  We present a self-consistent quantum optics approach to calculating the
surface enhanced Raman spectrum of molecules coupled to arbitrarily shaped
plasmonic systems. Our treatment is intuitive to use and provides fresh
analytical insight into the physics of the Raman scattering near metallic
surfaces and can be applied to a wide range of geometries including resonators,
waveguides, as well as hybrid photonic-plasmonic systems. Our general theory
demonstrates that the detected Raman spectrum originates from an interplay
between nonlinear light generation and propagation. Counter intuitively, at the
nonlinear generation stage, we show that the Stokes (anti-Stokes) signal at the
molecule location depends on the plasmonic enhancements, through the local
density of photon states (LDOS), at the anti-Stokes (Stokes) frequency.
However, when propagating from the vibrating molecule to the far field, the
Stokes (anti-Stokes) emission experiences a plasmonic enhancement at the Stokes
(anti-Stokes) frequency, as expected. We identify the limits of the commonly
known E^4 electric-field rule for Raman signal enhancement near plasmonic
surfaces at low pump powers, as well as a different E^8 rule at high pump
powers, and we clarify the role of the LDOS. Our theory uses a generalized
quantum master equation where the plasmonic system is treated as an
environmental bath that is described through the photonic Green function of the
medium. Therefore, any electrodynamics related physics, such as quenching and
propagation, are self-consistently included in the model. The presented
formalism is also capable of spatially describing the full Raman response in a
simple analytical way, which is typically not possible using simpler coupled
mode theories, even if one adopts a quantum picture.


  Public blockchains implement a fee mechanism to allocate scarce computational
resources across competing transactions. Most existing fee market designs
utilize a joint, fungible unit of account (e.g., gas in Ethereum) to price
otherwise non-fungible resources such as bandwidth, computation, and storage,
by hardcoding their relative prices. Fixing the relative price of each resource
in this way inhibits granular price discovery, limiting scalability and opening
up the possibility of denial-of-service attacks. As a result, many prominent
networks such as Ethereum and Solana have proposed multi-dimensional fee
markets. In this paper, we provide a principled way to design fee markets that
efficiently price multiple non-fungible resources. Starting from a loss
function specified by the network designer, we show how to compute dynamic
prices that align the network's incentives (to minimize the loss) with those of
the users and miners (to maximize their welfare), even as demand for these
resources changes. Our pricing mechanism follows from a natural decomposition
of the network designer's problem into two parts that are related to each other
via the resource prices. These results can be used to efficiently set fees in
order to improve network performance.


  We present the discovery of three new transiting giant planets, first
detected with the WASP telescopes, and establish their planetary nature with
follow up spectroscopy and ground-based photometric lightcurves. WASP-92 is an
F7 star, with a moderately inflated planet orbiting with a period of 2.17 days,
which has $R_p = 1.461 \pm 0.077 R_{\rm J}$ and $M_p = 0.805 \pm 0.068 M_{\rm
J}$. WASP-93b orbits its F4 host star every 2.73 days and has $R_p = 1.597 \pm
0.077 R_{\rm J}$ and $M_p = 1.47 \pm 0.029 M_{\rm J}$. WASP-118b also has a hot
host star (F6) and is moderately inflated, where $R_p = 1.440 \pm 0.036 R_{\rm
J}$ and $M_p = 0.513 \pm 0.041 M_{\rm J}$ and the planet has an orbital period
of 4.05 days. They are bright targets (V = 13.18, 10.97 and 11.07 respectively)
ideal for further characterisation work, particularly WASP-118b, which is being
observed by K2 as part of campaign 8. WASP-93b is expected to be tidally
migrating outwards, which is divergent from the tidal behaviour of the majority
of hot Jupiters discovered.


  Semiconductor quantum dots embedded in hybrid circular Bragg gratings are a
promising platform for the efficient generation of nonclassical light. The
scalable fabrication of multiple devices with similar performance is highly
desirable for their practical use as sources of single and entangled photons,
while the ability to operate at telecom wavelength is essential for their
integration with the existing fiber infrastructure. In this work we combine the
promising properties of broadband hybrid circular Bragg gratings with a
membrane-transfer process performed on 3" wafer scale. We develop and study
single-photon sources based on InAs/GaAs quantum dots emitting in the telecom
O-band, demonstrating bright single-photon emission with Purcell factor > 5 and
count rates up to 10 MHz. Furthermore, we address the question of
reproducibility by benchmarking the performance of 10 devices covering a wide
spectral range of 50 nm within the O-band.


  We study the $n$-dimensional Schr\"odinger equation with singular potential
$V_\lambda(x)=\lambda |x|^{-2}$. Its solution space is studied as a global
representation of $\widetilde{SL(2,\R)}\times O(n)$. A special subspace of
solutions for which the action globalizes is constructed via nonstandard
induction outside the semisimple category. The space of $K$-finite vectors is
calculated, obtaining conditions for $\lambda$ so that this space is non-empty.
The direct sum of solution spaces, over such admissible values of $\lambda$ is
studied as a representation of the $2n+1$-dimensional Heisenberg group.


  Accurate photo-z measurements are important to construct a large-scale
structure map of X-ray Universe in the ongoing SRG/eROSITA All-Sky Survey. We
present machine learning Random Forest-based models for probabilistic photo-z
predictions based on information from 4 large photometric surveys (SDSS,
Pan-STARRS, DESI Legacy Imaging Survey, and WISE). Our models are trained on
the large sample of $\approx$580000 quasars and galaxies selected from the SDSS
DR14 spectral catalog and take into account Galactic extinction and
uncertainties in photometric measurements for target objects. On the Stripe82X
test sample we obtained photo-z accuracy for X-ray sources: $NMAD=0.034$
(normalized median absolute deviation) and $n_{>0.15}=0.088$ (catastrophic
outliers fraction), which is almost $\sim2$ times better than best photo-z
results available in the literature.


  Modern astronomical experiments are designed to achieve multiple scientific
goals, from studies of galaxy evolution to cosmic acceleration. These goals
require data of many different classes of night-sky objects, each of which has
a particular set of observational needs. These observational needs are
typically in strong competition with one another. This poses a challenging
multi-objective optimization problem that remains unsolved. The effectiveness
of Reinforcement Learning (RL) as a valuable paradigm for training autonomous
systems has been well-demonstrated, and it may provide the basis for
self-driving telescopes capable of optimizing the scheduling for astronomy
campaigns. Simulated datasets containing examples of interactions between a
telescope and a discrete set of sky locations on the celestial sphere can be
used to train an RL model to sequentially gather data from these several
locations to maximize a cumulative reward as a measure of the quality of the
data gathered. We use simulated data to test and compare multiple
implementations of a Deep Q-Network (DQN) for the task of optimizing the
schedule of observations from the Stone Edge Observatory (SEO). We combine
multiple improvements on the DQN and adjustments to the dataset, showing that
DQNs can achieve an average reward of 87%+-6% of the maximum achievable reward
in each state on the test set. This is the first comparison of offline RL
algorithms for a particular astronomical challenge and the first open-source
framework for performing such a comparison and assessment task.


  Generating adversarial examples is the art of creating a noise that is added
to an input signal of a classifying neural network, and thus changing the
network's classification, while keeping the noise as tenuous as possible. While
the subject is well-researched in the 2D regime, it is lagging behind in the 3D
regime, i.e. attacking a classifying network that works on 3D point-clouds or
meshes and, for example, classifies the pose of people's 3D scans. As of now,
the vast majority of papers that describe adversarial attacks in this regime
work by methods of optimization. In this technical report we suggest a neural
network that generates the attacks. This network utilizes PointNet's
architecture with some alterations. While the previous articles on which we
based our work on have to optimize each shape separately, i.e. tailor an attack
from scratch for each individual input without any learning, we attempt to
create a unified model that can deduce the needed adversarial example with a
single forward run.


  The H-unistochastic matrices are a special class of symmetric bistochastic
matrices obtained by taking the square of the absolute value of each entry of a
Hermitian unitary matrix. We examine the geometric relationship of the convex
hull of the n by n H-unistochastic matrices relative to the larger convex set
of n by n symmetric bistochastic matrices. We show that any line segment in the
convex set of the n by n symmetric bistochastic matrices which passes through
the centroid of this convex set must spend at least two-thirds of its length in
the convex hull of the n by n H-unistochastic matrices when n is either three
or four and we prove a partial result for higher n. A class of completely
positive linear maps called the self-dual doubly stochastic maps is useful for
studying this problem. Some results on self-dual doubly stochastic maps are
given including a self-dual version of the Laudau-Streater theorem.


  This course of lectures has been taught for several years at the Lomonosov
Moscow State University; its modified version in 2021 is read in the Zhejiang
University (Hangzhou), in the framework of summer school on quantum computing.
The course is devoted to a new type of computations based on quantum mechanics.
Quantum computations are fundamentally different from classical ones in that
they occur in the space of so-called quantum states, and not in ordinary binary
strings. Quantum computing is a real process in which the mathematical
description is inextricably linked with quantum physics. Various forms of
quantum computing are considered: the Feynman gate model, fermionic and
adiabatic computations. A class of problems is described in which quantum
computing is not only more efficient than classical ones, but also cannot be
replaced by them. The course is designed for students of physics and
mathematics and natural science specialties as well as all those interested in
this subject. It requires familiarity with the basics of linear algebra and
mathematical analysis in the first two courses of the university.


  The paper is devoted to operators given formally by the expression
\begin{equation*} -\partial_x^2+\big(\alpha-\frac14\big)x^{-2}. \end{equation*}
This expression is homogeneous of degree minus 2. However, when we try to
realize it as a self-adjoint operator for real $\alpha$, or closed operator for
complex $\alpha$, we find that this homogeneity can be broken.
  This leads to a definition of two holomorphic families of closed operators on
$L^2({\mathbb R}_+)$, which we denote $H_{m,\kappa}$ and $H_0^\nu$, with
$m^2=\alpha$, $-1<\Re(m)<1$, and where $\kappa,\nu\in{\mathbb C}\cup\{\infty\}$
specify the boundary condition at $0$. We study these operators using their
explicit solvability in terms of Bessel-type functions and the Gamma function.
In particular, we show that their point spectrum has a curious shape: a string
of eigenvalues on a piece of a spiral. Their continuous spectrum is always
$[0,\infty[$. Restricted to their continuous spectrum, we diagonalize these
operators using a generalization of the Hankel transformation. We also study
their scattering theory.
  These operators are usually non-self-adjoint. Nevertheless, it is possible to
use concepts typical for the self-adjoint case to study them. Let us also
stress that $-1<\Re(m)<1$ is the maximal region of parameters for which the
operators $H_{m,\kappa}$ can be defined within the framework of the Hilbert
space $L^2({\mathbb R}_+)$.


  In the present paper, by approximating the derivatives in the Kou et al.
\cite{Kou} fourth-order method by central difference quotient, we obtain new
modification of this method free from derivatives. We prove the important fact
that the method obtained preserve their order of convergence, without
calculating any derivative. Finally, numerical tests confirm that our method
give the better performance as compare to other well known Steffensen type
methods.


  Forward-backward correlations of charged-particle multiplicities in symmetric
bins in pseudorapidity (eta) are studied in order to gain insight into the
underlying correlation structure of particle production in Au+Au collisions.
The PHOBOS detector is used to measure integrated multiplicities in bins
defined within eta<3, centered at eta and covering an interval Delta-eta. The
variance (sigma^2_C) of a suitably defined forward-backward asymmetry variable
is calculated as a function of eta, Delta-eta, and centrality. It is found to
be sensitive to short range correlations, and the concept of ``clustering'' is
used to interpret comparisons to phenomenological models.


  The goal of this work is to present an approach to the homogeneous Boltzmann
equation for Maxwellian molecules with a physical collision kernel which allows
us to construct unique solutions to the initial value problem in a space of
probability measures defined via the Fourier transform. In that space, the
second moment of a measure is not assumed to be finite, so infinite energy
solutions are not {\it a priori} excluded from our considerations. Moreover, we
study the large time asymptotics of solutions and, in a particular case, we
give an elementary proof of the asymptotic stability of self-similar solutions
obtained by A.V. Bobylev and C. Cercignani [J. Stat. Phys. {\bf 106} (2002),
1039--1071].


  Here we show, by performing ab initio classical field simulations that two
distinct superfluid phases, separated by thermal vortex-antivortex pair
creation, exist in experimentally producible quasi-2D Bose gas. These results
resolve the debate on the nature of the low temperature phase(s) of a trapped
interacting 2D Bose gas.


  In this paper, we consider the local bases of primitive nonpowerful sign
pattern matrices, show that there are "gaps" in the local base set and
characterize some sign pattern matrices with given local bases.


  We consider versions of the grasshopper problem (Goulko and Kent, 2017) on
the circle and the sphere, which are relevant to Bell inequalities. For a
circle of circumference $2\pi$, we show that for unconstrained lawns of any
length and arbitrary jump lengths, the supremum of the probability for the
grasshopper's jump to stay on the lawn is one. For antipodal lawns, which by
definition contain precisely one of each pair of opposite points and have
length $\pi$, we show this is true except when the jump length $\phi$ is of the
form $\pi\frac{p}{q}$ with $p,q$ coprime and $p$ odd. For these jump lengths we
show the optimal probability is $1 - 1/q$ and construct optimal lawns. For a
pair of antipodal lawns, we show that the optimal probability of jumping from
one onto the other is $1 - 1/q$ for $p,q$ coprime, $p$ odd and $q$ even, and
one in all other cases. For an antipodal lawn on the sphere, it is known (Kent
and Pital\'ua-Garc\'ia, 2014) that if $\phi = \pi/q$, where $q \in \mathbb N$,
then the optimal retention probability of $1-1/q$ for the grasshopper's jump is
provided by a hemispherical lawn. We show that in all other cases where $0<\phi
< \pi/2$, hemispherical lawns are not optimal, disproving the hemispherical
colouring maximality hypotheses (Kent and Pital\'ua-Garc\'ia, 2014). We discuss
the implications for Bell experiments and related cryptographic tests.


  Continuous variable quantum key distribution (CVQKD) is the sharing of secret
keys between different parties using the continuous amplitude and phase
quadratures of light. There are many protocols in which different modulation
schemes are used to implement CVQKD. However, there has been no tool for
comparison between different CVQKD protocols to determine the optimal protocol
for varying channels while simultaneously taking into account the effects of
different parameters. Here, a comparison tool has been developed to map regions
of positive secret key rate (SKR), given a channel's transmittance and excess
noise, where a user's modulation can be adjusted to guarantee a positive SKR in
an arbitrary environment. The method has been developed for discrete modulated
CVQKD (DM-CVQKD) protocols but can be extended to other current and future
protocols and security proofs.


  Analytic formulae are given for QCD corrections to the lepton spectra in
decays of polarised up and down type heavy quarks. These formulae are much
simpler than the published ones for the corrections to the spectra of charged
leptons originating from the decays of unpolarised quarks and polarised up type
quarks. Distributions of leptons in semileptonic $\Lambda_c$ and $\Lambda_b$
decays can be used as spin analysers for the corresponding heavy quarks. Thus
our results can be applied to the decays of polarised charm and bottom quarks.
For the charged leptons the corrections to the asymmetries are found to be
small in charm decays whereas for bottom decays they exhibit a non-trivial
dependence on the energy of the charged lepton. Short life-time enables
polarisation studies for the top quark. Our results are directly applicable for
processes involving polarised top quarks.


  We give the first rigorous construction of complete, embedded self-shrinking
hypersurfaces under mean curvature flow, since Angenent's torus in 1989. The
surfaces exist for any sufficiently large prescribed genus $g$, and are
non-compact with one end. Each has $4g+4$ symmetries and comes from
desingularizing the intersection of the plane and sphere through a great
circle, a configuration with very high symmetry. Each is at infinity asymptotic
to the cone in $\mathbb{R}^3$ over a $2\pi/(g+1)$-periodic graph on an equator
of the unit sphere $\mathbb{S}^2\subseteq\mathbb{R}^3$, with the shape of a
periodically "wobbling sheet". This is a dramatic instability phenomenon, with
changes of asymptotics that break much more symmetry than seen in minimal
surface constructions. The core of the proof is a detailed understanding of the
linearized problem in a setting with severely unbounded geometry, leading to
special PDEs of Ornstein-Uhlenbeck type with fast growth on coefficients of the
gradient terms. This involves identifying new, adequate weighted H\"older
spaces of asymptotically conical functions in which the operators invert, via a
Liouville-type result with precise asymptotics.


  A 2-complex $K$ has collapsing non-positive immersion if for every
combinatorial immersion $X\to K$, where $X$ is finite, connected and does not
allow collapses, either $\chi(X)\le 0$ or $X$ is point. This concept is due to
Wise who also showed that this property implies local indicability of the
fundamental group $\pi_1(K)$. In this paper we study a relative version of
collapsing non-positive immersion that can be applied to 2-complex pairs
$(L,K)$: The pair has relative collapsing non-positive immersion if for every
combinatorial immersion $f\colon X\to L$, where $X$ is finite, connected and
does not allow collapses, either $\chi(X)\le \chi(Y)$, where $Y$ is the
essential part of the preimage $f^{-1}(K)$, or $X$ is a point. We show that
under certain conditions a transitivity law holds: If $(L,K)$ has relative
collapsing non-positive immersion and $K$ has collapsing non-positive
immersion, then $L$ has collapsing non-positive immersion. This article is
partly motivated by the following open question: Do reduced injective labeled
oriented trees have collapsing non-positive immersion? We answer this question
in the affirmative for certain important special cases.


  In the paper we prove that every automorphism of and elementary adjoint
Chevalley group of types $A_l, D_l$, or $E_l$, over local commutative ring with
1/2 is a composition of a ring automorphism and conjugation by some matrix from
the normalizer of the Chevalley group in $\GL(V)$ ($V$ is the adjoint
representation space).


  Is the output of generative AI entitled to First Amendment protection? We're
inclined to say yes. Even though current AI programs are of course not people
and do not themselves have constitutional rights, their speech may potentially
be protected because of the rights of the programs' creators. But beyond that,
and likely more significantly, AI programs' speech should be protected because
of the rights of their users-both the users' rights to listen and their rights
to speak. In this short Article, we sketch the outlines of this analysis.


  We consider a class of leptogenesis models in which the lepton asymmetry
arises from dark matter annihilation processes which violate CP and lepton
number. Importantly, a necessary one-loop contribution to the annihilation
matrix element arises from absorptive final state interactions. We elucidate
the relationship between this one-loop contribution and the CP-violating phase.
As we show, the branching fraction for dark matter annihilation to leptons may
be small in these models, while still generating the necessary asymmetry.


  RoboJam is a machine-learning system for generating music that assists users
of a touchscreen music app by performing responses to their short
improvisations. This system uses a recurrent artificial neural network to
generate sequences of touchscreen interactions and absolute timings, rather
than high-level musical notes. To accomplish this, RoboJam's network uses a
mixture density layer to predict appropriate touch interaction locations in
space and time. In this paper, we describe the design and implementation of
RoboJam's network and how it has been integrated into a touchscreen music app.
A preliminary evaluation analyses the system in terms of training, musical
generation and user interaction.


  We study a cloud network with M distributed receiving antennas and L users,
which transmit their messages towards a centralized decoder (CD), where M>=L.
We consider that the cloud network applies the Compute-and-Forward (C&F)
protocol, where L antennas/relays are selected to decode integer equations of
the transmitted messages. In this work, we focus on the best relay selection
and the optimization of the Physical-Layer Network Coding (PNC) at the relays,
aiming at the throughput maximization of the network. Existing literature
optimizes PNC with respect to the maximization of the minimum rate among users.
The proposed strategy maximizes the sum rate of the users allowing nonsymmetric
rates, while the optimal solution is explored with the aid of the Pareto
frontier. The problem of relay selection is matched to a coalition formation
game, where the relays and the CD cooperate in order to maximize their profit.
Efficient coalition formation algorithms are proposed, which perform joint
relay selection and PNC optimization. Simulation results show that a
considerable improvement is achieved compared to existing results, both in
terms of the network sum rate and the players' profits.


  The size of higher twist corrections to the spin proton and neutron g1
structure functions and their role in determining the polarized parton
densities in the nucleon is discussed.


  Let $SP_n(\mathbb{C})$ be the symplectic group and
$\mathfrak{sp}_n(\mathbb{C})$ its Lie algebra. Let $B$ be a Borel subgroup of
$SP_n(\mathbb{C} )$, $\mathfrak{b}={\rm Lie}(B)$ and $\mathfrak n$ its
nilradical. Let $\mathcal X$ be a subvariety of elements of square 0 in
$\mathfrak n.$ $B$ acts adjointly on $\mathcal X$. In this paper we describe
topology of orbits $\mathcal X/B$ in terms of symmetric link patterns.
  Further we apply this description to the computations of the closures of
orbital varieties of nilpotency order 2 and to their intersections. In
particular we show that all the intersections of codimension 1 are irreducible.


  We consider a spontaneously broken gauge theory based on the standard model
(SM) group G = SU(2) x U(1) with scalar fields that carry arbitrary
representations of G, and we investigate some general properties of the charged
and neutral current involving these fields. In particular we derive the
conditions for having real or complex couplings of the Z boson to two different
neutral or charged scalar fields, and for the existence of CP-violating
Z-scalar-scalar couplings. Moreover, we study models with the same fermion
content as in the SM, with one SU(2) Higgs singlet, and an arbitrary number of
Higgs doublets. We show that the structure of the Z-Higgs boson and of the
Yukawa couplings in these models can be such that CP-violating Zb{\bar b}G form
factors which conserve chirality are induced at the one-loop level.


  According to electrodynamical equations in curved spacetime we consider the
coupling of a linearized weak gravitational wave (GW) to a Gaussian beam
passing through a static magnetic field. It is found that unlike the properties
of the "left-circular" and "right-circular" waves of the tangential
perturbative photon fluxes in the cylindrical polar coordinates, the resultant
effect of the tangential and radial perturbations can produce the unique
nonvanishing photon flux propagating along the direction of the electric field
of the Gaussian beam. This result might provide a larger detecting space for
the high-frequency GWs in GHz band. Moreover, we also discuss the relevant
noise issues.


  We investigate by numerical simulations and analytical calculations the
Bak-Sneppen model for biological evolution in scale-free networks. By using
large scale numerical simulations, we study the avalanche size distribution and
the activity time behavior at nodes with different connectivities. We argue the
absence of a critical barrier and its associated critical behavior for infinite
size systems. These findings are supported by a single site mean-field analytic
treatment of the model.


  We introduce a n-term quadrature to integrate inner products of n functions,
as opposed to a Gaussian quadrature to integrate 2n functions. We will
characterize and provide computational tools to construct the inner product
quadrature, and establish its connection to the Gaussian quadrature.


  We present the first subarcsecond-resolution mid-infrared (MIR) atlas of
local active galactic nuclei (AGN). Our atlas contains 253 AGN with a median
redshift of z=0.016, and includes all publicly available MIR imaging performed
to date with ground-based 8-m class telescopes, a total of 895 independent
measurements. Of these, more than 60% are published here for the first time. We
detect extended nuclear emission in at least 21% of the objects, while another
19% appear clearly point-like, and the remaining objects cannot be constrained.
Where present, elongated nuclear emission aligns with the ionization cones in
Seyferts. Subarcsecond resolution allows us to isolate the AGN emission on
scales of a few tens of parsecs and to obtain nuclear photometry in multiple
filters for the objects. Median spectral energy distributions (SEDs) for the
different optical AGN types are constructed and individual MIR 12 and 18micron
continuum luminosities are computed. These range over more than six orders of
magnitude. In comparison to the arcsecond-scale MIR emission as probed by
Spitzer, the continuum emission is much lower on subarcsecond scales in many
cases. The silicate feature strength is similar on both scales and generally
appears in emission (absorption) in type I (II) AGN. However, the polycyclic
aromatic hydrocarbon emission appears weaker or absent on subarcsecond scales.
The differences of the MIR SEDs on both scales are particularly large for
AGN/starburst composites and close-by (and weak) AGN. The nucleus dominates
over the total emission of the galaxy only at luminosities >=10^(44)erg/s. The
AGN MIR atlas is well suited not only for detailed investigation of individual
sources but also for statistical studies of AGN unification.


  In this paper, we compute the partition functions of $\mathcal{N}=1$ SUGRA
for different boundary topologies, i.e. sphere and torus, using super-Virasoro
TQFT. We use fusion and modular kernels of the super-Liouville theory to
compute the necklace-channel conformal block and showcase formalism by proving
that the inner product holds for superconformal blocks, defined as states in
the Hilbert space. Finally, we compute the out-of-time-order correlator for the
torus topology with superconformal primary insertions as matter using the tools
of super-Virasoro TQFT and investigate its early-time behaviour.


  NASA and other astrophysical data of the Cassiopeia A supernova remnant have
been rendered into a three-dimensional virtual reality (VR) and augmented
reality (AR) program, the first of its kind. This data-driven experience of a
supernova remnant allows viewers to walk inside the leftovers from the
explosion of a massive star, select the parts of the supernova remnant to
engage with, and access descriptive texts on what the materials are. The basis
of this program is a unique 3D model of the 340-year old remains of a stellar
explosion, made by combining data from the NASA Chandra X-ray Observatory,
Spitzer Space Telescope, and ground-based facilities. A collaboration between
the Smithsonian Astrophysical Observatory and Brown University allowed the 3D
astronomical data collected on Cassiopeia A to be featured in the VR/AR
program, which is an innovation in digital technologies with public, education,
and research-based impacts.


  The goal of this paper is to develop a coherent theory for inhomogeneous
Diophantine approximation on curves in $R^n$ akin to the well established
homogeneous theory. More specifically, the measure theoretic results obtained
generalize the fundamental homogeneous theorems of R.C. Baker (1978), Dodson,
Dickinson (2000) and Beresnevich, Bernik, Kleinbock, Margulis (2002). In the
case of planar curves, the complete Hausdorff dimension theory is developed


  Bell's theorem states that quantum mechanics is not a locally causal theory.
This state is often interpreted as nonlocality in quantum mechanics. Toner and
Bacon [Phys. Rev. Lett. \textbf{91}, 187904 (2003)] have shown that a shared
random-variables theory augmented by one bit of classical communication exactly
simulates the Bell correlation in a singlet state. In this paper, we show that
in Toner and Bacon protocol, one of the parties (Bob) can deduce another
party's (Alice) measurement outputs, if she only informs Bob of one of her own
outputs. Afterwards, we suggest a nonlocal version of Toner and Bacon protocol
wherein classical communications is replaced by nonlocal effects, so that
Alice's measurements cause instantaneous effects on Bob's outputs. In the
nonlocal version of Toner and Bacon's protocol, we get the same result again.
We also demonstrate that the same approach is applicable to Svozil's protocol.


  Chiral perturbation theory (ChPT) is the effective field theory of the strong
interactions at low energies. We will address the issue of a consistent power
counting scheme in a manifestly Lorentz-invariant formulation of baryon ChPT.
As applications we show how the inclusion of vector and axial-vector mesons in
the calculation of the nucleon electromagnetic and axial form factors,
respectively, lead to an improved description of the empirical data. Finally,
we will outline a systematic implementation of the Delta(1232) resonance into
the effective field theory program.


  We introduce the concept of degree of quantumness in quantum synchronization,
a measure of the quantum nature of synchronization in quantum systems.
Following techniques from quantum information, we propose the number of
non-commuting observables that synchronize as a measure of quantumness. This
figure of merit is compatible with already existing synchronization
measurements, and it captures different physical properties. We illustrate it
in a quantum system consisting of two weakly interacting cavity-qubit systems,
which are coupled via the exchange of bosonic excitations between the cavities.
Moreover, we study the synchronization of the expectation values of the Pauli
operators and we propose a feasible superconducting circuit setup. Finally, we
discuss the degree of quantumness in the synchronization between two quantum
van der Pol oscillators.


  There is a general consensus that SOA benefits could be reached but it is
unclear how to achieve this. Research shows that the problems with SOA
governance in practice are among the major reasons of SOA failures. Based on a
literature review, this study first proposes a list of SOA aspects to be
considered when implementing SOA governance. By adopting an interpretive
research methodology based on interviews, this research paper makes two
contributions: it addresses the practical matters that are major concerns for
organisations to achieve a higher maturity level with their SOA, and it reveals
the importance of the key SOA aspects in building strong governance and
consequently reaching a higher maturity level. The expected result should
deliver a theoretical contribution to SOA maturity in relation to SOA
governance; it could provide organisations with new awareness in assessing
their level of maturity and provide recommendations.


  We present photometric and spectroscopic observations of the type Ibn
supernova (SN) 2019uo, the second ever SN Ibn with flash ionization (He II, C
III, N III) features in its early spectra. SN 2019uo displays a rapid post-peak
luminosity decline of 0.1 mag d$^{-1}$ similar to most of the SNe Ibn, but is
fainter ($M^V_{max} = -18.30 \pm 0.24$ mag) than a typical SN Ibn and shows a
color evolution that places it between SNe Ib and the most extreme SNe Ibn. SN
2019uo shows P-cygni He I features in the early spectra which gradually evolves
and becomes emission dominated post peak. It also shows faster evolution in
line velocities as compared to most other members of the type Ibn subclass. The
bolometric light curve is fairly described by a $^{56}$Ni + circumstellar
interaction model.


  We present a class of mappings between models with topological mass mechanism
and purely topological models in arbitrary dimensions. These mappings are
established by directly mapping the fields of one model in terms of the fields
of the other model in closed expressions. These expressions provide the
mappings of their actions as well as the mappings of their propagators. For a
general class of models in which the topological model becomes the BF model the
mappings present arbitrary functions which otherwise are absent for
Chern-Simons like actions. This work generalizes the results of [1] for
arbitrary dimensions.


  Simulating pp collisions at LHC energies in the framework of the SUGRA model
and the detection of the produced leptons and jets by ATLAS we demonstrate that
a clean signature of SUSY can be obtained over a large domain of the parameter
space in the case of L-violating R parity breaking ($\lambda$ couplings). The
obtained signal allows the reconstruction of the SUSY particles and thereby the
precise determination of the model parameters $m_0, m_{1/2}, tan\beta$ and sign
$\mu$.


  Despite considerable advancements with deep neural language models, the
enigma of neural text degeneration persists when these models are tested as
text generators. The counter-intuitive empirical observation is that even
though the use of likelihood as training objective leads to high quality models
for a broad range of language understanding tasks, using likelihood as a
decoding objective leads to text that is bland and strangely repetitive.
  In this paper, we reveal surprising distributional differences between human
text and machine text. In addition, we find that decoding strategies alone can
dramatically effect the quality of machine text, even when generated from
exactly the same neural language model. Our findings motivate Nucleus Sampling,
a simple but effective method to draw the best out of neural generation. By
sampling text from the dynamic nucleus of the probability distribution, which
allows for diversity while effectively truncating the less reliable tail of the
distribution, the resulting text better demonstrates the quality of human text,
yielding enhanced diversity without sacrificing fluency and coherence.


  We continue to investigate the $\mathcal{N}=1$ deformations of
four-dimensional $\mathcal{N}=2$ superconformal field theories (SCFTs) labeled
by a nilpotent element of the flavor symmetry. This triggers a renormalization
group (RG) flow to an $\mathcal{N}=1$ SCFT. We systematically analyze all
possible deformations of this type for certain classes of $\mathcal{N}=2$
SCFTs: conformal SQCDs, generalized Argyres-Douglas theories and the $E_6$
SCFT. We find a number of examples where the amount of supersymmetry gets
enhanced to $\mathcal{N}=2$ at the end point of the RG flow. Most notably, we
find that the $SU(N)$ and $Sp(N)$ conformal SQCDs can be deformed to flow to
the Argyres-Douglas (AD) theories of type $(A_1, D_{2N-1})$ and $(A_1, D_{2N})$
respectively. This RG flow therefore allows us to compute the full
superconformal index of the $(A_1,D_N)$ class of AD theories. Moreover, we find
an infrared duality between $\mathcal{N}=1$ theories where the fixed point is
described by an $\mathcal{N}=2$ AD theory. We observe that the classes of
examples that exhibit supersymmetry enhancement saturate certain bounds for the
central charges implied by the associated two-dimensional chiral algebra.


  The recent state-of-the-art deep learning methods have significantly improved
brain tumor segmentation. However, fully supervised training requires a large
amount of manually labeled masks, which is highly time-consuming and needs
domain expertise. Weakly supervised learning with scribbles provides a good
trade-off between model accuracy and the effort of manual labeling. However,
for segmenting the hierarchical brain tumor structures, manually labeling
scribbles for each substructure could still be demanding. In this paper, we use
only two kinds of weak labels, i.e., scribbles on whole tumor and healthy brain
tissue, and global labels for the presence of each substructure, to train a
deep learning model to segment all the sub-regions. Specifically, we train two
networks in two phases: first, we only use whole tumor scribbles to train a
whole tumor (WT) segmentation network, which roughly recovers the WT mask of
training data; then we cluster the WT region with the guide of global labels.
The rough substructure segmentation from clustering is used as weak labels to
train the second network. The dense CRF loss is used to refine the weakly
supervised segmentation. We evaluate our approach on the BraTS2017 dataset and
achieve competitive WT dice score as well as comparable scores on substructure
segmentation compared to an upper bound when trained with fully annotated
masks.


  Baryon-to-meson Transition Distribution Amplitudes (TDAs) encoding valuable
new information on hadron structure appear as building blocks in the collinear
factorized description for several types of hard exclusive reactions. In this
paper, we address the possibility of accessing nucleon-to-pion ($\pi N$) TDAs
from $\bar{p}p \to e^+e^- \pi^0$ reaction with the future \={P}ANDA detector at
the FAIR facility. At high center of mass energy and high invariant mass
squared of the lepton pair $q^2$, the amplitude of the signal channel $\bar{p}p
\to e^+e^- \pi^0$ admits a QCD factorized description in terms of $\pi N$ TDAs
and nucleon Distribution Amplitudes (DAs) in the forward and backward kinematic
regimes. Assuming the validity of this factorized description, we perform
feasibility studies for measuring $\bar{p}p \to e^+e^- \pi^0$ with the
\={P}ANDA detector. Detailed simulations on signal reconstruction efficiency as
well as on rejection of the most severe background channel, i.e. $\bar{p}p \to
\pi^+\pi^- \pi^0$ were performed for the center of mass energy squared $s = 5$
GeV$^2$ and $s = 10$ GeV$^2$, in the kinematic regions $3.0 < q^2 < 4.3$
GeV$^2$ and $5 < q^2 < 9$ GeV$^2$, respectively, with a neutral pion scattered
in the forward or backward cone $| \cos\theta_{\pi^0}| > 0.5 $ in the
proton-antiproton center of mass frame. Results of the simulation show that the
particle identification capabilities of the \={P}ANDA detector will allow to
achieve a background rejection factor of $5\cdot 10^7$ ($1\cdot 10^7$) at low
(high) $q^2$ for $s=5$ GeV$^2$, and of $1\cdot 10^8$ ($6\cdot 10^6$) at low
(high) $q^2$ for $s=10$ GeV$^2$, while keeping the signal reconstruction
efficiency at around $40\%$. At both energies, a clean lepton signal can be
reconstructed with the expected statistics corresponding to $2$ fb$^{-1}$ of
integrated luminosity. (.../...)


  Unsupervised domain adaptive segmentation aims to improve the segmentation
accuracy of models on target domains without relying on labeled data from those
domains. This approach is crucial when labeled target domain data is scarce or
unavailable. It seeks to align the feature representations of the source domain
(where labeled data is available) and the target domain (where only unlabeled
data is present), thus enabling the model to generalize well to the target
domain. Current image- and video-level domain adaptation have been addressed
using different and specialized frameworks, training strategies and
optimizations despite their underlying connections. In this paper, we propose a
unified framework PiPa++, which leverages the core idea of ``comparing'' to (1)
explicitly encourage learning of discriminative pixel-wise features with
intraclass compactness and inter-class separability, (2) promote the robust
feature learning of the identical patch against different contexts or
fluctuations, and (3) enable the learning of temporal continuity under dynamic
environments. With the designed task-smart contrastive sampling strategy,
PiPa++ enables the mining of more informative training samples according to the
task demand. Extensive experiments demonstrate the effectiveness of our method
on both image-level and video-level domain adaption benchmarks. Moreover, the
proposed method is compatible with other UDA approaches to further improve the
performance without introducing extra parameters.


  In this paper, we study a type of reflected BSDE with a constraint and
introduce a new kind of nonlinear expectation via BSDE with a constraint and
prove the Doob-Meyer decomposition with respect to the super(sub)martingale
introduced by this nonlinear expectation. We then apply the results to the
pricing of American options in incomplete market.


  An unbounded one-dimensional solid-on-solid model with integer heights is
studied. Unbounded here means that there is no a priori restrictions on the
discret e gradient of the interface. The interaction Hamiltonian of the
interface is given by a finite range part, pr oportional to the sum of height
differences, plus a part of exponentially decaying long range potentials. The
evolution of the interface is a reversible Markov process. We prove that if
this system is started in the center of a box of size L after a time of order
L^3 it reaches, with a very large probability, the top or the bottom of the
box.


  We study the Schr\"odinger operators ${H}_{\lambda\mu}(K)$ with
$K\in\mathbb{T}^2$ being the fixed quasimomentum of a pair of particles,
associated with a system of two arbitrary particles on a two-dimensional
lattice $\mathbb{Z}^2$ with on-site and nearest-neighbor interactions of
strengths $\lambda\in\mathbb{R}$ and $\mu\in\mathbb{R}$, respectively. We
divide the $(\lambda,\mu)$-plane of parameters $\lambda$ and $\mu$ into
connected components, such that in each component, the Schr\"{o}dinger operator
$H_{\lambda\mu}(0)$ has a fixed number of eigenvalues. These eigenvalues are
located both below the bottom of the essential spectrum and above its top.
Additionally, we establish a sharp lower bound for the number of isolated
eigenvalues of $H_{\lambda\mu}(K)$ within each connected component.


  Motivated by questions originating from the study of a class of shallow
student-teacher neural networks, methods are developed for the analysis of
spurious minima in classes of gradient equivariant dynamics related to neural
nets. In the symmetric case, methods depend on the generic equivariant
bifurcation theory of irreducible representations of the symmetric group on $n$
symbols, $S_n$; in particular, the standard representation of $S_n$. It is
shown that spurious minima do not arise from spontaneous symmetry breaking but
rather through a complex deformation of the landscape geometry that can be
encoded by a generic $S_n$-equivariant bifurcation. We describe minimal models
for forced symmetry breaking that give a lower bound on the dynamic complexity
involved in the creation of spurious minima when there is no symmetry. Results
on generic bifurcation when there are quadratic equivariants are also proved;
this work extends and clarifies results of Ihrig & Golubitsky and Chossat,
Lauterback & Melbourne on the instability of solutions when there are quadratic
equivariants.


  In this Letter, we propose a new type of lossless metamaterial whose
effective permittivity is tunable from negative to positive values. Its optical
response is studied analytically and numerically. We further demonstrate that
this tunable metamaterial can significantly modulate the phase of an incident
pulse with negligible reflection loss, functioning as an efficient phase
shifter.


  We extend some inequalities for normal matrices and positive linear maps
related to the Russo-Dye theorem. The results cover the case of some positive
linear maps on a von Neumann algebra mapping any nonzero operator to an
unbounded operator.


  The spectra of octet and decuplet baryons are studied using SU(3) lattice QCD
at the quenched level. As an implementation to reduce the statistical
fluctuation, we employ the anisotropic lattice with $O(a)$ improved quark
action. In relation to $\Lambda(1405)$, we measure also the mass of the SU(3)
flavor-singlet negative-parity baryon, which is described as a three quark
state in the quenched lattice QCD, and its lowest mass is measured about 1.6
GeV. Since the experimentally observed negative-parity baryon $\Lambda(1405)$
is much lighter than 1.6 GeV, $\Lambda(1405)$ may include a large component of
a $N \bar K$ bound state rather than the three quark state. The mass splitting
between the octet and the decuplet baryons are also discussed in terms of the
current quark mass.


  In recent years, machine learning (ML) and neural networks (NNs) have gained
widespread use and attention across various domains, particularly in
transportation for achieving autonomy, including the emergence of flying taxis
for urban air mobility (UAM). However, concerns about certification have come
up, compelling the development of standardized processes encompassing the
entire ML and NN pipeline. This paper delves into the inference stage and the
requisite hardware, highlighting the challenges associated with IEEE 754
floating-point arithmetic and proposing alternative number representations. By
evaluating diverse summation and dot product algorithms, we aim to mitigate
issues related to non-associativity. Additionally, our exploration of
fixed-point arithmetic reveals its advantages over floating-point methods,
demonstrating significant hardware efficiencies. Employing an empirical
approach, we ascertain the optimal bit-width necessary to attain an acceptable
level of accuracy, considering the inherent complexity of bit-width
optimization.


  We review the results of the 1st Extreme Ultraviolet (EUV) Light Sources Code
Comparison Workshop, which was held online on 3rd November 2020. The goal of
this workshop was to provide a platform for specialists in EUV light source
plasma modeling to benchmark and validate their numerical codes using
well-defined case studies. Eight institutions spanning four countries
contributed data to the workshop. Two topics were addressed, namely (i) the
atomic kinetics and radiative properties of tin plasmas under EUV-generating
conditions and (ii) laser absorption in a fully ionized, one-dimensional
hydrogen plasma. In this paper, we summarize the key findings of the workshop
and outline plans for future iterations of this code comparison activity.


  The recent IceCube detection of TeV neutrino emission from the nearby active
galaxy NGC 1068 suggests that active galactic nuclei (AGN) could make a sizable
contribution to the diffuse flux of astrophysical neutrinos. The absence of TeV
$\gamma$-rays from NGC 1068 indicates neutrino production in the vicinity of
the supermassive black hole, where the high radiation density leads to
$\gamma$-ray attenuation. Therefore, any potential neutrino emission from
similar sources is not expected to correlate with high-energy $\gamma$-rays.
Disk-corona models predict neutrino emission from Seyfert galaxies to correlate
with keV X-rays, as they are tracers of coronal activity. Using through-going
track events from the Northern Sky recorded by IceCube between 2011 and 2021,
we report results from a search for individual and aggregated neutrino signals
from 27 additional Seyfert galaxies that are contained in the BAT AGN
Spectroscopic Survey (BASS). Besides the generic single power-law, we evaluate
the spectra predicted by the disk-corona model. Assuming all sources to be
intrinsically similar to NGC 1068, our findings constrain the collective
neutrino emission from X-ray bright Seyfert galaxies in the Northern
Hemisphere, but, at the same time, show excesses of neutrinos that could be
associated with the objects NGC 4151 and CGCG 420-015. These excesses result in
a 2.7$\sigma$ significance with respect to background expectations.


  This note is intended primarily for college calculus students right after the
introduction of the Intermediate Value Theorem, to show them how the
Intermediate Value Theorem is used repeatedly and straightforwardly to prove
the celebrated Sharkovsky's theorem on the periods of coexistent periodic
orbits of continuous maps on an interval. Furthermore, if the maps have a
periodic orbit P of odd period > 1, then we find more periodic points, in the
appendix, which constitute what we call the towers of periodic points
associated with P. These towers of periodic points have infinitely many layers.
In this note, no knowledge of Dynamical Systems Theory is required.
  In this revision, we add the result (Proposition 1 on page 9) that the
periodic orbits of continuous unimodal maps on the interval $[0, 1]$ of least
periods $\ge 2$ are nested in the sense that if $P$ and $Q$ are periodic orbits
of a continuous unimodal map on $[0, 1]$ of least periods $\ge 2$ and if $\max
P < \max Q$, then $[\min P, \max P] \subset [\min Q, \max Q]$.


  In this study, a refined approach for multicomponent fitting of active
galactic nuclei (AGN) spectra is presented utilizing the newly developed Python
code $fantasy$ (fully automated python tool for AGN spectra analysis). AGN
spectra are modeled by simultaneously considering the underlying broken
power-law continuum, predefined emission line lists, and an Fe II model, which
is here extended to cover the wavelength range 3700 - 11000 A. The Fe II model,
founded solely on atomic data, effectively describes the extensive emission of
the complex iron ion in the vicinity of the H$\gamma$ and H$\beta$ lines, as
well as near the H$\alpha$ line, which was previously rarely studied. The
proposed spectral fitting approach is tested on a sample of high-quality AGN
spectra from the Sloan Digital Sky Survey (SDSS) Data Release 17. The results
indicate that when Fe II emission is present near H$\beta$, it is also detected
redward from H$\alpha$, potentially contaminating the broad H$\alpha$ line
wings and thus affecting the measurements of its flux and width. The production
of Fe II emission is found to be strongly correlated with Eddington luminosity
and appears to be controlled by the similar mechanism as the hydrogen Balmer
lines. The study highlights the benefits of fitting AGN type 1 spectra with the
$fantasy$ code, pointing that it may be used as a robust tool for analyzing a
large number of AGN spectra in the coming spectral surveys.


  Green Peas are a new class of young, emission line galaxies that were
discovered by citizen volunteers in the Galaxy Zoo project. Their low stellar
mass, low metallicity and very high star formation rates make Green Peas the
nearby (z~0.2) analogs of the Lyman-break Galaxies (LBGs) which account for the
bulk of the star formation in the early universe (z~2-5). They thus provide
accessible laboratories in the nearby Universe for understanding star
formation, supernova feedback, particle acceleration and magnetic field
amplification in early galaxies. We report the first direct radio detection of
Green Peas with low frequency GMRT observations and our stacking detection with
archival VLA FIRST data. We show that the radio emission implies that these
extremely young galaxies already have magnetic fields (>30 muG) even larger
than that of the Milky Way. This is at odds with the present understanding of
magnetic field growth based on amplification of seed fields by dynamo action
over a galaxy's lifetime. Our observations strongly favor models with
pregalactic magnetic fields at muG levels.


  Active stresses can cause instabilities in contractile gels and living
tissues. Here we describe a generic hydrodynamic theory that treats these
systems as a mixture of two phases of varying activity and different mechanical
properties. We find that differential activity between the phases provides a
mechanism causing a demixing instability. We follow the nonlinear evolution of
the instability and characterize a phase diagram of the resulting patterns. Our
study complements other instability mechanisms in mixtures such as differential
growth, shape, motion or adhesion.


  The problem of inferring the outcome of a simultaneous measurement of two
non-commuting observables is addressed. We show that for certain pairs with
dense spectra, precise inferences of the measurement outcomes are possible in
pre-and post-selected ensembles, and if the selections involve entangled states
with some other system. We show that the problem is related to the problem of
assigning weak values to a continuous family of operators, and give explicit
examples where this problem is solvable. Some foundational implications are
briefly discussed.


  Let $X$ be one of the finite-dimensional simple graded Lie superalgebras of
Cartan type $W, S, H, K, HO, KO, SHO$ or $SKO$ over an algebraically closed
field of characteristic $p>3$. In this paper we prove that $X$ can be generated
by one element except the ones of type $W,$ $HO$, $KO$ or $SKO$ in certain
exceptional cases, in which $X$ can be generated by two elements. As a
subsidiary result, we also prove that certain classical Lie superalgebras or
their relatives can be generated by one or two elements.


  This study examines the finite $F$-representation type (abbr. FFRT) property
of a two-dimensional normal graded ring $R$ in characteristic $p>0$, using
notions from the theory of algebraic stacks. Given a graded ring $R$, we
consider an orbifold curve $\mathfrak C$, which is a root stack over the smooth
curve $C=\text{Proj} R$, such that $R$ is the section ring associated with a
line bundle $L$ on $\mathfrak C$. The FFRT property of $R$ is then rephrased
with respect to the Frobenius push-forwards $F^e_*(L^i)$ on the orbifold curve
$\mathfrak C$. As a result, we see that if the singularity of $R$ is not log
terminal, then $R$ has FFRT only in exceptional cases where the characteristic
$p$ divides a weight of $\mathfrak C$.


  We propose a discretization of the optimality principle in dynamic
programming based on radial basis functions and Shepard's moving least squares
approximation method. We prove convergence of the approximate optimal value
function to the true one and present several numerical experiments.


  We calculate the imaginary part of the retarded two-loop self-energy of a
static vector boson in a plasma of quarks and gluons of temperature T, using
the imaginary time formalism. We recombine various cuts of the self-energy to
generate physical processes. We demonstrate how cuts containing loops may be
reinterpreted in terms of interference between Order $\alpha$ tree diagrams and
the Born term along with spectators from the medium. We apply our results to
the rate of dilepton production in the limit of dilepton invariant mass E>>T.
We find that all infrared and collinear singularities cancel in the final
result obtained in this limit.


  In this work we present an evolutionary game inspired by the work of Carlo
Cipolla entitled The basic laws of human stupidity. The game expands the
classical scheme of two archetypical strategies, collaborators and defectors,
by including two additional strategies. One of these strategies is associated
to a stupid player that according to Cipolla is the most dangerous one as it
undermines the global wealth of the population. By considering a spatial
evolutionary game and imitation dynamics that go beyond the paradigm of a
rational player we explore the impact of Cipolla' s ideas and analyze the
extent of the damage that the stupid players inflict on the population


  We introduce and study a family of polytopes which can be seen as a
generalization of the permutahedron of type $B_d$. We highlight connections
with the largest possible diameter of the convex hull of a set of points in
dimension $d$ whose coordinates are integers between $0$ and $k$, and with the
computational complexity of multicriteria matroid optimization.


  We introduce the notion of an ordered face structure. The ordered face
structures to many-to-one computads are like positive face structures to
positive-to-one computads. This allow us to give an explicit combinatorial
description of many-to-one computads in terms of ordered face structures.


  The inclusive production rate of phi mesons from the decay of b hadrons
produced in Z0 decays was measured to be Br(b->phi+X) =
0.0282+-0.0013(stat.)+-0.0019(syst.), using data collected by the OPAL detector
at LEP.


  We show that three numerical semigroups <5,6,7,8>, <3,7,8 > and <3,5> are of
double covering type, i.e., the Weierstrass semigroups of ramification points
on double covers of curves. Combining this with the results of
Oliveira-Pimentel and Komeda we can determine the Weierstrass semigroups of the
ramification points on double covers of genus two curves.


  We propose a novel architecture for depth estimation from a single image. The
architecture itself is based on the popular encoder-decoder architecture that
is frequently used as a starting point for all dense regression tasks. We build
on AdaBins which estimates a global distribution of depth values for the input
image and evolve the architecture in two ways. First, instead of predicting
global depth distributions, we predict depth distributions of local
neighborhoods at every pixel. Second, instead of predicting depth distributions
only towards the end of the decoder, we involve all layers of the decoder. We
call this new architecture LocalBins. Our results demonstrate a clear
improvement over the state-of-the-art in all metrics on the NYU-Depth V2
dataset. Code and pretrained models will be made publicly available.


  The relaxation of field-line tension during magnetic reconnection gives rise
to a universal Fermi acceleration process involving the curvature drift of
particles. However, the efficiency of this mechanism is limited by the trapping
of energetic particles within flux-ropes. Using 3D fully kinetic simulations,
we demonstrate that the flux-rope kink instability leads to strong field-line
chaos in weak-guide-field regimes where the Fermi mechanism is most efficient,
thus allowing particles to transport out of flux-ropes and undergo further
acceleration. As a consequence, both ions and electrons develop clear power-law
energy spectra which contain a significant fraction of the released energy. The
low-energy bounds are determined by the injection physics, while the
high-energy cutoffs are limited only by the system size. These results have
strong relevance to observations of nonthermal particle acceleration in space
and astrophysics.


  We investigate the global dynamics from a measure-theoretic perspective for
smooth flows with invariant cones of rank k. For such systems, it is shown that
prevalent (or equivalently, almost all) orbits will be pseudo-ordered or
convergent to equilibria. This reduces to Hirsch's prevalent convergence
Theorem if the rank k=1; and implies an almost-sure Poincare-Bendixson Theorem
for the case k=2. These results are then applied to obtain an almost sure
Poincare-Bendixson theorem for high-dimensional differential equations.


  Recently Corteel and Welsh outlined a technique for finding new sum-product
identities by using functional relations between generating functions for
cylindric partitions and a theorem of Borodin. Here, we extend this framework
to include very general product-sides coming from work of Han and Xiong. In
doing so, we are led to consider structures such as weighted cylindric
partitions, symmetric cylindric partitions and weighted skew double shifted
plane partitions. We prove some new identities and obtain new proofs of known
identities, including the G\"ollnitz-Gordon and Little G\"ollnitz identities as
well as some beautiful Schmidt-type identities of Andrews and Paule.


  We study the transverse momenta and (pseudo)rapidity spectrum of the top
quark and their decay products, the tt-system, and the total number of jets in
proton-proton (pp) collisions at 13 TeV by using the Tsallis-Pareto-type
function and the three-source Landau hydrodynamic model, respectively. The
related parameters, such as the effective temperature of the interacting system
(T), the non-extensivity of the process (n) and the width ($\sigma$) of
(pseudo)rapidity distribution are extracted.


  A model is considered well-calibrated when its probability estimate aligns
with the actual likelihood of the output being correct. Calibrating language
models (LMs) is crucial, as it plays a vital role in detecting and mitigating
hallucinations of LMs as well as building more trustworthy models. However,
standard calibration techniques may not be suited for LM calibration. For
instance, post-processing methods such as temperature scaling do not reorder
the candidate generations. On the other hand, training-based methods require
fine-tuning the entire model, which is impractical for LMs of large scale. We
present LitCab, a lightweight calibration mechanism consisting of a single
linear layer that takes the input text representation and predicts a bias term,
which is then added to the LM output logits. LitCab improves model calibration
by only adding < 2% of the original model parameters. For evaluation, we
construct CaT, a benchmark consisting of eight text generation tasks, covering
responses ranging from short phrases to paragraphs. We test LitCab with
Llama2-7B, where it improves calibration across all tasks, reducing the average
ECE score by as large as 30%. We further conduct a comprehensive evaluation
with multiple popular open-sourced LMs from GPT and LLaMA families, yielding
the following key findings: (i) Larger models within the same family exhibit
better calibration on tasks with short generation tasks, but not necessarily
for longer ones. (ii) GPT-family models show superior calibration compared to
LLaMA, Llama2, and Vicuna models, despite having much fewer parameters. (iii)
Fine-tuning pretrained model (e.g., LLaMA) with samples of limited purpose
(e.g., conversations) may lead to worse calibration, highlighting the
importance of fine-tuning setups for calibrating LMs.


  In this note, we will do analysis of accessible singular points for a
polynomial Hamiltonian system obtained by taking a double covering of the
Painlev\'e I equation. We will show that this system passes the Painlev\'e
$\alpha$-test for all accessible singular points $P_i \ (i=1,2,3)$. We note its
holomorphy condition of the first Painlev\'e system.


  We present evidence for a new phenomenon in the propagation of
electromagnetic radiation across the Universe, a corkscrew rotation of the
plane of polarization not accounted for by conventional physics.


  The resonator-induced phase (RIP) gate is a multi-qubit entangling gate that
allows a high degree of flexibility in qubit frequencies, making it attractive
for quantum operations in large-scale architectures. We experimentally realize
the RIP gate with four superconducting qubits in a three-dimensional (3D)
circuit-quantum electrodynamics architecture, demonstrating high-fidelity
controlled-Z (CZ) gates between all possible pairs of qubits from two different
4-qubit devices in pair subspaces. These qubits are arranged within a wide
range of frequency detunings, up to as large as 1.8 GHz. We further show a
dynamical multi-qubit refocusing scheme in order to isolate out 2-qubit
interactions, and combine them to generate a four-qubit
Greenberger-Horne-Zeilinger state.


  X-ray computed tomography (XCT) has become a reliable metrology tool for
measuring internal flaws and other microstructural features in engineering
materials. However, tracking of material points to measure three-dimensional
(3D) deformations has hitherto relied on either artificially adding tracer
particles (speckles) or exploiting inherent microstructural features such as
inclusions. This has greatly limited the spatial resolution and magnitude of
the deformation measurements. Here we report a novel Flux Enhanced Tomography
for Correlation (FETC) technique that leverages the inherent inhomogeneities
within nominally homogeneous engineering polymers to track 3D material point
displacements without recourse to artificial speckles or microstructural
features such as inclusions. The FETC is then combined with a
Eulerian/Lagrangian transformation in a multi-step Digital Volume Correlation
(DVC) methodology to measure all nine components of the deformation gradient
within the volume of complex specimens undergoing extreme deformations. FETC is
a powerful technique that greatly expands the capabilities of laboratory-based
XCT to provide amongst other things the inputs required for data-driven
constitutive modelling approaches.


  We report a benchmark theoretical investigation of both adiabatic and
vertical electron affinities of five DNA and RNA nucleobases: adenine, guanine,
cytosine, thymine and uracil using state-of-the-art equation of motion coupled
cluster (EOMCC) method. We have calculated the vertical electron affinity
values of first five electron attached states of the DNA and RNA nucleobases
and only the first electron attached state is found to be energetically
accessible in gas phase. An analysis of the natural orbitals shows that the
first electron attached states of uracil and thymine are valence-bound type and
undergo significant structural changes on attachment of excess electron, which
is reflected in the deviation of the adiabatic electron affinity from the
vertical one. On the other hand, the first electron attached state of cytosine,
adenine and guanine are dipole-bound type and their structure remain unaffected
on attachment of an extra electron, which results in small deviation of
adiabatic electron affinity from that of the vertical one. Vertical and
adiabatic electron affinity values of all the DNA and RNA nucleobases are
negative implying that the first electron attached state are not stable, but
rather resonance states. Previously, reported theoretical studies had shown
scattered results for electron affinities of DNA and RNA bases, with large
deviations from experimental values. Our EOMCC computed values are in very good
agreement with experimental values and can be used as a reliable benchmark for
calibrating new theoretical methods.


  The extraction of useful deep features is important for many computer vision
tasks. Deep features extracted from classification networks have proved to
perform well in those tasks. To obtain features of greater usefulness,
end-to-end distance metric learning (DML) has been applied to train the feature
extractor directly. However, in these DML studies, there were no equitable
comparisons between features extracted from a DML-based network and those from
a softmax-based network. In this paper, by presenting objective comparisons
between these two approaches under the same network architecture, we show that
the softmax-based features perform competitive, or even better, to the
state-of-the-art DML features when the size of the dataset, that is, the number
of training samples per class, is large. The results suggest that softmax-based
features should be properly taken into account when evaluating the performance
of deep features.


  Full Configuration Interaction Quantum Monte Carlo (FCIQMC) has been
effectively applied to very large configuration interaction (CI) problems, and
was recently adapted for use as an active space solver and combined with
orbital optimisation. In this work, we detail an approach within FCIQMC to
allow for efficient sampling of fully internally-contracted multireference
perturbation theories within the same stochastic framework. Schemes are
described to allow for the close control over the resolution of stochastic
sampling of the effective higher-body intermediates within the active space. It
is found that while CASPT2 seems less amenable to a stochastic reformulation,
NEVPT2 is far more stable, requiring a similar number of walkers to converge
the NEVPT2 expectation values as to converge the underlying CI problem. We
demonstrate the application of the stochastic approach to the computation of
NEVPT2 within a (24,24) active space in a biologically relevant system, and
show that small numbers of walkers are sufficient for a faithful sampling of
the NEVPT2 energy to chemical accuracy, despite the active space already
exceeding the limits of practicality for traditional approaches. This raises
prospects of an efficient stochastic solver for multireference chemical
problems requiring large active spaces, with an accurate treatment of external
orbitals.


  Suppose $(M,\omega)$ is a compact symplectic manifold acted on by a compact
Lie group $K$ in a Hamiltonian fashion, with moment map $\mu: M \to \Lie(K)^*$
and Marsden-Weinstein reduction $M_{red} = \mu^{-1}(0)/K$. In this paper, we
assume that $M$ has a $K$-invariant K\"ahler structure. In an earlier paper, we
proved a formula (the residue formula) for $\eta_0 e^{\omega_0}[M_{red}]$ for
any $\eta_0 \in H^*(M_{red})$, where $\omega_0$ is the induced symplectic form
on $M_{red}$. Here we apply the residue formula in the special case $\eta_0 =
Td(M_{red})$; when $K$ acts freely on $\mu^{-1}(0)$ this yields a formula for
the Riemann-Roch number $RR (L_{red})$ of a holomorphic line bundle $L_{red}$
on $M_{red}$ that descends from a holomorphic line bundle $L$ on $M$ for which
$c_1(L) = \omega$. Using the holomorphic Lefschetz formula we similarly obtain
a formula for the $K$-invariant Riemann-Roch number $RR^K(L) $ of $L$. In the
case when the maximal torus $T$ of $K$ has dimension one (except in a few
special circumstances), we show the two formulas are the same. Thus in this
special case the residue formula is equivalent to the result of Guillemin and
Sternberg that $RR(L_{red}) = RR^K(L)$. (The residue formula was proved under
the assumption that 0 is a regular value of $\mu$, and was given in terms of
the restrictions of classes in the equivariant cohomology $H^*_T(M) $ of $M$ to
the


  We consider the task of estimating a structural model of dynamic decisions by
a human agent based upon the observable history of implemented actions and
visited states. This problem has an inherent nested structure: in the inner
problem, an optimal policy for a given reward function is identified while in
the outer problem, a measure of fit is maximized. Several approaches have been
proposed to alleviate the computational burden of this nested-loop structure,
but these methods still suffer from high complexity when the state space is
either discrete with large cardinality or continuous in high dimensions. Other
approaches in the inverse reinforcement learning (IRL) literature emphasize
policy estimation at the expense of reduced reward estimation accuracy. In this
paper we propose a single-loop estimation algorithm with finite time guarantees
that is equipped to deal with high-dimensional state spaces without
compromising reward estimation accuracy. In the proposed algorithm, each policy
improvement step is followed by a stochastic gradient step for likelihood
maximization. We show that the proposed algorithm converges to a stationary
solution with a finite-time guarantee. Further, if the reward is parameterized
linearly, we show that the algorithm approximates the maximum likelihood
estimator sublinearly. Finally, by using robotics control problems in MuJoCo
and their transfer settings, we show that the proposed algorithm achieves
superior performance compared with other IRL and imitation learning benchmarks.


  In the present note, we address the question about behavior of $L_3$-norm of
the velocity field as time $t$ approaches blow-up time $T$. It is known that
the upper limit of the above norm must be equal to infinity. We show that, for
blow-ups of type I, the lower limit of $L_3$-norm equals to infinity as well.


  The nonrelativistic motion of a charged particle around a dyon in (9+1)
spacetime is known as the nine-dimensional MICZ-Kepler problem. This problem
has been solved exactly by the variables-separation method in three different
coordinate systems, spherical, parabolic, and prolate spheroidal. In the
present study, we establish a relationship between the variable separation and
the algebraic structure of SO(10) symmetry. Each of the spherical, parabolic,
or prolate spheroidal bases is proved to be a set of eigenfunctions of a
corresponding nonuplet of algebraically-independent integrals of motion. This
finding also helps us establish connections between the bases by the algebraic
method. This connection, in turn, allows calculating complicated integrals of
confluent Heun, generalized Laguerre, and generalized Jacobi polynomials, which
are important in physics and analytics.


  For each integer $n \geq 3$, we exhibit a nonuniform arithmetic lattice in
$\mathrm{SO}(n,1)$ containing Zariski-dense surface subgroups.


  In this article, we study the Faraday effect in a binary composite consisting
of a dielectric matrix with metallic inclusions. We first use the replica trick
together with a variational method in order to compute the effective
permittivity tensor (in the quasi-static limit) of this composite in a static
magnetic field. In order to find the scaling exponents near the percolation
threshold, we use a high contrast or low frequency expansion combined with
scaling. The result of the two methods are in agreement and predict that near
the percolation threshold (and below, that is in the dielectric region), the
Faraday effect is greatly enhanced.


  We combine classic stability results for foliations with recent results on
deformations of Lie groupoids and Lie algebroids to provide a cohomological
characterization for rigidity of compact foliations on compact manifolds.


  In $T$*-type cuprate oxides with five oxygen coordination, little is known
about the relationship between the spin correlations and dope carriers. We
performed $^{139}$La-nuclear magnetic resonance (NMR) and electrical
resistivity measurements on an as-sintered (AS) and oxidation annealed (OA)
polycrystalline $T$*-type La$_{0.86}$Eu$_{0.86}$S$_{0.28}$CuO$_4$ (LESCO) to
investigate its magnetic and superconducting (SC) properties. Upon cooling, the
NMR spectrum of AS LESCO broadened below 3 K, at which the nuclear spin-lattice
relaxation rate $1/T_1$ against the temperature exhibited a maximum, thereby
indicating the appearance of static magnetism. The temperature dependence of
$1/T_1$ between 3 K and 20 K was similar to that of the resistivity displaying
the semiconducting behavior. Furthermore, the energy scale of the transport gap
and spin-dynamics estimated was found to be comparable. These results suggest a
close connection between the mobility of the doped carriers and low-energy
spin-dynamics, as reported for lightly doped $T$-type La$_{2-x}$Sr$_x$CuO$_4$.
In the OA SC sample, we confirmed the absence of a magnetic order and the
Korringa relation above 10 K. Therefore, in the $T$*-type LESCO with $x$ =
0.28, the magnetic state coupled with holes drastically turns to the weakly
correlated metallic state by oxidation annealing.


  A nonlinear reaction-diffusion system with cross-diffusion describing the
COVID-19 outbreak is studied using the Lie symmetry method. A complete Lie
symmetry classification is derived and it is shown that the system with
correctly-specified parameters admits highly nontrivial Lie symmetry operators,
which do not occur for all known reaction-diffusion systems. The symmetries
obtained are also applied for finding exact solutions of the system in the most
interesting case from applicability point of view. It is shown that the exact
solutions derived possess all necessary properties for describing the pandemic
spread under 1D approximation in space and lead to the distributions, which
qualitatively correspond to the measured data of the COVID-19 spread in
Ukraine.


  We develop the method of stochastic modified equations (SME), in which
stochastic gradient algorithms are approximated in the weak sense by
continuous-time stochastic differential equations. We exploit the continuous
formulation together with optimal control theory to derive novel adaptive
hyper-parameter adjustment policies. Our algorithms have competitive
performance with the added benefit of being robust to varying models and
datasets. This provides a general methodology for the analysis and design of
stochastic gradient algorithms.


  We present an investigation of clumpy galaxies in the Hubble Ultra Deep Field
at 0.5 $\leq z \leq$ 1.5 in the rest-frame far-ultraviolet (FUV) using HST WFC3
broadband imaging in F225W, F275W, and F336W. An analysis of 1,404 galaxies
yields 209 galaxies that host 403 kpc-scale clumps. These host galaxies appear
to be typical star-forming galaxies, with an average of 2 clumps per galaxy and
reaching a maximum of 8 clumps. We measure the photometry of the clumps, and
determine the mass, age, and star formation rates (SFR) utilizing the
SED-fitting code FAST. We find that clumps make an average contribution of 19%
to the total rest-frame FUV flux of their host galaxy. Individually, clumps
contribute a median of 5% to the host galaxy SFR and an average of $\sim$4% to
the host galaxy mass, with total clump contributions to the host galaxy stellar
mass ranging widely from less than 1% up to 93%. Clumps in the outskirts of
galaxies are typically younger, with higher star formation rates, than clumps
in the inner regions. The results are consistent with clump migration theories
in which clumps form through violent gravitational instabilities in gas-rich
turbulent disks, eventually migrate toward the center of the galaxies, and
coalesce into the bulge.


  Oftentimes, there is a need to experiment with different programming
languages and technologies when designing software applications. Such
experiments must be reproducible and share-able within a team workplace, and
manual effort should be minimized for setting up/tearing down said experiments.
  This paper solves this problem by presenting a cloud-based web service for
remote code execution, that is easily extensible to support any number of
programming languages and libraries. The service provides a fast, reproducible
solution for small software experiments and is amenable to collaboration in a
workplace (via sharable permalinks). The service is designed as a distributed
system to reliably support a large number of users, and efficiently manage
cloud-hosting costs with predictive auto-scaling while minimizing SLA
violations.


  An extensive empirical literature documents a generally negative correlation,
named the "leverage effect," between asset returns and changes of volatility.
It is more challenging to establish such a return-volatility relationship for
jumps in high-frequency data. We propose new nonparametric methods to assess
and test for a discontinuous leverage effect --- i.e. a relation between
contemporaneous jumps in prices and volatility. The methods are robust to
market microstructure noise and build on a newly developed price-jump
localization and estimation procedure. Our empirical investigation of six years
of transaction data from 320 NASDAQ firms displays no unconditional negative
correlation between price and volatility cojumps. We show, however, that there
is a strong relation between price-volatility cojumps if one conditions on the
sign of price jumps and whether the price jumps are market-wide or
idiosyncratic. Firms' volatility levels strongly explain the cross-section of
discontinuous leverage while debt-to-equity ratios have no significant
explanatory power.


  In this paper, a homogeneous system of n $\alpha$-order linear fractal
differential equation is defined and the set of its fundamental solutions
through the corresponding Wronskian matrix is described. Finally, the solutions
of some assigned autonomous homogeneous system are plotted to show the details
previously proved.


  We consider how to normalize the scattering amplitudes of 4D heterotic
superstrings in a Minkowski background. We fix the normalization of the vacuum
amplitude (the string partition function) at each genus, and of every vertex
operator describing a physical external string state in a way consistent with
unitarity of the $S$-matrix. We also provide an explicit expression for the map
relating the vertex operator of an incoming physical state to the vertex
operator describing the same physical state, but outgoing. This map is related
to hermitean conjugation and to the hermiticity properties of the scattering
amplitudes.


  Designing more efficient, reliable, and explainable neural network
architectures is critical to studies that are based on artificial intelligence
(AI) techniques. Previous studies, by post-hoc analysis, have found that the
best-performing ANNs surprisingly resemble biological neural networks (BNN),
which indicates that ANNs and BNNs may share some common principles to achieve
optimal performance in either machine learning or cognitive/behavior tasks.
Inspired by this phenomenon, we proactively instill organizational principles
of BNNs to guide the redesign of ANNs. We leverage the Core-Periphery (CP)
organization, which is widely found in human brain networks, to guide the
information communication mechanism in the self-attention of vision transformer
(ViT) and name this novel framework as CP-ViT. In CP-ViT, the attention
operation between nodes is defined by a sparse graph with a Core-Periphery
structure (CP graph), where the core nodes are redesigned and reorganized to
play an integrative role and serve as a center for other periphery nodes to
exchange information. We evaluated the proposed CP-ViT on multiple public
datasets, including medical image datasets (INbreast) and natural image
datasets. Interestingly, by incorporating the BNN-derived principle (CP
structure) into the redesign of ViT, our CP-ViT outperforms other
state-of-the-art ANNs. In general, our work advances the state of the art in
three aspects: 1) This work provides novel insights for brain-inspired AI: we
can utilize the principles found in BNNs to guide and improve our ANN
architecture design; 2) We show that there exist sweet spots of CP graphs that
lead to CP-ViTs with significantly improved performance; and 3) The core nodes
in CP-ViT correspond to task-related meaningful and important image patches,
which can significantly enhance the interpretability of the trained deep model.


  In this study, the Haldane model's edge states are utilized to illustrate
that a zero-energy localized state forms around a single vacancy in the model.
In order to complete this task, the conventional unit cell associated to the
Haldane hexagonal structure is transferred onto a two-leg ladder in momentum
space, effectively forming an extended Su-Schrieffer-Heeger~(SSH) lattice
through a one-dimensional Fourier transform. Through the application of a
suitable unitary transformation, the two-leg SSH ladder in momentum space is
converted into an equivalent lattice with two distinct on-site states with
different momentum that are suitable for the calculations. Ultimately, the
desired zero-energy localized mode formed around the vacant-site is represented
by a combination of the armchair edge states. Furthermore, the scenario
involving two vacant sites is investigated and it is revealed that an effective
hopping interaction exists between the localized states formed around the
on-site vacancies created along a zigzag chain in the lattice. This structure
can be likened to the structure of a quantum dot with two none-degenerate
energy levels. Such a hopping interaction is absent for the same vacancies
created on the armchair chains. Finally, it is shown that introducing vacancies
periodically on the sites of a zigzag row along a finite-width ribbon with the
Haldane structure leads to the emergence of an impurity band within the energy
gap.


  Trapped atomic ions are a proven and powerful tool for the fundamental
research of quantum physics. They have emerged in recent years as one of the
most promising candidates for several practical technologies including quantum
computers, quantum simulators, atomic clocks, mass spectrometers and quantum
sensors. Advanced fabrication techniques, taken from established and nascent
disciplines, are being deployed to create novel, reliable devices with a view
to large scale integration and commercial compatibility. This review will cover
the fundamentals of ion trapping before proceeding with a discussion of the
design of ion traps for the aforementioned applications. We will analyse
current microfabrication techniques that are being utilised, as well as various
considerations which motivate the choice of materials and processes. Finally,
we discuss current efforts to include advanced, on-chip features into next
generation ion traps.


  Recent observations of beating signals in the excitation energy transfer
dynamics of photosynthetic complexes have been interpreted as evidence for
sustained coherences that are sufficiently long-lived for energy transport and
coherence to coexist. The possibility that coherence may be exploited in
biological processes has opened up new avenues of exploration at the interface
of physics and biology. The microscopic origin of these long-lived coherences,
however, remains to be uncovered. Here we present such a mechanism and verify
it by numerically exact simulations of system-environment dynamics. Crucially,
the non-trivial spectral structures of the environmental fluctuations and
particularly discrete vibrational modes can lead to the generation and
sustenance of both oscillatory energy transport and electronic coherence on
timescales that are comparable to excitation energy transport. This suggests
that the non-trivial structure of protein environments plays a more significant
role for coherence in biological processes than previously believed.


  We demonstrate that a dark silhouette of the black hole illuminated by a thin
accretion disk and seen by a distant observer is, in fact, a silhouette of the
event horizon hemisphere. The boundary of this silhouette is a contour of the
event horizon equatorial circle if a thin accretion disk is placed in the black
hole equatorial plane. A luminous matter plunging into black hole from
different directions provides the observational opportunity for recovering a
total silhouette of the invisible event horizon globe. The event horizon
silhouette is projected on the celestial sphere within a position of the black
hole shadow. A relative position of brightest point in the accretion disk with
respect to the position of event horizon silhouette in the image of black hole
in the galaxy M87, observed by the Event Horizon Telescope, corresponds to a
rather high value of the black hole spin, $a\simeq0.75$.


  The Fatou-Julia decomposition is significant in the study of iterations of
holomorphic mappings. Such a decomposition can be also considered for
foliations in a unified manner. Although the decomposition will be fundamental
in the study, it is not easy to decide the decomposition. In this article, we
give a sufficient condition for open sets to be contained in Fatou sets. We
also discuss relations between Fatou--Julia decompositions and minimal sets.


  Spectrally-peaked proton beams ($E_{p}\approx 8$ MeV, $\Delta E\approx 4$
MeV) have been observed from the interaction of an intense laser ($> 10^{19 }$
Wcm$^{-2}$) with ultrathin CH foils, as measured by spectrally-resolved full
beam profiles. These beams are reproducibly generated for foil thicknesses
(5-100 nm), and exhibit narrowing divergence with decreasing target thickness
down to $\approx 8^\circ$ for 5 nm. Simulations demonstrate that the narrow
energy spread feature is a result of buffered acceleration of protons. Due to
their higher charge-to-mass ratio, the protons outrun a carbon plasma driven in
the relativistic transparency regime.


  Quantum Analogical Modeling (QAM) works under the assumption that the correct
exemplar-based description for a system of behavior minimizes the overall
uncertainty of the system. The measure used in QAM differs from the traditional
logarithmic measure of uncertainty; instead QAM uses a quadratic measure of
disagreement between pairs of exemplars. (This quadratic measure parallels the
squaring function holding between the amplitude and the probability for a state
function in quantum mechanics.) QAM eliminates all supracontexts (contextual
groupings of exemplars) that fail to minimize the number of disagreements. The
resulting system thus distinguishes between homogeneous and heterogeneous
supracontexts and uses only exemplars in homogeneous supracontexts to predict
behavior. This paper revises earlier work on QAM (in 2005) by showing that
homogeneity for a supracontext can be most simply determined by discovering
whether there are any heterogeneous pointers between any of the supracontext's
exemplars. A pointer for a pair of exemplars is heterogeneous whenever those
two exemplars are found in different subcontexts of the supracontext and take
different outcomes.


  This paper proposes a novel diffusion-based model, CompoDiff, for solving
zero-shot Composed Image Retrieval (ZS-CIR) with latent diffusion. This paper
also introduces a new synthetic dataset, named SynthTriplets18M, with 18.8
million reference images, conditions, and corresponding target image triplets
to train CIR models. CompoDiff and SynthTriplets18M tackle the shortages of the
previous CIR approaches, such as poor generalizability due to the small dataset
scale and the limited types of conditions. CompoDiff not only achieves a new
state-of-the-art on four ZS-CIR benchmarks, including FashionIQ, CIRR, CIRCO,
and GeneCIS, but also enables a more versatile and controllable CIR by
accepting various conditions, such as negative text, and image mask conditions.
CompoDiff also shows the controllability of the condition strength between text
and image queries and the trade-off between inference speed and performance,
which are unavailable with existing CIR methods. The code and dataset are
available at https://github.com/navervision/CompoDiff


  Quantum mechanical weak values of projection operators have been used to
answer which-way questions, e.g. to trace which arms in a multiple Mach-Zehnder
setup a particle may have traversed from a given initial to a prescribed final
state. I show that this procedure might lead to logical inconsistencies in the
sense that different methods used to answer composite questions, like Has the
particle traversed the way X or the way Y? , may result in different answers
depending on which methods are used to find the answer. I illustrate the
problem by considering some examples: the quantum pigeonhole framework of
Aharonov et al, the three-box problem, and Hardys paradox. To prepare the
ground for my main conclusion on the incompatibility in certain cases of weak
values and logic, I study the corresponding situation for strong/projective
measurements. In this case, no logical inconsistencies occur provided one is
always careful in specifying exactly to which ensemble or sample space one
refers. My results cast doubts on the utility of quantum weak values in
treating cases like the examples mentioned.


  Topology and many-body localization (MBL) have opened new avenues for
preserving quantum information at finite energy density. Resonant
delocalization plays a crucial role in destabilizing these phenomena. In this
work, we study the statistical properties of many-body resonances in a
disordered interacting Ising model - which can host symmetry protected
topological order - using a Clifford circuit encoding of the real space
renormalization group which allows the resonant properties of the wave
functions to be efficiently characterized. Our findings show that both the
trivial and topologically ordered MBL phases remain stable to the resonances,
but in the vicinity of the transition between them localization is destabilized
by resonance proliferation. Diverging susceptibility towards the development of
an avalanche instability suggests an intervening ergodic phase. We are also
able to access the local integrals of motion in the MBL phases and identify the
topological edge-mode operators in the ordered phase. Our results have
important implications for the stability of MBL and phase transitions between
distinct MBL phases with and without symmetries.


  Chiral anomaly is a very fundamental aspect of quantum theories with chiral
fermion, from the Standard Model to supersymmetric field theories or even
string theories. How such microscopic anomaly manifests itself in a macroscopic
many-body system with chiral fermions, is a highly nontrivial question that has
recently attracted significant interest. As it turns out, unusual transport
currents can be induced by chiral anomaly under suitable conditions in such
systems, with the notable example of the Chiral Magnetic Effect (CME) where a
vector current (e.g. electric current) is generated along an external magnetic
field. The CME has been enthusiastically studied in two very different physical
systems: the Dirac and Weyl semimetals in condensed matter physics as well as
the quark-gluon plasma in heavy ion collisions. In this contribution, we report
the latest theoretical and experimental status for the search of CME in heavy
ion collisions.


  We present a study of the $\pi\pi$ scattering amplitude in the $\sigma$ and
$\rho$ channels at finite temperature and nuclear density within a chiral
unitary framework. Meson resonances are dynamically generated in our approach,
which allows us to analyze the behavior of their associated scattering poles
when the system is driven towards chiral symmetry restoration. Medium effects
are incorporated in three ways: (a) by thermal corrections of the unitarized
scattering amplitudes, (b) by finite nuclear density effects associated to a
renormalization of the pion decay constant, and complementarily (c) by
extending our calculation of the scalar-isoscalar channel to account for finite
nuclear density and temperature effects in a microscopic many-body
implementation of pion dynamics. Our results are discussed in connection with
several phenomenological aspects relevant for nuclear matter and Heavy-Ion
Collision experiments, such as $\rho$ mass scaling vs broadening from dilepton
spectra and chiral restoration signals in the $\sigma$ channel. We also
elaborate on the molecular nature of $\pi\pi$ resonances.


  We prove that a connected properly immersed minimal surface in Euclidean
3-space with infinite symmetry group whose intersection with a ball of radius R
is less than 2\piR^2 is a plane, a catenoid or a Scherk singly-periodic minimal
surface. In particular, we prove that the only periodic minimal
desingularization of a pair of intersecting planes is Scherk's singly-periodic
minimal surface.


  In this paper, we propose a recurrent neural network (RNN)-based MIDI music
composition machine that is able to learn musical knowledge from existing
Beatles' songs and generate music in the style of the Beatles with little human
intervention. In the learning stage, a sequence of stylistically uniform,
multiple-channel music samples was modeled by a RNN. In the composition stage,
a short clip of randomly-generated music was used as a seed for the RNN to
start music score prediction. To form structured music, segments of generated
music from different seeds were concatenated together. To improve the quality
and structure of the generated music, we integrated music theory knowledge into
the model, such as controlling the spacing of gaps in the vocal melody,
normalizing the timing of chord changes, and requiring notes to be related to
the song's key (C major, for example). This integration improved the quality of
the generated music as verified by a professional composer. We also conducted a
subjective listening test that showed our generated music was close to original
music by the Beatles in terms of style similarity, professional quality, and
interestingness. Generated music samples are at https://goo.gl/uaLXoB.


  Argumentation theory is a powerful paradigm that formalizes a type of
commonsense reasoning that aims to simulate the human ability to resolve a
specific problem in an intelligent manner. A classical argumentation process
takes into account only the properties related to the intrinsic logical
soundness of an argument in order to determine its acceptability status.
However, these properties are not always the only ones that matter to establish
the argument's acceptability---there exist other qualities, such as strength,
weight, social votes, trust degree, relevance level, and certainty degree,
among others.


  The main issues in non-accelerator astroparticle physics are reviewed and
discussed. A short description is given of the experimental methods, of many
experiments and of their experimental results.