  Model averaging has received much attention in the past two decades, which
integrates available information by averaging over potential models. Although
various model averaging methods have been developed, there are few literatures
on the theoretical properties of model averaging from the perspective of
stability, and the majority of these methods constrain model weights to a
simplex. The aim of this paper is to introduce stability from statistical
learning theory into model averaging. Thus, we define the stability, asymptotic
empirical risk minimizer, generalization, and consistency of model averaging
and study the relationship among them. Our results indicate that stability can
ensure that model averaging has good generalization performance and consistency
under reasonable conditions, where consistency means model averaging estimator
can asymptotically minimize the mean squared prediction error. We also propose
a L2-penalty model averaging method without limiting model weights and prove
that it has stability and consistency. In order to reduce the impact of tuning
parameter selection, we use 10-fold cross-validation to select a candidate set
of tuning parameters and perform a weighted average of the estimators of model
weights based on estimation errors. The Monte Carlo simulation and an
illustrative application demonstrate the usefulness of the proposed method.


  Using the Morse-theoretic techniques introduced by Hitchin, we prove that the
moduli space of $\Sp(2p,2q)$-Higgs bundles over a compact Riemann surface of
genus $g\geq 2$ is connected. In particular, this implies that the moduli space
of representations of the fundamental group of the surface in $\Sp(2p,2q)$ is
connected.


  Deep neural networks (DNNs) have demonstrated exceptional success across
various tasks, underscoring the need to evaluate the robustness of advanced
DNNs. However, traditional methods using stickers as physical perturbations to
deceive classifiers present challenges in achieving stealthiness and suffer
from printing loss. Recent advancements in physical attacks have utilized light
beams such as lasers and projectors to perform attacks, where the optical
patterns generated are artificial rather than natural. In this study, we
introduce a novel physical attack, adversarial catoptric light (AdvCL), where
adversarial perturbations are generated using a common natural phenomenon,
catoptric light, to achieve stealthy and naturalistic adversarial attacks
against advanced DNNs in a black-box setting. We evaluate the proposed method
in three aspects: effectiveness, stealthiness, and robustness. Quantitative
results obtained in simulated environments demonstrate the effectiveness of the
proposed method, and in physical scenarios, we achieve an attack success rate
of 83.5%, surpassing the baseline. We use common catoptric light as a
perturbation to enhance the stealthiness of the method and make physical
samples appear more natural. Robustness is validated by successfully attacking
advanced and robust DNNs with a success rate over 80% in all cases.
Additionally, we discuss defense strategy against AdvCL and put forward some
light-based physical attacks.


  Accurately predicting the lifespan of lithium-ion batteries is crucial for
optimizing operational strategies and mitigating risks. While numerous studies
have aimed at predicting battery lifespan, few have examined the
interpretability of their models or how such insights could improve
predictions. Addressing this gap, we introduce three innovative models that
integrate shallow attention layers into a foundational model from our previous
work, which combined elements of recurrent and convolutional neural networks.
Utilizing a well-known public dataset, we showcase our methodology's
effectiveness. Temporal attention is applied to identify critical timesteps and
highlight differences among test cell batches, particularly underscoring the
significance of the "rest" phase. Furthermore, by applying cyclic attention via
self-attention to context vectors, our approach effectively identifies key
cycles, enabling us to strategically decrease the input size for quicker
predictions. Employing both single- and multi-head attention mechanisms, we
have systematically minimized the required input from 100 to 50 and then to 30
cycles, refining this process based on cyclic attention scores. Our refined
model exhibits strong regression capabilities, accurately forecasting the
initiation of rapid capacity fade with an average deviation of only 58 cycles
by analyzing just the initial 30 cycles of easily accessible input data.


  Multi-object tracking has been recently approached with the min-cost network
flow optimization techniques. Such methods simultaneously resolve multiple
object tracks in a video and enable modeling of dependencies among tracks.
Min-cost network flow methods also fit well within the "tracking-by-detection"
paradigm where object trajectories are obtained by connecting per-frame outputs
of an object detector. Object detectors, however, often fail due to occlusions
and clutter in the video. To cope with such situations, we propose to add
pairwise costs to the min-cost network flow framework. While integer solutions
to such a problem become NP-hard, we design a convex relaxation solution with
an efficient rounding heuristic which empirically gives certificates of small
suboptimality. We evaluate two particular types of pairwise costs and
demonstrate improvements over recent tracking methods in real-world video
sequences.


  We discuss aspects of secure quantum communication by proposing and analyzing
a quantum analog of the Vernam cipher (one-time-pad). The quantum Vernam cipher
uses entanglement as the key to encrypt quantum information sent through an
insecure quantum channel. First, in sharp contrast with the classical Vernam
cipher, the quantum key can be recycled securely. We show that key recycling is
intrinsic to the quantum cipher-text, rather than using entanglement as the
key. Second, the scheme detects and corrects for arbitrary transmission errors,
and it does so using only local operations and classical communication (LOCC)
between the sender and the receiver. The application to quantum message
authentication is discussed. Quantum secret sharing schemes with similar
properties are characterized. We also discuss two general issues, the relation
between secret communication and secret sharing, the classification of secure
communication protocols.


  The rise of social media has been argued to intensify uncivil and hostile
online political discourse. Yet, to date, there is a lack of clarity on what
incivility means in the political sphere. In this work, we utilize a
multidimensional perspective of political incivility, developed in the fields
of political science and communication, that differentiates between
impoliteness and political intolerance. We present state-of-the-art incivility
detection results using a large dataset of 13K political tweets, collected and
annotated per this distinction. Applying political incivility detection at
large-scale, we observe that political incivility demonstrates a highly skewed
distribution over users, and examine social factors that correlate with
incivility at subpopulation and user-level. Finally, we propose an approach for
modeling social context information about the tweet author alongside the tweet
content, showing that this leads to improved performance on the task of
political incivility detection. We believe that this latter result holds
promise for socially-informed text processing in general.


  Let $X$ be a product system over a quasi-lattice ordered groupoid $(G,P)$.
Under mild hypotheses, we associate to $X$ a $C^*$-algebra which is couniversal
for injective Nica covariant Toeplitz representations of $X$ which preserve the
gauge coaction. When $(G,P)$ is a quasi-lattice ordered group this couniversal
$C^*$-algebra coincides with the Cuntz-Nica-Pimsner algebra introduced by
Carlsen-Larsen-Sims-Vittadello, and under some mild amenability conditions with
that of Sims and Yeend. We prove related gauge invariant uniqueness theorems in
this general setup.


  We adress the maximization problem of expected utility from terminal wealth.
The special feature of this paper is that we consider a financial market where
the price process of risky assets can have a default time. Using dynamic
programming, we characterize the value function with a backward stochastic
differential equation and the optimal portfolio policies. We separately treat
the cases of exponential, power and logarithmic utility.


  Elastic crystalline membranes exhibit a buckling transition from sphere to
polyhedron. However, their morphologies are restricted to convex polyhedra and
are difficult to externally control. Here, we study morphological changes of
closed crystalline membrane of super-paramagnetic particles. The competition of
magnetic dipole-dipole interactions with the elasticity of this magnetoelastic
membrane leads to concave morphologies. Interestingly, as the magnetic field
strength increases, the symmetry of the buckled membrane decreases from 5-fold
to 3-fold, to 2-fold and, finally, to 1-fold rotational symmetry. This gives
the ability to switch the membrane morphology between convex and concave shapes
with specific symmetry and provides promising applications for membrane shape
control in the design of actuatable micro-containers for targeted delivery
systems.


  We have recently solved the inverse spectral problem for integrable PDEs in
arbitrary dimensions arising as commutation of multidimensional vector fields
depending on a spectral parameter $\lambda$. The associated inverse problem, in
particular, can be formulated as a non linear Riemann Hilbert (NRH) problem on
a given contour of the complex $\lambda$ plane. The most distinguished examples
of integrable PDEs of this type, like the dispersionless
Kadomtsev-Petviashivili (dKP), the heavenly and the 2 dimensional
dispersionless Toda equations, are real PDEs associated with Hamiltonian vector
fields. The corresponding NRH data satisfy suitable reality and symplectic
constraints. In this paper, generalizing the examples of solvable NRH problems
illustrated in \cite{MS4,MS5,MS6}, we present a general procedure to construct
solvable NRH problems for integrable real PDEs associated with Hamiltonian
vector fields, allowing one to construct implicit solutions of such PDEs
parametrized by an arbitrary number of real functions of a single variable.
Then we illustrate this theory on few distinguished examples for the dKP and
heavenly equations. For the dKP case, we characterize a class of similarity
solutions, a class of solutions constant on their parabolic wave front and
breaking simultaneously on it, and a class of localized solutions breaking in a
point of the $(x,y)$ plane. For the heavenly equation, we characterize two
classes of symmetry reductions.


  The WASP (Wide Angle Search for Planets) project is an exoplanet transit
survey that has been automatically taking wide field images since 2004. Two
instruments, one in La Palma and the other in South Africa, continually monitor
the night sky, building up light curves of millions of unique objects. These
light curves are used to search for the characteristics of exoplanetary
transits. This first public data release (DR1) of the WASP archive makes
available all the light curve data and images from 2004 up to 2008 in both the
Northern and Southern hemispheres. A web interface (www.wasp.le.ac.uk/public/)
to the data allows easy access over the Internet. The data set contains 3 631
972 raw images and 17 970 937 light curves. In total the light curves have 119
930 299 362 data points available between them.


  The basic idea behind Rayleigh's criterion on resolving two incoherent
optical point sources is that the overlap between the spatial modes from
different sources would reduce the estimation precision for the locations of
the sources, dubbed Rayleigh's curse. We generalize the concept of Rayleigh's
curse to the abstract problems of quantum parameter estimation with incoherent
sources. To manifest the effect of Rayleigh's curse on quantum parameter
estimation, we define the curse matrix in terms of quantum Fisher information
and introduce the global and local immunity to the curse accordingly. We
further derive the expression for the curse matrix and give the necessary and
sufficient condition on the immunity to Rayleigh's curse. For estimating the
one-dimensional location parameters with a common initial state, we demonstrate
that the global immunity to the curse on quantum Fisher information is
impossible for more than two sources.


  Understanding which inductive biases could be helpful for the unsupervised
learning of object-centric representations of natural scenes is challenging. In
this paper, we systematically investigate the performance of two models on
datasets where neural style transfer was used to obtain objects with complex
textures while still retaining ground-truth annotations. We find that by using
a single module to reconstruct both the shape and visual appearance of each
object, the model learns more useful representations and achieves better object
separation. In addition, we observe that adjusting the latent space size is
insufficient to improve segmentation performance. Finally, the downstream
usefulness of the representations is significantly more strongly correlated
with segmentation quality than with reconstruction accuracy.


  Estimation of distribution algorithms (EDA) as one of the EAs is a stochastic
optimization problem which establishes a probability model to describe the
distribution of solutions and randomly samples the probability model to create
offspring and optimize model and population. Reference Vector Guided
Evolutionary (RVEA) based on the EDA framework, having a better performance to
solve MaOPs. Besides, using the generative adversarial networks to generate
offspring solutions is also a state-of-art thought in EAs instead of crossover
and mutation. In this paper, we will propose a novel algorithm based on RVEA[1]
framework and using Distributional Adversarial Networks (DAN) [2]to generate
new offspring. DAN uses a new distributional framework for adversarial training
of neural networks and operates on genuine samples rather than a single point
because the framework also leads to more stable training and extraordinarily
better mode coverage compared to single-point-sample methods. Thereby, DAN can
quickly generate offspring with high convergence regarding the same
distribution of data. In addition, we also use Large-Scale Multi-Objective
Optimization Based on A Competitive Swarm Optimizer (LMOCSO)[3] to adopts a new
two-stage strategy to update the position in order to significantly increase
the search efficiency to find optimal solutions in huge decision space. The
propose new algorithm will be tested on 9 benchmark problems in Large scale
multi-objective problems (LSMOP). To measure the performance, we will compare
our proposal algorithm with some state-of-art EAs e.g., RM-MEDA[4], MO-CMA[10]
and NSGA-II.


  We report on the first measurements of the isotopic ratio 14N/15N in N2H+
toward a statistically significant sample of high-mass star forming cores. The
sources belong to the three main evolutionary categories of the high-mass star
formation process: high-mass starless cores, high-mass protostellar objects,
and ultracompact HII regions. Simultaneous measurements of 14N/15N in CN have
been made. The 14N/15N ratios derived from N2H+ show a large spread (from ~180
up to ~1300), while those derived from CN are in between the value measured in
the terrestrial atmosphere (~270) and that of the proto-Solar nebula (~440) for
the large majority of the sources within the errors. However, this different
spread might be due to the fact that the sources detected in the N2H+
isotopologues are more than those detected in the CN ones. The 14N/15N ratio
does not change significantly with the source evolutionary stage, which
indicates that time seems to be irrelevant for the fractionation of nitrogen.
We also find a possible anticorrelation between the 14N/15N (as derived from
N2H+) and the H/D isotopic ratios. This suggests that 15N enrichment could not
be linked to the parameters that cause D enrichment, in agreement with the
prediction by recent chemical models. These models, however, are not able to
reproduce the observed large spread in 14N/15N, pointing out that some
important routes of nitrogen fractionation could be still missing in the
models.


  Considering some modified Newtonian potentials and the Hubble law in writing
the total energy of a test mass located at the edge of a flat
Friedmann-Robertson-Walker universe, we obtain several modified Friedmann
equations. Interestingly enough, our study shows that the employed potentials,
while some of them have some successes in modelling the spiral galaxies
rotation curves, may also address an accelerated universe. This fact indicates
that dark energy and dark matter may have some common origins and aspects.


  Conditional models with one pair of conditional and conditioned factors in
Mukerjee et al. (2017) are extended to two pairs in this paper. The extension
includes the parametrization, effect hierarchy, sufficient conditions for
universal optimality, aberration, complementary set theory and the strategy for
finding minimum aberration designs. A catalog of 16-run minimum aberration
designs under conditional models is provided. For five to twelve factors, all
16-run minimum aberration designs under conditional models are also minimum
aberration under traditional models.


  The aim of this paper is to generalize results of C.-L. Chai about the
monodromy of Hecke invariant subvarieties to Shimura varieties of PEL-type.


  A hole in a graph is an induced subgraph which is a cycle of length at least
four. We prove that for every positive integer k, every triangle-free graph
with sufficiently large chromatic number contains holes of k consecutive
lengths.


  The internal thermal noise in LIGO's test masses is analyzed by a new
technique, a direct application of the Fluctuation-Dissipation Theorem to
LIGO's readout observable, $x(t)=$(longitudinal position of test-mass face,
weighted by laser beam's Gaussian profile). Previous analyses, which relied on
a normal-mode decomposition of the test-mass motion, were valid only if the
dissipation is uniformally distributed over the test-mass interior, and they
converged reliably to a final answer only when the beam size was a
non-negligible fraction of the test-mass cross section. This paper's direct
analysis, by contrast, can handle inhomogeneous dissipation and arbitrary beam
sizes. In the domain of validity of the previous analysis, the two methods give
the same answer for $S_x(f)$, the spectral density of thermal noise, to within
expected accuracy. The new analysis predicts that thermal noise due to
dissipation concentrated in the test mass's front face (e.g. due to mirror
coating) scales as $1/r_0^2$, by contrast with homogeneous dissipation, which
scales as $1/r_0$ ($r_0$ is the beam radius); so surface dissipation could
become significant for small beam sizes.


  The structure and evolution of aggregate grains formed within a plasma
environment are dependent upon the charge acquired by the micron-sized dust
grains during the coagulation process. The manner in which the charge is
arranged on developing irregular structures can affect the fractal dimension of
aggregates formed during collisions, which in turn influences the coagulation
rate and size evolution of the dust within the plasma cloud. This paper
presents preliminary models for the charge and size evolution of fractal
aggregates immersed in a plasma environment calculated using a modification to
the orbital-motion-limited (OML) theory. Primary electron and ion currents
incident on points on the aggregate surface are determined using a
line-of-sight (LOS) approximation: only those electron or ion trajectories
which are not blocked by another grain within the aggregate contribute to the
charging current. Using a self-consistent iterative approach, the equilibrium
charge and dipole moment are calculated for the dust aggregate. The charges are
then used to develop a heuristic charging scheme which can be implemented in
coagulation models. While most coagulation theories assume that it is difficult
for like-charged grains to coagulate, the OML_LOS approximation indicates that
the electric potentials of aggregate structures are often reduced enough to
allow significant coagulation to occur.


  It is typically assumed that radiation pressure driven winds are accelerated
to an asymptotic velocity of V ~ v_esc, where v_esc is the escape velocity from
the central source. We note that this is not the case for dusty shells and
clouds. Instead, if the shell or cloud is initially optically-thick to the UV
emission from the source of luminosity L, then there is a significant boost in
V that reflects the integral of the momentum absorbed as it is accelerated. For
shells reaching a generalized Eddington limit, we show that V ~ (4R_UV L/M_sh
c)^1/2, in both point-mass and isothermal-sphere potentials, where R_UV is the
radius where the shell becomes optically-thin to UV photons, and M_sh is the
mass of the shell. The asymptotic velocity significantly exceeds v_esc for
typical parameters, and can explain the ~1000-2000km/s outflows observed from
rapidly star-forming galaxies and active galactic nuclei if the surrounding
halo has low gas density. Similarly fast outflows from massive stars can be
accelerated on few - 10^3 yr timescales. These results carry over to clouds
that subtend only a small fraction of the solid angle from the source of
radiation and that expand as a consequence of their internal sound speed. We
further consider the dynamics of shells that sweep up a dense circumstellar or
circumgalactic medium. We calculate the "momentum ratio" Mdot v/(L/c) in the
shell limit and show that it can only significantly exceed ~2 if the effective
optical depth of the shell to re-radiated FIR photons is much larger than
unity. We discuss simple prescriptions for the properties of galactic outflows
for use in large-scale cosmological simulations. We also briefly discuss
applications to the dusty ejection episodes of massive stars, the disruption of
giant molecular clouds, and AGN.


  The branching process is the minimal model for propagation dynamics,
avalanches and criticality, broadly used in neuroscience. A simple extension of
it, adding inhibitory nodes, induces a much-richer phenomenology, including, an
intermediate phase, between quiescence and saturation, that exhibits the key
features of "asynchronous states" in cortical networks. Remarkably, in the
inhibition-dominated case, it exhibits an extremely-rich phase diagram, that
captures a wealth of non-trivial features of spontaneous brain activity, such
as collective excitability, hysteresis, tilted avalanche shapes, and partial
synchronization, allowing us to rationalize striking empirical findings within
a common and parsimonious framework.


  We investigate the possible sequels, for the hybrid compact stars consisting
of nucleons, hyperons and three flavour color-flavor-locked quarks phase under
global neutrality and chemical equilibrium conditions. The hadron equations of
state are computed within the framework of energy density functionals based on
the relativistic mean field theory by employing two different model
parameterizations. The quarks matter phase of equation of state is computed by
using Quarks Quasiparticle model derived from a non-relativistic energy
density-functional approach. A plausible set of hybrid equations of state for
superdense hadron-quarks matter is obtained and, which satisfies the
constraints provided by bulk nuclear matter, the observational data of
frequencies and maximum Gravitational mass 2$M_\odot$ with their extracted
radii, Keplerian limits, secular axisymmetric instability and limits of tidal
deformabilities from GW170817 binary neutron stars (BNS) merger. We obtained
structural properties of nonrotating and rotating compact stars, the
evolutionary sequences with constant baryonic mass star spinning down by
electromagnetic and gravitational radiations and, discuss the issues relating
to phase transition from hadrons to quarks matter phase. The internal structure
of rotating star with observed spin down frequencies, exhibiting shrinkage of
soft quarks core of compact stars are discussed for constant baryonic mass. We
present the theoretically computed limits of radii for the spin down
configurations of hybrid stars corresponding to the recently observed
millisecond pulsars. We also present and discuss the calculated results for
tidal deformability, $\Lambda$ and tidal parameters $\Lambda_1$, $\Lambda_2$ of
non spining hybrid star which are consistent with the waveform model analysis
of GW170817 BNS.


  The half filled Landau level is expected to be approximately particle-hole
symmetric, which requires an extension of the Halperin-Lee-Read (HLR) theory of
the compressible state observed at this filling. Recent work indicates that,
when particle-hole symmetry is preserved, the composite Fermions experience a
quantized $\pi$-Berry phase upon winding around the composite Fermi-surface,
analogous to Dirac fermions at the surface of a 3D topological insulator. In
contrast, the effective low energy theory of the composite fermion liquid
originally proposed by HLR lacks particle-hole symmetry and has vanishing Berry
phase. In this paper, we explain how thermoelectric transport measurements can
be used to test the Dirac nature of the composite Fermions by quantitatively
extracting this Berry phase. First we point out that longitudinal thermopower
(Seebeck effect) is non-vanishing due to the unusual nature of particle hole
symmetry in this context and is not sensitive to the Berry phase. In contrast,
we find that off-diagonal thermopower (Nernst effect) is directly related to
the topological structure of the composite Fermi surface, vanishing for zero
Berry phase and taking its maximal value for $\pi$ Berry phase. In contrast, in
purely electrical transport signatures the Berry phase contributions appear as
small corrections to a large background signal, making the Nernst effect a
promising diagnostic of the Dirac nature of composite fermions.


  We present the first survey of electric field data using the ARTEMIS
spacecraft in the solar wind to study inertial range turbulence. It was found
that the average perpendicular spectral index of the electric field depends on
the frame of measurement. In the spacecraft frame it is -5/3, which matches the
magnetic field due to the large solar wind speed in Lorentz transformation. In
the mean solar wind frame, the electric field is primarily due to the
perpendicular velocity fluctuations and has a spectral index slightly shallower
than -3/2, which is close to the scaling of the velocity. These results are an
independent confirmation of the difference in scaling between the velocity and
magnetic field, which is not currently well understood. The spectral index of
the compressive fluctuations was also measured and found to be close to -5/3,
suggesting that they are not only passive to the velocity but may also interact
nonlinearly with the magnetic field.


  In this paper, we discuss adaptive approximations of an elliptic eigenvalue
optimization problem in a phase-field setting by a conforming finite element
method. An adaptive algorithm is proposed and implemented in several two
dimensional numerical examples for illustration of efficiency and accuracy.
Theoretical findings consist in the vanishing limit of a subsequence of
estimators and the convergence of the relevant subsequence of
adaptively-generated solutions to a solution to the continuous optimality
system.


  This paper is devoted to a new family of reverse Hardy-Littlewood-Sobolev
inequalities which involve a power law kernel with positive exponent. We
investigate the range of the admissible parameters and characterize the optimal
functions. A striking open question is the possibility of concentration which
is analyzed and related with nonlinear diffusion equations involving mean field
drifts.


  Large Language Models (LLMs) are powerful tools for natural language
processing, enabling novel applications and user experiences. However, to
achieve optimal performance, LLMs often require adaptation with private data,
which poses privacy and security challenges. Several techniques have been
proposed to adapt LLMs with private data, such as Low-Rank Adaptation (LoRA),
Soft Prompt Tuning (SPT), and In-Context Learning (ICL), but their comparative
privacy and security properties have not been systematically investigated. In
this work, we fill this gap by evaluating the robustness of LoRA, SPT, and ICL
against three types of well-established attacks: membership inference, which
exposes data leakage (privacy); backdoor, which injects malicious behavior
(security); and model stealing, which can violate intellectual property
(privacy and security). Our results show that there is no silver bullet for
privacy and security in LLM adaptation and each technique has different
strengths and weaknesses.


  We study the structural properties like the gravitational mass, radius and
tidal deformability of dark matter (DM) admixed strange quark stars (SQSs). For
the purpose we consider the vector MIT Bag model to describe the strange quark
matter (SQM) and investigate the possible presence of accreted DM in the SQSs
consequently forming DM admixed SQSs. We introduce feeble interaction between
SQM and the accreted fermionic DM via a vector dark boson mediator. Considering
the present literature, in the context of possible presence of DM in SQSs, this
work is the first to consider interaction between DM and SQM in the DM admixed
SQSs. The mass of the DM fermion ($m_{\chi}$) and the vector mediator
($m_{\xi}$) and the coupling ($y_{\xi}$) between them are determined in
accordance with the constraint from Bullet cluster and the present day relic
abundance, respectively. We find that the presence of DM reduces both the mass
and radius of the star compared to the no-DM case. The massive the DM fermion,
the lower the values of maximum mass and radius of the DM admixed SQSs. For the
chosen values of $m_{\chi}$ and corresponding values of $m_{\xi}$ and
$y_{\xi}$, the computed structural properties of the DM admixed SQSs satisfy
all the various present day astrophysical constraints.We obtain massive DM
admixed SQSs configurations consistent with the GW190814 observational data.
Hence the secondary compact object associated with this event may be a DM
admixed SQS.


  We use ~88 arcmin**2 of deep (>~26.5 mag at 5 sigma) NICMOS data over the two
GOODS fields and the HDF South to conduct a search for bright z>~7 galaxy
candidates. This search takes advantage of an efficient preselection over 58
arcmin**2 of NICMOS H-band data where only plausible z>~7 candidates are
followed up with NICMOS J-band observations. ~248 arcmin**2 of deep
ground-based near-infrared data (>~25.5 mag, 5 sigma) is also considered in the
search. In total, we report 15 z-dropout candidates over this area -- 7 of
which are new to these search fields. Two possible z~9 J-dropout candidates are
also found, but seem unlikely to correspond to z~9 galaxies. The present z~9
search is used to set upper limits on the prevalence of such sources. Rigorous
testing is undertaken to establish the level of contamination of our selections
by photometric scatter, low mass stars, supernovae (SNe), and spurious sources.
The estimated contamination rate of our z~7 selection is ~24%. Through careful
simulations, the effective volume available to our z>~7 selections is estimated
and used to establish constraints on the volume density of luminous (L*(z=3),
or -21 mag) galaxies from these searches. We find that the volume density of
luminous star-forming galaxies at z~7 is 13_{-5}^{+8}x lower than at z~4 and
>25x lower (1 sigma) at z~9 than at z~4. This is the most stringent constraint
yet available on the volume density of >~L* galaxies at z~9. The present
wide-area, multi-field search limits cosmic variance to <20%. The evolution we
find at the bright end of the UV LF is similar to that found from recent Subaru
Suprime-Cam, HAWK-I or ERS WFC3/IR searches. The present paper also includes a
complete summary of our final z~7 z-dropout sample (18 candidates) identified
from all NICMOS observations to date (over the two GOODS fields, the HUDF,
galaxy clusters).


  When the logarithmic slope of the galaxy counts is lower than 0.4 (this is
the case in all filters at high magnitude), the magnification bias due to the
lens makes the number density of objects decrease. Consequently, the radial
distribution shows a typical depletion curve. We present simulations of
depletion curves obtained for a variety of different lens models and we show
how the model parameters affect the depletion area.


  Topological insulators are a novel class of quantum materials characterized
by protected gapless surface or edge states but insulating bulk states which is
due to presence of spin-orbit interactions and time-reversal symmetry. Such an
intriguing surface and bulk topology manifests itself in coupling with lattice
dynamics due to electron-phonon scattering. Here we report an in-depth
investigation of a topological nodal line semimetal PbTaSe2 via temperature,
polarization dependent Raman spectroscopy and temperature dependent single
crystal X-ray diffraction (SC-XRD) measurements. Our analysis shows signature
of electron-phonon coupling as reflected in the Fano asymmetry in line shape of
M1-M4 modes and anomalous temperature variation of line-width of P3-P4 modes.
Further polarization dependent phonon symmetry changes at different temperature
(6K and 300K), discontinuities in bulk phonon dynamics for P2-P5 modes and
disappearance of phonon modes i.e., M1-M5, on decreasing temperatures indicates
towards a thermally induced structural phase transition which is also supported
by the SC-XRD results. Hence based on our findings we propose that M1-M4 modes
are surface phonon modes, the material undergoes a thermally induced structural
phase transition from alpha to beta phase at T ~ 150 K or is in close proximity
to the beta phase and another transition below T(CDW+beta) ~ 100K which is
possibly due to the interplay of remanent completely commensurate charge
density wave (CCDW) of 1H-TaSe2 and beta phase.


  We consider a stochastic multi-armed bandit (MAB) problem motivated by
``large'' action spaces, and endowed with a population of arms containing
exactly $K$ arm-types, each characterized by a distinct mean reward. The
decision maker is oblivious to the statistical properties of reward
distributions as well as the population-level distribution of different
arm-types, and is precluded also from observing the type of an arm after play.
We study the classical problem of minimizing the expected cumulative regret
over a horizon of play $n$, and propose algorithms that achieve a rate-optimal
finite-time instance-dependent regret of $\mathcal{O}\left( \log n \right)$. We
also show that the instance-independent (minimax) regret is
$\tilde{\mathcal{O}}\left( \sqrt{n} \right)$ when $K=2$. While the order of
regret and complexity of the problem suggests a great degree of similarity to
the classical MAB problem, properties of the performance bounds and salient
aspects of algorithm design are quite distinct from the latter, as are the key
primitives that determine complexity along with the analysis tools needed to
study them.


  Recently, a novel mixed-synchronization phenomenon is observed in
counter-rotating nonlinear coupled oscillators. In mixed-synchronization state:
some variables are synchronized in-phase, while others are out-of-phase. We
have experimentally verified the occurrence of mixed-synchronization states in
coupled counter-rotating chaotic piecewise Rossler oscillator. Analytical
discussion on approximate stability analysis and numerical confirmation on the
experimentally observed behavior is also given.


  One-dimensional systems---ranging from travelling light to circuit cables and
from DNA to superstrings---are ubiquitous and critically important to the human
knowledge of the universe. However, our engagement with one-dimensional systems
in the research and education of spontaneous phase transitions, the phenomena
wherein materials can change rapidly between different phases (e.g., gas,
liquid, solid, etc.) on their own, has not been largely exercised, since it was
proven that one-dimensional systems do not contain phase transitions in the
textbook Ising model almost 100 years ago [1] and its quantum counterpart, the
Heisenberg model, over 50 years ago [2]. Recently, a spontaneous marginal phase
transition (MPT) was discovered in a one-dimensional Ising model containing
strong geometrical frustration [3]. Here, by exploring the symmetry of the new
mathematical structure underlying the MPT, I report the finding and
classification of an infinite number of MPT cases---with highly tunable
intriguing behaviors like phase reentrance, the dome shape of transition
temperature, pairing, and gauge freedom. These discoveries reveal the
possibility of building the MPT-based one-dimensional Ising Machine that can be
used to simulate the complex phenomena of phase competition in strongly
correlated systems and provide insights with its unambiguous exact solutions.
They also form a rich playground for exploring unconventional phase transitions
in one-dimensional Heisenberg models.


  We implemented various DFT+U schemes, including the ACBN0 self-consistent
density-functional version of the DFT+U method [Phys. Rev. X 5, 011006 (2015)]
within the massively parallel real-space time-dependent density functional
theory (TDDFT) code Octopus. We further extended the method to the case of the
calculation of response functions with real-time TDDFT+U and to the description
of non-collinear spin systems. The implementation is tested by investigating
the ground-state and optical properties of various transition metal oxides,
bulk topological insulators, and molecules. Our results are found to be in good
agreement with previously published results for both the electronic band
structure and structural properties. The self consistent calculated values of U
and J are also in good agreement with the values commonly used in the
literature. We found that the time-dependent extension of the self-consistent
DFT+U method yields improved optical properties when compared to the empirical
TDDFT+U scheme. This work thus opens a different theoretical framework to
address the non equilibrium properties of correlated systems.


  Chimera states are a captivating occurrence in which a system composed of
multiple interconnected elements exhibits a distinctive combination of
synchronized and desynchronized behavior. The emergence of these states can be
attributed to the complex interdependence between quantum entanglement and the
delicate balance of interactions among system constituents. The emergence of
discrete-time crystal (DTC) in typical many-body periodically driven systems
occurs when there is a breaking of time translation symmetry. Coexisting
coupled DTC and a ferromagnetic dynamically many-body localized (DMBL) phase at
distinct regions have been investigated under the controlled spin rotational
error of a disorder-free spin-1/2 chain for different types of spin-spin
interactions. We contribute a novel approach for the emergence of the
DTC-DMBL-chimeralike state, which is robust against external static fields in a
periodically driven quantum many-body system.


  The equilibrium shape of liquid drops on elastic substrates is determined by
minimising elastic and capillary free energies, focusing on thick
incompressible substrates. The problem is governed by three length scales: the
size of the drop $R$, the molecular size $a$, and the ratio of surface tension
to elastic modulus $\gamma/E$. We show that the contact angles undergo two
transitions upon changing the substrates from rigid to soft. The microscopic
wetting angles deviate from Young's law when $\gamma/Ea \gg 1$, while the
apparent macroscopic angle only changes in the very soft limit $\gamma/ER \gg
1$. The elastic deformations are worked out in the simplifying case where the
solid surface energy is assumed constant. The total free energy turns out lower
on softer substrates, consistent with recent experiments.


  Currently, pre-trained models can be considered the default choice for a wide
range of NLP tasks. Despite their SoTA results, there is practical evidence
that these models may require a different number of computing layers for
different input sequences, since evaluating all layers leads to overconfidence
in wrong predictions (namely overthinking). This problem can potentially be
solved by implementing adaptive computation time approaches, which were first
designed to improve inference speed. Recently proposed PonderNet may be a
promising solution for performing an early exit by treating the exit layer's
index as a latent variable. However, the originally proposed exit criterion,
relying on sampling from trained posterior distribution on the probability of
exiting from the $i$-th layer, introduces major variance in exit layer indices,
significantly reducing the resulting model's performance. In this paper, we
propose improving PonderNet with a novel deterministic Q-exit criterion and a
revisited model architecture. We adapted the proposed mechanism to ALBERT and
RoBERTa and compared it with recent methods for performing an early exit. We
observed that the proposed changes can be considered significant improvements
on the original PonderNet architecture and outperform PABEE on a wide range of
GLUE tasks. In addition, we also performed an in-depth ablation study of the
proposed architecture to further understand Lambda layers and their
performance.


  The Markov chain Monte Carlo methods offer practical procedures for detecting
signals characterized by a large number of parameters and under conditions of
low signal-to-noise ratio. We present a Metropolis-Hastings algorithm capable
of inferring the spin and orientation parameters of a neutron star from its
periodic gravitational wave signature seen by laser interferometric detectors


  The charge spin-separation, pseudogap formation and phase diagrams are
studied in two and four site Hubbard clusters using analytical diagonalization
and grand canonical ensemble method in a multidimensional parameter space of
temperature, magnetic field, on-site Coulomb interaction ($U\ge 0$), and
chemical potential. The numerically evaluated, exact expressions for charge and
spin susceptibilities provide clear evidence for the existence of true gaps in
the ground state and pseudogaps in a limited range of temperature.
  In particular, Mott-Hubbard type charge crossover, spin pseudogap and
magnetic correlations with antiferromagnetic (spin) pseudogap structure for two
and four site clusters closely resemble the pseudogap phenomena and the
normal-state phase diagram in high T$_c$ superconductors. ~ ~


  In this technical note, we consider the linear-quadratic time-inconsistent
mean-field type leader-follower Stackelberg differential game with an adapted
open-loop information structure. The objective functionals of the leader and
the follower include conditional expectations of state and control (mean field)
variables, and the cost parameters could be general nonexponential discounting
depending on the initial time. As stated in the existing literature, these two
general settings of the objective functionals induce time inconsistency in the
optimal solutions. Given an arbitrary control of the leader, we first obtain
the follower's (time-consistent) equilibrium control and its state feedback
representation in terms of the nonsymmetric coupled Riccati differential
equations (RDEs) and the backward stochastic differential equation (SDE). This
provides the rational behavior of the follower, characterized by the
forward-backward SDE (FBSDE). We then obtain the leader's explicit
(time-consistent) equilibrium control and its state feedback representation in
terms of the nonsymmetric coupled RDEs under the FBSDE constraint induced by
the follower. With the solvability of the nonsymmetric coupled RDEs, the
equilibrium controls of the leader and the follower constitute the
time-consistent Stackelberg equilibrium. Finally, the numerical examples are
provided to check the solvability of the nonsymmetric coupled RDEs.


  Kernel methods have had great success in Statistics and Machine Learning.
Despite their growing popularity, however, less effort has been drawn towards
developing kernel based classification methods on Riemannian manifolds due to
difficulty in dealing with non-Euclidean geometry. In this paper, motivated by
the extrinsic framework of manifold-valued data analysis, we propose a new
positive definite kernel on planar Kendall shape space $\Sigma_2^k$, called
extrinsic Veronese Whitney Gaussian kernel. We show that our approach can be
extended to develop Gaussian kernels on any embedded manifold. Furthermore,
kernel ridge regression classifier (KRRC) is implemented to address the shape
classification problem on $\Sigma_2^k$, and their promising performances are
illustrated through the real data analysis.


  In this study, we unveil an eccentric superradiance phenomenon in molecular
aggregates coupled to surface plasmon polaritons. Through the quantization of
electromagnetic fields in media, we demonstrate that superradiance can be
significantly enhanced by polaritons and its behavior distinguishably surpasses
the Dick's $N$ scaling law. To understand the mechanism of this anomalous
phenomenon, we derive an analytical expression of the superradiance rate, which
is general for molecular aggregates in arbitrary dispersive and absorbing
media. Furthermore, we show the importance of intermolecular distance for this
extraordinary superradiance.


  A second-order differential identity for the Riemann tensor is obtained, on a
manifold with symmetric connection. Several old and some new differential
identities for the Riemann and Ricci tensors descend from it. Applications to
manifolds with Recurrent or Symmetric structures are discussed. The new
structure of K-recurrency naturally emerges from an invariance property of an
old identity by Lovelock.


  I shortly review the application of a recently introduced constituent
quark-meson model to the determination of some strong coupling constants
governing the decays of charm heavy mesons with one pion in the final state. I
present the model directly through its rules for computing amplitudes. For a
detailed explanation of the model, the reader is referred to the original
papers.


  Motivated by the study of invariant rings of finite groups on the first Weyl
algebras $A_{1}$ (\cite{AHV}) and finding interesting families of new
noetherian rings, a class of algebras similar to $U(sl_{2})$ were introduced
and studied by Smith in \cite{S}. Since the introduction of these algebras,
research efforts have been focused on understanding their weight modules, and
many important results were already obtained in \cite{S} and \cite{Ku}. But it
seems that not much has been done on the part of nonweight modules. In this
note, we generalize Kostant's results in \cite{K} on the Whittaker model for
the universal enveloping algebras $U(\frak g)$ of finite dimensional semisimple
Lie algebras $\frak g$ to Smith's algebras. As a result, a complete
classification of irreducible Whittaker modules (which are definitely infinite
dimensional) for Smith's algebras is obtained, and the submodule structure of
any Whittaker module is also explicitly described.


  Thermo-optic microheater is indispensable in silicon photonic devices for
smart and reconfigurable photonic networks. Much efforts have been made to
improve the metallic microheater performance in the past decades. However,
because of the metallic nature of light absorption, placing the metallic
microheater very close to the waveguide for fast response is impractical and
has not been done experimentally. Here, we experimentally demonstrate a
metallic microheater placed very close to the waveguide based on parity-time
(PT) symmetry breaking. The intrinsic high loss of metallic heater ensures the
system will operate in the PT-symmetry-broken region, which guarantee the low
loss of light in the silicon waveguide. Moreover, heating at a close range
significantly reduces the response time. A fast response time of ~1 us is
achieved without introducing extra loss. The insertion loss is only 0.1 dB for
the long heater. The modulation bandwidth is 280 kHz, which is an order of
magnitude improvement when compared with that of the mainstream thermo-optic
phase shifters. To verify the capability of large-scale integration, a 1*8
phased array for beam steering is also demonstrated experimentally with the
PT-symmetry-broken metallic heaters. Our work provides a novel design concept
for low-loss fast-response optical switches with dissipative materials and
offers a new approach to enhance the performance of thermo-optic phase
shifters.


  The energy splitting $E_{0a}$ in two and four dimensional Ising models is
measured in a cylindrical geometry on finite lattices. By comparing to exact
results in the two dimensional Ising model we demonstrate that $E_{0a}$ can be
extracted very reliably from Monte Carlo calculations in practice. In four
dimensions we compare the measured $E_{0a}$ with two different theoretical
predictions on the finite size behavior of the energy splitting. We find that
our numerical data are in favor of the predictions based on the semiclassical
dilute instanton gas approximation.


  We calculate the effective mass of a single quantized vortex in the BCS
superconductor at finite temperature. Using the effective action for a vortex,
we arrive at the mass formula as the integral of the spectral function
$J(\omega)/\omega^3$ over frequency. The spectral function is given in terms of
the transition elements of the gradient of the Hamiltonian between
Bogoliubov-deGennes eigenstates. We show that core-core, and core-extended
transitions yield the vortex mass, near T=0, of order of electron mass
displaced by the normal core. The extended-extended states contributions are
linearly divergent with the low frequency cutoff $\omega_c$, in accordance with
the Ohmic character of the spectral function at low energies. We argue that the
mass and friction are closely related in this system and arise from the same
mechanism - interaction with the surrounding fermionic degrees of freedom.


  In this article, we will prove that if $G$ is a connected claw-free graph and
either $\sigma_6(G)\geq |G|-5$ or $\sigma_7(G)\geq |G|-2$, here $\sigma_k(G)$
is the minimmum degree sum of $k$ independent vertices in $G$, then $G$ has a
spanning tree with at most two branch vertices.


  We combine simultaneous constraints on stellar evolutionary status from
asteroseismology, and on nitrogen abundances derived from large spectroscopic
surveys, to follow nitrogen surface abundances all along the evolution of a
low-mass star, comparing model expectations with data. After testing and
calibrating the observed yields from the APOGEE survey, we first show that
nitrogen surface abundances follow the expected trend after the first dredge-up
occurred, i.e. that the more massive is the star the more nitrogen is enhanced.
Moreover, the behaviour of nitrogen data along the evolution confirms the
existence of non-canonical extra-mixing on the RGB for all low-mass stars in
the field. But more surprisingly, the data indicate that nitrogen has been
depleted between the RGB tip and the red clump. This may suggest that some
nitrogen has been burnt near or at the He flash episode.


  The rotational-fission of a rubble-pile asteroid can result in an "asteroid
pair", two un-bound asteroids sharing similar orbits. This mechanism might
exposes material that previously had never have been exposed to the weathering
conditions of space. Therefore, the surfaces of asteroid pairs offer the
opportunity to observe non-weathered fresh spectra. We report near-IR
spectroscopic observations of 31 asteroids in pairs. We analyze their spectral
slopes, 1 {\mu}m absorption band, taxonomy, and estimate the time elapsed since
their separation. Analyzing the 19 S-complex objects in our sample, we find two
fresh Q-type asteroids that are the first of their kind to be observed in the
main-belt over the full visible and near-IR range. This solidly demonstrates
that Q-type objects are not limited to the NEA population. The pairs in our
sample present a range of fresh and weathered surfaces with no clear evidence
for a correlation with the ages of the pairs. However, our sample includes old
pairs (1 to 2 My) that present low spectral slopes. This illustrates a
timescale of at least ~2 My before an object develops high spectral slope that
is typical for S-type asteroids.
  We discuss mechanisms that explain the existence of weathered pairs with
young dynamical ages and find that the "secondary fission" model (Jacobson &
Scheeres 2011) is the most robust with our observations since: 1) the secondary
members in our sample present fresh parameters that tend to be fresher than
their weathered primaries; 2) most of the fresh pairs in our sample have low
size ratios between the secondary and the primary; 3) 33% of the primaries in
our sample are fresh, similar to the prediction set by this model; 4) known
satellites orbit two of the pairs in our sample with low size ratio and fresh
surface; 5) there is no correlation between the weathering state and the
primary shape as predicted by other models.


  In this treatise we aim to build a hybrid network automated (self-adaptive)
security threats discovery and prevention system; by using unconventional
techniques and methods, including fuzzy logic and biological inspired
algorithms under the context of soft computing.


  We calculate the explicit expression of the effective potential in a
$\lambda\phi^4$ theory at finite temperature in a static universe for arbitrary
spacetime dimensions (2\leq D < 5). To study the combined effects of the
temperature and scale factor to the spontaneous symmetry breaking we evaluate
the effective potential at finite temperature in $R\otimes S^{D-1}$ and
$R\otimes H^{D-1}$. The phase structure of a $\lambda\phi^4$ theory is found by
observing the minimum of the effective potential with varying temperature and
scale factor. All the ring diagrams are resummed for $D\gtrsim 4$ to improve
the loop expansion at high temperature. For a conformally coupled and a
minimally coupled scalar field it is shown that temperature and positive
curvature suppress the symmetry breaking, while negative curvature enhances it.
The conformally coupled scalar has larger curvature effects than the minimally
coupled one.


  In this paper, we propose a new type of array antenna, termed the Random
Frequency Diverse Array (RFDA), for an uncoupled indication of target direction
and range with low system complexity. In RFDA, each array element has a narrow
bandwidth and a randomly assigned carrier frequency. The beampattern of the
array is shown to be stochastic but thumbtack-like, and its stochastic
characteristics, such as the mean, variance, and asymptotic distribution are
derived analytically. Based on these two features, we propose two kinds of
algorithms for signal processing. One is matched filtering, due to the
beampattern's good characteristics. The other is compressive sensing, because
the new approach can be regarded as a sparse and random sampling of target
information in the spatial-frequency domain. Fundamental limits, such as the
Cram\'er-Rao bound and the observing matrix's mutual coherence, are provided as
performance guarantees of the new array structure. The features and
performances of RFDA are verified with numerical results.


  The Coulomb-nuclear interference is studied as a function of the projectile
ground-state binding energy in the 8Li + 12C and 8Li + 208Pb breakup reactions,
by considering an arbitrary range for the 8Li ground-state binding energies
{\epsilon}b, varying from the experimental one 2.03 MeV down to 0.01 MeV.
Regardless the target mass, we first show that the Coulomb breakup cross
section is stronger dependent on {\epsilon}b than the nuclear breakup cross
section, due to the long-range nature of the Coulomb forces and to the
electromagnetic transition matrix elements. For example, in case of 8Li + 208Pb
reaction at Elab = 60MeV, it is found that |{\sigma}_int|\simeq
4\times{\sigma}_nucl$, while ${\sigma}_Coul\simeq 35\times{\sigma_nucl}$. This
shows clearly that small nuclear contribution in a Coulomb-dominated reaction
does not imply insignificant Coulomb-nuclear interference. Such result can be
mainly attributed to peripheral interference phenomenon, represented by a
function of the binding energy, which determines the peripheral range of
nuclear forces, where Coulomb and nuclear forces strongly interfere
destructively.


  Searches for the exclusive decays of the Higgs boson to an $\omega$ meson and
a photon or a $K^{*}$ meson and a photon can probe flavour-conserving and
flavour-violating Higgs boson couplings to light quarks, respectively. Searches
for these decays, along with the analogous $Z$ boson decay to an $\omega$ meson
and a photon, are performed with a $pp$ collision data sample corresponding to
integrated luminosities of up to 134 fb$^{-1}$ collected at $\sqrt{s}=13$ TeV
with the ATLAS detector at the CERN Large Hadron Collider. The obtained 95%
confidence-level upper limits on the respective branching fractions are ${\cal
B}(H\rightarrow\omega\gamma)< 5.5\times 10^{-4}$, ${\cal B}(H\rightarrow
K^{*}\gamma)< 2.2\times10^{-4}$ and ${\cal B}(Z\rightarrow
\omega\gamma)<3.9\times 10^{-6}$. The limits for $H\rightarrow \omega\gamma$
and $Z\rightarrow \omega\gamma$ are 370 times and 140 times the Standard Model
expected values, respectively. The result for $Z\rightarrow \omega\gamma$
corresponds to a two-orders-of-magnitude improvement over the limit obtained by
the DELPHI experiment at LEP.


  As a complementary study to that performed on the transverse momentum
($p_{\rm T}$) spectra of charged pions, kaons and protons in proton-proton (pp)
collisions at LHC energies 0.9, 2.76 and 7 TeV, we present a scaling behaviour
in the $p_{\rm T}$ spectra of strange particles ($K_{S}^{0}$, $\rm \Lambda$,
$\rm \Xi$ and $\phi$) at these three energies. This scaling behaviour is
exhibited when the spectra are expressed in a suitable scaling variable
$z=p_{\rm T}/K$, where the scaling parameter $K$ is determined by the quality
factor method and increases with the center of mass energy ($\sqrt{s}$). The
rates at which $K$ increases with $\mathrm{ln}\sqrt{s}$ for these strange
particles are found to be identical within errors. In the framework of the
colour string percolation model, we argue that these strange particles are
produced through the decay of clusters that are formed by the colour strings
overlapping. We observe that the strange mesons and baryons are produced from
clusters with different size distributions, while the strange mesons (baryons)
$K_{S}^{0}$ and $\phi$ ($\rm \Lambda$ and $\rm \Xi$) originate from clusters
with the same size distributions. The cluster's size distributions for strange
mesons are more dispersed than those for strange baryons. The scaling behaviour
of the $p_{\rm T}$ spectra for these strange particles can be explained by the
colour string percolation model in a quantitative way.


  Persistent multi-object tracking (MOT) allows autonomous vehicles to navigate
safely in highly dynamic environments. One of the well-known challenges in MOT
is object occlusion when an object becomes unobservant for subsequent frames.
The current MOT methods store objects information, like objects' trajectory, in
internal memory to recover the objects after occlusions. However, they retain
short-term memory to save computational time and avoid slowing down the MOT
method. As a result, they lose track of objects in some occlusion scenarios,
particularly long ones. In this paper, we propose DFR-FastMOT, a light MOT
method that uses data from a camera and LiDAR sensors and relies on an
algebraic formulation for object association and fusion. The formulation boosts
the computational time and permits long-term memory that tackles more occlusion
scenarios. Our method shows outstanding tracking performance over recent
learning and non-learning benchmarks with about 3% and 4% margin in MOTA,
respectively. Also, we conduct extensive experiments that simulate occlusion
phenomena by employing detectors with various distortion levels. The proposed
solution enables superior performance under various distortion levels in
detection over current state-of-art methods. Our framework processes about
7,763 frames in 1.48 seconds, which is seven times faster than recent
benchmarks. The framework will be available at
https://github.com/MohamedNagyMostafa/DFR-FastMOT.


  In this paper, we give novel certificates for triangular equivalence and rank
profiles. These certificates enable to verify the row or column rank profiles
or the whole rank profile matrix faster than recomputing them, with a
negligible overall overhead. We first provide quadratic time and space
non-interactive certificates saving the logarithmic factors of previously known
ones. Then we propose interactive certificates for the same problems whose
Monte Carlo verification complexity requires a small constant number of
matrix-vector multiplications, a linear space, and a linear number of extra
field operations. As an application we also give an interactive protocol,
certifying the determinant of dense matrices, faster than the best previously
known one.


  The combined effect of fluid elasticity and yield-stress on the flow past a
circular cylinder is studied by two-dimensional direct numerical simulation. We
analyze the effects of yield-stress, elasticity, shear-thinning, and
shear-thickening on the wake characteristics using the Saramito constitutive
model. The elastoviscoplastic (EVP) wake flow is studied at a moderate Reynolds
number (Re = 100) where two-dimensional vortex shedding occurs in the Newtonian
case. We find that in the shear-thinning elastoviscoplastic flow, when yield
stress increases, the drag coefficient and root mean square of the lift
coefficient both decrease, while the length of the recirculation bubble
$L_{RB}$ increases. These changes indicate that the wake oscillation amplitude
decreases with an increasing yield stress. For shear-thickening however, the
drag coefficient $C_D$ increases at a large Bingham number, and the wake
becomes chaotic. The comparison of viscoelastic fluid and EVP fluid reveals
that the polymer stresses, tr($\tau^p$), decay considerably less downstream of
the cylinder in the EVP case, indicating that significant stresses persist at
large distances. We observe that shear-thinning competes with elastic and yield
stresses and counteracts their effect, while shear-thickening enhances elastic
and yield stress effects, so that the flow pattern can change from periodic to
a chaotic flow.


  We use a high resolution collisionless simulation of a Virgo--like cluster in
a $\Lambda$CDM cosmology to determine the velocity and clustering properties of
the diffuse stellar component in the intracluster region at the present epoch.
The simulated cluster builds up hierarchically and tidal interactions between
member galaxies and the cluster potential produce a diffuse stellar component
free-flying in the intracluster medium. Here we adopt an empirical scheme to
identify tracers of the stellar component in the simulation and hence study its
properties. We find that at $z=0$ the intracluster stellar light is mostly
unrelaxed in velocity space and clustered in structures whose typical
clustering radii are about 50 kpc at R=400--500 kpc from the cluster center,
and predict the radial velocity distribution expected in spectroscopic
follow-up surveys. Finally, we compare the spatial clustering in the simulation
with the properties of the Virgo intracluster stellar population, as traced by
ongoing intracluster planetary nebulae surveys in Virgo. The preliminary
results indicate a substantial agreement with the observed clustering
properties of the diffuse stellar population in Virgo.


  We present a unified approach to $L^p$-solutions ($p > 1$) of
multidimensional backward stochastic differential equations (BSDEs) driven by
L\'evy processes and more general filtrations. New existence, uniqueness and
comparison results are obtained. The generator functions obey a time-dependent
extended monotonicity (Osgood) condition in the $y$-variable and have general
growth in $y$. Within this setting, the results generalize those of Royer
(2006), Yin and Mao (2008), Yao (2017), Kruse and Popier (2016/2017) and Geiss
and Steinicke (2018).


  Circumbinary planets are generally more likely to transit than equivalent
single-star planets, but practically the geometry and orbital dynamics of
circumbinary planets make the chance of observing a transit inherently
time-dependent. In this follow-up paper to Martin & Triaud (2015), the
time-dependence is probed deeper by analytically calculating when and for how
long the binary and planet orbits overlap, allowing for transits to occur. The
derived equations are applied to the known transiting circumbinary planets
found by Kepler to predict when future transits will occur, and whether they
will be observable by upcoming space telescopes TESS, CHEOPS and PLATO. The
majority of these planets spend less than 50% of their time in a transiting
configuration, some less than 20%. From this it is calculated that the known
Kepler eclipsing binaries likely host an additional ~ 17 - 30 circumbinary
planets that are similar to the ten published discoveries, and they will
ultimately transit some day, potentially during the TESS and PLATO surveys.


  Sparse approximation is the problem to find the sparsest linear combination
for a signal from a redundant dictionary, which is widely applied in signal
processing and compressed sensing. In this project, I manage to implement the
Orthogonal Matching Pursuit (OMP) algorithm and Sparse Representation-based
Classification (SRC) algorithm, then use them to finish the task of masked
image classification with majority voting. Here the experiment was token on the
AR data-set, and the result shows the superiority of OMP algorithm combined
with SRC algorithm over masked face image classification with an accuracy of
98.4%.


  Reliable quasi-static object manuipulation and robotic locomotion require
verification of the stability of equilibria under rigid contacts and friction.
In a recent paper, M. Posa, M. Tobenkin, and R. Tedrake demonstrated that
sums-of-squares (SOS) programming can be used to verify Lyapunov stability via
Lyapunov's direct method. This test was successfully applied to several simple
problems with a single point contact. At the same time it has been found that
this method is too conservative for several multi-contact systems. In this
paper, an extension of Lyapunov's direct method is proposed, which makes use of
several Lyapunov functions, and which allows \emph{temporary} increase of those
Lyapunov function along a motion trajectory. The proposed method remains
compatible with SOS programming techniques. The improved stability test is
successfully applied to a rigid body with 2 point contacts, for which the exact
conditions of Lyapunov stability are unknown.


  Bismuth vanadate (BiVO4) has emerged as a highly prospective material for
photoanodes in photoelectrochemical (PEC) water oxidation. However, current
limitations with this material lie in the difficulties in producing stable and
continuous BiVO4 layers with efficient carrier transfer kinetics, thereby
impeding its widespread application in water splitting processes. This study
introduces a new fabrication approach that yields continuous, monoclinic
nanostructured BiVO4 films, paving the way for their use as photoanodes in
efficient PEC water oxidation for hydrogen production under solar light
conditions. The fabrication involves the intercalation of vanadium (V) ions
into Bi2O3 films at 450oC. Upon interaction with V ions, the film undergoes a
transformation from tetragonal Bi2O3 to monoclinic scheelite BiVO4. This
synthesis method enables the fabrication of single monoclinic phase BiVO4 films
with thicknesses up to 270 nm. The engineered monoclinic BiVO4 film, devoid of
any pinholes that could cause carrier loss, exhibits a robust photocurrent of
1.0 mA/cm2 at 1.23 VRHE in a neutral electrolyte, without requiring additional
modifications or doping. Moreover, we demonstrate that the incorporation of a
cobalt phosphate (Co-Pi) co-catalyst into the BiVO4 photoanode significantly
enhances the lifetime of photogenerated holes by a factor of nine, resulting in
a further elevation of the photocurrent to 2.9 mA/cm2. This remarkable PEC
enhancement can be attributed to the surface state passivation by the Co-Pi
co-catalyst. Our fabrication approach opens up a new facile route for producing
large-scale, highly efficient BiVO4 photoanodes for PEC water splitting
technology.


  The finite amplitude method (FAM), which we have recently proposed (T.
Nakatsukasa, T. Inakura, and K. Yabana, Phys. Rev. C 76, 024318 (2007)),
simplifies significantly the fully self-consistent RPA calculation. Employing
the FAM, we are conducting systematic, fully self-consistent response
calculations for a wide mass region. This paper is intended to present a
computational scheme to be used in the systematic investigation and to show the
performance of the FAM for a realistic Skyrme energy functional. We implemented
the method in the mixed representation in which the forward and backward RPA
amplitudes are represented by indices of single-particle orbitals for occupied
states and the spatial grid points for unoccupied states. We solve the linear
response equation for a given frequency. The equation is a linear algebraic
problem with a sparse non-hermitian matrix, which is solved with an iterative
method. We show results of the dipole response for selected spherical and
deformed nuclei. The peak energies of the giant dipole resonance agree well
with measurements for heavy nuclei, while they are systematically
underestimated for light nuclei. We also discuss the width of the giant dipole
resonance in the fully self-consistent RPA calculation.


  We have identified galaxies near two quasars which are at the redshift of
damped Lyman-alpha (DLA) systems in the UV spectra of the quasars. Both
galaxies are actively forming stars. One galaxy has a luminosity close to the
break in the local galaxy luminosity function, L*, the other is significantly
fainter than L* and appears to be interacting with a nearby companion. Despite
the strong selection effects favoring spectroscopic identification of the most
luminous DLA galaxies, many of the spectroscopically-identified DLA galaxies in
the literature are sub-L*, suggesting that the majority of the DLA population
is probably sub-L*, in contrast to MgII absorbers at similar redshifts whose
mean luminosity is close to L*.


  We present CRUXEval (Code Reasoning, Understanding, and eXecution
Evaluation), a benchmark consisting of 800 Python functions (3-13 lines). Each
function comes with an input-output pair, leading to two natural tasks: input
prediction and output prediction. First, we propose a generic recipe for
generating our execution benchmark which can be used to create future variation
of the benchmark. Second, we evaluate twenty code models on our benchmark and
discover that many recent high-scoring models on HumanEval do not show the same
improvements on our benchmark. Third, we show that simple CoT and fine-tuning
schemes can improve performance on our benchmark but remain far from solving
it. The best setup, GPT-4 with chain of thought (CoT), achieves a pass@1 of 75%
and 81% on input and output prediction, respectively. In contrast, Code Llama
34B achieves a pass@1 of 50% and 46% on input and output prediction,
highlighting the gap between open and closed source models. As no model is
close to acing CRUXEval, we provide examples of consistent GPT-4 failures on
simple programs as a lens into its code reasoning capabilities and areas for
improvement.


  We construct a manifestly diffeomorphism invariant Wilsonian (Exact)
Renormalization Group for classical gravity, and begin the construction for
quantum gravity. We demonstrate that the effective action can be computed
without gauge fixing the diffeomorphism invariance, and also without
introducing a background space-time. We compute classical contributions both
within a background-independent framework and by perturbing around a fixed
background, and verify that the results are equivalent. We derive the exact
Ward identities for actions and kernels and verify consistency. We formulate
two forms of the flow equation corresponding to the two choices of classical
fixed-point: the Gaussian fixed point, and the scale invariant interacting
fixed point using curvature-squared terms. We suggest how this programme may
completed to a fully quantum construction.


  We study the exploration-exploitation dilemma in the linear quadratic
regulator (LQR) setting. Inspired by the extended value iteration algorithm
used in optimistic algorithms for finite MDPs, we propose to relax the
optimistic optimization of \ofulq and cast it into a constrained
\textit{extended} LQR problem, where an additional control variable implicitly
selects the system dynamics within a confidence interval. We then move to the
corresponding Lagrangian formulation for which we prove strong duality. As a
result, we show that an $\epsilon$-optimistic controller can be computed
efficiently by solving at most $O\big(\log(1/\epsilon)\big)$ Riccati equations.
Finally, we prove that relaxing the original \ofu problem does not impact the
learning performance, thus recovering the $\tilde{O}(\sqrt{T})$ regret of
\ofulq. To the best of our knowledge, this is the first computationally
efficient confidence-based algorithm for LQR with worst-case optimal regret
guarantees.


  We consider the graphs whose edges are marked by the integers (weights) from
$0$ to $q-1$ (zero corresponds to no-edge). Such graph is called additive if
its vertices can be marked in such a way that the weight of every edge is equal
to the modulo-$q$ sum of weights of the two incident vertices. By a switching
of a graph we mean the modulo-$q$ sum of the graph with some additive graph on
the same vertex set. A graph with $n$ vertices is called switching separable if
some of its switchings does not have a connected component of order $n$ or
$n-1$. We consider the following test for the switching separability: if
removing any vertex of a graph $G$ results in a switching separable graph, then
$G$ is switching separable itself. We prove this test for odd $q$ and
characterize the exceptions when $q$ is even. We establish a connection between
the switching separability of a graph and the reducibility of $(n-1)$-ary
quasigroups constructed from this graph.


  Semiconductor design companies are integrating proprietary intellectual
property (IP) blocks to build custom integrated circuits (IC) and fabricate
them in a third-party foundry. Unauthorized IC copies cost these companies
billions of dollars annually. While several methods have been proposed for
hardware IP obfuscation, they operate on the gate-level netlist, i.e., after
the synthesis tools embed the semantic information into the netlist. We propose
ASSURE to protect hardware IP modules operating on the register-transfer level
(RTL) description. The RTL approach has three advantages: (i) it allows
designers to obfuscate IP cores generated with many different methods (e.g.,
hardware generators, high-level synthesis tools, and pre-existing IPs). (ii) it
obfuscates the semantics of an IC before logic synthesis; (iii) it does not
require modifications to EDA flows. We perform a cost and security assessment
of ASSURE.


  Multilayer MoS2 possesses highly anisotropic thermal conductivities along
in-plane and cross-plane directions that could hamper heat dissipation in
electronics. With about 9% cross-plane compressive strain created by
hydrostatic pressure in a diamond anvil cell, we observed about 12 times
increase in the cross-plane thermal conductivity of multilayer MoS2. Our
experimental and theoretical studies reveal that this drastic change arises
from the greatly strengthened interlayer interaction and heavily modified
phonon dispersions along cross-plane direction, with negligible contribution
from electronic thermal conductivity, despite its enhancement of 4 orders of
magnitude. The anisotropic thermal conductivity in the multilayer MoS2 at
ambient environment becomes almost isotropic under highly compressive strain,
effectively transitioning from 2D to 3D heat dissipation. This strain tuning
approach also makes possible parallel tuning of structural, thermal and
electrical properties, and can be extended to the whole family of 2D Van der
Waals solids, down to two layer systems.


  This paper investigates bicovariant differential calculus on noncommutative
spaces of the Lie algebra type. For a given Lie algebra $g_0$ we construct a
Lie superalgebra $g=g_0\oplus g_1$ containing noncommutative coordinates and
one--forms. We show that $g$ can be extended by a set of generators $T_{AB}$
whose action on the enveloping algebra $U(g)$ gives the commutation relations
between monomials in $U(g_0)$ and one--forms. Realizations of noncommutative
coordinates, one--forms and the generators $T_{AB}$ as formal power series in a
semicompleted Weyl superalgebra are found. In the special case $dim(g_0)=
dim(g_1)$ we also find a realization of the exterior derivative on $U(g_0)$.
The realizations of these geometric objects yield a bicovariant differential
calculus on $U(g_0)$ as a deformation of the standard calculus on the Euclidean
space.


  I introduce an algorithm to detect one-way quantum information between two
interacting quantum systems, i.e. the direction and orientation of the
information transfer in arbitrary quantum dynamics. I then build an
information-theoretic quantifier of one-way information which satisfies a set
of desirable axioms. In particular, it correctly evaluates whether correlation
implies one-way quantum information, and when the latter is transferred between
uncorrelated systems. In the classical scenario, the quantity measures
information transfer between random variables. I also generalize the method to
identify and rank concurrent sources of quantum information flow in many-body
dynamics, enabling to reconstruct causal patterns in complex networks.


  We propose how to realize nonreciprocity for a weak input optical field via
nonlinearity and synthetic magnetism. We show that the photons transmitting
from a linear cavity to a nonlinear cavity (i.e., an asymmetric nonlinear
optical molecule) exhibit nonreciprocal photon blockade but no clear
nonreciprocal transmission. Both nonreciprocal transmission and nonreciprocal
photon blockade can be observed, when one or two auxiliary modes are coupled to
the asymmetric nonlinear optical molecule to generate an artificial magnetic
field. Similar method can be used to create and manipulate nonreciprocal
transmission and nonreciprocal photon blockade for photons bi-directionally
transport in a symmetric nonlinear optical molecule. Additionally, a photon
circulator with nonreciprocal photon blockade is designed based on nonlinearity
and synthetic magnetism. The combination of nonlinearity and synthetic
magnetism provides us an effective way towards the realization of quantum
nonreciprocal devices, e.g., nonreciprocal single-photon sources and
single-photon diodes.


  Rayleigh-Levy flights have played a significant role in cosmology as
simplified models for understanding how matter distributes itself under
gravitational influence. These models also exhibit numerous remarkable
properties that enable the prediction of a wide range of characteristics. Here,
we derive the one and two point statistics of extreme points within
Rayleigh-Levy flights spanning one to three dimensions, stemming directly from
fundamental principles. In the context of the mean field limit, we provide
straightforward closed-form expressions for Euler counts and their
correlations, particularly in relation to their clustering behaviour over long
distances. Additionally, quadratures allow for the computation of extreme value
number densities. A comparison between theoretical predictions in 1D and Monte
Carlo measurements shows remarkable agreement. Given the widespread use of
Rayleigh-Levy processes, these comprehensive findings offer significant promise
not only in astrophysics but also in broader applications beyond the field.


  In this brief note insightful remarks are made on the controversy on the
decomposition of the proton spin into the spin and orbital angular momenta of
quarks and gluons. It is argued that the difference in the perception on the
nature of the problem is the main reason for the persistent disputes. There is
no decomposition that simultaneously satisfies the twin principles of manifest
Lorentz covariance and gauge invariance, and partial considerations hide likely
inconsistencies. It is suggested that field equations and matter (i. e.
electron in QED and quarks in QCD) equations must be analyzed afresh rather
than beginning with the expressions of total angular momentum; canonical or
otherwise.


  A review study of NIST Statistical Test Suite is undertaken with a motivation
to understand all its test algorithms and to write their C codes independently
without looking at various sites mentioned in the NIST document. All the codes
are tested with the test data given in the NIST document and excellent
agreements have been found. The codes have been put together in a package
executable in MS Windows platform. Based on the package, exhaustive test runs
are executed on three PRNGs, e.g. LCG by Park & Miller, LCG by Knuth and BBSG.
Our findings support the present belief that BBSG is a better PRNG than the
other two.


  We present our results of deep 21 cm line (HI) observations of five early and
mixed-type dwarf galaxies in the nearby Sculptor group using the ATNF 64m
Parkes Radio Telescope. Four of these objects, ESO294-G010, ESO410-G005,
ESO540-G030, and ESO540-G032, were detected in HI with neutral hydrogen masses
in the range of 2-9x10^5 M_{\odot} ($M_{HI}/L_{B}$ = 0.08, 0.13, 0.16, and
0.18, respectively). These HI masses are consistent with the gas mass expected
from stellar outflows over a large period of time. Higher resolution radio data
from the Australia Telescope Compact Array were further analysed to measure
more accurate positions and the distribution of the HI gas. In the cases of
dwarfs ESO294-G010 and ESO540-G030, we find significant offsets of 290 pc and
460 pc, respectively, between the position of the HI peak flux and the center
of the stellar component. These offsets are likely to have internal cause such
as the winds from star-forming regions. The fifth object, the spatially
isolated dwarf elliptical Scl-dE1, remains undetected at our 3\sigma limit of
22.5 mJy km/s and thus must contain less than 10^5 M_{\odot} of neutral
hydrogen. This leaves Scl-dE1 as the only Sculptor group galaxy known where no
interstellar medium has been found to date. The object joins a list of similar
systems including the Local Group dwarfs Tucana and Cetus that do not fit into
the global picture of the morphology-density relation where gas-rich dwarf
irregulars are in relative isolation and gas-deficient dwarf ellipticals are
satellites of more luminous galaxies.


  This paper investigates an efficient exponential integrator generalized
multiscale finite element method for solving a class of time-evolving partial
differential equations in bounded domains. The proposed method first performs
the spatial discretization of the model problem using constraint energy
minimizing generalized multiscale finite element method (CEM-GMsFEM). This
approach consists of two stages. First, the auxiliary space is constructed by
solving local spectral problems, where the basis functions corresponding to
small eigenvalues are captured. The multiscale basis functions are obtained in
the second stage using the auxiliary space by solving local energy minimization
problems over the oversampling domains. The basis functions have exponential
decay outside the corresponding local oversampling regions. We shall consider
the first and second-order explicit exponential Runge-Kutta approach for
temporal discretization and to build a fully discrete numerical solution. The
exponential integration strategy for the time variable allows us to take full
advantage of the CEM-GMsFEM as it enables larger time steps due to its
stability properties. We derive the error estimates in the energy norm under
the regularity assumption. Finally, we will provide some numerical experiments
to sustain the efficiency of the proposed method.


  This paper studies a version of counting problem in dynamical system that is
of interest specially in conformal dynamical systems where functions of the
systems are angle preserving. Recently M. Pollicott and M. Urba\'{n}ski
published a result in this context for D-generic systems where the complex
transfer operator behaves nice on the critical line of the Poincare series.
Their result contains an asymptotic formula for the planer Apollonian circle
packing. We lift the D-generic condition in the paper to see how their
asymptotic formula changes. Further we observed an asymptotic of length closely
related to this counting problem.


  We introduce a very simple model of a dark halo. It is a close relative of
Hernquist's model, being generated by the same transformation but this time
applied to the logarithmic potential rather than the point mass. The density is
proportional to (distance)$^{-1}$ at small radii, whilst the rotation curve is
flat at large radii. Isotropic and radially anisotropic distributions functions
are readily found, and the intrinsic and line of sight kinematical quantities
are available as simple formulae. We also provide an analytical approximation
to the Hamiltonian as a function of the actions. As an application, we study
the kinematic properties of stellar haloes and tracers in elliptical galaxies.
We show that the radial velocity dispersion of a power-law population in a
galaxy with a flat rotation curve always tends to the constant value. This
holds true irrespective of the anisotropy or the lengthscales of the dark or
luminous matter. An analogous result holds for the line of sight or projected
velocity dispersion of a power-law surface brightness profile. The radial
velocity dispersion of Population II stars in the Milky Way is a strongly
declining function of Galactocentric radius. So, if the rotation curve is flat,
we conclude that the stellar halo density cannot follow a power-law at large
radii, but must decrease more sharply (like an Einasto profile) or be abruptly
truncated at large radii. Both the starcount and kinematic data of the Milky
Way stellar halo are well-represented by an Einasto profile with index
$m\approx 2$ and effective radius $\approx 20$ kpc.


  We present in this contribution the basic formul\ae\ for the analysis of
low--momentum charged-- and neutral--kaon interactions in hydrogen, including
as well a (brief) description of the problems left open by past experiments,
and of the improvements DA$\Phi$NE can be expected to offer over them.
Interactions in deuterium and other light nuclei will be only briefly
mentioned, and only in those respects touching directly upon the more
``elementary'' aspects of kaon--nucleon interactions.


  We discover an instability mechanism in suspensions of self-propelled
particles that does not involve active stress. Instead, it is driven by a
subtle interplay of inertia, swimmer motility, and concentration fluctuations,
through a crucial time lag between the velocity and the concentration field.
The resulting time-persistent state seen in our high-resolution numerical
simulations consists of self-sustained waves of concentration and orientation,
transiting from regular oscillations to wave turbulence. We analyze the
statistical features of this active turbulence, including an intriguing
connection to the Batchelor spectrum of passive scalars.


  We report the results from a 17O Nuclear Magnetic Resonance (NMR) study of
the high temperature superconducting cuprate (HTSC), RuSr2EuCu2O8. This
compound has recently been found to exhibit the coexistence of magnetic order
and superconductivity. At 9 T, the magnetic order in the RuO2 layers is
predominately ferromagnetic. We measured the 17O NMR spectra from 10 K to 330 K
and find the occurrence of an increasing 17O NMR shift with increasing
temperature for temperatures above ~200 K, providing direct evidence that
RuSr2RCu2O8 is similar to a very underdoped HTSC. The analysis of the NMR shift
and spectral width of the 17O NMR line gives a small but measurable hyperfine
field of ~9 mT from the Ru moment at the oxygen site in the copper oxygen
planes. We show that the 17O NMR linewidth is governed by dipolar contributions
from the Ru moment.


  Using a near-IR stellar library of 706 stars with a wide coverage of
atmospheric parameters, we study the behaviour of the Ca II triplet strength in
terms of effective temperature, surface gravity and metallicity. Empirical
fitting functions for recently defined line-strength indices, namely CaT*, CaT
and PaT, are provided. These functions can be easily implemented into stellar
populations models to provide accurate predictions for integrated Ca II
strengths. We also present a thorough study of the various error sources and
their relation to the residuals of the derived fitting functions. Finally, the
derived functional forms and the behaviour of the predicted Ca II are compared
with those of previous works in the field.


  We investigate the transport of intensity equation (TIE) and the transport of
phase equation (TPE) for solving the phase retrieval problem. Both the TIE and
the TPE are derived from the paraxial Helmholtz equation and relate phase
information to the intensity. The TIE is usually favored since the TPE is
nonlinear. The main contribution of this paper is a discussion of preferential
use of either one of the two equations or potential benefits of a hybrid use.
Moreover, we discuss the solution of the TPE with the method of characteristics
and with viscosity methods. Both the TIE and the viscosity method are
numerically implemented with finite element methods.


  A varactor-based tunable bandstop filter has been proposed in this article.
The proposed filter is based on a dualmode circuit developed by introducing
inductive and capacitive couplings into a notch filter. The frequency
tunability is achieved by using varactor diodes instead of the lumped
capacitors in the circuit. Next, the equivalent circuit model has been
implemented in planar microstrip technology using thin inductive traces and
varactor diodes. The fabricated filter prototype shows a continuous center
frequency tuning range of 0.66 - 0.99 GHz with a compact size of 0.12lg*0:16lg,
where lg is the guided wavelength at the middle frequency of the tuning range.


  We propose new dipole and quadrupole indices for interacting insulators with
point group symmetries. The proposed indices are defined in terms of many-body
quantum multipole operators combined with the generator of the point group
symmetry. Unlike the original multipole operators, these combined operators
commute with Hamiltonian under the symmetry and therefore their eigenvalues are
quantized. This enables a clear identification of nontrivial multipolar states.
We calculate the multipole indices in representative models and show their
effectiveness as order parameters. Furthermore, we demonstrate a bulk-boundary
correspondence: a non-zero index implies the existence of edge/corner states
under the the point group symmetry.


  We establish bounds on the density of states measure for Schr\"odinger
operators. These are deterministic results that do not require the existence of
the density of states measure, or, equivalently, of the integrated density of
states. The results are stated in terms of a "density of states outer-measure"
that always exists, and provides an upper bound for the density of states
measure when it exists. We prove log-H\"older continuity for this density of
states outer-measure in one, two, and three dimensions for Schr\"odinger
operators, and in any dimension for discrete Schr\"odinger operators.


  Table 1 in our paper, ApJ 648, 774 (2006) entitled "Intergalactic Photon
Spectra from the Far IR to the UV Lyman Limit for 0 < z < 6 and the Optical
Depth of the Universe to High Energy Gamma-Rays" had erroneous numbers for the
coefficients fitting the parametric form for the optical depth of the universe
to gamma-rays. The correct values for these parameters as described in the
original text are given here in a corrected table for various redshifts for the
baseline model (upper row) and fast evolution (lower row) for each individual
redshift. The parametric approximation is good for optical depths between 0.01
and 100 and for gamma-ray energies up to ~2 TeV for all redshifts but also for
energies up to ~10 TeV for redshifts less than 1.


  In 1985, van den Dries showed that the theory of the reals with a predicate
for the integer powers of two admits quantifier elimination in an expanded
language, and is hence decidable. He gave a model-theoretic argument, which
provides no apparent bounds on the complexity of a decision procedure. We
provide a syntactic argument that yields a procedure that is primitive
recursive, although not elementary. In particular, we show that it is possible
to eliminate a single block of existential quantifiers in time $2^0_{O(n)}$,
where $n$ is the length of the input formula and $2_k^x$ denotes $k$-fold
iterated exponentiation.


  This paper presents an investigation of the age-dependent size effect and
fracture characteristics of an ultra high performance concrete (UHPC). The
study is based on a unique set of experimental data connecting aging tests for
two curing protocols of one size and scaled size effect tests of one age. Both
aging and size effect studies are performed on notched three point bending
tests. Experimental data is augmented by state of the art simulations employing
a recently developed discrete element based early-age computational framework.
The framework is constructed by coupling a hygro-thermo-chemical (HTC) model
and the Lattice Discrete Particle Model (LDPM) through a set of aging
functions. The HTC component allows taking into account variable curing
conditions and predicts the maturity of concrete. The mechanical component,
LDPM, simulates the failure behavior of concrete at the length scale of major
heterogeneities. After careful calibration and validation the mesoscale
HTC-LDPM model is uniquely posed to perform predictive simulations. The
ultimate flexural strengths from experiments and simulations are analyzed by
the cohesive size effect curve (CSEC) method, and the classical size effect law
(SEL). The fracture energies obtained by LDPM, CSEC, SEL, and cohesive crack
analyses are compared and an aging formulation for fracture properties is
proposed. Based on experiments, simulations, and size effect analyses, the
age-dependence of size effect and the robustness of analytical size effect
methods are evaluated.


  This paper proposes a diffusive wetting model for the weakly-compressible
smoothed particle hydrodynamics (WCSPH) method to simulate individual water
entry/exit as well as the complete process from water entry to exit. The model
is composed of a physically consistent diffusive wetting equation to describe
the wetting evolution at the fluid-solid interface, a wetting-coupled
identification approach to determine the type of fluid particles by taking into
account the wetting degree of the contacted solid, and a numerical
regularization on the fluid particles at fully wetted fluid-solid interface.
The accuracy, efficiency, and versatility of the present model are validated
through qualitative and quantitative comparisons with experiments, including
the 3-D water entry of a sphere, the 2-D water entry/exit of a cylinder, and
the complete process from water entry to exit of a 2-D cylinder.


  Recently there has been a surge of interest in operations research (OR) and
the machine learning (ML) community in combining prediction algorithms and
optimization techniques to solve decision-making problems in the face of
uncertainty. This gave rise to the field of contextual optimization, under
which data-driven procedures are developed to prescribe actions to the
decision-maker that make the best use of the most recently updated information.
A large variety of models and methods have been presented in both OR and ML
literature under a variety of names, including data-driven optimization,
prescriptive optimization, predictive stochastic programming, policy
optimization, (smart) predict/estimate-then-optimize, decision-focused
learning, (task-based) end-to-end learning/forecasting/optimization, etc.
Focusing on single and two-stage stochastic programming problems, this review
article identifies three main frameworks for learning policies from data and
discusses their strengths and limitations. We present the existing models and
methods under a uniform notation and terminology and classify them according to
the three main frameworks identified. Our objective with this survey is to both
strengthen the general understanding of this active field of research and
stimulate further theoretical and algorithmic advancements in integrating ML
and stochastic programming.


  We study the level sets of prevalent H\"older functions. For a prevalent
$\alpha$-H\"older function on the unit interval, we show that the upper
Minkowski dimension of every level set is bounded from above by $1-\alpha$ and
Lebesgue positively many level sets have Hausdorff dimension equal to
$1-\alpha$.


  High resolution angle-resolved photoemission measurements have been carried
out on (La_1.4-xNd_0.6Sr_x)CuO_4, a model system with static stripes, and
(La_1.85Sr_0.15)CuO_4, a high temperature superconductor (T_c=40K) with dynamic
stripes. In addition to the straight segments near (pi, 0) and (0, pi)
antinodal regions, we have identified the existence of nodal spectral weight
and its associated Fermi surface in the electronic structure of both systems.
The ARPES spectra in the nodal region show well-defined Fermi cut-off,
indicating a metallic character of this charge-ordered state. This observation
of nodal spectral weight, together with the straight segments near antinodal
regions, reveals dual nature of the electronic structure of the stripes due to
the competition of order and disorder.