations
because only the string cores require high spatial resolution. Using dedicated
AMR simulations we obtain an over three order of magnitude leap in dynamic
range and provide evidence that axion strings radiate their energy with a
scale-invariant spectrum, to within $\sim$5% precision, leading to a mass
prediction in the range (40,180) microelectronvolts.


  We derive a Markovian master equation for driven open quantum systems based
on the Lewis-Riesenfeld invariants theory, which is available for arbitrary
driving protocols.The role of the Lewis-Riesenfeld invariants is to help us
bypass the time-ordering obstacle in expanding the propagator of the free
dynamics, such that the Lindblad operators in our driven-Markovian master
equation can be determined easily. We also illustrate that, for the driven open
quantum systems, the spontaneous emission and the thermal excitation induce the
transitions between eigenstates of the Lewis-Riesenfeld invariant, but not the
system Hamiltonian's. As an example, we present the driven-Markovian master
equation for a driven two-level system coupled to a heat reservoir. By
comparing to the exactly solvable models, the availability of the
driven-Markovian master equation is verified. Meanwhile, the adiabatic limit
and inertial limit of the driven-Markovian master equation are also discussed,
which result in the same Markovian master equations as those presented before
in the corresponding limits.


  We study the behavior of matrix string theory in the strong coupling region,
where it is expected to reduce to discrete light-cone type IIA superstring. In
the large $N$ limit, the reduction corresponds to the double-dimensional
reduction from wrapped supermembranes on $R^{10}\times S^1$ to type IIA
superstrings on $R^{10}$ in the light-cone gauge, which is shown classically,
however it is not obvious quantum mechanically. We analyze the problem in
matrix string theory by using the strong coupling ($1/g$) expansion. We find
that the quantum corrections do not cancel out at $\mathcal{O}(1/g^2)$.
Detailed calculations can be seen in Ref.\cite{UY}.


  In this paper we consider connected locally $G$-arc-transitive graphs with
vertices of valence 3 and 4, such that the kernel $G_{uv}^{[1]}$ of the action
of an edge-stabiliser on the neighourhood $\Gamma(u) \cup \Gamma(v)$ is
trivial. We find nineteen finitely presented groups with the property that any
such group $G$ is a quotient of one of these groups. As an application, we
enumerate all connected locally arc-transitive graphs of valence ${3,4}$ on at
most 350 vertices whose automorphism group contains a locally arc-transitive
subgroup $G$ with $G_{uv}^{[1]} = 1$.


  Private blockchain is driving the creation of business networks, resulting in
the creation of new value or new business models to the enterprises
participating in the network. Such business networks form when enterprises come
together to derive value through a network which is greater than the value that
can be derived solely by any single company. This results in a setting that
combines both competitive and cooperative behavior, and which we call strategic
coopetition. Traditionally, cooperative and competitive behavior have been
analyzed separately in game theory. In this article, we provide a formal model
enabling to jointly analyze these different types of behaviors and the
interdependencies between them. Using this model, we formally demonstrate and
analyze the incentives for both cooperative and competitive behavior.


  This study probes the chemical abundances of the neutron-capture elements
cerium and neodymium in the inner Milky Way from an analysis of a sample of
$\sim$2000 stars in the Galactic Bulge/bar spatially contained within
$|X_{Gal}|<$5 kpc, $|Y_{Gal}|<$3.5 kpc, and $|Z_{Gal}|<$1 kpc, and spanning
metallicities between $-$2.0$\lesssim$[Fe/H]$\lesssim$+0.5. We classify the
sample stars into low- or high-[Mg/Fe] populations and find that, in general,
values of [Ce/Fe] and [Nd/Fe] increase as the metallicity decreases for the
low- and high-[Mg/Fe] populations. Ce abundances show a more complex variation
across the metallicity range of our Bulge-bar sample when compared to Nd, with
the r-process dominating the production of neutron-capture elements in the
high-[Mg/Fe] population ([Ce/Nd]$<$0.0). We find a spatial chemical dependence
of Ce and Nd abundances for our sample of Bulge-bar stars, with low- and
high-[Mg/Fe] populations displaying a distinct abundance distribution. In the
region close to the center of the MW, the low-[Mg/Fe] population is dominated
by stars with low [Ce/Fe], [Ce/Mg], [Nd/Mg], [Nd/Fe], and [Ce/Nd] ratios. The
low [Ce/Nd] ratio indicates a significant contribution in this central region
from r-process yields for the low-[Mg/Fe] population. The chemical pattern of
the most metal-poor stars in our sample suggests an early chemical enrichment
of the Bulge dominated by yields from core-collapse supernovae and r-process
astrophysical sites, such as magneto-rotational supernovae.


  A direct numerical simulation (DNS) of a channel flow with one curved surface
was performed at moderate Reynolds number (Re_tau = 395 at the inlet). The
adverse pressure gradient was obtained by a wall curvature through a
mathematical mapping from physical coordinates to Cartesian ones. The code,
using spectral spanwise and normal discretization, combines the advantage of a
good accuracy with a fast integration procedure compared to standard numerical
procedures for complex geometries. The turbulent flow slightly separates on the
profile at the lower curved wall and is at the onset of separation at the
opposite flat wall. The thin separation bubble is characterized with a reversal
flow fraction. Intense vortices are generated near the separation line on the
lower wall but also at the upper wall. Turbulent normal stresses and kinetic
energy budget are investigated along the channel.


  This papers deals with a construction and convergence analysis of a finite
difference scheme for solving time-fractional porous medium equation. The
governing equation exhibits both nonlocal and nonlinear behaviour making the
numerical computations challenging. Our strategy is to reduce the problem into
a single one-dimensional Volterra integral equation for the self-similar
solution and then to apply the discretization. The main difficulty arises due
to the non-Lipschitzian behaviour of the equation's nonlinearity. By the
analysis of the recurrence relation for the error we are able to prove that
there exists a family of finite difference methods that is convergent for a
large subset of the parameter space. We illustrate our results with a concrete
example of a method based on the midpoint quadrature.


  The most startling examples of collective animal behaviour are provided by
very large and cohesive groups moving in three dimensions. Paradigmatic
examples are bird flocks, fish schools and insect swarms. However, because of
the sheer technical difficulty of obtaining 3D data, empirical studies
conducted to date have only considered loose groups of a few tens of animals.
Moreover, these studies were very seldom conducted in the field. Recently the
STARFLAG project achieved the 3D reconstruction of thousands of birds under
field conditions, thus opening the way to a new generation of quantitative
studies of collective animal behaviour. Here, we review the main technical
problems in 3D data collection of large animal groups and we outline some of
the methodological solutions adopted by the STARFLAG project. In particular, we
explain how to solve the stereoscopic correspondence - or matching - problem,
which was the major bottleneck of all 3D studies in the past.


  The Hopf Lemma for second order elliptic operators is proved to hold in
domains with $C^{1,\alpha}$, and even less regular, boundaries. It need not
hold for $C^1$ boundaries. Corresponding results are proved for second order
parabolic operators.


  We propose and experimentally demonstrate a reactive planning system for
bipedal robots on unexplored, challenging terrains. The system consists of a
low-frequency planning thread (5 Hz) to find an asymptotically optimal path and
a high-frequency reactive thread (300 Hz) to accommodate robot deviation. The
planning thread includes: a multi-layer local map to compute traversability for
the robot on the terrain; an anytime omnidirectional Control Lyapunov Function
(CLF) for use with a Rapidly Exploring Random Tree Star (RRT*) that generates a
vector field for specifying motion between nodes; a sub-goal finder when the
final goal is outside of the current map; and a finite-state machine to handle
high-level mission decisions. The system also includes a reactive thread to
obviate the non-smooth motions that arise with traditional RRT* algorithms when
performing path following. The reactive thread copes with robot deviation while
eliminating non-smooth motions via a vector field (defined by a closed-loop
feedback policy) that provides real-time control commands to the robot's gait
controller as a function of instantaneous robot pose. The system is evaluated
on various challenging outdoor terrains and cluttered indoor scenes in both
simulation and experiment on Cassie Blue, a bipedal robot with 20 degrees of
freedom. All implementations are coded in C++ with the Robot Operating System
(ROS) and are available at
https://github.com/UMich-BipedLab/CLF_reactive_planning_system.


  While neural architecture search methods have been successful in previous
years and led to new state-of-the-art performance on various problems, they
have also been criticized for being unstable, being highly sensitive with
respect to their hyperparameters, and often not performing better than random
search. To shed some light on this issue, we discuss some practical
considerations that help improve the stability, efficiency and overall
performance.


  We study optimal control strategies to optimize the relaxation rate towards
the fixed point of a quantum system in the presence of a non-Markovian
dissipative bath. Contrary to naive expectations that suggest that memory
effects might be exploited to improve optimal control effectiveness,
non-Markovian effects influence the optimal strategy in a non trivial way: we
present a necessary condition to be satisfied so that the effectiveness of
optimal control is enhanced by non-Markovianity subject to suitable unitary
controls. For illustration, we specialize our findings for the case of the
dynamics of single qubit amplitude damping channels. The optimal control
strategy presented here can be used to implement optimal cooling processes in
quantum technologies and may have implications in quantum thermodynamics when
assessing the efficiency of thermal micro-machines.


  The Optimal Optical Coronagraph (OOC) Workshop held at the Lorentz Center in
September 2017 in Leiden, the Netherlands, gathered a diverse group of 25
researchers working on exoplanet instrumentation to stimulate the emergence and
sharing of new ideas. In this second installment of a series of three papers
summarizing the outcomes of the OOC workshop (see
also~\citenum{ruane2018,snik2018}), we present an overview of common path
wavefront sensing/control and Coherent Differential Imaging techniques,
highlight the latest results, and expose their relative strengths and
weaknesses. We layout critical milestones for the field with the aim of
enhancing future ground/space based high contrast imaging platforms. Techniques
like these will help to bridge the daunting contrast gap required to image a
terrestrial planet in the zone where it can retain liquid water, in reflected
light around a G type star from space.


  Motivated by potential financial gain, companies may hire fraudster groups to
write fake reviews to either demote competitors or promote their own
businesses. Such groups are considerably more successful in misleading
customers, as people are more likely to be influenced by the opinion of a large
group. To detect such groups, a common model is to represent fraudster groups'
static networks, consequently overlooking the longitudinal behavior of a
reviewer thus the dynamics of co-review relations among reviewers in a group.
Hence, these approaches are incapable of excluding outlier reviewers, which are
fraudsters intentionally camouflaging themselves in a group and genuine
reviewers happen to co-review in fraudster groups. To address this issue, in
this work, we propose to first capitalize on the effectiveness of the HIN-RNN
in both reviewers' representation learning while capturing the collaboration
between reviewers, we first utilize the HIN-RNN to model the co-review
relations of reviewers in a group in a fixed time window of 28 days. We refer
to this as spatial relation learning representation to signify the
generalisability of this work to other networked scenarios. Then we use an RNN
on the spatial relations to predict the spatio-temporal relations of reviewers
in the group. In the third step, a Graph Convolution Network (GCN) refines the
reviewers' vector representations using these predicted relations. These
refined representations are then used to remove outlier reviewers. The average
of the remaining reviewers' representation is then fed to a simple fully
connected layer to predict if the group is a fraudster group or not. Exhaustive
experiments of the proposed approach showed a 5% (4%), 12% (5%), 12% (5%)
improvement over three of the most recent approaches on precision, recall, and
F1-value over the Yelp (Amazon) dataset, respectively.


  The evolution of the B-band galaxy luminosity function is measured using a
sample of more than 11,000 galaxies with spectroscopic redshifts from the DEEP2
Redshift Survey. The rest-frame M_B versus U-B color-magnitude diagram of DEEP2
galaxies shows that the color-magnitude bi-modality seen in galaxies locally is
still present at redshifts z > 1. Dividing the sample at the trough of this
color bimodality into predominantly red and blue galaxies, we find that the
luminosity function of each galaxy color type evolves differently. Blue counts
tend to shift to brighter magnitudes at constant number density, while the red
counts remain largely constant at a fixed absolute magnitude. Using Schechter
functions with fixed faint-end slopes we find that M*_B for blue galaxies
brightens by ~ 1.3 magnitudes per unit redshift, with no significant evolution
in number density. For red galaxies M*_B brightens somewhat less with redshift,
while the formal value of phi* declines. When the population of blue galaxies
is subdivided into two halves using the rest-frame color as the criterion, the
measured evolution of both blue subpopulations is very similar.


  A new weak Galerkin (WG) finite element method for solving the second-order
elliptic problems on polygonal meshes by using polynomials of boundary
continuity is introduced and analyzed. The WG method is utilizing weak
functions and their weak derivatives which can be approximated by polynomials
in different combination of polynomial spaces. Different combination gives rise
to different weak Galerkin finite element methods, which makes WG methods
highly flexible and efficient in practical computation. This paper explores the
possibility of certain combination of polynomial spaces that minimize the
degree of freedom in the numerical scheme, yet without losing the accuracy of
the numerical approximation. Error estimates of optimal order are established
for the corresponding WG approximations in both a discrete $H^1$ norm and the
standard $L^2$ norm. In addition, the paper also presents some numerical
experiments to demonstrate the power of the WG method. The numerical results
show a great promise of the robustness, reliability, flexibility and accuracy
of the WG method.


  We study the effect of thermalization on the rigidity of a randomly packed
soft repulsive sphere system around the jamming point by analyzing the
shear-modulus using the cloned liquid theory with the 1 step replica symmetry
breaking ansatz and molecular dynamics simulations. Contrarily to the usual
harmonic picture for solids, we found that the thermalized jamming system is
anomalously softer than at zero temperature such that the shear-modulus becomes
as small as the pressure down to vanishingly low temperatures.


  In order to ease the analysis of error propagation in neuromorphic computing
and to get a better understanding of spiking neural networks (SNN), we address
the problem of mathematical analysis of SNNs as endomorphisms that map spike
trains to spike trains. A central question is the adequate structure for a
space of spike trains and its implication for the design of error measurements
of SNNs including time delay, threshold deviations, and the design of the
reinitialization mode of the leaky-integrate-and-fire (LIF) neuron model. First
we identify the underlying topology by analyzing the closure of all
sub-threshold signals of a LIF model. For zero leakage this approach yields the
Alexiewicz topology, which we adopt to LIF neurons with arbitrary positive
leakage. As a result LIF can be understood as spike train quantization in the
corresponding norm. This way we obtain various error bounds and inequalities
such as a quasi isometry relation between incoming and outgoing spike trains.
Another result is a Lipschitz-style global upper bound for the error
propagation and a related resonance-type phenomenon.


  Tactile sensing is critical for robotic grasping and manipulation of objects
under visual occlusion. However, in contrast to simulations of robot arms and
cameras, current simulations of tactile sensors have limited accuracy, speed,
and utility. In this work, we develop an efficient 3D finite element method
(FEM) model of the SynTouch BioTac sensor using an open-access, GPU-based
robotics simulator. Our simulations closely reproduce results from an
experimentally-validated model in an industry-standard, CPU-based simulator,
but at 75x the speed. We then learn latent representations for simulated BioTac
deformations and real-world electrical output through self-supervision, as well
as projections between the latent spaces using a small supervised dataset.
Using these learned latent projections, we accurately synthesize real-world
BioTac electrical output and estimate contact patches, both for unseen contact
interactions. This work contributes an efficient, freely-accessible FEM model
of the BioTac and comprises one of the first efforts to combine
self-supervision, cross-modal transfer, and sim-to-real transfer for tactile
sensors.


  This paper explores the utilization of Temporal Graph Networks (TGN) for
financial anomaly detection, a pressing need in the era of fintech and
digitized financial transactions. We present a comprehensive framework that
leverages TGN, capable of capturing dynamic changes in edges within financial
networks, for fraud detection. Our study compares TGN's performance against
static Graph Neural Network (GNN) baselines, as well as cutting-edge hypergraph
neural network baselines using DGraph dataset for a realistic financial
context. Our results demonstrate that TGN significantly outperforms other
models in terms of AUC metrics. This superior performance underlines TGN's
potential as an effective tool for detecting financial fraud, showcasing its
ability to adapt to the dynamic and complex nature of modern financial systems.
We also experimented with various graph embedding modules within the TGN
framework and compared the effectiveness of each module. In conclusion, we
demonstrated that, even with variations within TGN, it is possible to achieve
good performance in the anomaly detection task.


  The von Neumann evolution equation for density matrix and the Moyal equation
for the Wigner function are mapped onto evolution equation for optical tomogram
of quantum state. The connection with known evolution equation for symplectic
tomogram of the quantum state is clarified. The stationary states corresponding
to quantum energy levels are associated with the probability representation of
the von Neumann and Moyal equations written for the optical tomograms.
Classical Liouville equation for optical tomogram is obtained. Example of
parametric oscillator is considered in detail.


  We classify the rational Cherednik algebras H_c(W) (and their spherical
subalgebras) up to isomorphism and Morita equivalence in case when W is the
symmetric group and `c' is a generic parameter value.


  We outline a general theory for the analysis of flow-distributed standing and
travelling wave patterns in one-dimensional, open plug-flows of oscillatory
chemical media. We treat both the amplitude and phase dynamics of small and
large-amplitude waves, considering both travelling and stationary waves on an
equal footing and emphasizing features that are generic to a variety of kinetic
models. We begin with a linear stability analysis for constant and periodic
boundary forcing, drawing attention to the implications for systems far from a
Hopf bifurcation. Among other results, we show that for systems far from a Hopf
bifurcation, the first absolutely unstable mode may be a stationary wave mode.
We then introduce a non-linear formalism for studying both travelling and
stationary waves and show that the wave forms and their amplitudes depend on a
single reduced transport parameter. Our formalism sheds light on cases where
neither the linearized analyis nor the kinematic theory of phase waves give an
adequate description, and it can be applied to study some of the more complex
types of bifurcations (Canards, period-doublings, etc.) in open flow systems.


  Constrained clustering has been well-studied for algorithms such as $K$-means
and hierarchical clustering. However, how to satisfy many constraints in these
algorithmic settings has been shown to be intractable. One alternative to
encode many constraints is to use spectral clustering, which remains a
developing area. In this paper, we propose a flexible framework for constrained
spectral clustering. In contrast to some previous efforts that implicitly
encode Must-Link and Cannot-Link constraints by modifying the graph Laplacian
or constraining the underlying eigenspace, we present a more natural and
principled formulation, which explicitly encodes the constraints as part of a
constrained optimization problem. Our method offers several practical
advantages: it can encode the degree of belief in Must-Link and Cannot-Link
constraints; it guarantees to lower-bound how well the given constraints are
satisfied using a user-specified threshold; it can be solved deterministically
in polynomial time through generalized eigendecomposition. Furthermore, by
inheriting the objective function from spectral clustering and encoding the
constraints explicitly, much of the existing analysis of unconstrained spectral
clustering techniques remains valid for our formulation. We validate the
effectiveness of our approach by empirical results on both artificial and real
datasets. We also demonstrate an innovative use of encoding large number of
constraints: transfer learning via constraints.


  I argue that black hole entropy counts only those states of a black hole that
can influence the outside, and attempt (with only partial success) to defend
this claim against various objections, all but one coming from string theory.
Implications for the nature of the Bekenstein bound are discussed, and in
particular the case for a holographic principle is challenged. Finally, a
generalization of black hole thermodynamics to "partial event horizons" in
general spacetimes without black holes is proposed.


  Quasicrystals lack translational symmetry, but can still exhibit long-ranged
order, promoting them to candidates for unconventional physics beyond the
paradigm of crystals.
  Here, we apply a real-space functional renormalization group approach to the
prototypical quasicrystalline Penrose tiling Hubbard model treating} competing
electronic instabilities in an unbiased, beyond-mean-field fashion.
{\color{red} Our work reveals a delicate interplay between charge and spin
degrees of freedom in quasicrystals}. Depending on the range of interactions
and hopping amplitudes, we unveil a rich phase diagram including
antiferromagnetic orderings, charge density waves and subleading,
superconducting pairing tendencies. For certain parameter regimes we find a
competition of phases, which is also common in crystals, but additionally
encounter phases coexisting in a spatially separated fashion and ordering
tendencies which mutually collaborate to enhance their strength. We therefore
establish that quasicrystalline structures open up a route towards this rich
ordering behavior uncommon to crystals and that an unbiased, beyond-mean-field
approach is essential to describe this physics of quasicrystals correctly.


  Let A = {rho_1,...,rho_n} be a given set of quantum states. We consider the
problem of finding necessary and sufficient conditions on another set B =
{sigma_1,...,sigma_n} that guarantee the existence of a physical transformation
taking rho_i to sigma_i for all i. Uhlmann has given an elegant such condition
when both sets comprise pure states. We give a simple proof of this condition
and develop some consequences. Then we consider multi-probabilistic
transformations between sets of pure states which leads to conditions for the
problem of transformability between A and B when one set is pure and the other
is arbitrary.


  Small aerosols drift down temperature or turbulence gradient since faster
particles fly longer distances before equilibration. That fundamental
phenomenon, called thermophoresis or turbophoresis, is widely encountered in
nature and used in industry. It is universally believed that particles moving
down the kinetic energy gradient must concentrate in minima (say, on walls in
turbulence). Here we show that this is incorrect: escaping minima is possible
for inertial particles whose time of equilibration is longer than the time to
reach the minimum. The best way out is always through: particles escape by
flying through minima or reflecting from walls. We solve the problem
analytically and find the phase transition as a sign change of the mean
velocity. That means separation: light particles concentrate in a minimum while
heavy particles spread away from it (gravity can reverse the effect). That
discovery changes understanding of that fundamental phenomenon and may find
numerous applications.


  The momentum-space topological invariants, which characterize the ground
state of the Standard Model, are continuous functions of two parameters,
generated by the hypercharge and by the weak charge. These invariants provide
the absence of the mass of the elementary fermionic particles in the symmetric
phase above the electroweak transition (the mass protection). All the
invariants become zero in the broken symmetry phase, as a result all the
elementary fermions become massive. Relation of the momentum-space invariants
to chiral anomaly is also discussed.


  Two of the most widely used Langevin integrators for molecular dynamics
simulations are the GROMACS Stochastic Dynamics (GSD) integrator and the
splitting method BAOAB. In this letter, we show that the GROMACS Stochastic
Dynamics integrator is equal to the less frequently used splitting method BAOA.
It immediately follows that GSD and BAOAB sample the same configurations and
have the same high configurational accuracy. Our numerical results indicate
that GSD/BAOA has higher kinetic accuracy than BAOAB.


  We propose a novel neural network architecture for detecting intrusions on
the CAN bus. The Controller Area Network (CAN) is the standard communication
method between the Electronic Control Units (ECUs) of automobiles. However, CAN
lacks security mechanisms and it has recently been shown that it can be
attacked remotely. Hence, it is desirable to monitor CAN traffic to detect
intrusions. In order to detect both, known and unknown intrusion scenarios, we
consider a novel unsupervised learning approach which we call CANet. To our
knowledge, this is the first deep learning based intrusion detection system
(IDS) that takes individual CAN messages with different IDs and evaluates them
in the moment they are received. This is a significant advancement because
messages with different IDs are typically sent at different times and with
different frequencies. Our method is evaluated on real and synthetic CAN data.
For reproducibility of the method, our synthetic data is publicly available. A
comparison with previous machine learning based methods shows that CANet
outperforms them by a significant margin.


  For radiography applications using fast neutrons simultaneously with gammas
we have developed a detector with 16 stilbene crystals in a 4$\times$4 2D array
with a 5~mm pitch and a depth of 25~mm. The crystal array is read out by
Silicon photomultipliers and custom signal processing electronics. The detector
prototype was tested using a custom D-D fast neutron generator at the Paul
Scherrer Institute. By applying a pulse shape discrimination algorithm the
detector is able to detect and distinguish fast neutrons and gammas
simultaneously. Various attenuating samples placed between the source and
detector with different materials and thicknesses were tested and the measured
macroscopic fast neutron cross sections were compared to what was expected.
Deviations were studied with the help of detailed Geant4 simulations. The
detection efficiency for D-D fast neutrons was measured to be around 10\%.


  Let $X$ be a compact K\"ahler manifold and $\om$ a smooth closed form of
bidegree $(1,1)$ which is nonnegative and big. We study the classes ${\mathcal
E}_{\chi}(X,\om)$ of $\om$-plurisubharmonic functions of finite weighted
Monge-Amp\`ere energy. When the weight $\chi$ has fast growth at infinity, the
corresponding functions are close to be bounded.
  We show that if a positive Radon measure is suitably dominated by the
Monge-Amp\`ere capacity, then it belongs to the range of the Monge-Amp\`ere
operator on some class ${\mathcal E}_{\chi}(X,\om)$. This is done by
establishing a priori estimates on the capacity of sublevel sets of the
solutions.
  Our result extends U.Cegrell's and S.Kolodziej's results and puts them into a
unifying frame. It also gives a simple proof of S.T.Yau's celebrated a priori
${\mathcal C}^0$-estimate.


  A symplecticity-preserving RG analysis is carried out to study a resonance
structure near an elliptic fixed point of a proto-type symplectic map in two
dimensions. Through analyzing fixed points of a reduced RG map, a topology of
the resonance structure such as a chain of resonant islands can be determined
analytically. An application of this analysis to the Henon map is also
presented.


  We report results of dissipative particle dynamics simulations and develop a
semi-analytical theory of an anisotropic flow in a parallel-plate channel with
two superhydrophobic striped walls. Our approach is valid for any local slip at
the gas sectors and an arbitrary distance between the plates, ranging from a
thick to a thin channel. It allows us to optimize area fractions, slip lengths,
channel thickness and texture orientation to maximize a transverse flow. Our
results may be useful for extracting effective slip tensors from global
measurements, such as the permeability of a channel, in experiments or
simulations, and may also find applications in passive microfluidic mixing.


  We use character theory of finite groups of Lie type to establish new results
on representation varieties of Fuchsian groups, and also on probabilistic
generation of groups of Lie type.


  In this paper, we investigate traces of cycle integrals of certain
meromorphic modular forms. By relating them to regularised theta lifts we
provide explicit formulae for them in terms of coefficients of harmonic Maass
forms.


  A careful study is made on the lattice of the phase diagram of QCD with two
staggered flavors, to investigate the order of the chiral transition of N_f=2
QCD. The specific heat and the susceptibility of the chiral condensate are
determined for different spatial sizes of the system, and a finite size scaling
analysis provides a determination of the (pseudo)critical indices. The result
is a strong indication that the chiral transition is first order.


  Kronheimer and Mrowka defined invariants of balanced sutured manifolds using
monopole and instanton Floer homology. Their invariants assign isomorphism
classes of modules to balanced sutured manifolds. In this paper, we introduce
refinements of these invariants which assign much richer algebraic objects
called projectively transitive systems of modules to balanced sutured manifolds
and isomorphisms of such systems to diffeomorphisms of balanced sutured
manifolds. Our work provides the foundation for extending these sutured Floer
theories to other interesting functorial frameworks as well, and can be used to
construct new invariants of contact structures and (perhaps) of knots and
bordered 3-manifolds.


  We present Epsilon, a system for general convex programming using fast linear
and proximal operators. As with existing convex programming frameworks, users
specify convex optimization problems using a natural grammar for mathematical
expressions, composing functions in a way that is guaranteed to be convex by
the rules of disciplined convex programming. Given such an input, the Epsilon
compiler transforms the optimization problem into a mathematically equivalent
form consisting only of functions with efficient proximal operators---an
intermediate representation we refer to as prox-affine form. By reducing
problems to this form, Epsilon enables solving general convex problems using a
large library of fast proximal and linear operators; numerical examples on many
popular problems from statistics and machine learning show that this often
improves running times by an order of magnitude or more vs. existing approaches
based on conic solvers.


  We consider membranes of spherical topology in uncompactified Matrix theory.
In general for large membranes Matrix theory reproduces the classical membrane
dynamics up to 1/N corrections; for certain simple membrane configurations, the
equations of motion agree exactly at finite N. We derive a general formula for
the one-loop Matrix potential between two finite-sized objects at large
separations. Applied to a graviton interacting with a round spherical membrane,
we show that the Matrix potential agrees with the naive supergravity potential
for large N, but differs at subleading orders in N. The result is quite
general: we prove a pair of theorems showing that for large N, after removing
the effects of gravitational radiation, the one-loop potential between
classical Matrix configurations agrees with the long-distance potential
expected from supergravity. As a spherical membrane shrinks, it eventually
becomes a black hole. This provides a natural framework to study Schwarzschild
black holes in Matrix theory.


  By mimicking brain-like cognition and exploiting parallelism,
hyperdimensional computing (HDC) classifiers have been emerging as a
lightweight framework to achieve efficient on-device inference. Nonetheless,
they have two fundamental drawbacks, heuristic training process and ultra-high
dimension, which result in sub-optimal inference accuracy and large model sizes
beyond the capability of tiny devices with stringent resource constraints. In
this paper, we address these fundamental drawbacks and propose a
low-dimensional computing (LDC) alternative. Specifically, by mapping our LDC
classifier into an equivalent neural network, we optimize our model using a
principled training approach. Most importantly, we can improve the inference
accuracy while successfully reducing the ultra-high dimension of existing HDC
models by orders of magnitude (e.g., 8000 vs. 4/64). We run experiments to
evaluate our LDC classifier by considering different datasets for inference on
tiny devices, and also implement different models on an FPGA platform for
acceleration. The results highlight that our LDC classifier offers an
overwhelming advantage over the existing brain-inspired HDC models and is
particularly suitable for inference on tiny devices.


  We study revenue optimization learning algorithms for posted-price auctions
with strategic buyers. We analyze a very broad family of monotone regret
minimization algorithms for this problem, which includes the previously best
known algorithm, and show that no algorithm in that family admits a strategic
regret more favorable than $\Omega(\sqrt{T})$. We then introduce a new
algorithm that achieves a strategic regret differing from the lower bound only
by a factor in $O(\log T)$, an exponential improvement upon the previous best
algorithm. Our new algorithm admits a natural analysis and simpler proofs, and
the ideas behind its design are general. We also report the results of
empirical evaluations comparing our algorithm with the previous state of the
art and show a consistent exponential improvement in several different
scenarios.


  In the multicore era, the time to computational results is increasingly
determined by how quickly operands are accessed by cores, rather than by the
speed of computation per operand. From high-performance computing (HPC) to
mobile application processors, low multicore utilization rates result from the
slowness of accessing off-chip operands, i.e. the memory wall. The APplication
AXcelerator (APAX) universal numerical encoder reduces computing's memory wall
by compressing numerical operands (integers and floats), thereby decreasing CPU
access time by 3:1 to 10:1 as operands stream between memory and cores. APAX
encodes numbers using a low-complexity algorithm designed both for time series
sensor data and for multi-dimensional data, including images. APAX encoding
parameters are determined by a profiler that quantifies the uncertainty
inherent in numerical datasets and recommends encoding parameters reflecting
this uncertainty. Compatible software, FPGA, and systemon-chip (SoC)
implementations efficiently support encoding rates between 150 MByte/sec and
1.5 GByte/sec at low power. On 25 integer and floating-point datasets, we
achieved encoding rates between 3:1 and 10:1, with average correlation of
0.999959, while accelerating computational "time to results."


  The gravitational redshift effect allows one to directly probe the
gravitational potential in clusters of galaxies. Following up on Wojtak et al.
[Nature (London) 477, 567 (2011)], we present a new measurement. We take
advantage of new data from the tenth data release of the Sloan Digital Sky
Survey and the Baryon Oscillation Spectroscopic Survey. We compare the
spectroscopic redshift of the brightest cluster galaxies (BCGs) with that of
galaxies at the outskirts of clusters, using a sample with an average cluster
mass of $10^{14} M_{\odot}$. We find that these galaxies have an average
relative redshift of -11 km/s compared with that of BCGs, with a standard
deviation of +7 and -5 km/s. Our measurement is consistent with that of Wojtak
et al. However, our derived standard deviation is larger, as we take into
account various systematic effects, beyond the size of the dataset. The result
is in good agreement with the predictions from general relativity.


  We have examined the sensitivity to the axion-like particle (ALP) couplings
to electroweak gauge bosons in the diphoton production at a future muon
collider. The collisions at the $\mu^+ \mu^-$ energies of 3 TeV, 14 TeV, and
100 TeV are addressed. The differential cross sections versus the invariant
mass of the final photons and total cross section versus minimal diphoton
invariant mass are presented. We have derived the exclusion regions for the
ALP-gauge boson coupling. The obtained bounds are much stronger than the
current experimental bounds in the ALP mass region 10 GeV -- 10 TeV. The
partial-wave unitarity constraints on the ALP-gauge boson coupling are
estimated. We have shown that the unitarity is not violated in the region of
the ALP coupling studied in the present paper.


  Grounding the reasoning ability of large language models (LLMs) for embodied
tasks is challenging due to the complexity of the physical world. Especially,
LLM planning for multi-agent collaboration requires communication of agents or
credit assignment as the feedback to re-adjust the proposed plans and achieve
effective coordination. However, existing methods that overly rely on physical
verification or self-reflection suffer from excessive and inefficient querying
of LLMs. In this paper, we propose a novel framework for multi-agent
collaboration that introduces Reinforced Advantage feedback (ReAd) for
efficient self-refinement of plans. Specifically, we perform critic regression
to learn a sequential advantage function from LLM-planned data, and then treat
the LLM planner as an optimizer to generate actions that maximize the advantage
function. It endows the LLM with the foresight to discern whether the action
contributes to accomplishing the final task. We provide theoretical analysis by
extending advantage-weighted regression in reinforcement learning to
multi-agent systems. Experiments on Overcooked-AI and a difficult variant of
RoCoBench show that ReAd surpasses baselines in success rate, and also
significantly decreases the interaction steps of agents and query rounds of
LLMs, demonstrating its high efficiency for grounding LLMs. More results are
given at https://read-llm.github.io/.


  Let $h : \mathbb{R}^2 \to \mathbb{R}^2$ be an orientation preserving
homeomorphism of the plane. For any bounded orbit
$\mathcal{O}(x)=\{h^n(x):n\in\mathbb{Z}\}$ there exists a fixed point
$x'\in\mathbb{R}^2$ of $h$ linked to $\mathcal{O}(x)$ in the sense of Gambaudo:
one cannot find a Jordan curve $C\subseteq\mathbb{R}^2$ around
$\mathcal{O}(x)$, separating it from $x'$, that is isotopic to $h(C)$ in
$\mathbb{R}^2\setminus\left(\mathcal{O}(x)\cup\{x'\}\right)$.


  I review the recent 5D self-tuning solutions of the cosmological constant
problem, and try to unify two cosmological constant problems within the
framework of the self-tuning solutions. One problem, the large cosmological
constant needed for inflation, is interpreted by starting with the parameters
allowing only the dS vacuum, and the vanishing cosmological constant at a true
vacuum is realized by changing parameters by exit from inflation at the brane
such that the self-tuning solution is allowed.


  We consider an $N$ by $N$ real or complex generalized Wigner matrix $H_N$,
whose entries are independent centered random variables with uniformly bounded
moments. We assume that the variance profile, $s_{ij}:=\mathbb{E} |H_{ij}|^2$,
satisfies $\sum_{i=1}^Ns_{ij}=1$, for all $1 \leq j \leq N$ and $c^{-1} \leq N
s_{ij} \leq c$ for all $ 1 \leq i,j \leq N$ with some constant $c \geq 1$. We
establish Gaussian fluctuations for the linear eigenvalue statistics of $H_N$
on global scales, as well as on all mesoscopic scales up to the spectral edges,
with the expectation and variance formulated in terms of the variance profile.
We subsequently obtain the universal mesoscopic central limit theorems for the
linear eigenvalue statistics inside the bulk and at the edges respectively.


  Suppose $\mu$ is an $\alpha$-dimensional fractal measure for some
$0<\alpha<n$. Inspired by the results proved by R. Strichartz in 1990, we
discuss the $L^p$-asymptotics of the Fourier transform of $fd\mu$ by estimating
bounds of
  $$\underset{L\rightarrow\infty}{\liminf}\ \frac{1}{L^k} \int_{|\xi|\leq L}\
|\widehat{fd\mu}(\xi)|^pd\xi,$$ for $f\in L^p(d\mu)$ and $2<p<2n/\alpha$. In a
different direction, we prove a Hardy type inequality, that is,
  $$\int\frac{|f(x)|^p}{(\mu(E_x))^{2-p}}d\mu(x)\leq C\
\underset{L\rightarrow\infty}{\liminf} \frac{1}{L^{n-\alpha}} \int_{B_L(0)}
|\widehat{fd\mu}(\xi)|^pd\xi$$ where $1\leq p\leq 2$ and
$E_x=E\cap(-\infty,x_1]\times(-\infty,x_2]...(-\infty,x_n]$ for
$x=(x_1,...x_n)\in\R^n$ generalizing the one dimensional results proved by
Hudson and Leckband in 1992.


  We give a characterization of positive definite integrable functions on a
product of two Gelfand pairs as an integral of positive definite functions on
one of the Gelfand pairs with respect to the Plancherel measure on the dual of
the other Gelfand pair.
  In the very special case where the Gelfand pairs are Euclidean groups and the
compact subgroups are reduced to the identity, the characterization is a much
cited result in spatio-temporal statistics due to Cressie, Huang and Gneiting.
  When one of the Gelfand pairs is compact the characterization leads to
results about expansions in spherical functions with positive definite
expansion functions, thereby recovering recent results of the author in
collaboration with Peron and Porcu. In the special case when the compact
Gelfand pair consists of orthogonal groups, the characterization is important
in geostatistics and covers a recent result of Porcu and White.


  We are interested in the long-time asymptotic behavior of
growth-fragmentation equations with a nonlinear growth term. We present
examples for which we can prove either the convergence to a steady state or
conversely the existence of periodic solutions. Thanks the General Relative
Entropy method applied to well chosen self-similar solutions, we show that the
equation can "asymptotically" be reduced to a system of ODEs. Then stability
results are proved by using a Lyapunov functional, and existence of periodic
solutions are proved thanks to the Poincar\'e-Bendixon theorem or by Hopf
bifurcation.


  We study the annihilation of electroweak dumbbells and the dependence of
their dynamics on initial dumbbell length and twist. Untwisted dumbbells decay
rapidly while maximally twisted dumbbells collapse to form a compact
sphaleron-like object, before decaying into radiation. The decay products of a
dumbbell include electromagnetic magnetic fields with energy that is a few
percent of the initial energy. The magnetic field from the decay of twisted
dumbbells carries magnetic helicity with magnitude that depends on the twist,
and handedness that depends on the decay pathway.


  We investigate the representation theory of a large class of pointed Hopf
algebras, extending results of Lusztig and others. We classify all simple
modules in a suitable category and determine the weight multiplicities; we
establish a complete reducibility theorem in this category.


  Several papers published since 2006 describe effects of magnetic fields on
elasmobranchs and assess their utility in reducing negative interactions
between sharks and humans, including bycatch reduction. Most of these repeat a
single untested hypothesis regarding physical mechanisms by which elasmobranchs
detect magnetic fields and also neglect careful consideration of
magnetoreception in teleosts. Several species of teleosts are known to have
magnetoreception based in biogenic magnetite, and direct magnetic field
detection also has support in several species of elasmobranchs. The overly
narrow focus of earlier papers on the unsupported hypothesis that
magnetoreception in elasmobranchs is based in the ampullae of Lorenzini creates
the impression that all teleosts will be insensitive to magnetic deterrents.
However, magnetite based magnetoreception has been demonstrated in several
teleosts, and is supported in others. Furthermore, electroreception is present
in many teleost species; therefore, the possibility of induction based indirect
magnetoreception should be considered. Finally, experiments reported as
demonstrating insensitivity in teleost species to magnetic deterrents suffer
from inadequate design and sample sizes to reject the hypothesis of magnetic
detection in any given species. Since adoption of deterrent hook technologies
depends on both deterrent effects in sharks and the absence of effects in
target teleosts, the hypothesis of detection in teleost species must be
independently tested with adequate sample sizes.


  Recent advancements in computer vision promise to automate medical image
analysis. Rheumatoid arthritis is an autoimmune disease that would profit from
computer-based diagnosis, as there are no direct markers known, and doctors
have to rely on manual inspection of X-ray images. In this work, we present a
multi-task deep learning model that simultaneously learns to localize joints on
X-ray images and diagnose two kinds of joint damage: narrowing and erosion.
Additionally, we propose a modification of label smoothing, which combines
classification and regression cues into a single loss and achieves 5% relative
error reduction compared to standard loss functions. Our final model obtained
4th place in joint space narrowing and 5th place in joint erosion in the global
RA2 DREAM challenge.


  With the ever-growing storage density, high-speed, and low-cost data access,
flash memory has inevitably become popular. Multi-level cell (MLC) NAND flash
memory, which can well balance the data density and memory stability, has
occupied the largest market share of flash memory. With the aggressive memory
scaling, however, the reliability decays sharply owing to multiple
interferences. Therefore, the control system should be embedded with a suitable
error correction code (ECC) to guarantee the data integrity and accuracy. We
proposed the pre-check scheme which is a multi-strategy polar code scheme to
strike a balance between reasonable frame error rate (FER) and decoding
latency. Three decoders namely binary-input, quantized-soft, and pure-soft
decoders are embedded in this scheme. Since the calculation of soft
log-likelihood ratio (LLR) inputs needs multiple sensing operations and
optional quantization boundaries, a 2-bit quantized hard-decision decoder is
proposed to outperform the hard-decoded LDPC bit-flipping decoder with fewer
sensing operations. We notice that polar codes have much lower computational
complexity compared to LDPC codes. The stepwise maximum mutual information
(SMMI) scheme is also proposed to obtain overlapped boundaries without
exhausting search. The mapping scheme using Gray code is employed and proved to
achieve better raw error performance compared to other alternatives. Hardware
architectures are also given in this paper.


  The parallel-tempering method has been applied to numerically study the
thermodynamic behavior of a three-dimensional disordered antiferromagnetic
Ising model with random fields at spin concentrations corresponding to regions
of both weak and strong structural disorder. An analysis of the low-temperature
behavior of the model convincingly shows that in the case of a weakly
disordered samples there is realized an antiferromagnetic ordered state, while
in the region of strong structural disorder the effects of random magnetic
fields lead to the realization of a new phase state of the system with a
complex domain structure consisting of antiferromagnetic and ferromagnetic
domains separated by regions of a spin-glass phase and characterized by a
spinglass ground state.


  IPMCs consist of a Nafion(R) ionic polymer film coated on both sides with a
thin layer of metallic electrodes. The polymer completely dissociates when it
is saturated with water, releasing small cations while anions remain bound to
the polymer chains. When this strip is subject to an orthogonal electric field,
the cations migrate towards the negative electrode, carrying water away by
osmosis. This leads to the bending of the strip. We have previously published a
modelling of this system based on the thermodynamics of irreversible processes.
In this paper, we use this model to simulate numerically the bending of a
strip. Since the amplitude of the deflection is large, we use a beam model in
large displacements. In addition, the material permittivity may increase with
ion concentration. We therefore test three permittivity models. We plot the
profiles of the cations concentration, pressure, electric potential and
induction, and we study the influence of the strip geometry on the tip
displacement and on the blocking force. The results we obtain are in good
agreement with the experimental data published in the literature. The variation
of these quantities with the imposed electric potential allow us to
discriminate between the three models.


  In light of the current discrepancies between the recent predictions based on
QCD factorisation (QCDF) and the experimental data for several non-leptonic
colour-allowed two-body $B$-meson decays, we obtain new determinations of the
non-factorisable soft-gluon contribution to the decays $\bar B_{s}^0 \to
D_{s}^+ \pi^-$ and $\bar B^0 \to D^+ K^-$, using the framework of light-cone
sum rule (LCSR), with a suitable three-point correlation function and $B$-meson
light-cone distribution amplitudes. In particular, we discuss the problem
associated with a double light-cone (LC) expansion of the correlator, and
motivate future determinations of the three-particle $B$-meson matrix element
with the gluon and the spectator quark aligned along different light-cone
directions. Performing a LC-local operator product expansion of the correlation
function, we find, for both modes considered, the non-factorisable part of the
amplitude to be sizeable and positive, however, with very large systematic
uncertainties. Furthermore, we also determine for the first time, using LCSR,
the factorisable amplitudes at LO-QCD, and thus the corresponding branching
fractions. Our predictions are in agreement with the experimental data and
consistent with the results based on QCDF, although again within very large
uncertainties. In this respect, we provide a rich outlook for future
improvements and investigations.