  This paper proposes an adaptive compact attention model for few-shot
video-to-video translation. Existing works in this domain only use features
from pixel-wise attention without considering the correlations among multiple
reference images, which leads to heavy computation but limited performance.
Therefore, we introduce a novel adaptive compact attention mechanism to
efficiently extract contextual features jointly from multiple reference images,
of which encoded view-dependent and motion-dependent information can
significantly benefit the synthesis of realistic videos. Our core idea is to
extract compact basis sets from all the reference images as higher-level
representations. To further improve the reliability, in the inference phase, we
also propose a novel method based on the Delaunay Triangulation algorithm to
automatically select the resourceful references according to the input label.
We extensively evaluate our method on a large-scale talking-head video dataset
and a human dancing dataset; the experimental results show the superior
performance of our method for producing photorealistic and temporally
consistent videos, and considerable improvements over the state-of-the-art
method.


  We derive, in path integral approach, the (anomalous) master Ward identity
associated with an infinite set of nonlocal conservation laws in
two-dimensional principal chiral models


  In this paper, ensembles of classifiers that exploit several data
augmentation techniques and four signal representations for training
Convolutional Neural Networks (CNNs) for audio classification are presented and
tested on three freely available audio classification datasets: i) bird calls,
ii) cat sounds, and iii) the Environmental Sound Classification dataset. The
best performing ensembles combining data augmentation techniques with different
signal representations are compared and shown to outperform the best methods
reported in the literature on these datasets. The approach proposed here
obtains state-of-the-art results in the widely used ESC-50 dataset. To the best
of our knowledge, this is the most extensive study investigating ensembles of
CNNs for audio classification. Results demonstrate not only that CNNs can be
trained for audio classification but also that their fusion using different
techniques works better than the stand-alone classifiers.


  This paper aims to contribute to further understanding of dynamism (the
dynamic behavior of system models) in the mathematical and conceptual modeling
of systems. This study is conducted in the context of the claim that software
engineering lacks underpinning scientific theories, both for the software it
produces and the processes by which it does so. The research literature
proposes that information theory can provide such a benefit for software
engineering. We explore the dynamism expressive power of conceptual modeling as
a software engineering tool that can represent physical systems in the Shannon
Weaver communication model (SWCM). Specifically, the modeled source in the SWCM
is a physical phenomenon (a change that can occur in the world, e.g., tossing a
coin) resulting in generating observable events and data of unaddressed
information. The resultant model reflects the feasibility of extending the SWCM
to be applied in conceptual modeling in software engineering.


  Here we present the new applications of the Egorychev method of coefficients
of integral representations and computation of combinatorial sums developed by
the author at the end of 1970's and its recent applications to the algebra and
the theory of holomorphic functions in C^n and others.


  A number of characteristics of the new fundamental interaction are described.
The interaction is carried by a massless pseudoscalar boson and extends to at
least the electron neutrino, proton, and neutron. A substantiation of the
existence of such an interaction is supported by an good agreement between the
theoretical and experimental rates of all the five observed processes with
solar neutrinos. A bright manifestation of the new interaction is expected in
the observation that its contribution to the rate of splitting of a number of
light stable nuclei by reactor antineutrinos is approximately six orders of
magnitude greater than the contribution of electroweak interaction.


  A Ribbon of enhanced energetic neutral atom (ENA) emissions was discovered by
the Interstellar Boundary Explorer (IBEX) in 2009, redefining our understanding
of the heliosphere boundaries and the physical processes occurring at the
interstellar interface. The Ribbon signal is intertwined with that of a
globally distributed flux (GDF) that spans the entire sky. To a certain extent,
Ribbon separation methods enabled examining its evolution independent of the
underlying GDF. Observations over a full solar cycle revealed the Ribbon's
evolving nature, with intensity variations closely tracking those of the solar
wind (SW) structure after a few years delay accounting for the SW-ENA recycling
process. In this work, we examine the Ribbon structure, namely, its ENA fluxes,
angular extent, width, and circularity properties for two years, 2009 and 2019,
representative of the declining phases of two adjacent solar cycles. We find
that, (i) the Ribbon ENA fluxes have recovered in the nose direction and south
of it down to ~ 25{\deg} (for energies below 1.7 keV) and not at mid and high
ecliptic latitudes; (ii) The Ribbon width exhibits significant variability as a
function of azimuthal angle; (iii) Circularity analysis suggests that the 2019
Ribbon exhibits a statistically consistent radius with that in 2009. The
Ribbon's partial recovery is aligned with the consensus of a heliosphere with
its closest point being southward of the nose region. The large variability of
the Ribbon width as a function of Azimuth in 2019 compared to 2009 is likely
indicative of small-scale processes within the Ribbon.


  Let $E \subseteq \mathbb{R}^n$ be a union of line segments and $F \subseteq
\mathbb{R}^n$ the set obtained from $E$ by extending each line segment in $E$
to a full line. Keleti's \textit{line segment extension conjecture} posits that
the Hausdorff dimension of $F$ should equal that of $E$. Working in
$\mathbb{R}^2$, we use effective methods to prove a strong packing dimension
variant of this conjecture, from which the generalized Kakeya conjecture for
packing dimension immediately follows. This is followed by several doubling
estimates in higher dimensions and connections to related problems.


  In this paper, we study the principal eigenvalue $\mu(\mathscr{F}_k^-,E)$ of
the fully nonlinear operator
  \[
  \mathscr{F}_k^-[u] = \mathcal{P}_k^-(\nabla^2 u) - h |\nabla u|
  \] on a set $E \Subset \mathbb{R}^n$, where $h \in [0,\infty)$ and
$\mathcal{P}_k^-(\nabla^2 u)$ is the sum of the smallest $k$ eigenvalues of the
Hessian $\nabla^2 u$. We prove a lower estimate for $\mu(\mathscr{F}_k^-,E)$ in
terms of a generalized Hausdorff measure $\mathscr{H}_\Psi(E)$, for suitable
$\Psi$ depending on $k$, moving some steps in the direction of the
conjecturally sharp estimate
  \[
  \mu(\mathscr{F}_k^-,E) \ge C \mathscr{H}^k(E)^{-2/k}.
  \] The theorem is used to study the spectrum of bounded submanifolds in
$\mathbb{R}^n$, improving on our previous work in the direction of a question
posed by S.T. Yau. In particular, the result applies to solutions of Plateau's
problem for CMC surfaces.


  The paper considers the distribution of a general linear combination of
central and non-central chi-square random variables by exploring the branch cut
regions that appear in the standard Laplace inversion process. Due to the
original interest from the directional statistics, the focus of this paper is
on the density function of such distributions and not on their cumulative
distribution function. In fact, our results confirm that the latter is a
special case of the former. Our approach provides new insight by generating
alternative characterizations of the probability density function in terms of a
finite number of feasible univariate integrals. In particular, the central
cases seem to allow an interesting representation in terms of the branch cuts,
while general degrees of freedom and non-centrality can be easily adopted using
recursive differentiation. Numerical results confirm that the proposed approach
works well while more transparency and therefore easier control in the accuracy
is ensured.


  In 1956 $\AA$. Pleijel gave his celebrated theorem showing that the
inequality in Courant's theorem on the number of nodal domains is strict for
large eigenvalues of the Laplacian. This was a consequence of a stronger result
giving an asymptotic upper bound for the number of nodal domains of the
eigenfunctions as the eigenvalues tend to $+\infty$. A similar question occurs
naturally for Schr"\odinger operators. The first significant result has been
obtained recently by the first author for the harmonic oscillator. The purpose
of this paper is to consider more general potentials which are radial. We will
analyze the case when the potential tends to $+\infty$ and the case when the
potential is negative and tends to zero, where the considered eigenfucntion are
associated to the eigenvalues below the essential spectrum.


  We report the discovery of a massive ultra-compact quiescent galaxy that has
been strongly-lensed into multiple images by a foreground galaxy at z = 0.960.
This system was serendipitously discovered as a set of extremely Ks-bright
high-redshift galaxies with red J - Ks colors using new data from the
UltraVISTA YJHKs near-infrared survey. The system was also previously
identified as an optically-faint lens/source system using the COSMOS ACS
imaging by Faure et al. (2008, 2011). Photometric redshifts for the three
brightest images of the source galaxy determined from twenty-seven band
photometry place the source at z = 2.4 +/- 0.1. We provide an updated lens
model for the system which is a good fit to the positions and morphologies of
the galaxies in the ACS image. The lens model implies that the magnification of
the three brightest images is a factor of 4 - 5. We use the lens model,
combined with the Ks-band image to constrain the size and Sersic profile of the
galaxy. The best-fit model is an ultra-compact galaxy (Re =
0.64^{+0.08}_{-0.18} kpc, lensing-corrected), with a Sersic profile that is
intermediate between a disk and bulge profile (n = 2.2^{+2.3}_{-0.9}). We
present aperture photometry for the source galaxy images which have been
corrected for flux contamination from the central lens. The best-fit stellar
population model is a massive galaxy (Log(M_{star}/M_{sol}) =
10.8^{+0.1}_{-0.1}, lensing-corrected) with an age of 1.0^{+1.0}_{-0.4} Gyr,
moderate dust extinction (Av = 0.8^{+0.5}_{-0.6}), and a low specific star
formation rate (Log(SSFR) < -11.0 yr^{-1}). This is typical of massive
"red-and-dead" galaxies at this redshift and confirms that this source is the
first bona fide strongly-lensed massive ultra-compact quiescent galaxy to be
discovered. We conclude with a discussion of the prospects of finding a larger
sample of these galaxies.


  Spin exchange interaction between atoms in a spin-1 Bose-Einstein condensate
causes atomic spin evolving periodically under the single spatial mode
approximation in the mean field theory. By applying fast magnetic pulses
according to a two-step or a four-step control protocol, we find analytically
that the spin dynamics is significantly suppressed for an arbitrary initial
state. Numerical calculations under single mode approximation are carried out
to confirm the validity and robustness of these protocols. This localization
method can be readily utilized to improve the sensitivity of a magnetometer
based on spin-1 Bose-Einstein condensates.


  The NPDGamma experiment measures the asymmetry in $\gamma$-ray emission in
the capture of polarized neutrons on liquid parahydrogen. The beam polarization
is measured using $^3$He spin analysis, but this measurement does not account
for the contribution of depolarization from spin-flip scattering primarily due
to orthohydrogen in the bulk liquid. This is a systematic effect that dilutes
the experimental asymmetry and is modeled using Monte Carlo. Methods for
tracking neutron spin in MCNPX were developed in order to calculate the average
neutron polarization upon capture for use as a multiplicative correction to the
measured beam polarization for the NPDGamma experiment.


  We study the phase behavior of hard spheres confined between two parallel
hard plates using extensive computer simulations. We determine the full
equilibrium phase diagram for arbitrary densities and plate separations from
one to five hard-sphere diameters using free energy calculations. We find a
first-order fluid-solid transition, which corresponds to either capillary
freezing or melting depending on the plate separation. The coexisting solid
phase consists of crystalline layers with either triangular or square symmetry.
Increasing the plate separation, we find a sequence of crystal structures from
n triangular to (n+1) square to (n+1) triangular, where n is the number of
crystal layers, in agreement with experiments on colloids. At high densities,
the transition between square to triangular phases are intervened by
intermediate structures, e.g., prism, buckled, and rhombic phases.


  Magnetic interactions between a protostar and its accretion disc tend to
induce warping in the disc and produce secular changes in the stellar spin
direction, so that the spin axis may not always be perpendicular to the disc.
This may help explain the recently observed spin-orbit misalignment in a number
of exoplanetary systems. We study the dynamics of warped protoplanetary discs
under the combined effects of magnetic warping/precession torques and internal
stresses in the disc, including viscous damping of warps and propagation of
bending waves. We show that when the outer disc axis is misaligned with the
stellar spin axis, the disc evolves towards a warped steady-state on a
timescale that depends on the disc viscosity or the bending wave propagation
speed, but in all cases is much shorter than the timescale for the spin
evolution (of order of a million years). Moreover, for the most likely physical
parameters characterizing magnetic protostars, circumstellar discs and their
interactions, the steady-state disc has a rather small warp, such that the
whole disc lies approximately in a single plane determined by the outer disc
boundary conditions, although more extreme parameters may give rise to larger
disc warps. In agreement with our recent analysis (Lai et al. 2010) based on
flat discs, we find that the back-reaction magnetic torques of the slightly
warped disc on the star can either align the stellar spin axis with the disc
axis or push it towards misalignment, depending on the parameters of the
star-disc system. This implies that newly formed planetary systems may have a
range of inclination angles between the stellar spin axis and the symmetry axis
of the planetary orbits.


  Although metamaterials have been widely used for controlling elastic waves
through bandgap engineering, the directed guidance of stress waves in
non-periodic structures has remained a challenge. This work demonstrates that
spatially graded metamaterials based on conformal mappings present a rich
design space for controlling and attenuating wave motion - without the need for
bandgaps. Conformal mappings transform an elementary unit cell by scaling and
rotation into graded lattices with approximately geometrically similar unit
cells. This self-similarity allows for control over the local wave dispersion
throughout the metamaterial. As a key mechanism, it is shown that elastic waves
cannot propagate through graded unit cells with significant size differences,
except at low frequencies. This is exploited to create low-pass elastic wave
guides, extending beyond classical bandgap engineering, since bandgaps are not
required to achieve wave guiding and attenuation. Experiments confirm the
low-pass elastic wave filtering capability of a planar truss metamaterial with
conformal grading. Finally, a systematic design of curved metamaterial surfaces
is presented, providing a flexible framework for programming low-pass
attenuation and wave guiding in three dimensions.


  This note is an expository account of the theory of staggered sheaves, based
on a series of lectures given by the author at RIMS (Kyoto) in October 2008.


  Recent work on unsupervised term discovery (UTD) aims to identify and cluster
repeated word-like units from audio alone. These systems are promising for some
very low-resource languages where transcribed audio is unavailable, or where no
written form of the language exists. However, in some cases it may still be
feasible (e.g., through crowdsourcing) to obtain (possibly noisy) text
translations of the audio. If so, this information could be used as a source of
side information to improve UTD. Here, we present a simple method for rescoring
the output of a UTD system using text translations, and test it on a corpus of
Spanish audio with English translations. We show that it greatly improves the
average precision of the results over a wide range of system configurations and
data preprocessing methods.


  This paper analyzes $\ell_1$ regularized linear regression under the
challenging scenario of having only adversarially corrupted data for training.
We use the primal-dual witness paradigm to provide provable performance
guarantees for the support of the estimated regression parameter vector to
match the actual parameter. Our theoretical analysis shows the
counter-intuitive result that an adversary can influence sample complexity by
corrupting the irrelevant features, i.e., those corresponding to zero
coefficients of the regression parameter vector, which, consequently, do not
affect the dependent variable. As any adversarially robust algorithm has its
limitations, our theoretical analysis identifies the regimes under which the
learning algorithm and adversary can dominate over each other. It helps us to
analyze these fundamental limits and address critical scientific questions of
which parameters (like mutual incoherence, the maximum and minimum eigenvalue
of the covariance matrix, and the budget of adversarial perturbation) play a
role in the high or low probability of success of the LASSO algorithm. Also,
the derived sample complexity is logarithmic with respect to the size of the
regression parameter vector, and our theoretical claims are validated by
empirical analysis on synthetic and real-world datasets.


  Data Science is a complex and evolving field, but most agree that it can be
defined as a combination of expertise drawn from three broad areascomputer
science and technology, math and statistics, and domain knowledge -- with the
purpose of extracting knowledge and value from data. Beyond this, the field is
often defined as a series of practical activities ranging from the cleaning and
wrangling of data, to its analysis and use to infer models, to the visual and
rhetorical representation of results to stakeholders and decision-makers. This
essay proposes a model of data science that goes beyond laundry-list
definitions to get at the specific nature of data science and help distinguish
it from adjacent fields such as computer science and statistics. We define data
science as an interdisciplinary field comprising four broad areas of expertise:
value, design, systems, and analytics. A fifth area, practice, integrates the
other four in specific contexts of domain knowledge. We call this the 4+1 model
of data science. Together, these areas belong to every data science project,
even if they are often unconnected and siloed in the academy.


  We solve explicitly the Almgren-Chriss optimal liquidation problem where the
stock price process follows a geometric Brownian motion. Our technique is to
work in terms of cash and to use functional analysis tools. We show that this
framework extends readily to the case of a stochastic drift for the price
process and the liquidation of a portfolio.


  We describe a multi-mode quantum memory for propagating microwave photons
that combines a solid-state spin ensemble resonantly coupled to a frequency
tunable single-mode microwave cavity. We first show that high efficiency
mapping of the quantum state transported by a free photon to the spin ensemble
is possible both for strong and weak coupling between the cavity mode and the
spin ensemble. We also show that even in the weak coupling limit unit
efficiency and faithful retrieval can be obtained through time reversal
inhomogeneous dephasing based on spin echo techniques. This is possible
provided that the cavity containing the spin ensemble and the transmission line
are impedance matched. We finally discuss the prospects for an experimental
implementation using a rare-earth doped crystal coupled to a superconducting
resonator.


  Slattery has generalized Brauer's theory of p-blocks of finite groups to
pi-blocks of pi-separable groups where pi is a set of primes. In this setting
we show that the order of a defect group of a pi-block B is bounded in terms of
the number of irreducible characters in B. This is a variant of Brauer's
Problem 21 and generalizes K\"ulshammer's corresponding theorem for p-blocks of
p-solvable groups. At the same time, our result generalizes Landau's classical
theorem on the number of conjugacy classes of an arbitrary finite group. The
proof relies on the classification of finite simple groups.


  We use a constructive method to obtain all but finitely many p-local
representation zeta functions of a family Mn of finitely generated nilpotent
groups with maximal nilpotency class. For representation dimensions coprime to
all primes p < n, we construct all irreducible representations of Mn by
defining a standard form for the matrices of these representations and, after
taking into account twisting and isomorphism, count these twist isoclasses to
obtain our p-local zeta functions.


  Given the increase in the use of personal data for training Deep Neural
Networks (DNNs) in tasks such as medical imaging and diagnosis, differentially
private training of DNNs is surging in importance and there is a large body of
work focusing on providing better privacy-utility trade-off. However, little
attention is given to the interpretability of these models, and how the
application of DP affects the quality of interpretations. We propose an
extensive study into the effects of DP training on DNNs, especially on medical
imaging applications, on the APTOS dataset.


  The collective and purely relaxational dynamics of quantum many-body systems
after a quench at temperature $T=0$, from a disordered state to various phases
is studied through the exact solution of the quantum Langevin equation of the
spherical and the $O(n)$-model in the limit $n\to\infty$. The stationary state
of the quantum dynamics is shown to be a non-equilibrium state. The quantum
spherical and the quantum $O(n)$-model for $n\to\infty$ are in the same
dynamical universality class. The long-time behaviour of single-time and
two-time correlation and response functions is analysed and the universal
exponents which characterise quantum coarsening and quantum ageing are derived.
The importance of the non-Markovian long-time memory of the quantum noise is
elucidated by comparing it with an effective Markovian noise having the same
scaling behaviour and with the case of non-equilibrium classical dynamics.


  To meet the requirements of time-frequency networks and enable frequency
downloadability for nodes along the link, we demonstrated the extraction of
stable frequency signals at nodes using a mode-locked laser under the condition
of 100 km laboratory fiber. The node consists of a simple structure that
utilizes widely used optoelectronic devices and enables plug-and-play
applications. In addition, the node can recover frequency signals with multiple
frequencies, which are useful for scenarios that require different frequencies.
Here, we experimentally demonstrated a short-term frequency instability of
$2.83\times {{10}^{-13}}$@1 s and a long-term frequency instability of
$1.18\times {{10}^{-15}}$@10,000 s at the node, which is similar to that at the
remote site of the frequency transfer system. At the same time, frequency
signals with different frequencies also achieved stable extraction with the
same performance at the node. Our results can support the distributed
application under large-scale time-frequency networks.


  We present a general theory to obtain good linear network codes utilizing the
osculating nature of algebraic varieties. In particular, we obtain from the
osculating spaces of Veronese varieties explicit families of equidimensional
vector spaces, in which any pair of distinct vector spaces intersects in the
same dimension.
  Linear network coding transmits information in terms of a basis of a vector
space and the information is received as a basis of a possible altered vector
space. Ralf Koetter and Frank R. Kschischang introduced a metric on the set af
vector spaces and showed that a minimal distance decoder for this metric
achieves correct decoding if the dimension of the intersection of the
transmitted and received vector space is sufficiently large.
  The obtained osculating spaces of Veronese varieties are equidistant in the
above metric. The parameters of the resulting linear network codes are
determined.


  In order to close the set of relativistic hydrodynamic equations,
constitutive relations for the dissipative fluxes are required. In this work we
outline the calculation of the corresponding closure for the heat flux in terms
of the gradients of the independent scalar state variables: number density and
temperature. The results are compared with the ones obtained using Marle's
approximation in which a relativistic correction factor is included for the
relaxation time parameter. It is shown how including such correction this
BGK-like model yields good results in the relativistic case and not only in the
non-relativistic limit as was previously found by other authors.


  Given a complete Heyting algebra we construct an algebraic tensor
triangulated category whose Bousfield lattice is the Booleanization of the
given Heyting algebra. As a consequence we deduce that any complete Boolean
algebra is the Bousfield lattice of some tensor triangulated category. Using
the same ideas we then give two further examples illustrating some interesting
behaviour of the Bousfield lattice.


  The reduced density matrix (RDM) is crucial in quantum many-body systems for
understanding physical properties, including all local physical quantity
information. This study aims to minimize various error constraints that causes
challenges in higher-order RDMs estimation in quantum computing. We identify
the optimal balance between statistical and systematic errors in higher-order
RDM estimation in particular when cumulant expansion is used to suppress the
sample complexity. Furthermore, we show via numerical demonstration of quantum
subspace methods for one and two dimensional Fermi Hubbard model that, biased
yet efficient estimations better suppress hardware noise in excited state
calculations. Our work paves a path towards cost-efficient practical quantum
computing that in reality is constrained by multiple aspects of errors.


  We consider the production of dark matter in association with a pair of top
quarks, mediated by a scalar or pseudoscalar particle in a generic Simplified
Model. We demonstrate that the difference of azimuthal angle between the two
leptons $\Delta \phi_{ll}$, in the dileptonic top decay mode, can directly
probe the CP-properties of the mediator. We estimate the constraints to
strength and CP-structure of dark matter production for these well-motivated
Simplified Models from the LHC Run II.


  We consider a two-dimensional singularly perturbed transmission problem with
two different diffusion coefficients, in a domain with smooth (analytic)
boundary. The solution will contain boundary layers only in the part of the
domain where the diffusion coefficient is high and interface layers along the
interface. Utilizing existing and newly derived regularity results for the
exact solution, we design a robust $hp$ finite element method for its
approximation. Under the assumption of analytic input data, we show that the
method converges at an e{xponential} rate, provided the mesh and polynomial
degree distribution are chosen appropriately. Numerical results illustrating
our theoretical findings are also included.


  (i) For the matrix Schr\"{o}dinger operator on the half line, it is shown
that if the potential exponentially decreases fast enough then only the
scattering matrix uniquely determines the self-adjoint potential and the
boundary condition. (ii) For the matrix Schr\"{o}dinger operator on the full
line, it is shown that if the potential exponentially decreases fast enough
then the scattering matrix (or equivalently, the transmission coefficient and
reflection coefficient) uniquely determine the potential. If the potential
vanishes on $(-\infty,0)$ then only the left reflection coefficient uniquely
determine the potential.


  BGP is vulnerable to a series of attacks. Many solutions have been proposed
in the past two decades, but the most effective remain largely undeployed. This
is due to three fundamental reasons: the solutions are too computationally
expensive for current routers, they require changes to BGP, and/or they do not
give the right incentives to promote deployment.
  In this abstract we propose a Software-Defined Networking (SDN) architecture
to secure BGP routing. Our solution, BGPSecX, targets an IXP and it includes
techniques to allow different IXPs to collaborate. With SDN we remove the
computational burden from routers and do not make changes to BGP. Targeting
IXPs and promoting inter-IXP collaboration enables the creation of incentives
to foster adoption of BGP security services.


  In this article we use the expansion for biquantization described in
Cattaneo-Felder [math.QA/0309180] for the case of symmetric spaces. We
introduce a function of two variables $E(X,Y)$ for any symmetric pairs. This
function has an expansion in terms of Kontsevich's diagrams. We recover most of
the known results though in a more systematic way by using some elementary
properties of this $E$ function. We prove that Cattaneo and Felder's star
product coincides with Rouviere's for any symmetric pairs. We generalize some
of Lichnerowicz's results for the commutativity of the algebra of invariant
differential operators and solve a long standing problem posed by M. Duflo for
the expression of invariant differential operators on any symmetric spaces in
exponential coordinates. We describe the Harish-Chandra homomorphism in the
case of symmetric spaces by using all these constructions. We develop a new
method to construct characters for algebras of invariant differential
operators. We apply these methods in the case of $\sigma$-stable polarizations.


  We propose a method for creating a matte -- the per-pixel foreground color
and alpha -- of a person by taking photos or videos in an everyday setting with
a handheld camera. Most existing matting methods require a green screen
background or a manually created trimap to produce a good matte. Automatic,
trimap-free methods are appearing, but are not of comparable quality. In our
trimap free approach, we ask the user to take an additional photo of the
background without the subject at the time of capture. This step requires a
small amount of foresight but is far less time-consuming than creating a
trimap. We train a deep network with an adversarial loss to predict the matte.
We first train a matting network with supervised loss on ground truth data with
synthetic composites. To bridge the domain gap to real imagery with no
labeling, we train another matting network guided by the first network and by a
discriminator that judges the quality of composites. We demonstrate results on
a wide variety of photos and videos and show significant improvement over the
state of the art.


  We propose to smooth the entire objective function, rather than only the
check function, in a linear quantile regression context. Not only does the
resulting smoothed quantile regression estimator yield a lower mean squared
error and a more accurate Bahadur-Kiefer representation than the standard
estimator, but it is also asymptotically differentiable. We exploit the latter
to propose a quantile density estimator that does not suffer from the curse of
dimensionality. This means estimating the conditional density function without
worrying about the dimension of the covariate vector. It also allows for
two-stage efficient quantile regression estimation. Our asymptotic theory holds
uniformly with respect to the bandwidth and quantile level. Finally, we propose
a rule of thumb for choosing the smoothing bandwidth that should approximate
well the optimal bandwidth. Simulations confirm that our smoothed quantile
regression estimator indeed performs very well in finite samples.


  We study first-passage time problems for a diffusive particle with stochastic
resetting with a finite rate $r$. The optimal search time is compared
quantitatively with that of an effective equilibrium Langevin process with the
same stationary distribution. It is shown that the intermittent, nonequilibrium
strategy with non-vanishing resetting rate is more efficient than the
equilibrium dynamics. Our results are extended to multiparticle systems where a
team of independent searchers, initially uniformly distributed with a given
density, looks for a single immobile target. Both the average and the typical
survival probability of the target are smaller in the case of nonequilibrium
dynamics.


  We study subgap transport from a superconductor through a double quantum dot
with large on-site Coulomb repulsion to two normal leads. Non-local
superconducting correlations in the double dot are induced by the proximity to
the superconducting lead, detectable in non-local Andreev transport that splits
Cooper pairs in locally separated, spin-entangled electrons. We find that the
$I$--$V$ characteristics are strongly asymmetric: for a large bias voltage of
certain polarity, transport is blocked by populating the double dot with states
whose spin symmetry is incompatible with the superconductor. Furthermore, by
tuning gate voltages one has access to splitting of the Andreev excitation
energies, which is visible in the differential conductance.


  Change point analysis is concerned with detecting and locating structure
breaks in the underlying model of a sequence of observations ordered by time,
space or other variables. A widely adopted approach for change point analysis
is to minimize an objective function with a penalty term on the number of
change points. This framework includes several well-established procedures,
such as the penalized log-likelihood using the (modified) Bayesian information
criterion (BIC) or the minimum description length (MDL). The resulting
optimization problem can be solved in polynomial time by dynamic programming or
its improved version, such as the Pruned Exact Linear Time (PELT) algorithm
(Killick, Fearnhead, and Eckley 2012). However, existing computational methods
often suffer from two primary limitations: (1) methods based on direct
implementation of dynamic programming or PELT are often time-consuming for long
data sequences due to repeated computation of the cost value over different
segments of the data sequence; (2) state-of-the-art R packages do not provide
enough flexibility for users to handle different change point settings and
models. In this work, we present the fastcpd package, aiming to provide an
efficient and versatile framework for change point detection in several
commonly encountered settings. The core of our algorithm is built upon PELT and
the sequential gradient descent method recently proposed by Zhang and Dawn
(2023). We illustrate the usage of the fastcpd package through several
examples, including mean/variance changes in a (multivariate) Gaussian
sequence, parameter changes in regression models, structural breaks in
ARMA/GARCH/VAR models, and changes in user-specified models.


  Multilingual BERT (mBERT) has shown reasonable capability for zero-shot
cross-lingual transfer when fine-tuned on downstream tasks. Since mBERT is not
pre-trained with explicit cross-lingual supervision, transfer performance can
further be improved by aligning mBERT with cross-lingual signal. Prior work
proposes several approaches to align contextualised embeddings. In this paper
we analyse how different forms of cross-lingual supervision and various
alignment methods influence the transfer capability of mBERT in zero-shot
setting. Specifically, we compare parallel corpora vs. dictionary-based
supervision and rotational vs. fine-tuning based alignment methods. We evaluate
the performance of different alignment methodologies across eight languages on
two tasks: Name Entity Recognition and Semantic Slot Filling. In addition, we
propose a novel normalisation method which consistently improves the
performance of rotation-based alignment including a notable 3% F1 improvement
for distant and typologically dissimilar languages. Importantly we identify the
biases of the alignment methods to the type of task and proximity to the
transfer language. We also find that supervision from parallel corpus is
generally superior to dictionary alignments.


  The celebrated Michaelis-Menten (MM) expression provides a fundamental
relation between the rate of enzyme catalysis and substrate concentration. The
validity of this classical expression is, however, restricted to macroscopic
amounts of enzymes and substrates and, thus, to processes with negligible
fluctuations. Recent experiments have measured fluctuations in the catalytic
rate to reveal that the MM equation, though valid for bulk amounts, is not
obeyed at the molecular level. In this mini-review, we show how new statistical
measures of fluctuations in the catalytic rate identify a regime in which the
MM equation is always violated. This regime, characterized by temporal
correlations between enzymatic turnovers, is absent for a single enzyme and
unobservably short in the classical limit.


  In this paper, we investigate solution stability for control problems of
partial differential equations with the cost functional not involving the usual
quadratic term for the control. We first establish a sufficient optimality
condition for the optimal control problems with bang-bang controls. Then we
obtain criteria for solution stability for the optimal control problems of
bang-bang controls under linear perturbations. We prove H\"older stability of
optimal controls in $L^1$.


  We study the information transmission through a quantum channel, defined over
a continuous alphabet and losing its energy en route, in presence of correlated
noise among different channel uses. We then show that entangled inputs improve
the rate of transmission of such a channel.


  Despite strong connections through shared application areas, research efforts
on power market optimization (e.g., unit commitment) and power network
optimization (e.g., optimal power flow) remain largely independent. A notable
illustration of this is the treatment of power generation cost functions, where
nonlinear network optimization has largely used polynomial representations and
market optimization has adopted piecewise linear encodings. This work combines
state-of-the-art results from both lines of research to understand the best
mathematical formulations of the nonlinear AC optimal power flow problem with
piecewise linear generation cost functions. An extensive numerical analysis of
non-convex models, linear approximations, and convex relaxations across
fifty-four realistic test cases illustrates that nonlinear optimization methods
are surprisingly sensitive to the mathematical formulation of piecewise linear
functions. The results indicate that a poor formulation choice can slow down
algorithm performance by a factor of ten, increasing the runtime from seconds
to minutes. These results provide valuable insights into the best formulations
of nonlinear optimal power flow problems with piecewise linear cost functions,
a important step towards building a new generation of energy markets that
incorporate the nonlinear AC power flow model.


  In this paper we study the optimal control of a parabolic initial-boundary
value problem of Allen--Cahn type with dynamic boundary conditions. Phase field
systems of this type govern the evolution of coupled diffuse phase transition
processes with nonconserved order parameters that occur in a container and on
its surface, respectively. It is assumed that the nonlinear function driving
the physical processes within the bulk and on the surface are double well
potentials of logarithmic type whose derivatives become singular at the
boundary of their respective domains of definition. For such systems, optimal
control problems have been studied in the past. We focus here on the situation
when the cost functional of the optimal control problem contains a
nondifferentiable term like the $L^1$-norm leading to sparsity of optimal
controls. For such cases, we derive second-order sufficient conditions for
locally optimal controls.


  This paper proposes bimorphic recursion, which is restricted polymorphic
recursion such that every recursive call in the body of a function definition
has the same type. Bimorphic recursion allows us to assign two different types
to a recursively defined function: one is for its recursive calls and the other
is for its calls outside its definition. Bimorphic recursion in this paper can
be nested. This paper shows bimorphic recursion has principal types and
decidable type inference. Hence bimorphic recursion gives us flexible typing
for recursion with decidable type inference. This paper also shows that its
typability becomes undecidable because of nesting of recursions when one
removes the instantiation property from the bimorphic recursion.


  The binary system AR Sco contains an M star and the only known radio-pulsing
white dwarf. The system shows emission from radio to X-rays, likely dominated
by synchrotron radiation. The mechanism that produces most of this emission
remains unclear. Two competing scenarios have been proposed: Collimated
outflows, and direct interaction between the magnetospheres of the white dwarf
and the M star. The two proposed scenarios can be tested via very long baseline
interferometric radio observations. We conducted a radio observation with the
Australian Long Baseline Array (LBA) on 20 Oct 2016 at 8.5 GHz to study the
compactness of the radio emission. Simultaneous data with the Australian
Telescope Compact Array (ATCA) were also recorded for a direct comparison of
the obtained flux densities. AR Sco shows radio emission compact on
milliarcsecond angular scales ($\lesssim 0.02\ \mathrm{AU}$, or $4\
\mathrm{R_{\odot}}$). The emission is orbitally modulated, with an average flux
density of $\approx 6.5\ \mathrm{mJy}$. A comparison with the simultaneous ATCA
data shows that no flux is resolved out on mas scales, implying that the radio
emission is produced in this compact region. Additionally, the obtained radio
light curves on hour timescales are consistent with the optical light curve.
The radio emission in AR Sco is likely produced in the magnetosphere of the M
star or the white dwarf, and we see no evidence for a radio outflow or
collimated jets significantly contributing to the radio emission.


  We describe a Bayesian approach to estimating quasar black hole mass
functions (BHMF) when using the broad emission lines to estimate black hole
mass. We show how using the broad line mass estimates in combination with
statistical techniques developed for luminosity function estimation leads to
statistically biased results. We derive the likelihood function for the BHMF
based on the broad line mass estimates, and derive the posterior distribution
for the BHMF, given the observed data. We develop our statistical approach for
a flexible model where the BHMF is modelled as a mixture of Gaussian functions.
Statistical inference is performed using markov chain monte carlo (MCMC)
methods. Our method has the advantage that it is able to constrain the BHMF
even beyond the survey detection limits at the adopted confidence level,
accounts for measurement errors and the intrinsic uncertainty in broad line
mass estimates, and provides a natural way of estimating the probability
distribution of any quantities derived from the BHMF. We conclude by using our
method to estimate the local active BHMF using the z < 0.5 Bright Quasar Survey
sources. At z = 0.2, the quasar BHMF falls off approximately as a power law
with slope ~ 2 for M_{BH} > 10^8. Our analysis implies that z < 0.5 broad line
quasars have a typical Eddington ratio of ~ 0.4 and a dispersion in Eddington
ratio of < 0.5 dex (abridged).


  We prove the existence of a continuous family of positive and generally
non-monotone travelling fronts in delayed reaction-diffusion equations
$u_t(t,x) = \Delta u(t,x)- u(t,x) + g(u(t-h,x)) (*)$, when $g \in C^2(R_+,R_+)$
has exactly two fixed points: $x_1= 0$ and $x_2= a >0$. Recently, non-monotonic
waves were observed in numerical simulations by various authors. Here, for a
wide range of parameters, we explain why such waves appear naturally as the
delay $h$ grows. For the case of $g$ with negative Schwarzian, our conditions
are rather optimal; we observe that the well known Mackey-Glass type equations
with diffusion fall within this subclass of $(*)$. As an example, we consider
the diffusive Nicholson's blowflies equation.


  There are two superanalogs of the general linear group: GL(m|n) and GQ(n).
For any supercommutative superalgebra C let G(C) be the set of C-points of the
supermanifold G. Here there are described the GQ(n; C)-invariant functions on
Q(n; C) and GL(n; C)-invariant functions on the odd subspace of Mat (n|n; C),
more exactly, the invariants of the action of Lie supergroups GQ(n) and GL(n|n)
on the supermanifolds corresponding to Q(n; C) and the odd subspace of Mat(n|n;
C). The obtained answer is interpreted in terms of GL(n; C)-invariants on Q(n;
C) and GL(n|n; C)-invariants on the odd subspace of Mat (n|n; C) described
functorially in (i.e., independently of) C.


  The feature of our method different from other fuzzy grey relation method for
supermixed multiple attribute group decision-making is that all of the
subjective and objective weights are obtained by interval grey number and that
the group decisionmaking is performed based on the relative approach degree of
grey TOPSIS, the relative approach degree of grey incidence and the relative
membership degree of grey incidence using 4-dimensional Euclidean distance. The
weighted Borda method is used to obtain final rank by using the results of four
methods. An example shows the applicability of the proposed approach.


  We calculate the ratios $E2/M1$ and $C2/M1$ of the multipole amplitudes for
electroproduction of the $\Delta$(1232) in the range of photon virtuality
$0<-K^2<1$~GeV$^2$ in a chiral chromodielectric model and a linear
$\sigma$-model. We find that relatively large experimental values can be
explained in terms of the pion contribution alone; the contribution arising
from d-state quark admixture remains below 10\%. We describe the pion cloud as
a coherent state and use spin and isospin projection to obtain the physical
nucleon and the $\Delta$. The $A_{1/2}$ and $A_{3/2}$ amplitudes are reasonably
well reproduced in the $\sigma$-model; in the chromodielectric model, however,
they are a factor of two too small.


  We consider the problem of local tunneling into cuprate superconductors,
combining model based calculations for the superconducting order parameter with
wavefunction information obtained from first principles electronic structure.
For some time it has been proposed that scanning tunneling microscopy (STM)
spectra do not reflect the properties of the superconducting layer in the
CuO$_2$ plane directly beneath the STM tip, but rather a weighted sum of
spatially proximate states determined by the details of the tunneling process.
These "filter" ideas have been countered with the argument that similar
conductance patterns have been seen around impurities and charge ordered states
in systems with atomically quite different barrier layers. Here we use a
recently developed Wannier function based method to calculate topographies,
spectra, conductance maps and normalized conductance maps close to impurities.
We find that it is the local planar Cu $d_{x^2-y^2}$ Wannier function,
qualitatively similar for many systems, that controls the form of the tunneling
spectrum and the spatial patterns near perturbations. We explain how, despite
the fact that STM observables depend on the materials-specific details of the
tunneling process and setup parameters, there is an overall universality in the
qualitative features of conductance spectra. In particular, we discuss why STM
results on Bi$_2$Sr$_2$CaCu$_2$O$_8$ and Ca$_{2-x}$Na$_x$CuO$_2$Cl$_2$ are
essentially identical.


  We look for the properties of empty space-time proceeding from the general
relativity principle. An infinite number of the so-called covariant ether
theories (CETs) has been found, which, like the special relativity theory
(SRT), satisfy all known experimental facts in the physics of empty space-time.
In this connection a new approach to the problem of experimental testing of SRT
is discussed. In particular, we show that covariant ether theories predict a
dependence of Thomas-Wigner angle on an absolute velocity of a reference frame
of observation. Hence, a measurement of this dependence is capable to
distinguish SRT and CETs. It has been shown that the Lorentz ether theory is
one of CETs, corresponding to the admissible Galilean transformations in
physical space-time. Hence, we conclude that SRT and Lorentz ether theory can
be distinguished experimentally, at least in principle. A crucial experiments,
based on the Moessbauer effect, has been proposed.


  A new (in)finite dimensional algebra which is a fundamental dynamical
symmetry of a large class of (continuum or lattice) quantum integrable models
is introduced and studied in details. Finite dimensional representations are
constructed and mutually commuting quantities - which ensure the integrability
of the system - are written in terms of the fundamental generators of the new
algebra. Relation with the deformed Dolan-Grady integrable structure recently
discovered by one of the authors and Terwilliger's tridiagonal algebras is
described. Remarkably, this (in)finite dimensional algebra is a
``$q-$deformed'' analogue of the original Onsager's algebra arising in the
planar Ising model. Consequently, it provides a new and alternative algebraic
framework for studying massive, as well as conformal, quantum integrable
models.


  Every year, millions of brain MRI scans are acquired in hospitals, which is a
figure considerably larger than the size of any research dataset. Therefore,
the ability to analyse such scans could transform neuroimaging research. Yet,
their potential remains untapped, since no automated algorithm is robust enough
to cope with the high variability in clinical acquisitions (MR contrasts,
resolutions, orientations, artefacts, subject populations). Here we present
SynthSeg+, an AI segmentation suite that enables, for the first time, robust
analysis of heterogeneous clinical datasets. In addition to whole-brain
segmentation, SynthSeg+ also performs cortical parcellation, intracranial
volume estimation, and automated detection of faulty segmentations (mainly
caused by scans of very low quality). We demonstrate SynthSeg+ in seven
experiments, including an ageing study on 14,000 scans, where it accurately
replicates atrophy patterns observed on data of much higher quality. SynthSeg+
is publicly released as a ready-to-use tool to unlock the potential of
quantitative morphometry.


  The current status of the scientific results of the Auger Observatory will be
discussed which include spectrum, anisotropy in arrival directions, chemical
composition analyses, and limits on neutrino and photon fluxes. A review of the
Observatory detection systems will be presented. Auger has started the
construction of its second phase which encompasses antennae for radio detection
of cosmic rays, high-elevation telescopes, and surface plus muon detectors.
Details will be presented on the latter, AMIGA (Auger Muons and Infill for the
Ground Array), an Auger project consisting of 85 detector pairs each one
composed of a surface water-Cherenkov detector and a buried muon counter. The
detector pairs are arranged in an array with spacings of 433 and 750 m in order
to perform a detailed study of the 10^17 eV to 10^19 eV spectrum region.
Preliminary results on the performance of the 750 m array of surface detectors
and the first muon counter prototype will be presented.


  We numerically calculate the density profile and excitation spectrum of a
two-species Bose-Einstein condensate for the parameters of recent experiments.
We find that the ground state density profile of this system becomes unstable
in certain parameter regimes, which leads to a phase transition to a new stable
state. This state displays spontaneously broken cylindrical symmetry. This
behavior is reflected in the excitation spectrum: as we approach the phase
transition point, the lowest excitation frequency goes to zero, indicating the
onset of instability in the density profile. Following the phase transition,
this frequency rises again.


  We formulate several open questions related to enumerative combinatorics,
which arise in the spectral analysis of Hill operators with trigonometric
polynomial potentials.


  In this paper, we study the orbit intersection problem for the linear space
and the algebraic group in positive characteristic. Let $K$ be an algebraically
closed field of positive characteristic and let $\Phi_1, \Phi_{2}: K^d
\longrightarrow K^{d}$ be affine maps, $\Phi_i({\bf x}) = A_i ({\bf x}) + {\bf
x_i}$ (where each $A_i$ is a $d\times d$ matrix and ${\bf x}\in K^d$). If none
of the eigenvalues of the matrices $A_i$ are roots of unity and each ${\bf a}_i
\in K^d$ is not $\Phi_i$-preperiodic, then we prove that the set $\left \{(n_1,
n_2) \in \Z^{2} \mid \Phi_1^{n_1}({\bf a}_1) = \Phi_{2}^{n_{2}}({\bf
a}_{2})\right\}$ is $p$-normal in $\mathbb{Z}^{2}$ of order at most $d$.
Further, let $\Phi_1, \Phi_{2}: \mathbb{G}_m^d \longrightarrow \mathbb{G}_m^d$
be regular self-maps and ${\bf a}_1, {\bf a}_2\in \mathbb{G}_m^d(K)$. Let
$\Phi_1^0$ and $\Phi_2^0$ be group endomorphisms of $\mathbb{G}_m^d$ and ${\bf
y}, {\bf z} \in \mathbb{G}_m^d(K)$ such that $\Phi_1({\bf x}) = \Phi_1^{0}({\bf
x}) + {\bf y}$ and $\Phi_2({\bf x}) = \Phi_2^{0}({\bf x}) + {\bf z}$. We show,
under some conditions on the roots of the minimal polynomial of $ \Phi_1^{0}$
and $\Phi_2^{0}$, that the set $ \{(n_1, n_{2}) \in \N_0^{2} \mid
\Phi_1^{n_1}({\bf a}_1) = \Phi_{2}^{n_{2}}({\bf a}_{2})\}$ (where ${\bf a}_1,
{\bf a}_2\in \mathbb{G}_m^d(K)$) is a finite union of singletons and
one-parameter linear families. To do so, we use results on linear equations
over multiplicative groups in positive characteristic and some results on
systems of polynomial-exponential equations.


  We address the issue of the cosmological bias between matter and galaxy
distributions, looking at dark-matter haloes as a first step to characterize
galaxy clustering. Starting from the linear density field at high redshift, we
follow the centre of mass trajectory of the material that will form each halo
at late times (proto-halo). We adopt a fluid-like description for the evolution
of perturbations in the proto-halo distribution, which is coupled to the matter
density field via gravity. We present analytical solutions for the density and
velocity fields, in the context of renormalized perturbation theory. We start
from the linear solution, then compute one-loop corrections for the propagator
and the power spectrum. Finally we analytically resum the propagator and we use
a suitable extension of the time-renormalization-group method (Pietroni 2008)
to resum the power spectrum. For halo masses M<10^{14} Msol/h our results at
z=0 are in good agreement with N-body simulations. Our model is able to predict
the halo-matter cross spectrum with an accuracy of 5 per cent up to k = 0.1
h/Mpc approaching the requirements of future galaxy redshift surveys.


  Following earlier results of Sondow, we propose another criterion of
irrationality for Euler's constant $\gamma$. It involves similar linear
combinations of logarithm numbers $L\_{n,m}$. To prove that $\gamma$ is
irrational, it suffices to prove that, for some fixed $m$, the distance of
$d\_n L\_{n,m}$ ($d\_n$ is the least common multiple of the $n$ first integers)
to the set of integers $\mathbf{Z}$ does not converge to 0. A similar result is
obtained by replacing logarithms numbers by rational numbers: it gives a
sufficient condition involving only rational numbers. Unfortunately, the
chaotic behavior of $d\_n$ is an obstacle to verify this sufficient condition.
All the proofs use in a large manner the theory of Pad\'e approximation.


  Log-likelihood ratio (LLR) computation for non-binary modulations over fading
channels is complicated. A measure of LLR accuracy on asymmetric binary
channels is introduced to facilitate good LLR approximations for non-binary
modulations. Considering piecewise linear LLR approximations, we prove
convexity of optimizing the coefficients according to this measure. For the
optimized approximate LLRs, we report negligible performance losses compared to
true LLRs.


  Multiplayer online games are ideal settings for studying the effects of
technological disruptions on social behavior. Software patches to online games
cause significant changes to the game's rules and require players to develop
new strategies to cope with these disruptions. We surveyed players, analyzed
the content of software patch notes, and analyzed changes to the character
selection behaviors in more than 53 million matches of Dota 2 in the days
before and after software patches over a 30-month period. We found that the
severity of patches is correlated with the magnitude of behavioral changes
following a patch. We discuss the opportunities of leveraging software patches
to online games as a valuable but overlooked empirical instrument for measuring
behavioral dynamics.


  We use the n-globe with its skeletal filtration to define the fundamental
globular omega--groupoid of a filtered space; the proofs use an analogous
fundamental cubical omega--groupoid due to the author and Philip Higgins. This
method also relates the construction to the fundamental crossed complex of a
filtered space, and this relation allows the proof that the crossed complex
associated to the free globular omega-groupoid on one element of dimension n is
the fundamental crossed complex of the n-globe.


  We present the first Spitzer-IRS spectral maps of the Herbig-Haro flow GGD 37
detected in lines of [Ne III], [O IV], [Ar III], and [Ne V]. The detection of
extended [O IV] (55 eV) and some extended emission in [Ne V] (97 eV) indicates
a shock temperature in excess of 100,000 K, in agreement with X-ray
observations, and a shock speed in excess of 200 km s-1. The presence of an
extended pho- toionization or collisional ionization region indicates that GGD
37 is a highly unusual protostellar outflow.


  Transition probabilities of the ground-state bands in $\gamma$-soft nuclei
are studied for the first time using the triaxial projected shell model
approach. It is observed that the angular-momentum dependence of the transition
quadrupole moment $Q_t$ is related to the triaxial deformation of the nuclear
mean-field potential. The introduction of the $\gamma$-degree of freedom in the
shell model basis is shown to have a little influence on the {\it constant}
behavior of the low-spin $Q_t$ in a well-deformed nucleus. However, the {\it
increasing} collectivity with spin for the low-spin states in a $\gamma$-soft
nucleus can only be explained by considering the triaxial mean-field
deformation.


  Electrical switching of N\'eel order in an antiferromagnetic insulator is
desirable as a basis for memory applications. Unlike electrically-driven
switching of ferromagnetic order via spin-orbit torques, electrical switching
of antiferromagnetic order remains poorly understood. Here we investigate the
low-field magnetic properties of 30 nm thick, c-axis oriented
$\alpha$-Fe$_2$O$_3$ Hall devices using a diamond nitrogen-vacancy (NV) center
scanning microscope. Using the canted moment of $\alpha$-Fe$_2$O$_3$ as a
magnetic handle on its N\'eel vector, we apply a saturating in-plane magnetic
field to create a known initial state before letting the state relax in low
field for magnetic imaging. We repeat this procedure for different in-plane
orientations of the initialization field. We find that the magnetic field
images are characterized by stronger magnetic textures for fields along
$[\bar{1}\bar{1}20]$ and $[11\bar{2}0]$, suggesting that despite the expected
3-fold magneto-crystalline anisotropy, our $\alpha$-Fe$_2$O$_3$ thin films have
an overall in-plane uniaxial anisotropy. We also study current-induced
switching of the magnetic order in $\alpha$-Fe$_2$O$_3$. We find that the
fraction of the device that switches depends on the current pulse duration,
amplitude and direction relative to the initialization field. Specifically, we
find that switching is most efficient when current is applied along the
direction of the initialization field.


  In this work, we present a new approach for competitive geometric routing in
wireless ad hoc networks. In general, it is well-known that any online routing
strategy performs very poor in the worst case. The main difficulty are
uncovered regions within the wireless ad hoc network, which we denote as radio
holes. Complex shapes of radio holes, for example zig-zag-shapes, make local
geometric routing even more difficult, i.e., forwarded messages in direction to
the destination might get stuck in a dead end or are routed along very long
detours, when there is no knowledge about the ad hoc network. To obtain
knowledge about the position and shape of radio holes, we make use of a hybrid
network approach. This approach assumes that we can not just make use of the ad
hoc network but also of some cellular infrastructure, which is used to gather
knowledge about the underlying ad hoc network. Communication via the cellular
infrastructure incurs costs as cell phone providers are involved. Therefore, we
use the cellular infrastructure only to compute routing paths in the ad hoc
network. The actual data transmission takes place in the ad hoc network. In
order to find good routing paths we aim at computing an abstraction of the ad
hoc network in which radio holes are abstracted by bounding boxes. The
advantage of bounding boxes as hole abstraction is that we only have to
consider a constant number of nodes per hole. We prove that bounding boxes are
a suitable hole abstraction that allows us to find $c$-competitive paths in the
ad hoc network in case of non-intersecting bounding boxes. In case of
intersecting bounding boxes, we show via simulations that our routing strategy
significantly outperforms the so far best online routing strategies for
wireless ad hoc networks. Finally, we also present a routing strategy that is
$c$-competitive in case of pairwise intersecting bounding boxes.


  Quantum synchronizable codes are quantum error-correcting codes that can
correct the effects of quantum noise as well as block synchronization errors.
We improve the previously known general framework for designing quantum
synchronizable codes through more extensive use of the theory of finite fields.
This makes it possible to widen the range of tolerable magnitude of block
synchronization errors while giving mathematical insight into the algebraic
mechanism of synchronization recovery. Also given are families of quantum
synchronizable codes based on punctured Reed-Muller codes and their ambient
spaces.


  The potential of a combined ozone O3 ultraviolet (UV) light reactor for
gas-phase oxidation of flue gas pollutants has been evaluated in this work. For
this, numerical simulations of a continuously stirred tank reactor (CSTR) have
been performed for the analysis of sulfur dioxide SO2 removal. Chemical
kinetics have been coupled with modeling of the radiation intensity
distribution produced by a UV lamp with five different radiation models. A grid
convergence study and an optimization of the number of discrete point light
sources employed for some of the radiation models was carried out. The effect
of residence time and reactor size on the removal of SO2 have also been
analyzed. Overall, results for the abatement of SO2 in an O3-UV reactor under
optimized conditions suggest that this approach is suitable for sustainable air
cleaning applications.


  We study the interplay between the Kondo and superconducting (SC) proximity
effects, taking place in a triangular triple quantum dot (TTQD) connected to
one normal and two SC leads. This system shows various quantum phases. Without
the SC leads, the lowest two states that belong to the different spin sectors,
$S=0$ and $S=1/2$, become energetically very close to each other near half
filling. The singlet one is a Kondo-screened state by conduction electrons from
the normal lead, and the doublet one is a resonating valence bond state with
unpaired free spin which remains unscreened. Furthermore, when one additional
electron enters the TTQD, the ground state becomes a doublet in which the $S=1$
local moment due to the Nagaoka ferromagnetism is partially screened by
conduction electrons.The Cooper pairs penetrating into the TTQD from the SC
leads reconstruct the wavefunctions and vary the phase boundaries between these
quantum states in the parameter space. We calculate ground-state phase diagrams
using the numerical renormalization group, and show that the SC proximity
effect induces a reentrant transition in-between the three- and four-electron
fillings.


  We propose a new practical algorithm for computing the Feigenbaum constants
{\alpha} and {\delta}, having significantly lower time and space complexity
than previously used methods. The algorithm builds upon well-known linear
algebra techniques, and is easily parallelizable. An implementation of it has
been developed and used to determine both constants to 10,000 decimal places.


  This paper presents two existence h-principles, the first for conformal
symplectic structures on closed manifolds, and the second for leafwise
conformal symplectic structures on foliated manifolds with non empty boundary.
The latter h-principle allows to linearly deform certain codimension-$1$
foliations to contact structures. These results are essentially applications of
the Borman-Eliashberg-Murphy h-principle for overtwisted contact structures and
of the Eliashberg-Murphy symplectization of cobordisms, together with tools
pertaining to foliated Morse theory, which are elaborated here.


  A new approach toward the noncoherent communications over the time varying
fading channels is presented. In this approach, the relationship between the
input signal space and the output signal space of a correlatively changing
fading channel is shown to be a nonlinear mapping between manifolds of
different dimensions. Studying this mapping, it is shown that using nonlinear
decoding algorithms for single input-multiple output (SIMO) and multiple input
multiple output (MIMO) systems, extra numbers of degrees of freedom (DOF) are
available. We call them the nonlinear degrees of freedom.


  It was shown that using multiphoton qubits, a nearly deterministic Bell-state
measurement can be performed with linear optics and on-off photodetectors
[Phys. Rev. Lett. 114, 113603 (2015)]. However, multiphoton qubits are
generally more fragile than single-photon qubits under a lossy environment. In
this paper, we propose and analyze a scheme to teleport multiphoton-qubit
information using hybrid entanglement with a loss-tolerant carrier qubit. We
consider three candidates for the carrier qubit: a coherent-state qubit, a
single-photon polarization qubit, and a vacuum-and-single-photon qubit. We find
that teleportation with the vacuum-and-single-photon qubit tolerates about 10
times greater photon losses than with the multiphoton qubit of the photon
number $N \geq 4$ in the high fidelity regime ($F\geq 90\%$). The
coherent-state qubit encoding may be even better than the
vacuum-and-single-photon qubit as the carrier when its amplitude is as small as
$\alpha<0.78$. We further point out that the fidelity of the teleported state
by our scheme is determined by loss in the carrier qubit while the success
probability depends on loss only in the multiphoton qubit to be teleported. Our
study implies that the hybrid architecture may complement the weaknesses of
each qubit encoding.


  We report on the adiabatic splitting of a BEC of $^{87}$Rb atoms by an
asymmetric double-well potential located above the edge of a perpendicularly
magnetized TbGdFeCo film atom chip. By controlling the barrier height and
double-well asymmetry the sensitivity of the axial splitting process is
investigated through observation of the fractional atom distribution between
the left and right wells. This process constitutes a novel sensor for which we
infer a single shot sensitivity to gravity fields of $\delta
g/g\approx2\times10^{-4}$. From a simple analytic model we propose improvements
to chip-based gravity detectors using this demonstrated methodology.


  The paper presents a numerical method for simulating flow and mechanics in
fractured rock. The governing equations that couple the effects in the rock
mass and in the fractures are obtained using the discrete fracture-matrix
approach. The fracture flow is driven by the cubic law, and the contact
conditions prevent fractures from self-penetration. A stable finite element
discretization is proposed for the displacement-pressure-flux formulation. The
resulting nonlinear algebraic system of equations and inequalities is decoupled
using a robust iterative splitting into the linearized flow subproblem, and the
quadratic programming problem for the mechanical part. The non-penetration
conditions are solved by means of dualization and an optimal quadratic
programming algorithm. The capability of the numerical scheme is demonstrated
on a benchmark problem for tunnel excavation with hundreds of fractures in 3D.
The paper's novelty consists in a combination of three crucial ingredients: (i)
application of discrete fracture-matrix approach to poroelasticity, (ii) robust
iterative splitting of resulting nonlinear algebraic system working for
real-world 3D problems, and (iii) efficient solution of its mechanical
quadratic programming part with a large number of fractures in mutual contact
by means of own solvers implemented into an in-house software library.


  We embark on systematic explorations of the behaviour of tetraquark mesons
(colour-singlet bound states of two quarks and two antiquarks) in the
(idealized) limit of a large number $N_c$ of colour degrees of freedom of
quantum chromodynamics. Considering the scattering of two ordinary mesons into
two ordinary mesons, we start off with formulating a set of selection criteria
that should enable us to unambiguously single out precisely those contributions
to all encountered scattering amplitudes that potentially will develop
tetraquark poles. Assuming that tetraquark mesons do exist and, if so, emerge
in the contributions compatible with our criteria at largest admissible order
of $N_c$, we deduce, for the categories of tetraquarks that exhibit either four
or only two different open quark flavours, that the decay rates of these
tetraquark types are, at least, of order $1/N_c^2$ and that internal
consistency requires all the members of the first species to exist pairwise,
distinguishable by their favoured two-ordinary-meson decay channels.


  Exoplanet direct imaging using adaptive optics (AO) is often limited by
non-common path aberrations (NCPAs) and aberrations that are invisible to
traditional pupil-plane wavefront sensors (WFSs). This can be remedied by
focal-plane (FP) WFSs that characterize aberrations directly from a final
science image. Photonic lanterns (PLs) can act as low-order FPWFSs with the
ability to direct some light to downstream science instruments. Using a PL on
the SEAL (Santa Cruz Extreme AO Laboratory) high-contrast imaging testbed, we
demonstrate (1) linear ranges and (2) closed-loop control. Additionally, we
simulate the use of the PL in a multi-wavefront sensor AO system, in which
multiple WFSs feed back to the same common-path deformable mirror. Building on
previous multi-WFS AO demonstrations on SEAL, we simulate a modulated pyramid
WFS to sense aberrations of high spatial order and large amplitude, and the PL
to sense low order aberrations including NCPAs. We assess adaptive optics
performance in this setting using three different PL wavefront reconstruction
algorithms. We also provide a new method to experimentally identify the
propagation matrix of a PL, making advanced model-based algorithms practical.
This work demonstrates the role of photonic technologies and multi-stage
wavefront sensing in the context of extreme AO and high contrast imaging.


  If $\psi$ is analytic on the open unit disk $\mathbb{D}$ and $\varphi$ is an
analytic self-map of $\mathbb{D}$, the weighted composition operator
$C_{\psi,\varphi}$ is defined by $C_{\psi,\varphi}f(z)=\psi(z)f (\varphi (z))$,
when $f$ is analytic on $\mathbb{D}$. In this paper, we study normal,
cohyponormal, hyponormal and normaloid weighted composition operators on the
Hardy and weighted Bergman spaces. First, for some weighted Hardy spaces
$H^{2}(\beta)$, we prove that if $C_{\psi,\varphi}$ is cohyponormal on
$H^{2}(\beta)$, then $\psi$ never vanishes on $\mathbb{D}$ and $\varphi$ is
univalent, when $\psi \not \equiv 0$ and $\varphi$ is not a constant function.
Moreover, for $\psi=K_{a}$, where $|a| < 1$, we investigate normal,
cohyponormal and hyponormal weighted composition operators $C_{\psi,\varphi}$.
After that, for $\varphi $ which is a hyperbolic or parabolic automorphism, we
characterize all normal weighted composition operators $C_{\psi,\varphi}$, when
$\psi \not \equiv 0$ and $\psi$ is analytic on $\overline{\mathbb{D}}$.
  Finally, we find all normal weighted composition operators which are bounded
below.


  In many real-world deployments of machine learning systems, data arrive
piecemeal. These learning scenarios may be passive, where data arrive
incrementally due to structural properties of the problem (e.g., daily
financial data) or active, where samples are selected according to a measure of
their quality (e.g., experimental design). In both of these cases, we are
building a sequence of models that incorporate an increasing amount of data. We
would like each of these models in the sequence to be performant and take
advantage of all the data that are available to that point. Conventional
intuition suggests that when solving a sequence of related optimization
problems of this form, it should be possible to initialize using the solution
of the previous iterate -- to "warm start" the optimization rather than
initialize from scratch -- and see reductions in wall-clock time. However, in
practice this warm-starting seems to yield poorer generalization performance
than models that have fresh random initializations, even though the final
training losses are similar. While it appears that some hyperparameter settings
allow a practitioner to close this generalization gap, they seem to only do so
in regimes that damage the wall-clock gains of the warm start. Nevertheless, it
is highly desirable to be able to warm-start neural network training, as it
would dramatically reduce the resource usage associated with the construction
of performant deep learning systems. In this work, we take a closer look at
this empirical phenomenon and try to understand when and how it occurs. We also
provide a surprisingly simple trick that overcomes this pathology in several
important situations, and present experiments that elucidate some of its
properties.


  A description of the dynamics of a collisionless, self-gravitating fluid is
developed and applied to follow the development of Large Scale Structures in
the Universe. Such description takes on one of the assumptions of the Adhesion
Approximation (AA) model, i.e., the introduction of an artificial viscosity
$\nu$ in the Euler equation, but extends it to deeper non-linear stages, where
the extrapolation of the linear relation $\psi=-\phi$ between the velocity and
the gravitational potentials -- at the basis of both the Zel'dovich and the
Adhesion models -- is no longer valid. This is achieved by expanding the
relation bewteen the gravitational potential $\phi$ and the velocity potential
$\psi$, in powers of the small viscosity $\nu$. When the results are compared
to the outcomes of an N-body simulation, the proposed extension of the Adhesion
approach provides a better description of small-scale, deeply non-linear
regions, as it is quantitatively shown by the computation of some statistical
indicators. At larger scales, the satisfactory description of the large scale
texture and of the voids given by the canonical Adhesion Approximation is
preserved in the extended model.


  We discuss spectroscopy and infrared photometry for a complete sample of ~
800 galaxies in close pairs objectively selected from the CfA2 redshift survey.
We use 2MASS to compare near infrared color-color diagrams for our sample with
the Nearby Field Galaxy Sample and with a set of IRAS flux-limited pairs from
Surace et al. We construct a basic statistical model to explore the physical
sources of the substantial differences among these samples. The model explains
the spread of near infrared colors and is consistent with a picture where
central star formation is triggered by the galaxy-galaxy interaction before a
merger occurs. For 160 galaxies we report new, deep JHK photometry within our
spectroscopic aperture and we use the combined spectroscopic and photometric
data to explore the physical conditions in the central bursts. We find a set of
objects with H-K >= 0.45 and with a large F(FIR)/F(H). We interpret the very
red H-K colors as evidence for 600-1000 K dust within compact star-forming
regions, perhaps similar to super-star clusters identified in individual
well-studied interacting galaxies. The galaxies in our sample are candidate
``hidden'' bursts or, possibly, ``hidden'' AGN. Over the entire pair sample,
both spectroscopic and photometric data show that the specific star formation
rate decreases with the projected separation of the pair. The data suggest that
the near infrared color-color diagram is also a function of the projected
separation; all of the objects with central near infrared colors indicative of
bursts of star formation lie at small projected separation.


  We formally study the problem of classification under adversarial
perturbations from a learner's perspective as well as a third-party who aims at
certifying the robustness of a given black-box classifier. We analyze a
PAC-type framework of semi-supervised learning and identify possibility and
impossibility results for proper learning of VC-classes in this setting. We
further introduce a new setting of black-box certification under limited query
budget, and analyze this for various classes of predictors and perturbation. We
also consider the viewpoint of a black-box adversary that aims at finding
adversarial examples, showing that the existence of an adversary with
polynomial query complexity can imply the existence of a sample efficient
robust learner.


  Energy efficiency is a corner stone of sustainability in data center and
high-performance networking. However, at present there is a notable structural
mismatch between network silicon development targets and network equipment
utilization patterns in the field. In particular, some aspects of network
energy utilization (eg load-proportional energy consumption) routinely stay out
of focus during system design and implementation. Drawing from hands-on
research and development in high-speed and grid networking, we identify a novel
approach to energy efficiency in network engineering. In this paper, we
demonstrate how the problem of efficient network system design can be dissected
into smaller sections based on timescales of traffic processing. The newly
proposed approach allows R&D efforts to be tightly paired to resources and
sustainability targets to improve energy efficiency in many classes of network
and telecom devices.


  We construct an effective Quantum Field Theory for the wrapping effects in
1+1 dimensional models of factorised scattering. The recently developed
graph-theoretical approach to TBA gives the perturbative desctiption of this
QFT. For the sake of simplicity we limit ourselves to scattering matrices for a
single neutral particle and no bound state poles, such as the sinh-Gordon one.
On the other hand, in view of applications to AdS/CFT, we do not assume that
the scattering matrix is of difference type. The effective QFT involves both
bosonic and fermionic fields and possesses a symmetry which makes it one-loop
exact. The corresponding path integral localises to a critical point determined
by the TBA equation.


  This report presents algorithms for generating small random samples without
replacement. It considers two cases. It presents an algorithm for sampling a
pair of distinct integers, and an algorithm for sampling a triple of distinct
integers. The worst case runtime of both algorithms is constant, while the
worst case runtime of common algorithms for the general case of sampling $k$
elements from a set of $n$ are linear in $n$. Java implementations of both
algorithms are included in the open source library $\rho\mu$.


  The study of detached eclipsing binaries is one of the most powerful ways to
investigate the properties of individual stars and stellar systems. We present
preliminary masses, radii and effective temperatures for the eclipsing binary
WW Aurigae, which is composed of two metallic-lined A-type stars. We also
reanalyse the data on HD 23642, an A-type eclipsing binary member of the
Pleiades open cluster with a metallic-lined component, and determine its
distance to be 139 +/- 4 pc. This is in agreement with the traditional Pleiades
distance, but in disagreement with distance to the Pleiades, and to HD 23642
itself, derived from Hipparcos trigonometrical parallaxes.


  In this paper, we establish the existence and uniqueness of weak solutions to
first-order discount mean field games and a stability result to give the
existence for the ergodic problem. We show an example to illustrate the
multiplicity of weak solutions to the ergodic problem. With this motivation, we
address a selection condition, which is a necessary condition that any limit of
solutions under subsequence satisfies. As an application, we show a nontrivial
example to get the convergence of weak solutions.


  We introduce and study soficity for Lie algebras, modelled after linear
soficity in associative algebras. We introduce equivalent definitions of
soficity, one involving metric ultraproducts and the other involving almost
representations. We prove that any Lie algebra of subexponential growth is
sofic. We also prove that a Lie algebra over a field of characteristic 0 is
sofic if and only if its universal enveloping algebra is linearly sofic.
Finally, we give explicit families of almost representations for the Witt and
Virasoro algebras.


  The function of constructing the hierarchy of objects is important to the
visual process of the human brain. Previous studies have successfully adopted
capsule networks to decompose the digits and faces into parts in an
unsupervised manner to investigate the similar perception mechanism of neural
networks. However, their descriptions are restricted to the 2D space, limiting
their capacities to imitate the intrinsic 3D perception ability of humans. In
this paper, we propose an Inverse Graphics Capsule Network (IGC-Net) to learn
the hierarchical 3D face representations from large-scale unlabeled images. The
core of IGC-Net is a new type of capsule, named graphics capsule, which
represents 3D primitives with interpretable parameters in computer graphics
(CG), including depth, albedo, and 3D pose. Specifically, IGC-Net first
decomposes the objects into a set of semantic-consistent part-level
descriptions and then assembles them into object-level descriptions to build
the hierarchy. The learned graphics capsules reveal how the neural networks,
oriented at visual perception, understand faces as a hierarchy of 3D models.
Besides, the discovered parts can be deployed to the unsupervised face
segmentation task to evaluate the semantic consistency of our method. Moreover,
the part-level descriptions with explicit physical meanings provide insight
into the face analysis that originally runs in a black box, such as the
importance of shape and texture for face recognition. Experiments on CelebA,
BP4D, and Multi-PIE demonstrate the characteristics of our IGC-Net.


  We study properties of the random metric space called the Brownian map. For
every h>0, we consider the connected components of the complement of the open
ball of radius h centered at the root, and we let N(h,r) be the number of those
connected components that intersect the complement of the ball of radius h+r.
We then prove that r^3N(h,r) converges as r tends to 0 to a constant times the
density at h of the profile of distances from the root. In terms of the
Brownian cactus, this gives asymptotics for the number of vertices at height h
that have descendants at height h+r. Our proofs are based on a similar
approximation result for local times of super-Brownian motion by upcrossing
numbers. Our arguments make a heavy use of the Brownian snake and its special
Markov property.


  Mathematical steps are developed to obtain optimised well tempered model
"temperaments", based on a musical Well Temperament definition by H. Kelletat,
that is derived from A. Werckmeister. This supports objective mathematical
ranking of historical temperaments. Historical temperaments that fit best with
mathematical models are often installed on organs. Musical appreciation and
mathematical ranking of historical temperaments are in agreement. The diatonic
C-major impurity of Well Temperaments lies between that of an elaborated
optimal model and that of Equal Temperament. Historical Well Temperaments join
these limits very closely and the list is amply filled in small rising steps.
Hence, it achieves little to develop new Well Temperaments. The developed RMS
computing modules can also be used for precise and accurate recognition of
historical temperaments.


  In this paper we present an early Apprenticeship Learning approach to mimic
the behaviour of different players in a short adaption of the interactive
fiction Anchorhead. Our motivation is the need to understand and simulate
player behaviour to create systems to aid the design and personalisation of
Interactive Narratives (INs). INs are partially observable for the players and
their goals are dynamic as a result. We used Receding Horizon IRL (RHIRL) to
learn players' goals in the form of reward functions, and derive policies to
imitate their behaviour. Our preliminary results suggest that RHIRL is able to
learn action sequences to complete a game, and provided insights towards
generating behaviour more similar to specific players.


  We describe Dalitz plots arising in studies of $D$-meson decays, and what we
have learned from them in recent years. After some mention of technique and
history, we focus on decay of the $D^\pm$ and $D_s^\pm$ mesons to the
$K^-K^+\pi^\pm$ final state, and on $D_s^\pm$ decay to $\pi^+\pi^-\pi^\pm$.
Some mention of other Dalitz plots involving $D$-meson decays is also made.


  We employ the analytic Bethe Anzats to construct eigenvalues of transfer
matrices with finite-dimensional atypical representations in the auxiliary
space for the putative long-range spin chain encoding anomalous dimensions of
all composite single-trace gauge invariant operators of the maximally
supersymmetric Yang-Mills theory. They obey an infinite fusion hierarchy which
can be reduced to a finite set of integral relations for a minimal set of
transfer matrices. This set is used to derive a finite systems of functional
equations for eigenvalues of nested Baxter polynomials.


  The Bethe equation is a nonlinear differential equation that plays an
important role in nuclear physics and a variety of applications related to it,
such as the description of the behavior of an energetic particle when it
penetrates into matter. Despite its importance, its unusual to find the exact
solution to this nonlinear equation in literature and practically all of them
are of experimental nature. In this paper, we solve this equation and present a
new approach to obtain the solution through the combined use of the Adomian
Decomposition Method and the Laplace Transform (LADM). In addition, we
illustrate our approach solving three examples, in which initial conditions are
considered within the typical numerical ranges derived from the applications.
Our results indicate that LADM is highly accurate and can be considered a very
useful and valuable method.


  Given an operad A of topological spaces, we consider A-monads in a
topological category C . When A is an A-infinity-operad, any A-monad K : C -> C
can be thought of as a monad up to coherent homotopies. We define the
completion functor with respect to an A-infinity-monad and prove that it is an
A-infinity-monad itself.


  We present a correction method for the pair density (PD) to get close to the
ground state one. The PD is corrected to be a variationally-best PD within the
search region that is extended by adding the uniformly-scaled PDs to its
elements. The corrected PD is kept N-representable and satisfies the virial
relation rigorously. The validity of the present method is confirmed by
numerical calculations of neon atom. It is shown that the root-mean-square
error of the electron-electron interaction and external potential energies,
which is a good benchmark for the error of the PD, is reduced by 69.7% without
additional heavy calculations.


  In the never-ending quest for tools that enable an ISP to smooth
troubleshooting and improve awareness of network behavior, very much effort has
been devoted in the collection of data by active and passive measurement at the
data plane and at the control plane level. Exploitation of collected data has
been mostly focused on anomaly detection and on root-cause analysis. Our
objective is somewhat in the middle. We consider traceroutes collected by a
network of probes and aim at introducing a practically applicable methodology
to quickly spot measurements that are related to high-impact events happened in
the network. Such filtering process eases further in- depth human-based
analysis, for example with visual tools which are effective only when handling
a limited amount of data. We introduce the empathy relation between traceroutes
as the cornerstone of our formal characterization of the traceroutes related to
a network event. Based on this model, we describe an algorithm that finds
traceroutes related to high-impact events in an arbitrary set of measurements.
Evidence of the effectiveness of our approach is given by experimental results
produced on real-world data.


  In the probe limit, we investigate the nonlinear electrodynamical effects of
the both exponential form and the logarithmic form on the holographic
paramagnetism-ferromagnetism phase transition in the background of a
Schwarzschild-AdS black hole spacetime. Moreover, by comparing the exponential
form of nonlinear electrodynamics with the logarithmic form of nonlinear
electrodynamics and the Born-Infeld nonlinear electrodynamics which has been
presented in Ref.~\cite{Wu:2016uyj}, we find that the higher nonlinear
electrodynamics correction makes the critical temperature smaller and the
magnetic moment harder form in the case without external field. Furthermore,
the increase of nonlinear parameter b will result in extending the period of
the external magnetic field. Especially, the effect of the exponential form of
nonlinear electrodynamics on the periodicity of hysteresis loop is more
noticeable.


  In this article, we derive a magnetic dipole model for two identical,
electrically conducting, and permeable spheres that are exposed to an
oscillating homogeneous magnetic field. Our model predicts both amplitude and
phase of the induced field outside the spheres. The description is provided for
parallel and transverse excitation relative to the axis through the sphere
centers. This geometric decomposition allows the application of arbitrary
excitation field directions. Our approach is based on one dipole per sphere.
The origins of these secondary dipole fields are proposed to be found at
positions slightly displaced from the sphere centers to consider the mutual
interaction. This displacement and the resulting phase of the dipole moments
strongly depend on the distance between the spheres as well as on
complex-valued first and second order response factors, which contain material
properties and the oscillation frequency. We demonstrate the usefulness of our
displaced dipole model in terms of efficiency and accuracy compared to other
computationally simple approaches.


  Some non-classical properties such as squeezing, sub-Poissonian photon
statistics or oscillations in photon-number distributions may survive longer in
a phase-sensitive environment than in a phase-insensitive environment. We
examine if entanglement, which is an inter-mode non-classical feature, can also
survive longer in a phase-sensitive environment. Differently from the
single-mode case, we find that making the environment phase-sensitive does not
aid in prolonging entanglement.


  We study the computational complexity of finding a competitive equilibrium
(CE) with chores when agents have linear preferences. CE is one of the most
preferred mechanisms for allocating a set of items among agents. CE with equal
incomes (CEEI), Fisher, and Arrow-Debreu (exchange) are the fundamental
economic models to study allocation problems, where CEEI is a special case of
Fisher and Fisher is a special case of exchange. When the items are goods
(giving utility), the CE set is convex even in the exchange model, facilitating
several combinatorial polynomial-time algorithms (starting with the seminal
work of Devanur, Papadimitriou, Saberi and Vazirani) for all of these models.
In sharp contrast, when the items are chores (giving disutility), the CE set is
known to be non-convex and disconnected even in the CEEI model. Further, no
combinatorial algorithms or hardness results are known for these models. In
this paper, we give two main results for CE with chores:
  1) A combinatorial algorithm to compute a $(1-\varepsilon)$-approximate CEEI
in time $\tilde{\mathcal{O}}(n^4m^2 / \varepsilon^2)$, where $n$ is the number
of agents and $m$ is the number of chores.
  2) PPAD-hardness of finding a $(1-1/\mathit{poly}(n))$-approximate CE in the
exchange model under a sufficient condition. To the best of our knowledge,
these results show the first separation between the CEEI and exchange models
when agents have linear preferences, assuming PPAD $\neq $ P.
  Finally, we show that our new insight implies a straightforward proof of the
existence of an allocation that is both envy-free up to one chore (EF1) and
Pareto optimal (PO) in the discrete setting when agents have factored bivalued
preferences.


  We briefly describe a three-family intersecting D6-brane model in Type IIA
theory on the T^6/(Z_2 x Z_2) orientifold with a realistic phenomenology. In
this model, the gauge symmetry can be broken down to the Standard Model (SM)
gauge symmetry close to the string scale, and the gauge coupling unification
can be achieved. We calculate the supersymmetry breaking soft terms, and the
corresponding low energy supersymmetric particle spectrum, which may be tested
at the Large Hadron Collider (LHC). The observed dark matter density may also
be generated. Finally, we can explain the SM quark masses and CKM mixings, and
the tau lepton mass. The neutrino masses and mixings may be generated via the
seesaw mechanism as well.


  Sorting is one of the most basic algorithms, and developing highly parallel
sorting programs is becoming increasingly important in high-performance
computing because the number of CPU cores per node in modern supercomputers
tends to increase. In this study, we have implemented two multi-threaded
sorting algorithms based on samplesort and compared their performance on the
supercomputer Fugaku. The first algorithm divides an input sequence into
multiple blocks, sorts each block, and then selects pivots by sampling from
each block at regular intervals. Each block is then partitioned using the
pivots, and partitions in different blocks are merged into a single sorted
sequence. The second algorithm differs from the first one in only selecting
pivots, where the binary search is used to select pivots such that the number
of elements in each partition is equal. We compare the performance of the two
algorithms with different sequential sorting and multiway merging algorithms.
We demonstrate that the second algorithm with BlockQuicksort (a quicksort
accelerated by reducing conditional branches) for sequential sorting and the
selection tree for merging shows consistently high speed and high parallel
efficiency for various input data types and data sizes.