  The use of symbolic knowledge representation and reasoning as a way to
resolve the lack of transparency of machine learning classifiers is a research
area that lately attracts many researchers. In this work, we use knowledge
graphs as the underlying framework providing the terminology for representing
explanations for the operation of a machine learning classifier. In particular,
given a description of the application domain of the classifier in the form of
a knowledge graph, we introduce a novel method for extracting and representing
black-box explanations of its operation, in the form of first-order logic rules
expressed in the terminology of the knowledge graph.


  Several deep observations such as those carried out at the
Canada-France-Hawaii Telescope (CFHT) have revealed prominent Low Surface
Brightness (LSB) fine structures that change the apparent morphology of
galaxies. Previous photometry surveys have developed observational techniques
which exploit the diffuse light detected in the external regions of galaxies.
In these studies the outer perturbations have been identified and classified
like tidal tails, stellar streams, and shells. These structures are tracers of
interacting and merging events and they keep a memory of the mass assembly of
galaxies. Cosmological numerical simulations are needed to estimate their
visibility time-scale (among other properties) in order to reconstruct the past
merger history of galaxies. In the present work, we analyze a hydrodynamical
cosmological simulation to build a comprehensive interpretation of the
properties of fine structures. We make a census of several types of LSB fine
structures by visual inspection of individual snapshots at various time. We
reconstruct the evolution of the number of fine structures detected around an
early-type galaxy and we compare with the merger history of the galaxy. We find
that most of fine structures are associated with major and intermediate mass
merger events. Their survival time scale ranges between 0.7 and 4 Gyr. Shells
and streams remain visible for a longer time than tidal tails. These estimates
of survival times provide clues to interpret the shape and frequency of fine
structures observed in deep images in terms of mass assembly. We find that the
detectability of stellar streams is the most sensitive to the surface
brightness limit. We see 2-3 times more streams with a surface brightness cut
of 33 mag arcsec$^{-2}$ than with 29 mag arcsec$^{-2}$. The detection of shells
display a strong dependence on the projection angle.


  Let $X=\mathbb{P}(\mathcal{O}_{\mathbb{P}^s} \oplus \bigoplus_{i=1}^r
\mathcal{O}_{\mathbb{P}^s}(a_i))$ be a Fano projective bundle over
$\mathbb{P}^s$ and denote by $Crit(X) \subset (\mathbb{C}^{\ast})^n$ the
solution scheme of the Landau-Ginzburg system of equations of $X$. We describe
a map $E : Crit(X) \rightarrow Pic(X)$ whose image $\mathcal{E}= \{E(z) | z \in
Crit(X) \}$ is the full strongly exceptional collection on $X$ found by Costa
and Mir$\acute{\textrm{o}}$-Roig. We further show that $Hom(E(z),E(w))$ for
$z,w \in Crit(X)$ can be described in terms of a monodromy group acting on
$Crit(X)$.


  We study the dynamics of the five-parameter quadratic family of
volume-preserving diffeomorphisms of R^3. This family is the unfolded normal
form for a bifurcation of a fixed point with a triple-one multiplier and also
is the general form of a quadratic three-dimensional map with a quadratic
inverse. Much of the nontrivial dynamics of this map occurs when its two fixed
points are saddle-foci with intersecting two-dimensional stable and unstable
manifolds that bound a spherical ``vortex-bubble''. We show that this occurs
near a saddle-center-Neimark-Sacker (SCNS) bifurcation that also creates, at
least in its normal form, an elliptic invariant circle. We develop a simple
algorithm to accurately compute these elliptic invariant circles and their
longitudinal and transverse rotation numbers and use it to study their
bifurcations, classifying them by the resonances between the rotation numbers.
In particular, rational values of the longitudinal rotation number are shown to
give rise to a string of pearls that creates multiple copies of the original
spherical structure for an iterate of the map.


  To undergo diffusive shock acceleration, electrons need to be pre-accelerated
to increase their energies by several orders of magnitude, else their
gyro-radii are smaller than the finite width of the shock. In oblique shocks,
where the upstream magnetic field orientation is neither parallel or
perpendicular to the shock normal, electrons can escape to the shock upstream,
modifying the shock foot to a region called the electron foreshock. To
determine the pre-acceleration in this region, we undertake PIC simulations of
oblique shocks while varying the obliquity and in-plane angles. We show that
while the proportion of reflected electrons is negligible for $\theta_{\rm Bn}
= 74.3^\circ$, it increases to $R \sim 5\%$ for $\theta_{\rm Bn} = 30^\circ$,
and that, via the electron acoustic instability, these electrons power
electrostatic waves upstream with energy density proportional to $R^{0.6}$ and
a wavelength $\approx 2 \lambda_{\rm{se}}$, where $\lambda_{\rm{se}}$ is the
electron skin length. While the initial reflection mechanism is typically a
combination of shock surfing acceleration and magnetic mirroring, we show that
once the electrostatic waves have been generated upstream they themselves can
increase the momenta of upstream electrons parallel to the magnetic field. In
$\lesssim 1\%$ of cases, upstream electrons are prematurely turned away from
the shock and never injected downstream. In contrast, a similar fraction are
re-scattered back towards the shock after reflection, re-interact with the
shock with energies much greater than thermal, and cross into the downstream.


  We study the distribution of the star formation rate and metallicity of
damped Lyman-alpha absorbers using cosmological SPH simulations of the Lambda
cold dark matter model in the redshift range z=0-4.5. Our approach includes a
phenomenological model of galactic wind. We find that there is a positive
correlation between the projected stellar mass density and the neutral hydrogen
column density (NHI) of DLAs for high NHI systems, and that there is a good
correspondence in the spatial distribution of stars and DLAs in the
simulations. The evolution of typical star-to-gas mass ratios in DLAs can be
characterised by an increase from about 2 at z=4.5 to 3 at z=3, to 10 at z=1,
and finally to 20 at z=0. We also find that the projected SFR density in DLAs
follows the Kennicutt law well at all redshifts, and the simulated values are
consistent with the recent observational estimates of this quantity by Wolfe et
al. (2003a,b). The rate of evolution in the mean metallicity of simulated DLAs
as a function of redshift is mild, and is consistent with the rate estimated
from observations. The predicted metallicity of DLAs is generally sub-solar in
our simulations, and there is a significant scatter in the distribution of DLA
metallicity for a given NHI. However, we find that the median metallicity of
simulated DLAs is close to that of Lyman-break galaxies, which is higher than
the values typically observed for DLAs by nearly an order of magnitude. This
discrepancy with observations could be due to an inadequate treatment of SN
feedback in our current simulations, perhaps indicating that metals are not
expelled efficiently enough from DLAs by outflows. Alternatively, the current
observations might be missing the majority of the high metallicity DLAs due to
selection effects. (abridged)


  Heun's equation naturally appears as special cases of Fuchsian system of
differential equations of rank two with four singularities by introducing the
space of initial conditions of the sixth Painlev\'e equation. Middle
convolutions of the Fuchsian system are related with an integral transformation
of Heun's equation.


  Contributions of the CODALEMA/EXTASIS experiment to the 35th International
Cosmic Ray Conference, 12-20 July 2017, Busan, South Korea.


  An investigation is launched into the fundamental characteristics of
operations on and between sets, with a focus on compact convex sets and star
sets (compact sets star-shaped with respect to the origin) in $n$-dimensional
Euclidean space $\R^n$. For example, it is proved that if $n\ge 2$, with three
trivial exceptions, an operation between origin-symmetric compact convex sets
is continuous in the Hausdorff metric, GL(n) covariant, and associative if and
only if it is $L_p$ addition for some $1\le p\le\infty$. It is also
demonstrated that if $n\ge 2$, an operation * between compact convex sets is
continuous in the Hausdorff metric, GL(n) covariant, and has the identity
property (i.e., $K*\{o\}=K=\{o\}*K$ for all compact convex sets $K$, where $o$
denotes the origin) if and only if it is Minkowski addition. Some analogous
results for operations between star sets are obtained. An operation called
$M$-addition is generalized and systematically studied for the first time.
Geometric-analytic formulas that characterize continuous and GL(n)-covariant
operations between compact convex sets in terms of $M$-addition are
established. The term "polynomial volume" is introduced for the property of
operations * between compact convex or star sets that the volume of $rK*sL$,
$r,s\ge 0$, is a polynomial in the variables $r$ and $s$. It is proved that if
$n\ge 2$, with three trivial exceptions, an operation between origin-symmetric
compact convex sets is continuous in the Hausdorff metric, GL(n) covariant,
associative, and has polynomial volume if and only if it is Minkowski addition.


  The TESS spacecraft observed the asynchronous polar CD Ind at a two-minute
cadence almost continuously for 28 days in 2018, covering parts of 5
consecutive cycles of the system's 7.3-day beat period. These observations
provide the first uninterrupted photometry of a full spin-orbit beat cycle of
an asynchronous polar. Twice per beat cycle, the accretion flow switched
between magnetic poles on the white dwarf, causing the spin pulse of the white
dwarf (WD) to alternate between two waveforms after each pole-switch. An
analysis of the waveforms suggests that one accretion region is continuously
visible when it is active, while the other region experiences lengthy
self-eclipses by the white dwarf. We argue that the previously accepted periods
for both the binary orbit and the WD spin have been misidentified, and while
the cause of this misidentification is a subtle and easily overlooked effect,
it has profound consequences for the interpretation of the system's accretion
geometry and doubles the estimated time to resynchronization. Moreover, our
timings of the photometric maxima do not agree with the quadratic ephemeris
from Myers et al. (2017), and it is possible that the optical spin pulse might
be an unreliable indicator of the white dwarf's rotation. Finally, we use
Doppler tomography of archival time-resolved spectra from 2006 to study the
accretion flow. While the accretion flow showed a wider azimuthal extent than
is typical for synchronous polars, it was significantly less extended than in
the three other asynchronous polars for which Doppler tomography has been
reported.


  Chen's iterated integrals are treated within synthetic differential geometry.
The main result is that iterated integrals produce a subcomplex of the de Rham
complex on the free path space as well as based path spaces.


  Label differential privacy (label-DP) is a popular framework for training
private ML models on datasets with public features and sensitive private
labels. Despite its rigorous privacy guarantee, it has been observed that in
practice label-DP does not preclude label inference attacks (LIAs): Models
trained with label-DP can be evaluated on the public training features to
recover, with high accuracy, the very private labels that it was designed to
protect. In this work, we argue that this phenomenon is not paradoxical and
that label-DP is designed to limit the advantage of an LIA adversary compared
to predicting training labels using the Bayes classifier. At label-DP
$\epsilon=0$ this advantage is zero, hence the optimal attack is to predict
according to the Bayes classifier and is independent of the training labels.
Our bound shows the semantic protection conferred by label-DP and gives
guidelines on how to choose $\varepsilon$ to limit the threat of LIAs below a
certain level. Finally, we empirically demonstrate that our result closely
captures the behavior of simulated attacks on both synthetic and real world
datasets.


  We describe new components of the Gieseker--Maruyama moduli scheme
$\mathcal{M}(n)$ of semistable rank 2 sheaves $E$ on $\mathbb{P}^3$ with
$c_1(E)=0$, $c_2(E)=n$ and $c_3(E)=0$ whose generic point corresponds to non
locally free sheaves. We show that such components grow in number as $n$ grows,
and discuss how they intersect the instanton component. As an application, we
prove that $\mathcal{M}(2)$ is connected, and identify a connected subscheme of
$\mathcal{M}(3)$ consisting of 7 irreducible components.


  We prove that coherent perfect absorption (CPA) without lasing is {\bf not}
possible in the PT-symmetric domain as the s-matrix is such that $|\det S(\pm
k)|=1$. We study coherent scattering from three complex potentials, one solved
analytically and the other two numerically. We conjecture that in the domain of
unbroken symmetry (when the potential has real discrete spectrum) neither
spectral singularity nor CPA can occur. We show that Scarf II potential is a
special model that can analytically and explicitly exhibit these as well as
other novel phenomena and their subtleties. \pacs{03.65-w, 03.65.Nk, 11.30.Er,
42.25.Bs, 42.79.Gn


  We investigate the hydrodynamics of the QCD plasma using dimensionless
numbers built from the thermodynamics and transport theory of the plasma and
characteristic dimensions of the fireball produced in heavy-ion collisions. We
find that by the usual measures, dissipation is strong, and the fireball is on
the borderline of equilibrium. As a result, the system is richer in phenomena
than ideal hydrodynamics would predict. One general implication is that it may
be possible to get a direct view of the QCD plasma phase rather than having to
infer its existence indirectly from signals that come from the freezeout
isotherm after the fireball has cooled into the hadronic phase.


  Two-loop renormalization group equations in gauge theories with multiple U(1)
groups are presented. Instead of normalizing the abelian gauge fields in
canonical forms, we retain kinetic-mixing terms and treat the mixing
coefficients as free parameters. The beta- and gamma-functions are then
obtained in a straightforward manner.


  In the incremental knapsack problem ($\IK$), we are given a knapsack whose
capacity grows weakly as a function of time. There is a time horizon of $T$
periods and the capacity of the knapsack is $B_t$ in period $t$ for $t = 1,
\ldots, T$. We are also given a set $S$ of $N$ items to be placed in the
knapsack. Item $i$ has a value of $v_i$ and a weight of $w_i$ that is
independent of the time period. At any time period $t$, the sum of the weights
of the items in the knapsack cannot exceed the knapsack capacity $B_t$.
Moreover, once an item is placed in the knapsack, it cannot be removed from the
knapsack at a later time period. We seek to maximize the sum of (discounted)
knapsack values over time subject to the capacity constraints. We first give a
constant factor approximation algorithm for $\IK$, under mild restrictions on
the growth rate of $B_t$ (the constant factor depends on the growth rate). We
then give a PTAS for $\IIK$, the special case of $\IK$ with no discounting,
when $T = O(\sqrt{\log N})$.


  The hypothesis is proposed that under the approximation that the quantum
equations of motion reduce to the classical ones, the quantum vacuum also
reduces to the classical vacuum--the empty space. The vacuum energy of QED is
studied under this hypothesis. A possible solution to the cosmological constant
problem is provided and a kind of parameterization of the cosmological
"constant" is derived.


  One of the most unexpected results in the field of stellar populations of the
last few years, is the discovery that some Magellanic-Cloud globular clusters
younger than ~400 Myr, exhibit bimodal main sequences (MSs) in their
color-magnitude diagrams (CMDs). Moreover, these young clusters host an
extended main sequence turn off (eMSTO) in close analogy with what is observed
in most ~1-2 Gyr old clusters of both Magellanic Clouds.
  We use high-precision Hubble-Space-Telescope photometry to study the young
star cluster NGC1866 in the Large Magellanic Cloud. We discover an eMSTO and a
split MS. The analysis of the CMD reveals that (i) the blue MS is the less
populous one, hosting about one-third of the total number of MS stars; (ii)
red-MS stars are more centrally concentrated than blue-MS stars; (iii) the
fraction of blue-MS stars with respect to the total number of MS stars drops by
a factor of ~2 in the upper MS with F814W <~19.7.
  The comparison between the observed CMDs and stellar models reveals that the
observations are consistent with ~200 Myr old highly-rotating stars on the
red-MS, with rotation close to critical value, plus a non-rotating stellar
population spanning an age interval between ~140 and 220 Myr, on the blue-MS.
Noticeable, neither stellar populations with different ages only, nor coeval
stellar models with different rotation rates, properly reproduce the observed
split MS and eMSTO. We discuss these results in the context of the eMSTO and
multiple MS phenomenon.


  In warm inflation, dissipation due to the interactions of the inflaton field
to other light degrees of freedom leads naturally to the enhancement of the
primordial spectrum during the last 10-20 efolds of inflation. We study this
effect in a variant of the Warm Little Inflaton model, where the inflaton
couples to light scalars, with a quartic chaotic potential. These large
fluctuations on re-entry will form light, evaporating Primordial Black Holes,
with masses lighter than $10^6$ g. But at the same time they will act as a
source for the tensors at second order. The enhancement is maximal near the end
of inflation, which result in a spectral density of Gravitational Waves (GW)
peaked at frequencies $f \sim O(10^3-10^5)$ Hz today, and with an amplitude
$\Omega_{GW} \sim 10^{-10}-10^{-8}$. Although the frequency range is outside
the reach of present and planned GW detectors, it might be reached in future
high-frequency gravitational waves detectors, designed to search for
cosmological stochastic GW backgrounds above MHz frequencies.


  We investigate continuous parameter dependence for solutions of general
boundary value problems for ordinary linear differential systems. The
generalization of Kiguradze's theorem (1987) on correctness of such problems
was obtained. Also sufficient conditions for the Green matrices of such
problems to converge uniformly to the Green matrix of the limiting problem were
found.


  Spatial scene understanding, including monocular depth estimation, is an
important problem in various applications, such as robotics and autonomous
driving. While improvements in unsupervised monocular depth estimation have
potentially allowed models to be trained on diverse crowdsourced videos, this
remains underexplored as most methods utilize the standard training protocol,
wherein the models are trained from scratch on all data after new data is
collected. Instead, continual training of models on sequentially collected data
would significantly reduce computational and memory costs. Nevertheless, naive
continual training leads to catastrophic forgetting, where the model
performance deteriorates on older domains as it learns on newer domains,
highlighting the trade-off between model stability and plasticity. While
several techniques have been proposed to address this issue in image
classification, the high-dimensional and spatiotemporally correlated outputs of
depth estimation make it a distinct challenge. To the best of our knowledge, no
framework or method currently exists focusing on the problem of continual
learning in depth estimation. Thus, we introduce a framework that captures the
challenges of continual unsupervised depth estimation (CUDE), and define the
necessary metrics to evaluate model performance. We propose a rehearsal-based
dual-memory method, MonoDepthCL, which utilizes spatiotemporal consistency for
continual learning in depth estimation, even when the camera intrinsics are
unknown.


  Existing fiducial markers solutions are designed for efficient detection and
decoding, however, their ability to stand out in natural environments is
difficult to infer from relatively limited analysis. Furthermore, worsening
performance in challenging image capture scenarios - such as poor exposure,
motion blur, and off-axis viewing - sheds light on their limitations. E2ETag
introduces an end-to-end trainable method for designing fiducial markers and a
complimentary detector. By introducing back-propagatable marker augmentation
and superimposition into training, the method learns to generate markers that
can be detected and classified in challenging real-world environments using a
fully convolutional detector network. Results demonstrate that E2ETag
outperforms existing methods in ideal conditions and performs much better in
the presence of motion blur, contrast fluctuations, noise, and off-axis viewing
angles. Source code and trained models are available at
https://github.com/jbpeace/E2ETag.


  We study a quantum game played by two players with restricted multiple
strategies. It is found that in this restricted quantum game Nash equilibrium
does not always exist when the initial state is entangled. At the same time, we
find that when Nash equilibrium exists the pay off function is usually
different from that in the classical counterpart except in some special cases.
This presents an explicit example where quantum game and classical game may
differ. When designing a quantum game with limited strategies, the allowed
strategy should be carefully chosen according to the type of initial state.


  We develop the WKB expansion to relate Quantum Field Theory variables with
those describing macroscopical matter. We find that, up to the first quantum
correction, free scalar fields correspond to perfect fluids with pressure. We
also find the law of motion for the associated particles which takes into
account deviations from the classical trajectories, showing that they do not
follow unaccelerated straight line trajectories.
  Keywords: Quantum Field Theory, Fluid dynamics.
  PACS number (s): 11.10.-z, 03.40.Gc


  Correlations between stellar properties and the occurrence rate of exoplanets
can be used to inform the target selection of future planet search efforts and
provide valuable clues about the planet formation process. We analyze a sample
of 1194 stars drawn from the California Planet Survey targets to determine the
empirical functional form describing the likelihood of a star harboring a giant
planet as a function of its mass and metallicity. Our stellar sample ranges
from M dwarfs with masses as low as 0.2 Msun to intermediate-mass subgiants
with masses as high as 1.9 Msun. In agreement with previous studies, our sample
exhibits a planet-metallicity correlation at all stellar masses; the fraction
of stars that harbor giant planets scales as f \propto 10^{1.2 [Fe/H]}. We can
rule out a flat metallicity relationship among our evolved stars (at 98%
confidence), which argues that the high metallicities of stars with planets are
not likely due to convective envelope "pollution." Our data also rule out a
constant planet occurrence rate for [Fe/H]< 0, indicating that giant planets
continue to become rarer at sub-Solar metallicities. We also find that planet
occurrence increases with stellar mass (f \propto Mstar), characterized by a
rise from 3.5% around M dwarfs (0.5 Msun) to 14% around A stars (2 Msun), at
Solar metallicity. We argue that the correlation between stellar properties and
giant planet occurrence is strong supporting evidence of the core accretion
model of planet formation.


  A new mechanism of black hole formation in a first order phase transition is
proposed. In vacuum bubble collisions the interaction of bubble walls leads to
the formation of nontrivial vacuum configuration. The consequent collapse of
this vacuum configuration induces the black hole formation with high
probability. The primordial black holes that have been created by this way at
the end of first order inflation could give essential contribution into the
total density of the early Universe. The possibilities to establish some
nontrivial restrictions on the inflation models with first order phase
transition are discussed.


  We consider the design of state feedback control laws for both the switching
signal and the continuous input of an unknown switched linear system, given
past noisy input-state trajectories measurements. Based on Lyapunov-Metzler
inequalities, we derive data-dependent bilinear programs whose solution
directly returns a provably stabilizing controller and ensures $\mathcal{H}_2$
or $\mathcal{H}_{\infty}$ performance. We further present relaxations that
considerably reduce the computational cost, still without requiring
stabilizability of any of the switching modes. Finally, we showcase the
flexibility of our approach on the constrained stabilization problem for a
perturbed linear system.


  We combine searches by the CDF and D0 Collaborations for the standard model
Higgs boson with mass in the range 90--200 GeV$/c^2$ produced in the
gluon-gluon fusion, $WH$, $ZH$, $t{\bar{t}}H$, and vector boson fusion
processes, and decaying in the $H\rightarrow b{\bar{b}}$, $H\rightarrow
W^+W^-$, $H\rightarrow ZZ$, $H\rightarrow\tau^+\tau^-$, and $H\rightarrow
\gamma\gamma$ modes. The data correspond to integrated luminosities of up to 10
fb$^{-1}$ and were collected at the Fermilab Tevatron in $p{\bar{p}}$
collisions at $\sqrt{s}=1.96$ TeV. The searches are also interpreted in the
context of fermiophobic and fourth generation models. We observe a significant
excess of events in the mass range between 115 and 140 GeV/$c^2$. The local
significance corresponds to 3.0 standard deviations at $m_H=125$ GeV/$c^2$,
consistent with the mass of the Higgs boson observed at the LHC, and we expect
a local significance of 1.9 standard deviations. We separately combine searches
for $H \to b\bar{b}$, $H \to W^+W^-$, $H\rightarrow\tau^+\tau^-$, and
$H\rightarrow\gamma\gamma$. The observed signal strengths in all channels are
consistent with the presence of a standard model Higgs boson with a mass of 125
GeV/$c^2$.


  The spin and flavor symmetries of the heavy quark effective theory are
employed to discuss the exclusive cross sections for pair production of heavy
mesons in photon-photon collision. The ratios of the exclusive cross sections
for heavy mesons are obtained explicitly and the validity of results is
discussed.


  The classical Hennessy-Milner theorem says that two states of an image-finite
transition system are bisimilar if and only if they satisfy the same formulas
in a certain modal logic. In this paper we study this type of result in a
general context, moving from transition systems to coalgebras and from
bisimilarity to coinductive predicates. We formulate when a logic fully
characterises a coinductive predicate on coalgebras, by providing suitable
notions of adequacy and expressivity, and give sufficient conditions on the
semantics. The approach is illustrated with logics characterising similarity,
divergence and a behavioural metric on automata.


  The modern primary voltage standard is based on the AC Josephson effect and
the ensuing Shapiro steps, where a microwave tone applied to a Josephson
junction yields a constant voltage $hf/2e$ ($h$ is Planck's constant and $e$
the electron charge) determined by only the microwave frequency $f$ and
fundamental constants. Duality arguments for current and voltage have long
suggested the possibility of dual Shapiro steps -- that a Josephson junction
device could produce current steps with heights determined only on the applied
frequency. In this report, we embed an ultrasmall Josephson junction in a high
impedance array of larger junctions to reveal dual Shapiro steps. For multiple
frequencies, we detect that the AC response of the circuit is synchronised with
the microwave tone at frequency $f$, and the corresponding emergence of flat
steps in the DC response with current $2ef$, equal to the tunnelling of a
Cooper pair per tone period. This work sheds new light on phase-charge duality,
omnipresent in condensed matter physics, and extends it to Josephson circuits.
Looking forward, it opens a broad range of possibilities for new experiments in
the field of circuit quantum electrodynamics and is an important step towards
the long-sought closure of the quantum metrology electrical triangle.


  Networks of solution-processed nanomaterials are important for multiple
applications in electronics, sensing and energy storage/generation. While it is
known that network morphology plays a dominant role in determining the physical
properties of printed networks, it remains difficult to quantify network
structure. Here, we utilise FIB-SEM nanotomography to characterise the
morphology of nanostructured networks. Nanometer-resolution 3D-images were
obtained from printed networks of graphene nanosheets of various sizes, as well
as networks of WS2 nanosheets, silver nanosheets and silver nanowires.
Important morphological characteristics, including network porosity,
tortuosity, pore dimensions and nanosheet orientation were extracted and linked
to network resistivity. By extending this technique to interrogate the
structure and interfaces within vertical printed heterostacks, we demonstrate
the potential of this technique for device characterisation and optimisation.


  This document contains the documentation of TOBI (Tools for BCI) Interface D
(TiD). TiD tries to establish a standardized interface for event transmission
in neuroscience experiments. It is designed in a client-server architecture.
Clients are connecting to a single server and events are delivered in a
"bus-like" manner. TiD events are based on XML messages. So TiD messages can
also get custom extended. A cross platform C++ library is available and
provides all TiD functionality. To avoid jitter effect, hampering event
processing, TiD was optimized towards performance. The documentation provides
further performance tweaks to decrease TiD message processing latency and also
decrease event timing jitter.


  The robust rank-order test (Fligner and Policello, 1981) was designed as an
improvement of the non-parametric Wilcoxon-Mann-Whitney U-test to be more
appropriate when the samples being compared have unequal variance. However, it
tends to be excessively liberal when the samples are asymmetric. This is likely
because the test statistic is assumed to have a standard normal distribution
for sample sizes > 12. This work proposes an on-the-fly method to obtain the
distribution of the test statistic from which the critical/p-value may be
computed directly. The method of likelihood maximization is used to estimate
the parameters of the parent distributions of the samples being compared. Using
these estimated populations, the null distribution of the test statistic is
obtained by the Monte-Carlo method. Simulations are performed to compare the
proposed method with that of standard normal approximation of the test
statistic. For small sample sizes (<= 20), the Monte-Carlo method outperforms
the normal approximation method. This is especially true for low values of
significance levels (< 5%). Additionally, when the smaller sample has the
larger standard deviation, the Monte-Carlo method outperforms the normal
approximation method even for large sample sizes (= 40/60). The two methods do
not differ in power. Finally, a Monte-Carlo sample size of 10^4 is found to be
sufficient to obtain the aforementioned relative improvements in performance.
Thus, the results of this study pave the way for development of a toolbox to
perform the robust rank-order test in a distribution-free manner.


  In this paper, we give the classification of circulant graphs
$C(\mathbb{Z}_{n},S)$ with $|S|=2$ and completely solve the dispersability of
circulant graphs $C(\mathbb{Z}_{n},\{1, k\})$.


  The LkH$\alpha$ 101 cluster takes its name from its more massive member, the
LkH$\alpha$ 101star, which is an $\sim15$ M$_\odot$ star whose true nature is
still unknown. The distance to the LkH$\alpha$ 101 cluster has been
controversial for the last few decades, with estimated values ranging from 160
to 800 pc. We have observed members and candidate members of the LkH$\alpha$
101 cluster with signs of magnetic activity, using the Very Long Baseline
Array, in order to measure their trigonometric parallax and, thus, obtain a
direct measurement of their distances. A young star member, LkH$\alpha$ 101 VLA
J043001.15+351724.6, was detected at four epochs as a single radio source. The
best fit to its displacement on the plane of the sky yields a distance of
535$\pm$29 pc. We argue that this is the distance to the LkH$\alpha$ 101
cluster.


  In this paper, we are interested in the generic initial ideals of
\textit{singular} projective curves with respect to the graded lexicographic
order. Let $C$ be a \textit{singular} irreducible projective curve of degree
$d\geq 5$ with the arithmetic genus $\rho_a(C)$ in $\p^r$ where $r\ge 3$. If
$M(I_C)$ is the regularity of the lexicographic generic initial ideal of $I_C$
in a polynomial ring $k[x_0,..., x_r]$ then we prove that $M(I_C)$ is
$1+\binom{d-1}{2}-\rho_a(C)$ which is obtained from the monomial $$ x_{r-3}
x_{r-1}\,^{\binom{d-1}{2}-\rho_a(C)}, $$ provided that $\dim\Tan_p(C)=2$ for
every singular point $p \in C$. This number is equal to one plus the number of
non-isomorphic points under a generic projection of $C$ into $\p^2$. %if
$\deg(C)=3,4$ then $M(I_C)= \deg(C)$ by the direct computation. Our result
generalizes the work of J. Ahn for \textit{smooth} projective curves and that
of A. Conca and J. Sidman \cite{CS} for \textit{smooth} complete intersection
curves in $\p^3$. The case of singular curves was motivated by \cite[Example
4.3]{CS} due to A. Conca and J. Sidman. We also provide some illuminating
examples of our results via calculations done with {\it Macaulay 2} and \texttt
{Singular} \cite{DGPS, GS}.


  We show that the orbital angular momentum (OAM) of a light field can be
thermalized in a nonlinear cylindrical multimode optical waveguide. We find,
that upon thermal equilibrium, the maximization of the optical entropy leads to
a generalized Rayleigh-Jeans distribution that governs the power modal
occupancies with respect to the discrete OAM charge numbers. This distribution
is characterized by a temperature that is by nature different from that
associated with the longitudinal electromagnetic momentum flow of the optical
field. Counterintuitively and in contrast to previous results, we demonstrate
that even under positive temperatures, the ground state of the fiber is not
always the most populated in terms of power. Instead, because of OAM, the
thermalization processes may favor higher order modes. A new equation of state
is derived along with an extended Euler equation -- resulting from the
extensivity of the entropy itself. By monitoring the nonlinear interaction
between two multimoded optical wavefronts with opposite spins, we show that the
exchange of angular momentum is dictated by the difference in OAM temperatures,
in full accord with the second law of thermodynamics. The theoretical analysis
presented here is corroborated by numerical simulations that take into account
the complex nonlinear dynamics of hundreds of modes. Our results may pave the
way towards high power optical sources with controllable orbital angular
momenta, and at a more fundamental level, could shed light on the physics of
other complex multimoded nonlinear bosonic systems that display additional
conservation laws.


  Some aspects of Mirror symmetry are reviewed, with an emphasis on more recent
results extending mirror transform to higher genus Riemann surfaces and its
relation to the Kodaira-Spencer theory of gravity (talk given in the Geometry
and Topology Conference, April 93, Harvard, in honor of Raoul Bott)


  Inspired by the work of Karamata, we consider an extremization problem
associated with the probability of intersecting two random chords inside a
circle of radius $r, \, r \in (0,1]$, where the endpoints of the chords are
drawn according to a given probability distribution on $\mathbb{S}^1$.
  We show that, for $r=1,$ the problem is degenerated in the sense that any
continuous measure is an extremiser, and that, for $r$ sufficiently close to
$1,$ the desired maximal value is strictly below the one for $r=1$ by a
polynomial factor in $1-r.$ Finally, we prove, by considering the auxiliary
problem of drawing a single random chord, that the desired maximum is $1/4$ for
$r \in (0,1/2).$ Connections with other variational problems and energy
minimization problems are also presented.


  We propose that condensed matter phenomena involving the spontaneous
emergence and dynamics of crystal lattices can be realized in the setting of
ultracold Bose-condensed atoms coupled to multimode cavities. Previously, it
was shown that in the case of a transversely pumped single-mode cavity, the
atoms self-organize at either the even or the odd antinodes of the cavity mode,
given sufficient pump intensity, and hence spontaneously break a discrete
translational symmetry. Here, we demonstrate that in multimode cavities the
self-organization brings the additional feature of continuous translational
symmetry breaking, via a variant of Brazovskii's transition, thus paving the
way for realizations of compliant lattices and associated phenomena, e.g.,
quantum melting, topological defects, frustration, glassiness, and even
supersolidity; such phenomena are absent in ultracold atomic systems when the
optical lattices are externally imposed. We apply a functional integral
approach to this many-body cavity QED system, which enables us, inter alia, to
calculate transition thresholds, explore fluctuations near this transition, and
determine how such fluctuations are manifest in the light emitted from the
cavity.


  We describe the characteristics and evolution of the magnetic field and
chromospheric emission in an active region core observed by the Solar Optical
Telescope on Hinode. Consistent with previous studies, we find that the moss is
unipolar, the spatial distribution of magnetic flux evolves slowly, and the
magnetic field is only moderately inclined. We show that the field line
inclination and horizontal component are coherent, and that the magnetic field
is mostly sheared in the inter-moss regions where the highest magnetic flux
variability is seen. Using extrapolations from SP magnetograms we show that the
magnetic connectivity in the moss is different than in the quiet Sun because
most of the magnetic field extends to significant coronal heights. The magnetic
flux, field vector, and chromospheric emission in the moss also appear highly
dynamic, but actually show only small scale variations in magnitude on
time-scales longer than the cooling times for hydrodynamic loops computed from
our extrapolations, suggesting high-frequency (continuous) heating events. Some
evidence is found for flux (Ca 2 intensity) changes on the order of 100--200 G
(DN) on time-scales of 20--30 mins that could be taken as indicative of
low-frequency heating. We find, however, that only a small fraction (10%) of
our simulated loops would be expected to cool on these time-scales, and we find
no clear evidence that the flux changes consistently produce intensity changes
in the chromosphere. The magnetic flux and chromospheric intensity in most
individual SOT pixels in the moss vary by less than ~ 20% and ~ 10%,
respectively, on loop cooling time-scales. In view of the high energy
requirements of the chromosphere, we suggest that these variations could be
sufficient for the heating of `warm' EUV loops, but that the high basal levels
may be more important for powering the hot core loops rooted in the moss.


  We present a complete-quantum description of multi-particle Szilard engine
which consists of a working substance and a Maxwell's demon. The demon is
modeled as a multi-level quantum system with specific quantum control and the
working substance consists of identical particles obeying Bose-Einstein or
Fermi-Dirac statistics. In this description, a reversible scheme to erase the
demon's memory by a lower temperature heat bath is used. We demonstrate that
(1) the quantum control of the demon can be optimized for single-particle
Szilard engine so that the efficiency of the demon-assisted thermodynamic cycle
could reach the Carnot cycle's efficiency; (2) the low-temperature behavior of
the working substance is very sensitive to the quantum statistics of the
particles and the insertion position of the partition.


  We investigate the impact on convective numerical simulations of
thermo-compositional diabatic processes. We focus our study on simulations with
a stabilizing temperature gradient and a destabilizing mean-molecular weight
gradient. We aim to establish the possibility for a reduced
temperature-gradient in such setups. A suite of 3D simulations were conducted
using a numerical hydrodynamic code. We used as a simplified test case, a
sample region of the secondary atmosphere of a hot rocky exoplanet within which
the chemical transition CO+O $\leftrightarrow$ CO$_{2}$ could occur. Newtonian
cooling and a chemical source term was used to maintain a negative mean
molecular weight gradient. Our results demonstrate that this setup can reduce
the temperature gradient, a result which does not converge away with resolution
or over time. We also show that the presence of the reduced temperature
gradient is a function of the forcing timescales. The above transition leads to
a bifurcation of the temperature profile when the chemical forcing is fast,
reminiscent of the bifurcation seen in the boiling crisis for steam/liquid
convection. With the reduced temperature gradient in these idealized setups,
there exists the possibility for an analogy of the reddening (currently
observed in the spectra of brown dwarfs) in the spectra of rocky exoplanet
atmospheres. Detailed 1D modelling is needed, in order to characterize the
equilibrium thermal and compositional gradients, the timescales, and the impact
of a realistic equation of state, in order to assess if the regime identified
here will develop in realistic situations. This possibility cannot, however, be
excluded a priori. This prediction is new for terrestrial atmospheres and
represents strong motivation for the use of diabatic models when analysing
atmospheric spectra of rocky exoplanets that will be observed with e.g. the
James Webb Space Telescope.


  PatchMatch Multi-View Stereo (PatchMatch MVS) is one of the popular MVS
approaches, owing to its balanced accuracy and efficiency. In this paper, we
propose Polarimetric PatchMatch multi-view Stereo (PolarPMS), which is the
first method exploiting polarization cues to PatchMatch MVS. The key of
PatchMatch MVS is to generate depth and normal hypotheses, which form local 3D
planes and slanted stereo matching windows, and efficiently search for the best
hypothesis based on the consistency among multi-view images. In addition to
standard photometric consistency, our PolarPMS evaluates polarimetric
consistency to assess the validness of a depth and normal hypothesis, motivated
by the physical property that the polarimetric information is related to the
object's surface normal. Experimental results demonstrate that our PolarPMS can
improve the accuracy and the completeness of reconstructed 3D models,
especially for texture-less surfaces, compared with state-of-the-art PatchMatch
MVS methods.


  Ionic liquid gating can markedly modulate the materials' carrier density so
as to induce metallization, superconductivity, and quantum phase transitions.
One of the main issues is whether the mechanism of ionic liquid gating is an
electrostatic field effect or an electrochemical effect, especially for oxide
materials. Recent observation of the suppression of the ionic liquid
gate-induced metallization in the presence of oxygen for oxide materials
suggests the electrochemical effect. However, in more general scenarios, the
role of oxygen in ionic liquid gating effect is still unclear. Here, we perform
the ionic liquid gating experiments on a non-oxide material: two-dimensional
ferromagnetic Cr2Ge2Te6. Our results demonstrate that despite the large
increase of the gate leakage current in the presence of oxygen, the oxygen does
not affect the ionic liquid gating effect (< 5 % difference), which suggests
the electrostatic field effect as the mechanism on non-oxide materials.
Moreover, our results show that the ionic liquid gating is more effective on
the modulation of the channel resistances compared to the back gating across
the 300 nm thick SiO2.


  This paper poses a theoretical characterization of the stochastic
reachability problem in terms of probability measures, capturing the
probability measure of the state of the system that satisfies the reachability
specification for all probabilities over a finite horizon. We achieve this by
constructing the level sets of the probability measure for all probability
values and, since our approach is only for autonomous systems, we can determine
the level sets via forward simulations of the system from a point in the state
space at some time step in the finite horizon to estimate the reach
probability. We devise a training procedure which exploits this forward
simulation and employ it to design a deep neural network (DNN) to predict the
reach probability provided the current state and time step. We validate the
effectiveness of our approach through three examples.


  We study the conjugation involution in Seiberg-Witten theory in the context
of the Ozsv\'ath-Szab\'o and Bloom's spectral sequence for the branched double
cover of a link $L$ in $S^3$. We prove that there exists a spectral sequence of
$\mathbb{F}[Q]/Q^2$-modules (where $Q$ has degree $-1$) which converges to
$\widetilde{\mathit{HMI}}_*(\Sigma(L))$, an involutive version of the monopole
Floer homology of the branched double cover, and whose $E^2$-page is a version
of Bar Natan's characteristic two Khovanov homology of the mirror of $L$. We
conjecture that an analogous result holds in the setting of
$\mathrm{Pin}(2)$-monopole Floer homology.


  We report exact diagonalization studies of inelastic light scattering in
few-electron quantum dots under the strong confinement regime characteristic of
self-assembled dots. We apply the orthodox (second-order) theory for scattering
due to electronic excitations, leaving for the future the consideration of
higher-order effects in the formalism (phonons, for example), which seem
relevant in the theoretical description of available experiments. Our numerical
results stress the dominance of monopole peaks in Raman spectra and the
breakdown of selection rules in open-shell dots. The dependence of these
spectra on the number of electrons in the dot and the incident photon energy is
explicitly shown. Qualitative comparisons are made with recent experimental
results.


  The Lukacs property of the free Poisson distribution is studied here. We
prove that if free $\X$ and $\Y$ are free Poisson distributed with suitable
parameters, then $\X+\Y$ and
$\left(\X+\Y\right)^{-\frac{1}{2}}\X\left(\X+\Y\right)^{-\frac{1}{2}}$ are
free. As as an auxiliary result we give joint cumulants of $\X$ and $\X^{-1}$
for free Poisson distributed $\X$. We also study the Lukacs property of the
free gamma distribution.


  The protection of private information is a crucial issue in data-driven
research and business contexts. Typically, techniques like anonymisation or
(selective) deletion are introduced in order to allow data sharing, e. g. in
the case of collaborative research endeavours. For use with anonymisation
techniques, the $k$-anonymity criterion is one of the most popular, with
numerous scientific publications on different algorithms and metrics.
Anonymisation techniques often require changing the data and thus necessarily
affect the results of machine learning models trained on the underlying data.
In this work, we conduct a systematic comparison and detailed investigation
into the effects of different $k$-anonymisation algorithms on the results of
machine learning models. We investigate a set of popular $k$-anonymisation
algorithms with different classifiers and evaluate them on different real-world
datasets. Our systematic evaluation shows that with an increasingly strong
$k$-anonymity constraint, the classification performance generally degrades,
but to varying degrees and strongly depending on the dataset and anonymisation
method. Furthermore, Mondrian can be considered as the method with the most
appealing properties for subsequent classification.


  We investigate the necessary conditions for the two spacetimes, which are
solutions to the Einstein field equations with an anisotropic matter source, to
be related to each other by means of a conformal transformation. As a result,
we obtain that if one of such spacetimes is a generalization of the
Robertson-Walker solution with vanishing acceleration and vorticity, then the
other one has to be in this class as well, i.e. the conformal factor will be a
constant function on the hypersurfaces orthogonal to the fluid flow lines. The
evolution equation for this function appears naturally as a direct consequence
of the conformal transformation of the Ricci tensor.


  We test and compare a number of existing models predicting the location of
magnetic reconnection at Earth's dayside magnetopause for various solar wind
conditions. We employ robust image processing techniques to determine the
locations where each model predicts reconnection to occur. The predictions are
then compared to the magnetic separators, the magnetic field lines separating
different magnetic topologies. The predictions are tested in distinct
high-resolution simulations with interplanetary magnetic field (IMF) clock
angles ranging from 30 to 165 degrees in global magnetohydrodynamic simulations
using the three-dimensional Block-Adaptive Tree Solarwind Roe-type Upwind
Scheme (BATS-R-US) code with a uniform resistivity, although the described
techniques can be generally applied to any self-consistent magnetosphere code.
Additional simulations are carried out to test location model dependence on IMF
strength and dipole tilt. We find that most of the models match large portions
of the magnetic separators when the IMF has a southward component, with the
models saying reconnection occurs where the local reconnection rate and
reconnection outflow speed are maximized performing best. When the IMF has a
northward component, none of the models tested faithfully map the entire
magnetic separator, but the maximum magnetic shear model is the best at mapping
the separator in the cusp region where reconnection has been observed.
Predictions for some models with northward IMF orientations improve after
accounting for plasma flow shear parallel to the reconnecting components of the
magnetic fields. Implications for observations are discussed.


  The aim of this thesis is to investigate how the structure of a digraph
affects its dichromatic number and to extend various results on undirected
colouring to digraphs.
  In the first part of this thesis, we examine how the dichromatic number
interacts with other metrics. First, we consider the degree, which is the
maximum number of neighbours of a vertex. In the undirected case, this
corresponds to Brooks' theorem, a celebrated theorem with multiple variations
and generalizations. In the directed case, there is no natural metric
corresponding to the maximum degree, so we explore how different notions of
maximum directed degree lead to either Brooks-like theorems or impossibility
results. We also investigate the maximum local-arc connectivity, a metric that
encompasses several degree-like metrics.
  The second part of this manuscript focuses on a directed analogue of the
Gy\'arf\'as-Sumner conjecture. The Gy\'arf\'as-Sumner conjecture tries to
characterize sets S of undirected graphs such that graphs with large enough
chromatic number must contain a graph of S. This conjecture is still largely
open. On digraphs, a corresponding conjecture was proposed by Aboulker,
Charbit, and Naserasr. We prove several subcases of this conjecture, mainly
demonstrating that certain classes of digraphs have bounded dichromatic number.
  In the last part of this thesis, we address the d-edge-defective-colouring
problem, which involves colouring edges of a multigraph such that, for any
vertex, no colour appears on more than d of its incident edges. When d equals
one, this corresponds to the infamous edge-colouring problem. Shannon
established a tight bound on the number of colours needed relative to the
maximum degree when d equals one, and we extend this result to any value of d.
We also explore this problem on simple graphs and prove results that extend
Vizing's theorem to any value of d.


  Mirror-prox (MP) is a well-known algorithm to solve variational inequality
(VI) problems. VI with a monotone operator covers a large group of settings
such as convex minimization, min-max or saddle point problems. To get a
convergent algorithm, the step-size of the classic MP algorithm relies heavily
on the problem dependent knowledge of the operator such as its smoothness
parameter which is hard to estimate. Recently, a universal variant of MP for
smooth/bounded operators has been introduced that depends only on the norm of
updates in MP. In this work, we relax the dependence to evaluating the norm of
updates to Bregman divergence between updates. This relaxation allows us to
extends the analysis of universal MP to the settings where the operator is not
smooth or bounded. Furthermore, we analyse the VI problem with a stochastic
monotone operator in different settings and obtain an optimal rate up to a
logarithmic factor.


  We present a sparse coding-based framework for motion style decomposition and
synthesis. Dynamic Time Warping is firstly used to synchronized input motions
in the time domain as a pre-processing step. A sparse coding-based
decomposition has been proposed, we also introduce the idea of core component
and basic motion. Decomposed motions are then combined, transfer to synthesize
new motions. Lastly, we develop limb length constraint as a post-processing
step to remove distortion skeletons. Our framework has the advantage of less
time-consuming, no manual alignment and large dataset requirement. As a result,
our experiments show smooth and natural synthesized motion.


  Manual identification of fission tracks has practical problems, such as
variation due to observer-observation efficiency. An automatic processing
method that could identify fission tracks in a photomicrograph could solve this
problem and improve the speed of track counting. However, separation of
non-trivial images is one of the most difficult tasks in image processing.
Several commercial and free softwares are available, but these softwares are
meant to be used in specific images. In this paper, an automatic method based
on starlet wavelets is presented in order to separate fission tracks in mineral
photomicrographs. Automatization is obtained by Matthews correlation
coefficient, and results are evaluated by precision, recall and accuracy. This
technique is an improvement of a method aimed at segmentation of scanning
electron microscopy images. This method is applied in photomicrographs of
epidote phenocrystals, in which accuracy higher than 89% was obtained in
fission track segmentation, even for difficult images. Algorithms corresponding
to the proposed method are available for download. Using the method presented
here, an user could easily determine fission tracks in photomicrographs of
mineral samples.


  We develop Few-Shot Learning models trained to recognize five or ten
different dynamic hand gestures, respectively, which are arbitrarily
interchangeable by providing the model with one, two, or five examples per hand
gesture. All models were built in the Few-Shot Learning architecture of the
Relation Network (RN), in which Long-Short-Term Memory cells form the backbone.
The models use hand reference points extracted from RGB-video sequences of the
Jester dataset which was modified to contain 190 different types of hand
gestures. Result show accuracy of up to 88.8% for recognition of five and up to
81.2% for ten dynamic hand gestures. The research also sheds light on the
potential effort savings of using a Few-Shot Learning approach instead of a
traditional Deep Learning approach to detect dynamic hand gestures. Savings
were defined as the number of additional observations required when a Deep
Learning model is trained on new hand gestures instead of a Few Shot Learning
model. The difference with respect to the total number of observations required
to achieve approximately the same accuracy indicates potential savings of up to
630 observations for five and up to 1260 observations for ten hand gestures to
be recognized. Since labeling video recordings of hand gestures implies
significant effort, these savings can be considered substantial.


  In many applications, geodesic hierarchical models are adequate for the study
of temporal observations. We employ such a model derived for manifold-valued
data to Kendall's shape space. In particular, instead of the Sasaki metric, we
adapt a functional-based metric, which increases the computational efficiency
and does not require the implementation of the curvature tensor. We propose the
corresponding variational time discretization of geodesics and employ the
approach for longitudinal analysis of 2D rat skulls shapes as well as 3D shapes
derived from an imaging study on osteoarthritis. Particularly, we perform
hypothesis test and estimate the mean trends.


  Daisy graphs of a rooted graph $G$ with the root $r$ were recently introduced
as a generalization of daisy cubes, a class of isometric subgraphs of
hypercubes. In this paper we first solve the problem posed in
\cite{Taranenko2020} and characterize rooted graphs $G$ with the root $r$ for
which all daisy graphs of $G$ with respect to $r$ are isometric in $G$. We
continue the investigation of daisy graphs $G$ (generated by $X$) of a Hamming
graph $H$ and characterize those daisy graphs generated by $X$ of cardinality 2
that are isometric in $H$. Finally, we give a characterization of isometric
daisy graphs of a Hamming graph $K_{k_1}\Box \ldots \Box K_{k_n}$ with respect
to $0^n$ in terms of an expansion procedure.


  A concern can be characterized as a developer's intent behind a piece of
code, often not explicitly captured in it. We discuss a technique of recording
concerns using source code annotations (concern annotations). Using two studies
and two controlled experiments, we seek to answer the following 3 research
questions: 1) Do programmers' mental models overlap? 2) How do developers use
shared concern annotations when they are available? 3) Does using annotations
created by others improve program comprehension and maintenance correctness,
time and confidence? The first study shows that developers' mental models,
recorded using concern annotations, overlap and thus can be shared. The second
study shows that shared concern annotations can be used during program
comprehension for the following purposes: hypotheses confirmation, feature
location, obtaining new knowledge, finding relationships and maintenance notes.
The first controlled experiment with students showed that the presence of
annotations significantly reduced program comprehension and maintenance time by
34%. The second controlled experiment was a differentiated replication of the
first one, focused on industrial developers. It showed a 33% significant
improvement in correctness. We conclude that concern annotations are a viable
way to share developers' thoughts.


  In kernel-centric operations, the uprobe component of eBPF frequently
encounters performance bottlenecks, largely attributed to the overheads borne
by context switches. Transitioning eBPF operations to user space bypasses these
hindrances, thereby optimizing performance. This also enhances configurability
and obviates the necessity for root access or privileges for kernel eBPF,
subsequently minimizing the kernel attack surface. This paper introduces
bpftime, a novel user-space eBPF runtime, which leverages binary rewriting to
implement uprobe and syscall hook capabilities. Through bpftime, userspace
uprobes achieve a 10x speed enhancement compared to their kernel counterparts
without requiring dual context switches. Additionally, this runtime facilitates
the programmatic hooking of syscalls within a process, both safely and
efficiently. Bpftime can be seamlessly attached to any running process,
limiting the need for either a restart or manual recompilation. Our
implementation also extends to interprocess eBPF Maps within shared memory,
catering to summary aggregation or control plane communication requirements.
Compatibility with existing eBPF toolchains such as clang and libbpf is
maintained, not only simplifying the development of user-space eBPF without
necessitating any modifications but also supporting CO-RE through BTF. Through
bpftime, we not only enhance uprobe performance but also extend the versatility
and user-friendliness of eBPF runtime in user space, paving the way for more
efficient and secure kernel operations.


  We introduce the relation ${\rho}_{\lambda}$-orthogonality in the setting of
normed spaces as an extension of some orthogonality relations based on norm
derivatives, and present some of its essential properties. Among other things,
we give a characterization of inner product spaces via the functional
${\rho}_{\lambda}$. Moreover, we consider a class of linear mappings preserving
this new kind of orthogonality. In particular, we show that a linear mapping
preserving ${\rho}_{\lambda}$-orthogonality has to be a similarity, that is, a
scalar multiple of an isometry.


  We show that Joseph-Lamprou's path model for representations of generalized
Kac-Moody algebras can be embedded into Littelmann's path model for certain
Kac-Moody algebras. Using this embedding, for Joseph-Lamprou's path crystals,
we give a decomposition rule for tensor product and a branching rule for
restriction to Levi subalgebras. Also, we obtain a characterization of standard
paths in terms of a certain monoid, which can be thought of as a generalization
of a Coxeter group.


  Perovskite solar cells have shown remarkable efficiencies beyond 22%, through
organic and inorganic cation alloying. However, the role of alkali-metal
cations is not well-understood. By using synchrotron-based nano-X-ray
fluorescence and complementary measurements, we show that when adding RbI
and/or CsI the halide distribution becomes homogenous. This homogenization
translates into long-lived charge carrier decays, spatially homogenous carrier
dynamics visualized by ultrafast microscopy, as well as improved photovoltaic
device performance. We find that Rb and K phase-segregate in highly
concentrated aggregates. Synchrotron-based X-ray-beam-induced current and
electron-beam-induced current of solar cells show that Rb clusters do not
contribute to the current and are recombination active. Our findings bring
light to the beneficial effects of alkali metal halides in perovskites, and
point at areas of weakness in the elemental composition of these complex
perovskites, paving the way to improved performance in this rapidly growing
family of materials for solar cell applications.


  Container technologies, like Docker, are becoming increasingly popular.
Containers provide exceptional developer experience because containers offer
lightweight isolation and ease of software distribution. Containers are also
widely used in production environments, where a different set of challenges
arise such as security, networking, service discovery and load balancing.
Container cluster management tools, such as Kubernetes, attempt to solve these
problems by introducing a new control layer with the container as the unit of
deployment. However, adding a new control layer is an extra configuration step
and an additional potential source of runtime errors. The virtual machine
technology offered by cloud providers is more mature and proven in terms of
security, networking, service discovery and load balancing. However, virtual
machines are heavier than containers for local development, are less flexible
for resource allocation, and suffer longer boot times. This paper presents an
alternative to containers that enjoy the best features of both approaches: (1)
the use of mature, proven cloud vendor technology; (2) no need for a new
control layer; and (3) as lightweight as containers. Our solution is i2kit, a
deployment tool based on the immutable infrastructure pattern, where the
virtual machine is the unit of deployment. The i2kit tool accepts a simplified
format of Kubernetes Deployment Manifests in order to reuse Kubernetes' most
successful principles, but it creates a lightweight virtual machine for each
Pod using Linuxkit. Linuxkit alleviates the drawback in size that using virtual
machines would otherwise entail, because the footprint of Linuxkit is
approximately 60MB. Finally, the attack surface of the system is reduced since
Linuxkit only installs the minimum set of OS dependencies to run containers,
and different Pods are isolated by hypervisor technology.


  Dykhne-Davis-Pechukas (DDP) method is a common approximation scheme for the
transition probability in two-level quantum systems, as realized in the
Landau-Zener effect, leading to an exponentially damping form comparable to the
Schwinger pair production rate. We analyze the foundation of the DDP method
using a modern complex technique inspired by the Lefschetz-thimble method. We
derive an alternative and more adaptive formula that is useful even when the
DDP method is inapplicable. As a benchmark, we study the modified Landau-Zener
model and compare results from the DDP and our methods. We then revisit a
derivation of the Schwinger Mechanism of particle production under electric
fields using the DDP and our methods. We find that the DDP method gets worse
for the Sauter type of short-lived electric pulse, while our method is still a
reasonable approximation. We also study the Dynamically Assisted Schwinger
Mechanism in two methods.


  We define here two new classes of saturated fusion systems, reduced fusion
systems and tame fusion systems. These are motivated by our attempts to better
understand and search for exotic fusion systems: fusion systems which are not
the fusion systems of any finite group. Our main theorems say that every
saturated fusion system reduces to a reduced fusion system which is tame only
if the original one is realizable, and that every reduced fusion system which
is not tame is the reduction of some exotic (nonrealizable) fusion system.


  We consider the possibility that the basic space of physics is not spacetime,
but configuration space. We illustrate this on the example with a system of
gravitationally interacting point particles. It turns out that such system can
be described by the minimal length action in a multidimensional configuration
space C with a block diagonal metric. Allowing for more general metrics and
curvatures of C, we step beyond the ordinary general relativity in spacetime.
The latter theory is then an approximation to the general relativity in C.
Other sorts of configuration spaces can also be considered, for instance those
associated with extended objects, such as strings and branes. This enables a
deeper understanding of the geometric principle behind string theory, and an
insight on the occurrence of Yang-Mills and gravitational fields at the
`fundamental level'.


  We derive the maximum accelerated particle energy from first-order and
second-order Fermi acceleration at nonrelativistic and relativistic shocks for
explosions taking place in a uniform surrounding medium. Second-order
stochastic processes in relativistic flows are shown to be capable of
accelerating cosmic rays to ultra-high energies. Cosmic rays above the knee of
the cosmic ray spectrum can be accelerated by the second-order Fermi mechanism
in relativistic flows, such as those occuring in gamma-ray bursts and unusual
supernovae like SN 1998bw.


  In this thesis, a theoretical treatment of the relation between
electrophoretic velocity and the potential of the double layer of colloidal
particles is presented.
  Translators' note: The theory of electrophoresis is one of the foundational
topics that underpinned the development of colloid and surface science and
ranks with the famous Derjaguin-Landau-Verwey-Overbeek (DLVO) theory of
colloidal stability. J. Th. G. Overbeek ("Theo" to all who knew him) was the
first to develop a complete theoretical analysis of the electrophoretic motion
of a charged spherical particle under the influence of an external electric
field. This provided the theoretical framework for a widely used experimental
method to characterize the state of charge and particle size of small colloidal
particles. The solution of this problem required mastery of fluid mechanics,
colloidal electrostatics, statistical thermodynamics and transport theory in
addition to solid applied mathematics. Theo carried out this study as his
doctoral thesis under H.R. Kruyt at Utrecht University. The thesis, in Dutch,
was later published as a monograph. Given the important pedagogic value and
historical status of this work, we felt that it deserved to enjoy a wide
readership.


  We continue the study of robust reductions initiated by Gavalda and Balcazar.
In particular, a 1991 paper of Gavalda and Balcazar claimed an optimal
separation between the power of robust and nondeterministic strong reductions.
Unfortunately, their proof is invalid. We re-establish their theorem.
  Generalizing robust reductions, we note that robustly strong reductions are
built from two restrictions, robust underproductivity and robust
overproductivity, both of which have been separately studied before in other
contexts. By systematically analyzing the power of these reductions, we explore
the extent to which each restriction weakens the power of reductions. We show
that one of these reductions yields a new, strong form of the Karp-Lipton
Theorem.


  A criterion for M\"uger centralizer of a fusion subcategory of a braided
non-degenerate fusion category is given. Along the way we extend some
identities on the space of class functions of a fusion category introduced by
Shimizu in \cite{scalg}. We also show that in a modular tensor category the
product of two conjugacy class sums is a linear combination of conjugacy class
sums with rational coefficients.


  We study a system of two coupled nonlinear Schr\"{o}dinger equations, where
one equation includes gain and the other one includes losses. Strengths of the
gain and the loss are equal, i.e., the resulting system is parity-time (${\cal
PT}$) symmetric. The model includes both linear and nonlinear couplings, such
that when all nonlinear coefficients are equal, the system represents the
${\cal PT}$-generalization of the Manakov model. In the one-dimensional case,
we prove the existence of a global solution to the Cauchy problem in energy
space $H^1$, such that the $H^1$-norm of the global solution may grow in time.
In the Manakov case, we show analytically that the $L^2$-norm of the global
solution is bounded for all times and numerically that the $H^1$-norm is also
bounded. In the two-dimensional case, we obtain a constraint on the $L^2$-norm
of the initial data that ensures the existence of a global solution in the
energy space $H^1$.


  In software development, the identification of source code file experts is an
important task. Identifying these experts helps to improve software maintenance
and evolution activities, such as developing new features, code reviews, and
bug fixes. Although some studies have proposed repository mining techniques to
automatically identify source code experts, there are still gaps in this area
that can be explored. For example, investigating new variables related to
source code knowledge and applying machine learning aiming to improve the
performance of techniques to identify source code experts. The goal of this
study is to investigate opportunities to improve the performance of existing
techniques to recommend source code files experts. We built an oracle by
collecting data from the development history and surveying developers of 113
software projects. Then, we use this oracle to: (i) analyze the correlation
between measures extracted from the development history and the developers
source code knowledge and (ii) investigate the use of machine learning
classifiers by evaluating their performance in identifying source code files
experts. First Authorship and Recency of Modification are the variables with
the highest positive and negative correlations with source code knowledge,
respectively. Machine learning classifiers outperformed the linear techniques
(F-Measure = 71% to 73%) in the public dataset, but this advantage is not clear
in the private dataset, with F-Measure ranging from 55% to 68% for the linear
techniques and 58% to 67% for ML techniques. Overall, the linear techniques and
the machine learning classifiers achieved similar performance, particularly if
we analyze F-Measure. However, machine learning classifiers usually get higher
precision while linear techniques obtained the highest recall values.


  This is an expository paper on the theory of gradient flows, and in
particular of those PDEs which can be interpreted as gradient flows for the
Wasserstein metric on the space of probability measures (a distance induced by
optimal transport). The starting point is the Euclidean theory, and then its
generalization to metric spaces, according to the work of Ambrosio, Gigli and
Savar{\'e}. Then comes an independent exposition of the Wasserstein theory,
with a short introduction to the optimal transport tools that are needed and to
the notion of geodesic convexity, followed by a precise desciption of the
Jordan-Kinderleher-Otto scheme, with proof of convergence in the easiest case:
the linear Fokker-Planck equation. A discussion of other gradient flows PDEs
and of numerical methods based on these ideas is also provided. The paper ends
with a new, theoretical, development, due to Ambrosio, Gigli, Savar{\'e},
Kuwada and Ohta: the study of the heat flow in metric measure spaces.


  The minimal geometric deformation (MGD) paradigm is here employed to survey
axion stars on fluid branes. The finite value of the brane tension provides
beyond-general relativity corrections to the density, compactness, radius, and
asymptotic limit of the gravitational mass function of axion stars, in a MGD
background. The brane tension also enhances the effective range and magnitude
of the axion field coupled to gravity. MGD axion stars are compatible to
mini-massive compact halo objects for almost all the observational range of
brane tension, however, a narrow range allows MGD axion star densities large
enough to produce stimulated decays of the axion to photons, with no analogy in
the general-relativistic (GR) limit. Besides, the gravitational mass and the
density of MGD axion stars are shown to be up to four orders of magnitude
larger than the GR axion stars, being also less sensitive to tidal disruption
events under collision with neutron stars, for lower values of the fluid brane
tension.


  We present an Evolutionary Placement Algorithm (EPA) for the rapid assignment
of sequence fragments (short reads) to branches of a given phylogenetic tree
under the Maximum Likelihood (ML) model. The accuracy of the algorithm is
evaluated on several real-world data sets and compared to placement by
pair-wise sequence comparison, using edit distances and BLAST.
  We test two versions of the placement algorithm, one slow and more accurate
where branch length optimization is conducted for each short read insertion and
a faster version where the branch lengths are approximated at the insertion
position. For the slow version, additional heuristic techniques are explored
that almost yield the same run time as the fast version, with only a small loss
of accuracy. When those additional heuristics are employed the run time of the
more accurate algorithm is comparable to that of a simple BLAST search for data
sets with a high number of short query sequences. Moreover, the accuracy of the
Evolutionary Placement Algorithm is significantly higher, in particular when
the taxon sampling of the reference topology is sparse or inadequate. Our
algorithm, which has been integrated into RAxML, therefore provides an equally
fast but more accurate alternative to BLAST for phylogeny-aware analysis of
short-read sequence data.


  Spatial interactions between agents (humans, animals, or machines) carry
information of high value to human or electronic observers. However, not all
the information contained in a pair of continuous trajectories is important and
thus the need for qualitative descriptions of interaction trajectories arises.
The Qualitative Trajectory Calculus (QTC) (Van de Weghe, 2004) is a promising
development towards this goal. Numerous variants of QTC have been proposed in
the past and QTC has been applied towards analyzing various interaction
domains. However, an inherent limitation of those QTC variations that deal with
lateral movements is that they are limited to two-dimensional motion;
therefore, complex three-dimensional interactions, such as those occurring
between flying planes or birds, cannot be captured. Towards that purpose, in
this paper QTC3Dis presented: a novel qualitative trajectory calculus that can
deal with full three-dimensional interactions. QTC3D is based on
transformations of the Frenet-Serret frames accompanying the trajectories of
the moving objects. Apart from the theoretical exposition, including definition
and properties, as well as computational aspects, we also present an
application of QTC3D towards modeling bird flight. Thus, the power of QTC is
now extended to the full dimensionality of physical space, enabling succinct
yet rich representations of spatial interactions between agents.


  Background The COVID-19 pandemic has increased mental distress globally. The
proportion of people reporting anxiety is 26%, and depression is 34% points.
Disentangling associational and causal contributions of behavior, COVID-19
cases, and economic distress on mental distress will dictate different
mitigation strategies to reduce long-term pandemic-related mental distress.
Methods We use the Household Pulse Survey (HPS) April 2020 to February 2021
data to examine mental distress among U.S. citizens attributable to COVID-19.
We combined HPS survey data with publicly available state-level weekly:
COVID-19 case and death data from the Centers for Disease Control, public
policies, and Apple and Google mobility data. Finally, we constructed economic
and mental distress measures to estimate structural models with lag dependent
variables to tease out public health policies' associational and causal path
coefficients on economic and mental distress. Findings From April 2020 to
February 2021, we found that anxiety and depression had steadily climbed in the
U.S. By design, mobility restrictions primarily affected public health policies
where businesses and restaurants absorbed the biggest hit. Period t-1 COVID-19
cases increased job loss by 4.1% and economic distress by 6.3% points in the
same period. Job-loss and housing insecurity in t-1 increased period t mental
distress by 29.1% and 32.7%, respectively. However, t-1 food insecurity
decreased mental distress by 4.9% in time t. The pandemic-related potential
causal path coefficient of period t-1 economic distress on period t depression
is 57.8%, and anxiety is 55.9%. Thus, we show that period t-1 COVID-19 case
information, behavior, and economic distress may be causally associated with
pandemic related period t mental distress.


  We present counterexamples to a 30-year-old conjecture of Las Vergnas [J.
Combin. Theory Ser. B, 1988] regarding the Tutte polynomial of binary matroids.


  The discovery at the LHC of a scalar particle with properties that are so far
consistent with the SM Higgs boson is one of the most important advances in the
history of particle physics. The challenge of future collider experiments is to
determine whether its couplings will show deviations from the SM Higgs, as this
would indicate new physics at the TeV scale, and also to probe the flavor
structure of the Yukawa couplings. As a benchmark alternative to the SM Higgs,
we consider a generic two Higgs doublet model (2HDM) and analyze the precision
to which the LHC14, an ILC250, 500, 1000 GeV and a 125 GeV Muon Collider (MC)
can determine the gauge and Yukawa couplings. We allow for correlations among
the couplings. We include the impact of a Higgs total width measurement,
indirectly at the LHC and ILC and by a direct scan at the MC. We also discuss
pattern relations among the couplings that can test for singlet or doublet
Higgs extensions of 2HDMs.


  Cassidy, Phan and Shelton associate to any regular cell complex X a quadratic
K-algebra R(X). They give a combinatorial solution to the question of when this
algebra is Koszul. The algebra R(X) is a combinatorial invariant but not a
topological invariant. We show that nevertheless, the property that R(x) be
Koszul is a topological invariant.
  In the process we establish some conditions on the types of local singular-
ities that can occur in cell complexes X such that R(X) is Koszul, and more
generally in cell complexes that are pure and connected by codimension one
faces.


  The Web has enabled the availability of a huge amount of useful information,
but has also eased the ability to spread false information and rumors across
multiple sources, making it hard to distinguish between what is true and what
is not. Recent examples include the premature Steve Jobs obituary, the second
bankruptcy of United airlines, the creation of Black Holes by the operation of
the Large Hadron Collider, etc. Since it is important to permit the expression
of dissenting and conflicting opinions, it would be a fallacy to try to ensure
that the Web provides only consistent information. However, to help in
separating the wheat from the chaff, it is essential to be able to determine
dependence between sources. Given the huge number of data sources and the vast
volume of conflicting data available on the Web, doing so in a scalable manner
is extremely challenging and has not been addressed by existing work yet.
  In this paper, we present a set of research problems and propose some
preliminary solutions on the issues involved in discovering dependence between
sources. We also discuss how this knowledge can benefit a variety of
technologies, such as data integration and Web 2.0, that help users manage and
access the totality of the available information from various sources.


  We introduce a new concept of frame operators for Banach spaces we call a
Hilbert-Schauder frame operator. This is a hybird between standard frame theory
for Hilbert spaces and Schauder frame theory for Banach spaces. Most of our
results involve basic structure properties of the Hilbert-Schauder frame
operator. Examples of Hilbert-Schauder frames include standard Hilbert frames
and classical bases of $\ell_p$ and $L^p$-spaces with $1< p \le 2$. Finally, we
give a new isomorphic characterization of Hilbert spaces.


  We study the magnetization dynamics in a nanocontact magnetic vortex
oscillators as function of temperature. Low temperature experiments reveal that
the dynamics at low and high currents differ qualitatively. At low currents, we
excite a temperature independent standard oscillation mode, consisting in the
gyrotropic motion of a free layer vortex about the nanocontact. Above a
critical current, a sudden jump of the frequency is observed, concomitant with
a substantial increase of the frequency versus current slope factor. Using
micromagnetic simulation and analytical modeling, we associate this new regime
to the creation of a vortex-antivortex pair in the pinned layer of the spin
valve. The vortex-antivortex distance depends on the Oersted field which favors
a separation, and on the exchange bias field, which favors pair merging. The
pair in the pinned layer provides an additional spin torque altering the
dynamics of the free layer vortex, which can be quantitatively accounted for by
an analytical model.


  Multi-modal learning has emerged as an increasingly promising avenue in
vision recognition, driving innovations across diverse domains ranging from
media and education to healthcare and transportation. Despite its success, the
robustness of multi-modal learning for visual recognition is often challenged
by the unavailability of a subset of modalities, especially the visual
modality. Conventional approaches to mitigate missing modalities in multi-modal
learning rely heavily on algorithms and modality fusion schemes. In contrast,
this paper explores the use of text-to-image models to assist multi-modal
learning. Specifically, we propose a simple but effective multi-modal learning
framework GTI-MM to enhance the data efficiency and model robustness against
missing visual modality by imputing the missing data with generative
transformers. Using multiple multi-modal datasets with visual recognition
tasks, we present a comprehensive analysis of diverse conditions involving
missing visual modality in data, including model training. Our findings reveal
that synthetic images benefit training data efficiency with visual data missing
in training and improve model robustness with visual data missing involving
training and testing. Moreover, we demonstrate GTI-MM is effective with lower
generation quantity and simple prompt techniques.


  In this paper, a set of Python methods is described that can be used to
compute the frequency response of an arbitrary biochemical network given any
input and output. Models can be provided in standard SBML or Antimony format.
The code takes into account any conserved moieties so that this software can be
used to also study signaling networks where moiety cycles are common. A utility
method is also provided to make it easy to plot standard Bode plots from the
generated results. The code also takes into account the possibility that the
phase shift could exceed 180 degrees which can result in ugly discontinuities
in the Bode plot. In the paper, some of the theory behind the method is
provided as well as some commentary on the code and several illustrative
examples to show the code in operation. Illustrative examples include linear
reaction chains of varying lengths and the effect of negative feedback on the
frequency response.
  Software License: MIT Open Source
  Availability: The code is available from
https://github.com/sys-bio/frequencyResponse.


  For an integral functional defined on functions $(u,v)\in W^{1,1}\times L^1$
featuring a prototypical strong interaction term between $u$ and $v$, we
calculate its relaxation in the space of functions with bounded variations and
Radon measures. Interplay between measures and discontinuities bring various
additional difficulties, and concentration effects in recovery sequences play a
major role for the relaxed functional even if the limit measures are absolutely
continuous with respect to the Lebesgue one.


  The estimation of multivariate GARCH time series models is a difficult task
mainly due to the significant overparameterization exhibited by the problem and
usually referred to as the "curse of dimensionality". For example, in the case
of the VEC family, the number of parameters involved in the model grows as a
polynomial of order four on the dimensionality of the problem. Moreover, these
parameters are subjected to convoluted nonlinear constraints necessary to
ensure, for instance, the existence of stationary solutions and the positive
semidefinite character of the conditional covariance matrices used in the model
design. So far, this problem has been addressed in the literature only in low
dimensional cases with strong parsimony constraints. In this paper we propose a
general formulation of the estimation problem in any dimension and develop a
Bregman-proximal trust-region method for its solution. The Bregman-proximal
approach allows us to handle the constraints in a very efficient and natural
way by staying in the primal space and the Trust-Region mechanism stabilizes
and speeds up the scheme. Preliminary computational experiments are presented
and confirm the very good performances of the proposed approach.


  The block maxima method in extreme value theory consists of fitting an
extreme value distribution to a sample of block maxima extracted from a time
series. Traditionally, the maxima are taken over disjoint blocks of
observations. Alternatively, the blocks can be chosen to slide through the
observation period, yielding a larger number of overlapping blocks. Inference
based on sliding blocks is found to be more efficient than inference based on
disjoint blocks. The asymptotic variance of the maximum likelihood estimator of
the Fr\'{e}chet shape parameter is reduced by more than 18%. Interestingly, the
amount of the efficiency gain is the same whatever the serial dependence of the
underlying time series: as for disjoint blocks, the asymptotic distribution
depends on the serial dependence only through the sequence of scaling
constants. The findings are illustrated by simulation experiments and are
applied to the estimation of high return levels of the daily log-returns of the
Standard & Poor's 500 stock market index.


  The Lanczos process has been analytically and exactly carried out for the
spin 1/2 isotropic XY chain in the thermodynamic limit, yielding a form for the
Lanczos coefficient $\beta^2(s)$. This coefficient has a monotonic variation
for real positive $s$ and confirms a general theorem on the ground state
properties of extensive Many-body Systems. The Taylor expansion of the
coefficient about s=0 has a finite radius of convergence, and ground state
estimates based on a finite truncation of this are shown to be asymptotic.


  We first obtain finiteness properties for the collection of closed normal
subgroups of a compactly generated locally compact group. Via these properties,
every compactly generated locally compact group admits an essentially chief
series - i.e. a finite normal series in which each factor is compact, discrete,
or a topological chief factor. Additionally, a Jordan-H\"{o}lder theorem holds
for the `large' factors in an essentially chief series.


  This document summarizes the findings of the Accelerator Working Group (AWG)
of the International Scoping Study (ISS) of a Future Neutrino Factory and
super-beam Facility. The work of the group took place at three plenary meetings
along with three workshops, and an oral summary report was presented at the
NuFact06 workshop held at UC-Irvine in August, 2006. The goal was to reach
consensus on a baseline design for a Neutrino Factory complex. One aspect of
this endeavor was to examine critically the advantages and disadvantages of the
various Neutrino Factory schemes that have been proposed in recent years.


  We study a multivariate, non-linear Hawkes process $Z^N$ on a
$q$-Erd\H{o}s-R\'{e}nyi-graph with $N$ nodes. Each vertex is either excitatory
(probability $p$) or inhibitory (probability $1-p$). If $p\neq\tfrac12$, we
take the mean-field limit of $Z^N$, leading to a multivariate point process
$\bar Z$. We rescale the interaction intensity by $N$ and find that the limit
intensity process solves a deterministic convolution equation and all
components of $\bar Z$ are independent. The fluctuations around the mean field
limit converge to the solution of a stochastic convolution equation. In the
critical case, $p=\tfrac12$, we rescale by $N^{1/2}$ and discuss difficulties,
both heuristically and numerically.


  The fundamental problem considered in this paper is "What is the
\textit{energy} consumed for the implementation of a \emph{compressive sensing}
decoding algorithm on a circuit?". Using the "information-friction" framework,
we examine the smallest amount of \textit{bit-meters} as a measure for the
energy consumed by a circuit. We derive a fundamental lower bound for the
implementation of compressive sensing decoding algorithms on a circuit. In the
setting where the number of measurements scales linearly with the sparsity and
the sparsity is sub-linear with the length of the signal, we show that the
\textit{bit-meters} consumption for these algorithms is order-tight, i.e., it
matches the lower bound asymptotically up to a constant factor. Our
implementations yield interesting insights into design of energy-efficient
circuits that are not captured by the notion of computational efficiency alone.


  Recent experimental studies have shown that well-annealed, unstrained Si(105)
surfaces appear disordered and atomically rough when imaged using scanning
tunnelling microscopy (STM). We construct new models for the Si(105) surface
that are based on single- and double-height steps separated by Si(001)
terraces, and propose that the observed surface disorder of Si(105) originates
from the presence of several structural models with different atomic-scale
features but similar energies. This degeneracy can be removed by applying
compressive strains, a result that is consistent with recent observations of
the structure of the Ge/Si(105) surface.


  Stable fold maps are fundamental tools in a generalization of the theory of
Morse functions on smooth manifolds and its application to studies of
topological properties of smooth manifolds. Round fold maps were introduced as
stable fold maps with singular value sets, defined as the set consisting of all
the singular values, of concentric spheres by the author in 2013; for example,
some special generic maps on spheres are regarded as round fold maps whose
singular value sets are connected. Algebraic invariants such as homology and
homotopy groups of manifolds admitting round fold maps and more precisely, the
homeomorphism and diffeomorphism types of manifolds admitting such maps having
appropriate differential topological structures were studied. Moreover,
explicit round fold maps into the Eucidean space of dimension larger than $1$
are constructed on some fundamental manifolds such as manifolds having the
structures of bundles over the standard sphere of dimension equal to the
Euclidean space whose fibers are closed smooth manifolds and manifolds of
dimension not smaller than twice the dimension of the Euclidean space
represented as the connected sum of manifolds having the structures of bundles
over the standard sphere of dimension equal to the Euclidean space whose fibers
are diffeomorphic to standard spheres. In this paper, we construct new explicit
fold maps on some fundamental manifolds including the manifolds before by using
extended methods of ones used in the constructions before.


  We consider systems of ODEs with the right hand side being Laurent
polynomials in several non-commutative unknowns. In particular, these unknowns
could be matrices of arbitrary size. An important example of such a system was
proposed by M. Kontsevich. We prove the integrability of the Kontsevich system
by finding a Lax pair, corresponding first integrals and commuting flows. We
also provide a pre-Hamiltonian operator which maps gradients of integrals for
the Kontsevich system to symmetries.


  We give a review on the thermal average of the annihilation cross-sections
for $3\rightarrow 2$ and general higher-order processes. Thermal average of
higher order annihilations highly depend on the velocity of dark matter,
especially, for the case with resonance poles. We show such examples for scalar
dark matter in gauged $Z_3$ models.


  For a digraph D and three parameters x, y, z in {0,1,+,-} we define the
digraph D^(x,y,z) and call it the (x,y,z)-transformation of D. We show that for
every r-regular digraph D the adjacency characteristic polynomial A(t,
D^(x,y,z)) of (x,y,z)-transformation of D is uniquely defined by r and the
adjacency characteristic polynomial A(t, D) of digraph D and we give a
description of this function A(t, D^(x,y,z)) = F(r, A(t, D)). We also obtain
similar results for some non-regular digraphs, namely, for so-called
digraph-functions and their inverse. Also using the (x,y,z)-transformations of
digraphs, we give various new constructions of non-isomorphic adjacency
cospectral digraphs.


  In this work we illustrate the detrimental impact of the Cooper pair's
spin-structure on the thermodynamic and topological properties of a
spin-triplet superconductor in an applied Zeeman field. We particularly focus
on the paradigmatic one-dimensional case (Kitaev chain) for which we
self-consistently retrieve the energetically preferred Cooper pair spin-state
in terms of the corresponding spin d-vector. The latter undergoes a substantial
angular and amplitude reorganization upon the variation of the strength and the
orientation of the field and results to a modification of the bulk topological
phase diagram. Markedly, when addressing the open chain we find that the
orientation of the d-vector varies spatially near the boundary, affecting in
this manner the appearance of Majorana fermions at the edge or even altering
the properties of the bulk region. Our analysis reveals the limitations and
breakdown of the bulk-boundary correspondence in interacting topological
systems.


  We consider the parity problem in one-dimensional, binary, circular cellular
automata: if the initial configuration contains an odd number of 1s, the
lattice should converge to all 1s; otherwise, it should converge to all 0s. It
is easy to see that the problem is ill-defined for even-sized lattices (which,
by definition, would never be able to converge to 1). We then consider only odd
lattices.
  We are interested in determining the minimal neighbourhood that allows the
problem to be solvable for any initial configuration. On the one hand, we show
that radius 2 is not sufficient, proving that there exists no radius 2 rule
that can possibly solve the parity problem from arbitrary initial
configurations. On the other hand, we design a radius 4 rule that converges
correctly for any initial configuration and we formally prove its correctness.
Whether or not there exists a radius 3 rule that solves the parity problem
remains an open problem.