  Over the past few decades, underwater image enhancement has attracted
increasing amount of research effort due to its significance in underwater
robotics and ocean engineering. Research has evolved from implementing
physics-based solutions to using very deep CNNs and GANs. However, these
state-of-art algorithms are computationally expensive and memory intensive.
This hinders their deployment on portable devices for underwater exploration
tasks. These models are trained on either synthetic or limited real world
datasets making them less practical in real-world scenarios. In this paper we
propose a shallow neural network architecture, \textbf{Shallow-UWnet} which
maintains performance and has fewer parameters than the state-of-art models. We
also demonstrated the generalization of our model by benchmarking its
performance on combination of synthetic and real-world datasets.


  We give a survey of the theory of finite quantum groupoids (weak Hopf
algebras), including foundations of the theory and applications to finite depth
subfactors, dynamical deformations of quantum groups, and invariants of knots
and 3-manifolds.


  Various possiblities for a distributed magnetometer network are considered.
We discuss strategies such as croudsourcing smartphone magnetometer data, the
use of trees as magnetometers, and performing interferometry using magnetometer
arrays to synthesize the magnetometers into a large-scale low-frequency radio
telescope. Geophysical and other applications of such a network are discussed.


  It is known that the frame flow on a closed $n$-dimensional Riemannian
manifold with negative sectional curvature is ergodic if $n$ is odd and $n \neq
7$. In this paper we study its ergodicity for $n \geq 4$ even and $n = 7$, and
we show that: if $n \equiv 2$ mod $4$, or $n=4$, the frame flow is ergodic if
the manifold is $\sim 0.3$-pinched, if $n \equiv 0$ mod $4$, it is ergodic if
the manifold is $\sim 0.6$-pinched, except in the three dimensions $n=7,8,134$,
where the respective pinching conditions are $0.4962...$, $0.6212...$, and
$0.5788...$. In particular, if $n = 4$ or $n \equiv 2$ mod $4$, this almost
solves a long-standing conjecture of Brin asserting that $1/4$-pinched
even-dimensional manifolds have an ergodic frame flow.


  It has been recently shown that there is a particular combination of
conformal invariants in six dimensions which accepts a generic Einstein space
as a solution. The Lagrangian of this Conformal Gravity theory -- originally
found by Lu, Pang and Pope (LPP) -- can be conveniently rewritten in terms of
products and covariant derivatives of the Weyl tensor. This allows one to
derive the corresponding Noether prepotential and Noether-Wald charges in a
compact form. Based on this expression, we calculate the Noether-Wald charges
of six-dimensional Critical Gravity at the bicritical point, which is defined
by the difference of the actions for Einstein-AdS gravity and the LPP Conformal
Gravity. When considering Einstein manifolds, we show the vanishing of the
Noether prepotential of Critical Gravity explicitly, which implies the
triviality of the Noether-Wald charges. This result shows the equivalence
between Einstein-AdS gravity and Conformal Gravity within its Einstein sector
not only at the level of the action but also at the level of the charges.


  Recently, a number of competitive methods have tackled unsupervised
representation learning by maximising the mutual information between the
representations produced from augmentations. The resulting representations are
then invariant to stochastic augmentation strategies, and can be used for
downstream tasks such as clustering or classification. Yet data augmentations
preserve many properties of an image and so there is potential for a suboptimal
choice of representation that relies on matching easy-to-find features in the
data. We demonstrate that greedy or local methods of maximising mutual
information (such as stochastic gradient optimisation) discover local optima of
the mutual information criterion; the resulting representations are also
less-ideally suited to complex downstream tasks. Earlier work has not
specifically identified or addressed this issue. We introduce deep hierarchical
object grouping (DHOG) that computes a number of distinct discrete
representations of images in a hierarchical order, eventually generating
representations that better optimise the mutual information objective. We also
find that these representations align better with the downstream task of
grouping into underlying object classes. We tested DHOG on unsupervised
clustering, which is a natural downstream test as the target representation is
a discrete labelling of the data. We achieved new state-of-the-art results on
the three main benchmarks without any prefiltering or Sobel-edge detection that
proved necessary for many previous methods to work. We obtain accuracy
improvements of: 4.3% on CIFAR-10, 1.5% on CIFAR-100-20, and 7.2% on SVHN.


  AgInSe2 nanorods (NRs) with diameter of 15 nm have been investigated for
their nonlinear optical responses by using Z-scan and transient absorption
techniques with femtosecond laser pulses of photon energy greater than the
bandgap. At excitation irradiance of 20 GW/cm2, AgInSe2 NRs reveal saturation
in the nonlinear absorption and optical Kerr nonlinearity with a recovery time
determined to be a few ten picoseconds. Such large saturable absorption and
Kerr nonlinearity exhibit a third-order susceptibility of 1.2 x 10-8 esu and a
figure of merit of 0.04 esu.cm.s-1, making AgInSe2 NRs a promising candidate
for saturable absorption devices.


  Many online comments on social media platforms are hateful, humorous, or
sarcastic. The sarcastic nature of these comments (especially the short ones)
alters their actual implied sentiments, which leads to misinterpretations by
the existing sentiment analysis models. A lot of research has already been done
to detect sarcasm in the text using user-based, topical, and conversational
information but not much work has been done to use inter-sentence contextual
information for detecting the same. This paper proposes a new state-of-the-art
deep learning architecture that uses a novel Bidirectional Inter-Sentence
Contextual Attention mechanism (Bi-ISCA) to capture inter-sentence dependencies
for detecting sarcasm in the user-generated short text using only the
conversational context. The proposed deep learning model demonstrates the
capability to capture explicit, implicit, and contextual incongruous words &
phrases responsible for invoking sarcasm. Bi-ISCA generates state-of-the-art
results on two widely used benchmark datasets for the sarcasm detection task
(Reddit and Twitter). To the best of our knowledge, none of the existing
state-of-the-art models use an inter-sentence contextual attention mechanism to
detect sarcasm in the user-generated short text using only conversational
context.


  Several interacting models of chiral bosons and gauge fields are investigated
on the noncommutative extended Minkowski spacetime which was recently proposed
from a new point of view of disposing noncommutativity. The models include the
bosonized chiral Schwinger model, the generalized chiral Schwinger model (GCSM)
and its gauge invariant formulation. We establish the Lagrangian theories of
the models, and then derive the Hamilton's equations in accordance with the
Dirac's method and solve the equations of motion, and further analyze the
self-duality of the Lagrangian theories in terms of the parent action approach.


  The hypothesis of the relation between the observed alignment of spots in the
X-ray films in cosmic ray emulsion experiments and the selection procedure of
the highest-energy particles itself together with the transverse momentum
conservation is tested in the framework of the HYDJET++ model. It is shown that
the high degree of alignment can appear at the reasonable values of transverse
momentum disbalance of selected most energetic particles.


  Order statistics of periodic, Gaussian noise with 1/f^{\alpha} power spectrum
is investigated. Using simulations and phenomenological arguments, we find
three scaling regimes for the average gap d_k=<x_k-x_{k+1}> between the k-th
and (k+1)-st largest values of the signal. The result d_k ~ 1/k known for
independent, identically distributed variables remains valid for 0<\alpha<1.
Nontrivial, \alpha-dependent scaling exponents d_k ~ k^{(\alpha -3)/2} emerge
for 1<\alpha<5 and, finally, \alpha-independent scaling, d_k ~ k is obtained
for \alpha>5. The spectra of average ordered values \epsilon_k=<x_1-x_k> ~
k^{\beta} is also examined. The exponent {\beta} is derived from the gap
scaling as well as by relating \epsilon_k to the density of near extreme
states. Known results for the density of near extreme states combined with
scaling suggest that \beta(\alpha=2)=1/2, \beta(4)=3/2, and beta(infinity)=2
are exact values. We also show that parallels can be drawn between \epsilon_k
and the quantum mechanical spectra of a particle in power-law potentials.


  Given a separable, AF-algebra A and an inductive limit action on A of a
finitely generated abelian group with finite Rokhlin dimension with commuting
towers, we give a local description of the associated crossed product
C*-algebra. In particular, when A is unital and $\alpha \in Aut(A)$ is
approximately inner and has the Rokhlin property, we conclude that $A
\rtimes_{\alpha} \mathbb{Z}$ is an A$\mathbb{T}$-algebra.


  In a previous paper we have presented a new method for solving a class of
Cauchy integral equations. In this work we discuss in detail how to manage this
method numerically, when only a finite and noisy data set is available:
particular attention is focused on the question of the numerical stability.


  We present the rest-frame UV and optical photometry and morphology of
low-redshift broad-line quasar host galaxies from the Sloan Digital Sky Survey
Reverberation Mapping project. Our sample consists of 103 quasars at $z<0.8$,
spanning a luminosity range of $-25\le M_g\le -17$ mag. We stack the
multi-epoch images in the $g$ and $i$ bands taken by the Canada-France-Hawaii
Telescope. The combined $g$-band ($i$-band) images reach a $5\sigma$ depth of
26.2 (25.2) mag, with a typical PSF size of $0.7"$ ($0.6"$). Each quasar is
decomposed into a PSF and a S\'ersic profile, representing the central AGN and
the host galaxy components, respectively. The systematic errors of the measured
host galaxy flux in the two bands are 0.23 and 0.18 mag. The relative errors of
the measured galaxy half-light radii ($R_e$) are about 13%. We estimate the
rest-frame $u$- and $g$-band flux of the host galaxies, and find that the
AGN-to-galaxy flux ratios in the $g$ band are between 0.9 to 4.4 (68.3%
confidence). These galaxies have high stellar masses $M_\ast =
10^{10}\sim10^{11}\, M_\odot$. They have similar color with star-forming
galaxies at similar redshifts, in consistent with AGN positive feedback in
these quasars. We find that the $M_*-M_\text{BH}$ relation in our sample is
shallower than the local $M_\text{Bulge}-M_\text{BH}$ relation. The S\'ersic
indices and the $M_*-R_e$ relation indicate that the majority of the host
galaxies are disk-like.


  Recently, integrating visual controls into text-to-image~(T2I) models, such
as ControlNet method, has received significant attention for finer control
capabilities. While various training-free methods make efforts to enhance
prompt following in T2I models, the issue with visual control is still rarely
studied, especially in the scenario that visual controls are misaligned with
text prompts. In this paper, we address the challenge of ``Prompt Following
With Visual Control" and propose a training-free approach named Mask-guided
Prompt Following (MGPF). Object masks are introduced to distinct aligned and
misaligned parts of visual controls and prompts. Meanwhile, a network, dubbed
as Masked ControlNet, is designed to utilize these object masks for object
generation in the misaligned visual control region. Further, to improve
attribute matching, a simple yet efficient loss is designed to align the
attention maps of attributes with object regions constrained by ControlNet and
object masks. The efficacy and superiority of MGPF are validated through
comprehensive quantitative and qualitative experiments.


  Recent lattice data indicates that volume occupied by topological fermionic
modes shrinks to zero in the continuum limit of vanishing lattice spacing. The
data apparently cannot be accommodated within, say, conventional instanton
model. We review field-theoretic arguments which demonstrate that the
topological fermionic modes are to shrink to a vanishing submanifold of the
whole four dimensional space provided that measurements are performed with high
resolution. Moreover, the data fit well the emerging overall picture of
lower-dimensional defects in the Euclidean vacuum of Yang-Mills theories. We
also mention results on localization of scalar particles.


  We prove that for any $t\ge 3$ there exist constants $c>0$ and $n_0$ such
that any $d$-regular $n$-vertex graph $G$ with $t\mid n\geq n_0$ and second
largest eigenvalue in absolute value $\lambda$ satisfying $\lambda\le c
d^{t}/n^{t-1}$ contains a $K_t$-factor, that is, vertex-disjoint copies of
$K_t$ covering every vertex of $G$.


  Quantum simulation, the simulation of quantum processes on quantum computers,
suggests a path forward for the efficient simulation of problems in
condensed-matter physics, quantum chemistry, and materials science. While the
majority of quantum simulation algorithms are deterministic, a recent surge of
ideas has shown that randomization can greatly benefit algorithmic performance.
In this work, we introduce a scheme for quantum simulation that unites the
advantages of randomized compiling on the one hand and higher-order
multi-product formulas, as they are used for example in
linear-combination-of-unitaries (LCU) algorithms or quantum error mitigation,
on the other hand. In doing so, we propose a framework of randomized sampling
that is expected to be useful for programmable quantum simulators and present
two new multi-product formula algorithms tailored to it. Our framework reduces
the circuit depth by circumventing the need for oblivious amplitude
amplification required by the implementation of multi-product formulas using
standard LCU methods, rendering it especially useful for early quantum
computers used to estimate the dynamics of quantum systems instead of
performing full-fledged quantum phase estimation. Our algorithms achieve a
simulation error that shrinks exponentially with the circuit depth. To
corroborate their functioning, we prove rigorous performance bounds as well as
the concentration of the randomized sampling procedure. We demonstrate the
functioning of the approach for several physically meaningful examples of
Hamiltonians, including fermionic systems and the Sachdev-Ye-Kitaev model, for
which the method provides a favorable scaling in the effort.


  Safety-critical applications such as autonomous vehicles and social robots
require fast computation and accurate probability density estimation on
trajectory prediction. To address both requirements, this paper presents a new
normalizing flow-based trajectory prediction model named FlowChain. FlowChain
is a stack of conditional continuously-indexed flows (CIFs) that are expressive
and allow analytical probability density computation. This analytical
computation is faster than the generative models that need additional
approximations such as kernel density estimation. Moreover, FlowChain is more
accurate than the Gaussian mixture-based models due to fewer assumptions on the
estimated density. FlowChain also allows a rapid update of estimated
probability densities. This update is achieved by adopting the \textit{newest
observed position} and reusing the flow transformations and its
log-det-jacobians that represent the \textit{motion trend}. This update is
completed in less than one millisecond because this reuse greatly omits the
computational cost. Experimental results showed our FlowChain achieved
state-of-the-art trajectory prediction accuracy compared to previous methods.
Furthermore, our FlowChain demonstrated superiority in the accuracy and speed
of density estimation. Our code is available at
\url{https://github.com/meaten/FlowChain-ICCV2023}


  The effect of the quantum feedback on the tightness of the variance-based
uncertainty, the possibility of using quantum feedback to prepare the state
with a better tightness, and the relationship between the tightness of the
uncertainty and the mixedness of the system are studied. It is found that the
tightness of Schrodinger-Robertson uncertainty (SUR) relation has a strict
liner relationship with the mixedness of the system. As for the Robertson
uncertainty relation (RUR), we find that the tightness can be enhanced by
tuning the feedback at the beginning of the evolution. In addition, we deduce
that the tightness of RUR has an inverse relationship with the mixedness and
the relationship turns into a strict linear one when the system reach the
steady state.


  We consider the one-loop effective potential at zero and finite temperature
in scalar field theories with anisotropic space-time scaling. For $z=2$, there
is a symmetry breaking term induced at one-loop at zero temperature and we find
symmetry restoration through a first-order phase transition at high
temperature. For $z=3$, we considered at first the case with a positive mass
term at tree level and found no symmetry breaking effects induced at one-loop,
and then we study the case with a negative mass term at tree level where we
cannot conclude about symmetry restoration effects at high temperature because
of the imaginary parts that appear in the effective potential for small values
of the scalar field.


  Applying thermal renormalization group (TRG) equations to $\phi^4$ theory
with spontaneous breaking symmetry, we investigate the critical behavior of the
damping rate for the plasmons with finite momentum at the symmetry-restoring
phase transition. From the TRG equation the IR cutoff provided by the external
momentum leads to that the momentum-dependent coupling constant stops running
in the critical region. As the result, the critical slowing down phenomenon
reflecting the inherently IR effect doesn't take place at the critical point
for the plasmon with finite external momentum.


  We present a simple derivation of the Hellmann-Feynman theorem at finite
temperature. We illustrate its validity by considering three relevant examples
which can be used in quantum mechanics lectures: the one-dimensional harmonic
oscillator, the one-dimensional Ising model and the Lipkin model. We show that
the Hellmann-Feynman theorem allows one to calculate expectation values of
operators that appear in the Hamiltonian. This is particularly useful when the
total free-energy is available, but there is not direct access to the thermal
average of the operators themselves.


  We calculate the time evolution of the $X(3872)$ abundance in the hot hadron
gas produced in the late stage of heavy ion collisions. We use effective field
Lagrangians to obtain the production and dissociation cross sections of
$X(3872)$. In this evaluation we include diagrams involving the anomalous
couplings $\pi D^*\bar{D}^*$ and $X \bar{D}^{\ast} D^{\ast}$ and also the
couplings of the $X(3872)$ with charged $D$ and $D^*$ mesons. With these new
terms the $X(3872)$ interaction cross sections are much larger than those found
in previous works. Using these cross sections as input in rate equations, we
conclude that during the expansion and cooling of the hadronic gas, the number
of $X(3872)$, originally produced at the end of the mixed QGP/hadron gas phase,
is reduced by a factor of 4.


  The Tip of the Red Giant (TRGB) method provides one of the most accurate and
precise means of measuring the distances to nearby galaxies. Here we present a
VIJHK absolute calibration of the TRGB based on observations of TRGB stars in
the Large Magellanic Cloud (LMC),grounded on detached eclipsing binaries
(DEBs). This paper presents a more detailed description of the method first
presented in Freedman et al. (2019) for measuring corrections for the total
line-of-sight extinction and reddening to the LMC. In this method, we use a
differential comparison of the red giant population in the LMC, first with red
giants in the Local Group galaxy, IC 1613, and then with those in the Small
Magellanic Cloud. As a consistency check, we derive an independent calibration
of the TRGB sequence using the SMC alone, invoking its geometric distance also
calibrated by DEBs. An additional consistency check comes from near-infrared
observations of Galactic globular clusters covering a wide range of
metallicities. In all cases we find excellent agreement in the zero-point
calibration. We then examine the recent claims by Yuan et al. (2019),
demonstrating that, in the case of the SMC, they corrected for extinction alone
while neglecting the essential correction for reddening as well. In the case of
IC 1613, we show that their analysis contains an incorrect treatment of
(over-correction for) metallicity. Using our revised (and direct) measurement
of the LMC TRGB extinction, we find a value of Ho = 69.6 +/-0.8 (+/-1.1% stat)
+/- 1.7 (+/-2.4% sys) km/s/Mpc.


  We present a new upper limit on the energy that may be extracted from a Kerr
black hole by means of particle collisions in the ergosphere (i.e., the
"collisional Penrose process"). Earlier work on this subject has focused
largely on particles with critical values of angular momentum falling into an
extremal Kerr black hole from infinity and colliding just outside the horizon.
While these collisions are able to reach arbitrarily high center-of-mass
energies, it is very difficult for the reaction products to escape back to
infinity, effectively limiting the peak efficiency of such a process to roughly
$130\%$. When we allow one of the initial particles to have impact parameter $b
> 2M$, and thus not get captured by the horizon, it is able to collide along
outgoing trajectories, greatly increasing the chance that the products can
escape. For equal-mass particles annihilating to photons, we find a greatly
increased peak energy of $E_{\rm out} \approx 6\times E_{\rm in}$. For Compton
scattering, the efficiency can go even higher, with $E_{\rm out} \approx
14\times E_{\rm in}$, and for repeated scattering events, photons can both be
produced {\it and} escape to infinity with Planck-scale energies.


  We consider general Gaussian latent tree models in which the observed
variables are not restricted to be leaves of the tree. Extending related recent
work, we give a full semi-algebraic description of the set of covariance
matrices of any such model. In other words, we find polynomial constraints that
characterize when a matrix is the covariance matrix of a distribution in a
given latent tree model. However, leveraging these constraints to test a given
such model is often complicated by the number of constraints being large and by
singularities of individual polynomials, which may invalidate standard
approximations to relevant probability distributions. Illustrating with the
star tree, we propose a new testing methodology that circumvents singularity
issues by trading off some statistical estimation efficiency and handles cases
with many constraints through recent advances on Gaussian approximation for
maxima of sums of high-dimensional random vectors. Our test avoids the need to
maximize the possibly multimodal likelihood function of such models and is
applicable to models with larger number of variables. These points are
illustrated in numerical experiments.


  With the development of high-definition display devices, the practical
scenario of Super-Resolution (SR) usually needs to super-resolve large input
like 2K to higher resolution (4K/8K). To reduce the computational and memory
cost, current methods first split the large input into local patches and then
merge the SR patches into the output. These methods adaptively allocate a
subnet for each patch. Quantization is a very important technique for network
acceleration and has been used to design the subnets. Current methods train an
MLP bit selector to determine the propoer bit for each layer. However, they
uniformly sample subnets for training, making simple subnets overfitted and
complicated subnets underfitted. Therefore, the trained bit selector fails to
determine the optimal bit. Apart from this, the introduced bit selector brings
additional cost to each layer of the SR network. In this paper, we propose a
novel method named Content-Aware Bit Mapping (CABM), which can remove the bit
selector without any performance loss. CABM also learns a bit selector for each
layer during training. After training, we analyze the relation between the edge
information of an input patch and the bit of each layer. We observe that the
edge information can be an effective metric for the selected bit. Therefore, we
design a strategy to build an Edge-to-Bit lookup table that maps the edge score
of a patch to the bit of each layer during inference. The bit configuration of
SR network can be determined by the lookup tables of all layers. Our strategy
can find better bit configuration, resulting in more efficient mixed precision
networks. We conduct detailed experiments to demonstrate the generalization
ability of our method. The code will be released.


  Certain towers of function fields with complete splitting of rational places
at each stage are constructed. Also, families oof towers with positive N/g
ratios are described.


  In this work, we introduce the \emph{interval permutation segment (IP-SEG)}
model that naturally generalizes the geometric intersection models of interval
and permutation graphs. We study properties of two graph classes that arise
from the IP-SEG model and present a family of forbidden subgraphs for these
classes. In addition, we present polynomial algorithms for the clique and
independent set problems on these classes, when the model is given as part of
the input.


  Using scanning tunneling microscopy (STM), we investigated the evolution of
electrical conductance between a Pb tip and Pb(111) surface from tunneling to
atomic point contact at a site that was defined with atomic precision. We found
that the conductance evolution depended on the contact site, for instance,
on-top, bridge, or hollow (hcp and fcc) sites in the Pb lattice. In the
transition from tunneling to contact regimes, the conductance measured at the
on-top site was enhanced. In the point contact regime, the hollow sites had
conductances larger than those of the other sites, and between the hollow
sites, the hcp site had a conductance larger than that of the fcc site. We also
observed the enhancement and reversal of the apparent height in atomically
resolved high-current STM images, consistent with the results of the
conductance traces. Our results indicate the importance of atomic configuration
in the conductance of atomic junctions and suggest that attractive chemical
interactions have a significant role in electron transport between contacting
atoms.


  The Cartesian squares (powers) of manifolds with the fixed point property
(f.p.p.) are considered. Examples of manifolds with the f.p.p. are constructed
whose symmetric squares fail to have the f.p.p..


  Optimal estimates on asymptotic behaviors of weak solutions both at the
origin and at the infinity are obtained to the following quasilinear elliptic
equations \begin{eqnarray*}
-\Delta_{p}u-\frac{\mu}{|x|^{p}}|u|^{p-2}u+m|u|^{p-2}u=f(u), & & x\in\R^{N},
\end{eqnarray*} where $1<p<N$, $0\leq\mu<\left((N-p)/p\right)^{p}$, $m>0$ and
$f$ is a continuous function.


  We clarify and further explore the CFT dual of shockwave geometries in
Anti-de Sitter. The shockwave is dual to a CFT state produced by a heavy local
operator inserted at a complex point. It can also be created by light
operators, smeared over complex positions. We describe the dictionary in both
cases, and compare to various calculations, old and new. In CFT, we analyze the
operator product expansion in the Regge limit, and find that the leading
contribution is exactly the shockwave operator, $\int du h_{uu}$, localized on
a bulk geodesic. For heavy sources this is a simple consequence of conformal
invariance, but for light operators it involves a smearing procedure that
projects out certain double-trace contributions to the OPE. We revisit
causality constraints in large-$N$ CFT from this perspective, and show that the
chaos bound in CFT coincides with a bulk condition proposed by Engelhardt and
Fischetti. In particular states, this reproduces known constraints on CFT
3-point couplings, and confirms some assumptions about double-trace operators
made in previous work.


  The Helmholtz free energy density is parametrized as a function of
temperature and baryon density near the chiral critical point of QCD. The
parametrization incorporates the expected critical exponents and amplitudes. An
expansion away from equilibrium states is achieved with Landau theory. This is
used to calculate the probability that the system is found at a density other
than the equilibrium one. Such fluctuations are predicted to be very large in
heavy ion collisions.


  For an odd prime $p$ and integers $d, k, m$ with gcd$(p,d)=1$ and $2\leq
k\leq \frac{p-1}{2}$, we consider the determinant
  \begin{equation*}
  S_{m,k}(d,p) = \left|(\alpha_i - \alpha_j)^m\right|_{1 \leq i,j \leq
\frac{p-1}{k}},
  \end{equation*}
  where $\alpha_i$ are distinct $k$-th power residues modulo $p$. In this
paper, we deduce some residue properties for the determinant $S_{m,k}(d,p)$ as
a generalization of certain results of Sun. Using these, we further prove some
conjectures of Sun related to
$$\left(\frac{\sqrt{S_{1+\frac{p-1}{2},2}(-1,p)}}{p}\right) \text{ and }
\left(\frac{\sqrt{S_{3+\frac{p-1}{2},2}(-1,p)}}{p}\right).$$ In addition, we
investigate the number of primes $p$ such that $p\ |\
S_{m+\frac{p-1}{k},k}(-1,p)$, and confirm another conjecture of Sun related to
$S_{m+\frac{p-1}{2},2}(-1,p)$.


  The Canonical Correlation Analysis (CCA) family of methods is foundational in
multiview learning. Regularised linear CCA methods can be seen to generalise
Partial Least Squares (PLS) and be unified with a Generalized Eigenvalue
Problem (GEP) framework. However, classical algorithms for these linear methods
are computationally infeasible for large-scale data. Extensions to Deep CCA
show great promise, but current training procedures are slow and complicated.
First we propose a novel unconstrained objective that characterizes the top
subspace of GEPs. Our core contribution is a family of fast algorithms for
stochastic PLS, stochastic CCA, and Deep CCA, simply obtained by applying
stochastic gradient descent (SGD) to the corresponding CCA objectives. Our
algorithms show far faster convergence and recover higher correlations than the
previous state-of-the-art on all standard CCA and Deep CCA benchmarks. These
improvements allow us to perform a first-of-its-kind PLS analysis of an
extremely large biomedical dataset from the UK Biobank, with over 33,000
individuals and 500,000 features. Finally, we apply our algorithms to match the
performance of `CCA-family' Self-Supervised Learning (SSL) methods on CIFAR-10
and CIFAR-100 with minimal hyper-parameter tuning, and also present theory to
clarify the links between these methods and classical CCA, laying the
groundwork for future insights.


  Quantum $r$-Airy structures can be constructed as modules of
$\mathcal{W}(\mathfrak{gl}_r)$-algebras via restriction of twisted modules for
the underlying Heisenberg algebra. In this paper we classify all such higher
quantum Airy structures that arise from modules twisted by automorphisms of the
Cartan subalgebra consisting of products of disjoint cycles of the same length.
An interesting feature of these higher quantum Airy structures is that the
dilaton shifts must be chosen carefully to satisfy a matrix invertibility
condition, with a natural choice being roots of unity. We explore how these
higher quantum Airy structures may provide a definition of the Chekhov, Eynard,
and Orantin topological recursion for reducible algebraic spectral curves. We
also study under which conditions quantum $r$-Airy structures that come from
modules twisted by arbitrary automorphisms can be extended to new quantum
$(r+1)$-Airy structures by appending a trivial one-cycle to the twist without
changing the dilaton shifts.


  We analyze the non-Markovianity degree for random unitary evolution of
d-level quantum systems. It is shown how non-Markovianity degree is
characterized in terms of local decoherence rates. In particular we derive a
sufficient condition for vanishing of the back ow of information.


  In recent years, vanadium oxides have gained immense attention in the field
of energy storage devices due to their low-cost, layered structure and
multi-valency despite their limited electrical conductivity and lower
structural stability. In this brief review, we have tried to focus on
electrochemical properties of the stoichiometric vanadium oxides along with
VO_x composites. The morphology engineering, doping with heteroatom and
formation of composites with carbon-based materials and/or conducting polymers
in enhancing the supercapacitive performances of the vanadium oxides are
discussed in details. Finally, the potentiality and challenges of vanadium
oxides nanocomposites for supercapacitor applications are discussed.


  Relative attribute models can compare images in terms of all detected
properties or attributes, exhaustively predicting which image is fancier, more
natural, and so on without any regard to ordering. However, when humans compare
images, certain differences will naturally stick out and come to mind first.
These most noticeable differences, or prominent differences, are likely to be
described first. In addition, many differences, although present, may not be
mentioned at all. In this work, we introduce and model prominent differences, a
rich new functionality for comparing images. We collect instance-level
annotations of most noticeable differences, and build a model trained on
relative attribute features that predicts prominent differences for unseen
pairs. We test our model on the challenging UT-Zap50K shoes and LFW10 faces
datasets, and outperform an array of baseline methods. We then demonstrate how
our prominence model improves two vision tasks, image search and description
generation, enabling more natural communication between people and vision
systems.


  Deep learning-based image reconstruction methods have achieved promising
results across multiple MRI applications. However, most approaches require
large-scale fully-sampled ground truth data for supervised training. Acquiring
fully-sampled data is often either difficult or impossible, particularly for
dynamic contrast enhancement (DCE), 3D cardiac cine, and 4D flow. We present a
deep learning framework for MRI reconstruction without any fully-sampled data
using generative adversarial networks. We test the proposed method in two
scenarios: retrospectively undersampled fast spin echo knee exams and
prospectively undersampled abdominal DCE. The method recovers more anatomical
structure compared to conventional methods.


  Over the last decades, the total variation (TV) evolved to one of the most
broadly-used regularisation functionals for inverse problems, in particular for
imaging applications. When first introduced as a regulariser, higher-order
generalisations of TV were soon proposed and studied with increasing interest,
which led to a variety of different approaches being available today. We review
several of these approaches, discussing aspects ranging from
functional-analytic foundations to regularisation theory for linear inverse
problems in Banach space, and provide a unified framework concerning
well-posedness and convergence for vanishing noise level for respective
Tikhonov regularisation. This includes general higher orders of TV, additive
and infimal-convolution multi-order total variation, total generalised
variation (TGV), and beyond. Further, numerical optimisation algorithms are
developed and discussed that are suitable for solving the Tikhonov minimisation
problem for all presented models. Focus is laid in particular on covering the
whole pipeline starting at the discretisation of the problem and ending at
concrete, implementable iterative procedures. A major part of this review is
finally concerned with presenting examples and applications where higher-order
TV approaches turned out to be beneficial. These applications range from
classical inverse problems in imaging such as denoising, deconvolution,
compressed sensing, optical-flow estimation and decompression, to image
reconstruction in medical imaging and beyond, including magnetic resonance
imaging (MRI), computed tomography (CT), magnetic-resonance positron emission
tomography (MR-PET), and electron tomography.


  REBCO high-temperature superconductors are promising for fully
superconducting high-field magnets, including ultra-high field magnets.
Non-insulated (NI) and metal-insulated (MI) windings are a good solution for
protection against electro-thermal quench. Design and optimization requires
numerical modelling of REBCO inserts for high-field magnets. Here, we detail a
fast and accurate two-dimensional (2D) cross-sectional model for the
electromagnetic response of NI and MI coils, which is based on the Minimum
Electro Magnetic Entropy Production (MEMEP). Benchmarking with an $A-V$
formulation method on a double pancake coil shows good agreement. We also
analyse a fully superconducting 32 T magnet with a REBCO insert and a
low-temperature superconducing (LTS) outsert. In particular, we analyze the
current density, the screening curren induced field (SCIF), and the AC loss. We
have shown that metal-insulated coils enable transfer of angular current in the
radial direction, and hence magnet protection, while keeping the same screening
currents and AC loss of isolated coils, even at relatively high ramp rates of 1
A/s. Surprisingly, soldered coils with low resistance between turns present
relatively low AC loss for over-current configuration, which might enable
higher generated magnetic fields. The numerical method presented here can be
applied to optimize high-field magnets regarding SCIF in MI or NI magnets. It
also serves as the basis for future electro-thermal modelling and multi-physics
modeling that also includes mechanical properties.


  Recent observations suggest that dense gas clouds can survive even in hot
galactic winds. Here we show that the inclusion of turbulent densities with
different statistical properties has significant effects on the evolution of
wind-swept clouds. We investigate how the initial standard deviation of the
log-normal density field influences the dynamics of quasi-isothermal clouds
embedded in supersonic winds. We compare uniform, fractal solenoidal, and
fractal compressive cloud models in both 3D and 2D hydrodynamical simulations.
We find that the processes of cloud disruption and dense gas entrainment are
functions of the initial density distribution in the cloud. Fractal clouds
accelerate, mix, and are disrupted earlier than uniform clouds. Within the
fractal cloud sample, compressive clouds retain high-density nuclei, so they
are more confined, less accelerated, and have lower velocity dispersions than
their solenoidal counterparts. Compressive clouds are also less prone to
Kelvin-Helmholtz and Rayleigh-Taylor instabilities, so they survive longer than
solenoidal clouds. By comparing the cloud properties at the destruction time,
we find that dense gas entrainment is more effective in uniform clouds than in
either of the fractal clouds, and it is more effective in solenoidal than in
compressive models. In contrast, mass loading into the wind is more efficient
in compressive cloud models than in uniform or solenoidal models. Overall, wide
density distributions lead to inefficient entrainment, but they facilitate mass
loading and favour the survival of very dense gas in hot galactic winds.


  We investigate the effect of surface waves generated by the Faraday
instability on a shear-thickening surfactant solution under vertical
vibrations. We show that a prolonged oscillation of the surface above the
instability onset leads to an increase of the fluid viscosity. This phenomenon
is evidenced by comparing the time needed for the instability to develop in the
fluid at rest and once the fluid has been shaken above onset: pre-shaking may
delay the instability by two orders of magnitude. A simple model based on a
time-dependent viscosity is proposed which accounts quantitatively for the
experimental observations.


  The Luminous Blue Variable stars exhibit behavior ranging from light curve
`microvariations' on timescales of tens of days, to `outbursts' accompanied by
mass loss of up to 10e-03 solar masses per year, occurring decades apart, to
`giant eruptions' such as seen in Eta Carinae ejecting one or more solar masses
and recurring on timescales of centuries. Here we review the work of the Los
Alamos group since 1993 to investigate pulsations and instabilities in massive
stars using linear pulsation models and non-linear hydrodynamic models. The
models predict pulsational variability that may be associated with the
microvariations. Using a nonlinear pulsation hydrodynamics code with a
time-dependent convection treatment, we show that, in some circumstances, the
Eddington limit is exceeded periodically in the pulsation driving region of the
stellar envelope, accelerating the outer layers, and perhaps initiating mass
loss or LBV outbursts. We discuss how pulsations and mass loss may be
responsible for the location of the Humphreys-Davidson Limit in the H-R
diagram. The `giant eruptions', however, must involve much deeper regions in
the stellar core to cause such large amounts of mass to be ejected. We review
and suggest some possible explanations, including mixing from gravity modes,
secular instabilities, the epsilon mechanism, or the SASI instability as
proposed for Type II supernovae. We outline future work and required stellar
modeling capabilities to investigate these possibilities.


  Algorithms for online learning typically require one or more boundedness
assumptions: that the domain is bounded, that the losses are Lipschitz, or
both. In this paper, we develop a new setting for online learning with
unbounded domains and non-Lipschitz losses. For this setting we provide an
algorithm which guarantees $R_{T}(u)\le \tilde
O(G\|u\|\sqrt{T}+L\|u\|^{2}\sqrt{T})$ regret on any problem where the
subgradients satisfy $\|g_{t}\|\le G+L\|w_{t}\|$, and show that this bound is
unimprovable without further assumptions. We leverage this algorithm to develop
new saddle-point optimization algorithms that converge in duality gap in
unbounded domains, even in the absence of meaningful curvature. Finally, we
provide the first algorithm achieving non-trivial dynamic regret in an
unbounded domain for non-Lipschitz losses, as well as a matching lower bound.
The regret of our dynamic regret algorithm automatically improves to a novel
$L^{*}$ bound when the losses are smooth.


  We present some novel rotating hairy black hole metric in $(2+1)$ dimensions,
which is an exact solution to the field equations of the Einstein-scalar-AdS
theory with a non-minimal coupling. The scalar potential is determined by the
metric ansatz and consistency of the field equations and cannot be prescribed
arbitrarily. In the simplified, critical case, the scalar potential contains
two independent constant parameters, which are respectively related to the mass
and angular momentum of the black hole in a particular way. As long as the
angular momentum does not vanish, the metric can have zero, one or two
horizons. The case with no horizon is physically uninteresting because of the
curvature singularity lying at the origin. We identified the necessary
conditions for at least one horizon to be present in the solution, which
imposes some bound on the mass-angular momentum ratio. For some particular
choice of parameters our solution degenerates into some previously known black
hole solutions.


  We report the detection of rest--frame 6.2 and 7.7 \micron emission features
arising from Polycyclic Aromatic Hydrocarbons (PAH) in the Spitzer/IRS spectrum
of an infrared-luminous Lyman break galaxy at z=3.01. This is currently the
highest redshift galaxy where these PAH emission features have been detected.
The total infrared luminosity inferred from the MIPS 24 \micron and radio flux
density is 2$\times10^{13}$ L$_{\odot}$, which qualifies this object as a
so--called hyperluminous infrared galaxy (HyLIRG). However, unlike local
HyLIRGs which are generally associated with QSO/AGNs and have weak or absent
PAH emission features, this HyLIRG has very strong 6.2 and 7.7 \micron PAH
emission. We argue that intense star formation dominates the infrared emission
of this source, although we cannot rule out the presence of a deeply obscured
AGN. This LBG appears to be a distorted system in the HST ACS F606W and F814W
images, possibly indicating that a significant merger or interaction is driving
the large IR luminosity.


  We have collected transit times for the TRAPPIST-1 system with the Spitzer
Space Telescope over four years. We add to these ground-based, HST and K2
transit time measurements, and revisit an N-body dynamical analysis of the
seven-planet system using our complete set of times from which we refine the
mass ratios of the planets to the star. We next carry out a photodynamical
analysis of the Spitzer light curves to derive the density of the host star and
the planet densities. We find that all seven planets' densities may be
described with a single rocky mass-radius relation which is depleted in iron
relative to Earth, with Fe 21 wt% versus 32 wt% for Earth, and otherwise
Earth-like in composition. Alternatively, the planets may have an Earth-like
composition, but enhanced in light elements, such as a surface water layer or a
core-free structure with oxidized iron in the mantle. We measure planet masses
to a precision of 3-5%, equivalent to a radial-velocity (RV) precision of 2.5
cm/sec, or two orders of magnitude more precise than current RV capabilities.
We find the eccentricities of the planets are very small; the orbits are
extremely coplanar; and the system is stable on 10 Myr timescales. We find
evidence of infrequent timing outliers which we cannot explain with an eighth
planet; we instead account for the outliers using a robust likelihood function.
We forecast JWST timing observations, and speculate on possible implications of
the planet densities for the formation, migration and evolution of the planet
system.


  The claim of the freedom of the will (understood as an individual who is
transcendent to Nature) in the name of XXth century scientific knowledge,
against the perspective of XVIIIth-XIXth century scientific materialism, is
analysed and refuted in the present paper. The hypothesis of reductionism finds
no obstacle within contemporary natural sciences. Determinism in classical
physics is irrefutable, unless classical physics is itself refuted. From
quantum mechanics, some authors argue that free will is possible because there
is an ontological indeterminism in the natural laws, and that the mind is
responsible for the wave function collapse of matter, which leads to a choice
among the different possibilities for the body. However, here I defend the
opposite thesis because indeterminism does not imply free will, and because the
considerations about an autonomous mind sending orders to the body is against
neuroscience or evolutionary theories about human beings. The quantum theory of
measurement can be interpreted without the intervention of human minds, but
other fields of science cannot contemplate the mentalist scenario. A fatalistic
or materialist view, which denies the possibility of a free will, makes much
more sense in scientific terms.


  Synthetic aperture radar tomography (TomoSAR) has been extensively employed
in 3-D reconstruction in dense urban areas using high-resolution SAR
acquisitions. Compressive sensing (CS)-based algorithms are generally
considered as the state of the art in super-resolving TomoSAR, in particular in
the single look case. This superior performance comes at the cost of extra
computational burdens, because of the sparse reconstruction, which cannot be
solved analytically and we need to employ computationally expensive iterative
solvers. In this paper, we propose a novel deep learning-based super-resolving
TomoSAR inversion approach, $\boldsymbol{\gamma}$-Net, to tackle this
challenge. $\boldsymbol{\gamma}$-Net adopts advanced complex-valued learned
iterative shrinkage thresholding algorithm (CV-LISTA) to mimic the iterative
optimization step in sparse reconstruction. Simulations show the height
estimate from a well-trained $\boldsymbol{\gamma}$-Net approaches the
Cram\'er-Rao lower bound while improving the computational efficiency by 1 to 2
orders of magnitude comparing to the first-order CS-based methods. It also
shows no degradation in the super-resolution power comparing to the
state-of-the-art second-order TomoSAR solvers, which are much more
computationally expensive than the first-order methods. Specifically,
$\boldsymbol{\gamma}$-Net reaches more than $90\%$ detection rate in moderate
super-resolving cases at 25 measurements at 6dB SNR. Moreover, simulation at
limited baselines demonstrates that the proposed algorithm outperforms the
second-order CS-based method by a fair margin. Test on real TerraSAR-X data
with just 6 interferograms also shows high-quality 3-D reconstruction with
high-density detected double scatterers.


  We revisit the kink-like parametrization of the deceleration parameter q(z),
which considers a transition, at $z_t$, from cosmic deceleration to
acceleration. In this parametrization the initial, at $z \gg z_t$, value of the
q-parameter is $q_i$, its final, z=-1, value is $q_f$ and the duration of the
transition is parametrized by $\tau$. By assuming a flat space geometry we
obtain constraints on the free parameters of the model using recent data from
type Ia supernovae, BAO, CMB and the Hubble parameter H(z). The use of H(z)
data introduces an explicit dependence of the combined likelihood on the
present value of the Hubble parameter $H_0$, allowing us to explore the
influence of different priors when marginalizing over this parameter. We also
study the importance of the CMB information in the results by considering data
from WMAP7, WMAP9 and Planck. We show that the contours and best fit do not
depend much on the different CMB data used and that the considered new BAO data
is responsible for most of the improvement in the results. Assuming a flat
space geometry, $q_i=1/2$ and expressing the present value of the deceleration
parameter $q_0$ as a function of the other three free parameters, we obtain
$z_t=0.67^{+0.10}_{-0.08}$, $\tau=0.26^{+0.14}_{-0.10}$ and
$q_0=-0.48^{+0.11}_{-0.13}$, at 68\% of confidence level, with an uniform prior
over $H_0$. If in addition we fix $q_f=-1$, as in flat $\Lambda$CDM, DGP and
Chaplygin quartessence that are special models described by our
parametrization, we get $z_t=0.66^{+0.03}_{-0.04}$, $\tau=0.33^{+0.04}_{-0.04}$
and $q_0=-0.54^{+0.05}_{-0.07}$, in excellent agreement with flat $\Lambda$CDM
for which $\tau=1/3$. We also obtain for flat wCDM, another dark energy model
described by our parametrization, the constraint on the equation of state
parameter -1.22 < w < -0.78 at more than 99% confidence level.


  As a concrete application of the holographic correspondence to manifolds
which are only asymptotically Anti-de Sitter, we take a closer look at the
quaternionic Taub-NUT space. This is a four dimensional, non-compact,
inhomogeneous, riemannian manifold with the interesting property of smoothly
interpolating between two symmetric spaces, AdS_4 itself and the coset
SU(2,1)/U(2). Even more interesting is the fact that the scalar curvature of
the induced conformal structure at the boundary (corresponding to a squashed
three-sphere) changes sign as we interpolate between these two limiting cases.
Using twistor methods, we construct the bulk-to-bulk and bulk-to-boundary
propagators for conformally coupled scalars on quaternionic Taub-NUT. This may
eventually enable us to calculate correlation functions in the dual strongly
coupled CFT on a squashed S^3 using the standard AdS/CFT prescription.


  The last decade has witnessed great experimental progress that has led to
measurements of cross sections--polarized as well as unpolarized--of of high
accuracy in several $NN \to NNx$ reaction channels. These data, naturally, pose
challenges to theorists to develop methods by which they can be understood and
explained in commensurate detail.
  In this work we review the status of the theory with special emphasis on
model--independent methods. We discuss in detail not only the many observables
involved in the reactions, but also the physical questions that can be
addressed by studying them in the various reaction channels. The special
advantages of nucleon--nucleon induced reactions are stressed. Foremost among
these is the use of the initial and final states as a spin/isospin filter. This
opens, for example, a window into the spin dependence of the hyperon--nucleon
interaction and the dynamics of the light scalar mesons.


  In this paper we present the high-level functionalities of a
quantum-classical machine learning software, whose purpose is to learn the main
features (the fingerprint) of quantum noise sources affecting a quantum device,
as a quantum computer. Specifically, the software architecture is designed to
classify successfully (more than 99% of accuracy) the noise fingerprints in
different quantum devices with similar technical specifications, or distinct
time-dependences of a noise fingerprint in single quantum machines.


  We identify a mechanism for a type of hysteresis which we predict to occur in
a variety of depinning transitions. We show that the phenomenon of one-way
hysteresis is generic to stress-overshoot models of the depinning transition,
and we show how to calculate the size of the hysteresis gap exactly in a large
class of models. Unlike thermodynamic phase transitions, the dynamic phase
transition is still {\em continuous} despite the presence of hysteresis because
the terms which produce the hysteresis are renormalization group irrelevant. We
discuss the experimental and numerical signatures of one-way hysteresis, which
includes microscopic nucleation.


  We introduce a new route-finding problem which considers perception and
travel costs simultaneously. Specifically, we consider the problem of finding
the shortest tour such that all objects of interest can be detected
successfully. To represent a viable detection region for each object, we
propose to use an entropy-based viewing score that generates a diameter-bounded
region as a viewing neighborhood. We formulate the detection-based trajectory
planning problem as a stochastic traveling salesperson problem with
neighborhoods and propose a center-visit method that obtains an approximation
ratio of O(DmaxDmin) for disjoint regions. For non-disjoint regions, our method
-provides a novel finite detour in 3D, which utilizes the region's minimum
curvature property. Finally, we show that our method can generate efficient
trajectories compared to a baseline method in a photo-realistic simulation
environment.


  Self-folding origami has emerged as a tool to make functional objects in
material science. The common idea is to pattern a sheet with creases and
activate them to have the object fold spontaneously into a desired
configuration. This article shows that collinear quadrilateral metasheets are
able to fold into the Miura-Ori configuration, if we only impose strain on part
of their creases. In this study, we define and determine the optimal pattern of
strain (OPS) on a collinear quadrilateral metasheet, that is the pattern of
minimum "functional" creases with which the self-folding metasheet can fold
into Miura-Ori state stably. By comparing the energy evolution along the
folding pathway of each possible folded state under OPS, we conclude that the
energy predominance of the desired Miura-Ori pathway during the initial period
of time accounts for why the OPS works. Furthermore, we measure the projected
force of the OPS on the intial flat metasheet and give insights on how to
determine the OPS using only local information of the initial flat state.


  We use tropical and non-archimedean geometry to study generic root counts of
families of polynomial equations. These families are given as morphisms of
schemes $X\to{Y}$ that factor through a closed embedding into a relative torus
over a parameter space $Y$. We prove a generalization of Bernstein's theorem
for these morphisms, showing that the root count of a single well-behaved
tropical fiber spreads to an open dense subset of $Y$. We use this to express
the generic root count of a wide class of square systems in terms of the
matroidal degree of an explicit variety. This in particular gives tropical
formulas for the birational intersection indices and volumes of Newton-Okounkov
bodies defined by Kaveh and Khovanskii, and the generic root counts of the
steady-state equations of chemical reaction networks. An important role in
these theorems is played by the notion of tropical flatness, which allows us to
infer generic properties of $X\to{Y}$ from a single tropical fiber. We show
that the tropical analogue of the generic flatness theorem holds, in the sense
that $X\to{{Y}}$ is tropically flat over an open dense subset of the Berkovich
analytification of $Y$.


  We study the excitation of the electric current of chiral fermions along the
external magnetic field, known as the chiral magnetic effect, in the presence
of the background axial-vector field. The calculation of the current is based
on the exact solution of the Dirac equation for these fermions accounting for
the external fields. First, this solution was obtained for massive particles
and, then, we consider the chiral limit, which is used in the anomalous current
computation. We obtain that, in this situation, the anomalous current does not
contain the direct contribution of the axial-vector field. This result is
compared with findings of other authors.


  We have considered phi^4 theory in higher dimensions. Using functional
diagrammatic approach, we computed the one-loop correction to effective
potential of the scalar field in five dimensions. It is shown that phi^4 theory
can be regularised in five dimensions. Temperature dependent one-loop
correction and critical temperature T_c are computed and T_c depends on the
fundamental scale M of the theory. A brief discussion of symmetry restoration
is also presented. The nature of phase transitions is examined and is of second
order


  We present an assessment of the CMB large scale anomalies in polarisation
using the two-point correlation function as a test case. We employ the state of
the art of large scale polarisation datasets: the first based on a Planck 2018
HFI 100 and 143 GHz cross-spectrum analysis, based on SRoll2 processing, and
the second from a map-based approach derived through a joint treatment of
Planck 2018 LFI and WMAP-9yr. We consider the well-known $S_{1/2}$ estimator,
which measures the distance of the two-point correlation function from zero at
angular scales larger than $60^{\circ}$, and rely on realistic simulations for
both datasets to assess confidence intervals. By focusing on the pure
polarisation field described by either the $Q$ and $U$ Stokes parameters or by
the local $E-$modes, we show that the first description is heavily influenced
by the quadrupole (which is poorly constrained in both datasets) while the
second one is more suited for an analysis containing higher multipoles up to
$\ell \sim 10$, limit above which both datasets become markedly noise
dominated. We find that both datasets exhibit a lack-of-correlation anomaly in
pure polarisation, similar to the one observed in temperature, which is better
constrained by the less noisy Planck HFI 100$\times$143 data, where its
significance lies at about $99.5\%$. We perform our analysis using realizations
that are either constrained or non-constrained by the observed temperature
field, and find similar results in the two cases.


  Some peculiarities of the exploitation of the entropy inequality in case of
weakly nonlocal continuum theories are investigated and refined. As an example
it is shown that the proper application of the Liu procedure leads to the
Ginzburg-Landau equation in case of a weakly nonlocal extension of the
constitutive space of the simplest internal variable theories.


  We classify minimal hypersurfaces in $R^n \times S^m$, $n,m \geq 2$, which
are invariant by the canonical action of $O(n) \times O(m)$. We also construct
compact and noncompact examples of invariant hypersurfaces of constant mean
curvature. We show that the minimal hypersurfaces and the noncompact constant
mean curvature hypersurfaces are all unstable.


  Distribution of quantum entanglement is investigated for an anisotropic
quantum XY model with variable range interactions and in the presence of a
uniform transverse magnetic field. We report the possibility of
\emph{qualitative} growth in the entanglement between distant sites with an
increase in the range of interactions that vary either exponentially or
polynomially as the distance between the sites increases. Interestingly, we
find that such entanglement enhancement is not ubiquitous and is dependent on
the factorization points, a specific set of system parameters where the
zero-temperature state of the system is fully separable. In particular, we
observe that at zero-temperature, when the system parameters are chosen beyond
the pair of factorization points, the increments in entanglement length due to
variable range interactions are more pronounced compared to the situation when
the parameters lie in between the factorization points. By employing the sum of
all the bipartite entanglements with respect to a single site, we also show
that the shareability of the bipartite entanglements are constrained, thereby
establishing their monogamous nature. Furthermore, we note that the
factorization points get reallocated depending on the laws of interaction
fall-offs and provide an ansatz for the same. We reveal that the temperature at
which the canonical equilibrium state becomes entangled from an unentangled one
increases with the increase in the range of interactions, thereby demonstrating
enhanced robustness in entanglement against temperature in the presence of
long-range interactions and only when the system parameters are chosen between
the pair of factorization points. We apply an energy-based entanglement witness
to provide a justification to the observed robustness with temperature.


  This paper addresses the asymptotic performance of popular spatial regression
estimators on the task of estimating the linear effect of an exposure on an
outcome under "spatial confounding" -- the presence of an unmeasured
spatially-structured variable influencing both the exposure and the outcome.
The existing literature on spatial confounding is informal and inconsistent;
this paper is an attempt to bring clarity through rigorous results on the
asymptotic bias and consistency of estimators from popular spatial regression
models. We consider two data generation processes: one where the confounder is
a fixed function of space and one where it is a random function (i.e., a
stochastic process on the spatial domain). We first show that the estimators
from ordinary least squares (OLS) and restricted spatial regression are
asymptotically biased under spatial confounding. We then prove a novel main
result on the consistency of the generalized least squares (GLS) estimator
using a Gaussian process (GP) covariance matrix in the presence of spatial
confounding under in-fill (fixed domain) asymptotics. The result holds under
very general conditions -- for any exposure with some non-spatial variation
(noise), for any spatially continuous confounder, using any choice of Mat\'ern
or square exponential Gaussian process covariance used to construct the GLS
estimator, and without requiring Gaussianity of errors. Finally, we prove that
spatial estimators from GLS, GP regression, and spline models that are
consistent under confounding by a fixed function will also be consistent under
confounding by a random function. We conclude that, contrary to much of the
literature on spatial confounding, traditional spatial estimators are capable
of estimating linear exposure effects under spatial confounding in the presence
of some noise in the exposure. We support our theoretical arguments with
simulation studies.


  Generalizing standard monadic second-order logic for Kripke models, we
introduce monadic second-order logic interpreted over coalgebras for an
arbitrary set functor. Similar to well-known results for monadic second-order
logic over trees, we provide a translation of this logic into a class of
automata, relative to the class of coalgebras that admit a tree-like supporting
Kripke frame. We then consider invariance under behavioral equivalence of
formulas; more in particular, we investigate whether the coalgebraic
mu-calculus is the bisimulation-invariant fragment of monadic second-order
logic. Building on recent results by the third author we show that in order to
provide such a coalgebraic generalization of the Janin-Walukiewicz Theorem, it
suffices to find what we call an adequate uniform construction for the functor.
As applications of this result we obtain a partly new proof of the
Janin-Walukiewicz Theorem, and bisimulation invariance results for the bag
functor (graded modal logic) and all exponential polynomial functors.
  Finally, we consider in some detail the monotone neighborhood functor, which
provides coalgebraic semantics for monotone modal logic. It turns out that
there is no adequate uniform construction for this functor, whence the
automata-theoretic approach towards bisimulation invariance does not apply
directly. This problem can be overcome if we consider global bisimulations
between neighborhood models: one of our main technical results provides a
characterization of the monotone modal mu-calculus extended with the global
modalities, as the fragment of monadic second-order logic for the monotone
neighborhood functor that is invariant for global bisimulations.


  Within the past few years, organizations in diverse industries have adopted
MapReduce-based systems for large-scale data processing. Along with these new
users, important new workloads have emerged which feature many small, short,
and increasingly interactive jobs in addition to the large, long-running batch
jobs for which MapReduce was originally designed. As interactive, large-scale
query processing is a strength of the RDBMS community, it is important that
lessons from that field be carried over and applied where possible in this new
domain. However, these new workloads have not yet been described in the
literature. We fill this gap with an empirical analysis of MapReduce traces
from six separate business-critical deployments inside Facebook and at Cloudera
customers in e-commerce, telecommunications, media, and retail. Our key
contribution is a characterization of new MapReduce workloads which are driven
in part by interactive analysis, and which make heavy use of query-like
programming frameworks on top of MapReduce. These workloads display diverse
behaviors which invalidate prior assumptions about MapReduce such as uniform
data access, regular diurnal patterns, and prevalence of large jobs. A
secondary contribution is a first step towards creating a TPC-like data
processing benchmark for MapReduce.


  We study the thermodynamic limit of random partition models for the instanton
sum of 4D and 5D supersymmetric U(1) gauge theories deformed by some physical
observables. The physical observables correspond to external potentials in the
statistical model. The partition function is reformulated in terms of the
density function of Maya diagrams. The thermodynamic limit is governed by a
limit shape of Young diagrams associated with dominant terms in the partition
function. The limit shape is characterized by a variational problem, which is
further converted to a scalar-valued Riemann-Hilbert problem. This
Riemann-Hilbert problem is solved with the aid of a complex curve, which may be
thought of as the Seiberg-Witten curve of the deformed U(1) gauge theory. This
solution of the Riemann-Hilbert problem is identified with a special solution
of the dispersionless Toda hierarchy that satisfies a pair of generalized
string equations. The generalized string equations for the 5D gauge theory are
shown to be related to hidden symmetries of the statistical model. The
prepotential and the Seiberg-Witten differential are also considered.


  The mass distribution of the rich cluster of galaxies Cl0024+1654 has
frequently been used to constrain the nature of dark matter yet a model
consistent with all the observational data has been difficult to construct. In
this paper we analyse the three-dimensional structure of this cluster using new
spectroscopic information on ~300 galaxies within a projected radius of 3
Mpc/h. These data reveal an unusual foreground component of galaxies separated
from the main cluster by 3000 km/s. We use numerical simulations to show that a
high speed collision along the line of sight between Cl0024+1654 and a second
cluster of slightly smaller mass can reproduce the observed peculiar redshift
distribution. The collision dramatically alters the internal mass distribution
of the bound remnants, creating constant density cores from initially cuspy
dark matter profiles and scattering galaxies to large projected radii. Our
results can reconcile the inferred mass profile from gravitational lensing with
predictions from hierarchical structure formation models, while at the same
time resolving the mass discrepancy that results from a comparison between
lensing, velocity dispersion and X-ray studies.


  We describe a magnetohydrodynamic (MHD) constrained energy functional for
equilibrium calculations that combines the topological constraints of ideal MHD
with elements of Taylor relaxation.
  Extremizing states allow for partially chaotic magnetic fields and
non-trivial pressure profiles supported by a discrete set of ideal interfaces
with irrational rotational transforms.
  Numerical solutions are computed using the Stepped Pressure Equilibrium Code,
SPEC, and benchmarks and convergence calculations are presented.


  Large language models (LLMs) have shown remarkable performance on many tasks
in different domains. However, their performance in closed-book biomedical
machine reading comprehension (MRC) has not been evaluated in depth. In this
work, we evaluate GPT on four closed-book biomedical MRC benchmarks. We
experiment with different conventional prompting techniques as well as
introduce our own novel prompting method. To solve some of the retrieval
problems inherent to LLMs, we propose a prompting strategy named Implicit
Retrieval Augmented Generation (RAG) that alleviates the need for using vector
databases to retrieve important chunks in traditional RAG setups. Moreover, we
report qualitative assessments on the natural language generation outputs from
our approach. The results show that our new prompting technique is able to get
the best performance in two out of four datasets and ranks second in rest of
them. Experiments show that modern-day LLMs like GPT even in a zero-shot
setting can outperform supervised models, leading to new state-of-the-art
(SoTA) results on two of the benchmarks.


  In the inner region of the disc of an active galactic nucleus (AGN), the
collision of two white dwarfs (WDs) through Jacobi capture might be inevitable,
leading to a Type Ia supernova (SN Ia) explosion. This transient event,
influenced by the disc gas and the gravity of the supermassive black hole
(SMBH), exhibits distinct characteristics compared to normal SNe Ia. The energy
of the explosion is mainly stored in the ejecta in the form of kinetic energy.
Typically, the ejecta is not effectively decelerated by the AGN disc and rushes
rapidly out of the AGN disc. However, under the influence of the SMBH, most of
the ejecta falls back toward the AGN disc. As the fallback ejecta becomes more
dispersed, it interacts with the disc gas, converting its kinetic energy into
thermal energy. This results in a high-energy transient characterized by a
rapid initial rise followed by a decay with $L\propto t^{-2.8}$. The time-scale
of the transient ranges from hours to weeks, depending on the mass of the SMBH.
This process generates high-energy radiation spanning from hard X-rays to the
soft $\gamma$ range. Additionally, the subsequent damage to the disc may result
in changing-look AGNs. Moreover, the falling back of SNe Ia ejecta onto the AGN
disc significantly increases the metallicity of the AGN and can even generate
heavy elements within the AGN discs.


  Human following on mobile robots has witnessed significant advances due to
its potentials for real-world applications. Currently most human following
systems are equipped with depth sensors to obtain distance information between
human and robot, which suffer from the perception requirements and noises. In
this paper, we design a wheeled mobile robot system with monocular pan-tilt
camera to follow human, which can stay the target in the field of view and keep
following simultaneously. The system consists of fast human detector, real-time
and accurate visual tracker, and unified controller for mobile robot and
pan-tilt camera. In visual tracking algorithm, both Siamese networks and
optical flow information are exploited to locate and regress human
simultaneously. In order in perform following with a monocular camera, the
constraint of human height is introduced to design the controller. In
experiments, human following are conducted and analysed in simulations and a
real robot platform, which demonstrate the effectiveness and robustness of the
overall system.


  We demonstrate a measure for the effective number of parameters constrained
by a posterior distribution in the context of cosmology. In the same way that
the mean of the Shannon information (i.e. the Kullback-Leibler divergence)
provides a measure of the strength of constraint between prior and posterior,
we show that the variance of the Shannon information gives a measure of
dimensionality of constraint. We examine this quantity in a cosmological
context, applying it to likelihoods derived from Cosmic Microwave Background,
large scale structure and supernovae data. We show that this measure of
Bayesian model dimensionality compares favourably both analytically and
numerically in a cosmological context with the existing measure of model
complexity used in the literature.


  We develop a fourth-order numerical integrator to simulate the coupled spin
and orbital motions of two rigid bodies having arbitrary mass distributions
under the influence of their mutual gravitational potential. We simulate the
dynamics of components in well-characterized binary and triple near-Earth
asteroid systems and use surface of section plots to map the possible spin
configurations of the satellites. For asynchronous satellites, the analysis
reveals large regions of phase space where the spin state of the satellite is
chaotic. For synchronous satellites, we show that libration amplitudes can
reach detectable values even for moderately elongated shapes. The presence of
chaotic regions in the phase space has important consequences for the evolution
of binary asteroids. It may substantially increase spin synchronization
timescales, explain the observed fraction of asynchronous binaries, delay
BYORP-type evolution, and extend the lifetime of binaries. The variations in
spin rate due to large librations also affect the analysis and interpretation
of lightcurve and radar observations.


  The appearance of wobbling motion and chirality in rotating triaxial nuclei
is explained. The discovery of a new mode, chiral wobbling, in $^{74}$Br, is
commented.


  We introduce a quench of the geometry of Landau level orbitals as a probe of
nonequilibrium dynamics of fractional quantum Hall (FQH) states. We show that
such geometric quenches induce coherent many-body dynamics of neutral degrees
of freedom of FQH fluids. The simplest case of mass anisotropy quench can be
experimentally implemented as a sudden tilt of the magnetic field, and the
resulting dynamics reduces to the harmonic motion of the spin-$2$ "graviton"
mode, i.e., the long wavelength limit of the Girvin-MacDonald-Platzman
magnetoroton. We derive an analytical description of the graviton dynamics
using the bimetric theory of FQH states, and find agreement with exact
numerical simulations at short times. We show that certain types of geometric
quenches excite higher-spin collective modes, thus establishing their existence
in a microscopic model and motivating an extension of geometric theories of FQH
states.


  We study the response function of the Einstein Telescope to kinematic Doppler
anisotropies, which represent one of the guaranteed properties of the
stochastic gravitational wave background. If the frequency dependence of the
stochastic background changes slope within the detector frequency band, the
Doppler anisotropic contribution to the signal can not be factorized in a part
depending on frequency, and a part depending on direction. For the first time,
we study the detector response function to Doppler anisotropies without making
any factorizable Ansatz. Moreover, we do not assume that kinematic effects are
small, and we derive general formulas valid for any relative velocity among
frames. We apply our findings to three well-motivated examples of background
profiles: power-law, broken power-law, and models with a resonance motivated by
primordial black hole scenarios. We derive the signal-to-noise ratio associated
with an optimal estimator for the detection of non-factorizable kinematic
anisotropies, and we study it for representative examples.


  We provide a framework for detecting relevant insurance companies in a
systemic risk perspective. Among the alternative methodologies for measuring
systemic risk, we propose a complex network approach where insurers are linked
to form a global interconnected system. We model the reciprocal influence
between insurers calibrating edge weights on the basis of specific risk
measures. Therefore, we provide a suitable network indicator, the Weighted
Effective Resistance Centrality, able to catch which is the effect of a
specific vertex on the network robustness. By means of this indicator, we
assess the prominence of a company in spreading and receiving risk from the
others.


  We propose algorithms, based on the multi-scale entanglement renormalization
ansatz, to obtain the ground state of quantum critical systems in the presence
of boundaries, impurities, or interfaces. By exploiting the theory of minimal
updates [G. Evenbly and G. Vidal, arXiv:1307.0831], the ground state is
completely characterized in terms of a number of variational parameters that is
independent of the system size, even though the presence of a boundary, an
impurity, or an interface explicitly breaks the translation invariance of the
host system. Similarly, computational costs do not scale with the system size,
allowing the thermodynamic limit to be studied directly and thus avoiding
finite size effects e.g. when extracting the universal properties of the
critical system.


  By processing in the frequency domain (FD), massive MIMO systems can approach
the theoretical per-user capacity using a single carrier modulation (SCM)
waveform with a cyclic prefix. Minimum mean squared error (MMSE) detection and
zero forcing (ZF) precoding have been shown to effectively cancel multi-user
interference while compensating for inter-symbol interference. In this paper,
we present a modified downlink precoding approach in the FD based on
regularized zero forcing (RZF), which reuses the matrix inverses calculated as
part of the FD MMSE uplink detection. By reusing these calculations, the
computational complexity of the RZF precoder is drastically lowered, compared
to the ZF precoder. Introduction of the regularization in RZF leads to a bias
in the detected data symbols at the user terminals. We show this bias can be
removed by incorporating a scaling factor at the receiver. Furthermore, it is
noted that user powers have to be optimized to strike a balance between noise
and interference seen at each user terminal. The resulting performance of the
RZF precoder exceeds that of the ZF precoder for low and moderate input
signal-to-noise ratio (SNR) conditions, and performance is equal for high input
SNR. These results are established and confirmed by analysis and simulation.


  Polar codes are the first class of constructive channel codes achieving the
symmetric capacity of the binary-input discrete memoryless channels. But the
analysis and construction of polar codes involve the complex
iterative-calculation. In this paper, by revisiting the error event of the
polarized channel, a new concept, named polar spectrum, is introduced from the
weight distribution of polar codes. Thus we establish a systematic framework in
term of the polar spectrum to analyze and construct polar codes. By using polar
spectrum, we derive the union bound and the union-Bhattacharyya (UB) bound of
the error probability of polar codes and the upper/lower bound of the symmetric
capacity of the polarized channel. The analysis based on the polar spectrum can
intuitively interpret the performance of polar codes under successive
cancellation (SC) decoding. Furthermore, we analyze the coding structure of
polar codes and design an enumeration algorithm based on the MacWilliams
identities to efficiently calculate the polar spectrum. In the end, two
construction metrics named UB bound weight (UBW) and simplified UB bound weight
(SUBW) respectively, are designed based on the UB bound and the polar spectrum.
Not only are these two constructions simple and explicit for the practical
polar coding, but they can also generate polar codes with similar (in SC
decoding) or superior (in SC list decoding) performance over those based on the
traditional methods.


  In this paper, we study the optimal secondary-link beamforming pattern that
balances between the SU's throughput and the interference it causes to PUs in
MIMO cognitive radio networks. In particular, we aim to maximize the throughput
of the SU, while keeping the interference temperature at the primary receivers
below a certain threshold.
  Unlike traditional MIMO systems, SUs may not have the luxury of knowing the
channel state information (CSI) on the links to PUs. This presents a key
challenge for a secondary transmitter to steer interference away from primary
receivers. In this paper, we consider three scenarios, namely when the
secondary transmitter has complete, partial, or no knowledge about the channels
to the primary receivers. In particular, when complete CSI is not available,
the interference-temperature constraints are to be satisfied with high
probability, thus resulting in chance constraints that are typically hard to
deal with. Our contribution is fourfold. First, by analyzing the distributional
characteristics of MIMO channels, we propose a unified homogeneous QCQP
formulation that can be applied to all three scenarios. The homogeneous QCQP
formulation, though non-convex, is amenable to semidefinite programming (SDP)
relaxation methods. Secondly, we show that the SDP relaxation admits no gap
when the number of primary links is no larger than two. Thirdly, we propose a
randomized polynomial-time algorithm for constructing a near-optimal solution
to the QCQP problem when there are more than two primary links. Finally, we
show that when the secondary transmitter has no CSI on the links to primary
receivers, the optimal solution to the QCQP problem can be found by a simple
matrix eigenvalue-eigenvector computation, which can be done much more
efficiently than solving the QCQP directly.


  In autonomous driving tasks, scene understanding is the first step towards
predicting the future behavior of the surrounding traffic participants. Yet,
how to represent a given scene and extract its features are still open research
questions. In this study, we propose a novel text-based representation of
traffic scenes and process it with a pre-trained language encoder.
  First, we show that text-based representations, combined with classical
rasterized image representations, lead to descriptive scene embeddings. Second,
we benchmark our predictions on the nuScenes dataset and show significant
improvements compared to baselines. Third, we show in an ablation study that a
joint encoder of text and rasterized images outperforms the individual encoders
confirming that both representations have their complementary strengths.


  HST WFPC2 archival F606W and F300W images obtained within one year prior to
the explosion of the nearby Type II supernova (SN) 2003gd in Messier 74 (NGC
628) have been analyzed to isolate the progenitor star. The SN site was located
using precise astrometry applied to the HST images. Two plausible candidates
are identified within 0.6" of the SN position in the F606W image. Neither
candidate was detected in the F300W image. SN 2003gd appears to be of Type
II-plateau (II-P), with age ~87 d on June 17 UT and with low reddening [E(B-V)
= 0.13 mag]. The most likely of the two progenitor candidates has M_V_0 ~ -3.5
mag (for an extinction-corrected distance modulus of 29.3 mag) and, based on
additional color information derived from a high-quality, archival ground-based
I-band image, we estimate that this star was a red supergiant with initial mass
M_ZAMS ~ 8 -- 9 Msun. This mass estimate is somewhat lower than, but relatively
consistent with, recent limits placed on the progenitor masses of other SNe
II-P, using HST data. Future HST imaging with the Advanced Camera for Surveys,
when the SN has faded considerably, will be extremely useful in pinpointing the
exact SN location and securing identification of the progenitor. If our
proposed candidate is confirmed, it will be only the sixth SN progenitor ever
directly identified.


  Four recent observational results have challenged our understanding of
high--redshift galaxies, as they require the presence of far more ultraviolet
photons than should be emitted by normal stellar populations. First, there is
significant ultraviolet emission from Lyman Break Galaxies (LBGs) at
wavelenghts shorter than 912\AA. Second, there is strong Lyman alpha emission
from extended ``blobs'' with little or no associated apparent ionizing
continuum. Third, there is a population of galaxies with unusually strong
Lyman-alpha emission lines. And fourth, there is a strong HeII (1640 \AA)
emission line in a composite of LBGs. The proposed explanations for the first
three observations are internally inconsistent, and the fourth puzzle has
remained hitherto unexplained. Here we show that all four problems are resolved
simultaneously if 10-30 percent of the stars in many galaxies at z ~ 3-4 are
mainly primordial - unenriched by elements heavier than helium ('metals'). Most
models of hierarchical galaxy formation assume efficient intra--galactic metal
mixing, and therefore do not predict metal-free star formation at redshifts
significantly below z ~5. Our results imply that micro-mixing of metals within
galaxies is inefficient on a ~ Gyr time-scale, a conclusion that can be
verified with higher resolution simulations, and future observations of the
HeII emission line.


  We calculate spectral energy distributions (SEDs) of steady accretion discs
at high accretion rates, as appropriate for bright QSOs, under the assumption
that the outer parts are heated sufficiently to maintain marginal gravitational
stability, presumably by massive stars formed within the disc. The SED is
independent of the nature of these auxiliary sources if their inputs are
completely thermalized. Standard assumptions are made for angular momentum
transport, with an alpha parameter less than unity. With these prescriptions,
the luminosity of the disc is sensitive to its opacity, in contrast to standard
discs powered by release of orbital energy alone. Compared to the latter, our
discs have a broader SED, with a second peak in the near-infrared that is
energetically comparable to the blue bump. The energy in the second peak
increases with the outer radius of the disc, provided that the accretion rate
is constant with radius. By comparing our computed SEDs with observed ones, we
limit the outer radius of the disc to be less than 10^5 Schwarzschild radii, or
about one parsec, in a typical QSO. We also discuss some properties of our
minimum-Q discs in the regions where auxiliary heating is dominant (10^3-10^5
Schwarzschild radii).


  Codispersion analysis is a new statistical method developed to assess spatial
covariation between two spatial processes that may not be isotropic or
stationary. Its application to anisotropic ecological datasets have provided
new insights into mechanisms underlying observed patterns of species
distributions and the relationship between individual species and underlying
environmental gradients. However, the performance of the codispersion
coefficient when there is noise or measurement error ("contamination") in the
data has been addressed only theoretically. Here, we use Monte Carlo
simulations and real datasets to investigate the sensitivity of codispersion to
four types of contamination commonly seen in many real-world environmental and
ecological studies. Three of these involved examining codispersion of a spatial
dataset with a contaminated version of itself. The fourth examined differences
in codisperson between plants and soil conditions, where the estimates of soil
characteristics were based on complete or thinned datasets. In all cases, we
found that estimates of codispersion were robust when contamination, such as
data thinning, was relatively low (<15\%), but were sensitive to larger
percentages of contamination. We also present a useful method for imputing
missing spatial data and discuss several aspects of the codispersion
coefficient when applied to noisy data to gain more insight about the
performance of codispersion in practice.


  Electrohydrodynamic 3D printing is an additive manufacturing technique with
enormous potential in plasmonics, microelectronics, and sensing applications,
thanks to its broad materials palette, high voxel deposition rate, and
compatibility with various substrates. However, the electric field used to
deposit material is concentrated at the depositing structure resulting in the
focusing of the charged droplets and geometry-dependent landing positions,
which complicates the fabrication of complex 3D shapes. The low level of
concordance between design and printout seriously impedes the development of
electrohydrodynamic 3D printing and rationalizes the simplicity of the designs
reported so far. In this work, we break the electric field centrosymmetry to
study the resulting deviation in the flight trajectory of the droplets.
Comparison of experimental outcomes with predictions of an FEM model provides
new insights into the droplet characteristics and unveils how the product of
droplet size and charge uniquely governs its kinematics. From these insights,
we develop reliable predictions of the jet trajectory and allow the computation
of optimized printing paths counterbalancing the electric field distortion,
thereby enabling the fabrication of geometries with unprecedented complexity.


  In this study, we propose an automatic diary generation system that uses
information from past joint experiences with the aim of increasing the
favorability for robots through shared experiences between humans and robots.
For the verbalization of the robot's memory, the system applies a large-scale
language model, which is a rapidly developing field. Since this model does not
have memories of experiences, it generates a diary by receiving information
from joint experiences. As an experiment, a robot and a human went for a walk
and generated a diary with interaction and dialogue history. The proposed diary
achieved high scores in comfort and performance in the evaluation of the
robot's impression. In the survey of diaries giving more favorable impressions,
diaries with information on joint experiences were selected higher than diaries
without such information, because diaries with information on joint experiences
showed more cooperation between the robot and the human and more intimacy from
the robot.


  Aging in spin glasses (and in some other systems) reveals astonishing effects
of `rejuvenation and memory' upon temperature changes. In this paper, we
propose microscopic mechanisms (at the scale of spin-spin interactions) which
can be at the origin of such phenomena. Firstly, we recall that, in a
frustrated system, the effective average interaction between two spins may take
different values (possibly with opposite signs) at different temperatures. We
give simple examples of such situations, which we compute exactly. Such
mechanisms can explain why new ordering processes (rejuvenation) seem to take
place in spin glasses when the temperature is lowered. Secondly, we emphasize
the fact that inhomogeneous interactions do naturally lead to a wide
distribution of relaxation times for thermally activated flips. `Memory spots'
spontaneously appear, in the sense that the flipping time of some spin clusters
becomes extremely long when the temperature is decreased. Such memory spots are
capable of keeping the memory of previous ordering at a higher temperature
while new ordering processes occur at a lower temperature. After a qualitative
discussion of these mechanisms, we show in the numerical simulation of a
simplified example that this may indeed work. Our conclusion is that certain
chaos-like phenomena may show up spontaneously in any frustrated and
inhomogeneous magnetic system, without impeding the occurrence of memory
effects.


  Traditional methods for unsupervised learning of finite mixture models
require to evaluate the likelihood of all components of the mixture. This
becomes computationally prohibitive when the number of components is large, as
it is, for example, in the sum-product (transform) networks. Therefore, we
propose to apply a combination of the expectation maximization and the
Metropolis-Hastings algorithm to evaluate only a small number of,
stochastically sampled, components, thus substantially reducing the
computational cost. The Markov chain of component assignments is sequentially
generated across the algorithm's iterations, having a non-stationary target
distribution whose parameters vary via a gradient-descent scheme. We put
emphasis on generality of our method, equipping it with the ability to train
both shallow and deep mixture models which involve complex, and possibly
nonlinear, transformations. The performance of our method is illustrated in a
variety of synthetic and real-data contexts, considering deep models, such as
mixtures of normalizing flows and sum-product (transform) networks.


  Background: Small asymmetry between neutrons and protons, caused by the
differences in masses and charges of the up and down constituent quarks leads
to the isospin symmetry breaking. The isospin non-conservation affects broad
range of observables from superallowed Fermi weak interaction to
isospin-forbidden electromagnetic rates. Its most profound and cleanest
manifestation are systematic shifts in masses and excitation energies of mirror
atomic nuclei.
  Purpose: Recently, we constructed the charge-dependent DFT that includes
class II and III local interactions and demonstrated that the model allows for
very accurate reproduction of Mirror and Triplet Displacement energies in a
very broad range of masses. The aim of this work is to further test the
charge-dependent functional by studying Mirror Energy Differences (MEDs) in
function of angular momentum $I$.
  Methods: To compute MEDs we use DFT-rooted no core configuration interaction
model. This post mean-field method restores rotational symmetry and takes into
account configuration mixing within a space that includes relevant
(multi)particle-(multi)hole Slater determinants.
  Results: We applied the model to $f_{7/2}$-shell mirror pairs of $A=43$,
$45$, $47$, and $49$ focusing on MEDs in low-spin part (below band crossing)
what allowed us to limit the model space to seniority one and three (one broken
pair) configurations.
  Conclusions: We demonstrate that, for spins $I\leq 15/2$ being subject of the
present study, our model reproduces well experimental MEDs which vary strongly
in function of $I$ and $A$. The quality of model's predictions is comparable to
the nuclear shell-model results by Bentley et al. Phys. Rev. C 92, 024310
(2015).


  The spin-polarized even-denominator fractional quantum Hall (FQH) states in
the second Landau level (LL), i.e. 5/2 and 7/2, may possess novel
quasi-particle excitations obeying non-Abelian statistics. However, the spin
polarization of the 7/2 FQH state has not been investigated experimentally and
the spin polarization of the 5/2 FQH state from tilted field experiments
remains controversial. Using a piezo-driven sample rotator with the lowest
electron temperature down to 25 mK, we studied the energy gap of the
even-denominator FQH states in the second LL by precise control of the tilted
angles with a resolution less than 0.1{\deg}. We observed two different energy
gap dependences on the in-plane magnetic field for 5/2, 7/2, other FQH states
(7/3 and 8/3) in the second LL and reentrant integer quantum Hall (RIQH) states
in the third LL. Though the transition fields vary from states, their
corresponding in-plane magnetic lengths are comparable to the quantum well
thickness of the sample, which may result from the influence of the
finite-thickness effect. At low in-plane magnetic fields, before the
conjectured finite-thickness effect starts to dominate, the energy gaps of both
5/2 and 7/2 states show a non-decreasing behavior, supporting spin-polarized
ground states. Our results also suggest that the 7/3, 8/3 FQH states, and the
RIQH states in the third LL are spin-polarized or partially spin-polarized.