  Numerical simulations of the quarkonium spin splittings are done in the
framework of lattice nonrelativistic quantum chromodynamics (NRQCD). At leading
order in the velocity expansion the spin splittings are of $O(M_Q v^4)$, where
$M_Q$ is the renormalized quark mass and $v^2$ is the mean squared quark
velocity. A systematic analysis is done of all next-to-leading order
corrections. This includes the addition of $O(M_Q v^6)$ relativistic
interactions, and the removal of $O(a^2 M_Q v^4)$ discretization errors in the
leading-order interactions. Simulations are done for both S- and P-wave mesons,
with a variety of heavy quark actions and over a wide range of lattice
spacings. Two prescriptions for the tadpole improvement of the action are also
studied in detail: one using the measured value of the average plaquette, the
other using the mean link measured in Landau gauge. Next-to-leading order
interactions result in a very large reduction in the charmonium splittings,
down by about 60% from their values at leading order. There are further
indications that the velocity expansion may be poorly convergent for
charmonium. Prelimary results show a small correction to the hyperfine
splitting in the Upsilon system.


  Following Weinstein, Boyarchenko-Weinstein and Imai-Tsushima, we construct a
family of affinoids in the Lubin-Tate perfectoid space and formal models such
that the cohomology of the reduction of each formal model realizes the local
Langlands correspondence and the local Jacquet-Langlands correspondence for
certain representations. In the terminology of the essentially tame local
Langlands correspondence, the representations treated here are characterized as
being parametrized by minimal admissible pairs in which the field extensions
are totally ramified.


  Physical artificial intelligence can prove to be one of the most important
challenges of the artificial intelligence. The governance of physical
artificial intelligence would define its responsible intelligent application in
the society.


  We present results for the effect of a second massive quark in the relation
between the pole and the minimal subtracted quark mass at the three loop level.
We also consider the analogous effect for the wave function renormalisation
constant. Some technical details of the calculation are given. Our result is
phenomenologically relevant for the bottom quark including virtual charm
effects.


  We design the phase shifts of an intelligent reflecting surface
(IRS)-assisted single-input-multiple-output communication system to minimize
the outage probability (OP) and to maximize the ergodic rate. Our phase shifts
design uses only statistical channel state information since these depend only
on the large-scale fading coefficients; the obtained phase shift design remains
valid for a longer time frame. We further assume that one has access to only
quantized phase values. The closed-form expressions for OP and ergodic rate are
derived for the considered system. Next, two optimization problems are
formulated to choose the phase shifts of IRS such that (i) OP is minimized and
(ii) the ergodic rate is maximized. We used the multi-valued particle swarm
optimization (MPSO) and particle swarm optimization (PSO) algorithms to solve
the optimization problems. Numerical simulations are performed to study the
impact of various parameters on the OP and ergodic rate. We also discuss
signaling overhead between BS and IRS controller. It is shown that the overhead
can be reduced up to $99.69 \%$ by using statistical CSI for phase shift design
and $5$ bits to represent the phase shifts without significantly compromising
on the performance.


  The dispersion relations of collective oscillations of the magnetic moment of
magnetic dots arranged in square-planar arrays and having magnetic moments
perpendicular to the array plane are calculated. The presence of the external
magnetic field perpendicular to the plane of array, as well as the uniaxial
anisotropy for single dot are taken into account. The ferromagnetic state with
all the magnetic moments parallel, and chessboard antiferromagnetic state are
considered. The dispersion relation yields information about the stability of
different states of the array. There is a critical magnetic field below which
the ferromagnetic state is unstable. The antiferromagnetic state is stable for
small enough magnetic fields. The dispersion relation is non-analytic as the
value of the wave vector approaches zero. Non-trivial Van Hove anomalies are
also found for both ferromagnetic and antiferromagnetic states.


  We define self-distributive structures in the categories of coalgebras and
cocommutative coalgebras. We obtain examples from vector spaces whose bases are
the elements of finite quandles, the direct sum of a Lie algebra with its
ground field, and Hopf algebras. The self-distributive operations of these
structures provide solutions of the Yang--Baxter equation, and, conversely,
solutions of the Yang--Baxter equation can be used to construct
self-distributive operations in certain categories.
  Moreover, we present a cohomology theory that encompasses both Lie algebra
and quandle cohomologies, is analogous to Hochschild cohomology, and can be
used to study deformations of these self-distributive structures. All of the
work here is informed via diagrammatic computations.


  The imaginary part of the effective action is investigated in the 4D chiral
U(1) theory using the CFA.


  We study some properties of the randomized series and their applications to
the geometric structure of Banach spaces. For $n\ge 2$ and $1<p<\infty$, it is
shown that $\ell_\infty^n$ is representable in a Banach space $X$ if and only
if it is representable in the Lebesgue-Bochner $L_p(X)$. New criteria for
various convexity properties in Banach spaces are also studied. It is proved
that a Banach lattice $E$ is uniformly monotone if and only if its
$p$-convexification $E^{(p)}$ is uniformly convex and that a K\"othe function
space $E$ is upper locally uniformly monotone if and only if its
$p$-convexification $E^{(p)}$ is midpoint locally uniformly convex.


  The uniform disconnectedness is an important invariant property under
bi-Lipschitz mapping, and the Assouad dimension $\dim _{A}X<1$ implies the
uniform disconnectedness of $X$. According to quasi-Lipschitz mapping, we
introduce the quasi-Assouad dimension $\dim _{qA}$ such that $\dim _{qA}X<1$
implies its quasi uniform disconnectedness. We obtain $\overline{\dim }
_{B}X\leq \dim _{qA}X\leq \dim _{A}X$ and compute the quasi-Assouad dimension
of Moran set.


  We derive sharp bounds for the accuracy of approximate eigenvectors (Ritz
vectors) obtained by the Rayleigh-Ritz process for symmetric eigenvalue
problems. Using information that is available or easy to estimate, our bounds
improve the classical Davis-Kahan $\sin\theta$ theorem by a factor that can be
arbitrarily large, and can give nontrivial information even when the
$\sin\theta$ theorem suggests that a Ritz vector might have no accuracy at all.
We also present extensions in three directions, deriving error bounds for
invariant subspaces, singular vectors and subspaces computed by a
(Petrov-Galerkin) projection SVD method, and eigenvectors of self-adjoint
operators on a Hilbert space.


  This paper introduces the first minimal solvers that jointly solve for
affine-rectification and radial lens distortion from coplanar repeated
patterns. Even with imagery from moderately distorted lenses, plane
rectification using the pinhole camera model is inaccurate or invalid. The
proposed solvers incorporate lens distortion into the camera model and extend
accurate rectification to wide-angle imagery, which is now common from consumer
cameras. The solvers are derived from constraints induced by the conjugate
translations of an imaged scene plane, which are integrated with the division
model for radial lens distortion. The hidden-variable trick with ideal
saturation is used to reformulate the constraints so that the solvers generated
by the Grobner-basis method are stable, small and fast.
  Rectification and lens distortion are recovered from either one conjugately
translated affine-covariant feature or two independently translated
similarity-covariant features. The proposed solvers are used in a \RANSAC-based
estimator, which gives accurate rectifications after few iterations. The
proposed solvers are evaluated against the state-of-the-art and demonstrate
significantly better rectifications on noisy measurements. Qualitative results
on diverse imagery demonstrate high-accuracy undistortions and rectifications.
The source code is publicly available at https://github.com/prittjam/repeats.


  Stochastic gradient descent (SGD) is a popular stochastic optimization method
in machine learning. Traditional parallel SGD algorithms, e.g., SimuParallel
SGD, often require all nodes to have the same performance or to consume equal
quantities of data. However, these requirements are difficult to satisfy when
the parallel SGD algorithms run in a heterogeneous computing environment;
low-performance nodes will exert a negative influence on the final result. In
this paper, we propose an algorithm called weighted parallel SGD (WP-SGD).
WP-SGD combines weighted model parameters from different nodes in the system to
produce the final output. WP-SGD makes use of the reduction in standard
deviation to compensate for the loss from the inconsistency in performance of
nodes in the cluster, which means that WP-SGD does not require that all nodes
consume equal quantities of data. We also analyze the theoretical feasibility
of running two other parallel SGD algorithms combined with WP-SGD in a
heterogeneous environment. The experimental results show that WP-SGD
significantly outperforms the traditional parallel SGD algorithms on
distributed training systems with an unbalanced workload.


  As recent generative models can generate photo-realistic images, people seek
to understand the mechanism behind the generation process. Interpretable
generation process is beneficial to various image editing applications. In this
work, we propose a framework to discover interpretable directions in the latent
space given arbitrary pre-trained generative adversarial networks. We propose
to learn the transformation from prior one-hot vectors representing different
attributes to the latent space used by pre-trained models. Furthermore, we
apply a centroid loss function to improve consistency and smoothness while
traversing through different directions. We demonstrate the efficacy of the
proposed framework on a wide range of datasets. The discovered direction
vectors are shown to be visually corresponding to various distinct attributes
and thus enable attribute editing.


  It is known that, when an excited atom spontaneously emits one photon, two
effects are produced. First, the atom's internal and external states are
entangled with the states of the emitted photon. Second, the atom receives a
momentum transfered from the photon. In this work, the dynamics of such an atom
in vacuum is studied. Through a specific calculation, it is demonstrated that
these effects cause the atom to experience, on average, a friction force
opposite to its initial velocity. Properties of the force are also discussed.


  In this paper, we establish a unilateral global bifurcation result for a
class of quasilinear periodic boundary problems with a sign-changing weight. By
the Ljusternik-Schnirelmann theory, we first study the spectrum of the periodic
$p$-Laplacian with the sign-changing weight. In particular, we show that there
exist two simple, isolated, principal eigenvalues $\lambda_0^+$ and
$\lambda_0^-$. Furthermore, under some natural hypotheses on perturbation
function, we show that $(\lambda_0^\nu,0)$ is a bifurcation point of the above
problems and there are two distinct unbounded sub-continua
$\mathscr{C}_\nu^{+}$ and $\mathscr{C}_\nu^{-}$, consisting of the continuum
$\mathscr{C}_\nu$ emanating from $(\lambda_0^\nu, 0)$, where $\nu\in\{+,-\}$.
As an application of the above result, we study the existence of one-sign
solutions for a class of quasilinear periodic boundary problems with the
sign-changing weight. Moreover, the uniqueness of one-sign solutions and the
dependence of solutions on the parameter $\lambda$ are also studied.


  We propose an efficient and scalable method for incrementally building a
dense, semantically annotated 3D map in real-time. The proposed method assigns
class probabilities to each region, not each element (e.g., surfel and voxel),
of the 3D map which is built up through a robust SLAM framework and
incrementally segmented with a geometric-based segmentation method. Differently
from all other approaches, our method has a capability of running at over 30Hz
while performing all processing components, including SLAM, segmentation, 2D
recognition, and updating class probabilities of each segmentation label at
every incoming frame, thanks to the high efficiency that characterizes the
computationally intensive stages of our framework. By utilizing a specifically
designed CNN to improve the frame-wise segmentation result, we can also achieve
high accuracy. We validate our method on the NYUv2 dataset by comparing with
the state of the art in terms of accuracy and computational efficiency, and by
means of an analysis in terms of time and space complexity.


  Hype over novel quantum technologies has prompted discussion on the likely
societal impacts of the sector. Calls to ensure the responsible development of
quantum technologies are complicated by a lack of concrete case studies or
real-world examples of irresponsible quantum. At this stage, responsible
quantum faces a situation reminiscent of the Collingridge dilemma. In this
dilemma, the moment in which discussion on societal risks and benefits can be
most impactful is also the time where the least information is available. The
flipside of this challenge is an opportunity to build processes for examining
the public good of quantum before the trajectory (and potential problems) of
the sector become locked in. Recent work in this space has argued that quantum
researchers and innovators must work with society to address uncertainties and
concerns. By engaging quantum stakeholders and understanding their perspectives
on responsibility, this paper seeks to support this proposition and enable
further dialogue on responsible development and use of quantum technologies.


  The anomalous momentum and doping dependence of the electron spectral
function and electron dispersion for copper oxide materials in the underdoped
regime are studied within the t-J model. It is shown that the electron spectrum
is changed with dopings, and the electron dispersion exhibits a flat band
around ($\pi$,0) point in the Brillouin zone, which leads to the normal-state
pseudogap formation. The theoretical results are consistent with the
experiments and numerical simulations.


  Meetings play a critical infrastructural role in the coordination of work. In
recent years, due to shift to hybrid and remote work, more meetings are moving
to online Computer Mediated Spaces. This has led to new problems (e.g. more
time spent in less engaging meetings) and new opportunities (e.g. automated
transcription/captioning and recap support). Recent advances in large language
models (LLMs) for dialog summarization have the potential to improve the
experience of meetings by reducing individuals' meeting load and increasing the
clarity and alignment of meeting outputs. Despite this potential, they face
technological limitation due to long transcripts and inability to capture
diverse recap needs based on user's context. To address these gaps, we design,
implement and evaluate in-context a meeting recap system. We first
conceptualize two salient recap representations -- important highlights, and a
structured, hierarchical minutes view. We develop a system to operationalize
the representations with dialogue summarization as its building blocks.
Finally, we evaluate the effectiveness of the system with seven users in the
context of their work meetings. Our findings show promise in using LLM-based
dialogue summarization for meeting recap and the need for both representations
in different contexts. However, we find that LLM-based recap still lacks an
understanding of whats personally relevant to participants, can miss important
details, and mis-attributions can be detrimental to group dynamics. We identify
collaboration opportunities such as a shared recap document that a high quality
recap enables. We report on implications for designing AI systems to partner
with users to learn and improve from natural interactions to overcome the
limitations related to personal relevance and summarization quality.


  A minimum dominating set in a graph is a minimum set of vertices such that
every vertex of the graph either belongs to it, or is adjacent to one vertex of
this set. This mathematical object is of high relevance in a number of
applications related to social networks analysis, design of wireless networks,
coding theory, and data mining, among many others. When vertex weights are
given, minimizing the total weight of the dominating set gives rise to a
problem variant known as the minimum weight dominating set problem. To solve
this problem, we introduce a hybrid matheuristic combining a tabu search with
an integer programming solver. The latter is used to solve subproblems in which
only a fraction of the decision variables, selected relatively to the search
history, are left free while the others are fixed. Moreover, we introduce an
adaptive penalty to promote the exploration of intermediate infeasible
solutions during the search, enhance the algorithm with perturbations and node
elimination procedures, and exploit richer neighborhood classes. Extensive
experimental analyses on a variety of instance classes demonstrate the good
performance of the algorithm, and the contribution of each component in the
success of the search is analyzed.


  We present results on the second-faintest pulsating subdwarf B (sdB) star
known, RAT J0455+1305, derived from photometric data obtained in 2009. It shows
both short and long periods oscillations, theoretically assigned as pressure
and gravity modes. We identify six short-period frequencies (with one being a
combination) and six long-period frequencies. This star is the fourth hybrid
sdB star discovered so far which makes it of special interest as each type of
mode probes a different part of the star. This star is similar to the sdB
hybrid pulsator Balloon 090100001 in that it exhibits short-period mode
groupings, which can be used to identify pulsation parameters and constrain
theoretical models.


  The detection of anomalies in unknown environments is a problem that has been
approached from different perspectives with variable results. Artificial Immune
Systems (AIS) present particularly advantageous characteristics for the
detection of such anomalies. This research is based on an existing detector
model, named Artificial Bioindicators System (ABS) which identifies and solves
its main weaknesses. An ABS based anomaly classifier model is presented,
incorporating elements of the AIS. In this way, a new model (R-ABS) is
developed which includes the advantageous capabilities of an ABS plus the
reactive capabilities of an AIS to overcome its weaknesses and disadvantages.
The RABS model was tested using the well-known DARPA'98 dataset, plus a dataset
built to carry out a greater number of experiments. The performance of the RABS
model was compared to the performance of the ABS model based on classical
sensitivity and specificity metrics, plus a response time metric to illustrate
the rapid response of R-ABS relative to ABS. The results showed a better
performance of R-ABS, especially in terms of detection time.


  We have developed a new HFB code that specifically addresses nuclear
structure physics near the driplines. The HFB equations are solved on a
two-dimensional lattice for axially symmetric even-even nuclei using B-Spline
techniques. The quasiparticle energy spectrum is obtained by direct
diagonalization of the HFB lattice Hamiltonian with LAPACK. The energy spectrum
extends high into the continuum, up to several thousand MeV. Calculations with
Skyrme forces and (density-dependent) delta pairing interactions are now
underway.


  Reliably predictive simulation of complex flows requires a level of model
sophistication and robustness exceeding the capabilities of current
Reynolds-averaged Navier-Stokes (RANS) models. The necessary capability can
often be provided by well-resolved large eddy simulation (LES), but, for many
flows of interest, such simulations are too computationally intensive to be
performed routinely. In principle, hybrid RANS/LES (HRL) models capable of
transitioning through arbitrary levels of modeled and resolved turbulence would
ameliorate both RANS deficiencies and LES expense. However, these HRL
approaches have led to a host of unique complications, in addition to those
already present in RANS and LES. This work proposes a modeling approach aimed
at overcoming such challenges. The approach presented here relies on splitting
the turbulence model into three distinct components: two responsible for the
standard subgrid model roles of either providing the unresolved stress or
dissipation and a third which reduces the model length scale by creating
resolved turbulence. This formulation renders blending functions unnecessary in
HRL. Further, the split-model approach both reduces the physics-approximation
burden on simple eddy-viscosity-based models and provides convenient
flexibility in model selection. In regions where the resolution is adequate to
support additional turbulence, fluctuations are generated at the smallest
locally resolved scales of motion. This active forcing drives the system
towards a balance between RANS and grid-resolved LES for any combination of
resolution and flow while the split-model formulation prevents local disruption
to the total stress. The model is demonstrated on fully-developed,
incompressible channel flow [1] and the periodic hill [2], in which it is shown
to produce accurate results and avoid common HRL shortcomings, such as model
stress depletion.


  The observable Universe is described by a collection of equal mass galaxies
linked into a common unit by their mutual gravitational interaction. The
partition function of this system is cast in terms of Ising model spin
variables and maps exactly onto a three-dimensional stochastic scalar classical
field theory. The full machinery of the renormalization group and critical
phenomena is brought to bear on this field theory allowing one to calculate the
galaxy-galaxy correlation function, whose critical exponent is predicted to be
between 1.530 to 1.862, compared to the phenomenological value of 1.6 to 1.8


  I review my work with Bruce Draine on dust emissivity at microwave
frequencies (3 cm - 3 mm). This emissivity explains the recently detected
"anomalous" component of the galactic foreground emission. Both small (a<0.001
micron) and large grains contribute to this emission. Small grains have
electric dipole moments and emit while they rotate; the microwave emission of
large grains is mostly due to magneto-dipole radiation. Most efficient
magneto-dipole emitters are strongly magnetic, e.g. ferrimagnetic or
ferromagnetic, materials. The relative role of the two mechanisms can be
established through observations of microwave emissivity from dark clouds. New
microwave window is a window of opportunity for interstellar studies. Magnetic
fields inside dark clouds may be successfully studied via microwave
polarization. Microwave emissivity constrains the abundance of strongly
magnetic materials. For instance, the available data at 90 GHz indicate that
not more than 5% of interstellar Fe is in the form of metallic iron grains or
inclusions (e.g., in ``GEMS''). Future missions, e.g. MAP and PLANCK, will
bring a wealth of microwave data that can be successfully used to study ISM.
Such a study would be appreciated by cosmologists who franticly try to remove
all foregrounds from their data.


  A LiDAR Statistical Barnes Objective Analysis (LiSBOA) for optimal design of
LiDAR scans and retrieval of the velocity statistical moments is proposed. The
LiSBOA represents an adaptation of the classical Barnes scheme for the
statistical analysis of unstructured experimental data in N-dimensional spaces
and it is a suitable technique for the evaluation over a structured Cartesian
grid of the statistics of scalar fields sampled through scanning LiDARs. The
LiSBOA is validated and characterized via a Monte Carlo approach applied to a
synthetic velocity field. This revisited theoretical framework for the Barnes
objective analysis enables the formulation of guidelines for optimal design of
LiDAR experiments and efficient application of the LiSBOA for the
post-processing of LiDAR measurements. The optimal design of LiDAR scans is
formulated as a two cost-function optimization problem including the
minimization of the percentage of the measurement volume not sampled with
adequate spatial resolution and the minimization of the error on the mean of
the velocity field. The optimal design of the LiDAR scans also guides the
selection of the smoothing parameter and the total number of iterations to use
for the Barnes scheme.


  We describe a general construction of irreducible unitary representations of
the group of currents with values in the semidirect product of a locally
compact subgroup $P_0$ and a one-parameter group ${\mathbb R {}}^*_+=\{r:r>0\}$
of automorphisms of $P_0$. This construction is determined by a a faithful
unitary representation of $P_0$ (canonical representation) whose images under
the action of the group of automorphisms tend to the identity representation as
$r\to 0$. We apply this construction to the groups of currents of the maximal
parabolic subgroups of the groups of motions of the $n$-dimensional real and
complex Lobachevsky spaces. The obtained representations of the groups of
parabolic currents can be uniquely extended to the groups of currents with
values in the semisimple groups O(n,1) and U(n,1). This gives a new description
of the representations of the groups of currents of these groups constructed in
the 70s and realized in the Fock space. The key role in our construction is
played by the so-called special representation of the parabolic subgroup $P$
and the remarkable $\sigma$-finite measure (Lebesgue measure) $\mathcal L$ in
the space of distributions.


  We perform an exhaustive study of the simplest, nontrivial problem in
advection-diffusion -- a finite absorber of arbitrary cross section in a steady
two-dimensional potential flow of concentrated fluid. This classical problem
has been studied extensively in the theory of solidification from a flowing
melt, and it also arises in Advection-Diffusion-Limited Aggregation. In both
cases, the fundamental object is the flux to a circular disk, obtained by
conformal mapping from more complicated shapes. We construct the first accurate
numerical solution using an efficient new method, which involves mapping to the
interior of the disk and using a spectral method in polar coordinates. Our
method also combines exact asymptotics and an adaptive mesh to handle boundary
layers. Starting from a well-known integral equation in streamline coordinates,
we also derive new, high-order asymptotic expansions for high and low P\'eclet
numbers ($\Pe$). Remarkably, the `high' $\Pe$ expansion remains accurate even
for such low $\Pe$ as $10^{-3}$. The two expansions overlap well near $\Pe =
0.1$, allowing the construction of an analytical connection formula that is
uniformly accurate for all $\Pe$ and angles on the disk with a maximum relative
error of 1.75%. We also obtain an analytical formula for the Nusselt number
($\Nu$) as a function of the P\'eclet number with a maximum relative error of
0.53% for all possible geometries. Because our finite-plate problem can be
conformally mapped to other geometries, the general problem of two-dimensional
advection-diffusion past an arbitrary finite absorber in a potential flow can
be considered effectively solved.


  We consider certain two-dimensional systems with self--dual points including
uniform and disordered $q$-state Potts models. For systems with continuous
energy density (such as the disordered versions) it is established that the
self--dual point exhibits critical behavior: Infinite susceptibility, vanishing
magnetization and power law bounds for the decay of correlations.


  We consider the task of breaking down a quantum computation given as an
isometry into C-NOTs and single-qubit gates, while keeping the number of C-NOT
gates small. Although several decompositions are known for general isometries,
here we focus on a method based on Householder reflections that adapts well in
the case of sparse isometries. We show how to use this method to decompose an
arbitrary isometry before illustrating that the method can lead to significant
improvements in the case of sparse isometries. We also discuss the classical
complexity of this method and illustrate its effectiveness in the case of
sparse state preparation by applying it to randomly chosen sparse states.


  The Abel transform is a mathematical operation that transforms a
cylindrically symmetric three-dimensional (3D) object into its two-dimensional
(2D) projection. The inverse Abel transform reconstructs the 3D object from the
2D projection. Abel transforms have wide application across numerous fields of
science, especially chemical physics, astronomy, and the study of laser-plasma
plumes. Consequently, many numerical methods for the Abel transform have been
developed, which makes it challenging to select the ideal method for a specific
application. In this work eight transform methods have been incorporated into a
single, open-source Python software package (PyAbel) to provide a direct
comparison of the capabilities, advantages, and relative computational
efficiency of each transform method. Most of the tested methods provide
similar, high-quality results. However, the computational efficiency varies
across several orders of magnitude. By optimizing the algorithms, we find that
some transform methods are sufficiently fast to transform 1-megapixel images at
more than 100 frames per second on a desktop personal computer. In addition, we
demonstrate the transform of gigapixel images.


  As the James Webb Space Telescope (JWST) came online last summer, we entered
a new era of astronomy. This new era is supported by data products of
unprecedented information content that require novel reduction and analysis
techniques. Recently, Niraula et al. 2022 (N22) highlighted the need for
upgraded opacity models to prevent facing a model-driven accuracy wall when
interpreting exoplanet transmission spectra. Here, we follow the same approach
as N22 to explore the sensitivity of inferences on the atmospheric properties
of WASP-39 b to the opacity models used. We find that the retrieval of the main
atmospheric properties from this first JWST exoplanet spectrum is mostly
unaffected by the current state of the community's opacity models. Abundances
of strong opacity sources like water and carbon dioxide are reliably
constrained within $\sim$0.30 dex, beyond the 0.50 dex accuracy wall reported
in N22. Assuming the completeness and accuracy of line lists, N22's accuracy
wall is primarily driven by model uncertainties on broadening coefficients and
far-wing behaviors, which we find to have marginal consequences for
interpreting the transmission spectra of large, hot, high-metallicity
atmospheres such as WASP-39 b, in opposition to emission spectra and climate
modeling which depend on deeper parts of a planetary atmosphere. The origin of
the opacity challenge in the retrieval of metal-rich hot Jupiters via
transmission spectroscopy will thus mostly stem from the incompleteness and
inaccuracy of line lists.


  The consumers' willingness to pay plays an important role in economic theory
and in setting policy. For a market, this function can often be estimated from
observed behavior -- preferences are revealed. However, economists would like
to measure consumers' willingness to pay for some goods where this can only be
measured through stated valuation. Confirmed convergence of valuations based on
stated preferences as compared to valuations based on revealed preferences is
rare, and it is important to establish circumstances under which one can expect
such convergence. By building a simple probabilistic model for the consumers'
likelihood of travel, we provide an approach that should make comparing stated
and revealed preferences easier in cases where the preference is tied to travel
or some other behavior whose cost can be measured. We implemented this approach
in a pilot study and found an estimate of willingness to pay for visiting an
environmentally enhanced recreational site based on actual travel in good
agreement with an estimate based on a survey using stated preferences. To use
the probabilistic model we used population statistics to adjust for the
relevant duration and thus compare stated and revealed responses.


  We present a sample of Cepheid variable stars towards M31 based on the first
year of regular M31 observations of the PS1 survey in the r_P1 and i_P1
filters. We describe the selection procedure for Cepheid variable stars from
the overall variable source sample and develop an automatic classification
scheme using Fourier decomposition and the location of the instability strip.
We find 1440 fundamental mode (classical \delta) Cep stars, 126 Cepheids in the
first overtone mode, and 147 belonging to the Population II types. 296 Cepheids
could not be assigned to one of these classes and 354 Cepheids were found in
other surveys. These 2009 Cepheids constitute the largest Cepheid sample in M31
known so far and the full catalog is presented in this paper. We briefly
describe the properties of our sample in its spatial distribution throughout
the M31 galaxy, in its age properties, and we derive an apparent
period-luminosity relation (PLR) in our two bands. The Population I Cepheids
nicely follow the dust pattern of the M31 disk, whereas the 147 Type II
Cepheids are distributed throughout the halo of M31. We outline the time
evolution of the star formation in the major ring found previously and find an
age gradient. A comparison of our PLR to previous results indicates a curvature
term in the PLR.


  The paper argues that attracting more economists and adopting a more-precise
definition of dynamic complexity might help econophysics acquire more attention
in the economics community and bring new lymph to economic research. It may be
necessary to concentrate less on the applications than on the basics of
economic complexity, beginning with expansion and deepening of the study of
small systems with few interacting components, while until thus far complexity
has been assumed to be a prerogative of complicated systems only. It is
possible that without a thorough analysis at that level, the understanding of
systems that are at the same time complex and complicated will continue to
elude economics and econophysics research altogether. To that purpose, the
paper initiates and frames a definition of dynamic complexity grounded on the
concept of non-linear dynamical system.


  Various theorems for the preservation of set-theoretic axioms under forcing
are proved, regarding both forcing axioms and axioms true in the Levy-Collapse.
These show in particular that certain applications of forcing axioms require to
add generic countable sequences high up in the set-theoretic hierarchy even
before collapsing everything down to $\aleph\_1$. Later we give applications,
among them the consistency of ${\rm MM}$ with $\aleph\_\omega$ not being
Jonsson which answers a question raised during Oberwolfach 2005.


  We present a simple physical model for populating dark matter halos with
Lyman Alpha Emiiters(LAEs) and predict the physical properties of LAEs at
z~3-7. The central tenet of this model is that the Ly-alpha luminosity is
proportional to the star formation rate (SFR) which is directly related to the
halo mass accretion rate. The only free parameter in our model is then the
star-formation efficiency (SFE). An efficiency of 2.5% provides the best-fit to
the Ly-alpha luminosity function (LF) at redshift z=3.1, and we use this SFE to
construct Ly-alpha LFs at other redshifts. Our model reproduce the Ly-alpha
LFs, stellar ages, SFR ~1-10; Msun/yr, stellar masses ~ 10^7-10^8 Msun and the
clustering properties of LAEs at z~3-7. We find the spatial correlation lengths
ro ~ 3-6 Mpc/h, in agreement with the observations. Finally, we estimate the
field-to-field variation ~ 30% for current volume and flux limited surveys,
again consistent with observations. Our results suggest that the star
formation, and hence Ly-alpha emission in LAEs is powered by the accretion of
new material, and that the physical properties of LAEs do not evolve
significantly over a wide range of redshifts. Relating the accreted mass,
rather than the total mass of halos, to the Ly-alpha luminosity of LAEs
naturally gives rise to the duty cycle of LAEs.


  We discuss how to calculate genuine multipartite quantum and classical
correlations in symmetric, spatially invariant, mixed $n$-qubit density
matrices. We show that the existence of symmetries greatly reduces the amount
of free parameters to be optimized in order to find the optimal measurement
that minimizes the conditional entropy in the discord calculation. We apply
this approach to the states exhibited dynamically during a thermodynamic
protocol to extract maximum work. We also apply the symmetry criterion to a
wide class of physically relevant cases of spatially homogeneous noise over
multipartite entangled states. Exploiting symmetries we are able to calculate
the nonlocal and genuine quantum features of these states and note some
interesting properties.


  This is a brief report on time-domain numerical simulations of
extreme-mass-ratio binaries based on finite element methods. We discuss a new
technique for solving the perturbative equations describing a point-like object
orbiting a non-rotating massive black hole and the prospects of using it for
the evaluation of the gravitational self-force responsible of the inspiral of
these binary systems. We also discuss the perspectives of transferring this
technology to the more astrophysically relevant case of a central rotating
massive black hole.


  We show that quantum vortex-loop proliferation may be one possible
explanation of the super-long-range proximity effect observed in an insulating
underdoped cuprate, using the dual theory of quantum vortices. As a test of
this scenario, we propose that a dual proximity effect experiment can confirm
the superfluid motion of the quantum vortices in the vortex-proliferated
insulator and can measure the divergent correlation lengths near the
superconductor-insulator transition.


  We analyse a class of estimators of the generalized diffusion coefficient for
fractional Brownian motion $B_t$ of known Hurst index $H$, based on weighted
functionals of the single time square displacement. We show that for a certain
choice of the weight function these functionals possess an ergodic property and
thus provide the true, ensemble-averaged, generalized diffusion coefficient to
any necessary precision from a single trajectory data, but at expense of a
progressively higher experimental resolution. Convergence is fastest around
$H\simeq0.30$, a value in the subdiffusive regime.


  In this project, we build a modular, scalable system that can collect, store,
and process millions of satellite images. We test the relative importance of
both of the key limitations constraining the prevailing literature by applying
this system to a data-rich environment. To overcome classic data availability
concerns, and to quantify their implications in an economically meaningful
context, we operate in a data rich environment and work with an outcome
variable directly correlated with key indicators of socioeconomic well-being.
We collect public records of sale prices of homes within the United States, and
then gradually degrade our rich sample in a range of different ways which mimic
the sampling strategies employed in actual survey-based datasets. Pairing each
house with a corresponding set of satellite images, we use image-based features
to predict housing prices within each of these degraded samples. To generalize
beyond any given featurization methodology, our system contains an independent
featurization module, which can be interchanged with any preferred image
classification tool.
  Our initial findings demonstrate that while satellite imagery can be used to
predict housing prices with considerable accuracy, the size and nature of the
ground truth sample is a fundamental determinant of the usefulness of imagery
for this category of socioeconomic prediction. We quantify the returns to
improving the distribution and size of observed data, and show that the image
classification method is a second-order concern. Our results provide clear
guidance for the development of adaptive sampling strategies in data-sparse
locations where satellite-based metrics may be integrated with standard survey
data, while also suggesting that advances from image classification techniques
for satellite imagery could be further augmented by more robust sampling
strategies.


  In this paper, we show that coding can be used in storage area networks
(SANs) to improve various quality of service metrics under normal SAN operating
conditions, without requiring additional storage space. For our analysis, we
develop a model which captures modern characteristics such as constrained I/O
access bandwidth limitations. Using this model, we consider two important
cases: single-resolution (SR) and multi-resolution (MR) systems. For SR
systems, we use blocking probability as the quality of service metric and
propose the network coded storage (NCS) scheme as a way to reduce blocking
probability. The NCS scheme codes across file chunks in time, exploiting file
striping and file duplication. Under our assumptions, we illustrate cases where
SR NCS provides an order of magnitude savings in blocking probability. For MR
systems, we introduce saturation probability as a quality of service metric to
manage multiple user types, and we propose the uncoded resolution- aware
storage (URS) and coded resolution-aware storage (CRS) schemes as ways to
reduce saturation probability. In MR URS, we align our MR layout strategy with
traffic requirements. In MR CRS, we code videos across MR layers. Under our
assumptions, we illustrate that URS can in some cases provide an order of
magnitude gain in saturation probability over classic non-resolution aware
systems. Further, we illustrate that CRS provides additional saturation
probability savings over URS.


  This paper introduces a computational framework to identify nonlinear
input-output operators that fit a set of system trajectories while satisfying
incremental integral quadratic constraints. The data fitting algorithm is thus
regularized by suitable input-output properties required for system analysis
and control design. This biased identification problem is shown to admit the
tractable solution of a regularized least squares problem when formulated in a
suitable reproducing kernel Hilbert space. The kernel-based framework is a
departure from the prevailing state-space framework. It is motivated by
fundamental limitations of nonlinear state-space models at combining the
fitting requirements of data-based modeling with the input-output requirements
of system analysis and physical modeling.


  Speech sound disorders are a common communication impairment in childhood.
Because speech disorders can negatively affect the lives and the development of
children, clinical intervention is often recommended. To help with diagnosis
and treatment, clinicians use instrumented methods such as spectrograms or
ultrasound tongue imaging to analyse speech articulations. Analysis with these
methods can be laborious for clinicians, therefore there is growing interest in
its automation. In this paper, we investigate the contribution of ultrasound
tongue imaging for the automatic detection of speech articulation errors. Our
systems are trained on typically developing child speech and augmented with a
database of adult speech using audio and ultrasound. Evaluation on typically
developing speech indicates that pre-training on adult speech and jointly using
ultrasound and audio gives the best results with an accuracy of 86.9%. To
evaluate on disordered speech, we collect pronunciation scores from experienced
speech and language therapists, focusing on cases of velar fronting and gliding
of /r/. The scores show good inter-annotator agreement for velar fronting, but
not for gliding errors. For automatic velar fronting error detection, the best
results are obtained when jointly using ultrasound and audio. The best system
correctly detects 86.6% of the errors identified by experienced clinicians. Out
of all the segments identified as errors by the best system, 73.2% match errors
identified by clinicians. Results on automatic gliding detection are harder to
interpret due to poor inter-annotator agreement, but appear promising. Overall
findings suggest that automatic detection of speech articulation errors has
potential to be integrated into ultrasound intervention software for
automatically quantifying progress during speech therapy.


  We investigate the $\theta$-dependence of 2-dimensional $CP^{N-1}$ models in
the large-$N$ limit by lattice simulations. Thanks to a recent algorithm
proposed by M. Hasenbusch to improve the critical slowing down of topological
modes, combined with simulations at imaginary values of $\theta$, we manage to
determine the vacuum energy density up the sixth order in $\theta$ and up to $N
= 51$. Our results support analytic predictions, which are known up to the
next-to-leading term in $1/N$ for the quadratic term in $\theta$ (topological
susceptibility), and up to the leading term for the quartic coefficient $b_2$.
Moreover, we give a numerical estimate of further terms in the $1/N$ expansion
for both quantities, pointing out that the $1/N$ convergence for the
$\theta$-dependence of this class of models is particularly slow.


  Phase change memory (PCM) is an emerging high speed, high density, high
endurance, and scalable non-volatile memory technology which utilizes the large
resistivity contrast between the amorphous and crystalline phases of
chalcogenide materials such as Ge2Sb2Te5 (GST). In addition to being used as a
standalone memory, there has been a growing interest in integration of PCM
devices on top of the CMOS layer for computation in memory and neuromorphic
computing. The large CMOS overhead for memory controllers is a limiting factor
for this purpose. Transferring functionality like routing, multiplexing, and
logic to the memory layer can substantially reduce the CMOS overhead, making it
possible to integrate 100s of GB of PCM storage on top of a conventional CPU.
In this work, we present computational analysis of a phase change device
concept that can perform toggle operations. The toggle functionality is
achieved using two physical mechanisms: (i) isolation of different read
contacts due to amorphization between different write contact pairs, and (ii)
thermal cross-talk between a molten region and a previously amorphized region.
Phase-change devices with six contacts can be implemented as toggle flip-flops,
multiplexer, or demultiplexer when interfaced with CMOS transistors. Here, we
demonstrate the operation of the device as a toggle flip-flop with 5
transistors, requiring ~50% of the footprint compared to conventional CMOS
alternatives, with the added advantage of non-volatility.


  The introduction of posit reopened the debate about the utility of IEEE754 in
specific domains. In this context, we propose a high-level language (Scala)
library that aims to reduce the effort of designing and testing new number
representation systems (NRSs). The library's efficiency is tested with three
new NRSs derived from Morris Tapered Floating-Point by adding a hidden exponent
bit. We call these NRSs MorrisHEB, MorrisBiasHEB, and MorrisUnaryHEB,
respectively. We show that they offer a better dynamic range, better decimal
accuracy for unary operations, more exact results for addition (37.61% in the
case of MorrisUnaryHEB), and better average decimal accuracy for inexact
results on binary operations than posit and IEEE754. Going through existing
benchmarks in the literature, and favorable/unfavorable examples for
IEEE754/posit, we show that these new NRSs produce similar (less than one
decimal accuracy difference) or even better results than IEEE754 and posit.
Given the entire spectrum of results, there are arguments for MorrisBiasHEB to
be used as a replacement for IEEE754 in general computations. MorrisUnaryHEB
has a more populated ``golden zone'' (+13.6%) and a better dynamic range (149X)
than posit, making it a candidate for machine learning computations.


  Optical spectroscopic sensors are a powerful tool to reveal light-matter
interactions in many fields, such as physics, biology, chemistry, and
astronomy. Miniaturizing the currently bulky spectrometers has become
imperative for the wide range of applications that demand in situ or even in
vitro characterization systems, a field that is growing rapidly. Benchtop
spectrometers are capable of offering superior resolution and spectral range,
but at the expense of requiring a large size. In this paper, we propose a novel
method that redesigns spectroscopic sensors via the use of programmable
photonic circuits. Drawing from compressive sensing theory, we start by
investigating the most ideal sampling matrix for a reconstructive spectrometer
and reveal that a sufficiently large number of sampling channels is a
prerequisite for both fine resolution and low reconstruction error. This number
is, however, still considerably smaller than that of the reconstructed spectral
pixels, benefitting from the nature of reconstruction algorithms. We then show
that the cascading of a few engineered MZI elements can be readily programmed
to create an exponentially scalable number of such sampling spectral responses
over an ultra-broad bandwidth, allowing for ultra-high resolution down to
single-digit picometers without incurring additional hardware costs.
Experimentally, we implement an on-chip spectrometer with a fully-programmable
6-stage cascaded MZI structure and demonstrate a < 10 pm resolution with a >
200 nm bandwidth using only 729 sampling channels. This achieves a
bandwidth-to-resolution ratio of over 20,000, which is, to our best knowledge,
about one order of magnitude greater than any reported miniaturized
spectrometers to date. We further illustrate that by employing
dispersion-engineered waveguide components, the device bandwidth can be
extended to over 400 nm.


  LoRaWAN has garnered tremendous attention owing to the low power consumption
of end nodes, long range, high resistance to multipath, low cost, and use of
license-free sub-GHz bands. Consequently, LoRaWAN is gradually replacing Wi-Fi
and Bluetooth in sundry IoT applications including utility metering, smart
cities, and localization. Localization, in particular, has already witnessed a
surge of alternatives to Global Navigation Satellite System (GNSS), based on
Wi-Fi, Bluetooth, Ultra Wide Band, 5G, etc. in indoor and low power domains due
to the poor indoor coverage and high power consumption of GNSS. With the need
for localization only shooting up with dense IoT deployments, LoRaWAN is seen
as a promising solution in this context. Indeed, many attempts employing
various techniques such as Time of Arrival (ToA), Time Difference of Arrival
(TDoA), and Received Signal Strength Index (RSSI) have been made to achieve
localization using LoRaWAN. However, a significant drawback in this scenario is
the lack of extensive data on path loss and signal propagation modeling,
particularly in Indian cityscapes. Another demerit is the use of GNSS at some
stage primarily for time synchronization of gateways. In this work, we attempt
to nullify these two disadvantages of LoRaWAN based localization. The first
part of this work presents experimental data of LoRaWAN transmissions inside a
typical city building to study signal propagation and path loss. The latter
part proposes a standalone GNSS-free localization approach using LoRaWAN that
is achieved by applying a collaborative, TDoA-based methodology. An additional
stationary node is introduced into the network to allow the synchronization of
gateways without GNSS. Finally, the distribution of localization error in a
triangle of gateways and the effect of timing resolution, time-on-air, and duty
cycle constraints on it are investigated.


  We find that spectra of certain Iron Low Ionization Broad Absorption Line
(FeLOBAL) QSOs, which are characterized by low--ionization emission and blue
shifted absorption lines, can be well matched with the spectral synthesis code
SYNOW. SYNOW is a resonance scattering code and assumes that line emission
comes from a single line forming region. This interpretation is novel as
traditionally line emission and absorption in BALQSOs are thought to come from
two different regions. We extend this analysis by using the detailed PHOENIX
code to model the spectra. We present a SYNOW fit and a preliminary model
result from PHOENIX.


  PSR J1811-1736 (P=104 ms) is an old (~1.89 Gyrs) binary pulsar (P_orb=18.8 d)
in a highly eccentric orbit (e=0.828) with an unidentified companion.
Interestingly enough, the pulsar timing solution yields an estimated companion
mass 0.93 M_{\odot}<M_C<1.5 M_{\odot}, compatible with that of a neutron star.
As such, it is possible that PSR J1811-1736 is a double neutron star (DNS)
system, one of the very few discovered so far. This scenario can be
investigated through deep optical/infrared (IR) observations. We used J, H,
K-band images, obtained as part of the UK Infrared Telescope (UKIRT) Infrared
Deep Sky Survey (UKIDSS), and available in the recent Data Release 9 Plus, to
search for its undetected companion of the PSR J1811-1736 binary pulsar. We
detected a possible companion star to PSR J1811-1736 within the 3 sigma radio
position uncertainty (1.32 arcsec), with magnitudes J=18.61+/-0.07,
H=16.65+/-0.03, and K=15.46+/-0.02. The star colours are consistent with either
a main sequence (MS) star close to the turn-off or a lower red giant branch
(RGB) star, at a pulsar distance of ~5.5 kpc and with a reddening of
E(B-V)~4.9. The star mass and radius would be compatible with the constraints
on the masses and orbital inclination of the binary system inferred from the
mass function and the lack of radio eclipses near superior conjunction. Thus,
it is possible that it is the companion to PSR J1811-1736. However, based on
the star density in the field, we estimated a quite large chance coincidence
probability of ~0.27 between the pulsar and the star, which makes the
association unlikely. No other star is detected within the 3 sigma pulsar radio
position down to J~20.5, H~19.4$ and K~18.6, which would allow us to rule out a
MS companion star earlier than a mid-to-late M spectral type.


  The scintillation light output of a pure and a Thallium doped Sodium Iodide
(NaI) crystal under irradiation with 5.486MeV \alpha -particles has been
measured over a temperature range from 1.7K to 300K. Estimates of the decay
time constant at three selected temperatures are given. For pure NaI an
increase in light yield towards low temperatures could be confirmed and
measured at higher precision. For NaI(Tl) below 60K an increase in light output
has been found.


  In this article, we study the Euler class of taut foliations on the Dehn
fillings of a $\mathbb{Q}$-homology solid torus. We give a necessary and
sufficient condition for the Euler class of a foliation transverse to the core
of the filling solid torus to vanish. We apply this condition to taut
foliations on Dehn fillings of hyperbolic fibered manifolds and obtain many new
left-orderable Dehn filling slopes on these manifolds. For instance, we show
that when $X$ is the exterior of a pretzel knot $P(-2,3,2r+1)$, $r\geq 3$,
$\pi_1(X(\alpha_n))$ is left-orderable for a sequence of positive slopes
$\alpha_n$ with $\alpha_0 =2g-2$ and $\alpha_n\to 2g-1$. Lastly, we prove that
given any $\mathbb{Q}$-homology solid torus, the set of slopes for which the
corresponding Dehn fillings admit a taut foliation transverse to the core with
zero Euler class is nowhere dense in $\mathbb{R}\cup \{\frac{1}{0}\}$.


  Quantum field theory currently has a single standard mathematical
characterization (the Standard Model), but no single accepted conceptual
framework to interpret the mathematics. Many of these conceptualizations rely
on intuitive concepts carried over from classical physics (such as "particle"
and "causality"). In this paper, instead of relying on classical concepts we
attempt to infer a conceptualization directly from the mathematics. This
reconceptualization leads to a physical reinterpretation of the paths involved
in the Standard Model's action integral as traces of an accumulative process
that occurs within an "extraverse", of which our observable spacetime is a
single "slice". We briefly outline a rigorous mathematical model which
validates the physical reinterpretation, and leads to predictions that are
potentially verifiable by experiment. We contrast our model with other popular
interpretations of quantum mechanics. We describe some of the metaphysical
consequences of our proposed perspective. Finally we present some speculations
about an alternative approach that could possibly lead to a more satisfying,
intuitively-graspable theory.


  In this article we have used stochastic gravitational wave background as a
unique probe to gain insight regarding the creation mechanism of primordial
black holes. We have considered the cumulative gravitational wave background
which consists of the primary part coming from the creation mechanism of the
primordial black holes and the secondary part coming from the different
mechanisms the primordial black holes go through. We have shown that in the
presence of light or ultra light scalar bosons, superradiant instability
generates the secondary part of the gravitational wave background which is the
most detectable. In order to show the unique features of the cumulative
background, we have considered the delayed vacuum decay during a first order
phase transition as the origin of primordial black holes. We have shown the
dependence of the features of the cumulative background, such as the mass of
the relevant light scalars, peak frequencies, etc. on the transition
parameters. We have also generated the cumulative background for a few
benchmark cases to further illustrate our claim.


  Let $L/K$ be a Galois extension of number fields and let
$G=\mathrm{Gal}(L/K)$. We show that under certain hypotheses on $G$, for a
fixed prime number $p$, Leopoldt's conjecture at $p$ for certain proper
intermediate fields of $L/K$ implies Leopoldt's conjecture at $p$ for $L$. We
also obtain relations between the Leopoldt defects of intermediate extensions
of $L/K$. By applying a result of Buchmann and Sands together with an explicit
description of units and a special case of the above results, we show that
given any finite set of prime numbers $\mathcal{P}$, there exists an infinite
family $\mathcal{F}$ of totally real $S_{3}$-extensions of $\mathbb{Q}$ such
that Leopoldt's conjecture for $F$ at $p$ holds for every $F \in \mathcal{F}$
and $p \in \mathcal{P}$.


  Combining precision measurements and the Higgs boson search limit, the
electroweak data has evolved to a point where new physics is favored whether
the 3.2 sigma A_{FB}^b anomaly is genuine or not. Such new physics could
greatly alter the inferred value of the Higgs boson mass.


  New similarity variables are introduced for the Einstein - Maxwell equations
with one Killing vector that reduce the non-linear partial differential
equations in three independent variables to ordinary differential equations.
These similarity variables are the extensions of those previously found for the
Einstein-Maxwell equations with two Killing vectors. The resulting equations
are then solved, providing new solutions of the Einstein - Maxwell equations
with one Killing Vector.


  Let $\tau_{D}(Z) $ be the first exit time of iterated Brownian motion from a
domain $D \subset \RR{R}^{n}$ started at $z\in D$ and let $P_{z}[\tau_{D}(Z)
>t]$ be its distribution. In this paper we establish the exact asymptotics of
$P_{z}[\tau_{D}(Z) >t]$ over bounded domains as an improvement of the results
in \cite{deblassie, nane2}, for $z\in D$ \begin{eqnarray}
  \lim_{t\to\infty} t^{-1/2}\exp({3/2}\pi^{2/3}\lambda_{D}^{2/3}t^{1/3})
P_{z}[\tau_{D}(Z)>t]= C(z),\nonumber \end{eqnarray} where
$C(z)=(\lambda_{D}2^{7/2})/\sqrt{3 \pi}(\psi(z)\int_{D}\psi(y)dy) ^{2}$. Here
$\lambda_{D}$ is the first eigenvalue of the Dirichlet Laplacian ${1/2}\Delta$
in $D$, and $\psi $ is the eigenfunction corresponding to $\lambda_{D}$ .
  We also study lifetime asymptotics of Brownian-time Brownian motion (BTBM),
$Z^{1}_{t}=z+X(|Y(t)|)$, where $X_{t}$ and $Y_{t}$ are independent
one-dimensional Brownian motions.


  We calculate Wilson loop (quark anti-quark potential) in dS/CFT
correspondence. The brane-world model is considered where bulk is two 5d
Euclidean de Sitter spaces and boundary (brane) is 4d de Sitter one. Starting
from the Nambu-Goto action, the calculation of the effective tension (average
energy) is presented. Unlike to the case of supergravity calculation of Wilson
loop in AdS/CFT set-up, there is no need to regularize the Nambu-Goto action
(the volume of de Sitter space is finite). It turns out that at sufficiently
small curvature of 5d background the energy (potential) is positive and linear
on the distance between quark and anti-quark what indicates to the possibility
of confinement.


  We present a numerical approximation of the solutions of the Euler equations
with a gravitational source term. On the basis of a Suliciu type relaxation
model with two relaxation speeds, we construct an approximate Riemann solver,
which is used in a first order Godunov-type finite volume scheme. This scheme
can preserve both stationary solutions and the low Mach limit to the
corresponding incompressible equations. In addition, we prove that our scheme
preserves the positivity of density and internal energy, that it is entropy
satisfying and also guarantees not to give rise to numerical checkerboard modes
in the incompressible limit. Later we give an extension to second order that
preserves positivity, asymptotic-preserving and well-balancing properties.
Finally, the theoretical properties are investigated in numerical experiments.


  We investigate the origin of diffusion in non-chaotic systems. As an example,
we consider 1-$d$ map models whose slope is everywhere 1 (therefore the
Lyapunov exponent is zero) but with random quenched discontinuities and
quasi-periodic forcing. The models are constructed as non-chaotic
approximations of chaotic maps showing deterministic diffusion, and represent
one-dimensional versions of a Lorentz gas with polygonal obstacles (e.g., the
Ehrenfest wind tree model). In particular, a simple construction shows that
these maps define non-chaotic billiards in space-time. The models exhibit, in a
wide range of the parameters, the same diffusive behavior of the corresponding
chaotic versions. We present evidence of two sufficient ingredients for
diffusive behavior in one-dimensional, non-chaotic systems: i) a finite-size,
algebraic instability mechanism, and ii) a mechanism that suppresses periodic
orbits.


  Adherence to the non-pharmaceutical interventions (NPIs) put in place to
mitigate the spreading of infectious diseases is a multifaceted problem.
Socio-demographic, socio-economic, and epidemiological factors can influence
the perceived susceptibility and risk which are known to affect behavior.
Furthermore, the adoption of NPIs is dependent upon the barriers, real or
perceived, associated with their implementation. We study the determinants of
NPIs adherence during the first wave of the COVID-19 Pandemic in Colombia,
Ecuador, and El Salvador. Analyses are performed at the level of municipalities
and include socio-economic, socio-demographic, and epidemiological indicators.
Furthermore, by leveraging a unique dataset comprising tens of millions of
internet Speedtest measurements from Ookla, we investigate the quality of the
digital infrastructure as a possible barrier to adoption. We use publicly
available data provided by Meta capturing aggregated mobility changes as a
proxy of adherence to NPIs. Across the three countries considered, we find a
significant correlation between mobility drops and digital infrastructure
quality. The relationship remains significant after controlling for several
factors including socio-economic status, population size, and reported COVID-19
cases. This finding suggests that municipalities with better connectivity were
able to afford higher mobility reductions. The link between mobility drops and
digital infrastructure quality is stronger at the peak of NPIs stringency. We
also find that mobility reductions were more pronounced in larger, denser, and
wealthier municipalities. Our work provides new insights on the significance of
access to digital tools as an additional factor influencing the ability to
follow social distancing guidelines during a health emergency


  The majority of primary Central Nervous System (CNS) tumors in the brain are
among the most aggressive diseases affecting humans. Early detection of brain
tumor types, whether benign or malignant, glial or non-glial, is critical for
cancer prevention and treatment, ultimately improving human life expectancy.
Magnetic Resonance Imaging (MRI) stands as the most effective technique to
detect brain tumors by generating comprehensive brain images through scans.
However, human examination can be error-prone and inefficient due to the
complexity, size, and location variability of brain tumors. Recently, automated
classification techniques using machine learning (ML) methods, such as
Convolutional Neural Network (CNN), have demonstrated significantly higher
accuracy than manual screening, while maintaining low computational costs.
Nonetheless, deep learning-based image classification methods, including CNN,
face challenges in estimating class probabilities without proper model
calibration. In this paper, we propose a novel brain tumor image classification
method, called SIBOW-SVM, which integrates the Bag-of-Features (BoF) model with
SIFT feature extraction and weighted Support Vector Machines (wSVMs). This new
approach effectively captures hidden image features, enabling the
differentiation of various tumor types and accurate label predictions.
Additionally, the SIBOW-SVM is able to estimate the probabilities of images
belonging to each class, thereby providing high-confidence classification
decisions. We have also developed scalable and parallelable algorithms to
facilitate the practical implementation of SIBOW-SVM for massive images. As a
benchmark, we apply the SIBOW-SVM to a public data set of brain tumor MRI
images containing four classes: glioma, meningioma, pituitary, and normal. Our
results show that the new method outperforms state-of-the-art methods,
including CNN.


  We establish a transference inequality conjectured by Badziahin and Bugeaud
relating exponents of rational approximation of points in geometric
progression.


  We use a sign-reversing involution to show that trees on the vertex set [n],
considered to be rooted at 1, in which no vertex has exactly one child are
counted by 1/n sum_{k=1}^{n} (-1)^(n-k) {n}-choose-{k} (n-1)!/(k-1)! k^(k-1).
This result corrects a persistent misprint in the Encyclopedia of Integer
Sequences.


  We propose a Few-shot Dynamic Neural Radiance Field (FDNeRF), the first
NeRF-based method capable of reconstruction and expression editing of 3D faces
based on a small number of dynamic images. Unlike existing dynamic NeRFs that
require dense images as input and can only be modeled for a single identity,
our method enables face reconstruction across different persons with few-shot
inputs. Compared to state-of-the-art few-shot NeRFs designed for modeling
static scenes, the proposed FDNeRF accepts view-inconsistent dynamic inputs and
supports arbitrary facial expression editing, i.e., producing faces with novel
expressions beyond the input ones. To handle the inconsistencies between
dynamic inputs, we introduce a well-designed conditional feature warping (CFW)
module to perform expression conditioned warping in 2D feature space, which is
also identity adaptive and 3D constrained. As a result, features of different
expressions are transformed into the target ones. We then construct a radiance
field based on these view-consistent features and use volumetric rendering to
synthesize novel views of the modeled faces. Extensive experiments with
quantitative and qualitative evaluation demonstrate that our method outperforms
existing dynamic and few-shot NeRFs on both 3D face reconstruction and
expression editing tasks. Code is available at
https://github.com/FDNeRF/FDNeRF.


  We investigate the triangular-lattice antiferromagnetic Ising model with a
spatially anisotropic next-nearest-neighbor ferromagnetic coupling, which was
first discussed by Kitatani and Oguchi. By employing the effective geometric
factor, we analyze the scaling dimensions of the operators around the
Berezinskii-Kosterlitz-Thouless (BKT) transition lines, and determine the
global phase diagram. Our numerical data exhibit that two types of
BKT-transition lines separate the intermediate critical region from the ordered
and disordered phases, and they do not merge into a single curve in the
antiferromagnetic region. We also estimate the central charge and perform some
consistency checks among scaling dimensions in order to provide the evidence of
the six-state clock universality. Further, we provide an analysis of the shapes
of boundaries based on the crossover argument.


  We present a scheme of quantum repeater that uses entangled multimode
coherent states which are obtained by electro-optic modulation of symmetric and
antisymmetric Schr\"odinger cat states. In this method subcarrier modes of the
phase modulated states generated by the remote parties are sent to a symmetric
beam splitter at the central node. The entangled coherent states are heraldedly
prepared by photon counting measurements at the output channels of the beam
splitter. We study how the effects of decoherence in the quantum channel affect
statistics of photocounts and corresponding fidelity. We show how the proposed
scheme can be useful for extending range of quantum key distribution with sub
carrier wave encoding by exploiting quantum teleportation with the generated
entanglement.


  In outburst sources, quasi-periodic oscillation (QPO) frequency is known to
evolve in a certain way: in the rising phase, it monotonically goes up till a
soft intermediate state is achieved. In the propagating oscillatory shock
model, oscillation of the Compton cloud is thought to cause QPOs. Thus, in
order to increase QPO frequency, Compton cloud must collapse steadily in the
rising phase. In decline phases, exactly opposite should be true. We
investigate cause of this evolution of the Compton cloud. The same viscosity
parameter which increases the Keplerian disk rate, also moves the inner edge of
the Keplerian component, thereby reducing the size of the Compton cloud and
reducing the cooling time scale. We show that cooling of the Compton cloud by
inverse Comptonization is enough for it to collapse sufficiently so as to
explain the QPO evolution. In the Two Component Advective Flow (TCAF)
configuration of Chakrabarti-Titarchuk, centrifugal force induced shock
represents boundary of the Compton cloud. We take the rising phase of 2010
outburst of Galactic black hole candidate H~1743-322 and find an estimation of
variation of $\alpha$ parameter of the sub-Keplerian flow to be monotonically
rising from $0.0001$ to $0.02$, well within the range suggested by
magneto-rotational instability. We also estimate the inward velocity of the
Compton cloud to be a few meters/second which is comparable to what is found in
several earlier studies of our group by empirically fitting the shock locations
with the time of observations.


  Deep multimodal learning has achieved great progress in recent years.
However, current fusion approaches are static in nature, i.e., they process and
fuse multimodal inputs with identical computation, without accounting for
diverse computational demands of different multimodal data. In this work, we
propose dynamic multimodal fusion (DynMM), a new approach that adaptively fuses
multimodal data and generates data-dependent forward paths during inference. To
this end, we propose a gating function to provide modality-level or
fusion-level decisions on-the-fly based on multimodal features and a
resource-aware loss function that encourages computational efficiency. Results
on various multimodal tasks demonstrate the efficiency and wide applicability
of our approach. For instance, DynMM can reduce the computation costs by 46.5%
with only a negligible accuracy loss (CMU-MOSEI sentiment analysis) and improve
segmentation performance with over 21% savings in computation (NYU Depth V2
semantic segmentation) when compared with static fusion approaches. We believe
our approach opens a new direction towards dynamic multimodal network design,
with applications to a wide range of multimodal tasks.


  By choosing appropriate deformed Maxwellian ion and electron distribution
functions depending on the two particle constants of motion, i.e. the energy
and toroidal angular momentum, we reduce the Vlasov axisymmetric equilibrium
problem for quasineutral plasmas to a transcendental Grad-Shafranov-like
equation. This equation is then solved numerically under the Dirichlet boundary
condition for an analytically prescribed boundary possessing a lower X-point to
construct tokamak equilibria with toroidal sheared ion flow and anisotropic
pressure. Depending on the deformation of the distribution functions these
steady states can have toroidal current densities either peaked on the magnetic
axis or hollow. These two kinds of equilibria may be regarded as a bifurcation
in connection with symmetry properties of the distribution functions on the
magnetic axis.


  Some polynomials $P$ with rational coefficients give rise to well defined
maps between cyclic groups, $\Z_q\longrightarrow\Z_r$, $x+q\Z\longmapsto
P(x)+r\Z$. More generally, there are polynomials in several variables with
tuples of rational numbers as coefficients that induce maps between commutative
groups. We characterize the polynomials with this property, and classify all
maps between two given finite commutative groups that arise in this way. We
also provide interpolation formulas and a Taylor-type theorem for the
calculation of polynomials that describe given maps.


  Electromagnetic radiation is known to be associated with certain
gravitational waves events, i.e. the collision of binary neutron stars.
Establishing this connection is non-trivial. However, if electromagnetic
counterparts could be produced by directly converting gravitons into photons,
then a simple smoking gun test exists linking the two events. This model uses
the general and conversion mechanism discussed by Raffelt and Stodolsky.
Furthermore, because this mechanism is generic to the symmetries of general
relativity and the standard model and because it assumes a quantised
gravitational field, we may probe both the existence of the graviton and the
scale at which quantum gravity effects (and thus very high-energy phenomena)
become relevant using simple low-energy experiments.


  The order from quantum disorders (OFQD) phenomenon is well-known and
ubiquitous in particle physics and frustrated magnetic systems. Typically, OFQD
transfers a spurious Goldstone mode into a pseudo-Goldstone mode with a tiny
gap. Here, we report an opposite phenomenon: OFQD transfers a spurious
quadratic mode into a true linear Goldstone mode with a very small velocity
(named slow-Goldstone mode). This new phenomenon is demonstrated in an
interacting bosonic system subjected to an Abelian flux. We develop a new and
systematic OFQD analysis to determine the true quantum ground state and the
whole excitation spectrum. In the weak-coupling limit, the superfluid ground
state has a 4-sublattice 90? coplanar spin structure, which supports 4 linear
Goldstone modes with 3 different velocities. One of which is generated by the
OFQD is much softer than the other 3 Goldstone modes, so it can be easily
detected in the cold atom or photonic experiments. In the strong-coupling
limit, the ferromagnetic Mott ground state with a true quadratic Goldstone
mode. We speculate that there could be some topological phases intervening
between the two symmetry broken states. These novel phenomena may be observed
in the current cold-atom or photonic experiments subjected to an Abelian flux
at the weak coupling limit where the heatings may be well under control.
Possible connections to Coleman-Weinberg potential in particle physics, 1/N
expansion of Sachdev-Ye-Kitaev models, and zero temperature quantum black hole
entropy are outlined.


  We study aspects of confinement in the M theory fivebrane version of QCD
(MQCD). We show heavy quarks are confined in hadrons (which take the form of
membrane-fivebrane bound states) for N=1 and softly broken N=2 SU(Nc) MQCD. We
explore and clarify the transition from the exotic physics of the latter to the
standard physics of the former. In particular, the many strings and
quark-antiquark mesons found in N=2 field theory by Douglas and Shenker are
reproduced. It is seen that in the N=1 limit all but one such meson disappears
while all of the strings survive. The strings of softly broken N=2, N=1, and
even non-supersymmetric SU(Nc) MQCD have a common ratio for their tensions as a
function of the amount of flux they carry. We also comment on the almost BPS
properties of the Douglas-Shenker strings and discuss the brane picture for
monopole confinement on N=2 QCD Higgs branches.


  In this work, we propose an approach to teaching global warming adapted to
the new high school curricula. The aim is to build a link between CO$_2$
emissions and the rise in the Earth's average temperature, based as far as
possible on explicit empirical evidence. We first present the existing teaching
approaches on the subject, which are then related to the a prioir students'
ideas, in particular: the non-evidence of interactions between gases and
radiation. The didactic choices structuring the approach are then exposed. They
are based on the interpretation of experiments carried out with an infrared
camera in a spectral range allowing the emission and absorption of CO$_2$ to be
seen.


  Noisy sensing, imperfect control, and environment changes are defining
characteristics of many real-world robot tasks. The partially observable Markov
decision process (POMDP) provides a principled mathematical framework for
modeling and solving robot decision and control tasks under uncertainty. Over
the last decade, it has seen many successful applications, spanning
localization and navigation, search and tracking, autonomous driving,
multi-robot systems, manipulation, and human-robot interaction. This survey
aims to bridge the gap between the development of POMDP models and algorithms
at one end and application to diverse robot decision tasks at the other. It
analyzes the characteristics of these tasks and connects them with the
mathematical and algorithmic properties of the POMDP framework for effective
modeling and solution. For practitioners, the survey provides some of the key
task characteristics in deciding when and how to apply POMDPs to robot tasks
successfully. For POMDP algorithm designers, the survey provides new insights
into the unique challenges of applying POMDPs to robot systems and points to
promising new directions for further research.


  In this work, we study non-asymptotic bounds on correlation between two time
realizations of stable linear systems with isotropic Gaussian noise.
Consequently, via sampling from a sub-trajectory and using \emph{Talagrands'}
inequality, we show that empirical averages of reward concentrate around steady
state (dynamical system mixes to when closed loop system is stable under linear
feedback policy ) reward , with high-probability. As opposed to common belief
of larger the spectral radius stronger the correlation between samples,
\emph{large discrepancy between algebraic and geometric multiplicity of system
eigenvalues leads to large invariant subspaces related to system-transition
matrix}; once the system enters the large invariant subspace it will travel
away from origin for a while before coming close to a unit ball centered at
origin where an isotropic Gaussian noise can with high probability allow it to
escape the current invariant subspace it resides in, leading to
\emph{bottlenecks} between different invariant subspaces that span
$\mathbb{R}^{n}$, to be precise : system initiated in a large invariant
subspace will be stuck there for a long-time: log-linear in dimension of the
invariant subspace and inversely to log of inverse of magnitude of the
eigenvalue. In the problem of Ordinary Least Squares estimate of system
transition matrix via a single trajectory, this phenomenon is even more evident
if spectrum of transition matrix associated to large invariant subspace is
explosive and small invariant subspaces correspond to stable eigenvalues. Our
analysis provide first interpretable and geometric explanation into intricacies
of learning and concentration for random dynamical systems on continuous, high
dimensional state space; exposing us to surprises in high dimensions


  Quantizing images into discrete representations has been a fundamental
problem in unified generative modeling. Predominant approaches learn the
discrete representation either in a deterministic manner by selecting the
best-matching token or in a stochastic manner by sampling from a predicted
distribution. However, deterministic quantization suffers from severe codebook
collapse and misalignment with inference stage while stochastic quantization
suffers from low codebook utilization and perturbed reconstruction objective.
This paper presents a regularized vector quantization framework that allows to
mitigate above issues effectively by applying regularization from two
perspectives. The first is a prior distribution regularization which measures
the discrepancy between a prior token distribution and the predicted token
distribution to avoid codebook collapse and low codebook utilization. The
second is a stochastic mask regularization that introduces stochasticity during
quantization to strike a good balance between inference stage misalignment and
unperturbed reconstruction objective. In addition, we design a probabilistic
contrastive loss which serves as a calibrated metric to further mitigate the
perturbed reconstruction objective. Extensive experiments show that the
proposed quantization framework outperforms prevailing vector quantization
methods consistently across different generative models including
auto-regressive models and diffusion models.


  Droplets can be levitated by their own vapour when placed onto a superheated
plate (the Leidenfrost effect). It is less known that the Leidenfrost effect
can likewise be observed over a liquid pool (superheated with respect to the
drop), which is the study case here. Emphasis is placed on an asymptotic
analysis in the limit of small evaporation numbers, which proves to be a
realistic one indeed for not so small drops. The global shapes are found to
resemble "superhydrophobic drops" that follow from the equilibrium between
capillarity and gravity. However, the morphology of the thin vapour layer
between the drop and the pool is very different from that of classical
Leidenfrost drops over a flat rigid substrate, and exhibits different scaling
laws. We determine analytical expressions for the vapour thickness as a
function of temperature and material properties, which are confirmed by
numerical solutions. Surprisingly, we show that deformability of the pool
suppresses the chimney instability of Leidenfrost drops.


  Determining the inner structure of protons and nuclei in terms of their
fundamental constituents has been one of the main tasks of high energy nuclear
and particle physics experiments. This quest started as a mapping of the
(average) parton densities as a function of longitudinal momentum fraction and
resolution scale. Recently, the field has progressed to more differential
imaging, where one important development is the description of the
event-by-event quantum fluctuations in the wave function of the colliding
hadron.
  In this Review, recent developments on the extraction of proton and nuclear
transverse geometry with event-by-event fluctuations from collider experiments
at high energy is presented. The importance of this fundamentally interesting
physics in other collider experiments like in studies of the properties of the
Quark Gluon Plasma is also illustrated.


  The triangular lattice compound TlYbS$_2$ was prepared as large single
crystals via a molten flux growth technique using sodium chloride. Anisotropic
magnetic susceptibility measurements down to 0.4 K indicate a complete absence
of long-range magnetic order. Despite this lack of long-range order,
short-range antiferromagnetic interactions are evidenced through broad
transitions, suggesting frustrated behavior. Variable magnetic field
measurements reveal metamagnetic behavior at temperatures less than 2 K.
Complex low temperature field-tunable magnetic behavior, in addition to no
observable long-range order down to 0.4 K, suggest that TlYbS$_2$ is a
frustrated magnet and a possible quantum spin liquid candidate.


  Over the past few years, the explosion in sparse tensor algebra workloads has
led to a corresponding rise in domain-specific accelerators to service them.
Due to the irregularity present in sparse tensors, these accelerators employ a
wide variety of novel solutions to achieve good performance. At the same time,
prior work on design-flexible sparse accelerator modeling does not express this
full range of design features, making it difficult to understand the impact of
each design choice and compare or extend the state-of-the-art.
  To address this, we propose TeAAL: a language and simulator generator for the
concise and precise specification and evaluation of sparse tensor algebra
accelerators. We use TeAAL to represent and evaluate four disparate
state-of-the-art accelerators -- ExTensor, Gamma, OuterSPACE, and SIGMA -- and
verify that it reproduces their performance with high accuracy. Finally, we
demonstrate the potential of TeAAL as a tool for designing new accelerators by
showing how it can be used to speed up vertex-centric programming accelerators
-- achieving $1.9\times$ on BFS and $1.2\times$ on SSSP over GraphDynS.


  We introduce Latxa, a family of large language models for Basque ranging from
7 to 70 billion parameters. Latxa is based on Llama 2, which we continue
pretraining on a new Basque corpus comprising 4.3M documents and 4.2B tokens.
Addressing the scarcity of high-quality benchmarks for Basque, we further
introduce 4 multiple choice evaluation datasets: EusProficiency, comprising
5,169 questions from official language proficiency exams; EusReading,
comprising 352 reading comprehension questions; EusTrivia, comprising 1,715
trivia questions from 5 knowledge areas; and EusExams, comprising 16,774
questions from public examinations. In our extensive evaluation, Latxa
outperforms all previous open models we compare to by a large margin. In
addition, it is competitive with GPT-4 Turbo in language proficiency and
understanding, despite lagging behind in reading comprehension and
knowledge-intensive tasks. Both the Latxa family of models, as well as our new
pretraining corpora and evaluation datasets, are publicly available under open
licenses at https://github.com/hitz-zentroa/latxa. Our suite enables
reproducible research on methods to build LLMs for low-resource languages.


  We classify totally geodesic and parallel hypersurfaces of four-dimensional
non-reductive homogeneous pseudo-Riemannian manifolds.


  This work studies the modeling of false data injection attacks (FDIAs) on
IEGSs. First, we introduce a static state estimation model and bad data
detection method for IEGSs. Then, we develop FDIAs on IEGSs with complete
network topology and parameter information. Next, we develop FDIAs on IEGSs
when intruders have only local network topology and parameter information of an
IEGS. Lastly, we explore FDIAs on IEGSs when intruders have only local network
topology information of an IEGS.


  Automated Market Makers (AMMs) are decentralized applications that allow
users to exchange crypto-tokens without the need for a matching exchange order.
AMMs are one of the most successful DeFi use cases: indeed, major AMM platforms
process a daily volume of transactions worth USD billions. Despite their
popularity, AMMs are well-known to suffer from transaction-ordering issues:
adversaries can influence the ordering of user transactions, and possibly
front-run them with their own, to extract value from AMMs, to the detriment of
users. We devise an effective procedure to construct a strategy through which
an adversary can maximize the value extracted from user transactions.


  Let (Zn) be a branching process with immigration in an independent and
identically distributed random environment. Under necessary moment conditions,
we show the exact convergence rate in the central limit theorem on logZn by
using the convergence rates of the logarithm of submartingale and the result of
the corresponding random walk on the Berry-Esseen bound.


  We report a detailed study of low-temperature (mK) transport properties of a
silicon double-dot system fabricated by phosphorous ion implantation. The
device under study consists of two phosphorous nanoscale islands doped to above
the metal-insulator transition, separated from each other and the source and
drain reservoirs by nominally undoped (intrinsic) silicon tunnel barriers.
Metallic control gates, together with an Al-AlOx single-electron transistor,
were positioned on the substrate surface, capacitively coupled to the buried
dots. The individual double-dot charge states were probed using source-drain
bias spectroscopy combined with non-invasive SET charge sensing. The system was
measured in linear (VSD = 0) and non-linear (VSD <> 0) regimes allowing
calculations of the relevant capacitances. Simultaneous detection using both
SET sensing and source-drain current measurements was demonstrated, providing a
valuable combination for the analysis of the system. Evolution of the triple
points with applied bias was observed using both charge and current sensing.
Coulomb diamonds, showing the interplay between the Coulomb charging effects of
the two dots, were measured using simultaneous detection and compared with
numerical simulations.


  It was recently shown that, for solving NP-complete problems, adiabatic paths
always exist without finite-order perturbative crossings between local and
global minima, which could lead to anticrossings with exponentially small
energy gaps if present. However, it was not shown whether such a path could be
found easily. Here, we give a simple construction that deterministically
eliminates all such anticrossings in polynomial time, space, and energy, for
any Ising models with polynomial final gap. Thus, in order for adiabatic
quantum optimization to require exponential time to solve any NP-complete
problem, some quality other than this type of anticrossing must be unavoidable
and necessitate exponentially long runtimes.


  This work presents the multiharmonic analysis and derivation of functional
type a posteriori estimates of a distributed eddy current optimal control
problem and its state equation in a time-periodic setting. The existence and
uniqueness of the solution of a weak space-time variational formulation for the
optimality system and the forward problem are proved by deriving inf-sup and
sup-sup conditions. Using the inf-sup and sup-sup conditions, we derive
guaranteed, sharp, and fully computable bounds of the approximation error for
the optimal control problem and the forward problem in the functional type a
posteriori estimation framework. We present here the first computational
results on the derived estimates.


  Weakly acyclic games generalize potential games and are fundamental to the
study of game theoretic control. In this paper, we present a generalization of
weakly acyclic games, and we observe its importance in multi-agent learning
when agents employ experimental strategy updates in periods where they fail to
best respond. While weak acyclicity is defined in terms of path connectivity
properties of a game's better response graph, our generalization is defined
using a generalized better response graph. We provide sufficient conditions for
this notion of generalized weak acyclicity in both two-player games and
$n$-player games. To demonstrate that our generalization is not trivial, we
provide examples of games admitting a pure Nash equilibrium that are not
generalized weakly acyclic. The generalization presented in this work is
closely related to the recent theory of satisficing paths, and the
counterexamples presented here constitute the first negative results in that
theory.


  This paper begins with a summary of a powerful formalism for the study of
electronic states in condensed matter physics called "Gauge Theory of
States/Phases of Matter." The chiral anomaly, which plays quite a prominent
role in that formalism, is recalled. I then sketch an application of the chiral
anomaly in 1+1 dimensions to quantum wires. Subsequently, some elements of the
quantum Hall effect in two-dimensional (2D) gapped ("incompressible") electron
liquids are reviewed. In particular, I discuss the role of anomalous chiral
edge currents and of anomaly inflow in 2D gapped electron liquids with
explicitly or spontaneously broken time reversal, i.e., in Hall- and Chern
insulators. The topological Chern-Simons action yielding the transport
equations valid in the bulk of such systems and the associated anomalous edge
action are derived. The results of a general classification of "abelian" Hall
insulators are outlined. After some remarks on induced Chern-Simons actions, I
sketch results on certain 2D chiral photonic wave guides. I then continue with
an analysis of chiral edge spin-currents and the bulk response equations in
time-reversal invariant 2D topological insulators of electron gases with
spin-orbit interactions. The "chiral magnetic effect" in 3D systems and
axion-electrodynamics are reviewed next. This prepares the ground for an
outline of a general theory of 3D topological insulators, including "axionic
insulators". Some remarks on Weyl semi-metals, which exhibit the chiral
magnetic effect, and on Mott transitions in 3D systems with dynamical
axion-like degrees of freedom conclude this review.}


  We investigate the influence of the projective invariance on the
renormalization properties of the theory. One-loop counterterms are calculated
in the most general case of interaction of gravity with scalar field.


  Iterated Function Systems (IFSs) have been at the heart of fractal geometry
almost from its origin, and several generalizations for the notion of IFS have
been suggested. Subdivision schemes are widely used in computer graphics and
attempts have been made to link fractals generated by IFSs to limits generated
by subdivision schemes. With an eye towards establishing connection between
non-stationary subdivision schemes and fractals, this paper introduces the
notion of "trajectories of maps defined by function systems" which may be
considered as a new generalization of the traditional IFS. The significance and
the convergence properties of 'forward' and 'backward' trajectories are
studied. In contrast to the ordinary fractals which are self-similar at
different scales, the attractors of these trajectories may have different
structures at different scales.


  Raman process is used for generation of nonclassical states and subsequent
applications due to its simplicity. In view of the experimental feasibility of
the off-resonant Raman process at single photon level useful in long distance
quantum communication and quantum memory, we perform here a detailed study of
possibility of generation of nonclassical states under off-resonance
conditions. Specifically, we have studied nonclassicality in the off-resonant
Raman process with the help of a characteristic function written using more
general solution than the conventional short-time solution under complete
quantum treatment and established the significance of frequency detuning
parameter in generation of nonclassical states. The obtained characteristic
function remains Gaussian and reveals that larger values of frequency detuning
parameters are favorable to induce nonclassicality in some cases. The single-
and two-mode squeezing and antibunching as well as intermodal entanglement are
reported in terms of experimentally accessible quantum noise fluctuations
considering either phonon mode coherent or chaotic. Subsequently, the joint
photon number and integrated intensity distributions are studied to analyze the
performance of pair generation in Stokes-phonon and pump-phonon modes. The
present study discusses the role of resonance conditions in generation of
nonclassical states and establishes that experimentally controllable detuning
parameter can be used to probe and enhance the generated nonclassicality.