  In this paper, we introduce an abstract fuzzy economy (generalized fuzzy
game) model with a countable space of actions and we study the existence of the
fuzzy equilibrium. As applications, two types of results are obtained. The
first ones concern the existence of the solutions for systems of generalized
quasi-variational inequalities with random fuzzy mappings which we define. The
last ones are new random fixed point theorems for correspondences with values
in complete countable metric spaces.


  Conditional generative adversarial networks (cGANs) have shown superior
results in class-conditional generation tasks. To simultaneously control
multiple conditions, cGANs require multi-label training datasets, where
multiple labels can be assigned to each data instance. Nevertheless, the
tremendous annotation cost limits the accessibility of multi-label datasets in
real-world scenarios. Therefore, in this study we explore the practical setting
called the single positive setting, where each data instance is annotated by
only one positive label with no explicit negative labels. To generate
multi-label data in the single positive setting, we propose a novel sampling
approach called single-to-multi-label (S2M) sampling, based on the Markov chain
Monte Carlo method. As a widely applicable "add-on" method, our proposed S2M
sampling method enables existing unconditional and conditional GANs to draw
high-quality multi-label data with a minimal annotation cost. Extensive
experiments on real image datasets verify the effectiveness and correctness of
our method, even when compared to a model trained with fully annotated
datasets.


  This paper considers approximately sparse signal and low-rank matrix's
recovery via truncated norm minimization $\min_{x}\|x_T\|_q$ and
$\min_{X}\|X_T\|_{S_q}$ from noisy measurements. We first introduce truncated
sparse approximation property, a more general robust null space property, and
establish the stable recovery of signals and matrices under the truncated
sparse approximation property. We also explore the relationship between the
restricted isometry property and truncated sparse approximation property. And
we also prove that if a measurement matrix $A$ or linear map $\mathcal{A}$
satisfies truncated sparse approximation property of order $k$, then the first
inequality in restricted isometry property of order $k$ and of order $2k$ can
hold for certain different constants $\delta_{k}$ and $\delta_{2k}$,
respectively. Last, we show that if $\delta_{t(k+|T^c|)}<\sqrt{(t-1)/t}$ for
some $t\geq 4/3$, then measurement matrix $A$ and linear map $\mathcal{A}$
satisfy truncated sparse approximation property of order $k$. Which should
point out is that when $T^c=\emptyset$, our conclusion implies that sparse
approximation property of order $k$ is weaker than restricted isometry property
of order $tk$.


  The dilatation operator of planar N=4 super Yang-Mills in the pure scalar
SO(6) sector is derived at the two-loop order. Representation theory allows for
eight free coefficients in an ansatz for the corresponding spin-chain
hamiltonian acting on three adjacent scalar states. While four out of these
follow from the known SU(2|3) sector two-loop dilatation operator, the
remaining four coefficients are derived by diagrammatic techniques and a match
to the known dimension of a length three primary operator. Finally, comments
upon the use of this result for the evaluation of three-point structure
functions of scalar operators at the one-loop order are given.


  In 1960, the mathematician Ernst Specker described a simple example of
nonclassical correlations which he dramatized using a parable about a seer who
sets an impossible prediction task to his daughter's suitors. We revisit this
example here, using it as an entree to three central concepts in quantum
foundations: contextuality, Bell-nonlocality, and complementarity.
Specifically, we show that Specker's parable offers a narrative thread that
weaves together a large number of results, including: the impossibility of
measurement-noncontextual and outcome-deterministic ontological models of
quantum theory (the Kochen-Specker theorem), in particular the proof of
Klyachko; the impossibility of Bell-local models of quantum theory (Bell's
theorem), especially the proofs by Mermin and Hardy; the impossibility of a
preparation-noncontextual ontological model of quantum theory; and the
existence of triples of positive operator valued measures (POVMs) that can be
measured jointly pairwise but not triplewise. Along the way, several novel
results are presented, including: a generalization of a theorem by Fine
connecting the existence of a joint distribution over outcomes of
counterfactual measurements to the existence of a noncontextual model; a
generalization of Klyachko's proof of the Kochen-Specker theorem; a proof of
the Kochen-Specker theorem in the style of Hardy's proof of Bell's theorem; a
categorization of contextual and Bell-nonlocal correlations in terms of
frustrated networks; a new inequality testing preparation noncontextuality; and
lastly, some results on the joint measurability of POVMs and the question of
whether these can be modeled noncontextually. Finally, we emphasize that
Specker's parable provides a novel type of foil to quantum theory, challenging
us to explain why the particular sort of contextuality and complementarity
embodied therein does not arise in a quantum world.


  We present a characterization of finite permutation groups which contain a
transitive dihedral subgroup.


  The ever-evolving internet of things (IoT) has led to the growth of numerous
wireless sensors, communicating through the internet infrastructure. When
designing a network using these sensors, one critical aspect is the longevity
and self-sustainability of these devices. For extending the lifetime of these
sensors, radio frequency energy harvesting (RFEH) technology has proved to be
promising. In this paper, we propose CURE, a novel framework for RFEH that
effectively combines the benefits of cell-free massive MIMO (CFmMIMO), unmanned
aerial vehicles (UAVs), and reconfigurable intelligent surfaces (RISs) to
provide seamless energy harvesting to IoT devices. We consider UAV as an access
point (AP) in the CFmMIMO framework. To enhance the signal strength of the RFEH
and information transfer, we leverage RISs owing to their passive reflection
capability. Based on an extensive simulation, we validate our framework's
performance by comparing the max-min fairness (MMF) algorithm for the amount of
harvested energy.


  We consider the classical discrete time lost-sales model under stationary
continuous demand and linear holding and penalty costs and positive constant
lead time. To date the optimal policy structure is only known implicitly by
solving numerically the Bellman equations. In this paper we derive the first
optimality equation for the lost-sales model. We propose a fixed
non-stockout-probability (FP3) policy, implying that each period the order size
ensures that P3, the probability of no-stockout at the end of the period of
arrival of this order, equals some target value. The FP3-policy can be computed
efficiently and accurately from an exact recursive expression and two-moment
fits to the emerging random variables. We use the lost-sales optimality
equation to compute the optimal FP3-policy. Comparison against the optimal
policy for discrete demand suggests that the fixed P3-policy is
close-to-optimal. An extensive numerical experiment shows that the FP3-policy
outperforms other policies proposed in literature in 97% of all cases. Under
the FP3-policy, the volatility of the replenishment process is much lower than
the volatility of the demand process. This cv-reduction holds a promise for
substantial cost reduction at upstream stages in the supply chain of the
end-item under consideration, compared to the situation with backlogging.


  In this paper, we consider flow and transport problems in thin domains. The
mathematical model considered in the paper is described by a system of
equations for velocity, pressure, and concentration, where the flow is
described by the Stokes equations and the transport is described by an unsteady
convection-diffusion equation with non-homogeneous boundary conditions on walls
(reactive boundaries). We start with the finite element approximation of the
problem on unstructured grids and use it as a reference solution for two and
three-dimensional model problems. Fine grid approximation resolves complex
geometries on the grid level and leads to a large discrete system of equations
that is computationally expensive to solve. To reduce the size of the discrete
systems, we develop a multiscale model reduction technique, where we construct
local multiscale basis functions to generate a lower-dimensional model on a
coarse grid. The proposed multiscale model reduction is based on the
Discontinuous Galerkin Generalized Multiscale Finite Element Method
(DG-GMsGEM). In DG-GMsFEM for flow problems, we start with constructing the
snapshot space for each interface between coarse grid cells to capture possible
flows. For the reduction of the snapshot space size, we perform a dimension
reduction via a solution of the local spectral problem and use eigenvectors
corresponding to the smallest eigenvalues as multiscale basis functions for the
approximation on the coarse grid. For the transport problem, we construct
multiscale basis functions for each interface between coarse grid cells and
present additional basis functions to capture non-homogeneous boundary
conditions on walls. Finally, we will present some numerical simulations for
three test geometries for two and three-dimensional problems to demonstrate the
method's performance.


  Simultaneous speech-to-speech translation is widely useful but extremely
challenging, since it needs to generate target-language speech concurrently
with the source-language speech, with only a few seconds delay. In addition, it
needs to continuously translate a stream of sentences, but all recent solutions
merely focus on the single-sentence scenario. As a result, current approaches
accumulate latencies progressively when the speaker talks faster, and introduce
unnatural pauses when the speaker talks slower. To overcome these issues, we
propose Self-Adaptive Translation (SAT) which flexibly adjusts the length of
translations to accommodate different source speech rates. At similar levels of
translation quality (as measured by BLEU), our method generates more fluent
target speech (as measured by the naturalness metric MOS) with substantially
lower latency than the baseline, in both Zh <-> En directions.


  The Erd\H{o}s-R\'enyi random graph is the simplest model for node degree
distribution, and it is one of the most widely studied. In this model, pairs of
$n$ vertices are selected and connected uniformly at random with probability
$p$, consequently, the degrees for a given vertex follow the binomial
distribution. If the number of vertices is large, the binomial can be
approximated by Normal using the Central Limit Theorem, which is often allowed
when $\min (np, n(1-p)) > 5$. This is true for every node independently.
However, due to the fact that the degrees of nodes in a graph are not
independent, we aim in this paper to test whether the degrees of per node
collectively in the Erd\H{o}s-R\'enyi graph have a multivariate normal
distribution MVN. A chi square goodness of fit test for the hypothesis that
binomial is a distribution for the whole set of nodes is rejected because of
the dependence between degrees. Before testing MVN we show that the covariance
and correlation between the degrees of any pair of nodes in the graph are
$p(1-p)$ and $1/(n-1)$, respectively. We test MVN considering two assumptions:
independent and dependent degrees, and we obtain our results based on the
percentages of rejected statistics of chi square, the $p$-values of Anderson
Darling test, and a CDF comparison. We always achieve a good fit of
multivariate normal distribution with large values of $n$ and $p$, and very
poor fit when $n$ or $p$ are very small. The approximation seems valid when $np
\geq 10$. We also compare the maximum likelihood estimate of $p$ in MVN
distribution where we assume independence and dependence. The estimators are
assessed using bias, variance and mean square error.


  We studied the formation of Y-junctions for transonic elastic strings. In
particular, using the gen-eral solution for these strings, which is described
by left- and right-moving modes, we obtained thedynamics of kinks and
Y-junctions. Considering the linearized ansatz for straight strings, we
con-structed the parameter region space for which the formation of Y-junctions
due to strings collisionsis allowed.


  We study small vibrations of a string with time-dependent length $\ell(t)$
and boundary damping. The vibrations are described by a 1-d wave equation in an
interval with one moving endpoint at a speed $\ell'(t)$ slower than the speed
of propagation of the wave c=1. With no damping, the energy of the solution
decays if the interval is expanding and increases if the interval is shrinking.
The energy decays faster when the interval is expanding and a constant damping
is applied at the moving end. However, to ensure the energy decay in a
shrinking interval, the damping factor $\eta$ must be close enough to the
optimal value $\eta=1$, corresponding to the transparent condition. In all
cases, we establish lower and upper estimates for the energy with explicit
constants.


  Recent data in the neutrino sector point towards a relatively large value of
the reactor angle, incompatible with a vanishing theta_ 13 at about 3 sigma. In
order to explain such a result, we propose a SUSY model based on the broken
L_e-L_mu-L_tau symmetry, where large deviations from the symmetric limit
theta_12 = pi/4, tan(theta_23) \sim O(1) and theta_13 = 0 mainly come from the
charged lepton sector. We show that a description of all neutrino data is
possible if the charged lepton mass matrix has a special pattern of complex
matrix elements.


  Emil Post's tag system problem is the question of whether or not a tag system
$\{N=3, P(0)=00, P(1)=1101\}$ has a configuration, simulation of which will
never halt or end up in a loop. For the past decades, there were several
attempts to find an answer to this question, including a recent study by
Wolfram (2021), during which the first $2^{84}$ initial configurations were
checked. This paper presents a family of configurations of this type in a form
of strings $a^{n} b c^{m}$, that evolve to $a^{n+1} b c^{m+1}$ after a finite
amount of steps. The proof of this behavior for all non-negative $n$ and $m$ is
described further in a paper as a finite verification procedure, which is
computationally bounded by 20000 iterations of tag. All corresponding code can
be found at
https://github.com/nikitakurilenko/post-tag-infinitely-growing-configurations.


  Consider a set represented by an inequality. An interesting phenomenon which
occurs in various settings in mathematics is that the interior of this set is
the subset where strict inequality holds, the boundary is the subset where
equality holds, and the closure of the set is the closure of its interior. This
paper discusses this phenomenon assuming the set is a Voronoi cell induced by
given sites (subsets), a geometric object which appears in many fields of
science and technology and has diverse applications. Simple counterexamples
show that the discussed phenomenon does not hold in general, but it is
established in a wide class of cases. More precisely, the setting is a
(possibly infinite dimensional) uniformly convex normed space with arbitrary
positively separated sites. An important ingredient in the proof is a strong
version of the triangle inequality due to Clarkson (1936), an interesting
inequality which has been almost totally forgotten.


  Using a generalized energy-conserving transition probability, it is shown how
nonadiabatic calculations, within the Wigner-Heisenberg representation of
quantum mechanics, can be reliably extended to far longer times than those
allowed by a primitive sampling scheme. Tackling the spin-boson model as a
paradigmatic example, substantial numerical evidence is provided that effective
integration of the dynamics can be achieved for a wide range of temperatures
and friction.


  The fact that simulations of condensed matter problems are limited to sizes
far smaller than the macroscopic systems being emulated does have one redeeming
feature: The specific dependence on N, the number of molecules being simulated,
is sometimes itself a valuable piece of information. The isotropic phase of
liquid crystals provides a case in point. Light scattering and 2d-IR
experiments on isotropic-phase samples display increasingly large orientational
fluctuations as the samples approach their nematic phase. The growing length
scale of those locally ordered domains is readily seen in simulation as an ever
slower convergence of the distribution of orientational order parameters with
N. The rare-event character of the largest fluctuations make them difficult to
sample accurately. We show in this paper how taking a large deviation theory
perspective enables us to leverage simulation-derived information more
effectively. A key insight of large deviation theory is that extracting the
desired measurable, in our case, the extent of orientational order, is
completely equivalent to finding the size of the conjugate field required to
equilibrate that amount of order - and that knowing the relationship between
the two gives us the relative free energy. Indeed, a variety of thermodynamic
integration strategies used to evaluate free energy differences in simulation
are essentially founded on this idea. However, rather than applying an
artificially imposed external field, we use a priori statistical mechanical
insights into the small and large-field limits of the equation of state to
construct a simulation-guided, interpolated, equation of state. The free
energies that result turn out to need simulation information derived mostly
from the most probable configurations, rather than from the infrequent events,
and therefore use simulation information far more efficiently than conventional
methods.


  Establishing correspondences between two images requires both local and
global spatial context. Given putative correspondences of feature points in two
views, in this paper, we propose Order-Aware Network, which infers the
probabilities of correspondences being inliers and regresses the relative pose
encoded by the essential matrix. Specifically, this proposed network is built
hierarchically and comprises three novel operations. First, to capture the
local context of sparse correspondences, the network clusters unordered input
correspondences by learning a soft assignment matrix. These clusters are in a
canonical order and invariant to input permutations. Next, the clusters are
spatially correlated to form the global context of correspondences. After that,
the context-encoded clusters are recovered back to the original size through a
proposed upsampling operator. We intensively experiment on both outdoor and
indoor datasets. The accuracy of the two-view geometry and correspondences are
significantly improved over the state-of-the-arts. Code will be available at
https://github.com/zjhthu/OANet.git.


  W+W-gamma production at LEP2 is studied using data collected with the DELPHI
detector at centre-of-mass energies between 189 GeV and 209 GeV, corresponding
to an integrated luminosity of about 600 pb^-1. Cross-sections are measured for
the production of W+W- with a hard, central and isolated photon in the final
state, and are found to be compatible with the Standard Model prediction. The
photon energy spectra are used to derive limits on anomalous contributions to
the W+W-Z0gamma and W+W-gammagamma vertices.


  We study in detail the influence of different chemical potentials (baryon,
charged, strange, and neutrino) on how and how fast a free gas of quarks in the
zero-temperature limit reaches the conformal limit. We discuss the influence of
non-zero masses, the inclusion of leptons, and different constraints, such as
charge neutrality, zero-net strangeness, and fixed lepton fraction. We also
investigate for the first time how the symmetry energy of the system under some
of these conditions approaches the conformal limit. Finally, we briefly discuss
what kind of corrections are expected from perturbative QCD as one goes away
from the conformal limit.


  Neutrinos from a supernova (SN) might undergo fast flavor conversions near
the collapsed stellar core. We perform a detailed study of this intriguing
possibility, analyzing time-dependent state-of-the-art 3D SN models of 9 and 20
Msun. Both models were computed with multi-D three-flavor neutrino transport
based on a two-moment solver, and both exhibit the presence of the
lepton-number emission self-sustained asymmetry (LESA). The transport solution
does not provide the angular distributions of the neutrino fluxes, which are
crucial to track the fast flavor instability. To overcome this limitation, we
use a recently proposed approach based on the angular moments of the
energy-integrated electron lepton-number distribution. With this method we find
the possibility of fast neutrino flavor instability at radii <~20 km, which is
well interior to the neutrinosphere. Our results confirm recent observations in
a 2D SN model and in 2D/3D models with fixed matter background, which were
computed with Boltzmann neutrino transport. However, the flavor unstable
locations are not isolated points as discussed previously, but thin skins
surrounding volumes where electron antineutrinos are more abundant than
electron neutrinos. These volumes grow with time and appear first in the
convective layer of the proto-neutron star (PNS), where a decreasing electron
fraction (Ye) and high temperatures favor the occurrence of regions with
negative neutrino chemical potential. Since Ye remains higher in the LESA
dipole direction, where convective lepton-number transport out from the
nonconvective PNS core slows down the deleptonization, flavor unstable
conditions become more widespread in the opposite hemisphere. This interesting
phenomenon deserves further investigation, since its impact on SN modeling and
possible consequences for SN dynamics and neutrino observations are presently
unclear. (abridged)


  We introduce PaLM 2, a new state-of-the-art language model that has better
multilingual and reasoning capabilities and is more compute-efficient than its
predecessor PaLM. PaLM 2 is a Transformer-based model trained using a mixture
of objectives. Through extensive evaluations on English and multilingual
language, and reasoning tasks, we demonstrate that PaLM 2 has significantly
improved quality on downstream tasks across different model sizes, while
simultaneously exhibiting faster and more efficient inference compared to PaLM.
This improved efficiency enables broader deployment while also allowing the
model to respond faster, for a more natural pace of interaction. PaLM 2
demonstrates robust reasoning capabilities exemplified by large improvements
over PaLM on BIG-Bench and other reasoning tasks. PaLM 2 exhibits stable
performance on a suite of responsible AI evaluations, and enables
inference-time control over toxicity without additional overhead or impact on
other capabilities. Overall, PaLM 2 achieves state-of-the-art performance
across a diverse set of tasks and capabilities.
  When discussing the PaLM 2 family, it is important to distinguish between
pre-trained models (of various sizes), fine-tuned variants of these models, and
the user-facing products that use these models. In particular, user-facing
products typically include additional pre- and post-processing steps.
Additionally, the underlying models may evolve over time. Therefore, one should
not expect the performance of user-facing products to exactly match the results
reported in this report.


  We study the strong consistency and asymptotic normality of a least squares
estimator of the drift coefficient in complex-valued Ornstein-Uhlenbeck
processes driven by fractional Brownian motion, extending the results of Chen,
Hu, Wang (2017) to the case of Hurst parameter H \in (1/4 , 1/2) and the
results of Hu, Nualart, Zhou (2019) to a two-dimensional case. When H \in (0,
1/4], it is found that the integrand of the estimator is not in the domain of
the standard divergence operator. To facilitate the proofs, we develop a new
inner product formula for functions of bounded variation in the reproducing
kernel Hilbert space of fractional Brownian motion with Hurst parameter H \in
(0, 1/2). This formula is also applied to obtain the second moments of the
so-called {\alpha}-order fractional Brownian motion and the {\alpha}-fractional
bridges with the Hurst parameter H \in (0, 1/2).


  Recently it was shown that by means of an STM it is experimentally possible
to stimulate clock transitions between the singlet and the non-magnetic triplet
state of a Heisenberg-coupled spin dimer (Bae et al., Science Advances 4,
eaau4159). This leads to more strongly protected clock transitions while
ordinary ones only provide first-order protection against magnetic noise.
However, large decoherence times of clock like states normally refer to
ensembles of spins which do not dephase. In the cited experiment only one
single dimer is manipulated and not an ensemble. For this reason we simulate
how a single dimer behaves in an environment of other spins which couple to the
dimer via dipolar interactions. We perform unitary time evolutions in the
complete Hilbert space including dimer and a reasonably large environment. We
will see that for a weak environment this approach confirms long decoherence
times for the clock like state, but with stronger couplings this statement does
not hold. As a reference we compare the behavior of the dimer with other,
non-clock like, superposition states. Furthermore, we show that the internal
dynamics of the bath plays an important role for the decoherence time of the
system. In a regime where the system is weakly coupled to the bath, stronger
interactions among environmental spins worsen the decoherence time up to a
certain degree, while if system and bath are strongly coupled, stronger
interactions in the environment improve decoherence times.


  The advent of vision-language pre-training techniques enhanced substantial
progress in the development of models for image captioning. However, these
models frequently produce generic captions and may omit semantically important
image details. This limitation can be traced back to the image-text datasets;
while their captions typically offer a general description of image content,
they frequently omit salient details. Considering the magnitude of these
datasets, manual reannotation is impractical, emphasizing the need for an
automated approach. To address this challenge, we leverage existing captions
and explore augmenting them with visual details using "frozen" vision experts
including an object detector, an attribute recognizer, and an Optical Character
Recognizer (OCR). Our proposed method, FuseCap, fuses the outputs of such
vision experts with the original captions using a large language model (LLM),
yielding comprehensive image descriptions. We automatically curate a training
set of 12M image-enriched caption pairs. These pairs undergo extensive
evaluation through both quantitative and qualitative analyses. Subsequently,
this data is utilized to train a captioning generation BLIP-based model. This
model outperforms current state-of-the-art approaches, producing more precise
and detailed descriptions, demonstrating the effectiveness of the proposed
data-centric approach. We release this large-scale dataset of enriched
image-caption pairs for the community.


  We examine the cosmological implications of measurements of the void-galaxy
cross-correlation at redshift $z=0.57$ combined with baryon acoustic
oscillation (BAO) data at $0.1<z<2.4$. We find direct evidence of the late-time
acceleration due to dark energy at $>10\sigma$ significance from these data
alone, independent of the cosmic microwave background and supernovae. Using a
nucleosynthesis prior on $\Omega_bh^2$, we measure the Hubble constant to be
$H_0=72.3\pm1.9\;{\rm km\,s}^{-1}{\rm Mpc}^{-1}$ from BAO+voids at $z<2$, and
$H_0=69.0\pm1.2\;{\rm km\,s}^{-1}{\rm Mpc}^{-1}$ when adding Lyman-$\alpha$ BAO
at $z=2.34$, both independent of the CMB. Adding voids to CMB, BAO and
supernova data greatly improves measurement of the dark energy equation of
state, increasing the figure of merit by >40%, but remaining consistent with
flat flat $\Lambda$ cold dark matter.


  We show a general form of neutrino mass matrix (M), whose matrix elements are
denoted by M_{ij} (i.j=e, mu, tau) as flavor neutrino masses, that induces
maximal CP violation as well as maximal atmospheric neutrino mixing. The masses
of M_{mu mu}, M_{tau tau} and M_{mu tau}+sigma M_{ee} (sigma =\pm 1) turn out
to be completely determined by M_{e mu} and M_{e tau} for given mixing angles.
The appearance of CP violation is found to originate from the interference
between the mu-tau symmetric part of M and its breaking part. If |M_{e
mu}|=|M_{e tau}|, giving either M_{e mu}=-sigma e^{i theta} M_{e tau} or M_{e
mu}=-sigma e^{i theta}M*_{e tau} with a phase parameter theta, is further
imposed, we find that |M_{mu mu}|=|M_{tau tau}|is also satisfied. These two
constraints can be regarded as an extended version of the constraints in the
mu-tau symmetric texture given by M_{e mu}=-sigma M_{e tau} and M_{mu
mu}=M_{tau tau}. Majorana CP violation becomes active if arg(M_{mu tau})\neq
arg(M_{e mu})+theta/2 for M_{e mu}=-sigma e^{i theta} M_{e tau} and if
arg(M_{mu tau})\neq theta/2 for M_{e mu}=-sigma e^{i theta} M*_{e tau}.


  The increase in demand for spectrum-based services forms a bottleneck in
wireless networks. Device-to-Device (D2D) caching networks tackle this problem
by exploiting user's behavior predictability and the possibility of sharing
data between them to alleviate the network congestion. However, capturing
mobility statistics allows Service Providers (SPs) to enhance their caching
strategies. In this work, we introduce a mobility-aware D2D caching network
where SP harnesses user demand and mobility statistics to minimize the incurred
service cost through an optimal caching policy. We investigate two caching
schemes: centralized and decentralized caching schemes. In the centralized
caching scheme, SP makes the caching decision towards its cost minimization to
increase its profit. However, the complexity of optimal caching policy grows
exponentially with the number of users. Therefore, we discuss a greedy caching
algorithm which has a polynomial order complexity. We also use this greedy
algorithm to establish upper and lower bounds on the proactive service gain
achieved by the optimal caching policy. In the decentralized caching scheme,
users take over and make their caching decisions, in a distributed fashion
affected by the SP pricing policy, towards their payment minimization. We
formulated the tension between the SP and users as a Stackelberg game. The Best
response analysis was used to identify a sub-game perfect Nash equilibrium
(SPNE) between users. The optimal solution of proposed model was found to
depend on the SP reward preference, which affects the assigned memory in users'
devices. We found some regimes for the reward value where the SPNE was
non-unique. A fair allocation caching policy was adopted to choose one of these
SPNEs. To understand the impact of user behavior, we investigated some special
cases to explore how user's mobility statistics affect their caching decision.


  The charging and dissolution of mineral surfaces in contact with flowing
liquids are ubiquitous in nature, as most minerals in water spontaneously
acquire charge and dissolve. Mineral dissolution has been studied extensively
under equilibrium conditions, even though non-equilibrium phenomena are
pervasive and substantially affect the mineral-water interface. Here we
demonstrate using interface-specific spectroscopy that liquid flow along a
calcium fluoride surface creates a reversible, spatial charge gradient, with
decreasing surface charge downstream of the flow. The surface charge gradient
can be quantitatively accounted for by a reaction-diffusion-advection model,
which reveals that the charge gradient results from a delicate interplay
between diffusion, advection, dissolution, and desorption/adsorption. The
underlying mechanism is expected to be valid for a wide variety of systems,
including groundwater flows in nature and microfluidic systems.


  We present a type system for strategy languages that express program
transformations as compositions of rewrite rules. Our row-polymorphic type
system assists compiler engineers to write correct strategies by statically
rejecting non meaningful compositions of rewrites that otherwise would fail
during rewriting at runtime. Furthermore, our type system enables reasoning
about how rewriting transforms the shape of the computational program. We
present a formalization of our language at its type system and demonstrate its
practical use for expressing compiler optimization strategies. Our type system
builds the foundation for many interesting future applications, including
verifying the correctness of program transformations and synthesizing program
transformations from specifications encoded as types.


  We study a problem of sequential frame synchronization for a frame
transmitted uniformly in $A$ slots. For a discrete memoryless channel (DMC),
Venkat Chandar et al showed that the frame length $N$ must scale with $A$ as
$e^{N \alpha(Q)} > A$ for the frame synchronization error to go to zero
(asymptotically with $A$). Here, $Q$ denotes the transition probabilities of
the DMC and $\alpha(Q)$, defined as the synchronization threshold,
characterizes the scaling needed of $N$ for asymptotic error free frame
synchronization. We show that the asynchronous communication framework permits
a natural tradeoff between the sync frame length $N$ and the channel (usually
parameterised by the input). For an AWGN channel, we study this tradeoff
between the sync frame length $N$ and the input symbol power $P$ and
characterise the scaling needed of the sync frame energy $E = N P$ for optimal
frame synchronisation.


  The modelling of electrokinetic flows is a critical aspect spanning many
industrial applications and research fields. This has introduced great demand
in flexible numerical solvers to describe these flows. The underlying phenomena
are microscopic, non-linear, and often involve multiple domains. Therefore
often model assumptions and several numerical approximations are introduced to
simplify the solution. In this work, we present a multi-domain multi-species
electrokinetic flow model including complex interface and bulk reactions. After
a dimensional analysis and an overview of some limiting regimes, we present a
set of general purpose finite-volume solvers, based on \of, capable of
describing an arbitrary number of electrochemical species over multiple
interacting (solid or fluid) domains \cite{spnpfoam}. We provide verification
of the computational approach for several cases involving electrokinetic flows,
reactions between species, and complex geometries. We first present three
one-dimensional verification test cases, and then show the capability of the
solver to tackle two- and three-dimensional electrically driven flows and ionic
transport in random porous structures. The purpose of this work is to lay the
foundation for a general-purpose open-source flexible modelling tool for
problems in electrochemistry and electrokinetics at different scales.


  In this article we review recent theoretical and experimental developments on
multilongitudinal-mode emission in ring cavity lasers, paying special attention
to class B lasers. We consider both homogeneously and inhomogeneously broadened
amplifying media as well as the limits of small and large cavity losses (i.e.,
we treat cases within and outside the uniform field limit approximation). In
particular we discuss up to what extent the experimental observations of
self-mode locking in erbium-doped fiber lasers carried out in recent years are
a manifestation of the Risken-Nummedal-Graham-Haken instability.


  Log parsing transforms log messages into structured formats, serving as a
crucial step for log analysis. Despite a variety of log parsing methods that
have been proposed, their performance on evolving log data remains
unsatisfactory due to reliance on human-crafted rules or learning-based models
with limited training data. The recent emergence of large language models
(LLMs) has demonstrated strong abilities in understanding natural language and
code, making it promising to apply LLMs for log parsing. Consequently, several
studies have proposed LLM-based log parsers. However, LLMs may produce
inaccurate templates, and existing LLM-based log parsers directly use the
template generated by the LLM as the parsing result, hindering the accuracy of
log parsing. Furthermore, these log parsers depend heavily on historical log
data as demonstrations, which poses challenges in maintaining accuracy when
dealing with scarce historical log data or evolving log data. To address these
challenges, we propose AdaParser, an effective and adaptive log parsing
framework using LLMs with self-generated in-context learning (SG-ICL) and
self-correction. To facilitate accurate log parsing, AdaParser incorporates a
novel component, a template corrector, which utilizes the LLM to correct
potential parsing errors in the templates it generates. In addition, AdaParser
maintains a dynamic candidate set composed of previously generated templates as
demonstrations to adapt evolving log data. Extensive experiments on public
large-scale datasets show that AdaParser outperforms state-of-the-art methods
across all metrics, even in zero-shot scenarios. Moreover, when integrated with
different LLMs, AdaParser consistently enhances the performance of the utilized
LLMs by a large margin.


  We construct finite time blowup solutions to the parabolic-elliptic
Keller-Segel system $$\partial_t u = \Delta u - \nabla \cdot (u \nabla
\mathcal{K}_u), \quad -\Delta \mathcal{K}_u = u \quad \textup{in}\;\;
\mathbb{R}^d,\; d = 3,4,$$ and derive the final blowup profile $$ u(r,T) \sim
c_d \frac{|\log r|^\frac{d-2}{d}}{r^2} \quad \textup{as}\;\; r \to 0, \;\; c_d
> 0.$$ To our knowledge this provides a new blowup solution for the
Keller-Segel system, rigorously answering a question by Brenner, Constantin,
Kadanoff, Schenkel, and
  Venkataramani (Nonlinearity, 1999).


  We extend the notions of CR GJMS operators and Q-curvature to the case of
partially integrable CR structures. The total integral of the CR Q-curvature
turns out to be a global invariant of compact nondegenerate partially
integrable CR manifolds equipped with an orientation of the bundle of contact
forms, which is nontrivial in dimension at least five. It is shown that its
variation is given by the curvature-type quantity called the CR obstruction
tensor, which is introduced in the author's previous work. Moreover, we
consider the linearized CR obstruction operator. Based on a
scattering-theoretic characterization, we discuss its relation to the CR
deformation complex of integrable CR manifolds. The same characterization is
also used to determine the Heisenberg principal symbol of the linearized CR
obstruction operator.


  We use a Carleman type inequality of Koch and Tataru to obtain quantitative
estimates of unique continuation for solutions of second order elliptic
equations with singular lower order terms. First we prove a three sphere
inequality and then describe two methods of propagation of smallness from sets
of positive measure.


  We make use of the Maupertuis -- Jacobi correspondence, well known in
Classical Mechanics, to simplify 2-D asymptotic formulas based on Maslov's
canonical operator, when constructing Lagrangian manifolds invariant with
respect to phase flows for Hamiltonians of the form $F(x,|p|)$. As examples we
consider Hamiltonians coming from the Schr\"odinger equation, the 2-D Dirac
equation for graphene and linear water wave theory.


  Accurate estimates of left ventricle elastances based on non-invasive
measurements are required for clinical decision-making during treatment of
valvular diseases. The present study proposes a parameter discovery approach
based on a lumped parameter model of the cardiovascular system in conjunction
with optimization and non-invasive, clinical input measurements to approximate
important cardiac parameters, including left ventricle elastances. A subset of
parameters of a multi-compartment lumped parameter model was estimated using
1st order Adam gradient descent and hybrid Adam and 2nd order quasi-Newton
limited-memory Broyden-Fletcher-Goldfarb-Shanno optimization routines.
Forward-mode automatic differentiation was used to estimate the Jacobian
matrices and compared to the common finite differences approach. Synthetic data
of healthy and diseased hearts were generated as proxies for non-invasive
clinical measurements and used to evaluate the algorithm. Twelve parameters
including left ventricle elastances were selected for optimization based on 99%
explained variation in mean left ventricle pressure and volume. The hybrid
optimization strategy yielded the best overall results compared to 1st order
optimization with automatic differentiation and finite difference approaches,
with mean absolute percentage errors ranging from 6.67% to 14,14%. Errors in
left ventricle elastance estimates for simulated aortic stenosis and mitral
regurgitation were smallest when including synthetic measurements for arterial
pressure and valvular flow rate at approximately 2% and degraded to roughly 5%
when including volume trends as well. However, the latter resulted in better
tracking of the left ventricle pressure waveforms and may be considered when
the necessary equipment is available.


  The competition between short-range and cavity-mediated infinite-range
interactions in a cavity-boson system leads to the existence of a superfluid
phase and a Mott-insulator phase within the self-organized regime. In this
work, we quantitatively compare the steady-state phase boundaries of this
transition measured in experiments and simulated using the Multiconfigurational
Time-Dependent Hartree Method for Indistinguishable Particles. To make the
problem computationally feasible, we represent the full system by the exact
many-body wave function of a two-dimensional four-well potential. We argue that
the validity of this representation comes from the nature of both the
cavity-atomic system and the Bose-Hubbard physics. Additionally we show that
the chosen representation only induces small systematic errors, and that the
experimentally measured and theoretically predicted phase boundaries agree
reasonably. We thus demonstrate a new approach for the quantitative numerical
determination of the superfluid--Mott-insulator phase boundary.


  We theoretically study reflection and transmission of light in a
one-dimensional disordered phase-conjugating medium. Using an invariant
imbedding approach a Fokker-Planck equation for the distribution of the probe
light reflectance and expressions for the average probabilities of reflection
and transmission are derived. A new crossover length scale for localization of
light is found, which depends on the competition between phase conjugation and
disorder. For weak disorder, our analytical results are in good agreement with
numerical simulations.


  Scientists are increasingly exploring and utilizing the massive parallelism
of general-purpose accelerators such as GPUs for scientific breakthroughs. As a
result, datacenters, hyperscalers, national computing centers, and
supercomputers have procured hardware to support this evolving application
paradigm. These systems contain hundreds to tens of thousands of accelerators,
enabling peta- and exa-scale levels of compute for scientific workloads. Recent
work demonstrated that power management (PM) can impact application performance
in CPU-based HPC systems, even when machines have the same architecture and SKU
(stock keeping unit). This variation occurs due to manufacturing variability
and the chip's PM. However, while modern HPC systems widely employ accelerators
such as GPUs, it is unclear how much this variability affects applications.
Accordingly, we seek to characterize the extent of variation due to GPU PM in
modern HPC and supercomputing systems. We study a variety of applications that
stress different GPU components on five large-scale computing centers with
modern GPUs: Oak Ridge's Summit, Sandia's Vortex, TACC's Frontera and Longhorn,
and Livermore's Corona. These clusters use a variety of cooling methods and GPU
vendors. In total, we collect over 18,800 hours of data across more than 90% of
the GPUs in these clusters. Regardless of the application, cluster, GPU vendor,
and cooling method, our results show significant variation: 8% (max 22%)
average performance variation even though the GPU architecture and vendor SKU
are identical within each cluster, with outliers up to 1.5X slower than the
median GPU. These results highlight the difficulty in efficiently using
existing GPU clusters for modern HPC and scientific workloads, and the need to
embrace variability in future accelerator-based systems.


  The absolute Galois group of the cyclotomic field $K={\mathbb Q}(\zeta_p)$
acts on the \'etale homology of the Fermat curve $X$ of exponent $p$. We study
a Galois cohomology group which is valuable for measuring an obstruction for
$K$-rational points on $X$. We analyze a $2$-nilpotent extension of $K$ which
contains the information needed for measuring this obstruction. We determine a
large subquotient of this Galois cohomology group which arises from Heisenberg
extensions of $K$. For $p=3$, we perform a Magma computation with ray class
fields, group cohomology, and Galois cohomology, which determines it
completely.


  Motivated by application of current superalgebras in the study of disordered
systems such as the random XY and Dirac models, we investigate $gl(2|2)$
current superalgebra at general level $k$. We construct its free field
representation and corresponding Sugawara energy-momentum tensor in the
non-standard basis. Three screen currents of the first kind are also presented.


  We consider the problem of universal joint clustering and registration of
images and define algorithms using multivariate information functionals. We
first study registering two images using maximum mutual information and prove
its asymptotic optimality. We then show the shortcomings of pairwise
registration in multi-image registration, and design an asymptotically optimal
algorithm based on multiinformation. Further, we define a novel multivariate
information functional to perform joint clustering and registration of images,
and prove consistency of the algorithm. Finally, we consider registration and
clustering of numerous limited-resolution images, defining algorithms that are
order-optimal in scaling of number of pixels in each image with the number of
images.


  We have investigated the magnetodynamic properties of
$\text{La}_{0.7}\text{Sr}_{0.3}\text{MnO}_3$ (LSMO) films of thickness 10, 15
and 30 nm grown on (111)-oriented SrTi$\text{O}_3$ (STO) substrates by pulsed
laser deposition. Ferromagnetic resonance (FMR) experiments were performed in
the temperature range 100--300 K, and the magnetodynamic damping parameter
$\alpha$ was extracted as a function of both film thickness and temperature. We
found that the damping is lowest for the intermediate film thickness of 15 nm
with $\alpha \approx 2 \cdot 10^{-3}$, where $\alpha$ is relatively constant as
a function of temperature well below the Curie temperature of the respective
films.


  We suggest that the gauge-invariant hedgehoglike structures in the Wilson
loops are physically interesting degrees of freedom in the Yang--Mills theory.
The trajectories of these ``hedgehog loops'' are closed curves corresponding to
center-valued (untraced) Wilson loops and are characterized by the center
charge and winding number. We show numerically in the SU(2) Yang--Mills theory
that the density of hedgehog structures in the thermal Wilson--Polyakov line is
very sensitive to the finite-temperature phase transition. The (additively
normalized) hedgehog line density behaves like an order parameter: the density
is almost independent of the temperature in the confinement phase and changes
substantially as the system enters the deconfinement phase. In particular, our
results suggest that the (static) hedgehog lines may be relevant degrees of
freedom around the deconfinement transition and thus affect evolution of the
quark-gluon plasma in high-energy heavy-ion collisions.


  We find $\mathcal{N}=1$ Lagrangian gauge theories that flow to generalized
Argyres-Douglas theories with $\mathcal{N}=2$ supersymmetry. We find that
certain SU quiver gauge theories flow to generalized Argyres-Douglas theories
of type $(A_{k-1}, A_{mk-1})$ and $(I_{m, k m}, S)$. We also find quiver gauge
theories of SO/Sp gauge groups flowing to the $(A_{2m-1}, D_{2mk+1})$,
$(A_{2m}, D_{2m(k-1)+k})$ and $D_{m(2k+2)}^{m(2k+2)}[m]$ theories.


  A key feature of a general nonlinear partially hyperbolic dynamical system is
the absence of differentiability of its invariant splitting. In this paper, we
show that often partial derivatives of the splitting exist and the splitting
depends smoothly on the dynamical system itself.


  In this paper, we classify EF topological orders for 3+1D bosonic systems
where some emergent pointlike excitations are fermions. (1) We argue that all
3+1D bosonic topological orders have gappable boundary. (2) All the pointlike
excitations in EF topological orders are described by the representations of
$G_f=Z_2^f\leftthreetimes_{e_2} G_b$ -- a $Z_2^f$ central extension of a finite
group $G_b$ characterized by $e_2\in H^2(G_b,Z_2)$. (3) We find that the EF
topological orders are classified by 2+1D anomalous topological orders
$\mathcal{A}_b^3$ on their unique canonical boundary. Here $\mathcal{A}_b^3$ is
a unitary fusion 2-category with simple objects labeled by $\hat
G_b=Z_2^m\leftthreetimes G_b$. $\mathcal{A}_b^3$ also has one invertible
fermionic 1-morphism for each object as well as quantum-dimension-$\sqrt 2$
1-morphisms that connect two objects $g$ and $gm$, where $g\in \hat G_b$ and
$m$ is the generator of $Z_2^m$. (4) When $\hat G_b$ is the trivial $Z_2^m$
extension, the EF topological orders are called EF1 topological orders, which
is classified by simple data $(G_b,e_2,n_3,\nu_4)$. (5) When $\hat G_b$ is a
non-trivial $Z_2^m$ extension, the EF topological orders are called EF2
topological orders, where some intersections of three stringlike excitations
must carry Majorana zero modes. (6) Every EF2 topological order with
$G_f=Z_2^f\leftthreetimes G_b$ can be associated with a EF1 topological order
with $G_f=Z_2^f\leftthreetimes \hat G_b$. (7) We find that all EF topological
orders correspond to gauged 3+1D fermionic symmetry protected topological (SPT)
orders with a finite unitary symmetry group. (8) We further propose that the
general classification of 3+1D topological orders with finite unitary
symmetries for bosonic and fermionic systems can be obtained by gauging or
partially gauging the finite symmetry group of 3+1D SPT phases of bosonic and
fermionic systems.


  We present high angular resolution X-ray images and spectra from two {\em
Chandra} ACIS-I observations of the X-ray jet in the nearby radio galaxy
Centaurus A. We find that the X-ray emission from the jet is composed of a low
surface brightness diffuse component extending continuously from within at
least 60 pc of the active nucleus into the NE radio lobe 4 kpc from the
nucleus, along with 31 discrete compact knots, most of which are extended at
the resolution of our observation. We find that there are small but significant
differences between the X-ray and radio morphologies of the inner jet at the
arcsecond level, making it unlikely that a single, spatially coincident
population of ultrarelativistic electrons is responsible for the emission in
both energy regimes. We suggest that the X-ray knots of the inner jet are
indeed the sites of particle acceleration and shocks, and the X-ray and radio
knot offsets are caused by a combination of particle diffusion and energy loss.
These offsets may be a common feature of all jets in radio galaxies, or at
least jets in FR I type galaxies, and may be fundamental to the physics of such
jets. The X-ray spectra of several regions of the jet are well fit by absorbed
power-law models with photon indices $\sim$2.2-2.5, although the spectrum of
one bright knot located $\sim$1 kpc from the nucleus (knot B) is harder (photon
index = 2.0).


  This is the text of a series of five lectures given by the author at the
"Second Annual Spring Institute on Noncommutative Geometry and Operator
Algebras" held at Vanderbilt University in May 2004. It is meant as an overview
of recent results illustrating the interplay between noncommutative geometry
and arithmetic geometry/number theory.


  A total set of $n$ states $|i\rangle$ and the corresponding projectors
$\Pi(i)=|i\rangle \langle i|$ are considered, in a quantum system with
$d$-dimensional Hilbert space $H(d)$. A partially known density matrix $\rho$
with given $p(i)={\rm Tr}[\rho \Pi(i)]$ (where $i=1,...,n$ and $d\le n\le
d^2-1$) is considered, and its ranking permutation is defined. It is used to
calculate the Choquet integral ${\cal C}(\rho)$ which is a positive
semi-definite Hermitian matrix. Comonotonicity is an important concept in the
formalism, which is used to formalise the vague concept of physically similar
density matrices. It is shown that ${\cal C}(\rho)/{\rm Tr}[{\cal C}(\rho)]$ is
a density matrix which is a good approximation to the partially known density
matrix $\rho$.


  In the presented field line map approach the simulation domain of a tokamak
is covered with a cylindrical grid, which is Cartesian within poloidal planes.
Standard finite-difference methods can be used for the discretisation of
perpendicular (w.r.t.~magnetic field lines) operators. The characteristic flute
mode property $\left(k_{\parallel}\ll k_{\perp}\right)$ of structures is
exploited computationally by a grid sparsification in the toroidal direction. A
field line following discretisation of parallel operators is then required,
which is achieved via a finite difference along magnetic field lines. This
includes field line tracing and interpolation or integration. The main emphasis
of this paper is on the discretisation of the parallel diffusion operator.
Based on the support operator method a scheme is constructed which exhibits
only very low numerical perpendicular diffusion. The schemes are implemented in
the new code GRILLIX, and extensive benchmarks are presented which show the
validity of the approach in general and GRILLIX in particular. The main
advantage of the approach is that it does not rely on field/flux-aligned, which
become singular on the separatrix/X-point. Most tokamaks are based on the
divertor concept, and the numerical treatment of the separatrix is therefore of
importance for simulations of the edge and scrape-off layer.


  We consider weighted ray-transforms $P\_W$ (weighted Radon transforms along
straight lines) in $\mathbb{R}^d, \, d\geq 2,$ with strictly positive weights
$W$. We construct an example of such a transform with non-trivial kernel in the
space of infinitely smooth compactly supported functions on $\mathbb{R}^d$. In
addition, the constructed weight $W$ is rotation-invariant continuous and is
infinitely smooth almost everywhere on $\mathbb{R}^d \times \mathbb{S}^{d-1}$.
In particular, by this construction we give counterexamples to some well-known
injectivity results for weighted ray transforms for the case when the
regularity of $W$ is slightly relaxed. We also give examples of continous
strictly positive $W$ such that $\dim \ker P\_W \geq n$ in the space of
infinitely smooth compactly supported functions on $\mathbb{R}^d$ for arbitrary
$n\in \mathbb{N}\cup \{\infty\}$, where $W$ are infinitely smooth for $d=2$ and
infinitely smooth almost everywhere for $d\geq 3$.


  A simple afterburner including radial flow to the randomized transverse
momentum obtained from event generators, Pythia and Hijing, has been
implemented to calculate the $p/\pi$ ratios and compare them with available
data. A coherent trend of qualitative agreement has been obtained in $pp$
collisions and in $Au+Au$ for various centralities. Those results indicate that
the radial flow does play an important role in the so called baryon puzzle
anomaly.


  Major part of a pancreatic islet is composed of beta cells that secrete
insulin, a key hormone regulating influx of nutrients into all cells in a
vertebrate organism to support nutrition, housekeeping or energy storage. Beta
cells constantly communicate with each other using both direct, short-range
interactions through gap junctions, and paracrine long-range signaling.
However, how these cell interactions shape collective sensing and cell behavior
in islets that leads to insulin release is unknown. When stimulated by specific
ligands, primarily glucose, beta cells collectively respond with expression of
a series of transient Ca$^{2+}$ changes on several temporal scales. Here we
analyze a set of Ca$^{2+}$ spike trains recorded in acute rodent pancreatic
tissue slice under physiological conditions. We found strongly correlated
states of co-spiking cells coexisting with mostly weak pairwise correlations
widespread across the islet. Furthermore, the collective Ca$^{2+}$ spiking
activity in islet shows on-off intermittency with scaling of spiking
amplitudes, and stimulus dependent autoassociative memory features. We use a
simple spin glass-like model for the functional network of a beta cell
collective to describe these findings and argue that Ca$^{2+}$ spike trains
produced by collective sensing of beta cells constitute part of the islet
metabolic code that regulates insulin release and limits the islet size.


  Compositional reasoning is a hallmark of human visual intelligence. Yet,
despite the size of large vision-language models, they struggle to represent
simple compositions by combining objects with their attributes. To measure this
lack of compositional capability, we design Cola, a text-to-image retrieval
benchmark to Compose Objects Localized with Attributes. To solve Cola, a model
must retrieve images with the correct configuration of attributes and objects
and avoid choosing a distractor image with the same objects and attributes but
in the wrong configuration. Cola contains about 1.2k composed queries of 168
objects and 197 attributes on around 30K images. Our human evaluation finds
that Cola is 83.33% accurate, similar to contemporary compositionality
benchmarks. Using Cola as a testbed, we explore empirical modeling designs to
adapt pre-trained vision-language models to reason compositionally. We explore
6 adaptation strategies on 2 seminal vision-language models, using
compositionality-centric test benchmarks - Cola and CREPE. We find the optimal
adaptation strategy is to train a multi-modal attention layer that jointly
attends over the frozen pre-trained image and language features. Surprisingly,
training multimodal layers on CLIP performs better than tuning a larger FLAVA
model with already pre-trained multimodal layers. Furthermore, our adaptation
strategy improves CLIP and FLAVA to comparable levels, suggesting that training
multimodal layers using contrastive attribute-object data is key, as opposed to
using them pre-trained. Lastly, we show that Cola is harder than a closely
related contemporary benchmark, CREPE, since simpler fine-tuning strategies
without multimodal layers suffice on CREPE but not on Cola. However, we still
see a significant gap between our best adaptation and human accuracy,
suggesting considerable room for further research.


  The Galactic Center was observed at 8.6 mum in order to detect a mid-infrared
(MIR) counterpart of Sgr A*, parallel to NIR observations. The goal was to set
constraints on possible emission mechanisms.Imaging data were acquired with the
adaptive optics assisted NIR instrument NACO and the MIR instrument VISIR at
the ESO VLT. We present MIR imaging data of an unprecedented quality in terms
of spatial resolution and sensitivity. An extended ridge of emission is found
to be present in the immediate vicinity of Sgr A* and thus renders any
detection of a point source difficult. No MIR point source related to Sgr A*
was detected during the observations. We derive a tight upper limit of 22+-4
mJy (dereddened) on any possible point source present during the observations
in the night of 4/5 June 2006. The absence of a flare in simultaneous
observations at 2.2 mum and the low limits on any possible variability in the
MIR suggest strongly that Sgr A* was in a quasi-quiescent state during this
night. During the night from 5 to 6 June 2006, Sgr A* was found to be variable
on a low level at 3.8 mum. No point source at 8.6 mum was detected during the
simultaneous MIR observations. Due to the poorer atmospheric conditions a
higher upper limit of 60+-30mJy was found for Sgr A* at 8.6 mum during the
second night. The observations are consistent with theoretical predictions. If
the published models are correct, the observations demonstrate successfully
that a 8.6 mum counterpart of Sgr A* can be easily detected in its flaring
state. Spectral indices derived from simultaneous observations of flaring
emission from Sgr A* at NIR and MIR wavelengths will enable us to distinguish
between different kinds of flare models.


  Nuclear image has emerged as a promising research work in medical field.
Images from different modality meet its own challenge. Positron Emission
Tomography (PET) image may help to precisely localize disease to assist in
planning the right treatment for each case and saving valuable time. In this
paper, a novel approach of Spatial Fuzzy C Means (PET SFCM) clustering
algorithm is introduced on PET scan image datasets. The proposed algorithm is
incorporated the spatial neighborhood information with traditional FCM and
updating the objective function of each cluster. This algorithm is implemented
and tested on huge data collection of patients with brain neuro degenerative
disorder such as Alzheimers disease. It has demonstrated its effectiveness by
testing it for real world patient data sets. Experimental results are compared
with conventional FCM and K Means clustering algorithm. The performance of the
PET SFCM provides satisfactory results compared with other two algorithms


  To investigate the impact of matter mixing on the formation of molecules in
the ejecta of SN 1987A, time-dependent rate equations for chemical reactions
are solved for one-zone and one-dimensional ejecta models of SN 1987A. The
latter models are based on the one-dimensional profiles obtained by
angle-averaging of the three-dimensional hydrodynamical models (Ono et al.
2020), which effectively reflect the 3D matter mixing; the impact is
demonstrated, for the first time, based on three-dimensional hydrodynamical
models. The distributions of initial seed atoms and radioactive $^{56}$Ni
influenced by the mixing could affect the formation of molecules. By comparing
the calculations for spherical cases and for several specified directions in
the bipolar-like explosions in the three-dimensional hydrodynamical models, the
impact is discussed. The decay of $^{56}$Ni, practically $^{56}$Co at later
phases, could heat the gas and delay the molecule formation. Additionally,
Compton electrons produced by the decay could ionize atoms and molecules and
could destruct molecules. Several chemical reactions involved with ions such as
H$^+$ and He$^+$ could also destruct molecules. The mixing of $^{56}$Ni plays a
non-negligible role in both the formation and destruction of molecules through
the processes above. The destructive processes of carbon monoxide and silicon
monoxide due to the decay of $^{56}$Ni generally reduce the amounts. However,
if the molecule formation is sufficiently delayed under a certain condition,
the decay of $^{56}$Ni could locally increase the amounts through a sequence of
reactions.


  Polymer Physics: Phenomenology of Polymeric Fluid Simulations is a review
volume that I am writing. I anticipate it will take a while to complete, so I
am supplying individual chapters when each is more-or-less completed.
  This Chapter considers collective coordinates and collective models for
isolated polymer chains. Collective coordinates can be effective tools for
isolating aspects of polymer motion that are less obvious if only the Cartesian
coordinates of the individual atoms or monomers are viewed. I treat Fourier,
Rouse, and Haar wavelets as suppliers of collective coordinates. One of the
sets of collective coordinates that i consider, the Rouse coordinates, follows
naturally from the Rouse model of polymer dynamics. We therefore consider the
Rouse model as well as its more important predecessor, the Kirkwood-Riseman
model. Haar wavelets are noteworthy because they allow one to isolate
individual regions of a polymer


  We consider a random matrix model which describes the competition between
chiral symmetry breaking and the formation of quark Cooper pairs in QCD at
finite density. We study the evolution of the phase structure in temperature
and chemical potential with variations of the strength of the interaction in
the quark-quark channel and demonstrate that the phase diagram can realize a
total of six different topologies. A vector interaction representing
single-gluon exchange reproduces a topology commonly encountered in previous
QCD models, in which a low-density chiral broken phase is separated from a
high-density diquark phase by a first-order line. The other five topologies
either do not possess a diquark phase or display a new phase and new critical
points. Since these five cases require large variations of the coupling
constants away from the values expected for a vector interaction, we conclude
that the phase diagram of finite density QCD has the topology suggested by
single-gluon exchange and that this topology is robust.


  Inspired by the question of whether one can create a visually informative map
in which distances reflect travel-times rather than physical proximity, we
examine whether it is possible to construct a meaningful travel time function
between points in a region. We argue that such a function should constitute a
mathematical metric, and we offer a reasonable candidate using a max-min
approach.


  Audio codecs are typically transform-domain based and efficiently code
stationary audio signals, but they struggle with speech and signals containing
dense transient events such as applause. Specifically, with these two classes
of signals as examples, we demonstrate a technique for restoring audio from
coding noise based on generative adversarial networks (GAN). A primary
advantage of the proposed GAN-based coded audio enhancer is that the method
operates end-to-end directly on decoded audio samples, eliminating the need to
design any manually-crafted frontend. Furthermore, the enhancement approach
described in this paper can improve the sound quality of low-bit rate coded
audio without any modifications to the existent standard-compliant encoders.
Subjective tests illustrate that the proposed enhancer improves the quality of
speech and difficult to code applause excerpts significantly.


  Atomic ensembles strongly interacting with light constitute rich
quantum-optical many-body systems, with the potential for observing cooperative
effects and dissipative nonequilibrium phase transitions. We theoretically
analyze the conditions under which a driven atomic ensemble in free space,
characterized by strong dipole-dipole interactions and large spatial extent,
can undergo a superradiant phase transition, also known as cooperative
resonance fluorescence. In an atomic array, stationary states that conserve the
collective pseudospin exhibit completely cooperative decay and undergo a
second-order phase transition in the large atom number limit. In contrast,
decay mechanisms on longer timescales that fail to conserve pseudospin can lead
to discontinuous first-order phase transition at a critical finite atom number,
disrupting cooperation despite sharing many similar observable characteristics.
A hallmark of the superradiant phase transition is an abrupt shift from total
light reflection off the atoms to rapidly increasing transmission, accompanied
by significant quantum fluctuations, as a function of light intensity.


  We show that zero-energy flows appear in many particle systems as same as in
single particle cases in 2-dimensions. Vortex patterns constructed from the
zero-energy flows can be investigated in terms of the eigenstates in conjugate
spaces of Gel'fand triplets. Stable patterns are written by the superposition
of zero-energy eigenstates. On the other hand vortex creations and
annihilations are described by the insertions of unstable eigenstates with
complex-energy eigenvalues into the stable patterns. Some concrete examples are
presented in the 2-dimensional parabolic potential barrier case. %, i.e., $-m
\gamma^2 (x^2+y^2)/2$. We point out three interesting properties of the
zero-energy flows; (i) the absolute economy as for the energy consumption, (ii)
the infinite variety of the vortex patterns, and (iii) the absolute stability
of the vortex patterns .


  Recently, instruction-following audio-language models have received broad
attention for audio interaction with humans. However, the absence of
pre-trained audio models capable of handling diverse audio types and tasks has
hindered progress in this field. Consequently, most existing works have only
been able to support a limited range of interaction capabilities. In this
paper, we develop the Qwen-Audio model and address this limitation by scaling
up audio-language pre-training to cover over 30 tasks and various audio types,
such as human speech, natural sounds, music, and songs, to facilitate universal
audio understanding abilities. However, directly co-training all tasks and
datasets can lead to interference issues, as the textual labels associated with
different datasets exhibit considerable variations due to differences in task
focus, language, granularity of annotation, and text structure. To overcome the
one-to-many interference, we carefully design a multi-task training framework
by conditioning on a sequence of hierarchical tags to the decoder for
encouraging knowledge sharing and avoiding interference through shared and
specified tags respectively. Remarkably, Qwen-Audio achieves impressive
performance across diverse benchmark tasks without requiring any task-specific
fine-tuning, surpassing its counterparts. Building upon the capabilities of
Qwen-Audio, we further develop Qwen-Audio-Chat, which allows for input from
various audios and text inputs, enabling multi-turn dialogues and supporting
various audio-central scenarios.


  The advancement of astronomical observations opens the possibility of testing
our current understanding of gravitational theory in the strong-field regime
and probing any deviation from general relativity. We explore to what extent
compact stars predicted by non-minimal derivative coupling (NMDC) gravity
theory agree with observed data. We investigate white dwarfs (WDs), neutron
stars (NSs), and quark stars (QSs) mass and radius in various values of
constant scalar $|Q_{\infty}|$ at coupling strength of $\eta=\pm1$. This study
focuses on the astrophysical impacts of altering maximum masses by values of
$|Q_{\infty}|$ and $\eta$. From an observational point of view, we found that
WD stars are consistent with ultra-cold WD data at $|Q_{\infty}| \lesssim 0.2$.
We also found that QS has a similar impact of mass-radius to NS, where the
modification is more significant at higher (central) density. For NS and QS
EoSs, the value $|Q_{\infty}|$ strongly alters the critical mass and might
eliminate the $M-\rho_c$ turning point in the negative $\eta$ case. In that
case, the sufficiently large $|Q_{\infty}|$ could predict $M>2.6 M_\odot$ NS
and QS, i.e., larger than GW190814 secondary counterpart. We suggest that the
lower mass gap in the gravitational wave and x-ray binary mass population data
might restrict the theory's $|Q_{\infty}|$.


  The effect of nucleon-nucleon correlations in symmetric nuclear matter at
finite temperature is studied beyond BCS theory. Starting from a Hartree-Fock
description of nuclear matter with the Gogny effective interaction, we add
correlations corresponding to the formation of preformed pairs and scattering
states above the superfluid critical temperature within the in-medium T-matrix
approach, which is analogous to the Nozieres-Schmitt-Rink theory. We calculate
the critical temperature for a BEC superfluid of deuterons, of a BCS superfluid
of nucleons, and in the crossover between these limits. The effect of the
correlations on thermodynamic properties (equation of state, energy, entropy)
and the liquid-gas phase transition is discussed. Our results show that
nucleon-nucleon correlations beyond BCS play an important role for the
properties of nuclear matter, especially in the low-density region.


  Using Koll\'ar's semipositivity results, we produce a number of nef and ample
tautological divisors on Hassett's spaces of weighted stable pointed curves. As
an application, we prove that Hassett's spaces are log canonical models of
Deligne-Mumford spaces of stable pointed curves.


  We propose a novel algorithm for image reconstruction in radio
interferometry. The ill-posed inverse problem associated with the incomplete
Fourier sampling identified by the visibility measurements is regularized by
the assumption of average signal sparsity over representations in multiple
wavelet bases. The algorithm, defined in the versatile framework of convex
optimization, is dubbed Sparsity Averaging Reweighted Analysis (SARA). We show
through simulations that the proposed approach outperforms state-of-the-art
imaging methods in the field, which are based on the assumption of signal
sparsity in a single basis only.


  The possibility to control electrokinetic transport through carbon and
hexagonal boron nitride (hBN) nanotubes has recently opened new avenues for
nanofluidic approaches to face outstanding challenges such as energy production
and conversion or water desalination. The $p$H-dependence of experimental
transport coefficients point to the sorption of hydroxide ions as the
microscopic origin of the surface charge and recent ab initio calculations
suggest that these ions behave differently on carbon and hBN, with only
physisorption on the former and both physi- and chemisorption on the latter.
Using classical non-equilibrium molecular dynamics simulations of interfaces
between an aqueous electrolyte and three models of hBN and graphite surfaces,
we demonstrate the major influence of the sorption mode of hydroxide ions on
the interfacial transport properties. Physisorbed surface charge leads to a
considerable enhancement of the surface conductivity as compared to its
chemisorbed counterpart, while values of the $\zeta$-potential are less
affected . The analysis of the MD results for the surface conductivity and
$\zeta$-potential in the framework of Poisson-Boltzmann-Stokes theory, as is
usually done to analyze experimental data, further confirms the importance of
taking into account both the mobility of surface hydroxide ions and the
decrease of the slip length with increasing titratable surface charge density.


  Most observational techniques in astronomy can be understood as exploiting
the various forms of the first-order correlation function g^(1). As however
demonstrated by the Narrabri Stellar Intensity Interferometer back in the
1960's by Hanbury Brown & Twiss, and which is the first experiment to measure
the second-order correlation function g^(2), light can carry more information
than simply its intensity, spectrum and polarization. Since this experiment,
theoretical and laboratory studies of non-classical properties of light have
become a very active field of research, namely quantum optics. Despite the
variety of results in this field, astrophysics remained focused essentially on
first-order coherence. In this paper, we study the possibility that quantum
properties of light could be observed in cosmic sources. We provide the basic
mathematical ingredients about the first and the second order correlation
functions, applied to the modern context of astronomical observations. The
exploitation of g^(2) is certainly richer than what a modern intensity
interferometer could bring and is particularly interesting for sources of
non-thermal light. We conclude by briefly presenting why microquasars in our
galaxy and their extragalactic parents can represent an excellent first target
in the optical/near-infrared where to observe non-thermal light, and test the
use of g^(2) in astrophysical sources.


  The main advantage of Constraint Programming (CP) approaches for sequential
pattern mining (SPM) is their modularity, which includes the ability to add new
constraints (regular expressions, length restrictions, etc). The current best
CP approach for SPM uses a global constraint (module) that computes the
projected database and enforces the minimum frequency; it does this with a
filtering algorithm similar to the PrefixSpan method. However, the resulting
system is not as scalable as some of the most advanced mining systems like
Zaki's cSPADE. We show how, using techniques from both data mining and CP, one
can use a generic constraint solver and yet outperform existing specialized
systems. This is mainly due to two improvements in the module that computes the
projected frequencies: first, computing the projected database can be sped up
by pre-computing the positions at which an symbol can become unsupported by a
sequence, thereby avoiding to scan the full sequence each time; and second by
taking inspiration from the trailing used in CP solvers to devise a
backtracking-aware data structure that allows fast incremental storing and
restoring of the projected database. Detailed experiments show how this
approach outperforms existing CP as well as specialized systems for SPM, and
that the gain in efficiency translates directly into increased efficiency for
other settings such as mining with regular expressions.


  Using the irreducible tensor-operator technique, we establish the relation
between different forms of spin tomograms. Quantizer and dequantizer operators
are presented in simple explicit forms and are specified for the low-spin
states. The kernel of the star-product is evaluated for qubits and qutrits and
its connection with a generic formula is found.


  Symbolic music understanding, which refers to the understanding of music from
the symbolic data (e.g., MIDI format, but not audio), covers many music
applications such as genre classification, emotion classification, and music
pieces matching. While good music representations are beneficial for these
applications, the lack of training data hinders representation learning.
Inspired by the success of pre-training models in natural language processing,
in this paper, we develop MusicBERT, a large-scale pre-trained model for music
understanding. To this end, we construct a large-scale symbolic music corpus
that contains more than 1 million music songs. Since symbolic music contains
more structural (e.g., bar, position) and diverse information (e.g., tempo,
instrument, and pitch), simply adopting the pre-training techniques from NLP to
symbolic music only brings marginal gains. Therefore, we design several
mechanisms, including OctupleMIDI encoding and bar-level masking strategy, to
enhance pre-training with symbolic music data. Experiments demonstrate the
advantages of MusicBERT on four music understanding tasks, including melody
completion, accompaniment suggestion, genre classification, and style
classification. Ablation studies also verify the effectiveness of our designs
of OctupleMIDI encoding and bar-level masking strategy in MusicBERT.


  Implicit schemes have been extensively used in building physics to compute
the solution of moisture diffusion problems in porous materials for improving
stability conditions. Nevertheless, these schemes require important
sub-iterations when treating non-linear problems. To overcome this
disadvantage, this paper explores the use of improved explicit schemes, such as
Dufort-Frankel, Crank-Nicolson and hyperbolisation approaches. A first case
study has been considered with the hypothesis of linear transfer. The
Dufort-Frankel, Crank-Nicolson and hyperbolisation schemes were compared to the
classical Euler explicit scheme and to a reference solution. Results have shown
that the hyperbolisation scheme has a stability condition higher than the
standard Courant-Friedrichs-Lewy (CFL) condition. The error of this schemes
depends on the parameter \tau representing the hyperbolicity magnitude added
into the equation. The Dufort-Frankel scheme has the advantages of being
unconditionally stable and is preferable for non-linear transfer, which is the
second case study. Results have shown the error is proportional to O(\Delta t).
A modified Crank-Nicolson scheme has been proposed in order to avoid
sub-iterations to treat the non-linearities at each time step. The main
advantages of the Dufort-Frankel scheme are (i) to be twice faster than the
Crank-Nicolson approach; (ii) to compute explicitly the solution at each time
step; (iii) to be unconditionally stable and (iv) easier to parallelise on
high-performance computer systems. Although the approach is unconditionally
stable, the choice of the time discretisation $\Delta t$ remains an important
issue to accurately represent the physical phenomena.


  Global actions were introduced by Bak in order to have a homotopy theory in a
purely algebraic setting. In this paper we apply his techniques in a particular
case: the (single domain) unimodular row global action. More precisely, we
compute the the path connected component and fundamental group for the
unimodular row global action. An explicit computation of the fundamental group
of the (connected component of) unimodular row global action is closely related
to stability questions in K-theory. This will be shown by constructing an exact
sequence with the fundamental group functor as the middle term and having
surjective stability for the functor K_2 on the left and injective stability
for the functor K_1 on the right.


  In this paper we study the symmetry parameters determining number,
distinguishing number, and cost of 2-distinguishing, for some variations on
hypercubes, namely Hamming graphs, powers of hypercubes, folded hypercubes,
enhanced hypercubes, augmented hypercubes and locally twisted hypercubes.


  We consider the following class of fractional parametric problems
\begin{equation*} \left\{ \begin{array}{ll} (-\Delta_{Dir})^{s} u= f(x,
u)+t\varphi_{1}+h &\mbox{ in } \Omega\\ u=0 &\mbox{ on } \partial \Omega,
\end{array} \right. \end{equation*} where $\Omega\subset \mathbb{R}^{N}$ is a
smooth bounded domain, $s\in (0, 1)$, $N> 2s$, $(-\Delta_{Dir})^{s}$ is the
fractional Dirichlet Laplacian, $f: \bar{\Omega} \times \mathbb{R} \rightarrow
\mathbb{R}$ is a locally Lipschitz nonlinearity having linear or superlinear
growth and satisfying Ambrosetti-Prodi type assumptions, $t\in \mathbb{R}$,
$\varphi_{1}$ is the first eigenfunction of the Laplacian with homogenous
boundary conditions, and $h:\Omega\rightarrow \mathbb{R}$ is a bounded
function. Using variational methods, we prove that there exists a $t_{0}\in
\mathbb{R}$ such that the above problem admits at least two distinct solutions
for any $t\leq t_{0}$. We also discuss the existence of solutions for a
fractional periodic Ambrosetti-Prodi type problem.


  Lock polynomials and lock Kohnert tableaux are natural analogues to key
polynomials and key Kohnert tableaux, respectively. In this paper, we compare
lock polynomials to the much-studied key polynomials and show that the
difference of a key polynomial and lock polynomial for the same composition is
monomial positive. We also examine the conditions for which key and lock
polynomials are symmetric or quasisymmetric. We accomplish these goals
combinatorially using key Kohnert tableaux and lock Kohnert tableaux. In
particular, for the difference of a key minus a lock, we focus on the behavior
of crystal operators on Kohnert tableaux. The Type A Demazure crystal can be
realized on the vertex set of key Kohnert tableaux, and we show with an
explicit combinatorial definition that a similar crystal-like structure exists
on the vertex set of lock Kohnert tableaux. Finally, we construct an injective,
weight-preserving map from lock Kohnert tableaux to key Kohnert tableaux that
intertwines the crystal operators.


  We solve an open problem concerning the relaxation time (inverse spectral
gap) of the zero range process in $\mathbf {Z}^d/L\mathbf {Z}^d$ with constant
rate, proving a tight upper bound of $O((\rho +1)^2L^2)$, where $\rho$ is the
density of particles.


  We prove vanishing of distributions on a split real reductive group which
change according to a non-degenerate character under the left action of the
unipotent radical of the Borel subgroup, and are equivariant under the right
action of a spherical subgroup, and eigen with respect to the center of the
universal enveloping algebra of the Lie algebra of G.
  This is a generalization of a result by Shalika, that concerned the group
case. Shalika's result was crucial in the proof of his multiplicity one
theorem. We view our result as a step in the study of multiplicities of
quasi-regular representations on spherical varieties.
  As an application we prove non-vanishing of spherical Bessel functions.


  We prove a version of the Ando-Choi-Effros lifting theorem respecting
subspaces, which in turn relies on Oja's principle of local reflexivity
respecting subspaces. To achieve this, we first develop a theory of pairs of
$M$-ideals. As a first consequence we get a version respecting subspaces of the
Michael-Pe{\l}czy\'nski extension theorem. Other applications are related to
linear and Lipschitz bounded approximation properties for a pair consisting of
a Banach space and a subspace. We show that in the separable case, the BAP for
such a pair is equivalent to the simultaneous splitting of an associated pair
of short exact sequences given by a construction of Lusky. We define a
Lipschitz version of the BAP for pairs, and study its relationship to the
(linear) BAP for pairs. The two properties are not equivalent in general, but
they are when the pair has an additional Lipschitz-lifting property in the
style of Godefroy and Kalton. We also characterize, in the separable case,
those pairs of a metric space and a subset whose corresponding pair of
Lipschitz-free spaces has the BAP.


  High energy photon colliders based on laser backscattering are a very natural
extension of a e+e- linear colliders and open new possibilities to study of the
matter. This option has been included in the pre-conceptual designs of linear
colliders and work on Technical Design Reports is in progress. The physics
motivation for photon colliders is quite clear though more studies are needed.
The proof of its technical feasibility and the search for the best solutions is
of first priority now. In this talk we discuss: physics motivation, laser
problems and new possible solutions, and generation of low emittance beams
needed for obtaining very high luminosities.


  We consider the ground state of simple quantum systems coupled to an
environment. In general the system is entangled with its environment. As a
consequence, even at zero temperature, the energy of the system is not sharp: a
projective measurement can find the system in an excited state. We show that
energy fluctuation measurements at zero temperature provide entanglement
information. For two-state systems which exhibit a persistent current in the
ground state, energy fluctuations and persistent current fluctuations are
closely related. The harmonic oscillator serves to illustrate energy
fluctuations in a system with an infinite number of states. In addition to the
energy distribution we discuss the energy-energy time-correlation function in
the zero-temperature limit.


  We investigate the ultimate estimation precision, characterized by the
quantum Fisher information, of a two-level atom as a detector which is coupled
to massless scalar field in the Minkowski vacuum. It has been shown that for an
inertial detector moving with a constant velocity, its quantum Fisher
information is completely unaffected by the velocity, however, it still decays
over time due to the decoherence caused by the interaction between the atom and
the field. In addition, for a uniformly accelerated detector ($w=0$) moving
along spatially straight line, the accelerated motion will reduce the quantum
Fisher information in the estimation of state parameters. However, when the
detector trajectory is generated by a combination of the linear accelerated
motion and a component of the four-velocity $w=dy/d\tau$, we find quite unlike
the previous results that, for the non-relativistic case $(w\ll1)$, the
acceleration could degrade the quantum Fisher information, while the
four-velocity component will suppress the degradation of the quantum Fisher
information, and thus could enhance the precision of parameters estimation.
Furthermore, in the case for ultra-relativistic velocities
$(w\rightarrow\infty)$, although the detector still interacts with the
environment, it behaves as if it were a closed system as a consequence of
relativity correction associated to the velocity, and the quantum Fisher
information in this case can be shield from the effect of the external
environment, and thus from the relativistic motion.


  Context. Although a bluer-when-brighter trend is commonly observed in
blazars, the opposite trend of redder-when-brighter has also been found in some
blazars. Aims. We investigate the frequency of the redder-when-brighter trend
in flat-spectrum radio quasars (FSRQs). Methods. We investigate the optical
variability of 29 FSRQs in the SDSS Stripe 82 region using SDSS DR7 released
multi-epoch data covering about nine years. We determined the spectral index by
fitting a powerlaw to SDSS ugriz photometric data, and explored the
relationship between the spectral index and source brightness. Results. For all
FSRQs studied, we detect variations in r band flux of overall amplitude between
0.24 mag and 3.46 mag in different sources. Fourteen of 29 FSRQs display a
bluer-when-brighter trend. However, only one source exhibits a
redder-when-brighter trend, which implies that this behavior is rare in our
FSRQ sample. In this source, the thermal emission from the accretion disk may
be responsible for the redder-when-brighter trend.


  Density functional theory calculations have been performed for the
structural, electronic, magnetic and ferroelectric properties of a
mixed-valence Fe(II)-Fe(III) formate framework [NH$_2$(CH$_3$)$_2$][Fe$^{\rm
III}$Fe$^{\rm II}$(HCOO)$_6$] (DMAFeFe). Recent experiments report a
spontaneous electric polarization and our calculations are in agreement with
the reported experimental value. Furthermore, we shed light into the
microscopic mechanism leading to the observed value and as well how to possibly
enhanced the polarization. The interplay between charge ordering, dipolar
ordering of DMA$^+$ cations and the induced structural distortions suggest new
interesting directions to explore in these complex multifunctional hybrid
perovskites.


  We implemented the protocol of entanglement assisted orientation in the space
proposed by Brukner et al (quant-ph/0603167). We used min-max principle to
evaluate the optimal entangled state and the optimal direction of polarization
measurements which violate the classical bound.


  The total phenols and flavonoids content of different polar solvent extracts
from Aurea Helianthus flowers, and their antioxidant activity were determined.
The ethanol extract of Aurea Helianthus flowers were suspended in water and
fractionated using different polar solvents; hexane, chloroform, ethyl acetate,
butanol and water. The parameters of each extract mentioned above were
determined using Floin-ciocalteu reagent(FCR) method, AlCl3 colorimetry method,
ferric reducing ability of plasma(FRAP) assay, total antioxidant activity(TAA)
assay and DPPH radical scavenging assay. The highest total phenols
content(516.21 mg GAE/g) and flavonoids content(326.06 mg QCE/g) were obtained
in ethyl acetate extract, the correlation between TPC and TFC assay was founded
to be 0.967. All polar solvent extracts of Aurea Helianthus flowers showed
significant antioxidant effects, the hightest inhibition was obtained in ethyl
acetate and choroform extracts and the lowest inhibition in the water extract.
There is a good correlation of total phenols and flavonoids content with
antioxidant activity. This work indicated that the polar solvent extracts of
Aurea Helianthus flowers contain high phenols and flavonoids content and
exhibited antioxidant activities in vitro, therefore, could be candidates for
use as natural antioxidant.


  In this work, we propose a covert communication scheme where the transmitter
attempts to hide its transmission to a full-duplex receiver, from a warden that
is to detect this covert transmission using a radiometer. Specifically, we
first derive the detection error rate at the warden, based on which the optimal
detection threshold for its radiometer is analytically determined and its
expected detection error rate over wireless fading channels is achieved in a
closed-form expression. Our analysis indicates that the artificial noise
deliberately produced by the receiver with a random transmit power, although
causes self-interference, offers the capability of achieving a positive
effective covert rate for any transmit power (can be infinity) subject to any
given covertness requirement on the expected detection error rate. This work is
the first study on the use of the full-duplex receiver with controlled
artificial noise for achieving covert communications and invites further
investigation in this regard.


  Fundamental mathematical constants like $e$ and $\pi$ are ubiquitous in
diverse fields of science, from abstract mathematics to physics, biology and
chemistry. For centuries, new formulas relating fundamental constants have been
scarce and usually discovered sporadically. Here we propose a novel and
systematic approach that leverages algorithms for deriving mathematical
formulas for fundamental constants and help reveal their underlying structure.
Our algorithms find dozens of well-known as well as previously unknown
continued fraction representations of $\pi$, $e$, Catalan's constant, and
values of the Riemann zeta function. Two example conjectures found by our
algorithm and so far unproven are: \begin{equation*} \frac{24}{\pi^2} = 2 +
7\cdot 0\cdot 1+ \frac{8\cdot1^4}{2 + 7\cdot 1\cdot 2 + \frac{8\cdot2^4}{2 +
7\cdot 2\cdot 3 + \frac{8\cdot3^4}{2 + 7\cdot 3\cdot 4 +
\frac{8\cdot4^4}{..}}}} \quad\quad,\quad\quad \frac{8}{7 \zeta(3)} = 1\cdot 1 -
\frac{1^6}{3\cdot 7 - \frac{2^6}{5\cdot 19 - \frac{3^6}{7\cdot 37 -
\frac{4^6}{..}}}} \end{equation*} We present two algorithms that proved useful
in finding conjectures: a Meet-In-The-Middle (MITM) algorithm and a Gradient
Descent (GD) tailored to the recurrent structure of continued fractions. Both
algorithms are based on matching numerical values and thus they conjecture
formulas without providing proofs and without requiring prior knowledge on any
underlying mathematical structure. This approach is especially attractive for
constants for which no mathematical structure is known, as it reverses the
conventional approach of sequential logic in formal proofs. Instead, our work
supports a different approach for research: algorithms utilizing numerical data
to unveil mathematical structures, thus trying to play the role of intuition of
great mathematicians of the past, providing leads to new mathematical research.


  For control systems that either have a fast explicit periodic dependence on
time and bounded controls or have periodic solutions and small controls, we
define an average control system that takes into account all possible
variations of the control, and prove that its solutions approximate all
solutions of the oscillating system as oscillations go faster. The dimension of
its velocity set is characterized geometrically. When it is maximum the average
system defines a Finsler metric, not twice differentiable in general. For
minimum time control, this average system allows one to give a rigorous proof
that averaging the Hamiltonian given by the maximum principle is a valid
approximation.


  Megrelishvili defines \emph{light groups} of isomorphisms of a Banach space
as the groups on which the Weak and Strong Operator Topologies coincide, and
proves that every bounded group of isomorphisms of Banach spaces with the Point
of Continuity Property (PCP) is light. We investigate this concept for
isomorphism groups $G$ of classical Banach spaces $X$ without the PCP,
specially isometry groups, and relate it to the existence of $G$-invariant LUR
or strictly convex renormings of $X$.


  We study the ballistic adsorption of a polydisperse mixture of spheres onto a
line. Within a mean-field approximation, the problem can be analytically solved
by means of a kinetic equation for the gap distribution. In the mean-field
approach, the adsorbed substrate as approximated as composed by {\em effective}
particles with the {\em same} size, equal to the average diameter of the
spheres in the original mixture. The analytic solution in the case of binary
mixtures agrees quantitatively with direct Monte Carlo simulations of the
model, and qualitatively with previous simulations of a related model in $d=2$.