  We consider a family of random line tessellations of the Euclidean plane
introduced in a much more formal context by Hug and Schneider [Geom. Funct.
Anal. 17, 156 (2007)] and described by a parameter \alpha\geq 1. For \alpha=1
the zero-cell (that is, the cell containing the origin) coincides with the
Crofton cell of a Poisson line tessellation, and for \alpha=2 it coincides with
the typical Poisson-Voronoi cell. Let p_n(\alpha) be the probability for the
zero-cell to have n sides. By the methods of statistical mechanics we construct
the asymptotic expansion of \log p_n(\alpha) up to terms that vanish as
n\to\infty. In the large-n limit the cell is shown to become circular. The
circle is centered at the origin when \alpha>1, but gets delocalized for the
Crofton cell, \alpha=1, which is a singular point of the parameter range. The
large-n expansion of \log p_n(1) is therefore different from that of the
general case and we show how to carry it out. As a corollary we obtain the
analogous expansion for the {\it typical} n-sided cell of a Poisson line
tessellation.


  We provide a formula for the $n^{th}$ term of the $k$-generalized
Fibonacci-like number sequence using the $k$-generalized Fibonacci number or
$k$-nacci number, and by utilizing the newly derived formula, we show that the
limit of the ratio of successive terms of the sequence tends to a root of the
equation $x + x^{-k} = 2$. We then extend our results to $k$-generalized
Horadam ($k$GH) and $k$-generalized Horadam-like ($k$GHL) numbers. In dealing
with the limit of the ratio of successive terms of $k$GH and $k$GHL, a lemma
due to Z. Wu and H. Zhang [8] shall be employed. Finally, we remark that an
analogue result for $k$-periodic $k$-nary Fibonacci sequence can also be
derived.


  We consider Approval Voting systems where each voter decides on a subset to
candidates he/she approves. We focus on the optimization problem of finding the
committee of fixed size k minimizing the maximal Hamming distance from a vote.
In this paper we give a PTAS for this problem and hence resolve the open
question raised by Carragianis et al. [AAAI'10]. The result is obtained by
adapting the techniques developed by Li et al. [JACM'02] originally used for
the less constrained Closest String problem. The technique relies on extracting
information and structural properties of constant size subsets of votes.


  We present a neural network approach for closed-loop deep brain stimulation
(DBS). We cast the problem of finding an optimal neurostimulation strategy as a
control problem. In this setting, control policies aim to optimize therapeutic
outcomes by tailoring the parameters of a DBS system, typically via electrical
stimulation, in real time based on the patient's ongoing neuronal activity. We
approximate the value function offline using a neural network to enable
generating controls (stimuli) in real time via the feedback form. The neuronal
activity is characterized by a nonlinear, stiff system of differential
equations as dictated by the Hodgkin-Huxley model. Our training process
leverages the relationship between Pontryagin's maximum principle and
Hamilton-Jacobi-Bellman equations to update the value function estimates
simultaneously. Our numerical experiments illustrate the accuracy of our
approach for out-of-distribution samples and the robustness to moderate shocks
and disturbances in the system.


  We study asymptotic behaviors of positive solutions to the Yamabe equation
and the $\sigma$k-Yamabe equation near isolated singular points and establish
expansions up to arbitrary orders. Such results generalize an earlier
pioneering work by Caffarelli, Gidas, and Spruck, and a work by Korevaar,
Mazzeo, Pacard, and Schoen, on the Yamabe equation, and a work by Han, Li, and
Teixeira on the $\sigma_k$-Yamabe equation. The study is based on a combination
of classification of global singular solutions and an analysis of linearized
operators at these global singular solutions. Such linearized equations are
uniformly elliptic near singular points for $1 \leq k \leq n/2$ and become
degenerate for $n/2 < k \leq n$. In a significant portion of the paper, we
establish a degree 1 expansion for the $\sigma_k$-Yamabe equation for $n/2 < k
< n$, generalizing a similar result for $k = 1$ by Korevaar, Mazzeo, Pacard,
and Schoen and for $2 \leq k \leq n/2$ by Han, Li, and Teixeira.


  Let $q$ be a power of a prime and $\mathbb{F}_q$ the finite field consisting
of $q$ elements. We prove explicit upper bounds on the number of incidences
between lines and Cartesian products in $\mathbb{F}_q^2$. We also use our
results on point-line incidences to give new sum-product type estimates
concerning sums of reciprocals.


  One of the frustrating things in the digital fabrication era is that its
media are neither affordable nor easily accessible and usable.
Three-dimensional (3D) fabrication media (DFM) such as 3D Printers and 3D
Scanners have experienced an upsurge in popularity, while the latter remain
expensive and hard to function. With this paper, we aim to present you the
RhoScanner Project - a an affordable and efficient Three-dimensional Projective
Scanner for Smart-phones, hence shedding light on the extended capabilities of
digital fabrication media on popular use.


  Measuring association, or the lack of it, between variables plays an
important role in a variety of research areas, including education, which is of
our primary interest in this paper. Given, for example, student marks on
several study subjects, we may for a number of reasons be interested in
measuring the lack of co-monotonicity (LOC) between the marks, which rarely
follow monotone, let alone linear, patterns. For this purpose, in this paper we
explore a novel approach based on a LOC index, which is related to, yet
substantially different from, Eckhard Liebscher's recently suggested
coefficient of monotonically increasing dependence. To illustrate the new
technique, we analyze a data-set of student marks on mathematics, reading and
spelling.


  Sub-percent level accuracy in shear measurement is required by the Stage-IV
weak lensing surveys. One important challenge is about suppressing the shear
bias on source images of low signal-to-noise ratios (SNR$\lesssim10$).
Previously, it has been demonstrated that the shear estimators defined in the
Fourier_Quad (FQ) method can achieve sub-percent accuracy at the very faint end
(SNR$\lesssim5$) through ensemble averaging. Later, it is found that we can
approach the minimum statistical error (the Cramer-Rao Bound) by symmetrizing
the full PDF of the FQ shear estimators (the PDF_SYM approach), instead of
taking ensemble averages. Recently, with a large amount of mock galaxy images,
we are able to identify some small amount of shear biases in the PDF_SYM
approach at the faint end. The multiplicative bias goes up to
$1-2\times10^{-2}$ at SNR $\lesssim 10$, and the anisotropy of the point spread
function (PSF) causes an additive bias that can reach a few times $10^{-4}$. We
find that these biases originate from the noise-source coupling in the galaxy
power spectrum. It turns out that this problem can be largely fixed by adding
additional terms to the FQ shear estimators. The resulting multiplicative and
additive biases can be significantly suppressed to the level of $10^{-3}$ and
$10^{-5}$ respectively. These corrections substantially extend the available
SNR range for accurate shear measurement with the PDF_SYM approach.


  The binding energy of three identical bosons is estimated by coupled
differential equations which generalise the Feshbach--Rubinow approximation.
This method turns out to be rather efficient, especially in the limit of
vanishing binding.


  Finding the set of the n items most dissimilar from each other out of a
larger population becomes increasingly difficult and computationally expensive
as either n or the population size grows large. Finding the set of the n most
dissimilar items is different than simply sorting an array of numbers because
there exists a pairwise relationship between each item and all other items in
the population. For instance, if you have a set of the most dissimilar n=4
items, one or more of the items from n=4 might not be in the set n=5. An exact
solution would have to search all possible combinations of size n in the
population, exhaustively. We present an open-source software called similarity
downselection (SDS), written in Python and freely available on GitHub. SDS
implements a heuristic algorithm for quickly finding the approximate set(s) of
the n most dissimilar items. We benchmark SDS against a Monte Carlo method,
which attempts to find the exact solution through repeated random sampling. We
show that for SDS to find the set of n most dissimilar conformers, our method
is not only orders of magnitude faster, but is also more accurate than running
the Monte Carlo for 1,000,000 iterations, each searching for set sizes n=3-7
out of a population of 50,000. We also benchmark SDS against the exact solution
for example small populations, showing SDS produces a solution close to the
exact solution in these instances.


  Recent AI-based text-to-image models not only excel at generating realistic
images, they also give designers more and more fine-grained control over the
image content. Consequently, these approaches have gathered increased attention
within the computer graphics research community, which has been historically
devoted towards traditional rendering techniques that offer precise control
over scene parameters such as objects, materials, and lighting, when generating
realistic images. While the quality of rendered images is traditionally
assessed through well-established image quality metrics, such as SSIM or PSNR,
the unique challenges presented by text-to-image models, which in contrast to
rendering interweave the control of scene and rendering parameters, necessitate
the development of novel image quality metrics. Therefore, within this survey,
we provide a comprehensive overview of existing text-to-image quality metrics
addressing their nuances and the need for alignment with human preferences.
Based on our findings, we propose a new taxonomy for categorizing these
metrics, which is grounded in the assumption that there are two main quality
criteria, namely compositionality and generality, which ideally map to human
preferences. Ultimately, we derive guidelines for practitioners conducting
text-to-image evaluation, discuss open challenges of evaluation mechanisms, and
surface limitations of current metrics.


  Extending an earlier estimate for the degree of approximation of overiterated
univariate Bernstein operators towards the same operator of degree one, it is
shown that an analogous result holds in the $d$-variate case. The method
employed can be carried over to many other cases and is not restricted to
Bernstein-type or similar methods.


  The extremely sensitive Chandra Deep Field-North (CDF-N) pencil-beam X-ray
survey is used to identify and characterize the X-ray emission from old
high-latitude main sequence Galactic stars. Our principal goal is to
investigate the expected long-term decay of magnetic activity of late-type
stars due to the gradual spindown of stellar rotation from a magnetized stellar
wind. Eleven X-ray sources constitute a well-defined sample of 2 G, 2 K0-K4,
and 7 M2-M5 stars with median distance around 300 pc. X-ray luminosities are
typically log Lx ~ 27 erg/s and is dominated by flares rather than quiescent
coronal emission. Models of the population indicates that the CDF-N stars are
the most magnetically active old disk stars. A substantial decline in X-ray
luminosities over the 1<t<11 Gyr age interval is required. This is the first
demonstration that the coronal and flaring components of stellar magnetic
activity -- and presumably the interior magnetic dynamos responsible for the
reconnecting fields at the stellar surface -- exhibit long-term decay over the
age of the Galactic disk. The model that best fits the magnitudes, spectral
types and X-ray luminosities of the sample has Lx ~ 1/t^2 erg/s which is faster
than the 1/t decay rate predicted from widely accepted rotational spindown
rates and X-ray-activity relations.


  A polygon C is an intersecting polygon for a set O of objects in the plane if
C intersects each object in O, where the polygon includes its interior. We
study the problem of computing the minimum-perimeter intersecting polygon and
the minimum-area convex intersecting polygon for a given set O of objects. We
present an FPTAS for both problems for the case where O is a set of possibly
intersecting convex polygons in the plane of total complexity n.
  Furthermore, we present an exact polynomial-time algorithm for the
minimum-perimeter intersecting polygon for the case where O is a set of n
possibly intersecting segments in the plane. So far, polynomial-time exact
algorithms were only known for the minimum perimeter intersecting polygon of
lines or of disjoint segments.


  We study an associating lattice gas (ALG) using Monte Carlo simulation and
solutions on Husimi lattices. In this model, the molecules have an
orientational degree of freedom and the interactions depend on the relative
orientations of nearest-neighbor molecules. We focus on the transition between
the high-density liquid (HDL) phase and the isotropic gas phase in the limit of
full occupancy ($\mu \to \infty$). Simulation results show a continuous phase
transition at $\tau_c=k_BT_c/\gamma=0.4763(1)$ (where $-\gamma$ is the bond
energy) between the low-temperature HDL phase, with a non-vanishing mean
orientation of the molecules, and the high-temperature isotropic phase. Results
for critical exponents and the Binder cumulant indicate that the transition
belongs to the three-state Potts model universality class, even though the ALG
Hamiltonian does not have the full permutation symmetry of the Potts model. In
contrast with simulation, the Husimi lattice results furnish a discontinuous
phase transition, characterized by a discontinuity of the nematic order
parameter. The transition temperatures ($\tau_c=0.51403$ and $0.51207$ for
trees built with triangles and hexagons, respectively) are slightly higher than
the one found via simulation. Since the Husimi lattice studies show that the
ALG phase diagram features a discontinuous gas-HDL line for finite $\mu$, three
possible scenarios arise. The first is that in the limit $\mu \to \infty$ the
first-order line ends in a critical point; the second is a change in the nature
of the transition at some finite chemical potential; the third is that the
entire line is one of continuous phase transitions. Results from other ALG
models and the fact that mean-field approximations show a discontinuous phase
transition for the three-state Potts model (known to possess a continuous
transition) lends some weight to the third alternative.


  In this paper, we describe the formalization of the axiom of choice and
several of its famous equivalent theorems in Morse-Kelley set theory. These
theorems include Tukey's lemma, the Hausdorff maximal principle, the maximal
principle, Zermelo's postulate, Zorn's lemma and the well-ordering theorem. We
prove the above theorems by the axiom of choice in turn, and finally prove the
axiom of choice by Zermelo's postulate and the well-ordering theorem, thus
completing the cyclic proof of equivalence between them. The proofs are checked
formally using the Coq proof assistant in which Morse-Kelley set theory is
formalized. The whole process of formal proof demonstrates that the Coq-based
machine proving of mathematics theorem is highly reliable and rigorous. The
formal work of this paper is enough for most applications, especially in set
theory, topology and algebra.


  Scanning tunneling microscopy and spectroscopy (STM/S) measurements in the
superconducting dichalcogenide 2H-NbS2 show a peculiar superconducting density
of states with two well defined features at 0.97 meV and 0.53 meV, located
respectively above and below the value for the superconducting gap expected
from single band s-wave BCS model (D=1.76kBTc=0.9 meV). Both features have a
continuous temperature evolution and disappear at Tc = 5.7 K. Moreover, we
observe the hexagonal vortex lattice with radially symmetric vortices and a
well developed localized state at the vortex cores. The sixfold star shape
characteristic of the vortex lattice of the compound 2H-NbSe2 is, together with
the charge density wave order (CDW), absent in 2H-NbS2.


  We show that the no-disturbance principle imposes a tradeoff between locally
contextual correlations violating the Klyachko-Can-Binicioglu-Shumovski
inequality and spatially separated correlations violating the
Clauser-Horne-Shimony-Holt inequality. The violation of one inequality forbids
the violation of the other. We also obtain the corresponding monogamy relation
imposed by quantum theory for a qutrit-qubit system. Our results show the
existence of fundamental monogamy relations between contextuality and
nonlocality that suggest that entanglement might be a particular form of a more
fundamental resource.


  The Alexander biquandle of a virtual knot or link is a module over a
2-variable Laurent polynomial ring which is an invariant of virtual knots and
links. The elementary ideals of this module are then invariants of virtual
isotopy which determine both the generalized Alexander polynomial (also known
as the Sawollek polynomial) for virtual knots and the classical Alexander
polynomial for classical knots. For a fixed monomial ordering $<$, the
Gr\"obner bases for these ideals are computable, comparable invariants which
fully determine the elementary ideals and which generalize and unify the
classical and generalized Alexander polynomials. We provide examples to
illustrate the usefulness of these invariants and propose questions for future
work.


  We prove the analog of Cram\'er's short intervals theorem for primes in
arithmetic progressions and prime ideals, under the relevant Riemann
Hypothesis. Both results are uniform in the data of the underlying structure.
Our approach is based mainly on the inertia property of the counting functions
of primes and prime ideals.


  We modify and generalize the known solution for the electromagnetic field
when a vacuum, stationary, axisymmetric black hole is immersed in a uniform
magnetic field to the case of nonvacuum black holes (of modified gravity) and
determine all linear terms of the vector potential in powers of the magnetic
field and the rotation parameter.


  Leaked passwords from data breaches can pose a serious threat to users if the
password is reused elsewhere. With more online services getting breached today,
there is still a lack of large-scale quantitative understanding of the risks of
password reuse across services. In this paper, we analyze a large collection of
28.8 million users and their 61.5 million passwords across 107 services. We
find that 38% of the users have reused exactly the same password across
different sites, while 20% have modified an existing password to create new
ones. In addition, we find that the password modification patterns are highly
consistent across different user demographics, indicating a high
predictability. To quantify the risk, we build a new training-based guessing
algorithm, and show that more than 16 million password pairs can be cracked
within just 10 attempts (30% of the modified passwords and all the reused
passwords).


  We investigate the Kepler problem using a symplectic structure consistent
with the commutation rules of the noncommutative quantum mechanics. We show
that a noncommutative parameter of the order of $10^{-58} \text m^2$ gives
observable corrections to the movement of the solar system. In this way,
modifications in the physics of smaller scales implies modifications at large
scales, something similar to the UV/IR mixing.


  On 2004 Dec. 27, the soft gamma repeater (SGR) 1806-20 emitted the brightest
giant flare (GF) ever detected from an SGR, with an (isotropic) energy release
$\sim 100$ times greater than the only two other known SGR GFs. It was followed
by a very bright, fading radio afterglow. Extensive follow-up radio
observations provided a wealth of information with unprecedented astrometric
precision, revealing the temporal evolution of the source size, along with
densely sampled light curves and spectra. Here we expand on our previous work
on this source, by explaining these observations within one self-consistent
dynamical model. In this scenario, the early radio emission is due to the
outflow ejected during the GF energizing a thin shell surrounding a
pre-existing cavity, where the observed steep temporal decay of the radio
emission seen beginning on day 9 is attributed to the adiabatic cooling of the
shocked shell. The shocked ejecta and external shell move outward together,
driving a forward shock into the ambient medium, and are eventually decelerated
by a reverse shock. As we show in Gelfand et al. (2005), the radio emission
from the shocked external medium naturally peaks when significant deceleration
occurs, and then decays relatively slowly. The dynamical modeling of the
collision between the ejecta and the external shell together with the observed
evolution of the source size (which is nicely reproduced in our model) suggest
that most of the energy in the outflow was in mildly relativistic material,
with an initial expansion velocity $v/c \lesssim 0.7d_{15}$, for a distance of
$15d_{15}$ kpc to SGR 1806-20. An initially highly relativistic outflow would
not have produced a long coasting phase at a mildly relativistic expansion
velocity, as was observed.


  Existing equivariant neural networks require prior knowledge of the symmetry
group and discretization for continuous groups. We propose to work with Lie
algebras (infinitesimal generators) instead of Lie groups. Our model, the Lie
algebra convolutional network (L-conv) can automatically discover symmetries
and does not require discretization of the group. We show that L-conv can serve
as a building block to construct any group equivariant feedforward
architecture. Both CNNs and Graph Convolutional Networks can be expressed as
L-conv with appropriate groups. We discover direct connections between L-conv
and physics: (1) group invariant loss generalizes field theory (2)
Euler-Lagrange equation measures the robustness, and (3) equivariance leads to
conservation laws and Noether current.These connections open up new avenues for
designing more general equivariant networks and applying them to important
problems in physical sciences


  We have developed two quantum classifier models for the $t\bar{t}H(b\bar{b})$
classification problem, both of which fall into the category of hybrid
quantum-classical algorithms for Noisy Intermediate Scale Quantum devices
(NISQ). Our results, along with other studies, serve as a proof of concept that
Quantum Machine Learning (QML) methods can have similar or better performance,
in specific cases of low number of training samples, with respect to
conventional ML methods even with a limited number of qubits available in
current hardware. To utilise algorithms with a low number of qubits -- to
accommodate for limitations in both simulation hardware and real quantum
hardware -- we investigated different feature reduction methods. Their impact
on the performance of both the classical and quantum models was assessed. We
addressed different implementations of two QML models, representative of the
two main approaches to supervised quantum machine learning today: a Quantum
Support Vector Machine (QSVM), a kernel-based method, and a Variational Quantum
Circuit (VQC), a variational approach.


  We examine the radiative corrections to an extension of the standard model
containing a Lorentz-violating axial vector parameter. At second order in this
parameter, the photon self-energy is known to contain terms that violate gauge
invariance. Previously, this has been treated as a pathology, but it is also
possible to take the gauge noninvariant terms at face value. These terms then
make Lorentz-violating contributions to the photon mass, and directly measured
limits on the photon mass can be used to set bounds on the Lorentz violation at
better than the 10^-22 GeV level.


  In this paper, we consider the polymodal version of Lambek calculus with
subexponential modalities initially introduced by Kanovich, Kuznetsov, Nigam,
and Scedrov and its quantale semantics. In our approach, subexponential
modalities have an interpretation in terms of quantic conuclei. We show that
this extension of Lambek calculus is complete w.r.t quantales with quantic
conuclei. Also, we prove a representation theorem for quantales with quantic
conuclei and show that Lambek calculus with subexponentials is relationally
complete. Finally, we extend this representation theorem to the category of
quantales with quantic conuclei.


  The history of the local medium, within a few hundred parsecs, is dominated
by the evolution of the Gould Belt. The event that triggered this star-forming
region and molded the gas distribution is still unknown. Its orientation and
extent are reasonably well determined and its expansion matches the space and
velocity distributions of many large HI and H2 clouds within half a kiloparsec.
The present rim coincides with most of the nearby OB associations, but their
mean velocity does not seem to be related to the Belt expansion. The Belt age
is uncertain by a factor of 2 because of the discrepancy found between the
dynamical timescale (20 to 30 Myr) and the stellar ages (30 to 60 Myr). The
stellar content is derived from kinematic studies for massive stars and from
X-ray observations for young solar-mass ones. Whether star formation is active
along the rim or spread over a larger fraction of the disc is debated. The Belt
flatness and its tilt remain very difficult to interpret. Various scenarii
involve the impact of a high-velocity cloud, a cascade of supernovae, the
dissolution of a rotating system, or the braking of a supercloud entering the
spiral arm. Because of the enhanced star formation, the Belt supernova rate
over the past few million years has been 3 to 4 times larger than the local
Galactic rate. The corresponding pulsars may be responsible for the population
of unknown gamma-ray sources associated with the Belt. The higher rate also
implies an enhanced cosmic-ray production locally.


  We study the zero-temperature phase diagram and fractional excitation when a
thin film of 3D topological insulator has two competing masses: T- symmetric
exciton condensation and T- breaking Zeeman effect. Two topologically distinct
phases are identified: in one, the quasiparticles can be viewed as in a quantum
spin Hall phase, and in the other a quantum anomalous Hall phase. The vortices
of the exciton order parameter can carry fractional charge and statistics of
electrons in both phases. When the system undergoes the quantum phase
transition between these two phases, the charges, statistics and the number of
fermionic zero mode of the excitonic vortices are also changed. We derive the
effective field theory for vortices and external gauge field by directly
integrating out fermions and present an explicit wave function for the
fermionic zero mode localized at the excitonic vortices with or without orbital
magnetic field. The quantum phase transition can be measured by optical Faraday
or Kerr effect experiments, and in closing we discuss the conditions required
to create the excitonic condensate.


  We have fabricated air-stable n-type, ambipolar carbon nanotube field effect
transistors (CNFETs), and used them in nanoscale memory cells. N-type
transistors are achieved by annealing of nanotubes in hydrogen gas and
contacting them by cobalt electrodes. Scanning gate microscopy reveals that the
bulk response of these devices is similar to gold-contacted p-CNFETs,
confirming that Schottky barrier formation at the contact interface determines
accessibility of electron and hole transport regimes. The transfer
characteristics and Coulomb Blockade (CB) spectroscopy in ambipolar devices
show strongly enhanced gate coupling, most likely due to reduction of defect
density at the silicon/silicon-dioxide interface during hydrogen anneal. The CB
data in the ``on''-state indicates that these CNFETs are nearly ballistic
conductors at high electrostatic doping. Due to their nanoscale capacitance,
CNFETs are extremely sensitive to presence of individual charge around the
channel. We demonstrate that this property can be harnessed to construct data
storage elements that operate at the few-electron level.


  The processes taking place inside the living cell are now understood to the
point where predictive computational models can be used to gain detailed
understanding of important biological phenomena. A key challenge is to
extrapolate this detailed knowledge of the individual cell to be able to
explain at the population level how cells interact and respond with each other
and their environment. In particular, the goal is to understand how organisms
develop, maintain and repair functional tissues and organs.
  In this paper we propose a novel computational framework for modeling
populations of interacting cells. Our framework incorporates mechanistic,
constitutive descriptions of biomechanical properties of the cell population,
and uses a coarse graining approach to derive individual rate laws that enable
propagation of the population through time. Thanks to its multiscale nature,
the resulting simulation algorithm is extremely scalable and highly efficient.
As highlighted in our computational examples, the framework is also very
flexible and may straightforwardly be coupled with continuous-time descriptions
of biochemical signalling within, and between, individual cells.


  Liquid crystal elastomers (LCEs) can undergo large reversible contractions
along their nematic director upon heating or illumination. A spatially
patterned director within a flat LCE sheet thus encodes a pattern of
contraction on heating, which can morph the sheet into a curved shell, akin to
how a pattern of growth sculpts a developing organism. Here we consider,
theoretically, numerically and experimentally, patterns constructed from
regions of radial and circular director, which, in isolation, would form cones
and anticones. The resultant surfaces contain curved ridges with sharp V-shaped
cross-sections, associated with the boundaries between regions in the patterns.
Such ridges may be created in positively and negatively curved variants and,
since they bear Gauss curvature (quantified here via the Gauss-Bonnet theorem),
they cannot be flattened without energetically prohibitive stretch. Our
experiments and numerics highlight that, although such ridges cannot be
flattened isometrically, they can deform isometrically by trading the
(singular) curvature of the V angle against the (finite) curvature of the ridge
line. Furthermore, in finite thickness sheets, the sharp ridges are inevitably
non-isometrically blunted to relieve bend, resulting in a modest smearing out
of the encoded singular Gauss curvature. We close by discussing the use of such
features as actuating linear features, such as probes, tongues and limbs, and
highlighting the similarities between these patterns of shape change and those
found during the morphogenesis of several biological systems.


  We generalize the belief-propagation algorithm to sparse random networks with
arbitrary distributions of motifs (triangles, loops, etc.). Each vertex in
these networks belongs to a given set of motifs (generalization of the
configuration model). These networks can be treated as sparse uncorrelated
hypergraphs in which hyperedges represent motifs. Here a hypergraph is a
generalization of a graph, where a hyperedge can connect any number of
vertices. These uncorrelated hypergraphs are tree-like (hypertrees), which
crucially simplify the problem and allow us to apply the belief-propagation
algorithm to these loopy networks with arbitrary motifs. As natural examples,
we consider motifs in the form of finite loops and cliques. We apply the
belief-propagation algorithm to the ferromagnetic Ising model on the resulting
random networks. We obtain an exact solution of this model on networks with
finite loops or cliques as motifs. We find an exact critical temperature of the
ferromagnetic phase transition and demonstrate that with increasing the
clustering coefficient and the loop size, the critical temperature increases
compared to ordinary tree-like complex networks. Our solution also gives the
birth point of the giant connected component in these loopy networks.


  We consider the problem of secure distributed matrix multiplication in which
a user wishes to compute the product of two matrices with the assistance of
honest but curious servers. In this paper, we answer the following question: Is
it beneficial to offload the computations if security is a concern? We answer
this question in the affirmative by showing that by adjusting the parameters in
a polynomial code we can obtain a trade-off between the user's and the servers'
computational time. Indeed, we show that if the computational time complexity
of an operation in $\mathbb{F}_q$ is at most $\mathcal{Z}_q$ and the
computational time complexity of multiplying two $n\times n$ matrices is
$\mathcal{O}(n^\omega \mathcal{Z}_q)$ then, by optimizing the trade-off, the
user together with the servers can compute the multiplication in
$\mathcal{O}(n^{4-\frac{6}{\omega+1}} \mathcal{Z}_q)$ time. We also show that
if the user is only concerned in optimizing the download rate, a common
assumption in the literature, then the problem can be converted into a simple
private information retrieval problem by means of a scheme we call Private
Oracle Querying. However, this comes at large upload and computational costs
for both the user and the servers.


  Nonlinear non-stationary equation describing evolution of weakly curved
premixed flames with arbitrary gas expansion, subject to the Landau-Darrieus
instability, is derived. The new equation respects all the conservation laws to
be satisfied across the flame front, as well as correctly takes into account
influence of vorticity, generated in the flame, on the flame front structure
and flame velocity. Analytical solutions of the derived equation are found.


  We consider the excitation of polariton wakefields due to a propagating
source in a semiconductor micro cavity. We show that two kinds of wakes are
possible, depending on the constituents fraction (either exciton or photon) of
the polariton wavefunction. The nature of the wakefields (pure excitonic or
polaritonic) can be controled by changing the speed of propagation of the
external pump. This process could be used as a diagnostic for the internal
parameters of the microcavity.


  We present several regularity results for a biological network formulation
model originally introduced by D. Cai and D. Hu in {\it Phys. Rev. Lett.}, {\bf
111}(2013), 138701. A consequence of these result is that a stationary weak
solution must be a classical one in two space dimensions. Our mathematical
analysis is based upon the weakly monotone function theory and Hardy space
methods.


  Here we report the observation of extraordinary superconductivity in a
pressurized commercial niobium-titanium alloy. We find that its zero-resistance
superconductivity persists from ambient pressure to the pressure as high as
261.7 GPa, a record high pressure up to which a known superconducting state can
continuously survives. Remarkably, at such an ultra-high pressure, although the
ambient pressure volume is shrunk by 45% without structural phase transition,
the superconducting transition temperature (TC) increases to ~19.1 K from ~9.6
K, and the critical magnetic field (HC2) at 1.8 K has been enhanced to 19 T
from 15.4 T. These results set new records for both of the TC and the HC2 among
all the known alloy superconductors composed of only transition metal elements.
The remarkable high pressure superconducting properties observed in the NbTi
alloy not only expand our knowledge on this important commercial superconductor
but also are helpful for a better understanding on the superconducting
mechanism.


  Observations indicate that massive galaxies at z~2 are more compact than
galaxies of comparable mass at z~0, with effective radii evolving by a factor
of ~3-5. This implies that galaxies grow significantly in size but relatively
little in mass over the past ~10 Gyr. Two main physical models have been
proposed in order to explain the observed evolution of massive galaxies:
"mergers" and "puffing-up" scenarios. Here we introduce another possibility,
and discuss the potential role of the central active galactic nucleus (AGN)
feedback on the evolution of its host galaxy. We consider triggering of star
formation, due to AGN feedback, with radiation pressure on dusty gas as the
driving feedback mechanism. In this picture, stars are formed in the
feedback-driven outflow at increasingly larger radii and build up the outer
regions of the host galaxy. The resulting increase in size and stellar mass can
be compared with the observed growth of massive galaxies. Star formation in the
host galaxy is likely obscured due to dust extinction and reddening. We suggest
a number of observational predictions of our model, and discuss possible
implications for AGN feedback-driven star formation.


  The throughput benefits of random linear network codes have been studied
extensively for wirelined and wireless erasure networks. It is often assumed
that all nodes within a network perform coding operations. In
energy-constrained systems, however, coding subgraphs should be chosen to
control the number of coding nodes while maintaining throughput. In this paper,
we explore the strategic use of network coding in the wireless packet erasure
relay channel according to both throughput and energy metrics. In the relay
channel, a single source communicates to a single sink through the aid of a
half-duplex relay. The fluid flow model is used to describe the case where both
the source and the relay are coding, and Markov chain models are proposed to
describe packet evolution if only the source or only the relay is coding. In
addition to transmission energy, we take into account coding and reception
energies. We show that coding at the relay alone while operating in a rateless
fashion is neither throughput nor energy efficient. Given a set of system
parameters, our analysis determines the optimal amount of time the relay should
participate in the transmission, and where coding should be performed.


  Spontaneous symmetry-breaking, where the ground state of a system has lower
symmetry than the underlying Hamiltonian, is ubiquitous in physics. It leads to
multiply-degenerate ground states, each with a different "broken" symmetry
labeled by an order parameter. The variation of this order parameter in space
leads to soliton-like features at the boundaries of different broken-symmetry
regions and also to topological point defects. Bilayer graphene is a
fascinating realization of this physics, with an order parameter given by its
interlayer stacking coordinate. Bilayer graphene has been a subject of intense
study because in the presence of a perpendicular electric field, a band gap
appears in its electronic spectrum [1-3] through a mechanism that is intimately
tied to its broken symmetry. Theorists have further proposed that novel
electronic states exist at the boundaries between broken-symmetry stacking
domains [4-5]. However, very little is known about the structural properties of
these boundaries. Here we use electron microscopy to measure with nanoscale and
atomic resolution the widths, motion, and topological structure of soliton
boundaries and topological defects in bilayer graphene. We find that each
soliton consists of an atomic-scale registry shift between the two graphene
layers occurring over 6-11 nm. We infer the minimal energy barrier to
interlayer translation and observe soliton motion during in-situ heating above
1000 {\deg}C. The abundance of these structures across a variety samples, as
well as their unusual properties, suggests that they will have substantial
effects on the electronic and mechanical properties of bilayer graphene.


  In this paper, we show that an odd Galois representation rhobar: Gal(Qbar/Q)
--> GL_2(F_9) satisfying certain local conditions at 3 and 5 is modular. Our
main tool is an idea of Taylor, which reduces the problem to that of exhibiting
points on a Hilbert modular surface which are defined over a solvable extension
of Q, and which satisfy certain reduction properties. As a corollary, we show
that Hilbert-Blumenthal abelian surfaces over Q with good ordinary reduction at
3 and 5 are modular.


  Representation learning on graphs, also called graph embedding, has
demonstrated its significant impact on a series of machine learning
applications such as classification, prediction and recommendation. However,
existing work has largely ignored the rich information contained in the
properties (or attributes) of both nodes and edges of graphs in modern
applications, e.g., those represented by property graphs. To date, most
existing graph embedding methods either focus on plain graphs with only the
graph topology, or consider properties on nodes only. We propose PGE, a graph
representation learning framework that incorporates both node and edge
properties into the graph embedding procedure. PGE uses node clustering to
assign biases to differentiate neighbors of a node and leverages multiple
data-driven matrices to aggregate the property information of neighbors sampled
based on a biased strategy. PGE adopts the popular inductive model for
neighborhood aggregation. We provide detailed analyses on the efficacy of our
method and validate the performance of PGE by showing how PGE achieves better
embedding results than the state-of-the-art graph embedding methods on
benchmark applications such as node classification and link prediction over
real-world datasets.


  We study the lattice of finite-index extensions of a given finitely generated
subgroup $H$ of a free group $F$. This lattice is finite and we give a
combinatorial characterization of its greatest element, which is the
commensurator of $H$. This characterization leads to a fast algorithm to
compute the commensurator, which is based on a standard algorithm from automata
theory. We also give a sub-exponential and super-polynomial upper bound for the
number of finite-index extensions of $H$, and we give a language-theoretic
characterization of the lattice of finite-index subgroups of $H$. Finally, we
give a polynomial time algorithm to compute the malnormal closure of $H$.


  This paper proposes to use cepstrum for artifact detection, recognition and
removal in prefrontal EEG. This work focuses on the artifact caused by eye
movement. A database containing artifact-free EEG and eye movement contaminated
EEG from different subjects is established. A cepstral analysis-based feature
extraction with support vector machine (SVM) based classifier is designed to
identify the artifacts from the target EEG signals. The proposed method
achieves an accuracy of 99.62% on the artifact detection task and a 82.79%
accuracy on the 6-category eye movement classification task. A statistical
value-based artifact removal method is proposed and evaluated on a public EEG
database, where an accuracy improvement of 3.46% is obtained on the 3-category
emotion classification task. In order to make a confident decision of each 5s
EEG segment, the algorithm requires only 0.66M multiplication operations.
Compared to the state-of-the-art approaches in artifact detection and removal,
the proposed method features higher detection accuracy and lower computational
cost, which makes it a more suitable solution to be integrated into a real-time
and artifact robust Brain-Machine Interface (BMI).


  Non-uniform estimates are obtained for Poisson, compound Poisson, translated
Poisson, negative binomial and binomial approximations to sums of of
m-dependent integer-valued random variables. Estimates for Wasserstein metric
also follow easily from our results. The results are then exemplified by the
approximation of Poisson binomial distribution, 2-runs and $m$-dependent
$(k_1,k_2)$-events.


  Collinear high-gradient ${\cal O} (GV/m)$ beam-driven wakefield methods for
charged-particle acceleration could be critical to the realization of compact,
cost-efficient, accelerators, e.g., in support of TeV-scale lepton colliders or
multiple-user free-electron laser facilities. To make these options viable, the
high accelerating fields need to be complemented with large transformer ratios
$>2$, a parameter characterizing the efficiency of the energy transfer between
a wakefield-exciting "drive" bunch to an accelerated "witness" bunch. While
several potential current distributions have been discussed, their practical
realization appears challenging due to their often discontinuous nature. In
this paper we propose several alternative current profiles which are smooth
which also lead to enhanced transformer ratios. We especially explore a
laser-shaping method capable of generating one the suggested distributions
directly out of a photoinjector and discuss a linac concept that could possible
drive a dielectric accelerator.


  A generalized version of the so-called chiral quark soliton model (CQSM) in
nuclear physics is introduced. The Hamiltonian of the generalized CQSM is given
by a Dirac type operator with a mass term being an operator-valued function.
Some mathematically rigorous results on the model are reported. The subjects
included are: (i) supersymmetric structure; (ii) spectral properties; (iii)
symmetry reduction; (iv) a unitarily equivalent model.


  Perspective differences exist among different cultures or languages. A lack
of mutual understanding among different groups about their perspectives on
specific values or events may lead to uninformed decisions or biased opinions.
Automatically understanding the group perspectives can provide essential
background for many downstream applications of natural language processing
techniques. In this paper, we study colingual groups and use language corpora
as a proxy to identify their distributional perspectives. We present a novel
computational approach to learn shared understandings, and benchmark our method
by building culturally-aware models for the English, Chinese, and Japanese
languages. On a held out set of diverse topics including marriage, corruption,
democracy, our model achieves high correlation with human judgements regarding
intra-group values and inter-group differences.


  To a given Pisot unit $\beta$ we associate a finite abelian group whose size
appears to be equal to the discriminant of $\beta$. We call it the Pisot group
and find its representation in the two-sided $\beta$-compactum in the case of
$\beta$ satisfying the relation $Fin(\beta)=\Bbb Z[\beta]\cap[0,1)$. As a
motivation for the definition, we show that the Pisot group is the kernel of
some important arithmetic coding of the toral automorphism given by the
companion matrix naturally associated with $\beta$.


  Transductive Few-Shot Learning (TFSL) has recently attracted increasing
attention since it typically outperforms its inductive peer by leveraging
statistics of query samples. However, previous TFSL methods usually encode
uniform prior that all the classes within query samples are equally likely,
which is biased in imbalanced TFSL and causes severe performance degradation.
  Given this pivotal issue, in this work, we propose a novel Conditional
Transport (CT) based imbalanced TFSL model called {\textbf P}rototypes-oriented
{\textbf U}nbiased {\textbf T}ransfer {\textbf M}odel (PUTM) to fully exploit
unbiased statistics of imbalanced query samples, which employs forward and
backward navigators as transport matrices to balance the prior of query samples
per class between uniform and adaptive data-driven distributions. For
efficiently transferring statistics learned by CT, we further derive a closed
form solution to refine prototypes based on MAP given the learned navigators.
The above two steps of discovering and transferring unbiased statistics follow
an iterative manner, formulating our EM-based solver.
  Experimental results on four standard benchmarks including miniImageNet,
tieredImageNet, CUB, and CIFAR-FS demonstrate superiority of our model in
class-imbalanced generalization.


  I estimate the accuracies on Higgs boson coupling constants that experiments
at the Large Hadron Collider and the International Linear Collider are capable
of reaching over the long term.


  We present two recent applications of lattice-gas modeling techniques to
electrochemical adsorption on catalytically active metal substrates: urea on
Pt(100) and (bi)sulfate on Rh(111). Both involve the specific adsorption of
small molecules or ions on well-characterized single-crystal electrodes, and
they provide a particularly good fit between the adsorbate geometry and the
substrate structure. The close geometric fit facilitates the formation of
ordered submonolayer adsorbate phases in a range of electrode potential
positive of the range in which an adsorbed monolayer of hydrogen is stable. In
both systems the ordered-phase region is separated from the adsorbed- hydrogen
region by a phase transition, signified in cyclic voltammograms by a sharp
current peak. Based on data from {\it in situ\/} radiochemical surface
concentration measurements, cyclic voltammetry, and scanning tunneling micro-
scopy, and {\it ex situ\/} Auger electron spectroscopy and low-energy electron
diffraction, we have developed specific lattice-gas models for the two systems.
These models were studied by group-theoretical ground-state calcu- lations and
numerical Monte Carlo simulations, and effective lattice-gas inter- action
parameters were determined so as to provide agreement with experiments.


  In this paper, we develop a momentum super space formalism for
$\mathcal{N}=1,2$ superconformal field theories in three dimensions. First, we
solve for super-correlators in the usual momentum superspace variables.
However, we found that expressing quantities in super space spinor helicity
variables greatly simplifies the analysis. Further, by performing a "half"
Fourier transform of the Grassmann coordinates which is analogous to the
Twistor transform, an even more remarkable simplification occurs. Using these
formalism, we first compute all three point correlation functions involving
conserved super-currents with arbitrary spins in $\mathcal{N}=1,2$ theories. We
discover interesting double copy relations in $\mathcal{N}=1$
super-correlators. Also, we discovered super double copy relations that take us
from $\mathcal{N}=1$ to $\mathcal{N}=2$ super-correlators. We also comment on
the connection of our results with the flat space super amplitudes in one
higher dimension.


  There is compelling evidence that active galactic nuclei (AGNs) in
high-density regions have undergone a different evolution than their
counterparts in the field, indicating that they are strongly affected by their
environment. To investigate the various factors that may affect the prevalence
of AGNs in cluster galaxies, we selected a sample of 19 thoroughly studied
X-ray-selected galaxy clusters from the LoCuSS survey. All these clusters are
considered massive, with $M_{500}\gtrsim 2\times10^{14} M_{solar}$, and span a
narrow redshift range between $z\sim$0.16 and 0.28. We divided the cluster
surroundings into two concentric annuli with a width of $R_{500}$ radius. We
further divided the cluster sample based on the presence of infalling
X-ray-detected groups, cluster mass, or dynamical state. We found that the
X-ray AGN fraction in the outskirts is consistent with the field, but it is
significantly lower in cluster centres, in agreement with previous results for
massive clusters. We show that these results do not depend on cluster mass.
Furthermore, we did not find any evidence of a spatial correlation between
infalling groups and AGNs. Nevertheless, a significant excess of X-ray AGNs is
found in the outskirts of relaxed clusters at the 2$\sigma$ confidence level,
compared both to non-relaxed clusters and to the field. Our results suggest
that the mechanisms that trigger AGN activity may vary between cluster centres
and the outskirts. Ram pressure can efficiently remove the gas from infalling
galaxies, thereby triggering AGN activity in some cases. However, the reduced
availability of gas globally diminishes the fraction of AGNs in cluster
centers. The surplus of X-ray AGNs identified in the outskirts of relaxed
clusters may be attributed to an increased frequency of galaxy mergers, a
notion that is further supported by the disturbed morphology observed in
several galaxies.


  In this article we consider semigroups of transformations of cellular
automata which act on a fixed shift space. In particular, we are interested in
two properties of these semigroups which relate to "largeness". The first
property is ID and the other property is maximal commutativity (MC). A
semigroup has the ID property if the only infinite invariant closed set (with
respect to the semigroup action) is the entire space. We shall consider two
examples of semigroups: one is spanned by cellular automata transformations
that represent multiplications by integers on the one-dimensional torus and the
other one consists of all the cellular automata transformations which are
linear (when the symbols set is the ring of integers mod n). It will be shown
that the two properties of these semigroups depend on the number of symbols s.
The multiplication semigroup is ID and MC if and only if s is not a power of
prime. The linear semigroup over the mentioned ring is always MC but is ID if
and only if s is prime. When the symbol set is endowed with a finite field
structure (when possible) the linear semigroup is both ID and MC. In addition,
we associate with each semigroup which acts on a one sided shift space a
semigroup acting on a two sided shift space, and vice versa, in such a way that
preserves the ID and the MC properties.


  We show that $\mathbb{P} ( \ell_X(0,T] \leq 1)=(c_X+o(1))T^{-(1-H)}$, where
$\ell_X$ is the local time measure at $0$ of any recurrent $H$-self-similar
real-valued process $X$ with stationary increments that admits a sufficiently
regular local time and $c_X$ is some constant depending only on $X$. A special
case is the Gaussian setting, i.e. when the underlying process is fractional
Brownian motion, in which our result settles a conjecture by Molchan [Commun.
Math. Phys. 205, 97-111 (1999)] who obtained the upper bound $1-H$ on the decay
exponent of $\mathbb{P} ( \ell_X(0,T] \leq 1)$. Our approach establishes a new
connection between persistence probabilities and Palm theory for self-similar
random measures, thereby providing a general framework which extends far beyond
the Gaussian case.


  The availability of a robust map-based localization system is essential for
the operation of many autonomously navigating vehicles. Since uncertainty is an
inevitable part of perception, it is beneficial for the robustness of the robot
to consider it in typical downstream tasks of navigation stacks. In particular
localization and mapping methods, which in modern systems often employ
convolutional neural networks (CNNs) for perception tasks, require proper
uncertainty estimates. In this work, we present uncertainty-aware Panoptic
Localization and Mapping (uPLAM), which employs pixel-wise uncertainty
estimates for panoptic CNNs as a bridge to fuse modern perception with
classical probabilistic localization and mapping approaches. Beyond the
perception, we introduce an uncertainty-based map aggregation technique to
create accurate panoptic maps, containing surface semantics and landmark
instances. Moreover, we provide cell-wise map uncertainties, and present a
particle filter-based localization method that employs perception
uncertainties. Extensive evaluations show that our proposed incorporation of
uncertainties leads to more accurate maps with reliable uncertainty estimates
and improved localization accuracy. Additionally, we present the Freiburg
Panoptic Driving dataset for evaluating panoptic mapping and localization
methods. We make our code and dataset available at:
\url{http://uplam.cs.uni-freiburg.de}


  Recent lattice QCD calculations from the HAL and NPLQCD Collaborations have
reported evidence for the existence of a bound state with strangeness -2 and
baryon number 2 at quark masses somewhat higher than the physical values. A
controlled chiral extrapolation of these lattice results to the physical point
suggested that the state, identified with the famed H dibaryon, is most likely
slightly unbound (by 13 $\pm$ 14 MeV) with respect to the $\Lambda--\Lambda$
threshold. We report the results of an updated analysis which finds the H
unbound by 26 $\pm$ 11 MeV. Apart from the insight it would give us into how
QCD is realized in Nature, the H is of great interest because of its potential
implications for the equation of state of dense matter and studies of neutron
stars. It may also explain the enhancement above the $\Lambda--\Lambda$
threshold already reported experimentally. It is clearly of great importance
that the latter be pursued in experiments at the new J-PARC facility.


  We consider a positive stationary generalized Ornstein--Uhlenbeck process
\[V_t=\mathrm{e}^{-\xi_t}\biggl(\int_0^t\mathrm{e}^{\xi_{s-}}\
,\mathrm{d}\eta_s+V_0\biggr)\qquadfor t\geq0,\] and the increments of the
integrated generalized Ornstein--Uhlenbeck process
$I_k=\int_{k-1}^k\sqrt{V_{t-}} \mathrm{d}L_t$, $k\in\mathbb{N}$, where
$(\xi_t,\eta_t,L_t)_{t\geq0}$ is a three-dimensional L\'{e}vy process
independent of the starting random variable $V_0$. The genOU model is a
continuous-time version of a stochastic recurrence equation. Hence, our models
include, in particular, continuous-time versions of $\operatorname {ARCH}(1)$
and $\operatorname {GARCH}(1,1)$ processes. In this paper we investigate the
asymptotic behavior of extremes and the sample autocovariance function of
$(V_t)_{t\geq0}$ and $(I_k)_{k\in\mathbb{N}}$. Furthermore, we present a
central limit result for $(I_k)_{k\in\mathbb{N}}$. Regular variation and point
process convergence play a crucial role in establishing the statistics of
$(V_t)_{t\geq0}$ and $(I_k)_{k\in\mathbb{N}}$. The theory can be applied to the
$\operatorname {COGARCH}(1,1)$ and the Nelson diffusion model.


  We fix $n$ and say a square in the two-dimensional grid indexed by $(x,y)$
has color $c$ if $x+y \equiv c \pmod{n}$. A {\it ribbon tile} of order $n$ is a
connected polyomino containing exactly one square of each color. We show that
the set of order-$n$ ribbon tilings of a simply connected region $R$ is in
one-to-one correspondence with a set of {\it height functions} from the
vertices of $R$ to $\mathbb Z^{n}$ satisfying certain difference restrictions.
It is also in one-to-one correspondence with the set of acyclic orientations of
a certain partially oriented graph.
  Using these facts, we describe a linear (in the area of $R$) algorithm for
determining whether $R$ can be tiled with ribbon tiles of order $n$ and
producing such a tiling when one exists. We also resolve a conjecture of Pak by
showing that any pair of order-$n$ ribbon tilings of $R$ can be connected by a
sequence of local replacement moves. Some of our results are generalizations of
known results for order-2 ribbon tilings (a.k.a. domino tilings). We also
discuss applications of multidimensional height functions to a broader class of
polyomino tiling problems.


  Understanding the relaxation process is the most important unsolved problem
in non-equilibrium quantum physics. Current understanding primarily concerns on
if and how an isolated quantum many-body system thermalize. However, there is
no clear understanding of what conditions and on which time-scale do
thermalization occurs. In this article, we simulate the quench dynamics of
one-dimensional Bose gas in an optical lattice from an{\it {ab initio}}
perspective by solving the time-dependent many-boson Schr\"odinger equation
using the multi-configurational time-dependent Hartree method for bosons
(MCTDHB). We direct a superfluid (SF) to Mott-insulator (MI) transition by
performing two independent quenches: an interaction quench when the interaction
strength is changed instantaneously, and a lattice depth quench where the depth
of the lattice is altered suddenly. We show that although the Bose-Hubbard
model predicts identical physics, the general many-body treatment shows
significant differences between the two cases. We observe that lattice depth
quench exhibits a large time-scale to reach the MI state and shows an
oscillatory phase collapse-revival dynamics and a complete absence of
thermalization that reveals through the analysis of the time-evolution of the
reduced one-body density matrix, two-body density, and entropy production. In
contrast, the interaction quench shows a swift transition to the MI state and
shows a clear signature of thermalization for strong quench values. We provide
a physical explanation for these differences and prescribe an analytical
fitting formula for the time required for thermalization.


  Let X be a Fano manifold with Picard number one such that the tangent bundle
T_X is big. If X admits a rational curve with trivial normal bundle, we show
that X is isomorphic to the del Pezzo threefold of degree five.


  A {\it universal labeling} of a graph $G$ is a labeling of the edge set in
$G$ such that in every orientation $\ell$ of $G$ for every two adjacent
vertices $v$ and $u$, the sum of incoming edges of $v$ and $u$ in the oriented
graph are different from each other. The {\it universal labeling number} of a
graph $G$ is the minimum number $k$ such that $G$ has {\it universal labeling}
from $\{1,2,\ldots, k\}$ denoted it by $\overrightarrow{\chi_{u}}(G) $. We have
$2\Delta(G)-2 \leq \overrightarrow{\chi_{u}} (G)\leq 2^{\Delta(G)}$, where
$\Delta(G)$ denotes the maximum degree of $G$. In this work, we offer a
provocative question that is:" Is there any polynomial function $f$ such that
for every graph $G$, $\overrightarrow{\chi_{u}} (G)\leq f(\Delta(G))$?".
Towards this question, we introduce some lower and upper bounds on their
parameter of interest. Also, we prove that for every tree $T$,
$\overrightarrow{\chi_{u}}(T)=\mathcal{O}(\Delta^3) $. Next, we show that for a
given 3-regular graph $G$, the universal labeling number of $G$ is 4 if and
only if $G$ belongs to Class 1. Therefore, for a given 3-regular graph $G$, it
is an $ \mathbf{NP} $-complete to determine whether the universal labeling
number of $G$ is 4. Finally, using probabilistic methods, we almost confirm a
weaker version of the problem.


  We investigate the correlation between integrated proton-neutron interactions
obtained by using the up-to-date experimental data of binding energies and the
$N_{\rm p} N_{\rm n}$, the product of valence proton number and valence neutron
number with respect to the nearest doubly closed nucleus. We make corrections
on a previously suggested formula for the integrated proton-neutron
interaction. Our results demonstrate a nice, nearly linear, correlation between
the integrated p-n interaction and $N_{\rm p} N_{\rm n}$, which provides us
with a firm foundation of the applicability of the $N_{\rm p} N_{\rm n}$ scheme
to nuclei far from the stability line.


  We present a novel approach to improve the performance of deep reinforcement
learning (DRL) based outdoor robot navigation systems. Most, existing DRL
methods are based on carefully designed dense reward functions that learn the
efficient behavior in an environment. We circumvent this issue by working only
with sparse rewards (which are easy to design), and propose a novel adaptive
Heavy-Tailed Reinforce algorithm for Outdoor Navigation called HTRON. Our main
idea is to utilize heavy-tailed policy parametrizations which implicitly induce
exploration in sparse reward settings. We evaluate the performance of HTRON
against Reinforce, PPO and TRPO algorithms in three different outdoor
scenarios: goal-reaching, obstacle avoidance, and uneven terrain navigation. We
observe in average an increase of 34.41% in terms of success rate, a 15.15%
decrease in the average time steps taken to reach the goal, and a 24.9%
decrease in the elevation cost compared to the navigation policies obtained by
the other methods. Further, we demonstrate that our algorithm can be
transferred directly into a Clearpath Husky robot to perform outdoor terrain
navigation in real-world scenarios.


  A refined form of the `Folk Theorem' that a smooth action by a compact Lie
group can be (canonically) resolved, by iterated blow up, to have unique
isotropy type is proved in the context of manifolds with corners. This
procedure is shown to capture the simultaneous resolution of all isotropy types
in a `resolution structure' consisting of equivariant iterated fibrations of
the boundary faces. This structure projects to give a similar resolution
structure for the quotient. In particular these results apply to give a
canonical resolution of the radial compactification, to a ball, of any finite
dimensional representation of a compact Lie group; such resolutions of the
normal action of the isotropy groups appear in the boundary fibers in the
general case.


  Natural images are characterized by the multiscaling properties of their
contrast gradient, in addition to their power spectrum. In this work we show
that those properties uniquely define an {\em intrinsic wavelet} and present a
suitable technique to obtain it from an ensemble of images. Once this wavelet
is known, images can be represented as expansions in the associated wavelet
basis. The resulting code has the remarkable properties that it separates
independent features at different resolution level, reducing the redundancy,
and remains essentially unchanged under changes in the power spectrum. The
possible generalization of this representation to other systems is discussed.


  We consider a supersymmetric type-I seesaw framework with non-universal
scalar masses at the GUT scale to explain the long-standing discrepancy of the
anomalous magnetic moment of the muon. We find that it is difficult to
accommodate the muon g-2 while keeping charged-lepton flavor violating
processes under control for the conventional SO(10)-based relation between the
up sector and neutrino sector. However, such tension can be relaxed by adding a
Georgi-Jarlskog factor for the Yukawa matrices, which requires a non-trivial
GUT-based model. In this model, we find that both observables are compatible
for small mixings, CKM-like, in the neutrino Dirac Yukawa matrix.


  Recently, huge attention has been drawn to improve optical sensing devices
based on photonic resonators in the presence of graphene. In this paper, based
on the transfer matrix approach and TE polarization for the incident
electromagnetic waves, we numerically evaluate the transmission and reflection
spectra for one-dimensional photonic resonators and surface plasmon resonances
with strained graphene, respectively. We proved that a relatively small strain
field in graphene can modulate linearly polarized resonant modes within the
photonic bandgap of the defective crystal. Moreover, we study the strain
effects on the surface plasmon resonances created by the evanescent wave
technique at the interference between a monolayer graphene and prism.


  Surgery for brain cancer is a major problem in neurosurgery. The diffuse
infiltration into the surrounding normal brain by these tumors makes their
accurate identification by the naked eye difficult. Since surgery is the common
treatment for brain cancer, an accurate radical resection of the tumor leads to
improved survival rates for patients. However, the identification of the tumor
boundaries during surgery is challenging. Hyperspectral imaging is a
noncontact, non-ionizing and non-invasive technique suitable for medical
diagnosis. This study presents the development of a novel classification method
taking into account the spatial and spectral characteristics of the
hyperspectral images to help neurosurgeons to accurately determine the tumor
boundaries in surgical-time during the resection, avoiding excessive excision
of normal tissue or unintentionally leaving residual tumor. The algorithm
proposed in this study to approach an efficient solution consists of a hybrid
framework that combines both supervised and unsupervised machine learning
methods. To evaluate the proposed approach, five hyperspectral images of
surface of the brain affected by glioblastoma tumor in vivo from five different
patients have been used. The final classification maps obtained have been
analyzed and validated by specialists. These preliminary results are promising,
obtaining an accurate delineation of the tumor area.


  When locally exciting a quantum lattice model, the excitation will propagate
through the lattice. The effect is responsible for a wealth of non-equilibrium
phenomena, and has been exploited to transmit quantum information through spin
chains. It is a commonly expressed belief that for local Hamiltonians, any such
propagation happens at a finite "speed of sound". Indeed, the Lieb-Robinson
theorem states that in spin models, all effects caused by a perturbation are
limited to a causal cone defined by a constant speed, up to exponentially small
corrections. In this work we show that for translationally invariant bosonic
models with nearest-neighbor interactions, this belief is incorrect: We prove
that one can encounter excitations which accelerate under the natural dynamics
of the lattice and allow for reliable transmission of information faster than
any finite speed of sound. The effect is only limited by the model's range of
validity (eventually by relativity). It also implies that in non-equilibrium
dynamics of strongly correlated bosonic models far-away regions may become
quickly entangled, suggesting that their simulation may be much harder than
that of spin chains even in the low energy sector.


  In this paper we employ a gaussian expansion within the finite-$U$
slave-bosons formalism to investigate the momentum structure of the
electron-phonon vertex function in the Hubbard model as function of $U$ and
$n$. The suppression of large momentum scattering and the onset a small-${\bf
q}$ peak structure, parametrized by a cut-off $q_c$, are shown to be
essentially ruled by the band narrowing factor $Z_{\rm MF}$ due to the
electronic correlation. A phase diagram of $Z_{\rm MF}$ and $q_c$ in the whole
$U$-$n$ space is presented. Our results are in more than qualitative agreement
with a recent numerical analysis and permit to understand some anomalous
features of the Quantum Monte Carlo data.


  We consider MCMC algorithms for certain particle systems which include both
attractive and repulsive forces, making their convergence analysis challenging.
We prove that a version of these algorithms on a bounded state space is
uniformly ergodic with an explicit quantitative convergence rate. We also prove
that a version on an unbounded state-space is still geometrically ergodic, and
then use the method of shift-coupling to obtain an explicit quantitative bound
on its convergence rate.


  The paradigmatic Luminous Blue Variable R127 in the Large Magellanic Cloud
has been found in the intermediate, peculiar early-B state, and substantially
fainter in visual light, signaling the final decline from its major outburst
that began between 1978 and 1980. This transformation was detected in 2008
January, but archival data show that it began between early 2005 and early
2007. In fact, significant changes from the maximum, peculiar A-type spectrum,
which was maintained from 1986 through 1998, had already begun the following
year, coinciding with a steep drop in visual light. We show detailed
correspondences between the spectrum and light, in which the decline mimics the
rise. Moreover, these trends are not monotonic but are characterized by
multiple spikes and dips, which may provide constraints on the unknown outburst
mechanism. Intensive photometric and spectroscopic monitoring of R127 should
now resume, to follow the decline presumably back to the quiescent Ofpe/WN9
state, in order to fully document the remainder of this unique observational
opportunity.


  The ribosome flow model (RFM) is a phenomenological model for the flow of
particles along a 1D chain of $n$ sites. It has been extensively used to study
ribosome flow along the mRNA molecule during translation. When the transition
rates along the chain are time-varying and jointly $T$-periodic the RFM
entrains, i.e., every trajectory of the RFM converges to a unique $T$-periodic
solution that depends on the transition rates, but not on the initial
condition. In general, entrainment to periodic excitations like the 24h solar
day or the 50Hz frequency of the electric grid is important in numerous natural
and artificial systems. An interesting question, called the gain of entrainment
(GOE) in the RFM, is whether proper coordination of the periodic translation
rates along the mRNA can lead to a larger average protein production rate.
Analyzing the GOE in the RFM is non-trivial and partial results exist only for
the RFM with dimensions $n=1,2$. We use a new approach to derive several
results on the GOE in the general $n$-dimensional RFM. Perhaps surprisingly, we
rigorously characterize several cases where there is no GOE, so to maximize the
average production rate in these cases, the best choice is to use constant
transition rates all along the chain.


  Let M be a translation surface. We show that certain deformations of M
supported on the set of all cylinders in a given direction remain in the
GL(2,R)-orbit closure of M. Applications are given concerning complete
periodicity, field of definition, and the number of of parallel cylinders which
may be found on a translation surface in a given orbit closure.
  The proof uses Eskin-Mirzakhani-Mohammadi's recent theorem on orbit closures
of translation surfaces, as well as results of Minsky-Weiss and Smillie-Weiss
on the dynamics of horocycle flow.


  We present a finite element method for Stokes equations using the
Crouzeix-Raviart element for the velocity and the continuous linear element for
the pressure. We show that the inf-sup condition is satisfied for this pair.
Two numerical experiments are presented to support the theoretical results.


  We prove some basic properties of the relative Nakayama-Zariski
decomposition. We apply them to the study of lc generalized pairs. We prove the
existence of log minimal models or Mori fiber spaces for (relative) lc
generalized pairs polarized by an ample divisor. This extends a result of
Hashizume-Hu to generalized pairs. We also show that, for any lc generalized
pair $(X,B+A,{\bf{M}})/Z$ such that $K_X+B+A+{\bf{M}}_X\sim_{\mathbb R,Z}0$ and
$B\geq 0,A\geq 0$, $(X,B,{\bf{M}})/Z$ has either a log minimal model or a Mori
fiber space. This is an analogue of a result of Birkar/Hacon-Xu and Hashizume
in the category of generalized pairs, and is later shown to be crucial to the
proof of the existence of lc generalized flips in full generality.


  In this study I proposed a filtering beliefs method for improving performance
of Partially Observable Markov Decision Processes(POMDPs), which is a method
wildly used in autonomous robot and many other domains concerning control
policy. My method search and compare every similar belief pair. Because a
similar belief have insignificant influence on control policy, the belief is
filtered out for reducing training time. The empirical results show that the
proposed method outperforms the point-based approximate POMDPs in terms of the
quality of training results as well as the efficiency of the method.


  We demonstrate that certain Virasoro characters (and their linear
combinations) in minimal and non-minimal conformal models which admit
factorized forms are manifestly related to the ADE series. This permits to
extract quasi-particle spectra of a Lie algebraic nature which resembles the
features of Toda field theory. These spectra possibly admit a construction in
terms of the $W_n$-generators. In the course of our analysis we establish
interrelations between the factorized characters related to the parafermionic
models, the compactified boson and the minimal models.


  The proliferation of large language models (LLMs) in the real world has come
with a rise in copyright cases against companies for training their models on
unlicensed data from the internet. Recent works have presented methods to
identify if individual text sequences were members of the model's training
data, known as membership inference attacks (MIAs). We demonstrate that the
apparent success of these MIAs is confounded by selecting non-members (text
sequences not used for training) belonging to a different distribution from the
members (e.g., temporally shifted recent Wikipedia articles compared with ones
used to train the model). This distribution shift makes membership inference
appear successful. However, most MIA methods perform no better than random
guessing when discriminating between members and non-members from the same
distribution (e.g., in this case, the same period of time). Even when MIAs
work, we find that different MIAs succeed at inferring membership of samples
from different distributions. Instead, we propose a new dataset inference
method to accurately identify the datasets used to train large language models.
This paradigm sits realistically in the modern-day copyright landscape, where
authors claim that an LLM is trained over multiple documents (such as a book)
written by them, rather than one particular paragraph. While dataset inference
shares many of the challenges of membership inference, we solve it by
selectively combining the MIAs that provide positive signal for a given
distribution, and aggregating them to perform a statistical test on a given
dataset. Our approach successfully distinguishes the train and test sets of
different subsets of the Pile with statistically significant p-values < 0.1,
without any false positives.


  Recent years have witnessed the emergence of textual commonsense knowledge
bases, aimed at providing more nuanced and context-rich knowledge. The
integration of external commonsense into language models has been shown to be a
key enabler in advancing the state-of-the-art for a wide range of NLP tasks.
However, incorporating textual commonsense descriptions is computationally
expensive, as compared to encoding conventional symbolic knowledge. In this
paper, we propose a method to improve its efficiency without modifying the
model. We group training samples with similar commonsense descriptions into a
single batch, thus reusing the encoded description across multiple samples. One
key observation is that the upper bound of batch partitioning can be reduced to
the classic {\it graph k-cut problem}. Consequently, we propose a spectral
clustering-based algorithm to solve this problem. Extensive experiments
illustrate that the proposed batch partitioning approach effectively reduces
the computational cost while preserving performance. The efficiency improvement
is more pronounced on larger datasets and on devices with more memory capacity,
attesting to its practical utility for large-scale applications.


  A voxelization based post-processing algorithm is proposed to analyze the
packing of non-spherical particle assemblies simulated using the Discrete
Element Method. Voxelization of the particle data allows for isolating the
geometric features of the granular assembly in various spatial sub-domains (2D
surface or 3D region) and investigate the localized packing behaviour.
Analyzing the local packing behaviour enables determining con-fined influences
such as the wall-effect, stacking behaviour, local expansion/contraction and
localized loading. The efficacy of the proposed technique to analyze practical
granular assemblies is demonstrated through the packing analysis of different
assemblies of superquadric cubes, superquadric ellipsoidals, and
multi-spherical coffee beans.


  Magnetic resonance imaging (MRI) has revolutionized biomedical science by
providing non-invasive, three-dimensional biological imaging. However, spatial
resolution in conventional MRI systems is limited to tens of microns, which is
insufficient for imaging on molecular and atomic scales. Here we demonstrate an
MRI technique that provides sub-nanometer spatial resolution in three
dimensions, with single electron-spin sensitivity. Our imaging method works
under ambient conditions and can measure ubiquitous 'dark' spins, which
constitute nearly all spin targets of interest and cannot otherwise be
individually detected. In this technique, the magnetic quantum-projection noise
of dark spins is measured using a single nitrogen-vacancy (NV) magnetometer
located near the surface of a diamond chip. The spatial distribution of spins
surrounding the NV magnetometer is imaged with a scanning magnetic-field
gradient. To evaluate the performance of the NV-MRI technique, we image the
three-dimensional landscape of dark electronic spins at and just below the
diamond surface and achieve an unprecedented combination of resolution (0.8 nm
laterally and 1.5 nm vertically) and single-spin sensitivity. Our measurements
uncover previously unidentified electronic spins on the diamond surface, which
can potentially be used as resources for improved magnetic imaging of samples
proximal to the NV-diamond sensor. This three-dimensional NV-MRI technique is
immediately applicable to diverse systems including imaging spin chains,
readout of individual spin-based quantum bits, and determining the precise
location of spin labels in biological systems.


  The sum theorem and its corollaries are proved for a countable family of
zero-dimensional (in the sense of small and large inductive bidimensions)
p-closed sets, using a new notion of relative normality whose topological
correspondent is also new. The notion of almost $n$-dimensionality is
considered from the bitopological point of view.
  Bitopological spaces in which every subset is i-open in its $j$-closure
(i.e.,(i,j)-submaximal spaces) are introduced and their properties are studied.
Based on the investigations begun in [5] and [14], sufficient conditions are
found for bitopological spaces to be(1,2)-Baire in the class of p-normal
spaces. Furthermore, (i,j)-I-spaces are introduced and both the relations
between(i,j)-submaximal, (i,j)-nodec and (i,j)-I-spaces, and their properties
are studied when two topologies on a set are either independent of each other
or interconnected by the inclusion, S-, C- and N-relations or by their
combinations.
  The final part of the paper deals with the questions of preservation of
$(i,j)$-submaximal and $(2,1)\dd I$-spaces to an image, of $D$-spaces to an
image and an inverse image for both the topological and the bitopological
cases. Two theorems are formulated containing, on the one hand, topological
conditions and, on the other hand, bitopological ones, under which a
topological space is a $D$-space.


  Wearable biosensor technology enables real-time, convenient, and continuous
monitoring of users behavioral signals. Such include signals relative to body
motion, body temperature, biological or biochemical markers, and individual
grip forces, which are studied in this paper. A four step pick and drop image
guided and robot assisted precision task has been designed for exploiting a
wearable wireless sensor glove system. Individual spatio temporal grip forces
are analyzed on the basis of thousands of individual sensor data, collected
from different locations on the dominant and non-dominant hands of each of
three users in ten successive task sessions. Statistical comparisons reveal
specific differences between grip force profiles of the individual users as a
function of task skill level (expertise) and time.


  We demonstrate the phenomenon of self organized criticality (SOC) in a simple
random walk model described by a random walk of a myopic ant. The ant acts on
the underlying lattice aiming at uniform digging of the surface but is
unaffected by the underlying lattice. In 1-d, 2-d and 3-d we have explored this
model and have obtained power laws in the time intervals between consecutive
events of `digging'. Being a simple random walk, the power laws in space
translate to power laws in time. We also study the finite size scaling of
asymptotic scale invariant process as well as dynamic scaling in this system.
This model differs qualitatively from the cascade models of SOC.


  Anderson localization marks a halt of diffusive wave propagation in
disordered systems. Despite extensive studies over the past 40 years, Anderson
localization of light in three dimensions has remained elusive, leading to the
question of its very existence. Recent orders-of-magnitude speed-up of
finite-difference time-domain calculations allows us to conduct brute-force
numerical simulations of light transport in fully disordered 3D systems with
unprecedented dimension and refractive index contrast. We demonstrate
three-dimensional localization of vector electromagnetic waves in random
packings of metallic spheres, in sharp contrast to the absence of localization
for dielectric spheres with a refractive index contrast up to 10. Our work
opens a wide range of avenues in both fundamental research related to Anderson
localization and potential applications using 3D localized light.


  The ultra-precise Gravity Probe B experiment measured the frame-dragging
effect and geodetic precession on four quartz gyros. We use this result to test
WEP II (Weak Equivalence Principle II) which includes rotation in the universal
free-fall motion. The free-fall E\"otv\"os parameter eta for rotating body is <
= 10**(-11) with four-order improvement over previous results. The anomalous
torque per unit angular momentum parameter lambda is constrained to (-0.05 +-
3.67) \times 10**(-15) s-1, (0.24 +- 0.98) \times 10**(-15) s-1, and (0 +- 3.6)
\times 10**(-13) s-1 respectively in the directions of geodetic effect,
frame-dragging effect and angular momentum axis; the dimensionless
frequency-dependence parameter {\kappa} is constrained to (1.75 +- 4.96) \times
10**(-17), (1.80 +- 1.34) \times 10**(-17), and (0 +- 3) \times 10**(-14)
respectively.


  Probing the gas and dust in proto-planetary disks is central for
understanding the process of planet formation. In disks surrounding solar type
protostars, the bulk of the disk mass resides in the outer midplane, which is
cold ($\leq$20 K), dense ($\geq 10^7$ cm$^{-3}$) and depleted of CO. Observing
the disk midplane has proved, therefore, to be a formidable challenge.
Ceccarelli et al. (2004) detected H$_2$D$^+$ emission in a proto-planetary disk
and claimed that it probes the midplane gas. Indeed, since all heavy-elements
bearing molecules condense out onto the grain mantles, the most abundant ions
in the disk midplane are predicted to be H$_3^+$ and its isotopomers. In this
article, we carry out a theoretical study of the chemical structure of the
outer midplane of proto-planetary disks. Using a self-consistent physical model
for the flaring disk structure, we compute the abundances of H$_3^+$ and its
deuterated forms across the disk midplane. We also provide the average column
densities across the disk of H$_3^+$, H$_2$D$^+$, HD$_2^+$ and D$_3^+$, and
line intensities of the ground transitions of the ortho and para forms of
H$_2$D$^+$ and HD$_2^+$ respectively. We discuss how the results depend on the
cosmic ray ionization rate, dust-to-gas ratio and average grain radius, and
general stellar/disk parameters. An important factor is the poorly understood
freeze-out of N$_2$ molecules onto grains, which we investigate in depth. We
finally summarize the diagnostic values of observations of the H$_3^+$
isotopomers.


  We present a Monte-Carlo technique to probe the cosmic Infrared background
radiation (CIB) with faint source confusion in deep, wide-field 4 micron
images. We report a detection of surface brightness fluctuations using an
ensemble of 5000 pixels. The brightness fluctuations do not show correlated
structure and appear to be dominated by galaxies. We estimate a lower limit
(95% C.L.) on CIB by modeling the number-count behavior of contributing sources
to the detected fluctuations.


  Recent work pre-training Transformers with self-supervised objectives on
large text corpora has shown great success when fine-tuned on downstream NLP
tasks including text summarization. However, pre-training objectives tailored
for abstractive text summarization have not been explored. Furthermore there is
a lack of systematic evaluation across diverse domains. In this work, we
propose pre-training large Transformer-based encoder-decoder models on massive
text corpora with a new self-supervised objective. In PEGASUS, important
sentences are removed/masked from an input document and are generated together
as one output sequence from the remaining sentences, similar to an extractive
summary. We evaluated our best PEGASUS model on 12 downstream summarization
tasks spanning news, science, stories, instructions, emails, patents, and
legislative bills. Experiments demonstrate it achieves state-of-the-art
performance on all 12 downstream datasets measured by ROUGE scores. Our model
also shows surprising performance on low-resource summarization, surpassing
previous state-of-the-art results on 6 datasets with only 1000 examples.
Finally we validated our results using human evaluation and show that our model
summaries achieve human performance on multiple datasets.


  We enumerate the number of RNA contact structures according to their genus,
i.e. the topological character of their pseudoknots. By using a recently
proposed matrix model formulation for the RNA folding problem, we obtain exact
results for the simple case of an RNA molecule with an infinitely flexible
backbone, in which any arbitrary pair of bases is allowed. We analyze the
distribution of the genus of pseudoknots as a function of the total number of
nucleotides along the phosphate-sugar backbone.


  Recent progresses in ultra low power microelectronics propelled the
development of several microsensors and particularly the self powered
microsystems (SPMS). One of their limitations is their size and their autonomy
due to short lifetime of the batteries available on the market. To ensure their
ecological energetic autonomy, a promising alternative is to scavenge the
ambient energy such as the mechanical one. Nowadays, few microgenerators
operate at low frequency. They are often rigid structures that can perturb the
application or the environment; none of them are perfectly flexible. Thus, our
objective is to create a flexible, non-intrusive scavenger using electroactive
polymers. The goal of this work is to design a generator which can provide
typically 100 ?W to supply a low consumption system. We report in this paper an
analytical model which predicts the energy produced by a simple electroactive
membrane, and some promising experimental results.


  We study the stability of explicit one-step integration schemes for the
linear finite element approximation of linear parabolic equations. The derived
bound on the largest permissible time step is tight for any mesh and any
diffusion matrix within a factor of $2(d+1)$, where $d$ is the spatial
dimension. Both full mass matrix and mass lumping are considered. The bound
reveals that the stability condition is affected by two factors. The first one
depends on the number of mesh elements and corresponds to the classic bound for
the Laplace operator on a uniform mesh. The other factor reflects the effects
of the interplay of the mesh geometry and the diffusion matrix. It is shown
that it is not the mesh geometry itself but the mesh geometry in relation to
the diffusion matrix that is crucial to the stability of explicit methods. When
the mesh is uniform in the metric specified by the inverse of the diffusion
matrix, the stability condition is comparable to the situation with the Laplace
operator on a uniform mesh. Numerical results are presented to verify the
theoretical findings.


  The Omnibus Directive is an essential part of the European Union's New Deal
for Consumers. The Directive introduces new regulations in trade, including
e-commerce, with the main goal being to increase transparency, fairness and
consumer protection. The authors critically draw attention to a significant
oversight in the Omnibus Directive, namely the lack of consideration of
recommendation systems. Recommendation engines can be a source of potentially
harmful practices affecting consumers, hence the need for a directive
extension. The proposals presented in this article include the introduction of
ethical supervision over recommendation systems to minimize the risk of
negative effects of their recommendations, as well as a clear explanation of
the criteria on which recommendations are made -- similar to search result
rankings.
  --
  Dyrektywa Omnibus stanowi istotn\k{a} cz\k{e}\'s\'c Nowego {\L}adu dla
Konsument\'ow (ang. \emph{New Deal for Consumers}) Unii Europejskiej. Dyrektywa
wprowadza nowe regulacje w handlu, w tym e-commerce, kt\'orych g{\l}\'ownym
celem jest zwi\k{e}kszenie przejrzysto\'sci, uczciwo\'sci i ochrony
konsument\'ow. Autorzy krytycznie zwracaj\k{a} uwag\k{e} na istotne zaniedbanie
w dyrektywie Omnibus, jakim jest brak uwzgl\k{e}dnienia system\'ow
rekomendacyjnych. Silniki rekomendacyjne mog\k{a} by\'c \'zr\'od{\l}em
potencjalnie szkodliwych praktyk uderzaj\k{a}cych w konsument\'ow, st\k{a}d
niezb\k{e}dne jest rozszerzenie dyrektywy. Propozycje przedstawione w
niniejszym artykule obejmuj\k{a} wprowadzenie etycznego nadzoru nad systemami
rekomenduj\k{a}cymi, aby zminimalizowa\'c ryzyko negatywnych skutk\'ow ich
rekomendacji, a tak\.ze jasne wyja\'snienie kryteri\'ow, na podstawie kt\'orych
dokonywane s\k{a} rekomendacje -- analogicznie do ranking\'ow wynik\'ow
wyszukiwania.


  The dynamic expansion architecture is becoming popular in class incremental
learning, mainly due to its advantages in alleviating catastrophic forgetting.
However, task confusion is not well assessed within this framework, e.g., the
discrepancy between classes of different tasks is not well learned (i.e.,
inter-task confusion, ITC), and certain priority is still given to the latest
class batch (i.e., old-new confusion, ONC). We empirically validate the side
effects of the two types of confusion. Meanwhile, a novel solution called Task
Correlated Incremental Learning (TCIL) is proposed to encourage discriminative
and fair feature utilization across tasks. TCIL performs a multi-level
knowledge distillation to propagate knowledge learned from old tasks to the new
one. It establishes information flow paths at both feature and logit levels,
enabling the learning to be aware of old classes. Besides, attention mechanism
and classifier re-scoring are applied to generate more fair classification
scores. We conduct extensive experiments on CIFAR100 and ImageNet100 datasets.
The results demonstrate that TCIL consistently achieves state-of-the-art
accuracy. It mitigates both ITC and ONC, while showing advantages in battle
with catastrophic forgetting even no rehearsal memory is reserved.


  We propose a formulation of 11-dimensional M-theory in terms of five-branes
with closed strings on their world-volume. We use this description to construct
the complete spectrum of BPS states in compactifications to six and five
dimensions. We compute the degeneracy for fixed charge and find it to be in
accordance with U-duality (which in our formulation is manifest in six
dimensions) and the statistical entropy formula of the corresponding black
hole. We also briefly comment on the four-dimensional case.


  Compliance is a strong requirement for human-robot interactions. Soft-robots
provide an opportunity to cover the lack of compliance in conventional
actuation mechanisms, however, the control of them is very challenging given
their intrinsic complex motions. Therefore, soft-robots require new approaches
to e.g., modeling, control, dynamics, and planning. One of the control
strategies that ensures compliance is the impedance control. During the task
execution in the presence of coupling force and position constraints, a dynamic
behavior increases the flexibility of the impedance control. This imposes some
additional constraints on the stability of the control system. To tackle them,
we propose a variable impedance control in configuration space for a modular
soft robot manipulator (MSRM) in the presence of model uncertainties and
external forces. The external loads are estimated in configuration space using
a momentum-based approach in order to reduce the calculation complexity, and
the adaptive back-stepping sliding mode (ABSM) controller is designed to guard
against uncertainties. Stability analysis is performed using Lyapunov theory
which guarantees not only the exponential stability of each state under the
designed control law, but also the global stability of the closed-loop system.
The system performance is benchmarked against other conventional control
methods, such as the sliding mode (SM) and inverse dynamics PD controllers. The
results show the effectiveness of the proposed variable impedance control in
stabilizing the position error and diminishing the impact of the external load
compared to SM and PD controllers.


  The propagation of a step pulse through a thick resonant absorber with
homogeneously broadened absorption line is considered. It is shown that a
specific subradiant state is naturally developed in the absorber due to the
formation of the spatial domains of the atomic coherence with opposite phases.
It is proposed to divide the absorber into slices in accord with these domains
and place the phase shifters in front of the first slice and between the other
slices. If the phase shifters are switched on simultaneously at a particular
moment of time, elapsed from the beginning of the step pulse, a strong sharp
pulse is generated at the output of the last slice of the absorber. The effect
is explained by the phasing of the atomic coherence along all slices of the
absorber, which transforms subradiant state of atom-field system to
superradiant state.


  In this paper we introduce learnable lattice vector quantization and
demonstrate its effectiveness for learning discrete representations. Our
method, termed LL-VQ-VAE, replaces the vector quantization layer in VQ-VAE with
lattice-based discretization. The learnable lattice imposes a structure over
all discrete embeddings, acting as a deterrent against codebook collapse,
leading to high codebook utilization. Compared to VQ-VAE, our method obtains
lower reconstruction errors under the same training conditions, trains in a
fraction of the time, and with a constant number of parameters (equal to the
embedding dimension $D$), making it a very scalable approach. We demonstrate
these results on the FFHQ-1024 dataset and include FashionMNIST and Celeb-A.