  In this work, the critical parameters for an incompressible flow of
shear-thickening power-law fluids across a channel confined circular cylinder
have been investigated numerically. The governing equations have been solved by
using finite volume method for wide range of power-law (n=1 - 1.8) fluids and
for two blockage ratio (b = 2 and 4). Transitional insights of channel confined
cylinder, in particular, critical parameters indicating transitions from
creeping to separating flows (i.e., onset of steady symmetric wake formation),
and from steady symmetric wake to unsteady asymmetric wake formation (i.e.,
onset of vortex formation) are investigated and presented in terms of the
critical Reynolds numbers (Re^c and Re_c). The relative impacts of unconfined
and confined flows on these critical parameters have also been explored. In
general, both onsets of the flow separation and wake asymmetry delayed with
increasing values of the power-law index (n) and the wall confinement. The
dependence of critical Re on n for the confined (finite b) flow are, however,
completely opposite to that for unconfined flow, i.e., critical Re decreased
with increasing n. The influence of power-law index on the onset of vortex is
quite stronger than that on onset of wake formation. For instance, Re^c for
b=(2, 4, \infty) altered from (12.5, 7.25, 6.25) to (30.5, 9.25, 0.75) and
corresponding changes with Re_c are noted from (84.5, 70.25, 46.5) to (449.5,
179.5, 33.5) as n varied from 1 to 1.8, respectively. Stokes paradox (i.e., no
creeping flow even as Re ~ 0) apparent with unconfined flow of power-law fluids
is non-relevant in confined flows. Finally, predictive correlations for
critical Re as a function of dimensionless parameters (n and b) are presented
for their easy use in engineering analysis.


  It is proved by Sakuma and Brooks that any closed orientable $3$-manifold
with a Heegaard splitting of genus $g$ admits a $2$-fold branched cover that is
a hyperbolic $3$-manifold and a genus $g$ surface bundle over the circle. This
paper concerns entropy of pseudo-Anosov monodromies for hyperbolic fibered
$3$-manifolds. We prove that there exist infinitely many closed orientable
$3$-manifolds $M$ such that the minimal entropy over all hyperbolic, genus $g$
surface bundles over the circle as $2$-fold branched covers of the $3$-manifold
$M$ is comparable to $1/g$.


  We examine the elliptic system given by \begin{eqnarray*} \qquad \left\{
\begin{array}{lcl}
  -\Delta u =\lambda f(v) \quad \mbox{ in } \Omega
  -\Delta v =\gamma f(u) \quad \mbox{ in } \Omega, u=v =0, \quad \mbox{ on }
\pOm \end{array}\right.
  \end{eqnarray*} where $\lambda,\gamma$ are positive parameters, $\Omega$ is a
smooth bounded domain in $\IR^N$ and $f$ is a $C^{2}$ positive, nondecreasing
and convex function in $[0,\infty)$ such that $\frac{f(t)}{t}\rightarrow\infty$
as $t\rightarrow\infty$. Assuming
  $$0<\tau_{-}:=\liminf_{t\rightarrow\infty} \frac{f(t)f"(t)}{f'(t)^{2}}\leq
\tau_{+}:=\limsup_{t\rightarrow\infty} \frac{f(t)f"(t)}{f'(t)^{2}}\leq 2,$$ we
show that the extremal solution $(u^*, v^*)$ associated to the above system is
smooth provided\\
$N<\frac{2\alpha_{*}(2-\tau_{+})+2\tau_{+}}{\tau_{+}}\max\{1,\tau_{+}\}$, where
$\alpha_{*}>1$ denotes the largest root of the $2^{nd}$ order polynomial
$$P_{f}(\alpha,\tau_{-},\tau_{+}):=(2-\tau_{-})^{2} \alpha^{2}-
4(2-\tau_{+})\alpha+4(1-\tau_{+}).$$ As a consequences, $u^*, v^*\in
L^\infty(\Omega)$ for $N<5$. Moreover, if $\tau_{-}=\tau_{+}$, then $u^*,
v^*\in L^\infty(\Omega)$ for $N<10$.


  We propose a convolutional neural network (CNN) denoising based method for
seismic data interpolation. It provides a simple and efficient way to break
though the lack problem of geophysical training labels that are often required
by deep learning methods. The new method consists of two steps: (1) Train a set
of CNN denoisers from natural image clean-noisy pairs to learn denoising; (2)
Integrate the trained CNN denoisers into project onto convex set (POCS)
framework to perform seismic data interpolation. The method alleviates the
demanding of seismic big data with similar features as applications of
end-to-end deep learning on seismic data interpolation. Additionally, the
proposed method is flexible for many cases of traces missing because missing
cases are not involved in the training step, and thus it is of plug-and-play
nature. These indicate the high generalizability of our approach and the
reduction of the need of the problem-specific training. Primary results on
synthetic and field data show promising interpolation performances of the
presented CNN-POCS method in terms of signal-to-noise ratio, de-aliasing and
weak-feature reconstruction, in comparison with traditional $f$-$x$ prediction
filtering and curvelet transform based POCS methods.


  Generalizing empirical findings to new environments, settings, or populations
is essential in most scientific explorations. This article treats a particular
problem of generalizability, called "transportability", defined as a license to
transfer information learned in experimental studies to a different population,
on which only observational studies can be conducted. Given a set of
assumptions concerning commonalities and differences between the two
populations, Pearl and Bareinboim (2011) derived sufficient conditions that
permit such transfer to take place. This article summarizes their findings and
supplements them with an effective procedure for deciding when and how
transportability is feasible. It establishes a necessary and sufficient
condition for deciding when causal effects in the target population are
estimable from both the statistical information available and the causal
information transferred from the experiments. The article further provides a
complete algorithm for computing the transport formula, that is, a way of
combining observational and experimental information to synthesize bias-free
estimate of the desired causal relation. Finally, the article examines the
differences between transportability and other variants of generalizability.


  Spatially-Coupled (SC)-LDPC codes are known to have outstanding
error-correction performance and low decoding latency. Whereas previous works
on LDPC and SC-LDPC codes mostly take either an asymptotic or a finite-length
design approach, in this paper we present a unified framework for jointly
optimizing the codes' thresholds and cycle counts to address both regimes. The
framework is based on efficient traversal and pruning of the code search space,
building on the fact that the performance of a protograph-based SC-LDPC code
depends on some characteristics of the code's partitioning matrix, which by
itself is much smaller than the code's full parity-check matrix. We then
propose an algorithm that traverses all nonequivalent partitioning matrices,
and outputs a list of codes, each offering an attractive point on the trade-off
between asymptotic and finite-length performance. We further extend the
framework to designing SC-LDPC codes with sub-block locality, which is a
recently introduced feature offering fast access to sub-blocks within the code
block. Our simulations show that our framework results in SC-LDPC codes that
outperform the state-of-the-art constructions, and that it offers the
flexibility to choose low-SNR, high-SNR, or in-between SNR region as the
primary design target.


  We recently developed original electroencephalogram indices focusing on
microwaves of flattish period (named $\tau$), which correlated with volatile
anesthesia concentration in dogs. However, this mechanism remains unclear.
$\tau$ was defined as a subthreshold wave and burst wave was defined as an
above-threshold wave. This study shows that these indices well quantified the
morphological features of local field potential waveforms in mice, and made it
possible to discriminate the specific waveforms of the state of consciousness;
awake, shallow sleep, rapid eye movement sleep, and non-rapid eye movement
sleep. In addition, examination of $\tau$ suggested that microwaves are local
fluctuations of the electrode that can be formed for each data sampling, and
that its amplitude may increase with the degree of arousal.


  We provide a complete description of anisotropic scaling limits of stationary
linear random field on ${\mathbb {Z}}^3$ with long-range dependence and moving
average coefficients decaying as $O(|t_i|^{-q_i})$ in the $i$th direction,
$i=1,2,3.$ The scaling limits are taken over rectangles in ${\mathbb {Z}}^3$
whose sides increase as $O(\lambda^{\gamma_i}), i=1,2,3$ when $\lambda \to
\infty$, for any fixed $\gamma_i >0, i=1,2,3 $. We prove that all these limits
are Gaussian RFs whose covariance structure essentially is determined by the
fulfillment or violation of the balance conditions $\gamma_i q_i = \gamma_j
q_j, 1 \le i < j \le 3$. The paper extends recent results in \cite{ps2015},
\cite{ps2016}, \cite{pils2016}, \cite{pils2017} on anisotropic scaling of
long-range dependent random fields from dimension 2 to dimension 3.


  We study Gaussian quantum steering in the Schwarzschild-de Sitter (SdS)
spacetime that is endowed with both a black hole event horizon (BEH) and a
cosmological event horizon (CEH), giving rise to two different Hawking
temperatures. It is shown that the Hawking effect of the black hole always
reduces the quantum steering, but the Hawking effect of the expanding universe
does not always play the same role. For the first time, we find that the
Hawking effect can improve quantum steering. We also find that the observer who
locates in the BEH has stronger steerability than the observer who locates in
CEH. Further, we study the steering asymmetry, and the conditions for two-way,
one-way and no-way steering in the SdS spacetime. Finally, we study the
Gaussian quantum steering in the scenario of effective equilibrium temperature.
We show that quantum steering reduces monotonically with the effective
temperature but now increases monotonically with the Hawking temperature of the
black hole, which banishes the belief that the Hawking effect can only destroy
quantum steering.


  We study the $\tau \to \nu_\tau A$ decay, with $A$ an axial-vector meson. We
produce the $a_1(1260)$ and $b_1(1235)$ resonances in the Cabibbo favored mode
and two $K_1(1270)$ states in the Cabibbo suppressed mode. We take advantage of
previous chiral unitary approach results where these resonances appear
dynamically from the vector and pseudoscalar meson interaction in s-wave.
Actually two different poles were obtained associated to the $K_1(1270)$
quantum numbers. We find that the unmeasured rates for $b_1(1235)$ production
are similar to those of the $a_1(1260)$ and for the two $K_1$ states we suggest
to separate the present information on the $\bar K \pi \pi$ invariant masses
into $\bar K^* \pi$ and $\rho K$ modes, the channels to which these two
resonances couple most strongly, predicting that these modes peak at different
energies and have different widths. These measurements should shed light on the
existence of these two $K_1$ states.


  It is well known that ``equivalent'' sprint race times run with different
accompanying wind speeds or at different altitudes are anything but equivalent
races. The drag force acting on a sprinter is a function of air density and the
relative wind speed, where the former has traditionally been calculated using
the race venue's elevation above sea level. However, air density variation is
dependent on more than just altitude. This work will quantify how changes in
air temperature, barometric pressure, and humidity levels influence 100 m
sprint performances. When these effects are considered in combination, the
corrections to performances can be very large. The results suggest that a
non-negligible difference in race times can be expected for ``equivalent''
performances run with the same wind speed at the same venue or physical
altitude, but under different atmospheric conditions.


  Every proper closed subgroup of a connected Hausdorff group must have index
at least c, the cardinality of the continuum. 70 years ago Markov conjectured
that a group G can be equipped with a connected Hausdorff group topology
provided that every subgroup of G which is closed in all Hausdorff group
topologies on G has index at least c. Counter-examples in the non-abelian case
were provided 25 years ago by Pestov and Remus, yet the problem whether
Markov's Conjecture holds for abelian groups G remained open. We resolve this
problem in the positive.


  The classical Cantor's intersection theorem states that in a complete metric
space $X$, intersection of every decreasing sequence of nonempty closed bounded
subsets, with diameter approaches zero, has exactly one point. In this article,
we deal with decreasing sequences $\{K_n\}$ of nonempty closed bounded subsets
of a metric space $X$, for which the Hausdorff distance $H(K_n, K_{n+1})$ tends
to $0$, as well as for which the excess of $K_n$ over $X\setminus K_n$ tends to
$0$. We achieve nonempty intersection properties in metric spaces. The obtained
results also provide partial generalizations of Cantor's theorem.


  Our study aims to recognize M-type stars which are classified as "UNKNOWN"
due to bad quality in Large sky Area Multi-Object fibre Spectroscopic Telescope
(LAMOST) DR5 V1. A binary nonlinear hashing algorithm based on Multi-Layer
Pseudo Inverse Learning (ML-PIL) is proposed to effectively learn spectral
features for the M-type star detection, which can overcome the bad fitting
problem of template matching, particularly for low S/N spectra. The key steps
and the performance of the search scheme are presented. A positive dataset is
obtained by clustering the existing M-type spectra to train the ML-PIL
networks. By employing this new method, we find 11,410 M-type spectra out of
642,178 "UNKNOWN" spectra, and provide a supplemental catalogue. Both the
supplemental objects and released M-type stars in DR5 V1 are composed a whole M
type sample, which will be released in the official DR5 to the public in June
2019, All the M-type stars in the dataset are classified to giants and dwarfs
by two suggested separators: 1) color diagram of H versus J~K from 2MASS; 2)
line indices CaOH versus CaH1, and the separation is validated with HRD derived
from Gaia DR2. The magnetic activities and kinematics of M dwarfs are also
provided with the EW of H_alpha emission line and the astrometric data from
Gaia DR2 respectively.


  Hyperspectral pansharpening is receiving a growing interest since the last
few years as testified by a large number of research papers and challenges. It
consists in a pixel-level fusion between a lower-resolution hyperspectral
datacube and a higher-resolution single-band image, the panchromatic image,
with the goal of providing a hyperspectral datacube at panchromatic resolution.
Thanks to their powerful representational capabilities, deep learning models
have succeeded to provide unprecedented results on many general purpose image
processing tasks. However, when moving to domain specific problems, as in this
case, the advantages with respect to traditional model-based approaches are
much lesser clear-cut due to several contextual reasons. Scarcity of training
data, lack of ground-truth, data shape variability, are some such factors that
limit the generalization capacity of the state-of-the-art deep learning
networks for hyperspectral pansharpening. To cope with these limitations, in
this work we propose a new deep learning method which inherits a simple
single-band unsupervised pansharpening model nested in a sequential band-wise
adaptive scheme, where each band is pansharpened refining the model tuned on
the preceding one. By doing so, a simple model is propagated along the
wavelength dimension, adaptively and flexibly, with no need to have a fixed
number of spectral bands, and, with no need to dispose of large, expensive and
labeled training datasets. The proposed method achieves very good results on
our datasets, outperforming both traditional and deep learning reference
methods. The implementation of the proposed method can be found on
https://github.com/giu-guarino/R-PNN


  Explicit encoding of group actions in deep features makes it possible for
convolutional neural networks (CNNs) to handle global deformations of images,
which is critical to success in many vision tasks. This paper proposes to
decompose the convolutional filters over joint steerable bases across the space
and the group geometry simultaneously, namely a rotation-equivariant CNN with
decomposed convolutional filters (RotDCF). This decomposition facilitates
computing the joint convolution, which is proved to be necessary for the group
equivariance. It significantly reduces the model size and computational
complexity while preserving performance, and truncation of the bases expansion
serves implicitly to regularize the filters. On datasets involving in-plane and
out-of-plane object rotations, RotDCF deep features demonstrate greater
robustness and interpretability than regular CNNs. The stability of the
equivariant representation to input variations is also proved theoretically
under generic assumptions on the filters in the decomposed form. The RotDCF
framework can be extended to groups other than rotations, providing a general
approach which achieves both group equivariance and representation stability at
a reduced model size.


  In this paper we examine the problem of valuing an exotic derivative known as
the American passport option where the underlying is driven by a L\'evy
process. The passport option is a call option on a trading account. We derive
the pricing equation, using the dynamic programming principle, and prove that
the option value is a viscosity solution of variational inequality. We also
establish the comparison principle, which yields uniqueness and the convexity
of the viscosity solution.


  We discuss Strassler's hypothesis of matching nonperturbative effects in
orbifold pairs of gauge theories which are perturbatively planar equivalent.
One of the examples considered is the parent N=1 SU(N) supersymmetric
Yang-Mills theory and its nonsupersymmetric orbifold daughter. We apply two
strategies allowing us to study nonperturbative effects: (i) low-energy
theorems; (ii) putting the theory on small-size T^4 or R^3 x S^1 the parent and
daughter theories are weakly coupled and amenable to quasiclassical treatment.
In all cases our consideration yields a mismatch between the parent and
daughter theories. Thus, regretfully, we present evidence against Strassler's
hypothesis.


  This paper focuses on explaining changes over time in globally-sourced,
annual temporal data, with the specific objective of identifying pivotal
factors that contribute to these temporal shifts. Leveraging such analytical
frameworks can yield transformative impacts, including the informed refinement
of public policy and the identification of key drivers affecting a country's
economic evolution. We employ Local Interpretable Model-agnostic Explanations
(LIME) to shed light on national happiness indices, economic freedom, and
population metrics, spanning variable time frames. Acknowledging the presence
of missing values, we employ three imputation approaches to generate robust
multivariate time-series datasets apt for LIME's input requirements. Our
methodology's efficacy is substantiated through a series of empirical
evaluations involving multiple datasets. These evaluations include comparative
analyses against random feature selection, correlation with real-world events
as elucidated by LIME, and validation through Individual Conditional
Expectation (ICE) plots, a state-of-the-art technique proficient in feature
importance detection.


  We present the explicit inverse of a class of symmetric tridiagonal matrices
which is almost Toeplitz, except that the first and last diagonal elements are
different from the rest. This class of tridiagonal matrices are of special
interest in complex statistical models which uses the first order
autoregression to induce dependence in the covariance structure, for instance,
in econometrics or spatial modeling. They also arise in interpolation problems
using the cubic spline. We show that the inverse can be expressed as a linear
combination of Chebyshev polynomials of the second kind and present results on
the properties of the inverse, such as bounds on the row sums, the trace of the
inverse and its square, and their limits as the order of the matrix increases.


  This paper examines the most probable route to chaos in high-dimensional
dynamical systems in a very general computational setting. The most probable
route to chaos in high-dimensional, discrete-time maps is observed to be a
sequence of Neimark-Sacker bifurcations into chaos. A means for determining and
understanding the degree to which the Landau-Hopf route to turbulence is
non-generic in the space of $C^r$ mappings is outlined. The results comment on
previous results of Newhouse, Ruelle, Takens, Broer, Chenciner, and Iooss.


  We explored the magnetic behavior of a common two-phase nanomagnetic system
by Monte Carlo computer simulation of a modified Heisenberg model on a 3D
complex lattice with single- and cluster-spins. The effect of exchange coupling
between two component magnetic phases was studied on the enhancement in Curie
temperature (ECT) of the intergranular amorphous region of a common
duplex-phase alloy system, with numerous nano-crystallites embedded in
amorphous matrix. The dependences of ECT were investigated systematically upon
the nanocrystallite size, the volume fraction and the interspace among
crystallites. It was observed that large crystallized volume fraction, small
grain size and thin inter-phase thickness lead to the obvious ECT of
intergranular amorphous region whereas the Curie temperature of
nanocrystallites declines slightly. There is a simulative empirical formula
which relates the reduced ECT to microstructure parameter and conforms to its
experimental counterpart within an order of magnitude. In addition, we also
simulated the demagnetization of a hard-soft nanocomposite system. We estimated
the influence of exchange coupling between two component phases on the
cooperativity of two-phase magnetizations and the coherent reversal of
magnetizations as well as coercivity and energy product.


  Optimal signaling for secrecy rate maximization in Gaussian MIMO wiretap
channels is considered. While this channel has attracted a significant
attention recently and a number of results have been obtained, including the
proof of the optimality of Gaussian signalling, an optimal transmit covariance
matrix is known for some special cases only and the general case remains an
open problem. An iterative custom-made algorithm to find a globally-optimal
transmit covariance matrix in the general case is developed in this paper, with
guaranteed convergence to a \textit{global} optimum. While the original
optimization problem is not convex and hence difficult to solve, its minimax
reformulation can be solved via the convex optimization tools, which is
exploited here. The proposed algorithm is based on the barrier method extended
to deal with a minimax problem at hand. Its convergence to a global optimum is
proved for the general case (degraded or not) and a bound for the optimality
gap is given for each step of the barrier method. The performance of the
algorithm is demonstrated via numerical examples. In particular, 20 to 40
Newton steps are already sufficient to solve the sufficient optimality
conditions with very high precision (up to the machine precision level), even
for large systems. Even fewer steps are required if the secrecy capacity is the
only quantity of interest. The algorithm can be significantly simplified for
the degraded channel case and can also be adopted to include the per-antenna
power constraints (instead or in addition to the total power constraint). It
also solves the dual problem of minimizing the total power subject to the
secrecy rate constraint.


  We present high-resolution Magellan/MIKE spectra of the four brightest
confirmed red giant stars in the ultra-faint dwarf galaxy Bootes II (Boo II).
These stars all inhabit the metal-poor tail of the Boo II metallicity
distribution function. The chemical abundance pattern of all detectable
elements in these stars is consistent with that of the Galactic halo. However,
all four stars have undetectable amounts of neutron-capture elements Sr and Ba,
with upper limits comparable to the lowest ever detected in the halo or in
other dwarf galaxies. One star exhibits significant radial velocity variations
over time, suggesting it to be in a binary system. Its variable velocity has
likely increased past determinations of the Boo II velocity dispersion. Our
four stars span a limited metallicity range, but their enhanced
{\alpha}-abundances and low neutron-capture abundances are consistent with the
interpretation that Boo II has been enriched by very few generations of stars.
The chemical abundance pattern in Boo II confirms the emerging trend that the
faintest dwarf galaxies have neutron-capture abundances distinct from the halo,
suggesting the dominant source of neutron-capture elements in halo stars may be
different than in ultra-faint dwarfs.


  The main aim of this thesis is to reveal some interesting aspects of the
purely affine theory of gravity and its cosmological implication. A particular
attention will be devoted to its consequences when applied to cosmological
inflation. Primarily, affine spacetime, composed of geodesics with no notion of
length and angle, accommodates gravity but not matter. The thesis study is
expected to reveal salient properties of matter dynamics in affine spacetime
and may reveal an intimate connection between vacuum state and metrical
gravity. An interesting application of the framework is the inflationary
regime, where it is shown that affine gravity prefers only a unique metric
tensor such that the transition from nonminimal to minimal coupling of the
inflaton is performed only via redefinition of the latter. This allows us to
avoid the use of the so called conformal frames. In fact, unlike metric
gravity, the metric tensor in affine gravity is generated and not postulated a
priori, thus this tensor is absent in the actions and conformal transformation
does not make sense. Last but not least, we try to show how metric gravity can
be induced through a simple structure that contains only affine connection and
scalar fields. General relativity arises classically only at the vacuum, and
this view of gravity may be considered as a new way to inducing metric
elasticity of space, not through quantum corrections as in standard induced
gravity, but only classically. The thesis is concluded by analyzing affine
gravity in a particular higher-dimensional manifold (product of two spaces) in
an attempt to understand both, the cosmological constant and matter
dynamically.


  In 1760, Leonhard Euler began to write beautiful Letters to a German Princess
on Diverse Subjects of Physics and Philosophy. Much has been written about
Euler and his work, but we wonder, who was the princess? How did she become
involved with the greatest mathematician of her time? The princess was a
fifteen year old named Friederike Charlotte von Brandenburg-Schwedt. In this
article we explore her story and the nature of the letters.


  A new southern star-formation region, located at an estimated distance of
~1.5 kpc in the Lynds 1664 dark cloud in Canis Major, is described. Lynds 1664
contains several compact star clusters, small stellar groups, and young stars
associated with reflection nebulae. Narrow-band H{\alpha} and [SII] images
obtained with 4-m CTIO telescope reveal more than 20 new Herbig-Haro objects
associated with several protostellar outflows.


  Quasars behind the Galactic plane (GPQs) are important astrometric references
and valuable probes of Galactic gas, yet the search for GPQs is difficult due
to severe extinction and source crowding in the Galactic plane. In this paper,
we present a sample of 204 spectroscopically confirmed GPQs at |b|<20{\deg},
191 of which are new discoveries. This GPQ sample covers a wide redshift range
from 0.069 to 4.487. For the subset of 230 observed GPQ candidates, the lower
limit of the purity of quasars is 85.2%, and the lower limit of the fraction of
stellar contaminants is 6.1%. Using a multicomponent spectral fitting, we
measure the emission line and continuum flux of the GPQs, and estimate their
single-epoch virial black hole masses. Due to selection effects raised from
Galactic extinction and target magnitude, these GPQs have higher black hole
masses and continuum luminosities in comparison to the SDSS DR7 quasar sample.
The spectral-fitting results and black hole mass estimates are compiled into a
main spectral catalog, and an extended spectral catalog of GPQs. The successful
identifications prove the reliability of both our GPQ selection methods and the
GPQ candidate catalog, shedding light on the astrometric and astrophysical
programs that make use of a large sample of GPQs in the future.


  We report the influence of the field effect on the dc resistance and Hall
coefficient in the strain-induced Mott insulating state of an organic
superconductor $\kappa$-(BEDT-TTF)$_{2}$Cu[N(CN)$_{2}$]Br. Conductivity obeys
the formula for activated transport $\sigma_{\Box} =
\sigma_{0}\exp(-W/k_{B}T)$, where $\sigma_{0}$ is a constant and $W$ depends on
the gate voltage. The gate voltage dependence of the Hall coefficient shows
that, unlike in conventional FETs, the effective mobility of dense hole
carriers ($\sim1.6\times 10^{14}$ cm$^{-2}$) is enhanced by a positive gate
voltage. This implies that carrier doping involves delocalization of intrinsic
carriers that were initially localized due to electron correlation.


  In this paper, we give the proof of the general Kastler-Kalau-Walze type
theorem and the Dabrowski-Sitarz-Zalecki type theorem on odd dimensional
compact manifolds with boundary.


  We prove that all entire smooth strictly convex self-shrinking solutions on
$\mathbb{R}^n$ to the Hessian quotient flows must be quadratic. This
generalizes the rigidity theorem for entire self-shrinking solutions to the
Lagrangian mean curvature flow in pseudo-Euclidean space due to Ding-Xin
\cite{DX}. Moreover, we show that our argument works for a larger class of
equations. In particular, we obtain rigidity results for entire self-shrinking
solutions on $\mathbb{C}^n$ to the K\"{a}hler-Ricci flow under certain
conditions.


  We investigate the rectification and negative differential effects of
full-counting statistics of conjugate thermal spin transport in a spin Seebeck
engine. The engine is made by an electron/magnon interface diode driven by a
temperature bias, of which the scaled cumulant generating function is
formulated in the framework of nonequilibrium Green's function. The strongly
fluctuating interfacial electron density of states induced by quantum dot is
responsible for these intriguing properties. This work is relevant for
designing efficient spin caloritronic engine and can broaden our view in
nonequilibrium thermodynamics and the nonlinear phenomenon in quantum transport
system.


  Machine learning (ML) algorithms are gaining increased importance in many
academic and industrial applications, and such algorithms are, accordingly,
becoming common components in computer science curricula. Learning ML is
challenging not only due to its complex mathematical and algorithmic aspects,
but also due to a) the complexity of using correctly these algorithms in the
context of real-life situations and b) the understanding of related social and
ethical issues. Cognitive biases are phenomena of the human brain that may
cause erroneous perceptions and irrational decision-making processes. As such,
they have been researched thoroughly in the context of cognitive psychology and
decision making; they do, however, have important implications for computer
science education as well. One well-known cognitive bias, first described by
Kahneman and Tversky, is the base rate neglect bias, according to which humans
fail to consider the base rate of the underlying phenomena when evaluating
conditional probabilities. In this paper, we explore the expression of the base
rate neglect bias in ML education. Specifically, we show that about one third
of students in an Introduction to ML course, from varied backgrounds (computer
science students and teachers, data science, engineering, social science and
digital humanities), fail to correctly evaluate ML algorithm performance due to
the base rate neglect bias. This failure rate should alert educators and
promote the development of new pedagogical methods for teaching ML algorithm
performance.


  The exact determination of ground states of small systems is used in a
scaling study of the random-field Ising model. While three variants of the
model are found to be in the same universality class in 3 dimensions, the
Gaussian and bimodal models behave distinctly in 4 dimensions with the latter
apparently having a discontinuous jump in the magnetization. A finite-size
scaling analysis is presented for this transition.


  We present a localization proof of the fact that the cohomology of the moduli
spaces of genus zero stable maps to projective spaces is entirely tautological.
In addition, we obtain a description of a Bialynicki-Birula stratification in
the context of Gathmann's moduli spaces of maps with prescribed contact order
to a fixed hyperplane.


  Stochastic differentiable approximation schemes are widely used for solving
high dimensional problems. Most of existing methods satisfy some desirable
properties, including conditional descent inequalities, and almost sure (a.s.)
convergence guarantees on the objective function, or on the involved gradient.
However, for non-convex objective functions, a.s. convergence of the iterates,
i.e., the stochastic process, to a critical point is usually not guaranteed,
and remains an important challenge. In this article, we develop a framework to
bridge the gap between descent-type inequalities and a.s. convergence of the
associated stochastic process. Leveraging a novel Kurdyka-Lojasiewicz property,
we show convergence guarantees of stochastic processes under mild assumptions
on the objective function. We also provide examples of stochastic algorithms
benefiting from the proposed framework and derive a.s. convergence guarantees
on the iterates.


  Lattice walks are used to model various physical phenomena. In particular,
walks within Weyl chambers connect directly to representation theory via the
Littelmann path model. We derive asymptotics for centrally weighted lattice
walks within the Weyl chamber corresponding to $A_2$ by using tools from
analytic combinatorics in several variables (ACSV). We find universality
classes depending on the weights of the walks, in line with prior results on
the weighted Gouyou-Beauchamps model. Along the way, we identify a type of
singularity within a multivariate rational generating function that is not yet
covered by the theory of ACSV. We conjecture asymptotics for this type of
singularity.


  Modern neuroscience is currently limited in its capacity to perform long
term, wide-field measurements of neuron electromagnetics with nanoscale
resolution. Quantum microscopy using the nitrogen vacancy centre (NV) can
provide a potential solution to this problem with electric and magnetic field
sensing at nano-scale resolution and good biocompatibility. However, the
performance of existing NV sensing technology does not allow for studies of
small mammalian neurons yet. In this paper, we propose a solution to this
problem by engineering NV quantum sensors in diamond nanopillar arrays. The
pillars improve light collection efficiency by guiding excitation/emission
light, which improves sensitivity. More importantly, they also improve the size
of the signal at the NV by removing screening charges as well as coordinating
the neuron growth to the tips of the pillars where the NV is located. Here, we
provide a growth study to demonstrate coordinated neuron growth as well as the
first simulation of nano-scopic neuron electric and magnetic fields to assess
the enhancement provided by the nanopillar geometry.


  The primary present-day observables upon which theories of galaxy evolution
are based are a system's morphology, dynamics, colour, and chemistry.
Individually, each provides an important constraint to any given model; in
concert, the four represent a fundamental (intractable) boundary condition for
chemodynamical simulations. We review the current state-of-the-art
semi-analytical and chemodynamical models for the Milky Way, emphasising the
strengths and weaknesses of both approaches.


  Breaking a complex bio-social phenomenon (epidemic) into its components,
considering the processes that determine its dynamics, formalizing the accepted
hypotheses in mathematical equations, selecting appropriate experimental and
statistical material, and constructing a mathematical model - those are typical
tasks of scientific research. A specific data processing method (balanced
identification) and appropriate information technology made it possible to
consider a number of models, determine the general biological laws of the
virus-human interaction (common to all populations), and the country specific
social features of epidemic management in the countries (or cities) under
consideration. As the initial data, only new cases are used. Data from
different countries is taken from official sources and processed in a uniform
way. The obtained estimates of the number of undetected infected are lower
estimates.


  This paper has been withdrawn due to an error in the proof of the main
theorem.


  Normalizing Flows (NFs) are flexible explicit generative models that have
been shown to accurately model complex real-world data distributions. However,
their invertibility constraint imposes limitations on data distributions that
reside on lower dimensional manifolds embedded in higher dimensional space.
Practically, this shortcoming is often bypassed by adding noise to the data
which impacts the quality of the generated samples. In contrast to prior work,
we approach this problem by generating samples from the original data
distribution given full knowledge about the perturbed distribution and the
noise model. To this end, we establish that NFs trained on perturbed data
implicitly represent the manifold in regions of maximum likelihood. Then, we
propose an optimization objective that recovers the most likely point on the
manifold given a sample from the perturbed distribution. Finally, we focus on
3D point clouds for which we utilize the explicit nature of NFs, i.e. surface
normals extracted from the gradient of the log-likelihood and the
log-likelihood itself, to apply Poisson surface reconstruction to refine
generated point sets.


  A self-consistent model is developed for the surface and bulk states of thin
Y_{1-y}Ca_yBa_2Cu_3O_{7-\delta} (YCBCO) films. The dispersions of the chain and
plane layers are modelled by tight-binding bands, and the electronic structure
is then calculated for a finite-thickness film. The dopant atoms are treated
within a virtual crystal approximation. Because YCBCO is a polar material,
self-consistent treatment of the long range Coulomb interaction leads to a
transfer of charge between the film surfaces, and to the formation of surface
states. The tight binding band parameters are constrained by the requirement
that the calculated band structure of surface states at CuO$_2$-terminated
surfaces be in agreement with photoemission experiments. The spectral function
and density of states are calculated and compared with experiments. Unlike the
case of Bi_2Sr_2CaCu_2O_8, where the surfaces are believed to be representative
of the bulk, the densities of states at the YCBCO surfaces are shown to be
qualitatively different from the bulk, and are sensitive to doping. The
calculated spectral function agrees closely with both bulk-sensitive and
surface-sensitive photoemission results, while the calculated density of states
for optimally-doped YCBCO agrees closely with tunneling experiments. We find
that some density of states features previously ascribed to competing order can
be understood as band structure effects.


  We study an equivalence class of iterated rational Darboux transformations
applied on the harmonic oscillator, showing that many choices of state adding
and state deleting transformations lead to the same transformed potential. As a
by-product, we derive new identities between determinants whose entries are
Hermite polynomials. These identities have a combinatorial interpretation in
terms of Maya diagrams, partitions and Durfee rectangles, and serve to
characterize the equivalence class of rational Darboux transformations. Since
the determinants have different orders, we analyze the problem of finding the
minimal order determinant in each equivalence class, or equivalently, the
minimum number of Darboux transformations. The solution to this problem has an
elegan graphical interpretation. The results are applied to provide alternative
and more efficient representations for exceptional Hermite polynomials and
rational solutions of the Painlev\'e IV equation.


  Motivated by an observation in "Vertices, sources and Green correspondents of
the simple modules for the large Mathieu groups", J. of Algebra 322, we
determine the source algebra, and therefore all the structure, of the blocks
without essential Brauer pairs where the simple modules of all the Brauer
corespondents have trivial sources.


  Galled trees are widely studied as a recombination model in population
genetics. This class of phylogenetic networks is generalized into galled
networks by relaxing a structural condition. In this work, a linear recurrence
formula is given for counting 1-galled networks, which are galled networks
satisfying the condition that each reticulate node has only one leaf
descendant. Since every galled network consists of a set of 1-galled networks
stacked one on top of the other, a method is also presented to count and
enumerate galled networks.


  We argue that a $SO(d)$ magnetic monopole in an asymptotically AdS space-time
is dual to a $d$-dimensional strongly coupled system in a solid state. In light
of this, it would be remiss of us not to dub such a field configuration
$solidon$. In the presence of mixed boundary conditions, a solidon
spontaneously breaks translations (among many other symmetries) and gives rise
to Goldstone excitations on the boundary$-$the phonons of the solid. We derive
the quadratic action for the boundary phonons in the probe limit and show that,
when the mixed boundary conditions preserve conformal symmetry, the
longitudinal and transverse sound speeds are related to each other as expected
from effective field theory arguments. We then include backreaction and
calculate the free energy of the solidon for a particular choice of mixed
boundary conditions, corresponding to a relevant multi-trace deformation of the
boundary theory. We find such free energy to be lower than that of thermal AdS.
This suggests that our solidon undergoes a solid-to-liquid first order phase
transition by melting into a Schwarzschild-AdS black hole as the temperature is
raised.


  A new variant of the pencil-beam (PB) algorithm for dose distribution
calculation for radiotherapy with protons and heavier ions, the grid-dose
spreading (GDS) algorithm, is proposed. The GDS algorithm is intrinsically
faster than conventional PB algorithms due to approximations in convolution
integral, where physical calculations are decoupled from simple grid-to-grid
energy transfer. It was effortlessly implemented to a carbon-ion radiotherapy
treatment planning system to enable realistic beam blurring in the field, which
was absent with the broad-beam (BB) algorithm. For a typical prostate
treatment, the slowing factor of the GDS algorithm relative to the BB algorithm
was 1.4, which is a great improvement over the conventional PB algorithms with
a typical slowing factor of several tens. The GDS algorithm is mathematically
equivalent to the PB algorithm for horizontal and vertical coplanar beams
commonly used in carbon-ion radiotherapy while dose deformation within the size
of the pristine spread occurs for angled beams, which was within 3 mm for a
single proton pencil beam of $30^\circ$ incidence, and needs to be assessed
against the clinical requirements and tolerances in practical situations.


  We investigate how Viro's integral calculus applies for the study of the
topology of stable maps. We also discuss several applications to Morin maps and
complex maps.


  The transition to turbulence in conduits is among the longest-standing
problems in fluid mechanics. Challenges in producing or saving energy hinge on
understanding promotion or suppression of turbulence. While a global picture
based on an intrinsically 3D subcritical mechanism is emerging for 3D
turbulence, subcritical turbulence is yet to even be observed when flows
approach two dimensions, e.g. under intense rotation or magnetic fields. Here,
stability analysis and direct numerical simulations demonstrate a subcritical
quasi-2D transition from laminar flow to turbulence, via a radically different
2D mechanism to the 3D case, driven by nonlinear Tollmien--Schlichting waves.
This alternative scenario calls for a new line of thought on the transition to
turbulence and should inspire new strategies to control transition in rotating
devices and nuclear fusion reactor blankets.


  The formula for the lens is derived based on the information of instantaneous
focal function. Focal function is an important tool in designing lenses with
extended depth of focus (EDoF) because this allows EDoF lens designers to try
out various mathematical curves using computers to optimize their design. Once
an optimal focal function information is obtained, the corresponding physical
EDoF lens can be fabricated using the lens equation formulated in this
presentation.


  In one of the several manifestations, the future cellular networks are
required to accommodate a massive number of devices; several orders of
magnitude compared to today's networks. At the same time, the future cellular
networks will have to fulfill stringent latency constraints. To that end, one
problem that is posed as a potential showstopper is extreme congestion for
requesting uplink scheduling over the physical random access channel (PRACH).
Indeed, such congestion drags along scheduling delay problems. In this paper,
the use of self-organized device-to-device (D2D) clustering is advocated for
mitigating PRACH congestion. To this end, the paper proposes two D2D clustering
schemes, namely; Random-Based Clustering (RBC) and Channel-Gain-Based
Clustering (CGBC). Accordingly, this paper sheds light on random access within
the proposed D2D clustering schemes and presents a case study based on a
stochastic geometry framework. For the sake of objective evaluation, the D2D
clustering is benchmarked by the conventional scheduling request procedure.
Accordingly, the paper offers insights into useful scenarios that minimize the
scheduling delay for each clustering scheme. Finally, the paper discusses the
implementation algorithm and some potential implementation issues and remedies.


  We present numerical results with a focus on power transfer between two
standard linear antenna arrays placed in the near field, where a much smaller
active multi-antenna feeder (AMAF) space feeds a far larger passive array
referred to as a reflective intelligent surface (RIS). The interest is in the
regime of focal length to diameter ratio ($F/D$) less than unity. We address
the question of center feed vs. end feed for array fed array antenna
architectures and present the following novel findings and contributions: 1. In
the regime of $F/D$ ratio less than one, the AMAF-RIS power transfer deviates
from the classical inverse square law. Furthermore, the behavior of the power
transmission coefficient is more sensitive to the $F/D$ ratio than to a
particular RIS size. 2. For an end feed, non-eigenmodes provide better beam
shapes than the eigenmodes, which are still inferior to beam shapes from the
center feed eigenmodes. 3. The center feed provides more power gain than an end
feed. This clearly illustrates that the center feed configuration should be
used for array fed arrays, in contrast to the classical parabolic geometry.


  This note complements and clarifies the results obtained in the original
paper {\it QCD Parameters Correlations from Heavy Quarkonia} [1] where, here,
we present a more detailed discussion of the \alpha_s-results obtained @ N2LO
at two different subtraction scales \mu=2.85 and 9.50 GeV from the
(pseudo)scalar heavy quarkonia mass-spliitings
M_{\chi_{0c(0b)}}-M_{\eta_{c(b)}}. We obtain from the
M_{\chi_{0c}}-M_{\eta_{c}} sum rule: \alpha_s(2.85)=0.262(9) -->
\alpha_s(M_\tau)=0.318(15) --> \alpha_s(M_Z)=0.1183(19)(3) and from the
M_{\chi_{0b}}-M_{\eta_{b}} one: \alpha_s(9.50)=0.180(8) -->
\alpha_s(M_\tau)=0.312(27) --> \alpha_s(M_Z)=0.1175(32)(3), in complete
agreement with the world average: \alpha_s(M_Z)=0.1181(11).


  In this paper, the nonlinear (orbital) stability of static 180^\circ N\'eel
walls in ferromagnetic films, under the reduced wave-type dynamics for the
in-plane magnetization proposed by Capella, Melcher and Otto [CMO07], is
established. It is proved that the spectrum of the linearized operator around
the static N\'eel wall lies in the stable complex half plane with non-positive
real part. This information is used to show that small perturbations of the
static N\'eel wall converge to a translated orbit belonging to the manifold
generated by the static wall.


  We study a two-player zero-sum stochastic differential game with asymmetric
information where the payoff depends on a controlled continuous-time Markov
chain X with finite state space which is only observed by player 1. This model
was already studied in Cardaliaguet et al. (2015) through an approximating
sequence of discrete-time games. Our first contribution is the proof of the
existence of the value in the continuous-time model based on duality
techniques. This value is shown to be the unique solution of the same
Hamilton-Jacobi equation with convexity constraints which characterized the
limit value obtained in Cardaliaguet et al. (2015). Our second main
contribution is to provide a simpler equivalent formulation for this
Hamilton-Jacobi equation using directional derivatives and exposed points,
which we think is interesting for its own sake as the associated comparison
principle has a very simple proof which avoids all the technical machinery of
viscosity solutions.


  In this work, by using techniques and results of differential geometry, we
propose a new numerical method on complete Riemannian manifolds to find zeros
of vector fields. Our algorithm generalizes the classical secant method


  We report the first direct spectroscopic measurement of the velocity
dispersion function (VDF) for the high-mass red sequence (RS) galaxy population
at redshift $z\sim0.55$. We achieve high precision by using a sample of 600,000
massive galaxies with spectra from the Baryon Oscillation Spectroscopic Survey
(BOSS) of the third Sloan Digital Sky Survey (SDSS-III), covering stellar
masses $M_*\gtrsim10^{11}~M_{\odot}$. We determine the VDF by projecting the
joint probability-density function (PDF) of luminosity $L$ and velocity
dispersion $\sigma$, i.e. $p(L,\sigma)$, defined by our previous measurements
of the RS luminosity function and $L-\sigma$ relation for this sample. These
measurements were corrected from red--blue galaxy population confusion,
photometric blurring, incompleteness and selection effects within a
forward-modeling framework that furthermore correctly accommodates the low
spectroscopic signal-to-noise ratio of individual BOSS spectra. Our $z\sim0.55$
RS VDF is in overall agreement with the $z\sim0$ early-type galaxy (ETG) VDF at
$\log_{10}\sigma\gtrsim2.47$, however the number density of $z=0.55$ RS
galaxies that we report is larger than that of $z=0$ ETG galaxies at
$2.35\gtrsim\log_{10}\sigma\gtrsim 2.47$. The extrapolation of an
intermediate-mass L-$\sigma$ relation towards the high-mass end in previous
low-z works may be responsible for this disagreement. Evolutionary
interpretation of this comparison is also subject to differences in the way the
respective samples are selected; these differences can be mitigated in future
work by analyzing $z=0$ SDSS data using the same framework presented in this
paper. We also provide the sample PDF for the RS population (i.e. uncorrected
for incompleteness), which is a key ingredient for gravitational lensing
analyses using BOSS.


  In this work, the successful heteroepitaxial growth of boron carbide (B x C)
on 4HSiC(0001) 4{\textdegree} off substrate using chemical vapor deposition
(CVD) is reported. Towards this end, a two-step procedure was developed,
involving the 4H-SiC substrate boridation under BCl 3 precursor at
1200{\textdegree}C, followed by conventional CVD under BCl 3 + C 3 H 8 at
1600{\textdegree}C. Such a procedure allowed obtaining reproducibly
monocrystalline (0001) oriented films of B x C with a step flow morphology at a
growth rate of 1.9 $\mu$m/h. Without the boridation step, the layers are
systematically polycrystalline. The study of the epitaxial growth mechanism
shows that a monocrystalline B x C layer is formed after boridation but covered
with a B-and Si-containing amorphous layer. Upon heating up to
1600{\textdegree}C, under pure H 2 atmosphere, the amorphous layer was
converted into epitaxial B x C and transient surface SiB x and Si crystallites.
These crystallites disappear upon CVD growth.


  We calculate the contributions of the neutral top-pion, predicted by
topcolor-assisted technicolor (TC2) theory, to top-charm production via the
processes $\gamma\gamma \longrightarrow\bar{t}c$ and $e^{+}e^{-}\longrightarrow
\gamma\gamma\longrightarrow \bar{t}c$ at the high energy linear $e^{+}e^{-}$
collider (LC) experiments. The cross section is of order $10^{-2}pb$ in most of
the parameter space of TC2 theory, which may be detected at the LC experiments.
So the process $e^{+}e^{-}\longrightarrow \bar{t}c$ can be used to detect the
signature of TC2 theory.


  HESS J0632+057 is a gamma-ray binary composed of a compact object orbiting a
Be star with a period of about $315$ days. Extensive X-ray and TeV gamma-ray
observations have revealed a peculiar light curve containing two peaks,
separated by a dip. We present the results of simultaneous observations in hard
X-rays with NuSTAR and in TeV gamma-rays with VERITAS, performed in November
and December 2017. These observations correspond to the orbital phases
$\phi\approx0.22$ and $0.3$, where the fluxes are rising towards the first
light-curve peak. A significant variation of the spectral index from
1.77$\pm$0.05 to 1.56$\pm$0.05 is observed in the X-ray data. The
multi-wavelength spectral energy distributions (SED) derived from the
observations are interpreted in terms of a leptonic model, in which the compact
object is assumed to be a pulsar and non-thermal radiation is emitted by
high-energy electrons accelerated at the shock formed by the collision between
the stellar and pulsar wind. The results of the SED fitting show that our data
can be consistently described within this scenario, and allow us to estimate
the magnetization of the pulsar wind at the location of the shock formation.
The constraints on the pulsar-wind magnetization provided by our results are
shown to be consistent with those obtained from other systems.


  We provide a new description of logarithmic topological Andr\'e-Quillen
homology in terms of the indecomposables of an augmented ring spectrum. The new
description allows us to interpret logarithmic TAQ as an abstract cotangent
complex, and leads to an base-change formula for logarithmic topological
Hochschild homology. The latter is analogous to results of Weibel-Geller for
Hochschild homology of discrete rings, and of McCarthy-Minasian and Mathew for
topological Hochschild homology. For example, our results imply that
logarithmic THH satisfies base-change for tamely ramified extensions of
discrete valuation rings.


  We report on the largest Swift AGN monitoring program, concerning UV/optical
variability in Seyferts. From 554 observations, over a 750d period, of the
Seyfert galaxy NGC 5548, we see (McHardy et al. 2014) a good overall
correlation between the X-ray and UV/optical bands,particularly on short
timescales (tens of days). The UVOT bands are found to lag behind X-rays with a
lag scaling as wavelength to the power 1.23 +/- 0.31, in excellent agreement
with that expected (1.33) if UV/optical variability arises from reprocessing of
X-rays by the accretion disc. However, the observed lags are ~3 times longer
than expected from a standard Shakura-Sunyaev disc, raising real concerns about
the detailed validity of this model. The results can be explained with a
slightly larger mass and accretion rate, and a hotter disc, or if the disc is
clumpy, thereby enhancing the emission from the outer regions.


  Motivated by the recent observation of the high energy electron and positron
excesses in cosmic ray by PAMELA and ATIC/PPB-BETS, we suggest an anomaly-free
scenario for the universal extra dimension that localizes the SM quarks and
splits the spectrum of KK quarks from KK leptons. When the SM quarks are "well
localized" at the boundaries, the most stringent bound of the model ($1/R >
510$ GeV) comes from the resonance search for the Tevatron dijet channels. Even
at the early stage of LHC, one can discover the second KK gluon for masses up
to 4 TeV.


  For Riemannian submanifolds of a semi-Riemannian manifold, we introduce the
concepts of \emph{total shear tensor} and \emph{shear operators} as the
trace-free part of the corresponding second fundamental form and shape
operators. The relationship between these quantities and the umbilical
properties of the submanifold is shown. Several novel notions of umbilical
submanifolds are then considered along with the classical concepts of totally
umbilical and pseudo-umbilical submanifolds.
  Then we focus on the case of co-dimension $2$, and we present necessary and
sufficient conditions for the submanifold to be umbilical with respect to a
normal direction. Moreover, we prove that the umbilical direction, if it
exists, is unique ---unless the submanifold is totally umbilical--- and we give
a formula to compute it explicitly. When the ambient manifold is Lorentzian we
also provide a way of determining its causal character. We end the paper by
illustrating our results on the Lorentzian geometry of the Kerr black hole.


  The topological aspects of Einstein gravity suggest that topological
invariance could be a more profound principle in understanding quantum gravity.
In this work, we explore a topological supergravity action that initially
describes a universe without Riemann curvature, which seems trivial. However,
we made a surprising discovery by introducing a small deformation parameter
$\lambda$, which can be regarded as an AdS generalization of supersymmetry
(SUSY). We find that the deformed topological quantum field theory (TQFT)
becomes unstable at low energy, resulting in the emergence of a classical
metric, whose dynamics are controlled by the Einstein equation. Our findings
suggest that a quantum theory of gravity could be governed by a UV fixed point
of a SUSY TQFT, and classical spacetime ceases to exist beyond the Planck
scale.


  The physical properties of an axisymmetric black-hole-ring system are studied
analytically within the framework of general relativity to second order in the
dimensionless mass ratio $\mu\equiv m/M$. In particular, we analyze the
asymptotic behaviors of the binding-energy and the total angular-momentum of
the two-body system in the vicinity of the light ring at $R=3M$, where the
circular orbit becomes null. We find that both quantities diverge {\it
quadratically} in $\mu(1-3M/R)^{-1}$ at the light ring. The reported divergent
behavior of the physical quantities stems from the second order spin-orbit
interaction between the black hole and the orbiting object (the dragging of
inertial frames by the orbiting ring). It is shown that this composed
black-hole-ring toy model captures some of the essential features of the
conservative dynamics of the (astrophysically more interesting)
black-hole-particle system. In particular, we show that both systems share the
{\it same} quadratic divergent behavior of the physical quantities near the
light ring. Moreover, we prove that both systems are characterized by the {\it
same} ratio ${{E^{(2)}(R\to 3M)}\over{J^{(2)}(R\to
3M)}}={{1}\over{3\sqrt{3}}}$, where $E^{(2)}$ and $J^{(2)}$ are the divergent
second order (self-interaction) expansion coefficients of the binding-energies
and the angular-momenta of the systems, respectively.


  The electronic state of WTe2, a candidate of type-II Weyl semimetal, is
investigated by using laser-based spin- and angle-resolved photoemission
spectroscopy (SARPES). We prepare the pair of WTe2 samples, one with (001)
surface and the other with (00-1) surface, by "sandwich method", and measure
the band structures of each surface separately. The Fermi arcs are observed on
both surfaces. We identify that the Fermi arcs on the two surfaces are both
originating from surface states. We further find a surface resonance band,
which connects with the Fermi-arc band, forming a Dirac-cone-like band
dispersion. Our results indicate that the bulk electron and hole bands are much
closer in momentum space than band calculations.


  We study the Poiseuille flow of a soft-glassy material above the jamming
point, where the material flows like a complex fluid with Herschel- Bulkley
rheology. Microscopic plastic rearrangements and the emergence of their spatial
correlations induce cooperativity flow behavior whose effect is pronounced in
presence of confinement. With the help of lattice Boltzmann numerical
simulations of confined dense emulsions, we explore the role of geometrical
roughness in providing activation of plastic events close to the boundaries. We
probe also the spatial configuration of the fluidity field, a continuum
quantity which can be related to the rate of plastic events, thereby allowing
us to establish a link between the mesoscopic plastic dynamics of the jammed
material and the macroscopic flow behaviour.


  The authors demonstrate quadratic mixing of weak time harmonic
electromagnetic fields applied to Superconducting Quantum Interference Filters,
manufactured from high-$T_{\mathrm{c}}$ grain boundary Josephson junctions and
operated in active microcooler. The authors use the parabolic shape of the dip
in the dc-voltage output around B=0 to mix \emph{quadratically} two external
rf-signals, at frequencies $f_{\mathrm{1}}$ and $f_{\mathrm{2}}$ well below the
Josephson frequency $f_{\mathrm{J}}$, and detect the corresponding mixing
signal at $| {f_{1}-f_{2}}| $. Quadratic mixing takes also place when the SQIF
is operated without magnetic shield. The experimental results are well
described by a simple analytical model based on the adiabatic approximation.


  Shaping codes are used to generate code sequences in which the symbols obey a
prescribed probability distribution. They arise naturally in the context of
source coding for noiseless channels with unequal symbol costs. Recently,
shaping codes have been proposed to extend the lifetime of flash memory and
reduce DNA synthesis time. In this paper, we study a general class of shaping
codes for noiseless finite-state channels with cost and i.i.d. sources. We
establish a relationship between the code rate and minimum average symbol cost.
We then determine the rate that minimizes the average cost per source symbol
(total cost). An equivalence is established between codes minimizing average
symbol cost and codes minimizing total cost, and a separation theorem is
proved, showing that optimal shaping can be achieved by a concatenation of
optimal compression and optimal shaping for a uniform i.i.d. source.


  This contains a new version of the so-called non-commutative Gauss algorithm
for polycyclic groups. Its results allow to read off the order and the index of
a subgroup in an (possibly infinite) polycyclic group.


In this paper, we studied N-soliton solutions of an integrable equation.


  In this paper, by means of the Melnikov functions we consider bifurcations of
harmonic or subharmonic solutions from a periodic solution of a planar
Hamiltonian system under impulsive perturbation. We give some sufficient
conditions under which a harmonic or subharmonic solution exists.


  We present the first light curve solution of 6 contact binary systems which
are chosen from the ASAS catalog. The photometric elements and the estimated
absolute parameters of all systems are obtained with the light curve analyses.
We calculated the values of degree of contact for the systems. The location of
the targets on the Hertzsprung-Russell diagram and the mass-radius plane is
compared to the other well-known contact binaries and the evolutionary status
of the systems are also discussed.


  To curb the spread of fake news on social media platforms, recent studies
have considered an online crowdsourcing fact-checking approach as one possible
intervention method to reduce misinformation. However, it remains unclear under
what conditions crowdsourcing fact-checking efforts deter the spread of
misinformation. To address this issue, we model such distributed fact-checking
as `peer policing' that will reduce the perceived payoff to share or
disseminate false information (fake news) and also reward the spread of
trustworthy information (real news). By simulating our model on synthetic
square lattices and small-world networks, we show that the presence of social
network structure enables fake news spreaders to be self-organized into echo
chambers, thereby providing a boost to the efficacy of fake news and thus its
resistance to fact-checking efforts. Additionally, to study our model in a more
realistic setting, we utilize a Twitter network dataset and study the
effectiveness of deliberately choosing specific individuals to be
fact-checkers. We find that targeted fact-checking efforts can be highly
effective, seeing the same level of success with as little as a fifth of the
number of fact-checkers, but it depends on the structure of the network in
question. In the limit of weak selection, we obtain closed-form analytical
conditions for critical threshold of crowdsourced fact-checking in terms of the
payoff values in our fact-checker/fake news game. Our work has practical
implications for developing model-based mitigation strategies for controlling
the spread of misinformation that interferes with the political discourse.


  This paper presents EdgeLoc, an infrastructure-assisted, real-time
localization system for autonomous driving that addresses the incompatibility
between traditional localization methods and deep learning approaches. The
system is built on top of the Robot Operating System (ROS) and combines the
real-time performance of traditional methods with the high accuracy of deep
learning approaches. The system leverages edge computing capabilities of
roadside units (RSUs) for precise localization to enhance on-vehicle
localization that is based on the real-time visual odometry. EdgeLoc is a
parallel processing system, utilizing a proposed uncertainty-aware pose fusion
solution. It achieves communication adaptivity through online learning and
addresses fluctuations via window-based detection. Moreover, it achieves
optimal latency and maximum improvement by utilizing auto-splitting
vehicle-infrastructure collaborative inference, as well as online distribution
learning for decision-making. Even with the most basic end-to-end deep neural
network for localization estimation, EdgeLoc realizes a 67.75\% reduction in
the localization error for real-time local visual odometry, a 29.95\% reduction
for non-real-time collaborative inference, and a 30.26\% reduction compared to
Kalman filtering. Finally, accuracy-to-latency conversion was experimentally
validated, and an overall experiment was conducted on a practical cellular
network. The system is open sourced at
https://github.com/LoganCome/EdgeAssistedLocalization.


  We present results from large-scale molecular dynamics (MD) simulations of
homogeneous vapor-to-liquid nucleation. The simulations contain between one and
eight billion Lennard-Jones (LJ) atoms, covering up to 1.2 {\mu}s (56 million
time-steps). They cover a wide range of supersaturation ratios, S=1.55 to 10^4,
and temperatures from kT = 0.3 to 1.0 {\epsilon} (where {\epsilon} is the depth
of the LJ potential, and k the Boltzmann constant). We have resolved nucleation
rates as low as 10^{17} cm^{-3} s^{-1} (in the argon system), and critical
cluster sizes as large as 100 atoms. Recent argon nucleation experiments probe
nucleation rates in an overlapping range, making the first direct comparison
between laboratory experiments and molecular dynamics simulations possible: We
find very good agreement within the uncertainties, which are mainly due to the
extrapolations of argon and LJ saturation curves to very low temperatures. The
self-consistent, modified classical nucleation model of Girshick and Chiu [J.
Chem. Phys. 93, 1273 (1990)] underestimates the nucleation rates by up to 9
orders of magnitudes at low temperatures, and at kT = 1.0 {\epsilon} it
overestimates them by up to 10^5. The predictions from a semi-phenomenological
model by Laaksonen et al. [Phys. Rev. E 49, 5517 (1994)] are much closer to our
MD results, but still differ by factors of up to 104 in some cases. At low
temperatures, the classical theory predicts critical clusters sizes, which
match the simulation results (using the first nucleation theorem) quite well,
while the semi-phenomenological model slightly underestimates them. At kT = 1.0
{\epsilon} the critical sizes from both models are clearly too small.
(abridged)


  We present several results on the mixing time of the Glauber dynamics for
sampling from the Gibbs distribution in the ferromagnetic Potts model. At a
fixed temperature and interaction strength, we study the interplay between the
maximum degree ($\Delta$) of the underlying graph and the number of colours or
spins ($q$) in determining whether the dynamics mixes rapidly or not. We find a
lower bound $L$ on the number of colours such that Glauber dynamics is rapidly
mixing if at least $L$ colours are used. We give a closely-matching upper bound
$U$ on the number of colours such that with probability that tends to 1, the
Glauber dynamics mixes slowly on random $\Delta$-regular graphs when at most
$U$ colours are used. We show that our bounds can be improved if we restrict
attention to certain types of graphs of maximum degree $\Delta$, e.g. toroidal
grids for $\Delta = 4$.


  We study the angular structure of polarization of light transmitted through a
nematic liquid crystal (NLC) cell by analyzing the polarization state as a
function of the incidence angles and the polarization of the incident wave. The
polarization resolved angular patterns emerging after the NLC cell illuminated
by the convergent light beam are described in terms of the polarization
singularities such as C-points (points of circular polarization) and L-lines
(lines of linear polarization). For the homeotropically aligned cell, the
Stokes polarimetry technique is used to measure the polarization resolved
conoscopic patterns at different values of the ellipticity of the incident
light impinging onto the cell. Using the exact analytical expressions for the
transfer matrix we show that variations of the ellipticity induce
transformations of the angular pattern exhibiting the effect of avoided L-line
crossings and characterized by topological events such as creation and
annihilation of the C-points. The predictions of the theory are found to be in
good agreement with the experimental results.


  One of the most interesting astronomical objects is the Galactic Center. We
concentrate our discussion on a theoretical analysis of observational data of
bright stars in the IR-band obtained with large telescopes. We also discuss the
importance of VLBI observations of bright structures which could characterize
the shadow at the Galactic Center. There are attempts to describe the Galactic
Center with alternative theories of gravity and in this case one can constrain
parameters of such theories with observational data for the Galactic Center. In
particular, theories of massive gravity are intensively developing and
theorists have overcome pathologies presented in initial versions of these
theories. In theories of massive gravity, a graviton is massive in contrast
with GR where a graviton is massless. Now these theories are considered as an
alternative to GR. For example, the LIGO-Virgo collaboration obtained the
graviton mass constraint of about $1.2 \times 10^{-22}$ eV in their first
publication about the discovery of the first gravitational wave detection event
that resulted of the merger of two massive black holes. Surprisingly, one could
obtain a consistent and comparable constraint of graviton mass at a level
around $m_{g} < 2.9 \times 10^{-21}$ eV from analysis of observational data on
the trajectory of the star S2 near the Galactic Center. Therefore, observations
of bright stars with existing and forthcoming telescopes such as the European
Extremely Large Telescope (E-ELT) and the Thirty Meter Telescope (TMT) are
extremely useful for investigating the structure of the Galactic Center in the
framework of GR, but these observations also give a tool to confirm, rule out
or constrain alternative theories of gravity.


  The monitoring of accelerations is essential for a variety of applications
ranging from inertial navigation to consumer electronics. The basic operation
principle of an accelerometer is to measure the displacement of a flexibly
mounted test mass; sensitive displacement measurement can be realized using
capacitive, piezo-electric, tunnel-current, or optical methods. While optical
readout provides superior displacement resolution and resilience to
electromagnetic interference, current optical accelerometers either do not
allow for chip-scale integration or require bulky test masses. Here we
demonstrate an optomechanical accelerometer that employs ultra-sensitive
all-optical displacement read-out using a planar photonic crystal cavity
monolithically integrated with a nano-tethered test mass of high mechanical
Q-factor. This device architecture allows for full on-chip integration and
achieves a broadband acceleration resolution of 10 \mu g/rt-Hz, a bandwidth
greater than 20 kHz, and a dynamic range of 50 dB with sub-milliwatt optical
power requirements. Moreover, the nano-gram test masses used here allow for
optomechanical back-action in the form of cooling or the optical spring effect,
setting the stage for a new class of motional sensors.


  Quantum phase slip (QPS) is the topological singularity of the complex order
parameter of a quasi-one-dimensional superconductor: momentary zeroing of the
modulus and simultaneous 'slip' of the phase by 2\pi. The QPS event(s) are the
dynamic equivalent of tunneling through a conventional Josephson junction
containing static in space and time weak link(s). Here we demonstrate the
operation of a superconducting single electron transistor (Cooper pair
transistor) without any tunnel junctions. Instead a pair of thin
superconducting titanium wires in QPS regime were used. The current-voltage
characteristics demonstrate the clear Coulomb blockade with magnitude of the
Coulomb gap modulated by the gate potential. The Coulomb blockade disappears
above the critical temperature, and at low temperatures can be suppressed by
strong magnetic field.


  The simplest little Higgs model predicts a light pseudoscalar boson $\eta$
and opens up some new decay modes for $Z$-boson, such as $Z \to \bar{f} f
\eta$, $Z\to \eta\eta\eta$, $Z\to \eta\gamma$ and $Z\to \eta gg$. We examine
these decay modes in the parameter space allowed by current experiments, and
find that the branching ratios can reach $10^{-7}$ for $Z\to \bar{b}b\eta$,
$10^{-8}$ for $Z\to \bar{\tau}\tau\eta$, and $10^{-8}$ for $Z\to \eta\gamma$,
which should be accessible at the GigaZ option of the ILC. However, the
branching ratios can reach $10^{-12}$ for $Z\to \eta\eta\eta$, and $10^{-11}$
for $Z\to \eta gg$, which are hardly accessible at the GigaZ option.


  In this paper, we study the global subsonic irrotational flows in a
multi-dimensional ($n\geq 2$) infinitely long nozzle with variable cross
sections. The flow is described by the inviscid potential equation, which is a
second order quasilinear elliptic equation when the flow is subsonic. First, we
prove the existence of the global uniformly subsonic flow in a general
infinitely long nozzle for arbitrary dimension for sufficiently small incoming
mass flux and obtain the uniqueness of the global uniformly subsonic flow.
Furthermore, we show that there exists a critical value of the incoming mass
flux such that a global uniformly subsonic flow exists uniquely, provided that
the incoming mass flux is less than the critical value. This gives a positive
answer to the problem of Bers on global subsonic irrotational flows in
infinitely long nozzles for arbitrary dimension. Finally, under suitable
asymptotic assumptions of the nozzle, we obtain the asymptotic behavior of the
subsonic flow in far fields by a blow-up argument. The main ingredients of our
analysis are methods of calculus of variations, the Moser iteration techniques
for the potential equation and a blow-up argument for infinitely long nozzles.


  To understand the recently established unique magnetic and superconducting
phase diagram of LaFeAsO$_{1-x}$H$_x$, we analyze the realistic multiorbital
tight-binding model for $x=0 \sim 0.4$ beyond the rigid band approximation.
Both the spin and orbital susceptibilities are calculated in the presence of
the Coulomb and charge quadrupole interactions. It is found that both orbital
and spin fluctuations strongly develop at both $x \sim 0$ and 0.4, due to the
strong violation of the rigid band picture in LaFeAsO$_{1-x}$H$_x$. Based on
this result, we discuss the experimental phase diagram, especially the
double-dome superconducting phase. Moreover, we show that the quadrupole
interaction is effectively produced by the vertex correction due to Coulomb
interaction, resulting in the mutual development of spin and orbital
fluctuations.


  It is shown that monotone Boolean functions on the Boolean cube capture the
expected number of primes, under he usual identification by binary expansion.
This answers a question posed by G.Kalai.


  Estimating city evacuation time is a non-trivial problem due to the
interaction between thousands of individual agents, giving rise to various
collective phenomena, such as bottleneck formation, intermittent flow and
stop-and-go waves. We present a mean field approach to draw relationships
between road network spatial attributes, number of evacuees and resultant
evacuation time estimate (ETE). We divide $50$ medium sized UK cities into a
total of $697$ catchment areas which we define as an area where all agents
share the same nearest exit node. In these catchment areas, 90% of agents are
within $5.4$ km of their designated exit node. We establish a characteristic
flow rate from catchment area attributes (population, distance to exit node and
exit node width) and a mean flow rate in free-flow regime by simulating total
evacuations using an agent based `queuing network' model. We use these
variables to determine a relationship between catchment area attributes and
resultant ETE. This relationship could enable emergency planners to make rapid
appraisal of evacuation strategies and help support decisions in the run up to
a crisis.


  We examine the relevance of tidal heating for large Trans-Neptunian Objects,
with a focus on its potential to melt and maintain layers of subsurface liquid
water. Depending on their past orbital evolution, tidal heating may be an
important part of the heat budget for a number of discovered and hypothetical
TNO systems and may enable formation of, and increased access to, subsurface
liquid water. Tidal heating induced by the process of despinning is found to be
particularly able to compete with heating due to radionuclide decay in a number
of different scenarios. In cases where radiogenic heating alone may establish
subsurface conditions for liquid water, we focus on the extent by which tidal
activity lifts the depth of such conditions closer to the surface. While it is
common for strong tidal heating and long lived tides to be mutually exclusive,
we find this is not always the case, and highlight when these two traits occur
together.


  Analytical eigensolutions for Morse oscillators are used to investigate
quantum resonance and revivals and show how Morse anharmonicity affects revival
times. A minimum semi-classical Morse revival time Tmin-rev found by Heller is
related to a complete quantum revival time Trev using a quantum deviation
parameter that in turn relates Trev to the maximum quantum beat period
Tmax-beat. Also, number theory of Farey and Thales-circle geometry of Ford is
shown to elegantly analyze and display fractional revivals. Such quantum
dynamical analysis may have applications for spectroscopy or quantum
information processing and computing.


  We have compiled a sample of 90 SNe Ia from 1997 to 1999 (up to SN 1999da)
and studied the peculiarity rate of SN 1991T, SN 1991bg and SN 1986G-like
objects. A Monte Carlo code is written to study the observational biases
involved in the evaluation of the intrinsic peculiarity rate of SNe Ia. We
found that the peculiarity rate of SNe Ia is higher than 30% and the luminosity
function of SNe Ia is flat.


  We consider two problems of estimation in high-dimensional Gaussian models.
The first problem is that of estimating a linear functional of the means of $n$
independent $p$-dimensional Gaussian vectors, under the assumption that most of
these means are equal to zero. We show that, up to a logarithmic factor, the
minimax rate of estimation in squared Euclidean norm is between $(s^2\wedge n)
+sp$ and $(s^2\wedge np)+sp$. The estimator that attains the upper bound being
computationally demanding, we investigate suitable versions of group
thresholding estimators that are efficiently computable even when the dimension
and the sample size are very large. An interesting new phenomenon revealed by
this investigation is that the group thresholding leads to a substantial
improvement in the rate as compared to the element-wise thresholding. Thus, the
rate of the group thresholding is $s^2\sqrt{p}+sp$, while the element-wise
thresholding has an error of order $s^2p+sp$. To the best of our knowledge,
this is the first known setting in which leveraging the group structure leads
to a polynomial improvement in the rate.
  The second problem studied in this work is the estimation of the common
$p$-dimensional mean of the inliers among $n$ independent Gaussian vectors. We
show that there is a strong analogy between this problem and the first one.
Exploiting it, we propose new strategies of robust estimation that are
computationally tractable and have better rates of convergence than the other
computationally tractable robust (with respect to the presence of the outliers
in the data) estimators studied in the literature. However, this tractability
comes with a loss of the minimax-rate-optimality in some regimes.


  Bruinier and Ono recently developed the theory of generalized Borcherds
products, which uses coefficients of certain Maass forms as exponents in
infinite product expansions of meromorphic modular forms. Using this, one can
use classical results on congruences of modular forms to obtain congruences for
Maass forms. In this note we work out the example of Ramanujan's mock theta
functions f and {\omega} in detail.


  We describe various classes of infinitely presented groups that are
condensation points in the space of marked groups. A well-known class of such
groups consists of finitely generated groups admitting an infinite minimal
presentation. We introduce here a larger class of condensation groups, called
infinitely independently presentable groups, and establish criteria which allow
one to infer that a group is infinitely independently presentable. In addition,
we construct examples of finitely generated groups with no minimal
presentation, among them infinitely presented groups with Cantor-Bendixson rank
1, and we prove that every infinitely presented metabelian group is a
condensation group.


  We develop a general formalism to treat, in general relativity, the linear
oscillations of a two-fluid star about static (non-rotating) configurations.
Such a formalism is intended for neutron stars, whose matter content can be
described, as a first approximation, by a two-fluid model: one fluid is the
neutron superfluid, which is believed to exist in the core and inner crust of
mature neutron stars; the other fluid is a conglomerate of all other
constituents (crust nuclei, protons, electrons, etc...). We obtain a system of
equations which govern the perturbations both of the metric and of the matter
variables, whatever the equation of state for the two fluids. As a first
application, we consider the simplified case of two non-interacting fluids,
each with a polytropic equation of state. We compute numerically the
quasi-normal modes (i.e. oscillations with purely outgoing gravitational
radiation) of the corresponding system. When the adiabatic indices of the two
fluids are different, we observe a splitting for each frequency of the
analogous single fluid spectrum. The analysis also substantiates the claim that
w-modes are largely due to spacetime oscillations.


  We present some laws relating the $\Cat$-indexed categories of left, right
and bi-actions: by defining $(A\comp M)x = Mx^{Ax}$ one gets a biclosed
monoidal action of $\Set^{X\op}$ on $(\Set^X)\op$, while $\B X$ and $\Cat/X$
act (partially) on their opposites by exponentials; both the inclusions $(\B
X,\B X)\to (\Set^{X\op},\Set^X) \to (\Cat/X,\Cat/X)$ preserve the (cartesian)
monoidal structures and the actions, and the same holds for substitutions along
functors. These strong morphisms of strong indexed monoidal actions have in
fact a wider range of applications; in particular, replacing $\Set$ with any
(co)complete symmetric monoidal closed category $\V$, we consider the pair of
indexed categories $(\V_0^{X\op},\V_0^X ; X\in\Cat)$ with the pair of biclosed
indexed monoidal actions of each one on the opposite of the other one and its
formal relationships with biactions and constant actions.
  Some of the resulting laws also hold in a fragment of biclosed bicategory
(with an object supporting a symmetric monoidal category) and are taken, in the
second part, as the basis for developing some abstract category theory.
Finally, we add $\Set^{X\op\tm X}$ to the picture and give a symmetrical
version of the comprehension adjunction.


  The decoherence rate is a nonlinear channel parameter that describes
quantitatively the decay of the off-diagonal elements of a density operator in
the decoherence basis. We address the question of how to experimentally access
such a nonlinear parameter directly without the need of complete process
tomography. In particular, we design a simple experiment working with two
copies of the channel, in which the registered mean value of a two-valued
measurement directly determines the value of the average decoherence rate. No
prior knowledge of the decoherence basis is required.


  Mid-Infrared (MIR) images of the Galactic center show extended gas and dust
features along with bright IRS sources. Some of these dust features are a part
of ionized clumpy streamers orbiting Sgr~A*, known as the mini-spiral. We
present their proper motions over 12 year time period and report their flux
densities in $N$-band filters {and derive their spectral indices}. The
observations were carried out by VISIR at ESO VLT. High-pass filtering led to
the detection of several resolved filaments and clumps along the mini-spiral.
Each source was fit by a 2-D Gaussian profile to determine the offsets and
aperture sizes. We perform aperture photometry to extract fluxes in two
different bands. We present the proper motions of the largest consistent set of
resolved and reliably determined sources. In addition to stellar orbital
motions, we identify a stream-like motion of extended clumps along the
mini-spiral. We also detect MIR counterparts of the radio tail components of
the IRS7 source. They show a clear kinematical deviation with respect to the
star. They likely represent Kelvin-Helmholtz instabilities formed downstream in
the shocked stellar wind. We also analyze the shape and the orientation of the
extended late-type IRS3 star that is consistent with the ALMA sub-mm detection
of the source. Its puffed-up envelope with the radius of $\sim 2\times
10^6\,R_{\odot}$ could be the result of the red-giant collision with a nuclear
jet, which was followed by the tidal prolongation along the orbit.


  A treatment of linearized gravity is given in the Randall-Sundrum background.
The graviton propagator is found in terms of the scalar propagator, for which
an explicit integral expression is provided. This reduces to the
four-dimensional propagator at long distances along the brane, and provides
estimates of subleading corrections. Asymptotics of the propagator off the
brane yields exponential falloff of gravitational fields due to matter on the
brane. This implies that black holes bound to the brane have a "pancake"-like
shape in the extra dimension, and indicates validity of a perturbative
treatment off the brane. Some connections with the AdS/CFT correspondence are
described.


  Fluid approximations to cosmic ray (CR) transport are often preferred to
kinetic descriptions in studies of the dynamics of the interstellar medium
(ISM) of galaxies, because they allow simpler analytical and numerical
treatments. Magnetohydrodynamic (MHD) simulations of the ISM usually
incorporate CR dynamics as an advection-diffusion equation for CR energy
density, with anisotropic, magnetic field-aligned diffusion with the diffusive
flux assumed to obey Fick's law. We compare test-particle and fluid simulations
of CRs in a random magnetic field. We demonstrate that a non-Fickian
prescription of CR diffusion, which corresponds to the telegraph equation for
the CR energy density, can be easily calibrated to match the test particle
simulations with great accuracy. In particular, we consider a random magnetic
field in the fluid simulation that has a lower spatial resolution than that
used in the particle simulation to demonstrate that an appropriate choice of
the diffusion tensor can account effectively for the unresolved (subgrid)
scales of the magnetic field. We show that the characteristic time which
appears in the telegraph equation can be physically interpreted as the time
required for the particles to reach a diffusive regime and we stress that the
Fickian description of the CR fluid is unable to describe complex boundary or
initial conditions for the CR energy flux.


  We evaluate the spectral properties of the Goldstino in a Bose-Fermi mixture
of cold atoms and molecules whose dynamics is governed by a supersymmetric
hamiltonian. Model independent results are obtained from sum rules obeyed by
the spectral function. We carry out specific calculations, at zero and finite
temperature, using the Random Phase Approximation, and obtain in particular
analytic expressions for the dispersion relation at small momentum. These
explicit calculations allow us to pin down more precisely the features of the
Goldstino that can be attributed to the supersymmetry alone, together with its
spontaneous breaking. The anomalous large effect of the Fermi sea at moderate
and large momenta is emphasized.


  We construct a nonlinear differential equation of matrix pairs
$(\mathcal{M}(t),\mathcal{L}(t))$ that is invariant (the
\textbf{Structure-Preserving Property}) in the class of symplectic matrix pairs
\begin{align*}
\mathbb{S}_{\mathcal{S}_1,\mathcal{S}_2}=\left\{\left(\mathcal{M},\mathcal{L}\right)|
\ \mathcal{M}=\left[% \begin{array}{cc}
  X_{12} & 0
  X_{22} & I \end{array}% \right]\mathcal{S}_2, \mathcal{L}=\left[%
\begin{array}{cc}
  I & X_{11}
  0 & X_{21} \end{array}% \right]\mathcal{S}_1\right.\nonumber \left. \text{
and }X=\left[% \begin{array}{cc}
  X_{11} & X_{12}
  X_{21} & X_{22} \end{array}% \right]\text{is Hermitian}\right\} \end{align*}
for certain fixed symplectic matrices $\mathcal{S}_1$ and $\mathcal{S}_2$. Its
solution also preserves invariant subspaces on the whole orbit (the
\textbf{Eigenvector-Preserving Property}). Such a flow is called a
\textit{structure-preserving flow} and is governed by a Riccati differential
equation (RDE). In addition, Radon's lemma leads to an explicit form.
Therefore, blow-ups for the structure-preserving flows may happen at a finite
$t$. To continue, we then utilize the Grassmann manifolds to extend the domain
of the structure-preserving flow to the whole $\mathbb{R}$ subtracting some
isolated points.


  To reduce cost in storing, processing and visualizing a large-scale point
cloud, we consider a randomized resampling strategy to select a representative
subset of points while preserving application-dependent features. The proposed
strategy is based on graphs, which can represent underlying surfaces and lend
themselves well to efficient computation. We use a general feature-extraction
operator to represent application-dependent features and propose a general
reconstruction error to evaluate the quality of resampling. We obtain a general
form of optimal resampling distribution by minimizing the reconstruction error.
The proposed optimal resampling distribution is guaranteed to be shift,
rotation and scale-invariant in the 3D space. We next specify the
feature-extraction operator to be a graph filter and study specific resampling
strategies based on all-pass, low-pass, high-pass graph filtering and graph
filter banks. We finally apply the proposed methods to three applications:
large-scale visualization, accurate registration and robust shape modeling. The
empirical performance validates the effectiveness and efficiency of the
proposed resampling methods.


  This paper reports the experimental, analytical, and numerical study of
resistive-nanoindentation tests performed on gold samples (bulk and thin film).
First, the relevant contributions to electrical contact resistance are
discussed and analytically described. A brief comparison of tests performed on
gold and on natively oxidized metals highlights the high reproducibility and
the voltage-independence of experiments on gold(thanks to its oxide-free
surface). Then, the evolution of contact resistance during nanoindentation is
fully explained in terms of electronic transport regimes: starting from
tunneling, electronic transport is then driven by ballistic conduction before
ending with pure diffusive conduction. The corresponding analytical
expressions, as well as their validity domains, are determined and compared
with experimental data,showing excellent agreement. From there, focus is made
on the diffusive regime. Resistive-nanoindentation outputs are fully described
by analytical and finite-element modeling. The developed numerical framework
allows a better understanding of the main parameters: it first assesses the
technique capabilities (validity domains, sensitivity to tip defect,
sensitivity to rheology, effect of an oxide layer, and so on), butit also
validates the different assumptions made on current line distribution. Finally,
it is shown that a simple calibration procedure allows a well-resolved
monitoring of the contact area during resistive-nanoindentation performed on
samples with complex rheologies (ductile thin film on an elastic substrate).
Comparison to analytical and numerical approaches highlights the strength of
resistive-nanoindentation for continuous area monitoring.


  We conduct simulations of turbulent mixing in the presence of a magnetic
field, grown by the small-scale dynamo. We show that the scalar gradient field,
$\nabla C$, which must be large for diffusion to operate, is strongly biased
perpendicular to the magnetic field, ${\mathbf B}$. This is true both early-on,
when the magnetic field is negligible, and at late times, when the field is
strong enough to back react on the flow. This occurs because $\nabla C$
increases within the plane of a compressive motion, but ${\mathbf B}$ increases
perpendicular to it. At late times the magnetic field resists compression,
making it harder for scalar gradients to grow and likely slowing mixing.


  We introduce a simple model for the size distribution of avalanches based on
the idea that the front of an avalanche can be described by a directed random
walk. The model captures some of the qualitative features of earthquakes,
avalanches and other self-organized critical phenomena in one dimension. We
find scaling laws relating the frequency, size and width of avalanches and an
exponent $4/3$ in the size distribution law.


  Using first-principles calculations, the phonon frequencies at the $\Gamma$
point and the dielectric tensor are determined and analysed for the cubic and
rhombohedral phases of BaTiO$_{3}$. The dipole-dipole interaction is then
separated \`a la Cochran from the remaining short-range forces, in order to
investigate their respective influence on lattice dynamics. This analysis
highlights the delicate balance of forces leading to an unstable phonon in the
cubic phase and demonstrates the extreme sensitivity of this close compensation
to minute effective charge changes. Within our decomposition, the stabilization
of the unstable mode in the rhombohedral phase or under isotropic pressure has
a different origin.


  We introduce an enriched analogue of Lam and Pylyavskyy's theory of
set-valued $P$-partitions. An an application, we construct a $K$-theoretic
version of Stembridge's Hopf algebra of peak quasisymmetric functions. We show
that the symmetric part of this algebra is generated by Ikeda and Naruse's
shifted stable Grothendieck polynomials. We give the first proof that the
natural skew analogues of these power series are also symmetric. A central tool
in our constructions is a "$K$-theoretic" Hopf algebra of labeled posets, which
may be of independent interest. Our results also lead to some new explicit
formulas for the involution $\omega$ on the ring of symmetric functions.