  A number of recent estimates of the total luminosities of galaxies in the
SDSS are significantly larger than those reported by the SDSS pipeline. This is
because of a combination of three effects: one is simply a matter of defining
the scale out to which one integrates the fit when defining the total
luminosity, and amounts on average to < 0.1 mags even for the most luminous
galaxies. The other two are less trivial and tend to be larger; they are due to
differences in how the background sky is estimated and what model is fit to the
surface brightness profile. We show that PyMorph sky estimates are fainter than
those of the SDSS DR7 or DR9 pipelines, but are in excellent agreement with the
estimates of Blanton et al. (2011). Using the SDSS sky biases luminosities by
more than a few tenths of a magnitude for objects with half-light radii > 7
arcseconds. In the SDSS main galaxy sample these are typically luminous
galaxies, so they are not necessarily nearby. This bias becomes worse when
allowing the model more freedom to fit the surface brightness profile. When
PyMorph sky values are used, then two component Sersic-Exponential fits to
E+S0s return more light than single component deVaucouleurs fits (up to ~0.2
mag), but less light than single Sersic fits (0.1 mag). Finally, we show that
PyMorph fits of Meert et al. (2015) to DR7 data remain valid for DR9 images.
Our findings show that, especially at large luminosities, these PyMorph
estimates should be preferred to the SDSS pipeline values.


  We investigate the stellar kinematics of a sample of galaxies extracted from
the hydrodynamic cosmological Magneticum Pathfinder simulations out to $5$
half-mass radii. We construct differential radial stellar spin profiles
quantified by the observationally widely used $\lambda_\mathrm{R}$ and the
closely related $(V/\sigma)$ parameters. We find three characteristic profile
shapes: profiles exhibiting a (i) peak within $2.5$ half-mass radii and a
subsequent decrease (ii) continuous increase that plateaus at larger radii
typically with a high amplitude (iii) completely flat behaviour typically with
low amplitude, in agreement with observations. This shows that the kinematic
state of the stellar component can vary significantly with radius, suggesting a
distinct interplay between in-situ star formation and ex-situ accretion of
stars. Following the evolution of our sample through time, we provide evidence
that the accretion history of galaxies with decreasing profiles is dominated by
the anisotropic accretion of low mass satellites that get disrupted beyond $
\sim 2.0$ half-mass radii, building up a stellar halo with non-ordered motion
while maintaining the central rotation already present at $z=2$. In fact, at
$z=2$ decreasing profiles are the predominant profile class. Hence, we can
predict a distinct formation pathway for galaxies with a decreasing profile and
show that the centre resembles an old embedded disk. Furthermore, we show that
the radius of the kinematic transition provides a good estimation for the
transition radius from in-situ stars in the centre to accreted stars in the
halo.


  We propose a method for efficiently incorporating constraints into a
stochastic gradient Langevin framework for the training of deep neural
networks. Constraints allow direct control of the parameter space of the model.
Appropriately designed, they reduce the vanishing/exploding gradient problem,
control weight magnitudes and stabilize deep neural networks and thus improve
the robustness of training algorithms and the generalization capabilities of
the trained neural network. We present examples of constrained training methods
motivated by orthogonality preservation for weight matrices and explicit weight
normalizations. We describe the methods in the overdamped formulation of
Langevin dynamics and the underdamped form, in which momenta help to improve
sampling efficiency. The methods are explored in test examples in image
classification and natural language processing.


  Las Cumbres Observatory Global Telescope (LCOGT) is a young organization
dedicated to time-domain observations at optical and (potentially) near-IR
wavelengths. To this end, LCOGT is constructing a world-wide network of
telescopes, including the two 2m Faulkes telescopes, as many as 17 x 1m
telescopes, and as many as 23 x 40cm telescopes. These telescopes initially
will be outfitted for imaging and (excepting the 40cm telescopes) spectroscopy
at wavelengths between the atmospheric UV cutoff and the roughly 1-micron limit
of silicon detectors. Since the first of LCOGT's 1m telescopes are now being
deployed, we lay out here LCOGT's scientific goals and the requirements that
these goals place on network architecture and performance, we summarize the
network's present and projected level of development, and we describe our
expected schedule for completing it. In the bulk of the paper, we describe in
detail the technical approaches that we have adopted to attain the desired
performance. In particular, we discuss our choices for the number and location
of network sites, for the number and sizes of telescopes, for the
specifications of the first generation of instruments, for the software that
will schedule and control the network's telescopes and reduce and archive its
data, and for the structure of the scientific and educational programs for
which the network will provide observations.


  We show that braid groups with at most 6 strands are CAT(0) using the close
connection between these groups, the associated non-crossing partition
complexes and the embeddability of their diagonal links into spherical
buildings of type A. Furthermore, we prove that the orthoscheme complex of any
bounded graded modular complemented lattice is CAT(0), giving a partial answer
to a conjecture of Brady and McCammond.


  Programmatic reinforcement learning (PRL) has been explored for representing
policies through programs as a means to achieve interpretability and
generalization. Despite promising outcomes, current state-of-the-art PRL
methods are hindered by sample inefficiency, necessitating tens of millions of
program-environment interactions. To tackle this challenge, we introduce a
novel LLM-guided search framework (LLM-GS). Our key insight is to leverage the
programming expertise and common sense reasoning of LLMs to enhance the
efficiency of assumption-free, random-guessing search methods. We address the
challenge of LLMs' inability to generate precise and grammatically correct
programs in domain-specific languages (DSLs) by proposing a Pythonic-DSL
strategy - an LLM is instructed to initially generate Python codes and then
convert them into DSL programs. To further optimize the LLM-generated programs,
we develop a search algorithm named Scheduled Hill Climbing, designed to
efficiently explore the programmatic search space to consistently improve the
programs. Experimental results in the Karel domain demonstrate the superior
effectiveness and efficiency of our LLM-GS framework. Extensive ablation
studies further verify the critical role of our Pythonic-DSL strategy and
Scheduled Hill Climbing algorithm.


  In two-component non-linear Schr\"odinger equations, the force exerted by
incident monochromatic plane waves on an embedded dark soliton and on
dark-bright-type solitons is investigated, both perturbatively and by numerical
simulations. When the incoming wave is non-vanishing only in the orthogonal
component to that of the embedded dark soliton, its acceleration is in the
opposite direction to that of the incoming wave. This somewhat surprising
phenomenon can be attributed to the well known "negative effective mass" of the
dark soliton. When a dark-bright soliton, whose effective mass is also
negative, is hit by an incoming wave non-vanishing in the component
corresponding to the dark soliton, the direction of its acceleration coincides
with that of the incoming wave. This implies that the net force acting on it is
in the opposite direction to that of the incoming wave. This rather
counter-intuitive effect is a yet another manifestation of negative radiation
pressure exerted by the incident wave, observed in other systems. When a
dark-bright soliton interacts with an incoming wave in the component of the
bright soliton, it accelerates in the opposite direction, hence the force is
"pushing" it now. We expect that these remarkable effects, in particular the
negative radiation pressure, can be experimentally verified in Bose-Einstein
condensates.


  The goal of this paper is to propose and test a new memetic algorithm for the
capacitated vehicle routing problem in parallel computing environment. In this
paper we consider simple variation of vehicle routing problem in which the only
parameter is the capacity of the vehicle and each client only needs one
package. We present simple reduction to prove the existence of polynomial-time
algorithm for capacity 2. We analyze the efficiency of the algorithm using
hierarchical Parallel Random Access Machine (PRAM) model and run experiments
with code written in CUDA (for capacities larger than 2).


  In principle, the answer to the posed titular question is undoubtedly 'yes.'
But in practice, requisite reference data for homogeneous systems have been
obtained with a treatment of intermolecular interactions that is different from
that typically employed for heterogeneous systems. In this article, we assess
the impact of the choice of truncation scheme when comparing water in
homogeneous and inhomogeneous environments. Specifically, we use explicit free
energy calculations and a simple mean field analysis to demonstrate that using
the 'cut-and-shift' version of the Lennard-Jones potential (common to most
simple point charge models of water) results in a systematic increase in the
melting temperature of ice I$_{\rm h}$. In addition, by drawing an analogy
between a change in cutoff and a change in pressure, we use existing literature
data for homogeneous ice nucleation at negative pressures to suggest that
enhancements due to heterogeneous nucleation may have been overestimated by
several orders of magnitude.


  We point out that if quantum field renormalization is taken into account, and
the counterterms are evaluated at the Hubble-radius crossing time or few
e-foldings after it, the predictions of slow-roll inflation for both the scalar
and tensorial power spectrum change significantly. This leads to a change in
the consistency condition that relates the tensor-to-scalar amplitude ratio
with spectral indices. A reexamination of the potentials $\bf{\phi^2, \phi^4}$,
shows that both are compatible with five-year WMAP data. Only when the
counterterms are evaluated at much larger times beyond the end of inflation one
recovers the standard predictions. The alternative predictions presented here
may soon come within the range of measurement of near-future experiments.


  We report {\em JWST}/NIRCam measurements of quasar host galaxy emissions and
supermassive black hole (SMBH) masses for six quasars at $5.9<z<7.1$ in the
\textit{Emission-line galaxies and Intergalactic Gas in the Epoch of
Reionization} (EIGER) project. We obtain deep NIRCam imaging in the F115W,
F200W, and F356W bands, as well as F356W grism spectroscopy of the quasars. We
use bright unsaturated stars to construct models of the point spread function
(PSF) and estimate the errors of these PSFs. We then measure or constrain the
fluxes and morphology of the quasar host galaxies by fitting the quasar images
as a point source plus an exponential disk. We successfully detect the host
galaxy of three quasars, which have host-to-quasar flux ratios of
$\sim1\%-5\%$. Spectral Energy Distribution (SED) fitting suggests that these
quasar host galaxies have stellar masses of $M_*\gtrsim10^{10}M_\odot$. For
quasars with host galaxy non-detections, we estimate the upper limits of their
stellar masses. We use the grism spectra to measure the {\hb} line profile and
the continuum luminosity, then estimate the SMBH masses for the quasars. Our
results indicate that the positive relation between SMBH masses and host galaxy
stellar masses already exists at redshift $z\gtrsim6$. The quasars in our
sample show a high black hole to stellar mass ratio of
$M_\text{BH}/M_*\sim0.15$, which is about $\sim2$ dex higher than local
relations. We find that selection effects only contribute partially to the high
$M_\text{BH}/M_*$ ratios of high-redshift quasars. This result hints at a
possible redshift evolution of the $M_\text{BH}-M_*$ relation.


  The Wang-Silk approximation, 1/Q ~ 1/Q_stars + 1/Q_gas, is frequently used
for estimating the effective Q parameter in two-component discs of stars and
gas. Here we analyse this approximation in detail, and show how its accuracy
depends on the radial velocity dispersions and Toomre parameters of the two
components. We then propose a much more accurate but still simple approximation
for the effective Q parameter, which further takes into account the stabilizing
effect of disc thickness. Our effective Q parameter is a natural generalization
of Toomre's Q, and as such can be used in a wide variety of contexts, e.g. for
predicting star formation thresholds in galaxies or for measuring the stability
level of galactic discs at low and high redshifts.


  We introduce an improved approach for obtaining smooth finite-temperature
spectral functions of quantum impurity models using the numerical
renormalization group (NRG) technique. It is based on calculating first the
Green's function on the imaginary-frequency axis, followed by an analytic
continuation to the real-frequency axis using Pad\'e approximants. The
arbitrariness in choosing a suitable kernel in the conventional broadening
approach is thereby removed and, furthermore, we find that the Pad\'e method is
able to resolve fine details in spectral functions with less artifacts on the
scale of omega ~ T. We discuss the convergence properties with respect to the
NRG calculation parameters (discretization, truncation cutoff) and the number
of Matsubara points taken into account in the analytic continuation. We test
the technique on the the single-impurity Anderson model and the Hubbard model
(within the dynamical mean-field theory). For the Anderson impurity model, we
discuss the shape of the Kondo resonance and its temperature dependence. For
the Hubbard model, we discuss the inner structure of the Hubbard bands in
metallic and insulating solutions at half-filling, as well as in the doped Mott
insulator. Based on these test cases we conclude that the Pad\'e approximant
approach provides more reliable results for spectral functions at low-frequency
scales of omega < T and that it is capable of resolving sharp spectral features
also at high frequencies. It outperforms broadening in most respects.


  The predictive power of mean-field theory is emphasized by comparing theory
with simulations under controlled conditions. The recently developed test-field
method is used to extract turbulent transport coefficients both in kinematic as
well as nonlinear and quasi-kinematic cases. A striking example of the
quasi-kinematic method is provided by magnetic buoyancy-driven flows that
produce an alpha effect and turbulent diffusion.


  We analyze to what extent the complex Langevin method, which is in principle
capable of solving the so-called sign problems, can be considered as reliable.
We give a formal derivation of the correctness and then point out various
mathematical loopholes. The detailed study of some simple examples leads to
practical suggestions about the application of the method.


  In this article one investigates Rugina's Orientation Table and one gives
particular examples for several of its seven models. Leon Walras's Economics of
Stable Equilibrium and Keynes's Economics of Disequilibrium are combined in
Rugina's Orientation Table in systems which are s% stable and 100-s% unstable,
where s may be 100, 95, 65, 50, 35, 5, and 0. The Classical Logic and Modern
Logic are united in Rugina's Integrated Logic, and then generalized in the
Neutrosophic Logic.


  Using standard results from statistics, we show that for any continuous
quantum system (Gaussian or otherwise) and any observable $A$ (position or
otherwise), the distribution $ \pi _{a}\left(t\right) $ of a time measurement
at a fixed state $a$ can be inferred from the distribution $ \rho _{t}\left(
a\right) $ of a state measurement at a fixed time $t$ via the transformation $
\pi _{a}\left( t\right) = \left\vert \frac{\partial }{\partial t} \int_{-\infty
}^{a}\rho _{t}\left( u\right) du \right\vert $. This finding suggests that the
answer to the long-lasting time-of-arrival problem is in fact readily available
in the standard formalism, secretly hidden within the Born rule, and therefore
does not require the introduction of an ad-hoc time operator or a commitment to
a specific (e.g., Bohmian) ontology. The generality and versatility of the
result are illustrated by applications to the time-of-arrival at a given
location for a free particle in a superposed state and to the time required to
reach a given velocity for a free-falling quantum particle. Our approach also
offers a potentially promising new avenue toward the design of an experimental
protocol for the yet-to-be-performed observation of the phenomenon of quantum
backflow.


  The successful theoretical supernova explosion models should be able to
explain any features of the emission from supernovae at any evolutionary stage.
We check several models from two different points of view. With the
multi-frequency radiation hydro code STELLA we calculate gamma-ray, bolometric
and broad-band UBVI light curves. Then we use the same models to calculate the
emission from young supernova remnants.
  Here we present new plots for gamma-ray luminosity from several SN Ia models
and recomputations of bolometric and UBVRI light curves of model 13C for SN
1993J.


  We investigate safe multi-agent reinforcement learning, where agents seek to
collectively maximize an aggregate sum of local objectives while satisfying
their own safety constraints. The objective and constraints are described by
{\it general utilities}, i.e., nonlinear functions of the long-term
state-action occupancy measure, which encompass broader decision-making goals
such as risk, exploration, or imitations. The exponential growth of the
state-action space size with the number of agents presents challenges for
global observability, further exacerbated by the global coupling arising from
agents' safety constraints. To tackle this issue, we propose a primal-dual
method utilizing shadow reward and $\kappa$-hop neighbor truncation under a
form of correlation decay property, where $\kappa$ is the communication radius.
In the exact setting, our algorithm converges to a first-order stationary point
(FOSP) at the rate of $\mathcal{O}\left(T^{-2/3}\right)$. In the sample-based
setting, we demonstrate that, with high probability, our algorithm requires
$\widetilde{\mathcal{O}}\left(\epsilon^{-3.5}\right)$ samples to achieve an
$\epsilon$-FOSP with an approximation error of $\mathcal{O}(\phi_0^{2\kappa})$,
where $\phi_0\in (0,1)$. Finally, we demonstrate the effectiveness of our model
through extensive numerical experiments.


  We prove that any element in the Chow ring of the Hilbert scheme
$\text{Hilb}_n$ of $n$ points on a smooth surface $S$ is a universal class,
i.e. the pushforward of a polynomial in the Chern classes of the universal
subscheme on $\text{Hilb}_n \times S^k$ for some $k \in \mathbb{N}$, with
coefficients pulled back from the Chow of $S^k$.


  We analyze combinatorial optimization problems with ordinal, i.e.,
non-additive, objective functions that assign categories (like good, medium and
bad) rather than cost coefficients to the elements of feasible solutions. We
review different optimality concepts for ordinal optimization problems and
discuss their similarities and differences. We then focus on two prevalent
optimality concepts that are shown to be equivalent. Our main result is a
bijective linear transformation that transforms ordinal optimization problems
to associated standard multi-objective optimization problems with binary cost
coefficients. Since this transformation preserves all properties of the
underlying problem, problem-specific solution methods remain applicable. A
prominent example is dynamic programming and Bellman's principle of optimality,
that can be applied, e.g., to ordinal shortest path and ordinal knapsack
problems. We extend our results to multi-objective optimization problems that
combine ordinal and real-valued objective functions.


  Motivated by recent experiments on photon statistics from individual dye
pairs planted on biomolecules and coupled by fluorescence resonance energy
transfer (FRET), we show here that the FRET dynamics can be modelled by
Gaussian random processes with colored noise. Using Monte-Carlo numerical
simulations, the photon intensity correlations from the FRET pairs are
calculated, and are turned out to be very close to those observed in
experiment. The proposed stochastic description of FRET is consistent with
existing theories for microscopic dynamics of the biomolecule that carries the
FRET coupled dye pairs.


  The earliest confirmed interstellar object, `Oumuamua, was discovered in the
Solar System by Pan-STARRS in 2017, allowing for a calibration of the abundance
of interstellar objects of its size $\sim 100\;$ m. This was followed by the
discovery of Borisov, which allowed for a similar calibration of its size $\sim
0.4 - 1 \mathrm{\; km}$. One would expect a much higher abundance of
significantly smaller interstellar objects, with some of them colliding with
Earth frequently enough to be noticeable. Based on the CNEOS catalog of bolide
events, we identify the $\sim 0.45$m meteor detected at 2014-01-08 17:05:34 UTC
as originating from an unbound hyperbolic orbit with 99.999\% confidence. The
U.S. Department of Defense has since verified that "the velocity estimate
reported to NASA is sufficiently accurate to indicate an interstellar
trajectory." We infer that the meteor had an asymptotic speed of $v_{\infty}
\sim 42.1 \pm 5.5\; \mathrm{km \; s^{-1}}$ outside of the solar system. Its
origin is approximately towards R.A. $49.4 \pm 4.1^{\circ}$ and declination
$11.2 \pm 1.8^{\circ}$, implying that its initial velocity vector was $58\pm6\;
\mathrm{km\;s^{-1}}$ away from the velocity of the Local Standard of Rest
(LSR). Its high LSR speed implies a possible origin from the deep interior of a
planetary system or a star in the thick disk of the Milky Way galaxy. The local
number density of its population is $10^{6{^{+0.75}_{-1.5}}} \;
\mathrm{AU^{-3}}$ or $9 \times 10^{21{^{+0.75}_{-1.5}}} \; \mathrm{pc^{-3}}$
(necessitating 0.2 -- 20 Earth masses of material to be ejected per local
star). We show that the detections of CNEOS 2014-01-08, `Oumuamua, and Borisov
collectively imply that the differential size distribution in good agreement
with a collisional distribution, with a power-law slope is $q \sim 3.6 \pm
0.5$, where the quoted uncertainty corresponds to $2 \sigma$.


  We consider the configuration space of the Skyrme model and give a simple
proof that loops generated by full spatial rotations are contractible in the
even-, and non-contractible in the odd-winding-number sectors.


  In this paper, we present a general derivation of multicontinuum equations
and discuss cell problems. We present constraint cell problem formulations in a
representative volume element and oversampling techniques that allow reducing
boundary effects. We discuss different choices of constraints for cell
problems. We present numerical results that show how oversampling reduces
boundary effects. Finally, we discuss the relation of the proposed methods to
our previously developed methods, Nonlocal Multicontinuum Approaches.


  Since the quark model was put forward, theoretical researchers have always
attached great importance to the study of hidden color channels (including
color octets and diquark structure). Because of the influence of color Van der
waals forces, the hidden color channel itself has strong attraction, which
provides a dynamic mechanism for the formation of resonance state or bound
state. In this paper, taking the $T_{cc}$ system as an example, under the
framework of multi-Gaussian expansion method, a set of relatively complete
color singlets (that is, the ground state of the color singlet plus its
corresponding higher-order component) is used to replace the contribution of
the color octet. Similarly, we endeavor to replace the diquark structure with a
relatively complete set of molecular states, encompassing both the ground state
and excited states. Our results demonstrate that the color octet structure can
be effectively replaced by a set of relatively complete color singlet bases,
while the diquark structure cannot be entirely substituted by an equivalently
comprehensive set of molecular state bases.


  While the light-front quark model (LFQM) is employed to calculate hadronic
transition matrix elements, the vertex functions must be pre-determined. In
this work we derive the vertex functions for all d-wave states in this model.
Especially, since both of $^3D_1$ and $^3S_1$ are $1^{--}$ mesons, the Lorentz
structures of their vertex functions are the same. Thus when one needs to study
the processes where $^3D_1$ is involved, all the corresponding formulas for
$^3S_1$ states can be directly applied, only the coefficient of the vertex
function should be replaced by that for $^3D_1$. The results would be useful
for studying the newly observed resonances which are supposed to be d-wave
mesons and furthermore the possible 2S-1D mixing in $\psi'$ with the LFQM.


  With the advent of quantum computing, and other advancements in computation
and processing capabilities of modern systems, there arises a need to develop
new trapdoor functions that will serve as the foundation for a new generation
of encryption schemes. This paper explores the possibility of one such
potential trapdoor function using concepts stemming from Reversible Cellular
Automata (RCA) -- specifically, the Critter's Rule set up in a Margolus
Neighborhood. The proposed block encryption algorithm discusses how sensitive
data can be manipulated and converted efficiently into a two dimensional
sequence of bits, that can be iteratively evolved using the rules of the RCA
and a private key to achieve a desirable level of encryption within a
reasonable runtime. The performance benchmark and analysis results exemplify
how well the proposed encryption algorithm stands against different forms of
attacks.


  We scrutinize the behavior of eigenvalues of an electron of Helium atom as it
interacts with electric field directed along $z$-axis and exposed to linearly
polarized intense laser field radiation. In order to achieve this, we freeze
one electron of the helium atom at its ionic ground state and the motion of the
second electron in the ion core is treated via a more general case of screened
Coulomb potential model. Using the Kramers-Henneberger (KH) unitary
transformation, which is semiclassical counterpart of the Block-Nordsieck
transformation in the quantized field formalism, the squared vector potential
that appears in the equation of motion is eliminated and the resultant equation
is expressed in KH frame. Within this frame, the resulting potential and the
corresponding wave function have been expanded in Fourier series and using
Ehlotzkys approximation, we obtain a laser-dressed potential to simulate
intense laser field. By fitting the more general case of screened Coulomb
potential model into the laser-dressed potential, and then expanding it in
Taylor series up to $\mathcal{O}(r^4,\alpha_0^9)$, we obtain the solution
(eigenvalues and wave function) of an electron of Helium atom under the
influence of external electric field and high-intensity laser field, within the
framework of perturbation theory formalism. We found that the variation in
frequency of laser radiation has no effect on the eigenvalues of an electron of
helium for a particular electric field intensity directed along $z$-axis. Also,
for a very strong external electric field and an infinitesimal screening
parameter, the system is strongly bound. This work has potential application in
the areas of atomic and molecular processes in external fields including
interactions with strong fields and short pulses.


  Detailed radiation analysis of instruments flown in space is critical to
ensure mission safety, often requiring the use of state-of-the-art particle
transport simulation tools. Geant4 is one of the most powerful toolkits to
simulate the interaction and the passage of particles through matter. This
framework however, is not prepared to receive Standard for The Exchange of
Product data (STEP) files, the most versatile Computer-Aided Design (CAD)
format, as inputs requiring previous conversion to other formats. This,
especially when the instruments have complex shapes, and/or a large number of
volumes may lead to loss of detail and under or overestimation of the
quantities under study. Though several solutions have been proposed to import
complex geometries into Geant4, so far, only commercial options are available.
In this paper we present a new tool, GUIMesh, that embeds FreeCAD libraries, an
open-source CAD editor, to tessellate volumes, and convert them to Geometry
Description Markup Language (GDML), a Geant4 readable format, in a
straightforward way. Several degrees of freedom are given to the user regarding
the mesh and choice of material. Different geometries were tested for p
material definition, geometry and navigation errors, successfully validating
the method used.


  We derive a model to describe the interaction of an rf-SQUID (radio frequency
superconducting quantum interference device) based metasurface with free space
electromagnetic waves. The electromagnetic fields are described on the base of
Maxwell's equations. For the rf-SQUID metasurface we rely on an equivalent
circuit model. After a detailed derivation, we show that the problem that is
described by a system of coupled differential equations is wellposed and,
therefore, has a unique solution. In the small amplitude limit, we provide
analytical expressions for reflection, transmission, and absorption depending
on the frequency. To investigate the nonlinear regime, we numerically solve the
system of coupled differential equations using a finite element scheme with
transparent boundary conditions and the Crank-Nicolson method. We also provide
a rigorous error analysis that shows convergence of the scheme at the expected
rates. The simulation results for the adiabatic increase of either the field's
amplitude or its frequency show that the metasurface's response in the
nonlinear interaction regime exhibits bistable behavior both in transmission
and reflection.


This paper has been withdrawn.


  Standard power systems are modeled using differential-algebraic equations
(DAE). Following a transient event, voltage collapse can occur as a bifurcation
of the transient load flow solutions which is marked by the system trajectory
reaching a singular surface in state space where the voltage causality is lost.
If the system is under such a risk, preventive control decisions such as
changes in AVR setpoints need to be taken to enhance the stability. In this
regard, the knowledge of sensitivity of critical clearing time (CCT) to
controllable system parameters can be of great help. The stability boundary of
DAE systems is more complicated than ODE systems where in addition to stable
manifolds of unstable equilibrium points (UEP) and periodic orbits, singular
surfaces play an important role. In the present work, we derive the expressions
for CCT sensitivity for a generic DAE model using trajectory sensitivities with
applications to power system transient stability analysis (TSA) and preventive
control. The results are illustrated for multiple test systems which are then
validated against computationally intensive time-domain simulations (TDS).


  The half filled Hubbard model is studied in the pair approximation of the
Cluster Variation Method. The use of the $SO(4)$ symmetry of the model makes
possible to give a complete analytical characterization of the ground state, by
means of explicit expressions for the double occupancy and the nearest neighbor
correlation functions. The finite temperature analysis is reduced to the
numerical solution of only two coupled transcendental equations. The behavior
of local magnetic moment, specific heat and correlation functions is given for
some typical cases in one and two dimensions. We obtain good qualitative
agreement with exact and numerical results in one dimension. The results for
finite temperatures show a rapid evolution, with increasing temperature, from a
strongly antiferromagnetic behavior to a disordered one; in the high
temperature region a maximum (which has been related to a "gradual"
metal--insulator transition) is found in the specific heat for very large
values of the Coulomb repulsion.


  We present a comprehensive study on the electronic and magnetic properties of
the EuCl$_3$ monolayer using first-principles calculations. By taking into
account the spin-orbit coupling (SOC) and the Hubbard effects, we elucidate the
influence of these interactions on the structural properties of EuCl$_3$
monolayer. Comparing the lattice parameters obtained with the PBE+SOC and
PBE+SOC+Hubbard effects reveals an increase in the lattice parameters when
including the Hubbard effect. In the absence of the Hubbard interaction, the
magnetic ground state of the EuCl$_3$ monolayer exhibits a preference for a
ferromagnetic (FM) configuration as determined by the PBE+SOC calculations.
However, the introduction of the Hubbard parameter leads to a shift in the
magnetic ground state preference towards an antiferromagnetic (AFM) N\'{e}el
state. Based on the calculated energy values, Monte Carlo simulations are
carried out to determine the N\'{e}el temperature $(T_N)$. Our simulations
yield a N\'{e}el temperature of \SI{390}{\kelvin} for the EuCl$_3$ monolayer,
indicating the temperature at which the transition from a paramagnetic phase to
an antiferromagnetic phase occurs. These results highlight the importance of
incorporating the SOC and the Hubbard effect in accurately describing the
electronic and magnetic properties of the EuCl$_3$ monolayer. Our results
contribute to a deeper understanding of the fundamental physics underlying the
behavior of this intriguing two-dimensional material and provide insights into
its potential applications in spintronics and magnetic devices.


  In this paper, we consider the momentum operator of a quantum particle
directed along the displacement of two of its neighbors. A modified open-path
path integral molecular dynamics is presented to sample the distribution of
this directional momentum distribution, where we derive and use a new estimator
for this distribution. Variationally enhanced sampling is used to obtain this
distribution for an example molecule, Malonaldehyde, in the very low
temperature regime where deep tunneling happens. We find no secondary feature
in the directional momentum distribution, and that its absence is due to
quantum entanglement through a further study of the reduced density matrix.


  Let $f\colon Y \to X$ be a proper flat morphism of locally noetherian
schemes. Then, the locus in $X$ over which $f$ is smooth is stable under
generization. We prove that under suitable assumptions on the formal fibers of
$X$, the same property holds for other local properties of morphisms, even if
$f$ is only closed and flat. Our proof of this statement reduces to a purely
local question known as Grothendieck's localization problem. To answer
Grothendieck's problem, we provide a general framework that gives a uniform
treatment of previously known cases of this problem, and also solves this
problem in new cases, namely for weak normality, seminormality,
$F$-rationality, and the property "Cohen-Macaulay and $F$-injective." For the
weak normality statement, we prove that weak normality always lifts from
Cartier divisors. We also solve Grothendieck's localization problem for
terminal, canonical, and rational singularities in equal characteristic zero.


  This is an introduction to the theory of Witt vectors. It includes a
construction of the Witt rings, the Frobenius and Verschiebung endomorphisms,
the canonical map from W to W^2 (its lambda-algebra structure), the relation to
strict p-rings, and an account of the Artin-Hasse exponential.


  In recent years the question of maximizing GCD sums regained interest due to
its firm link with large values of $L$-functions. In the present paper we
initiate the study of minimizing for positive weights~$w$ of normalized $L^1$-
norm the sum $\sum_{m_1 , m_2 \leqslant N}
w({m_1})w({m_2})\frac{(m_1,m_2)}{\sqrt{m_1m_2}} $. We consider as well the
intertwined question of minimizing a weighted version of the usual
multiplicative energy. We give three applications of our results. Firstly we
obtain a logarithmic refinement of Burgess' bound on character sums
$\displaystyle{\sum_{M<n\leqslant M+N}\chi(n)}$ improving previous results of
Kerr, Shparlinski and Yau. Secondly let us denote by $\theta (x,\chi)$ the
theta series associated to a Dirichlet character $\chi$ modulo $p$.
Constructing a suitable mollifier, we improve a result of Louboutin and the
second author and show that, for any $x>0$, there exists at least $ \gg p/(\log
p)^{ \delta+o(1)}$ (with $\delta=1-\frac{1+\log_2 2}{\log 2} \approx 0.08607$)
even characters such that $\theta(x,\chi) \neq 0$. Lastly we obtain lower
bounds on small moments of character sums.


  We present a novel pipeline for learning the conditional distribution of a
building roof mesh given pixels from an aerial image, under the assumption that
roof geometry follows a set of regular patterns. Unlike alternative methods
that require multiple images of the same object, our approach enables
estimating 3D roof meshes using only a single image for predictions. The
approach employs the PolyGen, a deep generative transformer architecture for 3D
meshes. We apply this model in a new domain and investigate the sensitivity of
the image resolution. We propose a novel metric to evaluate the performance of
the inferred meshes, and our results show that the model is robust even at
lower resolutions, while qualitatively producing realistic representations for
out-of-distribution samples.


  Networks are universally considered as complex structures of interactions of
large multi-component systems. In order to determine the role that each node
has inside a complex network, several centrality measures have been developed.
Such topological features are also important for their role in the dynamical
processes occurring in networked systems. In this paper, we argue that the
dynamical activity of the nodes may strongly reshape their relevance inside the
network making centrality measures in many cases misleading. We show that when
the dynamics taking place at the local level of the node is slower than the
global one between the nodes, then the system may lose track of the structural
features. On the contrary, when that ratio is reversed only global properties
such as the shortest distances can be recovered. From the perspective of
networks inference, this constitutes an uncertainty principle, in the sense
that it limits the extraction of multi-resolution information about the
structure, particularly in the presence of noise. For illustration purposes, we
show that for networks with different time-scale structures such as strong
modularity, the existence of fast global dynamics can imply that precise
inference of the community structure is impossible.


  Group lifting structures are introduced to provide an algebraic framework for
studying lifting factorizations of two-channel perfect reconstruction
finite-impulse-response (FIR) filter banks. The lifting factorizations
generated by a group lifting structure are characterized by Abelian groups of
lower and upper triangular lifting matrices, an Abelian group of unimodular
gain scaling matrices, and a set of base filter banks. Examples of group
lifting structures are given for linear phase lifting factorizations of the two
nontrivial classes of two-channel linear phase FIR filter banks, the whole- and
half-sample symmetric classes, including both the reversible and irreversible
cases. This covers the lifting specifications for whole-sample symmetric filter
banks in Parts 1 and 2 of the ISO/IEC JPEG 2000 still image coding standard.
The theory is used to address the uniqueness of lifting factorizations. With no
constraints on the lifting process, it is shown that lifting factorizations are
highly nonunique. When certain hypotheses developed in the paper are satisfied,
however, lifting factorizations generated by a group lifting structure are
shown to be unique. A companion paper applies the uniqueness results proven in
this paper to the linear phase group lifting structures for whole- and
half-sample symmetric filter banks.


  The paper is devoted to an adaptation of author's approach to Leray theorems
in bounded cohomology theory to infinite chains. The main results are a
stronger and more general form of Gromov's Vanishing-finiteness theorem and a
generalization of the first part of his Cutting-of theorem. The proofs are
elementary.


  Several Active Learning (AL) policies require retraining a target model
several times in order to identify the most informative samples and rarely
offer the option to focus on the acquisition of samples from underrepresented
classes. Here the Mining of Single-Class by Active Learning (MiSiCAL) paradigm
is introduced where an AL policy is constructed through deep reinforcement
learning and exploits quantity-accuracy correlations to build datasets on which
high-performance models can be trained with regards to specific classes.
MiSiCAL is especially helpful in the case of very large batch sizes since it
does not require repeated model training sessions as is common in other AL
methods. This is thanks to its ability to exploit fixed representations of the
candidate data points. We find that MiSiCAL is able to outperform a random
policy on 150 out of 171 COCO10k classes, while the strongest baseline only
outperforms random on 101 classes.


  This paper studies the level set Crouzeix conjecture, which is a weak version
of Crouzeix's conjecture that applies to finite compressions of the shift.
Amongst other results, this paper establishes the level set Crouzeix conjecture
for several classes of $3\times3$, $4\times4$, and $5\times5$ matrices
associated to compressions of the shift via a geometric analysis of their
numerical ranges. This paper also establishes Crouzeix's conjecture for several
classes of nilpotent matrices whose studies are motivated by related
compressions of shifts.


  We demonstrate amplification (and attenuation) of a probe signal by a driven
two-level quantum system in the Landau-Zener-St\"{u}ckelberg-Majorana regime by
means of an experiment, in which a superconducting qubit was strongly coupled
to a microwave cavity, in a conventional arrangement of circuit quantum
electrodynamics. Two different types of flux qubit, specifically a conventional
Josephson junctions qubit and a phase-slip qubit, show similar results, namely,
lasing at the working points where amplification takes place. The experimental
data are explained by the interaction of the probe signal with Rabi-like
oscillations. The latter are created by constructive interference of
Landau-Zener-St\"{u}ckelberg-Majorana (LZSM) transitions during the driving
period of the qubit. A detailed description of the occurrence of these
oscillations and a comparison of obtained data with both analytic and numerical
calculations are given.


  We embed Duquesne and Le Gall's stable tree into a binary compact continuum
random tree (CRT) in a way that solves an open problem posed by Goldschmidt and
Haas. This CRT can be obtained by applying a recursive construction method of
compact CRTs as presented in earlier work to a specific distribution of a
random string of beads, i.e. a random interval equipped with a random discrete
measure. We also express this CRT as a tree built by replacing all branch
points of a stable tree by rescaled i.i.d. copies of a Ford CRT. Some of these
developments are carried out in a space of infinity-marked metric spaces
generalising Miermont's notion of a k-marked metric space.


  The key results on lepton-pair production in ultra-relativistic nuclear
collisions are shortly reviewed, starting at the roots of pp collisions in the
seventies, and ending at the perspectives of the colliders RHIC and LHC. The
presence is dominated by the recent precision results from NA60 at the CERN
SPS, culminating in the first measurement of the in-medium rho spectral
function and the transverse flow of the associated thermal radiation. The
seeming cut-off of the flow above the rho may well be the first direct hint for
thermal radiation of partonic origin in nuclear collisions. The major
milestones in the theoretical developments are also covered.


  Deep-embedding methods aim to discover representations of a domain that make
explicit the domain's class structure and thereby support few-shot learning.
Disentangling methods aim to make explicit compositional or factorial
structure. We combine these two active but independent lines of research and
propose a new paradigm suitable for both goals. We propose and evaluate a novel
loss function based on the $F$ statistic, which describes the separation of two
or more distributions. By ensuring that distinct classes are well separated on
a subset of embedding dimensions, we obtain embeddings that are useful for
few-shot learning. By not requiring separation on all dimensions, we encourage
the discovery of disentangled representations. Our embedding method matches or
beats state-of-the-art, as evaluated by performance on recall@$k$ and few-shot
learning tasks. Our method also obtains performance superior to a variety of
alternatives on disentangling, as evaluated by two key properties of a
disentangled representation: modularity and explicitness. The goal of our work
is to obtain more interpretable, manipulable, and generalizable deep
representations of concepts and categories.


  We present a controller synthesis algorithm for reach-avoid problems for
piecewise linear discrete-time systems. Our algorithm relies on SMT solvers and
in this paper we focus on piecewise constant control strategies. Our algorithm
generates feedback control laws together with inductive proofs of unbounded
time safety and progress properties with respect to the reach-avoid sets. Under
a reasonable robustness assump- tion, the algorithm is shown to be complete.
That is, it either generates a controller of the above type along with a proof
of correctness, or it establishes the impossibility of the existence of such
controllers. To achieve this, the algorithm iteratively attempts to solve a
weakened and strengthened versions of the SMT encoding of the reach-avoid
problem. We present preliminary experimental results on applying this algorithm
based on a prototype implementation.


  We report here a systematic quantitative study on generation and
characteristics of an active muon source driven by the interaction of an
electron beam within the energy range of 1 to 10 GeV from laser wakefield
acceleration (LWFA) with a tungsten target, using Monte Carlo simulations. The
10GeV electron beam, achievable in near future, from LWFA using femtosecond
multi-PW lasers is employed to drive the bright source of muon pairs in a
compact setup. We show that a highly directional and intense source of
short-pulsed GeV muon pairs having peak brightness 5x10^17 pairs/s/cm^2/sr and
sub-100-ps duration could be produced using a quasi-monoenergetic 10-fs, 10-GeV
electron bunch with 1-mrad divergence and 100-pC charge. The muon pairs are
emitted from a point-like source with well-defined position and timing, and the
source has size and geometric emittance about 1 mm and 40 microns,
respectively. Such muon sources can greatly benefit applications in muon
radiography, studies on anomalous dipole moment and rare decays of muons,
neutrino oscillations, and an injector of a future compact muon collider.


  Based on light curves from the Swift Burst Analyser, we investigate whether a
`dip' feature commonly seen in the early-time hardness ratios of Swift-XRT data
could arise from the juxtaposition of the decaying prompt emission and rising
afterglow. We are able to model the dip as such a feature, assuming the
afterglow rises as predicted by Sari & Piran (1999). Using this model we
measure the initial bulk Lorentz factor of the fireball. For a sample of 23
GRBs we find a median value of Gamma_0=225, assuming a constant-density
circumburst medium; or Gamma_0=93 if we assume a wind-like medium.


  We present the final catalogue of the 2dF QSO Redshift Survey (2QZ), based on
Anglo-Australian Telescope 2dF spectroscopic observations of 44576
colour-selected (u b_J r) objects with 18.25<b_J<20.85 selected from APM scans
of UK Schmidt Telescope (UKST) photographic plates. The 2QZ comprises 23338
QSOs, 12292 galactic stars (including 2071 white dwarfs) and 4558 compact
narrow-emission-line galaxies. We obtained a reliable spectroscopic
identification for 86 per cent of objects observed with 2dF. We also report on
the 6dF QSO Redshift Survey (6QZ), based on UKST 6dF observations of 1564
brighter 16<b_J<18.25 sources selected from the same photographic input
catalogue. In total, we identified 322 QSOs spectroscopically in the 6QZ. The
completed 2QZ is, by more than a factor 50, the largest homogeneous QSO
catalogue ever constructed at these faint limits (b_J<20.85) and high QSO
surface densities (35 QSOs deg^-2). As such it represents an important resource
in the study of the Universe at moderate-to-high redshifts. As an example of
the results possible with the 2QZ, we also present our most recent analysis of
the optical QSO luminosity function and its cosmological evolution with
redshift. For a flat, Omega_m=0.3 and Omega_lam=0.7, Universe, we find that a
double power law with luminosity evolution that is exponential in look-back
time, t, of the form L*(z) exp(6.15t), equivalent to an e-folding time of 2Gyr,
provides an acceptable fit to the redshift dependence of the QSO luminosity
function over the range 0.4 < z < 2.1 and M_bJ<-22.5. Evolution described by a
quadratic in redshift is also an acceptable fit, with L*(z)~10^(1.39z-0.29z^2).


  Reinforcement learning (RL) applications, where an agent can simply learn
optimal behaviors by interacting with the environment, are quickly gaining
tremendous success in a wide variety of applications from controlling simple
pendulums to complex data centers. However, setting the right hyperparameters
can have a huge impact on the deployed solution performance and reliability in
the inference models, produced via RL, used for decision-making. Hyperparameter
search itself is a laborious process that requires many iterations and
computationally expensive to find the best settings that produce the best
neural network architectures. In comparison to other neural network
architectures, deep RL has not witnessed much hyperparameter tuning, due to its
algorithm complexity and simulation platforms needed. In this paper, we propose
a distributed variable-length genetic algorithm framework to systematically
tune hyperparameters for various RL applications, improving training time and
robustness of the architecture, via evolution. We demonstrate the scalability
of our approach on many RL problems (from simple gyms to complex applications)
and compared with Bayesian approach. Our results show that with more
generations, optimal solutions that require fewer training episodes and are
computationally cheap while being more robust for deployment. Our results are
imperative to advance deep reinforcement learning controllers for real-world
problems.


  Paper withdrawn due to conceptual mistakes. A corrected version will soon be
available at the gr-qc archive.


  Influence diagrams are decision theoretic extensions of Bayesian networks.
They are applied to diverse decision problems. In this paper we apply influence
diagrams to the optimization of a vehicle speed profile. We present results of
computational experiments in which an influence diagram was used to optimize
the speed profile of a Formula 1 race car at the Silverstone F1 circuit. The
computed lap time and speed profiles correspond well to those achieved by test
pilots. An extended version of our model that considers a more complex
optimization function and diverse traffic constraints is currently being tested
onboard a testing car by a major car manufacturer. This paper opens doors for
new applications of influence diagrams.


  In recent years, the usefulness of 3D shape estimation is being realized in
microscopic or close-range imaging, as the 3D information can further be used
in various applications. Due to limited depth of field at such small distances,
the defocus blur induced in images can provide information about the 3D shape
of the object. The task of `shape from defocus' (SFD), involves the problem of
estimating good quality 3D shape estimates from images with depth-dependent
defocus blur. While the research area of SFD is quite well-established, the
approaches have largely demonstrated results on objects with bulk/coarse shape
variation. However, in many cases, objects studied under microscopes often
involve fine/detailed structures, which have not been explicitly considered in
most methods. In addition, given that, in recent years, large data volumes are
typically associated with microscopy related applications, it is also important
for such SFD methods to be efficient. In this work, we provide an indication of
the usefulness of the Belief Propagation (BP) approach in addressing these
concerns for SFD. BP has been known to be an efficient combinatorial
optimization approach, and has been empirically demonstrated to yield good
quality solutions in low-level vision problems such as image restoration,
stereo disparity estimation etc. For exploiting the efficiency of BP in SFD, we
assume local space-invariance of the defocus blur, which enables the
application of BP in a straightforward manner. Even with such an assumption,
the ability of BP to provide good quality solutions while using non-convex
priors, reflects in yielding plausible shape estimates in presence of fine
structures on the objects under microscopy imaging.


  In Supergiant X-ray binaries (SgXB), a compact object captures a fraction of
the wind of an O/B supergiant on a close orbit. Proxies exist to evaluate the
efficiency of mass and angular momentum accretion but they depend so
dramatically on the wind speed that given the current uncertainties, they only
set loose constrains. Furthermore, they often bypass the impact of orbital and
shock effects on the flow structure. We study the wind dynamics and the angular
momentum gained as the flow is accreted. We identify the conditions for the
formation of a disc-like structure around the accretor and the observational
consequences for SgXB. We use recent results on the wind launching mechanism to
compute 3D streamlines, accounting for the gravitational and X-ray ionizing
influence of the compact companion on the wind. Once the flow enters the Roche
lobe of the accretor, we solve the hydrodynamics equations with cooling. A
shocked region forms around the accretor as the flow is beamed. For wind speeds
of the order of the orbital speed, the shock is highly asymmetric compared to
the axisymmetric bow shock obtained for a purely planar homogeneous flow. With
net radiative cooling, the flow always circularizes for wind speeds low enough.
Although the donor star does not fill its Roche lobe, the wind can be
significantly beamed and bent by the orbital effects. The net angular momentum
of the accreted flow is then sufficient to form a persistent disc-like
structure. This mechanism could explain the proposed limited outer extension of
the accretion disc in Cygnus X-1 and suggests the presence of a disc at the
outer rim of the neutron star magnetosphere in Vela X-1, with dramatic
consequences on the spinning up of the accretor.


  Abnormal hemoglobins can have major consequences for tissue delivery of
oxygen. Correct diagnosis of hemoglobinopathies with altered oxygen affinity
requires a determination of hemoglobin oxygen dissociation curve (ODC), which
relates the hemoglobin oxygen saturation to the partial pressure of oxygen in
the blood. Determination of the ODC of human hemoglobin is typically carried
out under conditions in which hemoglobin is in equilibrium with O2 at each
partial pressure. However, in the human body due to the fast transit of RBCs
through tissues hemoglobin oxygen exchanges occur under non-equilibrium
conditions. We describe the determination of non-equilibrium ODC, and show that
under these conditions Hb cooperativity has two apparent components in the
Adair, Perutz, and MWC models of Hb. The first component, which we call
sequential cooperativity, accounts for ~70% of Hb cooperativity, and emerges
from the constraint of sequential binding that is shared by the three models.
The second component, which we call conformational cooperativity, accounts for
~30% of Hb cooperativity, and is due either to a conformational equilibrium
between low affinity and high affinity tetramers (as in the MWC model), or to a
conformational change from low to high affinity once two of the tetramer sites
are occupied (Perutz model).


  Consider the moment map $\mu \colon T^*(\mathfrak{p} \times \mathbb{C}^n) \to
\mathfrak{p}^*$ for a parabolic subalgebra $\mathfrak{p}$ of
$\mathfrak{gl}_n(\mathbb{C})$. We prove that the preimage of $0$ under $\mu$ is
a complete intersection when $\mathfrak{p}$ has finitely many $P$-orbits, where
$P\subseteq \operatorname{GL}_n(\mathbb{C})$ is a parabolic subgroup such that
$\operatorname{Lie}(P) = \mathfrak{p}$, and give an explicit description of the
irreducible components. This allows us to study nearby fibers of $\mu$ as they
are equidimensional, and one may also construct GIT quotients $\mu^{-1}(0)
/\!\!/_{\chi} P$ by varying the stability condition $\chi$. Finally, we study a
variety analogous to the scheme studied by Wilson with connections to a
Calogero--Moser phase space where only some of particles interact.


  Recently, the direct detection of gravitational waves from black hole (BH)
mergers was announced by the Advanced LIGO Collaboration. Multi-messenger
counterparts of stellar-mass BH mergers are of interest, and it had been
suggested that a small disk or celestial body may be involved in the binary of
two BHs. To test such possibilities, we consider the fate of a wind powered by
an active mini-disk in a relatively short, super-Eddington accretion episode
onto a BH with ~10-100 solar masses. We show that its thermal emission could be
seen as a fast optical transient with the duration from hours to days. We also
find that the coasting outflow forms external shocks due to interaction with
the interstellar medium, whose synchrotron emission might be expected in the
radio band on a time scale of years. Finally, we also discuss a possible jet
component and the associated high-energy neutrino emission as well as
ultra-high-energy cosmic-ray acceleration.


  The effectiveness of a language model is influenced by its token
representations, which must encode contextual information and handle the same
word form having a plurality of meanings (polysemy). Currently, none of the
common language modelling architectures explicitly model polysemy. We propose a
language model which not only predicts the next word, but also its sense in
context. We argue that this higher prediction granularity may be useful for end
tasks such as assistive writing, and allow for more a precise linking of
language models with knowledge bases. We find that multi-sense language
modelling requires architectures that go beyond standard language models, and
here propose a structured prediction framework that decomposes the task into a
word followed by a sense prediction task. To aid sense prediction, we utilise a
Graph Attention Network, which encodes definitions and example uses of word
senses. Overall, we find that multi-sense language modelling is a highly
challenging task, and suggest that future work focus on the creation of more
annotated training datasets.


  We investigate deep inelastic lepton scattering from the nucleon within a
constituent quark picture, in which the internal structure of constituent
quarks is modeled by meson and diquark dressing. In a covariant framework this
structure leads to a breakdown of the factorization necessary for a convolution
formulation. We perform our analysis in time-ordered perturbation theory in the
infinite momentum frame where factorization of subprocesses is automatic.
Numerical results are compared with recent data on valence quark distributions
in the proton.


  We study the dynamic critical behavior of a Swendsen-Wang-type algorithm for
the Ashkin--Teller model. We find that the Li--Sokal bound on the
autocorrelation time ($\tau_{{\rm int},{\cal E}} \ge {\rm const} \times C_H$)
holds along the self-dual curve of the symmetric Ashkin--Teller model, and is
almost but not quite sharp. The ratio $\tau_{{\rm int},{\cal E}} / C_H$ appears
to tend to infinity either as a logarithm or as a small power ($0.05 \leq p
\leq 0.12$). In an appendix we discuss the problem of extracting estimates of
the exponential autocorrelation time.


  In open chaotic systems the number of long-lived resonance states obeys a
fractal Weyl law, which depends on the fractal dimension of the chaotic saddle.
We study the generic case of a mixed phase space with regular and chaotic
dynamics. We find a hierarchy of fractal Weyl laws, one for each region of the
hierarchical decomposition of the chaotic phase-space component. This is based
on our observation of hierarchical resonance states localizing on these
regions. Numerically this is verified for the standard map and a hierarchical
model system.


  In this study, we investigate the problem of min-max continuous optimization
in a black-box setting $\min_{x} \max_{y}f(x,y)$. A popular approach updates
$x$ and $y$ simultaneously or alternatingly. However, two major limitations
have been reported in existing approaches. (I) As the influence of the
interaction term between $x$ and $y$ (e.g., $x^\mathrm{T} B y$) on the
Lipschitz smooth and strongly convex-concave function $f$ increases, the
approaches converge to an optimal solution at a slower rate. (II) The
approaches fail to converge if $f$ is not Lipschitz smooth and strongly
convex-concave around the optimal solution. To address these difficulties, we
propose minimizing the worst-case objective function $F(x)=\max_{y}f(x,y)$
directly using the covariance matrix adaptation evolution strategy, in which
the rankings of solution candidates are approximated by our proposed worst-case
ranking approximation (WRA) mechanism. Compared with existing approaches,
numerical experiments show two important findings regarding our proposed
method. (1) The proposed approach is efficient in terms of $f$-calls on a
Lipschitz smooth and strongly convex-concave function with a large interaction
term. (2) The proposed approach can converge on functions that are not
Lipschitz smooth and strongly convex-concave around the optimal solution,
whereas existing approaches fail.


  We introduce a symplectic dual quaternion variational integrator(DQVI) for
simulating single rigid body motion in all six degrees of freedom. Dual
quaternion is used to represent rigid body kinematics and one-step Lie group
variational integrator is used to conserve the geometric structure, energy and
momentum of the system during the simulation. The combination of these two
becomes the first Lie group variational integrator for rigid body simulation
without decoupling translations and rotations. Newton-Raphson method is used to
solve the recursive dynamic equation. This method is suitable for real-time
rigid body simulations with high precision under large time step. DQVI respects
the symplectic structure of the system with excellent long-term conservation of
geometry structure, momentum and energy. It also allows the reference point and
6-by-6 inertia matrix to be arbitrarily defined, which is very convenient for a
variety of engineering problems.


  A recently proposed form of dual theory for the three dimensional
superconductor is rederived starting from the lattice electrodynamics and
studied by renormalization group. The superfluid density below and close to the
transition vanishes as inverse of the correlation length of the disorder field.
The corresponding universal amplitude is given by the fixed point value of the
dual charge, and it is calculated to the leading order. The continuum dual
theory predicts the divergence of the magnetic field penetration depth with the
XY exponent, in contradiction to the results obtained from the Ginzburg-Landau
theory for the superconducting order-parameter. Possible reasons for this
difference are discussed.


  In this study, direct-current reactive sputtered ZnO and ZnO1-x based thin
film (30 nm and 300 nm in thickness) memristor devices were produced and the
effects of oxygen vacancies and thickness on the memristive characteristics
were investigated. The oxygen deficiency of the ZnO1-x structure was confirmed
by SIMS analyses. The memristive characteristics of both the ZnO and ZnO1-x
devices were determined by time dependent current-voltage (I-V-t) measurements.
The distinctive pinched hysteresis I-V loops of memristors were observed in all
the fabricated devices. The typical homogeneous interface and filamentary types
of memristive behaviors were compared. In addition, conduction mechanisms,
on/off ratios and the compliance current were analyzed. The 30 nm ZnO based
devices with native oxygen vacancies showed the best on/off ratio. All of the
devices exhibited dominant Schottky emissions and weaker Poole-Frenkel
conduction mechanisms. Results suggested that the oxygen deficiency was
responsible for the Schottky emission mechanism. Moreover, the compliance
currents of the devices were related to the decreasing power consumption as the
oxygen vacancies increased.


  This paper presents a new generalized Armijo's line-search method, and
combines it with a phi-regulation defined to obtain a new algorithm solving the
very general non-linear non-smooth convex programming. For the algorithm
designed, the global convergence is proved and the algorithm has super-linear
convergent rate under very weak conditions. This paper generalized the results
of reference "Fukushima M and Qi LQ (1996) SIAM Journal of Optimization 6:
1106-20".


  We present a new scheme to perform noise resilient universal adiabatic
quantum computation using two-body interactions. To achieve this, we introduce
a new family of error detecting subsystem codes whose gauge generators and a
set of their logical operators - capable of encoding universal Hamiltonian
computations - can be implemented using two-body interactions. Logical
operators of the code are used to encode any given computational Hamiltonian,
and the gauge operators are used to construct a penalty Hamiltonian whose
ground subspace is protected against local-errors. In contrast to previous
approaches, the constructed penalty Hamiltonian does not necessarily commute
with the encoded computational Hamiltonians, but for our construction, the
undesirable effect of the penalty Hamiltonian on the computation can be
compensated by a simple modification of the implemented Hamiltonians. We also
investigate whether a similar scheme can be constructed by encoding the
computational Hamiltonian using only bare-logical operators of subsystem codes,
to guarantee that computational Hamiltonian commutes with the penalty
Hamiltonian. We prove a no-go theorem showing that restricting to two-body
interactions and using any general CSS-type subsystem codes, such a
construction cannot encode systems beyond an Ising chain in a transverse field.
We point out that such a chain is universal for Hamiltonian-based quantum
computation, but it is not universal for ground-state quantum computation.


  In this article, our main concern is to study the existence of bound and
ground state solutions for the following fractional system of Schr\"{o}dinger
equations with Hardy potentials: \begin{equation*} \left\{ \begin{aligned}
(-\Delta)^{s_{1}} u - \lambda_{1} \frac{u~~}{|x|^{2s_{1}}} -
u^{2_{s_{1}}^{*}-1} = \nu \alpha h(x) u^{\alpha-1}v^{\beta} & \quad \mbox{in} ~
\mathbb{R}^{N}, (-\Delta)^{s_{2}} v - \lambda_{2} \frac{v~~}{|x|^{2s_{2}}} -
v^{2_{s_{2}}^{*}-1} = \nu \beta h(x) u^{\alpha}v^{\beta-1} & \quad \mbox{in} ~
\mathbb{R}^{N}, u,v >0 \quad \mbox{in} ~ \mathbb{R}^{N} \setminus \{0\},
\end{aligned} \right. \end{equation*} where $s_{1},s_{2} \in
(0,1)~\text{and}~\lambda_{i}\in (0, \Lambda_{N,s_{i}})$ with $\Lambda_{N,s_{i}}
= 2 \pi^{N/2} \frac{\Gamma^{2}(\frac{N+2s_i}{4})
\Gamma(\frac{N+2s_i}{2})}{\Gamma^{2}(\frac{N-2s_i}{4}) ~|\Gamma(-s_{i})|},
(i=1,2)$. By imposing certain assumptions on the parameters and on the function
h, we obtain ground-state solutions using the concentration-compactness
principle and the mountain-pass theorem.


  We demonstrate a simple network-analyzer technique to make quantitative
measurements of the bias dependence of spin torque in a magnetic tunnel
junction. We apply a microwave current to exert an oscillating spin torque near
the ferromagnetic resonance frequency of the tunnel junction's free layer. This
produces an oscillating resistance that, together with an applied direct
current, generates a microwave signal that we measure with the network
analyzer. An analysis of the resonant response yields the strength and
direction of the spin torque at non-zero bias. We compare to measurements of
the spin torque vector by time-domain spin-torque ferromagnetic resonance.


  In our work, we propose a novel formulation for supervised dimensionality
reduction based on a nonlinear dependency criterion called Statistical Distance
Correlation, Szekely et. al. (2007). We propose an objective which is free of
distributional assumptions on regression variables and regression model
assumptions. Our proposed formulation is based on learning a low-dimensional
feature representation $\mathbf{z}$, which maximizes the squared sum of
Distance Correlations between low dimensional features $\mathbf{z}$ and
response $y$, and also between features $\mathbf{z}$ and covariates
$\mathbf{x}$. We propose a novel algorithm to optimize our proposed objective
using the Generalized Minimization Maximizaiton method of \Parizi et. al.
(2015). We show superior empirical results on multiple datasets proving the
effectiveness of our proposed approach over several relevant state-of-the-art
supervised dimensionality reduction methods.


  In a class of theories where the Higgs field emerges as a pseudo
Nambu-Goldstone boson, it is often assumed that interactions to generate the
top Yukawa coupling provide the Higgs potential as well. Such a scenario
generically requires a little cancellation in the leading contribution to the
Higgs potential, and the electroweak scale is generated by the balance between
the leading and the subleading contributions. We, instead, consider the
possibility that the contribution from the dark matter particle balances
against that from the top quark. The thermal relic of the new particle explains
the abundance of dark matter in a consistent region of the parameter space, and
the direct detection is found to be promising.


  The brief review of current experiments on search and studying of double beta
decay processes is done. Best present limits on $\langle m_{\nu} \rangle$ and
$\langle g_{ee} \rangle$ are presented. Prospects of search for neutrinoless
double beta decay in new experiments with sensitivity to $\langle
m_{\nu}\rangle$ at the level of $\sim$ 0.01-0.1 eV are discussed.


  This paper studies how to learn parameters in diagonal Gaussian mixture
models. The problem can be formulated as computing incomplete symmetric tensor
decompositions. We use generating polynomials to compute incomplete symmetric
tensor decompositions and approximations. Then the tensor approximation method
is used to learn diagonal Gaussian mixture models. We also do the stability
analysis. When the first and third order moments are sufficiently accurate, we
show that the obtained parameters for the Gaussian mixture models are also
highly accurate. Numerical experiments are also provided.


  A concise point kinetic model of the explosion of a prompt supercritical
sphere driven by a nuclear fission chain reaction is presented. The findings
are in good agreement with the data available for Trinity, the first detonation
of a nuclear weapon conducted by the United States Army as part of the
Manhattan project. Results are presented for an implosion device containing
pure plutonium-239, although the model can be easily applied to, e.g.,
uranium-235. The fizzle probability and corresponding yield of a fission bomb
containing plutonium recovered from reactor fuel and therefore containing
significant amounts of spontaneously fissioning plutonium-240 which can induce
a predetonation of the device is illustrated by adding a corresponding source
term in the presented model. Related questions whether a bomb could be made by
developing countries or terrorist organizations can be tackled this way.
Although the information needed to answer such questions is in the public
domain, it is difficult to extract a consistent picture of the subject for
members of organizations who are concerned about the proliferation of nuclear
explosives.


  Multiplicative relations in the cohomology ring of a manifold impose
constraints upon its stable systoles. Given a compact Riemannian manifold
(X,g), its real homology H_*(X,R) is naturally endowed with the stable norm.
Briefly, if h\in H_k(X,R) then the stable norm of h is the infimum of the
Riemannian k-volumes of real cycles representing h. The stable k-systole is the
minimum of the stable norm over nonzero elements in the lattice of integral
classes in H_k(X,R). Relying on results from the geometry of numbers due to W.
Banaszczyk, and extending work by M. Gromov and J. Hebda, we prove
metric-independent inequalities for products of stable systoles, where the
product can be as long as the real cup length of X.


  Euclid's proof can be reworked to construct infinitely many primes, in many
different ways, using ideas from arithmetic dynamics.
  After acceptance Soundararajan noted the beautiful and fast converging
formula: $$ \tau = a^{1/(d-1)} x_0 \cdot \lim_{n\to \infty} \prod_{m=1}^n
\left(\frac{x_m}{ax_{m-1}^d} \right)^{1/d^m} $$


  In this paper, we show how to construct the standard Laplacian on the unit
square in a self-similar manner. We rewrite the familiar mean value property of
planar harmonic functions in terms of averge values on small squares, from
which we could know how the planar self-similar resistance form and the
Laplacian look like. This approach combines the constructive
limit-of-difference-quotients method of Kigami for p.c.f. self-similar sets and
the method of averages introduced by Kusuoka and Zhou for the Sierpinski
carpet.


  We consider a wireless networked control system (WNCS) with multiple
controllers and multiple attackers. The dynamic interaction between the
controllers and the attackers is modeled as a linear quadratic (LQ) zero-sum
difference game with multiplicative randomness induced by the multiple-input
and multiple-output (MIMO) wireless fading channels of the controllers and
attackers. We focus on analyzing the existence and achievability of the value
of the zero-sum game. We first establish a general sufficient and necessary
condition for the existence of the game value. This condition relies on the
solvability of a modified game algebraic Riccati equation (MGARE) under an
implicit concavity constraint, which is generally difficult to verify due to
the intermittent controllability or almost sure uncontrollability caused by the
multiplicative randomness. We then introduce a new positive semidefinite (PSD)
kernel decomposition method induced by multiplicative randomness, through which
we obtain a closed-form tight verifiable sufficient condition. Under the
existence condition, we finally construct a saddle-point policy that is able to
achieve the game value in a certain class of admissible policies. We
demonstrate that the proposed saddle-point policy is backward compatible to the
existing strictly feedback stabilizing saddle-point policy.


  We provide bounds on the first Betti number and structure results for the
fundamental group of horizon cross-sections for extreme stationary vacuum black
holes in arbitrary dimension, without additional symmetry hypotheses. This is
achieved by exploiting a correspondence between the associated near-horizon
geometries and the mathematical notion of $m$-quasi Einstein metrics, in
addition to generalizations of the classical splitting theorem from Riemannian
geometry. Consequences are analyzed and refined classifications are given for
the possible topologies of these black holes.


  Group actions on a Smale space and the actions induced on the C*-algebras
associated to such a dynamical system are studied. We show that an effective
action of a discrete group on a mixing Smale space produces a strongly outer
action on the homoclinic algebra. We then show that for irreducible Smale
spaces, the property of finite Rokhlin dimension passes from the induced action
on the homoclinic algbera to the induced actions on the stable and unstable
C*-algebras. In each of these cases, we discuss the preservation of
properties---such as finite nuclear dimension, Z-stability, and classification
by Elliott invariants---in the resulting crossed products.


  Many recent semi-supervised learning (SSL) studies build teacher-student
architecture and train the student network by the generated supervisory signal
from the teacher. Data augmentation strategy plays a significant role in the
SSL framework since it is hard to create a weak-strong augmented input pair
without losing label information. Especially when extending SSL to
semi-supervised object detection (SSOD), many strong augmentation methodologies
related to image geometry and interpolation-regularization are hard to utilize
since they possibly hurt the location information of the bounding box in the
object detection task. To address this, we introduce a simple yet effective
data augmentation method, Mix/UnMix (MUM), which unmixes feature tiles for the
mixed image tiles for the SSOD framework. Our proposed method makes mixed input
image tiles and reconstructs them in the feature space. Thus, MUM can enjoy the
interpolation-regularization effect from non-interpolated pseudo-labels and
successfully generate a meaningful weak-strong pair. Furthermore, MUM can be
easily equipped on top of various SSOD methods. Extensive experiments on
MS-COCO and PASCAL VOC datasets demonstrate the superiority of MUM by
consistently improving the mAP performance over the baseline in all the tested
SSOD benchmark protocols.


  In 2000, Lukyanov conjectured that a certain ratio of $N$-fold integrals
should provide access, in the large-$N$ regime, to the ground state expectation
value of the exponential of the Sinh-Gordon quantum field in 1+1 dimensions and
finite volume $R$. This work aims at rigorously constructing the fundamental
objects necessary to address the large-$N$ analysis of such integrals. More
precisely, we construct and establish the main properties of the the
equilibrium measure minimising a certain $N$-dependent energy functional that
naturally arises in the study of the leading large-$N$ behaviour of the
Lukyanov integral. Our construction allows us to heuristically advocate the
leading term in the large-$N$ asymptotic behaviour of the mentioned ratio of
Lukyanov integrals, hence supporting Lukyanov's prediction -- obtained by other
means -- on the exponent $\sigma$ of the power-law $N^{\sigma}$ term of its
asymptotic expansion as $N\rightarrow + \infty$.


  Generating motion for robots that interact with objects of various shapes is
a complex challenge, further complicated when the robot's own geometry and
multiple desired behaviors are considered. To address this issue, we introduce
a new framework based on Geometric Projectors (GeoPro) for constrained
optimization. This novel framework allows for the generation of task-agnostic
behaviors that are compliant with geometric constraints. GeoPro streamlines the
design of behaviors in both task and configuration spaces, offering diverse
functionalities such as collision avoidance and goal-reaching, while
maintaining high computational efficiency. We validate the efficacy of our work
through simulations and Franka Emika robotic experiments, comparing its
performance against state-of-the-art methodologies. This comprehensive
evaluation highlights GeoPro's versatility in accommodating robots with varying
dynamics and precise geometric shapes. For additional materials, please visit:
https://www.xueminchi.com/publications/geopro


  Empirical studies on food expenditure are largely based on cross-section data
and for a few studies based on longitudinal (or panel) data the focus has been
on the conditional mean. While the former, by construction, cannot model the
dependencies between observations across time, the latter cannot look at the
relationship between food expenditure and covariates (such as income,
education, etc.) at lower (or upper) quantiles, which are of interest to
policymakers. This paper analyzes expenditures on total food (TF), food at home
(FAH), and food away from home (FAFH) using mean regression and quantile
regression models for longitudinal data to examine the impact of economic
recession and various demographic, socioeconomic, and geographic factors. The
data is taken from the Panel Study of Income Dynamics (PSID) and comprises of
2174 families in the United States (US) observed between 2001-2015. Results
indicate that age and education of the head, family income, female headed
family, marital status, and economic recession are important determinants for
all three types of food expenditure. Spouse education, family size, and some
regional indicators are important for expenditures on TF and FAH, but not for
FAFH. Quantile analysis reveals considerable heterogeneity in the covariate
effects for all types of food expenditure, which cannot be captured by models
focused on conditional mean. The study ends by showing that modeling
conditional dependence between observations across time for the same family
unit is crucial to reducing/avoiding heterogeneity bias and better model
fitting.


  The presence of optical polarization anisotropies, such as Faraday/Kerr
effects, linear birefringence, and magnetoelectric birefringence are evidence
for broken symmetry states of matter. The recent discovery of a Kerr effect
using near-IR light in the pseudogap phase of the cuprates can be regarded as a
strong evidence for a spontaneous symmetry breaking and the existence of an
anomalous long-range ordered state. In this work we present a high precision
study of the polarimetry properties of the cuprates in the THz regime. While no
Faraday effect was found in this frequency range to the limits of our
experimental uncertainty (1.3 milli-radian or 0.07$^\circ$), a small but
significant polarization rotation was detected that derives from an anomalous
linear dichroism. In YBa$_2$Cu$_3$O$_y$ the effect has a temperature onset that
mirrors the pseudogap temperature T$^*$ and is enhanced in magnitude in
underdoped samples. In $x=1/8$ La$_{2-x}$Ba$_{x}$CuO$_4$, the effect onsets
above room temperature, but shows a dramatic enhancement near a temperature
scale known to be associated with spin and charge ordered states. These
features are consistent with a loss of both C$_4$ rotation and mirror symmetry
in the electronic structure of the CuO$_2$ planes in the pseudogap state.


  The galaxy cluster Abell 523 (A523) hosts an extended diffuse synchrotron
source historically classified as a radio halo. Its radio power at 1.4 GHz
makes it one of the most significant outliers in the scaling relations between
observables derived from multi-wavelength observations of galaxy clusters: it
has a morphology that is different and offset from the thermal gas, and it has
polarized emission at 1.4 GHz typically difficult to observe for this class of
sources. A magnetic field fluctuating on large spatial scales (~ 1 Mpc) can
explain these peculiarities but the formation mechanism for this source is not
yet completely clear. To investigate its formation mechanism, we present new
observations obtained with the LOw Frequency ARray at 120-168 MHz and the
Jansky Very Large Array at 1-2 GHz, which allow us to study the spectral index
distribution of this source. According to our data the source is observed to be
more extended at 144 MHz than previously inferred at 1.4 GHz, with a total size
of about 1.8 Mpc and a flux density S_144MHz = (1.52 +- 0.31) Jy. The spectral
index distribution of the source is patchy with an average spectral index alpha
~ 1.2 between 144 MHz and 1.410 GHz, while an integrated spectral index alpha ~
2.1 has been obtained between 1.410 GHz and 1.782 GHz. A previously unseen
patch of steep spectrum emission is clearly detected at 144 MHz in the south of
the cluster. Overall, our findings suggest that we are observing an overlapping
of different structures, powered by the turbulence associated with the primary
and a possible secondary merger.


  The sources that drove cosmological reionization left clues regarding their
identity in the slope and inhomogeneity of the ultraviolet ionizing background
(UVB): Bright quasars (QSOs) generate a hard UVB with predominantly large-scale
fluctuations while Population II stars generate a softer one with smaller-scale
fluctuations. Metal absorbers probe the UVB's slope because different ions are
sensitive to different energies. Likewise, they probe spatial fluctuations
because they originate in regions where a galaxy-driven UVB is harder and more
intense. We take a first step towards studying the reionization-epoch UVB's
slope and inhomogeneity by comparing observations of 12 metal absorbers at
$z\sim6$ versus predictions from a cosmological hydrodynamic simulation using
three different UVBs: a soft, spatially-inhomogeneous "galaxies+QSOs" UVB; a
homogeneous "galaxies+QSOs" UVB (Haardt & Madau 2012); and a QSOs-only model.
All UVBs reproduce the observed column density distributions of CII, SiIV, and
CIV reasonably well although high-column, high-ionization absorbers are
underproduced, reflecting numerical limitations. With upper limits treated as
detections, only a soft, fluctuating UVB reproduces both the observed SiIV/CIV
and CII/CIV distributions. The QSOs-only UVB overpredicts both CIV/CII and
CIV/SiIV, indicating that it is too hard. The Haardt & Madau (2012) UVB
underpredicts CIV/SiIV, suggesting that it lacks amplifications near galaxies.
Hence current observations prefer a soft, fluctuating UVB as expected from a
predominantly Population II background although they cannot rule out a harder
one. Future observations probing a factor of two deeper in metal column density
will distinguish between the soft, fluctuating and QSOs-only UVBs.


  The aim of this paper is to determine the irreducible components of M_g(D_n),
the locus inside M_g of the curves admitting an effective action by the
dihedral group D_n. This is done by classifying pairs (H,H') of distinct
subgroups of the mapping class group Map_g, such that both H and H' are
isomorphic to D_n and the fixed point locus of H inside the Teichm\"uller space
T_g is contained in the fixed point locus of H'.


  We study physical properties of a Luttinger liquid in a superlattice which is
characterized by alternating two tunneling parameters. Employing the
Bosonization approach, we describe the corresponding Hubbard model by the
equivalent Tomonoga-Luttinger model. We analyze the spin-charge separation and
transport property as the difference between the two tunneling parameter
increases. We suggest that cold Fermi gases trapped in a bichromatic optical
lattice and coupled quantum dots offer the opportunity to measure these effects
in a convenient manner. We also study the classical Ising chain with two
tunneling parameters. We found that the classical two-point correlator
decreases as the difference between the two tunneling parameter increases.


  We prove the analyticity of the finite volume QCD partition function for
complex values of the theta-vacuum parameter. The absence of singularities
different from Lee-Yang zeros only permits ^ cusp singularities in the vacuum
energy density and never v cusps. This fact together with the Vafa-Witten
diamagnetic inequality implies the vanishing of the density of Lee-Yang zeros
at theta=0 and has an important consequence: the absence of a first order phase
transition at theta=0. The result provides a key missing link in the
Vafa-Witten proof of parity symmetry conservation in vector-like gauge theories
and follows from renormalizability, unitarity, positivity and existence of BPS
bounds. Generalizations of this theorem to other physical systems are also
discussed, with particular interest focused on the non-linear CPn sigma model.


  We study the electronic properties of strongly spin-orbit coupled electrons
on the elastic pyrochlore lattice. Akin to the Peierls transition in
one-dimensional systems, the coupling of the lattice to the electronic degrees
of freedom can stabilize a spontaneous deformation of the crystal. This
deformation corresponds to a breathing mode, which breaks the inversion
symmetry. We find that for intermediate values of the staggered strain, the
inversion-symmetry broken phase realizes a topological Weyl semimetal. In the
temperature-elasticity phase diagram, the Weyl semimetal shows a reentrant
phase behavior: it can be reached from a symmetric phase realized both at
higher and at lower temperatures. The symmetric phase is a Dirac semimetal,
which is protected by the non-symmorphic space group of the pyrochlore lattice.
Beyond a critical value of the staggered strain, the symmetry-broken phase is a
fully gapped trivial insulator. The surface states of the Weyl semimetal form
open Fermi arcs and we observe that their connectivity depends on the
termination of the crystal. In particular, for the $\{111\}$ films, the
semiclassical closed electronic orbits of the surface states in a magnetic
field cross the bulk either twice, four, six or twelve times. We demonstrate
how one can tune the number of bulk crossings through a Lifshitz-like
transition of the Fermi arcs, which we call Weyl-Lifshitz transition, by
applying a surface potential. Our results offer a route to a topological Weyl
semimetal in nonmagnetic materials and might be relevant for pyrochlore oxides
with heavy transition-metal ions such as alloys of iridates.


  Fluid antenna systems (FASs) can reconfigure their antenna locations freely
within a spatially continuous space. To keep favorable antenna positions, the
channel state information (CSI) acquisition for FASs is essential. While some
techniques have been proposed, most existing FAS channel estimators require
several channel assumptions, such as slow variation and angular-domain
sparsity. When these assumptions are not reasonable, the model mismatch may
lead to unpredictable performance loss. In this paper, we propose the
successive Bayesian reconstructor (S-BAR) as a general solution to estimate FAS
channels. Unlike model-based estimators, the proposed S-BAR is prior-aided,
which builds the experiential kernel for CSI acquisition. Inspired by Bayesian
regression, the key idea of S-BAR is to model the FAS channels as a stochastic
process, whose uncertainty can be successively eliminated by kernel-based
sampling and regression. In this way, the predictive mean of the regressed
stochastic process can be viewed as the maximum a posterior (MAP) estimator of
FAS channels. Simulation results verify that, in both model-mismatched and
model-matched cases, the proposed S-BAR can achieve higher estimation accuracy
than the existing schemes.


  In a series of publications the Cummings-Stell model (CSM), for a binary
mixture of associative fluids with steric effects, has been solved analytically
using the Percus-Yevick approximation (PYA). The solution consists in a square
well potential of width w, whose center is placed into the hard sphere shell
($r < \sigma$): at $L = \sigma / n$ (n = 1, ..., 4). This paper presents a
general solution, for any n, of the first order Difference Differential
Equation (DDE), for the auxiliary Baxter's function that appears in the CSM,
using recursive properties of these auxiliary functions and a matrix composed
by differential and shift operators (MDSO). This problem is common in some
other models of associative fluids such as the CSM for homogeneus and
inhomogeneus mixtures of sticky shielded hard spheres including solvent effects
under PYA, and in that of mean-spherical approximation (MSA), for chemical ion
association and dipolar dumbbells and polymers. The sticky potential implies a
discontinuity step at $L$ in the solution of auxiliary Baxter's functions so
that, one side, $L$ now is arbitrary and, for some additional effects, it can
be placed one or more sticky potentials at different positions into the hard
shell.


  The Matern family of covariance functions is currently the most commonly used
for the analysis of geostatistical data due to its ability to describe
different smoothness behaviors. Yet, in many applications the smoothness
parameter is set at an arbitrary value. This practice is due partly to
computational challenges faced when attempting to estimate all covariance
parameters and partly to unqualified claims in the literature stating that
geostatistical data have little or no information about the smoothness
parameter. This work critically investigates this claim and shows it is not
true in general. Specifically, it is shown that the information the data have
about the correlation parameters varies substantially depending on the true
model and sampling design and, in particular, the information about the
smoothness parameter can be large, in some cases larger than the information
about the range parameter. In light of these findings, we suggest to reassess
the aforementioned practice and instead establish inferences from data-based
estimates of both range and smoothness parameters, especially for strongly
dependent non-smooth processes observed on irregular sampling designs. A data
set of daily rainfall totals is used to motivate the discussion and gauge this
common practice.


  We study a generating function for the sum over fatgraphs with specified
valences of vertices and faces, inversely weighted by the order of their
symmetry group. A compact expression is found for general (i.e. non necessarily
connected) fatgraphs. This expression admits a matrix integral representation
which enables to perform semi--classical computations, leading in particular to
a closed formula corresponding to (genus zero, connected) trees.


  In this Letter we constrain for the first time both cosmology and modified
gravity theories conjointly, by combining the GW and electromagnetic
observations of GW170817. We provide joint posterior distributions for the
Hubble constant $H_0$, and two physical effects typical of modified gravity:
the gravitational wave (GW) friction, encoded by the parameter $\alpha_M$, and
several GW dispersion relations. Among the results of this analysis, we can
improve by 15\% the bound of the graviton mass with respect to measurement
using the same event, but fixing $H_0$. We obtain a value of
$m^2_g=2.08_{-4.25}^{+13.90} \cdot 10^{-44} \rm{eV^2/c^4}$ at 99.7\% confidence
level (CL), when marginalising over the Hubble constant and GW friction term
$\alpha_M$. We find poor constraints on $\alpha_M$, but demonstrate that for
all the GW dispersions relations considered, including massive gravity, the GW
must be emitted $\sim$ 1.74s before the Gamma-ray burst (GRB). Furthermore, at
the GW merger peak frequency, we show that the fractional difference between
the GW group velocity and $c$ is $\lesssim 10^{-17}$.


  Meson corrections on chiral condensate up to next-to-leading order in $1/N_c$
expansion at finite density are investigated in NJL model with chiral symmetry
explicitly breaking. Compared with the mean-field results, the chiral phase
transition is still of first order, while the properties at the critical
density of chiral phase transition are found to change significantly.


  We explore effects of random non-axisymmetric perturbations of kinetic
helicity (the $\alpha$ effect) and diffusive decay of bipolar magnetic regions
on generation and evolution of large-scale non-axisymmetric magnetic fields on
the Sun. Using a reduced 2D nonlinear mean-field dynamo model and assuming that
bipolar regions emerge due to magnetic buoyancy in situ of the large-scale
dynamo action, we show that fluctuations of the $\alpha$ effect can maintain
the non-axisymmetric magnetic fields through a solar-type $\alpha^{2}\Omega$
dynamo process. It is found that diffusive decay of bipolar active regions is
likely to be the primary source of the non-axisymmetric magnetic fields
observed on the Sun. Our results show that the non-axisymmetric dynamo model
with stochastic perturbations of the $\alpha$ effect can explain periods of
extremely high activity (`super-cycle' events) as well as periods of deep
decline of magnetic activity. We compare the models with synoptic observations
of solar magnetic fields for the last four activity cycles, and discuss
implications of our results for interpretation of observations of stellar
magnetic activity.