  The dynamics of coupled 2D chaotic maps with time-delay on a scalefree-tree
is studied, with different types of the collective behaviors already been
reported for various values of coupling strength [1]. In this work we focus on
the dynamics' time-evolution at the coupling strength of the stability
threshold and examine the properties of the regularization process. The
time-scales involved in the appearance of the regular state and the periodic
state are determined. We find unexpected regularity in the the system's final
steady state: all the period values turn out to be integer multiples of one
among given numbers. Moreover, the period value distribution follows a
power-law with a slope of -2.24.


  We consider a non-self-adjoint $H$ given as the perturbation of a
self-adjoint operator $H_0$. We suppose that $H$ is of the form $H=H_0+CWC$
where $C$ is a bounded, positive definite and relatively compact with respect
to $H_0$, and $W$ is bounded. We suppose that $C(H_0-z)^{-1}C$ is uniformly
bounded in $z\in\mathbb{C}\setminus\mathbb{R}$. We define the regularized wave
operators associated to $H$ and $H_0$ by
$W_\pm(H,H_0):=\displaystyle\mathbb{s}-\lim_{t\rightarrow\infty} e^{\pm
itH}r_\mp(H)\Pi_\mathrm{p}(H^\star)^\perp e^{\mp itH_0}$ where
$\Pi_\mathrm{p}(H^\star)$ is the projection onto the direct sum of all the
generalized eigenspace associated to eigenvalue of $H^\star$ and $r_\mp$ is a
rational function that regularizes the `incoming/outgoing spectral
singularities' of $H$. We prove the existence and study the properties of the
regularized wave operators. In particular we show that they are asymptotically
complete if $H$ does not have any spectral singularity.


  We consider decays of the lowest-lying positive parity 56-plet and negative
parity bf 70-plet excited baryons. For the 70-plet, we include both
single-quark and two-quark decay operators, and find, somewhat mysteriously,
that the two-quark operators are not phenomenologically important. Studies of
decays 70-plet to Delta(1232) + photon may strengthen or vitiate this
observation. For the 56-plet decays, now using only the single-quark operator,
we can predict many strong decays after fitting parameters on the assumption
that the Roper is a 3q state. Comparison of these predictions to experiment can
verify the structure of the 56-plet. As a sidelight, we show a large N_c
derivation of the old Gursey-Radicati mass formula.


  Human densepose estimation, aiming at establishing dense correspondences
between 2D pixels of human body and 3D human body template, is a key technique
in enabling machines to have an understanding of people in images. It still
poses several challenges due to practical scenarios where real-world scenes are
complex and only partial annotations are available, leading to incompelete or
false estimations. In this work, we present a novel framework to detect the
densepose of multiple people in an image. The proposed method, which we refer
to Knowledge Transfer Network (KTN), tackles two main problems: 1) how to
refine image representation for alleviating incomplete estimations, and 2) how
to reduce false estimation caused by the low-quality training labels (i.e.,
limited annotations and class-imbalance labels). Unlike existing works directly
propagating the pyramidal features of regions for densepose estimation, the KTN
uses a refinement of pyramidal representation, where it simultaneously
maintains feature resolution and suppresses background pixels, and this
strategy results in a substantial increase in accuracy. Moreover, the KTN
enhances the ability of 3D based body parsing with external knowledges, where
it casts 2D based body parsers trained from sufficient annotations as a 3D
based body parser through a structural body knowledge graph. In this way, it
significantly reduces the adverse effects caused by the low-quality
annotations. The effectiveness of KTN is demonstrated by its superior
performance to the state-of-the-art methods on DensePose-COCO dataset.
Extensive ablation studies and experimental results on representative tasks
(e.g., human body segmentation, human part segmentation and keypoints
detection) and two popular densepose estimation pipelines (i.e., RCNN and
fully-convolutional frameworks), further indicate the generalizability of the
proposed method.


  Using the publicly available eROSITA Final Equatorial Depth Survey (eFEDS)
data, we detected the stacked X-ray emissions at the position of 463 filaments
at a significance of 3.8 sigma based on the combination of all energy bands. In
parallel, we found that the probability of the measurement under the null
hypothesis is ~0.0017. The filaments were identified with galaxies in the Sloan
Digital Sky Survey survey, ranging from 30 Mpc to 100 Mpc in length at 0.2 < z
< 0.6. The stacking of the filaments was performed with the eFEDS X-ray
count-rate maps in the energy range between 0.4 - 2.3 keV after masking the
resolved galaxy groups and clusters and the identified X-ray point sources from
the ROSAT, Chandra, XMM-Newton, and eROSITA observations. In addition, diffuse
X-ray foreground and background emissions or any residual contribution were
removed by subtracting the signal in the region between 10 - 20 Mpc from the
filament spines. For the stacked signal, we performed an X-ray spectral
analysis, which indicated that the signal is associated with a thermal
emission. According to a model with the astrophysical plasma emission code for
the plasma emission and with a beta-model gas distribution with beta=2/3, the
detected X-ray signal can be interpreted as emission from hot gas in the
filaments with an average gas temperature of 1.0 (+0.3 -0.2) keV and a gas
overdensity of 21 +- 5 at the center of the filaments.


  In recent years, blazar surveys at radio and X-ray energies have greatly
increased our understanding of this type of active galaxy. The combination of
multi-wavelength data has shown that blazars follow a well defined sequence in
terms of their broad band spectral properties. Together with increasingly
detailed emission models, this information has provided not only tools with
which to identify potential sources of TeV emission but also predictions of
their gamma-ray flux. A list of such candidates has been used in this work to
investigate the best targets for TeV observations. Observations reported here
have resulted in upper limits which do not conflict with the latest model
predictions.


  We use published mid-IR and V-band flux ratios for images A and B of
Q2237+0305 to demonstrate that the size of the mid-IR emission region has a
scale comparable to or larger than the microlens Einstein Radius (ER, ~10^17 cm
for solar mass stars). Q2237+0305 has been monitored extensively in the R and
V-bands for ~15 years. The variability record shows significant microlensing
variability of the optical emission region, and has been used by several
studies to demonstrate that the optical emission region is much smaller than
the ER for solar-mass objects. For the majority of the monitoring history, the
optical flux ratios have differed significantly from those predicted by
macro-models. In contrast, recent observations in mid-IR show flux ratios
similar to those measured in the radio, and to predictions of some lens models,
implying that the mid-IR flux is emitted from a region that is at least 2
orders of magnitude larger than the optical emission region. We have calculated
the likeli-hood of the observed mid-IR flux ratio as a function of mid-IR
source size given the observed V-band flux ratio. The expected flux ratio for a
source having dimensions of ~1 ER is a sensitive function of the macro model
adopted. However we find that the probability of source size given the observed
flux ratios is primarily sensitive to the ratio of the macro-model
magnifications. The majority of published macro models for Q2237+0305 yield a
flux ratio for images B and A of 0.8 - 1.1. By combining probabilities from the
ratios A/B and C/D we infer that the diameter of a circular IR emission region
is >1ER with >95% confidence. For microlensing by low-mass stars, this source
size limit rules out non-thermal processes such as synchrotron as mechanisms
for mid-IR emission.


  We discuss the interplay of wave packet decoherence and decoherence induced
by quantum gravity via interactions with spacetime foam for high energy
astrophysical neutrinos. In this context we point out a compelling consequence
of the expectation that quantum gravity should break global symmetries, namely
that quantum-gravity induced decoherence may not only be the most sensitive
probe for quantum properties of spacetime, but also can provide both a powerful
tool for the search for new particles, including totally decoupled backgrounds
interacting only gravitationally, and at the same time a window into the
intricacies of black hole information processing.


  We study the hedging and valuation of European and American claims on a
non-traded asset $Y$, when a traded stock $S$ is available for hedging, with
$S$ and $Y$ following correlated geometric Brownian motions. This is an
incomplete market, often called a basis risk model. The market agent's risk
preferences are modelled using a so-called forward performance process (forward
utility), which is a time-decreasing utility of exponential type. Moreover, the
market agent (investor) does not know with certainty the values of the asset
price drifts. This market setting with drift parameter uncertainty is the
partial information scenario. We discuss the stochastic control problem
obtained by setting up the hedging portfolio and derive the optimal hedging
strategy. Furthermore, a (dual) forward indifference price representation of
the claim and its PDE are obtained. With these results, the residual risk
process representing the basis risk (hedging error), pay-off decompositions and
asymptotic expansions of the indifference price in the European case are
derived. We develop the analogous stochastic control and stopping problem with
an American claim and obtain the corresponding forward indifference price
valuation formula.


  We consider a network of evolving opinions. It includes multiple individuals
with first-order opinion dynamics defined in continuous time and evolving based
on a general exogenously defined time-varying underlying graph. In such a
network, for an arbitrary fixed initial time, a subset of individuals forms an
eminence grise coalition, abbreviated as EGC, if the individuals in that subset
are capable of leading the entire network to agreeing on any desired opinion,
through a cooperative choice of their own initial opinions. In this endeavor,
the coalition members are assumed to have access to full profile of the
underlying graph of the network as well as the initial opinions of all other
individuals. While the complete coalition of individuals always qualifies as an
EGC, we establish the existence of a minimum size EGC for an arbitrary
time-varying network; also, we develop a non-trivial set of upper and lower
bounds on that size. As a result, we show that, even when the underlying graph
does not guarantee convergence to a global or multiple consensus, a generally
restricted coalition of agents can steer public opinion towards a desired
global consensus without affecting any of the predefined graph interactions,
provided they can cooperatively adjust their own initial opinions. Geometric
insights into the structure of EGC's are given. The results are also extended
to the discrete time case where the relation with Decomposition-Separation
Theorem is also made explicit.


  Robot planning in partially observable domains is difficult, because a robot
needs to estimate the current state and plan actions at the same time. When the
domain includes many objects, reasoning about the objects and their
relationships makes robot planning even more difficult. In this paper, we
develop an algorithm called scene analysis for robot planning (SARP) that
enables robots to reason with visual contextual information toward achieving
long-term goals under uncertainty. SARP constructs scene graphs, a factored
representation of objects and their relations, using images captured from
different positions, and reasons with them to enable context-aware robot
planning under partial observability. Experiments have been conducted using
multiple 3D environments in simulation, and a dataset collected by a real
robot. In comparison to standard robot planning and scene analysis methods, in
a target search domain, SARP improves both efficiency and accuracy in task
completion. Supplementary material can be found at https://tinyurl.com/sarp22


  With increasing availability of high dimensional, multi-source data, the
identification of joint and data specific patterns of variability has become a
subject of interest in many research areas. Several matrix decomposition
methods have been formulated for this purpose, for example JIVE (Joint and
Individual Variation Explained), and its angle based variation, aJIVE. Although
the effect of data contamination on the estimated joint and individual
components has not been considered in the literature, gross errors and outliers
in the data can cause instability in such methods, and lead to incorrect
estimation of joint and individual variance components. We focus on the aJIVE
factorization method and provide a thorough analysis of the effect outliers on
the resulting variation decomposition. After showing that such effect is not
negligible when all data-sources are contaminated, we propose a robust
extension of aJIVE (RaJIVE) that integrates a robust formulation of the
singular value decomposition into the aJIVE approach. The proposed RaJIVE is
shown to provide correct decompositions even in the presence of outliers and
improves the performance of aJIVE. We use extensive simulation studies with
different levels of data contamination to compare the two methods. Finally, we
describe an application of RaJIVE to a multi-omics breast cancer dataset from
The Cancer Genome Atlas. We provide the R package RaJIVE with a ready-to-use
implementation of the methods and documentation of code and examples.


  In this paper, we focus on a typical cooperative communication system with
one pair of source and destination, where a unmanned aerial vehicle (UAV)
flying from a start location to an end location serves as a mobile relay. To
efficiently utilize energy in ambient environment, the UAV's transmission
capability is powered exclusively by radio signal transmitted from the source
via the power-splitting mechanism. In such a cooperative communication system,
we study the end-to-end cooperative throughput maximization problem by
optimizing the UAV's power profile, power-splitting ratio profile and
trajectory for both amplify-and-forward (AF) and decode-and-forward (DF)
protocols. The problem is decomposed into two subproblems: profile optimization
given trajectory and trajectory optimization given profile. The former one is
solved via the dual decomposition with in-depth analysis and the latter one is
solved via successive convex optimization, by which a lower bound is
iteratively maximized. Then the end-to-end cooperative throughput maximization
problem is solved by alternately solving the two subproblems. The numerical
results show that with the proposed optimal solution, choice for the UAV's
power profile and power-splitting ratio profile is more long-sighted than the
greedy strategy from our previous work and the successive optimization is able
to converge in a few rounds of iteration. Moreover, as for the end-to-end
cooperative throughput, the proposed optimal solution outperforms both static
and greedy strategies, especially for the AF protocol.


  The dynamic world model and its linear perturbations were first studied in
Einstein's gravity. In the system without pressure the relativistic equations
coincide exactly with the later known ones in Newton's gravity. Here we prove
that, except for the gravitational wave contribution, even to the second-order
perturbations, equations for the relativistic irrotational zero-pressure fluid
in a flat Friedmann background coincide exactly with the previously known
Newtonian equations. Thus, to the second order, we correctly identify the
relativistic density and velocity perturbation variables, and we expand the
range of applicability of the Newtonian medium without pressure to all
cosmological scales including the super-horizon scale. In the relativistic
analyses, however, we do not have a relativistic variable which corresponds to
the Newtonian potential to the second order. Mixed usage of different gauge
conditions is useful to make such proofs and to examine the result with
perspective. We also present the gravitational wave equation to the second
order. Since our correspondence includes the cosmological constant, our results
are relevant to currently favoured cosmology. Our result has an important
practical implication that one can use the large-scale Newtonian numerical
simulation more reliably even as the simulation scale approaches near horizon.


  In this work we consider the permutational properties of multipartite
entanglement monotones. Based on the fact that genuine multipartite
entanglement is a property of the entire multi-qubit system, we argue that
ideal definitions for its characterizing quantities must be
permutation-invariant. Using this criterion, we examine the three 4-qubit
entanglement monotones introduced by Osterloh and Siewert [Phys. Rev. A. 72,
012337]. By expressing them in terms of quantities whose permutational
properties can be easily derived, we find that one of these monotones is not
permutation-invariant. We propose a permutation-invariant entanglement monotone
to replace it, and show that our new monotone properly measures the genuine
4-qubit entanglement in 4-qubit cluster-class states. Our results provide some
useful insights in understanding multipartite entanglement.


  We describe a set of generators and defining relations for the group of
birational automorphisms of a general 15-nodal quartic surface in the complex
projective 3-dimensional space.


  We pursue the study of the high energy behaviour of the gluon propagator on
the lattice in the Landau gauge in the flavorless case (n_f=0). It was shown in
a precedin g paper that the gluon propagator did not reach three-loop
asymptotic scaling at an energy scale as high as 5 GeV.
  Our present high statistics analysis includes also a simulation at
$\beta=6.8$ ($a\simeq 0.03$ fm), which allows to reach $\mu \simeq 10$ GeV.
Special care has been devoted to the finite lattice-spacing artifacts as well
as to the finite volume effects, the latter being acute at $\beta=6.8$ where
the volume is bounded by technical limits. Our main conclusion is a strong
evidence that the gluon propagator has reached three-loop asymptotic scaling,
at $\mu$ ranging from 5.6 GeV to 9.5 GeV. We buttress up this conclusion on
several demanding criteria of asymptoticity, including scheme independence. Our
fit in the 5.6 GeV to 9.5 GeV window yields $\Lambda^{\bar{{\rm MS}}} =
  319 \pm 14 ^{+10}_{-20}$ MeV, in good agreement with our previous result,
$\Lambda^{\bar{{\rm MS}}} = 295 \pm 20 $ MeV, obtained from the three gluon
vertex, but it is significantly above the Schr\"odinger functional method
estimate : $238 \pm 19$ MeV. The latter difference is not understood.
Confirming our previous paper, we show that a fourth loop is necessary to fit
the whole ($2.8 \div 9.5$) GeV energy window.


  Quantum communication research has in recent years shifted to include
multi-partite networks for which questions of quantum network routing naturally
emerge. To understand the potential for multi-partite routing, we focus on the
most promising architectures for future quantum networks - those connecting
nodes close to each other. Nearest-neighbour networks such as rings, lines, and
grids, have been studied under different communication scenarios to facilitate
the sharing of quantum resources, especially in the presence of bottlenecks. We
here analyze the potential of nearest-neighbour quantum networks and identify
some serious limitations, by demonstrating that rings and lines cannot overcome
common bottleneck communication problems.


  It was proved by Brudno that entropy and Kolmogorov complexity for dynamical
systems are tightly related. We generalize his results to the case of arbitrary
computable amenable group actions. Namely, for an ergodic shift-action, the
asymptotic Kolmogorov complexity of a typical point is equal to the
Kolmogorov-Sinai entropy of the action. For topological shift actions, the
asymptotic Komogorov complexity of every point is bounded from above by the
topological entropy, and there is a point attaining this bound.


  This paper studies the Cauchy problem for three-dimensional viscous,
compressible, and heat conducting magnetohydrodynamic equations with vacuum as
far field density. We prove the global existence and uniqueness of strong
solutions provided that the quantity $\|\rho_0\|_{L^\infty}+\|b_0\|_{L^3}$ is
suitably small and the viscosity coefficients satisfy $3\mu>\lambda$. Here, the
initial velocity and initial temperature could be large. The assumption on the
initial density do not exclude that the initial density may vanish in a subset
of $\mathbb{R}^3$ and that it can be of a nontrivially compact support. Our
result is an extension of the works of Fan and Yu \cite{FY09} and Li et al.
\cite{LXZ13}, where the local strong solutions in three dimensions and the
global strong solutions for isentropic case were obtained, respectively. The
analysis is based on some new mathematical techniques and some new useful
energy estimates. This paper can be viewed as the first result concerning the
global existence of strong solutions with vacuum at infinity in some classes of
large data in higher dimension.


  We present a detailed analysis of the detached eclipsing binary CD Tau. A
large variety of observational data, in form of IR photometry, CORAVEL radial
velocity observations and high-resolution spectra, are combined with the
published light curves to derive accurate absolute dimensions and effective
temperature of the components, as well as the metal abundance of the system. We
obtain: MA=1.442(16) Mo, RA=1.798(17) Ro, TeffA=6200(50) K, MB=1.368(16) Msun,
RB=1.584(20) Run and TeffB=6200(50) K. The metal content of the system is
determined to be [Fe/H]=+0.08(15) dex. In addition, the eclipsing binary has a
K-type close visual companion at about 10-arcsec separation, which is shown to
be physically linked, thus sharing a common origin. The effective temperature
of the visual companion (Teff=5250(200) K) is determined from synthetic
spectrum fitting, and its luminosity (log L/Lo=-0.27(6)), and therefore its
radius (R=0.89(9) Ro), are obtained from comparison with the apparent magnitude
of the eclipsing pair. The observed fundamental properties of the eclipsing
components are compared with the predictions of evolutionary models, and we
obtain good agreement for an age of 2.6 Gyr and a chemical composition of
Z=0.026 and Y=0.26. Furthermore, we test the evolutionary models for solar-mass
stars and we conclude that the physical properties of the visual companion are
very accurately described by the same isochrone that fits the more massive
components.


  We introduce and investigate the orbit-closed $C$-numerical range, a natural
modification of the $C$-numerical range of an operator introduced for $C$
trace-class by Dirr and vom Ende. Our orbit-closed $C$-numerical range is a
conservative modification of theirs because these two sets have the same
closure and even coincide when $C$ is finite rank. Since Dirr and vom Ende's
results concerning the $C$-numerical range depend only on its closure, our
orbit-closed $C$-numerical range inherits these properties, but we also
establish more.
  For $C$ selfadjoint, Dirr and vom Ende were only able to prove that the
closure of their $C$-numerical range is convex, and asked whether it is convex
without taking the closure. We establish the convexity of the orbit-closed
$C$-numerical range for selfadjoint $C$ without taking the closure by providing
a characterization in terms of majorization, unlocking the door to a plethora
of results which generalize properties of the $C$-numerical range known in
finite dimensions or when $C$ has finite rank. Under rather special hypotheses
on the operators, we also show the $C$-numerical range is convex, thereby
providing a partial answer to the question posed by Dirr and vom Ende.


  We study four-derivative corrections to 5d $\mathcal{N}=2$ minimal gauged
supergravity using tools from conformal supergravity. There are two
supersymmetric invariants at the four-derivative order and we show explicitly
how to write down the action in the Poincar\'{e} frame in terms of their
coefficients. We apply our results in the context of holography where the
four-derivative terms in the supergravity action translate into corrections to
the conformal anomalies of the dual 4d $\mathcal{N}=1$ SCFT. We use these
results to study corrections to the entropy of the supersymmetric black string
solutions of minimal supergravity. We also discuss explicit embeddings of the
5d supergravity in string and M-theory and use them to fix the
higher-derivative coefficients in terms of the microscopic parameters.


  Submodular optimization has received significant attention in both practice
and theory, as a wide array of problems in machine learning, auction theory,
and combinatorial optimization have submodular structure. In practice, these
problems often involve large amounts of data, and must be solved in a
distributed way. One popular framework for running such distributed algorithms
is MapReduce. In this paper, we present two simple algorithms for cardinality
constrained submodular optimization in the MapReduce model: the first is a
$(1/2-o(1))$-approximation in 2 MapReduce rounds, and the second is a
$(1-1/e-\epsilon)$-approximation in $\frac{1+o(1)}{\epsilon}$ MapReduce rounds.


  The superscaling observed in inclusive electron scattering is described
within the dilute Fermi gas model with interaction between the particles. The
comparison with the relativistic Fermi gas (RFG) model without interaction
shows an improvement in the explanation of the scaling function $f(\psi ')$ in
the region $\psi ' < -1$, where the RFG result is $f(\psi ') = 0$. It is found
that the behavior of $f(\psi ')$ for $\psi ' < -1$ depends on the particular
form of the general power-law asymptotics of the momentum distribution
$n(k)\sim 1/ k^{4+m}$ at large $k$. The best agreement with the empirical
scaling function is found for $m\simeq 4.5$ in agreement with the asymptotics
of $n(k)$ in the coherent density fluctuation model where $m = 4$. Thus,
superscaling gives information about the asymptotics of $n(k)$ and the NN
forces.


  Laminar flow in devices fabricated from soft materials causes deformation of
the passage geometry, which affects the flow rate--pressure drop relation. For
a given pressure drop, in channels with narrow rectangular cross-section, the
flow rate varies as the cube of the channel height, so deformation can produce
significant quantitative effects, including nonlinear dependence on the
pressure drop [{Gervais, T., El-Ali, J., G\"unther, A. \& Jensen, K.\ F.}\ 2006
Flow-induced deformation of shallow microfluidic channels.\ \textit{Lab Chip}
\textbf{6}, 500--507]. Gervais et. al. proposed a successful model of the
deformation-induced change in the flow rate by heuristically coupling a Hookean
elastic response with the lubrication approximation for Stokes flow. However,
their model contains a fitting parameter that must be found for each channel
shape by performing an experiment. We present a perturbation approach for the
flow rate--pressure drop relation in a shallow deformable microchannel using
the theory of isotropic quasi-static plate bending and the Stokes equations
under a lubrication approximation (specifically, the ratio of the channel's
height to its width and of the channel's height to its length are both assumed
small). Our result contains no free parameters and confirms Gervais et. al.'s
observation that the flow rate is a quartic polynomial of the pressure drop.
The derived flow rate--pressure drop relation compares favorably with
experimental measurements.


  (Abridged) In this paper we present a compilation of results from our most
advanced neutron star merger simulations, including a description of the
employed numerical procedures and a more complete overview over a large number
of computed models. The three-dimensional hydrodynamic simulations were done
with a code based on the Piecewise Parabolic Method with up to five levels of
nested Cartesian grids. The simulations are basically Newtonian, but
gravitational-wave emission and the corresponding back-reaction are taken into
account. The use of a physical nuclear equation of state allows us to follow
the thermodynamic history of the stellar medium and to compute the energy and
lepton number loss due to the emission of neutrinos. The computed models differ
concerning the neutron star masses and mass ratios, the neutron star spins, the
numerical resolution expressed by the cell size of the finest grid and the
number of grid levels, and the calculation of the temperature from the solution
of the entropy equation instead of the energy equation. Our simulations show
that the details of the gravitational-wave emission are still sensitive to the
numerical resolution, even in our highest-quality calculations. The amount of
mass which can be ejected from neutron star mergers depends strongly on the
angular momentum of the system. Our results do not support the initial
conditions of temperature and proton-to-nucleon ratio assumed in recent work
for producing a solar r-process pattern for nuclei around and above the A
approx 130 peak. The improved models confirm our previous conclusion that
gamma-ray bursts are not powered by neutrino emission during the dynamical
phase of the merging of two neutron stars.


  Nestohedra are a family of convex polytopes that includes permutohedra,
associahedra, and graph associahedra. In this paper, we study an extension of
such polytopes, called extended nestohedra. We show that these objects are
indeed the boundaries of simple polytopes, answering a question of Lam and
Pylyavskyy. We also study the duals of (extended) nestohedra, giving a complete
characterization of isomorphisms (as simplicial complexes) between the duals of
extended nestohedra and a partial characterization of isomorphisms between the
duals of nestohedra and extended nestohedra. In addition, we give formulas for
their $f$-, $h$-, and $\gamma$-vectors. This includes showing that the
$f$-vectors of the extended nestohedron corresponding to a forest $F$ and the
nestohedron corresponding to the line graph of $F$ are the same, as well as
showing that all flag extended nestohedra have nonnegative $\gamma$-vectors,
thus proving Gal's conjecture for a large class of flag simple polytopes. We
also relate the $f$- and $h$-vectors of the nestohedra and extended nestohedra,
as well as give explicit formulas for the $h$- and $\gamma$-vectors in terms of
descent statistics for a certain class of flag extended nestohedra. Finally, we
define a partial ordering on partial permutations that is a join semilattice
quotient of the weak Bruhar order on the symmetric group, and such that any
linear extension of the partial order provides a shelling of the dual of the
stellohedron.


  We conduct a spectroscopic search of quasars observed by the Sloan Digital
Sky Survey (SDSS) with broad absorption line (BAL) troughs due to Mg II and
troughs due to Fe II that simultaneously exhibit strong Balmer narrow emission
lines (NELs). We find that in a redshift range of 0.4 less than or equal to z
less than or equal to 0.9 approximately 23 of the 70 Mg II BALs and 4 of a
subset of 15 Fe II BALs exhibit strong Balmer emission. We also find
significant fractions of Mg II BALs (approximately 23%) and those Mg II BALs
with Fe II troughs (approximately 27%) have strong continuum reddening, E(B -
V) greater than or equal to 0.1. From measurements of the Balmer decrement in
three objects, we find similarly significant reddening of the NEL region in
three of the four objects; the NELs in the fourth object are not measurable. We
also include one object in this study not taken from the SDSS sample that shows
Fe II absorption and strong narrow emission, but due to measurement uncertainty
and low continuum reddening the comparison is consistent but inconclusive. We
find a trend in both the Mg II and Fe II BAL samples between the NEL reddening
and continuum reddening. Because the narrow line reddening is consistent with
the continuum reddening in every object in the two SDSS samples, it suggests
that the reddening sources in these objects likely exist at larger radial
distances than the narrow line regions from the central nucleus.


  We consider a two dimensional semiconductor with a local attraction among the
carriers. We study the ground state of this system as a function of the
semiconductor gap. We find a direct transition from a superconducting to an
insulating phase for no doping at a critical value, the single particle
excitations being always gapped. For finite doping we find a smooth crossover.
We calculate the critical temperature due to both the particle excitations and
the Berezinkii-Kosterlitz-Thouless transition.


  The concept of a controlled flow of a dynamical system, especially when the
controlling process feeds information back about the system, is of central
importance in control engineering. In this paper we build on the ideas
presented by Bouten and van Handel (L. Bouten, R. van Handel, "On the
separation principle of quantum control", in Quantum Stochastics and
Information: Statistics, Filtering and Control, World Scientific, 2008) and
develop a general theory of quantum feedback. We elucidate the relationship
between the controlling processes $Z$ and the measured process $Y$, and to this
end make a distinction between what we call the input picture and the output
picture. We should that the input-output relations for the noise fields have
additional terms not present in the standard theory, but that the relationship
between the control processes and measured processes themselves are internally
consistent - we do this for the two main cases of quadrature measurement and
photon-counting measurement. The theory is general enough to include a
modulating filter which processes the measurement readout $Y$ before returning
to the system. This opens up the prospect of applying very general engineering
feedback control techniques to open quantum systems in a systematic manner, and
we consider a number of specific modulating filter problems. Finally, we give a
brief argument as to why most of the rules for making instantaneous feedback
connections (J. Gough, M.R. James, "Quantum Feedback Networks: Hamiltonian
Formulation", Commun. Math. Phys., 287, 1109, 2009) ought to apply for
controlled dynamical networks as well.


  This paper is devoted to the computation of compact binaries composed of one
black hole and one neutron star. The objects are assumed to be on exact
circular orbits. Standard 3+1 decomposition of Einstein equations is performed
and the conformal flatness approximation is used. The obtained system of
elliptic equations is solved by means of multi-domain spectral methods. Results
are compared with previous work both in the high mass ratio limit and for one
neutron star with very low compactness parameter. The accuracy of the present
code is shown to be greater than with previous codes. Moreover, for the first
time, some sequences containing one neutron star of realistic compactness are
presented and discussed.


  We show that every closed oriented smooth 4-manifold admits a complete
singular Poisson structure in each homotopy class of maps to the 2-sphere. The
rank of this structure is 2 outside a small singularity set, which consists of
finitely many circles and isolated points. The Poisson bivector has rank 0 on
the singularities, where we give its local form explicitly.


  Extending the work of Alon, Frieze abnd Welsh, we show that there are
randomized polynomial time approximation schemes for computing the Tutte
polynomial in subdense graphs with an minimal node degree of $\Omega\left (
\frac{n}{\sqrt{\log n}}\right )$ . The same holds for the partition function
$Z$ in the random cluster model with uniform edge probabilities and for the
associated distribution $\lambda (A),\: A \subseteq E$ whenever the underlying
graph $G=(V,E)$ is $c\cdot\frac{n}{\sqrt{\log (n)}}$-subdense. In the
superdense case with node degrees $n-o(n)$, we show that the Tutte polynomial
$T_G(x,y)$ is asymptotically equal to $Q=(x-1)(y-1)$. Moreover, we briefly
discuss the problem of approximating $Z$ in the case of $(\alpha, \beta
)$-power law graphs.


  Two properties of a dynamical system, rigidity and non-recurrence, are
examined in detail. The ultimate aim is to characterize the sequences along
which these properties do or do not occur for different classes of
transformations. The main focus in this article is to characterize explicitly
the structural properties of sequences which can be rigidity sequences or
non-recurrent sequences for some weakly mixing dynamical system. For ergodic
transformations generally and for weakly mixing transformations in particular
there are both parallels and distinctions between the class of rigid sequences
and the class of non-recurrent sequences. A variety of classes of sequences
with various properties are considered showing the complicated and rich
structure of rigid and non-recurrent sequences.


  We consider two particles interacting via a contact interaction that are
constrained to a sphere, or $S^2$. We determine their spectrum to arbitrary
precision and for arbitrary angular momentum. We show how the non-inertial
frame leads to non-trivial solutions for different angular momenta. Our results
represent an extension of the finite-volume L\"uscher formulas but now to a
non-trivial geometry. We apply our results to predict the spectrum of select
two-nucleon halo nuclei and compare with experimental results.


  This paper suggests a generalized distribution of response times to new
information $\sim t^{-b}$ for human populations in the absence of deadlines.
This has important implications for psychological and social studies as well
the study of dynamical networks such as the WWW.


  We investigate the effects of collective modes on the temperature relaxation
rates in fully coupled electron-ion systems. Firstly, the well-understood limit
of weakly coupled plasmas is considered and the coupled mode formula within the
random phase approximation is derived starting from the Lenard-Balescu kinetic
equation. We show how the frequency integration can be performed by standard
methods without applying additional approximations. Due to the well-defined
approximation scheme, the results can serve as a benchmark for more approximate
theories and numerical simulations in this limit. The coupled mode electron-ion
transfer rates show a considerable reduction compared to the Fermi-Golden Rule
approach for certain parameters and very small changes for other systems. We
demonstrate how these coupled mode effects are connected to the occurrence of
ion acoustic modes and under which conditions they occur. Interestingly,
coupled mode effects can also occur for plasmas with very high electron
temperatures; a regime, where the Landau-Spitzer approach is believed to give
accurate results. Finally, we extend the approach to systems with strongly
coupled ions by applying static local field corrections. This extension can
substantially increase the coupled mode effects.


  A formalism (zeta-complex analysis), allowing one to construct global
Einstein metrics by matching together local ones described in the papers Phys.
Lett. B 513(2001)142-146; Diff. Geom. Appl. 16(2002)95-120, is developed. With
this formalism the singularities of the obtained metrics are described
naturally as well.


  Designing an in-pipe climbing robot that manipulates sharp gears to study
complex line relationships. Traditional rolling/happening pipe climbing robots
tend to slide when exploring pipe curves. The proposed gearbox connects to the
farthest ground plane of a standard dual output gearbox. Instrumentation helps
achieve a very well-defined deceleration sequence in which the robot slides and
pulls as it moves forward. This instrument takes into account the forces
exerted on each track within the line relationship and intentionally modifies
the robot's track speed, unlocking the key to fine-tuning. This makes the 3
output transmissions take a lot of time. Deflection of the robot on a pipe
network with various bearings and non-slip pipe bends demonstrates the
integrity of the proposed structure.


  A variety is rationally connected if two general points can be joined by a
rational curve. A higher version of this notion is rational simple
connectedness, which requires suitable spaces of rational curves through two
points to be rationally connected themselves. We prove that smooth, complex,
weighted complete intersections of low enough degree are rationally simply
connected. This result has strong arithmetic implications for weighted complete
intersections defined over the function field of a smooth, complex curve.
Namely, it implies that these varieties satisfy weak approximation at all
places, that R-equivalence of rational points is trivial, and that the Chow
group of zero cycles of degree zero is zero.


  We investigate the dynamics of a cold trapped ion coupled to the quantized
field inside a high-finesse cavity, considering exact resonance between the
ionic internal levels and the field (carrier transition). We derive an
intensity-dependent hamiltonian in which terms proportional to the square of
the Lamb-Dicke parameter ($\eta$) are retained. We show that different
nonclassical effects arise in the dynamics of the ionic population inversion,
depending on the initial states of the vibrational motion/field and on the
values of $\eta$.


  We consider a simple pendulum whose suspension point undergoes fast
vibrations in the plane of motion of the pendulum. The averaged over the fast
vibrations system is a Hamiltonian system with one degree of freedom depending
on two parameters. We give complete description of bifurcations of phase
portraits of this averaged system.


  We consider the problem of creating document representations in which
inter-document similarity measurements correspond to semantic similarity. We
first present a novel subspace-based framework for formalizing this task. Using
this framework, we derive a new analysis of Latent Semantic Indexing (LSI),
showing a precise relationship between its performance and the uniformity of
the underlying distribution of documents over topics. This analysis helps
explain the improvements gained by Ando's (2000) Iterative Residual Rescaling
(IRR) algorithm: IRR can compensate for distributional non-uniformity. A
further benefit of our framework is that it provides a well-motivated,
effective method for automatically determining the rescaling factor IRR depends
on, leading to further improvements. A series of experiments over various
settings and with several evaluation metrics validates our claims.


  To violate Kirchhoff s law is very important in the areas of thermal
radiation. However, due to the weak nonreciprocity in natural materials, it is
necessary to engineer novel structures to break the balance between emission
and absorption. In this work, we introduce magneto-optical material into
Fibonacci photonic crystals. Assisted by the nonreciprocity of the
magneto-optical material and the excitation of Tamm plasmon polaritons, strong
nonreciprocal thermal radiation can be realized. The difference between
absorption and emission at wavelength of 16 {\mu}m can reach 0.9 at the
incident angle of 60o. The distributions of the magnetic field are also
calculated to verify the underlying physical origin. By engineering the
parameters of the structure, it is found that strong nonreciprocal thermal
radiation can be achieved at shorter wavelength and smaller incident angle. The
results indicate that the Fibonacci magnetophotonic crystals are the promising
candidate to engineer the nonreciprocal emission for various requirements.


  The noise of a device under test (DUT) is measured simultaneously with two
instruments, each of which contributes its own background. The average cross
power spectral density converges to the DUT power spectral density. This method
enables the extraction of the DUT noise spectrum, even if it is significantly
lower than the background. After a snapshot on practical experiments, we go
through the statistical theory and the choice of the estimator. A few
experimental techniques are described, with reference to phase noise and
amplitude noise in RF/microwave systems and in photonic systems. The set of
applications of this method is wide. The final section gives a short panorama
on radioastronomy, radiometry, quantum optics, thermometry (fundamental and
applied), semiconductor technology, metallurgy, etc. This report is intended as
a tutorial, as opposed to a report on advanced research, yet addressed to a
broad readership: technicians, practitioners, Ph.D. students, academics, and
full-time scientists.


  The automatic collection of stack traces in bug tracking systems is an
integral part of many software projects and their maintenance. However, such
reports often contain a lot of duplicates, and the problem of de-duplicating
them into groups arises. In this paper, we propose a new approach to solve the
deduplication task and report on its use on the real-world data from JetBrains,
a leading developer of IDEs and other software. Unlike most of the existing
methods, which assign the incoming stack trace to a particular group in which a
single most similar stack trace is located, we use the information about all
the calculated similarities to the group, as well as the information about the
timestamp of the stack traces. This approach to aggregating all available
information shows significantly better results compared to existing solutions.
The aggregation improved the results over the state-of-the-art solutions by 15
percentage points in the Recall Rate Top-1 metric on the existing NetBeans
dataset and by 8 percentage points on the JetBrains data. Additionally, we
evaluated a simpler k-Nearest Neighbors approach to aggregation and showed that
it cannot reach the same levels of improvement. Finally, we studied what
features from the aggregation contributed the most towards better quality to
understand which of them to develop further. We publish the implementation of
the suggested approach, and will release the newly collected industrial dataset
upon acceptance to facilitate further research in the area.


  In this letter we report {\it in situ} small--angle neutron scattering
results on the high--density (HDA) and low-density amorphous (LDA) ice
structures and on intermediate structures as found during the temperature
induced transformation of HDA into LDA. We show that the small--angle signal is
characterised by two $Q$ regimes featuring different properties ($Q$ is the
modulus of the scattering vector defined as $Q =
4\pi\sin{(\Theta)}/\lambda_{\rm i}$ with $\Theta$ being half the scattering
angle and $\lambda_{\rm i}$ the incident neutron wavelength). The very low--$Q$
regime ($< 5\times 10^{-2}$ \AA $^{-1}$) is dominated by a Porod--limit
scattering. Its intensity reduces in the course of the HDA to LDA
transformation following a kinetics reminiscent of that observed in wide--angle
diffraction experiments. The small--angle neutron scattering formfactor in the
intermediate regime of $5 \times 10^{-2} < Q < 0.5$ \AA$^{-1}$ HDA and LDA
features a rather flat plateau. However, the HDA signal shows an ascending
intensity towards smaller $Q$ marking this amorphous structure as
heterogeneous. When following the HDA to LDA transition the formfactor shows a
pronounced transient excess in intensity marking all intermediate structures as
strongly heterogeneous on a length scale of some nano--meters.


  We prove the following result: For a generic value of the parameter, the
Temperley-Lieb category has no non-zero, proper tensor ideal. When the
parameter $d$ is equal to $2\cos(\pi/n)$ for some $n \ge 3$, then the
Temperley-Lieb category has exactly one non-zero, proper ideal, namely the
ideal of negligible morphisms.


  The decay of $\Lambda$-hypernuclei without pion emission, known as Non
Mesonic Weak Decay (NMWD), gives an effective tool to investigate $\Delta$S=1
four-baryon interactions. It was theoretically suggested that the two-nucleon
induced mechanism could play a substantial role in reproducing the observed
NMWD decay rates and nucleon spectra, but at present no direct evidence of such
a mechanism has been obtained. The FINUDA experiment, exploiting the
possibility to detect both charged and neutral particles coming from the
hypernucleus decay, has allowed us to deduce the relative weight of the two
nucleon induced decay rate to the total NMWD rate. The value of
$\Gamma_{2N}$/$\Gamma_{NMWD}$=0.24$\pm$${0.03_{stat}}^{+0.03_{sys}}_{{-{0.02_{sys}}}}$
has been deduced, with an error reduced by a factor more than two compared with
the previous assessment.


  In this work we analyze the spectral level statistics of the one-dimensional
ionic Hubbard model, the Hubbard model with an alternating on-site potential.
In particular, we focus on the statistics of the gap ratios between consecutive
energy levels. This quantity is often used in order to signal whether a
many-body system is integrable or chaotic. A chaotic system has typically the
statistics of a Gaussian ensemble of random matrices while the spectral
properties of the integrable system follow a Poisson statistics. We find that
whereas the Hubbard model without alternating potential is known to be
integrable and its spectral properties follow a Poissonian statistics, the
presence of an alternating potential causes a drastic change in the spectral
properties which resemble the one of a Gaussian ensemble of random matrices.
However, to uncover this behavior one has to separately consider the blocks of
all symmetries of the ionic Hubbard model.


  We numerically investigate the evolution of the holographic subregion
complexity during a quench process in Einstein-Born-Infeld theory. Based on the
subregion CV conjecture, we argue that the subregion complexity can be treated
as a probe to explore the interior of the black hole. The effects of the
nonlinear parameter and the charge on the evolution of the holographic
subregion complexity are also investigated. When the charge is sufficiently
large, it not only changes the evolution pattern of the subregion complexity,
but also washes out the second stage featured by linear growth.


  The temperature dependence of electronic and magnetic properties of the
organic charge-transfer salt (DOEO)$_4$[HgBr$_4$]TCE was investigated using
magnetometry. Electronic transport properties revealed three distinct phases
which are related to different magnetic coupling phenomena. In the
low-temperature insulating phase (T<70 K) the antiferromagnetic coupling
between two distinct sites of magnetic moments causes antiferromagnetic order
below the N\'eel temperature T$_N$=40 K. In the temperature region 70-120 K the
(DOEO)$_4$[HgBr$_4$]TCE shows metallic-like behavior and with further
increasing of temperature it becomes a bad metal due to loss of itinerant
character and increase of hopping conductivity of charge carriers.


  On-line firms deploy suites of software platforms, where each platform is
designed to interact with users during a certain activity, such as browsing,
chatting, socializing, emailing, driving, etc. The economic and incentive
structure of this exchange, as well as its algorithmic nature, have not been
explored to our knowledge. We model this interaction as a Stackelberg game
between a Designer and one or more Agents. We model an Agent as a Markov chain
whose states are activities; we assume that the Agent's utility is a linear
function of the steady-state distribution of this chain. The Designer may
design a platform for each of these activities/states; if a platform is adopted
by the Agent, the transition probabilities of the Markov chain are affected,
and so is the objective of the Agent. The Designer's utility is a linear
function of the steady state probabilities of the accessible states minus the
development cost of the platforms. The underlying optimization problem of the
Agent -- how to choose the states for which to adopt the platform -- is an MDP.
If this MDP has a simple yet plausible structure (the transition probabilities
from one state to another only depend on the target state and the recurrent
probability of the current state) the Agent's problem can be solved by a greedy
algorithm. The Designer's optimization problem (designing a custom suite for
the Agent so as to optimize, through the Agent's optimum reaction, the
Designer's revenue), is NP-hard to approximate within any finite ratio;
however, the special case, while still NP-hard, has an FPTAS. These results
generalize from a single Agent to a distribution of Agents with finite support,
as well as to the setting where the Designer must find the best response to the
existing strategies of other Designers. We discuss other implications of our
results and directions of future research.


  Recurrent flooding has increased rapidly in coastal regions due to sea level
rise and climate change. A key metric for evaluating transportation system
degradation is accessibility, yet the lack of temporally and spatially
disaggregate data means that the impact of recurrent flooding on accessibility,
and hence transportation system performance: is not well understood. Using
crowdsourced WAZE flood incident data from the Hampton Roads region in
Virginia, this study (Part 1) examines changes in the roadway network
accessibility for travelers residing in 1,113 traffic analysis zones (TAZs)
across five time of day periods. Additionally, a social vulnerability index
framework is developed to understand the socioeconomic characteristics of TAZs
that experience high accessibility reduction under recurrent flooding.
  Results show that TAZs experience the most accessibility reduction under
recurrent flooding during the morning peak period (6 to 9am) with large
differences across different zones, ranging from 0 to 49.6 (percentage) for
work trips (with population weighted mean reduction of 1.71 percent) and 0 to
87.9 (percentage) for nonwork trips (with population weighted mean reduction of
0.81 percent). Furthermore, the social vulnerability analysis showed that zones
with higher percentages of lower socioeconomic status, unemployed, less
educated, and limited English proficiency residents experience greater
accessibility reduction for work trips. In contrast to previous studies that
aggregate the effects of recurrent flooding across a city, these results
demonstrate that there exists large spatial and temporal variation in recurrent
floodings impacts on accessibility. This study also highlights the need to
include social vulnerability analysis in assessing impacts of climate events,
to ensure equitable outcomes as investments are made to create resilient
transportation infrastructure.


  At the Advanced Superconducting Test Accelerator (ASTA) now under
construction at Fermilab, we anticipate the appearance of the microbunching
instability related to the longitudinal space charge (LSC) impedances. With a
photoinjector source and up to two chicane compressors planned, the conditions
should result in the shift of some microbunched features into the visible light
regime. The presence of longitudinal microstructures (microbunching) in the
electron beam or the leading edge spikes can result in strong, spatially
localized coherent enhancements of optical transition radiation (COTR) that
mask the actual beam profile. Several efforts on mitigation of the effects in
the diagnostics task have been identified. At ASTA we have designed the beam
profiling stations to have mitigation features based on spectral filtering,
scintillator choice, and the timing of the trigger to the digital camera's CCD
chip. Since the COTR is more intense in the NIR than UV we have selectable
bandpass filters centered at 420 nm which also overlap the spectral emissions
of the LYSO:Ce scintillators. By delaying the CCD trigger timing of the
integration window by 40-50 ns, we can reject the prompt OTR signal and
integrate on the delayed scintillator light predominately. This combination of
options should allow mitigation of COTR enhancements of order 100-1000 in the
distribution.


  We show that the crystallographic braid group $B_n/[P_n,P_n]$ embeds
naturally in the group of unrestricted virtual braids $UVB_n$, we give new
proofs of known results about the torsion elements of $B_n/[P_n,P_n]$, and we
characterise the torsion elements of $UVB_n$.


  The effects of spatial correlations of density fluctuations on merger
histories of dark matter haloes (so-called `{\it merger trees}') are analysed.
We compare the mass functions of dark haloes derived by a new method for
calculating merger trees, that proposed by Rodrigues \& Thomas (RT), with those
given by other methods such as the Block model, the Press-Schechter formula and
our own formula in which the mass functions are analytically expressed in a way
that takes into consideration the spatial correlations. It is found that the
mass functions given by the new method are well fit by those given by our
formula. We believe that new method (RT) {\it naturally} and correctly takes
into account the spatial correlations of the density fluctuations due to a
calculated, grid-based realisation of the density fluctuations and so is very
useful for estimating the merger tree accurately in a way that takes into
consideration spatial correlations.
  Moreover, by applying our formula, we present an analytic expression which
reproduces the mass function derived by the Block model. We therefore show
clearly why and how the mass functions given by the new method and the Block
model are different from each other. Furthermore, we note that the construction
of merger trees is sensitive to the criterion of collapse and merging of
overlapped haloes in cases in which two or more haloes happen to overlap. In
fact, it is shown that the mass function is very much affected when the
criterion of overlapping is changed.


  We experimentally demonstrate a quantum walk on a line in phase space using
one and two trapped ion. A walk with up to 23 steps is realized by subjecting
an ion to state-dependent displacement operations interleaved with quantum coin
tossing operations. To analyze the ion's motional state after each step we
apply a technique that directly maps the probability density distribution onto
the ion's internal state. The measured probability distributions and the
position's second moment clearly show the non-classical character of the
quantum walk. To further highlight the difference between the classical
(random) and the quantum walk, we demonstrate the reversibility of the latter.
Finally, we extend the quantum walk by using two ions, giving the walker the
additional possibility to stay instead of taking a step.


  A Maximum Distance Separable code over an alphabet $F$ is defined via an
encoding function $C:F^k \rightarrow F^n$ that allows to retrieve a message $m
\in F^k$ from the codeword $C(m)$ even after erasing any $n-k$ of its symbols.
The minimum possible alphabet size of general (non-linear) MDS codes for given
parameters $n$ and $k$ is unknown and forms one of the central open problems in
coding theory. The paper initiates the study of the alphabet size of codes in a
generalized setting where the coding scheme is required to handle a
pre-specified subset of all possible erasure patterns, naturally represented by
an $n$-vertex $k$-uniform hypergraph. We relate the minimum possible alphabet
size of such codes to the strong chromatic number of the hypergraph and analyze
the tightness of the obtained bounds for both the linear and non-linear
settings. We further consider variations of the problem which allow a small
probability of decoding error.


  Factorization of polynomials arises in numerous areas in symbolic
computation. It is an important capability in many symbolic and algebraic
computation. There are two type of factorization of polynomials. One is
convention polynomial factorization, and the other approximate polynomial
factorization.
  Conventional factorization algorithms use symbolic methods to get exact
factors of a polynomial while approximate factorization algorithms use
numerical methods to get approximate factors of a polynomial. Symbolic
computation often confront intermediate expression swell problem, which lower
the efficiency of factorization. The numerical computation is famous for its
high efficiency, but it only gives approximate results. In this paper, we
present an algorithm which use approximate method to get exact factors of a
multivariate polynomial. Compared with other methods, this method has the
numerical computation advantage of high efficiency for some class of
polynomials with factors of lower degree. The experimental results show that
the method is more efficient than {\it factor} in Maple 9.5 for polynomials
with more variables and higher degree.


  We discuss the construction and symmetries of su(3) Clebsch-Gordan
coefficients arising from the su(3) basis states constructed as triple tensor
products of two-dimensional harmonic oscillator states. Because of the su(2)
symmetry of the basis states, matrix elements and recursion relations are
easily expressed in terms of su(2) technology. As the Weyl group has a
particularly simple action on these states, Weyl symmetries of the su(3)
coupling coefficients generalizing the well known m-> -m symmetry of su(2)
coupling can be obtained, so that any coefficient can be obtained as a sum of
Weyl-reflected coefficients lying in the dominant Weyl sector. Some important
cases of multiplicity-free decomposition are discussed as examples of
applications.


  This paper considers polynomial optimization with unbounded sets. We give a
homogenization formulation and propose a hierarchy of Moment-SOS relaxations to
solve it. Under the assumptions that the feasible set is closed at infinity and
the ideal of homogenized equality constraining polynomials is real radical, we
show that this hierarchy of Moment-SOS relaxations has finite convergence, if
some optimality conditions (i.e., the linear independence constraint
qualification, strict complementarity and second order sufficiency conditions)
hold at every minimizer, including the one at infinity. Moreover, we prove
extended versions of Putinar-Vasilescu type Positivstellensatz for polynomials
that are nonnegative on unbounded sets. The classical Moment-SOS hierarchy with
denominators is also studied. In particular, we give a positive answer to a
conjecture of Mai, Lasserre and Magron in their recent work.


  The game of chess as always been viewed as an iconic representation of
intellectual prowess. Since the very beginning of computer science, the
challenge of being able to program a computer capable of playing chess and
beating humans has been alive and used both as a mark to measure
hardware/software progresses and as an ongoing programming challenge leading to
numerous discoveries. In the early days of computer science it was a topic for
specialists. But as computers were democratized, and the strength of chess
engines began to increase, chess players started to appropriate to themselves
these new tools. We show how these interactions between the world of chess and
information technologies have been herald of broader social impacts of
information technologies. The game of chess, and more broadly the world of
chess (chess players, literature, computer softwares and websites dedicated to
chess, etc.), turns out to be a surprisingly and particularly sharp indicator
of the changes induced in our everyday life by the information technologies.
Moreover, in the same way that chess is a modelization of war that captures the
raw features of strategic thinking, chess world can be seen as small society
making the study of the information technologies impact easier to analyze and
to grasp.


  We develop an approach in solving exactly the problem of three-body
oscillators including general quadratic interactions in the coordinates for
arbitrary masses and couplings. We introduce a unitary transformation of three
independent angles to end up with a diagonalized Hamiltonian. Using the
representation theory of the group $SU(3)$, we explicitly determine the
solutions of the energy spectrum. Considering the ground state together with
reduced density matrix, we derive the corresponding purity function that is
giving rise to minimal and maximal entanglement under suitable conditions. The
cases of realizing one variable among three is discussed and know results in
literature are recovered.


  We analyze how the CFL states in dense matter work in the direction of
enhancing the parameter space for absolutely stable phases (strange matter). We
find that the "CFL strange matter" phase can be the true ground state of
hadronic matter for a much wider range of the parameters of the model (the gap
of the QCD Cooper pairs $\Delta$, the strange quark mass $m_s$ and the Bag
Constant $B$) than the state without any pairing, and derive a full equation of
state and an accurate analytic approximation to the lowest order in $\Delta$
and $m_{s}$ which may be directly used for applications. The effects of pairing
on the equation of state are found to be small (as previously expected) but not
negligible and may be relevant for astrophysics.


  We investigate the behavior, as a small parameter tends to zero, of a
nonlocal Allen-Cahn equation. Given a rather general initial data, we perform a
rigorous analysis of both the generation and the motion of interface, and
obtain a new estimate for its thickness. The limit problem involves motion by
mean curvature together with a nonlocal effect (which allows the possibility of
nontrivial stationary state).


  Harvey, Hill, and Hill have found that unexpected interactions involving the
nucleon, photon, and weak gauge bosons at low energies emerge from gauging the
axial anomaly of QCD under the full electroweak symmetry of the Standard Model
(SM). In this contribution we consider how such interactions can be isolated
through a triple-product momentum correlation in neutron radiative beta-decay.
The correlation is both parity- and naively time-reversal-odd, so that it
vanishes in the Standard Model save for effects induced by final-state
interactions (FSI). Nevertheless, the correlation can be generated by sources
of CP violation beyond the Standard Model, and such couplings, being
spin-independent, are not constrained by the nonobservation of the neutron
electric dipole moment (EDM). We consider the sorts of limits on its strength
which can be determined at existing and anticipated facilities, as well as the
size of induced correlations from known FSI. We also briefly consider the
possibility of nuclear beta-decay studies as well as the prospects for
muon-induced reaction studies.


  We consider a dataset $S$ held by an agency, and a vector query of interest,
$f(S) \in \mathbb{R}^k$, to be posed by an analyst, which contains the
information required for certain planned statistical inference. The agency
releases the requested vector query with noise that guarantees a given level of
Differential Privacy -- DP$(\varepsilon,\delta)$ -- using the well-known
Gaussian mechanism. The analyst can choose to pose the vector query $f(S)$ or
to adjust it by a suitable transformation that can make the agency's response
more informative. For any given level of privacy DP$(\varepsilon,\delta)$
decided by the agency, we study natural situations where the analyst can
achieve better statistical inference by adjusting the query with a suitable
simple explicit transformation.


  Social media has been considered as a data source for tracking disease.
However, most analyses are based on models that prioritize strong correlation
with population-level disease rates over determining whether or not specific
individual users are actually sick. Taking a different approach, we develop a
novel system for social-media based disease detection at the individual level
using a sample of professionally diagnosed individuals. Specifically, we
develop a system for making an accurate influenza diagnosis based on an
individual's publicly available Twitter data. We find that about half (17/35 =
48.57%) of the users in our sample that were sick explicitly discuss their
disease on Twitter. By developing a meta classifier that combines text
analysis, anomaly detection, and social network analysis, we are able to
diagnose an individual with greater than 99% accuracy even if she does not
discuss her health.


  Placement is an essential task in modern chip design, aiming at placing
millions of circuit modules on a 2D chip canvas. Unlike the human-centric
solution, which requires months of intense effort by hardware engineers to
produce a layout to minimize delay and energy consumption, deep reinforcement
learning has become an emerging autonomous tool. However, the learning-centric
method is still in its early stage, impeded by a massive design space of size
ten to the order of a few thousand. This work presents MaskPlace to
automatically generate a valid chip layout design within a few hours, whose
performance can be superior or comparable to recent advanced approaches. It has
several appealing benefits that prior arts do not have. Firstly, MaskPlace
recasts placement as a problem of learning pixel-level visual representation to
comprehensively describe millions of modules on a chip, enabling placement in a
high-resolution canvas and a large action space. It outperforms recent methods
that represent a chip as a hypergraph. Secondly, it enables training the policy
network by an intuitive reward function with dense reward, rather than a
complicated reward function with sparse reward from previous methods. Thirdly,
extensive experiments on many public benchmarks show that MaskPlace outperforms
existing RL approaches in all key performance metrics, including wirelength,
congestion, and density. For example, it achieves 60%-90% wirelength reduction
and guarantees zero overlaps. We believe MaskPlace can improve AI-assisted chip
layout design. The deliverables are released at
https://laiyao1.github.io/maskplace.


  In this paper, we tackle the domain adaptive object detection problem, where
the main challenge lies in significant domain gaps between source and target
domains. Previous work seeks to plainly align image-level and instance-level
shifts to eventually minimize the domain discrepancy. However, they still
overlook to match crucial image regions and important instances across domains,
which will strongly affect domain shift mitigation. In this work, we propose a
simple but effective categorical regularization framework for alleviating this
issue. It can be applied as a plug-and-play component on a series of Domain
Adaptive Faster R-CNN methods which are prominent for dealing with domain
adaptive detection. Specifically, by integrating an image-level multi-label
classifier upon the detection backbone, we can obtain the sparse but crucial
image regions corresponding to categorical information, thanks to the weakly
localization ability of the classification manner. Meanwhile, at the instance
level, we leverage the categorical consistency between image-level predictions
(by the classifier) and instance-level predictions (by the detection head) as a
regularization factor to automatically hunt for the hard aligned instances of
target domains. Extensive experiments of various domain shift scenarios show
that our method obtains a significant performance gain over original Domain
Adaptive Faster R-CNN detectors. Furthermore, qualitative visualization and
analyses can demonstrate the ability of our method for attending on the key
regions/instances targeting on domain adaptation. Our code is open-source and
available at \url{https://github.com/Megvii-Nanjing/CR-DA-DET}.


  We prove a comparison theorem for super- and sub-solutions with non-vanishing
gradients to semilinear PDEs provided a nonlinearity $f$ is $L^p$ function with
$p > 1$. The proof is based on a strong maximum principle for solutions of
divergence type elliptic equations with VMO leading coefficients and with lower
order coefficients from a Kato class. An application to estimation of periodic
water waves profiles is given.


  One of the most fundamental quantum states of light is squeezed vacuum, in
which noise in one of the quadratures is less than the standard quantum noise
limit. Significant progress has been made in the generation of optical squeezed
vacuum and its utilization for numerous applications. However, it remains
challenging to generate, manipulate, and measure such quantum states in
nanophotonics with performances required for a wide range of scalable quantum
information systems. Here, we overcome this challenge in lithium niobate
nanophotonics by utilizing ultrashort-pulse phase-sensitive amplifiers for both
generation and all-optical measurement of squeezed states on the same chip. We
generate a squeezed state spanning over more than 25 THz of bandwidth
supporting only a few optical cycles, and measure a maximum of 4.9 dB of
squeezing ($\sim$11 dB inferred). This level of squeezing surpasses the
requirements for a wide range of quantum information systems. Our results on
generation and measurement of few-optical-cycle squeezed states in
nanophotonics enable a practical path towards scalable quantum information
systems with THz clock rates and open opportunities for studying non-classical
nature of light in the sub-cycle regime.


  This review covers a subset of the astrophysical phenomena where neutrinos
play a significant role and where the underlying microphysics is nuclear
physics. The current status of the solar neutrino problem, atmospheric neutrino
experiments, the role of neutrinos in determining the dynamics of type-II
supernovae, and recent developments in exploring neutrino propagation in
stochastic media are reviewed.


  In this paper we prove symmetry results for classical solutions of nonlinear
cooperative elliptic systems in a ball or in annulus in $\RN$, $N \geq 2 $.
More precisely we prove that solutions having Morse index $j \leq N $ are
foliated Schwarz symmetric if the nonlinearity is convex and a full coupling
condition is satisfied along the solution.


  Estimating 3d human pose from monocular images is a challenging problem due
to the variety and complexity of human poses and the inherent ambiguity in
recovering depth from the single view. Recent deep learning based methods show
promising results by using supervised learning on 3d pose annotated datasets.
However, the lack of large-scale 3d annotated training data captured under
in-the-wild settings makes the 3d pose estimation difficult for in-the-wild
poses. Few approaches have utilized training images from both 3d and 2d pose
datasets in a weakly-supervised manner for learning 3d poses in unconstrained
settings. In this paper, we propose a method which can effectively predict 3d
human pose from 2d pose using a deep neural network trained in a
weakly-supervised manner on a combination of ground-truth 3d pose and
ground-truth 2d pose. Our method uses re-projection error minimization as a
constraint to predict the 3d locations of body joints, and this is crucial for
training on data where the 3d ground-truth is not present. Since minimizing
re-projection error alone may not guarantee an accurate 3d pose, we also use
additional geometric constraints on skeleton pose to regularize the pose in 3d.
We demonstrate the superior generalization ability of our method by
cross-dataset validation on a challenging 3d benchmark dataset MPI-INF-3DHP
containing in the wild 3d poses.


  A detailed analysis highlighting the effect of optomechanical non-linearity
on the dynamical evolution of a hybrid electro-optomechanical system (EOMS) is
presented. The study, conducted over a wide range of parameter regime reveals
that the quadratic coupling term significantly alters the dynamics of the
system and thus cannot be ignored for any potential applications.


  The quantum-to-classical transition is considered from the point of view of
contractions of associative algebras. Various methods and ideas to deal with
contractions of associative algebras are discussed that account for a large
family of examples. As an instance of them, the commutative algebra of
functions in phase space, corresponding to classical physical observables, is
obtained as a contraction of the Moyal star-product which characterizes the
quantum case. Contractions of associative algebras associated to Lie algebras
are discussed, in particular the Weyl-Heisenberg and $SU(2)$ groups are
considered.


  The point estimates of ReLU classification networks---arguably the most
widely used neural network architecture---have been shown to yield arbitrarily
high confidence far away from the training data. This architecture, in
conjunction with a maximum a posteriori estimation scheme, is thus not
calibrated nor robust. Approximate Bayesian inference has been empirically
demonstrated to improve predictive uncertainty in neural networks, although the
theoretical analysis of such Bayesian approximations is limited. We
theoretically analyze approximate Gaussian distributions on the weights of ReLU
networks and show that they fix the overconfidence problem. Furthermore, we
show that even a simplistic, thus cheap, Bayesian approximation, also fixes
these issues. This indicates that a sufficient condition for a calibrated
uncertainty on a ReLU network is "to be a bit Bayesian". These theoretical
results validate the usage of last-layer Bayesian approximation and motivate a
range of a fidelity-cost trade-off. We further validate these findings
empirically via various standard experiments using common deep ReLU networks
and Laplace approximations.


  A relation between the precanonical quantization of pure Yang-Mills fields
and the functional Schr\"odinger representation in the temporal gauge is
discussed. It is shown that the latter can be obtained from the former when the
ultraviolet parameter $\varkappa$ introduced in precanonical quantization goes
to infinity. In this limiting case, the Schr\"odinger wave functional can be
expressed as the trace of the Volterra product integral of
Clifford-algebra-valued precanonical wave functions restricted to a certain
field configuration, and the canonical functional derivative Schr\"odinger
equation together with the quantum Gau\ss\ constraint are derived from the
Dirac-like precanonical Schr\"odinger equation.


  Within a scaling ansatz formalism plus Thomas-Fermi approximation, we
investigate the collective excitations of a harmonically trapped boson-fermion
mixture in the collisionless and hydrodynamic limit at low temperature. Both
the monopole and quadrupole modes are considered in the presence of spherical
as well as cylindrically symmetric traps. In the spherical traps, the frequency
of monopole mode coincides in the collisionless and hydrodynamic regime,
suggesting that it might be undamped in all collisional regimes. In contrast,
for the quadrupole mode, the frequency differs largely in these two limits. In
particular, we find that in the hydrodynamic regime the quadrupole oscillations
with equal bosonic and fermionic amplitudes generate an exact eigenstate of the
system, regardless of the boson-fermion interaction. This resembles the Kohn
mode for the dipole excitation. We discuss in some detail the behavior of
monopole and quadrupole modes as a function of boson-fermion coupling at
different boson-boson interaction strength. Analytic solutions valid at weak
and medium fermion-boson coupling are also derived and discussed.


  We show that certain classes of modules have universal models with respect to
pure embeddings.
  $Theorem.$ Let $R$ be a ring, $T$ a first-order theory with an infinite model
extending the theory of $R$-modules and $K^T=(Mod(T), \leq_{pp})$ (where
$\leq_{pp}$ stands for pure submodule). Assume $K^T$ has joint embedding and
amalgamation.
  If $\lambda^{|T|}=\lambda$ or $\forall \mu < \lambda( \mu^{|T|} < \lambda)$,
then $K^T$ has a universal model of cardinality $\lambda$.
  As a special case we get a recent result of Shelah [Sh17, 1.2] concerning the
existence of universal reduced torsion-free abelian groups with respect to pure
embeddings.
  We begin the study of limit models for classes of $R$-modules with joint
embedding and amalgamation. We show that limit models with chains of long
cofinality are pure-injective and we characterize limit models with chains of
countable cofinality. This can be used to answer Question 4.25 of [Maz].
  As this paper is aimed at model theorists and algebraists an effort was made
to provide the background for both.


  We continue the research of the relation
$\hspace{1mm}\widetilde{\mid}\hspace{1mm}$ on the set $\beta {\mathbb{N}}$ of
ultrafilters on ${\mathbb{N}}$, defined as an extension of the divisibility
relation. It is a quasiorder, so we see it as an order on the set of
$=_\sim$-equivalence classes, where ${\cal F}=_\sim{\cal G}$ means that ${\cal
F}$ and ${\cal G}$ are mutually
$\hspace{1mm}\widetilde{\mid}\hspace{1mm}$-divisible. Here we introduce a new
tool: a relation of congruence modulo an ultrafilter. We first recall the
congruence of ultrafilters modulo an integer and show that $=_\sim$-equivalent
ultrafilters do not necessarily have the same residue modulo $m\in
{\mathbb{N}}$. Then we generalize this relation to congruence modulo an
ultrafilter in a natural way. After that, using iterated nonstandard
extensions, we introduce a stronger relation, which has nicer properties with
respect to addition and multiplication of ultrafilters. Finally, we also
introduce a strengthening of $\hspace{1mm}\widetilde{\mid}\hspace{1mm}$ and
show that it also behaves well in relation to the congruence relation.


  It is observed that the shifted Poisson structure (antibracket) on the
solution complex of Klein-Gordon and linear Yang-Mills theory on globally
hyperbolic Lorentzian manifolds admits retarded/advanced trivializations
(analogs of retarded/advanced Green's operators). Quantization of the
associated unshifted Poisson structure determines a unique (up to equivalence)
homotopy algebraic quantum field theory (AQFT), i.e. a functor that assigns
differential graded $\ast$-algebras of observables and fulfills homotopical
analogs of the AQFT axioms. For Klein-Gordon theory the construction is
equivalent to the standard one, while for linear Yang-Mills it is richer and
reproduces the BRST/BV field content (gauge fields, ghosts and antifields).


  We investigate the formation, growth, merger history, movement, and
destruction of cosmic voids detected via the watershed transform code VIDE in a
cosmological N-body dark matter {\Lambda}CDM simulation. By adapting a method
used to construct halo merger trees, we are able to trace individual voids back
to their initial appearance and record the merging and evolution of their
progenitors at high redshift. For the scales of void sizes captured in our
simulation, we find that the void formation rate peaks at scale factor 0.3,
which coincides with a growth in the void hierarchy and the emergence of dark
energy. Voids of all sizes appear at all scale factors, though the median
initial void size decreases with time. When voids become detectable they have
nearly their present-day volumes. Almost all voids have relatively stable
growth rates and suffer only infrequent minor mergers. Dissolution of a void
via merging is very rare. Instead, most voids maintain their distinct identity
as annexed subvoids of a larger parent. The smallest voids are collapsing at
the present epoch, but void destruction ceases after scale factor 0.3. In
addition, voids centers tend to move very little, less than 0.01 of their
effective radii per ln a, over their lifetimes. Overall, most voids exhibit
little radical dynamical evolution; their quiet lives make them pristine probes
of cosmological initial conditions and the imprint of dark energy.


  Pre-main sequence evolutionary theory is not well-calibrated to observations.
With care, the observed quantities can be converted into effective temperature
and luminosity (i.e. the Hertzsprung-Russell diagram) which the theoretical
calculations also predict as a function of stellar mass and age. For a sample
of nearby young stellar clusters and associations ranging in age from <1 Myr to
>100 Myr, we have tested the loci of luminosity as a function of effective
temperature against various sets of predicted pre-main sequence isochrones. As
we found in Hillenbrand & White (2004) which tested stellar masses, here for
the stellar ages there are two conclusions: some evolutionary calculations fare
better than others in reproducing the empirical sequences, and systematic
differences between all pre-main sequence evolutionary calculations and the
data are apparent. We also simulate hypothetical clusters of varying star
formation history and compare the resulting HR diagram predictions to observed
clusters. Our efforts are directed towards quantitative assessment of
**apparent** luminosity spreads in star forming regions and young clusters,
which are often erroneously interpreted as **true** luminosity spreads
indicative of **true** age spreads.


  Person-job fit is to match candidates and job posts on online recruitment
platforms using machine learning algorithms. The effectiveness of matching
algorithms heavily depends on the learned representations for the candidates
and job posts. In this paper, we propose to learn comprehensive and effective
representations of the candidates and job posts via feature fusion. First, in
addition to applying deep learning models for processing the free text in
resumes and job posts, which is adopted by existing methods, we extract
semantic entities from the whole resume (and job post) and then learn features
for them. By fusing the features from the free text and the entities, we get a
comprehensive representation for the information explicitly stated in the
resume and job post. Second, however, some information of a candidate or a job
may not be explicitly captured in the resume or job post. Nonetheless, the
historical applications including accepted and rejected cases can reveal some
implicit intentions of the candidates or recruiters. Therefore, we propose to
learn the representations of implicit intentions by processing the historical
applications using LSTM. Last, by fusing the representations for the explicit
and implicit intentions, we get a more comprehensive and effective
representation for person-job fit. Experiments over 10 months real data show
that our solution outperforms existing methods with a large margin. Ablation
studies confirm the contribution of each component of the fused representation.
The extracted semantic entities help interpret the matching results during the
case study.


  The advances in attention-based encoder-decoder (AED) networks have brought
great progress to end-to-end (E2E) automatic speech recognition (ASR). One way
to further improve the performance of AED-based E2E ASR is to introduce an
extra text encoder for leveraging extensive text data and thus capture more
context-aware linguistic information. However, this approach brings a mismatch
problem between the speech encoder and the text encoder due to the different
units used for modeling. In this paper, we propose an embedding aligner and
modality switch training to better align the speech and text latent spaces. The
embedding aligner is a shared linear projection between text encoder and speech
encoder trained by masked language modeling (MLM) loss and connectionist
temporal classification (CTC), respectively. The modality switch training
randomly swaps speech and text embeddings based on the forced alignment result
to learn a joint representation space. Experimental results show that our
proposed approach achieves a relative 14% to 19% word error rate (WER)
reduction on Librispeech ASR task. We further verify its effectiveness on
spoken language understanding (SLU), i.e., an absolute 2.5% to 2.8% F1 score
improvement on SNIPS slot filling task.


  In this note I point out a highly accurate relation - to within 0.2 ppb -
between the recently discovered accurate experimental value of the fine
structure constant (1/a)_exp =137.035999710(96) and the precise solution (1/a)=
137.035999737 of a nonlinear equation for the fine structure constant generated
by the earlier suggested new universal flavor-electroweak phenomenological
constant a_o = exp(-5) as a source and hints from the new experimental data.
This perfect match for the experimental value (1/a)_exp lends additional
support to the basic notion of a new universal physical constant a_o.


  Results from IRAS and recent optical CCD surveys are examined to discuss the
distribution and origin of dust and ionized gas in elliptical galaxies. In
strong contrast with the situation among spiral galaxies, masses of dust in
elliptical galaxies as derived from optical extinction are an order of
magnitude LOWER than those derived from IRAS data. I find that this dilemma can
be resolved by assuming the presence of a diffusely distributed component of
dust which is not detectable in optical data.
  The morphology of dust lanes and their association with ionized gas in
elliptical galaxies argues for an external origin of BOTH components of the
ISM.


  What are the most general principles in set theory relating forceability and
truth? As with Solovay's celebrated analysis of provability, both this question
and its answer are naturally formulated with modal logic. We aim to do for
forceability what Solovay did for provability. A set theoretical assertion psi
is forceable or possible, if psi holds in some forcing extension, and
necessary, if psi holds in all forcing extensions. In this forcing
interpretation of modal logic, we establish that if ZFC is consistent, then the
ZFC-provable principles of forcing are exactly those in the modal theory known
as S4.2.


  We introduce inference trees (ITs), a new class of inference methods that
build on ideas from Monte Carlo tree search to perform adaptive sampling in a
manner that balances exploration with exploitation, ensures consistency, and
alleviates pathologies in existing adaptive methods. ITs adaptively sample from
hierarchical partitions of the parameter space, while simultaneously learning
these partitions in an online manner. This enables ITs to not only identify
regions of high posterior mass, but also maintain uncertainty estimates to
track regions where significant posterior mass may have been missed. ITs can be
based on any inference method that provides a consistent estimate of the
marginal likelihood. They are particularly effective when combined with
sequential Monte Carlo, where they capture long-range dependencies and yield
improvements beyond proposal adaptation alone.


  We study arbitrary order symmetry operators for the linear Schr\"odinger
equations with arbitrary number of spatial variables. We deduce determining
equations for coefficient functions of such operators and consider in detail
some cases when these equations can be explicitly solved. In addition, the
complete group classification of the nonlinear Schr\"odinger equation is
presented.


  The growing advances in VLSI technology and design tools have exponentially
expanded the application domain of digital signal processing over the past 10
years. This survey emphasises on the architectural and performance parameters
of VLSI for DSP applications such as speech processing, wireless communication,
analog to digital converters, etc


  Many-particle optical lattice clocks have the potential for unprecedented
measurement precision and stability due to their low quantum projection noise.
However, this potential has so far never been realized because clock stability
has been limited by frequency noise of optical local oscillators. By
synchronously probing two 87Sr lattice systems using a laser with a thermal
noise floor of 1e-15, we remove classically correlated laser noise from the
intercomparison, but this does not demonstrate independent clock performance.
With an improved optical oscillator that has a 1e-16 thermal noise floor, we
demonstrate an order of magnitude improvement over the best reported stability
of any independent clock, achieving a fractional instability of 1e-17 in 1000 s
of averaging time for synchronous or asynchronous comparisons. This result is
within a factor of 2 of the combined quantum projection noise limit for a 160
ms probe time with ~10^3 atoms in each clock. We further demonstrate that even
at this high precision, the overall systematic uncertainty of our clock is not
limited by atomic interactions. For the second Sr clock, which has a
cavity-enhanced lattice, the atomic-density-dependent frequency shift is
evaluated to be -3.11e-17 with an uncertainty of 8.2e-19.


  Network centrality plays an important role in many applications. Central
nodes in social networks can be influential, driving opinions and spreading
news or rumors.In hyperlinked environments, such as the Web, where users
navigate via clicks, central content receives high traffic, becoming targets
for advertising campaigns. While there is an extensive amount of work on
centrality measures and their efficient computation, controlling nodes'
centrality via network updates is a more recent and challenging problem.
Performing minimal modifications to a network to achieve a desired property
falls under the umbrella of network design problems. This paper is focused on
improving the coverage centrality of a set of nodes, which is the number of
pairs of nodes that have a shortest path passing through the set, by adding
edges to the network. We prove strong inapproximability results and propose a
greedy algorithm for maximizing coverage centrality. To ensure scalability to
large networks, we also design an efficient sampling algorithm for the problem.
In addition to providing an extensive empirical evaluation of our algorithms,
we also show that, under some realistic constraints, the proposed solutions
achieve almost-optimal approximation for coverage centrality maximization.


  Similarity solutions play an important role in many fields of science: we
consider here similarity in stochastic dynamics. Important issues are not only
the existence of stochastic similarity, but also whether a similarity solution
is dynamically attractive, and if it is, to what particular solution does the
system evolve. By recasting a class of stochastic PDEs in a form to which
stochastic centre manifold theory may be applied we resolve these issues in
this class. For definiteness, a first example of self-similarity of the
Burgers' equation driven by some stochastic forced is studied. Under suitable
assumptions, a stationary solution is constructed which yields the existence of
a stochastic self-similar solution for the stochastic Burgers' equation.
Furthermore, the asymptotic convergence to the self-similar solution is proved.
Second, in more general stochastic reaction-diffusion systems stochastic centre
manifold theory provides a framework to construct the similarity solution,
confirm its relevance, and determines the correct solution for any compact
initial condition. Third, we argue that dynamically moving the spatial origin
and dynamically stretching time improves the description of the stochastic
similarity. Lastly, an application to an extremely simple model of turbulent
mixing shows how anomalous fluctuations may arise in eddy diffusivities. The
techniques and results we discuss should be applicable to a wide range of
stochastic similarity problems.


  We present a highly efficient lattice Boltzmann (LB) kinetic model for
thermal liquid-vapor system. Three key components are as beow: (i) a discrete
velocity model by Kataoka \emph{et al.} [Phys. Rev. E \textbf{69},
035701(R)(2004)]; (ii) a forcing term $I_{i}$ aiming to describe the
interfacial stress and recover the van der Waals equation of state by Gonnella
\emph{et al.} [Phys. Rev. E \textbf{76}, 036703 (2007)]; and (iii) a Windowed
Fast Fourier Transform (WFFT) scheme and its inverse by our group [Phys. Rev. E
\textbf{84}, 046715 (2011)] for solving the spatial derivatives, together with
a second-order Runge-Kutta (RK) finite difference scheme for solving the
temporal derivative in the LB equation. The model is verified and validated by
well-known benchmark tests. The results recovered from the present model are
well consistent with previous ones[Phys. Rev. E \textbf{84}, 046715 (2011)] or
theoretical analysis. The usage of less discrete velocities, high-order RK
algorithm and WFFT scheme with 16th-order in precision makes the model more
efficient by about $10$ times and more accurate than the original one.


  La$_{1.67}$Sr$_{0.33}$CuO$_4$ is not a superconductor and its resistivity
follows a purely T$^2$ temperature dependence at very low temperatures.
La$_{1.71}$Sr$_{0.29}$CuO$_4$, on the other hand, has a superconducting ground
state together with a T-Linear term in its resistivity. The concomitant
emergence of these two features below a critical doping is mystifying. Here, I
notice that the electron-electron collision rate in the Fermi liquid above the
doping threshold is unusually large. The scattering time of nodal
quasi-particles expressed in a dimensionless parameter $\zeta$ is very close to
what has been found in liquid $^3$He at its melting pressure. In the latter
case, fermionic particles become dynamically distinguishable by excess of
interaction. Ceasing to be dynamically indistinguishable, nodal electrons will
be excluded from the Fermi sea. Such non-degenerate carriers will then scatter
the degenerate ones within a phase space growing linearly with temperature.


  Tool-assisted refactoring transformations must be trustworthy if programmers
are to be confident in applying them on arbitrarily extensive and complex code
in order to improve style or efficiency. We propose a simple, high-level but
rigorous, notation for defining refactoring transformations in Erlang, and show
that this notation provides an extensible, verifiable and executable
specification language for refactoring. To demonstrate the applicability of our
approach, we show how to define and verify a number of example refactorings in
the system.