  For the generalized oscillator, we prove a Rellich type theorem, or
characterize the order of growth of eigenfunctions. The proofs are given by an
extensive use of commutator arguments invented recently by Ito and Skibsted.
These arguments are simple and elementary and do not employ energy cut-offs or
microlocal analysis.


  The organization of the connectivity between mammalian cortical areas has
become a major subject of study, because of its important role in scaffolding
the macroscopic aspects of animal behavior and intelligence. In this study we
present a computational reconstruction approach to the problem of network
organization, by considering the topological and spatial features of each area
in the primate cerebral cortex as subsidy for the reconstruction of the global
cortical network connectivity. Starting with all areas being disconnected,
pairs of areas with similar sets of features are linked together, in an attempt
to recover the original network structure. Inferring primate cortical
connectivity from the properties of the nodes, remarkably good reconstructions
of the global network organization could be obtained, with the topological
features allowing slightly superior accuracy to the spatial ones. Analogous
reconstruction attempts for the C. elegans neuronal network resulted in
substantially poorer recovery, indicating that cortical area interconnections
are relatively stronger related to the considered topological and spatial
properties than neuronal projections in the nematode. The close relationship
between area-based features and global connectivity may hint on developmental
rules and constraints for cortical networks. Particularly, differences between
the predictions from topological and spatial properties, together with the
poorer recovery resulting from spatial properties, indicate that the
organization of cortical networks is not entirely determined by spatial
constraints.


  In terms of local cohomology, we give an explicit range as to when the
FI-homology of an FI-module attains its regularity.


  The paper studies compactness properties of the affine Sobolev inequality of
Gaoyong Zhang et al in the case $p=2$, and existence and regularity of related
minimizers, in particular, solutions to the nonlocal Dirichlet problems \[
-\sum_{i,j=1}^{N}(A^{-1}[u])_{ij}\frac{\partial^2u}{\partial x_i\partial x_j}=f
\mbox{ in }\Omega\subset\mathbb R^N, \] and \[
-\sum_{i,j=1}^{N}(A^{-1}[u])_{ij}\frac{\partial^2u}{\partial x_i\partial
x_j}=u^{q-1}\,,\quad u>0,\mbox{ in }\Omega\subset\mathbb R^N, \] where
$A_{ij}[u]=\int_\Omega\frac{\partial u}{\partial x_i}\frac{\partial u}{\partial
x_j}\mathrm{d}x$ and $q\in(2,\frac{2N}{N-2})$.


  When do syzygies depend on the characteristic of the field? Even for
well-studied families of examples, very little is known. For a family of random
monomial ideals, namely the Stanley--Reisner ideals of random flag complexes,
we prove that the Betti numbers asymptotically almost always depend on the
characteristic. Using this result, we also develop a heuristic for
characteristic dependence of asymptotic syzygies of algebraic varieties.


  We consider a stabilized finite element method for the Darcy problem on a
surface based on the Masud-Hughes formulation. A special feature of the method
is that the tangential condition of the velocity field is weakly enforced
through the bilinear form and that standard parametric continuous polynomial
spaces on triangulations can be used. We prove optimal order a priori estimates
that take the approximation of the geometry and the solution into account.


  Experimental studies of microdosimetry in therapeutic ion beams have been
performed using several detectors. The differences among them lie on the
shapes, the site sizes, and the material. Coin-shaped solid-state detectors
made of silicon or diamond with thickness varying from 0.3 to 10 microns, as
well as proportional counters with spherical and cylindrical sensitive volumes
filled with tissue-equivalent gas are the microdosimeters used in therapeutic
proton and carbon-ion beams. One goal of microdosimetry in the clinical
environment is providing repeatable specification of the radiation quality of
the radiation field. A methodology should be developed to provide,
independently from the heterogeneous information collected with the different
detectors, a detector-independent specification of the radiation quality.
Historically the specification of the radiation quality is provided either, in
terms of Linear Energy Transfer (LET) or in terms of lineal energy, y. First
this study focuses on identifying the correlation between the distributions of
LET and the lineal energy spectra as well as the correspondence between their
mean values calculated in frequency and in dose. The evaluation is based on the
method of LET analysis described by Kellerer making the adaptation to the
peculiarities of the therapeutic ion-beam where the pristine irradiation is
unidirectional and made of a single type of mono-energetic ions. The second
objective of this study is to interpret the spectrum collected by a slab and
estimate what the spectrum would be if it was collected by a detector different
in shape, material, or size. An example confirms the method starting from the
simulated lineal energy spectrum obtained for carbon ions in a slab detector of
graphite and converting it to the spectruma that would be obtained in the same
radiation field for spherical, cylindrical, and slab detector made of water.


  In this letter, we demonstrate a relation between the boundary curvature
$\kappa$ and the wrinkle wavelength $\lambda$ of a thin suspended film under
boundary confinement. Experiments are done with nanocrystalline diamond films
of thickness $t \approx 184$~nm grown on glass substrates. By removing portions
of the substrate after growth, suspended films with circular boundaries of
radius $R$ ranging from approximately 30 to 811 $\mu$m are made. Due to
residual stresses, the portions of film attached to the substrate are of
compressive prestrain $\epsilon_0 \approx 11 \times 10^{-4}$ and the suspended
portions of film are azimuthally wrinkled at their boundary. We find that
$\lambda$ monotonically decreases with $\kappa$ and present a model predicting
that $\lambda \propto t^{1/2}(\epsilon_0 + \Delta R \kappa)^{-1/4}$, where
$\Delta R$ denotes a penetration depth over which strain relaxes at a boundary.
This relation is in agreement with our experiments and may be adapted to other
systems such as plant leaves. Also, we establish a novel method for measuring
residual compressive strain in thin films.


  In recent years, hydrodynamic optical-field-ionized (HOFI) channels have
emerged as a promising technique to create laser waveguides suitable for
guiding tightly-focused laser pulses in a plasma, as needed for laser-plasma
accelerators. While experimental advances in HOFI channels continue to be made,
the underlying mechanisms and the roles of the main parameters remain largely
unexplored. In this work, we propose a start-to-end simulation pipeline of the
HOFI channel formation and the resulting guiding properties, and use it to
explore the underlying physics and the tunability of HOFI channels. This
approach is benchmarked against experimental measurements. HOFI channels are
shown to feature excellent guiding properties over a wide range of parameters,
making them a promising and tunable waveguide option for laser-plasma
accelerators.


  We describe a new method of constructing transcendental entire functions $A$
such that the differential equation $w"+Aw=0$ has two linearly independent
solutions with relatively few zeros. In particular, we solve a problem of Bank
and Laine by showing that there exist entire functions $A$ of any prescribed
order greater than $1/2$ such that the differential equation has two linearly
independent solutions whose zeros have finite exponent of convergence. We show
that partial results by Bank, Laine, Langley, Rossi and Shen related to this
problem are in fact best possible. We also improve a result of Toda and show
that the resulting estimate is best possible. Our method is based on gluing
solutions of the Schwarzian differential equation $S(F)=2A$ for infinitely many
coefficients $A$.


  Using a large deviations approach we calculate the probability distribution
of the mutual information of MIMO channels in the limit of large antenna
numbers. In contrast to previous methods that only focused at the distribution
close to its mean (thus obtaining an asymptotically Gaussian distribution), we
calculate the full distribution, including its tails which strongly deviate
from the Gaussian behavior near the mean. The resulting distribution
interpolates seamlessly between the Gaussian approximation for rates $R$ close
to the ergodic value of the mutual information and the approach of Zheng and
Tse for large signal to noise ratios $\rho$. This calculation provides us with
a tool to obtain outage probabilities analytically at any point in the $(R,
\rho, N)$ parameter space, as long as the number of antennas $N$ is not too
small. In addition, this method also yields the probability distribution of
eigenvalues constrained in the subspace where the mutual information per
antenna is fixed to $R$ for a given $\rho$. Quite remarkably, this eigenvalue
density is of the form of the Marcenko-Pastur distribution with square-root
singularities, and it depends on the values of $R$ and $\rho$.


  Using an enhanced Self-Organizing Map method, we provided suboptimal
solutions to the Traveling Salesman Problem. Besides, we employed
hyperparameter tuning to identify the most critical features in the algorithm.
All improvements in the benchmark work brought consistent results and may
inspire future efforts to improve this algorithm and apply it to different
problems.


  We investigate the geometric properties displayed by the magnetic patterns
developing on a two-dimensional Ising system, when a diffusive thermal dynamics
is adopted. Such a dynamics is generated by a random walker which diffuses
throughout the sites of the lattice, updating the relevant spins. Since the
walker is biased towards borders between clusters, the border-sites are more
likely to be updated with respect to a non-diffusive dynamics and therefore, we
expect the spin configurations to be affected. In particular, by means of the
box-counting technique, we measure the fractal dimension of magnetic patterns
emerging on the lattice, as the temperature is varied. Interestingly, our
results provide a geometric signature of the phase transition and they also
highlight some non-trivial, quantitative differences between the behaviors
pertaining to the diffusive and non-diffusive dynamics.


  One of the most important practical hallmarks of topological matter is the
presence of topologically protected, exponentially localised edge states at
interfaces of regions characterised by unequal topological invariants. Here, we
show that even when driven far from their equilibrium ground state, Chern
insulators can inherit topological edge features from their parent Hamiltonian.
In particular, we show that the asymptotic long-time approach of the
non-equilibrium steady state, governed by a Lindblad Master equation, can
exhibit edge-selective extremal damping. This phenomenon derives from edge
states of non-Hermitian extensions of the parent Chern insulator Hamiltonian.
The combination of (non-Hermitian) topology and dissipation hence allows to
design topologically robust, spatially localised damping patterns.


  A variety of statistical and machine learning methods are used to model crash
frequency on specific roadways with machine learning methods generally having a
higher prediction accuracy. Recently, heterogeneous ensemble methods (HEM),
including stacking, have emerged as more accurate and robust intelligent
techniques and are often used to solve pattern recognition problems by
providing more reliable and accurate predictions. In this study, we apply one
of the key HEM methods, Stacking, to model crash frequency on five lane
undivided segments (5T) of urban and suburban arterials. The prediction
performance of Stacking is compared with parametric statistical models (Poisson
and negative binomial) and three state of the art machine learning techniques
(Decision tree, random forest, and gradient boosting), each of which is termed
as the base learner. By employing an optimal weight scheme to combine
individual base learners through stacking, the problem of biased predictions in
individual base-learners due to differences in specifications and prediction
accuracies is avoided. Data including crash, traffic, and roadway inventory
were collected and integrated from 2013 to 2017. The data are split into
training, validation, and testing datasets. Estimation results of statistical
models reveal that besides other factors, crashes increase with density (number
per mile) of different types of driveways. Comparison of out-of-sample
predictions of various models confirms the superiority of Stacking over the
alternative methods considered. From a practical standpoint, stacking can
enhance prediction accuracy (compared to using only one base learner with a
particular specification). When applied systemically, stacking can help
identify more appropriate countermeasures.


  The promise of fault-tolerant quantum computing has made topological
superconductors the focus of intense research during the past decade. In this
context, topological Josephson junctions based on nanowires or on topological
insulators provide an alternative route for probing topological
superconductivity. As a hallmark of their topological nature, such junctions
exhibit a ground-state fermion parity that is $4\pi$-periodic in the
superconducting phase difference $\phi$. Finding unambiguous experimental
evidence for this $4\pi$-periodicity still proves a difficult task, however.
Here we propose a topological Josephson heat engine implemented by a
Josephson-Stirling cycle as an alternative thermodynamic approach to test the
ground-state parity. Using a Josephson junction based on a quantum spin Hall
(QSH) insulator, we show how the thermodynamic cycle can be used to test the
$4\pi$-periodicity of the topological ground state and to distinguish between
parity-conserving and non-parity-conserving engines. Interestingly, we find
that parity conservation generally boosts both the efficiency and power of the
topological heat engine with respect to its non-topological counterpart. Our
results, applicable not only to QSH-based junctions but also to any topological
Josephson junction, demonstrate the potential of the intriguing and fruitful
marriage between topology and coherent thermodynamics.


  In light of the grammar given by Ji for the $(\alpha,\beta)$-Eulerian
polynomials introduced by Carlitz and Scoville, we provide a labeling scheme
for increasing binary trees. In this setting, we obtain a combinatorial
interpretation of the $\gamma$-coefficients of the $\alpha$-Eulerian
polynomials in terms of forests of planted 0-1-2-plane trees, which specializes
to a combinatorial interpretation of the $\gamma$-coefficients of the
derangement polynomials in the same vein. By means of a decomposition of an
increasing binary tree into a forest, we find combinatorial interpretations of
the sums involving two identities of Ji, one of which can be viewed as
$(\alpha,\beta)$-extensions of the formulas of Petersen and Stembridge.


  We unify and extend previous bijections on plane quadrangulations to
bipartite and quasibipartite plane maps. Starting from a bipartite plane map
with a distinguished edge and two distinguished corners (in the same face or in
two different faces), we build a new plane map with a distinguished vertex and
two distinguished half-edges directed toward the vertex. The faces of the new
map have the same degree as those of the original map, except at the locations
of the distinguished corners, where each receives an extra degree. The idea
behind this bijection is to build a path from the distinguished elements, slit
the map along it, and sew back after sliding by one unit, thus mildly modifying
the structure of the map at the extremities of the sliding path. This bijection
provides a sampling algorithm for uniform maps with prescribed face degrees and
allow to recover Tutte's famous counting formula for bipartite and
quasibipartite plane maps.
  In addition, we explain how to decompose the previous bijection into two more
elementary ones, which each transfer a degree from one face of the map to
another face. In particular, these transfer bijections are simpler to
manipulate than the previous one and this point of view simplifies the proofs.


  We study the nonperturbative structure of the axial current and evaluate the
two-point light-cone distribution amplitudes (DA) associated with the
correlator \int d\xi
exp(-iq\xi)<0|\bar{\psi}(x)\Gamma\psi(y)J_{\mu}^{5}(\xi)|0> within the
instanton vacuum model in the leading order in O(1/N_c). Due to the built-in
chiral symmetry, four of eight axial DAs are related to that for pions.
Knowledge of these nonperturbative objects is important for phenomenological
study of high-energy neutrino interactions and semileptonic decays of heavy
quarks. We provide a code for evaluation of these DAs and an interpolation
formula valid in the region Q^2 < 1 GeV^2.


  Context: MATISSE, the mid-infrared spectro-imaging instrument of VLTI, was
designed to deliver its advertised performance when paired with an external
second generation fringe tracker. Science observation started in 2019,
demonstrating imaging capabilities and faint science target observations. Now,
The GRAVITY fringe tracker stabilizes the MATISSE fringes which allows using
all spectroscopic modes and improves sensitivity and data accuracy. Aims: We
present how the MATISSE and GRAVITY instruments were adapted to make the
GRAVITY fringe tracker work with MATISSE, under the umbrella of the aptly-named
GRA4MAT project, led by ESO in collaboration with the two instrument consortia.
Methods: We detail the software modifications needed to implement an
acquisition and observing sequence specific to GRA4MAT, including simultaneous
fringe tracking and chopping and a narrow off-axis capability inspired by the
galactic center and exoplanet capability of GRAVITY. We explain the modified
data collection and reduction processes. We show how we leveraged the recent
fringe tracker upgrade to implement features specific to its use with MATISSE,
e.g. fringe jumps mitigation with an improved group delay control and
simultaneous fringe tracking and chopping with a new state machine. Results: We
successfully demonstrate significant improvements to the MATISSE instrument.
Observations can now be performed at higher spectral resolutions of up to
$R\sim3300$ and across the full LM bands at once. Long detector integration
times, made possible with stabilized fringes, have improved the LM-bands
sensitivity by a factor of 10. Low flux biases in coherently-reduced N-band
data have been eliminated. The L-band transfer function is now higher and more
stable. We finally illustrate the scientific potential of GRA4MAT with a
preview of the first exoplanet observation made by MATISSE on $\beta$ Pictoris
b.


  Previous work has highlighted that existing post-hoc explanation methods
exhibit disparities in explanation fidelity (across 'race' and 'gender' as
sensitive attributes), and while a large body of work focuses on mitigating
these issues at the explanation metric level, the role of the data generating
process and black box model in relation to explanation disparities remains
largely unexplored. Accordingly, through both simulations as well as
experiments on a real-world dataset, we specifically assess challenges to
explanation disparities that originate from properties of the data: limited
sample size, covariate shift, concept shift, omitted variable bias, and
challenges based on model properties: inclusion of the sensitive attribute and
appropriate functional form. Through controlled simulation analyses, our study
demonstrates that increased covariate shift, concept shift, and omission of
covariates increase explanation disparities, with the effect pronounced higher
for neural network models that are better able to capture the underlying
functional form in comparison to linear models. We also observe consistent
findings regarding the effect of concept shift and omitted variable bias on
explanation disparities in the Adult income dataset. Overall, results indicate
that disparities in model explanations can also depend on data and model
properties. Based on this systematic investigation, we provide recommendations
for the design of explanation methods that mitigate undesirable disparities.


  The pencil-beam model is valid only when elementary Gaussian beams are small
enough with respect to lateral heterogeneity of a medium, which is not always
the case in heavy charged particle radiotherapy. This work addresses a solution
for this problem by applying our discovery of self-similar nature of Gaussian
distributions. In this method, Gaussian beams split into narrower and
deflecting daughter beams when their size has exceeded the lateral
heterogeneity limit. They will be automatically arranged with modulated areal
density for accurate and efficient dose calculations. The effectiveness was
assessed in an carbon-ion beam experiment in presence of steep range
compensation, where the splitting calculation reproduced the detour effect of
imperfect compensation amounting up to about 10% or as large as the lateral
particle disequilibrium effect. The efficiency was analyzed in calculations for
carbon-ion and proton radiations with a heterogeneous phantom model, where the
splitting calculations took about a minute and were factor of 5 slower than the
non-splitting ones. The beam-splitting method is reasonably accurate,
efficient, and general so that it can be potentially used in various
pencil-beam algorithms.


  After reviewing charge conjugation and the CPT theorem, we define Majorana
fermions and clarify the relationship of Majorana, Weyl, and Dirac fields.
Appearance of Majorana fermions in various scenarios of physics beyond the
Standard Model is discussed, including neutrino masses, baryon asymmetry of the
universe, grand unified theories, and supersymmetry.


  The aim of this paper is to introduce and to give some constructions results
of BiHom-X algebras by using Yau's twisting, Rota Baxter and Some elements of
centroids. Next, we define the bimodules of BiHom-left symmetric dialgebras,
BiHom-associative dialgebras and BiHom-tridendriform algebras. A sequence of
this kind of bimodules can be constructed. Their matched pairs are also
introduced and related relevant properties are given.


  We investigate the barycentric associativity property for functions with
indefinite arities and discuss the more general property of barycentric
preassociativity, a generalization of barycentric associativity which does not
involve any composition of functions. We also provide a generalization of
Kolmogoroff-Nagumo's characterization of the quasi-arithmetic mean functions to
barycentrically preassociative functions.


  This paper is based on our previous work on neural coding. It is a
self-organized model supported by existing evidences. Firstly, we briefly
introduce this model in this paper, and then we explain the neural mechanism of
language and reasoning with it. Moreover, we find that the position of an area
determines its importance. Specifically, language relevant areas are in the
capital position of the cortical kingdom. Therefore they are closely related
with autonomous consciousness and working memories. In essence, language is a
miniature of the real world. Briefly, this paper would like to bridge the gap
between molecule mechanism of neurons and advanced functions such as language
and reasoning.


  This paper, Part I of a series, describes a kinematic framework for the
theory of a Dense Plasma Focus which is very similar to the GV model in spirit
but which differs in its scope in four respects. First, the GV model derives
most of its results from the mathematical properties of the solution of a
certain partial differential equation derived from assumptions that apparently
represent conservation of momentum but are not a rigorous application of the
relevant physics. The present model is based on the scaling properties of the
standard equations of motion, which lead to mathematical results identical with
the GV model. Second, the GV model is purely kinematic in nature. The present
model is also kinematic like the GV model but it incorporates additional
insights borrowed from other physical theories, models and experiments. Third,
the GV model does not take into account the experimentally observed delay
between the start of current and start of plasma propagation and the existence
of a nonzero thickness of the dense plasma sheath. The present model
incorporates both these features in its kinematic structure. Fourth, the unlike
the GV model, the present model allows considerations of some modifications of
standard Mather type geometry. In addition to the current waveform, the
proposed model reproduces the height and radius of the pinch column, the ratio
of pinch density to fill density, the general appearance of the umbrella like
plasma profile and streak picture and formation of bounded 3-dimensional plasma
structures embedded within the pinch plasma without taking into account
microscopic details of physical phenomena


  In recent years, deep models have achieved remarkable success in various
vision tasks. However, their performance heavily relies on large training
datasets. In contrast, humans exhibit hybrid learning, seamlessly integrating
structured knowledge for cross-domain recognition or relying on a smaller
amount of data samples for few-shot learning. Motivated by this human-like
epistemic process, we aim to extend hybrid learning to computer vision tasks by
integrating structured knowledge with data samples for more effective
representation learning. Nevertheless, this extension faces significant
challenges due to the substantial gap between structured knowledge and deep
features learned from data samples, encompassing both dimensions and knowledge
granularity. In this paper, a novel Epistemic Graph Layer (EGLayer) is
introduced to enable hybrid learning, enhancing the exchange of information
between deep features and a structured knowledge graph. Our EGLayer is composed
of three major parts, including a local graph module, a query aggregation
model, and a novel correlation alignment loss function to emulate human
epistemic ability. Serving as a plug-and-play module that can replace the
standard linear classifier, EGLayer significantly improves the performance of
deep models. Extensive experiments demonstrates that EGLayer can greatly
enhance representation learning for the tasks of cross-domain recognition and
few-shot learning, and the visualization of knowledge graphs can aid in model
interpretation.


  This paper concentrates on the time series momentum or contrarian effects in
the Chinese stock market. We evaluate the performance of the time series
momentum strategy applied to major stock indices in mainland China and explore
the relation between the performance of time series momentum strategies and
some firm-specific characteristics. Our findings indicate that there is a time
series momentum effect in the short run and a contrarian effect in the long run
in the Chinese stock market. The performances of the time series momentum and
contrarian strategies are highly dependent on the look-back and holding periods
and firm-specific characteristics.


  We introduce the electron attachment equation-of-motion pair coupled cluster
doubles (EA-EOM-pCCD) ansatz, which allows us to inexpensively compute electron
affinities, energies of unoccupied orbitals, and electron attachment spectra.
We assess the accuracy of EA-EOM-pCCD for a representative data set of organic
molecules for which experimental data is available, as well as the electron
attachment process in uranyl dichloride. EA-EOM-pCCD provides more reliable
energies for the LUMO than its ionization potential EOM counterpart for the
HOMO. The advantage of EA-EOM-pCCD is demonstrated for rylene and rylene
diimide units of different chain lengths, where the differences between
theoretical and experimental EAs approach chemical accuracy.


  This work presents a first study of a radiative calculation for the
gravitational axial anomaly in the massless Abelian Higgs model. The two loop
contribution to the anomalous correlation function of one axial current and two
energy-momentum tensors, <A_alpha(z) T_\mu\nu(y) T_\rho\sigma(x)>, is computed
at an order that involves only internal matter fields. Conformal properties of
massless field theories are used in order to perform the Feynman diagram
calculations in the coordinate space representation. The two loop contribution
is found not to vanish, due to the presence of two independent tensor
structures in the anomalous correlator.


  Dimensionality reduction is an effective method for learning high-dimensional
data, which can provide better understanding of decision boundaries in
human-readable low-dimensional subspace. Linear methods, such as principal
component analysis and linear discriminant analysis, make it possible to
capture the correlation between many variables; however, there is no guarantee
that the correlations that are important in predicting data can be captured.
Moreover, if the decision boundary has strong nonlinearity, the guarantee
becomes increasingly difficult. This problem is exacerbated when the data are
matrices or tensors that represent relationships between variables. We propose
a learning method that searches for a subspace that maximizes the prediction
accuracy while retaining as much of the original data information as possible,
even if the prediction model in the subspace has strong nonlinearity. This
makes it easier to interpret the mechanism of the group of variables behind the
prediction problem that the user wants to know. We show the effectiveness of
our method by applying it to various types of data including matrices and
tensors.


  The existence of two different Cantor sets, one of them contained in the set
of Liouville numbers and the other one inside the set of Diophantine numbers,
is proved. Finally, a necessary and sufficient condition for the existence of a
Cantor set contained in a subset of the real line is given.


  We formulate and prove Serre's equivalence for $\mathbb{Z}$-graded rings.
When restricted to the usual case of $\mathbb{N}$-graded rings, our version of
Serre's equivalence also sharpens the usual one by replacing the condition that
$A$ be generated by $A_1$ over $A_0$ by a more natural condition, which we call
the Cartier condition. For $\mathbb{Z}$-graded rings coming from flips and
flops, this Cartier condition relates more naturally to the geometry of the
flip/flop in question. We also interpret Grothendieck duality as an instance of
Greenlees-May duality for graded rings. These form the basic setting for a
homological study of flips and flops in [Yeu20a, Yeu20b].


  We characterize co-Hopfian finitely generated torsion free nilpotent groups
in terms of their Lie algebra automorphisms, and construct many examples of
such groups.


  Numerical hydrodynamical simulations have proven a successful means of
reproducing many of the statistical properties of the Lyman-Alpha forest as
measured in high redshift quasar spectra. Pseudo-hydrodynamical methods based
only on simulating the dark matter component have been claimed to yield a
comparable level of success. We investigate the degree to which two
pseudo-methods, with and without allowing for a pseudo-gas pressure, are able
to match the predictions of fully hydrodynamical plus dark matter simulations.
We also address the requirements for convergence to the statistics of the
spectra and the inferred properties of the Lyman-Alpha forest as a function of
resolution and box size. Generally we find it is possible to reach agreement
with full hydrodynamic simulations at the 10% level in the cumulative
distributions of the flux and absorption line parameter statistics for readily
achievable particle and grid numbers, but difficult to do much better.


  We introduce DynaMITE-RL, a meta-reinforcement learning (meta-RL) approach to
approximate inference in environments where the latent state evolves at varying
rates. We model episode sessions - parts of the episode where the latent state
is fixed - and propose three key modifications to existing meta-RL methods:
consistency of latent information within sessions, session masking, and prior
latent conditioning. We demonstrate the importance of these modifications in
various domains, ranging from discrete Gridworld environments to
continuous-control and simulated robot assistive tasks, demonstrating that
DynaMITE-RL significantly outperforms state-of-the-art baselines in sample
efficiency and inference returns.


  We generalize the constructions of Eisenbud, Fl{\o}ystad, and Weyman for
equivariant minimal free resolutions over the general linear group, and we
construct equivariant resolutions over the orthogonal and symplectic groups. We
also conjecture and provide some partial results for the existence of an
equivariant analogue of Boij-S\"oderberg decompositions for Betti tables, which
were proven to exist in the non-equivariant setting by Eisenbud and Schreyer.
Many examples are given.


  This paper is a follow-up to (arXiv:2203.03687), in which the first author
studied primitive association schemes lying between a tensor power
$\mathcal{T}_m^d$ of the trivial association scheme and the Hamming scheme
$\mathcal{H}(m,d)$. A question which arose naturally in that study was whether
all primitive fusions of $\mathcal{T}_m^d$ lie between
$\mathcal{T}_{m^e}^{d/e}$ and $\mathcal{H}(m^d, d/e)$ for some $e \mid d$. This
note answers this question positively provided that $m$ is large enough. We
similarly classify primitive fusions of the $d$th tensor power of a Johnson
scheme on $\binom{m}{k}$ points provided $m$ is large enough in terms of $k$
and $d$.


  We examine the utility of multiple channels of communication in wireless
networks under the SINR model of interference. The central question is whether
the use of multiple channels can result in linear speedup, up to some
fundamental limit. We answer this question affirmatively for the data
aggregation problem, perhaps the most fundamental problem in sensor networks.
To achieve this, we form a hierarchical structure of independent interest, and
illustrate its versatility by obtaining a new algorithm with linear speedup for
the node coloring problem.


  Imitation learning holds great promise for addressing the complex task of
autonomous urban driving, as experienced human drivers can navigate highly
challenging scenarios with ease. While behavior cloning is a widely used
imitation learning approach in autonomous driving due to its exemption from
risky online interactions, it suffers from the covariate shift issue. To
address this limitation, we propose a context-conditioned imitation learning
approach that employs a policy to map the context state into the ego vehicle's
future trajectory, rather than relying on the traditional formulation of both
ego and context states to predict the ego action. Additionally, to reduce the
implicit ego information in the coordinate system, we design an ego-perturbed
goal-oriented coordinate system. The origin of this coordinate system is the
ego vehicle's position plus a zero mean Gaussian perturbation, and the x-axis
direction points towards its goal position. Our experiments on the real-world
large-scale Lyft and nuPlan datasets show that our method significantly
outperforms state-of-the-art approaches.


  The local structure of Ba6Ge25 has been studied by x-ray diffraction and the
atomic pair distribution function technique at 40 K and room temperature.
Unambiguous evidence has been found that two out of three types of Ba atoms in
Ba6Ge25 move off their positions and become locked in split sites at low
temperatures.


  We propose a machine learning framework to accelerate numerical computations
of time-dependent ODEs and PDEs. Our method is based on recasting
(generalizations of) existing numerical methods as artificial neural networks,
with a set of trainable parameters. These parameters are determined in an
offline training process by (approximately) minimizing suitable (possibly
non-convex) loss functions by (stochastic) gradient descent methods. The
proposed algorithm is designed to be always consistent with the underlying
differential equation. Numerical experiments involving both linear and
non-linear ODE and PDE model problems demonstrate a significant gain in
computational efficiency over standard numerical methods.


  Aim: To study the multimessenger nature of the signal that can result from
the phase transition of a neutron star to a quark star and their corresponding
astrophysical observations. Methods: The phase transition process is initiated
by the abrupt pressure and density changes at the star center, giving rise to a
shock which deconfines matter followed by a weak front converting excess down
to strange quarks to attain absolute stability. This process's effects are
investigated by understanding how the energy escapes from the star in the form
of neutrino-antineutrino annihilation. For such annihilation process, the
corresponding energy deposition rate is calculated. Structural changes due to
the energy loss have been investigated in the likes of misalignment angle
evolution of the star and its astrophysical observation through gravitational
waves. Results: The energy and time signature for the neutrino-antineutrino
annihilation is compared with the observed isotropic energy for a short
gamma-ray burst. The misalignment angle evolves to align the star's tilt axis,
which can lead to the sudden increase or decrease of radio intensity from the
pulsar. The corresponding gravitational wave emission, both continuous and
burst, all lead towards multimessenger signals coming from the phase
transition.


  As one of the most fundamental physical phenomena, the anomalous Hall effect
(AHE) typically occurs in ferromagnetic materials but is not expected in the
conventional superconductors. Here, we have observed a giant AHE in kagome
superconductor CsV3Sb5 with transition temperature (Tc) of 2.7 K. The anomalous
Hall conductivity reaches up to 2.1*10^4 {\Omega}-1 cm-1 which is larger than
those observed in most of the ferromagnetic metals. Strikingly, the emergence
of AHE exactly follows the higher-temperature charge-density-wave (CDW)
transition with TCDW ~ 94 K, indicating a strong correlation between the CDW
state and AHE. Furthermore, AHE disappears when the CDW transition is
completely suppressed at high pressure. The origin for AHE is attributed to
enhanced skew scattering in CDW state and large Berry curvature arose from the
kagome lattice. These discoveries make CsV3Sb5 as an ideal platform to study
the interplay among nontrivial band topology, CDW and unconventional
superconductivity.


  Integrating human feedback in models can improve the performance of natural
language processing (NLP) models. Feedback can be either explicit (e.g. ranking
used in training language models) or implicit (e.g. using human cognitive
signals in the form of eyetracking). Prior eye tracking and NLP research reveal
that cognitive processes, such as human scanpaths, gleaned from human gaze
patterns aid in the understanding and performance of NLP models. However, the
collection of real eyetracking data for NLP tasks is challenging due to the
requirement of expensive and precise equipment coupled with privacy invasion
issues. To address this challenge, we propose ScanTextGAN, a novel model for
generating human scanpaths over text. We show that ScanTextGAN-generated
scanpaths can approximate meaningful cognitive signals in human gaze patterns.
We include synthetically generated scanpaths in four popular NLP tasks spanning
six different datasets as proof of concept and show that the models augmented
with generated scanpaths improve the performance of all downstream NLP tasks.


  In this paper approximations of three classes of fractional derivatives (FD)
using modified Gauss integration (MGI) and Gauss-Laguerre integration (GLI) are
considered. The main solutions of these fractional derivatives depend on
inverse of Laplace transforms, which are handled by these procedures. In the
modified form of integration the weights and nodes are obtained by means of a
difference equation, which gives a proper approximation form for the inverse of
Laplace transform and hence the fractional derivatives. Theorem is established
to indicate the boundary of the error of the solutions. Numerical examples are
given to illuminate the results of the application of these methods.


  Galois images of polycyclic codes over a finite chain ring $S$ and their
annihilator dual are investigated. The case when a polycyclic codes is
Galois-disjoint over the ring $S,$ is characterized and, the trace codes and
restrictions of free polycyclic codes over $S$ are also determined givind an
analogue of Delsarte theorem among trace map, any S -linear code and its
annihilator dual.


  Let $a,b$ be positive, relatively prime, integers. We prove, using induction,
that for every $d > ab-a-b$ there exist $x,y\in\mathbb{Z}_{\geq 0}$, such that
$d=ax+by$.


  The existence of dark matter particles that carry phenomenologically relevant
self-interaction cross sections mediated by light dark sector states is
considered to be severely constrained through a combination of experimental and
observational data. The conclusion is based on the assumption of specific dark
matter production mechanisms such as thermal freeze-out together with an
extrapolation of a standard cosmological history beyond the epoch of primordial
nucleosynthesis. In this work, we drop these assumptions and examine the
scenario from the perspective of the current firm knowledge we have: results
from direct and indirect dark matter searches and cosmological and
astrophysical observations, without additional assumptions on dark matter
genesis or the thermal state of the very early universe. We show that even in
the minimal set-up, where dark matter particles self-interact via a kinetically
mixed vector mediator, a significant amount of parameter space remains allowed.
Interestingly, however, these parameter regions imply a meta-stable, light
mediator, which in turn calls for modified search strategies.


  Recently, a new approach for solving the three-body problem for (d,p)
reactions in the Coulomb-distorted basis in momentum space was proposed.
Important input quantities for such calculations are the scattering matrix
elements for proton- and neutron-nucleus scattering. We present a
generalization of the Ernst-Shakin-Thaler scheme in which a momentum space
separable representation of proton-nucleus scattering matrix elements can be
calculated in the Coulomb basis. The viability of this method is demonstrated
by comparing S-matrix elements obtained for p$+^{48}$Ca and p$+^{208}$Pb for a
phenomenological optical potential with corresponding coordinate space
calculations.


  In this paper, wall-modeled large-eddy simulation (WMLES) is carried out with
Ffowcs-Williams and Hawkings (FW-H) acoustic analogy to investigate the
turbulent flow and hydrodynamic noise of an axisymmetric body of revolution. We
first develop the numerical model based on high-order schemes and validate it
by benchmark test of the turbulent flow around a circular cylinder at Re=10000.
It demonstrates the capability of the present scheme to capture the primary
flow patterns and the acoustic noise in the far field. Then, we conduct the
numerical simulation for the turbulent flows around the DARPA SUBOFF without
appendages at the Reynolds number of Re=1.2*10^7. The numerical results such as
pressure coefficients and velocity fluctuations, are accurately predicted by
the present model, which shows closer agreement with the experimental data than
available WMLES solutions in the literature. For the parallel midbody of the
hull, the wall pressure fluctuation reveals a low-frequency broadband spectrum
with the majority of signal energy. The surface fluctuating pressure spectrum
scales to the power of Strouhal number at the different locations, which is
consistent with those in the turbulent boundary layer of the plate flows and
airfoils. Moreover, the acoustic signature in the far field is investigated
where the lowest sound pressure level (SPL) occurs in the upstream and
downstream directions while the highest is found in the mid-parallel plane.
SPLs are relatively close in the region of high acoustic pressure at the
transverse plane of x/D=0, which exhibits a maximum difference of 1.2 dB
between locations at different angles. In the vertical plane at z/D=0, the
directivity plot reveals a symmetrical dipole pattern with vertical
fluctuations stronger than the streamwise fluctuations.


  Machine learning (ML) force fields are one of the most common applications of
ML methods in the field of physical and chemical science. In the optimal case,
they are able to reach accuracy close to the first principles methods with
significantly lowered computational cost. However, often the training of the ML
methods rely on full atomic structures alongside their potential energies, and
applying the force information needs special modifications to standard
algorithms. Here we apply distance-based ML methods to predict force norms and
estimate the directions of the force vectors of the thiolate-protected gold
nanoclusters. The method relies only on local structural information without
energy evaluations. We apply the atomic ML forces on the structure optimization
of the gold-thiolate rings, $\text{Au}_{25}(\text{SCH}_{3})_{18}$ nanocluster
and two known structural isomers of the $\text{Au}_{38}(\text{SCH}_{3})_{24}$
nanocluster. The results demonstrate that the method is well-suited for the
structural optimizations of the gold-thiolate systems, where the atomic bonding
has a covalent nature in the ligand shell and at the metal-ligand interface.
The methodology could be seen as an early attempt to introduce equivariant
learning to distance-based ML methods.


  This paper considers the problem of minimizing an expectation function over a
closed convex set, coupled with a {\color{black} functional or expectation}
constraint on either decision variables or problem parameters. We first present
a new stochastic approximation (SA) type algorithm, namely the cooperative SA
(CSA), to handle problems with the constraint on devision variables. We show
that this algorithm exhibits the optimal ${\cal O}(1/\epsilon^2)$ rate of
convergence, in terms of both optimality gap and constraint violation, when the
objective and constraint functions are generally convex, where $\epsilon$
denotes the optimality gap and infeasibility. Moreover, we show that this rate
of convergence can be improved to ${\cal O}(1/\epsilon)$ if the objective and
constraint functions are strongly convex. We then present a variant of CSA,
namely the cooperative stochastic parameter approximation (CSPA) algorithm, to
deal with the situation when the constraint is defined over problem parameters
and show that it exhibits similar optimal rate of convergence to CSA. It is
worth noting that CSA and CSPA are primal methods which do not require the
iterations on the dual space and/or the estimation on the size of the dual
variables. To the best of our knowledge, this is the first time that such
optimal SA methods for solving functional or expectation constrained stochastic
optimization are presented in the literature.


  Outline:
  1. Thermal axions
  2. Axion field evolution
  3. The domain wall problem
  4. Cold axions
  5. Axion miniclusters
  6. Axion isocurvature perturbations


  In this paper, we propose a novel framework for multi-target multi-camera
tracking (MTMCT) of vehicles based on metadata-aided re-identification
(MA-ReID) and the trajectory-based camera link model (TCLM). Given a video
sequence and the corresponding frame-by-frame vehicle detections, we first
address the isolated tracklets issue from single camera tracking (SCT) by the
proposed traffic-aware single-camera tracking (TSCT). Then, after automatically
constructing the TCLM, we solve MTMCT by the MA-ReID. The TCLM is generated
from camera topological configuration to obtain the spatial and temporal
information to improve the performance of MTMCT by reducing the candidate
search of ReID. We also use the temporal attention model to create more
discriminative embeddings of trajectories from each camera to achieve robust
distance measures for vehicle ReID. Moreover, we train a metadata classifier
for MTMCT to obtain the metadata feature, which is concatenated with the
temporal attention based embeddings. Finally, the TCLM and hierarchical
clustering are jointly applied for global ID assignment. The proposed method is
evaluated on the CityFlow dataset, achieving IDF1 76.77%, which outperforms the
state-of-the-art MTMCT methods.


  Amphiphiles are molecules which have both hydrophilic and hydrophobic parts.
In water- and/or oil-like solvent, they self-assemble into extended sheet-like
structures due to the hydrophobic effect. The free energy of an amphiphilic
system can be written as a functional of its interfacial geometry, and phase
diagrams can be calculated by comparing the free energies following from
different geometries. Here we focus on bicontinuous structures, where one
highly convoluted interface spans the whole sample and thereby divides it into
two separate labyrinths. The main models for surfaces of this class are triply
periodic minimal surfaces, their constant mean curvature and parallel surface
companions, and random surfaces. We discuss the geometrical properties of each
of these types of surfaces and how they translate into the experimentally
observed phase behavior of amphiphilic systems.


  We describe the computing tasks involved in autonomous driving, examine
existing autonomous driving computing platform implementations. To enable
autonomous driving, the computing stack needs to simultaneously provide high
performance, low power consumption, and low thermal dissipation, at low cost.
We discuss possible approaches to design computing platforms that will meet
these needs.


  We analyze a market impact game between $n$ risk averse agents who compete
for liquidity in a market impact model with permanent price impact and
additional slippage. Most market parameters, including volatility and drift,
are allowed to vary stochastically. Our first main result characterizes the
Nash equilibrium in terms of a fully coupled system of forward-backward
stochastic differential equations (FBSDEs). Our second main result provides
conditions under which this system of FBSDEs has indeed a unique solution,
which in turn yields the unique Nash equilibrium. We furthermore obtain
closed-form solutions in special situations and analyze them numerically


  This study proposes a multi-field asymptotic homogenization for the analysis
of thermo-piezoelectric materials with periodic microstructures. The effect of
the microstructural heterogeneity is taken into account by means of periodic
perturbation functions, which derive from the solution of non homogeneous
recursive cell problems defined over the unit periodic cell. A strong coupling
is present between the micro displacement field and the micro electric
potential field, since the mechanical and the electric problems are fully
coupled in the asymptotically expanded microscale field equations. The micro
displacement, the electric potential, and the relative temperature fields have
been related to the macroscopic quantities and to their gradients in the
derived down-scaling relations. Average field equations of infinite order have
been obtained and the closed form of the overall constitutive tensors has been
determined for the equivalent first-order homogenized continuum. A formal
solution of such equations has been derived by means of an asymptotic expansion
of the macro fields. The accuracy of the proposed formulation is assessed in
relation to illustrative examples of a bi-material periodic microstructure
subjected to harmonic body forces, free charge densities, and heat sources,
whose periodicity is much greater than the characteristic microstructural size.
The good agreement obtained between the solution of the homogenized model and
the finite element solution of the original heterogeneous material problem
confirms the validity of the proposed formulation.


  We present the first results from a near-IR spectroscopic campaign of the
Cl1604 supercluster at z~0.9 and the cluster RX J1821.6+6827 at z~0.82 to
investigate the nature of [OII] 3727A emission in cluster galaxies at high
redshift. Of the 401 members in the two systems, 131 galaxies have detectable
[OII] emission with no other signs of current star-formation, as well as strong
absorption features indicative of a well-established older stellar population.
The combination of these features suggests that the primary source of [OII]
emission in these galaxies is not the result of star-formation, but rather due
to the presence of a LINER or Seyfert component. Using the NIRSPEC spectrograph
on the Keck II 10-m telescope, 19 such galaxies were targeted, as well as six
additional [OII]-emitting cluster members that exhibited other signs of ongoing
star-formation. Nearly half (~47%) of the 19 [OII]-emitting, absorption-line
dominated galaxies exhibit [OII] to Ha equivalent width ratios higher than
unity, the typical value for star-forming galaxies. A majority (~68%) of these
19 galaxies are classified as LINER/Seyfert based on the emission-line ratio of
[NII] and Ha, increasing to ~85% for red [OII]-emitting, absorption-line
dominated galaxies. The LINER/Seyfert galaxies exhibit L([OII])/L(Ha) ratios
significantly higher than that observed in populations of star-forming
galaxies, suggesting that [OII] is a poor indicator of star-formation in a
large fraction of high-redshift cluster members. We estimate that at least ~20%
of galaxies in high-redshift clusters contain a LINER/Seyfert component that
can be revealed with line ratios. We also investigate the effect this
population has on the star formation rate of cluster galaxies and the
post-starburst fraction, concluding that LINER/Seyferts must be accounted for
if these quantities are to be meaningful.


  Ischaemic stroke is a medical condition caused by occlusion of blood supply
to the brain tissue thus forming a lesion. A lesion is zoned into a core
associated with irreversible necrosis typically located at the center of the
lesion, while reversible hypoxic changes in the outer regions of the lesion are
termed as the penumbra. Early estimation of core and penumbra in ischaemic
stroke is crucial for timely intervention with thrombolytic therapy to reverse
the damage and restore normalcy. Multisequence magnetic resonance imaging (MRI)
is commonly employed for clinical diagnosis. However, a sequence singly has not
been found to be sufficiently able to differentiate between core and penumbra,
while a combination of sequences is required to determine the extent of the
damage. The challenge, however, is that with an increase in the number of
sequences, it cognitively taxes the clinician to discover symptomatic
biomarkers in these images. In this paper, we present a data-driven fully
automated method for estimation of core and penumbra in ischaemic lesions using
diffusion-weighted imaging (DWI) and perfusion-weighted imaging (PWI) sequence
maps of MRI. The method employs recent developments in convolutional neural
networks (CNN) for semantic segmentation in medical images. In the absence of
availability of a large amount of labeled data, the CNN is trained using an
adversarial approach employing cross-entropy as a segmentation loss along with
losses aggregated from three discriminators of which two employ relativistic
visual Turing test. This method is experimentally validated on the ISLES-2015
dataset through three-fold cross-validation to obtain with an average Dice
score of 0.82 and 0.73 for segmentation of penumbra and core respectively.


  Let G be an edge weighted undirected graph. For every pair of nodes consider
the shortest cycle containing these nodes in G. The cycle diameter of G is the
maximum length of a cycle in this set. Let H be a directed graph obtained by
directing the edges of G. The cycle diameter of H is similarly defined except
for that cycles are replaced by directed closed walks. Is there always an
orientation H of G whose cycle diameter is bounded by a constant times the
cycle diameter of G? We prove this property for planar graphs. These results
have implications on the problem of approximating an orientation with minimum
diameter


  In a previous paper, we have shown that any Boolean formula can be encoded as
a linear programming problem in the framework of Bayesian probability theory.
When applied to NP-complete algorithms, this leads to the fundamental
conclusion that P = NP. Now, we implement this concept in elementary arithmetic
and especially in multiplication. This provides a polynomial time deterministic
factoring algorithm, while no such algorithm is known to day. This result
clearly appeals for a revaluation of the current cryptosystems. The Bayesian
arithmetic environment can also be regarded as a toy model for quantum
mechanics.


  The success of an open source software (OSS) project requires effective
communication among its members. Given that OSS projects often have established
social status systems, much communication may happen between individuals of
different statuses, particularly, elite developers who have project management
privileges and ordinary project contributors. Since sociolinguistics literature
and our prior work have found that groups in different status would be likely
develop different language styles, which may hinder critical cross status
communication, and hereby influence the outcomes of the project. We seek to
develop an understanding of cross status communication, as well as its impacts
on the outcomes of an OSS project in terms of productivity and quality. The
anticipated results describe the linguistic similarities and differences of
cross status communication and reveal the relationships between these
linguistic similarities and differences and project outcomes.


  We describe the early results of an investigation into the spectral
characteristics of the hottest Am stars (A0 - A2) in an attempt to link the
HgMn and Am classes of chemical peculiarity. A limited sample of hot-Am stars
was searched for the presence of lines from the very heavy elements platinum
and mercury, as well as a search for lines from the rare-earth elements in HgMn
stars. Our analysis of the strong optical platinum and mercury lines in the
spectrum of the HgMn star HR 7775 has detected isotopic shifts that are
different from those found at ultraviolet wavelengths and, in the case of
mercury, vary with ionization stage.


  Let $W$ be a binary-input memoryless symmetric (BMS) channel with Shannon
capacity $I(W)$ and fix any $\alpha > 0$. We construct, for any sufficiently
small $\delta > 0$, binary linear codes of block length
$O(1/\delta^{2+\alpha})$ and rate $I(W)-\delta$ that enable reliable
communication on $W$ with quasi-linear time encoding and decoding. Shannon's
noisy coding theorem established the \emph{existence} of such codes (without
efficient constructions or decoding) with block length $O(1/\delta^2)$. This
quadratic dependence on the gap $\delta$ to capacity is known to be best
possible. Our result thus yields a constructive version of Shannon's theorem
with near-optimal convergence to capacity as a function of the block length.
This resolves a central theoretical challenge associated with the attainment of
Shannon capacity. Previously such a result was only known for the erasure
channel.
  Our codes are a variant of Ar{\i}kan's polar codes based on multiple
carefully constructed local kernels, one for each intermediate channel that
arises in the decoding. A crucial ingredient in the analysis is a strong
converse of the noisy coding theorem when communicating using random linear
codes on arbitrary BMS channels. Our converse theorem shows extreme
unpredictability of even a single message bit for random coding at rates
slightly above capacity.


  We propose a microscopic theory of interaction of long wave molecular phonons
with electrons in fullerides in the presence of disorder. Phonon relaxation
rate and frequency renormalization are discussed. Finite electronic bandwidth
reduces phonon relaxation rate at $q=0$. Electron-phonon coupling constants
with molecular modes in fullerides are estimated. The results are in good
agreement with photoemission experiments.


  In the present study, the information entropy for smoluchowski coagulation
equation is proposed based on the statistical physics. and the normalized
particle size distribution is a log-normal function at equilibrium from the
principle of maximum entropy and moment constraint. the parameters in the
particle size distribution are determined as simple constants, the result
reveals that the assumption that algebraic mean volume be unit in
self-preserving hypothesis is reasonable. based on the present definition of
the information entropy, the cercignani conjecture holds naturally for
smoluchowski coagulation equation. Together with the fact that the conjecture
is also true for Boltzmann equation, cercignani conjecture holds for any
two-body collision systems, which will benefit the understanding of Brownian
motion and molecule kinematic theory, such as the stability of the dissipative
system, and the mathematical theory of convergence to thermodynamic
equilibrium.


  We notice that the class of nontrivial groups without proper subgroups of
finite index is not elementary, because some groups in this class, such as
$\mathbb Q*\mathbb Q$, have ultrapowers that map homomorphically onto $\mathbb
Z/p\mathbb Z$ for every prime $p$. Also, some ultrapowers of certain simple
groups map homomorphically onto $\mathbb Z/2\mathbb Z$.


  We investigate theoretically the morphology of a thin nematic film adsorbed
at flat substrate patterned by stripes with alternating aligning properties,
normal and tangential respectively. We construct a simple "exactly-solvable"
effective interfacial model where the liquid crystal distortions are accounted
for via an effective interface potential. We find that chemically patterned
substrates can strongly deform the nematic-air interface. The amplitude of this
substrate-induced undulations increases with decreasing average film thickness
and with increasing surface pattern pitch. We find a regime where the
interfacial deformation may be described in terms of a material-independent
universal scaling function. Surprisingly, the predictions of the effective
interfacial model agree semi-quantitatively with the results of the numerical
solution of a full model based on the Landau-de Gennes theory coupled to a
square-gradient phase field free energy functional for a two phase system.


  The definiteness of bulk electrostatic potentials in solids under periodic
boundary conditions defined in an invariant manner has been proved in the
general case of triclinic symmetry. Some principal consequences following from
the universal potential correction arising are discussed briefly.


  We study a large class of models with an arbitrary (finite) number of degrees
of freedom, described by Hamiltonians which are polynomial in bosonic creation
and annihilation operators, and including as particular cases n-th harmonic
generation and photon cascades. For each model, we construct a complete set of
commuting integrals of motion of the Hamiltonian, fully characterize the common
eigenspaces of the integrals of motion, and show that the action of the
Hamiltonian in these common eigenspaces can be represented by a quasi-exactly
solvable reduced Hamiltonian, whose expression in terms of the usual generators
of sl(2) is computed explicitly.


  The original ALHAMBRA catalogue contained over 400,000 galaxies selected
using a synthetic F814W image, to the magnitude limit AB(F814W)$\approx$24.5.
Given the photometric redshift depth of the ALHAMBRA multiband data (<z>=0.86)
and the approximately $I$-band selection, there is a noticeable bias against
red objects at moderate redshift. We avoid this bias by creating a new
catalogue selected in the $K_s$ band. This newly obtained catalogue is
certainly shallower in terms of apparent magnitude, but deeper in terms of
redshift, with a significant population of red objects at $z>1$. We select
objects using the $K_s$ band images, which reach an approximate AB magnitude
limit $K_s \approx 22$. We generate masks and derive completeness functions to
characterize the sample. We have tested the quality of the photometry and
photometric redshifts using both internal and external checks. Our final
catalogue includes $\approx 95,000$ sources down to $K_s \approx 22$, with a
significant tail towards high redshift. We have checked that there is a large
sample of objects with spectral energy distributions that correspond to that of
massive, passively evolving galaxies at $z > 1$, reaching as far as $z \approx
2.5$. We have tested the possibility of combining our data with deep infrared
observations at longer wavelengths, particularly Spitzer IRAC data.


  A conjecture of Khang Tran [6] claims that for an arbitrary pair of
polynomials $A(z)$ and $B(z)$, every zero of every polynomial in the sequence
$\{P_n(z)\}_{n=1}^\infty$ satisfying the three-term recurrence relation of
length $k$ $$P_n(z)+B(z)P_{n-1}(z)+A(z)P_{n-k}(z)=0 $$ with the standard
initial conditions $P_0(z)=1$, $P_{-1}(z)=\dots=P_{-k+1}(z)=0$ which is not a
zero of $A(z)$ lies on the real (semi)-algebraic curve $\mathcal C \subset
\mathbb {C}$ given by $$\Im \left(\frac{B^k(z)}{A(z)}\right)=0\quad {\rm
and}\quad 0\le (-1)^k\Re \left(\frac{B^k(z)}{A(z)}\right)\le
\frac{k^k}{(k-1)^{k-1}}.$$ In this short note, we show that for the recurrence
relation (generalizing the latter recurrence of Tran) given by
$$P_n(z)+B(z)P_{n-\ell}(z)+A(z)P_{n-k}(z)=0, $$
  with coprime $k$ and $\ell$ and the same standard initial conditions as
above, every root of $P_n(z)$ which is not a zero of $A(z)B(z)$ belongs to the
real algebraic curve $\mathcal C_{\ell,k}$ given by $$\Im
\left(\frac{B^k(z)}{A^\ell(z)}\right)=0.$$


  In this paper, we report on the construction of a deep Artificial Neural
Network (ANN) to localize simulated gravitational wave signals in the sky with
high accuracy. We have modelled the sky as a sphere and have considered cases
where the sphere is divided into 18, 50, 128, 1024, 2048 and 4096 sectors. The
sky direction of the gravitational wave source is estimated by classifying the
signal into one of these sectors based on it's right ascension and declination
values for each of these cases. In order to do this, we have injected simulated
binary black hole gravitational wave signals of component masses sampled
uniformly between 30-80 solar mass into Gaussian noise and used the whitened
strain values to obtain the input features for training our ANN. We input
features such as the delays in arrival times, phase differences and amplitude
ratios at each of the three detectors Hanford, Livingston and Virgo, from the
raw time-domain strain values as well as from analytical versions of these
signals, obtained through Hilbert transformation. We show that our model is
able to classify gravitational wave samples, not used in the training process,
into their correct sectors with very high accuracy (>90%) for coarse angular
resolution using 18, 50 and 128 sectors. We also test our localization on test
samples with injection parameters of the published LIGO binary black hole
merger events GW150914, GW170818 and GW170823 for 1024, 2048 and 4096 sectors
and compare the result with that from BAYESTAR and Parameter Estimation (PE).
In addition, we report that the time taken by our model to localize one GW
signal is around 0.018 secs on 14 Intel Xeon CPU cores.


  The emergent spectra of close-in, giant exoplanets ("hot Jupiters") are
expected to be distinct from those of self-luminous objects with similar
effective temperatures because hot Jupiters are primarily heated from above by
their host stars rather than internally from the release of energy from their
formation. Theoretical models predict a continuum of dayside spectra for hot
Jupiters as a function of irradiation level, with the coolest planets having
absorption features in their spectra, intermediate-temperature planets having
emission features due to thermal inversions, and the hottest planets having
blackbody-like spectra due to molecular dissociation and continuum opacity from
the H- ion. Absorption and emission features have been detected in the spectra
of a number of individual hot Jupiters, and population-level trends have been
observed in photometric measurements. However, there has been no unified,
population-level study of the thermal emission spectra of hot Jupiters such as
has been done for cooler brown dwarfs and transmission spectra of hot Jupiters.
Here we show that hot Jupiter secondary eclipse spectra centered around a water
absorption band at 1.4 microns follow a common trend in water feature strength
with temperature. The observed trend is broadly consistent with model
predictions for how the thermal structures of solar-composition planets vary
with irradiation level. Nevertheless, the ensemble of planets exhibits some
degree of scatter around the mean trend for solar composition planets. The
spread can be accounted for if the planets have modest variations in
metallicity and/or elemental abundance ratios, which is expected from planet
formation models. (abridged abstract)


  The human brain is the most complex object of study we encounter today.
Mapping the neuronal-level connections between the more than 80 billion neurons
in the brain is a hopeless task for science. By the recent advancement of
magnetic resonance imaging (MRI), we are able to map the macroscopic
connections between about 1000 brain areas. The MRI data acquisition and the
subsequent algorithmic workflow contain several complex steps, where errors can
occur. In the present contribution, we describe and publish 1064 human
connectomes, computed from the public release of the Human Connectome Project.
Each connectome is available in 5 resolutions, with 83, 129, 234, 463, and 1015
anatomically labeled nodes. For error correction, we follow an averaging and
extreme value deleting strategy for each edge and for each connectome. The
resulting 5320 braingraphs can be downloaded from the
\url{https://braingraph.org} site. This dataset makes possible the access to
these graphs for scientists unfamiliar with neuroimaging- and
connectome-related tools: mathematicians, physicists, and engineers can use
their expertize and ideas in the analysis of the connections of the human
brain. Brain scientists also have a robust and large, multi-resolution set for
connectomical studies.


  Asteroseismology of 1.0-2.0 Msun red giants by the Kepler satellite has
enabled the first definitive measurements of interior rotation in both first
ascent red giant branch (RGB) stars and those on the Helium burning clump. The
inferred rotation rates are 10-30 days for the ~0.2Msun He degenerate cores on
the RGB and 30-100 days for the He burning core in a clump star. Using the MESA
code we calculate state-of-the-art stellar evolution models of low mass
rotating stars from the zero-age main sequence to the cooling white dwarf (WD)
stage. We include transport of angular momentum due to rotationally induced
instabilities and circulations, as well as magnetic fields in radiative zones
(generated by the Tayler-Spruit dynamo). We find that all models fail to
predict core rotation as slow as observed on the RGB and during core He
burning, implying that an unmodeled angular momentum transport process must be
operating on the early RGB of low mass stars. Later evolution of the star from
the He burning clump to the cooling WD phase appears to be at nearly constant
core angular momentum. We also incorporate the adiabatic pulsation code,
ADIPLS, to explicitly highlight this shortfall when applied to a specific
Kepler asteroseismic target, KIC8366239. The MESA inlist adopted to calculate
the models in this paper can be found at \url{https://authorea.com/1608/}
(bottom of the document).


  We present results of temperature resolved scattering studies of a liquid
crystalline block copolymer undergoing an order-disorder transition (ODT) in
the presence of magnetic fields and time-resolved measurements during
isothermal field annealing at sub-ODT temperatures. In each case, field
interactions produced strongly textured mesophases with the cylindrical
microdomains aligned parallel to the field. We find there is no measurable
field-induced shift in the ODT temperature ($T_{ODT}$) which suggests that
selective melting does not play a role in mesophase alignment during isothermal
experiments. Our data indicate instead that sub-ODT alignment occurs by slow,
large scale grain rotation whereas alignment during cooling from the disordered
melt is rapid and driven by the nucleation of weakly ordered but preferentially
aligned material. We identify an optimum sub-cooling that maximizes alignment
during isothermal field annealing. This is corroborated by a simple model
incorporating the competing effects of an exponentially decreasing mobility and
divergent, increasing magnetic anisotropy on cooling below $T_{ODT}$. The
absence of measurable field-effects on $T_{ODT}$ is consistent with rough
estimates derived from the relative magnitudes of the free energy due to field
interaction and the enthalpy of the isotropic-LC transition.


  In this paper we present a data-adaptive estimation procedure for estimation
of average treatment effects in a time-to-event setting based on generalized
random forests. In these kinds of settings, the definition of causal effect
parameters are complicated by competing risks; here we distinguish between
treatment effects on the crude and the net probabilities, respectively. To
handle right-censoring, and to switch between crude and net probabilities, we
propose a two-step procedure for estimation, applying inverse probability
weighting to construct time-point specific weighted outcomes as input for the
forest. The forest adaptively handles confounding of the treatment assigned by
applying a splitting rule that targets a causal parameter. We demonstrate that
our method is effective for a causal search through a list of treatments to be
ranked according to the magnitude of their effect. We further apply our method
to a dataset from the Danish health registries where it is of interest to
discover drugs with an unexpected protective effect against relapse of severe
depression.


  GPU clouds have become a popular computing platform because of the cost of
owning and maintaining high-performance computing clusters. Many cloud
architectures have also been proposed to ensure a secure execution environment
for guest applications by enforcing strong security policies to isolate the
untrusted hypervisor from the guest virtual machines (VMs). In this paper, we
study the impact of GPU chip's hardware faults on the security of cloud
"trusted" execution environment using Deep Neural Network (DNN) as the
underlying application. We show that transient hardware faults of GPUs can be
generated by exploiting the Dynamic Voltage and Frequency Scaling (DVFS)
technology, and these faults may cause computation errors, but they have
limited impact on the inference accuracy of DNN due to the robustness and
fault-tolerant nature of well-developed DNN models. To take full advantage of
these transient hardware faults, we propose the Lightning attack to locate the
fault injection targets of DNNs and to control the fault injection precision in
terms of timing and position. We conduct experiments on three commodity GPUs to
attack four widely-used DNNs. Experimental results show that the proposed
attack can reduce the inference accuracy of the models by as high as 78.3\% and
64.5\% on average. More importantly, 67.9\% of the targeted attacks have
successfully misled the models to give our desired incorrect inference result.
This demonstrates that the secure isolation on GPU clouds is vulnerable against
transient hardware faults and the computation results may not be trusted.


  Electron lenses are pulsed, magnetically confined electron beams whose
current-density profile is shaped to obtain the desired effect on the
circulating beam in high-energy accelerators. They were used in the Fermilab
Tevatron collider for abort-gap clearing, beam-beam compensation, and halo
scraping. A beam-beam compensation scheme based upon electron lenses is
currently being implemented in the Relativistic Heavy Ion Collider at
Brookhaven National Laboratory. This work is in support of a conceptual design
of hollow electron beam scraper for the Large Hadron Collider. It also applies
to the implementation of nonlinear integrable optics with electron lenses in
the Integrable Optics Test Accelerator at Fermilab. We consider the axial
asymmetries of the electron beam caused by the bends that are used to inject
electrons into the interaction region and to extract them. A distribution of
electron macroparticles is deposited on a discrete grid enclosed in a
conducting pipe. The electrostatic potential and electric fields are calculated
using numerical Poisson solvers. The kicks experienced by the circulating beam
are estimated by integrating the electric fields over straight trajectories.
These kicks are also provided in the form of interpolated analytical symplectic
maps for numerical tracking simulations, which are needed to estimate the
effects of the electron lens imperfections on proton lifetimes, emittance
growth, and dynamic aperture. We outline a general procedure to calculate the
magnitude of the transverse proton kicks, which can then be generalized, if
needed, to include further refinements such as the space-charge evolution of
the electron beam, magnetic fields generated by the electron current, and
longitudinal proton dynamics.


  We investigate the late-time behavior of the massive vector field in the
background of the Schwarzschild and Schwarzschild-de Sitter black holes. For
Schwarzschild black hole, at intermediately late times the massive vector field
is represented by three functions with different decay law $\Psi_{0} \sim
t^{-(\ell + 3/2)} \sin{m t}$, $\Psi_{1} \sim t^{-(\ell + 5/2)} \sin{m t}$,
$\Psi_{2} \sim t^{-(\ell + 1/2)} \sin{m t}$, while at asymptotically late times
the decay law $\Psi \sim t^{-5/6} \sin{(m t)}$ is universal, and does not
depend on the multipole number $\ell$. Together with previous study of massive
scalar and Dirac fields where the same asymptotically late-time decay law was
found, it means, that the asymptotically late-time decay law $\sim t^{-5/6}
\sin{(m t)}$ \emph{does not depend} also \emph{on the spin} of the field under
consideration. For Schwarzschild-de Sitter black holes it is observed two
different regimes in the late-time decay of perturbations: non-oscillatory
exponential damping for small values of $m$ and oscillatory quasinormal mode
decay for high enough $m$. Numerical and analytical results are found for these
quasinormal frequencies.


  Predictive simulations are essential for applications ranging from weather
forecasting to material design. The veracity of these simulations hinges on
their capacity to capture the effective system dynamics. Massively parallel
simulations predict the systems dynamics by resolving all spatiotemporal
scales, often at a cost that prevents experimentation. On the other hand,
reduced order models are fast but often limited by the linearization of the
system dynamics and the adopted heuristic closures. We propose a novel
systematic framework that bridges large scale simulations and reduced order
models to extract and forecast adaptively the effective dynamics (AdaLED) of
multiscale systems. AdaLED employs an autoencoder to identify reduced-order
representations of the system dynamics and an ensemble of probabilistic
recurrent neural networks (RNNs) as the latent time-stepper. The framework
alternates between the computational solver and the surrogate, accelerating
learned dynamics while leaving yet-to-be-learned dynamics regimes to the
original solver. AdaLED continuously adapts the surrogate to the new dynamics
through online training. The transitions between the surrogate and the
computational solver are determined by monitoring the prediction accuracy and
uncertainty of the surrogate. The effectiveness of AdaLED is demonstrated on
three different systems - a Van der Pol oscillator, a 2D reaction-diffusion
equation, and a 2D Navier-Stokes flow past a cylinder for varying Reynolds
numbers (400 up to 1200), showcasing its ability to learn effective dynamics
online, detect unseen dynamics regimes, and provide net speed-ups. To the best
of our knowledge, AdaLED is the first framework that couples a surrogate model
with a computational solver to achieve online adaptive learning of effective
dynamics. It constitutes a potent tool for applications requiring many
expensive simulations.


  We analyze the production cross sections and isotopic distributions of
projectile-like residues in the reactions $^{112}$Sn + $^{112}$Sn and
$^{124}$Sn + $^{124}$Sn at an incident beam energy of 1 GeV/nucleon measured
with the FRS fragment separator at the GSI laboratory. Calculations within the
statistical multifragmentation model (SMM) for an ensemble of excited sources
were performed with ensemble parameters determined previously for similar
reactions at 600 MeV/nucleon. The obtained good agreement with the experiment
establishes the universal properties of the excited spectator systems produced
during the dynamical stage of the reaction. It is furthermore confirmed that a
significant reduction of the symmetry-energy term at the freeze-out stage of
reduced density and high temperature is necessary to reproduce the experimental
isotope distributions. A trend of decreasing symmetry energy for large
neutron-rich fragments of low excitation energy is interpreted as a
nuclear-structure effect.


  This article emphasizes that NLP as a science seeks to make inferences about
the performance effects that result from applying one method (compared to
another method) in the processing of natural language. Yet NLP research in
practice usually does not achieve this goal: In NLP research articles,
typically only a few models are compared. Each model results from a specific
procedural pipeline (here named processing system) that is composed of a
specific collection of methods that are used in preprocessing, pretraining,
hyperparameter tuning, and training on the target task. To make generalizing
inferences about the performance effect that is caused by applying some method
A vs. another method B, it is not sufficient to compare a few specific models
that are produced by a few specific (probably incomparable) processing systems.
Rather, the following procedure would allow drawing inferences about methods'
performance effects: (1) A population of processing systems that researchers
seek to infer to has to be defined. (2) A random sample of processing systems
from this population is drawn. (The drawn processing systems in the sample will
vary with regard to the methods they apply along their procedural pipelines and
also will vary regarding the compositions of their training and test data sets
used for training and evaluation.) (3) Each processing system is applied once
with method A and once with method B. (4) Based on the sample of applied
processing systems, the expected generalization errors of method A and method B
are approximated. (5) The difference between the expected generalization errors
of method A and method B is the estimated average treatment effect due to
applying method A compared to method B in the population of processing systems.


  Real-world applications of computing can be extremely time-sensitive. It
would be valuable if we could accelerate such tasks by performing some of the
work ahead of time. Motivated by this, we propose a cost model for quantum
algorithms that allows quantum precomputation, i.e., for a polynomial amount of
"free" computation before the input to an algorithm is fully specified, and
methods for taking advantage of it. We analyze two families of unitaries that
are asymptotically more efficient to implement in this cost model than in the
standard one. The first example of quantum precomputation, based on density
matrix exponentiation, could offer an exponential advantage under certain
conditions. The second example uses a variant of gate teleportation to achieve
a quadratic advantage when compared with implementing the unitaries directly.
These examples hint that quantum precomputation may offer a new arena in which
to seek quantum advantage.


  Currently there is great interest in the outcomes and astrophysical
implications of mergers of double degenerate binaries. In a commonly adopted
approximation, the components of such binaries are represented by polytropes
with an index n=3/2. We present detailed comparisons of stellar mass-transfer
and merger simulations of polytropic binaries that have been carried out using
two very different numerical algorithms --- a finite-volume "grid" code and a
smoothed-particle hydrodynamics (SPH) code. We find that there is agreement in
both the ultimate outcomes of the evolutions and the intermediate stages if the
initial conditions for each code are chosen to match as closely as possible. We
find that even with closely matching initial setups, the time it takes to reach
a concordant evolution differs between the two codes because the initial depth
of contact cannot be matched exactly. There is a general tendency for SPH to
yield higher mass transfer rates and faster evolution to the final outcome. We
also present comparisons of simulations calculated from two different energy
equations: in one series we assume a polytropic equation of state and in the
other series an ideal gas equation of state. In the latter series of
simulations an atmosphere forms around the accretor which can exchange angular
momentum and cause a more rapid loss of orbital angular momentum. In the
simulations presented here, the effect of the ideal equation of state is to
de-stabilize the binary in both SPH and grid simulations, but the effect is
more pronounced in the grid code.


  MCMC methods are used in Bayesian statistics not only to sample from
posterior distributions but also to estimate expectations. Underlying functions
are most often defined on a continuous state space and can be unbounded. We
consider a regenerative setting and Monte Carlo estimators based on i.i.d.
blocks of a Markov chain trajectory. The main result is an inequality for the
mean square error. We also consider confidence bounds. We first derive the
results in terms of the asymptotic variance and then bound the asymptotic
variance for both uniformly ergodic and geometrically ergodic Markov chains.


  We present a scalable scheme to achieve photon distillation, i.e. the
preparation of a single photon with reduced indistinguishability error out of
multiple imperfect photons, based on multiphoton interference in Fourier
matrices. Our scheme achieves arbitrary error reduction in a single step,
removing the need to concatenate multiple rounds of the protocol. Our scheme
has resource costs linear in the error reduction, and a constant probability of
success for arbitrary error reductions. We find that the scheme both raises the
threshold of error correcting codes in photonic quantum computers, as well as
reduces the resources required to construct a photonic quantum computer, making
it highly promising for implementation in such devices.


  We consider the $W$-pair production for both $e^+e^-$ and hadron colliders in
the context of unparticle physics associated with the scale invariant sector
proposed by Georgi. We have shown that the unparticle contributions are quite
comparable with standard model (SM) specially for low values of non-integral
scaling dimension $ (d_{\cal U}) $ and hence it is worthwhile to explore in
future colliders.


  We have observed 51 high mass star forming cores associated with water masers
at 350 micron. The spectral energy distributions (SEDs) and dust continuum
normalized radial intensity profiles were modeled for 28 sources using a
one-dimensional dust radiative transfer code assuming a power law density
distribution in the envelope n = n_0 (r/r_0)^{-p}. The best fit density power
law exponent, p, ranged from 1.0 to 2.5 with a mean value of p = 1.72. We
determined the dust masses for the modeled cores and found a mean mass of 209
M_{sun}.


  An SO(10) supersymmetric grand unified model proposed earlier leading to the
solar solution involving ``just-so'' vacuum oscillations is reexamined to study
its ability to obtain the other possible solar solutions. It is found that all
four viable solar neutrino oscillation solutions can be achieved in the model
simply by modification of the right-handed Majorana neutrino mass matrix, M_R.
Whereas the small mixing and vacuum solutions are easily obtained with several
texture zeros in M_R, the currently-favored large mixing angle solution
requires a nearly geometric hierarchical form for M_R that leads by the seesaw
formula to a light neutrino mass matrix which has two or three texture zeros.
The form of the matrix which provides the ``fine-tuning'' necessary to achieve
the large mixing angle solution can be understood in terms of Froggatt-Nielsen
diagrams for the Dirac and right-handed Majorana neutrino mass matrices. The
solution fulfils several leptogenesis requirements which in turn can be
responsible for the baryon asymmetry in the universe.


  In these notes, we begin by recalling aspects of the classical theory of
metric Diophantine approximation; such as theorems of Khintchine, Jarn\'{\i}k,
Duffin-Schaeffer and Gallagher. We then describe recent strengthening of
various classical statements as well as recent developments in the area of
Diophantine approximation on manifolds. The latter includes the well
approximable, the badly approximable and the inhomogeneous aspects.


  There are many space subdivision and space partitioning techniques used in
many algorithms to speed up computations. They mostly rely on orthogonal space
subdivision, resp. using hierarchical data structures, e.g. BSP trees,
quadtrees, octrees, kd-trees, bounding volume hierarchies, etc. However in some
applications a non-orthogonal space subdivision can offer new ways for actual
speed up. In the case of convex polygon in E3 a simple Point-in-Polygon test is
of the O(N) complexity and the optimal algorithm is of O(lg N) computational
complexity. In the E3 case, the complexity is O(N) even for the convex
polyhedron as no ordering is defined. New Point-in-Convex Polygon and
Point-in-Convex Polyhedron algorithms are presented based on space subdivision
in the preprocessing stage resulting to O(1) run-time complexity. The presented
approach is simple to implement. Due to the principle of duality, dual
problems, e.g. line-convex polygon, line clipping, can be solved in a
similarly.


  It is shown that a simple closed curve in $\mathbb C^n$ that is a uniform
limit of rectifiable simple closed curves each of which has nontrivial
polynomial hull has itself nontrivial polynomial hull. In case the limit curve
is rectifiable, the hull of the limit is shown to be the limit of the hulls. It
is also shown that every rectifiable simple closed curve in $\mathbb C^n$,
$n\geq 2$, can be approximated in total variation norm by a polynomially
convex, rectifiable simple closed curve that coincides with the original curve
except on an arbitrarily small segment. As a corollary, it is shown that every
rectifiable arc in $\mathbb C^n$, $n\geq 2$, is contained in a polynomially
convex, rectifiable simple closed curve.


  Precise frequency and phase synchronization are among the important aspects
in a coherent distributed phased array antenna system, and are among the most
challenging to achieve for microwave frequencies and above. We propose a high
accuracy distributed Kalman filter (HA-DKF) in which the nodes in the array
perform consensus averaging on their locally shared measurements, the
innovation noise covariances, and the KF-predicted as well as the KF-updated
estimates and error covariances, yielding improved electrical state
synchronization compared to other works in the literature. We evaluate the
algorithm through simulation and show that it converges in fewer iterations and
yields better electrical state synchronization than other algorithms.


  We obtain a generalized Euler-Lagrange differential equation and
transversality optimality conditions for Herglotz-type higher-order variational
problems. Illustrative examples of the new results are given.


  We develop an effective field theory for lattice models, in which the only
non-vanishing diagrams exactly reproduce the topology of the lattice. The
Bethe-Peierls approximation appears naturally as the saddle point
approximation. The corrections to the saddle-point result can be obtained
systematically. We calculate the lowest loop corrections for magnetisation and
correlation function.


  Exponential dichotomy of a strongly continuous cocycle $\bFi$ is proved to be
equivalent to existence of a Ma\~{n}e sequence either for $\bFi$ or for its
adjoint. As a consequence we extend some of the classical results to general
Banach bundles. The dynamical spectrum of a product of two cocycles, one of
which is scalar, is investigated and applied to describe the essential spectrum
of the Euler equation in an arbitrary spacial dimension.


  We propose a thermal scalar equation of motion (EOM) that takes into account
curvature corrections for backgrounds supported by Ramond-Ramond fluxes. This
can be used to obtain the Hagedorn temperature for type II string theory on AdS
and pp-wave backgrounds. For Ramond-Ramond flux supported pp-waves we show that
the proposed thermal scalar EOM reproduces the leading curvature correction in
the Hagedorn temperature equation obtained from the type II string theory
spectrum. Furthermore, we use the thermal scalar EOM to obtain curvature
corrections to the Hagedorn temperature for the AdS$_5 \times S^5$ and AdS$_4
\times \mathbb{C} P^3$ backgrounds. These corrections match with strong
coupling results of the integrable dual field theories, recently obtained by
the Quantum Spectral Curve technique.


  We conducted an eye-tracking user study with 13 participants to investigate
the influence of stimulus-question ordering and question modality on
participants using visual question-answering (VQA) tasks. We examined cognitive
load, task performance, and gaze allocations across five distinct experimental
designs, aiming to identify setups that minimize the cognitive burden on
participants. The collected performance and gaze data were analyzed using
quantitative and qualitative methods. Our results indicate a significant impact
of stimulus-question ordering on cognitive load and task performance, as well
as a noteworthy effect of question modality on task performance. These findings
offer insights for the experimental design of controlled user studies in
visualization research.


  Protecting medical privacy can create obstacles in the analysis and
distribution of healthcare graphs and statistical inferences accompanying them.
We pose a graph simulation model which generates networks using degree and
property augmentation (GRANDPA) and provide a flexible R package that allows
users to create graphs that preserve vertex attribute relationships and
approximating retaining topological properties observed in the original graph
(e.g., community structure). We support our proposed algorithm using a case
study based on Zachary's karate network and a patient-sharing graph generated
from Medicare claims data in 2019. In both cases, we find that community
structure is preserved, and normalized root mean square error between
cumulative distributions of the degrees is low (0.0508 and 0.0514
respectively).


  Thermal fluctuations of nanomagnets driven by spin-polarized currents are
treated via the Landau-Lifshitz-Gilbert equation as generalized to include both
the random thermal noise field and Slonczewski spin-transfer torque terms. The
magnetization reversal time of such a nanomagnet is then evaluated for wide
ranges of damping by using a method which generalizes the solution of the
so-called Kramers turnover problem for mechanical Brownian particles, thereby
bridging the very low damping and intermediate damping Kramers escape rates, to
the analogous magnetic turnover problem. The reversal time is then evaluated
for a nanomagnet with the free energy density given in the standard form of
superimposed easy-plane and in-plane easy-axis anisotropies with the dc bias
field along the easy axis.


  Leveraging massive knowledge from large language models (LLMs), recent
machine learning models show notable successes in general-purpose task solving
in diverse domains such as computer vision and robotics. However, several
significant challenges remain: (i) most of these models rely on 2D images yet
exhibit a limited capacity for 3D input; (ii) these models rarely explore the
tasks inherently defined in 3D world, e.g., 3D grounding, embodied reasoning
and acting. We argue these limitations significantly hinder current models from
performing real-world tasks and approaching general intelligence. To this end,
we introduce LEO, an embodied multi-modal generalist agent that excels in
perceiving, grounding, reasoning, planning, and acting in the 3D world. LEO is
trained with a unified task interface, model architecture, and objective in two
stages: (i) 3D vision-language (VL) alignment and (ii) 3D
vision-language-action (VLA) instruction tuning. We collect large-scale
datasets comprising diverse object-level and scene-level tasks, which require
considerable understanding of and interaction with the 3D world. Moreover, we
meticulously design an LLM-assisted pipeline to produce high-quality 3D VL
data. Through extensive experiments, we demonstrate LEO's remarkable
proficiency across a wide spectrum of tasks, including 3D captioning, question
answering, embodied reasoning, navigation and manipulation. Our ablative
studies and scaling analyses further provide valuable insights for developing
future embodied generalist agents. Code and data are available on project page.