  Large Language Models (LLMs) are revolutionizing various domains, yet
verifying their answers remains a significant challenge, especially for
intricate open-ended tasks such as consolidation, summarization, and extraction
of knowledge. In this work, we propose CheckEmbed: an accurate, scalable, and
simple LLM verification approach. CheckEmbed is driven by a straightforward yet
powerful idea: in order to compare LLM solutions to one another or to the
ground-truth, compare their corresponding answer-level embeddings obtained with
a model such as GPT Text Embedding Large. This reduces a complex textual answer
to a single embedding, facilitating straightforward, fast, and meaningful
verification. We develop a comprehensive verification pipeline implementing the
CheckEmbed methodology. The CheckEmbed pipeline also comes with metrics for
assessing the truthfulness of the LLM answers, such as embedding heatmaps and
their summaries. We show how to use these metrics for deploying practical
engines that decide whether an LLM answer is satisfactory or not. We apply the
pipeline to real-world document analysis tasks, including term extraction and
document summarization, showcasing significant improvements in accuracy,
cost-effectiveness, and runtime performance compared to existing token-,
sentence-, and fact-level schemes such as BERTScore or SelfCheckGPT.


  We study the problem of coupling a stochastic block model with a planted
bisection to a uniform random graph having the same average degree. Focusing on
the regime where the average degree is a constant relative to the number of
vertices $n$, we show that the distance to which the models can be coupled
undergoes a phase transition from $O(\sqrt{n})$ to $\Omega(n)$ as the planted
bisection in the block model varies. This settles half of a conjecture of
Bollob\'{a}s and Riordan and has some implications for sparse graph limit
theory. In particular, for certain ranges of parameters, a block model and the
corresponding uniform model produce samples which must converge to the same
limit point. This implies that any notion of convergence for sequences of
graphs with $\Theta(n)$ edges which allows for samples from a limit object to
converge back to the limit itself must identify these models.


  As the demand of real time computing increases day by day, there is a major
paradigm shift in processing platform of real time system from single core to
multi-core platform which provides advantages like higher throughput, linear
power consumption, efficient utilization of processor cores and high
performance per unit cost over the many single core processors unit. Currently
available most popular real time schedulers for multi-core domain are
partitioned and global scheduling and these schedulers not suitable to
efficiently use this multi-core platform efficiently. Although,
semi-partitioned algorithms increases utilization bound by using spare
capacities left by partitioning via global scheduling, it has a inherent
disadvantage of off-line task splitting. Although, semi-partitioned algorithms
increases utilization bound by using spare capacities left by partitioning via
global scheduling, it has a inherent disadvantage of off-line task splitting.
To overcome these problems of multi-core real time scheduling algorithm new
dynamic cluster based multi-core real time scheduling algorithm proposed which
is hybrid scheduling approach. This paper discuss different multi-core
scheduling techniques and comparative analysis of these techniques with the
proposed dynamic cluster based real time multi-core scheduling


  In this work, we have studied the observational constraints on the Cardassian
Model for the dark energy. We have compared the model with existing Supernova
data. The dependence of the location of the Cosmic Microwave Background
Radiation (CMBR) peaks on the parameters of the model have also been studied.
We find, in particular, that observational data arising from Archeops for the
location of the first peak, BOOMERANG for the location of the third peak,
together with the Supernova data, constrain significantly the parameter space.


  We give a simple direct proof of uniqueness of tangent cones for singular
projectively Hermitian Yang-Mills connections on reflexive sheaves at isolated
singularities modelled on $\mu$-polystable holomorphic bundles over
$\mathbf{P}^{n-1}$.


  In this paper we review the hypercircle method of Prager and Synge. This
theory inspired several studies and induced an active research in the area of a
posteriori error analysis. In particular, we review the Braess--Sch\"oberl
error estimator in the context of the Poisson problem. We discuss adaptive
finite element schemes based on two variants of the estimator and we prove the
convergence and optimality of the resulting algorithms.


  We present a 45 ks Chandra observation of the quasar ULAS J1342+0928 at
z=7.54. We detect 14.0^{+4.8}_{-3.7} counts from the quasar in the
observed-frame energy range 0.5-7.0 keV (6-sigma detection), representing the
most distant non-transient astronomical source identified in X-rays to date.
The present data are sufficient only to infer rough constraints on the spectral
parameters. We find an X-ray hardness ratio of HR = -0.51^{+0.26}_{-0.28}
between the 0.5-2.0 keV and 2.0-7.0 keV ranges and derive a power-law photon
index of Gamma = 1.95^{+0.55}_{-0.53}. Assuming a typical value for
high-redshift quasars of Gamma = 1.9, ULAS J1342+0928 has a 2-10 keV rest-frame
X-ray luminosity of L_{2-10} = 11.6^{+4.3}_{-3.5} x 10^{44} erg/s. Its
X-ray-to-optical power-law slope is alpha_{OX}=-1.67^{+0.16}_{-0.10},
consistent with the general trend indicating that the X-ray emission in the
most bolometrically powerful quasars is weaker relative to their optical
emission.


  Recently, the stochastic Polyak step size (SPS) has emerged as a competitive
adaptive step size scheme for stochastic gradient descent. Here we develop
ProxSPS, a proximal variant of SPS that can handle regularization terms.
Developing a proximal variant of SPS is particularly important, since SPS
requires a lower bound of the objective function to work well. When the
objective function is the sum of a loss and a regularizer, available estimates
of a lower bound of the sum can be loose. In contrast, ProxSPS only requires a
lower bound for the loss which is often readily available. As a consequence, we
show that ProxSPS is easier to tune and more stable in the presence of
regularization. Furthermore for image classification tasks, ProxSPS performs as
well as AdamW with little to no tuning, and results in a network with smaller
weight parameters. We also provide an extensive convergence analysis for
ProxSPS that includes the non-smooth, smooth, weakly convex and strongly convex
setting.


  This paper investigates the physical reasons for the existence, the tightness
and the near universality of the FIR/radio correlation for late-type field
galaxies. We develop theoretical models for the radio and far-infrared (FIR)
emission of normal galaxies and study the influence of their main parameters on
the ratio of the two emissions. In addition, data are used from a sample of 114
late-type galaxies which allow an estimate of the mean energy densities of the
radiation field and the magnetic field, and of the dust opacity. These data
reveal, for the first time, a reasonably good, linear correlation between the
energy density of the radiation field and the energy density of the magnetic
field. Furthermore we find that on average the galaxies are marginally
optically thick for the non-ionizing UV light. Including their extended
magnetic halos, galaxies are also found to be on average marginally optically
thick regarding the radiative energy losses of the Cosmic Ray electrons.
Combining these semi-empirical results with the theoretical emission models we
show that in the optically thick case the linear correlation between the energy
densities of the radiation field and the magnetic field is a necessary
condition for the existence of the observed FIR/radio correlation. Furthermore
we show that the individual dispersion of the FIR to radio continuum ratio
caused by uncertainties of any single one of the parameters considered is
significantly less than the empirical dispersion of the FIR/radio correlation.
The radio and the FIR emission are mainly determined by their sources, i.e.
massive supernova precursor stars, because galaxies act in a reasonable
approximation as calorimeters for the stellar UV radiation and for the energy
flux of the Cosmic Ray electrons.


  The heavy element ashes of rp-process hydrogen and helium burning in
accreting neutron stars are compressed to high density where they freeze,
forming the outer crust of the star. We calculate the chemical separation on
freezing for a number of different nuclear mixtures resulting from a range of
burning conditions for the rp-process. We confirm the generic result that light
nuclei are preferentially retained in the liquid and heavy nuclei in the solid.
This is in agreement with the previous study of a 17-component mixture of
rp-process ashes by Horowitz et al. (2007), but extends that result to a much
larger range of compositions. We also find an alternate phase separation regime
for the lightest ash mixtures which does not demonstrate this generic
behaviour. With a few exceptions, we find that chemical separation reduces the
expected $Q_{\rm imp}$ in the outer crust compared to the initial rp-process
ash, where $Q_{\rm imp}$ measures the mean-square dispersion in atomic number
$Z$ of the nuclei in the mixture. We find that the fractional spread of $Z$
plays a role in setting the amount of chemical separation and is strongly
correlated to the divergence between the two/three-component approximations and
the full component model. The contrast in $Y_e$ between the initial rp-process
ashes and the equilibrium liquid composition is similar to that assumed in
earlier two-component models of compositionally driven convection, except for
very light compositions which produce nearly negligible convective driving. We
discuss the implications of these results for observations of accreting neutron
stars.


  Let $\Lambda^r_n$ be the path algebra of the linearly oriented quiver of type
$\mathbb{A}$ with $n$ vertices modulo the $r$-th power of the radical, and let
$\widetilde{\Lambda}^r_n$ be the path algebra of the cyclically oriented quiver
of type $\widetilde{\mathbb{A}}$ with $n$ vertices modulo the $r$-th power of
the radical. Adachi gave a recurrence relation for the number of $\tau$-tilting
modules over $\Lambda^r_n$. In this paper, we show that the same recurrence
relation also holds for the number of $\tau$-tilting modules over
$\widetilde{\Lambda}^r_n$. As an application, we give a new proof for a result
by Asai on recurrence formulae for the number of support $\tau$-tilting modules
over $\Lambda^r_n$ and $\widetilde{\Lambda}^r_n$.


  Although basketball is a dynamic process sport, with 5 plus 5 players
competing on both offense and defense simultaneously, learning some static
information is predominant for professional players, coaches and team mangers.
In order to have a deep understanding of field goal attempts among different
players, we propose a zero inflated Poisson model with clustered regression
coefficients to learn the shooting habits of different players over the court
and the heterogeneity among them. Specifically, the zero inflated model
recovers the large proportion of the court with zero field goal attempts, and
the mixture of finite mixtures model learn the heterogeneity among different
players based on clustered regression coefficients and inflated probabilities.
Both theoretical and empirical justification through simulation studies
validate our proposed method. We apply our proposed model to the National
Basketball Association (NBA), for learning players' shooting habits and
heterogeneity among different players over the 2017--2018 regular season. This
illustrates our model as a way of providing insights from different aspects.


  Loop Quantum Gravity (LQG) is an attempt to describe the quantum gravity
regime. Introducing a non-zero cosmological constant $\Lambda$ in this context
has been a withstanding problem. Other approaches, such as Chern-Simons
gravity, suggest that quantum groups can be used to introduce $\Lambda$ in the
game. Not much is known when defining LQG with a quantum group. Tensor
operators can be used to construct observables in any type of discrete quantum
gauge theory with a classical/quantum gauge group. We illustrate this by
constructing explicitly geometric observables for LQG defined with a quantum
group and show for the first time that they encode a quantized hyperbolic
geometry. This is a novel argument pointing out the usefulness of quantum
groups as encoding a non-zero cosmological constant. We conclude by discussing
how tensor operators provide the right formalism to unlock the LQG formulation
with a non-zero cosmological constant.


  Color-kinematics duality is a remarkable conjectured property of gauge theory
which, together with double copy, is at the heart of a wealth of new
developments in scattering amplitudes. So far, its validity has been verified
in most cases only empirically, lacking a first-principle understanding beyond
tree-level. In this paper we provide initial steps in a first-principle
understanding of color-kinematics duality and double-copy at loop level,
through a detailed analysis of the field-theory limit of the monodromy
relations of string theory at one loop. In this limit, we dissect the type of
Feynman graphs generated and the relations they obey. We find that graphs with
contact-terms are unavoidable and are generated in the field theory limit of
"bulk" contours which do not have a standard physical interpretation in string
perturbation theory. We show how they are related to ambiguities in the
definition of the loop momentum and that their role is precisely to cancel
those ambiguities.


  We present results of recurrence analysis of 46 active galactic nuclei (AGN)
using light curves from the 157-month catalog of the Swift Burst Alert
Telescope (BAT) in the 14-150 keV band. We generate recurrence plots and
compute recurrence plot metrics for each object. We use the surrogate data
method to compare all derived recurrence-based quantities to three sets of
stochastic light curves with identical power spectrum, flux distribution, or
both, in order to determine the presence of determinism, non-linearity,
entropy, and non-stationarity. We compare these quantities with known physical
characteristics of each system, such as black hole mass, Eddington ratio, and
bolometric luminosity, radio loudness, obscuration, and spectroscopic type. We
find that almost all AGN in this sample exhibit substantial higher-order modes
of variability than is contained in the power spectrum, with approximately half
exhibiting nonlinear or non-stationary behavior. We find that Type 2 AGN are
more likely to contain deterministic variability than Type 1 AGN while the same
distinction is not found between obscured and unobscured AGN. The complexity of
variability among Type 1 AGN is anticorrelated with Eddington ratio, while no
relationship is found among Type 2 AGN. The connections between the recurrence
properties and AGN class suggest that hard X-ray emission is a probe of
distinct accretion processes among classes of AGN, which supports
interpretations of changing-look AGN and challenges the traditional unification
model that classifies AGN only on viewing angle.


  Here we give an overview on the connection between wavelet theory and
representation theory for graph $C^{\ast}$-algebras, including the higher-rank
graph $C^*$-algebras of A. Kumjian and D. Pask. Many authors have studied
different aspects of this connection over the last 20 years, and we begin this
paper with a survey of the known results. We then discuss several new ways to
generalize these results and obtain wavelets associated to representations of
higher-rank graphs. In \cite{FGKP}, we introduced the "cubical wavelets"
associated to a higher-rank graph. Here, we generalize this construction to
build wavelets of arbitrary shapes. We also present a different but related
construction of wavelets associated to a higher-rank graph, which we anticipate
will have applications to traffic analysis on networks. Finally, we generalize
the spectral graph wavelets of \cite{hammond} to higher-rank graphs, giving a
third family of wavelets associated to higher-rank graphs.


  We present a computational method for studying transverse homoclinic orbits
for periodic solutions of delay differential equations, a phenomenon that we
refer to as the \emph{Poincar\'{e} scenario}. The strategy is geometric in
nature, and consists of viewing the connection as the zero of a nonlinear map,
such that the invertibility of its Fr\'{e}chet derivative implies the
transversality of the intersection. The map is defined by a projected boundary
value problem (BVP), with boundary conditions in the (finite dimensional)
unstable and (infinite dimensional) stable manifolds of the periodic orbit. The
parameterization method is used to compute the unstable manifold and the BVP is
solved using a discrete time dynamical system approach (defined via the
\emph{method of steps}) and Chebyshev series expansions. We illustrate this
technique by computing transverse homoclinic orbits in the cubic Ikeda and
Mackey-Glass systems.


  We study the transmission through different small systems as a function of
the coupling strength $v$ to the two attached leads. The leads are identical
with only one propagating mode $\xi^E_C$ in each of them. Besides the
conductance $G$, we calculate the phase rigidity $\rho$ of the scattering wave
function $\Psi^E_C$ in the interior of the system. Most interesting results are
obtained in the regime of strongly overlapping resonance states where the
crossover from staying to traveling modes takes place. The crossover is
characterized by collective effects. Here, the conductance is plateau-like
enhanced in some energy regions of finite length while corridors with zero
transmission (total reflection) appear in other energy regions. This
transmission picture depends only weakly on the spectrum of the closed system.
It is caused by the alignment of some resonance states of the system with the
propagating modes $\xi^E_C$ in the leads. The alignment of resonance states
takes place stepwise by resonance trapping, i.e. it is accompanied by the
decoupling of other resonance states from the continuum of propagating modes.
This process is quantitatively described by the phase rigidity $\rho$ of the
scattering wave function. Averaged over energy in the considered energy window,
$<G>$ is correlated with $1-<\rho>$. In the regime of strong coupling, only two
short-lived resonance states survive each aligned with one of the channel wave
functions $\xi^E_C$. They may be identified with traveling modes through the
system. The remaining $M-2$ trapped narrow resonance states are well separated
from one another.


  We investigate a large class of $\mathcal{N} = (2, 2)$ supersymmetric field
theories in two dimensions, which contains the Murugan-Stanford-Witten model,
and can be naturally regarded as a disordered generalization of the
two-dimensional Landau-Ginzburg models. We analyze the two and four-point
functions of chiral superfields, and extract from them the central charge, the
operator spectrum, and the chaos exponent in these models. Some of the models
exhibit a conformal manifold parameterized by the variances of the random
couplings. We compute the Zamolodchikov metrics on the conformal manifold, and
demonstrate that the chaos exponent varies nontrivally along the conformal
manifolds. Finally, we introduce and perform some preliminary analysis of a
disordered generalization of the gauged linear sigma models, and discuss the
low energy theories as ensemble averages of Calabi-Yau sigma models over
complex structure moduli space.


  Self-consistent mean-field models are a powerful tool in the investigation of
nuclear structure and low-energy dynamics. They are based on effective
energy-density functionals, often formulated in terms of effective
density-dependent nucleon-nucleon interactions. The free parameters of the
functional are adjusted to empirical data. A proper choice of these parameters
requires a comprehensive set of constraints covering experimental data on
finite nuclei, concerning static as well as dynamical properties, empirical
characteristics of nuclear matter, and observational information on
nucleosynthesis, neutron stars and supernovae. This work aims at a
comprehensive survey of the performance of one of the most successful
non-relativistic self-consistent method, the Skyrme-Hartree-Fock model (SHF),
with respect to these constraints. A full description of the Skyrme functional
is given and its relation to other effective interactions is discussed. The
validity of the application of SHF far from stability and in dense environments
beyond the nuclear saturation density is critically assessed. The use of SHF in
models extended beyond the mean field approximation by including some
correlations is discussed. Finally, future prospects for further development of
SHF towards a more consistent application of the existing and promisingly newly
developing constraints are outlined.


  Within the mini-superspace model, brane-like cosmology means performing the
variation with respect to the embedding (Minkowski) time $\tau$ before fixing
the cosmic (Einstein) time $t$. The departure from Einstein limit is
parameterized by the 'energy' conjugate to $\tau$, and characterized by a
classically disconnected Embryonic epoch. In contrast with canonical quantum
gravity, the wave-function of the brane-like Universe is (i) $\tau$-dependent,
and (ii) vanishes at the Big Bang. Hartle-Hawking and Linde proposals dictate
discrete 'energy' levels, whereas Vilenkin proposal resembles $\alpha$-particle
disintegration.


  While deep learning methods are increasingly being applied to tasks such as
computer-aided diagnosis, these models are difficult to interpret, do not
incorporate prior domain knowledge, and are often considered as a "black-box."
The lack of model interpretability hinders them from being fully understood by
target users such as radiologists. In this paper, we present a novel
interpretable deep hierarchical semantic convolutional neural network (HSCNN)
to predict whether a given pulmonary nodule observed on a computed tomography
(CT) scan is malignant. Our network provides two levels of output: 1) low-level
radiologist semantic features, and 2) a high-level malignancy prediction score.
The low-level semantic outputs quantify the diagnostic features used by
radiologists and serve to explain how the model interprets the images in an
expert-driven manner. The information from these low-level tasks, along with
the representations learned by the convolutional layers, are then combined and
used to infer the high-level task of predicting nodule malignancy. This unified
architecture is trained by optimizing a global loss function including both
low- and high-level tasks, thereby learning all the parameters within a joint
framework. Our experimental results using the Lung Image Database Consortium
(LIDC) show that the proposed method not only produces interpretable lung
cancer predictions but also achieves significantly better results compared to
common 3D CNN approaches.


  Cosmological and astrophysical measurements provide powerful constraints on
neutrino masses complementary to those from accelerators and reactors. Here we
provide a guide to these different probes, for each explaining its physical
basis, underlying assumptions, current and future reach.


  We have calculated inverse-Compton Doppler factors for 3C 279 using the
collection of VLBI data recently published by us, and the collection of
multiwavelength spectra recently published by Hartman et al. From the Doppler
factor and superluminal apparent speed, we then calculate the Lorentz factor
and angle to the line-of-sight of the parsec-scale relativistic jet. We model
the jet components as homogeneous spheres and the VLBI core as an unresolved
inhomogeneous conical jet. The conical-jet model can be made to match both the
observed X-ray emission and the VLBI properties of the core with a suitable
choice of Doppler factor, implying the core makes a significant contribution to
the X-ray emission. The parameters of the conical models indicate the jet is
particle dominated at the radii that produce significant emission, and is not
in equipartition. At the inner radius of the conical jet the magnetic field is
of order 0.1 G and the relativistic-particle number density is of order 10
cm^{-3}. When all components are included in the calculation, then on average
the core produces about half of the X-rays, with the other half being split
between the long-lived component C4 and the brightest inner-jet component. We
calculate an average speed and angle to the line-of-sight for the region of the
jet interior to 1 mas of v=0.992c (gamma=8) and 4 degrees, and an average speed
and angle to the line-of-sight for C4 (at a distance from the core of 3 mas) of
v=0.997c (gamma=13) and 2 degrees. These values imply average Doppler factors
of delta=12 for the inner jet, and delta=21 for C4.


  In this manuscript, we analyze the structural properties of $Z=119$
superheavy nuclei in the mass range of 284 $\le$ A $\le$ 375 within the
framework of axially deformed relativistic mean field theory (RMF) and
calculate the binding energy, radii, quadrupole deformation parameter,
separation energies and density profile. To investigate the phenomenon of shape
coexistence the RMF calculations are performed within three possible solutions
i.e. prolate, oblate and spherical configurations. To get a better
visualization of nucleon and total matter distribution, two-dimensional contour
representation of density distribution for $^{291}$119 and $^{303}$119 has been
made. Further, a competition between possible decay modes such as
$\alpha-$decay, $\beta-$decay and spontaneous fission (SF) of the isotopic
chain of $Z=119$ superheavy nuclei under study is systematically analyzed
within self-consistent relativistic mean field model.
  Our analysis confirmed that $\alpha-$decay is restricted within the mass
range 284 $\leq$ A $\leq$ 296 and thus being the dominant decay channel in this
mass range. There is no possibility of $\beta-$decay for the considered
isotopic chain. In addition, we forecasted the $\alpha-$decay chain of fission
survival nuclides i.e. $^{284-296}$119 and found as one $\alpha$ chain from
$^{284}$119 and $^{296}$119, two consistent $\alpha$ chains from $^{285}$119
and $^{295}$119, three consistent $\alpha$ chains from $^{286}$119 and
$^{294}$119, four consistent alpha chains from $^{287}$119, six consistent
alpha chains from $^{288-293}$119. Thus, such studies can be of great
significance to the experimentalists in very near future for synthesizing
$Z=119$ superheavy nuclei.


  Pilot contamination in the uplink (UL) can severely degrade the channel
estimation quality at the base station (BS) in a massive multi-input
multi-output (MIMO) system. Thus, it is critical to explore all possible
avenues to enable more orthogonal resources for the users to transmit
non-interfering UL pilots. In conventional designs, pilot orthogonality
typically assumes constant channel gains over time, which limits the amount of
orthogonal resources in the case of time-selective channels. To circumvent this
constraint, in this paper, we show how to enable orthogonal multiplexing of
pilots in the case of Doppler fading by aligning the power spectrum densities
(PSD) of different users. From the derived PSD aligning rules, we can see
multiple users can be sounded simultaneously without creating/suffering pilot
contamination even when these users are experiencing time-varying channels.
Furthermore, we provide analytical formulas characterizing the channel
estimation mean square error (MSE) performance. Computer simulations further
confirm us the PSD alignment can serve as one important decontamination
mechanism for the UL pilots in massive MIMO.


  We discuss the solution of eigenvalue problems associated with partial
differential equations that can be written in the generalized form
$\m{A}x=\lambda\m{B}x$, where the matrices $\m{A}$ and/or $\m{B}$ may depend on
a scalar parameter. Parameter dependent matrices occur frequently when
stabilized formulations are used for the numerical approximation of partial
differential equations. With the help of classical numerical examples we show
that the presence of one (or both) parameters can produce unexpected results.


  The main purpose of this paper is to prove an identity of symmetry for the
Frobenius-Euler polynomials.


  Cities and metropolitan areas are major drivers of creativity and innovation
in all possible sectors: scientific, technological, social, artistic, etc. The
critical concentration and proximity of diverse mindsets and opportunities,
supported by efficient infrastructures, enable new technologies and ideas to
emerge, thrive, and trigger further innovation. Though this pattern seems well
established, geography's role in the emergence and diffusion of new
technologies still needs to be clarified. An additional important question
concerns the identification of the innovation pathways of metropolitan areas.
Here, we explore the factors that influence the spread of technology among
metropolitan areas worldwide and how geography and political borders impact
this process. Our evidence suggests that political geography has been highly
important for the diffusion of innovation till around two decades ago, slowly
declining afterwards in favour of a more global innovation ecosystem. Further,
the visualisation of the evolution of countries and metropolitan areas in a 2d
space of competitiveness and diversification reveals the existence of two main
innovation pathways, discriminating between different strategies towards
progress. Our work provides insights for policymakers seeking to promote
economic growth and technological advancement through tailored investments in
prioritarian innovation areas.


  The phase diagram of the Blume--Capel model on a semi--infinite simple cubic
lattice with a (100) free surface is studied in the pair approximation of the
cluster variation method. Six main topologies are found, of which two are new,
due to the occurrence of a first order surface transition in the phase with
ordered bulk, separating two phases with large and small surface order
parameters. The latter is a new phase and is studied in some detail, giving the
behaviour of the order parameter profiles in two typical cases. A comparison is
made with the results of a low temperature expansion, where these are
available, showing a great increase in accuracy with respect to the mean field
approximation.


  We theoretically investigated Anomalous Hall Effect (AHE) and Spin Hall
Effect (SHE) transversally to the insulating spacer O, in magnetic tunnel
junctions of the form F/O/F where F are ferromagnetic layers and O represents a
tunnel barrier. We considered the case of purely ballistic (quantum mechanical)
transport, taking into account the assymetric scattering due to spin-orbit
interaction in the tunnel barrier. AHE and SHE in the considered case have a
surface nature due to proximity effect. Their amplitude is in first order of
the scattering potential. This contrasts with ferromagnetic metals wherein
these effect are in second (side-jump scattering) and third (skew scattering)
order on these potentials. The value of AHE voltage in insulating spacer may be
much larger than in metallic ferromagnetic electrodes. For the antiparallel
orientation of the magnetizations in the two F-electrodes, a spontaneous Hall
voltage exists even at zero applied voltage. Therefore an insulating spacer
sandwiched between two ferromagnetic layers can be considered as exhibiting a
spontaneous ferroelectricity.


  In this paper we prove relationships between two generalizations of
commutative valuation theory for noncommutative central simple algebras: (1)
Dubrovin valuation rings; and (2) the value functions called gauges introduced
by Tignol and Wadsworth in [TW1] and [TW2]. We show that if v is a valuation on
a field F with associated valuation ring V and v is defectless in a central
simple F-algebra A, and C is a subring of A, then the following are equivalent:
(a) C is the gauge ring of some minimal v-gauge on A, i.e., a gauge with the
minimal number of simple components of C/J(C); (b) C is integral over V with C
= B_1 \cap ... \cap B_xi$ where each B_i is a Dubrovin valuation ring of A with
center V, and the B_i satisfy Graeter's Intersection Property. Along the way we
prove the existence of minimal gauges whenever possible and we show how gauges
on simple algebras are built from gauges on central simple algebras.


  Global concern regarding ultrafine particles (UFPs), which are particulate
matter (PM) with a diameter of less than 100nm, is increasing. These
particles-with more serious health effects than PM less than 2.5 micrometers
(PM2.5)-are difficult to measure using the current methods because their
characteristics are different from those of other air pollutants. Therefore, a
new monitoring system is required to obtain accurate UFPs information, which
will raise the financial burden of the government and people. In this study, we
estimated the economic value of UFPs information by evaluating the
willingness-to-pay (WTP) for the UFPs monitoring and reporting system. We used
the contingent valuation method (CVM) and the one-and-one-half-bounded
dichotomous choice (OOHBDC) spike model. We analyzed how the respondents'
socio-economic variables, as well as their cognition level of PM, affected
their WTP. Therefore, we collected WTP data of 1,040 Korean respondents through
an online survey. The estimated mean WTP for building a UFPs monitoring and
reporting system is KRW 6,958.55-7,222.55 (USD 6.22-6.45) per household per
year. We found that people satisfied with the current air pollutant
information, and generally possessing relatively greater knowledge of UFPs,
have higher WTP for a UFPs monitoring and reporting system. The results can be
used to establish new policies response to PM including UFPs.


  The purpose of this paper is to investigate $(n+1)$-Lie algebras induced by
$n$-Lie algebras and trace maps. We highlight a comparison of their structure
properties (solvability, nilpotency) and the cohomology groups as well as
central extensions. Moreover, we provide for dimensions $n$, $n+1$ and $n+2$,
the classification of $n$-Lie algebras which are induced by $(n-1)$-Lie
algebras.


  Mathematical problems of digital terrain analysis include interpolation of
digital elevation models (DEMs), DEM generalization and denoising, and
computation of morphometric variables by calculation of partial derivatives of
elevation. Traditionally, these procedures are based on numerical treatments of
two-variable discrete functions of elevation. We developed a spectral
analytical method and algorithm based on high-order orthogonal expansions using
the Chebyshev polynomials of the first kind with the subsequent Fejer
summation. The method and algorithm are intended for DEM analytical treatment,
such as, DEM global approximation, denoising, and generalization as well as
computation of morphometric variables by analytical calculation of partial
derivatives. To test the method and algorithm, we used a DEM of the Northern
Andes including 230,880 points (the elevation matrix 480 $\times$ 481). DEMs
were reconstructed with 480, 240, 120, 60, and 30 expansion coefficients. The
first and second partial derivatives of elevation were analytically calculated
from the reconstructed DEMs. Models of horizontal curvature ($k_h$) were then
computed with the derivatives. A set of elevation and $k_h$ maps related to
different number of expansion coefficients well illustrates data generalization
effects, denoising, and removal of artifacts contained in the original DEM. The
test results demonstrated a good performance of the developed method and
algorithm. They can be utilized as a universal tool for analytical treatment in
digital terrain modeling.


  The projected ensemble is based on the study of the quantum state of a
subsystem $A$ conditioned on projective measurements in its complement. Recent
studies have observed that a more refined measure of the thermalization of a
chaotic quantum system can be defined on the basis of convergence of the
projected ensemble to a quantum state design, i.e. a system thermalizes when it
becomes indistinguishable, up to the $k$-th moment, from a Haar ensemble of
uniformly distributed pure states. Here we consider a random unitary circuit
with the brick-wall geometry and analyze its convergence to the Haar ensemble
through the frame potential and its mapping to a statistical mechanical
problem. This approach allows us to highlight a geometric interpretation of the
frame potential based on the existence of a fluctuating membrane, similar to
those appearing in the study of entanglement entropies. At large local Hilbert
space dimension $q$, we find that all moments converge simultaneously with a
time scaling linearly in the size of region $A$, a feature previously observed
in dual unitary models. However, based on the geometric interpretation, we
argue that the scaling at finite $q$ on the basis of rare membrane
fluctuations, finding the logarithmic scaling of design times $t_k = O(\log
k)$. Our results are supported with numerical simulations performed at $q=2$.


  In this research article the necessary and sufficient conditions for the norm
of composition operator $C_{\Phi}$ on $\mathcal{A}_{\alpha}^2(H)$ to be one are
obtained. Moreover, $C_{\Phi}$ is unitary on $\mathcal{A}_{\alpha}^2(H)$ if and
only if it is co-isometry. The necessary and sufficient condition for Hermitian
and normal composition operators on $\mathcal{A}_{\alpha}^2(H)$ are also
explored. Also, the characterization for boundeness of generalized weighted
composition operator is obtained under some condition on $\Phi.$


  A novel view for the emergence of chaos in Lorenz-like systems is presented.
For such purpose, the Lorenz problem is reformulated in a classical mechanical
form and it turns out to be equivalent to the problem of a damped and forced
one dimensional motion of a particle in a two-well potential, with a forcing
term depending on the ``memory'' of the particle past motion. The dynamics of
the original Lorenz system in the new particle phase space can then be
rewritten in terms of an one-dimensional first-exit-time problem. The emergence
of chaos turns out to be due to the discontinuous solutions of the
transcendental equation ruling the time for the particle to cross the
intermediate potential wall. The whole problem is tackled analytically deriving
a piecewise linearized Lorenz-like system which preserves all the essential
properties of the original model.


  The nuclei $^4$He, $^8$Be, $^{12}$C and $^{16}$O have been studied starting
from nucleon-nucleon interactions of $v_4$ type. The wave function is built as
the product of three terms, a Jastrow correlation factor, a linear correlation
factor and a model wave function. The correlation factors account for both the
short range repulsive and the spin and isospin dependence of the nuclear
potential. The model wave function is antisymmetric and has the values of the
angular momentum and parity of the state under description. For the model wave
function we have used two different schemes. The first one is based on a
Harmonic Oscillator shell model with and without deformation, and the second
one is based on the Margenau-Brink model of alpha clustering. Projection
operators of parity and total angular momentum are used. The performance of
these two models is studied and compared systematically. Wave functions for the
ground state and some members of its rotational band and some other bound
states of these nuclei have been obtained. Binding energies, root mean square
radius and the expectation value of the kinetic energy and the different
channels of the nuclear interactions and the one-- and two-- body densities are
reported. The two different model wave functions and the effects of the
different nucleon-nucleon correlations have been evaluated on those quantities.
All the results here presented have been obtained by using the Variational
Monte Carlo method.


  In the first part of this paper we consider a general stationary subcritical
cluster model in $\mathbb{R}^d$. The associated pair-connectedness function can
be defined in terms of two-point Palm probabilities of the underlying point
process. Using Palm calculus and Fourier theory we solve the Ornstein-Zernike
equation (OZE) under quite general distributional assumptions. In the second
part of the paper we discuss the analytic and combinatorial properties of the
OZE-solution in the special case of a Poisson driven random connection model.


  Automatic data augmentation (AutoAugment) strategies are indispensable in
supervised data-efficient training protocols of vision transformers, and have
led to state-of-the-art results in supervised learning. Despite the success,
its development and application on self-supervised vision transformers have
been hindered by several barriers, including the high search cost, the lack of
supervision, and the unsuitable search space. In this work, we propose
AutoView, a self-regularized adversarial AutoAugment method, to learn views for
self-supervised vision transformers, by addressing the above barriers. First,
we reduce the search cost of AutoView to nearly zero by learning views and
network parameters simultaneously in a single forward-backward step, minimizing
and maximizing the mutual information among different augmented views,
respectively. Then, to avoid information collapse caused by the lack of label
supervision, we propose a self-regularized loss term to guarantee the
information propagation. Additionally, we present a curated augmentation policy
search space for self-supervised learning, by modifying the generally used
search space designed for supervised learning. On ImageNet, our AutoView
achieves remarkable improvement over RandAug baseline (+10.2% k-NN accuracy),
and consistently outperforms sota manually tuned view policy by a clear margin
(up to +1.3% k-NN accuracy). Extensive experiments show that AutoView
pretraining also benefits downstream tasks (+1.2% mAcc on ADE20K Semantic
Segmentation and +2.8% mAP on revisited Oxford Image Retrieval benchmark) and
improves model robustness (+2.3% Top-1 Acc on ImageNet-A and +1.0% AUPR on
ImageNet-O). Code and models will be available at
https://github.com/Trent-tangtao/AutoView.


  Hecke algebras are usually defined algebraically, via generators and
relations. We give a new algebro-geometric construction of affine and
double-affine Hecke algebras (the former is known as the Iwahori-Hecke algebra,
and the latter was introduced by Cherednik [Ch1]). More generally, to any
generalized Cartan matrix A and a point q in a 1-dimensional complex algebraic
group \c we associate an associative algebra H. If A is of finite type and
\c=C^*, the algebra H is the affine Hecke algebra of the corresponding finite
root system. If A is of affine type and \c=C^* then H is, essentially, the
Cherednik algebra. The case \c=C corresponds to `degenerate' counterparts of
the above objects cosidered by Drinfeld [Dr] and Lusztig [L2]. Finally, taking
\c to be an elliptic curve one gets some new elliptic analogues of the affine
Hecke algebra.


  In this article we study the finite temperature and chemical potential
effects in a nonlocal Nambu-Jona-Lasinio (nNJL) model in the real time
formalism. We make the usual Wick rotation to get from imaginary to real time
formalism. In doing so, we need to define our regulator in the complex plane
q^2. This deffinition will be crucial in our later analysis. We study the poles
in the propagator of this model and conclude that only some of them are of
interst to us. Once we have a well defined model in real time formalism, we
look at the chiral condensate to find the temperature at which chiral symmetry
restoration will occur. We find a second order phase transition that turns to a
first order one for high enough values of the chemical potential.


  We present an N-body model for the barred Milky Way (MW) galaxy that
reproduces many of its properties, including the overall mass distribution, the
disc kinematics, and the properties of the central bar. Our high-resolution (N
~ 10^8 particles) simulation, performed with the Ramses code, starts from an
axisymmetric non-equilibrium configuration constructed within the AGAMA
framework. This is a self-consistent dynamical model of the MW defined by the
best available parameters for the dark matter halo, the stellar disc and the
bulge.
  For the known (stellar and gas) disc mass (4.5 x 10^10 Msun) and disc mass
fraction at R ~ 2.2 R_d (f_d ~ 0.3 - 0.6), the low mass limit does not yield a
bar in a Hubble time. The high mass limit adopted here produces a box/peanut
bar within about 2 Gyr with the correct mass (~10^10 Msun), size (~5 kpc) and
peak pattern speed (~ 40-45 km/s/kpc).
  In agreement with earlier work, the bar formation timescale scales inversely
with f_d (i.e. log [T/Gyr] ~ 0.60/f_d - 0.83 for 1 < f_d < 0.3). The disc
radial heating is strong, but, in contrast to earlier claims, we find that disc
vertical heating outside of the box/peanut bulge structure is negligible.
  The synthetic barred MW exhibits long-term stability, except for the slow
decline (roughly -2 km/s/kpc/Gyr) of the bar pattern speed, consistent with
recent estimates. If our model is indicative of the Milky Way, we estimate that
the bar first emerged 3-4 Gyr ago.


  We classify Enriques surfaces of zero entropy, or, equivalently, Enriques
surfaces with a virtually abelian automorphism group.


  Modern speech enhancement (SE) networks typically implement noise suppression
through time-frequency masking, latent representation masking, or
discriminative signal prediction. In contrast, some recent works explore SE via
generative speech synthesis, where the system's output is synthesized by a
neural vocoder after an inherently lossy feature-denoising step. In this paper,
we propose a denoising vocoder (DeVo) approach, where a vocoder accepts noisy
representations and learns to directly synthesize clean speech. We leverage
rich representations from self-supervised learning (SSL) speech models to
discover relevant features. We conduct a candidate search across 15 potential
SSL front-ends and subsequently train our vocoder adversarially with the best
SSL configuration. Additionally, we demonstrate a causal version capable of
running on streaming audio with 10ms latency and minimal performance
degradation. Finally, we conduct both objective evaluations and subjective
listening studies to show our system improves objective metrics and outperforms
an existing state-of-the-art SE model subjectively.


  KGCleaner is a framework to identify and correct errors in data produced and
delivered by an information extraction system. These tasks have been
understudied and KGCleaner is the first to address both. We introduce a
multi-task model that jointly learns to predict if an extracted relation is
credible and repair it if not. We evaluate our approach and other models as
instance of our framework on two collections: a Wikidata corpus of nearly 700K
facts and 5M fact-relevant sentences and a collection of 30K facts from the
2015 TAC Knowledge Base Population task. For credibility classification,
parameter efficient simple shallow neural network can achieve an absolute
performance gain of 30 $F_1$ points on Wikidata and comparable performance on
TAC. For the repair task, significant performance (at more than twice) gain can
be obtained depending on the nature of the dataset and the models.


  Signal extrapolation tasks arise in miscellaneous manners in the field of
image and video signal processing. But, due to the widespread use of low-power
and mobile devices, the computational complexity of an algorithm plays a
crucial role in selecting an algorithm for a given problem. Within the scope of
this contribution, we introduce the complex-valued Frequency Selective
Extrapolation for fast image and video signal extrapolation. This algorithm
iteratively generates a generic complex-valued model of the signal to be
extrapolated as weighted superposition of Fourier basis functions. We further
show that this algorithm is up to 10 times faster than the existent real-valued
Frequency Selective Extrapolation that takes the real-valued nature of the
input signals into account during the model generation. At the same time, the
quality which is achievable by the complex-valued model generation is similar
to the quality of the real-valued model generation.


  Recently de Boissieu et al. proposed an explanation for the broadening of
acoustic modes observed in quasicrystals (QC). It is the transcription of a
well-known model used for glasses. We raise two fundamental objections against
applying it to QC. After the text of the Comment we report the methodology that
has been used to thwart the publication of this Comment, which is perfectly
valid.


  We consider a one-dimensional (1D) autoignitive reaction wave in reactive
flow system comprising unburned premixed gas entering from the inlet boundary
and burned gas exiting from the outlet boundary. In such a 1D system at given
initial temperature, it is generally accepted that steady-state solutions can
only exist if the inlet velocity matches either the velocity of deflagration
wave, as determined by the burning rate eigenvalue in the subsonic regime or
the velocity of detonation wave as dictated by the Chapman-Jouguet (CJ)
condition in the supersonic regime. In this study, we developed the general
concept of "autoignitive reaction wave" and theoretically demonstrate that two
distinct regimes that can maintain steady-state solutions both in subsonic and
supersonic conditions. Based on this theory, we selected inlet velocities that
are predicted to yield either steady-state or flashback solutions, and
conducted numerical simulations. This novel approach revealed that steady-state
solutions are possible not only at the velocity of the deflagration wave in the
subsonic regime and the velocity of the detonation wave in the supersonic
regime, but also across a broad range of inlet velocities. Furthermore, we
identify a highly stable "autoignitive reaction wave" that emerges when the
inlet velocity surpasses the velocity of detonation wave, devoid of the typical
shock wave commonly seen in detonation waves. This "supersonic autoignitive
reaction wave" lacks the instability-inducing detonation cell structure,
suggesting the potential for the development of novel combustor concepts.


  We give estimates for the approximation numbers of composition operators on
the Hp spaces, 1 $\le$ p \textless{} $\infty$.


  Out-of-distribution (OOD) generalization has attracted increasing research
attention in recent years, due to its promising experimental results in
real-world applications. In this paper,we study the confidence set prediction
problem in the OOD generalization setting. Split conformal prediction (SCP) is
an efficient framework for handling the confidence set prediction problem.
However, the validity of SCP requires the examples to be exchangeable, which is
violated in the OOD setting. Empirically, we show that trivially applying SCP
results in a failure to maintain the marginal coverage when the unseen target
domain is different from the source domain. To address this issue, we develop a
method for forming confident prediction sets in the OOD setting and
theoretically prove the validity of our method. Finally, we conduct experiments
on simulated data to empirically verify the correctness of our theory and the
validity of our proposed method.


  The eigenfrequencies of nonradial oscillations are a powerful probe of a
star's interior structure. This is especially true when there exist
discontinuities such as at the neutron star (NS) ocean/crust boundary, as first
noted by McDermott, Van Horn & Hansen. The interface mode associated with this
boundary has subsequently been neglected in studies of stellar nonradial
oscillations. We revisit this mode, investigating its properties both
analytically and numerically for a simple NS envelope model. We find that it
acts like a shallow surface ocean wave, but with a large radial displacement at
the ocean/crust boundary due to flexing of the crust with shear modulus $\mu\ll
P$, the pressure. This displacement lowers the mode's frequency by a factor of
$\sim(\mu/P)^{1/2}\sim0.1$ in comparison to a shallow surface wave frequency on
a hard surface. The interface mode may be excited on accreting or bursting NSs
and future work on nonradial oscillations should consider this mode. Our work
also implies an additional mode on massive and/or cold white dwarfs with
crystalline cores, which may have a frequency between the f-mode and g-modes,
an otherwise empty part of the frequency domain.


  We report on IRAC-4.5mic, IRAC-8.0mic and MIPS-24mic deep observations of 16
Gamma-Ray Burst (GRBs) host galaxies performed with the Spitzer Space
Telescope, and we investigate in the thermal infrared the presence of evolved
stellar populations and dust-enshrouded star-forming activity associated with
these objects. Our sample is derived from GRBs that were identified with
sub-arcsec localization between 1997 and 2001, and only a very small fraction
(~20%) of the targeted sources is detected down to f_4.5mic ~3.5microJy and
f_24mic ~85microJy (3sigma). This likely argues against a population dominated
by massive and strongly-starbursting (i.e., SFR > ~100 Msol/yr) galaxies as it
has been recently suggested from submillimeter/radio and optical studies of
similarly-selected GRB hosts. Furthermore we find evidence that some GRBs do
not occur in the most infrared-luminous regions -- hence the most actively
star-forming environments -- of their host galaxies. Should the GRB hosts be
representative of all star-forming galaxies at high redshift, models of
infrared galaxy evolution indicate that > ~50% of GRB hosts should have f_24mic
> ~100microJy. Unless the identification of GRBs prior to 2001 was prone to
strong selection effects biasing our sample against dusty galaxies, we infer in
this context that the GRBs identified with the current techniques can not be
directly used as unbiased probes of the global and integrated star formation
history of the Universe.


  In 2009, Grant, Shallit, and Stoll constructed a large family of pseudorandom
sequences, called generalized Rudin--Shapiro sequences, for which they
established some results about the average of discrete correlation coefficients
of order 2 in cases where the size of the alphabet is a prime number or a
squarefree product of primes. We establish similar results for an even larger
family of pseudorandom sequences, constructed via difference matrices, in the
case of an alphabet of any size. The constructions generalize those from Grant
et al. In the case where the size of the alphabet is squarefree and where there
are at least two prime factors, we obtain an improvement in the error term by
comparison with the result of Grant et al.


  Back-support exoskeletons are commonly used in the workplace to reduce low
back pain risk for workers performing demanding activities. However, for the
assistance of tasks differing from lifting, back-support exoskeletons potential
has not been exploited extensively. This work focuses on the use of an active
back-support exoskeleton to assist carrying. Two control strategies are
designed that modulate the exoskeleton torques to comply with the task
assistance requirements. In particular, two gait phase detection frameworks are
exploited to adapt the assistance according to the legs' motion. The two
strategies are assessed through an experimental analysis on ten subjects.
Carrying task is performed without and with the exoskeleton assistance. Results
prove the potential of the presented controls in assisting the task without
hindering the gait movement and improving the usability experienced by users.
Moreover, the exoskeleton assistance significantly reduces the lumbar load
associated with the task, demonstrating its promising use for risk mitigation
in the workplace.


  Chart question answering (CQA) is a newly proposed visual question answering
(VQA) task where an algorithm must answer questions about data visualizations,
e.g. bar charts, pie charts, and line graphs. CQA requires capabilities that
natural-image VQA algorithms lack: fine-grained measurements, optical character
recognition, and handling out-of-vocabulary words in both questions and
answers. Without modifications, state-of-the-art VQA algorithms perform poorly
on this task. Here, we propose a novel CQA algorithm called parallel recurrent
fusion of image and language (PReFIL). PReFIL first learns bimodal embeddings
by fusing question and image features and then intelligently aggregates these
learned embeddings to answer the given question. Despite its simplicity, PReFIL
greatly surpasses state-of-the art systems and human baselines on both the
FigureQA and DVQA datasets. Additionally, we demonstrate that PReFIL can be
used to reconstruct tables by asking a series of questions about a chart.


  We analyze the dynamical evolution of a perturbed force-free magnetosphere of
a rotating black hole, which is described by the Blandford-Znajek solution in
the stationary limit. We find that the electromagnetic field perturbations can
be classified into two categories: "trapped modes" and "traveling waves". The
trapped modes are analogous to the vacuum (without plasma) electromagnetic
quasinormal modes in rotating black hole spacetimes, but with different
eigenfrequencies and wave functions, due to their coupling with the background
electromagnetic field and current. The traveling waves propagate freely to
infinity or the black hole horizon along specific null directions, and they are
closely related to the no-scattering Poynting flux solutions discovered by
Brennan, Gralla and Jacobson. Our results suggest that the Blandford-Znajek
solution is mode stable, and more importantly we expect this study to
illuminate the dynamical behavior of force-free magnetospheres as well as to
shed light on the path to new exact solutions.


  Gravitational interactions of higher spin fields are generically plagued by
inconsistencies. We present a simple framework that couples higher spins to a
broad class of gravitational backgrounds (including Ricci flat and Einstein)
consistently at the classical level. The model is the simplest example of a
Yang--Mills detour complex, which recently has been applied in the mathematical
setting of conformal geometry. An analysis of asymptotic scattering states
about the trivial field theory vacuum in the simplest version of the theory
yields a rich spectrum marred by negative norm excitations. The result is a
theory of a physical massless graviton, scalar field, and massive vector along
with a degenerate pair of zero norm photon excitations. Coherent states of the
unstable sector of the model do have positive norms, but their evolution is no
longer unitary and their amplitudes grow with time. The model is of
considerable interest for braneworld scenarios and ghost condensation models,
and invariant theory.


  Given a knot K in S^3, Seidel and Smith described in arXiv:1002.2648v3 a
graded cohomology group Kh_{symp,inv}(K), a variant of their symplectic
Khovanov cohomology group. They also constructed a spectral sequence converging
to the Heegaard Floer-hat homology group for the connected sum of the double
branched cover and a copy of S^{2}xS^{1} (with E^1-page isomorphic to a direct
summand of Kh_{symp,inv}(K)). In a previous paper (arXiv:1004.2476v5), we
showed that the higher pages of this spectral sequence are knot invariants.
Here we discuss a reduced version of the spectral sequence which directly
computes HF-hat of the double branched cover. Under some degeneration
conditions, one obtains a new absolute Maslov grading on that group. This
occurs when K is a two-bridge knot, and we compute the grading in this case. We
also extract some rational-valued knot invariants from this construction.


  Using polynomial interpolation, along with structural properties of the
family of positive real rational functions, we here show that a set of m nodes
in the open left half of the complex plane, can always be mapped to anywhere in
the complex plane by rational positive real functions whose degree is at most
m. Moreover, we introduce an easy-to-find parametrization in $R^{2m+3}$ of a
large subset of these interpolating functions.


  We provide the foundations of a Hilbert space theory for the short-time
Fourier transform (STFT) where the flat tori \begin{equation*}
\mathbb{T}_{N}^2=\mathbb{R}^2/(\mathbb{Z}\times N\mathbb{Z})=[0,1]\times
\lbrack 0,N] \end{equation*} act as phase spaces. We work on an $N$-dimensional
subspace $S_{N}$ of distributions periodic in time and frequency in the dual
$S_0'(\mathbb{R})$ of the Feichtinger algebra $S_0(\mathbb{R})$ and equip it
with an inner product. To construct the Hilbert space $S_{N}$ we apply a
suitable double periodization operator to $S_0(\mathbb{R})$. On $S_{N}$, the
STFT is applied as the usual STFT defined on $S_0'(\mathbb{R})$. This STFT is a
continuous extension of the finite discrete Gabor transform from the lattice
onto the entire flat torus. As such, sampling theorems on flat tori lead to
Gabor frames in finite dimensions. For Gaussian windows, one is lead to spaces
of analytic functions and the construction allows to prove a necessary and
sufficient Nyquist rate type result, which is the analogue, for Gabor frames in
finite dimensions, of a well known result of Lyubarskii and Seip-Wallst{\'e}n
for Gabor frames with Gaussian windows and which, for $N$ odd, produces an
explicit \emph{full spark Gabor frame}. The compactness of the phase space, the
finite dimension of the signal spaces and our sampling theorem offer practical
advantages in some applications. We illustrate this by discussing a problem of
current research interest: recovering signals from the zeros of their noisy
spectrograms.


  The radio millisecond pulsar J1713+0747 is regarded as one of the
highest-precision clocks in the sky, and is regularly timed for the purpose of
detecting gravitational waves. The International Pulsar Timing Array
collaboration undertook a 24-hour global observation of PSR J1713+0747 in an
effort to better quantify sources of timing noise in this pulsar, particularly
on intermediate (1 - 24 hr) timescales. We observed the pulsar continuously
over 24 hr with the Arecibo, Effelsberg, GMRT, Green Bank, LOFAR, Lovell,
Nancay, Parkes, and WSRT radio telescopes. The combined pulse times-of-arrival
presented here provide an estimate of what sources of timing noise, excluding
DM variations, would be present as compared to an idealized root-N improvement
in timing precision, where N is the number of pulses analyzed. In the case of
this particular pulsar, we find that intrinsic pulse phase jitter dominates
arrival time precision when the S/N of single pulses exceeds unity, as measured
using the eight telescopes that observed at L-band/1.4 GHz. We present first
results of specific phenomena probed on the unusually long timescale (for a
single continuous observing session) of tens of hours, in particular
interstellar scintillation, and discuss the degree to which scintillation and
profile evolution affect precision timing. This paper presents the data set as
a basis for future, deeper studies.


  We study the properties of certain graphs involving the sums of primes. Their
structure largely turns out to relate to the distribution of prime gaps and can
be roughly seen in Cram\'er's model as well. We also discuss generalizations to
the Gaussian integers.


  Systems composed of soft matter (e.g., liquids, polymers, foams, gels,
colloids, and most biological materials) are ubiquitous in science and
engineering, but molecular simulations of such systems pose particular
computational challenges, requiring time and/or ensemble-averaged data to be
collected over long simulation trajectories for property evaluation. Performing
a molecular simulation of a soft matter system involves multiple steps, which
have traditionally been performed by researchers in a "bespoke" fashion,
resulting in many published soft matter simulations not being reproducible
based on the information provided in the publications. To address the issue of
reproducibility and to provide tools for computational screening, we have been
developing the open-source Molecular Simulation and Design Framework (MoSDeF)
software suite. In this paper, we propose a set of principles to create
Transparent, Reproducible, Usable by others, and Extensible (TRUE) molecular
simulations. MoSDeF facilitates the publication and dissemination of TRUE
simulations by automating many of the critical steps in molecular simulation,
thus enhancing their reproducibility. We provide several examples of TRUE
molecular simulations: All of the steps involved in creating, running and
extracting properties from the simulations are distributed on open-source
platforms (within MoSDeF and on GitHub), thus meeting the definition of TRUE
simulations.


  We review results about protoplanetary disk models, protoplanet migration and
formation of giant planets with migrating cores. We first model the
protoplanetary nebula as an \alpha-accretion disk and present steady state
calculations for different values of \alpha and gas accretion rate through the
disk. We then review the current theories of protoplanet migration in the
context of these models, focusing on the gaseous disk-protoplanet tidal
interaction. According to these theories, the migration timescale may be
shorter than the planetary formation timescale. Therefore we investigate planet
formation in the context of a migrating core, considering both the growth of
the core and the build-up of the envelope in the course of the migration.


  In this paper, we study the Casimir force for a class of Lorentzian nonlocal
field theories. These theories include a continuum of massive excitations. In
this regard, the effect of continuum massive modes on Casimir force is of
interest. We focus on the simplest case of two absorbing parallel planes in 1+1
dimensions, and we show that unlike local field theories, the thickness of the
absorbing "walls" changes the value of Casimir force.


  The quintic equation with real coefficients $$x^5+5ax^3+5a^2x+b=0$$ is solved
in terms of radicals and the results used to sum a hypergeometric series for
several arguments.


  Given a singular variety I discuss the relations between quantum cohomology
of its resolution and smoothing. In particular, I explain how toric
degenerations helps with computing Gromov--Witten invariants, and the role of
this story in Fanosearch programme. The challenge is to formulate enumerative
symplectic geometry of complex $3$-folds in a way suitable for extracting
invariants under blowups, contractions, and transitions.


  The special nonlinear dynamical regimes, "bushes of normal modes", can exist
in the N-particle Hamiltonian systems with discrete symmetry. The dimension of
the bush can be essentially less than that of the whole mechanical system.
One-dimensional bushes represent the similar nonlinear normal modes introduced
by Rosenberg. A given bush can be excited by imposing the appropriate initial
conditions, and the energy of the initial excitation turns out to be trapped in
this bush.
  In the present paper, we consider all possible vibrational bushes in the
simple octahedral mechanical system and discuss their stability under
assumption that the interactions between particles are described by the
Lennard-Jones potential.


  This study aimed to develop a method to evaluate the sense of discrepancy to
the operation response quantitatively. We examined the availability of
event-related potential (P300), which is considered to reflect attention to
stimulation, to evaluate the sense of discrepancy to the product response to
the user's action. In the experiment using subjective evaluation and P300 to
investigate the sense of discrepancy due to the lack of operation response
(sound and vibration) to the shutter operation of the mirrorless single-lens
camera, it was confirmed that P300 amplitude corresponds to the degree of the
subjective sense of discrepancy. Our results showed that the P300 amplitude
could evaluate the sense of discrepancy to the operation response.


  As the largest organ in the human body, the skin provides the important
sensory channel for humans to receive external stimulations based on touch. By
the information perceived through touch, people can feel and guess the
properties of objects, like weight, temperature, textures, and motion, etc. In
fact, those properties are nerve stimuli to our brain received by different
kinds of receptors in the skin. Mechanical, electrical, and thermal stimuli can
stimulate these receptors and cause different information to be conveyed
through the nerves. Technologies for actuators to provide mechanical,
electrical or thermal stimuli have been developed. These include static or
vibrational actuation, electrostatic stimulation, focused ultrasound, and more.
Smart materials, such as piezoelectric materials, carbon nanotubes, and shape
memory alloys, play important roles in providing actuation for tactile
sensation. This paper aims to review the background biological knowledge of
human tactile sensing, to give an understanding of how we sense and interact
with the world through the sense of touch, as well as the conventional and
state-of-the-art technologies of tactile actuators for tactile feedback
delivery.


  Let k>2 be a fixed integer exponent and let \theta > 9/10. We show that a
positive integer N can be represented as a non-trivial sum or difference of 3
k-th powers, using integers of size at most B, in O(B^{\theta}N^{1/10}) ways,
providing that N << B^{3/13}. The significance of this is that we may take
\theta strictly less than 1. We also prove the estimate O(B^{10/k}), (subject
to N << B) which is better for large k.
  The results extend to representations by an arbitrary fixed nonsingular
ternary from. However ``non-trivial'' must then be suitably defined.
Consideration of the singular form x^{k-1}y-z^k allows us to establish an
asymptotic formula for (k-1)-free values of p^k+c, when p runs over primes,
answering a problem raised by Hooley.


  Ultra-massive hydrogen-rich (DA spectral type) white dwarf (WD) stars
($M_{\star} > 1M_{\odot}$) coming from single-star evolution are expected to
harbor cores made of $^{16}$O and $^{20}$Ne, resulting from semi-degenerate
carbon burning when the progenitor star evolves through the super asymptotic
giant branch (S-AGB) phase. These stars are expected to be crystallized by the
time they reach the ZZ Ceti instability strip ($T_{\rm eff} \sim 12\,500$ K).
Theoretical models predict that crystallization leads to a separation of
$^{16}$O and $^{20}$Ne in the core of ultra-massive WDs, which impacts their
pulsational properties. This property offers a unique opportunity to study the
processes of crystallization. Here, we present the first results of a detailed
asteroseismic analysis of the best-studied ultra-massive ZZ Ceti star
BPM~37093. As a second step, we plan to repeat this analysis using
ultra-massive DA WD models with C/O cores in order to study the possibility of
elucidating the core chemical composition of BPM~37093 and shed some light on
its possible evolutionary origin. We also plan to extend this kind of analyses
to other stars observed from the ground and also from space missions like
Kepler and TESS.


  We introduce a set of two-parameter models for the dark energy equation of
state (EOS) $w(z)$ to investigate time-varying dark energy. The models are
classified into two types according to their boundary behaviors at the redshift
$z=(0,\infty)$ and their local extremum properties. A joint analysis based on
four observations (SNe + BAO + CMB + $H_0$) is carried out to constrain all the
models. It is shown that all models get almost the same $\chi^2_{min}\simeq
469$ and the cosmological parameters $(\Omega_M, h, \Omega_bh^2)$ with the
best-fit results $(0.28, 0.70, 2.24)$, although the constraint results on two
parameters $(w_0, w_1)$ and the allowed regions for the EOS $w(z)$ are
sensitive to different models and a given extra model parameter. For three of
Type I models which have similar functional behaviors with the so-called CPL
model, the constrained two parameters $w_0$ and $w_1$ have negative correlation
and are compatible with the ones in CPL model, and the allowed regions of
$w(z)$ get a narrow node at $z\sim 0.2$. The best-fit results from the most
stringent constraints in Model Ia give $(w_0,w_1) = (-0.96^{+0.26}_{-0.21},
-0.12^{+0.61}_{-0.89})$ which may compare with the best-fit results $(w_0,w_1)
= (-0.97^{+0.22}_{-0.18}, -0.15^{+0.85}_{-1.33})$ in the CPL model. For four of
Type II models which have logarithmic function forms and an extremum point, the
allowed regions of $w(z)$ are found to be sensitive to different models and a
given extra parameter. It is interesting to obtain two models in which two
parameters $w_0$ and $w_1$ are strongly correlative and appropriately reduced
to one parameter by a linear relation $w_1 \propto (1+w_0)$.


  I have carried out a search for Planet 9 in the IRAS data. At the distance
range proposed for Planet 9, the signature would be a 60 micron unidentified
IRAS point source with an associated nearby source from the IRAS Reject File of
sources which received only a single hours-confirmed (HCON) detection. The
confirmed source should be detected on the first two HCON passes, but not on
the third, while the single HCON should be detected only on the third HCON. I
have examined the unidentified sources in three IRAS 60micron catalogues: some
can be identified with 2MASS galaxies, Galactic sources or as cirrus. The
remaining unidentified sources have been examined with the IRSA Scanpi tool to
check for the signature missing HCONs, and for association with IRAS Reject
File single HCONs. No matches of interest survive.
  For a lower mass planet (< 5 earth masses) in the distance range 200-400 AU,
we expect a pair or triplet of single HCONs with separations 2-35 arcmin.
Several hundred candidate associations are found and have been examined with
Scanpi. A single candidate for Planet 9 survives which satisfies the
requirements for detected and non-detected HCON passes. A fitted orbit suggest
a distance of 225+-15 AU and a mass of 3-5 earth masses. Dynamical simulations
are needed to explore whether the candidate is consistent with existing planet
ephemerides. If so, a search in an annulus of radius 2.5-4 deg centred on the
1983 position at visible and near infrared wavelengths would be worthwhile.


  We introduce a family of order $N\in \mathbb{N}$ Lax matrices that is indexed
by the natural number $k\in \{1,\ldots,N-1\}.$ For each value of $k$ they serve
as strong Lax matrices of a hierarchy of integrable difference systems in edge
variables that in turn lead to hierarchies of integrable difference systems in
vertex variables or in a combination of edge and vertex variables. Furthermore,
the entries of the Lax matrices are considered as elements of a division ring,
so we obtain hierarchies of discrete integrable systems extended in the
non-commutative domain.


  We investigate experimentally the influence of rotation on the penetration
depth of a spherical projectile impacting a granular medium. We show that a
rotational motion significantly increases the penetration depth achieved.
Moreover, we model our experimental results by modifying the frictional term of
the equation describing the penetration dynamics of an object in a granular
medium. In particular, we find that the frictional drag decreases linearly with
the velocity ratio between rotational (spin motion) and translational (falling
motion) velocities. The good agreement between our model and our experimental
measurements offers perspectives for estimating the depth that spinning
projectiles reach after impacting onto a granular ground, such as happens with
seeds dropped from aircraft or with landing probes.


  Conversational recommender systems (CRSs) have become crucial emerging
research topics in the field of RSs, thanks to their natural advantages of
explicitly acquiring user preferences via interactive conversations and
revealing the reasons behind recommendations. However, the majority of current
CRSs are text-based, which is less user-friendly and may pose challenges for
certain users, such as those with visual impairments or limited writing and
reading abilities. Therefore, for the first time, this paper investigates the
potential of voice-based CRS (VCRSs) to revolutionize the way users interact
with RSs in a natural, intuitive, convenient, and accessible fashion. To
support such studies, we create two VCRSs benchmark datasets in the e-commerce
and movie domains, after realizing the lack of such datasets through an
exhaustive literature review. Specifically, we first empirically verify the
benefits and necessity of creating such datasets. Thereafter, we convert the
user-item interactions to text-based conversations through the ChatGPT-driven
prompts for generating diverse and natural templates, and then synthesize the
corresponding audios via the text-to-speech model. Meanwhile, a number of
strategies are delicately designed to ensure the naturalness and high quality
of voice conversations. On this basis, we further explore the potential
solutions and point out possible directions to build end-to-end VCRSs by
seamlessly extracting and integrating voice-based inputs, thus delivering
performance-enhanced, self-explainable, and user-friendly VCRSs. Our study aims
to establish the foundation and motivate further pioneering research in the
emerging field of VCRSs. This aligns with the principles of explainable AI and
AI for social good, viz., utilizing technology's potential to create a fair,
sustainable, and just world.


  We use direct-summation N-body integrations to follow the evolution of binary
black holes at the centers of galaxy models with large, constant-density cores.
Particle numbers as large as 400K are considered. The results are compared with
the predictions of loss-cone theory, under the assumption that the supply of
stars to the binary is limited by the rate at which they can be scattered into
the binary's influence sphere by gravitational encounters. The agreement
between theory and simulation is quite good; in particular, we are able to
quantitatively explain the observed dependence of binary hardening rate on N.
We do not verify the recent claim of Chatterjee, Hernquist & Loeb (2003) that
the hardening rate of the binary stabilizes when N exceeds a particular value,
or that Brownian wandering of the binary has a significant effect on its
evolution. When scaled to real galaxies, our results suggest that massive black
hole binaries in gas-poor nuclei would be unlikely to reach gravitational-wave
coalescence in a Hubble time.


  The cascade of fluorescence photons by a two-level atom excited by coherent
laser light is reviewed. The discussion emphasizes the random nature of
resonance fluorescence and uses the distribution of delays between two
successively emitted photons as the primary characterization of the process.
Other characterizations such as photon counting and photon correlation are
deduced.


  A classical result due to Segre states that on a real cubic surface in
${\mathbb P}^3_\R$ there exists two kinds of real lines: elliptic and
hyperbolic lines. These two kinds of real lines are defined in an intrinsic
way, i.e., their definition does not depend on any choices of orientation data.
Segre's classification of smooth real cubic surfaces also shows that any such
surface contains at least 3 real lines. Starting from these remarks and
inspired by the classical problem mentioned above, our article has the
following goals:
  - We explain a general principle which leads to lower bounds in real
algebraic geometry,
  - We explain the reason for the appearance of intrinsic signs in the
classical problem treated by Segre, showing that the same phenomenon occurs in
a large class of enumerative problems in real algebraic geometry.
  - We illustrate these principles in the enumerative problem for real lines in
real hypersurfaces of degree $2m-3$ in ${\mathbb P}^m_\R$.


  The 2 into n scattering with final particles at rest is discussed. The
comparison with purely soft processes allows to identify symmetries responsible
for vanishing of certain 2 into n amplitudes. Some examples are given.


  We present in-hand manipulation tasks where a robot moves an object in grasp,
maintains its external contact mode with the environment, and adjusts its
in-hand pose simultaneously. The proposed manipulation task leads to complex
contact interactions which can be very susceptible to uncertainties in
kinematic and physical parameters. Therefore, we propose a robust in-hand
manipulation method, which consists of two parts. First, an in-gripper
mechanics model that computes a na\"ive motion cone assuming all parameters are
precise. Then, a robust planning method refines the motion cone to maintain
desired contact mode regardless of parametric errors. Real-world experiments
were conducted to illustrate the accuracy of the mechanics model and the
effectiveness of the robust planning framework in the presence of kinematics
parameter errors.


  We describe 'staq', a full-stack quantum processing toolkit written in
standard C++. 'staq' is a quantum compiler toolkit, comprising of tools that
range from quantum optimizers and translators to physical mappers for quantum
devices with restricted connectives. The design of 'staq' is inspired from the
UNIX philosophy of "less is more", i.e. 'staq' achieves complex functionality
via combining (piping) small tools, each of which performs a single task using
the most advanced current state-of-the-art methods. We also provide a set of
illustrative benchmarks.


  Regression testing is performed to provide confidence that changes in a part
of software do not affect other parts of the software. An execution of all
existing test cases is the best way to re-establish this confidence. However,
regression testing is an expensive process---there might be insufficient
resources (e.g., time, workforce) to allow for the re-execution of all test
cases. Regression test prioritization techniques attempt to re-order a
regression test suite based on some criteria so that highest priority test
cases are executed earlier.
  In this study, we want to prioritize test cases for regression testing based
on the dependency network of faults. In software testing, it is common that
some faults are consequences of other faults (leading faults). Moreover,
dependent faults can be removed if and only if the leading faults have been
removed. Our goal is to prioritize test cases so that test cases that exposed
leading faults (the most central faults in the fault dependency network) in the
system testing phase, are executed first in regression testing.
  We present ComReg, a test case prioritization technique based on the
dependency network of faults. We model a fault dependency network as a directed
graph and identify leading faults to prioritize test cases for regression
testing. We use a centrality aggregation technique which considers six network
representative centrality metrics to identify leading faults in the fault
dependency network. We also discuss the use of fault communities to select an
arbitrary percentage of the test cases from a prioritized regression test
suite. We conduct a case study that evaluates the effectiveness and
applicability of the proposed method.


  The magnitude homology, introduced by R. Hepworth and S. Willerton, offers a
topological invariant that enables the study of graph properties. Hypergraphs,
being a generalization of graphs, serve as popular mathematical models for data
with higher-order structures. In this paper, we focus on describing the
topological characteristics of hypergraphs by considering their magnitude
homology. We begin by examining the distances between hyperedges in a
hypergraph and establish the magnitude homology of hypergraphs. Additionally,
we explore the relationship between the magnitude and the magnitude homology of
hypergraphs. Furthermore, we derive several functorial properties of the
magnitude homology for hypergraphs. Lastly, we present the K\"{u}nneth theorem
for the simple magnitude homology of hypergraphs.


  Representation Learning (RL) plays a pivotal role in the success of many
problems including cyberattack detection. Most of the RL methods for
cyberattack detection are based on the latent vector of Auto-Encoder (AE)
models. An AE transforms raw data into a new latent representation that better
exposes the underlying characteristics of the input data. Thus, it is very
useful for identifying cyberattacks. However, due to the heterogeneity and
sophistication of cyberattacks, the representation of AEs is often
entangled/mixed resulting in the difficulty for downstream attack detection
models. To tackle this problem, we propose a novel mod called Twin Auto-Encoder
(TAE). TAE deterministically transforms the latent representation into a more
distinguishable representation namely the \textit{separable representation} and
the reconstructsuct the separable representation at the output. The output of
TAE called the \textit{reconstruction representation} is input to downstream
models to detect cyberattacks. We extensively evaluate the effectiveness of TAE
using a wide range of bench-marking datasets. Experiment results show the
superior accuracy of TAE over state-of-the-art RL models and well-known machine
learning algorithms. Moreover, TAE also outperforms state-of-the-art models on
some sophisticated and challenging attacks. We then investigate various
characteristics of TAE to further demonstrate its superiority.


  The way the human body is depicted in classical and modern paintings is
relevant for art historical analyses. Each artist has certain themes and
concerns, resulting in different poses being used more heavily than others. In
this paper, we propose a computer vision pipeline to analyse human pose and
representations in paintings, which can be used for specific artists or
periods. Specifically, we combine two pose estimation approaches (OpenPose and
DensePose, respectively) and introduce methods to deal with occlusion and
perspective issues. For normalisation, we map the detected poses and contours
to Leonardo da Vinci's Vitruvian Man, the classical depiction of body
proportions. We propose a visualisation approach for illustrating the
articulation of joints in a set of paintings. Combined with a hierarchical
clustering of poses, our approach reveals common and uncommon poses used by
artists. Our approach improves over purely skeleton based analyses of human
body in paintings.


  In [6], the authors construct a cochain complex
$C\!H^*(\mathcal{Z}_{\mathcal{K}})$ on the cohomology of a moment-angle complex
$\mathcal{Z}_{\mathcal{K}}$ and call the resulting cohomology the double
cohomology, $H\!H^*(\mathcal{Z}_{\mathcal{K}})$. In this paper, we study the
change of rank in double cohomology after gluing an $n$-simplex to a simplicial
complex $\mathcal{K}$ in certain conditions. As an application, we give a
positive answer to an open problem in [6]: For any even integer $r$, there
always exists a simlicial complex $\mathcal{K}$ such that $\operatorname{rank}
H\!H^*(\mathcal{Z}_{\mathcal{K}})=r$.


  The Fermi liquid theory formulated by Landau is a basic paradigm of the
behavior of an interacting many-body system. We present a new application of
this theory to calculate "Landau force" on a macroscopic object. We show that
immersing a pendulum in Fermi liquid can increase its oscillation frequency,
and evidence of this has been observed in mixtures of 3He and 4He.


  We prove that a closed oriented Einstein four-manifold is either
anti-self-dual or (after passing to a double Riemann cover if necessary)
K\"ahler-Einstein, provided that $\lambda_2 \geq -\frac{S}{12}$, where
$\lambda_2$ is the middle eigenvalue of the self-dual Weyl tensor $W^+$ and $S$
is the scalar curvature. The same conclusion holds for closed oriented
four-manifolds with $\delta W^+=0$.


  A recent Monte Carlo study of {\em quenched} QCD showed that the chiral
condensate is non-vanishing above $T_c$ in the phase where the average of the
Polyakov loop $P$ is complex. We show how this is related to the dependence of
the spectrum of the Dirac operator on the boundary conditions in Euclidean
time. We use a random matrix model to calculate the density of small
eigenvalues and the chiral condensate as a function of $\arg P$. The chiral
symmetry is restored in the $\arg P=2\pi/3$ phase at a higher $T$ than in the
$\arg P=0$ phase. In the phase $\arg P = \pi$ of the $SU(2)$ gauge theory the
chiral condensate stays nonzero for all~$T$.


  HI observations of the Virgo Cluster pair NGC 4532/DDO 137, conducted as part
of the Arecibo Legacy Fast ALFA Survey (ALFALFA), reveal an HI feature
extending ~500 kpc to the southwest. The structure has a total mass of up to 7
x 10^8 solar masses, equivalent to 10% of the pair HI mass. Optical R imaging
reveals no counterparts to a level of 26.5 magnitudes per square arcsec. The
structure is likely the result of galaxy harassment.


  In this article we study non-commutative vector sigma model with the most
general \phi^4 interaction on Moyal-Weyl spaces. We compute the 2- and 4-point
functions to all orders in the large N limit and then apply the approximate
Wilson renormalization group recursion formula to study the renormalized
coupling constants of the theory. The non-commutative Wilson-Fisher fixed point
interpolates between the commutative Wilson-Fisher fixed point of the Ising
universality class which is found to lie at zero value of the critical coupling
constant a_* of the zero dimensional reduction of the theory, and a novel
strongly interacting fixed point which lies at infinite value of a_*
corresponding to maximal non-commutativity beyond which the two-sheeted
structure of a_* as a function of the dilation parameter disappears.


  We study an extensive sample of 87 GRBs for which there are well sampled and
simultaneous optical and X-ray light-curves. We extract the cleanest possible
signal of the afterglow component, and compare the temporal behaviors of the
X-ray light-curve, observed by Swift XRT, and optical data, observed by UVOT
and ground-based telescopes for each individual burst. Overall we find 62\%
GRBs that are consistent with the standard afterglow model. When more advanced
modeling is invoked, up to 91\% of the bursts in our sample may be consistent
with the external shock model. A large fraction of these bursts are consistent
with occurring in a constant interstellar density medium (ISM) (61\%) while
only 39\% of them occur in a wind-like medium. Only 9 cases have afterglow
light-curves that exactly match the standard fireball model prediction, having
a single power law decay in both energy bands which are observed during their
entire duration. In particular, for the bursts with chromatic behavior
additional model assumptions must be made over limited segments of the
light-curves in order for these bursts to fully agree with the external shock
model. Interestingly, for 54\% of the X-ray and 40\% of the optical band
observations the end of the shallow decay ($t^{\sim-0.5}$) period coincides
with the jet break ($t^{\sim-p}$) time, causing an abrupt change in decay
slope. The fraction of the burst that consistent with the external shock model
is independent of the observational epochs in the rest frame of GRBs. Moreover,
no cases can be explained by the cooling frequency crossing the X-ray or
optical band.


  The evolution of plasma entropy and the process of plasma energy
re-distribution at the collisionless plasma shock front are evaluated based on
the high temporal resolution data from the four MMS spacecraft during the
crossing of the terrestrial bow shock. The ion distribution function has been
separated into the populations with different characteristic behavior in the
vicinity of the shock: the upstream core population, the reflected ions; the
gyrating ions; the ions trapped in the vicinity of the shock, and the
downstream core population. The values of ion and electron moments (density,
bulk velocity, and temperature) have been determined separately for these
populations. It was shown that the solar wind core population bulk velocity
slows down mainly in the ramp with the electrostatic potential increase but not
in the foot region as it was supposed. The reflected ion population determine
the foot region properties, so that the proton temperature peak in the foot
region is the effect of the relative motion of the different ion populations,
rather than an actual increase in the thermal speed of any of the ion
population. The ion entropy evaluated showed a significant increase across the
shock the enhancement of the ion entropy occurs in the foot of the shock front
and at the ramp, where the reflected ions are emerging in addition to the
upstream solar wind ions, the anisotropy growing to generate the bursts of
ion-scales electrostatic waves. The entropy of electrons across the shock
doesn't show significant change - electron heating goes almost adiabatically.


  Large scale molecular dynamics simulations of freely decaying turbulence in
three-dimensional space are reported. Fluid components are defined from the
microscopic states by eliminating thermal components from the coarse-grained
fields. The energy spectrum of the fluid components is observed to scale
reasonably well according to Kolmogorov scaling determined from the energy
dissipation rate and the viscosity of the fluid, even though the Kolmogorov
length is of the order of the molecular scale.


  Luminous red nova transients, presumably from stellar coalescence, exhibit
long-term precursor emission over hundreds of binary orbits, leading to
impulsive outbursts with durations similar to a single orbital period. In an
effort to understand these signatures, we present and analyze a hydrodynamic
model of unstable mass transfer from a giant-star donor onto a more compact
accretor in a binary system. Our simulation begins with mass transfer at the
Roche limit separation and traces a phase of runaway decay leading up to the
plunge of the accretor within the envelope of the donor. We characterize the
fluxes of mass and angular momentum through the system and show that the
orbital evolution can be reconstructed from measurements of these quantities.
The morphology of outflow from the binary changes significantly as the binary
orbit tightens. At wide separations, a thin stream of relatively high-entropy
gas trails from the outer Lagrange points. As the orbit tightens, the orbital
motion desynchronizes from the donor's rotation, and low-entropy ejecta trace a
broad fan of largely ballistic trajectories. An order-of-magnitude increase in
mass ejection rate accompanies the plunge of the accretor with the envelope of
the donor. We argue that this transition marks the precursor-to-outburst
transition observed in stellar coalescence transients.


  We solve the Landau problem for charged particles on odd-dimensional spheres
$S^{2k-1}$ in the background of constant SO(2k-1) gauge fields carrying the
irreducible representation $\left ( \frac{I}{2}, \frac{I}{2}, \cdots,
\frac{I}{2} \right)$. We determine the spectrum of the Hamiltonian, the
degeneracy of the Landau levels and give the eigenstates in terms of the Wigner
${\cal D}$-functions, and for odd values of $I$ the explicit local form of the
wave functions in the lowest Landau level (LLL). Spectrum of the Dirac operator
on $S^{2k-1}$ in the same gauge field background together with its degeneracies
is also determined and in particular the number of zero modes is found. We show
how the essential differential geometric structure of the Landau problem on the
equatorial $S^{2k-2}$ is captured by constructing the relevant projective
modules. For the Landau problem on $S^5$, we demonstrate an exact
correspondence between the union of Hilbert spaces of LLL's with $I$ ranging
from $0$ to $I_{max} = 2K$ or $I_{max} = 2K+1$ to the Hilbert spaces of the
fuzzy ${\mathbb C}P^3$ or that of winding number $\pm1$ line bundles over
${\mathbb C}P^3$ at level $K$, respectively.


  Understanding the proton spin composition from the quarks and gluons spin
polarization and their motion is important to test various kinds of sum rules
and nonperturbative properties of hadrons. At the Relativistic Heavy Ion
Collider (RHIC), we collide longitudinally polarized proton beams and measure
the double helicity asymmetry $A_{LL}$, which is an important physical quantity
for extracting the polarized parton distribution functions (PDFs) of the
proton. Direct photon, jet and charged pion production are good channels to
probe the gluon spin polarization inside the proton, with the ability to probe
also the sign of the gluon spin. Direct photon production is the theoretically
``cleanest'' channel, with little fragmentation contribution, but limited by
statistics. On the other hand, jet and charged pion production have more
statistics, but include more hard processes and hadronization effects. I will
present the recent measurements of direct photon, jet and charged pion
$A_{LL}$s at PHENIX and show their complementary roles in extracting the gluon
spin.


  In network science, graphs obtained by taking the Kronecker or tensor power
of the adjacency matrix of an initiator graph are used to construct complex
networks. In this paper, we analytically prove sufficient conditions under
which such Kronecker graphs can be searched by a continuous-time quantum walk
in optimal $\Theta(\sqrt{N})$ time. First, if the initiator is regular and its
adjacency matrix has a dominant principal eigenvalue, meaning its unique
largest eigenvalue asymptotically dominates the other eigenvalues in magnitude,
then the Kronecker graphs generated by this initiator can be quantum searched
with probability 1 in $\pi\sqrt{N}/2$ time, asymptotically, and we give the
critical jumping rate of the walk that enables this. Second, for any fixed
initiator that is regular, non-bipartite, and connected, the Kronecker graphs
generated by it are quantum searched in $\Theta(\sqrt{N})$ time. This greatly
extends the number of Kronecker graphs on which quantum walks are known to
optimally search. If the fixed, regular, connected initiator is bipartite,
however, then search on its Kronecker powers is not optimal, but is still
better than classical computer's $O(N)$ runtime if the initiator has more than
two vertices.