  In this work, we further investigate the application of the well-known
Richardson extrapolation (RE) technique to accelerate the convergence of
sequences resulting from linear multistep methods (LMMs) for numerically
solving initial-value problems of systems of ordinary differential equations.
By extending the ideas of our previous paper, we now utilize some advanced
versions of RE in the form of repeated RE (RRE). Assume that the underlying LMM
-- the base method -- has order $p$ and RE is applied $l$ times. Then we prove
that the accelerated sequence has convergence order $p+l$. The version we
present here is global RE (GRE, also known as passive RE), since the terms of
the linear combinations are calculated independently. Thus, the resulting
higher-order LMM-RGRE methods can be implemented in a parallel fashion and
existing LMM codes can directly be used without any modification. We also
investigate how the linear stability properties of the base method (e.g. $A$-
or $A(\alpha)$-stability) are preserved by the LMM-RGRE methods.


  We propose a GAN design which models multiple distributions effectively and
discovers their commonalities and particularities. Each data distribution is
modeled with a mixture of $K$ generator distributions. As the generators are
partially shared between the modeling of different true data distributions,
shared ones captures the commonality of the distributions, while non-shared
ones capture unique aspects of them. We show the effectiveness of our method on
various datasets (MNIST, Fashion MNIST, CIFAR-10, Omniglot, CelebA) with
compelling results.


  In this paper we discuss the geometry of affine Deligne Lusztig varieties
with very special level structure, determining their dimension and connected
and irreducible components. As application, we prove the Grothendieck
conjecture for Shimura varieties with very special level at $p$ and a function
field analogue.


  Let G be a planar triangle-free graph and let C be a cycle in G of length at
most 8. We characterize all situations where a 3-coloring of C does not extend
to a proper 3-coloring of the whole graph.


  We propose a nonperturbative quantum dissipation theory, in term of
hierarchical quantum master equation. It may be used with a great degree of
confidence to various dynamics systems in condensed phases. The theoretical
development is rooted in an improved semiclassical treatment of Drude bath,
beyond the conventional high temperature approximations. It leads to the new
theory a simple modification but important improvement over the conventional
stochastic Liouville equation theory, without extra numerical cost. Its broad
range of validity and applicability is extensively demonstrated with two--level
electron transfer model systems, where the new theory can be considered as the
modified Zusman equation. We also present a criterion, which depends only on
the system--bath coupling strength, characteristic bath memory time, and
temperature, to estimate the performance of the hierarchical quantum master
equation.


  The deployment of Artificial Neural Networks (ANNs) in safety-critical
applications poses a number of new verification and certification challenges.
In particular, for ANN-enabled self-driving vehicles it is important to
establish properties about the resilience of ANNs to noisy or even maliciously
manipulated sensory input. We are addressing these challenges by defining
resilience properties of ANN-based classifiers as the maximal amount of input
or sensor perturbation which is still tolerated. This problem of computing
maximal perturbation bounds for ANNs is then reduced to solving mixed integer
optimization problems (MIP). A number of MIP encoding heuristics are developed
for drastically reducing MIP-solver runtimes, and using parallelization of
MIP-solvers results in an almost linear speed-up in the number (up to a certain
limit) of computing cores in our experiments. We demonstrate the effectiveness
and scalability of our approach by means of computing maximal resilience bounds
for a number of ANN benchmark sets ranging from typical image recognition
scenarios to the autonomous maneuvering of robots.


  In this paper we perform a fusion between two important theoretical
methodologies, one related to the Frozen Wave beams, which are non-diffracting
beams whose longitudinal intensity pattern can be chosen a priori in an medium
(absorbing or not), and the other related to the Airy-Type pulses, which are
pulses resistant to dispersion effects in dispersive materials. As a result, a
new method emerges, capable of providing vortex pulses resistant to three
concomitant effects, i.e.: diffraction, dispersion and attenuation; while
concurrently the spatial variation of the wave intensity along its axis of
propagation can be engineered at will. The new approach can be seen as a
generalization of the Localized Waves theory in the paraxial regime and the new
pulses can have potential applications in different fields such as optics
communications, nonlinear optics, micromanipulation, and so on.


  This paper aims to unify and extend existing techniques for deriving upper
bounds on the transient of max-plus matrix powers. To this aim, we introduce
the concept of weak CSR expansions: A^t=CS^tR + B^t. We observe that most of
the known bounds (implicitly) take the maximum of (i) a bound for the weak CSR
expansion to hold, which does not depend on the values of the entries of the
matrix but only on its pattern, and (ii) a bound for the CS^tR term to
dominate. To improve and analyze (i), we consider various cycle replacement
techniques and show that some of the known bounds for indices and exponents of
digraphs apply here. We also show how to make use of various parameters of
digraphs. To improve and analyze (ii), we introduce three different kinds of
weak CSR expansions (named after Nachtigall, Hartman-Arguelles, and Cycle
Threshold). As a result, we obtain a collection of bounds, in general
incomparable to one another, but better than the bounds found in the
literature.


  We re-examine the kinematic variable m_T2 and its relatives in the light of
recent work by Cheng and Han. Their proof that m_T2 admits an equivalent, but
implicit, definition as the `boundary of the region of parent and daughter
masses that is kinematically consistent with the event hypothesis' is
far-reaching in its consequences. We generalize their result both to simpler
cases (m_T, the transverse mass) and to more complex cases (m_TGen). We further
note that it is possible to re-cast many existing and unpleasant proofs (e.g.
those relating to the existence or properties of "kink" and "crease" structures
in m_T2) into almost trivial forms by using the alternative definition. Not
only does this allow us to gain better understanding of those existing results,
but it also allows us to write down new (and more or less explicit) definitions
of (a) the variable that naturally generalizes m_T2 to the case in which the
parent or daughter particles are not identical, and (b) the inverses of m_T and
m_T2 -- which may be useful if daughter masses are known and bounds on parent
masses are required. We note the implications that these results may have for
future matrix-element likelihood techniques.


  We study theoretically the nonstationary circuit QED system in which the
artificial atom transition frequency, or the atom-cavity coupling, have a small
periodic time modulation, prescribed externally. The system formed by the atom
coupled to a single cavity mode is described by the Rabi Hamiltonian. We show
that, in the dispersive regime, when the modulation periodicity is tuned to the
`resonances', the system dynamics presents the dynamical Casimir effect,
resonant Jaynes-Cummings or resonant Anti-Jaynes-Cummings behaviors, and it can
be described by the corresponding effective Hamiltonians. In the resonant
atom-cavity regime and under the resonant modulation, the dynamics is similar
to the one occurring for a stationary two-level atom in a vibrating cavity, and
an entangled state with two photons can be created from vacuum. Moreover, we
consider the situation in which the atom-cavity coupling, the atomic frequency,
or both have a small nonperiodic time modulation, and show that photons can be
created from vacuum in the dispersive regime. Therefore, an analog of the
dynamical Casimir effect can be simulated in circuit QED, and several photons,
as well as entangled states, can be generated from vacuum due to the
anti-rotating term in the Rabi Hamiltonian.


  The language model (LM) approach based on acoustic and linguistic prompts,
such as VALL-E, has achieved remarkable progress in the field of zero-shot
audio generation. However, existing methods still have some limitations: 1)
repetitions, transpositions, and omissions in the output synthesized speech due
to limited alignment constraints between audio and phoneme tokens; 2)
challenges of fine-grained control over the synthesized speech with
autoregressive (AR) language model; 3) infinite silence generation due to the
nature of AR-based decoding, especially under the greedy strategy. To alleviate
these issues, we propose ELLA-V, a simple but efficient LM-based zero-shot
text-to-speech (TTS) framework, which enables fine-grained control over
synthesized audio at the phoneme level. The key to ELLA-V is interleaving
sequences of acoustic and phoneme tokens, where phoneme tokens appear ahead of
the corresponding acoustic tokens. The experimental findings reveal that our
model outperforms VALL-E in terms of accuracy and delivers more stable results
using both greedy and sampling-based decoding strategies. The code of ELLA-V
will be open-sourced after cleanups. Audio samples are available at
https://ereboas.github.io/ELLAV/.


  Dematerialization is the reduction in the quantity of materials needed to
produce something useful over time. Dematerialization fundamentally derives
from ongoing increases in technical performance but it can be counteracted by
demand rebound - increases in usage because of increased value (or decreased
cost) that also results from increasing technical performance. A major question
then is to what extent technological performance improvement can offset and is
offsetting continuously increasing economic consumption. This paper contributes
to answering this question by offering some simple quantitative extensions to
the theory of dematerialization. The paper then empirically examines the
materials consumption trends as well as cost trends for a large set of
materials and a few modern artifacts over the past decades. In each of 57 cases
examined, the particular combinations of demand elasticity and technical
performance rate improvement are not consistent with dematerialization.
Overall, the theory extension and empirical examination indicate that there is
no dematerialization occurring even for cases of information technology with
rapid technical progress. Thus, a fully passive policy stance that relies on
unfettered technological change is not supported by our results.


  We introduce G_2-vector fields, Rochesterian 1-forms and Rochesterian vector
fields on manifolds with a closed G_2-structure as analogues of symplectic
vector fields, Hamiltonian functions and Hamiltonian vector fields
respectively, and we show that the spaces of G_2-vector fields and of
Rochesterian vector fields are Lie subalgebras of the Lie algebra of vector
fields with the standard Lie bracket. We also define, in analogy with the
Poisson bracket on smooth real-valued functions from symplectic geometry, a
bracket operation on the space of Rochesterian 1-forms associated to the space
of Rochesterian vector fields and prove, despite the lack of a Jacobi identity,
a relationship between this bracket and diffeomorphisms which preserve
G_2-structures.


  Instructional videos provide detailed how-to guides for various tasks, with
viewers often posing questions regarding the content. Addressing these
questions is vital for comprehending the content, yet receiving immediate
answers is difficult. While numerous computational models have been developed
for Video Question Answering (Video QA) tasks, they are primarily trained on
questions generated based on video content, aiming to produce answers from
within the content. However, in real-world situations, users may pose questions
that go beyond the video's informational boundaries, highlighting the necessity
to determine if a video can provide the answer. Discerning whether a question
can be answered by video content is challenging due to the multi-modal nature
of videos, where visual and verbal information are intertwined. To bridge this
gap, we present the YTCommentQA dataset, which contains naturally-generated
questions from YouTube, categorized by their answerability and required
modality to answer -- visual, script, or both. Experiments with answerability
classification tasks demonstrate the complexity of YTCommentQA and emphasize
the need to comprehend the combined role of visual and script information in
video reasoning. The dataset is available at
https://github.com/lgresearch/YTCommentQA.


  It has been known since 2007 that the Wilson and Racah polynomials can be
characterized as basis functions for irreducible representations of the
quadratic symmetry algebra of the quantum superintegrable system on the
2-sphere, $H\Psi=E\Psi$, with generic 3-parameter potential. Clearly, the
polynomials are expansion coefficients for one eigenbasis of a symmetry
operator $L_1$ of $H$ in terms of an eigenbasis of another symmetry operator
$L_2$, but the exact relationship appears not to have been made explicit. We
work out the details of the expansion to show, explicitly, how the polynomials
arise and how the principal properties of these functions: the measure, 3-term
recurrence relation, 2nd order difference equation, duality of these relations,
permutation symmetry, intertwining operators and an alternate derivation of
Wilson functions -- follow from the symmetry of this quantum system. There is
active interest in the relation between multivariable Wilson polynomials and
the quantum superintegrable system on the $n$-sphere with generic potential,
and these results should aid in the generalization. Contracting function space
realizations of irreducible representations of this quadratic algebra to the
other superintegrable systems one can obtain the full Askey scheme of
orthogonal hypergeometric polynomials. All of these contractions of
superintegrable systems with potential are uniquely induced by Wigner Lie
algebra contractions of $so(3, C )$ and $e(2, C)$. All of the polynomials
produced are interpretable as quantum expansion coefficients. It is important
to extend this process to higher dimensions.


  We prove that the spaces of C1 symplectomorphisms and of C1 volume-preserving
diffeomorphisms of connected manifolds both contain residual subsets of
diffeomorphisms whose centralizers are trivial. (Les diff\'eomorphismes
conservatifs C1-g\'en\'eriques ont un centralisateur trivial. Nous montrons que
l'espace des symplectomorphismes de classe C1 et l'espace des
diff\'eomomorphismes de classe C1 pr\'eservant une forme volume contiennent
tous deux des sous-ensembles r\'esiduels de diff\'eomorphismes dont le
centralisateur est trivial.)


  The density perturbation of the universe has been considered in the framework
of a Finslerian cosmological model in which the background spacetime of the
universe is taken as the spatially flat FLRW spacetime with a Finslerian
perturbation. The inhomogeneity in the matter(energy) density arises naturally
in this consideration of gravity in the $( \alpha, \beta)$ - Finsler space for
the background spacetime of the universe. The resulting inhomogeneous matter
density indicates matter perturbation departing from the uniform density, and
it is caused by the Finslerian perturbation in the Riemannian spacetime, thus
ascertaining the geometrical origin of the growth of matter perturbation.


  Higgs boson production via weak boson fusion is sensitive to the tensor
structure of the HVV (V=W,Z) couplings, which distinguishes loop induced
vertices from SM expectations. At the CERN Large Hadron Collider this
information shows up most clearly in the azimuthal angle correlations of the
two forward and backward quark jets which are typical for weak boson fusion. We
calculate the next-to-leading order QCD corrections to this process, in the
presence of anomalous HVV couplings. Gluon emission does not significantly
change the azimuthal jet correlations.


  We have performed four-terminal conductance measurements of a one-dimensional
(1D) channel in which it is possible to modulate the potential profile using
three overlaying finger gates. In such a 1D ballistic structure we have
observed, {\em for the first time,} that the conductance steps show a gradual
decrease from $2e^2/h$ to $0.97 \times 2e^2/h$ with increasing negative finger
gate voltage in a short, clean 1D constriction. We suggest this phenomenon is
due to differing shifts of 1D subbands with changing spilt-gate voltage. Both a
simple analytical estimate for an adiabatic constriction and, realistic
modeling of the device, give the same magnitude of the conductance decrease as
observed in our experiments.


  The main goal of this study is to propose a mathematical model describing
paths of the axon growth cones and differences in the behavior of normal and
mutant axons. We introduce a probabilistic model for axon growing, such that
each family of axons is described as an ensemble of trajectories of a
continuous time random walk (CTRW) model under different parameters in the case
of normal and mutant axons. We describe different regimes in the model and
conclude how the behavior of axons depends on the parameters of the model.
Biological observations of the axonal growth process say us that the guiding
development of axons to their targets is operated by chemical signals from the
cellular environment. To simulate this control mechanism we propose the CTRW
model, where a random waiting time reflects a reaction time of the growth cones
on the neighboring chemical environment.


  We study a quantum repeater which is based on decoherence free quantum gates
recently proposed by Klein et al. [Phys. Rev. A 73, 012332 (2006)]. A number of
operations on the decoherence free subspace in this scheme makes use of an
ancilla qubit, which undergoes dephasing and thus introduces decoherence to the
system. We examine how this decoherence affects entanglement swapping and
purification as well as the performance of a quantum repeater. We compare the
decoherence free quantum repeater with a quantum repeater based on qubits that
are subject to decoherence and show that it outperforms the latter when
decoherence due to long waiting times of conventional qubits becomes
significant. Thus, a quantum repeater based on decoherence free subspaces is a
possibility to greatly improve quantum communication over long or even
intercontinental distances.


  A measurement of the shape of the differential decay rate and the associated
Isgur-Wise function for the decay
$\Lambda_b^0\to\Lambda_c^+\mu^-\overline{\nu}$ is reported, using data
corresponding to $3 fb^{-1}$ collected with the LHCb detector in proton-proton
collisions. The $\Lambda_c^+\mu^-\overline{\nu}$(+ anything) final states are
reconstructed through the detection of a muon and a $\Lambda_c^+$ baryon
decaying into $pK^-\pi^+$, and the decays
$\Lambda_b^0\to\Lambda_c^+\pi^+\pi^-\mu^-\overline{\nu}$ are used to determine
contributions from $\Lambda_b^0\to \Lambda_c^{\star+}\mu ^-\bar{\nu}$ decays.
The measured dependence of the differential decay rate upon the squared
four-momentum transfer between the heavy baryons, $q^2$, is compared with
expectations from heavy-quark effective theory and from unquenched lattice QCD
predictions.


  By using computers to do experimental manipulations on Fourier series, we
construct additional series with interesting properties. We construct several
series whose sums remain unchanged when the $n^{th}$ term is multiplied by
$\sin(n)/n$. One example is this classic series for $\pi/4$: \[
  \frac{\pi}{4} = 1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \dots = 1 \cdot
\frac{\sin(1)}{1} - \frac{1}{3} \cdot \frac{\sin(3)}{3} + \frac{1}{5} \cdot
\frac{\sin(5)}{5} - \frac{1}{7} \cdot \frac{\sin(7)}{7} + \dots . \] Another
example is \[ \sum_{n=1}^{\infty} \frac{\sin(n)}{n} = \sum_{n=1}^{\infty}
\left(\frac{\sin(n)}{n}\right)^2 = \frac{\pi-1}{2}. \] This paper also
discusses an included Mathematica package that makes it easy to calculate and
graph the Fourier series of many types of functions.


  In February 2007, the fourth stage of the Mainz Microtron, MAMI-C, started
operations with a first experiment. The new Harmonic Double-Sided Microtron
delivers an electron beam with energies up to 1.5 GeV while preserving the
excellent beam quality of the previous stages. The experimental program at MAMI
is focused on studies of the hadron structure in the domain of non-perturbative
QCD. In this paper, a few prominent selections of the extensive physics program
at MAMI-C will be presented.


  Divergence functions are interesting discrepancy measures. Even though they
are not true distances, we can use them to measure how separated two points
are. Curiously enough, when they are applied to random variables, they lead to
a notion of best predictor that coincides with usual best predictor in
Euclidean distance. Given a divergence function, we can derive from it a
Riemannian metric, which leads to a distance in which means and best predictors
do not coincide with their Euclidean counterparts. It is the purpose of this
note to study the Riemannian metric derived from the divergence function as
well as its use in prediction theory.


  We present that two spin defects (SDs) can be entangled through a magnon
polariton mode, within the strong coupling regime. The magnonic modes are
provided by an antiferromagnetic (AF) MnF$_{2}$ layer and their dispersion is
characterized by the layer's thickness. The macroscopic quantum electrodynamics
theory is used to describe the light-matter interactions, where the Green's
functions are its core element. The individual SD relaxes by exciting the
magnon polariton modes, exhibiting high enhancement values of the Purcell
factor. When two SDs are considered, an oscillatory population exchange is
observed between them, a sign of strong light-matter coupling, where the
concurrence value is used to quantify the level of entanglement. The thinner AF
layers can potentially be used to promote interactions between multiple spins
through long range coupling, this is a desired feature to fabricate high demand
applications in the fields of quantum measurement and computation.


  The modified eccentric connectivity index of a graph is defined as the sum of
the products of eccentricity with the total degree of neighboring vertices,
over all vertices of the graph. This is a generalization of eccentric
connectivity index. In this paper, we derive some upper and lower bounds for
the modified eccentric connectivity index in terms of some graph parameters
such as number of vertices, number of edges, radius, minimum degree, maximum
degree, total eccentricity, the first and second Zagreb indices, Weiner index
etc.


  In this work, we have characterized changes in the dynamics of a
two-dimensional relativistic standard map in the presence of dissipation and
specially when it is submitted to thermal effects modeled by a Gaussian noise
reservoir. By the addition of thermal noise in the dissipative relativistic
standard map (DRSM) it is possible to suppress typical stable periodic
structures (SPSs) embedded in the chaotic domains of parameter space for large
enough temperature strengths. Smaller SPSs are first affected by thermal
effects, starting from their borders, as a function of temperature. To estimate
the necessary temperature strength capable to destroy those SPSs we use the
largest Lyapunov exponent to obtain the critical temperature ($T_C$) diagrams.
For critical temperatures the chaotic behavior takes place with the suppression
of periodic motion, although, the temperature strengths considered in this work
are not so large to convert the deterministic features of the underlying system
into a stochastic ones.


  In the standard inflationary scenario with inflaton potential
$V(\Phi)=M^4-{1\over4}\lambda\Phi^4$, the resulting density perturbations
$\delta\rho/\rho$ are proportional to $\lambda^{1/2}$. Upper bounds on
$\delta\rho/\rho$ require $\lambda < 10^{-13}$. Ratra has shown that an
alternative treatment of reheating results in $\delta\rho/\rho \propto
\lambda^{-1}$, so that an upper bound on $\delta\rho/\rho$ does not put an
obvious upper bound on $\lambda$. We verify that $\delta\rho/\rho \propto
\lambda^{-1}$ is indeed a possibility, but show that $\lambda < 10^{-13}$ is
still required.


  The area law for entanglement provides one of the most important connections
between information theory and quantum many-body physics. It is not only
related to the universality of quantum phases, but also to efficient numerical
simulations in the ground state. Various numerical observations have led to a
strong belief that the area law is true for every non-critical phase in
short-range interacting systems. However, the area law for long-range
interacting systems is still elusive, as the long-range interaction results in
correlation patterns similar to those in critical phases. Here, we show that
for generic non-critical one-dimensional ground states with locally bounded
Hamiltonians, the area law robustly holds without any corrections, even under
long-range interactions. Our result guarantees an efficient description of
ground states by the matrix-product state in experimentally relevant long-range
systems, which justifies the density-matrix renormalization algorithm.


  Recent studies of non-Hermitian periodic lattices unveiled the non-Hermitian
skin effect (NHSE), in which the bulk modes under the periodic boundary
conditions (PBC) become skin modes under open boundary conditions (OBC). The
NHSE is a topological effect owing to the non-trivial spectral winding, and
such spectral behaviors appear naturally in non-reciprocal systems. Hence
prevailing approaches rely on non-reciprocity to achieve the NHSE. Here, we
report the experimental realization of the geometry-dependent skin effect
(GDSE) in a two-dimensional (2D) reciprocal system, in which the skin effect
occurs only at boundaries whose macroscopic symmetry mismatches with the
lattice symmetry. The role of spectral reciprocity and symmetry is revealed by
connecting reflective channels at given boundaries with the spectral topology
of the PBC spectrum. Our work highlights the vital role of reciprocity and
macroscopic geometry on the NHSE in systems with dimensions larger than one and
opens new routes for wave structuring using non-Hermitian effects.


  In our previous work, Hopf cyclic cohomology in braided monoidal categories,
we extended the formalism of Hopf cyclic cohomology due to Connes and Moscovici
and the more general case of Hopf cyclic cohomology with coefficients to the
context of abelian braided monoidal categories. In this paper we go one step
further in reducing the restriction of the ambient category being symmetric. We
let the ambient category to be non-symmetric but assume only the restriction on
the braid map for the Hopf algebra object (in that category) which is the main
player in the theory. In the case of Hopf cyclic cohomology with (nontrivial)
coefficients we also need to have similar restrictions on the braid map for the
object(s) providing the coefficients datum. We present a family of examples of
non-symmetric categories in which many objects with such a restrictions on the
braid map exist (anyonic vector spaces).


  We present a snapshot Hubble Space Telescope (HST) image of the galaxy
cluster A1201 (z=0.169), revealing a tangential arc 2arcsec from the brightest
cluster galaxy (BCG). Keck-ESI spectroscopy confirms that the arc is
gravitational in nature and that the source galaxy lies at z=0.451. We
construct a model of the gravitational potential of the cluster that faithfully
reproduces the observed arc morphology. Despite the relaxed appearance of the
cluster in the HST frame, the best fit ellipticity of the total matter
distribution is epsilon_total>0.5, in contrast to the light distribution of the
BCG epsilon_BCG=0.23+/-0.03 on 2'' scales. Further deep optical observations
and pointed X-ray spectro-imaging observations with Chandra are required to
determine whether this elongation is due to a single elongated dark matter
halo, or a more complex distribution of matter in the cluster core. We compare
the arc with a sample drawn from the published literature, and confirm that it
is unique among tangential systems in the small physical scales that it probes
(6kpc). In anticipation of a more thorough investigation of this cluster across
a broad range of physical scales, we use our fiducial lens model to estimate
the projected mass and mass-to-light ratio of the cluster within a radius of
6kpc, obtaining: M=(5.9^+0.9_-0.7)x10^11 M_o, M/L_V=9.4^+2.4_-2.1(M/L)_o.
Overall our results confirm the importance of HST snapshot surveys for
identifying rare lensing constraints on cluster mass distributions. In
combination with follow--up optical and X-ray observations, the arc in A1201
should help to increase our understanding of the physics of cluster cores.


  In this paper we describe a detailed analysis of the photometric
uncertainties present within the Sloan Digital Sky Survey (SDSS) imaging survey
based on repeat observations of approximately 200 square degrees of the sky. We
show that, for the standard SDSS aperture systems (petrocounts, counts_model,
psfcounts and cmodel_counts), the errors generated by the SDSS photometric
pipeline under-estimate the observed scatter in the individual bands. The
degree of disagreement is a strong function of aperture and magnitude (ranging
from 20% to more than a factor of 2). We also find that the photometry in the
five optical bands can be highly correlated for both point sources and
galaxies, although the correlation for point sources is almost entirely due to
variable objects. Without correcting for this covariance the SDSS color errors
could be in over-estimated by a factor of two to three. Combining these
opposing effects, the SDSS errors on the colors differ from the observed color
variation by approximately 10-20% for most apertures and magnitudes. We provide
a prescription to correct the errors derived from the SDSS photometric pipeline
as a function of magnitude and a semi-analytic method for generating the
appropriate covariance between the different photometric passbands. Given the
intrinsic nature of these correlations, we expect that all current and future
multi-band surveys will also observe strongly covariant magnitudes. The ability
of these surveys to complete their science goals is largely dependent on
color-based target selection and photometric redshifts; these results show the
importance of spending a significant fraction of early survey operations on
re-imaging to empirically determine the photometric covariance of any
observing/reduction pipeline.


  The azimuthal correlations of D mesons and charged particles were measured
with the ALICE detector in pp collisions at $\sqrt{s}=7$ TeV and p-Pb
collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV at the Large Hadron Collider. D$^0$,
D$^+$, and D$^{*+}$ mesons and their charge conjugates with transverse momentum
$3<p_{\rm T}<16$ GeV/$c$ and rapidity in the nucleon-nucleon centre-of-mass
system $|y_{\rm cms}|<0.5$ (pp collisions) and $-0.96<y_{\rm cms}<0.04$ (p-Pb
collisions) were correlated to charged particles with $p_{\rm T}>0.3$ Gev/$c$.
The properties of the correlation peak induced by the jet containing the D
meson, described in terms of the yield of charged particles in the peak and
peak width, are compatible within uncertainties between the two collision
systems, and described by Monte-Carlo simulations based on the PYTHIA, POWHEG
and EPOS 3 event generators.


  Semimetallic CeNiSn is shown to transform into a Kondo semiconductor upon the
substitution of few percent of Sb for Sn. The full-gap formation is not
decisively influenced by the atomic disorder introduced by the substitution.
Instead, the extra valence electrons introduced with the Sb doping (one per Sb
atom) contribute to the formation of the collective Kondo spin-singlet state at
low temperatures, as seen by a reduction of magnetic susceptibility. The
definition of the Kondo semiconductor is provided and the difference with
either the band-Kondo or the Mott-Hubbard insulators is stressed.


  We present a new method to extract anisotropic flow in heavy ion collisions
from the genuine correlation among a large number of particles. Anisotropic
flow is obtained from the zeroes in the complex plane of a generating function
of azimuthal correlations, in close analogy with the theory of phase
transitions by Lee and Yang. Flow is first estimated globally, i.e., averaged
over the phase space covered by the detector, and then differentially, as a
function of transverse momentum and rapidity for identified particles. The
corresponding estimates are less biased by nonflow correlations than with any
other method. The practical implementation of the method is rather
straightforward. Furthermore, it automatically takes into account most
corrections due to azimuthal anisotropies in the detector acceptance. The main
limitation of the method is statistical errors, which can be significantly
larger than with the ``standard'' method of flow analysis if the flow and/or
the event multiplicities are too small. In practice, we expect this to be the
most accurate method to analyze directed and elliptic flow in fixed-target
heavy-ion collisions between 100 MeV and 10 GeV per nucleon (at the Darmstadt
SIS synchrotron and the Brookhaven Alternating Gradient Synchrotron), and
elliptic flow at ultrarelativistic energies (at the Brookhaven Relativistic
Heavy Ion Collider, and the forthcoming Large Hadron Collider at CERN).


  This study aims to inspect and evaluate the integration of database queries
and their use in e-commerce product searches. It has been observed that
e-commerce is one of the most prominent trends, which have been emerged in the
business world, for the past decade. E-commerce has gained tremendous
popularity, as it offers higher flexibility, cost efficiency, effectiveness,
and convenience, to both, consumers and businesses. Large number of retailing
companies has adopted this technology, in order to expand their operations,
across of the globe; hence they needs to have highly responsive and integrated
databases. In this regard, the approach of database queries is found to be the
most appropriate and adequate techniques, as it simplifies the searches of
e-commerce products.


  The direct-coupling analysis is a powerful method for protein contact
prediction, and enables us to extract "direct" correlations between distant
sites that are latent in "indirect" correlations observed in a protein
multiple-sequence alignment. I show that the direct correlation can be obtained
by using a formulation analogous to the Ornstein-Zernike integral equation in
liquid theory. This formulation intuitively illustrates how the indirect or
apparent correlation arises from an infinite series of direct correlations, and
provides interesting insights into protein structure prediction.


  Using the close relationship between coactions of discrete groups and Fell
bundles, we introduce a procedure for inducing a C*-coaction of a quotient
group G/N of a discrete group G to a C*-coaction of G itself on an induced
C*-algebra. We show that induced coactions behave in many respects similarly to
induced actions. In particular, as an analogue of the well known imprimitivity
theorem for induced actions we prove that the crossed products of the original
and the induced coactions are always Morita equivalent. We also obtain
nonabelian analogues of a theorem of Olesen and Pedersen which show that there
is a duality between induced coactions and twisted actions in the sense of
Green. We further investigate amenability of Fell bundles corresponding to
induced coactions.


  Change of numeraire is a classical tool in mathematical finance.
Campi-Laachir-Martini established its applicability to martingale optimal
transport. We note that the results of Campi-Laachir-Martini extend to the case
of weak martingale transport. We apply this to shadow couplings, continuous
time martingale transport problems in the framework of Huesmann-Trevisan and in
particular to establish the correspondence between stretched Brownian motion
with its geometric counterpart.
  Note: We emphasize that we learned about the geometric stretched Brownian
motion gSBM (defined in PDE terms) in a presentation of Loeper \cite{Lo23}
before our work on this topic started. We noticed that a change of numeraire
transformation in the spirit of \cite{CaLaMa14} allows for an alternative
viewpoint in the weak optimal transport framework. We make our work public
following the publication of Backhoff-Loeper-Obloj's work \cite{BaLoOb24} on
arxiv.org. The article \cite{BaLoOb24} derives gSBM using PDE techniques as
well as through an independent probabilistic approach which is close to the one
we give in the present article.


  We demonstrate full suppression of dephasing tied to deformation potential
coupling of confined electrons to longitunidal acoustic (LA) phonons in optical
control experiments on large semiconductor quantum dots (QDs) with emission
compatible with the low-dispersion telecommunications band at 1.3~$\mu$m. By
exploiting the sensitivity of the electron-phonon spectral density to the size
and shape of the QD, we demonstrate a four-fold reduction in the threshold
pulse area required to enter the decoupled regime for exciton inversion using
adiabatic rapid passage (ARP). Our calculations of the quantum state dynamics
provide good agreement with our experimental results and indicate that the
symmetry of the QD wave function provides an additional means to engineer the
electron-phonon interaction. Our findings will support the development of
solid-state quantum emitters in future distributed quantum networks using
semiconductor QDs.


  The non-stationarity characteristic of the solar power renders traditional
point forecasting methods to be less useful due to large prediction errors.
This results in increased uncertainties in the grid operation, thereby
negatively affecting the reliability and increased cost of operation. This
research paper proposes a unified architecture for multi-time-horizon
predictions for short and long-term solar forecasting using Recurrent Neural
Networks (RNN). The paper describes an end-to-end pipeline to implement the
architecture along with the methods to test and validate the performance of the
prediction model. The results demonstrate that the proposed method based on the
unified architecture is effective for multi-horizon solar forecasting and
achieves a lower root-mean-squared prediction error compared to the previous
best-performing methods which use one model for each time-horizon. The proposed
method enables multi-horizon forecasts with real-time inputs, which have a high
potential for practical applications in the evolving smart grid.


  In a seminal 1965 paper, Motzkin and Straus established an elegant connection
between the clique number of a graph and the global maxima of a quadratic
program defined on the standard simplex. Since then, the result has been the
subject of intensive research and has served as the motivation for a number of
heuristics and bounds for the maximum clique problem. Most of the studies
available in the literature, however, focus typically on the local/global
solutions of the program, and little or no attention has been devoted so far to
the study of its Karush-Kuhn-Tucker (KKT) points. In contrast, in this paper we
study the properties of (a parameterized version of) the Motzkin-Straus program
and show that its KKT points can provide interesting structural information and
are in fact associated with certain regular sub-structures of the underlying
graph.


  To investigate the physical processes, we present observational results of
the sites S234, V582, and IRAS 05231+3512 situated toward l = 171.7 - 174.1
degrees. Based on the CO line data, we find that these sites are not physically
connected, and contain at least one filament (with length > 7 pc). The observed
line masses (M_line,obs) of the filaments associated with V582 and IRAS
05231+3512 are ~37 and ~28 M_sun/pc, respectively. These filaments are
characterized as thermally supercritical, and harbor several clumps. Groups of
infrared-excess sources and massive B-type stars are observed toward the
filament containing V582, while a very little star formation (SF) activity is
found around IRAS 05231+3512. Our results favour radial collapse scenario in
the filaments harboring V582 and IRAS 05231+3512. In the site S234, two
filaments (i.e. ns1 (M_line,obs ~130 M_sun/pc) and ns2 (M_line,obs ~45
M_sun/pc)) are identified as thermally supercritical. An extended temperature
structure at 27-30 K surrounds a relatively cold (~19 K) ~8.9 pc long filament
ns1. At least four condensations (M_clump ~70-300 M_sun) are seen in ns1, and
are devoid of the GMRT 610 MHz radio emission. The filament ns2 hosting clumps
is devoid of ongoing SF, and could be at an early stage of fragmentation. An
intense SF activity, having the SF efficiency ~3.3% and SF rate ~40-20
M_sun/Myr (for t_sf ~1-2 Myr), is observed in ns1. The feedback of massive
stars in S234 seems to explain the observed SF in the filament ns1.


  We present an interactive system enabling users to manipulate images to
explore the robustness and sensitivity of deep learning image classifiers.
Using modern web technologies to run in-browser inference, users can remove
image features using inpainting algorithms and obtain new classifications in
real time, which allows them to ask a variety of "what if" questions by
experimentally modifying images and seeing how the model reacts. Our system
allows users to compare and contrast what image regions humans and machine
learning models use for classification, revealing a wide range of surprising
results ranging from spectacular failures (e.g., a "water bottle" image becomes
a "concert" when removing a person) to impressive resilience (e.g., a "baseball
player" image remains correctly classified even without a glove or base). We
demonstrate our system at The 2018 Conference on Computer Vision and Pattern
Recognition (CVPR) for the audience to try it live. Our system is open-sourced
at https://github.com/poloclub/interactive-classification. A video demo is
available at https://youtu.be/llub5GcOF6w.


  Traditionally one defines the speed of a wave as a property of the medium.
Recent studies in photonics have challenged this idea, indicating that spatial
shaping of the optical wavefront has can alter the arrival time of single
photons when compared to an entangled reference photon. However, relying only
on time of flight measurements leads to ambiguity in the measurement. Unlike
photonics, one can directly measure the phase and intensity of sound,
permitting unambiguous measurements. We developed a bespoke 28-element
ultrasonic phased array transducer to generate short pulses that carrying
orbital angular momentum. Through spatial mapping, we observed pulse modulation
that indicates a localised change in phase velocity by over 10 m/s. We present
a geometrical argument for this effect, proposing that the phase velocity
varies to compensate for the effective path length increase arising from
spatial wavefront shaping. We expect that this pulse dispersion is a general
effect for any spatially shaped wavefront and that it could be utilised to
manipulate readings from pulse based sensor technologies such as SONAR, medical
ultrasound, and underwater communication systems.


  Semantic communications is considered as a promising technology to increase
the efficiency of next-generation communication systems, particularly targeting
human-machine and machine-type communications. In contrast to the
source-agnostic approach of conventional wireless communication systems,
semantic communication seeks to ensure that only the relevant information for
the underlying task is communicated to the receiver. Considering that most
semantic communication applications have strict latency, bandwidth, and power
constraints, a prominent approach is to model them as a joint source-channel
coding (JSCC) problem. Although JSCC has been a long-standing open problem in
communication and coding theory, remarkable performance gains have been shown
recently over existing separate source and channel coding systems, particularly
in low-latency and low-power scenarios. Recent progress is thanks to the
adoption of deep learning techniques for joint source-channel code design that
outperform the concatenation of state-of-the-art compression and channel coding
schemes, which are results of decades-long research efforts. In this article,
we present an adaptive deep learning based JSCC (DeepJSCC) architecture for
semantic communications, introduce its design principles, highlight its
benefits, and outline future research challenges that lie ahead.


  We show that an optical vortex beam, implemented classically, can be
transferred to the transverse amplitude of a heralded single photon. For this
purpose we have relied on the process of spontaneous parametric downconversion
(SPDC) for the generation of signal and idler photon pairs, using a pump in the
form of a Bessel-Gauss (BG) beam with orbital angular momentum (specifically,
with topological charge l = 1 and l = 2). We have designed our source so that
it operates within the short SPDC crystal regime for which, the amplitude and
phase of the pump may be transferred to a heralded single photon. In order to
verify the vortex nature of our heralded single photon, we have shown that the
conditional angular spectrum and the transverse intensity at the single-photon
level match similar measurements carried out for the pump. In addition, we have
shown that when our heralded single photon is diffracted through a triangular
aperture, the far-field singlephoton transverse intensity exhibits the expected
triangular arrangement of intensity lobes associated with the presence of
orbital angular momentum.


  Because an agents resources dictate what actions it can possibly take, it
should plan which resources it holds over time carefully, considering its
inherent limitations (such as power or payload restrictions), the competing
needs of other agents for the same resources, and the stochastic nature of the
environment. Such agents can, in general, achieve more of their objectives if
they can use --- and even create --- opportunities to change which resources
they hold at various times. Driven by resource constraints, the agents could
break their overall missions into an optimal series of phases, optimally
reconfiguring their resources at each phase, and optimally using their assigned
resources in each phase, given their knowledge of the stochastic environment.
In this paper, we formally define and analyze this constrained, sequential
optimization problem in both the single-agent and multi-agent contexts. We
present a family of mixed integer linear programming (MILP) formulations of
this problem that can optimally create phases (when phases are not predefined)
accounting for costs and limitations in phase creation. Because our
formulations multaneously also find the optimal allocations of resources at
each phase and the optimal policies for using the allocated resources at each
phase, they exploit structure across these coupled problems. This allows them
to find solutions significantly faster(orders of magnitude faster in larger
problems) than alternative solution techniques, as we demonstrate empirically.


  We write a Renormalization Group (RG) equation for the function f in a theory
of gravity in the f(R) truncation. Our equation differs from previous ones due
to the exponential parametrization of the quantum fluctuations and to the
choice of gauge. The cutoff procedure depends on three free parameters, and we
find that there exist discrete special choices of parameters for which the flow
equation has fixed points where f=f_0+f_1 R+f_2 R^2. For other values of the
parameters the solution seems to be continuously deformed.


  We prove a weak version of Lusztig's conjecture on explicit description of
the asymptotic Hecke algebras (both finite and affine), and explain its
relation to Lusztig's classification of character sheaves.


  For a suitable triangulated category $\mathcal{T}$ with a Serre functor $S$
and a full precovering subcategory $\mathcal{C}$ closed under summands and
extensions, an indecomposable object $C$ in $\mathcal{C}$ is called
Ext-projective if Ext$^1(C,\mathcal{C})=0$. Then there is no Auslander-Reiten
triangle in $\mathcal{C}$ with end term $C$. In this paper, we show that if,
for such an object $C$, there is a minimal right almost split morphism
$\beta:B\rightarrow C$ in $\mathcal{C}$, then $C$ appears in something very
similar to an Auslander-Reiten triangle in $\mathcal{C}$: an essentially unique
triangle in $\mathcal{T}$ of the form \begin{align*}
  \Delta= X\xrightarrow{\xi} B\xrightarrow{\beta} C\rightarrow \Sigma X,
\end{align*} where $X$ is an indecomposable not in $\mathcal{C}$ and $\xi$ is a
$\mathcal{C}$-envelope of $X$. Moreover, under some extra assumptions, we show
that removing $C$ from $\mathcal{C}$ and replacing it with $X$ produces a new
subcategory of $\mathcal{T}$ closed under extensions. We prove that this
process coincides with the classic mutation of $\mathcal{C}$ with respect to
the rigid subcategory of $\mathcal{C}$ generated by all the indecomposable
Ext-projectives in $\mathcal{C}$ apart from $C$.
  When $\mathcal{T}$ is the cluster category of Dynkin type $A_n$ and
$\mathcal{C}$ has the above properties, we give a full description of the
triangles in $\mathcal{T}$ of the form $\Delta$ and show under which
circumstances replacing $C$ by $X$ gives a new extension closed subcategory.


  We present a numerical study of conductance oscillations of transition metal
multilayers as a function of layer thickness. Using a material-specific
tight-binding model, we show that for disorder-free layers with random
thicknesses but clean interfaces, long-period oscillations in the conductance
can occur, which are reminiscent of those found in structures exhibiting GMR.
Using a heuristic effective mass model, we argue that these oscillations arise
from beating between the Fermi wavevector and a class of wavevectors
characteristic of the superlattice structure.


  A review of the uses of the CD kernel in the spectral theory of orthogonal
polynomials, concentrating on recent results.


  Millimeter-wave will be a key technology in next-generation wireless networks
thanks to abundant bandwidth availability. However, the use of large antenna
arrays with beamforming demands precise beam-alignment between transmitter and
receiver, and may entail huge overhead in mobile environments. This paper
investigates the design of an optimal interactive beam-alignment and data
communication protocol, with the goal of minimizing power consumption under a
minimum rate constraint. The base-station selects beam-alignment or data
communication and the beam parameters, based on feedback from the user-end.
Based on the sectored antenna model and uniform prior on the angles of
departure and arrival (AoD/AoA), the optimality of a fixed-length
beam-alignment phase followed by a data-communication phase is demonstrated.
Moreover, a decoupled fractional beam-alignment method is shown to be optimal,
which decouples over time the alignment of AoD and AoA, and iteratively scans a
fraction of their region of uncertainty. A heuristic policy is proposed for
non-uniform prior on AoD/AoA, with provable performance guarantees, and it is
shown that the uniform prior is the worst-case scenario. The performance
degradation due to detection errors is studied analytically and via simulation.
The numerical results with analog beams depict up to 4dB, 7.5dB, and 14 dB
gains over a state-of-the-art bisection method, conventional and interactive
exhaustive search policies, respectively, and demonstrate that the sectored
model provides valuable insights for beam-alignment design.


  The singular parabolic problem $u_t-\triangle u=\lambda{\frac{1+\delta|\nabla
u|^2}{(1-u)^2}}$ on a bounded domain $\Omega$ of $\mathbb{R}^n$ with Dirichlet
boundary condition, models the Microelectromechanical systems (MEMS) device
with fringing field. In this paper, we focus on the quenching behavior of the
solution to this equation. We first show that there exists a critical value
$\lambda_\delta^*>0$ such that if $0<\lambda<\lambda_\delta^*$, all solutions
exist globally; while for $\lambda>\lambda_\delta^*$, all the solution will
quench in finite time. The estimate of the quenching time in terms of large
voltage $\lambda$ is investigated. Furthermore, the quenching set is a compact
subset of $\Omega$, provided $\Omega$ is a convex bounded domain in
$\mathbb{R}^n$. In particular, if the domain $\Omega$ is radially symmetric,
then the origin is the only quenching point. We not only derive the one-side
estimate of the quenching rate, but also further study the refined asymptotic
behavior of the finite quenching solution.


  A finite group $R$ is a DCI-group if, whenever $S$ and $T$ are subsets of $R$
with the Cayley graphs ${\rm Cay}(R,S)$ and ${\rm Cay}(R,T)$ isomorphic, there
exists an automorphism $\varphi$ of $R$ with $S^\varphi=T$.
  Elementary abelian groups of order $p^4$ or smaller are known to be
DCI-groups, while those of sufficiently large rank are known not to be
DCI-groups. The only published proof that elementary abelian groups of order
$p^4$ are DCI-groups uses Schur rings and does not work for $p=2$ (which has
been separately proven using computers). This paper provides a simpler proof
that works for all primes. Some of the results in this paper also apply to
elementary abelian groups of higher rank, so may be useful for completing our
determination of which elementary abelian groups are DCI-groups.


  CP2K is an open source electronic structure and molecular dynamics software
package to perform atomistic simulations of solid-state, liquid, molecular and
biological systems. It is especially aimed at massively-parallel and
linear-scaling electronic structure methods and state-of-the-art ab-initio
molecular dynamics simulations. Excellent performance for electronic structure
calculations is achieved using novel algorithms implemented for modern
high-performance computing systems. This review revisits the main capabilities
of CP2k to perform efficient and accurate electronic structure simulations. The
emphasis is put on density functional theory and multiple post-Hartree-Fock
methods using the Gaussian and plane wave approach and its augmented
all-electron extension.


  Diffusion probabilistic models (DPMs) which employ explicit likelihood
characterization and a gradual sampling process to synthesize data, have gained
increasing research interest. Despite their huge computational burdens due to
the large number of steps involved during sampling, DPMs are widely appreciated
in various medical imaging tasks for their high-quality and diversity of
generation. Magnetic resonance imaging (MRI) is an important medical imaging
modality with excellent soft tissue contrast and superb spatial resolution,
which possesses unique opportunities for DPMs. Although there is a recent surge
of studies exploring DPMs in MRI, a survey paper of DPMs specifically designed
for MRI applications is still lacking. This review article aims to help
researchers in the MRI community to grasp the advances of DPMs in different
applications. We first introduce the theory of two dominant kinds of DPMs,
categorized according to whether the diffusion time step is discrete or
continuous, and then provide a comprehensive review of emerging DPMs in MRI,
including reconstruction, image generation, image translation, segmentation,
anomaly detection, and further research topics. Finally, we discuss the general
limitations as well as limitations specific to the MRI tasks of DPMs and point
out potential areas that are worth further exploration.


  The emission of the so-called extreme blazars challenges the particle
acceleration models. The hardness of its spectrum, $<2$, demands extreme
parameters using the standard one-zone SSC model in the high energy band. Some
authors use both two-zone or hadronic/leptohadronic models to relax these
extreme values. In this work, we present a leptohadronic two-zone model with
external radiation fields to explain the broadband emission, where the
contribution of two components forms the hard-spectrum in the $\gamma$-rays
band. The first is produced by the photopion process, where accelerated protons
in an inner blob located close to the core interact with the X-ray photons
coming from a pair plasma. This mechanism will be responsible for $\gamma$-rays
in the TeV's energies range. The second contribution is produced by an outer
blob, which corresponds to the source of X-rays and $\gamma$-rays with sub-TeV
energies via the standard SSC and EIC model. We exemplify our model with the
prototype extreme blazar 1ES 0229 +200 obtaining a good description of its
spectral energy distribution.


  Lie solvable restricted enveloping algebras were characterized by Riley and
Shalev except when the ground field is of characteristic 2. We resolve the
characteristic 2 case here which completes the classification. As an
application of our result, we obtain a characterization of ordinary Lie
algebras over any field whose enveloping algebra is Lie solvable.


  Over the past few years, deep neural networks (DNNs) have achieved tremendous
success and have been continuously applied in many application domains.
However, during the practical deployment in the industrial tasks, DNNs are
found to be erroneous-prone due to various reasons such as overfitting, lacking
robustness to real-world corruptions during practical usage. To address these
challenges, many recent attempts have been made to repair DNNs for version
updates under practical operational contexts by updating weights (i.e., network
parameters) through retraining, fine-tuning, or direct weight fixing at a
neural level. In this work, as the first attempt, we initiate to repair DNNs by
jointly optimizing the architecture and weights at a higher (i.e., block)
level.
  We first perform empirical studies to investigate the limitation of whole
network-level and layer-level repairing, which motivates us to explore a novel
repairing direction for DNN repair at the block level. To this end, we first
propose adversarial-aware spectrum analysis for vulnerable block localization
that considers the neurons' status and weights' gradients in blocks during the
forward and backward processes, which enables more accurate candidate block
localization for repairing even under a few examples. Then, we further propose
the architecture-oriented search-based repairing that relaxes the targeted
block to a continuous repairing search space at higher deep feature levels. By
jointly optimizing the architecture and weights in that space, we can identify
a much better block architecture. We implement our proposed repairing
techniques as a tool, named ArchRepair, and conduct extensive experiments to
validate the proposed method. The results show that our method can not only
repair but also enhance accuracy & robustness, outperforming the
state-of-the-art DNN repair techniques.


  GPUs in High-Performance Computing systems remain under-utilised due to the
unavailability of schedulers that can safely schedule multiple applications to
share the same GPU. The research reported in this paper is motivated to improve
the utilisation of GPUs by proposing a framework, we refer to as schedGPU, to
facilitate intra-node GPU co-scheduling such that a GPU can be safely shared
among multiple applications by taking memory constraints into account. Two
approaches, namely a client-server and a shared memory approach are explored.
However, the shared memory approach is more suitable due to lower overheads
when compared to the former approach.
  Four policies are proposed in schedGPU to handle applications that are
waiting to access the GPU, two of which account for priorities. The feasibility
of schedGPU is validated on three real-world applications. The key observation
is that a performance gain is achieved.
  For single applications, a gain of over 10 times, as measured by GPU
utilisation and GPU memory utilisation, is obtained. For workloads comprising
multiple applications, a speed-up of up to 5x in the total execution time is
noted. Moreover, the average GPU utilisation and average GPU memory utilisation
is increased by 5 and 12 times, respectively.


  A crucial step in single particle analysis (SPA) of cryogenic electron
microscopy (Cryo-EM), 2D classification and alignment takes a collection of
noisy particle images to infer orientations and group similar images together.
Averaging these aligned and clustered noisy images produces a set of clean
images, ready for further analysis such as 3D reconstruction. Fourier-Bessel
steerable principal component analysis (FBsPCA) enables an efficient,
adaptable, low-rank rotation operator. We extend the FBsPCA to additionally
handle translations. In this extended FBsPCA representation, we use a
probabilistic polar-coordinate Gaussian mixture model to learn soft clusters in
an unsupervised fashion using an expectation maximization (EM) algorithm. The
obtained rotational clusters are thus additionally robust to the presence of
pairwise alignment imperfections. Multiple benchmarks from simulated Cryo-EM
datasets show probabilistic PolarGMM's improved performance in comparisons with
standard single-particle Cryo-EM tools, EMAN2 and RELION, in terms of various
clustering metrics and alignment errors.


  Macroscopic arrays of cold atoms trapped in optical cavities can reach the
strong atom-light collective coupling regime thanks to the simultaneous
interactions of the cavity mode with the atomic ensemble. In a recent work we
reported a protocol that takes advantage of the strong and collective
atom-light interactions in cavity QED systems for precise electric field
sensing in the optical domain. We showed that it can provide between
$10$-$20$~dB of metrological gain over the standard quantum limit in current
cavity QED experiments operating with long-lived alkaline-earth atoms. Here, we
give a more in depth discussion of the protocol using both exact analytical
calculations and numerical simulations, and describe the precise conditions
under which the predicted enhancement holds after thoroughly accounting for
both photon loss and spontaneous emission, natural decoherence mechanisms in
current experiments. The analysis presented here not only serves to benchmark
the protocol and its utility in cavity QED arrays but also sets the conditions
required for its applicability in other experimental platforms such as arrays
of trapped ions.


  The spinless Salpeter equation supplemented by an instanton induced force is
used to describe the spectra of light mesons, including the pseudoscalar ones.
The coupling constants of the instanton induced potential, as well as the quark
constituent masses are not treated as simple free parameters but are calculated
from the underlying instanton theory. Quite good results are obtained provided
the quark are considered as effective degrees of freedom with a finite size. A
further test of the model is performed by calculating the electromagnetic mass
differences between S-wave mesons.


  The quasi-realistic free fermionic heterotic-string models provide some of
the most detailed examples to explore the phenomenology of string unification.
While providing a powerful tool to generate models and their spectra,
understanding the realisation of the free fermion models in a bosonic formalism
will provide important insight into their basic properties away from the free
fermion point. In this paper we elucidate bosonic equivalent of the basic
symmetry breaking pattern in the free fermion models from E8XE8 to
SO(16)XSO(16) and exhibit the connection of the free fermion models with
corresponding non--supersymmetric vacua by interpolations.


  Charge symmetry breaking (CSB) in the strong interaction occurs because of
the difference between the masses of the up and down quarks. The use of
effective field theories allows us to follow this influence of confined quarks
in hadronic and nuclear systems. The progress in observing and understanding
CSB is reviewed with particular attention to the recent successful observations
of CSB in measurements involving the production of a single neutral pion and to
the related theoretical progress.


  Distributed decision making in multi-agent networks has recently attracted
significant research attention thanks to its wide applicability, e.g. in the
management and optimization of computer networks, power systems, robotic teams,
sensor networks and consumer markets. Distributed decision-making problems can
be modeled as inter-dependent optimization problems, i.e., multi-agent
game-equilibrium seeking problems, where noncooperative agents seek an
equilibrium by communicating over a network. To achieve a network equilibrium,
the agents may decide to update their decision variables via proximal dynamics,
driven by the decision variables of the neighboring agents. In this paper, we
provide an operator-theoretic characterization of convergence with a
time-invariant communication network. For the time-varying case, we consider
adjacency matrices that may switch subject to a dwell time. We illustrate our
investigations using a distributed robotic exploration example.


  Some deep conjectures about quantum gravity are closely related to the role
of symmetries in the gravitational background, especially for quantum black
holes. In this paper, we systematically study the theory of quantum information
for a charged, chaotic system. We show how the quantum information in the whole
system has been represented by its charge sectors, using the theory of quantum
chaos and quantum error correction, with concrete examples in the context of
the complex SYK model. We discuss possible implications for black hole thought
experiments and conjectures about quantum gravity in the dynamical setup. We
believe this work will have potential applications from theories of quantum
gravity to quantum simulation in quantum devices.


  The 26 long-duration gamma-ray bursts (GRBs) with known redshifts form a
distinct cosmological set, selected differently than other cosmological probes
such as quasars and galaxies. Since the progenitors are now believed to be
connected with active star-formation and since burst emission penetrates dust,
one hope is that with a uniformly-selected sample, the large-scale redshift
distribution of GRBs can help constrain the star-formation history of the
Universe. However, we show that strong observational biases in ground-based
redshift discovery hamper a clean determination of the large-scale GRB rate and
hence the connection of GRBs to the star formation history. We then focus on
the properties of the small-scale (clustering) distribution of GRB redshifts.
When corrected for heliocentric motion relative to the local Hubble flow, the
observed redshifts appear to show a propensity for clustering: 8 of 26 GRBs
occurred within a recession velocity difference of 1000 km/s of another GRB.
That is, 4 pairs of GRBs occurred within 30 h_65^-1 Myr in cosmic time, despite
being causally separated on the sky. We investigate the significance of this
clustering. Comparison of the numbers of close redshift pairs expected from the
simulation with that observed shows no significant small-scale clustering
excess in the present sample; however, the four close pairs occur only in about
twenty percent of the simulated datasets (the precise significance of the
clustering is dependent upon the modeled biases). We conclude with some
impetuses and suggestions for future precise GRB redshift measurements.


  The hard core model in statistical physics is a probability distribution on
independent sets in a graph in which the weight of any independent set I is
proportional to lambda^(|I|), where lambda > 0 is the vertex activity. We show
that there is an intimate connection between the connective constant of a graph
and the phenomenon of strong spatial mixing (decay of correlations) for the
hard core model; specifically, we prove that the hard core model with vertex
activity lambda < lambda_c(Delta + 1) exhibits strong spatial mixing on any
graph of connective constant Delta, irrespective of its maximum degree, and
hence derive an FPTAS for the partition function of the hard core model on such
graphs. Here lambda_c(d) := d^d/(d-1)^(d+1) is the critical activity for the
uniqueness of the Gibbs measure of the hard core model on the infinite d-ary
tree. As an application, we show that the partition function can be efficiently
approximated with high probability on graphs drawn from the random graph model
G(n,d/n) for all lambda < e/d, even though the maximum degree of such graphs is
unbounded with high probability.
  We also improve upon Weitz's bounds for strong spatial mixing on bounded
degree graphs (Weitz, 2006) by providing a computationally simple method which
uses known estimates of the connective constant of a lattice to obtain bounds
on the vertex activities lambda for which the hard core model on the lattice
exhibits strong spatial mixing. Using this framework, we improve upon these
bounds for several lattices including the Cartesian lattice in dimensions 3 and
higher.
  Our techniques also allow us to relate the threshold for the uniqueness of
the Gibbs measure on a general tree to its branching factor (Lyons, 1989).


  We investigate an ultracold Fermi gas at unitarity confined in a periodic box
$V=L^3$ using renormalization group (RG) techniques. Within this approach we
can quantitatively assess the long range bosonic order parameter fluctuations
which dominate finite-size effects. We determine the finite-size and
particle-number dependence of universal quantities, such as the Bertsch
parameter and the fermion gap. Moreover, we analyze how these universal
observables respond to the variation of an external pairing source. Our results
indicate that the Bertsch parameter saturates rather quickly to its value in
the thermodynamic limit as a function of increasing box size. On the other
hand, we observe that the fermion gap shows a significantly stronger dependence
on the box size, in particular for small values of the pairing source. Our
results may contribute to a better understanding of finite-size and
particle-number effects present in Monte-Carlo simulations of ultracold Fermi
gases.


  The bulk viscosity in spin-one color-superconducting strange quark matter is
calculated by taking into account the interplay between the nonleptonic and
semi-leptonic week processes. In agreement with previous studies, it is found
that the inclusion of the semi-leptonic processes may result in non-negligible
corrections to the bulk viscosity in a narrow window of temperatures. The
effect is generally more pronounced for pulsars with longer periods. Compared
to the normal phase, however, this effect due to the semi-leptonic processes is
less pronounced in spin-one color superconductors. Assuming that the critical
temperature of the phase transition is much larger than 40 keV, the main effect
of spin-one color superconductivity in a wide range of temperatures is an
overall increase of the bulk viscosity with respect to the normal phase. The
corresponding enhancement factor reaches up to about 9 in the polar and
A-phases, about 25 in the planar phase and about 29 in the CSL phase. This
factor is determined by the suppression of the nonleptonic rate in
color-superconducting matter and, therefore, may be even larger if all quark
quasiparticles happen to be gapped.


  We have analysed 53 square degrees of imaging data from the Red-Sequence
Cluster Survey (RCS), and measured the excess correlations in the shapes of
galaxies on scales out to ~1.5 degrees. We separate the signal into an ``E''-
(lensing) and ``B''-mode (systematics), which allows us to study residual
systematics. On scales larger than 10 arcminutes, we find no ``B''-mode. On
smaller scales we find a small, but significant ``B''-mode. This signal is also
present when we select a sample of bright galaxies. These galaxies are rather
insensitive to observational distortions, and we therefore conclude that the
oberved ``B''-mode is likely to be caused by intrinsic alignments. We therefore
limit the cosmic shear analysis to galaxies with 22<R_C<24. We derive joint
constraints on Omega_m and sigma_8, by marginalizing over Gamma, Omega_Lambda
and the source redshift distribution, using different priors. We obtain a
conservative constraint of $\sigma_8=0.45^{+0.09}_{-0.12} \Omega_m^{-0.55}$
(95% confidence). A better constraint is derived when we use Gaussian priors
redshift distribution. For this choice of priors, we find
$\sigma_8=(0.46^{+0.05}_{-0.07})\Omega_m^{-0.52}$ (95% confidence). Using our
setof Gaussian priors, we find that we can place a lower bound on Gamma:
Gamma>0.1+0.16\Omega_m$ (95% confidence). Comparison of the RCS results with
three other recent cosmic shear measurements shows excellent agreement. The
current weak lensing results are also in good agreement with CMB measurements,
when we allow the reionization optical depth tau and the spectral index n_s to
vary. We present a simple demonstration of how the weak lensing results can be
used as a prior in the parameter estimation from CMB measurements to derive
constraints on the reionization optical depth tau. (abridged)


  In the paper we present the exact solutions of one-dimensional Nonlinear
Schr\"{o}dinger Equation. The solutions correspond to the Bogoliubov
excitations in Bose-gas with a local interaction. The obtained expression is
used for evaluating the transmission coefficient of the excitations across a
delta-functional potential barrier.


  Defect models have recently been declared dead (Watson 1997), because they
predict microwave background and matter fluctuations grossly out of line with
what we see. In this talk we apply the fact that many defects are automatically
destroyed at the time of radiation-matter transition, thus resurrecting the
defects model. Moreover, the resurrected version predicts a cosmological
constant, explains the apparent excess of hot clusters and the non-Gaussianity
observed in galaxy surveys. If this model is correct, then the MAP and PLANCK
missions will not measure what people expect them to (oscillations); rather,
they will measure a broad hump.


  We prove two inequalities between the Lyapunov exponents of a diffeomorphism
and its local recurrence properties. We give examples showing that each of the
inequalities is optimal.


  We consider gauge invariant quark two-point Green's functions in which the
gluonic phase factor follows a skew-polygonal line. Using a particular
representation for the quark propagator in the presence of an external gluon
field, functional relations between Green's functions with different numbers of
segments of the polygonal lines are established. An integral equation is
obtained for the Green's function having a phase factor along a single straight
line. The related kernels involve Wilson loops with skew-polygonal contours and
with functional derivatives along the sides of the contours.


  Surveys of Active Galactic Nuclei (AGN) in different observational regimes
seem to give different answers for the behaviour of the obscured fraction with
luminosity. Based on the complex spectra seen in recent studies, we note that
partial covering could significantly change the apparent luminosities of many
AGN, even after apparent X-ray absorption correction. We explore whether this
effect could reproduce the observed dependence of the obscured fraction on the
apparent X-ray luminosities seen between 2--10 keV. We can reproduce the
observed trend in a model where 33 per cent of AGN are unobscured, 30 per cent
are heavily buried, and 37 per cent have a range of intermediate partial
coverings. Our model is also tentatively successful at reproducing observed
trends in the X-ray vs. infrared luminosity ratio for AGN.


  Hierarchical Rate Splitting (HRS) schemes proposed in recent years have shown
to provide significant improvements in exploiting spatial diversity in wireless
networks and provide high throughput for all users while minimising
interference among them. Hence, one of the major challenges for such HRS
schemes is the necessity to know the optimal clustering of these users based
only on their Channel State Information (CSI). This clustering problem is known
to be NP hard and, to deal with the unmanageable complexity of finding an
optimal solution, in this work a scalable and much lighter clustering mechanism
based on Neural Network (NN) is proposed. The accuracy and performance metrics
show that the NN is able to learn and cluster the users based on the noisy
channel response and is able to achieve a rate comparable to other more complex
clustering schemes from the literature.


  The paper provides a link between ergodic theory and symplectic topology. A
classical notion of ergodic theory is a skew product map associated with a loop
in a group of transformations. We study skew products which come from loops in
the group of Hamiltonian diffeomorphisms of a symplectic manifold. Our main
question is which homotopy classes of loops can be represented by strictly
ergodic skew products. We prove an existence result, and find an obstruction
which arises from Hofer's geometry on the group of Hamiltonian diffeomorphisms.


  We formulate a Langevin description of dynamics of a speckle pattern
resulting from the multiple scattering of a coherent wave in a nonlinear
disordered medium. The speckle pattern exhibits instability with respect to
periodic excitations at frequencies $\Omega$ below some
$\Omega_{\mathrm{max}}$, provided that the nonlinearity exceeds some
$\Omega$-dependent threshold. A transition of the speckle pattern from a
stationary state to the chaotic evolution is predicted upon increasing
nonlinearity. The shortest typical time scale of chaotic intensity fluctuations
is of the order of $1/\Omega_\mathrm {max}$.


  In medical imaging, surface registration is extensively used for performing
systematic comparisons between anatomical structures, with a prime example
being the highly convoluted brain cortical surfaces. To obtain a meaningful
registration, a common approach is to identify prominent features on the
surfaces and establish a low-distortion mapping between them with the feature
correspondence encoded as landmark constraints. Prior registration works have
primarily focused on using manually labeled landmarks and solving highly
nonlinear optimization problems, which are time-consuming and hence hinder
practical applications. In this work, we propose a novel framework for the
automatic landmark detection and registration of brain cortical surfaces using
quasi-conformal geometry and convolutional neural networks. We first develop a
landmark detection network (LD-Net) that allows for the automatic extraction of
landmark curves given two prescribed starting and ending points based on the
surface geometry. We then utilize the detected landmarks and quasi-conformal
theory for achieving the surface registration. Specifically, we develop a
coefficient prediction network (CP-Net) for predicting the Beltrami
coefficients associated with the desired landmark-based registration and a
mapping network called the disk Beltrami solver network (DBS-Net) for
generating quasi-conformal mappings from the predicted Beltrami coefficients,
with the bijectivity guaranteed by quasi-conformal theory. Experimental results
are presented to demonstrate the effectiveness of our proposed framework.
Altogether, our work paves a new way for surface-based morphometry and medical
shape analysis.


  The internet of things (IoT) based wireless sensor networks (WSNs) face an
energy shortage challenge that could be overcome by the novel wireless power
transfer (WPT) technology. The combination of WSNs and WPT is known as wireless
rechargeable sensor networks (WRSNs), with the charging efficiency and charging
scheduling being the primary concerns. Therefore, this paper proposes a
probabilistic on-demand charging scheduling for integrated sensing and
communication (ISAC)-assisted WRSNs with multiple mobile charging vehicles
(MCVs) that addresses three parts. First, it considers the four attributes with
their probability distributions to balance the charging load on each MCV. The
distributions are residual energy of charging node, distance from MCV to
charging node, degree of charging node, and charging node betweenness
centrality. Second, it considers the efficient charging factor strategy to
partially charge network nodes. Finally, it employs the ISAC concept to
efficiently utilize the wireless resources to reduce the traveling cost of each
MCV and to avoid the charging conflicts between them. The simulation results
show that the proposed protocol outperforms cutting-edge protocols in terms of
energy usage efficiency, charging delay, survival rate, and travel distance.


  Raman scattering is the inelastic process where photons bounce off molecules,
losing energy and becoming red-shifted. This weak effect is unique to each
molecular species, making it an essential tool in e.g. spectroscopy and
label-free microscopy. The invention of the laser enabled a regime of
stimulated Raman scattering (SRS), where the efficiency is greatly increased by
inducing coherent molecular oscillations. However, this phenomenon required
high intensities due to the limited interaction volumes, and this limitation
was overcome by the emergence of anti-resonant fibres (ARFs) guiding light in a
small hollow channel over long distances. Based on their unique properties,
this Perspective reviews the transformative impact of ARFs on modern SRS-based
applications ranging from development of light sources and convertors for
spectroscopy and materials science, to quantum technologies for the future
quantum networks, providing insights into future trends and the expanding
horizons of the field.


  We consider optimal control problems involving two constraint sets: one
comprised of linear ordinary differential equations with the initial and
terminal states specified and the other defined by the control variables
constrained by simple bounds. When the intersection of these two sets is empty,
typically because the bounds on the control variables are too tight, the
problem becomes infeasible. In this paper, we prove that, under a
controllability assumption, the ``best approximation'' optimal control
minimizing the distance (and thus finding the ``gap'') between the two sets is
of bang--bang type, with the ``gap function'' playing the role of a switching
function. The critically feasible control solution (the case when one has the
smallest control bound for which the problem is feasible) is also shown to be
of bang--bang type. We present the full analytical solution for the critically
feasible problem involving the (simple but rich enough) double integrator. We
illustrate the overall results numerically on various challenging example
problems.


  The atomic transition from an excited state $|{\rm e}\rangle$ to the ground
state $|{\rm g}\rangle$ by emitting a neutrino pair and a photon, i.e., $|{\rm
e}\rangle \to |{\rm g}\rangle + |\gamma\rangle + |\nu^{}_i\rangle +
|\bar{\nu}^{}_j\rangle$ with $i, j = 1, 2, 3$, has been proposed by Yoshimura
and his collaborators as an alternative way to determine the absolute scale
$m^{}_0$ of neutrino masses. More recently, a statistical analysis of the fine
structure of the photon spectrum from this atomic process has been performed
[N. Song {\it et al.}, Phys.\ Rev.\ D {\bf 93}, 013020 (2016)] to
quantitatively examine the experimental requirements for a realistic
determination of absolute neutrino masses. In this paper, we show how to
improve the statistical analysis and demonstrate that the previously required
detection time can be reduced by one order of magnitude for the case of a
$3\sigma$ determination of $m_0^{} \sim 0.01~\text{eV}$ with an accuracy better
than $10\%$. Such an improvement is very encouraging for further investigations
on measuring absolute neutrino masses through atomic processes.


  We compare flavour singlet and non-singlet vector mesons from first
principles using lattice QCD. With N_f=2 flavours of light quark, this
addresses the omega-rho mass difference.
  Using maximally twisted-mass lattice QCD, we are able for the first time to
determine this mass difference precisely and we compare with experiment. We
also discuss omega-rho mixing effects arising within QCD through the u-d quark
mass difference.


  Many settings of interest involving humans and machines -- from virtual
personal assistants to autonomous vehicles -- can naturally be modelled as
principals (humans) delegating to agents (machines), which then interact with
each other on their principals' behalf. We refer to these multi-principal,
multi-agent scenarios as delegation games. In such games, there are two
important failure modes: problems of control (where an agent fails to act in
line their principal's preferences) and problems of cooperation (where the
agents fail to work well together). In this paper we formalise and analyse
these problems, further breaking them down into issues of alignment (do the
players have similar preferences?) and capabilities (how competent are the
players at satisfying those preferences?). We show -- theoretically and
empirically -- how these measures determine the principals' welfare, how they
can be estimated using limited observations, and thus how they might be used to
help us design more aligned and cooperative AI systems.


  The task of the challenge is to develop a voice anonymization system for
speech data which conceals the speaker's voice identity while protecting
linguistic content and emotional states. The organizers provide development and
evaluation datasets and evaluation scripts, as well as baseline anonymization
systems and a list of training resources formed on the basis of the
participants' requests. Participants apply their developed anonymization
systems, run evaluation scripts and submit evaluation results and anonymized
speech data to the organizers. Results will be presented at a workshop held in
conjunction with Interspeech 2024 to which all participants are invited to
present their challenge systems and to submit additional workshop papers.


  The constraints on the minimal supergravity model from the b->s+\gamma decay
are studied. A large domain in the parameter space for the model satisfies the
CLEO bound, BR(b->s+\gamma)<5.4X10^{-4}. However, the allowed domain is
expected to diminish significantly with an improved bound on this decay. The
dependence of the b->s+\gamma branching ratio on various parameters is studied
in detail. It is found that, for A_t<0 and the top quark mass within the
vicinity of the center of the CDF value, m_t^{pole}=174\pm17 GeV, there exists
only a small allowed domain because the light stop is tachyonic for most of the
parameter space. A similar phenomenon exists for a lighter top and A_t negative
when the GUT coupling constant is slightly reduced. For A_t>0, however, the
branching ratio is much less sensitive to small changes in m_t, and \alpha_G.


  We consider two types of discrete-time Markov chains where the state space is
a graded poset and the transitions are taken along the covering relations in
the poset. The first type of Markov chain goes only in one direction, either up
or down in the poset (an \emph{up chain} or \emph{down chain}). The second type
toggles between two adjacent rank levels (an \emph{up-and-down chain}).
  We introduce two compatibility concepts between the up-directed transition
probabilities (an \emph{up rule}) and the down-directed (a \emph{down rule}),
and we relate these to compatibility between up-and-down chains. This framework
is used to prove a conjecture about a limit shape for a process on Young's
lattice.
  Finally, we settle the questions whether the reverse of an up chain is a down
chain for some down rule and whether there exists an up or down chain at all if
the rank function is not bounded.


  A typical question addressed in this paper is the following. Suppose
$Z\subset Y\subset X$ are hyperbolic spaces where $Z$ is quasiconvex in both
$Y$ and $X$. Let $\HAT{Y}$ and $\HAT{X}$ denote the spaces obtained from $Y$
and $X$ respectively by coning off $Z$ as defined by Farb. {\em If the
inclusion of the coned-off spaces $\HAT{Y}\map \HAT{X}$ admits the
Cannon-Thurston (CT) map then does the inclusion $Y\map X$ also admit the
Cannon-Thurston map?} The main result of this paper answers this question
affirmatively provided $\HAT{Y}\map \HAT{X}$ satisfies Mitra's criterion for
the existence of CT maps, although the answer in general is negative.
  The main application of our theorem is in the context of acylindrical
complexes of hyperbolic groups. A. Martin proved a combination theorem for
developable, acylindrical complexes of hyperbolic groups. Suppose $(\mathcal G,
\YY)$ is an acylindrical complex of hyperbolic groups with universal cover $B$
which satisfy the hypotheses of Martin's theorem. Suppose $\YY_1\subset \YY$ is
a connected subcomplex such that the subcomplex of groups $(\mathcal G, \YY_1)$
also satisfies the hypotheses of Martin's theorem, it has universal cover $B_1$
and the natural homomorphism $\pi_1(\mathcal G, \YY_1)\map \pi_1(\mathcal G,
\YY)$ is injective. It follows from the main theorem of this paper that the
inclusion $\pi_1(\mathcal G, \YY_1)\map \pi_1(\mathcal G, \YY)$ admits the CT
map if the inclusion $B_1\rightarrow B$ satisfies Mitra's criterion. Also
$\pi_1(\mathcal G, \YY_1)$ is quasiconvex in $\pi_1(\mathcal G, \YY)$ if in
addition $B_1$ is qi embedded in $B$.


  We study the problem of Reinforcement Learning (RL) with linear function
approximation, i.e. assuming the optimal action-value function is linear in a
known $d$-dimensional feature mapping. Unfortunately, however, based on only
this assumption, the worst case sample complexity has been shown to be
exponential, even under a generative model. Instead of making further
assumptions on the MDP or value functions, we assume that our action space is
such that there always exist playable actions to explore any direction of the
feature space. We formalize this assumption as a ``ball structure'' action
space, and show that being able to freely explore the feature space allows for
efficient RL. In particular, we propose a sample-efficient RL algorithm
(BallRL) that learns an $\epsilon$-optimal policy using only
$\tilde{O}\left(\frac{H^5d^3}{\epsilon^3}\right)$ number of trajectories.


  We show variationally that instability of the ferromagnetic state in the
Hubbard model is largely controlled by softening of a long-wavelength spin-wave
excitation, except in the over-doped strong-coupling region where the
individual-particle excitation becomes unstable first. A similar conclusion is
drawn also for the double exchange ferromagnet. Generally the spin-wave
instability may be regarded as a precursor of the metal-insulator transition.


  Key-value relations are prevalent in Visually-Rich Documents (VRDs), often
depicted in distinct spatial regions accompanied by specific color and font
styles. These non-textual cues serve as important indicators that greatly
enhance human comprehension and acquisition of such relation triplets. However,
current document AI approaches often fail to consider this valuable prior
information related to visual and spatial features, resulting in suboptimal
performance, particularly when dealing with limited examples. To address this
limitation, our research focuses on few-shot relational learning, specifically
targeting the extraction of key-value relation triplets in VRDs. Given the
absence of a suitable dataset for this task, we introduce two new few-shot
benchmarks built upon existing supervised benchmark datasets. Furthermore, we
propose a variational approach that incorporates relational 2D-spatial priors
and prototypical rectification techniques. This approach aims to generate
relation representations that are more aware of the spatial context and unseen
relation in a manner similar to human perception. Experimental results
demonstrate the effectiveness of our proposed method by showcasing its ability
to outperform existing methods. This study also opens up new possibilities for
practical applications.


  We perform the quenched lattice QCD analysis on the nuclear force
(baryon-baryon interactions). We employ $20^3\times 24$ lattice at $\beta=5.7$
($a\simeq 0.19$ fm) with the standard gauge action and the Wilson quark action
with the hopping parameters $\kappa=0.1600, 0.1625, 0.1650$, and generate about
200 gauge configurations. We measure the temporal correlators of the two-baryon
system which consists of heavy-light-light quarks. We extract the inter-baryon
force as a function of the relative distance $r$. We also evaluate the
contribution to the nuclear force from each ``Feynman diagram'' such as the
quark-exchange diagram individually, and single out the roles of Pauli-blocking
effects or quark exchanges in the inter-baryon interactions.


  Conditions when application of cyclization procedure does not lead to the
periodic function are specified. Sufficient conditions under which obtained
function is periodic are stated.


  Direct searches for lepton flavor violating Higgs boson decays in the $\tau
\mu$ channel have been recently reported by the CMS collaboration. The results
display a slight excess of signal events with a significance of 2.5$\sigma$,
which translates into a branching ratio of about $1$%. By interpreting these
findings as a hint for beyond the standard model physics, we show that the
Type-III 2HDM is capable of reproducing such signal while at the same time
satisfying vacuum stability, perturbativity, electroweak precision data,
measured Higgs standard decay modes and low-energy lepton flavor violating
constraints. We have found that the allowed signal strength ranges for the
$b\bar b$, $WW^*$ and $ZZ^*$ standard channels shrink as soon as
BR$(h\to\tau\mu)\sim 1$% is enforced. Thus, we point out that if the excess
persists, improved measurements of these channels may be used to test our
Type-III 2HDM scenario.


  The electromagnetic characteristics of double-layer quantum Hall systems are
studied, with projection to the lowest Landau level taken into account and
intra-Landau-level collective excitations treated in the single-mode
approximation. It is pointed out that dipole-active excitations, both
elementary and collective, govern the long-wavelength features of quantum Hall
systems. In particular, the presence of the dipole-active interlayer
out-of-phase collective excitations, inherent to double-layer systems, modifies
the leading O(k) and O(k^{2}) long-wavelength characteristics (i.e., the
transport properties and characteristic scale) of the double-layer quantum Hall
states substantially. We apply bosonization techniques and construct from such
electromagnetic characteristics an effective theory, which consists of three
vector fields representing the three dipole-active modes, one interlayer
collective mode and two inter-Landau-level cyclotron modes. This effective
theory properly incorporates the spectrum of collective excitations on the
right scale of the Coulomb energy and, in addition, accommodates the favorable
transport properties of the standard Chern-Simons theories.


  Given a metric space $X$ of finite asymptotic dimension, we consider a
quasi-isometric invariant of the space called dimension function. The space is
said to have asymptotic Assouad-Nagata dimension less or equal $n$ if there is
a linear dimension function in this dimension. We prove that if $X$ is a
tree-graded space (as introduced by C. Drutu and M. Sapir) and for some
positive integer $n$ a function $f$ serves as an $n$-dimensional dimension
function for all pieces of $X$, then the function $300\cdot f$ serves as an
$n$-dimensional dimension function for $X$. As a corollary we find a formula
for the asymptotic Assouad-Nagata dimension of the free product of finitely
generated infinite groups: $asdim_{AN} (G*H)= max\{asdim_{AN} (G), asdim_{AN}
(H)\}.$


  The complementarity knapsack problem (CKP) is a knapsack problem with
real-valued variables and complementarity conditions between pairs of its
variables. We extend the polyhedral studies of De Farias et al. for CKP, by
proposing three new families of cutting-planes that are all obtained from a
combinatorial concept known as a pack. Sufficient conditions for these
inequalities to be facet-defining, based on the concept of a maximal switching
pack, are also provided. Moreover, we answer positively a conjecture by de
Farias et~al.~about the separation complexity of the inequalities introduced in
their work, and propose efficient separation algorithms for our newly defined
cutting-planes.


  Mismatch removal is a critical prerequisite in many feature-based tasks.
Recent attempts cast the mismatch removal task as a binary classification
problem and solve it through deep learning based methods. In these methods, the
imbalance between positive and negative classes is important, which affects
network performance, i.e., Fn-score. To establish the link between Fn-score and
loss, we propose to guide the loss with the Fn-score directly. We theoretically
demonstrate the direct link between our Guided Loss and Fn-score during
training. Moreover, we discover that outliers often impair global context in
mismatch removal networks. To address this issue, we introduce the attention
mechanism to mismatch removal task and propose a novel Inlier Attention Block
(IA Block). To evaluate the effectiveness of our loss and IA Block, we design
an end-to-end network for mismatch removal, called GLA-Net \footnote{Our code
will be available in Github later.}. Experiments have shown that our network
achieves the state-of-the-art performance on benchmark datasets.