  Most natural languages have a predominant or fixed word order. For example in
English the word order is usually Subject-Verb-Object. This work attempts to
explain this phenomenon as well as other typological findings regarding word
order from a functional perspective. In particular, we examine whether fixed
word order provides a functional advantage, explaining why these languages are
prevalent. To this end, we consider an evolutionary model of language and
demonstrate, both theoretically and using genetic algorithms, that a language
with a fixed word order is optimal. We also show that adding information to the
sentence, such as case markers and noun-verb distinction, reduces the need for
fixed word order, in accordance with the typological findings.


  Heavy quarks are a powerful probe for investigating the properties of the
Quark-Gluon Plasma created in heavy-ion collisions, since they are produced in
initial hard scattering processes and experience all the stages of the medium
evolution. ALICE has measured the production of $\mathrm{D}^0$, $\mathrm{D}^+$,
$\mathrm{D}^{*+}$, and $\mathrm{D}_{\mathrm{s}}^+$ mesons at central rapidity
in their hadronic decay channels in various collision systems and energies. We
present recent results for D-meson production measured by the ALICE
Collaboration in pp collisions at $\sqrt{s}=7$ and 2.76 TeV, Pb-Pb collisions
at $\sqrt{s_\mathrm{NN}}=2.76$ TeV and p-Pb collisions at
$\sqrt{s_\mathrm{NN}}=5.02$ TeV.


  Tiny flying insects, such as Drosophila melanogaster, fly by flapping their
wings at frequencies faster than their brains are able to process. To do so,
they rely on self-oscillation: dynamic instability, leading to emergent
oscillation, arising from muscle stretch-activation. Many questions concerning
this vital natural instability remain open. Does flight motor self-oscillation
necessarily lead to resonance - a state optimal in efficiency and/or
performance? If so, what state? And is self-oscillation even guaranteed in a
motor driven by stretch-activated muscle, or are there limiting conditions? In
this work, we use data-driven models of wingbeat and muscle behaviour to answer
these questions. Developing and leveraging novel analysis techniques, including
symbolic computation, we establish a fundamental condition for motor
self-oscillation common to a wide range of motor models. Remarkably, D.
melanogaster flight apparently defies this condition: a paradox of motor
operation. We explore potential resolutions to this paradox, and, within its
confines, establish that the D. melanogaster flight motor is likely not
resonant with respect to exoskeletal elasticity: instead, the muscular
elasticity plays a dominant role. Contrary to common supposition, the stiffness
of stretch-activated muscle is an obstacle to, rather than an enabler of, the
operation of the D. melanogaster flight motor.


  Considering a bidirectionally pumped ring microresonator, we provide a
concise derivation of the model equations allowing us to eliminate the
repetition rate terms and reduce the nonlinear interaction between the
counter-propagating waves to the power-dependent shifts of the resonance
frequencies. We present the simulation results of the soliton control by
swiping the frequency of the counter-propagating wave in the forward and
backward directions and with the soliton-blockade effect either present or not.
We highlight the non-reciprocity of the forward and backward scans.
Furthermore, we report the soliton crystals and breathers existing in the
vicinity of the blockade interval.


  We propose a twistor construction of surfaces in Lie sphere geometry based on
the linear system which copies equations of Wilczynski's projective frame. In
the particular case of Lie-applicable surfaces this linear system describes
joint eigenfunctions of a pair of commuting Schr\"odinger operators with
magnetic fields.


  We study the possibility of pre-merger localization of eccentric compact
binary coalescences by second-generation gravitational-wave detector networks.
Gravitational waves from eccentric binaries can be regarded as a sequence of
pulses, which are composed of various higher harmonic modes than ones with
twice the orbital frequency. The higher harmonic modes from a very early
inspiral phase will not only contribute to the signal-to-noise ratio, but also
allow us to localize the gravitational-wave source before the merger sets in.
This is due to the fact that high-frequency gravitational waves are essential
for the source localization via triangulation by ground-based detector
networks. We found that the single-detector signal-to-noise ratio exceeds 5 at
10 min before the merger for a 1.4--1.4 $M_\odot$ eccentric binary neutron
stars at 100 Mpc in optimal cases, and it can be localized up to 10 deg$^2$ at
half a minute before the merger by a four-detector network. We will even be
able to achieve $\sim$ 10 deg$^2$ at 10 min before the merger for a face-on
eccentric compact binary by a five-detector network.


  We examine the theta-expansion of the eleven-dimensional supervielbein. We
outline a systematic procedure which can be iterated to any order. We give
explicit expressions for the vielbein and three-form potential components up to
order ${\cal O}(\th^5)$. Furthermore we show that at each order in the number
of supergravity fields, in a perturbative expansion around flat space, it is
possible to obtain exact expressions to all orders in theta. We give the
explicit expression at linear order in the number of fields and we show how the
procedure can be iterated to any desired order. As a byproduct we obtain the
complete linear coupling of the supermembrane to the background supergravity
fields, covariantly in component form. We discuss the implications of our
results for M(atrix) theory.


  The Lorentz term raises the linear matter power on small scale which leads to
interesting signatures in the 21 cm signal. Numerical simulations of the
resuting nonlinear density field, the distribution of ionized hydrogen and the
21 cm signal at different values of redshift are presented for magnetic fields
with field strength B=5 nG, and spectral indices $n_B=-2.9, -2.2$ and -1.5
together with the adiabatic mode for the best fit data of Planck13+WP.
Comparing the averaged global 21 cm signal with the projected SKA1-LOW
sensitivities of the Square Kilometre Array (SKA) it might be possible to
constrain the magnetic field parameters.


  The main results of this paper are (I) a simulation algorithm which, under
quite general constraints, transforms algorithms running on the Congested
Clique into algorithms running in the MapReduce model, and (II) a distributed
$O(\Delta)$-coloring algorithm running on the Congested Clique which has an
expected running time of (i) $O(1)$ rounds, if $\Delta \geq \Theta(\log^4 n)$;
and (ii) $O(\log \log n)$ rounds otherwise. Applying the simulation theorem to
the Congested-Clique $O(\Delta)$-coloring algorithm yields an $O(1)$-round
$O(\Delta)$-coloring algorithm in the MapReduce model.
  Our simulation algorithm illustrates a natural correspondence between
per-node bandwidth in the Congested Clique model and memory per machine in the
MapReduce model. In the Congested Clique (and more generally, any network in
the $\mathcal{CONGEST}$ model), the major impediment to constructing fast
algorithms is the $O(\log n)$ restriction on message sizes. Similarly, in the
MapReduce model, the combined restrictions on memory per machine and total
system memory have a dominant effect on algorithm design. In showing a fairly
general simulation algorithm, we highlight the similarities and differences
between these models.


  The aim of this paper is to determine all irreducible spherical functions of
the pair (G,K)=(SU(n+1),U(n)), where the highest weight of their K-types are of
the form (m+l,...,m+l,m,...,m). Instead of looking at a spherical function \Phi
of type \pi we look at a matrix-valued function H defined on a section of the
K-orbits in an affine subvariety of P_n(C). The function H diagonalizes, hence
it can be identified with a column vector-valued function. The irreducible
spherical functions of type \pi turn out to be parameterized by S={(w,r)\in Z x
Z : 0\leq w, 0 \leq r \leq l, 0\leq m+w+r}. A key result to characterize the
associated function H_{w,r} is the existence of a matrix-valued polynomial
function \Psi of degree l such that F_{w,r}(t)=\Psi(t)^{-1}H_{w,r}(t) becomes
an eigenfunction of a matrix hypergeometric operator with eigenvalue
\lambda(w,r), explicitly given. In the last section we assume that m\ge 0 and
define the matrix polynomial P_w as the (l+1) x (l+1) matrix whose r-row is the
polynomial F_{w,r}. This leads to interesting families of matrix-valued
orthogonal Jacobi polynomials P_w^{\alpha,\beta} for \alpha,\beta>-1.


  Magnetic, radiation pressure, and thermal driving are the three mechanisms
capable of launching accretion disk winds. In X-ray binaries, radiation
pressure is often not significant, as in many systems the luminosity is too low
for driving due to continuum transitions yet too high for driving due to line
transitions. This leaves thermal and magnetic driving as the contender
launching mechanisms in these systems. Using Athena++, we perform axisymmetric
ideal MHD simulations that include radiative heating and cooling processes
appropriate for Compton heated winds to show that the inclusion of magnetic
fields into a thermally driven wind has the opposite effect of what one might
expect: rather than provide a velocity boost, the thermal wind is suppressed in
low plasma beta regions where the field lines are strong enough to reshape the
direction of the flow. Our analysis reveals that magneto-centrifugal launching
is present but weak, while the reduction in wind velocity is not due to the
change in gravitational potential through the magnetically imposed streamline
geometry, but rather due to the increased flow tube area just above the surface
of the disk, which is less conducive to acceleration. Our results suggest that
for magnetothermal wind models to be successful at producing fast dense
outflows in low mass X-ray binaries, the winds must be magnetically launched
well within the Compton radius.


  Radio relics are patches of diffuse synchrotron radio emission that trace
shock waves. Relics are thought to form when intra-cluster medium electrons are
accelerated by cluster merger induced shock waves through the diffusive shock
acceleration mechanism. In this paper, we present observations spanning 150 MHz
to 30 GHz of the `Sausage' and `Toothbrush' relics from the Giant Metrewave and
Westerbork telescopes, the Karl G. Jansky Very Large Array, the Effelsberg
telescope, the Arcminute Microkelvin Imager and Combined Array for Research in
Millimeter-wave Astronomy. We detect both relics at 30 GHz, where the previous
highest frequency detection was at 16 GHz. The integrated radio spectra of both
sources clearly steepen above 2 GHz, at the >6$\sigma$ significance level,
supports the spectral steepening previously found in the `Sausage' and the
Abell 2256 relic. Our results challenge the widely adopted simple formation
mechanism of radio relics and suggest more complicated models have to be
developed that, for example, involve re-acceleration of aged seed electrons.


  In order to extend our approach based on SU$*$(4), we were led to (real)
projective and (line) Complex geometry. So here we start from quadratic
Complexe which yield naturally the 'light cone'
$x_{1}^{2}+x_{2}^{2}+x_{3}^{2}-x_{0}^{2}=0$ when being related to (homogeneous)
point coordinates $x_{\alpha}^{2}$ and infinitesimal dynamics by tetrahedral
Complexe (or line elements). This introduces naturally projective
transformations by preserving anharmonic ratios. Referring to old work of
Pl{\"u}cker relating quadratic Complexe to optics, we discuss (linear)
symplectic symmetry and line coordinates, the main purpose and thread within
this paper, however, is the identification and discussion of special relativity
as direct invariance properties of line/Complex coordinates as well as their
relation to 'quantum field theory' by complexification of point coordinates or
Complexe. This can be established by the Lie mapping which relates
lines/Complexe to sphere geometry so that SU(2), SU(2)$\times$U(1),
SU(2)$\times$SU(2) and the Dirac spinor description emerge without additional
assumptions. We give a short outlook in that quadratic Complexe are related to
dynamics e.g.~power expressions in terms of six-vector products of Complexe,
and action principles may be applied. (Quadratic) products like
$F^{\mu\nu}F_{\mu\nu}$ or $F^{a\,\mu\nu}F^{a}_{\mu\nu}$, $1\leq a\leq 3$ are
natural quadratic Complex expressions ('invariants') which may be extended by
line constraints $\lambda k\cdot\epsilon=0$ with respect to an 'action
principle' so that we identify 'quantum field theory' with projective or
line/Complex geometry having applied the Lie mapping.


  We extend the formalism of embedded spin networks and spin foams to include
topological data that encode the underlying three-manifold or four-manifold as
a branched cover. These data are expressed as monodromies, in a way similar to
the encoding of the gravitational field via holonomies. We then describe
convolution algebras of spin networks and spin foams, based on the different
ways in which the same topology can be realized as a branched covering via
covering moves, and on possible composition operations on spin foams. We
illustrate the case of the groupoid algebra of the equivalence relation
determined by covering moves and a 2-semigroupoid algebra arising from a
2-category of spin foams with composition operations corresponding to a fibered
product of the branched coverings and the gluing of cobordisms. The spin foam
amplitudes then give rise to dynamical flows on these algebras, and the
existence of low temperature equilibrium states of Gibbs form is related to
questions on the existence of topological invariants of embedded graphs and
embedded two-complexes with given properties. We end by sketching a possible
approach to combining the spin network and spin foam formalism with matter
within the framework of spectral triples in noncommutative geometry.


  The tensor network states (TNS) methods combined with Monte Carlo (MC)
techniques have been proved a powerful algorithm for simulating quantum
many-body systems. However, because the ground state energy is a highly
non-linear function of the tensors, it is easy to get stuck in local minima
when optimizing the TNS of the simulated physical systems. To overcome this
difficulty, we introduce a replica-exchange molecular dynamics optimization
algorithm to obtain the TNS ground state, based on the MC sampling techniques,
by mapping the energy function of the TNS to that of a classical dynamical
system. The method is expected to effectively avoid local minima. We make
benchmark tests on a 1D Hubbard model based on matrix product states (MPS) and
a Heisenberg $J_1$-$J_2$ model on square lattice based on string bond states
(SBS). The results show that the optimization method is robust and efficient
compared to the existing results.


  Timing side-channel attacks exploit secret-dependent execution time to fully
or partially recover secrets of cryptographic implementations, posing a severe
threat to software security. Constant-time programming discipline is an
effective software-based countermeasure against timing side-channel attacks,
but developing constant-time implementations turns out to be challenging and
error-prone. Current verification approaches/tools suffer from scalability and
precision issues when applied to production software in practice. In this
paper, we put forward practical verification approaches based on a novel
synergy of taint analysis and safety verification of self-composed programs.
Specifically, we first use an IFDS-based lightweight taint analysis to prove
that a large number of potential (timing) side-channel sources do not actually
leak secrets. We then resort to a precise taint analysis and a safety
verification approach to determine whether the remaining potential side-channel
sources can actually leak secrets. These include novel constructions of
taint-directed semi-cross-product of the original program and its Boolean
abstraction, and a taint-directed self-composition of the program. Our approach
is implemented as a cross-platform and fully automated tool CT-Prover. The
experiments confirm its efficiency and effectiveness in verifying real-world
benchmarks from modern cryptographic and SSL/TLS libraries. In particular,
CT-Prover identify new, confirmed vulnerabilities of open-source SSL libraries
(e.g., Mbed SSL, BearSSL) and significantly outperforms the state-of-the-art
tools.


  Two-dimensional Talbot array illuminators (TAIs) were designed, fabricated,
and evaluated for high-resolution high-contrast x-ray phase imaging of soft
tissue at 10-20keV. The TAIs create intensity modulations with a high
compression ratio on the micrometer scale at short propagation distances. Their
performance was compared with various other wavefront markers in terms of
period, visibility, flux efficiency and flexibility to be adapted for limited
beam coherence and detector resolution. Differential x-ray phase contrast and
dark-field imaging were demonstrated with a one-dimensional, linear phase
stepping approach yielding two-dimensional phase sensitivity using Unified
Modulated Pattern Analysis (UMPA) for phase retrieval. The method was employed
for x-ray phase computed tomography reaching a resolution of 3$\mu$m on an
unstained murine artery. It opens new possibilities for three-dimensional,
non-destructive, and quantitative imaging of soft matter such as virtual
histology. The phase modulators can also be used for various other x-ray
applications such as dynamic phase imaging, super-resolution structured
illumination microscopy, or wavefront sensing.


  Measuring the distance between machine-produced and human language is a
critical open problem. Inspired by empirical findings from psycholinguistics on
the periodicity of entropy in language, we propose FACE, a set of metrics based
on Fourier Analysis of the estimated Cross-Entropy of language, for measuring
the similarity between model-generated and human-written languages. Based on an
open-ended generation task and the experimental data from previous studies, we
find that FACE can effectively identify the human-model gap, scales with model
size, reflects the outcomes of different sampling methods for decoding,
correlates well with other evaluation metrics and with human judgment scores.


  Non-equilibrium steady states are a focal point of research in the study of
open quantum systems. Previous variational algorithms for searching these
steady states have suffered from resource-intensive implementations due to
vectorization or purification of the system density matrix, requiring large
qubit resources and long-range coupling. In this work, we present a novel
variational quantum algorithm that efficiently searches for non-equilibrium
steady states by simulating the operator-sum form of the Lindblad equation. By
introducing the technique of random measurement, we are able to estimate the
nonlinear cost function while reducing the required qubit resources by half
compared to previous methods. Additionally, we prove the existence of the
parameter shift rule in our variational algorithm, enabling efficient updates
of circuit parameters using gradient-based classical algorithms. To demonstrate
the performance of our algorithm, we conduct simulations for dissipative
quantum transverse Ising and Heisenberg models, achieving highly accurate
results. Our approach offers a promising solution for effectively addressing
non-equilibrium steady state problems while overcoming computational
limitations and implementation challenges.


  Recent works have sought to realize certain families of orthogonal, symmetric
polynomials as partition functions of well-chosen classes of solvable lattice
models. Many of these use Boltzmann weights arising from the trigonometric
six-vertex model $R$-matrix (or generalizations or specializations of these
weights). In this paper, we seek new variants of bosonic models on lattices
designed for type B/C root systems, whose partition functions match the zonal
spherical function in type C. Under general assumptions, we find that this is
possible for all highest weights in rank $2$ and $3$, but not for higher rank.


  Non-autoregressive translation (NAT) models achieve comparable performance
and superior speed compared to auto-regressive translation (AT) models in the
context of sentence-level machine translation (MT). However, their abilities
are unexplored in document-level MT, hindering their usage in real scenarios.
In this paper, we conduct a comprehensive examination of typical NAT models in
the context of document-level MT and further propose a simple but effective
design of sentence alignment between source and target. Experiments show that
NAT models achieve high acceleration on documents, and sentence alignment
significantly enhances their performance.
  However, current NAT models still have a significant performance gap compared
to their AT counterparts. Further investigation reveals that NAT models suffer
more from the multi-modality and misalignment issues in the context of
document-level MT, and current NAT models struggle with exploiting document
context and handling discourse phenomena. We delve into these challenges and
provide our code at \url{https://github.com/baoguangsheng/nat-on-doc}.


  We show the equivalence of a previously derived exact expression for the
response of a non-relativistic system with harmonic forces and an infinite sum
of weighted $\delta$-functions corresponding to the spectrum. We forward
arguments, indicating that the Gersch-Rodriguez-Smith $1/q$-expansion of the
response does not converge and prove that this expansion is an asymptotic
series.


  We report on a microfluidic method that allows measurement of a small
concentration of large contaminants in suspensions of solid micrometer-scale
particles. To perform the measurement, we flow the colloidal suspension through
a series of constrictions, i.e. a microchannel of varying cross-section. We
show and quantify the role of large contaminants in the formation of clogs at a
constriction and the growth of the resulting filter cake. By measuring the time
interval between two clogging events in an array of parallel microchannels, we
are able to estimate the concentration of contaminants whose size is selected
by the geometry of the microfluidic device. This technique for characterizing
colloidal suspensions offers a versatile and rapid tool to explore the role of
contaminants on the properties of the suspensions.


  This paper develops and implements a nonparametric test of Random Utility
Models. The motivating application is to test the null hypothesis that a sample
of cross-sectional demand distributions was generated by a population of
rational consumers. We test a necessary and sufficient condition for this that
does not rely on any restriction on unobserved heterogeneity or the number of
goods. We also propose and implement a control function approach to account for
endogenous expenditure. An econometric result of independent interest is a test
for linear inequality constraints when these are represented as the vertices of
a polyhedron rather than its faces. An empirical application to the U.K.
Household Expenditure Survey illustrates computational feasibility of the
method in demand problems with 5 goods.


  We outline basic principles of a new method that gives a conceptual reasoning
for and, at the same time, proofs of (super)congruences for truncated sums of
arithmetic hypergeometric evaluations.


  Models often easily learn biases present in the training data, and their
predictions directly reflect this bias. We analyze gender bias in dialogue
data, and examine how this bias is actually amplified in subsequent generative
chit-chat dialogue models. We measure gender bias in six existing dialogue
datasets, and focus on the most biased one, the multi-player text-based fantasy
adventure dataset LIGHT, as a testbed for our bias mitigation techniques. The
LIGHT dataset is highly imbalanced with respect to gender, containing
predominantly male characters, likely because it is entirely collected by
crowdworkers and reflects common biases that exist in fantasy or medieval
settings. We consider three techniques to mitigate gender bias: counterfactual
data augmentation, targeted data collection, and bias controlled training. We
show that our proposed techniques mitigate gender bias in LIGHT by balancing
the genderedness of generated dialogue utterances and are particularly
effective in combination. We quantify performance using various evaluation
methods---such as quantity of gendered words, a dialogue safety classifier, and
human studies---all of which show that our models generate less gendered, but
equally engaging chit-chat responses.


  Being motivated by the multilayer RECOS (REctified-COrrelations on a Sphere)
transform, we develop a data-driven Saak (Subspace approximation with augmented
kernels) transform in this work. The Saak transform consists of three steps: 1)
building the optimal linear subspace approximation with orthonormal bases using
the second-order statistics of input vectors, 2) augmenting each transform
kernel with its negative, 3) applying the rectified linear unit (ReLU) to the
transform output. The Karhunen-Lo\'eve transform (KLT) is used in the first
step. The integration of Steps 2 and 3 is powerful since they resolve the sign
confusion problem, remove the rectification loss and allow a straightforward
implementation of the inverse Saak transform at the same time. Multiple Saak
transforms are cascaded to transform images of a larger size. All Saak
transform kernels are derived from the second-order statistics of input random
vectors in a one-pass feedforward manner. Neither data labels nor
backpropagation is used in kernel determination. Multi-stage Saak transforms
offer a family of joint spatial-spectral representations between two extremes;
namely, the full spatial-domain representation and the full spectral-domain
representation. We select Saak coefficients of higher discriminant power to
form a feature vector for pattern recognition, and use the MNIST dataset
classification problem as an illustrative example.


  This paper contributes multivariate versions of seven commonly used elastic
similarity and distance measures for time series data analytics. Elastic
similarity and distance measures are a class of similarity measures that can
compensate for misalignments in the time axis of time series data. We adapt two
existing strategies used in a multivariate version of the well-known Dynamic
Time Warping (DTW), namely, Independent and Dependent DTW, to these seven
measures.
  While these measures can be applied to various time series analysis tasks, we
demonstrate their utility on multivariate time series classification using the
nearest neighbor classifier. On 23 well-known datasets, we demonstrate that
each of the measures but one achieves the highest accuracy relative to others
on at least one dataset, supporting the value of developing a suite of
multivariate similarity and distance measures. We also demonstrate that there
are datasets for which either the dependent versions of all measures are more
accurate than their independent counterparts or vice versa. In addition, we
also construct a nearest neighbor-based ensemble of the measures and show that
it is competitive to other state-of-the-art single-strategy multivariate time
series classifiers.


  We establish the asymptotic behavior of the Andrews $G_k(q)$ function as
$q\to 1.$


  Electromagnetically induced transparency (EIT) and absorption (EIA) are
quantum coherence phenomena which result due to interference of excitation
pathways. Since the first realization of EIT in 1991 and EIA in 1998,
mechanisms behind these remarkable effects have been studied extensively,
therefore both are relatively easily achievable in controlled environments.
Combining EIT and EIA with Rydberg atoms have provided utility in various
research fields such as interacting many body systems, quantum optics and
quantum information science. We propose an analysis of Rydberg-EIT and
Rydberg-EIA effects in cold Cs and Rb atomic ensembles in a four-level ladder
type scheme with self-consistent mean field approach. Our results are
consistent with experimental realizations and provide a many-body method to
simulate EIT-EIA cross-over.


  In this paper we discuss epicycloid approximation of the trajectories of
charged particles in axisymmetric magnetic fields. Epicycloid trajectories are
natural in the Guiding Center approximation and we study in detail the errors
arising in this approach. We also discuss how using exact results for particle
motion in the equatorial plane of a magnetic dipole the accuracy of this
approximation can be significantly extended. We also show that the epicycloids
approximate the trajectory of a charged particle more accurately than the
position of the particle along the trajectory.


  We develop systematically to all orders the forward scattering description
for retarded amplitudes in field theories at zero temperature. Subsequently,
through the application of the thermal operator, we establish the forward
scattering description at finite temperature. We argue that, beyond providing a
graphical relation between the zero temperature and the finite temperature
amplitudes, this method is calculationally quite useful. As an example, we
derive the important features of the one loop retarded gluon self-energy in the
hard thermal loop approximation from the corresponding properties of the zero
temperature amplitude.


  Adversarial robustness of deep neural networks is an extensively studied
problem in the literature and various methods have been proposed to defend
against adversarial images. However, only a handful of defense methods have
been developed for defending against attacked videos. In this paper, we propose
a novel Over-and-Under complete restoration network for Defending against
adversarial videos (OUDefend). Most restoration networks adopt an
encoder-decoder architecture that first shrinks spatial dimension then expands
it back. This approach learns undercomplete representations, which have large
receptive fields to collect global information but overlooks local details. On
the other hand, overcomplete representations have opposite properties. Hence,
OUDefend is designed to balance local and global features by learning those two
representations. We attach OUDefend to target video recognition models as a
feature restoration block and train the entire network end-to-end. Experimental
results show that the defenses focusing on images may be ineffective to videos,
while OUDefend enhances robustness against different types of adversarial
videos, ranging from additive attacks, multiplicative attacks to physically
realizable attacks. Code: https://github.com/shaoyuanlo/OUDefend


  We study Green functions for the pressure of stationary Stokes systems in a
(possibly unbounded) domain $\Omega\subset \mathbb{R}^d$, where $d\ge 2$. We
construct the Green function when coefficients are merely measurable in one
direction and have Dini mean oscillation in the other directions, and $\Omega$
is such that the divergence equation is solvable there. We also establish
global pointwise bounds for the Green function and its derivatives when
coefficients have Dini mean oscillation and $\Omega$ has a $C^{1,\rm{Dini}}$
boundary. Green functions for the flow velocity of Stokes systems are also
considered.


  We report the discovery of Mothra, an extremely magnified monster star,
likely a binary system of two supergiant stars, in one of the strongly lensed
galaxies behind the galaxy cluster MACS0416. The star is in a galaxy with
spectroscopic redshift $z=2.091$ in a portion of the galaxy that is parsecs
away from the cluster caustic. The binary star is observed only on the side of
the critical curve with negative parity but has been detectable for at least
eight years, implying the presence of a small lensing perturber.
  Microlenses alone cannot explain the earlier observations of this object made
with the Hubble Space Telescope. A larger perturber with a mass of at least
$10^4$\,\Msun\ offers a more satisfactory explanation. Based on the lack of
perturbation on other nearby sources in the same arc, the maximum mass of the
perturber is $M< 2.5\times10^6$\,\Msun, making it the smallest substructure
constrained by lensing above redshift 0.3. The existence of this millilens is
fully consistent with the expectations from the standard cold dark matter
model. On the other hand, the existence of such small substructure in a cluster
environment has implications for other dark matter models. In particular, warm
dark matter models with particle masses below 8.7\,keV are excluded by our
observations. Similarly, axion dark matter models are consistent with the
observations only if the axion mass is in the range $0.5\times10^{-22}\, {\rm
eV} < m_a < 5\times10^{-22}\, {\rm eV}$.


  In this paper we study the light bending caused by a slowly rotating source
in the context of quadratic theories of gravity, in which the Einstein--Hilbert
action is extended by additional terms quadratic in the curvature tensors. The
deflection angle is computed employing the method based on the Gauss--Bonnet
theorem and working in the approximation of a weak lens; also, we assume that
the source and observer are at an infinite distance. The formalism presented is
very general and applies to any spacetime metric in the limit of weak
gravitational field and slow rotation. We find the explicit formula for the
deflection angle for several local and nonlocal theories, and also discuss some
phenomenological implications.


  We present calculations on energy- and time-resolved two-photon photoemission
spectra of images states in Cu(100) and Cu(111) surfaces. The surface is
modeled by a 1D effective potential and the states are propagated within a
real-space, real-time method. To obtain the energy resolved spectra we employ a
geometrical approach based on a subdivision of space into two regions. We treat
electronic inelastic effects by taking into account the scattering rates
calculated within a GW scheme. To get further insight into the decaying
mechanism we have also studied the effect of the variation of the classical
Hartree potential during the excitation. This effect turns out to be small.


  It has been found that an algorithm can generate true random numbers on
classical computer. The algorithm can be used to generate unbreakable message
PIN (personal identification number) and password.


  We show that if the conclusion of the well known Stampacchia Theorem, on
variational inequalities, holds on a Banach space X, then X is isomorphic to a
Hilbert space. Motivated by this we obtain a relevant result concerning
self-dual Banach spaces and investigate some connections between existing
notions of orthogonality and self-duality. Moreover, we revisit the notion of
the cosine of a linear operator and show that it can be used to characterize
Hilbert space structure. Finally, we present some consequences of our results
to quadratic forms and to evolution triples.


  In a recent paper, with Drago and Pinamonti we have introduced a
Wetterich-type flow equation for scalar fields on Lorentzian manifolds, using
the algebraic approach to perturbative QFT. The equation governs the flow of
the effective average action, under changes of a mass parameter k. Here we
introduce an analogous flow equation for gauge theories, with the aid of the
Batalin-Vilkovisky (BV) formalism. We also show that the corresponding
effective average action satisfies a Slavnov-Taylor identity in Zinn-Justin
form. We interpret the equation as a cohomological constraint on the functional
form of the effective average action, and we show that it is consistent with
the flow.


  We produced optical waveguides in the 167Er3+ :7LiYF4 crystal with diameters
ranging from 30 to 100 mkm by using the depressed-cladding approach with
femtosecond laser. These waveguides were studied (both inside and outside) by
stationary and coherent spectroscopy on the 809 nm optical transitions between
the hyperfine sublevels of 4I15/2 and 4I9/2 multiplets of 167Er3+ ions. It was
found that the spectra of 167Er3+ were slightly broadened and shifted inside
the waveguides compared to the bulk crystal spectra. We managed to observe a
two-pulse photon echo on this transition and determined phase relaxation times
for each of waveguides. The experimental results show that the created crystal
waveguides doped by rare-earth ions can be used in optical quantum memory and
integrated quantum schemes.


  We investigate an atom interferometer in which large momentum differences
between the arms are obtained by using quantum resonances in the atom optics
$\delta$-kicked rotor. The interferometer can potentially measure the Talbot
time (from which $h/m$ can be deduced), the local gravitational field, or can
serve as a narrow velocity filter. We present an analytical analysis in the
short pulse limit, and a numerical investigation for finite pulse durations.
The sensitivity of the interferometer is improved by a moderate violation of
the short pulse limit. Remarkably simple relations predict the optimal pulse
duration, and the sensitivity of the interferometer.


  In Bain [J. Math. Phys. 64, 023301 (2023)], we found asymptotics of one-point
correlation functions of the two-periodic weighted Aztec diamond in the
mesoscopic limit, where the linear size of the ordered region is of the same
order as the correlation length. In this paper, we follow up with a numerical
study of two-point correlation functions of dimers separated by a mesoscopic
distance.


  The dynamical properties of a model of dark energy in which two scalar fields
are coupled by a non-canonical kinetic term are studied. We show that overall
the addition of the coupling has only minor effects on the dynamics of the
two-field system for both potentials studied, even preserving many of the
features of the assisted quintessence scenario. The coupling of the kinetic
terms enlarges the regions of stability of the critical points. When the
potential is of an additive form, we find the kinetic coupling has an
interesting effect on the dynamics of the fields as they approach the
inflationary attractor, with the result that the combined equation of state of
the scalar fields can approach -1 during the transition from a matter dominated
universe to the recent period of acceleration.


  Although quasi-Keplerian discs are among the most common astrophysical
structures, computation of secular angular momentum transport within them
routinely presents a considerable practical challenge. In this work, we
investigate the secular small-inclination dynamics of a razor-thin particle
disc as the continuum limit of a discrete Lagrange-Laplace secular perturbative
theory and explore the analogy between the ensuing secular evolution --
including non-local couplings of self-gravitating discs -- and quantum
mechanics. We find the 'quantum' Hamiltonian that describes the time evolution
of the system and demonstrate the existence of a conserved inner product. The
lowest-frequency normal modes are numerically approximated by performing a Wick
rotation on the equations of motion. These modes are used to quantify the
accuracy of a much simpler local-coupling model, revealing that it predicts the
shape of the normal modes to a high degree of accuracy, especially in narrow
annuli, even though it fails to predict their eigenfrequencies.


  We present new near infrared spectroscopic measurements for 29 luminous
high-z quasars and use the data to discuss the size and other properties of the
NLRs in those sources. The high resolution spectra have been used to carefully
model the Fe II blends and to provide reliable [O III], Fe II and Hb
measurements. We find that about 2/3 of all high luminosity sources show strong
[O III] lines while the remaining objects show no or very weak such line. While
weak [O III] emitters are also found among lower luminosity AGN, we argue that
the implications for very high luminosity objects are different. In particular,
we suggest that the averaging of these two populations in other works gave rise
to claims of a Baldwin relationship in [O III] which is not confirmed by our
data. We also argue that earlier proposed relations of the type R_NLR \propto
L_[O III]^{1/2}, where R_NLR is the NLR radius, are theoretically sound yet
they must break down for R_NLR exceeding a few kpc. This suggests that the NLR
properties in luminous sources are different from those observed in nearby AGN.
In particular, we suggest that some sources lost their very large, dynamically
unbound NLR while others are in a phase of violent star-forming events that
produce a large quantity of high density gas in the central kpc. This gas is
ionized and excited by the central radiation source and its spectroscopic
properties may be different from those observed in nearby, lower luminosity
NLRs. We also discuss the dependence of EW(Hb) and Fe II/Hb on L, M_BH, and
accretion rate for a large sample of AGNs. The strongest dependence of the two
quantities is on the accretion rate and the Fe II/Hb correlation is probably
due to the EW(Hb) dependence on accretion rate. We show the most extreme values
measured so far of Fe II/Hb and address its correlation with EW([O III]).


  The beta-delayed charged particle emission from ^11Li has been studied with
emphasis on the three-body n+alpha+^6He and five-body 2alpha+3n channels from
the 10.59 and 18.15 MeV states in ^11Be. Monte Carlo simulations using an
R-matrix formalism lead to the conclusion that the ^AHe resonance states play a
significant role in the break-up of these states. The results exclude an
earlier assumption of a phase-space description of the break-up process of the
18.15 MeV state. Evidence for extra sequential decay paths is found for both
states.


  The daily activities performed by a disabled or elderly person can be
monitored by a smart environment, and the acquired data can be used to learn a
predictive model of user behavior. To speed up the learning, several
researchers designed collaborative learning systems that use data from multiple
users. However, disclosing the daily activities of an elderly or disabled user
raises privacy concerns. In this paper, we use state-of-the-art deep neural
network-based techniques to learn predictive human activity models in the
local, centralized, and federated learning settings. A novel aspect of our work
is that we carefully track the temporal evolution of the data available to the
learner and the data shared by the user. In contrast to previous work where
users shared all their data with the centralized learner, we consider users
that aim to preserve their privacy. Thus, they choose between approaches in
order to achieve their goals of predictive accuracy while minimizing the shared
data. To help users make decisions before disclosing any data, we use machine
learning to predict the degree to which a user would benefit from collaborative
learning. We validate our approaches on real-world data.


  We introduce G-L\'{e}vy processes which develop the theory of processes with
independent and stationary increments under the framework of sublinear
expectations. We then obtain the L\'{e}vy-Khintchine formula and the existence
for G-L\'{e}vy processes. We also introduce G-Poisson processes.


  We demonstrate that Zeeman ground-state spin levels in Nd3+:YVO4 provides the
possibility to create an efficient lambda-system for optical pumping
experiments. The branching ratio R in the lambda-system is measured
experimentally via absorption spectroscopy and is compared to a theoretical
model. We show that R can be tuned by changing the orientation of the magnetic
field. These results are applied to optical pumping experiments, where
significant improvement is obtained compared to previous experiments in this
system. The tunability of the branching ratio in combination with its good
coherence properties and the high oscillator strength makes Nd3+:YVO4 an
interesting candidate for various quantum information protocols.


  We explore the relationship between fibrations arising naturally from a
surjective morphism to an abelian variety. These fibrations encode geometric
information about the morphism. Our study focuses on the interplay of these
fibrations and presents several applications. Then we propose a generalization
of the Iitaka conjecture which predicts an equality of Kodaira dimension of
fibrations, and prove it when the base is a smooth projective variety of
maximal Albanese dimension.


  The study of charge-exchange injection of protons into accelerators started
in 1960 at the Institute of Nuclear Physics of the Siberian Branch of Russian
Academy of Science, as proposed by G. I. Budker in connection with the
development of the program of the VAPP-4 proton-antiproton collider. Since the
purpose was the accumulation of beams with a maximum intensity, and the record
intensity of the H- ion beams received by that time was only 70 {\mu}A, an
important part of the program was the development of methods to produce intense
beams of negative hydrogen ions. Charge-exchange injection of particles into
accelerators and storage rings is an important application of the
charge-exchange technology. Development of charge exchange injection with
compensation of ionization energy loss by RF acceleration voltage up to the
space charge limit is presented. Accumulation of coasting beam with space
charge compensation with weak focusing and strong focusing is described.
Accumulation of circulating beam in a storage ring with intensity above space
charge limit is presented. Observation, explanation and damping of e-p
instability (electron cloud effect) is discussed. Recent developments of charge
exchange injection are discussed. Laser ionization of H- in charge exchange
injection is reviewed.


  Given a non empty set $S$ of vertices of a graph, the partiality of a vertex
with respect to $S$ is the difference between maximum and minimum of the
distances of the vertex to the vertices of $S$. The vertices with minimum
partiality constitute the fair center of the set. Any vertex set which is the
fair center of some set of vertices is called a fair set. In this paper we
prove that the induced subgraph of any fair set is connected in the case of
trees and characterise block graphs as the class of chordal graphs for which
the induced subgraph of all fair sets are connected. The fair sets of $K_{n}$,
$K_{m,n}$, $K_{n}-e$, wheel graphs, odd cycles and symmetric even graphs are
identified. The fair sets of the Cartesian product graphs are also discussed.


  The flow of the low energy eigenstates of a $U_q[sl(2|1)]$ superspin chain
with alternating fundamental ($3$) and dual ($\bar{3}$) representations is
studied as function of a twist angle determining the boundary conditions. The
finite size spectrum is characterized in terms of scaling dimensions and quasi
momenta representing the two families of commuting transfer matrices for the
model which are even and odd under the interchange $3\leftrightarrow \bar{3}$,
respectively. Based on the extrapolation of our finite size data we find that
under a variation of the boundary conditions from periodic to antiperiodic for
the fermionic degrees of freedom levels from the continuous part of the
spectrum flow into discrete levels and vice versa.


  We discuss models of ultralight scalar Dark Matter (DM) with linear and
quadratic couplings to the Standard Model (SM). In addition to studying the
phenomenology of linear and quadratic interactions separately, we examine their
interplay. We review the different experiments that can probe such interactions
and present the current and expected future bounds on the parameter space. In
particular, we discuss the scalar field solution presented in [A. Hees, O.
Minazzoli, E. Savalle, Y. V. Stadnik and P. Wolf, Phys.Rev.D 98 (2018) 6,
064051], and extend it to theories that capture both the linear and the
quadratic couplings of the DM field to the SM. Furthermore, we discuss the
theoretical aspects and the corresponding challenges for natural models in
which the quadratic interactions are of phenomenological importance.


  A lattice Boltzmann model for amphiphilic fluid dynamics is presented. It is
a ternary model, in that it conserves mass separately for each chemical species
present (water, oil, amphiphile), and it maintains an orientational degree of
freedom for the amphiphilic species. Moreover, it models fluid interactions at
the microscopic level by introducing self-consistent forces between the
particles, rather than by positing a Landau free energy functional. This
combination of characteristics fills an important need in the hierarchy of
models currently available for amphiphilic fluid dynamics, enabling efficient
computer simulation and furnishing new theoretical insight. Several
computational results obtained from this model are presented and compared to
existing lattice-gas model results. In particular, it is noted that lamellar
structures, which are precluded by the Peierls instability in two-dimensional
systems with kinetic fluctuations, are not observed in lattice-gas models, but
are easily found in the corresponding lattice Boltzmann models. This points out
a striking difference in the phenomenology accessible to each type of model.


  By means of analyzing the notion of verbal products of groups, we show that
soficity, hyperlinearity, amenability, the Haagerup property, the Kazhdan's
property (T) and exactness are preserved under taking $k$-nilpotent products of
groups, while being orderable is not preserved. We also study these properties
for solvable and for Burnside products of groups. We then show that if two
discrete groups are sofic, or have the Haagerup property, their restricted
verbal wreath product arising from nilpotent, solvable and certain Burnside
products is also sofic or has the Haagerup property respectively. We also prove
related results for hyperlinear, linear sofic and weakly sofic approximations.
Finally, we give applications combining our work with the Shmelkin embedding to
show that certain quotients of free groups are sofic or have the Haagerup
property.


  We equip the polytope of $n\times n$ Markov matrices with the normalized
trace of the Lebesgue measure of $\mathbb{R}^{n^2}$. This probability space
provides random Markov matrices, with i.i.d. rows following the Dirichlet
distribution of mean $(1/n,...,1/n)$. We show that if $\bM$ is such a random
matrix, then the empirical distribution built from the singular values
of$\sqrt{n} \bM$ tends as $n\to\infty$ to a Wigner quarter--circle
distribution. Some computer simulations reveal striking asymptotic spectral
properties of such random matrices, still waiting for a rigorous mathematical
analysis. In particular, we believe that with probability one, the empirical
distribution of the complex spectrum of $\sqrt{n} \bM$ tends as $n\to\infty$ to
the uniform distribution on the unit disc of the complex plane, and that
moreover, the spectral gap of $\bM$ is of order $1-1/\sqrt{n}$ when $n$ is
large.


  Electron-positron pair production, in combined Sauter potential wells and an
oscillating one is imposed on a static Sauter potential, is investigated by
using the computational quantum field theory. We find that the gain number (the
difference of pair number under combined potentials to the simple addition of
pair number for each potential) of the created pairs depends strongly on the
depth of static potential and the frequency of oscillating potential. In
particular, it is more sensitive to the frequency compared with the depth. For
the low-frequency multiphoton regime, the gaining is almost positive and
exhibits interesting nonlinear characteristics on both depth and frequency. For
the single-photon regime, however, the gaining is almost negative and decreases
near linearly with depth while it exhibits an oscillation characteristic with
frequency. Furthermore, the optimal frequency and depth of gain number are
found and discussed.


  We show that for each positive integer $k$ there is a $k\times k$ matrix $B$
with $\pm 1$ entries such that putting $E$ to be the span of the rows of the
$k\times 2k$ matrix $[\sqrt{k}I_k,B]$, then $E,E^{\bot}$ is a Kashin splitting:
The $L_1^{2k}$ and the $L_2^{2k}$ are universally equivalent on both $E$ and
$E^{\bot}$. Moreover, the probability that a random $\pm 1$ matrix satisfies
the above is exponentially close to 1.


  Networks embedded in space can display all sorts of transitions when their
structure is modified. The nature of these transitions (and in some cases
crossovers) can differ from the usual appearance of a giant component as
observed for the Erdos-Renyi graph, and spatial networks display a large
variety of behaviors. We will discuss here some (mostly recent) results about
topological transitions, `localization' transitions seen in the shortest paths
pattern, and also about the effect of congestion and fluctuations on the
structure of optimal networks. The importance of spatial networks in real-world
applications makes these transitions very relevant and this review is meant as
a step towards a deeper understanding of the effect of space on network
structures.


  Power domination in graphs arises from the problem of monitoring an electric
power system by placing as few measurement devices in the system as possible. A
power dominating set of a graph is a set of vertices that observes every vertex
in the graph, following a set of rules for power system monitoring. A practical
problem of interest is to determine the minimum number of additional
measurement devices needed to monitor a power network when the network is
expanded and the existing devices remain in place. In this paper, we study the
problem of finding the smallest power dominating set that contains a given set
of vertices X. We also study the related problem of finding the smallest zero
forcing set that contains a given set of vertices X. The sizes of such sets in
a graph G are respectively called the restricted power domination number and
restricted zero forcing number of G subject to X. We derive several tight
bounds on the restricted power domination and zero forcing numbers of graphs,
and relate them to other graph parameters. We also present exact and
algorithmic results for computing the restricted power domination number,
including integer programs for general graphs and a linear time algorithm for
graphs with bounded treewidth. We also use restricted power domination to
obtain a parallel algorithm for finding minimum power dominating sets in trees.


  We establish new sufficient conditions for the applicability of the strong
law of large numbers (SLLN) for sequences of pairwise independent
non-identically distributed random variables. These results generalize
Etemadi's extension of Kolmogorov's SLLN for identically distributed random
variables. Some of the obtained results hold with an arbitrary norming sequence
in place of the classical normalization.


  This paper proposes a way of protecting probabilistic prediction models
against changes in the data distribution, concentrating on the case of
classification and paying particular attention to binary classification. This
is important in applications of machine learning, where the quality of a
trained prediction algorithm may drop significantly in the process of its
exploitation. Our techniques are based on recent work on conformal test
martingales and older work on prediction with expert advice, namely tracking
the best expert.


  A promising route to realize entangled magnetic states combines geometrical
frustration with quantum-tunneling effects. Spin-ice materials are canonical
examples of frustration, and Ising spins in a transverse magnetic field are the
simplest many-body model of quantum tunneling. Here, we show that the tripod
kagome lattice material Ho${_3}$Mg${_2}$Sb${_3}$O${_{14}}$ unites an ice-like
magnetic degeneracy with quantum-tunneling terms generated by an intrinsic
splitting of the Ho$^{3+}$ ground-state doublet, which is further coupled to a
nuclear spin bath. Using neutron scattering and thermodynamic experiments, we
observe a symmetry-breaking transition at $T^{\ast}\approx0.32$ K to a
remarkable state with three peculiarities: a concurrent recovery of magnetic
entropy associated with the strongly coupled electronic and nuclear degrees of
freedom; a fragmentation of the spin into periodic and ice-like components; and
persistent inelastic magnetic excitations down to $T\approx0.12$ K. These
observations deviate from expectations of classical spin fragmentation on a
kagome lattice, but can be understood within a model of dipolar kagome ice
under a homogeneous transverse magnetic field, which we survey with exact
diagonalization on small clusters and mean-field calculations. In
Ho${_3}$Mg${_2}$Sb${_3}$O${_{14}}$, hyperfine interactions dramatically alter
the single-ion and collective properties, and suppress possible quantum
correlations, rendering the fragmentation with predominantly single-ion quantum
fluctuations. Our results highlight the crucial role played by hyperfine
interactions in frustrated quantum magnets, and motivate further investigations
of the role of quantum fluctuations on partially-ordered magnetic states.


  Based on the most complete sample of Galactic open star clusters up to 1.8
kpc, we performed statistical analysis of the distribution of open cluster
parameters in order to understand the Galactic structure. The geometrical
characteristics of a large number of open clusters enable us to determine solar
offset and scale height and distribution of reddening material in the Galactic
neighbourhood.


  We have performed a Quantum Monte Carlo study of a two-dimensional bulk
sample of interacting 1/2-spin structureless fermions, a model of $^3$He
adsorbed on a variety of preplated graphite substrates. We have computed the
equation of state and the polarization energy using both the standard
fixed-node approximate technique and a formally exact methodology, relying on
bosonic imaginary-time correlation functions of operators suitably chosen in
order to extract fermionic energies. As the density increases, the fixed-node
approximation predicts a transition to an itinerant ferromagnetic fluid,
whereas the unbiased methodology indicates that the paramagnetic fluid is the
stable phase until crystallization takes place. We find that two-dimensional
$^3$He at zero temperature crystallizes from the paramagnetic fluid at a
density of 0.061 \AA$^{-2}$ with a narrow coexistence region of about 0.002
\AA$^{-2}$. Remarkably, the spin susceptibility turns out in very good
agreement with experiments.


  The Master Catalogue of stars towards the Magellanic Clouds (MC2) is a
multi-wavelength reference catalogue. The current paper presents the first
results of the MC2 project. We started with a massive cross-identification of
the two recently released near-infrared surveys: the DENIS Catalogue towards
the Magellanic Clouds (DCMC) with more than 1.3 million sources identified in
at least two of the three DENIS filters (I J Ks) and the 2nd Incremental
Release of the 2MASS point source catalogue (J H Ks) covering the same region
of the sky. Both point source catalogues provide an unprecedented wealth of
data on the stellar populations of the Magellanic Clouds (MCs). The
cross-matching procedure has been extended to optical wavelength ranges,
including the UCAC1 (USNO) and GSC2.2 catalogues. New cross-matching procedures
for very large catalogues have been developed and important results on the
astrometric and photometric accuracy of the cross-identified catalogues were
derived. The cross-matching of large surveys is an essential tool to improve
our understanding of their specific contents. This study has been partly
supported by the ASTROVIRTEL project that aims at improving access to
astronomical archives as virtual telescopes.


  In this paper we discuss the stability of an alternative pollution-free
procedure for computing spectra. The main difference with the Galerkin method
lies in the fact that it gives rise to a weak approximate problem which is
quadratic in the spectral parameter, instead of linear. Previous accounts on
this new procedure can be found in Levitin and Shargorodsky (2002)
[math.SP/0212087] and Boulton (2006) [math.SP/0503126].


  I review recent results on the spatial distribution of substructure in CDM
halos. I show that the spatial distribution of subhalos is anisotropic and
generally prolate with a long axis that is closely aligned with the long axis
of the total mass distribution of the host halo. I show that the correlation
between the subhalo distribution and the long axis of the host halo is strong
both in dissipationless and dissipational gasdynamical simulations. More
massive subhalos tend to be more strongly clustered along the major axis of the
host halo reflecting filamentary accretion. The anisotropy of subhalos has
potential implications for the interpretation of several observations in the
Local Group and beyond. For example, I show that while the mean projected mass
fraction in substructure in the central regions of CDM halos is fsub \approx
0.4%, fsub is a strong function of projection angle and is ~ 5 to 6 times
higher for projections that are nearly collinear with the major axis of the
host halo.


  Sparse-view CT is a promising strategy for reducing the radiation dose of
traditional CT scans, but reconstructing high-quality images from incomplete
and noisy data is challenging. Recently, 3D Gaussian has been applied to model
complex natural scenes, demonstrating fast convergence and better rendering of
novel views compared to implicit neural representations (INRs). Taking
inspiration from the successful application of 3D Gaussians in natural scene
modeling and novel view synthesis, we investigate their potential for
sparse-view CT reconstruction. We leverage prior information from the
filtered-backprojection reconstructed image to initialize the Gaussians; and
update their parameters via comparing difference in the projection space.
Performance is further enhanced by adaptive density control. Compared to INRs,
3D Gaussians benefit more from prior information to explicitly bypass learning
in void spaces and allocate the capacity efficiently, accelerating convergence.
3D Gaussians also efficiently learn high-frequency details. Trained in a
self-supervised manner, 3D Gaussians avoid the need for large-scale paired
data. Our experiments on the AAPM-Mayo dataset demonstrate that 3D Gaussians
can provide superior performance compared to INR-based methods. This work is in
progress, and the code will be publicly available.


  We give explicit harmonic representatives of Dolbeault cohomology of
Oeljeklaus-Toma manifolds and show that they are geometrically Dolbeault
formal. We also give explicit harmonic representatives of Bott-Chern cohomology
of Oeljeklaus-Toma manifolds of type $(s,1)$ and study the Angella-Tomassini
inequality.


  We re-examine the very stringent limits on the axion mass based on the
strength and duration of the neutrino signal from SN 1987A, in the light of new
measurements of the axial-vector coupling strength of nucleons, possible
suppression of axion emission due to many-body effects, and additional emission
processes involving pions. The suppression of axion emission due to nucleon
spin fluctuations induced by many-body effects degrades previous limits by a
factor of about 2. Emission processes involving thermal pions can strengthen
the limits by a factor of 3-4 within a perturbative treatment that neglects
saturation of nucleon spin fluctuations. Inclusion of saturation effects,
however, tends to make the limits less dependent on pion abundances. The
resulting axion mass limit also depends on the precise couplings of the axion
and ranges from 0.5x10**(-3) eV to 6x10**(-3) eV.


  This article describes the application of soft computing methods for solving
the problem of locating garbage accumulation points in urban scenarios. This is
a relevant problem in modern smart cities, in order to reduce negative
environmental and social impacts in the waste management process, and also to
optimize the available budget from the city administration to install waste
bins. A specific problem model is presented, which accounts for reducing the
investment costs, enhance the number of citizens served by the installed bins,
and the accessibility to the system. A family of single- and multi-objective
heuristics based on the PageRank method and two mutiobjective evolutionary
algorithms are proposed. Experimental evaluation performed on real scenarios on
the cities of Montevideo (Uruguay) and Bahia Blanca (Argentina) demonstrates
the effectiveness of the proposed approaches. The methods allow computing
plannings with different trade-off between the problem objectives. The computed
results improve over the current planning in Montevideo and provide a
reasonable budget cost and quality of service for Bahia Blanca.


  In this paper, a unified framework for particulate two-phase flow will be
presented with a wide range of solid-particle concentration from dilute to
dense limit. The two phase flow is simulated by two coupled flow solvers, i.e.,
the gas-kinetic scheme (GKS) for the gas phase and unified gas-kinetic
wave-particle method (UGKWP) for the particle phase. The GKS is a second-order
Navier-Stokes flow solver for the continuum flow. The UGKWP is a multiscale
method for all flow regimes. The wave and particle decomposition in UGKWP
depends on the cell's Knudsen number (Kn). At a small Kn number, the high
concentrated solid particle phase will be modeled by the Eulerian hydrodynamic
wave due to the intensive particle-particle collisions. At a large Kn number,
the dilute solid particle will be sampled and followed by the Lagrangian
particle formulation to capture the non-equilibrium transport. In the
transition regime, the distribution and evolution of particle and wave in UGKWP
are controlled by the local Kn number with a smooth transition between the
above limits. In the current scheme, the two phase model improves the previous
one in all following aspects: drag force model for different solid particle
concentrations; the frictional pressure in inter-particle contacts at high
solid-particle concentration; a flux limiting model to avoid solid particles'
over-packing; additional non-conservative nozzle and work terms for the gas
phase. Besides, the inter-particle collisions have been refined numerically for
the dense particle flow through the discretization of the collision term and
numerical flux function. The numerical scheme is tested in a series of typical
gas-particle problems. The results validate the accuracy and reliability of the
proposed method for gas-particle flow.


  The classical approach to solvability of a mathematical problem is to define
a method which includes certain rules of operation or algorithms. Then using
the defined method, one can show that some problems are solvable or not
solvable or undecidable depending on the particular method. With numerical
solutions implemented in a computer, it might be more practical to define
solvability of a mathematical problem as a complex decomposition problem. The
decomposition breaks the data into a simple part and a complex part. The simple
part is the solvable part by the method prescribed in the problem definition.
The complex part is the leftover of the simple part. Complex part can be viewed
as the "residual" of data or operator. It should be interpreted and not to be
discarded as useless. We will give different examples to illustrate the more
practical definition of solvability. The complex part is not noise and should
not be viewed as useless part of the data. It has its own merit in terms of
topological or geological interpretation. We have de-emphasized absolute
solvability and have emphasized the practical solvability where the simple and
complex parts both play important roles.


  Perceptual evaluation constitutes a crucial aspect of various
audio-processing tasks. Full reference (FR) or similarity-based metrics rely on
high-quality reference recordings, to which lower-quality or corrupted versions
of the recording may be compared for evaluation. In contrast, no-reference (NR)
metrics evaluate a recording without relying on a reference. Both the FR and NR
approaches exhibit advantages and drawbacks relative to each other. In this
paper, we present a novel framework called CORN that amalgamates these dual
approaches, concurrently training both FR and NR models together. After
training, the models can be applied independently. We evaluate CORN by
predicting several common objective metrics and across two different
architectures. The NR model trained using CORN has access to a reference
recording during training, and thus, as one would expect, it consistently
outperforms baseline NR models trained independently. Perhaps even more
remarkable is that the CORN FR model also outperforms its baseline counterpart,
even though it relies on the same training data and the same model
architecture. Thus, a single training regime produces two independently useful
models, each outperforming independently trained models


  Autoencoders are able to learn useful data representations in an unsupervised
matter and have been widely used in various machine learning and computer
vision tasks. In this work, we present methods to train Invertible Neural
Networks (INNs) as (variational) autoencoders which we call INN (variational)
autoencoders. Our experiments on MNIST, CIFAR and CelebA show that for low
bottleneck sizes our INN autoencoder achieves results similar to the classical
autoencoder. However, for large bottleneck sizes our INN autoencoder
outperforms its classical counterpart. Based on the empirical results, we
hypothesize that INN autoencoders might not have any intrinsic information loss
and thereby are not bounded to a maximal number of layers (depth) after which
only suboptimal results can be achieved.


  High frame rate 3-D ultrasound imaging technology combined with
super-resolution processing method can visualize 3-D microvascular structures
by overcoming the diffraction limited resolution in every spatial direction.
However, 3-D super-resolution ultrasound imaging using a full 2-D array
requires a system with large number of independent channels, the design of
which might be impractical due to the high cost, complexity, and volume of data
produced.
  In this study, a 2-D sparse array was designed and fabricated with 512
elements chosen from a density-tapered 2-D spiral layout. High frame rate
volumetric imaging was performed using two synchronized ULA-OP 256 research
scanners. Volumetric images were constructed by coherently compounding 9-angle
plane waves acquired in 3 milliseconds at a pulse repetition frequency of 3000
Hz. To allow microbubbles sufficient time to move between consequent compounded
volumetric frames, a 7-millisecond delay was introduced after each volume
acquisition. This reduced the effective volume acquisition speed to 100 Hz and
the total acquired data size by 3.3-fold. Localization-based 3-D
super-resolution images of two touching sub-wavelength tubes were generated
from 6000 volumes acquired in 60 seconds. In conclusion, this work demonstrates
the feasibility of 3D super-resolution imaging and super-resolved velocity
mapping using a customized 2D sparse array transducer.


  Minimum-weight cut (min-cut) is a basic measure of a network's connectivity
strength. While the min-cut can be computed efficiently in the sequential
setting [Karger STOC'96], there was no efficient way for a distributed network
to compute its own min-cut without limiting the input structure or dropping the
output quality: In the standard CONGEST model, existing algorithms with
nearly-optimal time (e.g. [Ghaffari, Kuhn, DISC'13; Nanongkai, Su, DISC'14])
can guarantee a solution that is $(1+\epsilon)$-approximation at best while the
exact $\tilde O(n^{0.8}D^{0.2} + n^{0.9})$-time algorithm [Ghaffari, Nowicki,
Thorup, SODA'20] works only on *simple* networks (no weights and no parallel
edges). Here $n$ and $D$ denote the network's number of vertices and
hop-diameter, respectively. For the weighted case, the best bound was $\tilde
O(n)$ [Daga, Henzinger, Nanongkai, Saranurak, STOC'19].
  In this paper, we provide an *exact* $\tilde O(\sqrt n + D)$-time algorithm
for computing min-cut on *weighted* networks. Our result improves even the
previous algorithm that works only on simple networks. Its time complexity
matches the known lower bound up to polylogarithmic factors. At the heart of
our algorithm are a clever routing trick and two structural lemmas regarding
the structure of a minimum cut of a graph. These two structural lemmas
considerably strengthen and generalize the framework of Mukhopadhyay-Nanongkai
[STOC'20] and can be of independent interest.


  The fast growth of Internet-connected embedded devices demands for new
capabilities at the network edge. These new capabilities are local processing,
efficient communications, and resource virtualization. The current work aims to
address these capabilities by designing and deploying a new management
proposal, which offers on-demand activation of offline Internet of Things (IoT)
fog computing assets via a Software Defined Networking (SDN) based solution
combined with containerization and sensor virtualization. We propose a testbed
as a proof of concept for the main functionalities of this novel solution. The
obtained results evidence that the current SDN-based solution can deploy with
success activation policies on computational edge containers, which are located
within the same network domain of the SDN controller. In addition, different
application-level scenarios are also investigated.


  I derive a system of pulsation equations for compact stars made up of an
arbitrary number of perfect fluids that can be used to study radial
oscillations and stability with respect to small perturbations. I assume
spherical symmetry and that the only inter-fluid interactions are
gravitational. My derivation is in line with Chandrasekhar's original
derivation for the pulsation equation of a single-fluid compact star and keeps
the contributions from the individual fluids manifest. I illustrate solutions
to the system of pulsations equations with one-, two-, and three-fluid
examples.


  We recently showed that several Local Group (LG) galaxies have much higher
radial velocities (RVs) than predicted by a 3D dynamical model of the standard
cosmological paradigm. Here, we show that 6 of these 7 galaxies define a thin
plane with root mean square thickness of only 101 kpc despite a widest extent
of nearly 3 Mpc, much larger than the conventional virial radius of the Milky
Way (MW) or M31. This plane passes within ${\sim 70}$ kpc of the MW-M31
barycentre and is oriented so the MW-M31 line is inclined by $16^\circ$ to it.
  We develop a toy model to constrain the scenario whereby a past MW-M31 flyby
in Modified Newtonian Dynamics (MOND) forms tidal dwarf galaxies that settle
into the recently discovered planes of satellites around the MW and M31. The
scenario is viable only for a particular MW-M31 orbital plane. This roughly
coincides with the plane of LG dwarfs with anomalously high RVs.
  Using a restricted $N$-body simulation of the LG in MOND, we show how the
once fast-moving MW and M31 gravitationally slingshot test particles outwards
at high speeds. The most distant such particles preferentially lie within the
MW-M31 orbital plane, probably because the particles ending up with the highest
RVs are those flung out almost parallel to the motion of the perturber. This
suggests a dynamical reason for our finding of a similar trend in the real LG,
something not easily explained as a chance alignment of galaxies with an
isotropic or mildly flattened distribution (probability $= {0.0015}$).


  We calculate the rapidity gap survival probability associated with the Higgs
decay and Higgs plus dijet production in proton-proton collisions by resumming
the leading non-global logarithms without any approximation to the number of
colors. For dijet production, depending on partonic subprocesses, the
probability involves various `color multipoles', i.e., the product of 4 ($qq\to
qq$) or 6 ($qg\to qg$) or 8 ($gg\to gg$) Wilson lines. We calculate all these
multipoles for a fixed dijet configuration and discuss the factorization of
higher multipoles into lower multipoles as well as the validity of the
large-$N_c$ approximation.


  Complex oxide heterointerfaces can host a rich of emergent phenomena, and
epitaxial growth is usually at the heart of forming these interfaces. Recently,
a strong crystalline-orientation-dependent two-dimensional superconductivity
was discovered at interfaces between KTaO3 single-crystal substrates and films
of other oxides. Unexpectedly, rare of these oxide films was epitaxially grown.
Here, we report the existence of superconductivity in epitaxially grown
LaVO3/KTaO3(111) heterostructures, with a superconducting transition
temperature of ~0.5 K. Meanwhile, no superconductivity was detected in the
(001)- and (110)-orientated LaVO3/KTaO3 heterostructures down to 50 mK.
Moreover, we find that for the LaVO3/KTaO3(111) interfaces to be conducting, an
oxygen-deficient growth environment and a minimum LaVO3 thickness of ~0.8 nm (~
2 unit cells) are needed.


  Continuous improvements of observations and modeling efforts have led to
tremendous strides in exoplanetary science. However, as instruments and
techniques advance laboratory data becomes more important to interpret
exoplanet observations and verify theoretical modeling. Though experimental
studies are often deferred due to their high costs and long timelines, it is
imperative that laboratory investigations are prioritized to ensure steady
advances in the field of exoplanetary science. This White Paper discusses the
importance of prioritizing exoplanetary laboratory efforts, and discusses
several experimental facilities currently performing exoplanetary research.


  We study homological structure of the filtrations of the spaces of
self-adjoint operators by the multiplicity of the ground state. We consider
only operators acting in a finite dimensional complex or real Hilbert space but
infinite dimensional generalizations are easily guessed.


  FT-Raman spectroscopy was employed to study (in-vitro) non-altered human
colorectal tissues aiming evaluate their spectral differences. The samples were
collected from 39 patients, adding 144 spectra. The results enable one
estabilish 3 well defined spectroscopic groups of what was consistently checked
by statistical (clustering) and biological (histopathology) analysis. The
similarity within each group was better than 90%. Groups 1 and 2 had 80% of
similarity while presenting both 70% of similarity to group 3. All groups
presented connective and epithelial tissues as histopathological
characteristic. Group 1 differs from others by the presence of soft muscle
while group 3 by presence of fatty tissue. Tissues from group 2 are composed by
samples with connective and epithelial tissues. This study is very relevant in
order to establish the non-altered or normal spectroscopic standard for future
studies and applications on optical biopsy and diagnosis of colorectal cancer.


  In math.RT/0302174 we developed a framework to study representations of
groups of the form $G((t))$, where $G$ is an algebraic group over a local field
$K$. The main feature of this theory is that natural representations of groups
of this kind are not on vector spaces, but rather on pro-vector spaces.
  In this paper we present some further constructions related to this theory.
The main results include: 1) General theorems insuring representability of
covariant functors, 2) Study of the functor of semi-invariants, which is an
analog of the functor of semi-infinite cohomology for infinite-dimensional Lie
algebras, 3) Construction of representations from the moduli space of
$G$-bundles on algebraic curve over $K$.


  Systematic study of the existing statistical data from direct numerical
simulations (DNS) lead to a logical and important classification of generic
turbulent boundary layers (TBL), namely Type A,B and C TBL, based on the
distribution patterns of time averaged wall shear stress. Among these three
types, Type A and B TBLs are investigated in terms of its universal statistical
laws of velocity and temperature with independency on both Reynolds (Re) and
Prandtl (Pr) numbers. With reference to the analysis by von Karman in
developing the conventional law of the wall for Type A TBL, the current study
first physically distinguishes the time averaged local velocity scale from the
ensemble averaged velocity scale, and properly defines the TBL temperature
scale based on wall heat flux, similar to the well known frictional velocity
scale based on wall shear stress. The unified law of the wall formulations are
then derived for the inner layer of Type A and B thermal TBLs using these
scales. The formulations are constructed by introducing the general damping and
enhancing functions in inner layer, and further, these functions are extended
to logarithmic coordinate based on the multiscale characteristics of TBL
velocity profiles. The validations of the law are conducted both by the DNS
guided near wall integration of Type B TBL governing equations, which uncovered
the Re and Pr independency mechanisms of the law. The research advances the
current understandings of the conventional TBL theory and develop the complete
analytical forms of law of the wall for Type A and B TBLs, including inner
layer, transition layer, logarithmic layer and wake layer.


  We study the Pareto frontier of two archetypal objectives in multi-armed
bandits, namely, regret minimization (RM) and best arm identification (BAI)
with a fixed horizon. It is folklore that the balance between exploitation and
exploration is crucial for both RM and BAI, but exploration is more critical in
achieving the optimal performance for the latter objective. To this end, we
design and analyze the BoBW-lil'UCB$(\gamma)$ algorithm. Complementarily, by
establishing lower bounds on the regret achievable by any algorithm with a
given BAI failure probability, we show that (i) no algorithm can simultaneously
perform optimally for both the RM and BAI objectives, and (ii)
BoBW-lil'UCB$(\gamma)$ achieves order-wise optimal performance for RM or BAI
under different values of $\gamma$. Our work elucidates the trade-off more
precisely by showing how the constants in previous works depend on certain
hardness parameters. Finally, we show that BoBW-lil'UCB outperforms a close
competitor UCB$_\alpha$ (Degenne et al., 2019) in terms of the time complexity
and the regret on diverse datasets such as MovieLens and Published Kinase
Inhibitor Set.


  Toward an improved understanding of the role of quantum information in nuclei
and exotic matter, we examine the magic (non-stabilizerness) in low-energy
strong interaction processes. As stabilizer states can be prepared efficiently
using classical computers, and include classes of entangled states, it is magic
and fluctuations in magic, along with entanglement, that determine resource
requirements for quantum simulations. As a measure of fluctuations in magic
induced by scattering, the "magic power" of the S-matrix is introduced. Using
experimentally-determined scattering phase shifts and mixing parameters, the
magic power in nucleon-nucleon and hyperon-nucleon scattering, along with the
magic in the deuteron, are found to exhibit interesting features. The
$\Sigma^-$-baryon is identified as a potential candidate catalyst for enhanced
spreading of magic and entanglement in dense matter, depending on in-medium
decoherence.


  For a dominant integral weight $\Lambda$ in a Lie algebra of affine type A
and rank $e$, and an interval $I_0$ in the residue set $I$, we define the face
for the interval $I_0$ to be the subgraph of the block-reduced crystal
$\widehat P(\Lambda)$ that is generated by $f_i$ for $i \in I_0$. We show that
such a face has an automorphism that preserves defects. For an interval of
length $2$, we also give a non-recursive construction of the $e$-regular
multipartitions with weights in the face, as well as a formula for the number
of $e$-regular multipartitions at each vertex of the face.
  For an affine Lie algebra of type $A$ we define and investigate the shape of
canonical basis elements, a sequence counting the number of multipartitions
with a given coefficient. For finite faces generated by $\Lambda$ with
$|I_0|=1,2$, we give a non-recursive closed formula for the canonical basis
elements.


  According to Rayleigh's criterion, rotating flows are linearly stable when
their specific angular momentum increases radially outward. The celebrated
magnetorotational instability opens a way to destabilize those flows, as long
as the angular velocity is decreasing outward. Using a short-wavelength
approximation we demonstrate that even flows with very steep positive shear can
be destabilized by azimuthal magnetic fields which are current-free within the
fluid. We illustrate the transition of this instability to a rotationally
enhanced kink-type instability in case of a homogeneous current in the fluid,
and discuss the prospects for observing it in a magnetized Taylor-Couette flow.


  This article presents the results of a study of signs on a Bronze Age slab
discovered in the vicinity of a heavily plowed mound near the settlement of
Pyatikhatki. The slab belongs to the Dolmen archaeological culture. In the
course of this research, it was proved that the Pyatikhatki slab is a unique
measuring tool, that combines elements of sundial and water clock. It has all
the cup marks of an analemmatic sundial, except for the presence of a precise
analemma, which at that time, it seems, could not yet be built. The vertical
gnomon moved only along the north-south line, and the time was determined
approximately. Most likely, this was due to the lack of accuracy in measuring
time using the water clock of that era. It is possible that it was their
imperfection that was the incentive for the development of a new type of watch
- a sundial, which would allow measuring time over a long period with a higher
accuracy.


  Quantum mechanical systems with position dependent masses (PDM) admitting two
parametric Lie symmetry groups are classified. Namely, all PDM systems are
specified which, in addition to their invariance w.r.t. a two parametric Lie
group, admit at least one second order integral of motion. The presented
classification is partially extended to the more generic systems which do not
accept any Lie group.


  For most practical optimisation problems local search outperforms random
sampling - despite the "No Free Lunch Theorem". This paper introduces a
property of search landscapes termed Neighbours' Similar Fitness (NSF) that
underlies the good performance of neighbourhood search in terms of local
improvement. Though necessary, NSF is not sufficient to ensure that searching
for improvement among the neighbours of a good solution is better than random
search. The paper introduces an additional (natural) property which supports a
general proof that, for NSF landscapes, neighbourhood search beats random
search.


  Security threats such as jamming and route manipulation can have significant
consequences on the performance of modern wireless networks. To increase the
efficacy and stealthiness of such threats, a number of extremely challenging,
cross-layer attacks have been recently unveiled. Although existing research has
thoroughly addressed many single-layer attacks, the problem of detecting and
mitigating cross-layer attacks still remains unsolved. For this reason, in this
paper we propose a novel framework to analyze and address cross-layer attacks
in wireless networks. Specifically, our framework consists of a detection and a
mitigation component. The attack detection component is based on a Bayesian
learning detection scheme that constructs a model of observed evidence to
identify stealthy attack activities. The mitigation component comprises a
scheme that achieves the desired trade-off between security and performance. We
specialize and evaluate the proposed framework by considering a specific
cross-layer attack that uses jamming as an auxiliary tool to achieve route
manipulation. Simulations and experimental results obtained with a test-bed
made up by USRP software-defined radios demonstrate the effectiveness of the
proposed methodology.


  The experiment of determination of the 64Zn(n,a)61Ni reaction cross section
in the 5.0-6.75 MeV neutron energy range was performed at the 4.5 MV Van de
Graaf accelerator at the Institute of Heavy Ion Physics, Peking University,
Beijing. Double section ionization chamber with grid was used for direct
registration of the reaction products. The cross sections and angular
distributions were extracted from the experimental data. The obtained values
were compared with the results of other authors and theoretical estimations.
The analysis of the experimental data and model calculations were carried out.


  Anelastic relaxation and $^{139}$La NQR relaxation measurements in
La$_{2-x}$Sr$_x$CuO$_4$ for Sr content x around 2 and 3 percent, are presented
and discussed in terms of spin and lattice excitations and ordering processes.
It is discussed how the phase diagram of La$_{2-x}$Sr$_x$CuO$_4$ at the
boundary between the antiferromagnetic (AF) and the spin-glass phase (x = 0.02)
could be more complicate than previous thought, with a transition to a
quasi-long range ordered state at T = 150 K, as indicated by recent neutron
scattering data. On the other hand, the $^{139}$La NQR spectra are compatible
with a transition to a conventional AF phase around T = 50 K, in agreement with
the phase diagram commonly accepted in the literature. In this case the
relaxation data, with a peak of magnetic origin in the relaxation rate around
150 K at 12 MHz and the anelastic counterparts around 80 K in the kHz range,
yield the first evidence in La$_{1.98}$Sr$_{0.02}$CuO$_4$ of freezing involving
simultaneously lattice and spin excitations. This excitation could correspond
to the motion of charged stripes.


  We study the effects of disorder on a Kitaev chain with longer-range hopping
and pairing terms which is capable of forming local zero energy excitations
and, hence, serves as a minimal model for localization-protected edge qubits.
The clean phase diagram hosts regions with 0, 1, and 2 Majorana zero-modes
(MZMs) per edge. Using a semi-analytic approach corroborated by numerical
calculations of the entanglement degeneracy, we show how phase boundaries
evolve under the influence of disorder. While in general the 2 MZM region is
stable with respect to moderate disorder, stronger values drive transition
towards the topologically trivial phase. We uncover regions where the addition
of disorder induces local zero-modes absent for the corresponding clean system.
Interestingly, we discover that disorder destroys any direct transition between
phases with zero and two MZMs by creating a tricritical point at the 2-0 MZM
boundary of the clean system. Finally, motivated by recent experiments, we
calculate the characteristic signatures of the disorder phase diagram as
measured in dynamical local and non-local qubit correlation functions. Our work
provides a minimal starting point to investigate the coherence properties of
local qubits in the presence of disorder.


  Incomplete multi-modal image segmentation is a fundamental task in medical
imaging to refine deployment efficiency when only partial modalities are
available. However, the common practice that complete-modality data is visible
during model training is far from realistic, as modalities can have imbalanced
missing rates in clinical scenarios. In this paper, we, for the first time,
formulate such a challenging setting and propose Preference-Aware
Self-diStillatION (PASSION) for incomplete multi-modal medical image
segmentation under imbalanced missing rates. Specifically, we first construct
pixel-wise and semantic-wise self-distillation to balance the optimization
objective of each modality. Then, we define relative preference to evaluate the
dominance of each modality during training, based on which to design task-wise
and gradient-wise regularization to balance the convergence rates of different
modalities. Experimental results on two publicly available multi-modal datasets
demonstrate the superiority of PASSION against existing approaches for modality
balancing. More importantly, PASSION is validated to work as a plug-and-play
module for consistent performance improvement across different backbones. Code
is available at https://github.com/Jun-Jie-Shi/PASSION.


  We have examined a method of direct extraction of accurate tight-binding
parameters from an ab-initio band-structure calculation. The linear muffin-tin
potential method, in its full-potential implementation, has been used to
provide the hamiltonian and overlap matrix elements in the momentum space.
These matrix elements are Fourier transformed to real space to produce the
tight-binding parameters. The feasibility of this method has been tested on the
intermetallic alloy NiAl, using spd orbitals for each atom. The parameters
generated for this alloy have been used as input to a real-space calculation of
the local density of states using the recursion method.


  We study 203 (of 442) Swift AGN and Cluster Survey extended X-ray sources
located in the SDSS DR8 footprint to search for galaxy over-densities in three
dimensional space using SDSS galaxy photometric redshifts and positions near
the Swift cluster candidates. We find 104 Swift clusters with a >3sigma galaxy
over-density. The remaining targets are potentially located at higher redshifts
and require deeper optical follow-up observations for confirmation as galaxy
clusters. We present a series of cluster properties including the redshift, BCG
magnitude, BCG-to-X-ray center offset, optical richness, and X-ray luminosity.
We also detect red sequences in ~85% of the 104 confirmed clusters. The X-ray
luminosity and optical richness for the SDSS confirmed Swift clusters are
correlated and follow previously established relations. The distribution of the
separations between the X-ray centroids and the most likely BCG is also
consistent with expectation. We compare the observed redshift distribution of
the sample with a theoretical model, and find that our sample is complete for z
<~ 0.3 and is still 80% complete up to z ~= 0.4, consistent with the SDSS
survey depth. These analysis results suggest that our Swift cluster selection
algorithm has yielded a statistically well-defined cluster sample for further
studying cluster evolution and cosmology. We also match our SDSS confirmed
Swift clusters to existing cluster catalogs, and find 42, 23 and 1 matches in
optical, X-ray and SZ catalogs, respectively, so the majority of these clusters
are new detections.


  We study coherent energy transfer of a single excitation and quantum
entanglement in a dimer, which consists of a donor and an acceptor modeled by
two two-level systems. Between the donor and the acceptor, there exists a
dipole-dipole interaction, which provides the physical mechanism for coherent
energy transfer and entanglement generation. The donor and the acceptor couple
to two independent heat baths with diagonal couplings that do not dissipate the
energy of the non-coupling dimer. Special attention is paid to the effect on
single-excitation energy transfer and entanglement generation of the energy
detuning between the donor and the acceptor and the temperatures of the two
heat baths. It is found that, the probability for single-excitation energy
transfer largely depends on the energy detuning in the low temperature limit.
Concretely, the positive and negative energy detunings can increase and
decrease the probability at the steady state, respectively. In the high
temperature limit, however, the effect of the energy detuning on the
probability is neglectably small. We also find that the probability is
neglectably dependent on the bath temperature difference of the two heat baths.
In addition, it is found that quantum entanglement can be generated in the
process of coherent energy transfer. As the bath temperature increases, the
generated steady state entanglement decreases. For a given bath temperature,
the steady-state entanglement decreases with the increasing of the absolute
value of the energy detuning.


  The Noether number of a representation is the largest degree of an element in
a minimal homogeneous generating set for the corresponding ring of invariants.
We compute the Noether number for an arbitrary representation of a cyclic group
of prime order, and as a consequence prove the "2p-3 conjecture".


  We address the important question of how to characterize the normal state of
fermionic superfluids under the influence of a strong effective magnetic field,
implemented through rapid rotation or novel artificial field techniques. We
consider the effects of crossing from BCS to BEC and the role of non-condensed
pairs, or pseudogap effects. Using a simple extension of Gor'kov theory we
demonstrate how these pairs organize above the transition $T_c$ into precursors
of a vortex configuration, which are associated with distortions of the ideal
Abrikosov lattice. This non-uniform normal state appears to enable "Bose
condensation" in a field which is otherwise problematic due to the effective
one-dimensionality of Landau level dispersion.


  Application of Machine Learning algorithms to the medical domain is an
emerging trend that helps to advance medical knowledge. At the same time, there
is a significant a lack of explainable studies that promote informed,
transparent, and interpretable use of Machine Learning algorithms. In this
paper, we present explainable multi-class classification of the Covid-19 mental
health data. In Machine Learning study, we aim to find the potential factors to
influence a personal mental health during the Covid-19 pandemic. We found that
Random Forest (RF) and Gradient Boosting (GB) have scored the highest accuracy
of 68.08% and 68.19% respectively, with LIME prediction accuracy 65.5% for RF
and 61.8% for GB. We then compare a Post-hoc system (Local Interpretable
Model-Agnostic Explanations, or LIME) and an Ante-hoc system (Gini Importance)
in their ability to explain the obtained Machine Learning results. To the best
of these authors knowledge, our study is the first explainable Machine Learning
study of the mental health data collected during Covid-19 pandemics.