  Both low frequency and high frequency impurity modes have been produced in a
SiN micromechanical cantilever array by illumination with either an infrared or
visible laser. When such laser-induced impurities are placed near a driven
intrinsic localized mode (ILM) it is either repelled or attracted. By measuring
the linear response spectrum for these two cases it was found that vibrational
hopping of the ILM takes place when the natural frequency of the ILM and an
even symmetry linear local mode are symmetrically located about the driven ILM
frequency so that parametric excitation of these two linear modes is enhanced,
amplifying the lateral motion of the ILM. Numerical simulations are consistent
with these signature findings. It is also demonstrated that the correct sign of
the observed interaction can be found with a harmonic lattice-impurity model
but the magnitude of the effect is enhanced in a nonlinear lattice.


  Quantification of anatomical shape changes currently relies on scalar global
indexes which are largely insensitive to regional or asymmetric modifications.
Accurate assessment of pathology-driven anatomical remodeling is a crucial step
for the diagnosis and treatment of many conditions. Deep learning approaches
have recently achieved wide success in the analysis of medical images, but they
lack interpretability in the feature extraction and decision processes. In this
work, we propose a new interpretable deep learning model for shape analysis. In
particular, we exploit deep generative networks to model a population of
anatomical segmentations through a hierarchy of conditional latent variables.
At the highest level of this hierarchy, a two-dimensional latent space is
simultaneously optimised to discriminate distinct clinical conditions, enabling
the direct visualisation of the classification space. Moreover, the anatomical
variability encoded by this discriminative latent space can be visualised in
the segmentation space thanks to the generative properties of the model, making
the classification task transparent. This approach yielded high accuracy in the
categorisation of healthy and remodelled left ventricles when tested on unseen
segmentations from our own multi-centre dataset as well as in an external
validation set, and on hippocampi from healthy controls and patients with
Alzheimer's disease when tested on ADNI data. More importantly, it enabled the
visualisation in three-dimensions of both global and regional anatomical
features which better discriminate between the conditions under exam. The
proposed approach scales effectively to large populations, facilitating
high-throughput analysis of normal anatomy and pathology in large-scale studies
of volumetric imaging.


  Gravitational-wave observations of merging compact binaries hold the key to
precision measurements of the objects' masses and spins. General-relativistic
precession, caused by spins misaligned with the orbital angular momentum, is
considered a crucial tracer for determining the binary's formation history and
environment, and it also improves mass estimates -- its measurement is
therefore of particular interest with wide-ranging implications. Precession
leaves a characteristic signature in the emitted gravitational-wave signal that
is even more pronounced in binaries with highly unequal masses. The recent
observations of GW190412 and GW190814 have confirmed the existence of such
asymmetric compact binaries. Here, we perform a systematic study to assess the
confidence in measuring precession in gravitational-wave observations of high
mass ratio binaries and, our ability to measure the mass of the lighter
companion in neutron star -- black hole type systems. Using Bayesian model
selection, we show that precession can be decisively identified for low-mass
binaries with mass ratios as low as $1:3$ and mildly precessing spins with
magnitudes $\lesssim 0.4$, even in the presence of systematic waveform errors.


  Let V be a normal affine surface which admits a C*- and a C+-action. In this
note we show that in many cases V can be embedded as a principal Zariski open
subset into a hypersurface of a weighted projective space. In particular, we
recover a result of D. Daigle and P. Russell.


  An intriguing property of deep neural networks is their inherent
vulnerability to adversarial inputs, which significantly hinders their
application in security-critical domains. Most existing detection methods
attempt to use carefully engineered patterns to distinguish adversarial inputs
from their genuine counterparts, which however can often be circumvented by
adaptive adversaries. In this work, we take a completely different route by
leveraging the definition of adversarial inputs: while deceiving for deep
neural networks, they are barely discernible for human visions. Building upon
recent advances in interpretable models, we construct a new detection framework
that contrasts an input's interpretation against its classification. We
validate the efficacy of this framework through extensive experiments using
benchmark datasets and attacks. We believe that this work opens a new direction
for designing adversarial input detection methods.


  In this paper, we will give the subconvexity bounds for self dual GL(3)
$L-$functions in the $t$ aspect as well as subconvexity bounds for self dual
$GL(3)\times GL(2)$ $L-$functions in the GL(2) spectral aspect.


  Data-intensive container-based cloud applications have become popular with
the increased use cases in the Internet of Things domain. Challenges arise when
engineering such applications to meet quality requirements, both classical ones
like performance and emerging ones like elasticity and resilience. There is a
lack of reference use cases, applications, and experiences when prototyping
such applications that could benefit the research community. Moreover, it is
hard to generate realistic and reliable workloads that exercise the resources
according to a specification. Hence, designing reference applications that
would exhibit similar performance behavior in such environments is hard. In
this paper, we present a work in progress towards a reference use case and
application for data-intensive containerized cloud applications having an
industrial motivation. Moreover, to generate reliable CPU workloads we make use
of ProtoCom, a well-known library for the generation of resource demands, and
report the performance under various quality requirements in a Kubernetes
cluster of moderate size. Finally, we present the scalability of the current
solution assuming a particular autoscaling policy. Results of the calibration
show high variability of the ProtoCom library when executed in a cloud
environment. We observe a moderate association between the occupancy of node
and the relative variability of execution time.


  This work presents a theoretical investigation of an active photonic grating
of the parity-time (PT) symmetric architecture. The analytical study of the
free-space mode propagation from the grating structure indicates the unique
bifurcation property due to the PT-symmetry modulation. It is shown that both
the gain/loss contrast and the lattice constant parameters are critical factors
to modulate the active photonic system in between the PT-symmetry to the
symmetry-broken phases. Furthermore, numerical simulations via the Rigorous
Coupled-Wave Analysis (RCWA) method discover the existence of a unique Spectral
Singularity (SS) phenomenon in this PT grating structure, which corresponds to
a non-trivial single-mode and near-zero bandwidth photonic resonant emission.
Also, the guiding procedure for fulfilling SS modes is found to be related to
the unique formation of the scattering matrix applied in the PT-symmetric
photonic gratings. This theoretical work takes a fresh look into the active
PT-symmetric photonic gratings focusing on the discovery of new free-space
emission modes rather than the commonly studied unidirectional properties,
which could contribute to the development of novel low-threshold and
super-coherent surface-emitting devices.


  Color-singlet gauge bosons with renormalizable couplings to quarks but not to
leptons must interact with additional fermions ("anomalons") required to cancel
the gauge anomalies. Analyzing the decays of such leptophobic bosons into
anomalons, I show that they produce final states involving leptons at the LHC.
Resonant production of a flavor-universal leptophobic $Z'$ boson leads to
cascade decays via anomalons, whose signatures include a leptonically decaying
$Z$, missing energy and several jets. A $Z'$ boson that couples to the
right-handed quarks of the first and second generations undergoes cascade
decays that violate lepton universality and include signals with two leptons
and jets, or with a Higgs boson, a lepton, a $W$ and missing energy.


  Recent works have considered the ability of transmitter Alice to communicate
reliably to receiver Bob without being detected by warden Willie. These works
generally assume a standard discrete-time model. But the assumption of a
discrete-time model in standard communication scenarios is often predicated on
its equivalence to a continuous-time model, which has not been established for
the covert communications problem. Here, we consider the continuous-time
channel directly and study if efficient covert communication can still be
achieved. We assume that an uninformed jammer is present to assist Alice, and
we consider additive white Gaussian noise (AWGN) channels between all parties.
For a channel with approximate bandwidth W, we establish constructions such
that O(WT) information bits can be transmitted covertly and reliably from Alice
to Bob in T seconds for two separate scenarios: 1) when the path-loss between
Alice and Willie is known; and 2) when the path-loss between Alice and Willie
is unknown.


  Measurements of azimuthal angular correlations are presented for
high-multiplicity pPb collisions at $\sqrt{s_\mathrm{NN}}=$ 5.02 TeV and
peripheral PbPb collisions at $\sqrt{s_\mathrm{NN}}=$ 2.76 TeV. The data used
in this work were collected with the CMS detector at the CERN LHC. Fourier
coefficients as functions of transverse momentum and pseudorapidity are studied
using the scalar product method, 4-, 6-, and 8-particle cumulants, and the
Lee-Yang zeros technique. The influence of event plane decorrelation is
evaluated using the scalar product method and found to account for most of the
observed pseudorapidity dependence.


  The first aim is to construct generalizations of Polya type point process by
applying a branching mechanism to these point processes. Conditions are given
under which these point processes satisfy an integration by parts formula.
Furthermore we compute their Palm kernels, which turn out to be superpositions
of different point processes. Secondly we identify all point processes whose
local characteristics agree with these of a fixed branching of a Polya type
point process as mixtures of branchings of Polya type point process and show
that in this case also they are characterized by an integration by parts
formula.


  We have carried out bound-state and low-energy quantum scattering
calculations on He + NH (triplet Sigma) in magnetic fields, with the NH
molecule in its n=1 rotationally excited states. We have explored the pattern
of levels as a function of magnetic field and identified the nearly good
quantum numbers in different regimes. We have used the bound-state calculations
to locate low-energy Feshbach resonances. When the magnetic field is used to
tune across such a resonance, the real and imaginary part of the scattering
length show asymmetric oscillations and peaks with amplitude between 1 and 3
Angstroms. The scattering length does not pass through a pole at resonance. The
resonant behavior is characterized by a complex resonant scattering length
a_res. The corresponding inelastic cross sections show troughs as well as peaks
near resonance. This may be important for efforts to achieve evaporative and
sympathetic cooling for molecules, because it offers the hope that inelastic
trap losses can be reduced by tuning close to a Feshbach resonance.


  This paper addresses the problem of navigation control of a general class of
2nd order uncertain nonlinear multi-agent systems in a bounded workspace, which
is a subset of $R^3$ , with static obstacles. In particular, we propose a
decentralized control protocol such that each agent reaches a predefined
position at the workspace, while using local information based on a limited
sensing radius. The proposed scheme guarantees that the initially connected
agents remain always connected. In addition, by introducing certain distance
constraints, we guarantee inter-agent collision avoidance as well as collision
avoidance with the obstacles and the boundary of the workspace. The proposed
controllers employ a class of Decentralized Nonlinear Model Predictive
Controllers (DNMPC) under the presence of disturbances and uncertainties.
Finally, simulation results verify the validity of the proposed framework.


  We should be in a golden age of scientific discovery, given that we have more
data and more compute power available than ever before, plus a new generation
of algorithms that can learn effectively from data. But paradoxically, in many
data-driven fields, the eureka moments are becoming increasingly rare.
Scientists are struggling to keep pace with the explosion in the volume and
complexity of scientific data. We describe here a few simple architectural
principles that we believe are essential in order to create effective, robust,
and flexible platforms that make the best use of emerging technology to deal
with the exponential growth of scientific data.


  We study the synchronization of coupled maps on a variety of networks
including regular one and two dimensional networks, scale free networks, small
world networks, tree networks, and random networks. For small coupling
strengths nodes show turbulent behavior but form phase synchronized clusters as
coupling increases. We identify two different ways of cluster formation,
self-organized clusters which have mostly intra-cluster couplings and driven
clusters which have mostly inter-cluster couplings. The synchronized clusters
may be of dominant self-organized type, dominant driven type or mixed type
depending on the type of network and the parameters of the dynamics. There are
some nodes of the floating type that show intermittent behaviour between
getting attached to some clusters and evolving independently. The residence
times of a floating node in a synchronized cluster show an exponential
distribution. We define different states of the coupled dynamics by considering
the number and type of synchronized clusters. For the local dynamics governed
by the logistic map we study the phase diagram in the plane of the coupling
constant ($\epsilon$) and the logistic map parameter ($\mu$). For large
coupling strengths and nonlinear coupling we find that the scale free networks
and the Caley tree networks lead to better cluster formation than the other
types of networks with the same average connectivity. For most of our study we
use the number of connections of the order of the number of nodes which allows
us to distinguish between the two mechanisms of cluster formation. As the
number of connections increases the number of nodes forming clusters and the
size of the clusters in general increase.


  The high sensitivity of the new generation of radio telescopes such as the
Square Kilometre Array (SKA) will allow cosmological weak lensing measurements
at radio wavelengths that are competitive with optical surveys. We present an
adaptation to radio data of lensfit, a method for galaxy shape measurement
originally developed and used for optical weak lensing surveys. This likelihood
method uses an analytical galaxy model and makes a Bayesian marginalisation of
the likelihood over uninteresting parameters. It has the feature of working
directly in the visibility domain, which is the natural approach to adopt with
radio interferometer data, avoiding systematics introduced by the imaging
process. As a proof of concept, we provide results for visibility simulations
of individual galaxies with flux density S >= 10 muJy at the phase centre of
the proposed SKA1-MID baseline configuration, adopting 12 frequency channels in
the band 950 - 1190 MHz. Weak lensing shear measurements from a population of
galaxies with realistic flux and scalelength distributions are obtained after
natural gridding of the raw visibilities. Shear measurements are expected to be
affected by "noise bias": we estimate the bias in the method as a function of
signal-to-noise ratio (SNR). We obtain additive and multiplicative bias values
that are comparable to SKA1 requirements for SNR > 18 and SNR > 30,
respectively. The multiplicative bias for SNR > 10 is comparable to that found
in ground-based optical surveys such as CFHTLenS, and we anticipate that
similar shear measurement calibration strategies to those used for optical
surveys may be used to good effect in the analysis of SKA radio interferometer
data.


  In models of oriented closed strings, anomaly cancellations are deeply linked
to the {\it modular invariance} of the torus amplitude. If open and/or
unoriented strings are allowed, there are no non-trivial modular
transformations in the additional genus-one amplitudes (Klein bottle, annulus
and M\"obius strip). As originally recognized by Green and Schwarz, in the
ten-dimensional type-I superstring the anomaly cancellation results from a
delicate interplay between the contributions of these additional surfaces. In
lower-dimensional models, the possible presence of a number of antisymmetric
tensors yields a generalization of the Green-Schwarz mechanism. I illustrate
these results by referring to some six-dimensional chiral models, and I
conclude by addressing the additional difficulties that one meets when trying
to extend the construction to chiral four-dimensional models. (Contribution to
''From Superstrings to Supergravity'', Erice, ITALY, december 5-12, 1992)


  Assume that $G$ is a finite group. For every $a, b \in\mathbb N,$ we define a
graph $\Gamma_{a,b}(G)$ whose vertices correspond to the elements of $G^a\cup
G^b$ and in which two tuples $(x_1,\dots,x_a)$ and $(y_1,\dots,y_b)$ are
adjacent if and only if $\langle x_1,\dots,x_a,y_1,\dots,y_b \rangle =G.$ We
study several properties of these graphs (isolated vertices, loops,
connectivity, diameter of the connected components) and we investigate the
relations between their properties and the group structure, with the aim of
understanding which information about $G$ are encoded by these graphs.


  We educe a perspective on how best to regulate the bank of tomorrow in frames
of debate launched by the International Centre for Financial Regulation and
Financial Times. Our goal is to create a conceptual framework for policymakers
and regulators to shape the international financial system in century of
globalization using the 1888 FT's motto: "Without fear and without favour." Our
prospect employs an analytical approach, which focuses on the origins and
evolution of banking system, its transformation over the recent decades,
subsequent encountering the limits to growth and redefinition of new strategic
boundaries of emerging financial industry. We identify the main reasons and
limitations, which led to the global financial crisis. We propose the new
research agendas with the aim to understand the situation in finances, evaluate
the created systemic damages, and find the possible ways to resolve the
existing problems through introduction of new banking regulation. We think that
the global economic and financial systems are highly nonlinear systems. In our
opinion, the frequency, phase and amplitude modulation during the mixing of
waves, which characterize the Kitchin, Juglar, Kuznets, Kondratiev economic
cycles, may result in origination of strong nonlinear dynamics in financial
system, accompanied by chaos- induced phenomena. These nonlinear effects have
to be taken to the account, when adding the liquidity to the financial system
in small quantas in series over time period during the Quantitative Easing
policy execution by central banks. We propose the Random Tax to be selectively
imposed on the profits, obtained by market agents during high-risk high-profit
speculative transactions. We expect that the Random Tax will stabilize the
financial system in conditions of free market capitalism.


  In this work, we introduce machine learning methods to implement readout of a
single qubit on $^{171}\mathrm{Yb^{+}}$ trapped-ion system. Different machine
learning methods including convolutional neural networks and fully-connected
neural networks are compared with traditional methods in the tests. The results
show that machine learning methods have higher fidelity, more robust readout
results in relatively short time. To obtain a 99% readout fidelity, neural
networks only take half of the detection time needed by traditional threshold
or maximum likelihood methods. Furthermore, we implement the machine learning
algorithms on hardware-based field-programmable gate arrays and an ARM
processor. An average readout fidelity of 99.5% (with $10^5$ magnitude trials)
within 171 $\mu$s is demonstrated on the embedded hardware system for
$^{171}\mathrm{Yb^{+}}$ ion trap.


  The need for wireless communication has driven the communication systems to
high performance. However, the main bottleneck that affects the communication
capability is the Fast Fourier Transform (FFT), which is the core of most
modulators. This paper presents FPGA implementation of pipeline digit-slicing
multiplier-less radix 22 DIF (Decimation In Frequency) SDF (single path delay
feedback) butterfly for FFT structure. The approach is taken, in order to
reduce computation complexity in butterfly multiplier, the digit-slicing
multiplier-less technique was utilized in the critical path of pipeline
Radix-22 DIF SDF FFT structure. The proposed design focused on the trade-off
between the speed and active silicon area for the chip implementation. The
multiplier input data was sliced into four blocks each one with four bits to
process at the same time in parallel. The new architecture was investigated and
simulated with MATLAB software. The Verilog HDL code in Xilinx ISE environment
was derived to describe the FFT Butterfly functionality and was downloaded to
Virtex II FPGA board. Consequently, the Virtex-II FG456 Proto board was used to
implement and test the design on the real hardware. As a result, from the
findings, the synthesis report indicates the maximum clock frequency of 555.75
MHz with the total equivalent gate count of 32,146 is a marked and significant
improvement over Radix 22 DIF SDF FFT butterfly. In comparison with the
conventional butterfly architecture design which can only run at a maximum
clock frequency of 200.102 MHz and the conventional multiplier can only run at
a maximum clock frequency of 221.140 MHz, the proposed system exhibits better
results.


  We have found several families of vortex soliton solutions in two-dimensional
discrete dissipative systems governed by the cubic-quintic complex
Ginzburg-Landau equation. There are symmetric and asymmetric solutions, and
some of them have simultaneously two different topological charges. Their
regions of existence and stability are determined. Additionally, we have
analyzed the relation- ship between dissipation and stability for a number of
solutions. We have obtained that dissipation favours the stability of the
solutions.


  We investigate the possible influence of very-high-energy physics on
inflationary predictions focussing on whether effective field theories can
allow effects which are parametrically larger than order H^2/M^2, where M is
the scale of heavy physics and H is the Hubble scale at horizon exit. By
investigating supersymmetric hybrid inflation models, we show that decoupling
does not preclude heavy-physics having effects for the CMB with observable size
even if H^2/M^2 << O(1%), although their presence can only be inferred from
observations given some a priori assumptions about the inflationary mechanism.
Our analysis differs from the results of hep-th/0210233, in which other kinds
of heavy-physics effects were found which could alter inflationary predictions
for CMB fluctuations, inasmuch as the heavy-physics can be integrated out here
to produce an effective field theory description of low-energy physics. We
argue, as in hep-th/0210233, that the potential presence of heavy-physics
effects in the CMB does not alter the predictions of inflation for generic
models, but does make the search for deviations from standard predictions
worthwhile.


  A description of all subsemigroups of $M_2(\mathbb{C})$ which are given by a
countable intersection of constructible sets is given. Furthermore, it is shown
that they are intersections of constructible semigroups.


  A critical step to building trustworthy deep neural networks is trust
quantification, where we ask the question: How much can we trust a deep neural
network? In this study, we take a step towards simple, interpretable metrics
for trust quantification by introducing a suite of metrics for assessing the
overall trustworthiness of deep neural networks based on their behaviour when
answering a set of questions. We conduct a thought experiment and explore two
key questions about trust in relation to confidence: 1) How much trust do we
have in actors who give wrong answers with great confidence? and 2) How much
trust do we have in actors who give right answers hesitantly? Based on insights
gained, we introduce the concept of question-answer trust to quantify
trustworthiness of an individual answer based on confident behaviour under
correct and incorrect answer scenarios, and the concept of trust density to
characterize the distribution of overall trust for an individual answer
scenario. We further introduce the concept of trust spectrum for representing
overall trust with respect to the spectrum of possible answer scenarios across
correctly and incorrectly answered questions. Finally, we introduce
NetTrustScore, a scalar metric summarizing overall trustworthiness. The suite
of metrics aligns with past social psychology studies that study the
relationship between trust and confidence. Leveraging these metrics, we
quantify the trustworthiness of several well-known deep neural network
architectures for image recognition to get a deeper understanding of where
trust breaks down. The proposed metrics are by no means perfect, but the hope
is to push the conversation towards better metrics to help guide practitioners
and regulators in producing, deploying, and certifying deep learning solutions
that can be trusted to operate in real-world, mission-critical scenarios.


  The shallow decay phase or plateau phase of early afterglows of gamma-ray
bursts (GRBs), discovered by Swift, is currently understood as being due to
energy injection to a relativistic blast wave. One natural scenario for energy
injection invokes a millisecond magnetar as the central engine of GRBs, because
the conventional model of a pulsar predicts a nearly constant
magnetic-dipole-radiation luminosity within the spin-down timescale. However,
we note that significant brightening occurs in some early afterglows, which
apparently conflicts with the above scenario. Here we propose a new model to
explain this significant brightening phenomena by considering a hyperaccreting
fallback disk around a newborn millisecond magnetar. We show that for typical
values of the model parameters, sufficient angular momentum of the accreted
matter is transferred to the magnetar and spins it up. It is this spin-up that
leads to a dramatic increase of the magnetic dipole radiation luminosity with
time and thus significant brightening of an early afterglow. Based on this
model, we carry out numerical calculations and fit well early afterglows of 12
GRBs assuming sufficiently strong fallback accretion. If the accretion is very
weak, our model turns out to be the conventional energy-injection scenario of a
pulsar. Therefore, our model can provide a unified explanation for the shallow
decay phase, plateaus, and significant brightening of early afterglows.


  The quantum state discrimination is an important part of quantum information
processing. We investigate the discrimination of coherent states through
Jaynes-Cummings (JC) model interaction between the field and the ancilla
without rotation wave approximation (RWA). We show that the minimum failure
probability can be reduced as RWA is eliminated from JC model and the non-RWA
terms accompanied by the quantum effects of fields (e.g. the virtual photon
process in the JC model without RWA) can enhance the state discrimination. The
JC model without RWA for unambiguous state discrimination is superior to
ambiguous state discrimination, particularly when the number of sequential
measurements increases. Unambiguous state discrimination implemented via the
non-RWA JC model is beneficial to saving resource cost.


  We determine which faithful irreducible representations $V$ of a simple
linear algebraic group $G$ are generically free for Lie($G$), i.e., which $V$
have an open subset consisting of vectors whose stabilizer in Lie($G$) is zero.
This relies on bounds on $\dim V$ obtained in prior work (part I), which reduce
the problem to a finite number of possibilities for $G$ and highest weights for
$V$, but still infinitely many characteristics. The remaining cases are handled
individually, some by computer calculation. These results were previously known
for fields of characteristic zero, although new phenomena appear in prime
characteristic; we provide a shorter proof that gives the result with very mild
hypotheses on the characteristic. (The few characteristics not treated here are
settled in part III.) These results are related to questions about invariants
and the existence of a stabilizer in general position.


  We tackle the problem of algorithmic fairness, where the goal is to avoid the
unfairly influence of sensitive information, in the general context of
regression with possible continuous sensitive attributes. We extend the
framework of fair empirical risk minimization to this general scenario,
covering in this way the whole standard supervised learning setting. Our
generalized fairness measure reduces to well known notions of fairness
available in literature. We derive learning guarantees for our method, that
imply in particular its statistical consistency, both in terms of the risk and
the fairness measure. We then specialize our approach to kernel methods and
propose a convex fair estimator in that setting. We test the estimator on a
commonly used benchmark dataset (Communities and Crime) and on a new dataset
collected at the University of Genova, containing the information of the
academic career of five thousand students. The latter dataset provides a
challenging real case scenario of unfair behaviour of standard regression
methods that benefits from our methodology. The experimental results show that
our estimator is effective at mitigating the trade-off between accuracy and
fairness requirements.


  Kernel methods are an important class of techniques in machine learning. To
be effective, good feature maps are crucial for mapping non-linearly separable
input data into a higher dimensional (feature) space, thus allowing the data to
be linearly separable in feature space. Previous work has shown that quantum
feature map design can be automated for a given dataset using NSGA-II, a
genetic algorithm, while both minimizing circuit size and maximizing
classification accuracy. However, the evaluation of the accuracy achieved by a
candidate feature map is costly. In this work, we demonstrate the suitability
of kernel-target alignment as a substitute for accuracy in genetic
algorithm-based quantum feature map design. Kernel-target alignment is faster
to evaluate than accuracy and doesn't require some data points to be reserved
for its evaluation. To further accelerate the evaluation of genetic fitness, we
provide a method to approximate kernel-target alignment. To improve
kernel-target alignment and root mean squared error, the final trainable
parameters of the generated circuits are further trained using COBYLA to
determine whether a hybrid approach applying conventional circuit parameter
training can easily complement the genetic structure optimization approach. A
total of eight new approaches are compared to the original across nine varied
binary classification problems from the UCI machine learning repository,
showing that kernel-target alignment and its approximation produce feature map
circuits enabling comparable accuracy to the previous work but with larger
margins on training data (in excess of 20\% larger) that improve further with
circuit parameter training.


  We give a geometric criterion to check the validity of integral Tate
conjecture for one cycles on separably rationally connected fibrations over a
curve, and to check that the Brauer-Manin obstruction is the only obstruction
to local-global principle for zero cycles on a separably rationally connected
variety defined over a global function field.
  We prove that the Brauer-Manin obstruction is the only obstruction to
local-global principle for zero cycles on all geometrically rational surfaces
defined over a global function field, and to Hasse principle for rational
points on del Pezzo surfaces of degree four defined over a global function
field of odd characteristic.
  Along the way, we also prove some results about the space of one cycles on a
separably rationally connected fibration over a curve, which leads to the
equality of the coniveau filtration and the strong coniveau filtration
(introduced by Benoist-Ottem and Voisin) on degree $3$ homology of such
varieties.


  Using a Wang-Landau entropic sampling scheme, we investigate the effects of
quenched bond randomness on a particular case of a triangular Ising model with
nearest- ($J_{nn}$) and next-nearest-neighbor ($J_{nnn}$) antiferromagnetic
interactions. We consider the case $R=J_{nnn}/J_{nn}=1$, for which the pure
model is known to have a columnar ground state where rows of nearest-neighbor
spins up and down alternate and undergoes a weak first-order phase transition
from the ordered to the paramagnetic state. With the introduction of quenched
bond randomness we observe the effects signaling the expected conversion of the
first-order phase transition to a second-order phase transition and using the
Lee-Kosterlitz method, we quantitatively verify this conversion. The emerging,
under random bonds, continuous transition shows a strongly saturating specific
heat behavior, corresponding to a negative exponent $\alpha$, and belongs to a
new distinctive universality class with $\nu=1.135(11)$, $\gamma/\nu=1.744(9)$,
and $\beta/\nu=0.124(8)$. Thus, our results for the critical exponents support
an extensive but weak universality and the emerged continuous transition has
the same magnetic critical exponent (but a different thermal critical exponent)
as a wide variety of two-dimensional (2d) systems without and with quenched
disorder.


  A formula is proposed to quantitatively estimate the signal emission rate of
Communicating Extra-Terrestrial Intelligent civilizations (CETIs) in the
Galaxy. I suggest that one possible type of CETI signal would be brief radio
bursts similar to fast radio bursts (FRBs). A dedicated search for FRB-like
artificial signals in the Galaxy for decades may pose a meaningful upper limit
on the emission rate of these signals by CETIs. The Fermi-Hart paradox is
answered in terms of not having enough observing times for this and other types
of signals. Whether humans should send FRB-like signals in the far future is
briefly discussed.


  We consider a random field, defined on an integer-valued d-dimensional
lattice, with covariance function satisfying a condition more general than
summability. Such condition appeared in the well-known Newman's conjecture
concerning the central limit theorem (CLT) for stationary associated random
fields. As was demonstrated by Herrndorf and Shashkin, the conjecture fails
already for d=1. In the present paper, we show the validity of modified
conjecture leaving intact the mentioned condition on covariance function. Thus
we establish, for any positive integer d, a criterion of the CLT validity for
the wider class of positively associated stationary fields. The uniform
integrability for the squares of normalized partial sums, taken over growing
parallelepipeds or cubes, plays the key role in deriving their asymptotic
normality. So our result extends the Lewis theorem proved for sequences of
random variables. A representation of variances of partial sums of a field
using the slowly varying functions in several arguments is employed in
essential way.


  We report the result of a systematic methanol observation toward IRAS
19312+1950. The properties of the SiO, H2O and OH masers of this object are
consistent with those of mass-losing evolved stars, but some other properties
are difficult to explain in the standard scheme of stellar evolution in its
late stage. Interestingly, a tentative detection of radio methanol lines was
suggested toward this object by a previous observation. To date, there are no
confirmed detections of methanol emission towards evolved stars, so
investigation of this possible detection is important to better understand the
circumstellar physical/chemical environment of IRAS 19312+1950. In this study,
we systematically observed multiple methanol lines of IRAS 19312+1950 in the
lambda=3mm, 7mm, and 13mm bands, and detected 6 lines including 4 thermal lines
and 2 class I maser lines. We derived basic physical parameters including
kinetic temperature and relative abundances by fitting a radiative transfer
model. According to the derived excitation temperature and line profiles, a
spherically expanding outflow lying at the center of the nebulosity is excluded
from the possibilities for methanol emission regions. The detection of class I
methanol maser emission suggests that a shock region is involved in the system
of IRAS 19312+1950. If the central star of IRAS 19312+1950 is an evolved star
as suggested in the past, the class I maser detected in the present observation
is the first case detected in an interaction region between an evolved star
outflow and ambient molecular gas.


  Nowadays the semi-tensor product (STP) approach to finite games has become a
promising new direction. This paper provides a comprehensive survey on this
prosperous field. After a brief introduction for STP and finite (networked)
games, a description for the principle and fundamental technique of STP
approach to finite games is presented. Then several problems and recent results
about theory and applications of finite games via STP are presented. A brief
comment about the potential use of STP to artificial intelligence is also
proposed.


  We consider the Burns-Flach formulation of the equivariant Tamagawa number
conjecture (ETNC). In their setup, a Tamagawa number is an element of a
relative K-group. We show that this relative group agrees with an ordinary
K-group, namely of the category of locally compact topological modules over the
order. Its virtual objects are an equivariant Haar measure in a precise sense.
We expect that all relative K-groups in the ETNC will have analoguous
interpretations. At present, we need to restrict to regular orders, e.g.
hereditary.


  The positivity of the energy in relativistic quantum mechanics implies that
wave functions can be continued analytically to the forward tube T in complex
spacetime. For Klein-Gordon particles, we interpret T as an extended (8D)
classical phase space containing all 6D classical phase spaces as symplectic
submanifolds. The evaluation maps $e_z: f\to f(z)$ of wave functions on T are
relativistic coherent states reducing to the Gaussian coherent states in the
nonrelativistic limit. It is known that no covariant probability interpretation
exists for Klein-Gordon particles in real spacetime because the time component
of the conserved "probability current" can attain negative values even for
positive-energy solutions. We show that this problem is solved very naturally
in complex spacetime, where $|f(x-iy)|^2$ is interpreted as a probability
density on all 6D phase spaces in T which, when integrated over the "momentum"
variables y, gives a conserved spacetime probability current whose time
component is a positive regularization of the usual one. Similar results are
obtained for Dirac particles, where the evaluation maps $e_z$ are spinor-valued
relativistic coherent states. For free quantized Klein-Gordon and Dirac fields,
the above formalism extends to n-particle/antiparticle coherent states whose
scalar products are Wightman functions. The 2-point function plays the role of
a reproducing kernel for the one-particle and antiparticle subspaces.


  For normal play, impartial games, we define penults as those positions in
which every option results in an immediate win for the other player. We explore
the number of tokens in penults of two positional games, Impartial Tic and
Impartial Tak. We obtain a complete classification in the former case. We then
explore winning strategies and further directions.


  Motivated by the problem of domino tilings of the Aztec diamond, a weighted
particle system is defined on $N$ lines, with line $j$ containing $j$
particles. The particles are restricted to lattice points from 0 to $N$, and
particles on successive lines are subject to an interlacing constraint. It is
shown that marginal distributions for this particle system can be computed
exactly. This in turn is used to give unified derivations of a number of
fundamental properties of the tiling problem, for example the evaluation of the
number of distinct configurations and the relation to the GUE minor process. An
interlaced particle system associated with the domino tiling of a certain half
Aztec diamond is similarly defined and analyzed.


  The general properties of a class of two-dimensional dilaton gravity (DG)
theories with multi-exponential potentials are studied and a subclass of these
theories, in which the equations of motion reduce to Toda and Liouville
equations, is treated in detail. A combination of parameters of the equations
should satisfy a certain constraint that is identified and solved for the
general model. It follows that in DG the integrable Toda equations, generally,
cannot appear without accompanying Liouville equations.
  The most difficult problem in the two-dimensional Toda-Liouville DG is to
solve the energy-momentum constraints. We discuss this problem using the
simplest examples and identify the main obstacles to finding its analytic
solution. Then we consider a subclass of integrable two-dimensional theories,
in which scalar matter satisfy the Toda equations while the two-dimensional
metric is trivial.
  We also show how the wave-like solutions of the general Toda-Liouville
systems can be simply derived. In DG, these solutions describe nonlinear waves
coupled to gravity as well as static states and cosmologies. For the static
states and cosmologies we propose and study a more general one-dimensional
Toda-Liouville model typically emerging in one-dimensional reductions of
higher-dimensional gravity and supergravity theories. A special attention is
paid to making the analytic structure of the solutions of the Toda equations as
simple and transparent as possible, with the aim to gain a better understanding
of realistic theories reduced to dimensions 1+1 and 1+0 or 0+1.


  We present followup imaging of two bright (L > L*) galaxy candidates at z > 8
from the Brightest of Reionizing Galaxies (BoRG) survey with the F098M filter
on HST/WFC3. The F098M filter provides an additional constraint on the flux
blueward of the spectral break, and the observations are designed to
discriminate between low- and high-z photometric redshift solutions for these
galaxies. Our results confirm one galaxy, BoRG 0116+1425 747, as a highly
probable z ~ 8 source, but reveal that BoRG 0116+1425 630 - previously the
brightest known z > 8 candidate (mAB = 24.5) - is likely to be a z ~ 2
interloper. As this source was substantially brighter than any other z > 8
candidate, removing it from the sample has a significant impact on the derived
UV luminosity function in this epoch. We show that while previous BoRG results
favored a shallow power-law decline in the bright end of the luminosity
function prior to reionization, there is now no evidence for departure from a
Schechter function form and therefore no evidence for a difference in galaxy
formation processes before and after reionization.


  The field limit of superconducting radio-frequency cavity made of type II
superconductor with a large Ginzburg-Landau parameter is studied with taking
effects of nano-scale surface topography into account. If the surface is
ideally flat, the field limit is imposed by the superheating field. On the
surface of cavity, however, nano-defects almost continuously distribute and
suppress the superheating field everywhere. The field limit is imposed by an
effective superheating field given by the product of the superheating field for
ideal flat surface and a suppression factor that contains effects of
nano-defects. A nano-defect is modeled by a triangular groove with a depth
smaller than the penetration depth. An analytical formula for the suppression
factor of bulk and multilayer superconductors are derived in the framework of
the London theory. As an immediate application, the suppression factor of the
dirty Nb processed by the electropolishing is evaluated by using results of
surface topographic study. The estimated field limit is consistent with the
present record field of nitrogen-doped Nb cavities. Suppression factors of
surfaces of other bulk and multilayer superconductors, and those after various
surface processing technologies can also be evaluated by using the formula.


  Scalar Field Dark Matter (SFDM), comprised of ultralight ($\gtrsim 10^{-22}$
eV) bosons, is distinguished from massive ($\gtrsim$ GeV), collisionless Cold
Dark Matter (CDM) by its novel structure-formation dynamics as Bose-Einstein
condensate (BEC) and quantum superfluid with wave-like properties, described by
the Gross-Pitaevski and Poisson (GPP) equations. In the free-field (fuzzy)
limit of SFDM (FDM), structure is inhibited below the de Broglie wavelength
$\lambda_{\text{deB}}$, but resembles CDM on larger scales. Virialized haloes
have solitonic cores of radius $\sim \lambda_{\text{deB}}$ that follow the
ground-state attractor solution of GPP, surrounded by CDM-like envelopes. As
superfluid, SFDM is irrotational (vorticity-free) but can be unstable to vortex
formation. We previously showed this can happen in halo cores, from angular
momentum arising during structure formation, when repulsive self-interaction
(SI) is present to support them out to a second length scale
$\lambda_{\text{SI}}$ with $\lambda_{\text{SI}} > \lambda_{\text{deB}}$ (the
Thomas-Fermi regime), but only if SI is strong enough. This suggested FDM cores
(without SI) would not form vortices. FDM simulations later found vortices, but
only outside halo cores, consistent with our previous suggestion based upon
TF-regime analysis. We extend that analysis now to FDM, to show explicitly that
vortices should not arise in solitonic cores from angular momentum, modelling
them as either Gaussian spheres or compressible, ($n = 2$)-polytropic,
irrotational Riemann-S ellipsoids. We find that, for typical halo spin
parameters, angular momentum per particle is below $\hbar$, the minimum
required even for one singly-quantized vortex in the centre. Even for larger
angular momentum, however, vortex formation is not energetically favoured.


  In this paper, we consider model-free federated reinforcement learning for
tabular episodic Markov decision processes. Under the coordination of a central
server, multiple agents collaboratively explore the environment and learn an
optimal policy without sharing their raw data. Despite recent advances in
federated Q-learning algorithms achieving near-linear regret speedup with low
communication cost, existing algorithms only attain suboptimal regrets compared
to the information bound. We propose a novel model-free federated Q-learning
algorithm, termed FedQ-Advantage. Our algorithm leverages reference-advantage
decomposition for variance reduction and operates under two distinct
mechanisms: synchronization between the agents and the server, and policy
update, both triggered by events. We prove that our algorithm not only requires
a lower logarithmic communication cost but also achieves an almost optimal
regret, reaching the information bound up to a logarithmic factor and
near-linear regret speedup compared to its single-agent counterpart when the
time horizon is sufficiently large.


  For each Dynkin diagram $D$, we define a ''cluster configuration space''
${\mathcal{M}}_D$ and a partial compactification ${\widetilde
{\mathcal{M}}}_D$. For $D = A_{n-3}$, we have ${\mathcal{M}}_{A_{n-3}} =
{\mathcal{M}}_{0,n}$, the configuration space of $n$ points on ${\mathbb P}^1$,
and the partial compactification ${\widetilde {\mathcal{M}}}_{A_{n-3}}$ was
studied in this case by Brown. The space ${\widetilde {\mathcal{M}}}_D$ is a
smooth affine algebraic variety with a stratification in bijection with the
faces of the Chapoton-Fomin-Zelevinsky generalized associahedron. The regular
functions on ${\widetilde {\mathcal{M}}}_D$ are generated by coordinates
$u_\gamma$, in bijection with the cluster variables of type $D$, and the
relations are described completely in terms of the compatibility degree
function of the cluster algebra. As an application, we define and study cluster
algebra analogues of tree-level open string amplitudes.


  We present an analysis of Galactic bulge stars from Hubble Space Telescope
(HST) Wide Field Camera 3 (WFC3) observations of the Stanek window
(l,b=[0.25,-2.15]) from two epochs approximately two years apart. This dataset
is adjacent to the provisional Wide-field Infrared Survey Telescope (WFIRST)
microlensing field. Proper motions are measured for approximately 115,000 stars
down to 28th mag in V band and 25th mag in I band, with accuracies of 0.5 mas
yr$^{-1}$ (20 km s$^{-1}$) at I $\approx$ 21. A cut on the longitudinal proper
motion $\mu_l$ allows us to separate disk and bulge populations and produce
bulge-only star counts that are corrected for photometric completeness and
efficiency of the proper-motion cut. The kinematic dispersions and surface
density in the field are compared to the nearby SWEEPS sight-line, finding a
marginally larger than expected gradient in stellar density. The observed bulge
star counts and kinematics are further compared to the Besan\c{c}on, Galaxia,
and GalMod Galactic population synthesis models. We find that most of the
models underpredict low-mass bulge stars by $\sim$33% below the main-sequence
turnoff, and upwards of $\sim$70% at redder J and H wavebands. While
considering inaccuracies in the Galactic models, we give implications for the
exoplanet yield from the WFIRST microlensing mission.


  The 3D Morphable Model (3DMM), which is a Principal Component Analysis (PCA)
based statistical model that represents a 3D face using linear basis functions,
has shown promising results for reconstructing 3D faces from single-view
in-the-wild images. However, 3DMM has restricted representation power due to
the limited number of 3D scans and the global linear basis. To address the
limitations of 3DMM, we propose a straightforward learning-based method that
reconstructs a 3D face mesh through Free-Form Deformation (FFD) for the first
time. FFD is a geometric modeling method that embeds a reference mesh within a
parallelepiped grid and deforms the mesh by moving the sparse control points of
the grid. As FFD is based on mathematically defined basis functions, it has no
limitation in representation power. Thus, we can recover accurate 3D face
meshes by estimating appropriate deviation of control points as deformation
parameters. Although both 3DMM and FFD are parametric models, it is difficult
to predict the effect of the 3DMM parameters on the face shape, while the
deformation parameters of FFD are interpretable in terms of their effect on the
final shape of the mesh. This practical advantage of FFD allows the resulting
mesh and control points to serve as a good starting point for 3D face modeling,
in that ordinary users can fine-tune the mesh by using widely available 3D
software tools. Experiments on multiple datasets demonstrate how our method
successfully estimates the 3D face geometry and facial expressions from 2D face
images, achieving comparable performance to the state-of-the-art methods.


  In this work, we introduce a new realization of exactly-solvable
time-dependent Hamiltonians based on the solutions of the fourth Painlev\'e and
the Ermakov equations. The latter is achieved by introducing a shape-invariant
condition between an unknown quantum invariant and a set of third-order
intertwining operators with time-dependent coefficients. The new quantum
invariant is constructed by adding a deformation term to the well-known
parametric oscillator invariant. Such a deformation depends explicitly on time
through the solutions of the Ermakov equation, which ensures the regularity of
the new time-dependent potential of the Hamiltonian at each time. On the other
hand, with the aid of the proper reparametrization, the fourth Painlev\'e
equation appears, the parameters of which dictate the spectral behavior of the
quantum invariant. In particular, the eigenfunctions of the third-order ladder
operators lead to several sequences of solutions to the Schr\"odinger equation,
determined in terms of the solutions of a Riccati equation, Okamoto
polynomials, or nonlinear bound states of the derivative nonlinear
Schr\"odinger equation. Remarkably, it is noticed that the solutions in terms
of the nonlinear bound states lead to a quantum invariant with equidistant
eigenvalues, which contains both an (N+1)-dimensional and an infinite sequence
of eigenfunctions. The resulting family of time-dependent Hamiltonians is such
that, to the authors' knowledge, have been unnoticed in the literature of
stationary and nonstationary systems.


  We contrast the distinct frameworks of materials design and physical learning
in creating elastic networks with desired stable states. In design, the desired
states are specified in advance and material parameters can be optimized on a
computer with this knowledge. In learning, the material physically experiences
the desired stable states in sequence, changing the material so as to stabilize
each additional state. We show that while designed states are stable in
networks of linear Hookean springs, sequential learning requires specific
non-linear elasticity. We find that such non-linearity stabilizes states in
which strain is zero in some springs and large in others, thus playing the role
of Bayesian priors used in sparse statistical regression. Our model shows how
specific material properties allow continuous learning of new functions through
deployment of the material itself.


  Because most large galaxies contain a central black hole, and galaxies often
merge, black-hole binaries are expected to be common in galactic nuclei.
Although they cannot be imaged, periodicities in the light curves of quasars
have been interpreted as evidence for binaries, most recently in PG~1302-102,
with a short rest-frame optical period of 4 years. If the orbital period
matches this value, then for the range of estimated black hole masses the
components would be separated by 0.007-0.017 pc, implying relativistic orbital
speeds. There has been much debate over whether black hole orbits could be
smaller than 1 pc. Here we show that the amplitude and the sinusoid-like shape
of the variability of PG~1302-102 can be fit by relativistic Doppler boosting
of emission from a compact, steadily accreting, unequal-mass binary. We predict
that brightness variations in the ultraviolet light curve track those in the
optical, but with a 2-3 times larger amplitude. This prediction is relatively
insensitive to the details of the emission process, and is consistent with
archival UV data. Follow-up UV and optical observations in the next few years
can test this prediction and confirm the existence of a binary black hole in
the relativistic regime.


  Power-law behaviors are common in many disciplines, especially in network
science. Real-world networks, like disease spreading among people, are more
likely to be interconnected communities, and show richer power-law behaviors
than isolated networks. In this paper, we look at the system of two communities
which are connected by bridge links between a fraction $r$ of bridge nodes, and
study the effect of bridge nodes to the final state of the
Susceptible-Infected-Recovered model, by mapping it to link percolation. By
keeping a fixed average connectivity, but allowing different transmissibilities
along internal and bridge links, we theoretically derive different power-law
asymptotic behaviors of the total fraction of the recovered $R$ in the final
state as $r$ goes to zero, for different combinations of internal and bridge
link transmissibilities. We also find crossover points where $R$ follows
different power-law behaviors with $r$ on both sides when the internal
transmissibility is below but close to its critical value, for different bridge
link transmissibilities. All of these power-law behaviors can be explained
through different mechanisms of how finite clusters in each community are
connected into the giant component of the whole system, and enable us to pick
effective epidemic strategies and to better predict their impacts.


  We derive an upper bound on the support of matrix coefficients of
suprecuspidal representations of the general linear group over a
non-archimedean local field. The results are in par with those which can be
obtained from the Bushnell--Kutzko classification of supercuspidal
representations, but they are proved independently.


  Here we show an example of a young asteroid cluster located in a dynamically
stable region, which was produced by partial disruption of a primitive body
about 30 km in size. We estimate its age to be only 1.9 +/- 0.3 Myr, thus its
post-impact evolution should have been very limited. The large difference in
size between the largest object and the other cluster members means that this
was a cratering event. The parent body had a large orbital inclination, and was
subject to collisions with typical impact speeds higher by a factor of 2 than
in the most common situations encountered in the main belt. For the first time
we have at disposal the observable outcome of a very recent event to study
high-speed collisions involving primitive asteroids, providing very useful
constraints to numerical simulations of these events and to laboratory
experiments.


  We prove an atomic type decomposition for the noncommutative martingale Hardy
space $\h_p$ for all $0<p<2$ by an explicit constructive method using algebraic
atoms as building blocks. Using this elementary construction, we obtain a weak
form of the atomic decomposition of $\h_p$ for all $0< p < 1,$ and provide a
constructive proof of the atomic decomposition for $p=1$. We also study
$(p,\8)_c$-atoms, and show that every $(p,2)_c$-atom can be decomposed into a
sum of $(p,\8)_c$-atoms; consequently, for every $0<p\le 1$, the
$(p,q)_c$-atoms lead to the same atomic space for all $2\le q\le\8$. As
applications, we obtain a characterization of the dual space of the
noncommutative martingale Hardy space $\h_p$ ($0<p<1$) as a noncommutative
Lipschitz space via the weak form of the atomic decomposition. Our constructive
method can also be applied to proving some sharp martingale inequalities.


  Stabilization of equilibrium solution to parabolic like equations via
proportional boundary feedbacks.


  As part of the ML Reproducibility Challenge 2020, we investigated the ICML
2020 paper "Learning De-biased Representations with Biased Representations" by
Bahng et al., where the authors formalize and attempt to tackle the so called
"cross bias generalization" problem with a new approach they introduce called
ReBias. This report contains results of our attempts at reproducing the work in
the application area of Image Recognition, specifically on the datasets biased
MNIST and ImageNet. We compare ReBias with other methods - Vanilla, Biased,
RUBi (as implemented by the authors), and conclude with a discussion concerning
the validity of the claims made by the paper. We were able to reproduce results
reported for the biased MNIST dataset to within 1% of the original values
reported in the paper. Like the authors, we report results averaged over 3
runs. However, in a later section, we provide some additional results that
appear to weaken the central claim of the paper with regards to the biased
MNIST dataset. We were not able to reproduce results for ImageNet as in the
original paper, but based on communication with the authors, provide a
discussion as to the reasons for the same. This work attempts to be useful to
other researchers aiming to use ReBias for their own research purposes,
advising on certain possible pitfalls that may be encountered in the process.


  We examine the wavelength dependence of radial light profiles based on
S\'ersic index $n$ measurements of 1067 galaxies with M$_*\geq$
10$^{9.5}$M$_\odot$ and in the redshift range $0.5 < z < 3$. The sample and
rest-frame optical light profiles are drawn from CANDELS$+$3D-HST; rest-frame
near-infrared light profiles are inferred from CEERS JWST/NIRCam imaging. $n$
shows only weak dependence on wavelength, regardless of redshift, galaxy mass
and type: on average, star-forming galaxies have $n = 1-1.5$ and quiescent
galaxies have $n = 3-4$ in the rest-frame optical and near-infrared. The strong
correlation at all wavelengths between $n$ and star-formation activity implies
a physical connection between the radial stellar mass profile and
star-formation activity. The main caveat is that the current sample is too
small to discern trends for the most massive galaxies (M$_* > 10^{11}M_\odot$).


  The existence of nonzero localised periodic solutions for general
one-dimensional discrete nonlinear Klein-Gordon systems with convex on-site
potentials is proved. The existence problem of localised solutions is expressed
in terms of a fixed point equation for an operator on some appropriate function
space which is solved by means of Schauder's Fixed Point Theorem.


  We apply the theory of Lie point symmetries for the study of a family of
partial differential equations which are integrable by the hyperbolic
reductions method and are reduced to members of the Painlev\'{e} transcendents.
The main results of this study is that from the application of the similarity
transformations provided by the Lie point symmetries all the members of the
family of the partial differential equations are reduced to second-order
differential equations which are maximal symmetric and can be linearized.


  We prove the "existence of a piece of Scri near $i^0$" (with most likely poor
differentiability of the conformally rescaled metric) for general
asymptotically flat data with well-defined energy-momentum. The proof uses
scaling and a gluing construction to reduce the problem to Bieri's stability
theorem.


  In this manuscript, we introduce the notion of fundamental cases to study the
unitary dual of $U(p,q)$. As applications, we prove of a conjecture of
Salamanca-Riba and Vogan stated in 1998, as well as the fundamental
parallelepiped (FPP) conjecture of Vogan in 2023 for $U(p,q)$.


  Evaluation of a product integral with values in the Lie group SU(1,1) yields
the explicit solution to the impedance form of the Schr\"odinger equation.
Explicit formulas for the transmission coefficient and $S$-matrix of the
classical one-dimensional Schr\"odinger operator with arbitrary compactly
supported potential are obtained as a consequence. The formulas involve
operator theoretic analogues of the standard hyperbolic functions, and provide
a new window on acoustic and quantum scattering in one dimension.


  In a recent paper, Bilu et al. studied a conjecture of Marques and Lengyel on
the $p$-adic valuation of the Tribonacci sequence. In this article, we do a
similar study on the $p$-adic valuation of third order linear recurrence
sequences by considering a generalisation of the conjecture of Marques and
Lengyel for third order linear recurrence sequences. We obtain analogues of the
results of Bilu et al. for certain third order linear recurrence sequences.
Also, as a consequence of the conjecture, we prove that the solution set of the
Diophantine equation given by $x_n=m!$ in positive integers $n,m$ is finite for
certain third order linear recurrence sequences $(x_n)$.


  We study percolation in the following random environment: let $Z$ be a
Poisson process of constant intensity in the plane, and form the Voronoi
tessellation of the plane with respect to $Z$. Colour each Voronoi cell black
with probability $p$, independently of the other cells. We show that the
critical probability is 1/2. More precisely, if $p>1/2$ then the union of the
black cells contains an infinite component with probability 1, while if $p<1/2$
then the distribution of the size of the component of black cells containing a
given point decays exponentially. These results are analogous to Kesten's
results for bond percolation in the square lattice.
  The result corresponding to Harris' Theorem for bond percolation in the
square lattice is known: Zvavitch noted that one of the many proofs of this
result can easily be adapted to the random Voronoi setting. For Kesten's
results, none of the existing proofs seems to adapt. The methods used here also
give a new and very simple proof of Kesten's Theorem for the square lattice; we
hope they will be applicable in other contexts as well.


  The majority of systems rely on user authentication on passwords, but
passwords have so many weaknesses and widespread use that easily raise
significant security concerns, regardless of their encrypted form. Users hold
the same password for different accounts, administrators never check password
files for flaws that might lead to a successful cracking, and the lack of a
tight security policy regarding regular password replacement are a few problems
that need to be addressed. The proposed research work aims at enhancing this
security mechanism, prevent penetrations, password theft, and attempted
break-ins towards securing computing systems. The selected solution approach is
two-folded; it implements a two-factor authentication scheme to prevent
unauthorized access, accompanied by Honeyword principles to detect corrupted or
stolen tokens. Both can be integrated into any platform or web application with
the use of QR codes and a mobile phone.


  The extraction of brain functioning features is a crucial step in the
definition of brain-computer interfaces (BCIs). In the last decade, functional
connectivity (FC) estimators have been increasingly explored based on their
ability to capture synchronization between multivariate brain signals. However,
the underlying neurophysiological mechanisms and the extent to which they can
improve performance in BCI-related tasks, is still poorly understood. To
address this gap in knowledge, we considered a group of 20 healthy subjects
during an EEG-based hand motor imagery (MI) task. We studied two
well-established FC estimators, i.e. spectral- and imaginary-coherence, and
investigated how they were modulated by the MI task. We characterized the
resulting FC networks by extracting the strength of connectivity of each EEG
sensor and compared the discriminant power with respect to standard power
spectrum features. At the group level, results showed that while
spectral-coherence based network features were increasing the controlateral
motor area, those based on imaginary-coherence were decreasing. We demonstrated
that this opposite, but complementary, behavior was respectively determined by
the increase in amplitude and phase synchronization between the brain signals.
At the individual level, we proved that including these network connectivity
features in the classification of MI mental states led to an overall
improvement in accuracy. Taken together, our results provide fresh insights
into the oscillatory mechanisms subserving brain network changes during MI and
offer new perspectives to improve BCI performance.


  Charmed meson decays into a pseudoscalar meson P and a tensor meson T are
studied. The charm to tensor meson transition form factors are evaluated in the
Isgur-Scora-Grinstein-Wise (ISGW) quark model. It is shown that the
Cabibbo-allowed decay $D_s^+\to f_2(1270)\pi^+$ is dominated by the
W-annihilation contribution and has the largest branching ratio in $D\to TP$
decays. We argue that the Cabibbo-suppressed mode $D^+\to f_2(1270)\pi^+$
should be suppressed by one order of magnitude relative to $D_s^+\to
f_2(1270)\pi^+$. When the finite width effect of the tensor resonances is taken
into account, the decay rate of $D\to TP$ is generally enhanced by a factor of
$2\sim 3$. Except for $D_s^+\to f_2(1270)\pi^+$, the predicted branching ratios
of $D\to TP$ decays are in general too small by one to two orders of magnitude
compared to experiment. However, it is very unlikely that the $D\to T$
transition form factors can be enhanced by a factor of $3\sim 5$ within the
ISGW quark model to account for the discrepancy between theory and experiment.
As many of the current data are still preliminary and lack sufficient statistic
significance, more accurate measurements are needed to pin down the issue.


  Automated story generation is the problem of automatically selecting a
sequence of events, actions, or words that can be told as a story. We seek to
develop a system that can generate stories by learning everything it needs to
know from textual story corpora. To date, recurrent neural networks that learn
language models at character, word, or sentence levels have had little success
generating coherent stories. We explore the question of event representations
that provide a mid-level of abstraction between words and sentences in order to
retain the semantic information of the original data while minimizing event
sparsity. We present a technique for preprocessing textual story data into
event sequences. We then present a technique for automated story generation
whereby we decompose the problem into the generation of successive events
(event2event) and the generation of natural language sentences from events
(event2sentence). We give empirical results comparing different event
representations and their effects on event successor generation and the
translation of events to natural language.


  The advent of Web 3.0, claiming for personalization in interactive systems
(Lassila & Hendler, 2007), and the need for systems capable of interacting in a
more natural way in the future society flooded with computer systems and
devices (Harper et al., 2008) show that great advances in HCI should be done.
This chapter presents some contributions of LIA for the future of HCI,
defending that using common sense knowledge is a possibility for improving HCI,
especially because people assign meaning to their messages based on their
common sense and, therefore, the use of this knowledge in developing user
interfaces can make them more intuitive to the end-user. Moreover, as common
sense knowledge varies from group to group of people, it can be used for
developing applications capable of giving different feedback for different
target groups, as the applications presented along this chapter illustrate,
allowing, in this way, interface personalization taking into account cultural
issues. For the purpose of using common sense knowledge in the development and
design of computer systems, it is necessary to provide an architecture that
allows it. This chapter presents LIAs approaches for common sense knowledge
acquisition, representation and use, as well as for natural language
processing, contributing with those ones who intent to get into this
challenging world to get started.


  We study a notion of local time for a continuous path, defined as a limit of
suitable discrete quantities along a general sequence of partitions of the time
interval. Our approach subsumes other existing definitions and agrees with the
usual (stochastic) local times a.s. for paths of a continuous semimartingale.
We establish pathwise version of the It\^o-Tanaka, change of variables and
change of time formulae. We provide equivalent conditions for existence of
pathwise local time. Finally, we study in detail how the limiting objects, the
quadratic variation and the local time, depend on the choice of partitions. In
particular, we show that an arbitrary given non-decreasing process can be
achieved a.s. by the pathwise quadratic variation of a standard Brownian motion
for a suitable sequence of (random) partitions; however, such degenerate
behavior is excluded when the partitions are constructed from stopping times.


  Model predictive control (MPC) provides a useful means for controlling
systems with constraints, but suffers from the computational burden of
repeatedly solving an optimization problem in real time. Offline (explicit)
solutions for MPC attempt to alleviate real time computational challenges using
either multiparametric programming or machine learning. The multiparametric
approaches are typically applied to linear or quadratic MPC problems, while
learning-based approaches can be more flexible and are less memory-intensive.
Existing learning-based approaches offer significant speedups, but the
challenge becomes ensuring constraint satisfaction while maintaining good
performance. In this paper, we provide a neural network parameterization of MPC
policies that explicitly encodes the constraints of the problem. By exploring
the interior of the MPC feasible set in an unsupervised learning paradigm, the
neural network finds better policies faster than projection-based methods and
exhibits substantially shorter solve times. We use the proposed policy to solve
a robust MPC problem, and demonstrate the performance and computational gains
on a standard test system.


  During Eugene Garfield's (EG's) lengthy career as information scientist, he
published about 1,500 papers. In this study, we use the impressive oeuvre of EG
to introduce a new type of bibliometric networks: keyword co-occurrences
networks based on the context of citations, which are referenced in a certain
paper set (here: the papers published by EG). The citation context is defined
by the words which are located around a specific citation. We retrieved the
citation context from Microsoft Academic. To interpret and compare the results
of the new network type, we generated two further networks: co-occurrence
networks which are based on title and abstract keywords from (1) EG's papers
and (2) the papers citing EG's publications. The comparison of the three
networks suggests that papers of EG and citation contexts of papers citing EG
are semantically more closely related to each other than to titles and
abstracts of papers citing EG. This result accords with the use of citations in
research evaluation that is based on the premise that citations reflect the
cognitive influence of the cited on the citing publication.


  We propose a measure of divergence of probability distributions for
quantifying the dissimilarity of two chaotic attractors. This measure is
defined in terms of a generalized entropy. We illustrate our procedure by
considering the effect of additive noise in the well known H\'enon attractor.
Comparison of two H\'enon attractors for slighly different parameter values,
has shown that the divergence has complex scaling structure. Finally, we show
how our approach allows to detect non-stationary events in a time series.


  Motivated by recent experiments with two-component Bose-Einstein condensates,
we study fully-connected spin models subject to an additional constraint. The
constraint is responsible for the Hilbert space dimension to scale only
linearly with the system size. We discuss the unconventional statistical
physical and thermodynamic properties of such a system, in particular the
absence of concentration of the underlying probability distributions. As a
consequence, expectation values are less suitable to characterize such systems,
and full distribution functions are required instead. Sharp signatures of phase
transitions do not occur in such a setting, but transitions from singly peaked
to doubly peaked distribution functions of an "order parameter" may be present.


  We investigate effects of D-term contributions to the mixed modulus-anomaly
mediated supersymmetry breaking scenario. In the original scenario, the
tachyonic slepton problem in the pure anomaly mediated supersymmetry breaking
is cured by modulus contributions. We generalize the scenario so as to include
contributions from the D-terms of U(1)_Y and the gauged U(1)_{B-L} which is
motivated in a grand unified theory based on a higher rank gauge group such as
SO(10). As a consequence of additional $D$-term contributions to scalar masses,
we obtain various soft supersymmetry breaking mass spectra, which are different
from those obtained in the conventional mixed modulus-anomaly mediated
supersymmetry breaking. Especially, we find that the lightest superpartner
(LSP) neutralinos can be various types, such as Higgsino-like, wino-like and
bino-like degenerating with the next LSP sfermions.


  We present a very sensitive and scalable method to measure the population of
highly excited Rydberg states in a thermal vapor cell of rubidium atoms. We
detect the Rydberg ionization current in a 5 mm electrically contacted cell.
The measured current is found to be in excellent agreement with a theory for
the Rydberg population based on a master equation for the three level problem
including an ionization channel and the full Doppler distributions at the
corresponding temperatures. The signal-to-noise ratio of the current detection
is substantially better than purely optical techniques.


  Dunsiger and co-workers have criticised our paper on magnetic monopole
dynamics spin ice [S. T. Bramwell et al., Nature, 461 956 (2009)]. We consider
their criticisms and results but show that these do not warrant any revision of
our earlier conclusions. In contrast, we point out that their conclusion of a
`new' type of spin dynamics in spin ice is inconsistent with established facts.


  We present an encompassing treatment of D-brane charges in supersymmetric
SO(3) WZW models. There are two distinct supersymmetric CFTs at each even
level: the standard bosonic SO(3) modular invariant tensored with free
fermions, as well as a novel twisted model. We calculate the relevant twisted
K-theories and find complete agreement with the CFT analysis of D-brane
charges. The K-theoretical computation in particular elucidates some important
aspects of N=1 supersymmetric WZW models on non-simply connected Lie groups.


  Misclassification of medicine is perilous to the health of a patient, more so
if the said patient is visually impaired or simply did not recognize the color,
shape or type of medicine strip. This paper proposes a method for
identification of medicine strips by 2-D cepstral analysis of their images
followed by performing classification that has been done using the K-Nearest
Neighbor (KNN), Support Vector Machine (SVM) and Logistic Regression (LR)
Classifiers. The 2-D cepstral features extracted are extremely distinct to a
medicine strip and consequently make identifying them exceptionally accurate.
This paper also proposes the Color Gradient and Pill shape Feature (CGPF)
extraction procedure and discusses the Binary Robust Invariant Scalable
Keypoints (BRISK) algorithm as well. The mentioned algorithms were implemented
and their identification results have been compared.


  The one-band extended Hubbard model in two dimensions near band-filling 1/2
is solved in the fluctuation exchange approximation, including the long-range
(1/r) part of the Coulomb interaction, up to 4th neighbor distance. Our results
suggest that d_(x^2 - y^2) pairing in the Hubbard model is robust against the
inclusion of long-range Coulomb interactions with moderate 1st neighbor
repulsion strength V_1. d_(x^2 - y^2) pairing is suppressed only at large V_1
(>~ 0.25U-0.4U), due to incipient charge density wave instabilities.


  Even though making artificial micrometric swimmers has been made possible by
using various propulsion mechanisms, guiding their motion in the presence of
thermal fluctuations still remains a great challenge. Such a task is essential
in biological systems, which present a number of intriguing solutions that are
robust against noisy environmental conditions as well as variability in
individual genetic makeup. Using synthetic Janus particles driven by an
electric field, we present a feedback-based particle guiding method, quite
analogous to the "run-and-tumbling" behavior of Escherichia coli but with a
deterministic steering in the tumbling phase: the particle is set to the "run"
state when its orientation vector aligns with the target, while the transition
to the "steering" state is triggered when it exceeds a tolerance angle
{\alpha}. The active and deterministic reorientation of the particle is
achieved by a characteristic rotational motion that can be switched on and off
by modulating the AC frequency of the electric field, first reported in this
work. Relying on numerical simulations and analytical results, we show that
this feedback algorithm can be optimized by tuning the tolerance angle
{\alpha}. The optimal resetting angle depends on signal to noise ratio in the
steering state, and it is demonstrated in the experiment. Proposed method is
simple and robust for targeting, despite variability in self-propelling speeds
and angular velocities of individual particles.


  In the context of eternal inflation, cosmological predictions depend on the
choice of measure to regulate the diverging spacetime volume. The spectrum of
inflationary perturbations is no exception, as we demonstrate by comparing the
predictions of the fat geodesic and causal patch measures. To highlight the
effect of the measure---as opposed to any effects related to a possible
landscape of vacua---we take the cosmological model, including the model of
inflation, to be fixed. We also condition on the average CMB temperature
accompanying the measurement. Both measures predict a 1-point expectation value
for the gauge-invariant Newtonian potential, which takes the form of a
(scale-dependent) monopole, in addition to a related contribution to the
3-point correlation function, with the detailed form of these quantities
differing between the measures. However, for both measures both effects are
well within cosmic variance. Our results make clear the theoretical relevance
of the measure, and at the same time validate the standard inflationary
predictions in the context of eternal inflation.


  This paper considers the optimal scaling problem for high-dimensional random
walk Metropolis algorithms for densities which are differentiable in Lp mean
but which may be irregular at some points (like the Laplace density for
example) and/or are supported on an interval. Our main result is the weak
convergence of the Markov chain (appropriately rescaled in time and space) to a
Langevin diffusion process as the dimension d goes to infinity. Because the
log-density might be non-differentiable, the limiting diffusion could be
singular. The scaling limit is established under assumptions which are much
weaker than the one used in the original derivation of [6]. This result has
important practical implications for the use of random walk Metropolis
algorithms in Bayesian frameworks based on sparsity inducing priors.


  Magnetic Resonance Imaging (MRI) has evolved as a clinical standard-of-care
imaging modality for cardiac morphology, function assessment, and guidance of
cardiac interventions. All these applications rely on accurate extraction of
the myocardial tissue and blood pool from the imaging data. Here we propose a
framework for left ventricle (LV) segmentation from cardiac cine-MRI. First, we
segment the LV blood pool using iterative graph cuts, and subsequently use this
information to segment the myocardium. We formulate the segmentation procedure
as an energy minimization problem in a graph subject to the shape prior
obtained by label propagation from an average atlas using affine registration.
The proposed framework has been validated on 30 patient cardiac cine-MRI
datasets available through the STACOM LV segmentation challenge and yielded
fast, robust, and accurate segmentation results.


  Observations of low-metallicity halo stars have revealed a puzzling result:
the abundance of \li7 in these stars is at least three times lower than their
predicted primordial abundance. It is unclear whether the cause of this
disagreement is a lack of understanding of lithium destruction mechanisms in
stars or the non-standard physics behind the Big Bang Nucleosynthesis (BBN).
Uncertainties related to the destruction of lithium in stars can be
circumvented if lithium abundance is measured in the "pristine" gas of the low
metallicity systems. The first measurement in one such system, the Small
Magellanic Cloud (SMC), was found to be at the level of the pure expected
primordial value, but is on the other hand, just barely consistent with the
expected galactic abundance for the system at the SMC metallicity, where
important lithium quantity was also produced in interactions of galactic cosmic
rays (GCRs) and presents an addition to the already present primordial
abundance. Due to the importance of the SMC lithium measurement for the
resolution of the lithium problem, we here draw attention to the possibility of
another post-BBN production channel of lithium, which could present an
important addition to the observed SMC lithium abundance. Besides standard
galactic cosmic rays, additional post-BBN production of lithium might come from
cosmic rays accelerated in galaxy-galaxy interactions. This might be important
for a system such is the SMC, which has experienced galaxy harassment in its
history...(abridged)


  It is not always clear how to adjust for control data in causal inference,
balancing the goals of reducing bias and variance. We show how, in a setting
with repeated experiments, Bayesian hierarchical modeling yields an adaptive
procedure that uses the data to determine how much adjustment to perform. The
result is a novel analysis with increased statistical efficiency compared to
the default analysis based on difference estimates. We demonstrate this
procedure on two real examples, as well as on a series of simulated datasets.
We show that the increased efficiency can have real-world consequences in terms
of the conclusions that can be drawn from the experiments. We also discuss the
relevance of this work to causal inference and statistical design and analysis
more generally.


  We analyze two-color spatially localized modes formed by parametrically
coupled fundamental and second-harmonic fields excited at quadratic (or chi-2)
nonlinear interfaces embedded into a linear layered structure --- a
quasi-one-dimensional quadratic nonlinear photonic crystal. For a periodic
lattice of nonlinear interfaces, we derive an effective discrete model for the
amplitudes of the fundamental and second-harmonic waves at the interfaces (the
so-called discrete chi-2 equations), and find, numerically and analytically,
the spatially localized solutions --- discrete gap solitons. For a single
nonlinear interface in a linear superlattice, we study the properties of
two-color localized modes, and describe both similarities and differences with
quadratic solitons in homogeneous media.


  We have developed a model in which the quantum fluctuations of the proton
structure are characterised by hot spots, whose number grows with decreasing
Bjorken-$x$. Our model reproduces the $F_2(x,Q^2)$ data from HERA at the
relevant scale, as well as the exclusive and dissociative $\mathrm{J/}\psi$
photoproduction data from H1 and ALICE. Our model predicts that for
$W_{\gamma\mathrm{p}} \approx 500$ GeV, the dissociative $\mathrm{J/}\psi$
cross section reaches a maximum and then decreases steeply with energy, which
is in qualitatively good agreement to a recent observation that the
dissociative $\mathrm{J/}\psi$ background in the exclusive $\mathrm{J/}\psi$
sample measured in photoproduction by ALICE decreases as energy increases. Our
prediction provides a clear signature for gluon saturation at LHC energies.


  This study actually draws from and builds on an earlier paper (Kumar and
Bhattacharya, 2002). Here we have basically added a neutrosophic dimension to
the problem of determining the conditional probability that a financial fraud
has been actually committed, given that no Type I error occurred while
rejecting the null hypothesis H0: The observed first-digit frequencies
approximate a Benford distribution; and accepting the alternative hypothesis
H1: The observed first-digit frequencies do not approximate a Benford
distribution. We have also suggested a conceptual model to implement such a
neutrosophic fraud detection system.


  We discuss the escape rate of the Brownian motion on a hyperbolic space. We
point out that the escape rate is determined by using the Brownian expression
of the radial part and a generalized Kolmogorov's test for the one dimensional
Brownian motion.


  In this paper, we investigate the distributed convex optimization problem
over a multi-agent system with Markovian switching communication networks. The
objective function is the sum of each agent's local objective function, which
cannot be known by other agents. The communication network is assumed to switch
over a set of weight-balanced directed graphs with a Markovian property.We
propose a consensus sub-gradient algorithm with two time-scale step-sizes to
handle the uncertainty due to the Markovian switching topologies and the
absence of global gradient information. With a proper selection of step-sizes,
we prove the almost sure convergence of all agents' local estimates to the same
optimal solution when the union graph of the Markovian network' states is
strongly connected and the Markovian network is irreducible. Simulations are
given for illustration of the results.


  We present a broad study of collider processes that embed $2 \to 2$
scattering amplitudes involving top quarks in the Electroweak sector. We
parametrise the modified interactions using the Standard Model Effective Field
Theory framework and discuss how the New Physics effects lead to unitarity
violating behaviour at the amplitude level. For each scattering amplitude we
compute the helicity amplitudes in the high energy limit paying special
attention to the effects of the higher dimensional operators. We also discuss
whether and to what extent the unitarity violating effects are retained in
physical processes at colliders.


  By the use of the gauge/gravity duality, we calculate the imaginary part of
heavy quarkonium potential and thermal width with the effect of gluon
condensate which is absent in AdS$_{5}$ background. Our results show that the
dropping gluon condensate reduces the absolute value of imaginary potential and
therefore decreases the thermal width both in "exact" and "approximate"
approach implying that the heavy quarkonium has a weaker bound with the
increase of gluon condensate. In addition, the thermal width will disappear at
a critical condensate value, which indicates the dissociation of quarkonium. We
conclude that increasing gluon condensate will lead to easier dissociation of
heavy quarkonium for fixed temperature.


  Magnetic nanoparticles have emerged as a promising approach to improving
cancer treatment. However, many novel nanoparticle designs fail in clinical
trials due to a lack of understanding of how to overcome the in vivo transport
barriers. To address this shortcoming, we develop a novel computational model
aimed at the study of magnetic nanoparticles in vitro and in vivo. In this
paper, we present an important building block for this overall goal, namely an
efficient computational model of the in-flow capture of magnetic nanoparticles
by a cylindrical permanent magnet in an idealised test setup. We use a
continuum approach based on the Smoluchowski advection-diffusion equation,
combined with a simple approach to consider the capture at an impenetrable
boundary, and derive an analytical expression for the magnetic force of a
cylindrical magnet of finite length on the nanoparticles. This provides a
simple and numerically efficient way to study different magnet configurations
and their influence on the nanoparticle distribution in three dimensions. Such
an in silico model can increase insight into the underlying physics, help to
design novel prototypes and serve as a precursor to more complex systems in
vivo and in silico.


  In this paper, we construct a winning condition $W$ over a finite set of
colors such that, first, every finite arena has a strategy with 2 states of
general memory which is optimal w.r.t.~$W$, and second, there exists no $k$
such that every finite arena has a strategy with $k$ states of chromatic memory
which is optimal w.r.t.~$W$.


  We study experimentally the reproducible conductance fluctuations between the
quantum Hall plateaus in the conductance of two-terminal submicron silicon
MOSFETs. For the dramatic fluctuations at the insulator-to-first-plateau
transition we find a conductance distribution that is approximately uniform
between zero and $e^2/h$. We point out that this is consistent with the
prediction of random $S$-matrix theory for a conductor with single-channel
leads in a magnetic field.


  Multimodal registration is a challenging problem in medical imaging due the
high variability of tissue appearance under different imaging modalities. The
crucial component here is the choice of the right similarity measure. We make a
step towards a general learning-based solution that can be adapted to specific
situations and present a metric based on a convolutional neural network. Our
network can be trained from scratch even from a few aligned image pairs. The
metric is validated on intersubject deformable registration on a dataset
different from the one used for training, demonstrating good generalization. In
this task, we outperform mutual information by a significant margin.


  In addition to the emission of gravitational waves (GWs) the coalescence and
merger of two neutron stars will produce a variety of electromagnetic (EM)
signals. In this work we combine a large set of numerical relativity
simulations performed by different groups and we present fits for the mass,
kinetic energy, and the velocities of the dynamical ejected material.
Additionally, we comment on the geometry and composition of the ejecta and
discuss the influence of the stars' individual rotation.
  The derived fits can be used to approximate the luminosity and lightcurve of
the kilonovae (macronovae) and to estimate the main properties of the radio
flares. This correlation between the binary parameters and the EM signals
allows in case of a GW detection to approximate possible EM counterparts when
first estimates of the masses are available. After a possible kilonovae
observation our results could also be used to restrict the region of the
parameter space which has to be covered by numerical relativity simulations.


  A nonlinearly generalized Camassa-Holm equation, depending an arbitrary
nonlinearity power $p \neq 0$, is considered. This equation reduces to the
Camassa-Holm equation when $p=1$ and shares one of the Hamiltonian structures
of the Camassa-Holm equation. Two main results are obtained. A classification
of point symmetries is presented and a peakon solution is derived, for all
powers $p \neq 0$.


  We study the energy gap opening in the electronic spectrum of graphene
bilayers caused by asym- metric doping. Both substitutional impurities (boron
acceptors and nitrogen donors) and adsorbed potassium donors are considered.
The gap evolution with dopant concentration is compared to the situation in
which the asymmetry between the layers is induced by an external electric
field. The effects of adsorbed potassium are similar to that of an electric
field, but substitutional impurities behave quite differently, showing smaller
band gaps and a large sensitivity to disorder and sublattice occupation.


  We study the phase diagram of a one-dimensional balls-in-boxes (BIB) model
that has been proposed as an effective model for the spatial-volume dynamics of
(2+1)-dimensional causal dynamical triangulations (CDT). The latter is a
statistical model of random geometries and a candidate for a nonperturbative
formulation of quantum gravity, and it is known to have an interesting phase
diagram, in particular including a phase of extended geometry with classical
properties. Our results corroborate a previous analysis suggesting that a
particular type of potential is needed in the BIB model in order to reproduce
the droplet condensation typical of the extended phase of CDT. Since such a
potential can be obtained by a minisuperspace reduction of a (2+1)-dimensional
gravity theory of the Ho\v{r}ava-Lifshitz type, our result strengthens the link
between CDT and Ho\v{r}ava-Lifshitz gravity.


  A q-difference analogue of the Painlev\'e III equation is considered. Its
derivations, affine Weyl group symmetry, and two kinds of special function type
solutions are discussed.


  We discuss the role of two different types of diagram in the proton-proton
double parton scattering (DPS) cross section - single and double perturbative
splitting graphs. Using explicit calculations of simple graphs from these
classes we show that the treatment of these graphs by the 'double PDF'
framework for describing the DPS cross section, introduced a number of years
ago by Snigirev and collaborators, is unsatisfactory. We suggest that a
contribution from single perturbative splitting graphs should be included in
the DPS cross section, albeit with a different geometrical prefactor to the
contribution from 'zero perturbative splitting' graphs.


  In the Intriligator-Seiberg-Shih model, we parametrize spontaneous breaking
of $U(1)_R$ symmetry with two gauge singlets with R-charges 1 and --1. These
singlets can play the role of the messengers. The messenger scale is
dynamically generated, and hence there is no hierarchy problem between the
supersymmetry breaking scale and the messenger scale. In the gauge mediation
scenario, supersymmetry breaking scale turns out to be around
$\mathcal{O}(10^6)\textrm{GeV}$.