  For wireless networks with multiple sources, an omnidirectional relay scheme
is developed, where each node can simultaneously relay different messages in
different directions. This is accomplished by the decode-and-forward relay
strategy, with each relay binning the multiple messages to be transmitted, in
the same spirit of network coding. Specially for the all-source all-cast
problem, where each node is an independent source to be transmitted to all the
other nodes, this scheme completely eliminates interference in the whole
network, and the signal transmitted by any node can be used by any other node.
For networks with some kind of symmetry, assuming no beamforming is to be
performed, this omnidirectional relay scheme is capable of achieving the
maximum achievable rate.


  A review is presented of the current experimental status of the top quark
sector of the standard model. The measurements summarized include searches for
electroweak single top production, the latest results on the ttbar production
cross section, and searches for new physics in top quark production and decay.
In addition, the recent measurement of the top quark mass to a precision of
0.7% is highlighted


  It is conjectured that every cusped hyperbolic 3-manifold admits a geometric
triangulation, i.e. it is decomposed into positive volume ideal hyperbolic
tetrahedra. Here, we show that sufficiently highly twisted knots admit a
geometric triangulation. In addition, by extending work of Gueritaud and
Schleimer, we also give quantified versions of this result for infinite
families of examples.


  We present multi-frequency, multi-epoch radio imaging of the complex radio
source B2151+174 in the core of the cluster, Abell 2390 (z~0.23). From new and
literature data we conclude that the FRII-powerful radio source is the
combination of a compact, core-dominated `medium-symmetric object' (MSO) with a
more extended, steeper spectrum mini-halo. B2151+174 is unusual in a number of
important aspects: i) it is one of the most compact and flat spectrum sources
in a cluster core known; ii) it shows a complex, compact twin-jet structure in
a north-south orientation; iii) the orientation of the jets is 45deg misaligned
with apparent structure (ionization cones and dust disk) of the host galaxy on
larger scales. Since the twin-jet of the MSO has its northern half with an
apparent `twist', it might be that precession of the central supermassive black
hole explains this misalignement.
  B2151+174 may be an example of the early stage (10^3-10^4 yrs duration) of a
`bubble' being blown into the ICM where the plasma has yet to expand.


  $SU(N_c)$ colour-singlet restriction, along with flavour and spin symmetry,
on thermal partonic ensemble is shown to recombine the partons with internal
colour structure into colour-singlet multi-quark clusters which can be
identified with various hadronic modes at a given temperature. This provides a
possible basis for recombination model for hadronization of quark-gluon plasma.
This also leads to a natural explanation for the ratio of (anti)protons to
pions and the quark number scaling of the elliptic flow coefficient in
relativistic heavy-ion collisions.


  We study a novel large dimensional approximate factor model with regime
changes in the loadings driven by a latent first order Markov process. By
exploiting the equivalent linear representation of the model, we first recover
the latent factors by means of Principal Component Analysis. We then cast the
model in state-space form, and we estimate loadings and transition
probabilities through an EM algorithm based on a modified version of the
Baum-Lindgren-Hamilton-Kim filter and smoother that makes use of the factors
previously estimated. Our approach is appealing as it provides closed form
expressions for all estimators. More importantly, it does not require knowledge
of the true number of factors. We derive the theoretical properties of the
proposed estimation procedure, and we show their good finite sample performance
through a comprehensive set of Monte Carlo experiments. The empirical
usefulness of our approach is illustrated through three applications to large
U.S. datasets of stock returns, macroeconomic variables, and inflation indexes.


  In this article we obtain a fundamental measure functional for the model of
aligned hard hexagons in the plane. Our aim is not just to provide a functional
for a new, admittedly academic, model, but to investigate the structure of
fundamental measure theory. A model of aligned hard hexagons has similarities
with the hard disk model. Both share "lost cases", i.e. admit configurations of
three particles in which there is pairwise overlap but not triple overlap.
These configurations are known to be problematic for fundamental measure
functionals, which are not able to capture their contribution correctly. This
failure lies in the inability of these functionals to yield a correct low
density limit of the third order direct correlation function. Here we derive
the functional by projecting aligned hard cubes on the plane x+y+z=0. The
correct dimensional crossover behavior of these functionals permits us to
follow this strategy. The functional of aligned hard cubes, however, does not
have lost cases, so neither had the resulting functional for aligned hard
hexagons. The latter exhibits, in fact, a peculiar structure as compared to the
one for hard disks. It depends on a uniparametric family of weighted densities
through a new term not appearing in the functional for hard disks. Apart from
studying the freezing of this system, we discuss the implications of the
functional structure for new developments of fundamental measure theory.


  We prove that any symplectic automorphism of finite order of an irreducible
holomorphic symplectic manifold of O'Grady's 10-dimensional deformation type is
trivial.


  We propose a general notion of dissipativity with dynamic supply rates for
nonlinear systems. This extends classical dissipativity with static supply
rates and dynamic supply rates of miscellaneous quadratic forms. The main
results of this paper concern Lyapunov and asymptotic stability analysis for
nonlinear feedback dissipative systems that are characterised by dissipation
inequalities with respect to compatible dynamic supply rates but involving
possibly different and independent auxiliary systems. Importantly,
dissipativity conditions guaranteeing stability of the state of the feedback
systems, without concerns on the stability of the state of the auxiliary
systems, are provided. The key results also specialise to a simple coupling
test for the interconnection of two nonlinear systems described by dynamic
(Psi, Pi, Upsilon, Omega)-dissipativity, and are shown to recover several
existing results in the literature, including small-gain, passivity indices,
static (Q, S, R)-dissipativity, dissipativity with terminal costs, etc.
Comparison with the input-output approach to feedback stability analysis based
on integral quadratic constraints is also made.


  We characterize the space of multipliers from the Hardy space of Dirichlet
series $\mathcal H_p$ into $\mathcal H_q$ for every $1 \leq p,q \leq \infty$.
For a fixed Dirichlet series, we also investigate some structural properties of
its associated multiplication operator. In particular, we study the norm, the
essential norm, and the spectrum for an operator of this kind. We exploit the
existing natural identification of spaces of Dirichlet series with spaces of
holomorphic functions in infinitely many variables and apply several methods
from complex and harmonic analysis to obtain our results. As a byproduct we get
analogous statements on such Hardy spaces of holomorphic functions.


  In this paper, locally repairable codes with all-symbol locality are studied.
Methods to modify already existing codes are presented. Also, it is shown that
with high probability, a random matrix with a few extra columns guaranteeing
the locality property, is a generator matrix for a locally repairable code with
a good minimum distance. The proof of this gives also a constructive method to
find locally repairable codes.


  We calculate the systematic errors in the weak gravitational lensing power
spectrum which would be caused by spatially varying calibration (i.e.
multiplicative) errors, such as might arise from uncorrected seeing or
extinction variations. The systematic error is fully described by the angular
two-point correlation function of the systematic in the case of the 2D lensing
that we consider here. We investigate three specific cases: Gaussian,
``patchy'' and exponential correlation functions. In order to keep systematic
errors below statistical errors in future LSST-like surveys, the spatial
variation of calibration should not exceed 3% rms. This conclusion is
independently true for all forms of correlation function we consider. The
relative size the E- and B-mode power spectrum errors does, however, depend
upon the form of the correlation function, indicating that one cannot repair
the E-mode power spectrum systematics by means of the B-mode measurements.


  Nanostructures, such a quantum dots or nanoparticles, made of
three-dimensional topological insulators (3DTIs) have been recently attracting
increasing interest, especially for their optical properties. In this paper we
calculate the energy spectrum, the surface states and the dipole matrix
elements for optical transitions with in-plane polarization of 3DTI
nanocylinders of finite height L and radius R. We first derive an effective 2D
Hamiltonian by exploiting the cylindrical symmetry of the problem. We develop
two approaches: the first one is an exact numerical tight-binding model
obtained by discretising the Hamiltonian. The second one, which allows us to
obtain analytical results, is an approximated model based on a large-R
expansion and on an effective boundary condition to account for the finite
height of the nanocylinder. We find that the agreement between the two models,
as far as eigenenergies and eigenfunctions are concerned, is excellent for the
lowest absolute value of the longitudinal component of the angular momentum.
Finally, we derive analytical expressions for the dipole matrix elements by
first considering the lateral surface alone and the bases alone, and then for
the whole nanocylinder. In particular, we focus on the two limiting cases of
tall and squat nanocylinders. The latter case is compared with the numerical
results finding a good agreement.


  We present an abundance analysis of light elements in He-rich stars. The
analysis is based on both low and high resolution observations collected at
ESO, La Silla, Chile in the optical region and includes 6 standards and 21
He-rich stars. Light-element abundances display a diverse pattern: they range
from under-solar up to above-solar values.


  We report on the discovery of three new millisecond pulsars (namely
J1748-2446aj, J1748-2446ak and J1748-2446al) in the inner regions of the dense
stellar system Terzan 5. These pulsars have been discovered thanks to a method,
alternative to the classical search routines, that exploited the large set of
archival observations of Terzan 5 acquired with the Green Bank Telescope over 5
years (from 2010 to 2015). This technique allowed the analysis of stacked power
spectra obtained by combining ~206 hours of observation. J1748-2446aj has a
spin period of ~2.96 ms, J1748-2446ak of ~1.89 ms (thus it is the fourth
fastest pulsar in the cluster) and J1748-2446al of ~5.95 ms. All the three
millisecond pulsars are isolated and currently we have timing solutions only
for J1748-2446aj and J1748-2446ak. For these two systems, we evaluated the
contribution to the measured spin-down rate of the acceleration due to the
cluster potential field, thus estimating the intrinsic spin-down rates, which
are in agreement with those typically measured for millisecond pulsars in
globular clusters. Our results increase to 37 the number of pulsars known in
Terzan 5, which now hosts 25% of the entire pulsar population identified, so
far, in globular clusters.


  Recent progress in two-dimensional superconductors with atomic-scale
thicknesses is reviewed mainly from the experimental point of view. The
superconducting systems treated here involve a variety of materials and forms:
elemental-metal ultrathin films and atomic layers on semiconductor surfaces;
interfaces and superlattices of heterostructures made of cuprates, perovskite
oxides, and rare-earth metal heavy-fermion compounds; interfaces of
electric-double-layer transistors; graphene and atomic sheets of
transition-metal dichalcogenide; iron selenide and organic conductors on oxide
and metal surfaces, respectively. Unique phenomena arising from the ultimate
two-dimensionality of the system and the physics behind them are discussed.


  The celebrated result by Biane-Bougerol-O'Connell relates Duistermaat-Heckman
(DH) measures for coadjoint orbits of a compact Lie group $G$ with the
multi-dimensional Pitman transform of the Wiener process on its Cartan
subalgebra. The DH theory admits several non-trivial generalizations. In this
paper, we consider the case of $G=SU(2)$, and we give an interpretation of DH
measures for $SU(2) \cong S^3$ valued moment maps in terms of an interesting
stochastic process on the unit disc, and an interpretation of the DH measures
for Poisson $\mathbb{H}^3$ valued moment maps (in the sense of Lu) in terms of
a stochastic process on the interior of a hyperbola.


  Historically, true context-sensitive parsing has seldom been applied to
programming languages, due to its inherent complexity. However, many mainstream
programming and markup languages (C, Haskell, Python, XML, and more) possess
context-sensitive features. These features are traditionally handled with
ad-hoc code (e.g., custom lexers), outside of the scope of parsing theory.
  Current grammar formalisms struggle to express context-sensitive features.
Most solutions lack context transparency: they make grammars hard to write,
maintain and compose by hardwiring context through the entire grammar. Instead,
we approach context-sensitive parsing through the idea that parsers may recall
previously matched input (or data derived therefrom) in order to make parsing
decisions. We make use of mutable parse state to enable this form of recall.
  We introduce principled stateful parsing as a new transactional discipline
that makes state changes transparent to parsing mechanisms such as backtracking
and memoization. To enforce this discipline, users specify parsers using
formally specified primitive state manipulation operations.
  Our solution is available as a parsing library named Autumn. We illustrate
our solution by implementing some practical context-sensitive grammar features
such as significant whitespace handling and namespace classification.


  This paper, investigates the conditional quantile estimation of a scalar
random response and a functional random covariate (i.e. valued in some
infinite-dimensional space) whenever {\it functional stationary ergodic data
with random censorship} are considered. We introduce a kernel type estimator of
the conditional quantile function. We establish the strong consistency with
rate of this estimator as well as the asymptotic normality which induces a
confidence interval that is usable in practice since it does not depend on any
unknown quantity. An application to electricity peak demand interval prediction
with censored smart meter data is carried out to show the performance of the
proposed estimator.


  To solve the hierarchy problem, extra-dimensional models must explain why the
new dimensions stabilize to the right size, and the known mechanisms for doing
so require bulk scalars that couple to the branes. Because of these couplings
the energetics of dimensional stabilization competes with the energetics of the
Higgs vacuum, with potentially observable effects. These effects are
particularly strong for one or two extra dimensions because the bulk-Higgs
couplings can then be super-renormalizable or dimensionless. Experimental reach
for such extra-dimensional Higgs `portals' are stronger than for gravitational
couplings because they are less suppressed at low-energies. We compute how
Higgs-bulk coupling through such a portal with two extra dimensions back-reacts
onto properties of the Higgs boson. When the KK mass is smaller than the Higgs
mass, mixing with KK modes results in an invisible Higgs decay width,
missing-energy signals at high-energy colliders, and new mechanisms of energy
loss in stars and supernovae. Astrophysical bounds turn out to be complementary
to collider measurements, with observable LHC signals allowed by existing
constraints. We comment on the changes to the Higgs mass-coupling relationship
caused by Higgs-bulk mixing, and how the resulting modifications to the running
of Higgs couplings alter vacuum-stability and triviality bounds.


  We bring fresh insight into the ensemble properties of PbS colloidal quantum
dots with a critical review of the literature on semiconductors followed by
systematic comparisons between steady-state photocurrent and photoluminescence
measurements. Our experiments, performed with sufficiently low powers to
neglect nonlinear effects, indicate that the photoluminescence spectra have no
other noticeable contribution beside the radiative recombination of thermalized
photocarriers (i.e. photocarriers in thermodynamic quasi-equilibrium). A
phenomenological model based on the local Kirchhoff law is proposed that makes
it possible to identify the nature of the thermalized photocarriers and to
extract their temperatures from the measurements. Two regimes are observed: for
highly compact assemblies of PbS quantum dots stripped from organic ligands,
the thermalization concerns photocarriers distributed over a wide energy range.
With PbS quantum dots cross-linked with 1,2-ethanedithiol or longer organic
ligand chains, the thermalization concerns solely the fundamental exciton and
can quantitatively explain all the observations, including the precise Stokes
shift between the absorbance and luminescence maxima.


  We consider the R\'enyi entropies $S_n(\ell)$ in the one dimensional spin-1/2
Heisenberg XX chain in a magnetic field. The case n=1 corresponds to the von
Neumann ``entanglement'' entropy. Using a combination of methods based on the
generalized Fisher-Hartwig conjecture and a recurrence relation connected to
the Painlev\'e VI differential equation we obtain the asymptotic behaviour,
accurate to order ${\cal O}(\ell^{-3})$, of the R\'enyi entropies $S_n(\ell)$
for large block lengths $\ell$. For n=1,2,3,10 this constitutes the 3,6,10,48
leading terms respectively. The o(1) contributions are found to exhibit a rich
structure of oscillatory behaviour, which we analyze in some detail both for
finite $n$ and in the limit $n\to\infty$.


  By the growing trend of online shopping and e-commerce websites,
recommendation systems have gained more importance in recent years in order to
increase the sales ratios of companies. Different algorithms on recommendation
systems are used and every one produce different results. Every algorithm on
this area have positive and negative attributes. The purpose of the research is
to test the different algorithms for choosing the best one according as
structure of dataset and aims of developers. For this purpose, threshold and
k-means based collaborative filtering and content-based filtering algorithms
are utilized on the dataset contains 100*73421 matrix length. What are the
differences and effects of these different algorithms on the same dataset? What
are the challenges of the algorithms? What criteria are more important in order
to evaluate a recommendation systems? In the study, we answer these crucial
problems with the case study.


  We show that a stochastic flow which is generated by a stochastic
differential equation on $\R^d$ with bounded volatility has a random attractor
provided that the drift component in the direction towards the origin is larger
than a certain strictly positive constant $\beta$ outside a large ball. Using a
similar approach, we provide a lower bound for the linear growth rate of the
inner radius of the image of a large ball under a stochastic flow in case the
drift component in the direction away from the origin is larger than a certain
strictly positive constant $\beta$ outside a large ball. To prove the main
result we use chaining techniques in order to control the growth of the
diameter of subsets of the state space under the flow.


  We demonstrate one-dimensional Doppler cooling of a beam of buffer-gas cooled
Barium monofluoride (BaF) molecules. The dependences of the cooling efficiency
with the laser detuning, the bias filed and the laser intensity are carefully
measured. We numerical simulate our experiment with a Monte Carlo method, and
find the theoretic predictions consists with our experimental data. This result
represents a key step towards further cooling and trapping of BaF molecules.


  In this work we focus on the surface roughness correction to the near-field
radiative heat transfer between a nanoparticle and a material with a rough
surface utilizing a direct perturbation theory up to second order in the
surface profile. We discuss the different distance regimes for the local
density of states above the rough material and the heat flux analytically and
numerically. We show that the heat transfer rate is larger than that
corresponding to a flat surface at short distances. At larger distances it can
become smaller due to surface polariton scattering by the rough surface. For
distances much smaller than the correlation length of the surface profile, we
show that the results converge to a proximity approximation, whereas in the
opposite limit the rough surface can be replaced by an equivalent surface
layer.


  We discuss a supersymmetric unified model based on a product gauge group
SU(5)\times SU(5)\times SU(5), where the gauge symmetry breaking is achieved
without the adjoint or higher-dimensional Higgs field, and the doublet-triplet
splitting in the Higgs masses is realized by the use of the discrete symmetry.
In this article we present an explicit model for realistic fermion masses with
the discrete symmetries Z_7\times Z_2. It is shown that all the observed masses
and mixing angles for quarks and leptons, including neutrinos, are well
described by the breaking of the symmetries imposed in the model. Especially,
the maximal and large mixing angles in the atmospheric and solar neutrino
oscillations are obtained as the most preferred values, and the typical value
of the neutrino mixing element U_{e3} is 0.1-0.3. We also point out the
non-trivial relations among the \mu-parameter for the Higgs mass, the charged
fermion hierarchies, and the neutrino masses. These relations suggest that the
scale of \mu is of order of the weak scale.


  The limitations on the production and profitability of entanglement in a
harmonic chain under strong driving are considered. We report on the limits of
attainable entanglement for a given set of squeezings of the eigenmodes,
showing that the higher the entanglement the more oscillatory and thus less
easy to profit from. We also comment on propagation properties of entanglement,
discussing the role of fast rotating terms and illustrating several issues with
the example of a sudden switch of the coupling.


  We propose a new mechanism for baryogenesis in supersymmetric extensions of
the standard model, that does not depend on (super)GUT interactions. It occurs
by the non-perturbative electroweak reprocessing of a lepton asymmetry. This
lepton asymmetry is generated by the effects of lepton number violating induced
operators, arising from "see-saw" (s)neutrino masses, which act on scalar
condensate oscillations along flat directions of the supersymmetric standard
model.


  The dynamics of a cloud of ultra-cold two-level atoms is studied at
off-resonant laser driving to a Rydberg state. We find that resonant excitation
channels lead to strongly peaked spatial correlations associated with the
buildup of asymmetric excitation structures. These aggregates can extend over
the entire ensemble volume, but are in general not localized relative to the
system boundaries. The characteristic distances between neighboring excitations
depend on the laser detuning and on the interaction potential. These properties
lead to characteristic features in the spatial excitation density, the Mandel
$Q$ parameter, and the total number of excitations. As an application an
implementation of the three-atom CSWAP or Fredkin gate with Rydberg atoms is
discussed. The gate not only exploits the Rydberg blockade, but also utilizes
the special features of an asymmetric geometric arrangement of the three atoms.
We show that continuous-wave off-resonant laser driving is sufficient to create
the required spatial arrangement of atoms out of a homogeneous cloud.


  Oracle Bone Inscriptions is one of the oldest existing forms of writing in
the world. However, due to the great antiquity of the era, a large number of
Oracle Bone Inscriptions (OBI) remain undeciphered, making it one of the global
challenges in the field of paleography today. This paper introduces a novel
approach, namely Puzzle Pieces Picker (P$^3$), to decipher these enigmatic
characters through radical reconstruction. We deconstruct OBI into foundational
strokes and radicals, then employ a Transformer model to reconstruct them into
their modern (conterpart)\textcolor{blue}{counterparts}, offering a
groundbreaking solution to ancient script analysis. To further this endeavor, a
new Ancient Chinese Character Puzzles (ACCP) dataset was developed, comprising
an extensive collection of character images from seven key historical stages,
annotated with detailed radical sequences. The experiments have showcased
considerable promising insights, underscoring the potential and effectiveness
of our approach in deciphering the intricacies of ancient Chinese scripts.
Through this novel dataset and methodology, we aim to bridge the gap between
traditional philology and modern document analysis techniques, offering new
insights into the rich history of Chinese linguistic heritage.


  In 1985, Leggett and Garg put forward the concept of macroscopic realism
(macrorealism) and, in analogy to Bell's theorem, derived a necessary condition
in terms of inequalities, which are now known as the Leggett-Garg inequalities.
In this paper, we discuss another necessary condition called no-signaling in
time. It solely bases on comparing the probability distribution for a
macrovariable at some time for the cases where previously a measurement has or
has not been performed. Although the concept is analogous to the no-signaling
condition in the case of Bell tests, it can be violated according to quantum
mechanical predictions even in situations where no violation of Leggett-Garg
inequalities is possible.


  We describe a novel way to measure the mass of heavy, long-lived neutral
particles that decay to photons using collider experiments. We focus on a Light
Neutralino and Gravitino model in a Gauge Mediated Supersymmetry Breaking
scenario where the neutralino has a long-lifetime (O(ns)) as it is not excluded
by current experiments. To illustrate our method and give sensitivity estimates
we use recent CDF results and a production mechanism where sparticles are
produced via $\phi_{i} \rightarrow \widetilde{\chi}^{1}_{0}
\widetilde{\chi}^{1}_{0} \rightarrow (\gamma \widetilde{G})(\gamma
\widetilde{G})$ in which $\phi_{i}$ indicates a neutral scalar boson,
$\widetilde{\chi}^{1}_{0}$ is the lightest neutralino and $\widetilde{G}$ is
the gravitino, as a full set of background shapes and rates are available.
Events can be observed in the exclusive photon plus Missing $E_{T}$ final state
where one photon arrives at the detector with a delayed time of arrival.
Surprisingly, a simple measurement of the slope of the delayed-time
distribution with the full CDF dataset is largely insensitive to all but the
$\widetilde{\chi}^{1}_{0}$ mass and allows for the possibility of determining
its mass to approximately 25% of itself.


  For $(n+1)$-webs by curves in an ambiant $n$-dimensional manifold, we first
define a generalization of the well known Blaschke curvature of the dimension
two, which vanishes iff the web has the maximum possible rank which is one.
But, contrary to the dimension two where all 3-webs of rank one are locally
isomorphic, we prove that there are infinitely many classes of isomorphism for
germs of 4-webs by curves of rank one in the dimension three : we provide a
procedure for building all of them, up to isomorphism, and give examples of
invariants of these classes allowing in particular to distinguish the so-called
quadrilateral webs among them.


  Convolutional Neural Network (CNN) models often lack the ability to
incorporate human input, which can be addressed by Augmented Reality (AR)
headsets. However, current AR headsets face limitations in processing power,
which has prevented researchers from performing real-time, complex image
recognition tasks using CNNs in AR headsets. This paper presents a method to
deploy CNN models on AR headsets by training them on computers and transferring
the optimized weight matrices to the headset. The approach transforms the image
data and CNN layers into a one-dimensional format suitable for the AR platform.
We demonstrate this method by training the LeNet-5 CNN model on the MNIST
dataset using PyTorch and deploying it on a HoloLens AR headset. The results
show that the model maintains an accuracy of approximately 98%, similar to its
performance on a computer. This integration of CNN and AR enables real-time
image processing on AR headsets, allowing for the incorporation of human input
into AI models.


  Energy efficient communication technology has attracted much attention due to
the explosive growth of energy consumption in current wireless communication
systems. In this letter we focus on fairness-based energy efficiency and aim to
maximize the minimum user energy efficiency in the multicell multiuser joint
beamforming system, taking both dynamic and static power consumptions into
account. This optimization problem is a non-convex fractional programming
problem and hard to tackle. In order to find its solution, the original problem
is transformed into a parameterized polynomial subtractive form by exploiting
the relationship between the user rate and the minimum mean square error, and
using the fractional programming theorem. Furthermore, an iterative algorithm
with proved convergence is developed to achieve a near-optimal performance.
Numerical results validate the effectiveness of the proposed solution and show
that our algorithm significantly outperforms the max-min rate optimization
algorithm in terms of maximizing the minimum energy efficiency.


  As antibiotic resistance grows more frequent for common bacterial infections,
alternative treatment strategies such as phage therapy have become more widely
studied in the medical field. While many studies have explored the efficacy of
antibiotics, phage therapy, or synergistic combinations of phages and
antibiotics, the impact of virus competition on the efficacy of antibiotic
treatment has not yet been considered. Here, we model the synergy between
antibiotics and two viral types, temperate and chronic, in controlling
bacterial infections. We demonstrate that while combinations of antibiotic and
temperate viruses exhibit synergy, competition between temperate and chronic
viruses inhibits bacterial control with antibiotics. In fact, our model reveals
that antibiotic treatment may counterintuitively increase the bacterial load
when a large fraction of the bacteria develop antibiotic-resistance.


  In this paper, the oxidation-assisted dealloying (OAD) of Cu0.7Al0.3 films
with different microstructures which were obtained by high vacuum annealing at
different temperatures were studied using powder X-ray diffraction,
field-emission scanning electron microscopy and energy dispersive X-ray
analysis. It was observed that different microstructures such as eutectic
mixture or solid solution, the grain size of Cu or Al component in
eutectic-mixture Cu0.7Al0.3 films affected the corrosion morphology greatly. It
thus provided a practical route to fabricate flexible CuO porous
nanostructure-films (PNFs) with controllable pore size, porosity, block size
and shape. Further, the underlying OAD mechanisms for the structure-resultant
different corrosion morphologies of Cu0.7Al0.3 films were also explored. In
these senses, the study is suggestive and crucial to both the mechanism
understanding of OAD process and the technical controlling of PNF fabrication.


  The design and implementation of Deep Learning (DL) models is currently
receiving a lot of attention from both industrials and academics. However, the
computational workload associated with DL is often out of reach for low-power
embedded devices and is still costly when run on datacenters. By relaxing the
need for fully precise operations, Approximate Computing (AxC) substantially
improves performance and energy efficiency. DL is extremely relevant in this
context, since playing with the accuracy needed to do adequate computations
will significantly enhance performance, while keeping the quality of results in
a user-constrained range. This chapter will explore how AxC can improve the
performance and energy efficiency of hardware accelerators in DL applications
during inference and training.


  It is generally accepted that the main cause of ultracold neutron (UCN)
losses in storage traps is the upscattering to the thermal energy range by
hydrogen adsorbed on the surface of the trap walls. However, the data on which
this conclusion is based are poor and contradictory. Here, we report a
measurement, performed at the Los Alamos National Laboratory UCN source, of the
average energy of the flux of upscattered neutrons after the interaction of UCN
with hydrogen bound in semicrystalline polymer PMP (tradename TPX),
[C$_{6}$H$_{12}$]$_n$. Our analysis, performed with the MCNP code based on the
application of the neutron scattering law to UCN upscattered by bound hydrogen
in semicrystalline polyethylene, [C$_{2}$H$_{4}$]$_n$, leads us to a flux
average energy value of 26$\pm3$ meV in contradiction with previously reported
experimental values of 10 to 13 meV and in agreement with the theoretical
models of neutron heating implemented in the MCNP code.


  A new framework is introduced for constructing interpretable and truly
reliable reduced models for multiscale problems in situations without scale
separation. Hydrodynamic approximation to the kinetic equation is used as an
example to illustrate the main steps and issues involved. To this end, a set of
generalized moments are constructed first to optimally represent the underlying
velocity distribution. The well-known closure problem is then solved with the
aim of best capturing the associated dynamics of the kinetic equation. The
issue of physical constraints such as Galilean invariance is addressed and an
active learning procedure is introduced to help ensure that the dataset used is
representative enough. The reduced system takes the form of a conventional
moment system and works regardless of the numerical discretization used.
Numerical results are presented for the BGK (Bhatnagar--Gross--Krook) model and
binary collision of Maxwell molecules. We demonstrate that the reduced model
achieves a uniform accuracy in a wide range of Knudsen numbers spanning from
the hydrodynamic limit to free molecular flow.


  We report enhanced superconductivity in bilayer thin films consisting of
superconducting La$_{1.6-x}$Nd$_{0.4}$Sr$_{x}$CuO$_{4}$ with 0.06 $\leq x<$
0.20 and metallic but non-superconducting La$_{1.55}$Sr$_{0.45}$CuO$_{4}$.
These bilayers show a maximum increase in superconducting transition
temperature ($T_c$) of more than 200% for $x$ = 0.06 while no change in $T_c$
is observed for the bilayers with $x\geq$ 0.20. The analysis of the critical
current and kinetic inductance data suggests 2-3 unit cells thick interfacial
layer electronically perturbed to have a higher $T_c$. A simple charge transfer
model with cation intermixing explains the observed $T_c$ in bilayers. Still
the unusually large thickness of interfacial superconducting layers can not be
explained in terms of this model. We believe the stripe relaxation as well as
the proximity effect also influence the superconductivity of the interface.


  Fractional extensions of the cable equation have been proposed in the
literature to describe transmembrane potential in spiny dendrites. The
anomalous behavior has been related in the literature to the geometrical
properties of the system, in particular, the density of spines, by experiments,
computer simulations, and in comb-like models.~The same PDE can be related to
more than one stochastic process leading to anomalous diffusion behavior. The
time-fractional diffusion equation can be associated to a continuous time
random walk (CTRW) with power-law waiting time probability or to a special case
of the Erd\'ely-Kober fractional diffusion, described by the ggBm. In this
work, we show that time fractional generalization of the cable equation arises
naturally in the CTRW by considering a superposition of Markovian processes and
in a {\it ggBm-like} construction of the random variable.


  While natural languages are compositional, how state-of-the-art neural models
achieve compositionality is still unclear. We propose a deep network, which not
only achieves competitive accuracy for text classification, but also exhibits
compositional behavior. That is, while creating hierarchical representations of
a piece of text, such as a sentence, the lower layers of the network distribute
their layer-specific attention weights to individual words. In contrast, the
higher layers compose meaningful phrases and clauses, whose lengths increase as
the networks get deeper until fully composing the sentence.


  The neutrino floor is a theoretical lower limit on WIMP-like dark matter
models that are discoverable in direct detection experiments. It is commonly
interpreted as the point at which dark matter signals become hidden underneath
a remarkably similar-looking background from neutrinos. However, it has been
known for some time that the neutrino floor is not a hard limit, but can be
pushed past with sufficient statistics. As a consequence, some have recently
advocated for calling it the "neutrino fog" instead. The downside of current
methods of deriving the neutrino floor are that they rely on arbitrary choices
of experimental exposure and energy threshold. Here we propose to define the
neutrino floor as the boundary of the neutrino fog, and develop a calculation
free from these assumptions. The technique is based on the derivative of a
hypothetical experimental discovery limit as a function of exposure, and leads
to a neutrino floor that is only influenced by the systematic uncertainties on
the neutrino flux normalisations. Our floor is broadly similar to those found
in the literature, but differs by almost an order of magnitude in the sub-GeV
range, and above 20~GeV.


  We investigate the Lax equation in the context of infinite-dimensional Lie
algebras. Explicit solutions are discussed in the sequentially complete
asymptotic estimate context, and an integral expansion (sums of iterated
Riemann integrals over nested commutators with correction term) is derived for
the situation that the Lie algebra is inherited by an infinite-dimensional Lie
group in Milnor's sense. In the context of Banach Lie groups (and Lie groups
with suitable regularity properties), we generalize the
Baker-Campbell-Dynkin-Hausdorff formula to the product integral (with
additional nilpotency assumption in the non-Banach case). We combine this
formula with the results obtained for the Lax equation to derive an explicit
representation of the product integral in terms of the exponential map. An
important ingredient in the non-Banach case is an integral transformation that
we introduce. This transformation maps continuous Lie algebra-valued curves to
smooth ones and leaves the product integral invariant. This transformation is
also used to prove a regularity statement in the asymptotic estimate context.


  In the standard approach, predictions of perturbative Quantum Chromodynamics
for ratios of cross sections are computed as the ratio of fixed-order
predictions for the numerator and the denominator. Beyond the lowest order in
the perturbative expansion, the result does, however, not correspond to a
fixed-order prediction for the ratio. This article describes how exact
fixed-order results for ratios of arbitrary cross sections can be obtained. The
general method for computations in any order of the perturbative expansion is
derived, and results for next-to-leading order and next-to-next-to-leading
order calculations are given. The approach is applied to theory predictions for
various multi-jet cross section ratios measured at hadron colliders. The two
methods are compared with each other and with the experimental data.
Recommendations are made how to obtain improved theory predictions with more
realistic uncertainty estimates.


  Face mask use by the general public for limiting the spread of the COVID-19
pandemic is controversial, though increasingly recommended, and the potential
of this intervention is not well understood. We develop a compartmental model
for assessing the community-wide impact of mask use by the general,
asymptomatic public, a portion of which may be asymptomatically infectious.
Model simulations, using data relevant to COVID-19 dynamics in the US states of
New York and Washington, suggest that broad adoption of even relatively
ineffective face masks may meaningfully reduce community transmission of
COVID-19 and decrease peak hospitalizations and deaths. Moreover, mask use
decreases the effective transmission rate in nearly linear proportion to the
product of mask effectiveness (as a fraction of potentially infectious contacts
blocked) and coverage rate (as a fraction of the general population), while the
impact on epidemiologic outcomes (death, hospitalizations) is highly nonlinear,
indicating masks could synergize with other non-pharmaceutical measures. Masks
are found to be useful with respect to both preventing illness in healthy
persons and preventing asymptomatic transmission. Hypothetical mask adoption
scenarios suggest that immediate near universal (80%) adoption of moderately
(50%) effective masks could prevent on the order of 17--45% of projected deaths
over two months in New York, while decreasing the peak daily death rate by
34--58%, absent other changes in epidemic dynamics. Our results suggest use of
face masks by the general public is potentially of high value in curtailing
community transmission and the burden of the pandemic. The community-wide
benefits are likely to be greatest when face masks are used in conjunction with
other non-pharmaceutical practices (such as social-distancing), and when
adoption is nearly universal (nation-wide) and compliance is high.


  Inflection point inflation generically includes a deviation from slow-roll
when the inflaton approaches the inflection point. Such deviations are shown to
be generated by transitions between singular trajectories. The effects on the
power spectrum are studied within the context of universality classes for
small-field models. These effects are shown to scale with universality
parameters, and can explain the anomalously low power at large scales observed
in the CMB. The reduction of power is related to the inflection point's basin
of attraction. Implications for the likelihood of inflation are discussed.


  The quark delocalization and color screening model, a quark potential model,
is used for a systematic search of dibaryon candidates in the $u,d$ and $s$
three flavor world. Color screening which appears in unquenched lattice gauge
calculations and quark delocalization (which is similar to electron
delocalization in molecular physics) are both included. Flavor symmetry
breaking and channel coupling effects are studied. The model is constrained not
only by baryon ground state properties but also by the $N$-$N$ scattering phase
shifts. The deuteron and zero energy di-nucleon resonance are both reproduced
qualitatively. The model predicts two extreme types of dibaryonic systems:
``molecular'' like the deuteron, and highly delocalized six-quark systems among
which only a few narrow dibaryon resonances occur in the $u,d$ and $s$ three
flavor world. Possible high spin dibaryon resonances are emphasized.


  Motivation is given for trying a theory of gravity with a preferred reference
frame (``ether'' for short). One such theory is summarized, that is a scalar
bimetric theory. Dynamics is governed by an extension of Newton's second law.
In the static case, geodesic motion is recovered together with Newton's
attraction field. In the static spherical case, Schwarzschild's metric is got.
An asymptotic scheme of post-Minkowskian (PM) approximation is built by
associating a conceptual family of systems with the given weakly-gravitating
system. It is more general than the post-Newtonian scheme in that the velocity
may be comparable with $c$. This allows to justify why the 0PM approximation of
the energy rate may be equated to the rate of the Newtonian energy, as is
usually done. At the 0PM approximation of this theory, an isolated system loses
energy by quadrupole radiation, without any monopole or dipole term. It seems
plausible that the observations on binary pulsars (the pulse data) could be
nicely fitted with a timing model based on this theory.


  Deep metric learning (DML) has received much attention in deep learning due
to its wide applications in computer vision. Previous studies have focused on
designing complicated losses and hard example mining methods, which are mostly
heuristic and lack of theoretical understanding. In this paper, we cast DML as
a simple pairwise binary classification problem that classifies a pair of
examples as similar or dissimilar. It identifies the most critical issue in
this problem--imbalanced data pairs. To tackle this issue, we propose a simple
and effective framework to sample pairs in a batch of data for updating the
model. The key to this framework is to define a robust loss for all pairs over
a mini-batch of data, which is formulated by distributionally robust
optimization. The flexibility in constructing the uncertainty decision set of
the dual variable allows us to recover state-of-the-art complicated losses and
also to induce novel variants. Empirical studies on several benchmark data sets
demonstrate that our simple and effective method outperforms the
state-of-the-art results. Codes are available at:
https://github.com/qiqi-helloworld/A-Simple-and-Effective-Framework-for-Pairewise-Distance-Metric-Learning


  Denote by $x$ a random infinite path in the graph of Pascal's triangle (left
and right turns are selected independently with fixed probabilities) and by
$d_n(x)$ the binomial coefficient at the $n$'th level along the path $x$. Then
for a dense $G_{\delta}$ set of $\theta$ in the unit interval, $\{d_n(x)\theta
\}$ is almost surely dense but not uniformly distributed modulo 1.


  Beyond the Sun-Earth line, spacecraft equipped with various solar telescopes
are intended to be deployed at several different vantage points in the
heliosphere to carry out coordinated, multi-view observations of the Sun and
its dynamic activities. In this context, we investigate solar visibility by
imaging instruments onboard the spacecraft orbiting the Sun-Earth Lagrange
points L1, L4 and L5, respectively. An optimal arrival time for vertical
periodic orbits stationed at L4 and L5 is determined based on geometric
considerations that ensure maximum visibility of solar poles or higher
latitudes per year. For a different set of orbits around the three Lagrange
points (L1, L4 and L5), we calculate the visibility of the solar surface (i.e.,
observation days per year) as a function of the solar latitude. We also analyze
where the solar limb viewed from one of the three Sun-Earth Lagrange points
under consideration is projected onto the solar surface visible to the other
two. This analysis particularly aims at determining the feasibility of studying
solar eruptions, such as flares and coronal mass ejections, with coordinated
observations of off-limb erupting coronal structures and their on-disk magnetic
footpoints. In addition, visibility analysis of a feature (such as sunspots) on
the solar surface is made for multiple spacecraft in various types of orbits
with different inclinations to quantify the improvement in continuous tracking
of the target feature for studying its long-term evolution from emergence,
growth and to decay. A comprehensive comparison of observations from single
(L1), double (L1 and L4) and multi-space missions (L1, L4 and L5) is carried
out through our solar visibility analysis, and this may help us to design
future space missions of constructing multiple solar observatories at the
Sun-Earth Lagrange points.


  A spatially homogeneous and anisotropic Bianchi type I universe is considered
while it is filled by pressureless dark matter (DM) and Tsallis holographic
dark energy (DE) interacting with each other throughout a sign-changeable
mutual interaction. Various infra-red (IR) cutoffs are studied, and it has been
obtained that while the current universe can classically be stable for some
cases, all models display classical instability by themselves at the future
($z\rightarrow-1$). Moreover, we find out that some models can cross the
phantom line. In order to have a more comprehensive study, the statefinder
diagnostic and the $\omega_D-{\omega}^{\prime}_{D}$ plane are also investigated
showing that the model parameters significantly affect the evolution
trajectories in the $r-s$ and $\omega_D-{\omega}^{\prime}_{D}$ planes.


  We will investigate numerically a seesaw model with $A_4$ flavor symmetry to
find allowed regions satisfying the current experimental neutrino oscillation
data, then use them to predict physical consequences. Namely, the lightest
active neutrino mass has order of $\mathcal{O}(10^{-2})$ eV. The effective
neutrino mass $|\langle m\rangle|$ associated with neutrinoless double beta
decay is in the range of $[0.002 \;\mathrm{eV},0.038\;\mathrm{eV}]$ and
$[0.048\;\mathrm{eV},0.058\;\mathrm{eV}]$ corresponding to the normal and the
inverted hierarchy schemes. Other relations among relevant physical quantities
are shown, so that they can be determined if some of them are confirmed
experimentally. The recent data of the baryon asymmetry of the Universe
($\eta_B$) can be explained via leptogenesis caused by the effect of the
renormalization group evolution on the Dirac Yukawa couplings, provided the
right handed neutrino mass scale $M_0$ is ranging from $\mathcal{O}(10^8)$ GeV
to $\mathcal{O}(10^{12})$ GeV for $\tan\beta =3$. This allowed $M_0$ range
distinguishes with the scale of $\mathcal{O}(10^{13})$ GeV concerned by other
effects that also generate the consistent $\eta_B$ from leptogenesis. The
branching ratio of the decay $ \mu \rightarrow\,e\gamma$ may reach the future
experimental sensitivity in the very light values of $M_0$. Hence, it will be
inconsistent with the $M_0$ range predicted from the $\eta_B$ data whenever
this decay is detected experimentally.


  A pair of surgeries on a knot is chirally cosmetic if they result in
homeomorphic manifolds with opposite orientations. Using recent methods of
Ichihara, Ito, and Saito, we show that, except for the (2,5) and (2,7)-torus
knots, the genus 2 and 3 alternating odd pretzel knots do not admit any
chirally cosmetic surgeries. Further, we show that for a fixed genus, at most
finitely many alternating odd pretzel knots admit chirally cosmetic surgeries.


  The presence of occluders significantly impacts object recognition accuracy.
However, occlusion is typically treated as an unstructured source of noise and
explicit models for occluders have lagged behind those for object appearance
and shape. In this paper we describe a hierarchical deformable part model for
face detection and landmark localization that explicitly models part occlusion.
The proposed model structure makes it possible to augment positive training
data with large numbers of synthetically occluded instances. This allows us to
easily incorporate the statistics of occlusion patterns in a discriminatively
trained model. We test the model on several benchmarks for landmark
localization and detection including challenging new data sets featuring
significant occlusion. We find that the addition of an explicit occlusion model
yields a detection system that outperforms existing approaches for occluded
instances while maintaining competitive accuracy in detection and landmark
localization for unoccluded instances.


  It is well-known that a paracompact space $X$ is of covering dimension at
most $n$ if and only if any map $f\colon X\to K$ from $X$ to a simplicial
complex $K$ can be pushed into its $n$-skeleton $K^{(n)}$. We use the same idea
to characterize asymptotic dimension in the coarse category of arbitrary coarse
spaces. Continuity of the map $f$ is replaced by variation of $f$ on elements
of a uniformly bounded cover. The same way one can generalize Property A of
G.Yu to arbitrary coarse spaces.


  Oscillating shape motion of a freely falling water droplet has long
fascinated and inspired scientists. We propose dynamic non-linear equations for
closed, two dimensional surfaces in gravity and apply it to analyze shape
dynamics of freely falling water drops. The analytic solutions qualitatively
well explain why drops oscillate among prolate/oblate morphologies and display
a number of features consistent with experiments.


  We predict the observational signatures of galaxy scale outflows powered by
active galactic nuclei (AGN). Most of the emission is produced by the forward
shock driven into the ambient interstellar medium (ISM) rather than by the
reverse shock. AGN powered galactic winds with energetics suggested by
phenomenological feedback arguments should produce spatially extended 1-10 keV
X-ray emission of 10^(41-44) erg/s, significantly in excess of the spatially
extended X-ray emission associated with normal star forming galaxies. The
presence of such emission is a direct test of whether AGN outflows
significantly interact with the ISM of their host galaxy. We further show that
even radio quiet quasars should have a radio luminosity comparable to or in
excess of the far infrared-radio correlation of normal star forming galaxies.
This radio emission directly constrains the total kinetic energy flux in
AGN-powered galactic winds. Radio emission from AGN wind shocks can also
explain the recently highlighted correlations between radio luminosity and the
kinematics of AGN narrow-line regions in radio quiet quasars.


  The use of large language models in medical dialogue generation has garnered
significant attention, with a focus on improving response quality and fluency.
While previous studies have made progress in optimizing model performance for
single-round medical Q&A tasks, there is a need to enhance the model's
capability for multi-round conversations to avoid logical inconsistencies. To
address this, we propose an approach called preference learning from process
feedback~(PLPF), which integrates the doctor's diagnostic logic into LLMs. PLPF
involves rule modeling, preference data generation, and preference alignment to
train the model to adhere to the diagnostic process. Experimental results using
Standardized Patient Testing show that PLPF enhances the diagnostic accuracy of
the baseline model in medical conversations by 17.6%, outperforming traditional
reinforcement learning from human feedback. Additionally, PLPF demonstrates
effectiveness in both multi-round and single-round dialogue tasks, showcasing
its potential for improving medical dialogue generation.


  We present Mezzo, a typed programming language of ML lineage. Mezzo is
equipped with a novel static discipline of duplicable and affine permissions,
which controls aliasing and ownership. This rules out certain mistakes,
including representation exposure and data races, and enables new idioms, such
as gradual initialization, memory re-use, and (type)state changes. Although the
core static discipline disallows sharing a mutable data structure, Mezzo offers
several ways of working around this restriction, including a novel dynamic
ownership control mechanism which we dub "adoption and abandon".


  In this manuscript we study the vector - vector interaction within the hidden
gauge formalism in a coupled channel unitary approach. In the sector
$C=1,S=1,J=2$ we get a pole in the T-matrix around $2572$ MeV that we identify
with the $D^*_{s2}(2573)$, coupling strongly to the
$D^*K^*$($D^*_s\phi$($\omega$)) channels. In addition we obtain resonances in
other exotic sectors which have not been studied before such as $C=1,S=-1$,
$C=2,S=0$ and $C=2,S=1$. This 'flavor-exotic' states are interpreted as
$D^*\bar{K^*}$, $D^*D^*$ and $D^*_sD^*$ molecular states but have not been
observed yet. In total we obtain nine states with different spin, isospin,
charm and strangeness of non $C=0,S=0$ and $C=1,S=0$ character, which have been
reported before.


  We have investigated the mass-metallicity (M-Z) relation using galaxies at
0.4<z<1.0 from the Gemini Deep Deep Survey and Canada-France Redshift Survey.
Deep K and z' band photometry allowed us to measure stellar masses for 69
galaxies. From a subsample of 56 galaxies, for which metallicity of the
interstellar medium is also measured, we identified a strong correlation
between mass and metallicity, for the first time in the distant Universe. This
was possible because of the larger base line spanned by the sample in terms of
metallicity (a factor of 7) and mass (a factor of 400) than in previous works.
This correlation is much stronger and tighter than the luminosity-metallicity,
confirming that stellar mass is a more meaningful physical parameter than
luminosity. We find clear evidence for temporal evolution in the M-Z relation
in the sense that at a given mass, a galaxy at z=0.7 tends to have lower
metallicity than a local galaxy of similar mass. We use the z=0.1 SDSS M-Z
relation, and a small sample of z=2.3 Lyman break galaxies with known mass and
metallicity, to propose an empirical redshift-dependent M-Z relation, according
to which the stellar mass and metallicity in small galaxies evolve for a longer
time than in massive galaxies. This relation predicts that the generally metal
poor damped Lyman-alpha galaxies have stellar masses of the order of 10^8.8
M_sun (with a dispersion of 0.7 dex) all the way from z=0.2 to z=4. The
observed redshift evolution of the M-Z relation can be reproduced remarkably
well by a simple closed-box model where the key assumption is an e-folding time
for star formation which is higher or, in other words, a period of star
formation that lasts longer in less massive galaxies than in more massive
galaxies. Such a picture supports the downsizing scenario for galaxy formation.


  One of the fundamental problems of modern physics is how the classical world,
the 2nd Law of Thermodynamics and the whole irreversibility emerges from the
quantum reality with reversible evolution. This relates to the problem of
measurement transforming quantum, non-copyable data, towards intersubjective,
copyable classical knowledge. We use the quantum state discrimination to show
in a central system model how it's evolution leads to the broadcasting of the
classical information. We analyze the process of orthogonalization and
decoherence, their time scales and dependence on the environment.


  We compute the modular Hamiltonians of regions having the future horizon
lying on a null plane. For a CFT this is equivalent to regions with boundary of
arbitrary shape lying on the null cone. These Hamiltonians have a local
expression on the horizon formed by integrals of the stress tensor. We prove
this result in two different ways, and show that the modular Hamiltonians of
these regions form an infinite dimensional Lie algebra. The corresponding group
of unitary transformations moves the fields on the null surface locally along
the null generators with arbitrary null line dependent velocities, but act non
locally outside the null plane. We regain this result in greater generality
using more abstract tools on algebraic quantum field theory. Finally, we show
that modular Hamiltonians on the null surface satisfy a Markov property that
leads to the saturation of the strong sub-additive inequality for the entropies
and to the strong super-additivity of the relative entropy.


  The moir\'e Hubbard model describes correlations in certain homobilayer
twisted transition metal dichalcogenides. Using exact diagonalization and
density matrix renormalization group methods, we find magnetic Mott insulating
and metallic phases, which, upon doping exhibit intertwined charge and spin
ordering and, in some regimes, pair binding of holes. The phases are highly
tunable via an interlayer potential difference. Remarkably, the hole binding
energy is found to be highly tunable revealing an experimentally accessible
regime where holes become attractive. In this attractive regime, we study the
superconducting correlation function and point out the possibility of weak
superconductivity.


  tau -> (3 pions) nu_tau decays are analysed within the framework of the
resonance effective theory of QCD. We work out the relevant Lagrangian that
describes the axial-vector current hadronization contributing to these
processes, in particular the local a_1(1260)-rho(770)-Goldstone interactions.
The new coupling constants are constrained by imposing the asymptotic behaviour
of the corresponding spectral function within QCD. Hence we compare the
theoretical framework with the experimental data, obtaining a good quality fit
from the ALEPH spectral function and branching ratio. We also get values for
the mass and on-shell width of the a_1(1260) resonance. In this way we are able
to provide the structure functions that have been measured by OPAL and CLEO-II
and we find an excellent agreement.


  Brill-Noether theory studies the existence and deformations of curves in
projective spaces; its basic object of study is $\mathcal{W}^r_{d,g}$, the
moduli space of smooth genus $g$ curves with a choice of degree $d$ line bundle
having at least $(r+1)$ independent global sections. The Brill-Noether theorem
asserts that the map $\mathcal{W}^r_{d,g} \rightarrow \mathcal{M}_g$ is
surjective with general fiber dimension given by the number $\rho = g -
(r+1)(g-d+r)$, under the hypothesis that $0 \leq \rho \leq g$. One may
naturally conjecture that for $\rho < 0$, this map is generically finite onto a
subvariety of codimension $-\rho$ in $\mathcal{M}_g$. This conjecture fails in
general, but seemingly only when $-\rho$ is large compared to $g$. This paper
proves that this conjecture does hold for at least one irreducible component of
$\mathcal{W}^r_{d,g}$, under the hypothesis that $0 < -\rho \leq \frac{r}{r+2}
g - 3r+3$. We conjecture that this result should hold for all $0 < -\rho \leq g
+ C$ for some constant $C$, and we give a purely combinatorial conjecture that
would imply this stronger result.


  It is shown that for the reason of neutrinos being left-handed and their
gauge-couplings being parity-violated, linearly polarized photons acquire their
circular polarization by interacting with neutrinos. Calculating the ratio of
linear and circular polarizations of laser photons interacting with either
Dirac or Majorana neutrino beam, we obtain this ratio for the Dirac neutrino
case, which is about twice less than the ratio for the Majorana neutrino case.
Based on this ratio, we discuss the possibility of using advanced laser
facilities and the T2K neutrino experiment to measure the circular polarization
of laser beams interacting with neutrino beams in ground laboratories. This
could be an additional and useful way to gain some insight into the physics of
neutrinos, for instance their Dirac or Majorana nature.


  We study the effect of thermal phase fluctuation on the electron spectral
function $A(k,\omega)$ in a d-wave superconductor with Monte Carlo simulation.
The phase degree of freedom is modeled by a XY-type model with build-in d-wave
character. We find a ridge-like structure emerges abruptly on the underlying
Fermi surface in $A(k,\omega=0)$ above the KT-transition temperature of the XY
model. Such a ridge-like structure, which shares the same characters with the
Fermi arc observed in the pseudogap phase of the underdoped cuprates, is found
to be caused by the vortex-like phase fluctuation of the XY model.


  We study the nonleptonic two-body weak decays of $\Lambda_b$ by modifying the
MIT bag model without introducing new parameters to construct the momentum
eigenstates of the baryons. We find that the branching ratios of $\Lambda_b^0
\to \Lambda_c^+ \pi^-$, $\Lambda_c^+ K^-$, $p \pi^-$ and $pK^-$ are
$(4.5\pm0.2)\times 10^{-3}$, $(3.4\pm 0.1)\times 10^{-4}$, $(5.0\pm 0.5)\times
10^{-6}$ and $(6.0\pm 0.7) \times 10^{-6}$, which are all well consistent with
the current experimental data, respectively. We also explore P and CP
asymmetries for the decays of $\Lambda_b^0 \to p (\pi^-,K^-)$. In particular,
we obtain that the direct CP-violating rate asymmetries in $\Lambda_b^0 \to p
\pi^-$ and $\Lambda_b^0 \to p K^-$ are around $-4.4\%$ and $6.7\%$, in
comparison with $(-2.5\pm2.9)\%$ and $(-2.5\pm2.2)\%$ from the Particle Data
Group in 2020, respectively.


  We perform a comparison of the properties of galaxies in compact groups,
loose groups and in the field to deepen our understanding of the physical
mechanisms acting upon galaxy evolution in different environments. We select
samples of galaxies in compact groups identified by McConnachie et al., loose
groups identified by Zandivarez and Martinez, and field galaxies from the Sloan
Digital Sky Survey. We compare properties of the galaxy populations in these
different environments: absolute magnitude, colour, size, surface brightness,
stellar mass and concentration. We also study the fraction of red and early
type galaxies, the luminosity function, the colour-luminosity and
luminosity-size relations. The population of galaxies in compact groups differ
from that of loose groups and the field. The fraction of read and early type
galaxies is higher in compact groups. On average, galaxies in compact groups
are systematically smaller, more concentrated and have higher surface
brightness than galaxies in the field and in loose groups. For fixed absolute
magnitude, or fixed surface brightness, galaxies in compact groups are smaller.
The physical mechanisms that transform galaxies into earlier types could be
more effective within compact groups given the high densities and low velocity
dispersion that characterise that particular environment, this could explain
the large fraction of red and early type galaxies we found in compact groups.
Galaxies inhabiting compact groups have undergone a major transformation
compared to galaxies that inhabit loose groups.


  In this paper, we discuss the representability almost everywhere (a.e.) in
the plane of an irreducible algebraic function as the Cauchy transform of a
signed measure supported on a finite number of compact semi-analytic curves and
a finite number of isolated points. We discuss the existence of critical
trajectories of a family of quadratic differentials.


  RNA viruses are known to replicate with extremely high mutation rates. These
rates are actually close to the so-called error threshold. This threshold is in
fact a critical point beyond which genetic information is lost through a
second-order phase transition, which has been dubbed the ``error catastrophe.''
Here we explore this phenomenon using a field theory approximation to the
spatially extended Swetina-Schuster quasispecies model [J. Swetina and P.
Schuster, Biophys. Chem. {\bf 16}, 329 (1982)], a single-sharp-peak landscape.
In analogy with standard absorbing-state phase transitions, we develop a
reaction-diffusion model whose discrete rules mimic the Swetina-Schuster model.
The field theory representation of the reaction-diffusion system is
constructed. The proposed field theory belongs to the same universality class
than a conserved reaction-diffusion model previously proposed [F. van Wijland
{\em et al.}, Physica A {\bf 251}, 179 (1998)]. From the field theory, we
obtain the full set of exponents that characterize the critical behavior at the
error threshold. Our results present the error catastrophe from a new point of
view and suggest that spatial degrees of freedom can modify several mean field
predictions previously considered, leading to the definition of characteristic
exponents that could be experimentally measurable.


  [HHM20] discovered, for 7 pairs (C,D) of seemingly distinct standard
electoral control types, that C and D are identical: For each input I and each
election system, I is a Yes instance of both C and D, or of neither.
Surprisingly this had gone undetected, even as the field was score-carding how
many std. control types election systems were resistant to; various "different"
cells on such score cards were, unknowingly, duplicate effort on the same
issue. This naturally raises the worry that other pairs of control types are
also identical, and so work still is being needlessly duplicated.
  We determine, for all std. control types, which pairs are, for elections
whose votes are linear orderings of the candidates, always identical. We show
that no identical control pairs exist beyond the known 7. We for 3 central
election systems determine which control pairs are identical ("collapse") with
respect to those systems, and we explore containment/incomparability
relationships between control pairs. For approval voting, which has a different
"type" for its votes, [HHM20]'s 7 collapses still hold. But we find 14
additional collapses that hold for approval voting but not for some election
systems whose votes are linear orderings. We find 1 additional collapse for
veto and none for plurality. We prove that each of the 3 election systems
mentioned have no collapses other than those inherited from [HHM20] or added
here. But we show many new containment relationships that hold between some
separating control pairs, and for each separating pair of std. control types
classify its separation in terms of containment (always, and strict on some
inputs) or incomparability.
  Our work, for the general case and these 3 important election systems,
clarifies the landscape of the 44 std. control types, for each pair collapsing
or separating them, and also providing finer-grained information on the
separations.


  Agricultural commodity futures are often settled by delivery. Quality options
that allow the futures short to deliver one of several underlying assets are
commonly used in such contracts to prevent manipulation. Inclusion of these
options reduces the price of the futures contract and leads to degraded
contract hedging performance. Valuation of these options is a first step in
assessing the impact of the quality options embedded into a futures contract.
This paper demonstrates a Monte Carlo simulation based approach to estimate the
value of a quality option. In order to improve simulation efficiency, the
technique of antithetic variables is used. This approach can help in the
assessment of the impact of embedded quality options.


  In random matrix theory, Marchenko-Pastur law states that random matrices
with independent and identically distributed entries have a universal
asymptotic eigenvalue distribution under large dimension limit, regardless of
the choice of entry distribution. This law provides useful insight for physics
research, because the large $N$ limit proved to be a very useful tool in
various theoretical models. We present an alternative proof of Marchenko-
Pastur law using Feynman diagrams, which is more familiar to the physics
community. We also show that our direct diagrammatic approach can readily
generalize to six types of restricted random matrices, which are not all
covered by the original Marchenko-Pastur law.


  Fitting a function by using linear combinations of a large number $N$ of
`simple' components is one of the most fruitful ideas in statistical learning.
This idea lies at the core of a variety of methods, from two-layer neural
networks to kernel regression, to boosting. In general, the resulting risk
minimization problem is non-convex and is solved by gradient descent or its
variants. Unfortunately, little is known about global convergence properties of
these approaches.
  Here we consider the problem of learning a concave function $f$ on a compact
convex domain $\Omega\subseteq {\mathbb R}^d$, using linear combinations of
`bump-like' components (neurons). The parameters to be fitted are the centers
of $N$ bumps, and the resulting empirical risk minimization problem is highly
non-convex. We prove that, in the limit in which the number of neurons
diverges, the evolution of gradient descent converges to a Wasserstein gradient
flow in the space of probability distributions over $\Omega$. Further, when the
bump width $\delta$ tends to $0$, this gradient flow has a limit which is a
viscous porous medium equation. Remarkably, the cost function optimized by this
gradient flow exhibits a special property known as displacement convexity,
which implies exponential convergence rates for $N\to\infty$, $\delta\to 0$.
  Surprisingly, this asymptotic theory appears to capture well the behavior for
moderate values of $\delta, N$. Explaining this phenomenon, and understanding
the dependence on $\delta,N$ in a quantitative manner remains an outstanding
challenge.


  We consider the problem of estimating a dose-response curve, both globally
and locally at a point. Continuous treatments arise often in practice, e.g. in
the form of time spent on an operation, distance traveled to a location or
dosage of a drug. Letting A denote a continuous treatment variable, the target
of inference is the expected outcome if everyone in the population takes
treatment level A=a. Under standard assumptions, the dose-response function
takes the form of a partial mean. Building upon the recent literature on
nonparametric regression with estimated outcomes, we study three different
estimators. As a global method, we construct an
empirical-risk-minimization-based estimator with an explicit characterization
of second-order remainder terms. As a local method, we develop a two-stage,
doubly-robust (DR) learner. Finally, we construct a mth-order estimator based
on the theory of higher-order influence functions. Under certain conditions,
this higher order estimator achieves the fastest rate of convergence that we
are aware of for this problem. However, the other two approaches are easier to
implement using off-the-shelf software, since they are formulated as two-stage
regression tasks. For each estimator, we provide an upper bound on the
mean-square error and investigate its finite-sample performance in a
simulation. Finally, we describe a flexible, nonparametric method to perform
sensitivity analysis to the no-unmeasured-confounding assumption when the
treatment is continuous.


  Most existing necessary conditions for optimal control based on adjoining
methods require both state information and costate information, yet the lack of
costates for a given feasible trajectory in practice impedes the determination
of optimality. This paper establishes a novel theoretical framework for
time-optimal control of controllable linear systems, proposing the augmented
switching law that represents the input control and the feasibility in a
compact form. Given a feasible trajectory, the disturbed trajectory under the
constraints of augmented switching law is guaranteed to be feasible, resulting
in a novel state-centric necessary condition without dependence on costate
information. A first order necessary condition is proposed that the Jacobian
matrix of the augmented switching law is not full row rank, which also results
in an approach to optimizing a given feasible trajectory further. The proposed
necessary condition is applied to the chain-of-integrators systems with full
box constraints, contributing to some conclusions challenging to reason by
traditional costate-based necessary conditions.


  We study simply interpolating sequences for the Dirichlet space in the unit
disc. In particular we are interested in comparing three different sufficient
conditions for simply interpolating sequences. The first one is the the so
called one box condition, the second is the column bounded propererty for the
associated Grammian matrix and the third one is a restricted version of the one
box condition introduced by Bishop and, independently, by Marshall and
Sundberg. We prove that the one box condition implies the column bounded
property which in turn implies the restricted on box condition of
Bishop-Marshall-Sundberg, and we give two counterexamples which show that the
reverse implications fail even for weakly separated sequences.


  Many physicists believe that the EPR experiment exhibits instantaneous
non-local effects. I argue below that an application of Born's Rule to EPR
shows no such instantaneous effects and that EPR is consistent with full
Lorentz invariance. I then discuss how it is possible to understand the EPR
correlations for non-commuting spin components without recourse to non-local
effects. Finally, I use these results to discuss the Free Will Theorem, which I
formulate in a new way.


  Spectroscopic factors (SF) play an important role in nuclear physics and
astrophysics. The traditional method of extracting SF from direct transfer
reactions suffers from serious ambiguities. We discuss a modified method which
is based on including the asymptotic normalization coefficient (ANC) of the
overlap functions into the transfer analysis. In the modified method the
contribution of the external part of the reaction amplitude, typically
dominant, is fixed and the SF is determined from fitting the internal part. We
illustrate the modified method with $(d,p)$ reactions on ${}^{208}{\rm Pb},
{}^{12}{\rm C}$, and ${}^{84}{\rm Se}$ targets at different energies. The
modified method allows one to extract the SF, which do not depend on the shape
of the single-particle nucleon-target interaction, and has the potential of
improving the reliability and accuracy of the structure information. This is
specially important for nuclei on dripline, where not much is known.


  An explicit description of all Walsh polynomials generating tight wavelet
frames is given. An algorithm for finding the corresponding wavelet functions
is suggested, and a general form for all wavelet frames generated by an
appropriate Walsh polynomial is described. Approximation properties of tight
wavelet frames are also studied. In contrast to the real setting, it appeared
that a wavelet tight frame decomposition has an arbitrary large approximation
order whenever all wavelet functions are compactly supported.


  Safety remains a central obstacle preventing widespread use of RL in the real
world: learning new tasks in uncertain environments requires extensive
exploration, but safety requires limiting exploration. We propose Recovery RL,
an algorithm which navigates this tradeoff by (1) leveraging offline data to
learn about constraint violating zones before policy learning and (2)
separating the goals of improving task performance and constraint satisfaction
across two policies: a task policy that only optimizes the task reward and a
recovery policy that guides the agent to safety when constraint violation is
likely. We evaluate Recovery RL on 6 simulation domains, including two
contact-rich manipulation tasks and an image-based navigation task, and an
image-based obstacle avoidance task on a physical robot. We compare Recovery RL
to 5 prior safe RL methods which jointly optimize for task performance and
safety via constrained optimization or reward shaping and find that Recovery RL
outperforms the next best prior method across all domains. Results suggest that
Recovery RL trades off constraint violations and task successes 2 - 20 times
more efficiently in simulation domains and 3 times more efficiently in physical
experiments. See https://tinyurl.com/rl-recovery for videos and supplementary
material.


  In this paper, we generalize the Cosmetic Surgery Conjecture to an $n$-cusped
hyperbolic $3$-manifold and prove it under the assumption of another well-known
conjecture in number theory, so called the Zilber-Pink Conjecture. For $n=1$
and $2$, we show them without the assumption.


  This paper discusses reformulations of the problem of coloring plane maps
with four colors. The context is the edge-coloring with three colors of cubic
graphs such that three distinct colors occur at each vertex. We include
discussion of the Eliahou-Kryuchkov conjecture, the Penrose formula, the vector
cross product formulation and the reformulations in terms of formations and
factorizations due to G. Spencer-Brown. The latter includes a proof of the
Spencer-Brown parity lemma and discussion of the parity-pass algorithm.


  This note announces results on the relations between the approach of
Beilinson and Drinfeld to the geometric Langlands correspondence based on
conformal field theory, the approach of Kapustin and Witten based on $N=4$ SYM,
and the AGT-correspondence. The geometric Langlands correspondence is described
as the Nekrasov-Shatashvili limit of a generalisation of the AGT-correspondence
in the presence of surface operators. Following the approaches of Kapustin -
Witten and Nekrasov - Witten we interpret some aspects of the resulting picture
using an effective description in terms of two-dimensional sigma models having
Hitchin's moduli spaces as target-manifold.


  Large pre-trained language models for textual data have an unconstrained
output space; at each decoding step, they can produce any of 10,000s of
sub-word tokens. When fine-tuned to target constrained formal languages like
SQL, these models often generate invalid code, rendering it unusable. We
propose PICARD (code and trained models available at
https://github.com/ElementAI/picard), a method for constraining auto-regressive
decoders of language models through incremental parsing. PICARD helps to find
valid output sequences by rejecting inadmissible tokens at each decoding step.
On the challenging Spider and CoSQL text-to-SQL translation tasks, we show that
PICARD transforms fine-tuned T5 models with passable performance into
state-of-the-art solutions.


  The a.c. electric field distribution is studied in a composite, containing
materials with small local losses. The possibility that 2D two-component system
can have effective absorption in the absence of local absorption was evidented.
We study the second and higher moments of electric field and show that they
diverge with the decrease of local absorption. The 3D system near the
percolation threshold is also discussed. The observation of giant field
fluctuations in granular films is explained.


  We propose to model time-varying periodic and oscillatory processes by means
of a hidden Markov model where the states are defined through the spectral
properties of a periodic regime. The number of states is unknown along with the
relevant periodicities, the role and number of which may vary across states. We
address this inference problem by a Bayesian nonparametric hidden Markov model
assuming a sticky hierarchical Dirichlet process for the switching dynamics
between different states while the periodicities characterizing each state are
explored by means of a trans-dimensional Markov chain Monte Carlo sampling
step. We develop the full Bayesian inference algorithm and illustrate the use
of our proposed methodology for different simulation studies as well as an
application related to respiratory research which focuses on the detection of
apnea instances in human breathing traces.


  We present a nucleosynthesis study of the merger of a 0.4 solar masses helium
white dwarf with a 0.8 solar masses carbon-oxygen white dwarf, coupling the
thermodynamic history of Smoothed Particle Hydrodynamics particles with a
post-processing code. The resulting chemical abundance pattern, particularly
for oxygen and fluorine, is in qualitative agreement with the observed
abundances in R Coronae Borealis stars.


  Polynomials whose coefficients, roots, and critical points lie in the ring of
rational integers are called nice polynomials. In this paper, we present a
general method for investigating such polynomials. We extend our results from
the ring of rational integers to rings of algebraic integers that are unique
factorization domains, with special interest in the ring of Gaussian integers.
We apply our method to establish strong properties of nice polynomials whose
degree is a prime power. We present a considerable reduction of the system of
equations for nice polynomials of arbitrary degree with three roots. We
establish properties of nice antisymmetric polynomials, and properties of the
averages of the roots of the derivatives of nice polynomials. Finally, we
present new examples of nice polynomials obtained with the help of a computer,
after a considerable simplification of the computation by our method.


  We propose a method to conduct uniform inference for the (optimal) value
function, that is, the function that results from optimizing an objective
function marginally over one of its arguments. Marginal optimization is not
Hadamard differentiable (that is, compactly differentiable) as a map between
the spaces of objective and value functions, which is problematic because
standard inference methods for nonlinear maps usually rely on Hadamard
differentiability. However, we show that the map from objective function to an
$L_p$ functional of a value function, for $1 \leq p \leq \infty$, are Hadamard
directionally differentiable. As a result, we establish consistency and weak
convergence of nonparametric plug-in estimates of Cram\'er-von Mises and
Kolmogorov-Smirnov test statistics applied to value functions. For practical
inference, we develop detailed resampling techniques that combine a bootstrap
procedure with estimates of the directional derivatives. In addition, we
establish local size control of tests which use the resampling procedure. Monte
Carlo simulations assess the finite-sample properties of the proposed methods
and show accurate empirical size and nontrivial power of the procedures.
Finally, we apply our methods to the evaluation of a job training program using
bounds for the distribution function of treatment effects.


  A recent comment on our work (Phys. Rev. Lett., vol. 110, 016601 (2013)) by
A.A.Aligia claims that we "made mistakes in the evaluation of the lesser
quantities". It is further claimed that the distribution function of the
single-particle selfenergy of the interacting region in the Fermi liquid
regime, e.g. at small bias voltage, low temperature, and small frequency, is
continuous. These claims are based on a comparison of the particle-hole
symmetric case with results obtained from the approach of A.A.Aligia. We
disagree with these claims and show that the discrepancies that the comment
alludes to originate from a violation of Ward identities by the method employed
in the comment. A comparison of our approach with the numerical renormalization
group shows perfect agreement for the symmetric case.


  Cell polarization is a critical process that separates molecules into two
distinct regions in prokaryotic and eukaryotic cells, guiding biological
processes such as cell division and cell differentiation. Although several
underlying antagonistic reaction-diffusion networks capable of setting up cell
polarization have been identified experimentally and theoretically, our
understanding of how to manipulate pattern stability and asymmetry remains
incomplete, especially when only a subset of network components are known. Here
we present numerical results to show that the polarized pattern of an
antagonistic 2-node network collapses into a homogeneous state when subjected
to single-sided self-regulation, single-sided additional regulation, or unequal
system parameters. However, polarity can be restored through a combination of
two modifications that have opposing effects. Additionally, spatially
inhomogeneous parameters favoring respective domains stabilize their interface
at designated locations. To connect our findings to cell polarity studies of
the nematode Caenorhabditis elegans zygote, we reconstituted a 5-node network
where a 4-node circuit with full mutual inhibitions between anterior and
posterior is modified by a mutual activation in the anterior and an additional
mutual inhibition between the anterior and the posterior. Once again, a generic
set of kinetic parameters moves the interface towards either the anterior or
posterior end, yet a polarized pattern can be stabilized through spatial tuning
of one or more parameters coupled to intracellular or extracellular cues. A
user-friendly software, PolarSim, is introduced to facilitate the exploration
of networks with alternative node numbers, parameter values, and regulatory
pathways.


  We explore the emergence of persistent infection in a patch of population,
where the disease progression of the individuals is given by the SIRS model and
an individual becomes infected on contact with another infected individual. We
investigate the persistence of contagion qualitatively and quantitatively,
under varying degrees of heterogeneity in the initial population. We observe
that when the initial population is uniform, consisting of individuals at the
same stage of disease progression, infection arising from a contagious seed
does not persist. However when the initial population consists of randomly
distributed refractory and susceptible individuals, a single source of
infection can lead to sustained infection in the population, as heterogeneity
facilitates the de-synchronization of the phases in the disease cycle of the
individuals. We also show how the average size of the window of persistence of
infection depends on the degree of heterogeneity in the initial composition of
the population. In particular, we show that the infection eventually dies out
when the entire initial population is susceptible, while even a few
susceptibles among an heterogeneous refractory population gives rise to a large
persistent infected set.


  We see how nested sequents, a natural generalisation of hypersequents, allow
us to develop a systematic proof theory for modal logics. As opposed to other
prominent formalisms, such as the display calculus and labelled sequents,
nested sequents stay inside the modal language and allow for proof systems
which enjoy the subformula property in the literal sense. In the first part we
study a systematic set of nested sequent systems for all normal modal logics
formed by some combination of the axioms for seriality, reflexivity, symmetry,
transitivity and euclideanness. We establish soundness and completeness and
some of their good properties, such as invertibility of all rules,
admissibility of the structural rules, termination of proof-search, as well as
syntactic cut-elimination. In the second part we study the logic of common
knowledge, a modal logic with a fixpoint modality. We look at two infinitary
proof systems for this logic: an existing one based on ordinary sequents, for
which no syntactic cut-elimination procedure is known, and a new one based on
nested sequents. We see how nested sequents, in contrast to ordinary sequents,
allow for syntactic cut-elimination and thus allow us to obtain an ordinal
upper bound on the length of proofs.


  A spin-isospin dependent three-dimensional approach has been applied for
formulation of the three-nucleon bound state and a new expression for Faddeev
equation based on three-nucleon free basis state has been obtained. Then the
three-nucleon wave function has been obtained as a function of five independent
variables.


  The STAR experiment at the Relativistic Heavy Ion Collider (RHIC) at
Brookhaven National Laboratory (BNL) is carrying out a spin physics program
colliding transversely or longitudinally polarized proton beams at = 200-500
GeV to gain deeper insigh t into the spin structure and dynamics of the proton.
These studies provide fundamental insight into Quantum Chromodynamics (QCD).
One of the main objectives is the determination of the polarized gluon
distribution function, g, through the measurement of the longitudinal
double-spin asymmetry, ALL, for various processes. Inclusive hadron and jet
production from polarized pp collision data collected so far at = 200 GeV using
the STAR detector at RHIC have placed important constraints on g. Di-jet
producti on provides direct access to the initial parton kinematics at leading
order (LO) QCD and thus provides sensitivity to the Bjorken-x dependence of g.
The status of the mid-rapidity di-jet cross section analysis from the 2005 RHIC
run and the longitudinal d ouble-spin asymmetry at mid-rapidity for the 2006
data sample are discussed in these proceedings. Projections on future di-jet
measurements at STAR are provided.


  We introduce SAGE; a Generative LLM for inferring attribute values for
products across world-wide e-Commerce catalogs. We introduce a novel
formulation of the attribute-value prediction problem as a Seq2Seq
summarization task, across languages, product types and target attributes. Our
novel modeling approach lifts the restriction of predicting attribute values
within a pre-specified set of choices, as well as, the requirement that the
sought attribute values need to be explicitly mentioned in the text. SAGE can
infer attribute values even when such values are mentioned implicitly using
periphrastic language, or not-at-all-as is the case for common-sense defaults.
Additionally, SAGE is capable of predicting whether an attribute is
inapplicable for the product at hand, or non-obtainable from the available
information. SAGE is the first method able to tackle all aspects of the
attribute-value-prediction task as they arise in practical settings in
e-Commerce catalogs. A comprehensive set of experiments demonstrates the
effectiveness of the proposed approach, as well as, its superiority against
state-of-the-art competing alternatives. Moreover, our experiments highlight
SAGE's ability to tackle the task of predicting attribute values in zero-shot
setting; thereby, opening up opportunities for significantly reducing the
overall number of labeled examples required for training.


  We seek to understand the evolution of Wolf-Rayet central stars by comparing
the diffuse X-ray emission from their wind-blown bubbles with that from their
hydrogen-rich counterparts with predictions from hydrodynamical models. We
simulate the dynamical evolution of heat-conducting wind-blown bubbles using a
post-AGB-model of 0.595~Msun, allowing for variations of its evolutionary
timescale and wind power. For Wolf-Rayet central stars, the wind is
hydrogen-poor, more dense, and slower compared to O-type central stars. We use
the CHIANTI software to compute the X-ray properties of bubble models along the
evolutionary paths and explicitly allow for non-equilibrium ionisation of key
chemical elements. A sample of 12 planetary nebulae with diffuse X-ray emission
-- seven harbouring an O-type and five a Wolf-Rayet nucleus -- is used to test
the bubble models. The properties of most hydrogen-rich bubbles (X-ray
temperature, X-ray luminosity, size) and their central stars (photon and wind
luminosity) are fairly well represented by bubble models of our 0.595~Msun AGB
remnant. The bubble evolution of Wolf-Rayet objects is different, thanks to the
high radiation cooling of their carbon- and oxygen-rich winds. The bubble
formation is delayed, and eventually, evaporation begins, leading to chemically
stratified bubbles. The bubbles of the youngest Wolf-Rayet objects appear
chemically uniform, the chemically stratified bubbles of the evolved Wolf-rayet
objects have excessively low characteristic temperatures that cannot be
explained by our modelling. The formation of nebulae with O-type nuclei follows
mainly a single path, but the formation pathways leading to the Wolf-Rayet-type
objects appear diverse.


  We investigate the one-dimensional Hubbard model with an additional
bond-charge interaction, recently considered in the description of compounds
that exhibit strong 1D features above the temperature of ordered phases. The
partition function of the model is exactly calculated for a value of the
bond-charge coupling; the behavior of the specific heat and spin susceptibility
as a function of temperature is derived at arbitrary filling, and particularly
discussed across the occurring metal-insulator transition. The results show
that the bond-charge terms weaken the spin excitations of the system.


  Federated learning (FL) allows multiple clients to collaboratively learn a
globally shared model through cycles of model aggregation and local model
training, without the need to share data. Most existing FL methods train local
models separately on different clients, and then simply average their
parameters to obtain a centralized model on the server side. However, these
approaches generally suffer from large aggregation errors and severe local
forgetting, which are particularly bad in heterogeneous data settings. To
tackle these issues, in this paper, we propose a novel FL framework that uses
online Laplace approximation to approximate posteriors on both the client and
server side. On the server side, a multivariate Gaussian product mechanism is
employed to construct and maximize a global posterior, largely reducing the
aggregation errors induced by large discrepancies between local models. On the
client side, a prior loss that uses the global posterior probabilistic
parameters delivered from the server is designed to guide the local training.
Binding such learning constraints from other clients enables our method to
mitigate local forgetting. Finally, we achieve state-of-the-art results on
several benchmarks, clearly demonstrating the advantages of the proposed
method.