  We propose the Graph2Graph Transformer architecture for conditioning on and
predicting arbitrary graphs, and apply it to the challenging task of
transition-based dependency parsing. After proposing two novel Transformer
models of transition-based dependency parsing as strong baselines, we show that
adding the proposed mechanisms for conditioning on and predicting graphs of
Graph2Graph Transformer results in significant improvements, both with and
without BERT pre-training. The novel baselines and their integration with
Graph2Graph Transformer significantly outperform the state-of-the-art in
traditional transition-based dependency parsing on both English Penn Treebank,
and 13 languages of Universal Dependencies Treebanks. Graph2Graph Transformer
can be integrated with many previous structured prediction methods, making it
easy to apply to a wide range of NLP tasks.


  We introduce a variant of the proximal gradient method in which the quadratic
term is diagonal but may be indefinite, and is safeguarded by a trust region.
Our method is a special case of the proximal quasi-Newton trust-region method
of arXiv:2103.15993v3. We provide closed-form solution of the step computation
in certain cases where the nonsmooth term is separable and the trust region is
defined in infinity norm, so that no iterative subproblem solver is required.
Our analysis expands upon that of arXiv:2103.15993v3 by generalizing the
trust-region approach to problems with bound constraints. We provide an
efficient open-source implementation of our method, named TRDH, in the Julia
language in which Hessians approximations are given by diagonal quasi-Newton
updates. TRDH evaluates one standard proximal operator and one indefinite
proximal operator per iteration. We also analyze and implement a variant named
iTRDH that performs a single indefinite proximal operator evaluation per
iteration. We establish that iTRDH enjoys the same asymptotic worst-case
iteration complexity as TRDH. We report numerical experience on unconstrained
and bound-constrained problems, where TRDH and iTRDH are used both as
standalone and subproblem solvers. Our results illustrate that, as standalone
solvers, TRDH and iTRDH improve upon the quadratic regularization method R2 of
arXiv:2103.15993v3 but also sometimes upon their quasi-Newton trust-region
method, referred to here as TR-R2, in terms of smooth objective value and
gradient evaluations. On challenging nonnegative matrix factorization, binary
classification and data fitting problems, TRDH and iTRDH used as subproblem
solvers inside TR improve upon TR-R2 for at least one choice of diagonal
approximation.


  We introduce a structural approach to study Lagrangian submanifolds of the
complex hyperquadric in arbitrary dimension by using its family of
non-integrable almost product structures. In particular, we define local angle
functions encoding the geometry of the Lagrangian submanifold at hand. We prove
that these functions are constant in the special case that the Lagrangian
immersion is the Gauss map of an isoparametric hypersurface of a sphere and
give the relation with the constant principal curvatures of the hypersurface.
We also use our techniques to classify all minimal Lagrangian submanifolds of
the complex hyperquadric which have constant sectional curvatures and all
minimal Lagrangian submanifolds for which all, respectively all but one, local
angle functions coincide.


  Hadoop is a popular MapReduce framework for developing parallel applications
in distributed environments. Several advantages of MapReduce such as
programming ease and ability to use commodity hardware make the applicability
of soft computing methods for parallel and distributed systems easier than
before. In this paper, we present the results of an experimental study on
running soft computing algorithms using Hadoop. This study shows how a simple
genetic algorithm running on Hadoop can be used to produce solutions for high
dimensional optimization problems. In addition, a simple but effective
technique, which did not need MapReduce chains, has been proposed.


  We iteratively derive the product-form solutions of stationary distributions
of priority multiclass queueing networks with multi-sever stations. The
networks are Markovian with exponential interarrival and service time
distributions. These solutions can be used to conduct performance analysis or
as comparison criteria for approximation and simulation studies of large scale
networks with multi-processor shared-memory switches and cloud computing
systems with parallel-server stations. Numerical comparisons with existing
Brownian approximating model are provided to indicate the effectiveness of our
algorithm.


  Existing approaches to fairness in stochastic multi-armed bandits (MAB)
primarily focus on exposure guarantee to individual arms. When arms are
naturally grouped by certain attribute(s), we propose Bi-Level Fairness, which
considers two levels of fairness. At the first level, Bi-Level Fairness
guarantees a certain minimum exposure to each group. To address the unbalanced
allocation of pulls to individual arms within a group, we consider meritocratic
fairness at the second level, which ensures that each arm is pulled according
to its merit within the group. Our work shows that we can adapt a UCB-based
algorithm to achieve a Bi-Level Fairness by providing (i) anytime Group
Exposure Fairness guarantees and (ii) ensuring individual-level Meritocratic
Fairness within each group. We first show that one can decompose regret bounds
into two components: (a) regret due to anytime group exposure fairness and (b)
regret due to meritocratic fairness within each group. Our proposed algorithm
BF-UCB balances these two regrets optimally to achieve the upper bound of
$O(\sqrt{T})$ on regret; $T$ being the stopping time. With the help of
simulated experiments, we further show that BF-UCB achieves sub-linear regret;
provides better group and individual exposure guarantees compared to existing
algorithms; and does not result in a significant drop in reward with respect to
UCB algorithm, which does not impose any fairness constraint.


  We consider derivations $\partial$ on Conway's field $\mathbf{No}$ of surreal
numbers such that the ordered differential field $(\mathbf{No},\partial)$ has
constant field $\mathbb{R}$ and is a model of the model companion of the theory
of $H$-fields with small derivation. We show that this determines
$(\mathbf{No},\partial)$ uniquely up to isomorphism, and that this structure is
absolutely homogeneous universal for models of this theory with constant field
$\mathbb{R}$.


  We present a combined experimental-theoretical study demonstrating the role
of site disorder, off-stoichiometry and strain on the optical behavior of
magnetoelectric gallium ferrite. Optical properties such as band-gap,
refractive indices and dielectric constants were experimentally obtained by
performing ellipsometric studies over the energy range 0.8 eV to 4.2 eV on
pulsed laser deposited epitaxial thin films of stoichiometric gallium ferrite
with b-axis orientation and the data was compared with theoretical results.
Calculations on the ground state structure show that the optical activity in
GaFeO3 arises primarily from O2p-Fe3d transitions. Further, inclusion of site
disorder and epitaxial strain in the ground state structure significantly
improves the agreement between the theory and the room temperature experimental
data substantiating the presence of site-disorder in the experimentally derived
strained GaFeO3 films at room temperature. We attribute the modification of the
ground state optical behavior upon inclusion of site disorder to the
corresponding changes in the electronic band structure, especially in Fe3d
states leading to a lowered band-gap of the material.


  The quantum dynamics of fermionic or bosonic many-body systems following
external excitation can be successfully studied using two-time nonequilibrium
Green's functions (NEGF) or single-time reduced density matrix methods.
Approximations are introduced via a proper choice of the many-particle
self-energy or decoupling of the BBGKY hierarchy. These approximations are
based on Feynman's diagram approaches or on cluster expansions into
single-particle and correlation operators. Here, we develop a different
approach where, instead of equations of motion for the many-particle NEGF (or
density operators), single-time equations for the correlation functions of
fluctuations are analyzed. We present a derivation of the first two equations
of the alternative hierarchy of fluctuations and discuss possible decoupling
approximations. In particular, we derive the polarization approximation (PA)
which is shown to be equivalent to the single-time version [following by
applying the generalized Kadanoff-Baym ansatz (GKBA)] of the nonequilibrium
$GW$ approximation with exchange effects of NEGF theory, for weak coupling. The
main advantage of the quantum fluctuations approach is that the standard
ensemble average can be replaced by a semiclassical average over different
initial realizations, as was demonstrated before by Lacroix and co-workers [see
e.g. D. Lacroix et al., Phys. Rev. B, 2014, 90, 125112]. Here, we introduce the
stochastic $GW$ (SGW) approximation and the stochastic polarization
approximation (SPA) which are demonstrated to be equivalent to the single-time
$GW$ approximation without and with exchange, respectively, in the weak
coupling limit. Our numerical tests confirm that our approach has the same
favorable linear scaling with the computation time as the recently developed
G1-G2 scheme [Schluenzen et al., Phys. Rev. Lett., 2020, 124, 076601].


  The recently observed large Rashba-type spin splitting in the BiTeX (X = I,
Br, Cl) bulk states due to the absence of inversion asymmetry and large charge
polarity enables observation of the transition in Fermi surface topology from
spindle-torus to torus with varying the carrier density. These BiTeX systems
with high spin-orbit energy scales offer an ideal platform for achieving
practical spintronic applications and realizing non-trivial phenomena such as
topological superconductivity and Majorana fermions. Here we use Shubnikov-de
Haas oscillations to investigate the electronic structure of the bulk
conduction band of BiTeCl single crystals with different carrier densities. We
observe the topological transition of the Fermi surface (FS) from a
spindle-torus to a torus. The Landau level fan diagram reveals the expected
non-trivial {\pi} Berry phase for both the inner and outer FSs. Angle-dependent
oscillation measurements reveal three-dimensional FS topology when the Fermi
level lies in the vicinity of the Dirac point. All the observations are
consistent with large Rashba spin-orbit splitting in the bulk conduction band.


  In this paper we introduce the AMADEUS strategy, which has been used to
produce scientific writing tools for non-native users of English for 15 years,
and emphasize a learn-by-doing approach through which students and novice
writers can improve their scientific writing. More specifically, we provide a
9-step recipe for the students to compile writing material according to a
procedure that has proven efficient in scientific writing courses.


  The notion of Nash equilibria plays a key role in the analysis of strategic
interactions in the framework of $N$ player games. Analysis of Nash equilibria
is however a complex issue when the number of players is large. In this article
we emphasize the role of optimal transport theory in: 1) the passage from Nash
to Cournot-Nash equilibria as the number of players tends to infinity, 2) the
analysis of Cournot-Nash equilibria.


  Skip connections are an essential component of current state-of-the-art deep
neural networks (DNNs) such as ResNet, WideResNet, DenseNet, and ResNeXt.
Despite their huge success in building deeper and more powerful DNNs, we
identify a surprising security weakness of skip connections in this paper. Use
of skip connections allows easier generation of highly transferable adversarial
examples. Specifically, in ResNet-like (with skip connections) neural networks,
gradients can backpropagate through either skip connections or residual
modules. We find that using more gradients from the skip connections rather
than the residual modules according to a decay factor, allows one to craft
adversarial examples with high transferability. Our method is termed Skip
Gradient Method(SGM). We conduct comprehensive transfer attacks against
state-of-the-art DNNs including ResNets, DenseNets, Inceptions,
Inception-ResNet, Squeeze-and-Excitation Network (SENet) and robustly trained
DNNs. We show that employing SGM on the gradient flow can greatly improve the
transferability of crafted attacks in almost all cases. Furthermore, SGM can be
easily combined with existing black-box attack techniques, and obtain high
improvements over state-of-the-art transferability methods. Our findings not
only motivate new research into the architectural vulnerability of DNNs, but
also open up further challenges for the design of secure DNN architectures.


  We study the dynamics of Dirac-Born-Infeld (DBI) dark energy interacting with
dark matter. The DBI dark energy model considered here has a scalar field with
a nonstandard kinetic energy term, and has potential and brane tension that are
power-law functions. The new feature considered here is an interaction between
the DBI dark energy and dark matter through a phenomenological interaction
between the DBI scalar field and the dark matter fluid. We analyze two
different types of interactions between the DBI scalar field and the dark
matter fluid. In particular we study the phase-space diagrams of and look for
critical points of the phase space that are both stable and lead to
accelerated, late-time expansion. In general we find that the interaction
between the two dark components does not appear to give rise to late-time
accelerated expansion. However, the interaction can make the critical points in
the phase space of the system stable. Whether such stabilization occurs or not
depends on the form of the interaction between the two dark components.


  Rigorously quantifying the information in high contrast imaging data is
important for informing follow-up strategies to confirm the substellar nature
of a point source, constraining theoretical models of planet-disk interactions,
and deriving planet occurrence rates. However, within the exoplanet direct
imaging community, non-detections have almost exclusively been defined using a
frequentist detection threshold (i.e. contrast curve) and associated
completeness. This can lead to conceptual inconsistencies when included in a
Bayesian framework. A Bayesian upper limit is such that the true value of a
parameter lies below this limit with a certain probability. The associated
probability is the integral of the posterior distribution with the upper limit
as the upper bound. In summary, a frequentist upper limit is a statement about
the detectability of planets while a Bayesian upper limit is a statement about
the probability of a parameter to lie in an interval given the data. The latter
is therefore better suited for rejecting hypotheses or theoretical models based
on their predictions. In this work we emphasize that Bayesian statistics and
upper limits are more easily interpreted and typically more constraining than
the frequentist approach. We illustrate the use of Bayesian analysis in two
different cases: 1) with a known planet location where we also propose to use
model comparison to constrain the astrophysical nature of the point source and
2) gap-carving planets in TW Hya. To finish, we also mention the problem of
combining radial velocity and direct imaging observations.


  Based on the Fermi observational data we reveal meaningful constraints for
the dependence of the macroscopic conductivity $(\sigma)$ of dissipative pulsar
magnetosphere models on the corresponding spin-down rate, $\dot{\mathcal{E}}$.
Our models are refinements of the FIDO (Force-Free Inside, Dissipative Outside)
models whose dissipative regions are restricted on the equatorial current-sheet
outside the light-cylinder. Taking into account the observed cutoff-energies of
all the Fermi-pulsars and assuming that a) the corresponding $\gamma-$ray
pulsed emission is due to curvature radiation at the radiation-reaction-limit
regime and b) this emission is produced at the equatorial current-sheet near
the light-cylinder, we show that the \emph{Fermi}-data provide clear
indications about the corresponding accelerating electric-field components. A
direct comparison between the \emph{Fermi} cutoff-energies and the model ones
reveals that $\sigma$ increases with $\dot{\mathcal{E}}$ for high
$\dot{\mathcal{E}}$-values while it saturates for low ones. This comparison
indicates also that the corresponding gap-width increases toward low
$\dot{\mathcal{E}}$-values. Assuming the Goldreich-Julian flux for the emitting
particles we calculate the total $\gamma-$ray luminosity $(L_{\gamma})$. A
comparison between the dependence of the Fermi $L_{\gamma}$-values and the
model ones on $\dot{\mathcal{E}}$ indicates an increase of the emitting
particle multiplicity with $\dot{\mathcal{E}}$. Our modeling guided by the
\emph{Fermi}-data alone, enhances our understanding of the physical mechanisms
behind the high energy emission in pulsar magnetospheres.


  We employ robust weak gravitational lensing measurements to improve
cosmological constraints from measurements of the galaxy cluster mass function
and its evolution, using X-ray selected clusters detected in the ROSAT All-Sky
Survey. Our lensing analysis constrains the absolute mass scale of such
clusters at the 8 per cent level, including both statistical and systematic
uncertainties. Combining it with the survey data and X-ray follow-up
observations, we find a tight constraint on a combination of the mean matter
density and late-time normalization of the matter power spectrum,
$\sigma_8(\Omega_m/0.3)^{0.17}=0.81\pm0.03$, with marginalized, one-dimensional
constraints of $\Omega_m=0.26\pm0.03$ and $\sigma_8=0.83\pm0.04$. For these two
parameters, this represents a factor of two improvement in precision with
respect to previous work, primarily due to the reduced systematic uncertainty
in the absolute mass calibration provided by the lensing analysis. Our new
results are in good agreement with constraints from cosmic microwave background
(CMB) data, both WMAP and Planck (plus WMAP polarization), under the assumption
of a flat $\Lambda$CDM cosmology with minimal neutrino mass. Consequently, we
find no evidence for non-minimal neutrino mass from the combination of cluster
data with CMB, supernova and baryon acoustic oscillation measurements,
regardless of which all-sky CMB data set is used (and independent of the recent
claimed detection of B-modes on degree scales). We also present improved
constraints on models of dark energy (both constant and evolving),
modifications of gravity, and primordial non-Gaussianity. Assuming flatness,
the constraints for a constant dark energy equation of state from the cluster
data alone are at the 15 per cent level, improving to $\sim 6$ per cent when
the cluster data are combined with other leading probes.


  A quantum-mechanical version of Einstein's 1905 theory of Brownian motion is
presented. Starting from the Hamiltonian dynamics of an isolated composite of
objective and environmental systems, subdynamics for the objective system is
derived in the spirit of Einstein. The resulting master equation is found to
have the Lindblad structure.


  With the widespread adoption of mobility-on-demand (MoD) services and the
advancements in autonomous vehicle (AV) technology, the research interest into
the AVs based MoD (AMoD) services has grown immensely. Often agent-based
simulation frameworks are used to study the AMoD services using the trip data
of current Taxi or MoD services. For reliable results of AMoD simulations, a
realistic city network and travel times play a crucial part. However, many
times the researchers do not have access to the actual network state
corresponding to the trip data used for AMoD simulations reducing the
reliability of results. Therefore, this paper introduces a spatio-temporal
optimization strategy for scaling the link-level network travel times using the
simulated trip data without additional data sources on the network state. The
method is tested on the widely used New York City (NYC) Taxi data and shows
that the travel times produced using the scaled network are very close to the
recorded travel times in the original data. Additionally, the paper studies the
performance differences of AMoD simulation when the scaled network is used. The
results indicate that realistic travel times can significantly impact AMoD
simulation outcomes.


  We consider sequential decision making under uncertainty, where the goal is
to optimize over a large decision space using noisy comparative feedback. This
problem can be formulated as a $K$-armed Dueling Bandits problem where $K$ is
the total number of decisions. When $K$ is very large, existing dueling bandits
algorithms suffer huge cumulative regret before converging on the optimal arm.
This paper studies the dueling bandits problem with a large number of arms that
exhibit a low-dimensional correlation structure. Our problem is motivated by a
clinical decision making process in large decision space. We propose an
efficient algorithm CorrDuel which optimizes the exploration/exploitation
tradeoff in this large decision space of clinical treatments. More broadly, our
approach can be applied to other sequential decision problems with large and
structured decision spaces. We derive regret bounds, and evaluate performance
in simulation experiments as well as on a live clinical trial of therapeutic
spinal cord stimulation. To our knowledge, this marks the first time an online
learning algorithm was applied towards spinal cord injury treatments. Our
experimental results show the effectiveness and efficiency of our approach.


  We study thermodynamics of nuclear matter in a two-flavored parity doublet
model within the mean field approximation. Parameters of the model are chosen
to reproduce correctly the properties of the nuclear ground state. The model
predicts two phase transitions in nuclear matter, a liquid-gas phase transition
at normal nuclear density and a chiral transition at higher density. At finite
temperature the pion decay constant exhibits a considerable reduction at
intermediate values of chemical potential, which is traced back to the presence
of the liquid-gas transition, and approaches zero at higher chemical potential
associated with the chiral symmetry restoration. A "transition" from meson-rich
to baryon-rich matter is also discussed.


  In this work, we consider a variant of the classical Longest Common
Subsequence problem called Doubly-Constrained Longest Common Subsequence
(DC-LCS). Given two strings s1 and s2 over an alphabet A, a set C_s of strings,
and a function Co from A to N, the DC-LCS problem consists in finding the
longest subsequence s of s1 and s2 such that s is a supersequence of all the
strings in Cs and such that the number of occurrences in s of each symbol a in
A is upper bounded by Co(a). The DC-LCS problem provides a clear mathematical
formulation of a sequence comparison problem in Computational Biology and
generalizes two other constrained variants of the LCS problem: the Constrained
LCS and the Repetition-Free LCS. We present two results for the DC-LCS problem.
First, we illustrate a fixed-parameter algorithm where the parameter is the
length of the solution. Secondly, we prove a parameterized hardness result for
the Constrained LCS problem when the parameter is the number of the constraint
strings and the size of the alphabet A. This hardness result also implies the
parameterized hardness of the DC-LCS problem (with the same parameters) and its
NP-hardness when the size of the alphabet is constant.


  We generalize a result of Tibor Gallai as follows: for any finite set of
points $\mathcal{S}$ in the plane, if the plane is colored in finitely many
colors, then there exist $2^{\aleph_0}$ monochromatic subsets of the plane
homothetic to $\mathcal{S}$. Furthermore, we prove an even stronger result for
$n$-dimensional Euclidean space.


  We demonstrate the existence of hidden topological angles (HTAs) in a large
class of quantum field theories and quantum mechanical systems. HTAs are
distinct from theta-parameters in the lagrangian. They arise as invariant angle
associated with saddle points of the complexified path integral and their
descent manifolds (Lefschetz thimbles). Physical effects of HTAs become most
transparent upon analytic continuation in $n_f$ to non-integer number of
flavors, reducing in the integer $n_f$ limit to a $\mathbb Z_2$ valued phase
difference between dominant saddles. In ${\cal N}=1$ super Yang-Mills theory we
demonstrate the microscopic mechanism for the vanishing of the gluon
condensate. The same effect leads to an anomalously small condensate in a
QCD-like $SU(N)$ gauge theory with fermions in the two-index representation.
The basic phenomenon is that, contrary to folklore, the gluon condensate can
receive both positive and negative contributions in a semi-classical expansion.
In quantum mechanics, a HTA leads to a difference in semi-classical expansion
of integer and half-integer spin particles.


  Lipid vesicles appear ubiquitously in biological systems. Understanding how
the mechanical and intermolecular interations deform vesicle membrane is a
fundamental question in biophysics. In this article we developed a fast
algorithm to compute the surface configurations of lipid vesicles by
introducing the surface harmonic functions to approximate the surfaces. This
parameterization of the surfaces allows an analytical computation of the
membrane curvature energy and its gradient for the efficient minimization of
the curvature energy using a nonlinear conjugate gradient method. Our approach
drastically reduces the degrees of freedom for approximating the membrane
surfaces compared to the previously developed finite element and finite
difference methods. Vesicle deformations with a reduced volume larger than 0.65
can be well approximated by using as small as 49 surface harmonic functions.
The method thus has a great potential to reduce the computational expense of
tracking multiple vesicles which deform for their interaction with external
fields.


  We show that the functor from bialgebras to vector spaces sending a bialgebra
to its subspace of primitives has monadic length at most 2.


  Localization lengths of the electrons and holes in InGaN/GaN quantum wells
have been calculated using numerical solutions of the effective mass
Schr\"odinger equation. We have treated the distribution of indium atoms as
random and found that the resultant fluctuations in alloy concentration can
localize the carriers. By using a locally varying indium concentration function
we have calculated the contribution to the potential energy of the carriers
from band gap fluctuations, the deformation potential and the spontaneous and
piezoelectric fields. We have considered the effect of well width fluctuations
and found that these contribute to electron localization, but not to hole
localization. We also simulate low temperature photoluminescence spectra and
find good agreement with experiment.


  An information theory description of finite systems explicitly evolving in
time is presented. We impose a MaxEnt variational principle on the Shannon
entropy at a given time while the constraints are set at a former time. The
resulting density matrix contains explicit time odd components in the form of
collective flows. As a specific application we consider the dynamics of the
expansion in connection with heavy ion experiments. Lattice gas and classical
molecular dynamics simulations are shown.


  Integrable systems are derived from inelastic flows of timelike, spacelike,
and null curves in 2- and 3- dimensional Minkowski space. The derivation uses a
Lorentzian version of a geometrical moving frame method which is known to yield
the modified Korteveg-de Vries (mKdV) equation and the nonlinear Schrodinger
(NLS) equation in 2- and 3- dimensional Euclidean space, respectively. In
2-dimensional Minkowski space, timelike/spacelike inelastic curve flows are
shown to yield the defocusing mKdV equation and its bi-Hamiltonian
integrability structure, while inelastic null curve flows are shown to give
rise to Burgers' equation and its symmetry integrability structure. In
3-dimensional Minkowski space, the complex defocusing mKdV equation and the NLS
equation along with their bi-Hamiltonian integrability structures are obtained
from timelike inelastic curve flows, whereas spacelike inelastic curve flows
yield an interesting variant of these two integrable equations in which complex
numbers are replaced by hyperbolic (split-complex) numbers.


  The understanding of the nanoscale physical properties of biomolecules and
biomaterials will ultimately promote the research in the biological sciences.
In this review, we focused on theory, simulation, and experiments involving
nanoscale materials inspired by biological systems. Specifically, self-assembly
in living and synthetic materials, bio-functionalized nanomaterials and probing
techniques that use nanomaterials are discussed.


  The paper is concerned with `geometrization' of smooth (i.e. with open
stabilizers) representations of the automorphism group of universal domains,
and with the properties of `geometric' representations of such groups. As an
application, we calculate the cohomology groups of several classes of smooth
representations of the automorphism group of an algebraically closed extension
of infinite transcendence degree of an algebraically closed field.


  In this paper we describe how to include funding and margining costs into a
risk-neutral pricing framework for counterparty credit risk. We consider
realistic settings and we include in our models the common market practices
suggested by the ISDA documentation without assuming restrictive constraints on
margining procedures and close-out netting rules. In particular, we allow for
asymmetric collateral and funding rates, and exogenous liquidity policies and
hedging strategies. Re-hypothecation liquidity risk and close-out amount
evaluation issues are also covered. We define a comprehensive pricing framework
which allows us to derive earlier results on funding or counterparty risk. Some
relevant examples illustrate the non trivial settings needed to derive known
facts about discounting curves by starting from a general framework and without
resorting to ad hoc hypotheses. Our main result is a bilateral collateralized
counterparty valuation adjusted pricing equation, which allows to price a deal
while taking into account credit and debt valuation adjustments along with
margining and funding costs in a coherent way. We find that the equation has a
recursive form, making the introduction of an additive funding valuation
adjustment difficult. Yet, we can cast the pricing equation into a set of
iterative relationships which can be solved by means of standard least-square
Monte Carlo techniques.


  This paper presents a novel model training solution, denoted as
Adaptive-Gravity, for enhancing the robustness of deep neural network
classifiers against adversarial examples. We conceptualize the model
parameters/features associated with each class as a mass characterized by its
centroid location and the spread (standard deviation of the distance) of
features around the centroid. We use the centroid associated with each cluster
to derive an anti-gravity force that pushes the centroids of different classes
away from one another during network training. Then we customized an objective
function that aims to concentrate each class's features toward their
corresponding new centroid, which has been obtained by anti-gravity force. This
methodology results in a larger separation between different masses and reduces
the spread of features around each centroid. As a result, the samples are
pushed away from the space that adversarial examples could be mapped to,
effectively increasing the degree of perturbation needed for making an
adversarial example. We have implemented this training solution as an iterative
method consisting of four steps at each iteration: 1) centroid extraction, 2)
anti-gravity force calculation, 3) centroid relocation, and 4) gravity
training. Gravity's efficiency is evaluated by measuring the corresponding
fooling rates against various attack models, including FGSM, MIM, BIM, and PGD
using LeNet and ResNet110 networks, benchmarked against MNIST and CIFAR10
classification problems. Test results show that Gravity not only functions as a
powerful instrument to robustify a model against state-of-the-art adversarial
attacks but also effectively improves the model training accuracy.


  Following a previous work evidencing that short poly-propylene glycol (PPG)
chains incorporated to crude SBR-silica nanocomposites act as filler-network
softeners without changing their structure, we propose in the present letter to
examine more operative cross-linked materials. We first evidence that the
adsorption of PPG onto silica deactivates progressively the particle's
catalytic effect on vulcanization, without perturbing however the cross-link
density distribution that we investigate through multiple-quantum NMR. In
addition, electron microscopy confirms that silica structure is conserved after
vulcanization and that it does not depend on the PPG content either. Composites
containing various amount of PPG can thus be seen as structurally identical,
both from a matrix and filler point of view - which is confirmed by small and
medium amplitude oscillation shear rheology showing strikingly identical
viscoelastic properties. PPG signature only appears above 100% in tensile
deformation where it is seen to soften dramatically the filler network. Our
discovery makes it consequently possible to decorrelate the mechanical behavior
of reinforced rubbers under normal conditions of use and urgent needs of energy
dissipation.


  We report here the results of deep optical spectroscopy of the very extended
emission-line region (VEELR) found serendipitously around the Seyfert 2 galaxy
NGC 4388 in the Virgo cluster using the Subaru Telescope. The H-alpha recession
velocities of most of the filaments of the region observed are highly
blue-shifted with respect to the systemic velocity of the galaxy. The velocity
field is complicated, and from the kinematic and morphological points of view,
there seem to be several streams of filaments: low velocity (v = -100 km/s)
filaments, high velocity (v = -300 km/s) filaments, and a very high velocity (v
> -500 km/s) cloud complex. The emission-line ratios of the VEELR filaments are
well explained by power-law photoionization models with solar abundances,
suggesting that the Seyfert nucleus of NGC 4388 is the dominant ionization
source of the VEELR and that the VEELR gas has moderate metallicity. In
addition to photoionization, shock heating probably contributes to the
ionization of the gas. In particular, the filaments outside the ionization cone
of the Seyfert nucleus are mainly excited by shocks. We conclude that the VEELR
was formerly the disk gas of NGC 4388, which has been stripped by ram pressure
due to the interaction between the hot intra-cluster medium (ICM) and the
galaxy. The velocity field and the morphology of the VEELR closely resemble
snapshots from some numerical simulations of this process. In the case of NGC
4388, the ram pressure-stripped gas, which is normally seen as extended HI
filaments, happens to be exposed and ionized by the radiation from the AGN, and
so can be seen as optical emission-line gas.


  Although the energetic feedback from active galactic nuclei (AGN) is believed
to have a profound effect on the evolution of galaxies and clusters of
galaxies, details of the AGN heating remain elusive. Here, we study NGC 193 - a
nearby lenticular galaxy - based on X-ray (Chandra) and radio (VLA and GMRT)
observations. These data reveal the complex AGN outburst history of the galaxy:
we detect a pair of inner X-ray cavities, an outer X-ray cavity, a shock front,
and radio lobes extending beyond the inner cavities. We suggest that the inner
cavities were produced ~78 Myr ago by a weaker AGN outburst, while the outer
cavity, the radio lobes, and the shock front are due to a younger (13-26 Myr)
and (4-8) times more powerful outburst. Combining this with the observed
morphology of NGC 193, we conclude that NGC 193 likely represents the first
example of a second, more powerful, AGN outburst overrunning an older, weaker
outburst. These results help to understand how the outburst energy is
dissipated uniformly in the core of galaxies, and therefore may play a crucial
role in resolving how AGN outbursts suppress the formation of large cooling
flows at cluster centers.


  In this work the stochastic generalization of single Hodgkin-Huxley neuron is
further extended to unidirectionally coupled neurons. Our main focus is to
elucidate the role of channel noise in the kinetics and energetics of spiking
of action potential and the synchronization between two coupled neurons. We
have found that the size of the patch is playing the pivotal role in
synchronization and metabolic energy consumption. For example, there exists
three different patch size ranges in which coupled neuron system behaves in a
different manner from noise enhanced phase to dead range state before reaching
the deterministic limit. We have also found that the sodium and potassium
channel blockers have characteristic kinetic and energetic effects on
synchronization process and metabolic energy consumption rate which has been
validated with the simulated data.


  In this work, the triangle singularity mechanism is investigated in the
$\psi(2S) \to p \bar{p} \eta / p \bar{p} \pi^0$ process. The triangle loop
composed by $J/\psi$, $\eta$ and $p$ has a singularity in the physical
kinematic range for the $\psi(2S) \to p \bar{p} \eta / p \bar{p} \pi^0$
process, and it would generate a very narrow peak in the invariant mass
spectrum of $p\eta (\pi)$ around $1.56387$ GeV, which is far away from both the
threshold and relative resonances. In these processes, all the involved
vertices are constrained by the experimental data. Thus, we can make a precise
model independent prediction here. It turns out that the peak in the $p\eta$
invariant mass spectrum is visible, while it is very small in the $p\pi^0$
invariant mass spectrum. We expect this effect shown in $p \bar{p} \eta$ final
state can be observed by the Beijing Spectrometer (BESIII) and Super Tau-Charm
Facility (STCF) in the future.


  A new recurrence relation for exceptional orthogonal polynomials is proposed,
which holds for type 1, 2 and 3. As concrete examples, the recurrence relations
are given for Xj-Hermite, Laguerre and Jacobi polynomials in j = 1,2 case.


  In this article we give a uniform proof why the shift map on Floer homology
trajectory spaces is scale smooth. This proof works for various Floer
homologies, periodic, Lagrangian, Hyperk\"ahler, elliptic or parabolic, and
uses Hilbert space valued Sobolev theory.


  We study spectral properties of the Fokker-Planck operator that describes
particles diffusing in a quenched random velocity field. This random operator
is non-Hermitian and has eigenvalues occupying a finite area in the complex
plane. We calculate the eigenvalue density and averaged one-particle Green's
function, for weak disorder and dimension d>2. We relate our results to the
time-evolution of particle density, and compare them with numerical
simulations.


  Let $$ F(x, y) = \prod\limits_{k = 0}^{n - 1}(\delta_kx - \gamma_ky) $$ be a
binary form of degree $n \geq 1$, with complex coefficients, written as a
product of $n$ linear forms in $\mathbb C[x, y]$. Let $$ h_F = \prod\limits_{k
= 0}^{n - 1}\sqrt{|\gamma_k|^2 + |\delta_k|^2} $$ denote the height of $F$ and
let $A_F$ denote the area of the fundamental region of $F$: $$ \left\{(x, y)
\in \mathbb R^2 \colon |F(x, y)| \leq 1\right\}. $$ We prove that $h_F^{2/n}A_F
\geq \left(2^{1 + (r/n)}\right)\pi$, where $r$ is the number of roots of $F$ on
the real projective line $\mathbb R\mathbb P^1$, counting multiplicity.


  Red Dwarf (dM) stars are overwhelmingly the most numerous stars in our
Galaxy. These cool, faint and low mass stars make up more than 80% of all
stars. Also dM stars have extremely long life times (longer than 50-100 Gyr).
Determining the number of red dwarfs with planets and assessing planetary
habitability (a planet's potential to develop and sustain life) is critically
important because such studies would indicate how common life is in the
universe. Our program - "Living with a Red Dwarf" - addresses these questions
by investigating the long-term nuclear evolution and the coronal and
chromospheric properties of red dwarf stars with widely different ages (~50 Myr
-- 12 Gyr). One major focus of the program is to study the magnetic-dynamo
generated coronal and chromospheric X-ray--FUV/UV emissions and flare
properties of a sample of dM0--5 stars. Observations carried out by FUSE of a
number of young to old dM stars provide important data for understanding
transition region heating in these stars with deep convective zones as well as
providing measures of FUV irradiances. Also studied are the effects of
X-ray--FUV emissions on possible hosted planets and impacts of this radiation
on their habitability. Using these data we are constructing irradiance tables
(X-UV irradiances) that can be used to model the effects of XUV radiation on
planetary atmospheres and possible life on planetary surfaces. The initial
results of this program are discussed.


  A new model is presented for simulating coherent synchrotron radiation (CSR)
in one dimension. The method is based on convolving an integrated Green
function (IGF) with the longitudinal charge density. Since it is based on an
IGF, the accuracy of this approach is determined by how well one resolves the
charge density and not by resolving the single particle wake function. Since
short-range wakefield effects are included analytically, the approach can be
much more efficient than ordinary (non-IGF) approaches in situations where the
wake function and charge density have disparate spatial scales. Two cases are
presented: one derived from the full wake including short-range effects, and
one derived from the asymptotic wake. In the latter case the algorithm contains
the same physics as others based on the asymptotic approximation, but requires
only the line charge density and not its derivative. Examples are presented
that illustrate the limitations of the asymptotic-wake approximation, and that
illustrate how microbunching can increase the CSR fields by orders of magnitude
depending on the microbunching wavelength.


  We propose a novel approach for group elevator scheduling by formulating it
as the maximization of submodular function under a matroid constraint. In
particular, we propose to model the total waiting time of passengers using a
quadratic Boolean function. The unary and pairwise terms in the function denote
the waiting time for single and pairwise allocation of passengers to elevators,
respectively. We show that this objective function is submodular. The matroid
constraints ensure that every passenger is allocated to exactly one elevator.
We use a greedy algorithm to maximize the submodular objective function, and
derive provable guarantees on the optimality of the solution. We tested our
algorithm using Elevate 8, a commercial-grade elevator simulator that allows
simulation with a wide range of elevator settings. We achieve significant
improvement over the existing algorithms.


  A map $\phi$ on an associative ring is called a multiplicative Lie derivation
if $\phi([x,y])=[\phi(x),y]+[x,\phi(y)]$ holds for any elements $x,y$, where
$[x,y]=xy-yx$ is the Lie product. In the paper, we discuss the multiplicative
Lie derivations on the triangular 3-matrix rings $\mathcal T={\mathcal
T}_3(\mathcal R_i; \mathcal M_{ij})$. Under the standard assumption
$Q_i\mathcal Z(\mathcal T)Q_i=\mathcal Z(Q_i\mathcal T Q_i)$, $i=1,2,3$, we
show that every multiplicative Lie derivation $\varphi:\mathcal T\to\mathcal T$
has the standard form $\varphi=\delta+\gamma$ with $\delta $ a derivation and
$\gamma$ a center valued map vanishing each commutator.


  Human data forms the backbone of machine learning. Data protection laws thus
have strong bearing on how ML systems are governed. Given that most
requirements in data protection laws accompany the processing of personal data,
organizations have an incentive to keep their data out of legal scope. This
makes the development and application of certain privacy-preserving
techniques--data protection techniques--an important strategy for ML
compliance. In this paper, we examine the impact of a rhetoric that deems data
wrapped in these techniques as data that is "good-to-go". We show how their
application in the development of ML systems--from private set intersection as
part of dataset curation to homomorphic encryption and federated learning as
part of model computation--can further support individual monitoring and data
consolidation. With data accumulation at the core of how the ML pipeline is
configured, we argue that data protection techniques are often instrumentalized
in ways that support infrastructures of surveillance, rather than in ways that
protect individuals associated with data. Finally, we propose technology and
policy strategies to evaluate data protection techniques in light of the
protections they actually confer. We conclude by highlighting the role that
technologists might play in devising policies that combat surveillance ML
technologies.


  X-ray observations of hot gas in galaxy clusters often show steeper
temperature gradients across cold fronts -- contact discontinuities, driven by
the differential gas motions. These sharp (a few kpc wide) surface
brightness/temperature discontinuities would be quickly smeared out by the
electron thermal conduction in unmagnetized plasma, suggesting significant
suppression of the heat flow across the discontinuities. In fact, the character
of the gas flow near cold fronts is favorable for suppression of conduction by
aligning magnetic field lines along the discontinuities. We argue that a
similar mechanism is operating in the bulk of the gas. Generic 3D random
isotropic and incompressible motions increase the temperature gradients (in
some places) and at the same time suppress the local conduction by aligning the
magnetic field lines perpendicular to the local temperature gradient. We show
that the suppression of the effective conductivity in the bulk of the gas can
be linked to the increase of the frozen magnetic field energy density. On
average the rate of decay of the temperature fluctuations $\mathrm{d}\langle
\delta T^2 \rangle /\mathrm{d}t$ decreases as $\langle B^2 \rangle ^{-1/5}$.


  Recent studies have shown that, relative position encoding performs well in
selective state space model scanning algorithms, and the architecture that
balances SSM and Attention enhances the efficiency and effectiveness of the
algorithm, while the sparse activation of the mixture of experts reduces the
training cost. I studied the effectiveness of using different position
encodings in structured state space dual algorithms, and the more effective
SSD-Attn internal and external function mixing method, and designed a more
efficient cross domain mixture of experts. I found that the same matrix is very
wonderful in different algorithms, which allows us to establish a new hybrid
sparse architecture: Cheems. Compared with other hybrid architectures, it is
more efficient and more effective in language modeling tasks.


  We develop a theory for drying-induced stresses in sessile, poroelastic drops
undergoing evaporation on rigid surfaces. Using a lubrication-like
approximation, the governing equations of three-dimensional nonlinear
poroelasticity are reduced to a single thin-film equation for the drop
thickness. We find that thin drops experience compressive elastic stresses but
the total in-plane stresses are tensile. The mechanical response of the drop is
dictated by the initial profile of the solid skeleton, which controls the
in-plane deformation, the dominant components of elastic stress, and sets a
limit on the depth of delamination that can potentially occur. Our theory
suggests that the alignment of desiccation fractures in colloidal drops is
selected by the shape of the drop at the point of gelation. We propose that the
emergence of three distinct fracture patterns in dried blood drops is a
consequence of a non-monotonic drop profile at gelation. We also show that
depletion fronts, which separate wet and dry solid, can invade the drop from
the contact line and localise the generation of mechanical stress during
drying. Finally, the finite element method is used to explore the stress
profiles in drops with large contact angles.


  Code summaries are brief natural language descriptions of source code pieces.
The main purpose of code summarization is to assist developers in understanding
code and to reduce documentation workload. In this paper, we design a novel
multi-task learning (MTL) approach for code summarization through mining the
relationship between method code summaries and method names. More specifically,
since a method's name can be considered as a shorter version of its code
summary, we first introduce the tasks of generation and informativeness
prediction of method names as two auxiliary training objectives for code
summarization. A novel two-pass deliberation mechanism is then incorporated
into our MTL architecture to generate more consistent intermediate states fed
into a summary decoder, especially when informative method names do not exist.
To evaluate our deliberation MTL approach, we carried out a large-scale
experiment on two existing datasets for Java and Python. The experiment results
show that our technique can be easily applied to many state-of-the-art neural
models for code summarization and improve their performance. Meanwhile, our
approach shows significant superiority when generating summaries for methods
with non-informative names.


  We consider spectrum-angular characteristics of the undulator-type radiation
emitted by a bunch of relativistic charged particles because of interacting
with the nonsynchronous spatial harmonics of the transverse wakefields excited
by this bunch as it moves in a periodic structure. The conditions acceptable
for possible experimental verification when incoherent undulator-type radiation
power exceeds power loss associated with exciting the wakefields are discussed.


  We present a derivation of 2PN/RM metric field equations from the Einstein
field equation in General Relativity. We use the exponential parametrization
and the $c^{-3}$ isotropic spatial coordinates such as in IAU2000
recommendations.


  This paper addresses the problem of copying an unknown assembly of primitives
with known shape and appearance using information extracted from a single
photograph by an off-the-shelf procedure for object detection and pose
estimation. The proposed algorithm uses a simple combination of physical
stability constraints, convex optimization and Monte Carlo tree search to plan
assemblies as sequences of pick-and-place operations represented by STRIPS
operators. It is efficient and, most importantly, robust to the errors in
object detection and pose estimation unavoidable in any real robotic system.
The proposed approach is demonstrated with thorough experiments on a UR5
manipulator.


  We study how the precision of the exoplanet radius determination is affected
by our present knowledge of limb darkening in two cases: when we fix the limb
darkening coefficients and when we adjust them. We also investigate the effects
of spots in one-colour photometry. We study the effect of limb darkening on the
planetary radius determination both via analytical expressions and by numerical
experiments. We also compare some of the existing limb darkening tables. When
stellar spots affect the fit, we replace the limb darkening coefficients,
calculated for the unspotted cases, with effective limb darkening coefficients
to describe the effect of the spots. There are two important cases. (1) When
one fixes the limb darkening values according to some theoretical predictions,
the inconsistencies of the tables do not allow us to reach accuracy in the
planetary radius of better than 1-10% (depending on the impact parameter) if
the host star's surface effective temperature is higher than 5000 K. Below 5000
K the radius ratio determination may contain even 20% error. (2) When one
allows adjustment of the limb darkening coefficients, the a/Rs ratio, the
planet-to-stellar radius ratio, and the impact parameter can be determined with
sufficient accuracy (<1%), if the signal-to-noise ratio is high enough.
However, the presence of stellar spots and faculae can destroy the agreement
between the limb darkening tables and the fitted limb darkening coefficients,
but this does not affect the precision of the planet radius determination. We
also find that it is necessary to fit the contamination factor, too. We
conclude that the present inconsistencies of theoretical stellar limb darkening
tables suggests one should not fix the limb darkening coefficients. When one
allows them to be adjusted, then the planet radius, impact parameter, and the
a/Rs can be obtained with the required precision.


  By combining NRQCD factorization and collinear factorization, we compute a
series of relativistic corrections for $J/\psi$ hadroproduction to all orders
in $v^2$ at large $p_T$ limit. The $v^2$ expansion converges well for all
channels. We find that the ratio of relativistic correction term to the
corresponding leading term is independent of kinematic variables for any
channel, which generalizes the proportional relations found in previous works
to all orders.


  The primary objectives of the ExoplANETS-A project are to: establish new
knowledge on exoplanet atmospheres; establish new insight on influence of the
host star on the planet atmosphere; disseminate knowledge, using online,
web-based platforms. The project, funded under the EU's Horizon-2020 programme,
started in January 2018 and has a duration ~3 years. We present an overview of
the project, the activities concerning the host stars and some early results on
the host stars.


  In this paper, direction-of-arrival estimation using nested array is studied
in the framework of sparse signal representation. With the vectorization
operator, a new real-valued nonnegative sparse signal recovery model which has
a wider virtual array aperture is built. To leverage celebrated compressive
sensing algorithms, the continuous parameter space has to be discretized to a
number of fixed grid points, which inevitably incurs modeling error caused by
off-grid gap. To remedy this issue, a block alternating optimization method is
put forth that jointly estimates the sparse signal and refines the locations of
grid points. Specifically, inspired by the majorization minimization, the
proposed method iteratively minimizes a surrogate function majorizing the given
objective function, where only a single block of variables are updated per
iteration while the remaining ones are kept fixed. The proposed method features
affordable computational complexity, and numerical tests corroborate its
superior performance relative to existing alternatives in both overdetermined
and underdetermined scenarios.


  How many copies of a quantum process are necessary and sufficient to
construct an approximate classical description of it? We extend the result of
Surawy-Stepney, Kahn, Kueng, and Guta (2022) to show that
$\tilde{\mathcal{O}}(d_{\text{in}}^3d_{\text{out}}^3/\varepsilon^2)$ copies are
sufficient to learn any quantum channel $C^{d_{\text{in}}\times d_{\text{in}}}
\rightarrow C^{d_{\text{out}}\times d_{\text{out}}}$ to within $\varepsilon$ in
diamond norm. Moreover, we show that $\Omega(d_{\text{in}}^3
d_{\text{out}}^3/\varepsilon^2)$ copies are necessary for any strategy using
incoherent non-adaptive measurements. This lower bound applies even for
ancilla-assisted strategies.


  Time scales associated with many-body fast neutrino flavor conversions in
core-collapse supernova are explored in the context of an effective two-flavor
model with axial symmetry. We present a preliminary study of time scales
obtained from a linear stability analysis and from the distributions of
Loschmidt echo crossing times (intimately connected to dynamical phase
transitions in non-equilibrium systems) determined by time evolution with the
exact many-body Hamiltonian. Starting from a tensor-product initial state
describing systems of $N$ neutrinos, with $N/2$ electron-type and $N/2$
heavy-type, with uniform angular distributions, the Loschmidt echo crossing
times, $t_{\mathcal{L}_{\times}}$, are found to exhibit two distinct time
scales that are exponentially separated. The second peak structure at longer
times, effectively absent for $N=4$, develops with increasing $N$. When
re-scaled in terms of $\log t_{\mathcal{L}_{\times}}$, the distributions are
found to become increasingly well described by the sum of two stable
distributions. The distribution of Loschmidt echo crossing times differs
somewhat from the results of the (numerical) linear stability analysis, which
exhibits a peak at finite frequency and a second peak consistent with zero
frequency. The exact analysis suggests that the zero-frequency instability
manifests itself as a modest flavor-conversion time scale.


  An efficient reflective elastic metasurface with tunable focusing point is
proposed. The metasurface is based on electric resonators embedded in a
stretchable elastic substrate. The focal length is controlled by mean of the
stretching applied applied to the sample. The results predicted by theory and
numerical simulations are experimentally verified. Our proposal shows that
smart engineering elastic metamaterials are an effective platform for new
functional devices based on metamaterials.


  The processing of signals on graph edges is challenging considering that
Graph Signal Processing techniques are defined only on the graph nodes.
Leveraging the Line Graph to transform a graph edge signal onto the node of its
edge-to-vertex dual, we propose the Line Graph Least Mean Square (LGLMS)
algorithm for online time-varying graph edge signal prediction. By setting up
an $l_2$-norm optimization problem, LGLMS forms an adaptive algorithm as the
graph edge analogy of the classical adaptive LMS algorithm. Additionally, the
LGLMS inherits all the GSP concepts and techniques that can previously be
deployed on the graph nodes, but without the need to redefine them on the graph
edges. Experimenting with transportation graphs and meteorological graphs, with
the signal observations having noisy and missing values, we confirmed that
LGLMS is suitable for the online prediction of time-varying edge signals.


  The dynamics of internal waves in stratified media, such as the ocean or
atmosphere, is highly dependent on the topography of their floor. A closed-form
analytical solution can be derived only in cases when the water distribution
density and the shape of the floor are modeled with specific functions. In a
general case when the characteristics of stratified media and the boundary
conditions are arbitrary, the dynamics of internal waves can be only
approximated with numerical methods. However, numerical solutions do not
describe the wave field qualitatively. At the same time, the need for a
qualitative analysis of the far field of internal waves arises in studies
applying remote sensing methods in space-based radar applications. In this
case, the dynamics of internal waves can be described using asymptotic models.
In this paper, we derive asymptotic solutions to the problem of characterizing
the far field of internal gravity waves propagating in a stratified medium with
a smoothly varying floor.


  To resolve the discrepancies of the superconducting order parameter in
quasi-two-dimensional NbSe_2, comprehensive specific-heat measurements have
been carried out. By analyzing both the zero-field and mixed-state data with
magnetic fields perpendicular to and parallel to the c axis of the crystal and
using the two-gap model, we conclude that (1) more than one energy scale of the
order parameter is required for superconducting NbSe_2 due to the thermodynamic
consistency; (2)delta_L=1.26 meV and delta_S=0.73 meV are obtained; (3)
N_S(0)/N(0)=11%~20%; (4) The observation of the kink in gamma(H) curve suggests
that the two-gap scenario is more favorable than the anisotropic s-wave model
to describe the gap structure of NbSe_2; and (5)delta_S is more isotropic and
has a three-dimensional-like feature and is located either on the Se or the
bonding Nb Fermi sheets.


  We report on a study of neutron-rich nuclei around doubly magic 132Sn in
terms of the shell model employing a realistic effective interaction derived
from the CD-Bonn nucleon-nucleon potential. The short-range repulsion of the
bare potential is renormalized by constructing a low-momentum potential,
V-low-k, that is used directly as input for the calculation of the effective
interaction. We present results for the four nuclei beyond the N=82 shell
closure 134Sn, 134Sb, 136Sb, and 136Te. Comparison shows that our results are
in very good agreement with the experimental data presently available for these
exotic nuclei. We also present our predictions of the hitherto unknown spectrum
of 136Sn.


  We calculate cosmic ray transport with a collisional Boltzmann Transport
Equation, including E-M forces. We apply the Crank-Nicholson Method to solve
this equation. At each time step, the spatial distribution of cosmic rays is
applied to the ZEUS 2D magnetohydrodynamics model, which is then utilized to
calculate the resulting E-M field. Finally, the field is applied to the initial
equation. This sequence is repeated over many time steps until a steady state
is reached. We consider results from t = 0 until steady state for an isotropic
low energy cosmic ray flux, and also for an enhanced cosmic ray flux impinging
on one side of a molecular cloud. This cosmic ray flux is used to determine an
ionization rate of interstellar hydrogen by cosmic rays, zeta. Astrochemical
implications are briefly mentioned.


  Seam-cutting methods have been proven effective in the composition step of
image stitching, especially for images with parallax. However, the
effectiveness of seam-cutting usually depends on that images can be roughly
aligned such that there exists a local region where a plausible seam can be
found. For images with large parallax, current alignment methods often fall
short of expectations. In this paper, we propose a local alignment and
stitching method guided by seam quality evaluation. First, we use existing
image alignment and seam-cutting methods to calculate an initial seam and
evaluate the quality of pixels along the seam. Then, for pixels with low
qualities, we separate their enclosing patches in the aligned images and
locally align them by extracting modified dense correspondences via SIFT flow.
Finally, we composite the aligned patches via seam-cutting and merge them into
the original aligned result to generate the final mosaic. Experiments show that
compared with the state-of-the-art seam-cutting methods, our result is more
plausible and with fewer artifacts. The code will be available at
https://github.com/tlliao/Seam-guided-local-alignment.


  We investigate the propagation of gravitational waves on a black hole
background within the low energy effective field theory of gravity, where
effects from heavy fields are captured by higher dimensional curvature
operators. Depending on the spin of the particles integrated out, the speed of
gravitational waves at low energy can be either superluminal or subluminal as
compared to the causal structure observed by other species. Interestingly
however, gravitational waves are always exactly luminal at the black hole
horizon, implying that the horizon is identically defined for all species. We
further compute the corrections on quasinormal frequencies caused by the higher
dimensional curvature operators and highlight the corrections arising from the
low energy effective field.


  A hypergraph $H$ is properly colored if for every vertex $v\in V(H)$, all the
edges incident to $v$ have distinct colors. In this paper, we show that if
$H_{1}$, \cdots, $H_{s}$ are properly-colored $k$-uniform hypergraphs on $n$
vertices, where $n\geq3k^{2}s$, and $e(H_{i})>{{n}\choose {k}}-{{n-s+1}\choose
{k}}$, then there exists a rainbow matching of size $s$, containing one edge
from each $H_i$. This generalizes some previous results on the Erd\H{o}s
Matching Conjecture.


  Bekenstein has proposed the bound S < pi M_P^2 L^2 on the total entropy S in
a volume L^3. This non-extensive scaling suggests that quantum field theory
breaks down in large volume. To reconcile this breakdown with the success of
local quantum field theory in describing observed particle phenomenology, we
propose a relationship between UV and IR cutoffs such that an effective field
theory should be a good description of Nature. We discuss implications for the
cosmological constant problem. We find a limitation on the accuracy which can
be achieved by conventional effective field theory: for example, the minimal
correction to (g-2) for the electron from the constrained IR and UV cutoffs is
larger than the contribution from the top quark.


  Ellenberg, Venkatesh, and Westerland have established a weak form of the
function field analogue of the Cohen--Lenstra heuristic, on the distribution of
imaginary number fields with $\ell$-parts of their class groups isomorphic to a
fixed group. They first explain how this follows from an asymptotic point count
for certain Hurwitz schemes, and then establish this asymptotic by using the
Grothendieck--Lefschetz trace formula to translate it into a difficult
homological stability problem in algebraic topology, which they nonetheless
solve.
  These are the notes accompanying my talk at the S\'eminaire Bourbaki, which
focus on the remarkable homological stability theorem for Hurwitz spaces.


  Prompting and Multiple Choices Questions (MCQ) have become the preferred
approach to assess the capabilities of Large Language Models (LLMs), due to
their ease of manipulation and evaluation. Such experimental appraisals have
pointed toward the LLMs' apparent ability to perform causal reasoning or to
grasp uncertainty. In this paper, we investigate whether these abilities are
measurable outside of tailored prompting and MCQ by reformulating these issues
as direct text completion - the foundation of LLMs. To achieve this goal, we
define scenarios with multiple possible outcomes and we compare the prediction
made by the LLM through prompting (their Stated Answer) to the probability
distributions they compute over these outcomes during next token prediction
(their Revealed Belief). Our findings suggest that the Revealed Belief of LLMs
significantly differs from their Stated Answer and hint at multiple biases and
misrepresentations that their beliefs may yield in many scenarios and outcomes.
As text completion is at the core of LLMs, these results suggest that common
evaluation methods may only provide a partial picture and that more research is
needed to assess the extent and nature of their capabilities.


  We present a theory for the rate of energy exchange between electrons and
ions -- also known as the electron-ion coupling factor -- in physical systems
ranging from hot solid metals to plasmas, including liquid metals and warm
dense matter. The paper provides the theoretical foundations of a recent work
[J. Simoni and J. Daligault, Phys. Rev. Lett. {\bf 122}, 205001 (2019)], where
first-principles quantum molecular dynamics calculations based on this theory
were presented for representative materials and conditions. We first derive a
general expression for the electron-ion coupling factor that includes
self-consistently the quantum mechanical and statistical nature of electrons,
the thermal and disorder effects, and the correlations between particles. We
show that our theory reduces to well-known models in limiting cases. In
particular, we show that it simplifies to the standard electron-phonon coupling
formula in the limit of hot solids with lattice and electronic temperatures
much greater than the Debye temperature, and that it extends the
electron-phonon coupling formula beyond the harmonic phonon approximation. For
plasmas, we show that the theory readily reduces to well-know Spitzer formula
in the hot plasma limit, to the Fermi golden rule formula in the limit of weak
electron-ion interactions, and to other models proposed to go beyond the latter
approximation. We explain that the electron-ion coupling is particularly well
adapted to averaged atom models, which offer an effective way to include
non-ideal interaction effects to the standard models and at a much reduced
computational cost in comparison to first-principles quantum molecular dynamics
simulations.


  Ultrafast optical control of the structural and electronic properties of
various quantum materials has recently sparked great interest. In particular,
photoinduced quantum phase transition between distinct topological phases has
been considered as a promising route to realize ultrafast topological quantum
computers. Here we use first-principles and effective Hamiltonian methods to
show that in ZrTe$_5$, a layered topological material, lattice distortions
corresponding to all three types of zone-center infrared optical phonon modes
can drive the system from the strong or weak topological insulating phase to a
Weyl semimetal by breaking the global inversion symmetry. Thus achieved Weyl
phases are robust, highly tunable and one of the cleanest ones due to the
proximity of the Weyl points to the Fermi level and a lack of other carriers.
We further show that the amount of infrared-mode pumping necessary to induce
such Weyl phases can be reduced if used in conjunction with an A$_g$ Raman-mode
pumping that first drives the system to the Dirac semimetal state. We also find
that Berry curvature dipole moment (BCDM), induced by the dynamical inversion
symmetry breaking, gives rise to various nonlinear effects that oscillate with
the amplitude of the phonon modes. These nonlinear effects present a novel
switch for controlling the Weyltronics enabled quantum system.


  By a $B$-regular variety, we mean a smooth projective variety over $C$
admitting an algebraic action of the upper triangular Borel subgroup $B \subset
SL_2(C)$ such that the unipotent radical in $B$ has a unique fixed point. A
result of M. Brion and the first author describes the equivariant cohomology
algebra (over $C$) of a $B$-regular variety $X$ as the coordinate ring of a
remarkable affine curve in $X \times P^1$. The main result of this paper uses
this fact to classify the $B$-invariant subvarieties $Y$ of a $B$-regular
variety $X$ for which the restriction map $i_Y:H^*(X) \to H^*(Y)$ is
surjective.


  This dissertation is concerned with the study of program equivalence and
algebraic effects as they arise in the theory of programming languages.
Algebraic effects represent impure behaviour in a functional programming
language, such as input and output, exceptions, nondeterminism etc. all treated
in a generic way. Program equivalence aims to identify which programs can be
considered equal in some sense. This question has been studied for a long time
but has only recently been extended to languages with algebraic effects, which
are a newer development. Much work remains to be done in order to understand
program equivalence in the presence of algebraic effects. In particular, there
is no characterisation of contextual equivalence using a logic. We define a
logic whose formulas express properties of higher-order programs with algebraic
effects. We then investigate three notions of program equivalence for algebraic
effects: logical equivalence induced by the aforementioned logic, applicative
bisimilarity and contextual equivalence. For the programming language used in
this dissertation, we prove that they all coincide. Therefore, the main novel
contribution of the dissertation is defining the first logic for algebraic
effects whose induced program equivalence coincides with contextual
equivalence.


  Designing a synthetic crown is a time-consuming, inconsistent, and
labor-intensive process. In this work, we present a fully automatic method that
not only learns human design dental crowns, but also improves the consistency,
functionality, and esthetic of the crowns. Following success in point cloud
completion using the transformer-based network, we tackle the problem of the
crown generation as a point-cloud completion around a prepared tooth. To this
end, we use a geometry-aware transformer to generate dental crowns. Our main
contribution is to add a margin line information to the network, as the
accuracy of generating a precise margin line directly,determines whether the
designed crown and prepared tooth are closely matched to
allowappropriateadhesion.Using our ground truth crown, we can extract the
margin line as a spline and sample the spline into 1000 points. We feed the
obtained margin line along with two neighbor teeth of the prepared tooth and
three closest teeth in the opposing jaw. We also add the margin line points to
our ground truth crown to increase the resolution at the margin line. Our
experimental results show an improvement in the quality of the designed crown
when considering the actual context composed of the prepared tooth along with
the margin line compared with a crown generated in an empty space as was done
by other studies in the literature.


  We present a novel description of nuclear many-body systems, both for nuclear
matter and finite nuclei, emphasizing the connection with the condensate
structure of the QCD ground state and spontaneous chiral symmetry breaking.
Lorentz scalar and vector mean-fields are introduced in accordance with QCD sum
rules. Nuclear binding arises from pionic fluctuations, using in-medium chiral
perturbation theory up to three-loop order. Ground state properties of $^{16}$O
and $^{40}$Ca are calculated. The built-in QCD constraints reduce the number of
input parameters significantly in comparison with purely phenomenological
relativistic mean-field approaches.


  We apply the Nakajima-Zwanzig approach to open quantum systems to study
steady-state transport across generic multi-level junctions coupled to bosonic
or fermionic reservoirs. The method allows for a unified diagrammatic
formulation in Liouville space, with diagrams being classified according to an
expansion in the coupling strength between the reservoirs and the junction.
Analytical, approximate expressions are provided up to fourth order for the
steady-state boson transport that generalize to multi-level systems the known
results for the low-temperature thermal conductance in the spin-boson model.
The formalism is applied to the problem of heat transport in a qubit-resonator
junction modeled by the quantum Rabi model. Nontrivial transport features
emerge as a result of the interplay between the qubit-oscillator detuning and
coupling strength. For quasi-degenerate spectra, nonvanishing steady-state
coherences cause a suppression of the thermal conductance.


  We analyze anew experiments on the NMR in cuprates and find an important
information on their phase separation and its stripe character hidden in the
dependence of $1/^{63}T_{1}$ on degree of doping. In a broad class of materials
$1/^{63}T_{1}$ is the sum of two terms: the temperature independent one
attributed to ``incommensurate'' stripes that occur at external doping, and an
``universal'' temperature dependent term ascribed to moving metallic and AF
sub-phases. We argue that the frustrated first order phase transition in a
broad temperature interval bears a dynamical character.


  POINT-AGAPE is an Anglo-French collaboration which is employing the Isaac
Newton Telescope (INT) to conduct a pixel-lensing survey towards M31. In this
paper we investigate what we can learn from pixel-lensing observables about the
MACHO mass and fractional contribution in M31 and the Galaxy for the case of
spherically-symmetric near-isothermal haloes. We employ detailed pixel-lensing
simulations which include many of the factors which affect the observables. For
a maximum MACHO halo we predict an event rate in V of up to 100 per season for
M31 and 40 per season for the Galaxy. However, the Einstein radius crossing
time is generally not measurable and the observed full-width half-maximum
duration provides only a weak tracer of lens mass. Nonetheless, we find that
the near-far asymmetry in the spatial distribution of M31 MACHOs provides
significant information on their mass and density contribution. We present a
likelihood estimator for measuring the fractional contribution and mass of both
M31 and Galaxy MACHOs which permits an unbiased determination to be made of
MACHO parameters, even from data-sets strongly contaminated by variable stars.
If M31 does not have a significant population of MACHOs in the mass range
0.001-1 Solar masses strong limits will result from the first season of INT
observations. Simulations based on currently favoured density and mass values
indicate that, after three seasons, the M31 MACHO parameters should be
constrained to within a factor four uncertainty in halo fraction and an order
of magnitude uncertainty in mass (90% confidence). Interesting constraints on
Galaxy MACHOs may also be possible. For a campaign lasting ten years,
comparable to the lifetime of current LMC surveys, reliable estimates of MACHO
parameters in both galaxies should be possible. (Abridged)


  We study RR flux backgrounds in two dimensional type 0 string theories. In
particular, we study the relation between the 0A matrix model and the extremal
black hole in two dimensions. Using T-duality we find a dual flux background in
type 0B theory and propose its matrix model description. When the Fermi level
is set to zero this system remains weakly coupled and exhibits a larger
symmetry related to the structure of flux vacua. Finally, we construct a two
dimensional type IIB background as an orbifold of the 0B background.


  We study the topological phase of bright soliton with arbitrary velocity
under the self-steepening effect. Such topological phase can be described by
the topological vector potential and effective magnetic field. We find that the
point-like magnetic fields corresponds to the density peak of such bright
solitons, where each elementary magnetic flux is {\pi}. Remarkably, we show
that two bright solitons can generate an additional topological field due to
the phase jump between them. Our research provided the possibility to use
bright solitons to explore topological properties.


  We perform Brownian dynamics simulations of active stiff polymers undergoing
run-reverse dynamics, and so mimic bacterial swimming, in porous media. In
accord with recent experiments of \emph{Escherichia coli}, the polymer dynamics
are characterized by trapping phases interrupted by directed hopping motion
through the pores. We find that the effective translational diffusivities of
run-reverse agents can be enhanced up to two orders in magnitude, compared to
their non-reversing counterparts, and exhibit a non-monotonic behavior as a
function of the reversal rate, which we rationalize using a coarse-grained
model. Furthermore, we discover a geometric criterion for the optimal
spreading, which emerges when their run lengths are comparable to the longest
straight path available in the porous medium. More significantly, our criterion
unifies results for porous media with disparate pore sizes and shapes and thus
provides a fundamental principle for optimal transport of microorganisms and
cargo-carriers in densely-packed biological and environmental settings.


  We establish a cutting lemma for definable families of sets in distal
structures, as well as the optimality of the distal cell decomposition for
definable families of sets on the plane in $o$-minimal expansions of fields.
Using it, we generalize the results in [J. Fox, J. Pach, A. Sheffer, A. Suk,
and J. Zahl. "A semi-algebraic version of Zarankiewicz's problem"] on the
semialgebraic planar Zarankiewicz problem to arbitrary $o$-minimal structures,
in particular obtaining an $o$-minimal generalization of the
Szemer\'edi-Trotter theorem.


  Quantum mechanical uncertainty relations for position and momentum are
expressed in the form of inequalities involving the Renyi entropies. The proof
of these inequalities requires the use of the exact expression for the
(p,q)-norm of the Fourier transformation derived by Babenko and Beckner.
Analogous uncertainty relations are derived for angle and angular momentum and
also for a pair of complementary observables in N-level systems. All these
uncertainty relations become more attractive when expressed in terms of the
symmetrized Renyi entropies.


  We study the implications of endogenous pricing for learning and welfare in
the classic herding model . When prices are determined exogenously, it is known
that learning occurs if and only if signals are unbounded. By contrast, we show
that learning can occur when signals are bounded as long as non-conformism
among consumers is scarce. More formally, learning happens if and only if
signals exhibit the vanishing likelihood property introduced bellow. We discuss
the implications of our results for potential market failure in the context of
Schumpeterian growth with uncertainty over the value of innovations.


  We present an optimal transport approach for mesh adaptivity and shock
capturing of compressible flows. Shock capturing is based on a viscosity
regularization of the governing equations by introducing an artificial
viscosity field as solution of the Helmholtz equation. Mesh adaptation is based
on the optimal transport theory by formulating a mesh mapping as solution of
Monge-Ampere equation. The marriage of optimal transport and viscosity
regularization for compressible flows leads to a coupled system of the
compressible Euler/Navier-Stokes equations, the Helmholtz equation, and the
Monge-Ampere equation. We propose an iterative procedure to solve the coupled
system in a sequential fashion using homotopy continuation to minimize the
amount of artificial viscosity while enforcing positivity-preserving and
smoothness constraints on the numerical solution. We explore various mesh
monitor functions for computing r-adaptive meshes in order to reduce the amount
of artificial dissipation and improve the accuracy of the numerical solution.
The hybridizable discontinuous Galerkin method is used for the spatial
discretization of the governing equations to obtain high-order accurate
solutions. Extensive numerical results are presented to demonstrate the optimal
transport approach on transonic, supersonic, hypersonic flows in two
dimensions. The approach is found to yield accurate, sharp yet smooth solutions
within a few mesh adaptation iterations.


  For signals belonging to balls in smoothness classes and noise with enough
moments, the asymptotic behavior of the minimax quadratic risk among
soft-threshold estimates is investigated. In turn, these results, combined with
a median filtering method, lead to asymptotics for denoising heavy tails via
wavelet thresholding. Some further comparisons of wavelet thresholding and of
kernel estimators are also briefly discussed.


  The baryon to photon ratio in the present Universe is very accurately
measured to be $(6.065 \pm 0.090) \times 10^{-10}$. We study the possible
origin of this baryon asymmetry in the neutrino sector through the generic
mechanism of baryogenesis through leptogenesis. We consider both type I and
type II seesaw origin of neutrino masses within the framework of left right
symmetric models (LRSM). Using the latest best fit global neutrino oscillation
data of mass squared differences, mixing angles and Dirac CP phase, we compute
the predictions for baryon to photon ratio keeping the Majorana CP phases as
free parameters for two different choices of lightest neutrino mass eigenvalue
for both normal and inverted hierarchical patterns of neutrino masses. We do
our calculation with and without lepton flavor effects being taken into
account. We choose different diagonal Dirac neutrino mass matrix for different
flavor effects in such a way that the lightest right handed neutrino mass is in
the appropriate range. We also study the predictions for baryon asymmetry when
the neutrino masses arise from a combination of both type I and type II seesaw
(with dominating type I term) and discriminate between several combinations of
Dirac and Majorana CP phases by demanding successful predictions for baryon
asymmetry.


  Our aims are twofold: To determine the physical parameters of PMS members in
young open clusters (YOCs), and to check and compare the performances of
different model isochrones.
  We compare UBVRI photometric observations of YOCs to theoretical isochrones
in the photometric diagrams. The comparison simultaneously provides membership
assignments for MS and PMS stars, and estimates for the masses, ages, and
spatial distribution of the candidate members.
  The relations found between the different cluster parameters show that the
procedure applied to assign cluster membership, and to measure physical
parameters for the selected members, is well founded.


  A survey is given of the various aspects of W-boson physics at the next
generation of linear colliders. In particular, it is indicated how the W boson
can help us improve our understanding of the mechanism of mass generation and
the structure of the non-abelian gauge-boson interactions. Also the topics of
radiative corrections and gauge invariance are briefly addressed.


  We propose a new formalism of quantum subsystems which allows to unify the
existing and new methods of reduced description of quantum systems. The main
mathematical ingredients are completely positive maps and correlation
functions. In this formalism generalized quantum systems can be composed and
there is a notion of generalized entanglement. Models of fermionic and bosonic
systems and also quantum systems described by the SU(2) symmetry are studied.


  Magnetic resonance imaging (MRI) is an important medical imaging modality,
but its acquisition speed is quite slow due to the physiological limitations.
Recently, super-resolution methods have shown excellent performance in
accelerating MRI. In some circumstances, it is difficult to obtain
high-resolution images even with prolonged scan time. Therefore, we proposed a
novel super-resolution method that uses a generative adversarial network (GAN)
with cyclic loss and attention mechanism to generate high-resolution MR images
from low-resolution MR images by a factor of 2. We implemented our model on
pelvic images from healthy subjects as training and validation data, while
those data from patients were used for testing. The MR dataset was obtained
using different imaging sequences, including T2, T2W SPAIR, and mDIXON-W. Four
methods, i.e., BICUBIC, SRCNN, SRGAN, and EDSR were used for comparison.
Structural similarity, peak signal to noise ratio, root mean square error, and
variance inflation factor were used as calculation indicators to evaluate the
performances of the proposed method. Various experimental results showed that
our method can better restore the details of the high-resolution MR image as
compared to the other methods. In addition, the reconstructed high-resolution
MR image can provide better lesion textures in the tumor patients, which is
promising to be used in clinical diagnosis.


  We consider the stochastic heat equation $$\frac{\partial Y_t(x)}{\partial t}
= \frac{1}{2} \Delta_x Y_t(x) + Y_{t-}(x)^{\beta} \dot{L}^{\alpha}$$ with $t
\ge 0$, $x \in \mathbb{R}$ and $L^{\alpha}$ being an $\alpha$-stable white
noise without negative jumps. Under appropriate non-negative initial
conditions, when $\alpha \in (1,2)$ and $\beta \in (\frac{1}{\alpha}, 1)$ we
prove that weak uniqueness holds for the above using the approximating duality
approach developed by Mytnik (Ann. Probab. (1998) 26 968-984).


  Edge intelligence is an emerging network architecture that integrates
sensing, communication, computing components, and supports various machine
learning applications, where a fundamental communication question is: how to
allocate the limited wireless resources (such as time, energy) to the
simultaneous model training of heterogeneous learning tasks? Existing methods
ignore two important facts: 1) different models have heterogeneous demands on
training data; 2) there is a mismatch between the simulated environment and the
real-world environment. As a result, they could lead to low learning
performance in practice. This paper proposes the learning centric wireless
resource allocation (LCWRA) scheme that maximizes the worst learning
performance of multiple tasks. Analysis shows that the optimal transmission
time has an inverse power relationship with respect to the generalization
error. Finally, both simulation and experimental results are provided to verify
the performance of the proposed LCWRA scheme and its robustness in real
implementation.


  Moir\'e materials such as magic angle twisted bilayer graphene (MATBG)
exhibit remarkable phenomenology, but present significant challenges for
certain experimental methods, particularly scanning probes such as scanning
tunneling microscopy (STM). Typical STM studies that can image tens of
thousands of atomic unit cells can image roughly ten moir\'e cells, making data
analysis statistically fraught. Here, we propose a method to mitigate this
problem by aggregating STM conductance data from several bias voltages, and
then using the unsupervised machine learning method of gaussian mixture model
clustering to draw maximal insight from the resulting dataset. We apply this
method, using as input coarse-grained bond variables respecting the point group
symmetry, to investigate nematic ordering tendencies in MATBG for both charge
neutral and hole-doped samples. For the charge-neutral dataset, the clustering
reveals the surprising coexistence of multiple types of nematicity that are
unrelated by symmetry, and therefore generically nondegenerate. By contrast,
the clustering in the hole doped data is consistent with long range order of a
single type. Beyond its value in analyzing nematicity in MATBG, our method has
the potential to enhance understanding of symmetry breaking and its spatial
variation in a variety of moir\'e materials.


  We revisit the singlet-doublet dark matter model with a special emphasis on
the effect of CP violation on the dark matter phenomenology. The CP violation
in the dark sector induces a pseudoscalar interaction of a fermionic dark
matter candidate with the SM Higgs boson. The pseudoscalar interaction helps
the dark matter candidate evade the strong constraints from the dark matter
direct detection experiments. We show that the model can explain the measured
value of the dark matter density even if dark matter direct detection
experiments do not observe any signal. We also show that the electron electric
dipole moment is an important complement to the direct detection for testing
this model. Its value is smaller than the current upper bound but within the
reach of future experiments.


  We establish sharp remainder terms of the $L^{2}$-Caffarelli-Kohn-Niren\-berg
inequalities on homogeneous groups, yielding the inequalities with best
constants. Our methods also give new sharp Caffarelli-Kohn-Nirenberg type
inequalities in $\mathbb{R}^{n}$ with arbitrary quasi-norms. We also present
explicit examples to illustrate our results for different weights and in
abelian cases.


  Commercially successful magnetic tunnel junction can harness the unmatched
capabilities of molecular device elements by solving decade-old fabrication
issues. Utilization of magnetic tunnel junction as a testbed for molecules also
enables unprecedented magnetic studies of molecular spintronics devices. This
paper utilizes magnetic force microscopy (MFM) to vividly show that
organometallic molecules when bridged between two ferromagnetic electrodes
along the magnetic tunnel junction edges, transformed the magnetic electrodes
itself. Molecules impacted several hundred-micron areas of ferromagnetic
electrodes at room temperature. Complementary, magnetic resonance and
magnetometer studies supported the dramatic MFM results. Molecule induced
changes in the magnetic electrodes impacted the transport of the magnetic
tunnel junction and stabilized as much as six orders smaller current at room
temperature. Magnetic tunnel junction based molecular devices can be a gateway
to a vast range of commercially viable futuristic logic and memory devices that
are controlled by the molecular quantum states near room temperature.


  We investigate some basic questions about the interaction of regular and
rational relations on words. The primary motivation comes from the study of
logics for querying graph topology, which have recently found numerous
applications. Such logics use conditions on paths expressed by regular
languages and relations, but they often need to be extended by rational
relations such as subword or subsequence. Evaluating formulae in such extended
graph logics boils down to checking nonemptiness of the intersection of
rational relations with regular or recognizable relations (or, more generally,
to the generalized intersection problem, asking whether some projections of a
regular relation have a nonempty intersection with a given rational relation).
  We prove that for several basic and commonly used rational relations, the
intersection problem with regular relations is either undecidable (e.g., for
subword or suffix, and some generalizations), or decidable with
non-primitive-recursive complexity (e.g., for subsequence and its
generalizations). These results are used to rule out many classes of graph
logics that freely combine regular and rational relations, as well as to
provide the simplest problem related to verifying lossy channel systems that
has non-primitive-recursive complexity. We then prove a dichotomy result for
logics combining regular conditions on individual paths and rational relations
on paths, by showing that the syntactic form of formulae classifies them into
either efficiently checkable or undecidable cases. We also give examples of
rational relations for which such logics are decidable even without syntactic
restrictions.


  This paper proposes embedded Gaussian Process Barrier States (GP-BaS), a
methodology to safely control unmodeled dynamics of nonlinear system using
Bayesian learning. Gaussian Processes (GPs) are used to model the dynamics of
the safety-critical system, which is subsequently used in the GP-BaS model. We
derive the barrier state dynamics utilizing the GP posterior, which is used to
construct a safety embedded Gaussian process dynamical model (GPDM). We show
that the safety-critical system can be controlled to remain inside the safe
region as long as we can design a controller that renders the BaS-GPDM's
trajectories bounded (or asymptotically stable). The proposed approach
overcomes various limitations in early attempts at combining GPs with barrier
functions due to the abstention of restrictive assumptions such as linearity of
the system with respect to control, relative degree of the constraints and
number or nature of constraints. This work is implemented on various examples
for trajectory optimization and control including optimal stabilization of
unstable linear system and safe trajectory optimization of a Dubins vehicle
navigating through an obstacle course and on a quadrotor in an obstacle
avoidance task using GP differentiable dynamic programming (GP-DDP). The
proposed framework is capable of maintaining safe optimization and control of
unmodeled dynamics and is purely data driven.


  Continuous odour measurements both of emissions as well as ambient
concentrations are seldom realised, mainly because of their high costs. They
are therefore often substituted by concentration measurements of odorous
substances. Then a conversion of the chemical concentrations C (mg m-3) into
odour concentrations COD (ouE m-3) and odour intensities OI is necessary. Four
methods to convert the concentrations of single substances to the odour
concentrations and odour intensities of an odorous mixture are investigated:
(1) direct use of measured concentrations, (2) the sum of the odour activity
value SOAV, (3) the sum of the odour intensities SOI, and (4) the equivalent
odour concentration EOC, as a new method. The methods are evaluated with
olfactometric measurements of seven substances as well as their mixtures. The
results indicate that the SOI and EOC conversion methods deliver reliable
values. These methods use not only the odour threshold concentration but also
the slope of the Weber-Fechner law to include the sensitivity of the odour
perception of the individual substances. They fulfil the criteria of an
objective conversion without the need of a further calibration by additional
olfactometric measurements.


  In this paper we construct small amplitude periodic internal waves traveling
at the boundary region between two rotational and homogeneous fluids with
different densities. Within a period, the waves we obtain have the property
that the gradient of the stream function associated to the fluid beneath the
interface vanishes, on the wave surface, at exactly two points. Furthermore,
there exists a critical layer which is bounded from above by the wave profile.
Besides, we prove, without excluding the presence of stagnation points, that if
the vorticity function associated to each fluid in part is real-analytic,
bounded, and non-increasing, then capillary-gravity steady internal waves are a
priori real-analytic. Our new method provides the real-analyticity of capillary
and capillary-gravity waves with stagnation points traveling over a homogeneous
rotational fluid under the same restrictions on the vorticity function.


  The quantization of vector bundles is defined. Examples are constructed for
the well controlled case of equivariant vector bundles over compact coadjoint
orbits. (Coadjoint orbits are symplectic spaces with a transitive, semisimple
symmetry group.) In preparation for the main result, the quantization of
coadjoint orbits is discussed in detail.
  This subject should not be confused with the quantization of the total space
of a vector bundle such as the cotangent bundle.