  We consider a Hubbard-like model of strongly-interacting spinless fermions
and hardcore bosons on a square lattice, such that nearest neighbor occupation
is forbidden. Stripes (lines of holes across the lattice forming antiphase
walls between ordered domains) are a favorable way to dope this system below
half-filling. The problem of a single stripe can be mapped to a spin-1/2 chain,
which allows understanding of its elementary excitations and calculation of the
stripe's effective mass for transverse vibrations. Using Lanczos exact
diagonalization, we investigate the excitation gap and dispersion of a hole on
a stripe, and the interaction of two holes. We also study the interaction of
two, three, and four stripes, finding that they repel, and the interaction
energy decays with stripe separation as if they are hardcore particles moving
in one (transverse) direction. To determine the stability of an array of
stripes against phase separation into particle-rich phase and hole-rich liquid,
we evaluate the liquid's equation of state, finding the stripe-array is not
stable for bosons but is possibly stable for fermions.


  In this paper, imposing hermitian conjugate relations on the two-parameter
deformed quantum group GL_{p,q}(2) is studied. This results in a
non-commutative phase associated with the unitarization of the quantum group.
After the achievement of the quantum group U_{p,q}(2) with pq real via a
non-commutative phase, the representation of the algebra is built by means of
the action of the operators constituting the U_{p,q}(2) matrix on states.


  We derive a formula for the virtual class of the moduli space of rubber maps
to $[\mathbb{P}^1/G]$ pushed forward to the moduli space of stable maps to
$BG$. As an application, we show that the Gromov-Witten theory of
$[\mathbb{P}^1/G]$ relative to $0$ and $\infty$ are determined by known
calculations.


  Modern X-ray telescopes have detected hundreds of thousands of X-ray sources
in the universe. However, current methods to classify these sources using the
X-ray data themselves suffer problems - detailed X-ray spectroscopy of
individual sources is too time-consuming, while hardness ratios often lack
accuracy, and can be difficult to use effectively. These methods fail to use
the power of X-ray CCD detectors to identify X-ray emission lines and
distinguish line-dominated spectra (from chromospherically active stars,
supernova remnants, etc.) from continuum-dominated ones (e.g., compact objects
or active galactic nuclei [AGN]). In this paper, we probe the use of artificial
neural networks (ANN) in differentiating Chandra spectra of young stars in the
Chandra Orion Ultradeep Project (COUP) survey from AGN in the Chandra Deep
Field South (CDFS) survey. We use these surveys to generate 100,000 artificial
spectra of stars and AGN and train our ANN models to separate the two kinds of
spectra. We find that our methods reach an accuracy of approx. 92% in
classifying simulated spectra of moderate-brightness objects in typical
exposures, but their performance slightly decreases on the observed COUP and
CDFS spectra (approx. 91%), due in large part to the relatively high background
of these long-exposure datasets. We also investigate the performance of our
methods with changing properties of the spectra such as the net source counts,
the relative contribution of background, the absorption column of the sources,
etc. We conclude that these methods have substantial promise for application to
large X-ray surveys.


  We report on the unambiguous observation of the sub-cycle ionization bursts
in sequential strong-field double ionization of H$_2$ and their disentanglement
in molecular frame photoelectron angular distributions. This observation was
made possible by the use of few-cycle laser pulses with a known
carrier-envelope phase in combination with multi-particle coincidence momentum
imaging. The approach demonstrated here will allow sampling of the
intramolecular electron dynamics and the investigation of charge-state specific
Coulomb-distortions on emitted electrons in polyatomic molecules.


  In this paper, we provide sufficient conditions for the functions $\psi$ and
$\phi$ to be the approximate duals in the Hardy space $H^p(\mathbb{R})$ for all
$0<p\leq1$. Based on these conditions, we obtain the wavelet series expansion
in the Hardy space with the approximate duals. The important properties of our
approach include the following: (i) our results work for any $0<p\leq1$; (ii)
we do not assume that the functions $\psi$ and $\phi$ are exact duals; (iii) we
provide a tractable bound for the operator norm of the associated wavelet frame
operator so that it is possible to check the suitability of the functions
$\psi$ and $\phi$.


  CoVaR (conditional value-at-risk) is a crucial measure for assessing
financial systemic risk, which is defined as a conditional quantile of a random
variable, conditioned on other random variables reaching specific quantiles. It
enables the measurement of risk associated with a particular node in financial
networks, taking into account the simultaneous influence of risks from multiple
correlated nodes. However, estimating CoVaR presents challenges due to the
unobservability of the multivariate-quantiles condition. To address the
challenges, we propose a two-step nonparametric estimation approach based on
Monte-Carlo simulation data. In the first step, we estimate the unobservable
multivariate-quantiles using order statistics. In the second step, we employ a
kernel method to estimate the conditional quantile conditional on the order
statistics. We establish the consistency and asymptotic normality of the
two-step estimator, along with a bandwidth selection method. The results
demonstrate that, under a mild restriction on the bandwidth, the estimation
error arising from the first step can be ignored. Consequently, the asymptotic
results depend solely on the estimation error of the second step, as if the
multivariate-quantiles in the condition were observable. Numerical experiments
demonstrate the favorable performance of the two-step estimator.


  In the work presented here, we have studied the impact of right handed
neutrinos, which are introduced to account for the evidence of neutrino masses,
on charged lepton flavour violating observables. In particular, we have focused
on the loop induced decays of the Z boson into two leptons of different
flavour. We have performed a numerical study of the rates predicted for these
processes within the Inverse Seesaw model, specifically considering scenarios
where $ \mu -e $ transitions are suppressed. Our conclusion, after comparison
with the most relevant experimental constraints, is that branching ratios as
large as $ 10^{-7} $ can be predicted in the $ \tau -\mu $ or $ \tau -e $
channels, together with heavy neutrinos having masses of the TeV order. Such
rates could be accessible at next generation colliders.


  The time delays of gravitationally lensed quasars are generally believed to
be unique numbers whose measurement is limited only by the quality of the light
curves and the models for the contaminating contribution of gravitational
microlensing to the light curves. This belief is incorrect -- gravitational
microlensing also produces changes in the actual time delays on the ~day(s)
light-crossing time scale of the emission region. This is due to a combination
of the inclination of the disk relative to the line of sight and the
differential magnification of the temperature fluctuations producing the
variability. We demonstrate this both mathematically and with direct
calculations using microlensing magnification patterns. Measuring these delay
fluctuations can provide a physical scale for microlensing observations,
removing the need for priors on either the microlens masses or the component
velocities. That time delays in lensed quasars are themselves time variable
likely explains why repeated delay measurements of individual lensed quasars
appear to vary by more than their estimated uncertainties. This effect is also
an important new systematic problem for attempts to use time delays in lensed
quasars for cosmology or to detect substructures (satellites) in lens galaxies.


  We calculate the quantum heat generation, the interaction force and the
frictional torque for two rotating spherical nanoparticles with a radius $R$.
In contrast to the static case, when there is an upper limit in the radiative
heat transfer between the particles, for two rotating nanoparticles the quantum
heat generation rate diverges when the angular velocity becomes equal to the
poles in the photon emission rate. These poles arise for the separation $d
<d_0= R(3/\varepsilon''(\omega_0))^{1/3}$ (where $\varepsilon''(\omega_0)$ is
the imaginary part of the dielectric function for the particle material at the
surface phonon or plasmon polariton frequency $\omega_0$ ) due to the anomalous
Doppler effect and the mutual polarization of the particles and they exist even
for the particles with losses. Similar singularities exist also for the
interaction force and the frictional torque. The obtained results can be
important for biomedical applications.


  In this Letter we investigate the role of recombination energy during a
common envelope event. We confirm that taking this energy into account helps to
avoid the formation of the circumbinary envelope commonly found in previous
studies. For the first time, we can model a complete common envelope event,
with a clean compact double white dwarf binary system formed at the end. The
resulting binary orbit is almost perfectly circular. In addition to considering
recombination energy, we also show that between 1/4 and 1/2 of the released
orbital energy is taken away by the ejected material. We apply this new method
to the case of the double-white dwarf system WD 1101+364, and we find that the
progenitor system at the start of the common envelope event consisted of a
$\sim1.5M_\odot$ red giant star in a $\sim 30$ day orbit with a white dwarf
companion.


  We consider the quantized enveloping algebra $U_q(\widehat{\mathfrak{sl}}_2)$
and its basic module $V(\Lambda_0)$. This module is infinite-dimensional,
irreducible, integrable, and highest-weight. We describe $V(\Lambda_0)$ using a
$q$-shuffle algebra in the following way. Start with the free associative
algebra $\mathbb V$ on two generators $x,y$. The standard basis for $\mathbb V$
consists of the words in $x,y$. In 1995 M. Rosso introduced an associative
algebra structure on $\mathbb V$, called a $q$-shuffle algebra. For $u,v\in
\lbrace x,y\rbrace$ their $q$-shuffle product is $u\star v = uv+q^{(u,v)}vu$,
where $( u,v) =2$ (resp. $(u,v) =-2$) if $u=v$ (resp.
  $u\not=v$).
  Let $\mathbb U$ denote the subalgebra of the $q$-shuffle algebra $\mathbb V$
  that is generated by $x, y$. Rosso showed that the algebra $\mathbb U$ is
isomorphic to the positive part of $U_q(\widehat{\mathfrak{sl}}_2)$.
  In our first main result, we turn $\mathbb U$ into a
$U_q(\widehat{\mathfrak{sl}}_2)$-module. Let $\bf U$ denote the
$U_q(\widehat{\mathfrak{sl}}_2)$-submodule of $\mathbb U$ generated by the
empty word. In our second main result, we show that the
$U_q(\widehat{\mathfrak{sl}}_2)$-modules $\bf U$ and $V(\Lambda_0)$ are
isomorphic. Let $\bf V$ denote the subspace of $\mathbb V$ spanned by the words
that do not begin with $y$ or $xx$. In our third main result, we show that $\bf
U = \mathbb U \cap {\bf V}$.


  A new cosmological model leads to testable predictions that are different
from those of both standard cosmology and models with a cosmological constant.
The prediction that q_0=0 is the same as in other ``coasting universe'' models,
but arises without the need for any exotic form of matter or other ad hoc
assumptions.


  During Phase-2 of the LHC, known as the High Luminosity LHC (HL-LHC), the
accelerator will increase its instantaneous luminosity to 5 $\times$ 10$^{34}$
cm$^{-2}$ s$^{-1}$, delivering an integrated luminosity of 3000 fb$^{-1}$ over
10 years of operation starting from 2027. In view of the HL-LHC, the CMS muon
system will be upgraded to sustain efficient muon triggering and reconstruction
performance. Resistive Plate Chambers (RPCs) serve as dedicated detectors for
muon triggering due to their excellent timing resolution, and will extend
$|\eta|$ (pseudorapidity) up to a region of 2.4. Before Long Shutdown 3 (LS3),
the RE3/1 and RE4/1 stations of the endcap will be equipped with new improved
Resistive Plate Chambers (iRPCs) having different design and geometry than the
present RPC system. The iRPC geometry configuration improves the detector's
rate capability and its ability to survive the harsh background conditions of
the HL-LHC. Also, new electronics equipped with excellent timing precision
measurements with a resolution of less than 150 ps are developed to readout the
RPC detectors from both sides of the strips to allow for good spatial
resolution along them. The performance of the iRPC has been studied with gamma
radiation at the Gamma Irradiation Facility (GIF++) at CERN. Ongoing longevity
studies will help to certify the iRPCs for the HL-LHC running period. The main
detector parameters such as the currents, rate and resistivity are regularly
monitored as a function of the integrated charge. Preliminary results of the
detector performance will be presented.


  We propose a new scheme for realizing nonlocal nondegenerate optical
parametric amplifier by means of genuine four-mode entanglement. The
nondegenerate optical parametric amplifier is regarded as a unitary
transformation from two input fields to two outputs. Two inputs and two outputs
are located at the remote stations respectively. Employing off-line four-mode
entanglement, homodyne detection, classical communication and local
displacement, the nonlocal nondegenerate optical parametric amplifier can be
achieved. This scheme can be implemented with a setup that is experimentally
accessible at present.


  Synthesis of the biological "energy currency molecule" adenosine triphosphate
ATP is accomplished by FoF1-ATP synthase. In the plasma membrane of Escherichia
coli, proton-driven rotation of a ring of 10 c subunits in the Fo motor powers
catalysis in the F1 motor. While F1 uses 120 degree stepping, Fo models predict
a step-by-step rotation of c subunits 36 degree at a time, which is here
demonstrated by single-molecule fluorescence resonance energy transfer.


  A remarkable result of Stanley shows that the set of maximal chains in the
non-crossing partition lattice of type $A$ is Schur-positive, where descents
are defined by a distinguished edge labeling. A bijection between these chains
and labeled trees was presented by Goulden and Yong. Using Adin-Roichman's
variant of Bj\"orner's $EL$-labeling, we show that the subset of maximal chains
in the non-crossing partition lattice of type $A$, whose underlying tree is a
convex caterpillar, is Schur-positive.


  We demonstrate how to model the toppling activity in avalanching systems by
stochastic differential equations (SDEs). The theory is developed as a
generalization of the classical mean field approach to sandpile dynamics by
formulating it as a generalization of Itoh's SDE. This equation contains a
fractional Gaussian noise term representing the branching of an avalanche into
small active clusters, and a drift term reflecting the tendency for small
avalanches to grow and large avalanches to be constricted by the finite system
size. If one defines avalanching to take place when the toppling activity
exceeds a certain threshold the stochastic model allows us to compute the
avalanche exponents in the continum limit as functions of the Hurst exponent of
the noise. The results are found to agree well with numerical simulations in
the Bak-Tang-Wiesenfeld and Zhang sandpile models. The stochastic model also
provides a method for computing the probability density functions of the
fluctuations in the toppling activity itself. We show that the sandpiles do not
belong to the class of phenomena giving rise to universal non-Gaussian
probability density functions for the global activity. Moreover, we demonstrate
essential differences between the fluctuations of total kinetic energy in a
two-dimensional turbulence simulation and the toppling activity in sandpiles.


  We define some formal moduli space of quasi-isogenies of isoclinic
$p$-divisible groups with a non-reductive group as the "structure group". We
then formulate new Arithmetic Fundamental Lemma conjectures for Bessel
subgroups in the context of the arithmetic Gan-Gross-Prasad conjectures. Some
(very limited) evidence is presented.


  We have numerically investigated the dynamics of vortices in a clean layered
superconductor placed in a perpendicular magnetic field. We describe the
energetics using a Ginzburg-Landau free energy functional in the lowest Landau
level approximation. The dynamics are determined using the time-dependent
Ginzburg-Landau approximation, and thermal fluctuations are incorporated via a
Langevin term. The c-axis conductivity at nonzero frequencies, as calculated
from the Kubo formalism, shows a strong but not divergent increase as the
melting temperature $T_M$ is approached from above, followed by an apparently
discontinuous drop at the vortex lattice freezing temperature. The
discontinuity is consistent with the occurrence of a first-order freezing. The
calculated equilibrium properties agree with previous Monte Carlo studies using
the same Hamiltonian. We briefly discuss the possibility of detecting this
fluctuation conductivity experimentally.


  We show that complex, massive spin-1 fields minimally coupled to Einstein's
gravity with a negative cosmological constant, admit asymptotically anti-de
Sitter self-gravitating solutions. Focusing on 4-dimensional spacetimes, we
start by obtaining analytical solutions in the test-field limit, where the
Proca field equations can be solved in a fixed anti-de Sitter background, and
then find fully non-linear solutions numerically. These solutions are a natural
extension of the recently found asymptotically flat Proca stars and share
similar properties with scalar boson stars. In particular, we show that they
are stable against spherically symmetric linear perturbations for a range of
fundamental frequencies limited by their point of maximum mass. We finish with
an overview of the behavior of Proca stars in $5$ dimensions.


  In this article, spherically symmetric thin-shell wormholes supported by a
generalized Chaplygin gas are constructed and their stability under
perturbations preserving the symmetry is studied. Wormholes with charge and
with a cosmological constant are analyzed and the results are compared with
those obtained for the original Chaplygin gas, which was considered in a
previous work. For some values of the parameters, one stable configuration is
also present and a new extra unstable solution is found.


  The importance of inference in Machine Learning (ML) has led to an explosive
number of different proposals in ML, and particularly in Deep Learning. In an
attempt to reduce the complexity of Convolutional Neural Networks, we propose a
Volterra filter-inspired Network architecture. This architecture introduces
controlled non-linearities in the form of interactions between the delayed
input samples of data. We propose a cascaded implementation of Volterra
Filtering so as to significantly reduce the number of parameters required to
carry out the same classification task as that of a conventional Neural
Network. We demonstrate an efficient parallel implementation of this Volterra
Neural Network (VNN), along with its remarkable performance while retaining a
relatively simpler and potentially more tractable structure. Furthermore, we
show a rather sophisticated adaptation of this network to nonlinearly fuse the
RGB (spatial) information and the Optical Flow (temporal) information of a
video sequence for action recognition. The proposed approach is evaluated on
UCF-101 and HMDB-51 datasets for action recognition, and is shown to outperform
state of the art CNN approaches.


  Future intelligent autonomous systems (IAS) are inevitably deciding on moral
and legal questions, e.g. in self-driving cars, health care or human-machine
collaboration. As decision processes in most modern sub-symbolic IAS are
hidden, the simple political plea for transparency, accountability and
governance falls short. A sound ecosystem of trust requires ways for IAS to
autonomously justify their actions, that is, to learn giving and taking reasons
for their decisions. Building on social reasoning models in moral psychology
and legal philosophy such an idea of >>Reasonable Machines<< requires novel,
hybrid reasoning tools, ethico-legal ontologies and associated argumentation
technology. Enabling machines to normative communication creates trust and
opens new dimensions of AI application and human-machine interaction.
  Keywords: Trusthworthy and Explainable AI, Ethico-Legal Governors, Social
Reasoning Model, Pluralistic and Expressive Normative Reasoning


  The effect of radiation polarization attended with the motion of spinning
charge in the magnetic field could be viewed through the classical theory of
self-interaction. The quantum expression for the polarization time follows from
the semiclassical relation $T_{QED}\sim \hbar c^{3}/\mu_{B}^2\omega_{c}^3$, and
needs quantum explanation neither for the orbit nor for the spin motion. In our
approach the polarization emerges as a result of natural selection in the
ensenmble of elastically scattered electrons among which the group of particles
that bear their spins in the 'right' directions has the smaller probability of
radiation. The evidence of non-complete polarization degree is also obtained.


  The Horndeski theory of gravity is known as the most general scalar-tensor
theory with second-order field equations. Recently, it was demonstrated by
Gleyzes et al. that the Horndeski theory can further be generalized in such a
way that although field equations are of third order, the number of propagating
degrees of freedom remains the same. We study small-scale gravity in the
generalized Horndeski theory, focusing in particular on an impact of the new
derivative interaction beyond Horndeski on the Vainshtein screening mechanism.
In the absence of the quintic galileon term and its generalization, we show
that the new interaction does not change the qualitative behavior of gravity
outside and near the source: the two metric potentials coincide, $\Phi = \Psi
\;(\sim r^{-1})$, while the gravitational coupling is given by the cosmological
one and hence is time-dependent in general. We find, however, that the
gravitational field inside the source shows a novel behavior due to the
interaction beyond Horndeski: the gravitational attraction is not determined
solely from the enclosed mass and two potentials do not coincide, indicating
breaking of the screening mechanism.


  We discuss N=2 SU(2) Yang-Mills gauge theories coupled with N_f (=2,3)
massive hypermultiplets in the weak coupling limit. We determine the exact
massive prepotentials and the monodromy matrices around the weak coupling
limit. We also study that the double scaling limit of these massive theories
and find that the massive N_f -1 theory can be obtained from the massive N_f
theory. New formulae for the massive prepotentials and the monodromy matrices
are proposed. In these formulae, N_f dependences are clarified.


  We present the analysis result of a gravitational binary-lensing event
OGLE-2005-BLG-018. The light curve of the event is characterized by 2 adjacent
strong features and a single weak feature separated from the strong features.
The light curve exhibits noticeable deviations from the best-fit model based on
standard binary parameters. To explain the deviation, we test models including
various higher-order effects of the motions of the observer, source, and lens.
From this, we find that it is necessary to account for the orbital motion of
the lens in describing the light curve. From modeling of the light curve
considering the parallax effect and Keplerian orbital motion, we are able to
measure not only the physical parameters but also a complete orbital solution
of the lens system. It is found that the event was produced by a binary lens
located in the Galactic bulge with a distance $6.7\pm 0.3$ kpc from the Earth.
The individual lens components with masses $0.9\pm 0.3\ M_\odot$ and $0.5\pm
0.1\ M_\odot$ are separated with a semi-major axis of $a=2.5 \pm 1.0$ AU and
orbiting each other with a period $P=3.1 \pm 1.3$ yr. The event demonstrates
that it is possible to extract detailed information about binary lens systems
from well-resolved lensing light curves.


  We consider a class of stochastic control problems where the state process is
a probability measure-valued process satisfying an additional martingale
condition on its dynamics, called measure-valued martingales (MVMs). We
establish the `classical' results of stochastic control for these problems:
specifically, we prove that the value function for the problem can be
characterised as the unique solution to the Hamilton-Jacobi-Bellman equation in
the sense of viscosity solutions. In order to prove this result, we exploit
structural properties of the MVM processes. Our results also include an
appropriate version of It\^o's lemma for controlled MVMs. We also show how
problems of this type arise in a number of applications, including
model-independent derivatives pricing, the optimal Skorokhod embedding problem,
and two player games with asymmetric information.


  We develop a theoretical basis for understanding the spin relaxation
processes in Kondo lattice systems with heavy fermions as experimentally
observed by electron spin resonance (ESR). The Kondo effect leads to a common
energy scale that regulates a logarithmic divergence of different spin kinetic
coefficients and supports a collective spin motion of the Kondo ions with
conduction electrons. We find that the relaxation rate of a collective spin
mode is greatly reduced due to a mutual cancelation of all the divergent
contributions even in the case of the strongly anisotropic Kondo interaction.
The contribution to the ESR linewidth caused by the local magnetic field
distribution is subject to motional narrowing supported by ferromagnetic
correlations. The developed theoretical model successfully explains the ESR
data of YbRh2Si2 in terms of their dependence on temperature and magnetic
field.


  We use quasiclassical methods of superconductivity to study the
superconducting proximity effect from a topological $p$-wave superconductor
into a disordered one-dimensional metallic wire. We demonstrate that the
corresponding Eilenberger equations with disorder reduce to a closed non-linear
equation for the superconducting component of the matrix Green's function.
Remarkably, this equation is formally equivalent to a classical mechanical
system (i.e., Newton's equations), with the Green function corresponding to a
coordinate of a fictitious particle and the coordinate along the wire
corresponding to time. This mapping allows to obtain exact solutions in the
disordered nanowire in terms of elliptic functions. A surprising result that
comes out of this solution is that the $p$-wave superconductivity
proximity-induced into the disordered metal remains long-range, decaying as
slowly as the conventional $s$-wave superconductivity. It is also shown that
impurity scattering leads to the appearance of a zero-energy peak.


  We propose and study a quantum pump which emulates a traditional paddlewheel,
that can be implemented with ultracold atoms in waveguides. We use wavepacket
propagation to study its single-mode dynamics, which also determines its
multimode current for mesoscopic setups. Energy flow with or without particle
transport is possible. The spectrum reveals unusual features such as nonuniform
Floquet side-bands and counter-intuitive scattering. Explanations are found by
examining the scattering dynamics comparatively using quantum, classical and
semiclassical pictures, indicating a rich system and experimentally accessible
method to explore quantum versus classical dynamics.


  We construct a semiclassical theory for the transport of topological
junctions starting from a microscopic Hamiltonian that comprehensively includes
the interplay among the Majorana qubit, the Josephson phase, and the
dissipation process. With the path integral approach, we derive a set of
semiclassical equations of motion that can be used to calculate the time
evolution of the Josephson phase and the Majorana qubit. In the equations we
reveal rich dynamical phenomena such as the qubit induced charge pumping, the
effective spin-orbit torque, and the Gilbert damping. We demonstrate the
influence of these dynamical phenomena on the transport signatures of the
junction. We apply the theory to study the Shapiro steps of the junction, and
find the suppression of the first Shapiro step due to the dynamical feedback of
the Majorana qubit.


  In this paper,based on the available mathematical works on geometry and
topology of hyperbolic manifolds and discrete groups, some results of Freedman
et al (hep-th/9804058) are reproduced and broadly generalized. Among many new
results the possibility of extension of work of Belavin, Polyakov and
Zamolodchikov to higher dimensions is investigated. Known in physical
literature objections against such extension are removed and the possibility of
an extension is convincingly demonstrated.


  We investigate the distribution of eigenvalues of the weighted Laplacian on
closed weighted Riemannian manifolds of nonnegative Bakry-\'Emery Ricci
curvature. We derive some universal inequalities among eigenvalues of the
weighted Laplacian on such manifolds. These inequalities are quantitative
versions of the previous theorem by the author with Shioya. We also study some
geometric quantity, called multi-way isoperimetric constants, on such manifolds
and obtain similar universal inequalities among them. Multi-way isoperimetric
constants are generalizations of the Cheeger constant. Extending and following
the heat semigroup argument by Ledoux and E. Milman, we extend the Buser-Ledoux
result to the $k$-th eigenvalue and the $k$-way isoperimetric constant. As a
consequence the $k$-th eigenvalue of the weighted Laplacian and the $k$-way
isoperimetric constant are equivalent up to polynomials of $k$ on closed
weighted manifolds of nonnegative Bakry-\'Emery Ricci curvature.


  Considering the constraints from the experimental data on $\mu\rightarrow
e\gamma$, $\mu\rightarrow3e$, $\mu-e$ conversion etc., we analyze the Lepton
Flavor Violating decays $\phi(J/\Psi,\Upsilon(1S)) \rightarrow
e^+\mu^-(\mu^+\tau^-)$ in the scenarios of the minimal supersymmetric
extensions of Standard Model with seesaw Mechanism. Numerically, there is
parameter space that the LFV processes of
$J/\Psi(\Upsilon)\rightarrow\mu^+\tau^-$ can reach the upper experimental
bounds, meanwhile the theoretical predictions on $\mu\rightarrow e\gamma$,
$\mu\rightarrow3e$, $\mu-e$ conversion satisfy the present experimental bounds.
For searching of new physics, Lepton Flavor Violating processes
$J/\Psi(\Upsilon)\rightarrow\mu^+\tau^-$ may be more promising and effective
channels.


  In two recent articles [PRL 90, 026802 (2003); PRB 69, 085307 (2004)], we
developed a transport theory for an extended tunnel junction between two
interacting fractional-quantum-Hall edge channels, obtaining analytical results
for the conductance. Ponomarenko and Averin (PA) have expressed disagreement
with our theoretical approach and question the validity of our results
(cond-mat/0602532). Here we show why PA's critique is unwarranted.


  We measure the non-axisymmetry in the luminosity distribution in the inner
few kpc of the remnants of advanced mergers of galaxies with a view to
understand the relaxation in the central regions. For this, we analyze the
images from the 2MASS archival data for a selected sample of 12 merging
galaxies, which show signs of interaction but have a single nucleus. The
central regions are fitted by elliptical isophotes whose centres are allowed to
vary to get the best fit. The centres of isophotes show a striking sloshing
pattern with a spatial variation of up to 20-30 % within the central 1 kpc.
This indicates mass asymmetry and a dynamically unrelaxed behaviour. Next, we
Fourier-analyze the galaxy images while keeping the centre constant and measure
the deviation from axisymmetry in terms of the fractional Fourier amplitudes
(A_1, A_2 etc) as a function of radius. All mergers show a high value of
lopsidedness (upto A_1 ~ 0.2) in the central 5 kpc. The m=2 asymmetry is even
stronger, with values of A_2 upto ~ 0.3, and in three cases these are shown to
represent bars. The corresponding values denoting non-axisymmetry in inner
regions of a control sample of eight non-merger galaxies are found to be
several times smaller. Surprisingly, this central asymmetry is seen even in
mergers where the outer regions have relaxed into a smooth elliptical-like
r^{1/4} profile or a spiral-like exponential profile. Thus the central
asymmetry is long-lived, estimated to be ~ 1 Gyr, and hence lasts for over 100
local dynamical timescales. These central asymmetries are expected to play a
key role in the future dynamical evolution of the central region of a merger,
and can help in feeding a central AGN.


  This is a review of the properties of 2d quantum quasiperiodic
antiferromagnets as reported in studies that have been carried out in the last
decade. Many results have been obtained for perfectly ordered as well as for
disordered two dimensional bipartite quasiperiodic tilings. The theoretical
methods used include spin wave theory, and renormalization group along with
Quantum Monte Carlo simulations. These methods all show that the ground state
of these unfrustrated antiferromagnets have N\'eel type order but with a highly
complex spatial distribution of local staggered magnetization. The ground state
properties, excitation energies and spatial dependence, structure factor, and
local susceptibilities are presented. The effects of introducing geometrical
disorder on the magnetic properties are discussed.


  Provably solving stochastic convex optimization problems with constraints is
essential for various problems in science, business, and statistics. Recently
proposed XOR-Stochastic Gradient Descent (XOR-SGD) provides a convergence rate
guarantee solving the constraints-free version of the problem by leveraging
XOR-Sampling. However, the task becomes more difficult when additional equality
and inequality constraints are needed to be satisfied. Here we propose XOR-PGD,
a novel algorithm based on Projected Gradient Descent (PGD) coupled with the
XOR sampler, which is guaranteed to solve the constrained stochastic convex
optimization problem still in linear convergence rate by choosing proper step
size. We show on both synthetic stochastic inventory management and real-world
road network design problems that the rate of constraints satisfaction of the
solutions optimized by XOR-PGD is $10\%$ more than the competing approaches in
a very large searching space. The improved XOR-PGD algorithm is demonstrated to
be more accurate and efficient than both XOR-SGD and SGD coupled with MCMC
based samplers. It is also shown to be more scalable with respect to the number
of samples and processor cores via experiments with large dimensions.


  Efficient molecular featurization is one of the major issues for machine
learning models in drug design. Here we propose persistent Ricci curvature
(PRC), in particular Ollivier persistent Ricci curvature (OPRC), for the
molecular featurization and feature engineering, for the first time. Filtration
process proposed in persistent homology is employed to generate a series of
nested molecular graphs. Persistence and variation of Ollivier Ricci curvatures
on these nested graphs are defined as Ollivier persistent Ricci curvature.
Moreover, persistent attributes, which are statistical and combinatorial
properties of OPRCs during the filtration process, are used as molecular
descriptors, and further combined with machine learning models, in particular,
gradient boosting tree (GBT). Our OPRC-GBT model is used in the prediction of
protein-ligand binding affinity, which is one of key steps in drug design.
Based on three most-commonly used datasets from the well-established
protein-ligand binding databank, i.e., PDBbind, we intensively test our model
and compare with existing models. It has been found that our model are better
than all machine learning models with traditional molecular descriptors.


  We revisit two classical problems: the determination of the law of the
underlying with respect to a risk-neutral measure on the basis of option
prices, and the pricing of options with convex payoffs in terms of prices of
call options with the same maturity (all options are European). The formulation
of both problems is expressed in a language loosely inspired by the theory of
inverse problems, and several proofs of the corresponding solutions are
provided that do not rely on any special assumptions on the law of the
underlying and that may, in some cases, extend results currently available in
the literature.


  In this Letter we present results from INTEGRAL and RXTE observations of the
spectral and timing behavior of the High Mass X-ray Binary A 0535+26 during its
August/September 2005 normal (type I) outburst with an average flux
F(5-100keV)~400mCrab. The search for cyclotron resonance scattering features
(fundamental and harmonic) is one major focus of the paper. Our analysis is
based on data from INTEGRAL and RXTE Target of Opportunity Observations
performed during the outburst. The pulse period is determined. X-ray pulse
profiles in different energy ranges are analyzed. The broad band INTEGRAL and
RXTE pulse phase averaged X-ray spectra are studied. The evolution of the
fundamental cyclotron line at different luminosities is analyzed. The pulse
period P is measured to be 103.39315(5)s at MJD 53614.5137. Two absorption
features are detected in the phase averaged spectra at E_1~45keV and
E_2~100keV. These can be interpreted as the fundamental cyclotron resonance
scattering feature and its first harmonic and therefore the magnetic field can
be estimated to be B~4x10^12G.


  Depthwise convolutions are widely used in lightweight convolutional neural
networks (CNNs). The performance of depthwise convolutions is mainly bounded by
the memory access rather than the arithmetic operations for classic
convolutions so that direct algorithms are often more efficient than indirect
ones (matrix multiplication-, Winograd-, and FFT-based convolutions) with
additional memory accesses. However, the existing direct implementations of
depthwise convolutions on ARMv8 architectures feature a bad trade-off between
register-level reuse of different tensors, which usually leads to sub-optimal
performance. In this paper, we propose new direct implementations of depthwise
convolutions by means of implicit padding, register tiling, etc., which contain
forward propagation, backward propagation and weight gradient update
procedures. Compared to the existing ones, our new implementations can incur
much less communication overhead between registers and cache. Experimental
results on two ARMv8 CPUs show that our implementations can averagely deliver
4.88x and 16.4x performance improvement over the existing direct ones in open
source libraries and matrix multiplications-based ones in Pytorch,
respectively.


  What happens to an autonomous vehicle (AV) if its data are adversarially
compromised? Prior security studies have addressed this question through mostly
unrealistic threat models, with limited practical relevance, such as white-box
adversarial learning or nanometer-scale laser aiming and spoofing. With growing
evidence that cyber threats pose real, imminent danger to AVs and
cyber-physical systems (CPS) in general, we present and evaluate a novel AV
threat model: a cyber-level attacker capable of disrupting sensor data but
lacking any situational awareness. We demonstrate that even though the attacker
has minimal knowledge and only access to raw data from a single sensor (i.e.,
LiDAR), she can design several attacks that critically compromise perception
and tracking in multi-sensor AVs. To mitigate vulnerabilities and advance
secure architectures in AVs, we introduce two improvements for security-aware
fusion: a probabilistic data-asymmetry monitor and a scalable track-to-track
fusion of 3D LiDAR and monocular detections (T2T-3DLM); we demonstrate that the
approaches significantly reduce attack effectiveness. To support objective
safety and security evaluations in AVs, we release our security evaluation
platform, AVsec, which is built on security-relevant metrics to benchmark AVs
on gold-standard longitudinal AV datasets and AV simulators.


  We consider accretion onto the white dwarfs in cataclysmic variables in
relation to nova eruptions, dwarf nova outbursts, hibernation and non-radial
oscillations.


  We discuss how confinement property of QCD results in the rational
unitarization scheme and how unitarity saturation leads to appearance of a
hadron liquid phase at very high temperatures.


  The electronic structure and magnetic properties of disordered
Fe$_{x}$Pd$_{100-x}$ alloys $(50 < x < 85)$ are investigated in the framework
of density functional theory using the full potential local orbital method
(FPLO). Disorder is treated in the coherent potential approximation (CPA). Our
calculations explain the experimental magnetization data. The origin of the
tetragonal distortion in the Fe-Pd magnetic shape memory alloys is found to be
a Jahn-Teller like effect which allows the system to reduce its band energy in
a narrow composition range. Prospects for an optimization of the alloys'
properties by adding third elements are discussed.


  This article addresses the problem of average consensus in a multi-agent
system when the desired consensus quantity is a time varying signal. Recently,
the EDCHO protocol leveraged high order sliding modes to achieve exact
consensus under a constrained set of initial conditions, limiting its
applicability to static networks. In this work, we propose REDCHO, an extension
of the previous protocol which is robust to mismatch in the initial conditions,
making it suitable to use cases in which connection and disconnection of agents
is possible. The convergence properties of the protocol are formally explored.
Finally, the effectiveness and advantages of our proposal are shown with
concrete simulation examples showing the benefits of REDCHO against other
methods in the literature.


  We propose a novel data-driven approach for analyzing synchrotron Laue X-ray
microdiffraction scans based on machine learning algorithms. The basic
architecture and major components of the method are formulated mathematically.
We demonstrate it through typical examples including polycrystalline BaTiO$_3$,
multiphase transforming alloys and finely twinned martensite. The computational
pipeline is implemented for beamline 12.3.2 at the Advanced Light Source,
Lawrence Berkeley National Lab. The conventional analytical pathway for X-ray
diffraction scans is based on a slow pattern by pattern crystal indexing
process. This work provides a new way for analyzing X-ray diffraction 2D
patterns, independent of the indexing process, and motivates further studies of
X-ray diffraction patterns from the machine learning prospective for the
development of suitable feature extraction, clustering and labeling algorithms.


  Most idealized studies of stratified shear instabilities assume that the
shear interface and the buoyancy interface are coincident. We discuss the role
of asymmetry on the evolution of shear instabilities. Using linear stability
theory and direct numerical simulations, we show that asymmetric shear
instabilities exhibit features of both Holmboe and Kelvin-Helmholtz (KH)
instabilities, and develop a framework to determine whether the instabilities
are more Holmboe-like or more KH-like. Further, the asymmetric instabilities
produce asymmetric mixing that exhibits features of both overturning and
scouring flows and that tends to realign the shear and buoyancy interfaces. In
all but the symmetric KH simulations, we observe a collapse in the distribution
of gradient Richardson number ($Ri_g$), suggesting that asymmetry reduces the
parameter dependence of KH-driven mixing events. The observed dependence of the
turbulent dynamics on small-scale details of the shear and stratification has
important implications for the interpretation of oceanographic data.


  We define an interesting class of semigroups of operators in Banach spaces,
namely, the randomly generated semigroups. This class contains as a remarkable
subclass a special type of quantum dynamical semigroups introduced by
Kossakowski in the early 1970s. Each randomly generated semigroup is
associated, in a natural way, with a pair formed by a representation or an
antirepresentation of a locally compact group in a Banach space and by a
convolution semigroup of probability measures on this group. Examples of
randomly generated semigroups having important applications in physics are
briefly illustrated.


  This manuscript presents a new framework towards automated digital
documentation and progress reporting of mechanical pipes in building
construction projects, using smartphones. New methods were proposed to optimize
video frame rate to achieve a desired image overlap; define metric scale for 3D
reconstruction; extract pipes from point clouds; and classify pipes according
to their planned bill of quantity radii. The effectiveness of the proposed
methods in both laboratory (six pipes) and construction site (58 pipes)
conditions was evaluated. It was observed that the proposed metric scale
definition achieved sub-millimeter pipe radius estimation accuracy. Both
laboratory and field experiments revealed that increasing the defined image
overlap improved point cloud quality, pipe classification quality, and pipe
radius/length estimation. Overall, it was found possible to achieve pipe
classification F-measure, radius estimation accuracy, and length estimation
percent error of 96.4%, 5.4mm, and 5.0%, respectively, on construction sites
using at least 95% image overlap.


  Controlling magnetism and spin structures in strongly correlated systems by
using electric field is of fundamental importance but challenging. Here, a
high-spin ruthenate phase is achieved via a solid ionic chemical junction at
SrRuO3/SrTiO3 interface with distinct formation energies and diffusion barriers
of oxygen vacancies, analogue to electronic band alignment in semiconductor
heterojunction. Oxygen vacancies trapped within this interfacial SrRuO3
reconstruct Ru-4d electronic structure and orbital occupancy, leading to an
enhanced magnetic moment. Furthermore, an interfacial magnetic phase can be
switched reversibly by electric-field-rectifying oxygen migration in a
solid-state ionic gating device, providing a framework for atomic design of
functionalities in strongly correlated oxides using a way of solid chemistry.


  Here we report our recent study on the spectral energy distribution (SED) of
the high frequency BL Lac object Mrk 421 in different luminosity states. We
used a full-fledged chi2-minimization procedure instead of more commonly used
"eyeball" fit to model the observed flux of the source (from optical to very
high energy), with a Synchrotron-Self-Compton (SSC) emission mechanism. Our
study shows that the synchrotron power and peak frequency remain constant with
varying source activity, and the magnetic field decreases with the source
activity while the break energy of electron spectrum and the Doppler factor
increase. Since a lower magnetic field and higher density of electrons result
in increased electron-photon scattering efficiency, the Compton power
increases, so does the total emission.


  We develop the first stochastic incremental method for calculating the
Moore-Penrose pseudoinverse of a real matrix. By leveraging three alternative
characterizations of pseudoinverse matrices, we design three methods for
calculating the pseudoinverse: two general purpose methods and one specialized
to symmetric matrices. The two general purpose methods are proven to converge
linearly to the pseudoinverse of any given matrix. For calculating the
pseudoinverse of full rank matrices we present two additional specialized
methods which enjoy a faster convergence rate than the general purpose methods.
We also indicate how to develop randomized methods for calculating approximate
range space projections, a much needed tool in inexact Newton type methods or
quadratic solvers when linear constraints are present. Finally, we present
numerical experiments of our general purpose methods for calculating
pseudoinverses and show that our methods greatly outperform the Newton-Schulz
method on large dimensional matrices.


  Tensor algebra lies at the core of computational science and machine
learning. Due to its high usage, entire libraries exist dedicated to improving
its performance. Conventional tensor algebra performance boosts focus on
algorithmic optimizations, which in turn lead to incremental improvements. In
this paper, we describe a method to accelerate tensor algebra a different way:
by outsourcing operations to an optical microchip. We outline a numerical
programming language developed to perform tensor algebra computations that is
designed to leverage our optical hardware's full potential. We introduce the
language's current grammar and go over the compiler design. We then show a new
way to store sparse rank-n tensors in RAM that outperforms conventional array
storage (used by C++, Java, etc.). This method is more memory-efficient than
Compressed Sparse Fiber (CSF) format and is specifically tuned for our optical
hardware. Finally, we show how the scalar-tensor product, rank-$n$ Kronecker
product, tensor dot product, Khatri-Rao product, face-splitting product, and
vector cross product can be compiled into operations native to our optical
microchip through various tensor decompositions.


  All existing transformer-based approaches to NLP using subword tokenisation
algorithms encode whitespace (word boundary information) through the use of
special space symbols (such as \#\# or \_) forming part of tokens. These
symbols have been shown to a) lead to reduced morphological validity of
tokenisations, and b) give substantial vocabulary redundancy. As such, removing
these symbols has been shown to have a beneficial effect on the processing of
morphologically complex words for transformer encoders in the pretrain-finetune
paradigm. In this work, we explore whether word boundary information is at all
useful to such models. In particular, we train transformer encoders across four
different training scales, and investigate several alternative approaches to
including word boundary information, evaluating on a range of tasks across
different domains and problem set-ups: GLUE (for sentence-level
classification), NER (for token-level classification), and two classification
datasets involving complex words (Superbizarre and FLOTA). Overall, through an
extensive experimental setup that includes the pre-training of 29 models, we
find no substantial improvements from our alternative approaches, suggesting
that modifying tokenisers to remove word boundary information isn't leading to
a loss of useful information.


  The Poisson equation on manifolds plays an fundamental role in many
applications. Recently, we proposed a novel numerical method called the Point
Integral method (PIM) to solve the Poisson equations on manifolds from point
clouds. In this paper, we prove the convergence of the point integral method
for solving the Poisson equation with the Dirichlet boundary condition.


  The role of the top quark in the Standard Model predictions for electroweak
precision observables is reviewed and the implications of the experimental data
for the indirect determination of the top mass range is discussed.


  We investigate the dynamics of spin glasses from the `rheological' point of
view, in which aging is suppressed by the action of small, non-conservative
forces. The different features can be expressed in terms of the scaling of
relaxation times with the magnitude of the driving force, which plays the role
of the critical parameter. Stated in these terms, ultrametricity loses much of
its mystery and can be checked rather easily. This approach also seems a
natural starting point to investigate what would be the real-space structures
underlying the hierarchy of time scales. We study in detail the appearance of
this many-scale behavior in a mean-field model, in which dynamic ultrametricity
is clearly present. A similar analysis is performed on numerical results
obtained for a 3D spin glass: In that case, our results are compatible with
either that dynamic ultrametricity is absent or that it develops so slowly that
even in experimental time-windows it is still hardly observable.


  We present preliminary results for the masses and decay constants of the
$\eta$ and $\eta^\prime$ mesons using CLS $N_f = 2+1$ ensembles. One of the
major challenges in these calculations are the large statistical fluctuations
due to disconnected quark loops. We tackle these by employing a combination of
noise reduction techniques which are tuned to minimize the statistical error at
a fixed cost. On the analysis side we carefully assess excited states
contributions by using a direct fit approach.


  We present a detailed analysis of the star formation history (SFH) of three
fields in M33 located ~ 4 - 6 visual scale lengths from its nucleus. These
fields were imaged with the Advanced Camera for Surveys on the Hubble Space
Telescope and reach ~ 2.5 magnitudes below the red clump of core helium burning
stars. The observed color-magnitude diagrams are modeled as linear combinations
of individual synthetic populations with different ages and metallicities. To
gain a better understanding of the systematic errors we have conducted the
analysis with two different sets of stellar evolutionary tracks which we
designate as Padova (Girardi et al. 2000) and Teramo (Pietrinferni et al.
2004). The precise details of the results depend on which tracks are used but
we can make several conclusions that are fairly robust despite the differences.
Both sets of tracks predict the mean age to increase and the mean metallicity
to decrease with radius. Allowing age and metallicity to be free parameters and
assuming star formation began ~ 14 Gyr ago, we find that the mean age of all
stars and stellar remnants increases from ~ 6 Gyr to ~ 8 Gyr and the mean
global metallicity decreases from ~ -0.7 to ~ -0.9. The fraction of stars
formed by 4.5 Gyr ago increases from ~ 65% to ~ 80%. The mean star formation
rate 80 - 800 Myr ago decreases from ~ 30% of the lifetime average to just ~
5%. The random errors on these estimates are ~ 10%, 1.0 Gyr, and 0.1 dex. By
comparing the results of the two sets of stellar tracks for the real data and
for test populations with known SFH we have estimated the systematic errors to
be 15%, 1.0 Gyr, and 0.2 dex. These do not include uncertainties in the
bolometric corrections or variations in alpha-element abundance which deserve
future study.


  We give yet another proof of the list-color version of Brooks' theorem that
is due, independently, to Vizing and to Erd\H{o}s, Rubin and Taylor, via a
famous theorem of Dirac on chordal graphs.


  Time-resolved optical spectroscopy of collective and single-particle
excitations of 1T-TaS2 and 2H-TaSe2 reveals the presence of a large gap in the
excitation spectrum on the femtosecond timescale, associated with the formation
of various degrees of CDW order. In common with superconducting cuprates,
excitations with energies less than the full gap show much slower relaxation.
This separation of timescales cannot be explained in a quasi-2D Fermi-Liquid
picture with an anisotropic gap but rather suggests the formation of a
fluctuating spatially inhomogeneous state eventually forming a long-range
ordered state at low temperatures.


  This paper considers the problem of controlling the operation of
inverter-interfaced distributed energy resources (DERs) in a distribution grid,
to achieve operational and performance goals with limited system-level
information. We develop an online feedback optimization method to drive the
DERs' power setpoints to solutions of an AC optimal power flow (OPF) problem
based only on voltage measurements (and without requiring measurements of the
power consumption of non-controllable assets). The proposed method - grounded
on the theory of control barrier functions - is based on a continuous
approximation of the projected gradient flow, appropriately modified to
accommodate measurements from the power network. We provide results in terms of
local exponential stability, and assess the robustness to errors in the
measurements and in the system Jacobian matrix. We show that the proposed
method ensures anytime satisfaction of the voltage constraints when no model
and measurement errors are present; if these errors are present and are small,
the voltage violation is practically negligible. We also discuss extensions of
the framework to virtual power plant setups. Numerical experiments on a 93-bus
distribution system and with realistic load and production profiles show a
superior performance in terms of voltage regulation relative to existing
methods.


  To handle the different types of surface reconstruction tasks, we have
replicated as well as modified a few of reconstruction methods and have made
comparisons between the traditional method and data-driven method for
reconstruction the surface of an object with dense point cloud as input. On top
of that, we proposed a system using tightly-coupled SLAM as an input to
generate deskewed point cloud and odometry and a Truncated Signed Distance
Function based Surface Reconstruction Library. To get higher accuracy,
IMU(Inertial Measurement Unit) pre-integration and pose graph optimization are
conduct in the SLAM part. With the help of the Robot Operating System, we could
build a system containing those two parts, which can conduct a real-time
outdoor surface reconstruction.


  We demonstrate the coherent control and electrical readout of the nuclear
spins of ionized phosphorus donors in natural silicon. By combining pulsed
illumination with coherent electron spin manipulation, we selectively ionize
the donor depending on its nuclear spin state, exploiting a spin-dependent
recombination process via a spin pair at the Si/SiO2 interface. The
nuclear-spin coherence time of the ionized donor is 18 ms, two orders of
magnitude longer than in the neutral donor state, rendering the ionized donor a
potential resource as a quantum memory. The presented experimental techniques
allow for spectroscopy of ionized-donor nuclear spins, increase the sensitivity
of electrically detected electron nuclear double resonance by more than two
orders of magnitude, and give experimental access to the lifetime of parallel
electron spin pairs.


  We study critical points of $F(4)$ gauged supergravity in six dimensions
coupled to three vector multiplets. Scalar fields are described by
$\mathbb{R}^+\times \frac{SO(4,3)}{SO(4)\times SO(3)}$ coset space, and the
gauge group is given by $SO(3)_R\times SO(3)$ with $SO(3)_R$ being the
R-symmetry. The maximally supersymmetric critical point with all scalars
vanishing preserves the full $SO(3)_R\times SO(3)$ symmetry. This is dual to a
superconformal field theories (SCFT$_5$) arising from a near horizon geometry
of the D4-D8 brane system in type I$'$ theory with an enhanced global symmetry
$E_1\sim SU(2)$. Apart from this trivial critical point, we identify a new
supersymmetric critical point preserving the full supersymmetry with the
$SO(3)_R\times SO(3)$ symmetry broken to its diagonal subgroup. This critical
point should correspond to a new SCFT in five dimensions. We study an RG flow
solution interpolating between the SCFT with $E_1$ symmetry and the new
supersymmetric critical point. The flow describes a supersymmetric deformation
driven by a vacuum expectation value of relevant operators of dimension $3$. We
identify the dual operators with the mass terms for hypermultiplet scalars in
the dual field theory. The solution provides an example of analytic
supersymmetric RG flows in AdS$_6$/CFT$_5$ correspondence.


  We consider estimation of a functional of the data distribution based on
i.i.d. observations. We assume the target function can be defined as the
minimizer of the expectation of a loss function over a class of $d$-variate
real valued cadlag functions that have finite sectional variation norm. For all
$k=0,1,\ldots$, we define a $k$-th order smoothness class of functions as
$d$-variate functions on the unit cube for which each of a sequentially defined
$k$-th order Radon-Nikodym derivative w.r.t. Lebesgue measure is cadlag and of
bounded variation. For a target function in this $k$-th order smoothness class
we provide a representation of the target function as an infinite linear
combination of tensor products of $\leq k$-th order spline basis functions
indexed by a knot-point, where the lower (than $k$) order spline basis
functions are used to represent the function at the $0$-edges. The $L_1$-norm
of the coefficients represents the sum of the variation norms across all the
$k$-th order derivatives, which is called the $k$-th order sectional variation
norm of the target function. This generalizes the zero order spline
representation of cadlag functions with bounded sectional variation norm to
higher order smoothness classes. We use this $k$-th order spline representation
of a function to define the $k$-th order spline sieve minimum loss estimator
(MLE), Highly Adaptive Lasso (HAL) MLE, and Relax HAL-MLE. For first and higher
order smoothness classes, in this article we analyze these three classes of
estimators and establish pointwise asymptotic normality and uniform convergence
at dimension free rate $n^{-k^*/(2k^*+1)}$ up till a power of $\log n$
depending on the dimension, where $k^*=k+1$, assuming appropriate
undersmoothing is used in selecting the $L_1$-norm. We also establish
asymptotic linearity of plug-in estimators of pathwise differentiable features
of the target function.


  We investigate the clustering structure of species sampling sequences
$(\xi_n)_n$, with general base measure. Such sequences are exchangeable with a
species sampling random probability as directing measure. The clustering
properties of these sequences are interesting for Bayesian nonparametrics
applications, where mixed base measures are used, for example, to accommodate
sharp hypotheses in regression problems and provide sparsity. In this paper, we
prove a stochastic representation for $(\xi_n)_n$ in terms of a latent
exchangeable random partition. We provide explicit expression of the EPPF of
the partition generated by $(\xi_n)_n$ in terms of the EPPF of the latent
partition. We investigate the asymptotic behaviour of the total number of
blocks and of the number of blocks with fixed cardinality in the partition
generated by $(\xi_n)_n$.


  The origin of spin-orbit interaction of light at a conventional optical
interface lies in the transverse nature of the photon polarization: The
polarizations associated with the plane-wave components experience slightly
different rotations in order to satisfy the transversality after reflection or
refraction. Recent advances in topological photonic materials provide crucial
opportunities to reexamine the spin-orbit interaction of light at the unique
optical interface. Here, we establish a general model to describe the
spin-orbit interaction of light in the photonic Dirac metacrystal. We find a
giant photonic spin Hall effect near the Dirac points when a Gaussian beam
impinges at the interface of the photonic Dirac metacrystal. The giant photonic
spin Hall effect is attribute to the strong spin-orbit interaction of light,
which manifests itself as the large polarization rotations of different
plane-wave components. We believe that these results may provide insight into
the fundamental properties of the spin-orbit interaction of light in the
topological photonic systems.


  We have studied the magnetic field or disorder induced insulating and
metallic phases in amorphous Ta superconducting thin films. The evolution of
the nonlinear transport in the insulating phase exhibits a non-monotonic
behavior as the magnetic field is increased. We suggest that this observation
could be an evidence of the presence of localized Cooper pairs in the
insulating phase. As the metallic phase intervenes the superconducting and
insulating states in Ta films, this result further reveals that Cooper pairs
also exist in the metallic ground state.


  Online Bayesian bipartite matching is a central problem in digital
marketplaces and exchanges, including advertising, crowdsourcing, ridesharing,
and kidney exchange. We introduce a graph neural network (GNN) approach that
emulates the problem's combinatorially-complex optimal online algorithm, which
selects actions (e.g., which nodes to match) by computing each action's
value-to-go (VTG) -- the expected weight of the final matching if the algorithm
takes that action, then acts optimally in the future. We train a GNN to
estimate VTG and show empirically that this GNN returns high-weight matchings
across a variety of tasks. Moreover, we identify a common family of graph
distributions in spatial crowdsourcing applications, such as rideshare, under
which VTG can be efficiently approximated by aggregating information within
local neighborhoods in the graphs. This structure matches the local behavior of
GNNs, providing theoretical justification for our approach.


  This paper analyzes two modeling approaches for occupant behaviour in
buildings. It compares a purely statistical approach with a multi-agent social
simulation based approach. The study concerns the door openings in an office.


  We present a growth model for special Cosserat rods that allows for induced
rotation of cross-sections. The growth law considers two controls, one for
lengthwise growth and other for rotations. This is explored in greater detail
for straight rods with helical and hemitropic material symmetries by
introduction of a symmetry preserving growth to account for the microstructure.
The example of a guided-guided rod possessing a chiral microstructure is
considered to study its deformation due to growth. We show the occurrence of
growth induced out-of-plane buckling in such rods.


  We consider triangulations of closed surfaces in which every vertex is
incident to exactly $d$ edges.
  These triangulations can be identified with subgroups of the triangle group
$\langle a,b,c\mid a^2,b^2,c^2,(ab)^3,(ac)^2,(bc)^d\rangle$ that intersect
$\langle a,b\rangle$, $\langle a,c\rangle$, and $\langle b,c\rangle$ trivially.
  The term geodesic duality refers to an external symmetry introduced by Wilson
in 1979. Our main result is the characterisation of all subgroups corresponding
to geodesic self--dual regular triangulations, together with a complete
enumeration for $d < 10$.


  We present ALMA observations of cold dust and molecular gas in four
high-luminosity, heavily reddened (A$_{\rm{V}} \sim 2.5-6$ mag) Type 1 quasars
at $z\sim2.5$ with virial M$_{\rm{BH}} \sim 10^{10}$M$_\odot$, to test whether
dusty, massive quasars represent the evolutionary link between submillimetre
bright galaxies (SMGs) and unobscured quasars. All four quasars are detected in
both the dust continuum and in the $^{12}$CO(3-2) line. The mean dust mass is
6$\times$10$^{8}$M$_\odot$ assuming a typical high redshift quasar spectral
energy distribution (T=41K, $\beta$=1.95 or T=47K, $\beta$=1.6). The implied
star formation rates are very high - $\gtrsim$1000 M$_\odot$ yr$^{-1}$ in all
cases. Gas masses estimated from the CO line luminosities cover
$\sim$1-5$\times10^{10}$($\alpha_{\rm{CO}} / 0.8$)M$_\odot$ and the gas
depletion timescales are very short - $\sim5-20$Myr. A range of gas-to-dust
ratios is observed in the sample. We resolve the molecular gas in one quasar -
ULASJ2315$+$0143 ($z=2.561$) - which shows a strong velocity gradient over
$\sim$20 kpc. The velocity field is consistent with a rotationally supported
gas disk but other scenarios, e.g. mergers, cannot be ruled out at the current
resolution of these data. In another quasar - ULASJ1234+0907 ($z=2.503$) - we
detected molecular line emission from two millimetre bright galaxies within 200
kpc of the quasar, suggesting that this quasar resides in a significant
over-density. The high detection rate of both cold dust and molecular gas in
these sources, suggests that reddened quasars could correspond to an early
phase in massive galaxy formation associated with large gas reservoirs and
significant star formation.


  We consider the single-handed spinor field in interaction with its own
gravitational field described by the set of field equations given by Weyl field
equations written in terms of derivatives that are covariant with respect to
the gravitational connection plus Einstein field equations soured with the
energy tensor of the spinor: for the Weyl spinor and the ensuing spacetime of
Weyl-Lewis-Papapetrou structure, we will find all exact solutions. The obtained
solution for the metric tensor is that of a PP-wave spacetime while the spinor
field is a flag-dipole.


  We add the magnetic field axis to the holographic model for a doped
superconductor proposed by Kiritsis and Li. We explore the resulting
superconducting dome, in a particular region of parameters in which the
equations for the superconductor can be mapped into the previously known
undoped case.


  Automatic modulation classification (AMC) is an important task for modern
communication systems; however, it is a challenging problem when signal
features and precise models for generating each modulation may be unknown. We
present a new biologically-inspired AMC method without the need for models or
manually specified features --- thus removing the requirement for expert prior
knowledge. We accomplish this task using regularized stacked sparse denoising
autoencoders (SSDAs). Our method selects efficient classification features
directly from raw in-phase/quadrature (I/Q) radio signals in an unsupervised
manner. These features are then used to construct higher-complexity abstract
features which can be used for automatic modulation classification. We
demonstrate this process using a dataset generated with a software defined
radio, consisting of random input bits encoded in 100-sample segments of
various common digital radio modulations. Our results show correct
classification rates of > 99% at 7.5 dB signal-to-noise ratio (SNR) and > 92%
at 0 dB SNR in a 6-way classification test. Our experiments demonstrate a
dramatically new and broadly applicable mechanism for performing AMC and
related tasks without the need for expert-defined or modulation-specific signal
information.


  Language models excel at generating coherent text, and model compression
techniques such as knowledge distillation have enabled their use in
resource-constrained settings. However, these models can be biased in multiple
ways, including the unfounded association of male and female genders with
gender-neutral professions. Therefore, knowledge distillation without any
fairness constraints may preserve or exaggerate the teacher model's biases onto
the distilled model. To this end, we present a novel approach to mitigate
gender disparity in text generation by learning a fair model during knowledge
distillation. We propose two modifications to the base knowledge distillation
based on counterfactual role reversal$\unicode{x2014}$modifying teacher
probabilities and augmenting the training set. We evaluate gender polarity
across professions in open-ended text generated from the resulting distilled
and finetuned GPT$\unicode{x2012}$2 models and demonstrate a substantial
reduction in gender disparity with only a minor compromise in utility. Finally,
we observe that language models that reduce gender polarity in language
generation do not improve embedding fairness or downstream classification
fairness.


  Overlapped Speech Detection (OSD) is an important part of speech applications
involving analysis of multi-party conversations. However, most of existing OSD
systems are trained and evaluated on small datasets with limited application
domains, which led to the robustness of them lacks benchmark for evaluation and
the accuracy of them remains inadequate in realistic acoustic environments. To
solve these problem, we conduct a study of large-scale learning (LSL) in OSD
tasks and propose a new general OSD system named CF-OSD with LSL based on
Conformer network and LSL. In our study, a large-scale test set consisting of
151h labeled speech of different styles, languages and sound-source distances
is produced and used as a new benchmark for evaluating the generality of OSD
systems. Rigorous comparative experiments are designed and used to evaluate the
effectiveness of LSL in OSD tasks and define the OSD model of our general OSD
system. The experiment results show that LSL can significantly improve the
accuracy and robustness of OSD systems, and the CF-OSD with LSL system
significantly outperforms other OSD systems on our proposed benchmark.
Moreover, our system has also achieved state-of-the-art performance on existing
small dataset benchmarks, reaching 81.6\% and 53.8\% in the Alimeeting testset
and DIHARD II evaluation set, respectively.


  New type of nonlinear (anharmonic) excitations -- bushes of vibrational modes
-- in physical systems with point or space symmetry are discussed. All infrared
active and Raman active bushes for C60 fulerene are found by means of special
group-theoretical methods.


  We study the transition from the cholesteric phase to two TGB$_C$ phases near
the upper critical twist $k_{c2}$: the Renn-Lubensky TGB$_C$ phase, with layer
normal rotating in a plane perpendicular to the pitch axis, and the Bordeaux
TGB$_C$ phase, with the layer normal rotating on a cone parallel to the pitch
axis. We calculate properties, including order-parameter profiles, of both
phases.


  We present a statistical study of chromospheric evaporation in solar flares
using simultaneous observations by the RHESSI X-ray telescope and the IRIS UV
spectrograph. The results are compared with radiation hydrodynamic flare models
from the F-CHROMA RADYN database. For each event, we study spatially-resolved
Doppler shifts of spectral lines formed in the transition region
(C\,II\,1334.5\,{\AA}) and hot coronal plasma (Fe\,XXI\,1354.1\,{\AA}) to
investigate the dynamics of the solar atmosphere during the flare impulsive
phase. We estimate the energy fluxes deposited by high-energy electrons using
X-ray imaging spectroscopy and assuming the standard thick-target model. Using
the RADYN flare models, the RH 1.5D radiative transfer code and the Chianti
atomic line database, we calculate C\,II and Fe\,XXI line profiles and compare
with the observations. While the RADYN models predict a correlation between the
Doppler shifts and deposited energy flux for both lines, this was only observed
in the C II data. Several quantitative discrepancies are found between the
observations and models: the Fe\,XXI Doppler shifts are substantially stronger
in the models than in the data; the C\,II mean blueshifts are absent in the
observations but predicted by the models. The transition energy between
`gentle' and `explosive' evaporation regimes estimated from the observations
($2-8\times{}10^{9}$~erg~cm$^{-2}$~s$^{-1}$) and derived from the models
($2.2-10.1\times{}10^{9}$~erg~cm$^{-2}$~s$^{-1}$) are comparable with each
other. The results illustrate relationships among the processes of
chromospheric evaporation, response of the colder layers, and the flare energy
flux deposited by high-energy electrons, although demonstrating discrepancy
between analyzed observations and RADYN models.


  In this note we provide an explicit lower bound on the spectral gap of
one-dimensional Schr\"odinger operators with non-negative bounded potentials
and subject to Neumann boundary conditions.


  To govern smart contracts running on Ethereum, multiple Ethereum Request for
Comment (ERC) standards have been developed, each containing a set of rules to
guide the behaviors of smart contracts. Violating the ERC rules could cause
serious security issues and financial loss, signifying the importance of
verifying smart contracts follow ERCs. Today's practices of such verification
are to either manually audit each single contract or use expert-developed,
limited-scope program-analysis tools, both of which are far from being
effective in identifying ERC rule violations. This paper presents a tool named
AuditGPT that leverages large language models (LLMs) to automatically and
comprehensively verify ERC rules against smart contracts. To build AuditGPT, we
first conduct an empirical study on 222 ERC rules specified in four popular
ERCs to understand their content, their security impacts, their specification
in natural language, and their implementation in Solidity. Guided by the study,
we construct AuditGPT by separating the large, complex auditing process into
small, manageable tasks and design prompts specialized for each ERC rule type
to enhance LLMs' auditing performance. In the evaluation, AuditGPT successfully
pinpoints 418 ERC rule violations and only reports 18 false positives,
showcasing its effectiveness and accuracy. Moreover, AuditGPT beats an auditing
service provided by security experts in effectiveness, accuracy, and cost,
demonstrating its advancement over state-of-the-art smart-contract auditing
practices.


  Color gradients in elliptical galaxies in distant clusters ($z=0.37-0.56$)
are examined by using the archival deep imaging data of Wide Field Planetary
Camera 2 (WFPC2) on-board the Hubble Space Telescope (HST). Obtained color
gradients are compared with the two model gradients to examine the origin of
the color gradients. In one model, a color gradient is assumed to be caused by
a metallicity gradient of stellar populations, while in the other one, it is
caused by an age gradient. Both of these model color gradients reproduce the
average color gradient seen in nearby ellipticals, but predict significantly
different gradients at a redshift larger than $\sim$0.3. Comparison between the
observed gradients and the model gradients reveals that the metallicity
gradient is much more favorable as the primary origin of color gradients in
elliptical galaxies in clusters. The same conclusion has been obtained for
field ellipticals by using those at the redshift from 0.1 to 1.0 in the Hubble
Deep Field-North by Tamura et al. (2000). Thus, it is also suggested that the
primary origin of the color gradients in elliptical galaxies does not depend on
galaxy environment.


  The rise of Large Language Models (LLMs) has sparked interest in their
application to sequential recommendation tasks as they can provide supportive
item information. However, due to the inherent complexities of sequential
recommendation, such as sequential patterns across datasets, noise within
sequences, and the temporal evolution of user preferences, existing LLM
reasoning strategies, such as in-context learning and chain-of-thought are not
fully effective. To address these challenges, we introduce a novel reasoning
principle: Dynamic Reflection with Divergent Thinking within a
retriever-reranker framework. Our approach starts with a collaborative
in-context demonstration retriever, which collects sequences exhibiting
collaborative behaviors as in-context examples. Following this, we abstract
high-level user preferences across multiple aspects, providing a more nuanced
understanding of user interests and circumventing the noise within the raw
sequences. The cornerstone of our methodology is dynamic reflection, a process
that emulates human learning through probing, critiquing, and reflecting, using
user feedback to tailor the analysis more effectively to the target user in a
temporal manner. We evaluate our approach on three datasets using six
pre-trained LLMs. The superior performance observed across these models
demonstrates the efficacy of our reasoning strategy, notably achieved without
the need to fine-tune the LLMs. With our principle, we managed to outperform
GPT-Turbo-3.5 on three datasets using 7b models e.g., Vicuna-7b and Openchat-7b
on NDCG@10. This research not only highlights the potential of LLMs in
enhancing sequential recommendation systems but also underscores the importance
of developing tailored reasoning strategies to fully harness their
capabilities.


  We review quantum information processing with cold neutral particles, that
is, atoms or polar molecules. First, we analyze the best suited degrees of
freedom of these particles for storing quantum information, and then we discuss
both single- and two-qubit gate implementations. We focus our discussion mainly
on collisional quantum gates, which are best suited for atom-chip-like devices,
as well as on gate proposals conceived for optical lattices. Additionally, we
analyze schemes both for cold atoms confined in optical cavities and hybrid
approaches to entanglement generation, and we show how optimal control theory
might be a powerful tool to enhance the speed up of the gate operations as well
as to achieve high fidelities required for fault tolerant quantum computation.


  Policy makers focus on stable strategies as the ones adopted by rational
players. If there are many such solutions an important question is how to
select amongst them. We study this question for the Multicommodity Flow
Coalition Game, used to model cooperation between autonomous systems (AS) in
the Internet. In short, strategies are flows in a capacitated network. The
payoff to a node is the total flow which it terminates. Markakis-Saberi show
this game is balanced and hence has a non-empty core by Scarf's Theorem. In the
transferable utility (TU) version this gives a polynomial-time algorithm to
find core elements, but for ASs side payments are not natural. Finding core
elements in NTU games tends to be computationally more difficult. For this
game, the only previous result gives a procedure to find a core element when
the supply graph is a path. We extend their work with an algorithm,
Incorporate, which produces many different core elements.
  We use our algorithm to evaluate specific instances by generating many core
vectors. We call these the Empirical Core for a game. We find that sampled core
vectors are more consistent with respect to social welfare (SW) than for
fairness (minimum payout). For SW they tend to do as well as the optimal linear
program value $LP_{sw}$. In contrast, there is a larger range in fairness for
the empirical core; the fairness values tend to be worse than the optimal
fairness LP value $LP_{fair}$. We study this discrepancy in the setting of
general graphs with single-sink demands. In this setting we give an algorithm
which produces core vectors that simultaneously maximize SW and fairness. This
leads to the following bicriteria result for general games. Given any
core-producing algorithm and any $\lambda \in (0,1)$, one can produce an
approximate core vector with fairness (resp. social welfare) at least $\lambda
LP_{fair}$ (resp $(1-\lambda) LP_{sw}$).


  Strain has a strong effect on the properties of materials and the performance
of electronic devices. Their ever shrinking size translates into a constant
demand for accurate and precise measurement methods with very high spatial
resolution. In this regard, transmission electron microscopes are key
instruments thanks to their ability to map strain with sub-nanometer
resolution. Here we present a novel method to measure strain at the nanometer
scale based on the diffraction of electron Bessel beams. We demonstrate that
our method offers a strain sensitivity better than $2.5 \cdot 10^{-4}$ and an
accuracy of $1.5 \cdot 10^{-3}$, competing with, or outperforming, the best
existing methods with a simple and easy to use experimental setup.


  Landauer's Principle that information loss from a computation implies entropy
increase can be rigorously proved from mathematical physics. However, carefully
examining its detailed formulation reveals that the traditional identification
of logically reversible computational operations with bijective transformations
of the full digital state space is actually not the correct logical-level
characterization of the full set of classical computational operations that can
be carried out physically with asymptotically zero energy dissipation. To find
the correct logical conditions for physical reversibility, we must account for
initial-state probabilities when applying the Principle. The minimal
logical-level requirement for the physical reversibility of deterministic
computational operations is that the subset of initial states that exhibit
nonzero probability in a given statistical operating context must be
transformed one-to-one into final states. Thus, any computational operation is
conditionally reversible relative to any sufficiently-restrictive precondition
on its initial state, and the minimum dissipation required for any
deterministic operation by Landauer's Principle asymptotically approaches 0
when the probability of meeting any preselected one of its suitable
preconditions approaches 1. This realization facilitates simpler designs for
asymptotically thermodynamically reversible computational hardware, compared to
designs that are restricted to using only fully-bijective operations such as
Toffoli type operations. Thus, this more general framework for reversible
computing provides a more effective theoretical foundation to use for the
design of practical reversible computers than does the more restrictive
traditional model of reversible logic. In this paper, we formally develop the
theoretical foundations of the generalized model, and briefly survey some of
its applications.


  Deep neural networks are a key component of behavior prediction and motion
generation for self-driving cars. One of their main drawbacks is a lack of
transparency: they should provide easy to interpret rationales for what
triggers certain behaviors. We propose an architecture called Attentional
Bottleneck with the goal of improving transparency. Our key idea is to combine
visual attention, which identifies what aspects of the input the model is
using, with an information bottleneck that enables the model to only use
aspects of the input which are important. This not only provides sparse and
interpretable attention maps (e.g. focusing only on specific vehicles in the
scene), but it adds this transparency at no cost to model accuracy. In fact, we
find slight improvements in accuracy when applying Attentional Bottleneck to
the ChauffeurNet model, whereas we find that the accuracy deteriorates with a
traditional visual attention model.


  Existence of a complex structure on the $6$ dimensional sphere is proved in
this paper. The proof is based on re-interpreting a hypothetical complex
structure as a classical ground state of a Yang--Mills--Higgs-like theory on
$S^6$. This classical vacuum solution is then constructed by Fourier expansion
(dimensional reduction) from the obvious one of a similar theory on the $14$
dimensional exceptional compact Lie group ${\rm G}_2$.


  The data model of an application, the nature and format of data stored across
executions, is typically a very rigid part of its early specification, even
when prototyping, and changing it after code that relies on it was written can
prove quite expensive and error-prone.
  Code and data in a running Lisp image can be dynamically modified. A
MOP-based persistence library can bring this dynamicity to the data model. This
enables to extend the easy prototyping way of development to the storage of
data and helps avoiding interruptions of service. This article presents the
conditions to do this portably and transparently.


  Let $K$ be an algebraically closed field and $\mathrm{M}(2,K)$ be the
$2\times 2$ matrix algebra over $K$ and $\mathrm{GL}(2,K)$ be the invertible
elements in $\mathrm{M}(2,K)$. We explore the image of polynomials with
constants, namely from the free algebra $\mathrm{M}(2,K)\langle x, y\rangle$.
In this article, we compute the images of the polynomial maps given by (a)
generalized sum of powers $Ax^{k_1} + By^{k_2}$ and (b) generalized commutator
map $Axy -Byx$, where $A$, $B$ are non-zero elements of $\mathrm{M}(2,K)$. We
compute this in the first case by fixing a simultaneous conjugate pair for $A,
B$ and it turns out that it is surjective in most of the cases. In the second
case, we show that the image of the map is always a vector space.


  Based on the dominant paradigm, all the wearable IoT devices used in the
healthcare sector also known as the internet of medical things (IoMT) are
resource constrained in power and computational capabilities. The IoMT devices
are continuously pushing their readings to the remote cloud servers for
real-time data analytics, that causes faster drainage of the device battery.
Moreover, other demerits of continuous centralizing of data include exposed
privacy and high latency. This paper presents a novel Federated Filtering
Framework for IoMT devices which is based on the prediction of data at the
central fog server using shared models provided by the local IoMT devices. The
fog server performs model averaging to predict the aggregated data matrix and
also computes filter parameters for local IoMT devices. Two significant
theoretical contributions of this paper are the global tolerable perturbation
error (${To{l_F}}$) and the local filtering parameter ($\delta$); where the
former controls the decision-making accuracy due to eigenvalue perturbation and
the later balances the tradeoff between the communication overhead and
perturbation error of the aggregated data matrix (predicted matrix) at the fog
server. Experimental evaluation based on real healthcare data demonstrates that
the proposed scheme saves upto 95\% of the communication cost while maintaining
reasonable data privacy and low latency.


  We show that the Cox ring of the moduli of $SL_2(\C)$ quasi-parabolic
principal bundles on a marked curve is generated by conformal blocks of level 1
and 2. We show that the ideal which vanishes on these generators is generated
by forms of degrees $2, 3, 4.$


  We investigate an example of noise-induced stabilization in the plane that
was also considered in (Gawedzki, Herzog, Wehr 2010) and (Birrell, Herzog, Wehr
2011). We show that despite the deterministic system not being globally stable,
the addition of additive noise in the vertical direction leads to a unique
invariant probability measure to which the system converges at a uniform,
exponential rate. These facts are established primarily through the
construction of a Lyapunov function which we generate as the solution to a
sequence of Poisson equations. Unlike a number of other works, however, our
Lyapunov function is constructed in a systematic way, and we present a
meta-algorithm we hope will be applicable to other problems. We conclude by
proving positivity properties of the transition density by using Malliavin
calculus via some unusually explicit calculations.


  A complete numerical description of the charge and spin dynamics of a
two-electron system confined in narrow nanowire quantum dots under oscillating
electric field is presented in the context of recent electric dipole spin
resonance experiments. We find that the spin-orbit coupling results in lifting
the spin blockade by phonon mediated relaxation provided that the initially
occupied state is close in energy to the ground state. This leads to
suppression of the blockade from the triplet state with spins polarized
parallel to the external magnetic field B. At higher B, after singlet-triplet
ground-state transition a new channel for lifting the Pauli blockade opens
which results in an appearance of additional resonance lines. The calculated
signatures of this transition are consistent with recent experimental results
[S. M. Frolov et al., Phys. Rev. Lett. 109, 236805 (2012)].


  We first review the Coset Space Dimensional Reduction (CSDR) programme and
present the best model constructed so far based on the $\mathcal{N} = 1$,
$10$-dimensional $E_8$ gauge theory reduced over the nearly-K\"ahler manifold
$SU(3)/U(1)\times U(1)$ with the additional use of the Wilson flux mechanism.
Then we present the corresponding programme in the case that the extra
dimensions are considered to be fuzzy coset spaces and the best model that has
been constructed in this framework too. In both cases the best model appears to
be the trinification GUT $SU(3)^3$.


  With the advent of machine learning, there have been several recent attempts
to learn effective and generalizable heuristics. Local Heuristic A* (LoHA*) is
one recent method that instead of learning the entire heuristic estimate,
learns a "local" residual heuristic that estimates the cost to escape a region
(Veerapaneni et al 2023). LoHA*, like other supervised learning methods,
collects a dataset of target values by querying an oracle on many planning
problems (in this case, local planning problems). This data collection process
can become slow as the size of the local region increases or if the domain
requires expensive collision checks. Our main insight is that when an A* search
solves a start-goal planning problem it inherently ends up solving multiple
local planning problems. We exploit this observation to propose an efficient
data collection framework that does <1/10th the amount of work (measured by
expansions) to collect the same amount of data in comparison to baselines. This
idea also enables us to run LoHA* in an online manner where we can iteratively
collect data and improve our model while solving relevant start-goal tasks. We
demonstrate the performance of our data collection and online framework on a 4D
$(x, y, \theta, v)$ navigation domain.


  The purpose of this note is to give counterexamples to the containment
$I^{(3)}\subset I^2$ over the real numbers.


  Antiferromagnetically coupled Ising s =3 spins on a triangular lattice are
very close to ordering at zero temperature. The low temperature behaviour of a
triangular lattice with Ising spins s =3 has been simulated by using both
Glauber and Kawasaki dynamics. The formation of misfit clusters, which are
essential for destabilizing the ordered state, are inhibited by the use of
Kawasaki dynamics. The sublattice susceptibilities and the sublattice order
parameter are found to depend qualitatively on the dynamics used so that robust
ordering occurs when Kawasaki dynamics are employed. The thermal behaviour that
is found for the spin model with Kawasaki dynamics gives insight into the
observed ordering of side chains seen in a tetraphilic liquid crystal.


  This paper presents a study of the structure dynamics in BaFe$_2$Se$_3$. We
combined first-principle calculations, infrared measurements and a thorough
symmetry analysis. Our study confirms that $Pnma$ cannot be the space group of
BaFe$_2$Se$_3$, even at room temperature. The phonons assignment requires $Pm$
to be the BaFe$_2$Se$_3$ space group, not only in the magnetic phase, but also
in the paramagnetic phase at room temperature. This is due to a strong coupling
between a short range spin-order along the ladders, and the lattice degrees of
freedom associated with the Fe-Fe bond length. This coupling induces a change
in the bond-length pattern from an alternated trapezoidal one (as in $Pnma$) to
an alternated small/large rectangular one. Out of the two patterns, only the
latter is fully compatible with the observed block-type magnetic structure.
Finally, we propose a complete symmetry analysis of the BaFe$_2$Se$_3$ phase
diagram in the 0-600\,K range.


  Closed-form approximations to the expected per-terminal
signal-to-interference-plus-noise-ratio (SINR) and ergodic sum spectral
efficiency of a large multiuser multiple-input multiple-output system are
presented. Our analysis assumes correlated Ricean fading with maximum ratio
combining on the uplink, where the base station (BS) is equipped with a uniform
linear array (ULA) with physical size restrictions. Unlike previous studies,
our model caters for the presence of unequal correlation matrices and unequal
Rice factors for each terminal. As the number of BS antennas grows without
bound, with a finite number of terminals, we derive the limiting expected
per-terminal SINR and ergodic sum spectral efficiency of the system. Our
findings suggest that with restrictions on the size of the ULA, the expected
SINR saturates with increasing operating signal-to-noise-ratio (SNR) and BS
antennas. Whilst unequal correlation matrices result in higher performance, the
presence of strong line-of-sight (LoS) has an opposite effect. Our analysis
accommodates changes in system dimensions, SNR, LoS levels, spatial correlation
levels and variations in fixed physical spacings of the BS array.


  The aim of this paper is to present a possible framework for incorporating a
superspace formulation of supersymmetry into the formalism of noncommutative
geometry \`a la Alain Connes. In analogy with the almost-commutative (AC)
manifold construction of field theory, a base space is taken to be the
superspace $\mathbb{R}^{3 | 2}$, with associated 2-point (Grassmann valued)
finite space. The data of the spectral triple is explored, including
decorations, i.e. algebra, Hilbert space, grading, real structure, and Dirac
operator. The gauge fields arising from the inner fluctuations of the Dirac
operator are computed. And both the SUSY invariant spectral action and
fermionic actions are calculated.