  Five elementary lectures delivered at TASI 2011 on the Standard Model, its
extensions to neutrino masses, flavor symmetries, and Grand-Unification.


  Let F be a non-archimedean local field and G be the group GL(N,F). Let \pi be
a smooth complex representation of G lying in the Bernstein block B(\pi) of
some simple type in the sense of Bushnell and Kutzko. Refining the approach of
the second author and U. Stuhler, we canonically attach to \pi a subset X_\pi
of the Bruhat-Tits building X of G, as well as a G-equivariant coefficient
system C[\pi ] on X_\pi. Roughly speaking the coefficient system is obtained by
taking isotypic components of \pi according to some representations constructed
from the Bushnell and Kutzko type of \pi . We conjecture that when \pi has
central character, the augmented chain complex associate to C[\pi ] is a
projective resolution of \pi in the category B(\pi). Moreover we reduce this
conjecture to a technical lemma of representation theoretic nature. We prove
this lemma when \pi is an irreducible discrete series of G. We then attach to
any irreducible discrete series \pi of G an explicit pseudo-coefficient f_\pi
and obtain a Lefschetz type formula for the value of the Harish-Chandra
character of \pi at a regular elliptic element. In contrast to that obtained by
U. Stuhler and the second author, this formula allows explicit character value
computations.


  The influence of triaxial deformation $\gamma$ on the purely collective form
of wobbling motion in even-even nuclei are discussed based on the triaxial
rotor model. It is found that the harmonic approximation is realized well when
$\gamma=30^{\circ}$ for the properties of energy spectra and electric
quadrupole transition probabilities, while this approximation gets bad when
$\gamma$ deviates from $30^{\circ}$. A recent data from Coulomb excitation
experiment, namely $3_1^+$ and $2_2^+$ for the $^{110}$Ru are studied and might
be suggested as the bandhead of the wobbling bands. In addition, two types of
angular momentum geometries for wobbling motion, stemming from different
$\gamma$ values, are exhibited by azimuthal plots.


  We have observed the decay $K_L\to \mu^+\mu^- \gamma \gamma$ at the KTeV
experiment at Fermilab. This decay presents a formidable background to the
search for new physics in $K_L\to\pi^0\mu^+\mu^-$. The 1997 data yielded a
sample of 4 signal events, with an expected background of 0.155 $\pm$ 0.081
events. The branching ratio is ${\mathcal B}(K_L\to \mu^+\mu^- \gamma \gamma$)
$ = (10.4^{+7.5}_{-5.9} {\rm (stat)} \pm 0.7 {\rm (sys)})\times 10^{-9}$ with
$m_{\gamma\gamma} \geq 1 {\rm MeV/c}^2$, consistent with a QED calculation
which predicts $(9.1\pm 0.8)\times 10^{-9}$.


  The compound ZrTe$_5$ has recently been connected to a charge-density-wave
(CDW) state with intriguing transport properties. Here, we investigate quantum
oscillations in ultrasound measurements that microscopically originate from
electron-phonon coupling and analyze how these would be affected by the
presence or absence of a CDW. We calculate the phonon self-energy due to
electron-phonon coupling, and from there deduce the sound-velocity
renormalization and sound attenuation. We find that the theoretical predictions
for a metallic Dirac model resemble the experimental data on a quantitative
level for magnetic fields up to the quantum-limit regime.


  Hierarchical polymer structures such as pNIPAM microgels have been
extensively studied for their ability to undergo significant structural and
physical transformations that can be controlled by external stimuli such as
temperature, pH or solvent composition. However, direct three-dimensional
visualization of individual particles in situ have so far been hindered by
insufficient resolution, with optical microscopy, or contrast, with electron
microscopy. In recent years superresolution microscopy techniques have emerged
that in principle can provide nanoscopic optical resolution. Here we report on
the in-situ superresolution microscopy of dye-labeled submicron sized pNIPAM
microgels revealing the internal microstructure during swelling and collapse of
individual particles. Using direct STochastic Optical Reconstruction Microscopy
(dSTORM) we demonstrate a lateral optical resolution of 30nm and an axial
resolution of 60nm.


  With the rapid progress of quantum information these recent years, it becomes
more and more relevant to dedicate efforts in introducing this research topic
to undergraduate students. However, as if in various fields of physics the
theoretical learning is closely accompanied with experimental illustrations,
such a teaching method can be expensive to organise for quantum information. We
propose one way to circumvent these difficulties by using the recently made
available 5-qubit quantum processor of IBM, in order to illustrate quantum
information tasks, by actually implementing them on the superconducting chip
through the web interface of the IBM Quantum Experience. We focus on the
realization of a quantum teleportation protocol on this device, analyze the
results and discuss the issues encountered, providing a complete analysis of
this software as a pedagogical tool.


  We describe some classes of PDE that display hidden symmetry, with reduced
equations having additional symmetry operators compared to the initial
equations. Relations between the concepts of hidden and conditional symmetry,
and between hidden symmetry and equivalence of classes of equations, is
discussed. In particular, we describe equations having hidden and conditional
symmetry under rotations and boosts in the Lorentz and Euclid groups.


  Dynamic rupture simulations generate synthetic waveforms that account for
non-linear source, path, and site complexity. Here, we analyze millions of
spatially dense waveforms from 3D dynamic rupture simulations in a novel way to
illuminate the spectral fingerprints of earthquake physics. We define a
Brune-type equivalent near-field corner frequency ($f_c$) to analyze the
spatial variability of ground motion spectra and unravel their link to source
complexity. We first investigate a simple 3D strike-slip setup, including an
asperity and a barrier, and illustrate basic relations between source
properties and $f_c$ variations. Next, we analyze > 13,000,000 synthetic
near-field strong motion waveforms generated in three high-resolution dynamic
rupture simulations of real earthquakes, namely, the $M_w$ 7.1 2019 Ridgecrest
mainshock, the $M_w$ 6.4 Searles Valley foreshock, and the $M_w$ 7.3 1992
Landers earthquake. All scenarios consider 3D fault geometries, topography,
off-fault plasticity, viscoelastic attenuation, 3D velocity structure, and
resolve frequencies up to 1-2 Hz. Our analysis reveals pronounced and localized
patterns of elevated $f_c$, specifically in the vertical components. We
validate such $f_c$ variability in observed near-fault spectra. Using isochrone
analysis, we identify the complex dynamic mechanisms that explain the rays of
elevated $f_c$ and cause unexpectedly impulsive, localized, vertical ground
motions. While the vertical high frequencies are also associated with path
effects, rupture directivity, and coalescence of multiple rupture fronts, we
show that they are dominantly caused by rake-rotated surface-breaking rupture
fronts that decelerate due to fault heterogeneities or geometric complexity.
Our findings highlight the potential of spatially dense ground motion
observations for furthering our understanding of earthquake physics directly
from near-field data.


  Let {\nu} be a normal function on a complex manifold X. The infinitesimal
invariant of {\nu} has a well-defined zero locus inside the tangent bundle TX.
When X is quasi-projective, and {\nu} is admissible, we show that this zero
locus is constructible in the Zariski topology.


  The sensitivity of ongoing searches for gravitational wave (GW) sources in
the ultra-low frequency regime ($10^{-9}$ Hz to $10^{-7}$ Hz) using Pulsar
Timing Arrays (PTAs) will continue to increase in the future as more well-timed
pulsars are added to the arrays. It is expected that next-generation radio
telescopes, namely, the Five-hundred-meter Aperture Spherical radio Telescope
(FAST) and the Square Kilometer Array (SKA), will grow the number of well-timed
pulsars to $O(10^3)$. The higher sensitivity will result in greater distance
reach for GW sources, uncovering multiple resolvable GW sources in addition to
an unresolved population. Data analysis techniques are, therefore, required
that can search for and resolve multiple signals present simultaneously in PTA
data. The multisource resolution problem in PTA data analysis poses a unique
set of challenges such as non-uniformly sampled data, a large number of
so-called pulsar phase parameters that arise from the inaccurately measured
distances to the pulsars, and poor separation of signals in the Fourier domain
due to a small number of cycles in the observed waveforms.


  The $r$-neighbour bootstrap percolation process on a graph $G$ starts with an
initial set $A_0$ of "infected" vertices and, at each step of the process, a
healthy vertex becomes infected if it has at least $r$ infected neighbours
(once a vertex becomes infected, it remains infected forever). If every vertex
of $G$ eventually becomes infected, then we say that $A_0$ percolates.
  We prove a conjecture of Balogh and Bollob\'as which says that, for fixed $r$
and $d\to\infty$, every percolating set in the $d$-dimensional hypercube has
cardinality at least $\frac{1+o(1)}{r}\binom{d}{r-1}$. We also prove an
analogous result for multidimensional rectangular grids. Our proofs exploit a
connection between bootstrap percolation and a related process, known as weak
saturation. In addition, we improve on the best known upper bound for the
minimum size of a percolating set in the hypercube. In particular, when $r=3$,
we prove that the minimum cardinality of a percolating set in the
$d$-dimensional hypercube is $\left\lceil\frac{d(d+3)}{6}\right\rceil+1$ for
all $d\geq3$.


  While the mechanical distortions change the electronic properties of graphene
significantly, the effects of electronic manipulation on its mechanical
properties have not been known. Using first-principles calculation methods, we
show that, when graphene expands isotropically under equibiaxial strain, both
the electron and hole doping can maintain or improve its ideal strength
slightly and enhance the critical breaking strain dramatically. Contrary to the
isotropic expansions, the electron doping decreases the ideal strength as well
as critical strain of uniaxially strained graphene while the hole doping
increases the both. Distinct failure mechanisms depending on type of strains
are shown to be origins of the different doping induced mechanical stabilities.
Our findings may resolve a contradiction between recent experimental and
theoretical results on the strength of graphene.


  In this paper, we are interested in the speed of convergence of the
stochastic billiard evolving in a convex set K. This process can be described
as follows: a particle moves at unit speed inside the set K until it hits the
boundary, and is randomly reflected, independently of its position and previous
velocity. We focus on convex sets in R 2 with a curvature bounded from above
and below. We give an explicit coupling for both the continuous-time process
and the embedded Markov chain of hitting points on the boundary, which leads to
an explicit speed of convergence to equilibrium.


  We analyze the properties of the shallow decay segment with a sample of 53
long Swift GRBs. We show that the distributions of its characteristics are
log-normal or normal, and its isotropic X-ray energy (E_{iso,X}) is linearly
correlated with the prompt gamma-ray energy, but with a steeper photon spectrum
except for some X-ray flashes. No significant spectral evolution is observed
from this phase to the follow-up phase, and the follow-up phase is usually
consistent with the external shock models, implying that this segment likely
due to a refreshed external shock. Within this scenario, the data are generally
consistent with a roughly constant injection luminosity up to the end of this
phase $t_b$. A positive correlation between E_{iso, X} and t_b also favors this
scenario. Among the 13 bursts that have well-sampled optical light curves, 6
have an optical break around t_b and the breaks are consistent with being
achromatic. However, the other 7 bursts either do not show an optical break or
have a break at a different epoch than t_b. This raises a concern to the energy
injection scenario, suggesting that the optical and X-ray emissions may not be
the same component at least for a fraction of bursts. There are 4 significant
outliers in the sample, and this shallow decau phase in these bursts is
immediately followed by a very steep decay after t_b, which is inconsistent
with any external shock model. The optical data of these bursts evolve
independently from the X-ray data. These X-ray plateaus likely have an internal
origin and demand continuous operation of a long-term GRB central engine. We
conclude that the observed shallow decay phase likely has diverse physical
origins(Abridged).


  Modern software engineering of electronic structure codes has seen a paradigm
shift from monolithic workflows towards object-based modularity. Software
objectivity allows for greater flexibility in the application of electronic
structure calculations, with particular benefits when integrated with
approaches for data-driven analysis. Here, we discuss different approaches to
create "deep" modular interfaces that connect big-data workflows and electronic
structure codes, and explore the diversity of use cases that they can enable.
We present two such interface approaches for the semi-empirical electronic
structure package, DFTB+. In one case, DFTB+ is applied as a library and
provides data to an external workflow; and in another, DFTB+ receives data via
external bindings and processes the information subsequently within an internal
workflow. We provide a general framework to enable data exchange workflows for
embedding new machine-learning-based Hamiltonians within DFTB+, or to enabling
deep integration of DFTB+ in multiscale embedding workflows. These modular
interfaces demonstrate opportunities in emergent software and workflows to
accelerate scientific discovery by harnessing existing software capabilities.


  Biometric systems based on iris recognition are currently being used in
border control applications and mobile devices. However, research in iris
recognition is stymied by various factors such as limited datasets of bonafide
irides and presentation attack instruments; restricted intra-class variations;
and privacy concerns. Some of these issues can be mitigated by the use of
synthetic iris data. In this paper, we present a comprehensive review of
state-of-the-art GAN-based synthetic iris image generation techniques,
evaluating their strengths and limitations in producing realistic and useful
iris images that can be used for both training and testing iris recognition
systems and presentation attack detectors. In this regard, we first survey the
various methods that have been used for synthetic iris generation and
specifically consider generators based on StyleGAN, RaSGAN, CIT-GAN, iWarpGAN,
StarGAN, etc. We then analyze the images generated by these models for realism,
uniqueness, and biometric utility. This comprehensive analysis highlights the
pros and cons of various GANs in the context of developing robust iris matchers
and presentation attack detectors.


  Host-to-host variability with respect to interactions between microorganisms
and multicellular hosts are commonly observed in infection and in homeostasis.
However, the majority of mechanistic models used in analyzing
host-microorganism relationships, as well as most of the ecological theories
proposed to explain co-evolution of host and microbes, are based on averages
across a host population. By assuming that observed variations are random and
independent, these models overlook the role of inter-host differences. Here we
analyze mechanisms underlying host-to-host variations, using the
well-characterized experimental infection model of polymicrobial otitis media
(OM) in chinchillas, in combination with population dynamic models and a
Maximum Entropy (MaxEnt) based inference scheme. We find that the nature of the
interactions among bacterial species critically regulates host-to-host
variations of these interactions. Surprisingly, seemingly unrelated phenomena,
such as the efficiency of individual bacterial species in utilizing nutrients
for growth and the microbe-specific host immune response, can become
interdependent in a host population. The latter finding suggests a potential
mechanism that could lead to selection of specific strains of bacterial species
during the coevolution of the host immune response and the bacterial species.


  We use CO and H alpha velocity fields to study the gas kinematics in the
spiral arms and interarms of M51 (NGC 5194), and fit the 2D velocity field to
estimate the radial and tangential velocity components as a function of spiral
phase (arm distance). We find large radial and tangential streaming velocities,
which are qualitatively consistent with the predictions of density wave theory
and support the existence of shocks. The streaming motions are complex, varying
significantly across the galaxy as well as along and between arms. Aberrations
in the velocity field indicate that the disk is not coplanar, perhaps as far in
as 20\arcsec\ (800 pc) from the center. Velocity profile fits from CO and H
alpha are typically similar, suggesting that most of the H alpha emission
originates from regions of recent star formation. We also explore vortensity
and mass conservation conditions. Vortensity conservation, which does not
require a steady state, is empirically verified. The velocity and density
profiles show large and varying mass fluxes, which are inconsistent with a
steady flow for a single dominant global spiral mode. We thus conclude that the
spiral arms cannot be in a quasi-steady state in any rotating frame, and/or
that out of plane motions may be significant.


  The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) is a
major facility to carry out spectroscopic surveys for cosmology and galaxy
evolution studies. The seventh data release of the LAMOST ExtraGAlactic Survey
(LEGAS) is currently available and including redshifts of 193\,361 galaxies.
These sources are spread over $\sim 11\,500$ deg$^2$ of the sky, largely
overlapping with other imaging (SDSS, HSC) and spectroscopic (BOSS) surveys.
The estimated depth of the galaxy sample, $r\sim17.8$, the high signal-to-noise
ratio, and the spectral resolution $R=1800$, make the LAMOST spectra suitable
for galaxy velocity dispersion measurements, which are invaluable to study the
structure and formation of galaxies and to determine their central dark matter
(DM) content. We present the first estimates of central velocity dispersion of
$\sim86\,000$ galaxies in LAMOST footprint. We have used a wrap-up procedure to
perform the spectral fitting using \textsc{pPXF}, and derive velocity
dispersion measurements. Statistical errors are also assessed by comparing
LAMOST velocity dispersion estimates with the ones of SDSS and BOSS over a
common sample of $\sim51\,000$ galaxies. The two datasets show a good
agreement, within the statistical errors, in particular when velocity
dispersion values are corrected to 1 effective radius aperture. We also present
a preliminary Mass-$\sigma$ relation and find consistency with previous
analyses based on local galaxy samples. These first results suggest that LAMOST
spectra are suitable for galaxy velocity dispersion measurements to complement
the available catalogs of galaxy internal kinematics in the northern
hemisphere. We plan to expand this analysis to next LAMOST data releases.


  We propose an extended Hubbard model on a 2D Kagome lattice with an
additional ring-exchange term. The particles can be either bosons or spinless
fermions . At a special filling fraction of 1/6 the model is analyzed in the
lowest non-vanishing order of perturbation theory. Such ``undoped'' model is
closely related to the Quantum Dimer Model. We show how to arrive at an exactly
soluble point whose ground state manifold is the extensively degenerate
``d-isotopy space'', a necessary precondition for for a certain type of
non-Abelian topological order. Near the ``special'' values, $d = 2 \cos
\pi/(k+2)$, this space is expected to collapse to a stable topological phase
with anyonic excitations closely related to SU(2) Chern-Simons theory at level
k.


  We study the spin-wave dispersion of localized spins in a disordered
double-exchange model using the perturbation theory with respect to the
strength of the disorder potential. We calculate the dispersion upto the
next-leading order, and extensively examine the case of one-dimension. We show
that in that case, disorder yields anomalous gapped-like behavior at the Fermi
wavenumber of the conduction electrons.


  In an open-world setting, it is inevitable that an intelligent agent (e.g., a
robot) will encounter visual objects, attributes or relationships it does not
recognize. In this work, we develop an agent empowered with visual curiosity,
i.e. the ability to ask questions to an Oracle (e.g., human) about the contents
in images (e.g., What is the object on the left side of the red cube?) and
build visual recognition model based on the answers received (e.g., Cylinder).
In order to do this, the agent must (1) understand what it recognizes and what
it does not, (2) formulate a valid, unambiguous and informative language query
(a question) to ask the Oracle, (3) derive the parameters of visual classifiers
from the Oracle response and (4) leverage the updated visual classifiers to ask
more clarified questions. Specifically, we propose a novel framework and
formulate the learning of visual curiosity as a reinforcement learning problem.
In this framework, all components of our agent, visual recognition module (to
see), question generation policy (to ask), answer digestion module (to
understand) and graph memory module (to memorize), are learned entirely
end-to-end to maximize the reward derived from the scene graph obtained by the
agent as a consequence of the dialog with the Oracle. Importantly, the question
generation policy is disentangled from the visual recognition system and
specifics of the environment. Consequently, we demonstrate a sort of double
generalization. Our question generation policy generalizes to new environments
and a new pair of eyes, i.e., new visual system. Trained on a synthetic
dataset, our results show that our agent learns new visual concepts
significantly faster than several heuristic baselines, even when tested on
synthetic environments with novel objects, as well as in a realistic
environment.


  While conventional shared demand-responsive transportation (SDRT) systems
mostly operate on a door-to-door policy, the usage of meeting points for the
pick-up and drop-off of user groups can offer several advantages, like fewer
stops and less total travelled mileage. Moreover, it offers the possibility to
select only feasible and well-defined locations where a safe (de-)boarding is
possible. This paper presents a three-step workflow for solving the SDRT
problem with meeting points (SDRT-MP). Firstly, the customers are clustered
into similar groups, then meeting (and divergence) points are determined for
each cluster. Finally, a parallel neighbourhood search algorithm is applied to
create the vehicle routes. Further, a simulation with realistic pick-up and
drop-off locations based on map data is performed in order to demonstrate the
impact of using meeting points for SDRT systems in contrast to the door-to-door
service. Although the average passenger travel time is higher due to enhanced
walking and waiting times, the experiment highlights a reduction of operator
resources required to serve all customers.


  We discuss the dependence of pure Yang-Mills equation of state on the choice
of gauge algebra. In the confined phase, we generalize to an arbitrary simple
gauge algebra Meyer's proposal of modelling the Yang-Mills matter by an ideal
glueball gas in which the high-lying glueball spectrum is approximated by a
Hagedorn spectrum of closed-bosonic-string type. Such a formalism is undefined
above the Hagedorn temperature, corresponding to the phase transition toward a
deconfined state of matter in which gluons are the relevant degrees of freedom.
Under the assumption that the adjoint string tension and the typical energy
scale of the running coupling are gauge-algebra independent, we discuss about
how the behavior of thermodynamical quantities such as the trace anomaly should
depend on the gauge algebra in both the confined and deconfined phase. The
obtained results compare favourably with recent and accurate lattice data in
the $\mathfrak{su}(3)$ case and support the idea that the more the gauge
algebra has generators, the more the phase transition is of first-order type.


  A three dimensional mesoscopic model is applied to study the properties of
short DNA chains in a confining environment. The cylindrical channel is
represented by a hard-wall repulsive potential incorporated in the system
Hamiltonian. The macroscopic helical parameters are computed performing
statistical averages over the ensemble of microscopic base pair fluctuations.
The average molecule elongation, measured by the end-to-end distance, is
derived as a function of the channel potential parameters both for a
homogeneous and a heterogeneous chain. The overall results suggest that the
mesoscopic model, with the channel potential term, yields consistent
quantitative estimates for the stretching and twisting of short chains.


  The homology of a Garside monoid, thus of a Garside group, can be computed
efficiently through the use of the order complex defined by Dehornoy and
Lafont. We construct a categorical generalization of this complex and we give
some computational techniques which are useful for reducing computing time.
  We then use this construction to complete results of Salvetti, Callegaro and
Marin regarding the homology of exceptional complex braid groups. We most
notably study the case of the Borchardt braid group $B(G_{31})$ through its
associated Garside category.


  We study gaugino condensation in presence of an anomalous $U(1)$ gauge group
and find that global supersymmetry is dynamically broken. An example of
particular interest is provided by effective string models with 4-dimensional
Green-Schwarz anomaly cancellation mechanism. The structure of the hidden
sector is constrained by the anomaly cancellation conditions and the scale of
gaugino condensation is shifted compared with the usual case. We explicitly
compute the resulting soft supersymmetry breaking terms.


  Let $f \colon X \to A$ be a morphism from a smooth projective variety to an
abelian variety (over the field of complex numbers). We show that the sheaves
$f_* \omega_X^{\otimes m}$ become globally generated after pullback by an
isogeny. We use this to deduce a decomposition theorem for these sheaves when
$m \ge 2$, analogous to that obtained by Chen-Jiang when $m = 1$. This is in
turn applied to effective results for pluricanonical linear series on irregular
varieties with canonical singularities.


  The paper observes an almost Hermitian manifold as an example of a
generalized Riemannian manifold and examines the application of a
quarter-symmetric connection on the almost Hermitian manifold. The almost
Hermitian manifold with quarter-symmetric connection preserving the generalized
Riemannian metric is actually the K\"ahler manifold. Observing the six linearly
independent curvature tensors with respect to the quarter-symmetric connection,
we construct tensors that do not depend on the quarter-symmetric connection
generator. One of them coincides with the Weyl projective curvature tensor of
symmetric metric $g$. Also, we obtain the relations between the Weyl projective
curvature tensor and the holomorphically projective curvature tensor. Moreover,
we examine the properties of curvature tensors when some tensors are hybrid.


  We study the morphology of the chain-like aggregates formed when a external
constant and uniaxial magnetic field is applied to a magneto-rheological (MR)
fluid. In order to characterize the conformation of the aggregates, we study
the evolution of various fractal dimensions during aggregation and
disaggregation processes (i.e., when the applied field is switched on and off),
using video-microscopy and image analysis. Experiments have been performed by
varying the values of two external parameters: the magnetic field amplitude and
particle concentration. We found that the box-counting dimension, related with
how the aggregates occupy the surrounding space, depends on the ratio
$R_1/R_0$. During the first stage of the disaggregation process, when the
particles are moving by Brownian motion inside the aggregate, Family-Vicsek
scaling function is verified.


  We present an algorithm to compute the minimum orbital intersection distance
(MOID), or global minimum of the distance between the points lying on two
Keplerian ellipses. This is achieved by finding all stationary points of the
distance function, based on solving an algebraic polynomial equation of $16$th
degree. The algorithm tracks numerical errors appearing on the way, and treats
carefully nearly degenerate cases, including practical cases with almost
circular and almost coplanar orbits. Benchmarks confirm its high numeric
reliability and accuracy, and that regardless of its error--controlling
overheads, this algorithm pretends to be one of the fastest MOID computation
methods available to date, so it may be useful in processing large catalogs.


  The circular twin paradox and Thomas Precession are presented in a way that
makes both accessible to students in introductory relativity courses. Both are
discussed by examining what happens during travel around a polygon and then in
the limit as the polygon tends to a circle. Since relativistic predictions
based on these examples can be verified in experiments with macroscopic objects
such as atomic clocks and the gyroscopes on Gravity Probe B, they are
particularly convincing to introductory students.


  Light travel time delays distort the apparent shapes of HII regions
surrounding bright quasars during early stages of cosmic reionization.
Individual HII regions may remain undetectable in forthcoming redshifted 21 cm
experiments. However, the systematic deformation along the line of sight may be
detectable statistically, either by stacking tomographic 21cm images of quasars
identified, for example, by JWST, or as small-scale anisotropy in the
three-dimensional 21cm power spectrum. Here we consider the detectability of
this effect. The anisotropy is largest when HII regions are large and expand
rapidly, and we find that if bright quasars contributed to the early stages of
reionization, then they can produce significant anisotropy, on scales
comparable to the typical sizes of HII regions of the bright quasars (approx.
30 Mpc and below). The effect therefore cannot be ignored when analyzing future
21cm power spectra on small scales. If 10 percent of the volume of the IGM at
redshift z=10 is ionized by quasars with typical ionizing luminosity of S= 5 x
10^{56} photons/second, the distortions can enhance by more than 10 percent the
21cm power spectrum in the radial (redshift) direction, relative to the
transverse directions. The level of this anisotropy exceeds that due to
redshift-space distortion, and has the opposite sign. We show that on-going
experiments such as MWA should be able to detect this effect. A detection would
reveal the presence of bright quasars, and shed light on the ionizing yield and
age of the ionizing sources, and the distribution and small-scale clumping of
neutral intergalactic gas in their vicinity.


  We devise a two dimensional model that mimics the recently observed power law
distributions for the amplitudes and durations of the acoustic emission signals
observed during martensitic transformation [ Vives {\it et al}, Phys. Rev.
Lett. {\bf 72}, 1694 (1994)]. We include a threshold mechanism arising from the
athermal nature of transformation, long-range interaction between the
transformed domains, inertial effects, and dissipation arising due to the
motion of the interface. The model exhibits thermal hysteresis of the
transformation, and more importantly, it shows that the energy is released in
the form of avalanches with power law distributions for their amplitudes and
durations. Computer simulations also reveal morphological features similar to
those observed in real systems.


  In [Meurant, Pape\v{z}, Tich\'y; Numerical Algorithms 88, 2021], we presented
an adaptive estimate for the energy norm of the error in the conjugate gradient
(CG) method. In this paper, we extend the estimate to algorithms for solving
linear approximation problems with a general, possibly rectangular matrix that
are based on applying CG to a system with a positive (semi-)definite matrix
build from the original matrix. We show that the resulting estimate preserves
its key properties: it can be very cheaply evaluated, and it is numerically
reliable in finite-precision arithmetic under some mild assumptions. We discuss
algorithms based on Hestenes-Stiefel-like implementation (often called CGLS and
CGNE in the literature) as well as on bidiagonalization (LSQR and CRAIG), and
both unpreconditioned and preconditioned variants. The numerical experiments
confirm the robustness and very satisfactory behaviour of the estimate.


  We highlight a practical yet rarely discussed problem in dialogue state
tracking (DST), namely handling unknown slot values. Previous approaches
generally assume predefined candidate lists and thus are not designed to output
unknown values, especially when the spoken language understanding (SLU) module
is absent as in many end-to-end (E2E) systems. We describe in this paper an E2E
architecture based on the pointer network (PtrNet) that can effectively extract
unknown slot values while still obtains state-of-the-art accuracy on the
standard DSTC2 benchmark. We also provide extensive empirical evidence to show
that tracking unknown values can be challenging and our approach can bring
significant improvement with the help of an effective feature dropout
technique.


  A model for classical impurities moving in Bose-Einstein Condensate (BEC) is
proposed in the framework of quantum field theory and is solved within the
Bogoliubov approximation at zero temperature. Several formulae are obtained for
physical quantities such as the occupation number, the dissipation, the free
energy, and the depletion. To illustrate this model two examples are studied;
an impurity moving with i) a constant velocity and ii) a constant acceleration.
Landau's criterion for energy dissipation accompanying the motion of impurities
due to creation of quasi-particles in a superfluid, which was proposed on the
basis of purely phenomenological argument, is obtained in the frame work of an
exact quantum mechanical model.


  Let $\mathfrak{g}$ be a simple complex Lie algebra and let $\mathfrak{t}
\subset \mathfrak{g}$ be a toral subalgebra of $\mathfrak{g}$. As a
$\mathfrak{t}$-module $\mathfrak{g}$ decomposes as \[\mathfrak{g} =
\mathfrak{s} \oplus \big(\oplus_{\nu \in \mathcal{R}} \mathfrak{g}^\nu\big)\]
where $\mathfrak{s} \subset \mathfrak{g}$ is the reductive part of a parabolic
subalgebra of $\mathfrak{g}$ and $\mathcal{R}$ is the Kostant root system
associated to $\mathfrak{t}$. When $\mathfrak{t}$ is a Cartan subalgebra of
$\mathfrak{g}$ the decomposition above is nothing but the root decomposition of
$\mathfrak{g}$ with respect to $\mathfrak{t}$; in general the properties of
$\mathcal{R}$ resemble the properties of usual root systems. In this note we
study the following problem: "Given a subset $\mathcal{S} \subset \mathcal{R}$,
is there a parabolic subalgebra $\mathfrak{p}$ of $\mathfrak{g}$ containing
$\mathcal{M} = \oplus_{\nu \in \mathcal{S}} \mathfrak{g}^\nu$ and whose
reductive part equals $\mathfrak{s}$?". Our main results is that, for a
classical simple Lie algebra $\mathfrak{g}$ and a saturated $\mathcal{S}
\subset \mathcal{R}$, the condition
$(\operatorname{Sym}^\cdot(\mathcal{M}))^{\mathfrak{s}} = \mathbf{C}$ is
necessary and sufficient for the existence of such a $\mathfrak{p}$. In
contrast, we show that this statement is no longer true for the exceptional Lie
algebras $\mathrm{F}_4, \mathrm{E}_6, \mathrm{E}_7$, and $\mathrm{E}_8$.
Finally, we discuss the problem in the case when $\mathcal{S}$ is not
saturated.


  Using the discrete element method (DEM), we study the splash processes
induced by the impact of a grain on two types of granular beds, namely,
randomly packed and FCC-structured beds.Good correspondence is obtained between
our numerical results and the findings of previous experiments, and it is
demonstrated that the packing structure of the granular bed strongly affects
the splash process.The mean ejection angle for the randomly packed bed is
consistent with previous experimental results. The FCC-structured bed yields a
larger mean ejection angle; however, the latter result has not been confirmed
experimentally. Furthermore, the ejection angle distributions and the vertical
ejection speeds for individual grains vary depending on the relative timing at
which the grains are ejected after the initial impact. Obvious differences are
observed between the distributions of grains ejected during the earlier and
later splash periods: the form of the vertical ejection speed distribution
varies from a power-law form to a lognormal form with time, and more than 80\%
of the kinetic energy of all ejected grains is used for earlier ejected grains.


  Quenched chiral perturbation theory is extended to include heavy-light
mesons. Non-analytic corrections to the decay constants, Isgur-Wise function
and masses and mixing of heavy mesons are then computed. The results are used
to estimate the error due to quenching in lattice computations of these
quantities. For reasonable choices of parameters, it is found that quenching
has a strong effect on $f_{B_s}/f_B$, reducing it by as much as $28\%$. The
errors are essentially negligible for the Isgur-Wise function and the mixing
parameter.


  Spider is a balloon-borne array of six telescopes that will observe the
Cosmic Microwave Background. The 2400 antenna-coupled bolometers in the
instrument will make a polarization map of the CMB with ~degree resolution at
150 GHz and 95 GHz. Polarization modulation is achieved via a cryogenic
sapphire half-wave plate (HWP) skyward of the primary optic. In this thesis,
the design, construction, and lab testing of the HWP system are discussed. The
polarization modulation of these optical stacks is modeled using a physical
optics calculation and Mueller matrices. Performance tests in both the lab and
integrated in the flight cryostat show consistency with the model.


  We discuss a number of long-standing theoretical questions about collapse to
black holes in the Brans-Dicke theory of gravitation. Using a new numerical
code, we show that Oppenheimer-Snyder collapse in this theory produces black
holes that are identical to those of general relativity in final equilibrium,
but are quite different from those of general relativity during dynamical
evolution. We find that there are epochs during which the apparent horizon of
such a black hole passes {\it outside\/} the event horizon, and that the
surface area of the event horizon {\it decreases\/} with time. This behavior is
possible because theorems which prove otherwise assume $R_{ab}l^al^b \ge 0$ for
all null vectors $l^a$. We show that dynamical spacetimes in Brans-Dicke theory
can violate this inequality, even in vacuum, for any value of $\omega$.


  Production of Bloch waves during a rapid quench is studied by analytical and
numerical methods. The density of Bloch waves decays exponentially with the
quench time. It also strongly depends on temperature. Very few textures are
produced for temperatures lower than a characteristic temperature proportional
to the square of the magnetic field.


  The escape mechanism of orbits in a star cluster rotating around its parent
galaxy in a circular orbit is investigated. A three degrees of freedom model is
used for describing the dynamical properties of the Hamiltonian system. The
gravitational field of the star cluster is represented by a smooth and
spherically symmetric Plummer potential. We distinguish between ordered and
chaotic orbits as well as between trapped and escaping orbits, considering only
unbounded motion for several energy levels. The Smaller Alignment Index (SALI)
method is used for determining the regular or chaotic nature of the orbits. The
basins of escape are located and they are also correlated with the
corresponding escape time of the orbits. Areas of bounded regular or chaotic
motion and basins of escape were found to coexist in the $(x,z)$ plane. The
properties of the normally hyperbolic invariant manifolds (NHIMs), located in
the vicinity of the index-1 Lagrange points $L_1$ and $L_2$, are also explored.
These manifolds are of paramount importance as they control the flow of stars
over the saddle points, while they also trigger the formation of tidal tails
observed in star clusters. Bifurcation diagrams of the Lyapunov periodic orbits
as well as restrictions of the Poincar\'e map to the NHIMs are deployed for
elucidating the dynamics in the neighbourhood of the saddle points. The
extended tidal tails, or tidal arms, formed by stars with low velocity which
escape through the Lagrange points are monitored. The numerical results of this
work are also compared with previous related work.


  We develop the geometric formulation of the Standard Model Effective Field
Theory (SMEFT). Using this approach we derive all-orders results in the
$\sqrt{2 \langle H^\dagger H \rangle}/\Lambda$ expansion relevant for studies
of electroweak precision and Higgs data.


  With a given holomorphic section of a Hermitian vector bundle, one can
associate a residue current by means of Cauchy-Fantappi\`e-Leray type formulas.
In this paper we define products of such residue currents. We prove that, in
the case of a complete intersection, the product of the residue currents of a
tuple of sections coincides with the residue current of the direct sum of the
sections.


  Deep neural networks (DNNs) have transformed several artificial intelligence
research areas including computer vision, speech recognition, and natural
language processing. However, recent studies demonstrated that DNNs are
vulnerable to adversarial manipulations at testing time. Specifically, suppose
we have a testing example, whose label can be correctly predicted by a DNN
classifier. An attacker can add a small carefully crafted noise to the testing
example such that the DNN classifier predicts an incorrect label, where the
crafted testing example is called adversarial example. Such attacks are called
evasion attacks. Evasion attacks are one of the biggest challenges for
deploying DNNs in safety and security critical applications such as
self-driving cars. In this work, we develop new methods to defend against
evasion attacks. Our key observation is that adversarial examples are close to
the classification boundary. Therefore, we propose region-based classification
to be robust to adversarial examples. For a benign/adversarial testing example,
we ensemble information in a hypercube centered at the example to predict its
label. In contrast, traditional classifiers are point-based classification,
i.e., given a testing example, the classifier predicts its label based on the
testing example alone. Our evaluation results on MNIST and CIFAR-10 datasets
demonstrate that our region-based classification can significantly mitigate
evasion attacks without sacrificing classification accuracy on benign examples.
Specifically, our region-based classification achieves the same classification
accuracy on testing benign examples as point-based classification, but our
region-based classification is significantly more robust than point-based
classification to various evasion attacks.


  We show that the sizable $D$-term contributions to sfermion mass spectrum can
be signatures of certain GUT, $E_6\times SU(2)_F\times U(1)_A$ GUT. Note that
these $D$-term contributions deviate the degenerate sfermion masses among
different generations in this model. This is different from the previous works
which have argued the $D$-term contributions, which deviate masses only between
sfermions with different quantum charges, as a signature of GUT with larger
rank unification group. Such $D$-terms are strongly constrained by the FCNC
processes if the SUSY breaking scale is the weak scale. However, in $E_6\times
SU(2)_F\times U(1)_A$, natural SUSY type sfermion mass spectrum is obtained,
and if the masses of ${\bf 10}_3$ sfermions are larger than $O(1{\rm TeV})$ to
realize 126 GeV Higgs and the other sfermion masses are $O(10{\rm TeV})$, then
sizable $D$-term contribution is allowed. If the deviations by these $D$-terms
can be observed in future experiments like 100 TeV proton collider or muon
collider, we may confirm the $E_6\times SU(2)_F\times U(1)_A$ GUT.


  In this paper, we characterize infinite-dimensional manifolds modeled on
absorbing sets in non-separable Hilbert spaces by using the discrete cells
property, which is a general position property. Moreover, we study the discrete
(locally finite) approximation property, which is an extension of the discrete
cells property.


  Few-shot language learners adapt knowledge from a pre-trained model to
recognize novel classes from a few-labeled sentences. In such settings,
fine-tuning a pre-trained language model can cause severe over-fitting. In this
paper, we propose an Embedding Hallucination (EmbedHalluc) method, which
generates auxiliary embedding-label pairs to expand the fine-tuning dataset.
The hallucinator is trained by playing an adversarial game with the
discriminator, such that the hallucinated embedding is indiscriminative to the
real ones in the fine-tuning dataset. By training with the extended dataset,
the language learner effectively learns from the diverse hallucinated
embeddings to overcome the over-fitting issue. Experiments demonstrate that our
proposed method is effective in a wide range of language tasks, outperforming
current fine-tuning methods. Further, we show that EmbedHalluc outperforms
other methods that address this over-fitting problem, such as common data
augmentation, semi-supervised pseudo-labeling, and regularization. The code
will be made available at: https://github.com/yiren-jian/EmbedHalluc.


  In this paper, we propose a coding scheme based on polar codes for empirical
coordination of autonomous devices. We consider a two-node network with a noisy
link in which the input and output signals have to be coordinated with the
source and the reconstruction. In the case of strictly causal encoding, we show
that polar codes achieve the empirical coordination region, provided that a
vanishing rate of common randomness is available.


  We study all-optical switching based on the dynamical properties of discrete
vector solitons in waveguide arrays. We employ the concept of the polarization
mode instability and demonstrate simultaneous switching and amplification of a
weak signal by a strong pump of the other polarization.


  Fractals and quasiperiodic structures share self-similarity as a structural
property. Motivated by the link between Fibonacci fractals and quasicrystals
which are scaled by the golden mean ratio $\frac{1+\sqrt{5}}{2}$, we introduce
and characterize a family of metallic-mean ratio fractals. We calculate the
spatial properties of this generalized family, including their boundaries,
which are also fractal. We then demonstrate how these fractals can be related
to aperiodic tilings, and show how we can decorate them to produce new, fractal
tilings.


  Recent experiments strongly suggest that a Fermi surface reconstruction and
multiple Fermi pockets are important common features of the underdoped
high-temperature cuprate superconductors. A related theoretical work [Phys.
Rev. B 79, 134512 (2009)] has demonstrated that a number of hallmark phenomena
observed in the underdoped cuprates appear naturally in the scenario of a
paired electron pocket co-existing with unpaired hole pockets. We propose
Gutzwiller-projected wave-functions to describe this two-fluid state as well as
two competing states in its vicinity. It is argued that a pseudogap state
constructed from these wave-functions may be selected by energetics at finite
temperatures due to spin fluctuations.


  In this work, we have validated the application of Hertzian contact mechanics
models and corrections in the framework of linear elasticity for the analysis
of force vs indentation curves acquired using spherical indenters by means of
finite elements simulations. We have systematically investigated the impact of
both large indentations and vertical spatial confinement (bottom effect) on the
accuracy of the nanomechanical analysis performed with the Hertz model for the
parabolic indenter compared to the Sneddon model for the spherical indenter.We
carried out a comprehensive characterization of the corrections for the Hertz
model proposed in the literature in the framework of linearized force vs
indentation curves, as well as a validation of a linearized form of the Sneddon
model for the spherical indenter and of the combined correction for large
indentations and bottom effect.Our results show that the corrected Hertz model
in combination with the use of a spherical indenter allows to accurately
quantify the Young's modulus of elasticity of linearly elastic samples and
represent a powerful toolkit to analyse experimental data acquired using
micrometre-sized colloidal probes on samples with variable thickness at
arbitrarily large indentations.


  We suggest that the exclusive Higgs + light (or b)-jet production at the LHC,
$pp \to h+j(j_b)$, is a rather sensitive probe of the light-quarks Yukawa
couplings and of other forms of new physics (NP) in the Higgs-gluon $hgg$ and
quark-gluon $qqg$ interactions. We study the Higgs $p_T$-distribution in $pp
\to h+j(j_b) \to \gamma \gamma + j(j_b)$, i.e., in $h+j(j_b)$ production
followed by the Higgs decay $h \to \gamma \gamma$, employing the
($p_T$-dependent) signal strength formalism to probe various types of NP which
are relevant to these processes and which we parameterize either as scaled
Standard Model (SM) couplings (the kappa-framework) and/or through new higher
dimensional effective operators (the SMEFT framework). We find that the
exclusive $h+j(j_b)$ production at the 13 TeV LHC is sensitive to various NP
scenarios, with typical scales ranging from a few TeV to ${\cal O}(10)$ TeV,
depending on the flavor, chirality and Lorentz structure of the underlying
physics.


  An effective paradigm for simulating the dynamics of robots that locomote and
manipulate is multi-rigid body simulation with rigid contact. This paradigm
provides reasonable tradeoffs between accuracy, running time, and simplicity of
parameter selection and identification. The Stewart-Trinkle/Anitescu-Potra time
stepping approach is the basis of many existing implementations. It
successfully treats inconsistent (Painleve-type) contact configurations,
efficiently handles many contact events occurring in short time intervals, and
provably converges to the solution of the continuous time differential
algebraic equations (DAEs) as the integration step size tends to zero. However,
there is currently no means to determine when the solution has largely
converged, i.e., when smaller integration steps would result in only small
increases in accuracy.
  The present work describes an approach that computes the event times (when
the set of active equations in a DAE changes) of all contact/impact events for
a multi-body simulation, toward using integration techniques with error control
to compute a solution with desired accuracy.
  We also describe a first-order, variable integration approach that ensures
that rigid bodies with convex polytopic geometries never interpenetrate. This
approach permits taking large steps when possible and takes small steps when
contact is complex.


  Multi-agent market simulators usually require careful calibration to emulate
real markets, which includes the number and the type of agents. Poorly
calibrated simulators can lead to misleading conclusions, potentially causing
severe loss when employed by investment banks, hedge funds, and traders to
study and evaluate trading strategies. In this paper, we propose a world model
simulator that accurately emulates a limit order book market -- it requires no
agent calibration but rather learns the simulated market behavior directly from
historical data. Traditional approaches fail short to learn and calibrate
trader population, as historical labeled data with details on each individual
trader strategy is not publicly available. Our approach proposes to learn a
unique "world" agent from historical data. It is intended to emulate the
overall trader population, without the need of making assumptions about
individual market agent strategies. We implement our world agent simulator
models as a Conditional Generative Adversarial Network (CGAN), as well as a
mixture of parametric distributions, and we compare our models against previous
work. Qualitatively and quantitatively, we show that the proposed approaches
consistently outperform previous work, providing more realism and
responsiveness.


This paper has been withdrawn by the author(s), due an error in the proof.


  This paper presents a study of how the theory of categories leads to the
creation of non classical logical systems. In particular, the case of the
elementary topos of graphs, where there are three other truth values different
from false and true. The approach in this article to the theory of categories
avoids specialized mathematical training to understand it, since it seeks to
make accessible the main ideas of this branch of mathematics to other
disciplines of knowledge. This work was presented by the second author, under
the title of "Logic and Categories", at the I Colloquium on Logic, Epistemology
and Methodology organized by the School of Philosophy of the University sity of
Costa Rica.


  Machines are a long way from robustly solving open-world perception-control
tasks, such as first-person view (FPV) aerial navigation. While recent advances
in end-to-end Machine Learning, especially Imitation and Reinforcement Learning
appear promising, they are constrained by the need of large amounts of
difficult-to-collect labeled real-world data. Simulated data, on the other
hand, is easy to generate, but generally does not render safe behaviors in
diverse real-life scenarios. In this work we propose a novel method for
learning robust visuomotor policies for real-world deployment which can be
trained purely with simulated data. We develop rich state representations that
combine supervised and unsupervised environment data. Our approach takes a
cross-modal perspective, where separate modalities correspond to the raw camera
data and the system states relevant to the task, such as the relative pose of
gates to the drone in the case of drone racing. We feed both data modalities
into a novel factored architecture, which learns a joint low-dimensional
embedding via Variational Auto Encoders. This compact representation is then
fed into a control policy, which we trained using imitation learning with
expert trajectories in a simulator. We analyze the rich latent spaces learned
with our proposed representations, and show that the use of our cross-modal
architecture significantly improves control policy performance as compared to
end-to-end learning or purely unsupervised feature extractors. We also present
real-world results for drone navigation through gates in different track
configurations and environmental conditions. Our proposed method, which runs
fully onboard, can successfully generalize the learned representations and
policies across simulation and reality, significantly outperforming baseline
approaches.
  Supplementary video: https://youtu.be/VKc3A5HlUU8


  We address the problem of timing-based localization in wireless networks,
when an unknown fraction of data is corrupted by nonideal signal conditions.
While timing-based techniques enable accurate localization, they are also
sensitive to such corrupted data. We develop a robust method that is applicable
to a range of localization techniques, including time-of-arrival,
time-difference-of-arrival and time-difference in schedule-based transmissions.
The method is nonparametric and requires only an upper bound on the fraction of
corrupted data, thus obviating distributional assumptions of the corrupting
noise distribution. The robustness of the method is demonstrated in numerical
experiments.


  Charged particles scattering on moving inhomogenities of the magnetised
interstellar medium can gain energy through the process of second-order Fermi
acceleration. This energy gain depletes in turn the magnetic wave spectrum
around the resonance wave-vector $k\sim 1/R_L$, where $R_L$ is the Larmor
radius of the charged particle. This energy transfer can prohibit the cascading
of magnetic turbulence to smaller scales, leading to a drop in the diffusion
coefficient and allowing the efficient exchange of charged dark matter
particles in the disk and the halo. As a result, terrestial limits from direct
detection experiments apply to charged dark matter. Together with the
no-observation of a drop in the diffusion coefficient, this excludes charged
dark matter for $10^3 GeV\lesssim m/q \lesssim 10^{11} GeV$, even if the
charged dark matter abundance is only a small part of the total relic
abundance.


  We consider the decays $h\to\gamma\gamma,\gamma Z$ in the context of an
extension of the standard model with two inert doublets and an additional $S_3$
symmetry. This model has contributions for these processes through new charged
scalar-loops. Comparing our $h\to\gamma\gamma$ with the more precise available
experimental data we can predict the behaviour of $h\to\gamma Z$ due that they
depend on the same parameters, our estimation for this channel is 1.05 times
the standard model value, but can be up to 1.16 if consider the $+1\sigma$
uncertainty from the $h\to\gamma\gamma$ data, and down to 0.96 if consider
$-1\sigma$.


  We have carried out high-resolution observations along one-dimensional cuts
through the three Galactic supershells GS 064-01-97, GS 090-28-17, and GS
174+02-64 in the HI 21 cm and CO J=1-0 lines. By comparing the HI data with
IRAS data, we have derived the distributions of the I_100 and tau_100 excesses,
which are, respectively, the 100 mum intensity and 100 mum optical depth in
excess of what would be expected from HI emission. We have found that both the
I_100 and tau_100 excesses have good correlations with the CO integrated
intensity W_CO in all three supershells. But the I_100 excess appears to
underestimate H_2 column density N(H_2) by factors of 1.5-3.8. This factor is
the ratio of atomic to molecular infrared emissivities, and we show that it can
be roughly determined from the HI and IRAS data. By comparing the tau_100
excess with W_CO, we derive the conversion factor X = N(H_2)/W_CO = 0.26-0.66
in the three supershells. In GS 090-28-17, which is a very diffuse shell, our
result suggests that the region with N(H_2) < 3*10^20 cm^-2 does not have
observable CO emission, which appears to be consistent with previous results
indicating that diffuse molecular gas is not observable in CO. Our results show
that the molecular gas has a 60/100 mum color temperature T_d lower than the
atomic gas. The low value of T_d might be due either to the low equilibrium
temperature or to the lower abundance of small grains, or a combination of
both.


  In an earlier paper I proposed a highly symmetric semi-classical initial
condition to describe the universe in the period leading up to the electroweak
transition and completely determine all cosmology after that. Nothing beyond
the Standard Model is assumed. Inflation is not needed. The initial symmetry
allows no adjustable parameters. It is a complete theory of the Standard Model
cosmological epoch, predictive and falsifiable. Here, the time evolution of the
initial condition is calculated in the classical approximation. The fields with
nontrivial classical values are the SU(2)-weak gauge field (the cosmological
gauge field or CGF) and the Higgs field. The CGF produces the electroweak
transition then evolves as a non-relativistic perfect fluid
($w_{\mathrm{CGF}}\approx 0$). At the present time, i.e. when $H=H_{0}$, the
CGF energy density satisfies $\Omega_{\Lambda}+\Omega_{\mathrm{CGF}}=1$. The
CGF is the dark matter. The dark matter is a classical phenomenon of the
Standard Model. The classsical universe contains only the dark matter, no
ordinary matter. At next to leading order the fluctuations of the Standard
Model fields will provide a calculable, relatively small amount of ordinary
matter such that
$\Omega_{\Lambda}+\Omega_{\mathrm{CGF}}+\Omega_{\mathrm{ordinary}}=1$.


  We propose a multi-particle self-consistent Hamiltonian (derived from an
N-body description) that is applicable for periodic structures such as
traveling-wave tubes (TWTs), gyrotrons, free-electron lasers, or particle
accelerators. We build a 1D symplectic multi-particle algorithm to simulate the
nonlinear wave-particle interaction in the time domain occurring in an
experimental 3-meters long helix TWT. Our algorithm is efficient thanks to a
drastic reduction model. A 3D helix version of our reduction model is provided.
Finally, we establish an explicit expression of the electromagnetic power in
the time domain and in non-monochromatic (non-"continuous waveform") regime.


  A crucial ingredient in the recent discovery by Ablowitz, Halburd, Herbst and
Korhonen \cite{AHH}, \cite {HK-2} that a connection exists between discrete
Painlev\'e equations and (finite order) Nevanlinna theory is an estimate of the
integrated average of $\log^+|f(z+1)/f(z)|$ on $|z|=r$. We obtained essentially
the same estimate in our previous paper \cite{CF} independent of Halburd et al
\cite{HK-1}. We continue our study in this paper by establishing complete
asymptotic relations amongst the logarithmic differences, difference quotients
and logarithmic derivatives for finite order meromorphic functions. In addition
to the potential applications of our new estimates in integrable systems, they
are also of independent interest. In particular, our findings show that there
are marked differences between the growth of meromorphic functions with
Nevanlinna order smaller and greater than one. We have established a
"difference" analogue of the classical Wiman-Valiron type estimates for
meromorphic functions with order less than one, which allow us to prove all
entire solutions of linear difference equations (with polynomial coefficients)
of order less than one must have positive rational order of growth. We have
also established that any entire solution to a first order algebraic difference
equation (with polynomial coefficients) must have a positive order of growth,
which is a "difference" analogue of a classical result of P\'olya.


  In this work, we investigate how flexible assets within a residential
building influence the long-term impact of operation. We use a measured-peak
grid tariff (MPGT) that puts a cost on the highest single-hour peak import over
the month. We apply a mathematical model of a Home Energy Management System
(HEMS) together with Stochastic Dynamic Programming (SDP), which calculates the
long-term impact of operating as a non-linear expected future cost curve (EFCC)
from the end of the scheduling period to the start. The proposed model is
applied to a case study for a Norwegian building with smart control of a
battery energy storage system (BESS), Electric vehicle (EV) charging and space
heating (SH). Each of the flexible assets are investigated individually with
MPGT and for an energy-based grid tariff. The results showed that EV charging
has the highest peak-power impact in the system, decreasing the total
electricity cost by 14.6% with MPGT when controllable compared to a reference
case with passive charging. It is further shown how the EFCC helps achieve
optimal timing and level of the peak demand, where it co-optimizes both
real-time pricing and the MPGT.


  We study Gauss maps of order $k$, associated to a projective variety $X$
embedded in projective space via a line bundle $L.$ We show that if $X$ is a
smooth, complete complex variety and $L$ is a $k$-jet spanned line bundle on
$X$, with $k\geq 1,$ then the Gauss map of order $k$ has finite fibers, unless
$X=\mathbb{P}^n$ is embedded by the Veronese embedding of order $k$. In the
case where $X$ is a toric variety, we give a combinatorial description of the
Gauss maps of order $k$, its image and the generic fibers.


  This is the second one in our series of papers on indirect quantum control
assisted by quantum accessor. In this paper we propose and study a new class of
indirect quantum control(IDQC) scheme based on the initial states preparation
of the accessor. In the present scheme, after the initial state of the accessor
is properly prepared, the system is controlled by repeatedly switching on and
off the interaction between the system and the accessor. This is different from
the protocol of our first paper, where we manipulate the interaction between
the controlled system and the accessor. We prove the controllability of the
controlled system for the proposed indirect control scheme. Furthermore, we
give an example with two coupled spins qubits to illustrate the scheme, the
concrete control process and the controllability.


  Protolanguage reconstruction is central to historical linguistics. The
comparative method, one of the most influential theoretical and methodological
frameworks in the history of the language sciences, allows linguists to infer
protoforms (reconstructed ancestral words) from their reflexes (related modern
words) based on the assumption of regular sound change. Not surprisingly,
numerous computational linguists have attempted to operationalize comparative
reconstruction through various computational models, the most successful of
which have been supervised encoder-decoder models, which treat the problem of
predicting protoforms given sets of reflexes as a sequence-to-sequence problem.
We argue that this framework ignores one of the most important aspects of the
comparative method: not only should protoforms be inferable from cognate sets
(sets of related reflexes) but the reflexes should also be inferable from the
protoforms. Leveraging another line of research -- reflex prediction -- we
propose a system in which candidate protoforms from a reconstruction model are
reranked by a reflex prediction model. We show that this more complete
implementation of the comparative method allows us to surpass state-of-the-art
protoform reconstruction methods on three of four Chinese and Romance datasets.


  The notion of observers' and their measurements is closely tied to the
Lorentzian metric geometry of spacetime, which in turn has its roots in the
symmetries of Maxwell's theory of electrodynamics. Modifying either the one,
the other, or both ingredients to our modern understanding of physics, requires
also a reformulation of the observer model used. In this presentation we will
consider a generalized theory of electrodynamics, so called local and linear
premetric, or area metric, electrodynamics and its corresponding spacetime
structure. On this basis we will describe an observer's measurement of time and
spatial length. A general algorithm how to determine observer measurements will
be outlined and explicitly applied to a first order premetric perturbation of
Maxwell electrodynamics. The later contains for example the photon sector of
the minimal standard model extension. Having understood an observer's
measurement of time and length we will derive the relativistic observables time
dilation and length contraction. In the future a modern relativistic
description of the classical tests of special relativity shall be performed,
including a consistent observer model.


  Let $p$ be an odd prime and let $k$ be a field of characteristic $p$. We
provide a practical algebraic description of the representation ring of
$k\mathrm{SL}_2(\mathbb{F}_p)$ modulo projectives. We then investigate a family
of modular plethysms of the natural $k\mathrm{SL}_2(\mathbb{F}_p)$-module $E$
of the form $\nabla^{\nu}\mathrm{Sym}^l E$ for a partition $\nu$ of size less
than $p$ and $0\leq l\leq p-2$. Within this family we classify both the modular
plethysms of $E$ which are projective and the modular plethysms of $E$ which
have only one non-projective indecomposable summand which is moreover
irreducible. We generalise these results to similar classifications where
modular plethysms of $E$ are replaced by $k\mathrm{SL}_2(\mathbb{F}_p)$-modules
of the form $\nabla^{\nu} V$, where $V$ is a non-projective indecomposable
$k\mathrm{SL}_2(\mathbb{F}_p)$-module and $|\nu|<p$.


  Near the band edge of photonic crystal waveguides, localized modes appear due
to disorder. We demonstrate a new method to elucidate spatial profile of the
localized modes in such systems using precise local tuning. Using deconvolution
with the known thermal profile, the spatial profile of a localized mode with
quality factor ($Q$) $>10^5$ is successfully reconstructed with a resolution of
$2.5 \ \mu $m.


  To achieve continuous massive data transmission with significantly reduced
data payload, the users can adopt semantic communication techniques to compress
the redundant information by transmitting semantic features instead. However,
current works on semantic communication mainly focus on high compression ratio,
neglecting the wireless channel effects including dynamic distortion and
multi-user interference, which significantly limit the fidelity of semantic
communication. To address this, this paper proposes a diffusion model
(DM)-based channel enhancer (DMCE) for improving the performance of multi-user
semantic communication, with the DM learning the particular data distribution
of channel effects on the transmitted semantic features. In the considered
system model, multiple users (such as road cameras) transmit semantic features
of multi-source data to a receiver by applying the joint source-channel coding
(JSCC) techniques, and the receiver fuses the semantic features from multiple
users to complete specific tasks. Then, we propose DMCE to enhance the channel
state information (CSI) estimation for improving the restoration of the
received semantic features. Finally, the fusion results at the receiver are
significantly enhanced, demonstrating a robust performance even under low
signal-to-noise ratio (SNR) regimes, enabling the generation of effective
object segmentation images. Extensive simulation results with a traffic
scenario dataset show that the proposed scheme can improve the mean
Intersection over Union (mIoU) by more than 25\% at low SNR regimes, compared
with the benchmark schemes.


  Nowadays, vehicles have complex in-vehicle networks (IVNs) with millions of
lines of code controlling almost every function in the vehicle including
safety-critical functions. It has recently been shown that IVNs are becoming
increasingly vulnerable to cyber-attacks capable of taking control of vehicles,
thereby threatening the safety of the passengers. Several countermeasures have
been proposed in the literature in response to the arising threats, however,
hurdle requirements imposed by the industry is hindering their adoption in
practice. In particular, detecting attacks on IVNs is challenged by strict
resource constraints and utterly complex communication patterns that vary even
for vehicles of the same model. In addition, existing solutions suffer from two
main drawbacks. First, they depend on the underlying vehicle configuration, and
second, they are incapable of detecting certain attacks of a stealthy nature.
In this paper, we propose CASAD, a CAN-Aware Stealthy-Attack Detection
mechanism that does not abide by the strict specifications predefined for every
vehicle model and addresses key real-world deployability challenges. Our fast,
lightweight, and system-agnostic approach learns the normal behavior of IVN
dynamics from historical data and detects deviations by continuously monitoring
IVN traffic. We demonstrate the effectiveness of CASAD by conducting various
experiments on a CAN bus prototype, a 2018 Volvo XC60, and publicly available
data from two real vehicles. Our approach is experimentally shown to be
effective against different attack scenarios, including the prompt detection of
stealthy attacks, and has considerable potential applicability to real
vehicles.


  Let H be a complex Hilbert space, B(H) and S(H) be the spaces of all bounded
operators and all self-adjoint operators on H, respectively. We give the
concrete forms of the maps on B(H) and also S(H) which preserve the spectrum of
certain products of operators.


  Causal models bring many benefits to decision-making systems (or agents) by
making them interpretable, sample-efficient, and robust to changes in the input
distribution. However, spurious correlations can lead to wrong causal models
and predictions. We consider the problem of inferring a causal model of a
reinforcement learning environment and we propose a method to deal with
spurious correlations. Specifically, our method designs a reward function that
incentivizes an agent to do an intervention to find errors in the causal model.
The data obtained from doing the intervention is used to improve the causal
model. We propose several intervention design methods and compare them. The
experimental results in a grid-world environment show that our approach leads
to better causal models compared to baselines: learning the model on data from
a random policy or a policy trained on the environment's reward. The main
contribution consists of methods to design interventions to resolve spurious
correlations.


  This paper introduces \textit{online bilevel optimization} in which a
sequence of time-varying bilevel problems is revealed one after the other. We
extend the known regret bounds for online single-level algorithms to the
bilevel setting. Specifically, we provide new notions of \textit{bilevel
regret}, develop an online alternating time-averaged gradient method that is
capable of leveraging smoothness, and give regret bounds in terms of the
path-length of the inner and outer minimizer sequences.


  In the present work we report a study on the viscous extended holographic
Ricci dark energy (EHRDE) model under the assumption of existence of bulk
viscosity in the linear barotropic fluid and the EHRDE in the framework of
standard Eckart theory of relativistic irreversible thermodynamics and it has
been observed that the non-equilibrium bulk viscous pressure is significantly
smaller than the local equilibrium pressure. We have studied the equation of
state (EoS) parameter and observed that the EoS behaves like "quintom" and is
consistent with the constraints set by observational data sets from SNLS3, BAO
and Planck + WMAP9 + WiggleZ measurements in the reference S. Kumar and L. Xu,
\emph{Phys. Lett. B},\textbf{737}, 244 (2014). Analysis of statefinder
parameters has shown the possibility of attainment of $\Lambda$CDM phase under
current model and at the same time it has been pointed out that the for $z=0$
i.e. current universe, the statefinder pair is different from that of
$\Lambda$CDM and the $\Lambda$CDM can be attained in a later stage of the
universe. An analysis of stability has shown that although the viscous EHRDE
along with viscous barotropic is classically unstable in the present epoch, it
can lead to a stable universe in very late stage. Considering an universe
enveloped by event horizon we have observed validity of generalized second law
of thermodynamics.


  Radio astronomy has experienced phenomenal progress in recent years due to
advances in digital technologies and processing speed, the development of new
technologies, and the prospect for new powerful facilities A new generation of
radio interferometers is opening new windows to the Universe. LOFAR, the world
largest telescope, extended the classical radio window at low frequencies. ALMA
started a new era at millimetre wavelengths and the planned SKA will
revolutionize the sciences of the Universe, well beyond the traditional limits
of astronomy. Radio astronomy research is making leaps with enhancements in
resolution, sensitivity, and image fidelity. In Germany, the community has
access to excellent facilities and training opportunities. The Effelsberg
telescope remains the flagship of radio astronomical research at centimeter
wavelengths and serves as a test bed for new technologies, LOFAR has notably
expanded the German community and now includes six German stations and a LOFAR
long term archive coordinated by the GLOW consortium. The SKA will be a
transformational astronomical facility in the coming decade(s), and the German
community is looking forward to broadly participate in SKA-enabled research.


  Let E be an elliptic curve over Q. In 1988, Koblitz conjectured a precise
asymptotic for the number of primes p up to x such that the order of the group
of points of E over the finite field F_p is prime. This is an analogue of the
Hardy and Littlewood twin prime conjecture in the case of elliptic curves.
  Koblitz's conjecture is still widely open. In this paper we prove that
Koblitz's conjecture is true on average over a two-parameter family of elliptic
curves. One of the key ingredients in the proof is a short average distribution
result in the style of Barban-Davenport-Halberstam, where the average is taken
over twin primes and their differences.


  The accuracy of Optical Character Recognition (OCR) is crucial to the success
of subsequent applications used in text analyzing pipeline. Recent models of
OCR post-processing significantly improve the quality of OCR-generated text,
but are still prone to suggest correction candidates from limited observations
while insufficiently accounting for the characteristics of OCR errors. In this
paper, we show how to enlarge candidate suggestion space by using external
corpus and integrating OCR-specific features in a regression approach to
correct OCR-generated errors. The evaluation results show that our model can
correct 61.5% of the OCR-errors (considering the top 1 suggestion) and 71.5% of
the OCR-errors (considering the top 3 suggestions), for cases where the
theoretical correction upper-bound is 78%.


  Object detection has witnessed significant progress by relying on large,
manually annotated datasets. Annotating such datasets is highly time consuming
and expensive, which motivates the development of weakly supervised and
few-shot object detection methods. However, these methods largely underperform
with respect to their strongly supervised counterpart, as weak training signals
\emph{often} result in partial or oversized detections. Towards solving this
problem we introduce, for the first time, an online annotation module (OAM)
that learns to generate a many-shot set of \emph{reliable} annotations from a
larger volume of weakly labelled images. Our OAM can be jointly trained with
any fully supervised two-stage object detection method, providing additional
training annotations on the fly. This results in a fully end-to-end strategy
that only requires a low-shot set of fully annotated images. The integration of
the OAM with Fast(er) R-CNN improves their performance by $17\%$ mAP, $9\%$
AP50 on PASCAL VOC 2007 and MS-COCO benchmarks, and significantly outperforms
competing methods using mixed supervision.


  The Susceptible-Infected (SI) and Susceptible-Infected-Recovered (SIR) models
provide two distinct representations of epidemic evolution, distinguished by
the lack of spontaneous recovery in the SI model. Here we introduce a new
active matter epidemic model, the ``Susceptible-Cleric-Zombie-Recovered''
(SCZR) model, in which spontaneous recovery is absent but zombies can recover
with probability $\gamma$ via interaction with a cleric. Upon interacting with
a zombie, both susceptibles and clerics can enter the zombie state with
probability $\beta$ and $\alpha$, respectively. By changing the intial fraction
of clerics or their healing ability rate $\gamma$, we can tune the SCZR model
between SI dynamics, in which no susceptibles or clerics remain at long times,
and SIR dynamics, in which no zombies remain at long times. The model is
relevant to certain real world diseases such as HIV where spontaneous recovery
is impossible but where medical interventions by a limited number of caregivers
can reduce or eliminate the spread of infection.


  Federated learning (FL) is a powerful distributed machine learning framework
where a server aggregates models trained by different clients without accessing
their private data. Hierarchical FL, with a client-edge-cloud aggregation
hierarchy, can effectively leverage both the cloud server's access to many
clients' data and the edge servers' closeness to the clients to achieve a high
communication efficiency. Neural network quantization can further reduce the
communication overhead during model uploading. To fully exploit the advantages
of hierarchical FL, an accurate convergence analysis with respect to the key
system parameters is needed. Unfortunately, existing analysis is loose and does
not consider model quantization. In this paper, we derive a tighter convergence
bound for hierarchical FL with quantization. The convergence result leads to
practical guidelines for important design problems such as the client-edge
aggregation and edge-client association strategies. Based on the obtained
analytical results, we optimize the two aggregation intervals and show that the
client-edge aggregation interval should slowly decay while the edge-cloud
aggregation interval needs to adapt to the ratio of the client-edge and
edge-cloud propagation delay. Simulation results shall verify the design
guidelines and demonstrate the effectiveness of the proposed aggregation
strategy.


  The frequency with which people interact with technology means that users may
develop interface habits, i.e. fast, automatic responses to stable interface
cues. Design guidelines often assume that interface habits are beneficial.
However, we lack quantitative evidence of how the development of habits
actually affect user performance and an understanding of how changes in the
interface design may affect habit development. Our work quantifies the effect
of habit formation and disruption on user performance in interaction. Through a
forced choice lab study task (n=19) and in the wild deployment (n=18) of a
notificationdialog experiment on smartphones, we show that people become more
accurate and faster at option selection as they develop an interface habit.
Crucially this performance gain is entirely eliminated once the habit is
disrupted. We discuss reasons for this performance shift and analyse some
disadvantages of interface habits, outlining general design patterns on how to
both support and disrupt them.Keywords: Interface habits, user behaviour,
breaking habit, interaction science, quantitative research.


  Majorana Bound States are predicted to appear as boundary states of the
Kitaev model. Here we show that a pi-Josephson Junction, inserted in a
topologically non trivial model ring, sustains a Majorana Bound State, which is
robust with respect to local and non local perturbations. The realistic
structure could be based on a High Tc Superconductor tricrystal structure,
similar to the one used to spot the d-wave order parameter. The presence of the
Majorana Bound State changes the ground state of the topologically non trivial
ring in a measurable way, with respect to that of a conventional one.


  We study strong gravitational lensing by a class of static wormhole
geometries. Analytical approaches to the same are developed, and the results
differ substantially from strong lensing by black holes, first reported by
Bozza. We consider two distinct situations, one in which the observer and the
source are on the same side of the wormhole throat, and the other in which they
are on opposite sides. Distinctive features in our study arise from the fact
that photon and antiphoton spheres might be present on both sides of the
wormhole throat, and that the throat might itself act as a photon sphere. We
show that strong gravitational lensing thus opens up a rich variety of
possibilities of relativistic image formation, some of which are novel, and are
qualitatively distinct from black hole lensing. These can serve as clear
indicators of exotic wormhole geometries.


  The fundamentals of the Maximum Entropy principle as a rule for assigning and
updating probabilities are revisited. The Shannon-Jaynes relative entropy is
vindicated as the optimal criterion for use with an updating rule. A
constructive rule is justified which assigns the probabilities least sensitive
to coarse-graining. The implications of these developments for interpreting
physics laws as rules of inference upon incomplete information are briefly
discussed.


  We present a general approach for the construction of the exact
local-energy-density functionals for a uniform N-dimensional electronic system
in a magnetic field. For arbitrary dimension, we obtain explicit expressions
for the matter, kinetic, and exchange density functionals. In the zero-field
limit, we recover the usual N-dimensional Thomas-Fermi theory. As an
application of our results, we develop a current-density-functional theory, in
the spirit of the Thomas-Fermi-Dirac approximation, for an inhomogeneous
many-electron system in a magnetic field.


  We present and analyse new optical images of the dust envelope surrounding
the high mass-loss carbon star IRC+10216. This envelope is seen due to external
illumination by galactic light. Intensity profiles and colors of the nebula
were obtained in the UBV bandpasses. The data are compared with the results of
a radiative transfer model calculating multiple scattering of interstellar
field photons by dust grains with a single radius. The data show that the
observed radial shape of the nebula, especially its half maximum radius, does
not depend on wavelength (within experimental errors), suggesting that grains
scatter in the grey regime, etc, etc (this abstract has been shortened)


  We study Voronoi diagrams for distance functions that add together two convex
functions, each taking as its argument the difference between Cartesian
coordinates of two planar points. When the functions do not grow too quickly,
then the Voronoi diagram has linear complexity and can be constructed in
near-linear randomized expected time. Additionally, the level sets of the
distances from the sites form a family of pseudocircles in the plane, all cells
in the Voronoi diagram are connected, and the set of bisectors separating any
one cell in the diagram from each of the others forms an arrangement of
pseudolines in the plane. We apply these results to the smoothed distance or
biotope transform metric, a geometric analogue of the Jaccard distance whose
Voronoi diagrams can be used to determine the dilation of a star network with a
given hub. For sufficiently closely spaced points in the plane, the Voronoi
diagram of smoothed distance has linear complexity and can be computed
efficiently. We also experiment with a variant of Lloyd's algorithm, adapted to
smoothed distance, to find uniformly spaced point samples with exponentially
decreasing density around a given point.


  2D materials provide a platform for strong light--matter interactions,
creating wide-ranging design opportunities via new-material discoveries and new
methods for geometrical structuring. We derive general upper bounds to the
strength of such light--matter interactions, given only the optical
conductivity of the material, including spatial nonlocality, and otherwise
independent of shape and configuration. Our material figure of merit shows that
highly doped graphene is an optimal material at infrared frequencies, whereas
single-atomic-layer silver is optimal in the visible. For quantities ranging
from absorption and scattering to near-field spontaneous-emission enhancements
and radiative heat transfer, we consider canonical geometrical structures and
show that in certain cases the bounds can be approached, while in others there
may be significant opportunity for design improvement. The bounds can encourage
systematic improvements in the design of ultrathin broadband absorbers, 2D
antennas, and near-field energy harvesters.


  We introduce several definitions of energy density of Brody curves and show
that they give the same value in an appropriate situation.


  We introduce a new template for the detection of gravitational waves from
compact binary systems which is based on Chebyshev polynomials of the first
kind. As well as having excellent convergence properties, these polynomials are
also very closely related to the elusive minimax polynomial. In this study we
have limited ourselves to the test-mass regime, where we model a test particle
in a circular equatorial orbit around a Schwarzschild black hole. Our objective
is to model the numerical gravitational wave flux function, starting with the
post-Newtonian expansion from Black Hole Perturbation Theory. We introduce a
new Chebyshev approximation to the flux function, which due to a process called
Chebyshev economization gives a better model than either post-Newtonian or Pade
based methods. A graphical examination of the new flux function shows that it
gives an excellent fit to the numerical flux, but more importantly we find that
at the last stable orbit the error is reduced, < 1.8%, at all orders of
approximation. We also find that the templates constructed using the Chebyshev
approximation give better fitting factors, in general > 0.99, and smaller
errors, < 1/10%, in the estimation of the Chirp mass when compared to a
fiducial exact waveform, constructed using the numerical flux and the exact
expression for the orbital energy function, again at all orders of
approximation. We also show that in the test-mass case, the new Chebyshev
template is superior to both PN and Pade approximant templates, especially at
lower orders of approximation.


  The Neural Tangent Kernel (NTK), defined as $\Theta_\theta^f(x_1, x_2) =
\left[\partial f(\theta, x_1)\big/\partial \theta\right] \left[\partial
f(\theta, x_2)\big/\partial \theta\right]^T$ where $\left[\partial f(\theta,
\cdot)\big/\partial \theta\right]$ is a neural network (NN) Jacobian, has
emerged as a central object of study in deep learning. In the infinite width
limit, the NTK can sometimes be computed analytically and is useful for
understanding training and generalization of NN architectures. At finite
widths, the NTK is also used to better initialize NNs, compare the conditioning
across models, perform architecture search, and do meta-learning.
Unfortunately, the finite width NTK is notoriously expensive to compute, which
severely limits its practical utility. We perform the first in-depth analysis
of the compute and memory requirements for NTK computation in finite width
networks. Leveraging the structure of neural networks, we further propose two
novel algorithms that change the exponent of the compute and memory
requirements of the finite width NTK, dramatically improving efficiency. Our
algorithms can be applied in a black box fashion to any differentiable
function, including those implementing neural networks. We open-source our
implementations within the Neural Tangents package (arXiv:1912.02803) at
https://github.com/google/neural-tangents.


  The mass-luminosity relation for late-type stars has long been a critical
tool for estimating stellar masses. However, there is growing need for both a
higher-precision relation and a better understanding of systematic effects
(e.g., metallicity). Here we present an empirical relationship between Mks and
mass spanning $0.075M_\odot<M<0.70M_\odot$. The relation is derived from 62
nearby binaries, whose orbits we determine using a combination of Keck/NIRC2
imaging, archival adaptive optics data, and literature astrometry. From their
orbital parameters, we determine the total mass of each system, with a
precision better than 1% in the best cases. We use these total masses, in
combination with resolved Ks magnitudes and system parallaxes, to calibrate the
mass-Mks relation. The result can be used to determine masses of single stars
with a precision of 2-3%, which we confirm by a comparison to dynamical masses
from the literature. The precision is limited by scatter around the best-fit
relation beyond mass uncertainties, perhaps driven by intrinsic variation in
the mass-Mks relation or underestimated measurement errors. We find the effect
of [Fe/H] on the mass-Mks relation is likely negligible for metallicities in
the Solar neighborhood (0.0+/-2.2% change in mass per dex change in [Fe/H]).
This weak effect is consistent with predictions from the Dartmouth Stellar
Evolution Database, but inconsistent with those from MESA Isochrones and
Stellar Tracks. A sample of binaries with a wider range of abundances will be
required to discern the importance of metallicity in extreme populations (e.g.,
in the Galactic Halo or thick disk).


  A new method is presented for describing vibrational effects in x-ray
absorption spectroscopy (XAS) and resonant inelastic x-ray scattering (RIXS)
using a combination of the classical Franck-Condon (FC) approximation and
classical trajectories run on the core-excited state. The formulation of RIXS
is an extension of the semiclassical Kramers-Heisenberg (SCKH) formalism of
Ref. {Ljungberg_2010} to the resonant case, retaining approximately the same
computational cost. To overcome difficulties with connecting the absorption and
emission processes in RIXS the classical FC approximation is used for the
absorption, which is seen to work well provided that a zero-point-energy
correction is included.
  In the case of core-excited states with dissociative character the method is
capable of closely reproducing the main features for one-dimensional test
systems, compared to the quantum mechanical formulation. Due to the good
accuracy combined with the relatively low computational cost, the method has
large potential of being used for complex systems with many degrees of freedom,
such as liquids and surface adsorbates.


  Infinite derivative theory of gravity is a modification to the general theory
of relativity. Such modification maintains the massless graviton as the only
true physical degree of freedom and avoids ghosts. Moreover, this class of
modified gravity can address classical singularities. In this thesis some
essential aspects of an infinite derivative theory of gravity are studied.
Namely, we considered the Hamiltonian formalism, where the true physical
degrees of freedom for infinite derivative scalar models and infinite
derivative gravity are obtained. Furthermore, the Gibbons-Hawking-York boundary
term for the infinite derivative theory of gravity was obtained. Finally, we
considered the thermodynamical aspects of the infinite derivative theory of
gravity over different backgrounds. Throughout the thesis, our methodology is
applied to general relativity, Gauss-Bonnet and f(R) theories of gravity as a
check and validation.


  Here, we propose a two-dimensional tungsten boride (WB4) lattice, with the
Gibbs free energy for the adsorption of atomic hydrogen, tending to be the
ideal value of 0 eV at 3% strained state, to host a better hydrogen evolution
reaction activity. Based on first-principles calculations, it is demonstrated
that the multiple d-p-pi and d-p-sigma Dirac conjugations of WB4 lattice
ensures its excellent electronic transport characteristics. Meanwhile, coupling
with the d-orbitals of W, the p-orbitals of borophene subunits in WB4 lattice
can modulate the d band center to get a good HER performance. Our results not
only provide a versatile platform for hosting multiple Dirac semimetal states
with a sandwich configuration, but also offer a guiding principle for
discovering the relationship between intrinsic properties of the active centre
and the catalytic activity of metal layer from the emerging field of
low-dimensional noble-metal-free lattices.


  In this work we address three questions: can we successfully describe
(observed) deviations from the standard model in the SMEFT language? Can we
learn something about the underlying, beyond the standard model, physics using
the SMEFT language? If no deviation is observed, how to proceed? Given the
myriad of viable BSM options with extended scalar sectors, we suggest a
widespread use of SMEFT not just as a global fitting tool (that could miss out
on deviations from extended scalar sectors) but also as a bookkeeping framework
in which the results from SMEFT fits to individual observables are provided,
reported, and archived in a consistent way. The compatibility of such
individual results can then be assessed in the light of BSM models with
extended scalar sectors.


  In a magnetization vs. temperature (M vs. T) experiment, the blocking region
of a magnetic nanoparticle (MNP) assembly is the interval of T values were the
system begins to respond to an applied magnetic field H when heating the sample
from the lower reachable temperature. The location of this region is determined
by the anisotropy energy barrier depending on the applied field H, the volume
V, the magnetic anisotropy constant K of the MNPs and the observing time of the
technique. In the general case of a polysized sample, a representative blocking
temperature value $T_B$ can be estimated from ZFC-FC experiments as a way to
determine the effective anisotropy constant.
  In this work, a numerical solved Stoner-Wolfharth two level model with
thermal agitation is used to simulate ZFC-FC curves of monosized and polysized
samples and to determine the best method for obtaining a representative $T_B$
value of polysized samples. The results corroborate a technique based on the T
derivative of the difference between ZFC and FC curves proposed by Micha et
al(the good) and demonstrate its relation with two alternative methods: the ZFC
maximum (the bad) and inflection point (the ugly). The derivative method is
then applied to experimental data, obtaining the $T_B$ distribution of a
polysized $Fe_3O_4$ MNP sample suspended in hexane with an excellent agreement
with TEM characterization.