  With the recent paradigm shift from cytotoxic drugs to new generation of
target therapy and immuno-oncology therapy during oncology drug developments,
patients with various cancer (sub)types may be eligible to participate in a
basket trial if they have the same molecular target. Bayesian hierarchical
modeling (BHM) are widely used in basket trial data analysis, where they
adaptively borrow information among different cohorts (subtypes) rather than
fully pool the data together or doing stratified analysis based on each cohort.
Those approaches, however, may have the risk of over shrinkage estimation
because of the invalidated exchangeable assumption. We propose a two-step
procedure to find the balance between pooled and stratified analysis. In the
first step, we treat it as a clustering problem by grouping cohorts into
clusters that share the similar treatment effect. In the second step, we use
shrinkage estimator from BHM to estimate treatment effects for cohorts within
each cluster under exchangeable assumption. For clustering part, we adapt the
mixture of finite mixtures (MFM) approach to have consistent estimate of the
number of clusters. We investigate the performance of our proposed method in
simulation studies and apply this method to Vemurafenib basket trial data
analysis.


  Modern data-driven tools are transforming application-specific polymer
development cycles. Surrogate models that can be trained to predict the
properties of new polymers are becoming commonplace. Nevertheless, these models
do not utilize the full breadth of the knowledge available in datasets, which
are oftentimes sparse; inherent correlations between different property
datasets are disregarded. Here, we demonstrate the potency of multi-task
learning approaches that exploit such inherent correlations effectively,
particularly when some property dataset sizes are small. Data pertaining to 36
different properties of over $13, 000$ polymers (corresponding to over $23,000$
data points) are coalesced and supplied to deep-learning multi-task
architectures. Compared to conventional single-task learning models (that are
trained on individual property datasets independently), the multi-task approach
is accurate, efficient, scalable, and amenable to transfer learning as more
data on the same or different properties become available. Moreover, these
models are interpretable. Chemical rules, that explain how certain features
control trends in specific property values, emerge from the present work,
paving the way for the rational design of application specific polymers meeting
desired property or performance objectives.


  The instability of mixing in the Kuramoto model of coupled phase oscillators
is the key to understanding a range of spatiotemporal patterns, which feature
prominently in collective dynamics of systems ranging from neuronal networks,
to coupled lasers, to power grids. In this paper, we describe a codimension-2
bifurcation of mixing whose unfolding, in addition to the classical scenario of
the onset of synchronization, also explains the formation of clusters and
chimeras. We use a combination of linear stability analysis and Penrose
diagrams to identify and analyze a variety of spatiotemporal patterns including
stationary and traveling coherent clusters and twisted states, as well as their
combinations with regions of incoherent behavior called chimera states. The
linear stability analysis is used to estimate of the velocity distribution
within these structures. Penrose diagrams, on the other hand, predict
accurately the basins of their existence. Furthermore, we show that network
topology can endow chimera states with nontrivial spatial organization. In
particular, we present twisted chimera states, whose coherent regions are
organized as stationary or traveling twisted states. The analytical results are
illustrated with numerical bifurcation diagrams computed for the Kuramoto model
with uni-, bi-, and tri-modal frequency distributions and all-to-all and
nonlocal nearest-neighbor connectivity.


  For an ordered point set in a Euclidean space or, more generally, in an
abstract metric space, the ordered Yao graph is obtained by connecting each of
the points to its closest predecessor by a directed edge. We show that for
every set of $n$ points in $\mathbb{R}^d$, there exists an order such that the
corresponding ordered Yao graph has maximum degree at least $\log{n}/(4d)$.
Apart from the $1/(4d)$ factor, this bound is the best possible. As for the
abstract setting, we show that for every $n$-element metric space, there exists
an order such that the corresponding ordered Yao graph has maximum degree
$\Omega(\sqrt{\log{n}/\log\log{n}})$.


  Associative memories are data structures that allow retrieval of stored
messages from part of their content. They thus behave similarly to human brain
that is capable for instance of retrieving the end of a song given its
beginning. Among different families of associative memories, sparse ones are
known to provide the best efficiency (ratio of the number of bits stored to
that of bits used). Nevertheless, it is well known that non-uniformity of the
stored messages can lead to dramatic decrease in performance. We introduce
several strategies to allow efficient storage of non-uniform messages in
recently introduced sparse associative memories. We analyse and discuss the
methods introduced. We also present a practical application example.


  We generalize the first part of A. Connes paper (math/9811068) on the zeroes
of the Riemann zeta function from a number field $k$ to any simple algebra $M$
over $k$. To a given automorphic representation $\pi$ of the reductive group
$M^\times$ of invertible elements of $M$ we find a Hilbert space $H_\pi$ and an
operator $D_\pi$ (Polya-Hilbert operator), which is the infinitesimal generator
of a canonical flow such that the spectrum of $D_\pi$ coincides with the purely
imaginary zeroes of the function $L(\pi,\rez{2} +z)$. As a byproduct we get
holomorphicity of all automorphic $L$-functions, not only the cuspidal ones.


  In this paper we provide a generalization of the Douglas-Rachford splitting
(DRS) and the primal-dual algorithm (Vu 2013, Condat 2013) for solving monotone
inclusions in a real Hilbert space involving a general linear operator. The
proposed method allows for primal and dual non-standard metrics and activates
the linear operator separately from the monotone operators appearing in the
inclusion. In the simplest case when the linear operator has full range, it
reduces to classical DRS. Moreover, the weak convergence of primal-dual
sequences to a Kuhn-Tucker point is guaranteed, generalizing the main result in
Svaiter (2011). Inspired by Gabay (1983), we also derive a new Split-ADMM
(SADMM) by applying our method to the dual of a convex optimization problem
involving a linear operator which can be expressed as the composition of two
linear operators. The proposed SADMM activates one linear operator implicitly
and the other one explicitly, and we recover ADMM when the latter is set as the
identity. Connections and comparisons of our theoretical results with respect
to the literature are provided for the main algorithm and SADMM. The
flexibility and efficiency of both methods is illustrated via a numerical
simulations in total variation image restoration and a sparse minimization
problem.


  Consider a conformal map from the unit disk onto a quasidisk. We determine a
range of critical complex powers with respect to which the derivative is
integrable. The results fit into the picture predicted by a circular analogue
of Brennan's conjecture.


  We study the structure of thermal spectral function of the stress-energy
tensor in ${\cal N}=4$ supersymmetric Yang-Mills theory at intermediate 't
Hooft coupling and infinite number of colors. In gauge-string duality, this
analysis reduces to the study of classical bulk supergravity with
higher-derivative corrections, which correspond to (inverse) coupling
corrections on the gauge theory side. We extrapolate the analysis of
perturbative leading-order corrections to intermediate coupling by
non-perturbatively solving the equations of motion of metric fluctuations dual
to the stress-energy tensor at zero spatial momentum. We observe the emergence
of a separation of scales in the analytic structure of the thermal correlator
associated with two types of characteristic relaxation modes. As a consequence
of this separation, the associated spectral function exhibits a narrow
structure in the small frequency region which controls the dynamics of
transport in the theory and may be described as a transport peak typically
found in perturbative, weakly interacting thermal field theories. We compare
our results with generic expectations drawn from perturbation theory, where
such a structure emerges as a consequence of the existence of quasiparticles.


  Novel 2D material CrI3 reveals unique combination of 2D ferromagnetism and
robust excitonic response. We demonstrate that the possibility of the formation
of magnetic topological defects, such as Neel skyrmions, together with large
excitonic Zeeman splitting, leads to giant scattering asymmetry, which is the
necessary prerequisite for the excitonic anomalous Hall effect. In addition,
the diamagnetic effect breaks the inversion symmetry, and in certain cases can
result in exciton localization on the skyrmion. This enables the formation of
magnetoexcitonic quantum dots with tunable parameters.


  The CP-odd nucleon potential for different models of CP violation in the one
meson exchange approximation is studied. It is shown that the main contribution
is due to the $\pi$-meson exchange which leads to a simple one parameter CP-odd
nucleon potential.


  In order to capture as much information as possible large galaxy surveys have
been increasing their volume and redshift depth. To face this challenge theory
has responded by making cosmological simulations of huge computational volumes
with equally increasing the number of dark matter particles and supercomputing
resources. Thus, it is taken for granted that the ideal situation is when a
single computational box encompasses the whole effective volume of the
observational survey, e.g., ~50 Gpch^3 for the DESI and Euclid surveys. Here we
study the effects of missing long-waves in a finite volume using several
relevant statistics: the abundance of dark matter halos, the PDF, the
correlation function and power spectrum, and covariance matrices. Finite volume
effects can substantially modify the results if the computational volumes are
less than ~(500Mpch)^3. However, the effects become extremely small and
practically can be ignored when the box-size exceeds ~1Gpch^3. We find that the
average power spectra of dark matter fluctuations show remarkable lack of
dependence on the computational box-size with less than 0.1% differences
between 1Gpch and 4Gpch boxes. No measurable differences are expected for the
halo mass functions for these volumes. The covariance matrices are scaled
trivially with volume, and small corrections due to super-sample modes can be
added. We conclude that there is no need to make those extremely large
simulations when a box-size of 1-1.5Gpch is sufficient to fulfil most of the
survey science requirements.


  We give a new application of the theory of holomorphic motions to the study
the distortion of level lines of harmonic functions and stream lines of ideal
planar fluid flow. In various settings, we show they are in fact quasilines -
the quasiconformal images of the real line. These methods also provide quite
explicit global estimates on the geometry of these curves.


  We show the convergence properties of the eigenvalues of the Dirac operator
on a spin manifold with a Riemannian flow when the metric is collapsed along
the flow.


  Most formal methods see the correctness of a software system as a binary
decision. However, proving the correctness of complex systems completely is
difficult because they are composed of multiple components, usage scenarios,
and environments. We present QuAC, a modular approach for quantifying the
correctness of service-oriented software systems by combining software
architecture modeling with deductive verification. Our approach is based on a
model of the service-oriented architecture and the probabilistic usage
scenarios of the system. The correctness of a single service is approximated by
a coverage region, which is a formula describing which inputs for that service
are proven to not lead to an erroneous execution. The coverage regions can be
determined by a combination of various analyses, e.g., formal verification,
expert estimations, or testing. The coverage regions and the software model are
then combined into a probabilistic program. From this, we can compute the
probability that under a given usage profile no service is called outside its
coverage region. If the coverage region is large enough, then instead of
attempting to get 100% coverage, which may be prohibitively expensive, run-time
verification or testing approaches may be used to deal with inputs outside the
coverage region. We also present an implementation of QuAC for Java using the
modeling tool Palladio and the deductive verification tool KeY. We demonstrate
its usability by applying it to a software simulation of an energy system.


  This paper is devoted to the analysis of the integrability of D1-brane on
group manifold. We consider D1-brane as principal chiral model, determine
corresponding equations of motions and find Lax connection. Then we calculate
the Poisson brackets of Lax connection and we find that it has similar
structure as in case of principal chiral model. As the second example we
consider more general background with non-zero NS-NS two form. We again show
that D1-brane theory is integrable on this background and determine Poisson
brackets of Lax connection.


  We propose a covariant technique to excavate physical bosonic string states
by entire trajectories rather than individually. The approach is based on Howe
duality: the string's spacetime Lorentz algebra commutes with a certain
inductive limit of $sp(\bullet)$, with the Virasoro constraints forming a
subalgebra of the Howe dual algebra $sp(\bullet)$. There are then infinitely
many simple trajectories of states, which are lowest-weight representations of
$sp(\bullet)$ and hence of the Virasoro algebra. Deeper trajectories are
recurrences of the simple ones and can be probed by suitable
trajectory-shifting operators built out of the Howe dual algebra generators. We
illustrate the formalism with a number of subleading trajectories and compute a
sample of tree-level amplitudes.


  In the present paper we consider the system {\Delta}u - W_u (u) = 0, where u:
R^n to R^n, for a class of potentials W: R^n to R that possess several global
minima and are invariant under a general finite reflection group G. We
establish existence of nontrivial entire solutions connecting the global minima
of W along certain directions at infinity.


  To interpret uncertainty estimates from differentiable probabilistic models,
recent work has proposed generating Counterfactual Latent Uncertainty
Explanations (CLUEs). However, for a single input, such approaches could output
a variety of explanations due to the lack of constraints placed on the
explanation. Here we augment the original CLUE approach, to provide what we
call $\delta$-CLUE. CLUE indicates $\it{one}$ way to change an input, while
remaining on the data manifold, such that the model becomes more confident
about its prediction. We instead return a $\it{set}$ of plausible CLUEs:
multiple, diverse inputs that are within a $\delta$ ball of the original input
in latent space, all yielding confident predictions.


  By including the contribution of the thermal cloud to the Lagrangian of the
condensate of a Bose gas, we extend the time-dependent variational method at
zero temperature to study temperature-dependent low collective excitation
modes. A Gaussian trial wave function of the condensate and a static
distribution density of the thermal cloud are used, and analytical expressions
for temperature-dependent excitation frequencies obtained. Theoretical results
are compared with measurements in the JILA and MIT experiments.


  In this article we study the expected rank problem under full information.
Our approach uses the planar Poisson approach from Gnedin (2007) to derive the
expected rank of a stopping rule that is one of the simplest non-trivial
examples combining rank dependent rules with threshold rules. This rule attains
an expected rank lower than the best upper bounds obtained in the literature so
far, in particular we obtain an expected rank of 2.32614.


  We study the effect of exponentially correlated noise on $xy-$model in the
limit of small correlation time discussing the order-disorder transition in
mean-field and the topological transition in two dimensions. We map the steady
states of the non-equilibrium dynamics into an effective equilibrium theory. In
mean-field, the critical temperature increases with the noise correlation time
$\tau$ indicating that memory effects promote ordering. This finding is
confirmed by numerical simulations. The topological transition temperature in
two dimensions remains untouched. However, finite size effects induce a
crossover in the vortices proliferation that is confirmed by numerical
simulations.


  The thermal resistivity of manganites and cuprates is shown to correlate with
local lattice distortions and the presence of localized holes as determined
from neutron diffraction and nuclear quadrupole resonance. Oxygen doping
dependent studies of heat conduction in Y-123 and Hg cuprates suggest that a
fraction of the holes in the CuO$_2$ planes are localized near the planar hole
concentration $p=1/8$. The results are consistent with the formation of
short-ranged, static stripe domains that are pinned near oxygen vacancy
clusters.


  It is expected that infinite distance limits in the moduli space of quantum
gravity are accompanied by a tower of light states. In view of the emergent
string conjecture, this tower must either induce a decompactification or
correspond to the emergence of a tensionless critical string. We study the
consistency conditions implied by this conjecture on the asymptotic behavior of
quantum gravity under dimensional reduction. If the emergent string descends
from a (2+1)-dimensional membrane in a higher-dimensional theory, we find that
such a membrane must parametrically decouple from the Kaluza-Klein scale. We
verify this censorship against emergent membrane limits, where the membrane
would sit at the Kaluza-Klein scale, in the hypermultiplet moduli space of
Calabi-Yau 3-fold compactifications of string/M-theory. At the classical level,
a putative membrane limit arises, up to duality, from an M5-brane wrapping the
asymptotically shrinking special Lagrangian 3-cycle corresponding to the
Strominger-Yau-Zaslow fiber of the Calabi-Yau. We show how quantum corrections
in the moduli space obstruct such a limit and instead lead to a
decompactification to 11 dimensions, where the role of the M5- and M2-branes
are interchanged.


  We introduce a new quasi-isometry invariant $\subcorank X$ of a metric space
$X$ called {\it subexponential corank}. A metric space $X$ has subexponential
corank $k$ if roughly speaking there exists a continuous map $g:X\to T$ such
that for each $t\in T$ the set $g^{-1}(t)$ has subexponential growth rate in
$X$ and the topological dimension $\dim T=k$ is minimal among all such maps.
Our main result is the inequality $\hyprank X\le\subcorank X$ for a large class
of metric spaces $X$ including all locally compact Hadamard spaces, where
$\hyprank X$ is maximal topological dimension of $\di Y$ among all $\CAT(-1)$
spaces $Y$ quasi-isometrically embedded into $X$ (the notion introduced by M.
Gromov in a slightly stronger form). This proves several properties of
$\hyprank$ conjectured by M. Gromov, in particular, that any Riemannian
symmetric space $X$ of noncompact type possesses no quasi-isometric embedding
$\hyp^n\to X$ of the standard hyperbolic space $\hyp^n$ with $n-1>\dim X-\rank
X$.


  A comparison is made of the probability of the process of two neutrino double
beta decay for $^{82}$Se in direct (counter) and geochemical experiments. It is
shown that the probability is systematically lower in geochemical experiments,
which characterize the probability of $\beta\beta(2\nu)$ decay a few billions
years ago. The experimental data for $^{130}$Te are also analyzed. It is shown
that geochemical measurements on young minerals give lower values of $T_{1/2}$
($^{130}$Te) and $T_{1/2}$ ($^{82}$Se) as compared to measurements on old
minerals. It is proposed that this could be due to a change in the weak
interaction constant with time. Possibilities of new, precise measurements be
performed with the aid of counters and geochemical experiments are discussed.


  Nobody knows how language works, but many theories abound. Transformers are a
class of neural networks that process language automatically with more success
than alternatives, both those based on neural computations and those that rely
on other (e.g. more symbolic) mechanisms. Here, I highlight direct connections
between the transformer architecture and certain theoretical perspectives on
language. The empirical success of transformers relative to alternative models
provides circumstantial evidence that the linguistic approaches that
transformers embody should be, at least, evaluated with greater scrutiny by the
linguistics community and, at best, considered to be the currently best
available theories.


  In recent years, Arm-based processors have arrived on the HPC scene, offering
an alternative the existing status quo, which was largely dominated by x86
processors. In this paper, we evaluate the Arm ecosystem, both the hardware
offering and the software stack that is available to users, by benchmarking a
production HPC platform that uses Marvell's ThunderX2 processors. We
investigate the performance of complex scientific applications across multiple
nodes, and we also assess the maturity of the software stack and the ease of
use from a users' perspective. This papers finds that the performance across
our benchmarking applications is generally as good as, or better, than that of
well-established platforms, and we can conclude from our experience that there
are no major hurdles that might hinder wider adoption of this ecosystem within
the HPC community.


  We analyze the possibility of $CP$ violation induced by heavy Majorana
neutrinos in the decays of the Higgs particle into top-quark, $W$- and
$Z$-boson pairs. In the framework of various ``see-saw" models with interfamily
mixings, we find that Majorana neutrinos may give rise to sizable $CP$-odd
observables at the one-loop electroweak order. Numerical estimates of these
$CP$-violating effects that may be detected in high-energy colliders are
presented.


  We use the persistent homology method of topological data analysis and
dimensional analysis techniques to study data of syntactic structures of world
languages. We analyze relations between syntactic parameters in terms of
dimensionality, of hierarchical clustering structures, and of non-trivial
loops. We show there are relations that hold across language families and
additional relations that are family-specific. We then analyze the trees
describing the merging structure of persistent connected components for
languages in different language families and we show that they partly correlate
to historical phylogenetic trees but with significant differences. We also show
the existence of interesting non-trivial persistent first homology groups in
various language families. We give examples where explicit generators for the
persistent first homology can be identified, some of which appear to correspond
to homoplasy phenomena, while others may have an explanation in terms of
historical linguistics, corresponding to known cases of syntactic borrowing
across different language subfamilies.


  In this paper we extend the calculation of the geometric Waldspurger periods
from our paper math/0510110 to the case of ramified coverings. We give some
applications to the study of Whittaker coefficients of the theta-lifting of
automorphic sheaves from PGL_2 to the metaplectic group Mp_2, they agree with
our conjectures from arXiv:1211.1596. In the process of the proof, we get some
new automorphic sheaves for GL_2 in the ramified setting. We also formulate
stronger conjectures about Waldspurger periods and geometric theta-lifting for
the dual pair (SL_2, Mp_2).


  Magnetic impurities in superconductors are of increasing interest due to
emergent Yu-Shiba-Rusinov (YSR) states and Majorana zero modes for
fault-tolerant quantum computation. However, a direct relationship between the
YSR multiple states and magnetic anisotropy splitting of quantum impurity spins
remains poorly characterized. By using scanning tunneling microscopy, we
resolve systematically individual transition-metal (Fe, Cr and Ni) impurities
induced YSR multiplets as well as their Zeeman effects in K$_3$C$_{60}$
superconductor. The YSR multiplets show identical $d$ orbital-like wave
functions that are symmetry-mismatched to the threefold K$_3$C$_{60}$(111) host
surface, breaking point-group symmetries of the spatial distribution of YSR
bound states in real space. Remarkably, we identify an unprecedented
fermion-parity-preserving quantum phase transition between ground states with
opposite signs of the uniaxial magnetic anisotropy that can be manipulated by
an external magnetic field. These findings can be readily understood in terms
of anisotropy splitting of quantum impurity spins, and thus elucidate the
intricate interplay between the magnetic anisotropy and YSR multiplets.


  Static contact angle hysteresis (CAH) is widely attributed to surface
roughness and chemical contamination. In the latter case, chemical defects
create free-energy barriers that prevent the contact line motion.
Electrowetting studies have demonstrated the similar ability of electric fields
to alter the surface free-energy landscape. Yet, the increase of apparent
static CAH by electric fields remains unseen. Here, we report the observation
and theoretical analysis of electrowetting hysteresis. This phenomenon enables
the continuous and dynamic control of CAH, not only for fundamental studies but
also to manufacture sticky-on-demand surfaces for sample collection.


  We construct an evidently positive multiple series as a generating function
for partitions satisfying the multiplicity condition in Schur's partition
theorem.
  Refinements of the series when parts in the said partitions are classified
according to their parities or values mod 3 are also considered.
  Direct combinatorial interpretations of the series are provided.


  The rendering of Sanskrit poetry from text to speech is a problem that has
not been solved before. One reason may be the complications in the language
itself. We present unique algorithms based on extensive empirical analysis, to
synthesize speech from a given text input of Sanskrit verses. Using a
pre-recorded audio units database which is itself tremendously reduced in size
compared to the colossal size that would otherwise be required, the algorithms
work on producing the best possible, tunefully rendered chanting of the given
verse. His would enable the visually impaired and those with reading
disabilities to easily access the contents of Sanskrit verses otherwise
available only in writing.


  In the large N_c limit, the variables required to analyze the low energy
structure of QCD in the framework of an effective field theory necessarily
include the degrees of freedom of the eta'. We evaluate the decay constants of
the pseudoscalar nonet to one loop within this extended framework and show
that, as a consequence of the anomalous dimension of the singlet axial current,
some of the effective coupling constants depend on the running scale of QCD.
The calculation relies on a simultaneous expansion in powers of momenta, quark
masses and 1/N_c.
  Talk given at the Workshop on Nonperturbative Methods in Quantum Field
Theory, NITP/CSSM, University of Adelaide, Australia, Feb. 1998.


  We present application of a highly-scalable overlapping grid-based
nonconforming Schwarz-spectral element method (Schwarz-SEM) to study the
dynamics of rotating ellipsoidal particles. The current study is one of the
first to explore the effect of rotation on ellipsoidal particles using fully
resolved simulations (direct numerical simulation). The rotating ellipsoidal
particles show substantial difference in the dynamics of the flow, when
compared against non-rotating particles. The difference is primarily due to
periodic attachment and separation of the flow to the surface of the particle
for the rotating cases, which results in a higher drag on the particles when
compared to the corresponding non-rotating cases. The dynamics is also
different from a rotating spherical particle, where a steady shear layer
develops near the surface of the sphere. For the rotating ellipsoidal
particles, this mechanism results in a phase-difference between the position of
observed maximum and minimum drag, and the position of expected maximum and
minimum drag (i.e., maximum and minimum projected area). A similar
phase-difference is also observed for the lift acting on the rotating
ellipsoidal particles. The results presented here demonstrate the importance of
explicitly modeling the shape and rotation of particles when we study the
dynamics of non-spherical particles. Finally, the study also validates the use
of non-conforming Schwarz-SEM for tackling problems in fully resolved
particulate flow dynamics.


  We propose a novel scheme to simulate Z_2 topological insulators via
one-dimensional (1D) cavity optomechanical cells array. The direct mapping
between 1D cavity optomechanical cells array and 2D quantum spin Hall (QSH)
system can be achieved by using diagonalization and dimensional reduction
methods. We show that the topological features of the present model can be
captured using a 1D generalized Harper equation with an additional SU(2) guage
structure. Interestingly, spin pumping of effective photon-phonon bosons can be
naturally derived after scanning the additional periodic parameter, which means
that we can realize the transition between different QSH edge states.


  One of the central tenets of conventional theories of superconductivity,
including most models proposed for the recently discovered iron-pnictide
superconductors, is the notion that only electronic excitations with energies
comparable to the superconducting energy gap are affected by the transition.
Here we report the results of a comprehensive spectroscopic ellipsometry study
of a high-quality crystal of superconducting
$\textrm{Ba}_{0.68}\textrm{K}_{0.32}\textrm{Fe}_2\textrm{As}_2$ that challenges
this notion. We observe a superconductivity-induced suppression of an
absorption band at an energy of $2.5\ \textrm{eV}$, two orders of magnitude
above the superconducting gap energy $2\Delta\sim 20\ \textrm{meV}$. Based on
density-functional calculations, this band can be assigned to transitions from
As-p to Fe-d orbitals crossing the Fermi surface. We identify a related effect
at the spin-density-wave transition in parent compounds of the 122 family. This
suggests that As-p states deep below the Fermi level contribute to the
formation of the superconducting and spin-density-wave states in the iron
arsenides.


  Nonadiabatic holonomic quantum computation has received increasing attention
due to its robustness against control errors. However, all the previous schemes
have to use at least two sequentially implemented gates to realize a general
one-qubit gate. Based on two recent works, we construct two Hamiltonians and
experimentally realized nonadiabatic holonomic gates by a single-shot
implementation in a two-qubit nuclear magnetic resonance (NMR) system. Two
noncommuting one-qubit holonomic gates, rotating along $\hat{x}$ and $\hat{z}$
axes respectively, are implemented by evolving a work qubit and an ancillary
qubit nonadiabatically following a quantum circuit designed. Using a sequence
compiler developed for NMR quantum information processor, we optimize the whole
pulse sequence, minimizing the total error of the implementation. Finally, all
the nonadiabatic holonomic gates reach high unattenuated experimental
fidelities over $98\%$


  The competing influence of two types of interactions on surface diffusion is
investigated: one of them, epsilon, acts between adsorbed particles, while the
other one, eta, between activated and adsorbed particles. To this end, a
specific lattice-gas model on a triangular, square, and hexagonal lattice is
considered with an attractive epsilon and an attractive or repulsive eta, both
restricted to nearest neighbors. For all three lattices the influence is
qualitatively the same. Namely, when eta is neglected, then epsilon is shown to
decelerate diffusion with a rate exponential in epsilon and inverse
temperature. Moreover, when eta is present and epsilon is fixed, then a
sufficiently attractive eta (relative to epsilon) accelerates diffusion
exponentially fast in eta and inverse temperature. However, quite surprisingly,
a repulsive or slightly attractive eta has practically no effect on diffusion.
Finally, when eta is set proportional to epsilon via a parameter $a$, surface
diffusion is exponentially accelerated (decelerated) for $a$ above (below) a
threshold value equal to 4, 5/4, and 7/8 for the three lattices. Thus, an eta
of strength comparable to epsilon is enough to boost diffusion on the square
and hexagonal lattices, while an eta of a rather large strength is needed for
the boost on the triangular lattice.


  We investigate the effect of free electrons on the quality factor (Q) of a
metallic nanomechanical resonator in the form of a thin elastic beam. The
flexural and longitudinal modes of the beam are modeled using thin beam
elasticity theory, and simple perturbation theory is used to calculate the rate
at which an externally excited vibration mode decays due to its interaction
with free electrons. We find that electron-phonon interaction significantly
affects the Q of longitudinal modes, and may also be of significance to the
damping of flexural modes in otherwise high-Q beams. The finite geometry of the
beam is manifested in two important ways. Its finite length breaks translation
invariance along the beam and introduces an imperfect momentum conservation law
in place of the exact law. Its finite width imposes a quantization of the
electronic states that introduces a temperature scale for which there exists a
crossover from a high-temperature macroscopic regime, where electron-phonon
damping behaves as if the electrons were in the bulk, to a low-temperature
mesoscopic regime, where damping is dominated by just a few dissipation
channels and exhibits sharp non-monotonic changes as parameters are varied.
This suggests a novel scheme for probing the electronic spectrum of a nanoscale
device by measuring the Q of its mechanical vibrations.


  The effect of gravitational wave of extremely low frequency on time delays
between different locations on the Einstein ring in a lens system with an
aligned source-deflector-observer configuration is investigated. The observer
will observe an Einstein ring from the lens system aligned in a highly
symmetric configuration. Time delays between different locations on the
Einstein ring cannot emerge without gravitational wave of cosmological
wavelength propagating through the lens system. Otherwise, different locations
on the Einstein ring will show time delays. Our previous studies showed that
time delays from different locations on the Einstein ring in the presence of
gravitational wave of cosmological wavelength present a special relationship.
But this result is limited to a specific aligned source-deflector-observer
configuration where the source and the observer are equidistant from the
deflector and the gravitational wave has special direction of propagation and
polarization. In order to investigate the property in the general case, we
extend to the general condition that the source and the observer aren't
equidistant from the deflector and the direction and polarization of the
gravitational wave is arbitrary in the present work. Results in this work show
that time delays between different locations on the Einstein ring with the
general condition present the same relationship as that in our previous
studies.


  We show that astrophysical gravitational waves can undergo an anomalous
modulation when propagating through cosmic gauge field dark energy. A
sufficiently strong effect, dependent on the gauge field energy density, would
appear as a redshift-dependent opacity, thereby impacting the use of
gravitational wave standard sirens to constrain the expansion history of the
Universe. We investigate a particular model of cosmic gauge field dark energy
and show that at early times it behaves like dark radiation, whereas a novel
interaction causes it to drive cosmic acceleration at late times. Joint
constraints on the cosmological scenario due to type 1a supernovae, baryon
acoustic oscillations, and cosmic microwave background data are presented. In
view of these constraints, we show that standard siren luminosity distances in
the redshift range 0.5 < z < 1.5 would systematically dim by up to 1%, which
may be distinguishable by third-generation gravitational wave detectors.


  The proper enforcement of motorcycle helmet regulations is crucial for
ensuring the safety of motorbike passengers and riders, as roadway cyclists and
passengers are not likely to abide by these regulations if no proper
enforcement systems are instituted. This paper presents the development and
evaluation of a real-time YOLOv5 Deep Learning (DL) model for detecting riders
and passengers on motorbikes, identifying whether the detected person is
wearing a helmet. We trained the model on 100 videos recorded at 10 fps, each
for 20 seconds. Our study demonstrated the applicability of DL models to
accurately detect helmet regulation violators even in challenging lighting and
weather conditions. We employed several data augmentation techniques in the
study to ensure the training data is diverse enough to help build a robust
model. The proposed model was tested on 100 test videos and produced an mAP
score of 0.5267, ranking 11th on the AI City Track 5 public leaderboard. The
use of deep learning techniques for image classification tasks, such as
identifying helmet-wearing riders, has enormous potential for improving road
safety. The study shows the potential of deep learning models for application
in smart cities and enforcing traffic regulations and can be deployed in
real-time for city-wide monitoring.


  Minkowski Space is the simplest four-dimensional Lorentzian Manifold, being
topologically trivial and globally flat, and hence the simplest model of
spacetime--from a General-Relativistic point of view. But this does not mean
that it is altogether structurally trivial. In fact, it has a very rich
structure, parts of which will be spelled out in detail in this contribution.
This will contain elementary aspects of affine spaces, various paths to the
Poincare group, the lattices of causally and chronologically complete regions,
and last but not least, the Noether-Herglotz theorem.


  This paper shows how to write Maxwell's Equations in Hamilton's Quaternions.
The fact that the quaternion product is non-commuting leads to distinct left
and right derivatives which must both be included in the theory. A new field
component is then revealed, which reduces part of the degree of freedom found
in the gauge, but which can then be used to explain thermoelectricity,
suggesting that the theory of heat has just as fundamental a connection to
electromagnetism as the magnetic field has to the electric field, for the new
theory now links thermal, electric, and magnetic phenomena altogether in one
set of elementary equations. This result is based on an initial hypothesis,
named ``The Quaternion Axiom,'' that postulates physical space is a quaternion
structure.


  Recently, several groups identified a tentative $\gamma$-ray line signal with
energy $\sim 130$ GeV in the central Galaxy from the Fermi-LAT data. %The
morphology study shows that the signal is consistent with dark matter
%annihilation, but with an offset $\sim 220$ pc ($1.5^{\circ}$) of the %center
from the Galactic center Sgr A$^{\star}$, Such a $\gamma-$ray line can be
interpreted as the signal of dark matter annihilation. However, the offset
$\sim 220$ pc ($1.5^{\circ}$) of the center of the most prominent signal region
from the Galactic center Sgr A$^{\star}$ has been thought to challenge the dark
matter annihilation interpretation. Considering the fact that such a 130 GeV
$\gamma$-ray line signal consists of only $\sim14$ photons, we suggest that the
"imperfect" consistency of these photons with the expected dark matter
distribution is due to the limited statistics. The offset will be smaller as
more signal photons have been collected in the near future. Our Monte Carlo
simulation supports the above speculation.


  The appearance of traffic jams on chains with a shunted section between two
simple chain segments in the maximum current phase is studied in the framework
of the Totally Asymmetric Simple Exclusion Process. The conditions for the
occurrence of this phenomenon are investigated both within the effective rates
approximation and numerically for arbitrary length of the shortcut. The problem
is interesting on its own because the conditions for coexistence of low- and
high density phases are essentially different from those for a simple chain
between two reservoirs. Our main results are: (1) For any values of the
external rates in the domain of the maximum current phase, there exists a
position of the shortcut where the shunted segment is in a phase of coexistence
with a completely delocalized domain wall; (2) The main features of the
coexistence phase and the density profiles in the whole network are well
described by the domain wall theory. Apart from the negligible inter-chain
correlations, they depend only on the current through the shortcut; (3) The
model displays an unexpected feature: the current through the longer shunted
segment is larger than the current through the shortcut; (4) From the viewpoint
of vehicular traffic, most comfortable conditions for the drivers are provided
when the shortcut is shifted downstream from the position of coexistence, when
both the shunted segment and the shortcut exhibit low-density lamellar flow.
Most unfavorable is the opposite case of upstream shifted shortcut, when both
the shunted segment and the shortcut are in a high-density phase describing
congested traffic of slowly moving cars. The above results are relevant also to
phenomena like crowding of molecular motors moving along twisted
protofilaments.


  In this paper, we propose a novel framework named DRL-CPG to learn
disentangled latent representation for controllable person image generation,
which can produce realistic person images with desired poses and human
attributes (e.g., pose, head, upper clothes, and pants) provided by various
source persons. Unlike the existing works leveraging the semantic masks to
obtain the representation of each component, we propose to generate
disentangled latent code via a novel attribute encoder with transformers
trained in a manner of curriculum learning from a relatively easy step to a
gradually hard one. A random component mask-agnostic strategy is introduced to
randomly remove component masks from the person segmentation masks, which aims
at increasing the difficulty of training and promoting the transformer encoder
to recognize the underlying boundaries between each component. This enables the
model to transfer both the shape and texture of the components. Furthermore, we
propose a novel attribute decoder network to integrate multi-level attributes
(e.g., the structure feature and the attribute representation) with
well-designed Dual Adaptive Denormalization (DAD) residual blocks. Extensive
experiments strongly demonstrate that the proposed approach is able to transfer
both the texture and shape of different human parts and yield realistic
results. To our knowledge, we are the first to learn disentangled latent
representations with transformers for person image generation.


  We present theory and experiments demonstrating the existence of invariant
manifolds that impede the motion of microswimmers in two-dimensional fluid
flows. One-way barriers are apparent in a hyperbolic fluid flow that block the
swimming of both smooth-swimming and run-and-tumble \emph{Bacillus subtilis}
bacteria. We identify key phase-space structures, called swimming invariant
manifolds (SwIMs), that serve as separatrices between different regions of
long-time swimmer behavior. When projected into $xy$-space, the edges of the
SwIMs act as one-way barriers, consistent with the experiments.


  The work is dedicated to the derivation of the 'functional' integral
representation of the disorder parameter. This derivation resolves the problem
of the choice of the so called modifed action as well as the problem of the
choice of the boundary conditions along the 'time' direction. The question of
the gauge fixing in the functional integral representation is also discussed.


  Given a compact set $K$ in the plane, which does not contain any triple of
points forming a vertical and a horizontal segment, and a map $f\in C(K)$, we
give a construction of functions $g,h\in C(\mathbb R)$ such that
$f(x,y)=g(x)+h(y)$ for all $(x,y)\in K$. This provides a constructive proof of
a part of Sternfeld's theorem on basic embeddings in the plane. In our proof
the set $K$ is approximated by a finite set of points.


  Semantic segmentation is an extensively studied task in computer vision, with
numerous methods proposed every year. Thanks to the advent of deep learning in
semantic segmentation, the performance on existing benchmarks is close to
saturation. A natural question then arises: Does the superior performance on
the closed (and frequently re-used) test sets transfer to the open visual world
with unconstrained variations? In this paper, we take steps toward answering
the question by exposing failures of existing semantic segmentation methods in
the open visual world under the constraint of very limited human labeling
effort. Inspired by previous research on model falsification, we start from an
arbitrarily large image set, and automatically sample a small image set by
MAximizing the Discrepancy (MAD) between two segmentation methods. The selected
images have the greatest potential in falsifying either (or both) of the two
methods. We also explicitly enforce several conditions to diversify the exposed
failures, corresponding to different underlying root causes. A segmentation
method, whose failures are more difficult to be exposed in the MAD competition,
is considered better. We conduct a thorough MAD diagnosis of ten PASCAL VOC
semantic segmentation algorithms. With detailed analysis of experimental
results, we point out strengths and weaknesses of the competing algorithms, as
well as potential research directions for further advancement in semantic
segmentation. The codes are publicly available at
\url{https://github.com/QTJiebin/MAD_Segmentation}.


  In \cite{christlieb2019kernel}, the authors developed a class of high-order
numerical schemes for the Hamilton-Jacobi (H-J) equations, which are
unconditionally stable, yet take the form of an explicit scheme. This paper
extends such schemes, so that they are more effective at capturing sharp
gradients, especially on nonuniform meshes. In particular, we modify the
weighted essentially non-oscillatory (WENO) methodology in the previously
developed schemes by incorporating an exponential basis and adapting the
previously developed nonlinear filters used to control oscillations. The main
advantages of the proposed schemes are their effectiveness and simplicity,
since they can be easily implemented on higher-dimensional nonuniform meshes.
We perform numerical experiments on a collection of examples, including H-J
equations with linear, nonlinear, convex and non-convex Hamiltonians. To
demonstrate the flexibility of the proposed schemes, we also include test
problems defined on non-trivial geometry.


  A recent unambiguous detection of X-ray rotational modulation of the
supersaturated star VXR45 (P = 0.223 days) has shown that its corona has
discrete dark and bright X-ray regions. We suggest that due to the rapid
rotation, the X-ray emitting corona has been centrifugally stripped away,
creating open field regions that are dark in X-rays. This leads naturally both
to a significant rotational modulation in X-rays but also to the lower X-ray
luminosity of supersaturated stars compared to those rotating more slowly. To
demonstrate the effect, we take as an example a more slowly rotating star for
which surface magnetograms are available. We extrapolate the potential coronal
magnetic field based on these magnetograms and determine for a hydrostatic,
isothermal atmosphere the structure of the density and of the optically-thin
X-ray emission. We show that if the rotation rate of this star were increased,
the magnitude of the X-ray luminosity would decrease while its rotational
modulation would increase in a way that is consistent with the recent
observations of VXR45.


  Driving scene understanding task involves detecting static elements such as
lanes, traffic signs, and traffic lights, and their relationships with each
other. To facilitate the development of comprehensive scene understanding
solutions using multiple camera views, a new dataset called Road Genome
(OpenLane-V2) has been released. This dataset allows for the exploration of
complex road connections and situations where lane markings may be absent.
Instead of using traditional lane markings, the lanes in this dataset are
represented by centerlines, which offer a more suitable representation of lanes
and their connections. In this study, we have introduced a new approach called
TopoMask for predicting centerlines in road topology. Unlike existing
approaches in the literature that rely on keypoints or parametric methods,
TopoMask utilizes an instance-mask based formulation with a transformer-based
architecture and, in order to enrich the mask instances with flow information,
a direction label representation is proposed. TopoMask have ranked 4th in the
OpenLane-V2 Score (OLS) and ranked 2nd in the F1 score of centerline prediction
in OpenLane Topology Challenge 2023. In comparison to the current
state-of-the-art method, TopoNet, the proposed method has achieved similar
performance in Frechet-based lane detection and outperformed TopoNet in
Chamfer-based lane detection without utilizing its scene graph neural network.


  It is known that the Collatz Conjecture (and the study of similar maps, here
called "Hydra maps") can be stated in terms of solution sets of functional
equations; or, equivalently, the fixed points of linear operators on spaces of
analytic functions. Rather than studying potential fixed points of such
operators, we examine their effect on the singularities of functions. To that
end, we introduce the notion of a "dreamcatcher", an object which encodes the
location and "virtual residue" of the singularities of an analytic function of
a specified growth rate along the boundary of the function's region of
convergence. Dreamcatchers can be given rigorous footing as elements of the
Hilbert space L2(Q/Z) of complex-valued functions on Q/Z which are
square-integrable with respect to the counting measure on Q/Z. The
aforementioned linear operators (called here "permutation operators") are shown
to "conserve" the singularities of their fixed points, in the sense that the
dreamcatcher of a fixed point is itself the fixed point of the operator induced
on L2(Q/Z) (the "dreamcatcher operator") by the permutation operator. Using
Pontryagin duality and p-adic analysis, the fixed points of the operators
acting on dreamcatchers for simple-pole-like singularities are completely
determined for a large class of Hydra maps in the case where the fixed points
are finitely supported on Q/Z. This enables qualitative conclusions to be made
about those Hydra maps' orbit classes in the non-negative integers.


  We examine the evolution of variously-sized radio galaxies [i.e., compact
symmetric objects (CSOs), medium-size symmetric objects (MSOs), Fanaroff-Riley
type II radio galaxies (FRIIs)], by comparing the relation between the hot spot
size and the projected linear size with a coevolution model of hot spots and a
cocoon. We take account of the deceleration effect by the cocoon head growth.
We find that the advance speed of hot spots and lobes inevitably show the
deceleration phase (CSO-MSO phase) and the acceleration phase (MSO-FRII phase).
This is ascribed to the change of the power-law index of ambient density
profile in the MSO phase ($\sim $1 kpc). It is also found that the cocoon shape
becomes nearly spherical or disrupted for MSOs, while an elongated morphology
is predicted for CSOs and FRIIs. This seems to be consistent with the higher
fraction of distorted morphology of MSOs than that of CSOs and FRI.
  Finally, we predict that only CSOs whose initial advance speed is higher than
about 0.1c can evolve into FRIIs, comparing the hot spot speed with the sound
speed of the ambient medium.


  A free electron can form a bound state with an atomic center $A$ upon photo
emission (radiative recombination). In the presence of a neighboring atom $B$,
such a bound state can, under certain conditions, be also formed via resonant
transfer of energy to $B$, with its subsequent relaxation through radiative
decay (two-center dielectronic recombination). This two-center process is very
efficient in the 'static' case where $A$ and $B$ form a weakly bound system,
dominating over single-center radiative recombination up to internuclear
distances as large as several nanometers. Here we study its dynamic variant in
which recombination occurs when a beam of species $A$ collides with a gas of
atoms $B$ and show that, even though the average distance between $A$ and $B$
in collisions is orders of magnitude larger than the typical size of a bound
system, the two-center recombination can still outperform the single-center
radiative recombination.


  In this paper, we continue to construct the low-energy effective field
theories (EFTs) of the canonical seesaw models, which are natural extensions of
the Standard Model (SM) to accommodate tiny but nonzero neutrino masses.
Different from three right-handed neutrino singlets in the type-I seesaw model,
the Higgs triplet in the type-II seesaw model participates directly in the
electroweak gauge interactions, rendering the EFT construction more
challenging. By integrating out the heavy Higgs triplet in the
functional-integral formalism, we carry out a complete one-loop matching of the
type-II seesaw model onto the so-called Standard Model Effective Field Theory
(SMEFT). It turns out that 41 dimension-six operators (barring flavor
structures and Hermitian conjugates) in the Warsaw basis of the SMEFT can be
obtained, covering all those 31 dimension-six operators in the case of type-I
seesaw model. The Wilson coefficients for 41 dimension-six operators are
computed up to $\mathcal{O}\left( M^{-2}_\Delta \right)$ with $M^{}_\Delta$
being the mass scale of the Higgs triplet. Moreover, the branching ratios of
rare radiative decays of charged leptons $l^-_\alpha \to l^-_\beta + \gamma$
are calculated in the EFT and compared with that in the full theory in order to
demonstrate the practical application and the correctness of our EFT
construction.


  This paper investigates the potential privacy risks associated with
forecasting models, with specific emphasis on their application in the context
of smart grids. While machine learning and deep learning algorithms offer
valuable utility, concerns arise regarding their exposure of sensitive
information. Previous studies have focused on classification models,
overlooking risks associated with forecasting models. Deep learning based
forecasting models, such as Long Short Term Memory (LSTM), play a crucial role
in several applications including optimizing smart grid systems but also
introduce privacy risks. Our study analyzes the ability of forecasting models
to leak global properties and privacy threats in smart grid systems. We
demonstrate that a black box access to an LSTM model can reveal a significant
amount of information equivalent to having access to the data itself (with the
difference being as low as 1% in Area Under the ROC Curve). This highlights the
importance of protecting forecasting models at the same level as the data.


  In this paper, we consider the small viscosity limit problem for the
isentropic compressible Navier-Stokes equations in a 2D exterior domain with
impermeable boundary conditions , and the corresponding Euler equations have
vortex sheet solutions.We obtain that away from the boundary and the contact
discontinuous the isentropic compressible viscous flow can be approximated by
the corresponding inviscid flow, near the boundary (the contact discontinuous)
there is a boundary layer (vortex layer)for the angular velocity in the leading
order expansion of solution, while the radial velocity and the pressure do not
have boundary layers (vortex layers) in the leading order. We rigorously
justify the asymptotic behavior of solutions in the $L^{\infty}$ space for the
small viscosities limit in the Lagrangian coordinates.


  This paper presents Global Benchmark Database (GBD), a comprehensive suite of
tools for provisioning and sustainably maintaining benchmark instances and
their metadata. The availability of benchmark metadata is essential for many
tasks in empirical research, e.g., for the data-driven compilation of
benchmarks, the domain-specific analysis of runtime experiments, or the
instance-specific selection of solvers. In this paper, we introduce the data
model of GBD as well as its interfaces and provide examples of how to interact
with them. We also demonstrate the integration of custom data sources and
explain how to extend GBD with additional problem domains, instance formats and
feature extractors.


  An experimentally realizable prototype nanophotonic circuit consisting of a
receiving and an emitting nano antenna connected by a two-wire optical
transmission line is studied using finite-difference time- and frequency-domain
simulations. To optimize the coupling between nanophotonic circuit elements we
apply impedance matching concepts in analogy to radio frequency technology. We
show that the degree of impedance matching, and in particular the impedance of
the transmitting nano antenna, can be inferred from the experimentally
accessible standing wave pattern on the transmission line. We demonstrate the
possibility of matching the nano antenna impedance to the transmission line
characteristic impedance by variations of the antenna length and width
realizable by modern microfabrication techniques. The radiation efficiency of
the transmitting antenna also depends on its geometry but is independent of the
degree of impedance matching. Our systems approach to nanophotonics provides
the basis for realizing general nanophotonic circuits and a large variety of
derived novel devices.


  Finite alphabet iterative decoders (FAIDs) for LDPC codes were recently shown
to be capable of surpassing the Belief Propagation (BP) decoder in the error
floor region on the Binary Symmetric channel (BSC). More recently, the
technique of decimation which involves fixing the values of certain bits during
decoding, was proposed for FAIDs in order to make them more amenable to
analysis while maintaining their good performance. In this paper, we show how
decimation can be used adaptively to further enhance the guaranteed error
correction capability of FAIDs that are already good on a given code. The new
adaptive decimation scheme proposed has marginally added complexity but can
significantly improve the slope of the error floor performance of a particular
FAID. We describe the adaptive decimation scheme particularly for 7-level FAIDs
which propagate only 3-bit messages and provide numerical results for
column-weight three codes. Analysis suggests that the failures of the new
decoders are linked to stopping sets of the code.


  In the present paper, we prove that on a fixed pointed stable curve of
characteristic $p>0$, there exists a duality between dormant
$\mathfrak{sl}_n$-opers ($1 < n <p-1$) and dormant
$\mathfrak{sl}_{(p-n)}$-opers. Also, we prove that there exists a unique (up to
isomorphism) dormant $\mathfrak{sl}_{(p-1)}$-oper on a fixed pointed stable
curve of characteristic $p>0$.


  The conductance of a tunnel point-contact in an STM-like geometry having a
single defect placed below the surface is investigated theoretically. The
effect of multiple electron scattering by the defect after reflections by the
metal surface is taken into account. In the approximation of s-wave scattering
the dependence of the conductance on the applied voltage and the position of
the defect is obtained. The results are illustrated for a model s-wave phase
shift describing Kondo-resonance scattering. We demonstrate that multiple
electron scattering by the magnetic impurity plays a decisive role in the
point-contact conductance at voltages near the Kondo resonance. We find that
the sign and shape of the Kondo anomaly depends on the position of the defect.


  We unveil the microscopic origin of largely debated magnetism in the
Mo$_{3}$O$_{8}$ cluster systems. Upon considering an extended Hubbard model at
1/6 filling on the anisotropic kagom\'e lattice formed by the Mo atoms, we
argue that its ground state is determined by the competition between kinetic
energy and intersite Coulomb interactions, which is controlled by the
trimerisation of the kagom\'e lattice into the Mo$_{3}$O$_{13}$ clusters. Based
on first-principles calculations, we show that the strong interaction limit is
realised in LiZn$_{2}$Mo$_{3}$O$_{8}$ revealing a plaquette charge order with
unpaired spins at the resonating hexagons, whose origin is solely related to
the opposite signs of intracluster and intercluster hoppings, in contrast to
all previous scenarios. On the other hand, both Li$_{2}$InMo$_{3}$O$_{8}$ and
Li$_{2}$ScMo$_{3}$O$_{8}$ are demonstrated to fall into the weak interaction
limit where the electrons are well localised at the Mo$_{3}$O$_{13}$ clusters.
While the former is found to exhibit long-range antiferromagnetic order, the
latter is more likely to reveal short-range order with quantum spin liquid-like
excitations. Our results not only reproduce most of the experimentally observed
features of these unique materials, but will also help to describe various
properties in other quantum cluster magnets.


  The thresholded feature has recently emerged as an extremely efficient, yet
rough empirical approximation, of the time-consuming sparse coding inference
process. Such an approximation has not yet been rigorously examined, and
standard dictionaries often lead to non-optimal performance when used for
computing thresholded features. In this paper, we first present two theoretical
recovery guarantees for the thresholded feature to exactly recover the nonzero
support of the sparse code. Motivated by them, we then formulate the Dictionary
Learning for Thresholded Features (DLTF) model, which learns an optimized
dictionary for applying the thresholded feature. In particular, for the $(k,
2)$ norm involved, a novel proximal operator with log-linear time complexity
$O(m\log m)$ is derived. We evaluate the performance of DLTF on a vast range of
synthetic and real-data tasks, where DLTF demonstrates remarkable efficiency,
effectiveness and robustness in all experiments. In addition, we briefly
discuss the potential link between DLTF and deep learning building blocks.


  A recent theorem of Foscolo-Haskins-Nordstr\"om which constructs complete
$G_2$-holonomy orbifolds from circle bundles over Calabi-Yau cones can be
utilised to construct and investigate a large class of generalisations of the
$M$-theory flop transition. We see that in many cases a UV perturbative gauge
theory appears to have an infrared dual described by a smooth $G_2$-holonomy
background in $M$-theory. Various physical checks of this proposal are carried
out affirmatively.


  The so called gamma metric corresponds to a two-parameter family of axially
symmetric, static solutions of Einstein's equations found by Bach. It contains
the Schwarzschild solution for a particular value of one of the parameters,
that rules a deviation from spherical symmetry.
  It is shown that there is invariantly definable singular behaviour beyond the
one displayed by the Kretschmann scalar when a unique, hypersurface orthogonal,
timelike Killing vector exists. In this case, a particle can be defined to be
at rest when its world-line is a corresponding Killing orbit. The norm of the
acceleration on such an orbit proves to be singular not only for metrics that
deviate from Schwarzschild's metric, but also on approaching the horizon of
Schwarzschild metric itself, in contrast to the discontinuous behaviour of the
curvature scalar.


  We construct a tractable model to describe the rate at which a knotted
polymer is ejected from a spherical capsid via a small pore. Knots are too
large to fit through the pore and must reptate to the end of the polymer for
ejection to occur. The reptation of knots is described by symmetric exclusion
on the line, with the internal capsid pressure represented by an additional
biased particle that drives knots to the end of the chain. We compute the exact
ejection speed for a finite number of knots L and find that it scales as 1/L.
We also construct a continuum theory for many knots that matches the exact
discrete theory for large L.


  We consider the reduced Allen-Cahn action functional, which appears as the
sharp interface limit of the Allen-Cahn action functional and can be understood
as a formal action functional for a stochastically perturbed mean curvature
flow. For suitable evolutions of generalized hypersurfaces this functional
consists of the sum of the squares of the mean curvature and of the velocity
vector, integrated over time and space. For given initial and final conditions
we investigate the corresponding action minimization problem. We give a
generalized formulation and prove compactness and lower semicontinuity
properties of the action functional. Furthermore we characterize the
Euler-Lagrange equation for smooth stationary points and investigate conserved
quantities. Finally we present an explicit example and consider concentric
spheres as initial and final data and characterize in dependence of the given
time span the properties of the minimal rotationally symmetric connection.


  In this paper, we investigate numerically a diffuse interface model for the
Navier-Stokes equation with fluid-fluid interface when the fluids have
different densities \cite{Lowengrub1998}. Under minor reformulation of the
system, we show that there is a continuous energy law underlying the system,
assuming that all variables have reasonable regularities. It is shown in the
literature that an energy law preserving method will perform better for
multiphase problems. Thus for the reformulated system, we design a $C^0$ finite
element method and a special temporal scheme where the energy law is preserved
at the discrete level. Such a discrete energy law (almost the same as the
continuous energy law) for this variable density two-phase flow model has never
been established before with $C^0$ finite element. A Newton's method is
introduced to linearise the highly non-linear system of our discretization
scheme. Some numerical experiments are carried out using the adaptive mesh to
investigate the scenario of coalescing and rising drops with differing density
ratio. The snapshots for the evolution of the interface together with the
adaptive mesh at different times are presented to show that the evolution,
including the break-up/pinch-off of the drop, can be handled smoothly by our
numerical scheme. The discrete energy functional for the system is examined to
show that the energy law at the discrete level is preserved by our scheme.


  This paper is concerned with approximations of the Boltzmann equation based
on the method of moments. We propose a generalization of the setting of the
moment-closure problem from relative entropy to {\phi}-divergences and a
corresponding closure procedure based on minimization of {\phi}-divergences.
The proposed description encapsulates as special cases Grad's classical closure
based on expansion in Hermite polynomials and Levermore's entropy-based
closure. We establish that the generalization to divergence-based closures
enables the construction of extended thermodynamic theories that avoid
essential limitations of the standard moment-closure formulations such as
inadmissibility of the approximate phase-space distribution, potential loss of
hyperbolicity and singularity of flux functions at local equilibrium. The
divergence-based closure leads to a hierarchy of tractable symmetric hyperbolic
systems that retain the fundamental structural properties of the Boltzmann
equation.


  In this paper, we present an efficient quantum compression method for
identically prepared states with arbitrary dimentional.


  We consider the propagation of electromagnetic waves through a
dilaton-Maxwell domain wall of the type introduced by Gibbons and Wells [G.W.
Gibbons and C.G. Wells, Class. Quant. Grav. 11, 2499-2506 (1994)]. It is found
that if such a wall exists within our observable universe, it would be absurdly
thick, or else have a magnetic field in its core which is much stronger than
observed intergalactic fields. We conclude that it is highly improbable that
any such wall is physically realized.


  With A Multi-Phase Transport (AMPT) model we investigate the relation between
the magnitude, fluctuations and correlations of the initial state spatial
anisotropy $\varepsilon_{n}$ and the final state anisotropic flow coefficients
$v_{n}$ in Au+Au collisions at $\sqrt{s_{_{\rm NN}}}=$ 200 GeV. It is found
that the relative eccentricity fluctuations in AMPT account for the observed
elliptic flow fluctuations, in agreement with measurements of the STAR
collaboration. In addition, the studies based on 2- and multi-particle
correlations and event-by-event distributions of the anisotropies suggest that
the Elliptic-Power function is a promising candidate of the underlying
probability density function of the event-by-event distributions of
$\varepsilon_{n}$ as well as $v_{n}$. Furthermore, the correlations between
different order symmetry planes and harmonics in the initial coordinate space
and final state momentum space are presented. Non-zero values of these
correlations have been observed. The comparison between our calculations and
data will, in the future, shed new insight into the nature of the fluctuations
of the Quark-Gluon Plasma produced in heavy ion collisions.


  We investigate threshold-based multi-trial decoding of concatenated codes
with an inner Maximum-Likelihood decoder and an outer error/erasure
(L+1)/L-extended Bounded Distance decoder, i.e. a decoder which corrects e
errors and t erasures if e(L+1)/L + t <= d - 1, where d is the minimum distance
of the outer code and L is a positive integer. This is a generalization of
Forney's GMD decoding, which was considered only for L = 1, i.e. outer Bounded
Minimum Distance decoding. One important example for (L+1)/L-extended Bounded
Distance decoders is decoding of L-Interleaved Reed-Solomon codes. Our main
contribution is a threshold location formula, which allows to optimally erase
unreliable inner decoding results, for a given number of decoding trials and
parameter L. Thereby, the term optimal means that the residual codeword error
probability of the concatenated code is minimized. We give an estimation of
this probability for any number of decoding trials.


  In this work, a new theoretical approach to study the non-equilibrium
transport properties of nanoscale systems coupled to metallic electrodes with
strong electron-phonon interactions is presented. The proposed approach
consists in a resummation of the dominant Feynman diagrams from the exact
preturbative expansion. This scheme is compared with methods that can be found
in the literature. It shows a good agreement with these methods in the range
where they are known to provide good results, for a wide range of parameters.
Also, it is compared with path-integral Monte Carlo calculations giving a
relatively good agreement for polaronic and non polaronic regimes. Some
preliminary results for the current noise obtained with our method are
presented.


  We have investigated the electronic structures of LaBi and LuBi, employing
the full-potential all electron method as implemented in Wien2k. Using this, we
have studied in detail both the bulk and the surface states of these materials.
From our band structure calculations we find that LuBi, like LaBi, is a
compensated semi-metal with almost equal and sizable electron and hole pockets.
In analogy with experimental evidence in LaBi, we thus predict that LuBi will
also be a candidate for extremely large magneto-resistance (XMR), which should
be of immense technological interest. Our calculations reveal that LaBi,
despite being gapless in the bulk spectrum, displays the characteristic
features of a $\mathbb{Z}_{2}$ topological semi-metal, resulting in gapless
Dirac cones on the surface, whereas LuBi only shows avoided band inversion in
the bulk and is thus a conventional compensated semi-metal with extremely large
magneto-resistance.


  We study the existence and the regularity of the biharmonic Green kernel in a
Brelot biharmonic space whose associated harmonic spaces have Green kernels. We
show by some examples that this kernel does not always exist. We then introduce
and study the adjoint of the given biharmonic space. This study was initiated
by Smyrnelis, however, it seems that several results were incomplete and we
clarify them here.


  We review the experimental as well as the phenomenology status of Generalized
Parton Distributions (GPDs), focusing on recent data on Deeply Virtual Compton
Scattering and Deep Virtual Meson Production. We also describe the various
strategies for extraction of GPDs from these data. Finally we conclude with a
summary of we know about GPDs and the experimental outlook in the years to
come.


  We present the characterization of the band structure of GaAs/AlAs
quantum-wire 1D superlattices performed by magnetophonon resonance with pulsed
magnetic fields up to 35 T. The samples, generated by the "atomic saw method"
from original quantum-well 2D superlattices, underwent substantial
modifications of their energy bands built up on the X-states of the bulk. We
have calculated the band structure by a finite element method and we have
studied the various miniband structures built up of the masses m_t and m_l of
GaAs and AlAs at the point X. From an experimental point of view, the main
result is that in the 2D case we observe only resonances when the magnetic
field B is applied along the growth axis whereas in the 1D case we obtain
resonances in all magnetic field configurations. The analysis of the maxima (or
minima for B // E) in the resistivity rho_xy as a function of B allows us to
account, qualitatively and semi-quantitatively, for the band structure
theoretically expected.


  For an integer k >= 1, the k-th interlacing adjoint of a digraph G is the
digraph i_k(G) with vertex-set V(G)^k, and arcs ((u_1, ..., u_k), (v_1, ...,
v_k)) such that (u_i,v_i) \in A(G) for i = 1, ..., k and (v_i, u_{i+1}) \in
A(G) for i = 1, ..., k-1. For every k we derive upper and lower bounds for the
chromatic number of i_k(G) in terms of that of G. In particular, we find tight
bounds on the chromatic number of interlacing adjoints of transitive
tournaments. We use this result in conjunction with categorial properties of
adjoint functors to derive the following consequence. For every integer ell,
there exists a directed path Q_{\ell} of algebraic length ell which admits
homomorphisms into every directed graph of chromatic number at least 4. We
discuss a possible impact of this approach on the multifactor version of the
weak Hedetniemi conjecture.


  The paper deals with the analysis of Burgers' equation on acyclic metric
graphs. The main goal is to establish the existence of weak solutions in the
$TV$ -- class of regularity. A key point is transmission conditions in vertices
obeying the Kirchhoff law. First, we consider positive solutions at arbitrary
acyclic networks and highlight two kinds of vertices, describing two mechanisms
of flow splitting at the vertex. Next we design rules at vertices for solutions
of arbitrary sign for any subgraph of hexagonal grid, which leads to a
construction of general solutions with $TV$ -- regularity for this class of
networks. Introduced transmission conditions are motivated by the change of the
energy estimation.


  It is shown that if a real value PL-invariant of closed combinatorial
manifolds admits a local formula that depends only on the f-vector of the link
of each vertex, then the invariant must be a constant times the Euler
characteristic.


  We solve two variants of the Reifenberg problem for all coefficient groups.
We carry out the direct method of the calculus of variation and search a
solution as a weak limit of a minimizing sequence. This strategy has been
introduced by De Lellis, De Philippis, De Rosa, Ghiraldin and Maggi and allowed
them to solve the Reifenberg problem. We use an analogous strategy which allows
to take into account the free boundary. Moreover, we show that the Reifenberg
class is closed under weak convergence without restriction on the coefficient
group.


  In this paper, we propose a binarized neural network learning method called
BiDet for efficient object detection. Conventional network binarization methods
directly quantize the weights and activations in one-stage or two-stage
detectors with constrained representational capacity, so that the information
redundancy in the networks causes numerous false positives and degrades the
performance significantly. On the contrary, our BiDet fully utilizes the
representational capacity of the binary neural networks for object detection by
redundancy removal, through which the detection precision is enhanced with
alleviated false positives. Specifically, we generalize the information
bottleneck (IB) principle to object detection, where the amount of information
in the high-level feature maps is constrained and the mutual information
between the feature maps and object detection is maximized. Meanwhile, we learn
sparse object priors so that the posteriors are concentrated on informative
detection prediction with false positive elimination. Extensive experiments on
the PASCAL VOC and COCO datasets show that our method outperforms the
state-of-the-art binary neural networks by a sizable margin.


  Sum-rank Hamming codes are introduced in this work. They are essentially
defined as the longest codes (thus of highest information rate) with minimum
sum-rank distance at least $ 3 $ (thus one-error-correcting) for a fixed
redundancy $ r $, base-field size $ q $ and field-extension degree $ m $ (i.e.,
number of matrix rows). General upper bounds on their code length, number of
shots or sublengths and average sublength are obtained based on such
parameters. When the field-extension degree is $ 1 $, it is shown that sum-rank
isometry classes of sum-rank Hamming codes are in bijective correspondence with
maximal-size partial spreads. In that case, it is also shown that sum-rank
Hamming codes are perfect codes for the sum-rank metric. Also in that case,
estimates on the parameters (lengths and number of shots) of sum-rank Hamming
codes are given, together with an efficient syndrome decoding algorithm. Duals
of sum-rank Hamming codes, called sum-rank simplex codes, are then introduced.
Bounds on the minimum sum-rank distance of sum-rank simplex codes are given
based on known bounds on the size of partial spreads. As applications, sum-rank
Hamming codes are proposed for error correction in multishot
matrix-multiplicative channels and to construct locally repairable codes over
small fields, including binary.


  In paper a new definition of reduced Pade approximant and algorithm for its
computing is proposed. Our approach is based on the investigation of the kernel
structure of the Toeplitz matrix. It is shown that the reduced Pade approximant
always has nice properties which classical Pade approximant possesses only in
the normal case. The new algorithm allows us to avoid Froissart doublets
appearance induced by computer roundoff in the non-normal Pade table.


  All investigators working on the foundations of quantum mechanics agree that
the theory has profoundly modified our conception of reality. But there ends
the consensus. The unproblematic formalism of the theory gives rise to a number
of very different interpretations, each of which has consequences on the notion
of reality. This paper analyses how the Copenhagen interpretation, von
Neumann's state vector collapse, Bohm and de Broglie's pilot wave and Everett's
many worlds modify, each in its own way, the classical conception of reality,
whose local character, in particular, requires revision.


  Next POI recommendation intends to forecast users' immediate future movements
given their current status and historical information, yielding great values
for both users and service providers. However, this problem is perceptibly
complex because various data trends need to be considered together. This
includes the spatial locations, temporal contexts, user's preferences, etc.
Most existing studies view the next POI recommendation as a sequence prediction
problem while omitting the collaborative signals from other users. Instead, we
propose a user-agnostic global trajectory flow map and a novel Graph Enhanced
Transformer model (GETNext) to better exploit the extensive collaborative
signals for a more accurate next POI prediction, and alleviate the cold start
problem in the meantime. GETNext incorporates the global transition patterns,
user's general preference, spatio-temporal context, and time-aware category
embeddings together into a transformer model to make the prediction of user's
future moves. With this design, our model outperforms the state-of-the-art
methods with a large margin and also sheds light on the cold start challenges
within the spatio-temporal involved recommendation problems.


  The latest FermiLab muon $g-2$ result shows a $5\sigma$ discrepancy with a
``widely advertised" Standard Model prediction. We consider a supersymmetric
$SU(4)_c \times SU(2)_L \times SU(2)_R$ model in which this discrepancy is
resolved by including contributions to muon $g-2$ from a relatively light SUSY
sector. A variety of realistic coannihilation scenarios can reproduce the
observed dark matter relic abundance. With a significantly reduced discrepancy,
of order $1 \sigma$ or less, the Higgsino-like dark matter solutions are also
viable. We provide benchmark points for these solutions that will be probed in
the direct detection dark matter experiments and collider searches.


  We numerically calculated the full capacitance matrices for both
one-dimensional (1D) and two-dimensional (2D) quantum-dot arrays. We found it
is necessary to use the full capacitance matrix in modeling coupled quantum dot
arrays due to weaker screening in these systems in comparison with arrays of
normal metal tunnel junctions. The static soliton potential distributions in
both 1D and 2D arrays are well approximated by the unscreened (1/r) coulomb
potential, instead of the exponential fall-off expected from the often used
nearest neighbor approximation. The Coulomb potential approximation also
provides a simple expression for the full inverse capacitance matrix of uniform
quantum dot arrays. In terms of dynamics, we compare the current-voltage (I-V)
characteristics of voltage biased 1D arrays using either the full capacitance
matrix or its nearest neighbor approximation. The I-V curves show clear
differences and the differences become more pronounced when larger arrays are
considered.


  We compute the density dependence of the quark condensate and how it changes
under the influence of isospin-asymmetric nuclear matter. This is achieved by
the calculation of the relevant Feynman diagrams using in-medium chiral
perturbation theory. We find that the absolute value of the quark condensate
decreases in nuclear matter by around 35% at normal nuclear density, in
agreement with previous model-independent calculations. We also present an
quantitative estimation of the difference of up- and down quark in-medium
condensates.


  The question is raised about whether the pulse delay in a saturable absorber
has anything to do with the "slow light" and group velocity reduction. We also
wonder why the 40-years-old trivial interpretation of the effect remains so far
ignored.


  We estimated the contribution of binary systems to the velocity dispersion
inside OB-associations derived from Gaia DR2 proper motions. The maximum
contribution to the velocity dispersion is given by the systems with the period
of revolution of P=5.9 yr whose components shift by a distance of about the
diameter of the system during the base-line time of Gaia DR2 observations. We
employed two methods to study the motion of the photocenter of the binary
system: the first one uses the total displacement between the initial and final
visibility periods and the second one is based on solving a system of n
equations defining the displacements at the times t_n. The first and second
methods yield very similar sigma_bn values of 0.90 and 0.87 km s-1,
respectively. Taking into account the fact that orbits are elliptical slightly
decreases the inferred sigma_bn. We estimated the eccentricity-averaged
sigma_bn value to be sigma_bn=0.81 km s-1 assuming that the orbital
eccentricities of massive binary systems are distributed uniformly in the [0,
0.9] interval. The choice of the exponent gamma in the power-law distribution,
p_q ~ q^gamma, of the component-mass ratios q=M_2/M_1 of binary systems appears
to have little effect on sigma_bn. A change of gamma from 0 (flat distribution)
to -2.0 (preponderance of systems with low-mass components) changes sigma_bn
from 0.90 to 1.07 km s-1.


  Motivated by the recent LHCb results of lepton flavour violation on b decays
into s and b decays into c transitions we study the lepton flavour violating
(LFV) baryonic decays {Lambda}_b decays into {Lambda}l_i^+ l_j^- in
non-universal Z^' model. We discuss the two-fold decay distribution of
{Lambda}_b decays into {Lambda}l_i^+ l_j^- decays in terms of transversity
amplitudes. From this distribution we study the differential branching ratio
and lepton side forward-backward asymmetry in new physics (NP). The predicted
values of the observables are very interesting and that might emboss the
footprints of NP more aesthetically.


  We consider a two-parameter one-dimensional Hamiltonian with uncorrelated
diagonal disorder and {\it non-random} long-range inter-site interaction
$J_{mn}=J/|m-n|^{\mu}$. The model is critical at $1<\mu<3/2$ and reveals the
localization-delocalization transition with respect to the disorder magnitude.
To detect the transition we analyze level and wave function statistics. It is
demonstrated also that in the marginal case ($\mu = 3/2$) all states are
localized.


  The planned JEM-EUSO (Extreme Universe Space Observatory onboard the ISS
Japanese Experimental Module) will measure the energy spectra of cosmic rays up
to the range of 1000 EeV and will search for direction to their sources. It
will observe the extensive air showers generated in the atmosphere by high
energy cosmic ray primary particle from the space. The instantaneous aperture
of the telescope will exceed by one order the aperture of the largest ground
based detectors. JEM-EUSO apparatus is a large telescope with a diameter of 2.5
m with fast UV camera. Slovakia is responsible for the determination of the UV
background, which influences the operational efficiency of the experiment and
for the analysis of fake trigger events.


  We prove that three automorphisms of the rooted binary tree defined by a
certain 3-state automaton generate a free non-Abelian group of rank 3.


  Recently the Galois module structure of square power classes of a field $K$
has been computed under the action of $\text{Gal}(K/F)$ in the case where
$\text{Gal}(K/F)$ is the Klein $4$-group. Despite the fact that the modular
representation theory over this group ring includes an infinite number of
non-isomorphic indecomposable types, the decomposition for square power classes
includes at most $9$ distinct summand types. In this paper we determine the
multiplicity of each summand type in terms of a particular subspace of
$\text{Br}(F)$, and show that all "unexceptional" summand types are possible.


  This paper presents an analysis of the Overton policy document database,
describing the makeup of materials indexed and the nature in which they cite
academic literature. We report on various aspects of the data, including
growth, geographic spread, language representation, the range of policy source
types included, and the availability of citation links in documents.
Longitudinal analysis over established journal category schemes is used to
reveal the scale and disciplinary focus of citations and determine the
feasibility of developing field-normalized citation indicators. We examine how
well self-reported funding outcomes collected by UK funders corresponds to data
indexed in the Overton database, and if peer-review assessment of impact as
measured by the UK Research Excellence Framework (REF) 2014 correlates with
derived citation metrics. Our findings show that for some research topics, such
as health, economics, social care and the environment, Overton contains a core
set of policy documents with sufficient citation linkage to academic literature
to support various citation analysis that may be informative in research
evaluation, impact assessment, and policy review. The data indexed in Overton
agrees with that collected via self-reporting of funding outcomes, and
correlates with peer-review assessment of impact in some disciplines.


  The moduli space $\mathcal{M}_d$ of degree $d\geq2$ rational maps can
naturally be endowed with a measure $\mu_\mathrm{bif}$ detecting maximal
bifurcations, called the bifurcation measure. We prove that the support of the
bifurcation measure $\mu_\mathrm{bif}$ has positive Lebesgue measure. To do so,
we establish a general sufficient condition for the conjugacy class of a
rational map to belong to the support of $\mu_\mathrm{bif}$ and we exhibit a
large set of Collet-Eckmann rational maps which satisfy this condition. As a
consequence, we get a set of Collet-Eckmann rational maps of positive Lebesgue
measure which are approximated by hyperbolic rational maps.


  Much of social science is centered around terms like ``ideology'' or
``power'', which generally elude precise definition, and whose contextual
meanings are trapped in surrounding language. This paper explores the use of
large language models (LLMs) to flexibly navigate the conceptual clutter
inherent to social scientific measurement tasks. We rely on LLMs' remarkable
linguistic fluency to elicit ideological scales of both legislators and text,
which accord closely to established methods and our own judgement. A key aspect
of our approach is that we elicit such scores directly, instructing the LLM to
furnish numeric scores itself. This approach affords a great deal of
flexibility, which we showcase through a variety of different case studies. Our
results suggest that LLMs can be used to characterize highly subtle and diffuse
manifestations of political ideology in text.


  We present an all-dielectric photonic crystal structure that supports
two-dimensionally confined helical topological edge states. The topological
properties of the system are controlled by the crystal parameters. An interface
between two regions of differing band topologies gives rise to topological edge
states confined in a dielectric slab that propagate around sharp corners
without backscattering. Three dimensional finite-difference time-domain
calculations show these edges to be confined in the out-of-plane direction by
total internal reflection. Such nanoscale photonic crystal architectures could
enable strong interactions between photonic edge states and quantum emitters.


  In a recent experimental study (Gomez del Campo et al, PRL 86, 43 (2001)) of
the reaction 17F(p,2p)16O, two-proton events were measured from excitations
near a 1-, E*=6.15 MeV state in 18Ne. We calculate by means of R-matrix theory
the resonant two-proton production cross section and branching ratios. We
conclude that it is unlikely that two-proton production via population of the
1- state is sufficient to explain the observed two-proton events. Alternative
sources of such events are discussed.


  Current statistics can be calculated in various ways. Event-based approaches
use the statistics of the number of events occuring during a given time.
Time-based approaches use the statistics of the time needed to reach a given
number of events. By analyzing normal as well as anomalous statistics of
nonequilibrium currents through a two level system in contact with two
different reservoirs, we investigate the conditions under which these different
statistics do or do not yield identical predictions. We rely on the continuous
time random walk formulation introduced in our earlier work [Phys. Rev. E 77,
051119 (2008)].


  Thanks to their improved data efficiency, equivariant neural networks have
gained increased interest in the deep learning community. They have been
successfully applied in the medical domain where symmetries in the data can be
effectively exploited to build more accurate and robust models. To be able to
reach a much larger body of patients, mobile, on-device implementations of deep
learning solutions have been developed for medical applications. However,
equivariant models are commonly implemented using large and computationally
expensive architectures, not suitable to run on mobile devices. In this work,
we design and test an equivariant version of MobileNetV2 and further optimize
it with model quantization to enable more efficient inference. We achieve
close-to state of the art performance on the Patch Camelyon (PCam) medical
dataset while being more computationally efficient.


  Let $X_{1},..,X_{n}$ denote an i.i.d. sample with light tail distribution and
$S_{1}^{n}$ denote the sum of its terms; let $a_{n}$ be a real sequence\ going
to infinity with $n.$\ In a previous paper (\cite{BoniaCao}) it is proved that
as $n\rightarrow\infty$, given $\left(S_{1}^{n}/n>a_{n}\right) $ all terms
$X_{i_{\text{}}}$ concentrate around $a_{n}$ with probability going to 1. This
paper explores the asymptotic distribution of $X_{1}$ under the conditioning
events $\left(S_{1}^{n}/n=a_{n}\right) $ and $\left(S_{1}^{n}/n\geq
a_{n}\right)$ . It is proved that under some regulatity property, the
asymptotic conditional distribution of $X_{1}$ given
$\left(S_{1}^{n}/n=a_{n}\right) $ can be approximated in variation norm by the
tilted distribution at point $a_{n}$, extending therefore the classical LDP
case developed in Diaconis and Freedman (1988) . Also under
$\left(S_{1}^{n}/n\geq a_{n}\right) $ the dominating point property holds.
  It also considers the case when the $X_{i}$'s are $\mathbb{R}^{d}-$valued,
$f$ is a real valued function defined on $\mathbb{R}^{d}$ and the conditioning
event writes $\left(U_{1}^{n}/n=a_{n}\right) $ or $\left(U_{1}^{n}/n\geq
a_{n}\right)$ with $U_{1}^{n}:=\left(f(X_{1})+..+f(X_{n})\right) /n$ and
$f(X_{1})$ has a light tail distribution$.$ As a by-product some attention is
paid to the estimation of high level sets of functions.


  Much of the nontrivial dynamics of the one dimensional Complex
Ginzburg-Landau Equation (CGLE) is dominated by propagating structures that are
characterized by local ``twists'' of the phase-field. I give a brief overview
of the most important properties of these various structures, formulate a
number of experimental challenges and address the question how such structures
may be identified in experimental space-time data sets.


  We study properties of the single-site reduced density matrix in the
Bose-Bose resonance model as a function of system parameters. This model
describes a single-component Bose gas with a resonant coupling to a diatomic
molecular state, here defined on a lattice. A main goal is to demonstrate that
the eigenstates of the single-site reduced density matrix have structures that
are characteristic for the various quantum phases of this system. Since the
Hamiltonian conserves only the global particle number but not the number of
bosons and molecules individually, these eigenstates, referred to as optimal
modes, can be nontrivial linear combinations of bare eigenstates of the
molecular and boson particle number. We numerically analyze the optimal modes
and their weights, the latter giving the importance of the corresponding state,
in the ground state of the Bose-Bose resonance model. We find that the
single-site von Neumann entropy is sensitive to the location of the phase
boundaries. We explain the structure of the optimal modes and their weight
spectra using perturbation theory and via a comparison to results for the
single-component Bose-Hubbard model. We further study the dynamical evolution
of the optimal modes and of the single-site entanglement entropy in two quantum
quenches that cross phase boundaries of the model and show that these
quantities are thermal in the steady state. For our numerical calculations, we
use the density matrix renormalization group method for ground-state
calculations and time evolution in a Krylov subspace for the quench dynamics as
well as exact diagonalization.


  We consider a diffuse interface approximation for the lipid phases of
rotationally symmetric two-phase bilayer membranes and rigorously derive its
$\Gamma$-limit. In particular, we prove that limit vesicles are $C^1$ across
interfaces, which justifies a regularity assumption that is widely made in
formal asymptotic and numerical studies. Moreover, a limit membrane may consist
of several topological spheres, which are connected at the axis of revolution
and resemble complete buds of the vesicle.