  We consider the task of learning a dynamical system from high-dimensional
time-course data. For instance, we might wish to estimate a gene regulatory
network from gene expression data measured at discrete time points. We model
the dynamical system non-parametrically as a system of additive ordinary
differential equations. Most existing methods for parameter estimation in
ordinary differential equations estimate the derivatives from noisy
observations. This is known to be challenging and inefficient. We propose a
novel approach that does not involve derivative estimation. We show that the
proposed method can consistently recover the true network structure even in
high dimensions, and we demonstrate empirical improvement over competing
approaches.


  The stability of a quasicrystalline structure, recently obtained in a
molecular-dynamics simulation of rapid cooling of a binary melt, is analyzed
for binary hard-sphere mixtures within a density-functional approach. It is
found that this quasicrystal is metastable relative to crystalline and fluid
phases for diameter ratios above 0.83. Such trend is partially reversed for
lower diameter ratios, since the quasicrystal becomes stable with respect to
the crystal but does not reach a coexistence with the fluid.


  Well-motivated electroweak dark matter is often hosted by an extended
electroweak sector which also contains new lepton pairs with masses near the
weak scale. In this paper, we explore such electroweak dark matter via
combining dark matter direct detections and high-luminosity LHC probes of new
lepton pairs. Using $Z$- and $W$-associated electroweak processes with two or
three lepton final states, we show that dependent on the overall coupling
constant, dark matter mass up to $170-210$ GeV can be excluded at $2\sigma$
level and up to $175-205$ GeV can be discovered at $5\sigma$ level at the 14
TeV LHC with integrated luminosities 300 fb$^{-1}$ and 3000 fb$^{-1}$,
respectively.


  The compounds $A_2$[FeCl$_5$(H$_2$O)] with $A=$ K, Rb, Cs are identified as
new linear magnetoelectric materials. We present a detailed investigation of
their linear magnetoelectric properties by measurements of pyroelectric
currents, dielectric constants and magnetization. The anisotropy of the linear
magnetoelectric effect of the K-based and Rb-based compound is consistent with
the magnetic point group $m'm'm'$, already reported in literature. A symmetry
analysis of the magnetoelectric effect of the Cs-based compound allows to
determine the magnetic point group $mmm'$ and to develop a model for its
magnetic structure. In addition, magnetic-field versus temperature phase
diagrams are derived and compared to the closely related multiferroic
(NH$_4$)$_2$[FeCl$_5$(H$_2$O)].


  The ring configurations for classical two-dimensional atoms are calculated
within the Thomson model and compared with the results from `exact' numerical
simulations. The influence of the functional form of the confinement potential
and the repulsive interaction potential between the particles on the
configurations is investigated. We also give exact results on those eigenmodes
of the system whose frequency does not depend on the number of particles in the
system.


  This paper introduces a novel control framework for Lagrangian variable speed
limits in hybrid traffic flow environments utilizing automated vehicles (AVs).
The framework was validated using a fleet of 100 connected automated vehicles
as part of the largest coordinated open-road test designed to smooth traffic
flow. The framework includes two main components: a high-level controller
deployed on the server side, named Speed Planner, and low-level controllers
called vehicle controllers deployed on the vehicle side. The Speed Planner
designs and updates target speeds for the vehicle controllers based on
real-time Traffic State Estimation (TSE) [1]. The Speed Planner comprises two
modules: a TSE enhancement module and a target speed design module. The TSE
enhancement module is designed to minimize the effects of inherent latency in
the received traffic information and to improve the spatial and temporal
resolution of the input traffic data. The target speed design module generates
target speed profiles with the goal of improving traffic flow. The vehicle
controllers are designed to track the target speed meanwhile responding to the
surrounding situation. The numerical simulation indicates the performance of
the proposed method: the bottleneck throughput has increased by 5.01%, and the
speed standard deviation has been reduced by a significant 34.36%. We further
showcase an operational study with a description of how the controller was
implemented on a field-test with 100 AVs and its comprehensive effects on the
traffic flow.


  Anisotropic bursts of gravitational radiation produced by events such as
super-massive black hole mergers leave permanent imprints on space. Such
gravitational wave "memory" (GWM) signals are, in principle, detectable through
pulsar timing as sudden changes in the apparent pulse frequency of a pulsar. If
an array of pulsars is monitored as a GWM signal passes over the Earth, the
pulsars would simultaneously appear to change pulse frequency by an amount that
varies with their sky position in a quadrupolar fashion. Here we describe a
search algorithm for such events and apply the algorithm to approximately six
years of data from the Parkes Pulsar Timing Array. We find no GWM events and
set an upper bound on the rate for events which could have been detected. We
show, using simple models of black hole coalescence rates, that this
non-detection is not unexpected.


  We construct a quantum system of spherical spins with a continuous local
symmetry. The model is exactly soluble in the thermodynamic limit and exhibits
a number of interesting properties. We show that the local symmetry is
spontaneously broken at finite as well as zero temperatures, implying the
existence of classical and quantum phase transitions with a nontrivial critical
behavior. The dynamical generation of gauge fields and the equivalence with the
$CP^{(\mathcal{N}-1)}$ model in the limit $\mathcal{N}\rightarrow\infty$ are
investigated. The dynamical generation of gauge fields is a consequence of the
restoration of the local symmetry.


  The low redshift Universe (z<~0.5) is not a dull place. Processes leading to
the suppression of star formation and morphological transformation are
prevalent: this is particularly evident in the dramatic upturn in the fraction
of S0-type galaxies in clusters. However, until now, the process and
environment of formation has remained unidentified. We present a HST-based
morphological analysis of galaxies in the redshift-space selected group and
field environments at z~0.4. Groups contain a much higher fraction of S0s at
fixed luminosity than the lower density field, with >99.999% confidence. Indeed
the S0 fraction in groups is at least as high as in z~0.4 clusters and X-ray
selected groups, which have more luminous Intra Group Medium (IGM). An 97%
confident excess of S0s at >=0.3Mpc from the group centre at fixed luminosity,
tells us that formation is not restricted to, and possibly even avoids, the
group cores. Interactions with a bright X-ray emitting IGM cannot be important
for the formation of the majority of S0s in the Universe. In contrast to S0s,
the fraction of elliptical galaxies in groups at fixed luminosity is similar to
the field, whilst the brightest ellipticals are strongly enhanced towards the
group centres (>99.999% confidence within 0.3Mpc). We conclude that the group
and sub-group environments must be dominant for the formation of S0 galaxies,
and that minor mergers, galaxy harassment and tidal interactions are the most
likely responsible mechanisms. This has implications not only for the inferred
pre-processing of cluster galaxies, but also for the global morphological and
star formation budget of galaxies: as hierarchical clustering progresses, more
galaxies will be subject to these transformations as they enter the group
environment.


  We show that the low-frequency modes of a sub-Ohmic bosonic heat bath
generate an effective dynamical asymmetry for an intrinsically symmetric
quantum spin -1/2. An initially fully polarized spin first decays towards a
quasiequilibrium determined by the dynamical asymmetry, thereby showing
coherent damped oscillations on the (fast) time scale of the spin splitting. On
top of this, the dynamical asymmetry itself decays on an ultraslow time scale
and vanishes asymptotically since the global equilibrium phase is symmetric. We
quantitatively study the nature of the initial fast decay to the
quasiequilibrium and discuss the features of ultraslow dynamics of the
quasiequilibrium itself. The dynamical asymmetry is more pronounced for smaller
values of the sub-Ohmic exponent and for lower temperatures, which emphasizes
the quantum many-body nature of the effect. The symmetry breaking is related to
the dynamic crossover between coherent and overdamped relaxation of the spin
polarization and is not connected to the localization quantum phase transition.
In addition to this delocalized phase, we identify a novel phase which is
characterized by damped coherent oscillations in the localized phase. This
allows for a sketch of the zero-temperature phase diagram of the sub-Ohmic
spin-boson model with four distinct phases.


  Predictive marker patterns in imaging data are a means to quantify disease
and progression, but their identification is challenging, if the underlying
biology is poorly understood. Here, we present a method to identify predictive
texture patterns in medical images in an unsupervised way. Based on deep
clustering networks, we simultaneously encode and cluster medical image patches
in a low-dimensional latent space. The resulting clusters serve as features for
disease staging, linking them to the underlying disease. We evaluate the method
on 70 T1-weighted magnetic resonance images of patients with different stages
of liver steatosis. The deep clustering approach is able to find predictive
clusters with a stable ranking, differentiating between low and high steatosis
with an F1-Score of 0.78.


  On a manifold or a closed subset of a Euclidean vector space, a retraction
enables to move in the direction of a tangent vector while staying on the set.
Retractions are a versatile tool to perform computational tasks such as
optimization, interpolation, and numerical integration. This paper studies two
known definitions of retraction on a closed subset of a Euclidean vector space,
one being weaker than the other. Specifically, it shows that, in the context of
constrained optimization, the weaker definition should be preferred as it
inherits the main property of the other while being less restrictive.


  We present a simple modification of the Altarelli-Feruglio $A_4$ flavor
symmetry model using a minimal number of parameters congruous with the
symmetries of the original theory. The resulting model is consistent with all
presently known data on neutrino masses and mixings. Furthermore, it makes
testable tight predictions for future experiments aimed at improving the
measurements of $\sin^2\theta_{12}$, $\sin^2\theta_{13}$, $\delta_{\rm CP}$ and
the neutrinoless double-beta decay parameter $|m_{ee}|$. Our model exploits the
unique possibility of multiple allowed, yet qualitatively different,
contractions of fields charged under the $A_4$ discrete symmetry.


  Using the Birmanexact sequence for pure mapping class groups, we construct a
universal Cannon--Thurston map onto the boundary of a curve complex for a
surface with punctures we call surviving curve complex. Along the way we prove
hyperbolicity of this complex and identify its boundary as a space of
laminations. As a corollary we obtain a universal Cannon--Thurston map to the
boundary of the ordinary curve complex, extending earlier work of the second
author with Mj and Schleimer.


  The framework of shifted boundary conditions has proven to be a very powerful
tool for the non-perturbative investigation of thermal quantum field theories.
For instance, it has been successfully considered for the determination of the
equation of state of SU(3) Yang-Mills theory with high accuracy. The set-up can
be generalized to QCD and it is expected to lead to a similar breakthrough. We
present first results for QCD with three flavours of non-perturbatively
O($a$)-improved Wilson fermions and shifted boundary conditions.


  Training and deploying machine learning models that meet fairness criteria
for protected groups are fundamental in modern artificial intelligence. While
numerous constraints and regularization terms have been proposed in the
literature to promote fairness in machine learning tasks, most of these methods
are not amenable to stochastic optimization due to the complex and nonlinear
structure of constraints and regularizers. Here, the term "stochastic" refers
to the ability of the algorithm to work with small mini-batches of data.
Motivated by the limitation of existing literature, this paper presents a
unified stochastic optimization framework for fair empirical risk minimization
based on f-divergence measures (f-FERM). The proposed stochastic algorithm
enjoys theoretical convergence guarantees. In addition, our experiments
demonstrate the superiority of fairness-accuracy tradeoffs offered by f-FERM
for almost all batch sizes (ranging from full-batch to batch size of one).
Moreover, we show that our framework can be extended to the case where there is
a distribution shift from training to the test data. Our extension is based on
a distributionally robust optimization reformulation of f-FERM objective under
$L_p$ norms as uncertainty sets. Again, in this distributionally robust
setting, f-FERM not only enjoys theoretical convergence guarantees but also
outperforms other baselines in the literature in the tasks involving
distribution shifts. An efficient stochastic implementation of $f$-FERM is
publicly available.


  Second-generation theoretical technologies -- heavy quark expansions, QCD sum
rules and QCD simulations on the lattice -- are arriving on the scene, allowing
a treatment of charm decays that is genuinely based on QCD. The availability of
those theoretical tools strengthens the case for the need for comprehensive
precision measurements of charm decays. It is pointed out that the decays of
charm mesons as well as of charm baryons have to be systematically analysed to
gain control over theoretical uncertainties. A $\tau$-charm factory with
$E_{c.m.}\leq 5.5$ GeV is optimally suited for such a program. It would lead to
a deeper understanding of QCD that would also prepare us better for exploiting
the discovery potential anticipated in beauty decays. In addition it is quite
conceivable (though certainly not guaranteed) that there arise fundamental
surprises, such as non-canonical rare $D$ decays, $D^0$-$\bar D^0$ oscillations
and CP violation in charm decays which would dramatically alter our perspective
on Nature's fundamental forces.


  We compute polarization maps for molecular cloud cores modeled as magnetized
singular isothermal toroids, under the assumption that the emitting dust grains
are aspherical and aligned with the large-scale magnetic field. We show that,
depending on the inclination of the toroid with the line-of-sight, the bending
of the magnetic field lines resulting from the need to counteract the inward
pull of gravity naturally produces a depolarization effect toward the centre of
the map. We compute the decrease of polarization degree with increasing
intensity for different viewing angles and frequencies, and we show that an
outward increasing temperature gradient, as expected in starless cores heated
by the external radiation field, enhances the decrease of polarization. We
compare our results with recent observations, and we conclude that this
geometrical effect, together with other mechanisms of depolarization, may
significantly contribute to the decrease of polarization degrees with intensity
observed in the majority of molecular cloud cores. Finally, we consider the
dependence of the polarization degree on the dust temperature gradient
predicted for externally heated clouds, and we briefly comment on the limits of
the Chandrasekhar-Fermi formula to estimate the magnetic field strength in
molecular cloud cores.


  The 256 dimensional M2-brane multiplet contains solitons of many different
intrinsic spins. Using the broken supersymmetry transformations of the
M2-brane, we find supergravity solutions which explicitly display these spins.
This amounts to quantizing the fermionic zero modes and computing the back
reaction on the metric and gauge potential. These spacetime fields are
therefore operator valued and acquire a conventional classical meaning only
after taking expectations in given BPS states. Our spinning spacetimes are not
of the standard Kerr form -- there is a non-vanishing gravitino. Nevertheless,
the solutions have angular momentum and magnetic dipole moments with a g-factor
of 2. We use probe techniques to study scattering of spinning BPS M2-branes.
The static interactions cancel between like-sign branes at leading order, but
there are static spin-spin forces between branes and anti-branes. The general
probe-background Lagrangian contains gravitational spin-spin and magnetic
dipole-dipole forces, as well as gravitino exchanges which allow branes to
change fermion number.


  Using duality theory techniques we derive simple, closed-form formulas for
bounding the optimal revenue of a monopolist selling many heterogeneous goods,
in the case where the buyer's valuations for the items come i.i.d. from a
uniform distribution and in the case where they follow independent (but not
necessarily identical) exponential distributions. We apply this in order to get
in both these settings specific performance guarantees, as functions of the
number of items $m$, for the simple deterministic selling mechanisms studied by
Hart and Nisan [EC 2012], namely the one that sells the items separately and
the one that offers them all in a single bundle.
  We also propose and study the performance of a natural randomized mechanism
for exponential valuations, called Proportional. As an interesting corollary,
for the special case where the exponential distributions are also identical, we
can derive that offering the goods in a single full bundle is the optimal
selling mechanism for any number of items. To our knowledge, this is the first
result of its kind: finding a revenue-maximizing auction in an additive setting
with arbitrarily many goods.


  The interplay between topological defects, such as dislocations or
disclinations, and the electronic degrees of freedom in graphene has been
extensively studied. In the literature, for the study of this kind of problems,
it is in general used either a gauge theory or a curved spatial Riemannian
geometry approach, where, in the geometric case, the information about the
defects is contained in the metric and the spin-connection. However, these
topological defects can also be associated to a Riemann-Cartan geometry where
curvature and torsion plays an important role. In this article we study the
interplay between a wedge dislocations in a planar graphene sheet and the
properties of its electronic degrees of freedom. Our approach relies in its
relation with elasticity theory through the so called elastic-gauge, where
their typical coefficients, as for example the Poisson's ratio, appear directly
in the metric, and consequently also in the electronic spectrum.


  We give a short proof of a conjecture of Lubin concerning certain families of
$p$-adic power series that commute under composition. We prove that if the
family is full (large enough), there exists a Lubin-Tate formal group such that
all the power series in the family are endomorphisms of this group. The proof
uses ramification theory and some $p$-adic Hodge theory.


  The number of Ultra-Diffuse Galaxies (UDGs) in clusters is of significant
importance to constrain models of their formation and evolution. Furthermore,
their distribution inside clusters may tell us something about their
interactions with their environments. In this work we revisit the abundance of
UDGs in a more consistent way than in previous studies. We add new data of UDGs
in eight clusters from the Kapteyn IAC WEAVE INT Clusters Survey (KIWICS),
covering a mass range in which only a few clusters have been studied before,
and complement these with a compilation of works in the literature to
homogeneously study the relation between the number of UDGs and the mass of
their host cluster. Overall, we find that the slope of the number of
UDGs$-$cluster mass relation is consistent with being sublinear when
considering galaxy groups or linear if they are excluded, but we argue that
most likely the behavior is sublinear. When systematically studying the
relation between the projected distance to the innermost UDG and M$_{200}$ for
each cluster, we find hints that favor a picture in which massive clusters
destroy UDGs in their centres.


  Motivated by the recent observation of superconductivity in the pressurized
trilayer La$_4$Ni$_3$O$_{10}$ Ruddlesden-Popper (RP) nickelate, we explore its
structural, electronic, and magnetic properties as a function of hydrostatic
pressure from first-principles calculations. We find that in both the bilayer
and trilayer nickelates, an orthorhombic(monoclinic)-to-tetragonal transition
under pressure takes place concomitantly with the onset of superconductivity.
The electronic structure of La$_4$Ni$_3$O$_{10}$ can be understood using a
molecular trimer basis wherein $n$ molecular subbands arise as the $d_{z^2}$
orbitals hybridize strongly along the $c$-axis within the trilayer. The
magnetic tendencies indicate that the ground state at ambient pressure is
formed by nonmagnetic inner planes and stripe-ordered outer planes that are
antiferromagnetically coupled along the $c$ axis, resulting in an unusual
$\uparrow$, 0, $\downarrow$ stacking that is consistent with the spin density
wave model suggested by neutron diffraction. Such a state is destabilized by
the pressures wherein superconductivity arises. Despite the presence of
$d_{z^2}$ states at the Fermi level, the $d_{x^2-y^2}$ orbitals also play a key
role in the electronic structure of La$_4$Ni$_3$O$_{10}$. This active role of
the $d_{x^2-y^2}$ states in the low-energy physics of the trilayer RP
nickelate, together with the distinct electronic behavior of inner and outer
planes, resembles the physics of multilayer cuprates.


  Large Vision-Language Models (LVLMs) suffer from hallucination issues,
wherein the models generate plausible-sounding but factually incorrect outputs,
undermining their reliability. A comprehensive quantitative evaluation is
necessary to identify and understand the extent of hallucinations in these
models. However, existing benchmarks are often limited in scope, focusing
mainly on object hallucinations. Furthermore, current evaluation methods
struggle to effectively address the subtle semantic distinctions between model
outputs and reference data, as well as the balance between hallucination and
informativeness. To address these issues, we introduce a multi-dimensional
benchmark covering objects, attributes, and relations, with challenging images
selected based on associative biases. Moreover, we propose a large language
model (LLM)-based two-stage evaluation framework that generalizes the popular
CHAIR metric and incorporates both faithfulness and coverage into the
evaluation. Experiments on 10 established LVLMs demonstrate that our evaluation
metric is more comprehensive and better correlated with humans than existing
work when evaluating on our challenging human-annotated benchmark dataset. Our
work also highlights the critical balance between faithfulness and coverage of
model outputs, and encourages future works to address hallucinations in LVLMs
while keeping their outputs informative.


  Data warehousing and OLAP applications must nowadays handle complex data that
are not only numerical or symbolic. The XML language is well-suited to
logically and physically represent complex data. However, its usage induces new
theoretical and practical challenges at the modeling, storage and analysis
levels, and a new trend toward XML warehousing has been emerging for a couple
of years. Unfortunately, no standard XML data warehouse architecture emerges.
In this paper, we propose a unified XML warehouse reference model that
synthesizes and enhances related work, and fits into a global XML warehousing
and analysis approach we have developed. We also present a software platform
that is based on this model, as well as a case study that illustrates its
usage.


  There is a recent and growing literature on large-width asymptotic properties
of Gaussian neural networks (NNs), namely NNs whose weights are initialized as
Gaussian distributions. Two popular problems are: i) the study of the
large-width distributions of NNs, which characterizes the infinitely wide limit
of a rescaled NN in terms of a Gaussian stochastic process; ii) the study of
the large-width training dynamics of NNs, which characterizes the infinitely
wide dynamics in terms of a deterministic kernel, referred to as the neural
tangent kernel (NTK), and shows that, for a sufficiently large width, the
gradient descent achieves zero training error at a linear rate. In this paper,
we consider these problems for $\alpha$-Stable NNs, namely NNs whose weights
are initialized as $\alpha$-Stable distributions with $\alpha\in(0,2]$. First,
for $\alpha$-Stable NNs with a ReLU activation function, we show that if the
NN's width goes to infinity then a rescaled NN converges weakly to an
$\alpha$-Stable stochastic process. As a difference with respect to the
Gaussian setting, our result shows that the choice of the activation function
affects the scaling of the NN, that is: to achieve the infinitely wide
$\alpha$-Stable process, the ReLU activation requires an additional logarithmic
term in the scaling with respect to sub-linear activations. Then, we study the
large-width training dynamics of $\alpha$-Stable ReLU-NNs, characterizing the
infinitely wide dynamics in terms of a random kernel, referred to as the
$\alpha$-Stable NTK, and showing that, for a sufficiently large width, the
gradient descent achieves zero training error at a linear rate. The randomness
of the $\alpha$-Stable NTK is a further difference with respect to the Gaussian
setting, that is: within the $\alpha$-Stable setting, the randomness of the NN
at initialization does not vanish in the large-width regime of the training.


  In the article "Construction of the discrete hull for the combinatorics of a
regular pentagonal tiling of the plane" we gave the construction of a discrete
hull for a combinatorial pentagonal tiling of the plane. In this paper, we give
the construction of a continuous hull for the same combinatorial tiling.


  We describe all connected graphs whose edge ideals are almost normally
torsionfree. We also prove that the facet ideal of a special odd cycle is
almost normally torsionfree. Finally, we determine the t-spread principal Borel
ideals generated in degree 3 which are almost normally torsionfree.


  The halo mass function from N-body simulations of collisionless matter is
generally used to retrieve cosmological parameters from observed counts of
galaxy clusters. This neglects the observational fact that the baryonic mass
fraction in clusters is a random variable that, on average, increases with the
total mass (within an overdensity of 500). Considering a mock catalog that
includes tens of thousands of galaxy clusters, as expected from the forthcoming
generation of surveys, we show that the effect of a varying baryonic mass
fraction will be observable with high statistical significance. The net effect
is a change in the overall normalization of the cluster mass function and a
milder modification of its shape. Our results indicate the necessity of taking
into account baryonic corrections to the mass function if one wants to obtain
unbiased estimates of the cosmological parameters from data of this quality. We
introduce the formalism necessary to accomplish this goal. Our discussion is
based on the conditional probability of finding a given value of the baryonic
mass fraction for clusters of fixed total mass. Finally, we show that combining
information from the cluster counts with measurements of the baryonic mass
fraction in a small subsample of clusters (including only a few tens of
objects) will nearly optimally constrain the cosmological parameters.


  We investigate the deformation of wavefronts of sound waves in rotating
Bose-Einstein condensates. In irrational fluid flows Berry et al. identified
this kind of deformation as the hydrodynamic analogue of the Aharonov-Bohm
effect. We study this effect in Bose-Einstein condensates and obtain the
Aharonov-Bohm phase shift at all wavelengths. We show that this deformation of
wave fronts is seen in both phase and density fluctuations. For wavelengths
larger than the healing length, the phase fluctuations experience a phase shift
of the order of $2\pi$ times the winding number. We also consider lattices of
vortices. If the angular momentum of the vortices are aligned, the total phase
shift is $2\pi$ times the number of vortices in the condensate. Because of this
behaviour the hydrodynamic Aharonov-Bohm can be utilized as a probe for quantum
vorticity, whose experimental realization could offers an alternative route to
investigate quantum turbulence in the laboratory.


  We propose a class of Pad\'e interpolation problems whose solutions are
expressible in terms of determinants of hypergeometric series.


  In this note we would like to give an explicit lower bound by using a lower
saturated subset of \mathbb{R}_{\geq 0}^n.


  Atom Trap Trace Analysis (ATTA), a novel method based upon laser trapping and
cooling, is used to count individual atoms of 41Ca present in biomedical
samples with isotopic abundance levels between 10^-8 and 10^-10. ATTA is
calibrated against Resonance Ionization Mass Spectrometry, demonstrating a good
agreement between the two methods. The present ATTA system has a counting
efficiency of 2x10^-7. Within one hour of observation time, its 3-sigma
detection limit on the isotopic abundance of 41Ca reaches 4.5x10^-10.


  Although it seems counter-intuitive, categorical colours do not exist as
external physical entities but are very much the product of our brains. Our
cortical machinery segments the world and associate objects to specific colour
terms, which is not only convenient for communication but also increases the
efficiency of visual processing by reducing the dimensionality of input scenes.
Although the neural substrate for this phenomenon is unknown, a recent study of
cortical colour processing has discovered a set of neurons that are
isoresponsive to stimuli in the shape of 3D-ellipsoidal surfaces in
colour-opponent space. We hypothesise that these neurons might help explain the
underlying mechanisms of colour naming in the visual cortex.
  Following this, we propose a biologically-inspired colour naming model where
each colour term - e.g. red, green, blue, yellow, etc. - is represented through
an ellipsoid in 3D colour-opponent space. This paradigm is also supported by
previous psychophysical colour categorisation experiments whose results
resemble such shapes. "Belongingness" of each pixel to different colour
categories is computed by a non-linear sigmoidal logistic function. The final
colour term for a given pixel is calculated by a maximum pooling mechanism. The
simplicity of our model allows its parameters to be learnt from a handful of
segmented images. It also offers a straightforward extension to include further
colour terms. Additionally, ellipsoids of proposed model can adapt to image
contents offering a dynamical solution in order to address phenomenon of colour
constancy. Our results on the Munsell chart and two datasets of real-world
images show an overall improvement comparing to state-of-the-art algorithms.


  Several technical aspects concerning the evaluation of the overlap between
two mean field wave functions of the Hartree Fock Bogoliubov type, are
discussed. The limit when several orbitals become fully occupied is derived as
well as the formula to reduce the dimensionality of the problem when exactly
empty orbitals are present. The formalism is also extended to deal with the
case where the bases of each of the wave functions are different. Several
practical results concerning the evaluation of pfaffians as well as the
canonical decomposition of norm overlaps are also discussed in the appendices.


  We propose a new kinetic BGK-type model for a mixture of four monatomic
gases, undergoing a bimolecular and reversible chemical reaction. The elastic
and reactive interactions are described separately by distinct relaxation terms
and the mechanical operator is the sum of binary BGK contributions, one for
each pair of interacting species. In this way, our model separately
incorporates the effects of mechanical processes and chemical reactions.
Additionally, it retains the effects of interspecies interactions which are
proper of the mixture. The dependence of Maxwellian attractors on the main
macroscopic fields is explicitly expressed by assuming that the exchange rates
for momentum and energy of mechanical and chemical operators coincide with the
ones of the corresponding Boltzmann terms. Under suitable hypotheses, the
entropy dissipation is proven by means of an H-functional prescribing the
relaxation of the distribution functions to the equilibrium.


  High control in the preparation and manipulation of states is an experimental
and theoretical important task in many quantum protocols. Shortcuts to
adiabaticity methods allow to obtain desirable states of a adiabatic dynamics
but in short time scales. In this work the problem of considering this
technique for two-coupled bosonic modes is addressed. By using a symplectic
transformation it is possible to decouple the modes and find the driving
Hamiltonian that drives the system through a transitionless dynamics in a
finite time. Two paradigmatic examples are discusses, the position-position and
the magnetic field couplings, as well as it is shown that the driving
Hamiltonian for each case contains local and global contributions accounting
for coherence in the energy basis and entanglement effects, respectively.


  We propose to use the near-threshold electron scattering data for atoms to
guide the reliable experimental determination of their electron affinities
(EAs), extracted using the Wigner Threshold Law, from laser photodetachment
threshold spectroscopy measurements. Data from the near-threshold electron
elastic scattering from W, Te, Rh, Sb and Sn atoms calculated using our complex
angular momentum method, wherein is embedded the electron-electron correlations
and core polarization interaction, are used as illustrations. We conclude with
a remark on the relativistic effects on the EA calculation for the heavy At
atom.


  Based on a parametric point-wise decomposition, a kind of isospectral
deformation, of the exact one-particle probability density of an externally
confined, analytically solvable interacting two-particle model system we
introduce the associated parametric ($p$) one-matrix and apply it in the
conventional M\"uller-type partitioning of the pair-density. Using the
Schr\"odinger Hamiltonian of the correlated system, the corresponding
approximate ground-state energy $E_p$ is then calculated. The
optimization-search performed on $E_p$ with such restricted informations has a
robust performance and results in the exact ($ex$) ground-state energy for the
correlated model system $E_p=E_{ex}$.


  In the emerging field of molecular communication (MC), testbeds are needed to
validate theoretical concepts, motivate applications, and guide further
modeling efforts. To this end, this paper presents a flexible and extendable
in-vessel testbed for flow-based macroscopic MC, abstractly modeling, e.g., a
part of a chemical reactor or a blood vessel. Signaling is based on injecting
non-reactive superparamagnetic iron oxide nanoparticles (SPIONs) dispersed in
an aqueous suspension into a tube with background flow. A commercial magnetic
susceptometer is used for non-intrusive downstream signal reception. To shed
light on the operation of the testbed, we identify the physical mechanisms
governing the transmission, propagation, and reception of the
information-carrying SPIONs. Moreover, to facilitate system design, we propose
a closed-form parametric expression for the end-to-end channel impulse response
(CIR). The proposed CIR model is shown to consistently capture the
experimentally observed distance-dependent impulse response peak heights and
peak decays for transmission distances from 5cm to 40cm. Moreover, to validate
our testbed, reliable communication is demonstrated based on experimental data
for model-agnostic and model-based detection methods.


  The equivalence of finite automata and regular expressions dates back to the
seminal paper of Kleene on events in nerve nets and finite automata from 1956.
In the present paper we tour a fragment of the literature and summarize results
on upper and lower bounds on the conversion of finite automata to regular
expressions and vice versa. We also briefly recall the known bounds for the
removal of spontaneous transitions (epsilon-transitions) on non-epsilon-free
nondeterministic devices. Moreover, we report on recent results on the average
case descriptional complexity bounds for the conversion of regular expressions
to finite automata and brand new developments on the state elimination
algorithm that converts finite automata to regular expressions.


  When a luminous source is extended, its distortions by weak gravitational
lensing are richer than a mere combination of magnification and shear. In a
recent work, we proposed an elegant formalism based on complex analysis to
describe and calculate such distortions. The present article further elaborates
this finite-beam approach, and applies it to a realistic cosmological model. In
particular, the cosmic correlations of image distortions beyond shear are
predicted for the first time. These constitute new weak-lensing observables,
sensitive to very-small-scale features of the distribution of matter in the
Universe. While the major part of the analysis is performed in the
approximation of circular sources, a general method for extending it to
noncircular sources is presented and applied to the astrophysically relevant
case of elliptic sources.


  Despite being a fundamental tool in soft matter research, quartz crystal
microbalance (QCM) analyses of discrete macromolecules in liquid so far lack a
firm theoretical basis. Currently, acoustic signals are qualitatively
interpreted using ad-hoc frameworks based on effective electrical circuits,
effective springs and trapped-solvent models with abundant fitting parameters.
Nevertheless, due to its extreme sensitivity, the QCM technique pledges to
become an accurate predictive tool. Using unsteady low Reynolds hydrodynamics
we derive analytical expressions for the acoustic impedance of adsorbed
discrete spheres. Our theory is successfully validated against 3D simulations
and a plethora of experimental results covering more than a decade of research
on proteins, viruses, liposomes, massive nanoparticles, with sizes ranging from
few to hundreds of nanometers. The excellent agreement without fitting
constants clearly indicates that the acoustic response is dominated by the
hydrodynamic impedance, thus, deciphering the secondary contribution of
physico-chemical forces will first require a hydrodynamic-reinterpretation of
QCM.


  The orbital M1 collective mode predicted for deformed clusters in a schematic
model is studied in a self-consistent random-phase-approximation approach which
fully exploits the shell structure of the clusters. The microscopic mechanism
of the excitation is clarified and the close correlation with E2 mode
established. The study shows that the M1 strength of the mode is fragmented
over a large energy interval. In spite of that, the fraction remaining at low
energy, well below the overwhelming dipole plasmon resonance, is comparable to
the strength predicted in the schematic model. The importance of this result in
view of future experiments is stressed.


  We demonstrate that the combination of two-body collisions and applied Rabi
pulses makes it possible to prepare arbitrary Dicke (spin) states as well as
maximally entangled states by appropriate sequencing of external fields.


  In this paper, we have proposed a public key cryptography using recursive
block matrices involving generalized Fibonacci numbers over a finite field Fp.
For this, we define multinacci block matrices, a type of upper triangular
matrix involving multinacci matrices at diagonal places and obtained some of
its algebraic properties. Moreover, we have set up a method for key element
agreement at end users, which makes the cryptography more efficient. The
proposed cryptography comes with a large keyspace and its security relies on
the Discrete Logarithm Problem(DLP).


  We study the hyperfine interaction between the nuclear spins and the
electrons in a HgTe quantum well, which is the prime experimentally realized
example of a two-dimensional topological insulator. The hyperfine interaction
is a naturally present, internal source of broken time-reversal symmetry from
the point of view of the electrons. The HgTe quantum well is described by the
so-called Bernevig-Hughes-Zhang (BHZ) model. The basis states of the BHZ model
are combinations of both S- and P-like symmetry states, which means that three
kinds of hyperfine interactions play a role: (i) The Fermi contact interaction,
(ii) the dipole-dipole like coupling and (iii) the electron orbital to
nuclear-spin coupling. We provide benchmark results for the forms and
magnitudes of these hyperfine interactions within the BHZ model, which give a
good starting point for evaluating hyperfine interactions in any HgTe
nanostructure. We apply our results to the helical edge states of a HgTe
two-dimensional topological insulator and show how their total hyperfine
interaction becomes anisotropic and dependent on the orientation of the sample
edge within the plane. Moreover, for the helical edge states the hyperfine
interactions due to the P-like states can dominate over the S-like contribution
in certain circumstances.


  Monte Carlo simulations and dynamical mean-field approximations are performed
to study the phase transition in a driven lattice gas with nearest-neighbor
exclusion on a square lattice. A slight extension of the microscopic dynamics
with allowing the next-nearest-neighbor hops results in dramatic changes.
Instead of the phase separation into high- and low-density regions in the
stationary state the system exhibits a continuous transition belonging to the
Ising universality class for any driving. The relevant features of phase
diagram are reproduced by an improved mean-field analysis.


  Several proposals for studying neutrinos with large detectors are currently
under discussion. We suggest that they could provide a precise measurement of
the electroweak mixing angle as well as a probe for new physics, such as
non-standard neutrino interactions (NSI), and the electroweak gauge structure.
We illustrate this explicitly for the case of the LENA proposal, either with an
artificial radioactive source or by using the solar neutrino flux.


  During the last years, through the combined effort of the insight, coming
from physical intuition and computer simulation, and the exploitation of
rigorous mathematical methods, the main features of the mean field
Sherrington-Kirkpatrick spin glass model have been firmly established. In
particular, it has been possible to prove the existence and uniqueness of the
infinite volume limit for the free energy, and its Parisi expression, in terms
of a variational principle, involving a functional order parameter. Even the
expected property of ultrametricity, for the infinite volume states, seems to
be near to a complete proof. The main structural feature of this model, and
related models, is the deep phenomenon of spontaneous replica symmetry breaking
(RSB), discovered by Parisi many years ago. By expanding on our previous work,
the aim of this paper is to investigate a general frame, where replica symmetry
breaking is embedded in a kind of mechanical scheme of the Hamilton-Jacobi
type. Here, the analog of the "time" variable is a parameter characterizing the
strength of the interaction, while the "space" variables rule out
quantitatively the broken replica symmetry pattern. Starting from the simple
cases, where annealing is assumed, or replica symmetry, we build up a
progression of dynamical systems, with an increasing number of space variables,
which allow to weaken the effect of the potential in the Hamilton-Jacobi
equation, as the level of symmetry braking is increased. This new machinery
allows to work out mechanically the general K-step RSB solutions, in a
different interpretation with respect to the replica trick, and lightens easily
their properties as existence or uniqueness.


  The tensor force is implemented into the time-dependent Hartree-Fock (TDHF)
theory so that both exotic and stable collision partners, as well as their
dynamics in heavy-ion fusion, can be described microscopically. The role of
tensor force on fusion dynamics is systematically investigated for
$^{40}\mathrm{Ca}+\mathrm{^{40}Ca}$, $^{40}\mathrm{Ca}+\mathrm{^{48}Ca}$,
$^{48}\mathrm{Ca}+\mathrm{^{48}Ca}$, $^{48}\mathrm{Ca}+\mathrm{^{56}Ni}$, and
$^{56}\mathrm{Ni}+\mathrm{^{56}Ni}$ reactions which vary by the total number of
spin-unsaturated magic numbers in target and projectile. A notable effect on
fusion barriers and cross sections is observed by the inclusion of tensor
force. The origin of this effect is analyzed. The influence of isoscalar and
isovector tensor terms is investigated with the T$IJ$ forces. These effects of
tensor force in fusion dynamics are essentially attributed to the shift of
low-lying vibration states of colliding partners and nucleon transfer in the
asymmetric reactions. Our calculations of above-barrier fusion cross sections
also show that tensor force does not significantly affect the dynamical
dissipation at near-barrier energies.


  Algebraic Geometric codes associated to a recently discovered class of
maximal curves are investigated. As a result, some linear codes with better
parameters with respect to the previously known ones are discovered, and 70
improvements on MinT's tables are obtained.


  Use-cases in the Internet of Things (IoT) typically involve a high number of
interconnected, heterogeneous devices. Due to the criticality of many IoT
scenarios, systems and applications need to be tested thoroughly before
rollout. Existing staging environments and testing frameworks are able to
emulate network properties but fail to deliver actual network-wide traffic
control to test systems application independently. To extend existing
frameworks, we present the distributed traffic replaying tool IoTreeplay.
  The tool embeds TCPLivePlay into an environment that allows the synchronous
replaying of network traffic with multiple endpoints and connections. Replaying
takes place in a user-defined network or testbed containing IoT use-cases.
Network traffic can be captured and compared to the original trace to evaluate
accuracy and reliability. The resulting implementation is able to accurately
replay connections within a maximum transmission rate but struggles with
deviations from regular TCP connections, like packet loss or connection reset.
An evaluation has been performed, measuring individual and aggregated delays
between packets, based on the recorded timestamps.


  Facial biometrics are an essential components of smartphones to ensure
reliable and trustworthy authentication. However, face biometric systems are
vulnerable to Presentation Attacks (PAs), and the availability of more
sophisticated presentation attack instruments such as 3D silicone face masks
will allow attackers to deceive face recognition systems easily. In this work,
we propose a novel Presentation Attack Detection (PAD) algorithm based on 3D
point clouds captured using the frontal camera of a smartphone to detect
presentation attacks. The proposed PAD algorithm, VoxAtnNet, processes 3D point
clouds to obtain voxelization to preserve the spatial structure. Then, the
voxelized 3D samples were trained using the novel convolutional attention
network to detect PAs on the smartphone. Extensive experiments were carried out
on the newly constructed 3D face point cloud dataset comprising bona fide and
two different 3D PAIs (3D silicone face mask and wrap photo mask), resulting in
3480 samples. The performance of the proposed method was compared with existing
methods to benchmark the detection performance using three different evaluation
protocols. The experimental results demonstrate the improved performance of the
proposed method in detecting both known and unknown face presentation attacks.


  In a poisoning attack, an adversary with control over a small fraction of the
training data attempts to select that data in a way that induces a corrupted
model that misbehaves in favor of the adversary. We consider poisoning attacks
against convex machine learning models and propose an efficient poisoning
attack designed to induce a specified model. Unlike previous model-targeted
poisoning attacks, our attack comes with provable convergence to {\it any}
attainable target classifier. The distance from the induced classifier to the
target classifier is inversely proportional to the square root of the number of
poisoning points. We also provide a lower bound on the minimum number of
poisoning points needed to achieve a given target classifier. Our method uses
online convex optimization, so finds poisoning points incrementally. This
provides more flexibility than previous attacks which require a priori
assumption about the number of poisoning points. Our attack is the first
model-targeted poisoning attack that provides provable convergence for convex
models, and in our experiments, it either exceeds or matches state-of-the-art
attacks in terms of attack success rate and distance to the target model.


  We introduce the appropriate framework for pathwise comparison of multiple
server queues under general stationary ergodic assumptions. We show in what
sense it is better to have more servers for a system under FCFS ('First Come,
First Served') or equivalently, more queues in a system of parallel queues
under the JSW ('Join the Shortest Workload') allocation policy. This comparison
result is based on the recursive representation of Kiefer and Wolfowitz, and on
a non-mass conservative generalization of the Schur-Convex semi-ordering. We
also show that the latter result does not hold true in general, for the larger
class of systems applying the semi-cyclic allocation policy introduced by
Scheller-Wolf in \cite{SW03}.


  We study two uncoupled oscillators, horizontal and vertical, residing in
rectilinear polygons (with only vertical and horizontal sides) and impacting
elastically from their boundary. The main purpose of the article is to analyze
the occurrence of resonance in such systems, depending on the shape of the
analytical potentials that determine the oscillators. We define resonant energy
levels; roughly speaking, these are levels for which the resonance phenomenon
occurs more often than rarely. We focus on unimodal analytic potentials with
the minimum at zero. The most important result of the work describes the size
of the set of resonance levels in the form of the following trichotomy: it is
mostly empty or is one-element or is large, i.e. non-empty and open. We also
indicate which classes of potentials each of the three possibilities can occur
in. From this point of view, the last case (strongly resonant) is the most
interesting. Then, the potentials belong to a special class of potentials,
denoted by $\mathcal{SP}$, which seems unknown in the literature. The presented
results appear to be new, even in the simplest case, when the uncoupled
oscillators are not trapped in any set.


  The Gauss map $g$ of a surface $\Sigma$ in $\mathbb{R}^4$ takes its values in
the Grassmannian of oriented 2-planes of $\mathbb{R}^4$: $G^+(2,4)$. We give
geometric criteria of stability for minimal surfaces in $\mathbb{R}^4$ in terms
of $g$. We show in particular that if the spherical area of the Gauss map
$|g(\Sigma)|$ of a minimal surface is smaller than $2\pi$ then the surface is
stable by deformations which fix the boundary of the surface.This answers a
question of Barbosa and Do Carmo in $\mathbb{R}^4$.


  We find general geometric conditions on a convex body of revolution K, in
dimensions four and six, so that its intersection body IK is not a polar
zonoid. We exhibit several examples of intersection bodies which are are not
polar zonoids.


  We show that if G is a finite group and A is a subset of G with no
non-trivial solutions to xz=yy then |A| < |G|/(log log |G|)^c.


  Digital Geometry software should reflect the generality of the underlying
mathe- matics: mapping the latter to the former requires genericity. By
designing generic solutions, one can effectively reuse digital geometry data
structures and algorithms. We propose an image processing framework focused on
the Generic Programming paradigm in which an algorithm on the paper can be
turned into a single code, written once and usable with various input types.
This approach enables users to design and implement new methods at a lower
cost, try cross-domain experiments and help generalize results


  We study the types of non-integrable $\mathrm{G}$-structures on Riemannian
manifolds. In particular, geometric types admitting a connection with totally
skew-symmetric torsion are characterized. 8-dimensional manifolds equipped with
a $\Spin(7)$-structure play a special role. Any geometry of that type admits a
unique connection with totally skew-symmetric torsion. Under weak conditions on
the structure group we prove that this geometry is the only one with this
property. Finally, we discuss the automorphism group of a Riemannian manifold
with a fixed non-integrable $\mathrm{G}$-structure.


  We analytically solve the position-dependent mass (PDM) 1D Schr\"odinger
equation for a new class of hyperbolic potentials $V_q^p(x) =
-V_0\frac{\sinh^px}{\cosh^qx}, \, p= -2, 0, \dots q$ [see C. A. Downing, J.
Math. Phys. 54 072101 (2013)] among which several hyperbolic single- and
double-wells. For a solitonic mass distribution, $m(x)=m_0\,\text{sech}^2(x)$,
we obtain exact analytic solutions to the resulting differential equations. For
several members of the class, the quantum mechanical problems map into
confluent Heun differential equations. The PDM Poschl-Teller potential is
considered and exactly solved as a particular case.


  This work presents a polyelectrolyte (PE) model based on a freely jointed
chain (FJC) in which the beads are ionizable and the bonds are rigid.
Electrostatic interactions considered are of the short range type up to
next-nearest neighbours using a Debye-H\"uckel (DH) potential. Exact
expressions for the conformational and protonation properties are obtained as a
function of the pH using the transfer matrix method and the integration of the
angular variables. For the finite cases with low N values, relevant differences
arise on both the protonation curve and the end to end distance due to the end
effects. However, when increasing N a rather rapid convergence is observed to
the infinite chain limiting case.


  This paper is devoted to primal conditions of error bounds for a general
function. In terms of Bouligand tangent cones, lower Hadamard directional
derivatives and the Hausdorff-Pompeiu excess of subsets, we provide several
necessary and/or sufficient conditions of error bounds with mild assumptions.
Then we use these primal results to characterize error bounds for
composite-convex functions (i.e. the composition of a convex function with a
continuously differentiable mapping). It is proved that the primal
characterization of error bounds can be established via Bouligand tangent
cones, directional derivatives and the Hausdorff-Pompeiu excess if the mapping
is metrically regular at the given point. The accurate estimate on the error
bound modulus is also obtained.


  We propose an evolutionary coordination game to formalize a simplified model
of the evolution of strategies during human courtship. The dynamics, derived
from the consideration of experimental observations on human social behavior
driven by self-esteem, turns out to be non-payoff monotonic. This property
gives rise to nontrivial evolution in the players' strategies, which we study
both numerically and analytically.


  The present work deals with a non-equilibrium thermodynamics that is
associated with the scenario of warm inflation. The premise is that an
adiabatic radiation production process holds exactly i.e. the radiation
dilution is exactly counterbalanced by a dissipation term. Under this
hypothesis, it is found that radiation particle number, temperature, radiation
energy density and pressure are all conserved -- a contradiction to the very
nature of the warm inflation dynamics. However, such exact adiabatic radiation
production process never happens in any realistic analysis of warm inflation.
In the slow roll approximation this holds at best at the zeroth order. Finally
it is shown that a variable cosmological constant may accommodate the
quasi-stable process in warm inflation with non-equilibrium thermodynamic
description.


  The representation sets of a central square C-loop are investigated. Isotopes
of central square C-loops of exponent 4 are shown to be both C-loops and
A-loops.


  We establish global well-posedness and scattering for solutions to the
mass-critical nonlinear Hartree equation $iu_t+\Delta u=\pm(|x|^{-2}*|u|^2)u$
for large spherically symmetric $L^2_x(\Bbb{R}^d)$ initial data; in the
focusing case we require, of course, that the mass is strictly less than that
of the ground state.


  We introduce a multi-locus genetically acquired phenotype, submitted to
mutations and with selective value, in an age-structured model for biological
aging. This phenotype describes a single-trait effect of the environment on an
individual, and we study the resulting distribution of this trait among the
population. In particular, our simulations show that the appearance of a double
phenotypic attractor in the ecology induces the emergence of a stable
polymorphism, as observed in the Galapagos finches. In the presence of this
polymorphism, the simulations generate short-term speciation, when mating
preferences are also allowed to suffer mutations and acquire selective value.


  Numerous authors have considered the problem of determining the Lebesgue
space mapping properties of the operator $\mathcal{A}$ given by convolution
with affine arc-length measure on some polynomial curve in Euclidean space.
Essentially, $\mathcal{A}$ takes weighted averages over translates of the
curve. In this paper a variant of this problem is discussed where averages over
both translates and dilates of a fixed curve are considered. The sharp range of
estimates for the resulting operator is obtained in all dimensions, except for
an endpoint. The techniques used are redolent of those previously applied in
the study of $\mathcal{A}$. In particular, the arguments are based upon the
refinement method of Christ, although a significant adaptation of this method
is required to fully understand the additional smoothing afforded by averaging
over dilates.


  Duality is a central concept in the theory of session types. Since a flaw was
found in the original definition of duality for recursive types, several other
definitions have been published. As their connection is not obvious, we compare
the competing definitions, discuss tradeoffs, and prove some equivalences. Some
of the results are mechanized in Agda.


  We show that the stochastic background of gravitational waves, produced in
the early cosmological epochs, strictly depends on the assumed theory of
gravity. In particular, the specific form of the function f(R), where R is the
Ricci scalar, is related to the evolution and the production mechanism of
gravitational waves. Using a neural network algorithm which only requires
non-Gaussian nature and independence of the input signals we conclude that, in
order to detect a CSB signal, the interferometric sensitivity of detector like
VIRGO will be improved.


  We consider Hamiltonian systems with two degrees of freedom of point vortex
type \[
  \kappa_j \dot{z}_j = J \nabla_{z_j} H_\Omega(z_1,z_2), \quad j=1,2, \] for
$z_1,z_2$ in a domain $\Omega\subset\mathbb{R}^2$. In the classical point
vortex context the Hamiltonian $H_\Omega$ is of the form \[
  H_\Omega(z_1,z_2) = -\frac{\kappa_1 \kappa_2}{\pi} \log |z_1-z_2| - 2\kappa_1
\kappa_2g(z_1,z_2) - \kappa_1^2 h(z_1) - \kappa_2^2 h(z_2), \] where
$g:\Omega\times\Omega\to\mathbb{R}$ is the regular part of a hydrodynamic Green
function in $\Omega$, $h:\Omega\to\mathbb{R}$ is the Robin function:
$h(z)=g(z,z)$, and $\kappa_1$, $\kappa_2$ are the vortex strengths.
  We prove the existence of infinitely many periodic solutions with prescribed
minimal period that are superpositions of a slow motion of the center of
vorticity close to a star-shaped level line of $h$ and of a fast rotation of
the two vortices around their center of vorticity. The proofs are based on a
recent higher dimensional version of the Poincar\'e-Birkhoff theorem due to
Fonda and Ure\~na.


  This paper is a continuation of our work concerning the logical and
computational foundations of multi-step fuzzy inference. We bring further
results on the implementation of the Mamdani-Assilian type of fuzzy rules and
inference in Goedel logic with truth constants. In our previous work, we have
provided translation of Mamdani-Assilian fuzzy rules to formulae of Goedel
logic, and subsequently, to suitable clausal form. Moreover, we have outlined a
class of problems regarding general properties of fuzzy inference and shown its
reduction to a class of deduction/unsatisfiability problems. We now focus on
solving such problems using an adapted hyperresolution calculus.


  The resonant laser cooling of circular accelerator beams of relativistic
charged particle is studied. It is shown that in the approximation of the given
external electromagnetic wave amplitude (small gain free electron laser) the
emittance of a beam of charged particles decreases. In the field of particle
energy about 100 in the mass energy units the beam energy losses are
negligible. The discovered effect can be used for cooling of charged particle
beams in various accelerators. The significant cooling rates are possible to
achieve by placing of the cooling device in the appropriate points of the
accelerator orbit. Resonant laser cooling for various cases are considered.
This method of charged particle beams cooling can be applied to circular
accelerators of electron and various relativistic heavy particle beams and has
significantly, about 3-4 orders of magnitude, shorter cooling time in
comparison to any other cooling method.


  The harmonic oscillator with a time-dependent frequency has a family of
linear quantum invariants for the time-dependent Schr\"{o}dinger equation,
which are determined by any two independent solutions to the classical equation
of motion. Ermakov and Pinney have shown that a general solution to the
time-dependent oscillator with an inverse cubic term can be expressed in terms
of two independent solutions to the time-dependent oscillator. We explore the
connection between linear quantum invariants and the Ermakov-Pinney solution
for the time-dependent harmonic oscillator. We advance a novel method to
construct Ermakov-Pinney solutions to a class of time-dependent oscillators and
the wave functions for the time-dependent Schr\"{o}dinger equation. We further
show that the first and the second P\"{o}schl-Teller potentials belong to a
special class of exact time-dependent oscillators. A perturbation method is
proposed for any slowly-varying time-dependent frequency.


  Unrestricted mutation of shared state is a source of many well-known
problems. The predominant safe solutions are pure functional programming, which
bans mutation outright, and flow sensitive type systems, which depend on
sophisticated typing rules. Mutable value semantics is a third approach that
bans sharing instead of mutation, thereby supporting part-wise in-place
mutation and local reasoning, while maintaining a simple type system. In the
purest form of mutable value semantics, references are second-class: they are
only created implicitly, at function boundaries, and cannot be stored in
variables or object fields. Hence, variables can never share mutable state.
  Because references are often regarded as an indispensable tool to write
efficient programs, it is legitimate to wonder whether such a discipline can
compete other approaches. As a basis for answering that question, we
demonstrate how a language featuring mutable value semantics can be compiled to
efficient native code. This approach relies on stack allocation for static
garbage collection and leverages runtime knowledge to sidestep unnecessary
copies.


  The Scaled Agile Framework (SAFe) is a framework for scaling agile methods in
large organizations. We have found several experience reports and white papers
describing SAFe adoptions in different banks, which indicates that SAFe is
being used in the banking industry. However, there is a lack of academic
publications on the topic, the banking industry is missing in the scientific
reports analyzing SAFe transformations. To fill this gap, we present a study on
the main challenges with a SAFe transformation at a large full-service bank. We
identify the challenges in the bank under study and compare the findings with
experience reports from other banks, as well as with research on SAFe
transformations in other domains. Many of the challenges reported in this paper
overlap with the generic SAFe challenges, including management and
organization, education and training, culture and mindset, requirements
engineering, quality assurance, and systems architecture. However, we also
report some novel challenges specific to the banking domain, e.g., the risk of
jeopardizing customer relations, stability, and trust of external stakeholders.
This study validates several SAFe-related challenges reported in previous work
in the banking context. It also brings up some novel challenges specific to the
banking industry. Therefore, we believe our results are particularly useful to
practitioners responsible for SAFe transformations at other banks.


  A method to obtain particle sizes from images that are used for particle
tracking velocimetry is proposed. This is an open source method, developed to
use together with the open source software OpenPTV. First, the analysis of
different factors that affect the estimation of the particle size is made.
Then, a transformation is proposed to estimate the sizes from information
obtained in OpenPTV. The method requires an extra calibration with a flat
target containing circles of different sizes, but if the calibration is
successful, the sizes of particles can be estimated reliable within certain
limits. For example, for solid of non-translucent particles, sizes can be
estimated with an error of maximum 10 %, as long as the particle diameter
correspond to at least three pixels width in the obtained images. For
translucent particles some extra assumptions will be needed in the
transformation.


  In this paper, we are concerned with the sign-changing solutions of
variational inequality problems. In order to give the existence results of the
sign-changing solutions for variational inequality problems, we first construct
a suitable penalty problem related to the variational inequality, and prove the
existence of a sign-changing solution for this penalty problem using the
invariant set of descending flow method. Secondly, we perform a series of
estimates on the sign-changing solution sequence of the penalty problem, and
prove that the limit of convergence of the sign-changing solution sequence is
the sign-changing solution of the original variational inequality problem.
Variational inequality problems have extensive and important applications. In
this paper, we used penalty method and the method of invariant set of
descending flow to obtain the existence results for solutions of a variational
inequality. In particular, we obtain the existence results for sign-changing
solutions of variational inequalities for the first time based on the method of
invariant set of descending flow.


  We prove that the lubrication approximation is perturbed by a non-regular
roughness of the boundary. We show how the flow may be accelerated using
adequate rugosity profiles on the bottom. We explicit the possible effects of
some abrupt changes in the profile. The limit system is mathematically
justified through a variant of the notion of two-scale convergence. Finally, we
present some numerical results, illustrating the limit system in the
three-dimensional case.


  A cascadic tensor multigrid method and an economic cascadic tensor multigrid
method is presented for solving the image restoration models. The methods use
quadratic interpolation as prolongation operator to provide more accurate
initial values for the next fine grid level, and constructs a
preserving-edge-denoising operator to obtain better edges and remove noise. The
experimental results show that the new methods not only improves computational
efficiency but also achieve better restoration quality.


  It is shown, that recently constructed PST Lagrangians for chiral
supergravities follow directly from earlier Kavalov-Mkrtchyan Lagrangians by an
Ansatz for the $\theta $ tensor by expressing this in terms of the PST scalar.
The susy algebra which included earlier $\alpha$-symmetry in the commutator of
supersymmetry transformations, is now shown to include both PST symmetries,
which arise from the single $\alpha$-symmetry term. The Lagrangian for the
5-brane is not described by this correspondence, and probably can be obtained
from more general Lagrangians, posessing $\alpha$-symmetry.


  The purpose of this research article is to discover how the econophysics
analysis can complement the econometrics models in application to the risk
management in the central banks and financial institutions, operating within
the nonlinear dynamical financial system. We consider the modern risk
management models and show the appropriate techniques to calculate the various
existing risks in the finances. We make a few comments on the possible
limitations in the models of statistical modeling of volatility such as the
Autoregressive Conditional Heteroskedasticity (GARCH) model, because of the
nonlinearities appearance in the nonlinear dynamical financial systems. We
propose that the various types of nonlinearities, which can originate in the
financial and economical systems, have to be taken to the detailed
consideration during the Cost of Capital calculation in the finances and
economics. We propose the new theory of nonlinear dynamic volatilities and the
new nonlinear dynamic chaos (NDC) volatility model for the statistical modeling
of financial volatility with the aim to determine the Value at Risk.


  In this paper we study the cosmological evolution of the universe filled with
a perfect fluid in the Eddington-inspired Born-Infeld gravity. Applying an
alternative method in which the evolution of the scale factor for this theory
is linked to the cosmographic parameters, we obtain a dynamical dark energy
solution where the singularity (through a regular bounce or a loitering phase)
still can be avoided for $\kappa>0$ with $w>0$. For the range $-1<w<0$, the
results lead us to universes that experience an unlimited rate of expansion
with finite density. Also, we obtain a possible maximum value of
$H=4.338\times10^{-43}/t_{\text{Planck}}$ at the cosmic bounce point.


  Let $x_1, x_2, \dots, x_n$ be the eigenvalues of a signed graph $\Gamma$ of
order $n$. The energy of $\Gamma$ is defined as
$E(\Gamma)=\sum^{n}_{j=1}|x_j|.$ Let $\mathcal{P}_n^4$ be obtained by
connecting a vertex of the negative circle $(C_4,{\overline{\sigma}})$ with a
terminal vertex of the path $P_{n-4}$. In this paper, we show that for $n=4,6$
and $n \geq 8,$ $\mathcal{P}_n^4$ has the maximal energy among all connected
unicyclic $n$-vertex signed graphs, except the cycles $C_5^+, C_7^+.$


  Humans rely heavily on shape information to recognize objects. Conversely,
convolutional neural networks (CNNs) are biased more towards texture. This is
perhaps the main reason why CNNs are vulnerable to adversarial examples. Here,
we explore how shape bias can be incorporated into CNNs to improve their
robustness. Two algorithms are proposed, based on the observation that edges
are invariant to moderate imperceptible perturbations. In the first one, a
classifier is adversarially trained on images with the edge map as an
additional channel. At inference time, the edge map is recomputed and
concatenated to the image. In the second algorithm, a conditional GAN is
trained to translate the edge maps, from clean and/or perturbed images, into
clean images. Inference is done over the generated image corresponding to the
input's edge map. Extensive experiments over 10 datasets demonstrate the
effectiveness of the proposed algorithms against FGSM and $\ell_\infty$ PGD-40
attacks. Further, we show that a) edge information can also benefit other
adversarial training methods, and b) CNNs trained on edge-augmented inputs are
more robust against natural image corruptions such as motion blur, impulse
noise and JPEG compression, than CNNs trained solely on RGB images. From a
broader perspective, our study suggests that CNNs do not adequately account for
image structures that are crucial for robustness. Code is available
at:~\url{https://github.com/aliborji/Shapedefense.git}.


  We identify exact gauge-instanton-like solutions to (super)-string theory
using the method of dimensional reduction. We find in particular the Polyakov
instanton of 3d QED, and a class of generalized Yang-Mills merons. We discuss
their marginal deformations, and show that for the $3d$ instanton they
correspond to a dissociation of vector- and axial-magnetic charges.


  In this paper, a new method of detection of election fraud is proposed. This
method is based on the calculation of the ratio of two standard normal random
variables; estimation of parameters of obtained sample and comparison of these
estimates with known theoretical values of parameters. Also in the paper, there
is an example of the application of the method.


  This paper is devoted to the study of the sign of the Green's function
related to a general linear $n^{\rm th}$-order operator, depending on a real
parameter, $T_n[M]$, coupled with the $(k,n-k)$ boundary value conditions.
  If operator $T_n[\bar M]$ is disconjugate for a given $\bar M$, we describe
the interval of values on the real parameter $M$ for which the Green's function
has constant sign.
  One of the extremes of the interval is given by the first eigenvalue of
operator $T_n[\bar M]$ satisfying $(k,n-k)$ conditions.
  The other extreme is related to the minimum (maximum) of the first
eigenvalues of $(k-1,n-k+1)$ and $(k+1,n-k-1)$ problems.
  Moreover if $n-k$ is even (odd) the Green's function cannot be non-positive
(non-negative).
  To illustrate the applicability of the obtained results, we calculate the
parameter intervals of constant sign Green's functions for particular
operators. Our method avoids the necessity of calculating the expression of the
Green's function.
  We finalize the paper by presenting a particular equation in which it is
shown that the disconjugation hypothesis on operator $T_n[\bar M]$ for a given
$\bar M$ cannot be eliminated.


  The Schwinger limit could be approached by focusing to its diffraction limit
the light reflected by a plasma mirror irradiated by a multi-petawatt laser. We
explore numerically the interaction between such intense light and matter. We
find that the interaction with a relativistic counterpropagative electron beam
would enable the exploration of the fully nonperturbative regime of
strong-field quantum electrodynamics (SF-QED), while the interaction with an
initially solid target leads to a profusion of SF-QED effects that retroact on
the laser-plasma interaction. We observe in both scenarios the formation of
relativistic attosecond electron-positron jets with very high densities.


  The arbitrary functions principle says that the fractional part of $nX$
converges stably to an independent random variable uniformly distributed on the
unit interval, as soon as the random variable $X$ possesses a density or a
characteristic function vanishing at infinity. We prove a similar property for
random variables defined on the Wiener space when the stochastic measure
$dB\_s$ is crumpled on itself.


  We study the effects of perturbative reheating on the evolution of the
curvature perturbation \zeta, in two-field inflation models. We use numerical
methods to explore the sensitivity of f_NL, n_s and r to the reheating process,
and present simple qualitative arguments to explain our results. In general, if
a large non-Gaussian signal exists at the start of reheating, it will remain
non zero at the end of reheating. Unless all isocurvature modes have completely
decayed before the start of reheating, we find that the non-linearity
parameter, f_NL, can be sensitive to the reheating timescale, and that this
dependence is most appreciable for `runaway' inflationary potentials that only
have a minimum in one direction. For potentials with a minimum in both
directions, f_NL can also be sensitive to reheating if a mild hierarchy exists
between the decay rates of each field. Within the class of models studied, we
find that the spectral index n_s, is fairly insensitive to large changes in the
field decay rates, indicating that n_s is a more robust inflationary
observable, unlike the non-linearity parameter f_NL. Our results imply that the
statistics of \zeta, especially f_NL, can only be reliably used to discriminate
between models of two-field inflation if the physics of reheating are properly
accounted for.


  Despite wide-scale deployment of phasor measurement unit technology, locating
the sources of low frequency forced oscillations in power systems is still an
open research topic. The dissipating energy flow method is one source location
technique which has performed remarkably well in both simulation and real time
application at ISO New England. The method has several deficiencies, though,
which are still poorly understood. This paper borrows the concepts of passivity
and positive realness from the controls literature in order to interpret the
dissipating energy flow method, pinpoint the reasons for its deficiencies, and
set up a framework for improving the method. The theorems presented in this
paper are then tested via simulation on a simple infinite bus power system
model.


  Despite the demonstrated editing capacity in the latent space of a pretrained
GAN model, inverting real-world images is stuck in a dilemma that the
reconstruction cannot be faithful to the original input. The main reason for
this is that the distributions between training and real-world data are
misaligned, and because of that, it is unstable of GAN inversion for real image
editing. In this paper, we propose a novel GAN prior based editing framework to
tackle the out-of-domain inversion problem with a composition-decomposition
paradigm. In particular, during the phase of composition, we introduce a
differential activation module for detecting semantic changes from a global
perspective, \ie, the relative gap between the features of edited and unedited
images. With the aid of the generated Diff-CAM mask, a coarse reconstruction
can intuitively be composited by the paired original and edited images. In this
way, the attribute-irrelevant regions can be survived in almost whole, while
the quality of such an intermediate result is still limited by an unavoidable
ghosting effect. Consequently, in the decomposition phase, we further present a
GAN prior based deghosting network for separating the final fine edited image
from the coarse reconstruction. Extensive experiments exhibit superiorities
over the state-of-the-art methods, in terms of qualitative and quantitative
evaluations. The robustness and flexibility of our method is also validated on
both scenarios of single attribute and multi-attribute manipulations.


  For a class of degenerate diffusion processes of rank 2, i.e. when only
Poisson brackets of order one are needed to span the whole space, we obtain a
parametrix representation of the density from which we derive some explicit
Gaussian controls that characterize the additional singularity induced by the
degeneracy. We then give a local limit theorem with the usual convergence rate
for an associated Markov chain approximation. The key point is that the "weak"
degeneracy allows to exploit the techniques first introduced by Konakov and
Molchanov and then developed by Konakov and Mammen that rely on Gaussian
approximations.


  We present new Bayesian Last Layer models in the setting of multivariate
regression under heteroscedastic noise, and propose an optimization algorithm
for parameter learning. Bayesian Last Layer combines Bayesian modelling of the
predictive distribution with neural networks for parameterization of the prior,
and has the attractive property of uncertainty quantification with a single
forward pass. The proposed framework is capable of disentangling the aleatoric
and epistemic uncertainty, and can be used to transfer a canonically trained
deep neural network to new data domains with uncertainty-aware capability.


  We report thickness dependent metal insulator transition in Ga doped ZnO
(Ga:ZnO) thin films grown by pulsed laser deposition technique. From the
electrical transport measurements, we find that while the thinnest film
exhibits a resistivity of 0.05 $\Omega$-cm, lying in the insulating regime, the
thickest has resistivity of $6.6\times10^{-4}\Omega$-cm which shows metallic
type of conduction. Our analysis reveals that the Mott's variable range hopping
(VRH) model governs the insulating behavior in the thinner Ga:ZnO whereas the
2D weak localization phenomena is appropriate to explain the electron transport
in the thicker Ga:ZnO. Magnetoresistance study further confirms the presence of
strong localization in 6 nm film while weak localization is observed in 20 nm
and above thicker films. From the density functional calculations, it is found
that due to surface reconstruction and Ga doping, strong crystalline disorder
sets in very thin films to introduce localized states and thereby, restricts
the donor electron mobility.


  The fundamental matrix can be estimated from point matches. The current gold
standard is to bootstrap the eight-point algorithm and two-view projective
bundle adjustment. The eight-point algorithm first computes a simple linear
least squares solution by minimizing an algebraic cost and then projects the
result to the closest rank-deficient matrix. We propose a single-step method
that solves both steps of the eight-point algorithm. Using recent results from
polynomial global optimization, our method finds the rank-deficient matrix that
exactly minimizes the algebraic cost. In this special case, the optimization
method is reduced to the resolution of very short sequences of convex linear
problems which are computationally efficient and numerically stable. The
current gold standard is known to be extremely effective but is nonetheless
outperformed by our rank-constrained method for bootstrapping bundle
adjustment. This is here demonstrated on simulated and standard real datasets.
With our initialization, bundle adjustment consistently finds a better local
minimum (achieves a lower reprojection error) and takes less iterations to
converge.


  New data are presented on the p(e,e'p)\pi^0 reaction at threshold at a
four-momentum transfer of Q^2=0.05 GeV^2/c^2. The data were taken with the
three-spectrometer setup of the A1 Collaboration at the Mainz Microtron MAMI.
The complete center of mass solid angle was covered up to a center of mass
energy of 4 MeV above threshold. Combined with measurements at three different
values of the virtual photon polarization \epsilon, the structure functions
\sigma_T, \sigma_L, \sigma_{TT}, and \sigma_{TL} are determined. The results
are compared with calculations in Heavy Baryon Chiral Perturbation Theory and
with a phenomenological model. The measured cross section is significantly
smaller than both predictions.


  We prove an analog of the holomorphic Lefschetz formula for endofunctors of
smooth compact dg-categories. We deduce from it a generalization of the
Lefschetz formula of V. Lunts that takes the form of a reciprocity law for a
pair of commuting endofunctors. As an application, we prove a version of
Lefschetz formula proposed by Frenkel and Ngo. Also, we compute explicitly the
ingredients of the holomorphic Lefschetz formula for the dg-category of matrix
factorizations of an isolated singularity w(x). We apply this formula to get
some restrictions on the Betti numbers of a Z/2-equivariant module over
k[[x_1,...,x_n]]/(w) in the case when w(-x)=w(x).


  Let G:=SO(n,1)^\circ and \Gamma be a geometrically finite Zariski dense
subgroup with critical exponent delta bigger than (n-1)/2. Under a spectral gap
hypothesis on L^2(\Gamma \ G), which is always satisfied for delta>(n-1)/2 for
n=2,3 and for delta>n-2 for n>= 4, we obtain an {\it effective} archimedean
counting result for a discrete orbit of \Gamma in a homogeneous space H\G,
where H is the trivial group, an affine symmetric subgroup or a horospherical
subgroup. More precisely, we show that for any effectively well-rounded family
{B_T} of compact subsets in H\G, there exists \eta>0 such that #[e]\G\cap
B_T=M(B_T) +O(M(B_T)^{1-\eta}) for an explicit measure M on H\G, which depends
on Gamma. We also apply affine sieve and describe the distribution of almost
primes on orbits of \Gamma in arithmetic settings.
  One of key ingredients in our approach is an effective asymptotic formula for
the matrix coefficients of L^2(\Gamma \ G) that we prove by combining methods
from spectral analysis, harmonic analysis and ergodic theory. An effective
mixing for the Bowen-Margulis-Sullivan measure is also obtained as an
application of our methods.


  The impact of the resummed next-to-leading logarithmic small-$x$
contributions to the anomalous dimension $\gamma_{gg}$ is evaluated for the
unpolarized parton densities and structure functions of the nucleon. These new
terms diminish the gluon distribution and overcompensate the contribution
caused by the resummed leading logarithmic small-$x$ anomalous dimension and
the quarkonic anomalous dimensions beyond next-to-leading order.


  Computational Fluid Dynamics (CFD) simulations using turbulence models are
commonly used in engineering design. Of the different turbulence modeling
approaches that are available, eddy viscosity based models are the most common
for their computational economy. Eddy viscosity based models utilize many
simplifications for this economy such as the gradient diffusion and the
isotropic eddy viscosity hypotheses. These simplifications limit the degree to
which eddy viscosity models can replicate turbulence physics and lead to model
form uncertainty. The Eigenspace Perturbation Method (EPM) has been developed
for purely physics based estimates of this model form uncertainty in turbulence
model predictions. Due to its physics based nature, the EPM weighs all
physically possible outcomes equally leading to overly conservative uncertainty
estimates in many cases. In this investigation we use data driven Machine
Learning (ML) approaches to address this limitation. Using ML models, we can
weigh the physically possible outcomes by their likelihood leading to better
calibration of the uncertainty estimates. Specifically, we use ML models to
predict the degree of perturbations in the EPM over the flow domain. This work
focuses on a Convolutional Neural Network (CNN) based model to learn the
discrepancy between Reynolds Averaged Navier Stokes (RANS) and Direct Numerical
Simulation (DNS) predictions. This model acts as a marker function, modulating
the degree of perturbations in the EPM. We show that this physics constrained
machine learning framework performs better than the purely physics or purely ML
alternatives, and leads to less conservative uncertainty bounds with improved
calibration.


  The DAMA experiment clearly observes a small oscillatory signal. The observed
yearly modulation is in phase with the Earth's motion around the Sun. Recent
reference [Vavra, 2014] suggested that the DAMA experiment observes a WIMP of
much smaller mass than what Xenon 10, Xenon 100, LUX and CDMS experiments can
possibly reach. Scattering would occur on proton or oxygen target present in
the NaI(Tl) crystal as OH-contamination at a few ppm level. This paper
elaborates further on the idea that the OH-molecule could act as a very
sensitive detection mechanism for neutrons or WIMPs, and suggests a calibration
procedure to prove this idea. We also propose a new detector concept to detect
a low mass WIMP.


  We revisit the possibility of producing observable tensor modes through a
continuous particle production process during inflation. Particularly, we focus
on the multi-field realization of inflation where a spectator pseudo-scalar
$\sigma$ induces a significant amplification of the ${\rm U}(1)$ gauge fields
through the coupling $\propto \sigma F_{\mu\nu}\tilde{F}^{\mu\nu}$. In this
model, both the scalar $\sigma$ and the Abelian gauge fields are
gravitationally coupled to the inflaton sector, therefore they can only affect
the primordial scalar and tensor fluctuations through their mixing with
gravitational fluctuations. Recent studies on this scenario show that the
sourced contributions to the scalar correlators can be dangerously large to
invalidate a large tensor power spectrum through the particle production
mechanism. In this paper, we re-examine these recent claims by explicitly
calculating the dominant contribution to the scalar power and bispectrum.
Particularly, we show that once the current limits from CMB data are taken into
account, it is still possible to generate a signal as large as $r \approx
10^{-3}$ and the limitations on the model building are more relaxed than what
was considered before.


  The $\beta$-decay half-lives of neutron-rich nuclei with $20 \leqslant Z
\leqslant 50$ are systematically investigated using the newly developed fully
self-consistent proton-neutron quasiparticle random phase approximation (QRPA),
based on the spherical relativistic Hartree-Fock-Bogoliubov (RHFB) framework.
Available data are reproduced by including an isospin-dependent proton-neutron
pairing interaction in the isoscalar channel of the RHFB+QRPA model. With the
calculated $\beta$-decay half-lives of neutron-rich nuclei a remarkable
speeding up of $r$-matter flow is predicted. This leads to enhanced $r$-process
abundances of elements with $A \gtrsim 140$, an important result for the
understanding of the origin of heavy elements in the universe.


  The rates-across-sites assumption in phylogenetic inference posits that the
rate matrix governing the Markovian evolution of a character on an edge of the
putative phylogenetic tree is the product of a character-specific scale factor
and a rate matrix that is particular to that edge. Thus, evolution follows
basically the same process for all characters, except that it occurs faster for
some characters than others. To allow estimation of tree topologies and edge
lengths for such models, it is commonly assumed that the scale factors are not
arbitrary unknown constants, but rather unobserved, independent, identically
distributed draws from a member of some parametric family of distributions. A
popular choice is the gamma family. We consider an example of a clock-like tree
with three taxa, one unknown edge length, and a parametric family of scale
factor distributions that contain the gamma family. This model has the property
that, for a generic choice of unknown edge length and scale factor
distribution, there is another edge length and scale factor distribution which
generates data with exactly the same distribution, so that even with infinitely
many data it will be typically impossible to make correct inferences about the
unknown edge length.


  We review the classical observational results for isotopic abundance
variations for several elements in CP stars. We concentrate on the "newest"
anomaly, in calcium. The cosmically very rare isotope, Ca-48 can rival and even
dominate the more common, alpha nuclide, Ca-40. Relevant examples are found in
the hot, non-magnetic HgMn stars, and the field horizontal-branch star, Feige
86. The calcium anomaly is also present in cool, magnetic stars, including the
notorious HD 101065, Przybylski's star.


  This paper studies the utility of the processes $\gamma \gamma \to \gamma
\gamma$, $\gamma Z$, and $ZZ$ in searching for sources of CP violation arising
from energy scales beyond the production thresholds of planned future
colliders. In the context of an effective Lagrangian approach we consider the
most general set of CP odd SU(2) $\times$ U(1) operators that give rise to
genuinely quartic gauge boson couplings which can be probed in $2 \to 2$
scattering processes at a $\gamma \gamma $ collider. We study each process in
detail, emphasizing the complementary information that is obtained by varying
the initial beam polarizations. Finally, we compare our results to other
constraints in the literature on CP odd gauge boson interactions and quartic
gauge boson couplings; the search reaches obtained here are typically stronger
and nicely complement previous studies which have focused primarily on $W$
boson, top quark, or Higgs production.


  The molecular structure of moving contact lines (MCLs) and the emergence of a
corresponding macroscopic dissipation have made the MCL a paradigm of fluid
dynamics. Through novel averaging techniques that remove capillary waves
smearing we achieve an unprecedented resolution in molecular dynamics (MD)
simulations and find that they match with the continuum description obtained by
finite element method (FEM) down to molecular scales. This allows us to
distinguish dissipation at the liquid-solid interface (Navier-slip) and at the
contact line, the latter being negligible for the rather smooth substrate
considered.


  We propose a novel method to determine the structure of symbols for any
family of polylogarithmic Feynman integrals. Using the d log-bases and simple
formulas for the leading order and next-to-leading contributions to the
intersection numbers, we give a streamlined procedure to compute the entries in
the coefficient matrices of canonical differential equations, including the
symbol letters and the rational coefficients. We also provide a selection rule
to decide whether a given matrix element must be zero. The symbol letters are
deeply related to the poles of the integrands and also have interesting
connections to the geometry of Newton polytopes. Our method can be applied to
many cutting-edge multi-loop calculations. The simplicity of our results also
hints at the possible underlying structure in perturbative quantum field
theories.


  We combine the exceptional depth of the Hubble Ultra Deep Field (HUDF) images
and the deep GRism ACS Program for Extragalactic Science (GRAPES) grism
spectroscopy to explore the stellar populations of 34 bulges belonging to
late-type galaxies at z=0.8-1.3. The sample is selected based on the presence
of a noticeable 4000A break in their GRAPES spectra, and by visual inspection
of the HUDF images. The HUDF images are used to measure bulge color and Sersic
index. The narrow extraction of the GRAPES data around the galaxy center
enables us to study the spectrum of the bulges in these late-type galaxies,
minimizing the contamination from the disk of the galaxy. We use the low
resolution (R~50) spectral energy distribution (SED) around the 4000A break to
estimate redshifts and stellar ages. The SEDs are compared with models of
galactic chemical evolution to determine the stellar mass, and to characterize
the age distribution. We find that, (1) the average age of late-type bulges in
our sample is ~1.3 Gyr with stellar masses in the range log(M)=6.5-10 solar.
(2) Late-type bulges are younger than early-type galaxies at similar redshifts
and lack a trend of age with respect to redshift, suggesting a more extended
period of star formation. (3) Bulges and inner disks in these late-type
galaxies show similar stellar populations, and (4) late-type bulges are better
fitted by exponential surface brightness profiles. The overall picture emerging
from the GRAPES data is that, in late-type galaxies at z=1, bulges form through
secular evolution and disks via an inside-out process.


  We systematically investigate the parameter space of neutrino and charged
lepton mass matrices for textures motivated by an extended quark-lepton
complementarity. As the basic hypothesis, we postulate that all mixing angles
in U_l and U_nu be either maximal or described by powers of a single small
quantity epsilon ~ theta_C. All mass hierarchies are described by this epsilon
as well. In this study, we do not assume specific forms for U_l and U_nu, such
as large mixing coming from the neutrino sector only. We perform a systematic
scan of the 262,144 generated mixing matrices for being compatible with current
experimental data, and find a sample of 2,468 possibilities. We then analyze
and classify the effective charged lepton and neutrino mass textures, where we
especially focus on a subset of models getting under pressure for small
theta_13. In addition, we predict the mixing angle distributions from our
sample of all valid textures, and study the robustness of this prediction. We
also demonstrate how our procedure can be extended to predictions of the Dirac
and Majorana phases in U_PMNS. For instance, we find that CP conservation in
neutrino oscillations is preferred, and we can impose a lower bound on the
mixing matrix element for neutrinoless double beta decay.