  Sleep-wake cycle detection is a key step when extrapolating sleep patterns
from actigraphy data. Numerous supervised detection algorithms have been
developed with parameters estimated from and optimized for a particular
dataset, yet their generalizability from sensor to sensor or study to study is
unknown. In this paper, we propose and validate an unsupervised algorithm --
CircaCP -- to detect sleep-wake cycles from minute-by-minute actigraphy data.
It first uses a robust cosinor model to estimate circadian rhythm, then
searches for a single change point (CP) within each cycle. We used CircaCP to
estimate sleep/wake onset times (S/WOTs) from 2125 indviduals' data in the MESA
Sleep study and compared the estimated S/WOTs against self-reported S/WOT event
markers. Lastly, we quantified the biases between estimated and self-reported
S/WOTs, as well as variation in S/WOTs contributed by the two methods, using
linear mixed-effects models and variance component analysis.
  On average, SOTs estimated by CircaCP were five minutes behind those reported
by event markers, and WOTs estimated by CircaCP were less than one minute
behind those reported by markers. These differences accounted for less than
0.2% variability in SOTs and in WOTs, taking into account other sources of
between-subject variations. By focusing on the commonality in human circadian
rhythms captured by actigraphy, our algorithm transferred seamlessly from
hip-worn ActiGraph data collected from children in our previous study to
wrist-worn Actiwatch data collected from adults. The large between- and
within-subject variability highlights the need for estimating individual-level
S/WOTs when conducting actigraphy research. The generalizability of our
algorithm also suggests that it could be widely applied to actigraphy data
collected by other wearable sensors.


  The long-time behaviour of spin-spin correlators in the slow relaxation of
systems undergoing phase-ordering kinetics is studied in geometries of finite
size. A phenomenological finite-size scaling ansatz is formulated and tested
through the exact solution of the kinetic spherical model, quenched to below
the critical temperature, in $2<d<4$ dimensions.


  A Bayesian Survival Analysis method is motivated and developed for analysing
sequences of scores made by a batsman in test or first class cricket. In
particular, we expect the presence of an effect whereby the distribution of
scores has more probability near zero than a geometric distribution, due to the
fact that batting is more difficult when the batsman is new at the crease. A
Metropolis-Hastings algorithm is found to be efficient at estimating the
proposed parameters, allowing us to quantify exactly how large this
early-innings effect is, and how long a batsman needs to be at the crease in
order to ``get their eye in''. Applying this model to several modern players
shows that a batsman is typically only playing at about half of their potential
ability when they first arrive at the crease, and gets their eye in
surprisingly quickly. Additionally, some players are more ``robust'' (have a
smaller early-innings effect) than others, which may have implications for
selection policy.


  We analyze flavor-changing-neutral-current (FCNC) effects in the $b\to s$
transitions that are induced by family non-universal $U(1)'$ gauge symmetries.
After systematically developing the necessary formalism, we present a
correlated analysis for the $\Delta B =1, 2$ processes. We adopt a
model-independent approach in which we only require family-universal charges
for the first and second generations and small fermion mixing angles. We
analyze the constraints on the resulting parameter space from $B_s - \bar B_s$
mixing and the time-dependent CP asymmetries of the penguin-dominated $B_d \to
(\pi, \phi, \eta', \rho, \omega, f_0)K_S$ decays. Our results indicate that the
currently observed discrepancies in some of these modes with respect to the
Standard Model predictions can be consistently accommodated within this general
class of models.


  The Fibonacci cube $\Gamma_n$ is the subgraph of the hypercube induced by the
binary strings that contain no two consecutive 1's. The Lucas cube $\Lambda_n$
is obtained from $\Gamma_n$ by removing vertices that start and end with 1. We
characterize maximal induced hypercubes in $\Gamma_n$ and $\Lambda_n$ and
deduce for any $p\leq n$ the number of maximal $p$-dimensional hypercubes in
these graphs.


  In this paper, we present our approach to systematically measure numerous
performance parameters of MCP-PMTs. The experimental setups, the analyses and
selected results are discussed. Although the techniques used may be different
in other locations, the document is intended as a guide for comparable
measurements with other types of MCP-PMTs. Measurements are shown for the
following performance parameters: spectral and spatial quantum efficiency,
collection efficiency, gain as a function of voltage, position and magnetic
field, time resolution, rate capability and lifetime. By using a dedicated
3-axis stepper and an FPGA-based DAQ system, also inner PMT parameters are
measured as a function of the active area, such as relative detection
efficiency, dark count rate, time resolution, recoil electron and afterpulse
distributions, as well as charge sharing and electronic crosstalk. In addition,
some of the parameters are investigated inside a strong magnetic field. For
many of these measurements, the change of most setup parameters and the
subsequent analysis can be controlled semi-automatically by software scripts.


  Generating wind power scenarios is very important for studying the impacts of
multiple wind farms that are interconnected to the grid. We develop a graph
convolutional generative adversarial network (GCGAN) approach by leveraging
GAN's capability in generating large number of realistic scenarios without
using statistical modeling. Unlike existing GAN-based wind power data
generation approaches, we design GAN's hidden layers to match the underlying
spatial and temporal characteristics. We advocate the use of graph filters to
embed the spatial correlation among multiple wind farms, and a one-dimensional
(1D) convolutional layer to represent the temporal feature filters. The
proposed graph and feature filter design significantly reduce the GAN model
complexity, leading to improvements in training efficiency and computation
complexity. Numerical results using real wind power data from Australia
demonstrate that the scenarios generated by the proposed GCGAN exhibit more
realistic spatial and temporal statistics than other GAN-based outputs.


  The recent experiment of Stettenheim, et al. showed that, contrary to
conventional belief, the coupling of a quantum electronic device to its
substrate can have important effects on the noise power spectrum, since the
substrate functions as a mechanical oscillator. We carry out a theoretical
analysis of this coupling in the case of a quantum point contact (QPC). First
we derive the noise power spectrum from the Hamiltonian without making the
Markovian approximation, and obtain numerical results that reproduce the
experimental data. Next we investigate the nature of the coupling. In most
previous analyses, the coupling of an electronic device to a mechanical
oscillator has been modeled as a position coupling. We model it both as a
position coupling and as a momentum coupling and compare the results. We find
that, as long as one includes backaction between position and momentum, the
assumed mode of coupling makes little difference, since the backaction
transmits momentum fluctuations to position fluctuations and vice versa.
Finally, we ask whether the salient features of the model persist in the
Markovian approximation. We find that a Markovian analysis confirms the
QPC-substrate coupling, but underestimates the noise floor and leads to
excessively sharp and narrow noise peaks around the resonant frequencies.


  Traditional molecular string representations, such as SMILES, often pose
challenges for AI-driven molecular design due to their non-sequential depiction
of molecular substructures. To address this issue, we introduce Sequential
Attachment-based Fragment Embedding (SAFE), a novel line notation for chemical
structures. SAFE reimagines SMILES strings as an unordered sequence of
interconnected fragment blocks while maintaining compatibility with existing
SMILES parsers. It streamlines complex generative tasks, including scaffold
decoration, fragment linking, polymer generation, and scaffold hopping, while
facilitating autoregressive generation for fragment-constrained design, thereby
eliminating the need for intricate decoding or graph-based models. We
demonstrate the effectiveness of SAFE by training an 87-million-parameter
GPT2-like model on a dataset containing 1.1 billion SAFE representations.
Through targeted experimentation, we show that our SAFE-GPT model exhibits
versatile and robust optimization performance. SAFE opens up new avenues for
the rapid exploration of chemical space under various constraints, promising
breakthroughs in AI-driven molecular design.


  Topic of the thesis is a theoretical description of the ultracold atomic
gases in one- and two-dimensional optical lattices in the presence of the
disorder leading to the Anderson localization. The disorder is created by
interaction of the main fraction of atoms with the second immobilized fraction
distributed randomly over the lattice.
  In low-dimensional systems there is no transition from the Anderson localized
to the conducting phase, although in the presence of correlations a discrete
set of extended states can exist. The first part of the thesis is devoted to
properties of such states. In the finite size lattices, the presence of those
states results in the appearance of `windows of transport' -- energy ranges, in
which the localization length is longer than the system size.The analytical
method of determining the extended states energies for correlations of
generalized $N$-mers type is presented, along with a proof that indeed those
states are extended in the infinite system. Subsequently, the way of
experimental creation of this type of correlations is proposed, as well as the
technique of generation of the disorder in the tunneling amplitudes, which
significantly enhances tunability of the proposed energy filters.
  The second part of the thesis describes the method which allows to simulate a
specific type of the disorder: random magnetic field. Systems of such a class,
created in a two dimensional lattice using simultaneous fast periodic
modulation of the lattice height and interactions with immobilized species, may
allow in future to investigate the range of topics from the condensed matter
physics, for example fractional quantum Hall effect at half-filling. In the
thesis, the most interesting features observed upon investigation of such
systems are presented. Especially, the anomalously low localization length for
correlated disorder is explained.


  Inspired by scientific collaboration networks, especially our empirical
analysis of the network of econophysicists, an evolutionary model for weighted
networks is proposed. Both degree-driven and weight-driven models are
considered. Compared with the BA model and other evolving models with
preferential attachment, there are two significant generalizations. First,
besides the new vertex added in at every time step, old vertices can also
attempt to build up new links, or to reconnect the existing links. The
reconnection between both new-old and old-old nodes are recorded and the
connecting times on every link is converted into the weight of the link. This
provides a natural way for the evolution of edge weight. Second, besides degree
and the weight of vertices, a path-related local information is also used as a
reference in the preferential attachment. The path-related preferential
attachment mechanism significantly increases the clustering coefficient of the
network. The model shows the scale-free phenomena in degree and weight
distribution. It also gives well qualitatively consistent behavior with the
empirical results.


  We present results of a study of charged particle track and vertex
reconstruction with a beam telescope made of four layers of 50 micron-thin CMOS
monolithic pixel sensors using the 120 GeV protons at the FNAL Meson Test Beam
Facility. We compare our results to the performance requirements of a future
e+e- linear collider in terms of particle track extrapolation and vertex
reconstruction accuracies.


  To test the quantum nature of gravity in a lab requires witnessing the
entanglement between the two test masses (nano-crystals) solely due to the
gravitational interaction kept at a distance in a spatial superposition. The
protocol is known as the quantum gravity-induced entanglement of masses (QGEM).
One of the main backgrounds in the QGEM experiment is electromagnetic (EM)
induced entanglement and decoherence. The EM interactions can entangle the two
neutral masses via dipole-dipole vacuum-induced interactions, such as the
Casimir-Polder interaction. To mitigate the EM-induced interactions between the
two nano-crystals, we enclose the two interferometers in a Faraday cage and
separate them by a conducting plate. However, any imperfection on the surface
of a nano-crystal, such as a permanent dipole moment will also create an EM
background interacting with the conducting plate in the experimental box. These
interactions will further generate EM-induced dephasing which we wish to
mitigate. In this paper, we will consider a parallel configuration of the QGEM
experiment, where we will estimate the EM-induced dephasing rate, run-by-run
systematic errors which will induce dephasing, and also provide constraints on
the size of the superposition in a model-independent way of creating the
spatial superposition.


  In prediction of forest parameters with data from remote sensing (RS),
regression models have traditionally been trained on a small sample of ground
reference data. This paper proposes to impute this sample of true prediction
targets with data from an existing RS-based prediction map that we consider as
pseudo-targets. This substantially increases the amount of target training data
and leverages the use of deep learning (DL) for semi-supervised regression
modelling. We use prediction maps constructed from airborne laser scanning
(ALS) data to provide accurate pseudo-targets and free data from Sentinel-1's
C-band synthetic aperture radar (SAR) as regressors. A modified U-Net
architecture is adapted with a selection of different training objectives. We
demonstrate that when a judicious combination of loss functions is used, the
semi-supervised imputation strategy produces results that surpass traditional
ALS-based regression models, even though \sen data are considered as inferior
for forest monitoring. These results are consistent for experiments on
above-ground biomass prediction in Tanzania and stem volume prediction in
Norway, representing a diversity in parameters and forest types that emphasises
the robustness of the approach.


  The Kadomtsev pinch, namely the Z-pinch profile marginally stable to
interchange modes, is revisited in light of observations from axisymmetric MHD
modeling of the FuZE sheared-flow-stabilized Z-pinch experiment. We show that
Kadomtsev's stability criterion, cleanly derived by the minimum energy
principle but of opaque physical significance, has an intuitive interpretation
in the specific entropy analogous to the Schwarzschild-Ledoux criterion for
convective stability of adiabatic pressure distributions in the fields of
astrophysics, meteorology, and oceanography. By analogy, the Kadomtsev profile
may be described as magnetoadiabatic in the sense that plasma pressure is
polytropically related to area-averaged current density from the ideal MHD
stability condition on the specific entropy. Further, the non-ideal stability
condition of the entropy modes is shown to relate the specific entropy gradient
to the ideal interchange stability function. Hence, the combined activity of
the ideal interchange and non-ideal entropy modes drives both the specific
entropy and specific magnetic flux gradients to zero in the marginally stable
state. The physical properties of Kadomtsev's pinch are reviewed in detail and
following from this the localization of pinch confinement, i.e., pinch size and
inductance, is quantified by the ratio of extensive magnetic and thermal
energies. In addition, results and analysis of axisymmetric MHD modeling of the
FuZE Z-pinch experiment are presented where pinch structure is found to consist
of a near-marginal flowing core surrounded by a super-magnetoadiabatic low-beta
sheared flow.


  We generalize the Wedderburn rank reduction formula by replacing the inverse
with the Moore--Penrose pseudoinverse. In particular, this allows one to remove
the non--singularity of a certain matrix from assumptions. The results implies
in a straightforward way Nystroem, CUR decompositions, meta-factorization, and
a result of Ameli, Shadden. We investigate which properties of the matrix are
inherited by the generalized Wedderburn reduction. Reductions leading to the
best low-rank approximation are explicitly described in terms of singular
vectors. We give a self--contained calculation of the range and the nullspace
of the projection $A(BA)^+B$ and prove that any projection can be expressed in
this way.


  We construct finite- and infinite-dimensional non-relativistic extensions of
the Newton-Hooke and Carroll (A)dS algebras using the algebra expansion method,
starting from the (anti-)de Sitter relativistic algebra in D dimensions. These
algebras are also shown to be embedded in different affine Kac-Moody algebras.
In the three-dimensional case, we construct Chern-Simons actions invariant
under these symmetries. This leads to a sequence of non-relativistic gravity
theories, where the simplest examples correspond to extended Newton-Hooke and
extended (post-)Newtonian gravity together with their Carrollian counterparts.


  Recent advances in artificial intelligence (AI), especially in generative
language modelling, hold the promise of transforming government. Given the
advanced capabilities of new AI systems, it is critical that these are embedded
using standard operational procedures, clear epistemic criteria, and behave in
alignment with the normative expectations of society. Scholars in multiple
domains have subsequently begun to conceptualize the different forms that AI
applications may take, highlighting both their potential benefits and pitfalls.
However, the literature remains fragmented, with researchers in social science
disciplines like public administration and political science, and the
fast-moving fields of AI, ML, and robotics, all developing concepts in relative
isolation. Although there are calls to formalize the emerging study of AI in
government, a balanced account that captures the full depth of theoretical
perspectives needed to understand the consequences of embedding AI into a
public sector context is lacking. Here, we unify efforts across social and
technical disciplines by first conducting an integrative literature review to
identify and cluster 69 key terms that frequently co-occur in the
multidisciplinary study of AI. We then build on the results of this
bibliometric analysis to propose three new multifaceted concepts for
understanding and analysing AI-based systems for government (AI-GOV) in a more
unified way: (1) operational fitness, (2) epistemic alignment, and (3)
normative divergence. Finally, we put these concepts to work by using them as
dimensions in a conceptual typology of AI-GOV and connecting each with emerging
AI technical measurement standards to encourage operationalization, foster
cross-disciplinary dialogue, and stimulate debate among those aiming to rethink
government with AI.


  This paper introduces the front-propagation algorithm, a novel eXplainable AI
(XAI) technique designed to elucidate the decision-making logic of deep neural
networks. Unlike other popular explainability algorithms such as Integrated
Gradients or Shapley Values, the proposed algorithm is able to extract an
accurate and consistent linear function explanation of the network in a single
forward pass of the trained model. This nuance sets apart the time complexity
of the front-propagation as it could be running real-time and in parallel with
deployed models. We packaged this algorithm in a software called
$\texttt{front-prop}$ and we demonstrate its efficacy in providing accurate
linear functions with three different neural network architectures trained on
publicly available benchmark datasets.


  Propensity score weighting is a tool for causal inference to adjust for
measured confounders. Survey data are often collected under complex sampling
designs such as multistage cluster sampling, which presents challenges for
propensity score modeling and estimation. In addition, for clustered data,
there may also be unobserved cluster effects related to both the treatment and
the outcome. When such unmeasured confounders exist and are omitted in the
propensity score model, the subsequent propensity score adjustment will be
biased. We propose a calibrated propensity score weighting adjustment for
multi-stage clustered data in the presence of unmeasured cluster-level
confounders. The propensity score is calibrated to balance design-weighted
covariate distributions and cluster effects between treatment groups. In
particular, we consider a growing number of calibration constraints increasing
with the number of clusters, which is necessary for removing asymptotic bias
that is associated with the unobserved cluster-level confounders. We show that
our estimator is robust in the sense that the estimator is consistent without
correct specification of the propensity score model. We extend the results to
the multiple treatments case. In simulation studies we show that the proposed
estimator is superior to other competitors. We estimate the effect of School
Body Mass Index Screening on prevalence of overweight and obesity for
elementary schools in Pennsylvania.


  Spectral and transport properties of doped (or gated) graphene with long
range charged impurities are discussed within the self-consistent Born
approximation. It is shown how, for impurity concentrations $n_{imp}\gtrsim n$
a finite DOS appears at the Dirac point, the one-particle lifetime no longer
scales linearly with the Fermi momentum, and the lineshapes in the spectral
function become non-lorentzian. These behaviors are different from the results
calculated within the Born approximation. We also calculate the optical
conductivity from the Kubo formula by using the self-consistently calculated
spectral function in the presence of charged impurities.


  Quantum annealing (QA) is a generic method for solving optimization problems
using fictitious quantum fluctuation. The current device performing QA involves
controlling the transverse field; it is classically simulatable by using the
standard technique for mapping the quantum spin systems to the classical ones.
In this sense, the current system for QA is not powerful despite utilizing
quantum fluctuation. Hence, we developed a system with a time-dependent
Hamiltonian consisting of a combination of the formulated Ising model and the
"driver" Hamiltonian with only quantum fluctuation. In the previous study, for
a fully connected spin model, quantum fluctuation can be addressed in a
relatively simple way. We proved that the fully connected antiferromagnetic
interaction can be transformed into a fluctuating transverse field and is thus
classically simulatable at sufficiently low temperatures. Using the fluctuating
transverse field, we established several ways to simulate part of the
nonstoquastic Hamiltonian on classical computers. We formulated a
message-passing algorithm in the present study. This algorithm is capable of
assessing the performance of QA with part of the nonstoquastic Hamiltonian
having a large number of spins. In other words, we developed a different
approach for simulating the nonstoquastic Hamiltonian without using the quantum
Monte Carlo technique. Our results were validated by comparison to the results
obtained by the replica method.


  We present a biased atomic qubit, universally implementable across all atomic
platforms, encoded as a `spin-cat' within ground state Zeeman levels. The key
characteristic of our configuration is the coupling of the ground state spin
manifold of size $F_g \gg 1$ to an excited Zeeman spin manifold of size $F_e =
F_g - 1$ using light. This coupling results in eigenstates of the driven atom
that include exactly two dark states in the ground state manifold, which are
decoupled from light and immune to spontaneous emission from the excited
states. These dark states constitute the `spin-cat', leading to the designation
`dark spin-cat'. We demonstrate that under strong Rabi drive and for large
$F_g$, the `dark spin-cat' is autonomously stabilized against common noise
sources and encodes a qubit with significantly biased noise. Specifically, the
bit-flip error rate decreases exponentially with $F_g$ relative to the
dephasing rate. We provide an analysis of dark spin-cats, their robustness to
noise, and discuss bias-preserving single qubit and entangling gates,
exemplified on a Rydberg tweezer platform.


  Given the Laplacian on a planar, convex domain with piecewise linear boundary
subject to mixed Dirichlet-Neumann boundary conditions, we provide a sufficient
condition for its lowest eigenvalue to dominate the lowest eigenvalue of the
Laplacian with the complementary boundary conditions (i.e. with Dirichlet
replaced by Neumann and vice versa). The application of this result to
triangles gives an affirmative partial answer to a recent conjecture. Moreover,
we prove a further observation of similar flavor for right triangles.


  Speech emotion recognition (SER) often experiences reduced performance due to
background noise. In addition, making a prediction on signals with only
background noise could undermine user trust in the system. In this study, we
propose a Noise Robust Speech Emotion Recognition system, NRSER. NRSER employs
speech enhancement (SE) to effectively reduce the noise in input signals. Then,
the signal-to-noise-ratio (SNR)-level detection structure and waveform
reconstitution strategy are introduced to reduce the negative impact of SE on
speech signals with no or little background noise. Our experimental results
show that NRSER can effectively improve the noise robustness of the SER system,
including preventing the system from making emotion recognition on signals
consisting solely of background noise. Moreover, the proposed SNR-level
detection structure can be used individually for tasks such as data selection.


  We describe, study, and experiment with an algorithm for finding all
solutions of systems of polynomial equations using homotopy continuation and
monodromy. This algorithm follows a framework developed in previous work and
can operate in the presence of a large number of failures of the homotopy
continuation subroutine. We give special attention to parallelization and
probabilistic analysis of a model adapted to parallelization and failures.
Apart from theoretical results, we developed a simulator that allows us to run
a large number of experiments without recomputing the outcomes of the
continuation subroutine.


  We present an analysis of infrared/optical/ultraviolet spectra of the two
images of the first gravitationally lensed quasar Q0957+561A, B. The Hubble
Space Telescope observations of Q0957+561A and Q0957+561B are separated in time
by the known time delay in this system, so we can directly deduce the flux
ratios. These flux ratios of images lead to important information on the dark
halo of the main lens galaxy (a giant elliptical at redshift z = 0.36). Our
measurements for the continuum are in good agreement with extinction in the
elliptical galaxy and a small fraction of mass in collapsed objects (no need
for gravitational microlensing). From the continuum and emission line ratios,
we also show evidence in favour of the existence of a network of compact dusty
clouds.


  We explore the possibility that the Fast Radio Bursts (FRBs) are powered by
magnetic reconnection in magnetars, triggered by Axion Quark Nugget (AQN) dark
matter. In this model, the magnetic reconnection is ignited by the shock wave
which develops when the nuggets' Mach number $M \gg 1$. These shock waves
generate very strong and very short impulses expressed in terms of pressure
$\Delta p/p\sim M^2$ and temperature $\Delta T/T\sim M^2$ in the vicinity of
(would be) magnetic reconnection area. We find that the proposed mechanism
produces a coherent emission which is consistent with current data, in
particular the FRB energy requirements, the observed energy distribution, the
frequency range and the burst duration. Our model allows us to propose
additional tests which future data will be able to challenge.


  Using a formalism that was recently developed in a companion paper, we
rigorously prove the equivalence, in the linear regime, of a number of
apparently different relativistic hydrodynamic theories proposed in the
literature. In particular, we show that Hydro+ is indistinguishable from the
Israel-Stewart theory for bulk viscosity, which in turn is indistinguishable
from a reacting mixture. The two-fluid model for superfluidity coincides with
the Israel-Stewart theory for heat conduction in the limit of infinite
conductivity, and this explains why the latter has a second sound. Also,
MIS$^*$ is equivalent to the Burgers model for viscoelasticity, and this
implies that the former must exhibit an elastic behavior at high frequencies.
Additionally, we show that if the degrees of freedom and the conservation laws
of a hydrodynamic theory have the same geometric character as those of the
Israel-Stewart theory, then such theory must be indistinguishable from the
Israel-Stewart theory in the linear regime. This explains why all second-order
theories turn out to be identical near equilibrium. Finally, we construct the
first linearized model for a relativistic supersolid that is proven to be
causal, stable, and strongly hyperbolic.


  Efficient thermoelectric materials require a rare and contraindicated
combination of materials properties: large electrical conductivity, large
Seebeck coefficient, and low thermal conductivity. One strategy to achieve the
first two properties is via low-energy electronic bands containing both flat
and dispersive parts in different regions of crystal momentum space, known as a
pudding-mold band structure. Here, we illustrate that BaPdS$_2$ successfully
achieves the pudding-mold band structure, contributing to a large
thermoelectric power factor, due to its anisotropic crystal structure
containing zig-zag chains of edge-sharing square planar PdS$_4$ units. In
addition, BaPdS$_2$ exhibits ultralow lattice thermal conductivity, and thus
also achieves the third property, due to extremely soft and anharmonic
interactions in its transverse acoustic phonon branch. We predict a remarkably
large thermoelectric figure of merit, with peak values between 2 and 3 for two
of the three crystallographic directions, suggesting BaPdS$_2$ warrants
experimental investigation.


  We develop a general embedding method based on the Friedman-Pippenger tree
embedding technique (1987) and its algorithmic version, essentially due to
Aggarwal et al. (1996), enhanced with a roll-back idea allowing to sequentially
retrace previously performed embedding steps. We use this method to obtain the
following results.
  -We show that the size-Ramsey number of logarithmically long subdivisions of
bounded degree graphs is linear in their number of vertices, settling a
conjecture of Pak (2002).
  -We give a deterministic, polynomial time online algorithm for finding
vertex-disjoint paths of prescribed length between given pairs of vertices in
an expander graph. Our result answers a question of Alon and Capalbo (2007).
  -We show that relatively weak bounds on the spectral ratio of $d$-regular
graphs force the existence of a topological minor of $K_t$ where $t=(1-o(1))d$.
We also exhibit a construction which shows that the theoretical maximum $t=d+1$
cannot be attained even if $\lambda=O(\sqrt{d})$. This answers a question of
Fountoulakis, K\"uhn and Osthus (2009).


  The freezing mechanism suggested for a fluid composed of hard disks [Huerta
et al., Phys. Rev. E, 2006, 74, 061106] is used here to probe the
fluid-to-solid transition in a hard-dumbbell fluid composed of overlapping hard
disks with a variable length between disk centers. Analyzing the trends in the
shape of second maximum of the radial distribution function of the planar
hard-dumbbell fluid it has been found that the type of transition could be
sensitive to the length of hard-dumbbell molecules. From the ${NpT}$ Monte
Carlo simulations data we show that if a hard-dumbbell length does not exceed
15% of the disk diameter, the fluid-to-solid transition scenario follows the
case of a hard-disk fluid, i.e., the isotropic hard-dumbbell fluid experiences
freezing. However, for a hard-dumbbell length larger than 15% of disk diameter,
there is evidence that fluid-to-solid transition may change to continuous
transition, i.e., such an isotropic hard-dumbbell fluid will avoid freezing.


  We call a log variety (X, D) algebraically hyperbolic if there exists a
positive number e such that 2g(C) - 2 + i(C, D) >= e deg(C) for all curves C on
X, where i(C, D) is the number of the intersections between D and the
normalization of C. Among other things, we proved that (P^2, D) is
algebraically hyperbolic for a very general curve D of degree at least 5. More
specifically, we showed that 2g(C) - 2 + i(C, D) >= (deg(D) - 4) deg C for all
curves C on P^2. For example, fix a very general quintic curve D and then for
any map f: C = P^1 --> P^2, there are at least deg(f) + 2 distinct points on C
that map to points on D by f.


  Suppose $p\geq1$, $w=P[F]$ is a harmonic mapping of the unit disk
$\mathbb{D}$ satisfying $F$ is absolutely continuous and $\dot{F}\in L^p(0,
2\pi)$, where $\dot{F}(e^{it})=\frac{\mathrm{d}}{\mathrm{d}t}F(e^{it})$. In
this paper, we obtain Bergman norm estimates of the partial derivatives for
$w$, i.e., $\|w_z\|_{L^p}$ and $\|\overline{w_{\bar{z}}}\|_{L^p}$, where $1\leq
p<2$. Furthermore, if $w$ is a harmonic quasiregular mapping of $\mathbb{D}$,
then we show that $w_z$ and $\overline{w_{\bar{z}}}$ are in the Hardy space
$H^p$, where $1\leq p\leq\infty$. The corresponding Hardy norm estimates,
$\|w_z\|_{p}$ and $\|\overline{w_{\bar{z}}}\|_{p}$, are also obtained.


  We consider the 1+1 dimensional supersymmetric matrix field theory obtained
from a dimensional reduction of ten dimensional ${\cal N} = 1$ super
Yang-Mills, which is a matrix model candidate for non-perturbative Type IIA
string theory. The gauge group here is U($N$), where $N$ is sent to infinity.
We adopt light-cone coordinates to parametrize the string world sheet, and
choose to work in the light-cone gauge. Quantizing this theory via Discretized
Light-Cone Quantization (DLCQ) introduces an integer, K, which restricts the
light-cone momentum-fraction of constituent quanta to be integer multiples of
1/K. We show how a double scaling limit involving the integers $K$ and $N$
implies the existence of an extra (free) parameter in the Yang-Mills theory,
which plays the role of an effective string coupling constant. The formulation
here provides a natural framework for studying quantitatively string dynamics
and conventional Yang-Mills in a unified setting.


  Bi-presymplectic chains of one-forms of co-rank one are considered. The
conditions in which such chains represent some Liouville integrable systems and
the conditions in which there exist related bi-Hamiltonian chains of vector
fields are derived. To present the construction of bi-presymplectic chains, the
notion of dual Poisson-presymplectic pair is used and the concept of
d-compatibility of Poisson bivectors and d-compatibility of presymplectic forms
is introduced. It is shown that bi-presymplectic representation of related flow
leads directly to the construction of separation coordinates in purely
algorithmic way. As an illustration bi-presymplectic and bi-Hamiltonian chains
in ${\mathbb R}^3$ are considered in detail.


  Designing controllers for systems affected by model uncertainty can prove to
be a challenge, especially when seeking the optimal compromise between the
conflicting goals of identification and control. This trade-off is explicitly
taken into account in the dual control problem, for which the exact solution is
provided by stochastic dynamic programming. Due to its computational
intractability, we propose a sampling-based approximation for systems affected
by both parametric and structural model uncertainty. The approach proposed in
this paper separates the prediction horizon in a dual and an exploitation part.
The dual part is formulated as a scenario tree that actively discriminates
among a set of potential models while learning unknown parameters. In the
exploitation part, achieved information is fixed for each scenario, and
open-loop control sequences are computed for the remainder of the horizon. As a
result, we solve one optimization problem over a collection of control
sequences for the entire horizon, explicitly considering the knowledge gained
in each scenario, leading to a dual model predictive control formulation.


  Relativistic thermodynamics as result of some recent computer simulations is
derived.


  The knowledge of the exact structure of the optical system PSF enables a
high-quality image reconstruction in fluorescence microscopy. Accurate PSF
models account for the vector nature of light and the phase and amplitude
modifications. Most existing real-space-based PSF models fall into a sampling
pitfall near the centre position, yielding to the violation of the energy
conservation. In this work, we present novel, to the best of our knowledge,
Fourier-based techniques for computing vector PSF and compare them to the
state-of-the-art. Our methods are shown to satisfy the physical condition of
the imaging process. They are reproducible, computationally efficient, and easy
to implement and easy to modify to represent various imaging modalities.


  In a 1983 paper the author has established a (decategorified) Satake
equivalence for affine Hecke algebras. In this paper we give new proofs for
some results of that paper, one based on the theory of J-rings and one based on
the known character formula for rational representations of a reductive group
in positive, large, characteristic. We also give an extension of that character
formula to disconnected groups.


  Often, corruption is described as taking place within or supported by a
network: A collection of individuals structured in such a way as to enable the
transaction of bribes for favors. Surprisingly, despite the network
nomenclature, corruption is rarely analyzed from the network perspective using
the tools of network science. Here, we will argue that analyzing corruption
from the perspective of network science is beneficial to its understanding. In
passing this chapter, a contribution to the Liber Amicorum in honor of Leo
Huberts, then gives a very short introduction into social network analysis.


  Extracting latent low-dimensional structure from high-dimensional data is of
paramount importance in timely inference tasks encountered with `Big Data'
analytics. However, increasingly noisy, heterogeneous, and incomplete datasets
as well as the need for {\em real-time} processing of streaming data pose major
challenges to this end. In this context, the present paper permeates benefits
from rank minimization to scalable imputation of missing data, via tracking
low-dimensional subspaces and unraveling latent (possibly multi-way) structure
from \emph{incomplete streaming} data. For low-rank matrix data, a subspace
estimator is proposed based on an exponentially-weighted least-squares
criterion regularized with the nuclear norm. After recasting the non-separable
nuclear norm into a form amenable to online optimization, real-time algorithms
with complementary strengths are developed and their convergence is established
under simplifying technical assumptions. In a stationary setting, the
asymptotic estimates obtained offer the well-documented performance guarantees
of the {\em batch} nuclear-norm regularized estimator. Under the same unifying
framework, a novel online (adaptive) algorithm is developed to obtain multi-way
decompositions of \emph{low-rank tensors} with missing entries, and perform
imputation as a byproduct. Simulated tests with both synthetic as well as real
Internet and cardiac magnetic resonance imagery (MRI) data confirm the efficacy
of the proposed algorithms, and their superior performance relative to
state-of-the-art alternatives.


  In this study, we demonstrate the concept of combining optical combs with
optical vortices for the first time. By combining the advantages of the both
light sources, we realize an optical vortex comb technology for arbitrary
spatiotemporal phase manipulation. This idea corresponds to simultaneous
control of the longitudinal and transverse modes of light based on the high
controllability of the optical comb. As a proof-of-concept experiment, we
applied an optical vortex comb to the generation and rotational control of a
ring-shaped optical lattice. Furthermore, to demonstrate the utility of this
technique, a rotational optical manipulation of microspheres was demonstrated
using the optical ring lattice as an optical tweezer light. Here, we present a
new applicability of the optical comb by utilizing its characteristics far
beyond the conventional range.


  A key measure of performance and comfort in a road traffic network is the
travel time that the users of the network experience to complete their
journeys. Travel times on road traffic networks are stochastic, highly
variable, and dependent on several parameters. It is, therefore, necessary to
have good indicators and measures of their variations. In this article, we
extend a recent approach for the derivation of deterministic bounds on the
travel time in a road traffic network (Farhi, Haj-Salem and Lebacque 2013). The
approach consists in using an algebraic formulation of the cell-transmission
traffic model on a ring road, where the car-dynamics is seen as a linear
min-plus system. The impulse response of the system is derived analytically,
and is interpreted as what is called a service curve in the network calculus
theory (where the road is seen as a server). The basic results of the latter
theory are then used to derive an upper bound for the travel time through the
ring road.
  We consider in this article open systems rather than closed ones. We define a
set of elementary traffic systems and an operator for the concatenation of such
systems. We show that the traffic system of any road itinerary can be built by
concatenating a number of elementary traffic systems. The concatenation of
systems consists in giving a service guarantee of the resulting system in
function of service guarantees of the composed systems. We illustrate this
approach with a numerical example, where we compute an upper bound for the
travel time on a given route in a urban network.


  Foundation vision or vision-language models are trained on large unlabeled or
noisy data and learn robust representations that can achieve impressive zero-
or few-shot performance on diverse tasks. Given these properties, they are a
natural fit for active learning (AL), which aims to maximize labeling
efficiency. However, the full potential of foundation models has not been
explored in the context of AL, specifically in the low-budget regime. In this
work, we evaluate how foundation models influence three critical components of
effective AL, namely, 1) initial labeled pool selection, 2) ensuring diverse
sampling, and 3) the trade-off between representative and uncertainty sampling.
We systematically study how the robust representations of foundation models
(DINOv2, OpenCLIP) challenge existing findings in active learning. Our
observations inform the principled construction of a new simple and elegant AL
strategy that balances uncertainty estimated via dropout with sample diversity.
We extensively test our strategy on many challenging image classification
benchmarks, including natural images as well as out-of-domain biomedical images
that are relatively understudied in the AL literature. We also provide a highly
performant and efficient implementation of modern AL strategies (including our
method) at https://github.com/sanketx/AL-foundation-models.


  We consider non-spherically symmetric perturbations of the uncharged black
string/flat black brane in the large dimension (D) limit of general relativity.
We express the perturbations in a simplified form using variables introduced by
Ishibashi and Kodama. We apply the large D limit to the equations, and show
that this leads to decoupling of the equations in the near-horizon and
asymptotic regions. It also enables use of matched asymptotic expansions to
obtain approximate analytical solutions and to analyze stability of the black
string/brane. For a large class of non-spherically symmetric perturbations, we
prove that there are no instabilities in the large D limit. For the rest, we
provide additional matching arguments that indicate that the black string/brane
is stable. In the \emph{static} limit, we show that for \emph{all}
non-spherically symmetric perturbations, there is no instability. This is proof
that the Gross-Perry-Yaffe mode for semiclassical black hole perturbations is
the unique unstable mode even in the large D limit. This work is also a direct
analytical indication that the only instability of the black string is the
Gregory-Laflamme instability.


  Finding the stability number of a graph, i.e., the maximum number of vertices
of which no two are adjacent, is a well known NP-hard combinatorial
optimization problem. Since this problem has several applications in real life,
there is need to find efficient algorithms to solve this problem. Recently,
Gaar and Rendl enhanced semidefinite programming approaches to tighten the
upper bound given by the Lov\'asz theta function. This is done by carefully
selecting some so-called exact subgraph constraints (ESC) and adding them to
the semidefinite program of computing the Lov\'asz theta function.
  First, we provide two new relaxations that allow to compute the bounds faster
without substantial loss of the quality of the bounds. One of these two
relaxations is based on including violated facets of the polytope representing
the ESCs, the other one adds separating hyperplanes for that polytope.
  Furthermore, we implement a branch and bound (B&B) algorithm using these
tightened relaxations in our bounding routine. We compare the efficiency of our
B&B algorithm using the different upper bounds. It turns out that already the
bounds of Gaar and Rendl drastically reduce the number of nodes to be explored
in the B&B tree as compared to the Lov\'asz theta bound. However, this comes
with a high computational cost. Our new relaxations improve the run time of the
overall B&B algorithm, while keeping the number of nodes in the B&B tree small.


  Algorithmic decidability is established for two order-theoretic properties of
downward closed subsets defined by finitely many obstructions in two infinite
posets. The properties under consideration are: (a) being atomic, i.e. not
being decomposable as a union of two downward closed proper subsets, or,
equivalently, satisfying the joint embedding property; and (b) being well
quasi-ordered. The two posets are: (1) words over a finite alphabet under the
consecutive subword ordering; and (2) finite permutations under the consecutive
subpermutation ordering. Underpinning the four results are characterisations of
atomicity and well quasi-order for the subpath ordering on paths of a finite
directed graph.


  Quantum phase slips are the primary excitations in one-dimensional
superfluids and superconductors at low temperatures. They have been well
characterized in most condensed-matter systems, and signatures of their
existence has been recently observed in superfluids based on quantum gases too.
In this review we briefly summarize the main results obtained on the
investigation of phase slips from superconductors to quantum gases. In
particular we focus our attention on recent experimental results of the
dissipation in one-dimensional Bose superfluids flowing along a shallow
periodic potential, which show signatures of quantum phase slips.


  Functioning is gaining recognition as an important indicator of global
health, but remains under-studied in medical natural language processing
research. We present the first analysis of automatically extracting
descriptions of patient mobility, using a recently-developed dataset of free
text electronic health records. We frame the task as a named entity recognition
(NER) problem, and investigate the applicability of NER techniques to mobility
extraction. As text corpora focused on patient functioning are scarce, we
explore domain adaptation of word embeddings for use in a recurrent neural
network NER system. We find that embeddings trained on a small in-domain corpus
perform nearly as well as those learned from large out-of-domain corpora, and
that domain adaptation techniques yield additional improvements in both
precision and recall. Our analysis identifies several significant challenges in
extracting descriptions of patient mobility, including the length and
complexity of annotated entities and high linguistic variability in mobility
descriptions.


  In this paper we introduce the first results that use data extracted directly
from numerical simulations as inputs to the analytic twisted disk model of
Zhuravlev & Ivanov. In both numerical and analytic approaches, fully
relativistic models of tilted and twisted disks having a moderate effective
viscosity around a slowly rotating Kerr black hole are considered.
Qualitatively, the analytic model demonstrates the same dynamics as the
simulations, although with some quantitative offset. Namely, the GRMHD
simulations generally give smaller variations of tilt and twist across the
disk. When the black hole and the disk rotate in the same sense, the simulated
tilted disk and analytic model show no sign of Bardeen-Petterson alignment,
even in the innermost parts of the disk, where the characteristic time for
relaxation to a quasi-stationary configuration is of the same order as the
computation time. In the opposite case, when the direction of the disk's
rotation is opposite to that of black hole, a partial alignment is observed, in
agreement with previous theoretical estimates. Thus, both fully numerical and
analytic schemes demonstrate that the Bardeen-Petterson effect may not be
possible for the case of prograde rotation provided that disk's effective
viscosity is sufficiently small. This may have implications in modeling of
different astrophysical phenomena, such as disk spectra and jet orientation.


  Screening mammography improves breast cancer outcomes by enabling early
detection and treatment. However, false positive callbacks for additional
imaging from screening exams cause unnecessary procedures, patient anxiety, and
financial burden. This work demonstrates an AI algorithm that reduces false
positives by identifying mammograms not suspicious for breast cancer. We
trained the algorithm to determine the absence of cancer using 123,248 2D
digital mammograms (6,161 cancers) and performed a retrospective study on
14,831 screening exams (1,026 cancers) from 15 US and 3 UK sites. Retrospective
evaluation of the algorithm on the largest of the US sites (11,592 mammograms,
101 cancers) a) left the cancer detection rate unaffected (p=0.02,
non-inferiority margin 0.25 cancers per 1000 exams), b) reduced callbacks for
diagnostic exams by 31.1% compared to standard clinical readings, c) reduced
benign needle biopsies by 7.4%, and d) reduced screening exams requiring
radiologist interpretation by 41.6% in the simulated clinical workflow. This
work lays the foundation for semi-autonomous breast cancer screening systems
that could benefit patients and healthcare systems by reducing false positives,
unnecessary procedures, patient anxiety, and expenses.


  Facial Expression Analysis remains a challenging task due to unexpected
task-irrelevant noise, such as identity, head pose, and background. To address
this issue, this paper proposes a novel framework, called Norface, that is
unified for both Action Unit (AU) analysis and Facial Emotion Recognition (FER)
tasks. Norface consists of a normalization network and a classification
network. First, the carefully designed normalization network struggles to
directly remove the above task-irrelevant noise, by maintaining facial
expression consistency but normalizing all original images to a common identity
with consistent pose, and background. Then, these additional normalized images
are fed into the classification network. Due to consistent identity and other
factors (e.g. head pose, background, etc.), the normalized images enable the
classification network to extract useful expression information more
effectively. Additionally, the classification network incorporates a Mixture of
Experts to refine the latent representation, including handling the input of
facial representations and the output of multiple (AU or emotion) labels.
Extensive experiments validate the carefully designed framework with the
insight of identity normalization. The proposed method outperforms existing
SOTA methods in multiple facial expression analysis tasks, including AU
detection, AU intensity estimation, and FER tasks, as well as their
cross-dataset tasks. For the normalized datasets and code please visit
{https://norface-fea.github.io/}.


  The superfluid--Mott-insulator phase transition of ultracold spin-1 bosons
with ferromagnetic and antiferromagnetic interactions in an optical lattice is
theoretically investigated. Two counterpropagating linearly polarized laser
beams with the angle $\theta$ between the polarization vectors
(lin-$\theta$-lin configuration), driving an $F_g=1$ to $F_e=1$ internal atomic
transition, create the optical lattice and at the same time couple atomic
ground states with magnetic quantum numbers $m=\pm 1$. Due to the coupling the
system can be described as a two-component one. At $\theta=0$ the system has a
continuous isospin symmetry, which can be spontaneously broken, thereby fixing
the number of particles in the atomic components. The phase diagram of the
system and the spectrum of collective excitations, which are density waves and
isospin waves, are worked out. In the case of ferromagnetic interactions, the
superfluid--Mott-insulator phase transition is always second order, but in the
case of antiferromagnetic interactions for some values of system parameters it
is first order and the superfluid and Mott phases can coexist. Varying the
angle $\theta$ one can control the populations of atomic components and
continuously turn on and tune their asymmetry.


  In order to develop provably safe human-in-the-loop systems, accurate and
precise models of human behavior must be developed. In the case of intelligent
vehicles, one can imagine the need for predicting driver behavior to develop
minimally invasive active safety systems or to safely interact with other
vehicles on the road. We present a optimization based method for approximating
the stochastic reachable set for human-in-the-loop systems. This method
identifies the most precise subset of states that a human driven vehicle may
enter, given some dataset of observed trajectories. We phrase this problem as a
mixed integer linear program, which can be solved using branch and bound
methods. The resulting model uncovers the most representative subset that
encapsulates the likely trajectories, up to some probability threshold, by
optimally rejecting outliers in the dataset. This tool provides set predictions
consisting of trajectories observed from the nonlinear dynamics and behaviors
of the human driven car, and can account for modes of behavior, like the driver
state or intent. This allows us to predict driving behavior over long time
horizons with high accuracy. By using this realistic data and flexible
algorithm, a precise and accurate driver model can be developed to capture
likely behaviors. The resulting prediction can be tailored to an individual for
use in semi-autonomous frameworks or generally applied for autonomous planning
in interactive maneuvers.


  We emphasize the difficulties of an experiment that can definitely
discriminate between local realistic hidden variables theories and quantum
mechanics using the Bell CHSH inequalities and a real measurement apparatus. In
particular we analyze some examples in which the noise in real instruments can
alter the experimental results, and the nontrivial problem to find a real "fair
sample" of particles to test the inequalities.


  We present a series of numerical simulations using a shock physics smoothed
particle hydrodynamics (SPH) code, investigating energetic impacts on small
celestial bodies characterised by diverse internal structures, ranging from
weak and homogeneous compositions to rubble-pile structures with varying
boulder volume packing. Our findings reveal that the internal structure of
these rubble-pile bodies significantly influences the impact outcomes.
Specifically, we observe that the same impact energy can either
catastrophically disrupt a target with a low boulder packing (<30 vol%), or
result in the ejection of only a small fraction of material from a target with
the same mass but high boulder packing (>40 vol%). This finding highlights the
pivotal role played by the rubble-pile structure, effectively acting as a bulk
shear strength, which governs the size and behaviour of the resulting impact.
Consequently, understanding and characterising the internal structure of
asteroids will be of paramount importance for any future efforts to deflect or
disrupt an asteroid on a collision course with Earth.


  We study a variant of the variational model for the quasi-static growth of
brittle fractures proposed by Francfort and Marigo. The main feature of our
model is that, in the discrete-time formulation, in each step we do not
consider absolute minimizers of the energy, but, in a sense, we look for local
minimizers which are sufficiently close to the approximate solution obtained in
the previous step. This is done by introducing in the variational problem an
additional term which penalizes the $L^2$-distance between the approximate
solutions at two consecutive times. We study the continuous-time version of
this model, obtained by passing to the limit as the time step tends to zero,
and show that it satisfies (for almost every time) some minimality conditions
which are slightly different from those considered in Francfort and Marigo and
in our previous paper, but are still enough to prove (under suitable regularity
assumptions on the crack path) that the classical Griffith's criterion holds at
the crack tips. We prove also that, if no initial crack is present and if the
data of the problem are sufficiently smooth, no crack will develop in this
model, provided the penalization term is large enough.


  Recompositing channel state information (CSI) from the beamforming feedback
matrix (BFM), which is a compressed version of CSI and can be captured because
of its lack of encryption, is an alternative way of implementing
firmware-agnostic WiFi sensing. In this study, we propose the use of camera
images toward the accuracy enhancement of CSI recomposition from BFM. The key
motivation for this vision-aided CSI recomposition is to draw a first-hand
insight that the BFM does not fully involve spatial information to recomposite
CSI and that this could be compensated by camera images. To leverage the camera
images, we use multimodal deep learning, where the two modalities, i.e., images
and BFMs, are integrated to recomposite the CSI. We conducted experiments using
IEEE 802.11ac devices. The experimental results confirmed that the
recomposition accuracy of the proposed multimodal framework is improved
compared to the single-modal framework only using images or BFMs.


  Dark matter made from non-thermally produced bosons can have very low,
possibly sub-eV masses. Axions and hidden photons are prominent examples of
such "dark" very weakly interacting light (slim) particles (WISPs). A suitable
mechanism for their non-thermal production is the misalignment mechanism. Their
dominant interaction with Standard Model (SM) particles is via photons. In this
note we want to go beyond these standard examples and discuss a wide range of
scalar and pseudo-scalar bosons interacting with SM matter fermions via
derivative interactions. Suitably light candidates arise naturally as
pseudo-Nambu-Goldstone bosons. In particular we are interested in examples,
inspired by familons, whose interactions have a non-trivial flavor structure.


  The most profound effect of disorder on the elastic response of solids is the
nonaffinity of local displacements whereby the atoms (particles, network
junctions) do not simply follow the macroscopic strain, as they do in perfect
crystals, but undergo additional displacements which result in a softening of
response. Whether disorder can produce further effects has been an open and
difficult question due to our poor understanding of nonaffinity. Here we
present a systematic analysis of this problem by allowing both network disorder
and lattice coordination to vary continuously under account of nonaffinity. In
one of its limits, our theory, supported by numerical simulations, shows that
in lattices close to the limit of mechanical stability the elastic response
stiffens proportionally to the degree of disorder. This result has important
implications in a variety of areas: from understanding the glass transition
problem to the mechanics of biological networks such as the cytoskeleton.


  We investigate linear interference effects between a nonlinear plane wave and
bright solitons, which are admitted by pair-transition coupled two-component
Bose-Einstein condensate. We demonstrate the interference effects can induce
several localized waves possessing distinctive wave structures, mainly
including anti-dark soliton, W-shaped soliton, multi-peak soliton, Kuznetsov-Ma
like breather, and multi-peak breather. Especially, the explicit conditions for
them are clarified by a phase diagram based on the linear interference
properties. Furthermore, the interactions between these localized waves are
discussed. The detailed analysis indicate that soliton-soliton interaction
induced phase shift brings the collision between these localized waves be
inelastic for soliton involving collision, and be elastic for breathers. These
characters come from that the profile of solitons depend on relative phase
between bright soliton and plane wave, and the profile of breathers do not
depend on the relative phase. These results would motivate more discussions on
linear interference between other nonlinear waves. Especially, the solitons or
breathers obtained here are not related with modulational instability. The
underlying reasons are discussed in detail.


  We have computed line emission cooling rates for the main cooling species in
models of interstellar molecular clouds. The models are based on numerical
simulations of super-sonic magneto-hydrodynamic (MHD) turbulence. Non-LTE
radiative transfer calculations have been performed to properly account for the
complex density and velocity structures in the MHD simulations. Three models
are used. Two of the models are based on MHD simulations with different
magnetic field strength and the third includes the computation of self-gravity
(in the super-Alfvenic regime of turbulence). The density and velocity fields
in the simulations are determined self-consistently by the dynamics of
super-sonic turbulence. The models are intended to represent molecular clouds
with linear size L~6 pc and mean density <n>~300 cm^-3, with the density
exceeding 10^4 cm^-3 in the densest cores. We present 12CO, 13CO, C18O, O2, OI,
CI and H2O cooling rates in isothermal clouds with kinetic temperatures 10-80K.
Analytical approximations are derived for the cooling rates. The inhomogeneity
of the models reduces photon trapping and enhances the cooling in the densest
parts of the clouds. Compared with earlier models the cooling rates are less
affected by optical depth effects and are therefore higher. The main effects
comes, however, from the density variation since cooling efficiency increases
with density. This is very important for the cooling of the clouds as a whole
since most cooling is provided by gas with density above the average.


  The mass transference principle, discovered by Beresnevich and Velani [Ann
Math (2), 2006], is a landmark result in Diophantine approximation that allows
us to obtain the Hausdorff measure theory of $\limsup$ set. Another important
tool is the notion of large intersection property, introduced and
systematically studied by Falconer [J. Lond. Math. Soc. (2), 1994]. The former
mainly focuses on passing between full (Lebesgue) measure and full Hausdorff
measure statements, while the latter transfers full Hausdorff content statement
to Hausdorff dimension. From this perspective, the proofs of the two results
are quite similar but often treated in different ways.
  In this paper, we establish a general mass transference principle from the
viewpoint of Hausdorff content, aiming to provide a unified proof for the
aforementioned results. More precisely, this principle allows us to transfer
the Hausdorff content bounds of a sequence of open sets $E_n$ to the full
Hausdorff measure statement and large intersection property for $\limsup E_n$.
One of the advantages of our approach is that the verification of the Hausdorff
content bound does not require the construction of Cantor-like subset,
resulting in a much simpler proof. As an application, we provide simpler proofs
for several mass transference principles.


  The universal quantum computation model based on quantum walk by Childs has
opened the door for a new way of studying the limitations and advantages of
quantum computation, as well as for its intermediate-term simulation. In recent
years, the growing interest in noisy intermediate-scale quantum computers
(NISQ) has lead to intense efforts being directed at understanding the
computational advantages of open quantum systems. In this work, we extend the
quantum walk model to open noisy systems in order to provide such a tool for
the study of NISQ computers. Our method does not use explicit purification, and
allows to ignore the environment degrees of freedom and obtain a much more
efficient implementation (linear rather than exponential in the runtime), which
employs no ancillas hence provides direct access to the entanglement properties
of the system. In our scheme, the quantum walk amplitudes represent elements of
the density matrix rather than the wavefunction of a pure state. Despite the
non-trivial manifestation of the normalization requirement in this setting, we
model the application of general unitary gates and nonunitary channels, with an
explicit implementation protocol for channels that are commonly used in noise
models.


  To understand how nonlocal Coulomb interactions affect the phase diagram of
correlated electron materials, we report on a method to approximate a
correlated lattice model with nonlocal interactions by an effective Hubbard
model with on-site interactions U* only. The effective model is defined by the
Peierls-Feynman-Bogoliubov variational principle. We find that the local part
of the interaction U is reduced according to U*=U-V', where V' is a weighted
average of nonlocal interactions. For graphene, silicene and benzene we show
that the nonlocal Coulomb interaction can decrease the effective local
interaction by more than a factor of 2 in a wide doping range.


  Using high-resolution resonant inelastic x-ray scattering (RIXS), we
performed a momentum-resolved study of magnetic excitations in the model
spin-1/2 2D antiferromagnetic insulator Sr_2CuCl_2O_2. We identify both a
single-spin-wave feature and a multi-magnon continuum, and show that the X-ray
polarization can be used to distinguish these two contributions in the
cross-section. The spin-waves display a large (70 meV) dispersion between the
zone-boundary points ($\pi$,0) and ($\pi$/2,$\pi$/2). Employing an extended
$t$-$t'$-$t"$-$U$ one-band Hubbard model, we find significant electronic
hopping beyond nearest-neighbor Cu ions. We conclude that sizeable extended
magnetic interactions are present in \scoc{} and probably important in all
undoped cuprates.


  New analysis methods for the vibrational dynamics from molecular dynamics are
proposed and applied to liquid H$_{2}$O. The internal modes of H$_{2}$O are
amplitude-modulated by Langevin dynamics with the frequency of the H$_{2}$O
libration (~600 cm$^{-1}$) and its first overtone (~1200 cm$^{-1}$). The
carrier signal is frequency-modulated by the variation of the hydrogen bond
strength due to thermal motion and by dephasing collisions. The standard power
spectra of the bond parameters yield broadened normal modes due to a
superposition of several perturbations. Here, the oscillating bond lengths and
angles are demodulated by the spline interpolation of the minima or maxima.
Additionally, a zero-crossing method is described, which yields the spectrum of
the frequency modulated carrier without Fourier transform by directly
converting the oscillation periods.


  Recent attacks on power grids demonstrated the vulnerability of the grids to
cyber and physical attacks. To analyze this vulnerability, we study
cyber-physical attacks that affect both the power grid physical infrastructure
and its underlying Supervisory Control And Data Acquisition (SCADA) system. We
assume that an adversary attacks an area by: (i) disconnecting some lines
within that area, and (ii) obstructing the information (e.g., status of the
lines and voltage measurements) from within the area to reach the control
center. We leverage the algebraic properties of the AC power flows to introduce
the efficient EXPOSE Algorithm for detecting line failures and recovering
voltages inside that attacked area after such an attack. The EXPOSE Algorithm
outperforms the state-of-the-art algorithm for detecting line failures using
partial information under the AC power flow model in terms of scalability and
accuracy. The main advantages of the EXPOSE Algorithm are that its running time
is independent of the size of the grid and number of line failures, and that it
provides accurate information recovery under some conditions on the attacked
area. Moreover, it approximately recovers the information and provides the
confidence of the solution when these conditions do not hold.


  The evolution of social media users' behavior over time complicates
user-level comparison tasks such as verification, classification, clustering,
and ranking. As a result, na\"ive approaches may fail to generalize to new
users or even to future observations of previously known users. In this paper,
we propose a novel procedure to learn a mapping from short episodes of user
activity on social media to a vector space in which the distance between points
captures the similarity of the corresponding users' invariant features. We fit
the model by optimizing a surrogate metric learning objective over a large
corpus of unlabeled social media content. Once learned, the mapping may be
applied to users not seen at training time and enables efficient comparisons of
users in the resulting vector space. We present a comprehensive evaluation to
validate the benefits of the proposed approach using data from Reddit, Twitter,
and Wikipedia.


  We study the effect of backward scatterings in the tunneling at a point
contact between the edges of a second level hierarchical fractional quantum
Hall states. A universal scaling dimension of the tunneling conductance is
obtained only when both of the edge channels propagate in the same direction.
It is shown that the quasiparticle tunneling picture and the electron tunneling
picture give different scaling behaviors of the conductances, which indicates
the existence of a crossover between the two pictures. When the direction of
two edge-channels are opposite, e.g. in the case of MacDonald's edge
construction for the $\nu=2/3$ state, the phase diagram is divided into two
domains giving different temperature dependence of the conductance.


  Non-Gaussian states of light, such as GKP states, are essential resources for
optical continuous-variable quantum computing. The ability to efficiently
produce these states would open up tremendous prospects for quantum
technologies in general and fault-tolerant quantum computing in particular.
This letter demonstrates a versatile method using a quantum memory cavity to
overcome the probabilistic nature of the breeding protocols and generate
non-Gaussian states at high rates with scalability perspectives. The
performances of our experimental setup are illustrated with the generation of
Schr\"odinger cat states of amplitude alpha = 1.63 with a fidelity of more than
60% at a generation rate in the kHz range, which is higher than the state of
the art for such states.


  In this work we have obtained the set of new exact solutions of the Einstein
equations that generalize the known Lemaitre-Tolman-Bondi solution for the
certain case of nonzero pressure under zero spatial curvature. These solutions
are pretending to describe the black hole immersed in the nonstatic
cosmological background and give a possibility to investigate the problems
concerning the effects of the cosmological expansion in gravitationally bounded
systems. They may also be used as a seed models in the problem of structure
formation in the universe at the epoch of matter and radiation decoupling. It
was shown that each of the solutions obtained contains either the
Reissner-Nordstrom or the Schwarzschild black hole in the central region of the
space. It is demonstrated that the approach of the mass function use in solving
the Einstein equations allows clear physical interpretation of the resulting
solutions that is of much benefit to any their further application.


  We study conditions for which the mapping torus of a 6-manifold endowed with
an $SU(3)$-structure is a locally conformal calibrated $G_2$-manifold, that is,
a 7-manifold endowed with a $G_2$-structure $\varphi$ such that $d \varphi = -
\theta \wedge \varphi$ for a closed non-vanishing 1-form $\theta$. Moreover, we
show that if $(M, \varphi)$ is a compact locally conformal calibrated
$G_2$-manifold with $\mathcal{L}_{\theta^{\#}} \varphi =0$, where
${\theta^{\#}}$ is the dual of $\theta$ with respect to the Riemannian metric
$g_{\varphi}$ induced by $\varphi$, then $M$ is a fiber bundle over $S^1$ with
a coupled $SU(3)$-manifold as fiber.


  In this paper, the minimum mean square error (MMSE) channel estimation for
intelligent reflecting surface (IRS) assisted wireless communication systems is
investigated. In the considered setting, each row vector of the equivalent
channel matrix from the base station (BS) to the users is shown to be Bessel
$K$ distributed, and all these row vectors are independent of each other. By
introducing a Gaussian scale mixture model, we obtain a closed-form expression
for the MMSE estimate of the equivalent channel, and determine analytical upper
and lower bounds on the mean square error. Using the central limit theorem, we
conduct an asymptotic analysis of the MMSE estimate, and show that the upper
bound on the mean square error of the MMSE estimate is equal to the asymptotic
mean square error of the MMSE estimation when the number of reflecting elements
at the IRS tends to infinity. Numerical simulations show that the gap between
the upper and lower bounds are very small, and they almost overlap with each
other at medium signal-to-noise ratio (SNR) levels and moderate number of
elements at the IRS.


  We study $L^2$-constraint minimizing problems related to elliptic systems. We
introduce a new rearrangement to show $H^1$-precompactness of any minimizing
sequences. Some strict inequality for the new rearrangement is obtained. It is
a key to exclude the dichotomy of minimizing sequences.


  Recently, Co-based honeycomb magnets have been proposed as promising
candidate materials to host the Kitaev spin liquid state. One of the
front-runners is BaCo$_2$(AsO$_4$)$_2$ (BCAO), where it was suggested that the
exchange processes between Co$^{2+}$ ions via the surrounding edge-sharing
oxygen octahedra could give rise to bond-dependent Kitaev interactions. In this
work, we present and analyze comprehensive inelastic neutron scattering studies
of BCAO with fields in the honeycomb plane. Combining the constraints from the
magnon excitations in the high-field polarized state and the inelastic spin
structure factor measured in zero magnetic field, we examine two leading
theoretical models: the Kitaev-type \JKG model and the \XXZ model. We show that
the existing experimental data can be consistently accounted for by the \XXZ
model but not by the \JKG model, and we discuss the implications of these
results for the realization of a spin liquid phase in BCAO and more generally
for the realization of the Kitaev model in cobaltates.


  We show that the interplay of strong Hubbard interaction $U$ and spin-orbit
coupling $\lambda$ in systems with $d^4$ electronic configuration leads to
several unusual magnetic phases. Most notably, we find that competition between
superexchange and spin-orbit coupling leads to a phase transition from a
non-magnetic state predicted by atomic physics to a novel magnetic state in the
large $U$ limit. We show that the local moment changes dramatically across this
phase transition, challenging the conventional wisdom that local moments are
robust against small perturbations in a Mott insulator. The Hund's coupling
plays an important role in determining the nature of the magnetism. We identify
candidate materials and present predictions for Resonant X-ray Scattering (RXS)
signatures of the unusual magnetism in $d^4$ Mott insulators.


  We analyze the morphology of the Magneto-rotational Instability (MRI) for a
stratified viscous plasma disk configuration in differential rotation, taking
into account the so-called corotation theorem for the background profile. In
order to select the intrinsic Alfv\'enic nature of MRI, we deal with an
incompressible plasma and we adopt a formulation of the local perturbation
analysis based on the use of the magnetic flux function as a dynamical
variable. Our study outlines, as consequence of the corotation condition, a
marked asymmetry of the MRI with respect to the equatorial plane, particularly
evident in a complete damping of the instability over a positive critical
height on the equatorial plane. We also emphasize how such a feature is already
present (although less pronounced) even in the ideal case, restoring a
dependence of the MRI on the stratified morphology of the gravitational field.


  In this work we investigate an inverse problem of recovering a time-dependent
potential in a semilinear subdiffusion model from an integral measurement of
the solution over the domain. The model involves the Djrbashian--Caputo
fractional derivative in time. Theoretically, we prove a novel conditional
Lipschitz stability result, and numerically, we develop an easy-to-implement
fixed point iteration for recovering the unknown coefficient. In addition, we
establish rigorous error bounds on the discrete approximation. These results
are obtained by crucially using smoothing properties of the solution operators
and suitable choice of a weighted $L^p(0,T)$ norm. The efficiency and accuracy
of the scheme are showcased on several numerical experiments in one- and
two-dimensions.


  The low-rank matrix optimization with affine manifold (rank-MOA) aims to
minimize a continuously differentiable function over a low-rank set
intersecting with an affine manifold. This paper is devoted to the optimality
analysis for rank-MOA. As a cornerstone, the intersection rule of the
Fr\'{e}chet normal cone to the feasible set of the rank-MOA is established
under some mild linear independence assumptions. Aided with the resulting
explicit formulae of the underlying normal cone, the so-called F-stationary
point and the \alpha-stationary point of rank-MOA are investigated and the
relationship with local/global minimizers are then revealed in terms of
first-order optimality conditions. Furthermore, the second-order optimality
analysis, including the necessary and the sufficient conditions, is proposed
based on the second-order differentiation information of the model. All these
results will enrich the theory of low-rank matrix optimization and give
potential clues to designing efficient numerical algorithms for seeking low
rank solutions. Meanwhile, two specific applications of the rank-MOA are
discussed to illustrate our proposed optimality analysis.


  We discuss interacting and non-interacting one dimensional atomic systems
trapped in an optical lattice plus a parabolic potential. We show that, in the
tight-binding approximation, the non-interacting problem is exactly solvable in
terms of Mathieu functions. We use the analytic solutions to study the
collective oscillations of ideal bosonic and fermionic ensembles induced by
small displacements of the parabolic potential. We treat the interacting boson
problem by numerical diagonalization of the Bose-Hubbard Hamiltonian. From
analysis of the dependence upon lattice depth of the low-energy excitation
spectrum of the interacting system, we consider the problems of
"fermionization" of a Bose gas, and the superfluid-Mott insulator transition.
The spectrum of the noninteracting system turns out to provide a useful guide
to understanding the collective oscillations of the interacting system,
throughout a large and experimentally relevant parameter regime.


  To go beyond the simple model for the fold as two flexible surfaces or faces
linked by a crease that behaves as an elastic hinge, we carefully shape and
anneal a crease within a polymer sheet and study its mechanical response.
First, we carry out an experimental study that consists on recording both the
shape of the fold in various loading configurations and the associated force
needed to deform it. Then, an elastic model of the fold is built upon a
continuous description of both the faces and the crease as a thin sheet with a
non flat reference configuration. The comparison between the model and
experiments yields the local fold properties and explains the significant
differences we observe between tensile and compression regimes. Furthermore, an
asymptotic study of the fold deformation enables us to determine the local
shape of the crease and identify the origin of its mechanical behaviour.


  Structured illumination has been widely used for optical sectioning and 3D
surface recovery. In a typical implementation, multiple images under
non-uniform pattern illumination are used to recover a single object section.
Axial scanning of the sample or the objective lens is needed for acquiring the
3D volumetric data. Here we demonstrate the use of axially-shifted pattern
illumination (asPI) for virtual volumetric confocal imaging without axial
scanning. In the reported approach, we project illumination patterns at a
tilted angle with respect to the detection optics. As such, the illumination
patterns shift laterally at different z sections and the sample information at
different z-sections can be recovered based on the captured 2D images. We
demonstrate the reported approach for virtual confocal imaging through a
diffusing layer and underwater 3D imaging through diluted milk. We show that we
can acquire the entire confocal volume in ~1s with a throughput of 420
megapixels per second. Our approach may provide new insights for developing
confocal light ranging and detection systems in degraded visual environments.


  We discuss the neutron skins of 48Ca and 208Pb. We review and critically
examine modern predictions and empirical constraints, with special attention to
the different interpretations of the findings from the PREX-II experiment and
the recently reported value of the neutron skin in 48Ca extracted from the CREX
experiment. We argue that, in the spirit of the ab initio philosophy, the path
to understanding the behavior of dense neutron-rich matter must not circumvent
fundamental nuclear forces. Based only on that argument, a thick neutron skin
in 208Pb is highly unlikely.


  This is a brief review of recent theoretical efforts to understand
persistence in nonequilibrium systems. Some of the recent experimental results
are also briefly mentioned. I also discuss recent generalizations of
persistence in various directions and conclude with a summary of open
questions.


  Direct detection experiments search for the interactions of Dark Matter (DM)
particles with nuclei in terrestrial detectors. But if these interactions are
sufficiently strong, DM particles may scatter in the Earth, affecting their
distribution in the lab. We present a new analytic calculation of this
`Earth-scattering' effect in the regime where DM particles scatter at most once
before reaching the detector. We perform the calculation self-consistently,
taking into account not only those particles which are scattered away from the
detector, but also those particles which are deflected towards the detector.
Taking into account a realistic model of the Earth and allowing for a range of
DM-nucleon interactions, we present the EarthShadow code, which we make
publicly available, for calculating the DM velocity distribution after
Earth-scattering. Focusing on low-mass DM, we find that Earth-scattering
reduces the direct detection rate at certain detector locations while
increasing the rate in others. The Earth's rotation induces a daily modulation
in the rate, which we find to be highly sensitive to the detector latitude and
to the form of the DM-nucleon interaction. These distinctive signatures would
allow us to unambiguously detect DM and perhaps even identify its interactions
in regions of the parameter space within the reach of current and future
experiments.


  This paper analyses a model for the intensity of distribution for rays
propagating without absorption in a random medium. The random medium is
modelled as a dynamical map. After $N$ iterations, the intensity is modelled as
a sum $S$ of ${\cal N}$ contributions from different trajectories, each of
which is a product of $N$ independent identically distributed random variables
$x_k$, representing successive focussing or de-focussing events. The number of
ray trajectories reaching a given point is assumed to proliferate
exponentially: ${\cal N}=\Lambda^N$, for some $\Lambda>1$. We investigate the
probability distribution of $S$. We find a phase transition as parameters of
the model are varied. There is a phase where the fluctuations of $S$ are
suppressed as $N\to \infty$, and a phase where the $S$ has large fluctuations,
for which we provide a large deviation analysis.


  Let $\tau$ be a linear map from a unital $C^*$-algebra $\CMcal A$ to a von
Neumann algebra $\mathematical B$ and let $\CMcal C$ be a unital $C^*$-algebra.
A map $T$ from a Hilbert $\CMcal A$-module $E$ to a von Neumann $\CMcal
C$-$\CMcal B$ module $F$ is called a $\tau$-map if $$\langle
T(x),T(y)\rangle=\tau(\langle x, y\rangle)~\mbox{for all}~x,y\in E.$$ A
Stinespring type theorem for $\tau$-maps and its covariant version are obtained
when $\tau$ is completely positive. We show that there is a bijective
correspondence between the set of all $\tau$-maps from $E$ to $F$ which are
$(u',u)$-covariant with respect to a dynamical system $(G,\eta,E)$ and the set
of all $(u',u)$-covariant $\widetilde{\tau}$-maps from the crossed product
$E\times_{\eta} G$ to $F$, where $\tau$ and $\widetilde{\tau}$ are completely
positive.


  Purpose: This study evaluates the effectiveness and impact of automated
order-based protocol assignment for magnetic resonance imaging (MRI) exams
using natural language processing (NLP) and deep learning (DL).
  Methods: NLP tools were applied to retrospectively process orders from over
116,000 MRI exams with 200 unique sub-specialized protocols ("Local" protocol
class). Separate DL models were trained on 70\% of the processed data for
"Local" protocols as well as 93 American College of Radiology ("ACR") protocols
and 48 "General" protocols. The DL Models were assessed in an "auto-protocoling
(AP)" inference mode which returns the top recommendation and in a "clinical
decision support (CDS)" inference mode which returns up to 10 protocols for
radiologist review. The accuracy of each protocol recommendation was computed
and analyzed based on the difference between the normalized output score of the
corresponding neural net for the top two recommendations.
  Results: The top predicted protocol in AP mode was correct for 82.8%, 73.8%,
and 69.3% of the test cases for "General", "ACR", and "Local" protocol classes,
respectively. Higher levels of accuracy over 96% were obtained for all protocol
classes in CDS mode. However, at current validation performance levels, the
proposed models offer modest, positive, financial impact on large-scale imaging
networks.
  Conclusions: DL-based protocol automation is feasible and can be tuned to
route substantial fractions of exams for auto-protocoling, with higher accuracy
with more general protocols. Economic analyses of the tested algorithms
indicate that improved algorithm performance is required to yield a practical
exam auto-protocoling tool for sub-specialized imaging exams.


  An experimental study on how reconstructed image signal and noise scale with
acquisition and reconstruction parameters is proposed. Monte-carlo simulation
is performed to emphasize that the measured noise is shot-noise.


  We study the Thermodynamic Bethe Ansatz (TBA) equations for pure $T\bar{T}$
perturbations of some simple integrable quantum field theories with a single
bosonic or fermionic particle, in particular the massive sinh-Gordon model and
its ultraviolet (UV) limit which is a deformation of the conformally invariant
free massless boson. Whereas the TBA equations for $T\bar{T}$ deformations of
massive theories are in principle known, the TBA equations we propose for the
deformations of conformal field theories (CFT's) are relatively new and require
a special factorization in rapidity variables of the CDD factor for the
scattering of the massless particles. The latter TBA equations can be solved
exactly and reproduce the known results for the ground state energy on a
cylinder of circumference $R$ which were previously obtained using different
methods based for instance on the Burgers differential equation. Special
attention is paid to the c-theorem in this context which is discussed in some
detail. For positive infra-red (IR) central charge $c_{IR}$, for flows
consistent with the c-theorem the ground state energy develops a (previously
known) square-root singularity towards the UV, which strongly suggests the
theories are UV incomplete in these physically important cases. We suggest that
the singularity indicates a tachyonic vacuum instability. Other cases with
$c_{IR} < 0$ do not have this singularity and are interpreted as being UV
complete with $c_{UV} = 0$. We extend our results to a continuously variable
$c_{IR}$ by introducing a chemical potential and suggest this as a possible toy
model for the $T\bar{T}$ perturbed Liouville theory.


  We demonstrate a three-dimensional Kosterlitz-Thouless (KT) transition in the
random field XY model driven out of thermal equilibrium. By employing the
spin-wave approximation and functional renormalization group approach, in the
weak disorder regime, the three-dimensional driven random field XY model is
found to exhibit a quasi-long-range order phase, wherein the correlation
function shows power-law decay with a non-universal exponent that depends on
the disorder strength. This result is consistent with that reported in a
previous numerical study. We further develop a phenomenological theory of the
three-dimensional KT transition by taking into account the effect of vortices.
The point of this theory is that the cross-section of the system with respect
to a plane perpendicular to the driving direction is essentially identical to
the two-dimensional pure XY model.


  Motivated by recent experimental findings in chemical synthesis of colloidal
particles, we draw an analogy between self-assembly processes occurring in
biological systems (e.g. protein folding) and a new exciting possibility in the
field of material science. We consider a self-assembly process whose elementary
building blocks are decorated patchy colloids of various types, that
spontaneously drive the system toward a unique and predetermined targeted
macroscopic structure.
  To this aim, we discuss a simple theoretical model -- the Kern-Frenkel model
-- describing a fluid of colloidal spherical particles with a pre-defined
number and distribution of solvophobic and solvophilic regions on their
surface. The solvophobic and solvophilic regions are described via a
short-range square-well and a hard-sphere potentials, respectively.
  Integral equation and perturbation theories are presented to discuss
structural and thermodynamical properties, with particular emphasis on the
computation of the fluid-fluid (or gas-liquid) transition in the
temperature-density plane.
  The model allows the description of both one and two attractive caps, as a
function of the fraction of covered attractive surface, thus interpolating
between a square-well and a hard-sphere fluid, upon changing the coverage.
  By comparison with Monte Carlo simulations, we assess the pros and the cons
of both integral equation and perturbation theories in the present context of
patchy colloids, where the computational effort for numerical simulations is
rather demanding.


  Deep neural networks (DNNs) are vulnerable to backdoor attacks, where
adversaries can maliciously trigger model misclassifications by implanting a
hidden backdoor during model training. This paper proposes a simple yet
effective input-level backdoor detection (dubbed IBD-PSC) as a `firewall' to
filter out malicious testing images. Our method is motivated by an intriguing
phenomenon, i.e., parameter-oriented scaling consistency (PSC), where the
prediction confidences of poisoned samples are significantly more consistent
than those of benign ones when amplifying model parameters. In particular, we
provide theoretical analysis to safeguard the foundations of the PSC
phenomenon. We also design an adaptive method to select BN layers to scale up
for effective detection. Extensive experiments are conducted on benchmark
datasets, verifying the effectiveness and efficiency of our IBD-PSC method and
its resistance to adaptive attacks. Codes are available at
\href{https://github.com/THUYimingLi/BackdoorBox}{BackdoorBox}.


  We analyze the molecular H$_2$ emission and the stellar kinematics in a data
cube of the nuclear region of M104, the Sombrero galaxy, obtained with NIFS on
the Gemini-north telescope. After a careful subtraction of the stellar
continuum, the only emission line we detected in the data cube was H$_2 \lambda
21218$. An analysis of this emission revealed the existence of a rotating
molecular torus/disk, aproximately co-planar with a dusty structure detected by
us in a previous work. We interpret these two structures as being associated
with the same obscuring torus/disk. The kinematic maps provided by the
Penalized Pixel Fitting method revealed that the stellar kinematics in the
nuclear region of M104 appears to be the result of the superposition of a
"cold" rotating disk and a "hot" bulge. Using a model of a thin eccentric disk,
we reproduced the main properties of the maps of the stellar radial velocity
and of the stellar velocity dispersion, specially within a distance of 0.2"
from the kinematic axis (in regions at larger distances, the limitations of a
model of a thin rotating disk become more visible). The general behavior of the
$h_3$ map, which is significantly noisier than the other maps, was also
reproduced by our model (although the discrepancies, in this case, are
considerably higher). With our model, we obtained a mass of (9.0 +/- 2.0) x
10^8 Mo for the supermassive black hole of M104, which is compatible, at
$1\sigma$ or $2\sigma$ levels, with the values obtained by previous studies.


  The state-of-the-art deep neural networks are vulnerable to common
corruptions (e.g., input data degradations, distortions, and disturbances
caused by weather changes, system error, and processing). While much progress
has been made in analyzing and improving the robustness of models in image
understanding, the robustness in video understanding is largely unexplored. In
this paper, we establish a corruption robustness benchmark, Mini Kinetics-C and
Mini SSV2-C, which considers temporal corruptions beyond spatial corruptions in
images. We make the first attempt to conduct an exhaustive study on the
corruption robustness of established CNN-based and Transformer-based
spatial-temporal models. The study provides some guidance on robust model
design and training: Transformer-based model performs better than CNN-based
models on corruption robustness; the generalization ability of spatial-temporal
models implies robustness against temporal corruptions; model corruption
robustness (especially robustness in the temporal domain) enhances with
computational cost and model capacity, which may contradict the current trend
of improving the computational efficiency of models. Moreover, we find the
robustness intervention for image-related tasks (e.g., training models with
noise) may not work for spatial-temporal models.


  Although data may be abundant, complete data is less so, due to missing
columns or rows. This missingness undermines the performance of downstream data
products that either omit incomplete cases or create derived completed data for
subsequent processing. Appropriately managing missing data is required in order
to fully exploit and correctly use data. We propose a Multiple Imputation model
using Denoising Autoencoders to learn the internal representation of data.
Furthermore, we use the novel mechanisms of Metamorphic Truth and Imputation
Feedback to maintain statistical integrity of attributes and eliminate bias in
the learning process. Our approach explores the effects of imputation on
various missingness mechanisms and patterns of missing data, outperforming
other methods in many standard test cases.