  There has been much debate over the form of the quantum area spectrum for a
black hole horizon, with the evenly spaced conception of Bekenstein having
featured prominently in the discourse. In this letter, we refine a very
recently proposed method for calibrating the Bekenstein form of the spectrum.
Our refined treatment predicts, as did its predecessor, a uniform spacing
between adjacent spectral levels of $8\pi$ in Planck units; notably, an outcome
that already has a pedigree as a proposed ``universal'' value for this
intrinsically quantum-gravitational measure. Although the two approaches are
somewhat similar in logic and quite agreeable in outcome, we argue that our
version is conceptually more elegant and formally simpler than its precursor.
Moreover, our rendition is able to circumvent a couple of previously unnoticed
technical issues and, as an added bonus, translates to generic theories of
gravity in a very direct manner.


  In the analysis of survey data, sampling weights are needed for consistent
estimation of the population. However, the original inverse probability weights
from the survey sample design are typically modified to account for
non-response, to increase efficiency by incorporating auxiliary population
information, and to reduce the variability in estimates due to extreme weights.
It is often the case that no single set of weights can be found which
successfully incorporates all of these modifications because together they
induce a large number of constraints and restrictions on the feasible solution
space. For example, a unique combination of categorical variables may not be
present in the sample data, even if the corresponding population level
information is available. Additional requirements for weights to fall within
specified ranges may also lead to fewer population level adjustments being
incorporated. We present a framework and accompanying computational methods to
address this issue of constraint achievement or selection within a restricted
space that will produce revised weights with reasonable properties. By
combining concepts from generalized raking, ridge and lasso regression,
benchmarking of small area estimates, augmentation of state-space equations,
path algorithms, and data-cloning, this framework simultaneously selects
constraints and provides diagnostics suggesting why a fully constrained
solution is not possible. Combinatoric operations such as brute force
evaluations of all possible combinations of constraints and restrictions are
avoided. We demonstrate this framework by applying alternative methods to
post-stratification for the National Survey on Drug Use and Health. We also
discuss strategies for scaling up to even larger data sets. Computations were
performed in R and code is available from the authors.


  Two years of Kepler data of KIC 8054146 (delta Sct/gamma Dor hybrid) revealed
349 statistically significant frequencies between 0.54 and 191.36 c/d (6.3
microHz to 2.21 mHz). The 117 low frequencies cluster in specific frequency
bands, but do not show the equidistant period spacings predicted for gravity
modes of successive radial order, n, and reported for at least one other hybrid
pulsator. The four dominant low frequencies in the 2.8 to 3.0 c/d (32 to 35
microHz) range show strong amplitude variability with timescales of months and
years. These four low frequencies also determine the spacing of the higher
frequencies in and beyond the delta Sct pressure-mode frequency domain. In
fact, most of the higher frequencies belong to one of three families with
spacings linked to a specific dominant low frequency. In the Fourier spectrum,
these family regularities show up as triplets, high-frequency sequences with
absolutely equidistant frequency spacings, side lobes (amplitude modulations)
and other regularities in frequency spacings. Furthermore, within two families
the amplitude variations between the low and high frequencies are related. We
conclude that the low frequencies (gravity modes, rotation) and observed high
frequencies (mostly pressure modes) are physically connected. This unusual
behavior may be related to the very rapid rotation of the star: from a
combination of high and low-resolution spectroscopy we determined that KIC
8054146 is a very fast rotator (v sin i = 300 +/- 20 km/s) with an effective
temperature of 7600 +/- 200 K and a surface gravity log g of 3.9 +/- 0.3.
Several astrophysical ideas explaining the origin of the relationship between
the low and high frequencies are explored.


  This paper proposes a novel deep reinforcement learning (RL) architecture,
called Value Prediction Network (VPN), which integrates model-free and
model-based RL methods into a single neural network. In contrast to typical
model-based RL methods, VPN learns a dynamics model whose abstract states are
trained to make option-conditional predictions of future values (discounted sum
of rewards) rather than of future observations. Our experimental results show
that VPN has several advantages over both model-free and model-based baselines
in a stochastic environment where careful planning is required but building an
accurate observation-prediction model is difficult. Furthermore, VPN
outperforms Deep Q-Network (DQN) on several Atari games even with
short-lookahead planning, demonstrating its potential as a new way of learning
a good state representation.


  As an important type of reinforcement learning algorithms, actor-critic (AC)
and natural actor-critic (NAC) algorithms are often executed in two ways for
finding optimal policies. In the first nested-loop design, actor's one update
of policy is followed by an entire loop of critic's updates of the value
function, and the finite-sample analysis of such AC and NAC algorithms have
been recently well established. The second two time-scale design, in which
actor and critic update simultaneously but with different learning rates, has
much fewer tuning parameters than the nested-loop design and is hence
substantially easier to implement. Although two time-scale AC and NAC have been
shown to converge in the literature, the finite-sample convergence rate has not
been established. In this paper, we provide the first such non-asymptotic
convergence rate for two time-scale AC and NAC under Markovian sampling and
with actor having general policy class approximation. We show that two
time-scale AC requires the overall sample complexity at the order of
$\mathcal{O}(\epsilon^{-2.5}\log^3(\epsilon^{-1}))$ to attain an
$\epsilon$-accurate stationary point, and two time-scale NAC requires the
overall sample complexity at the order of
$\mathcal{O}(\epsilon^{-4}\log^2(\epsilon^{-1}))$ to attain an
$\epsilon$-accurate global optimal point. We develop novel techniques for
bounding the bias error of the actor due to dynamically changing Markovian
sampling and for analyzing the convergence rate of the linear critic with
dynamically changing base functions and transition kernel.


  There is evidence of a second neutral pion from: (1) the anomalous branching
ratios in the reactions p-bar p -> pi pi and p-bar d -> pi pi N, and (2) the
1960's results of Tsai-Chu et al. for antinucleon annihilation stars in
emulsions. The anomaly of (1) is eliminated if the two neutral pions in the
reactions p-bar p -> pi_0 pi_0 and p-bar d -> pi_0 pi_0 n are not identical.
Tsai-Chu et al. observed a second neutral pion that ``decays more rapidly into
electron pairs with larger opening angles and more frequently into double
pairs.'' One antineutron annihilation event produced three neutral particles
(each with a mass of 135 +/- 14 MeV), and each decayed into four electrons with
much wider opening angles than those of the internal conversion electrons seen
in pi-zero decays. The larger opening angles and much more frequent double pair
production could be caused by neutral pions with a lifetime so short that they
sometimes decay into photon pairs before they can leave the annihilation
nucleus (e.g., Ag) of the emulsion. We discuss several methods of searching for
this second neutral pion.


  Static analysis tools have gained popularity among developers for finding
potential bugs, but their widespread adoption is hindered by the accomnpanying
high false alarm rates (up to 90%). To address this challenge, previous studies
proposed the concept of actionable warnings, and apply machine-learning methods
to distinguish actionable warnings from false alarms. Despite these efforts,
our preliminary study suggests that the current methods used to collect
actionable warnings are rather shaky and unreliable, resulting in a large
proportion of invalid actionable warnings. In this work, we mined 68,274
reversions from Top-500 Github C repositories to create a substantia actionable
warning dataset and assigned weak labels to each warning's likelihood of being
a real bug. To automatically identify actionable warnings and recommend those
with a high probability of being real bugs (AWHB), we propose a two-stage
framework called ACWRecommender. In the first stage, our tool use a pre-trained
model, i.e., UniXcoder, to identify actionable warnings from a huge number of
SA tool's reported warnings. In the second stage, we rerank valid actionable
warnings to the top by using weakly supervised learning. Experimental results
showed that our tool outperformed several baselines for actionable warning
detection (in terms of F1-score) and performed better for AWHB recommendation
(in terms of nDCG and MRR). Additionaly, we also performed an in-the-wild
evaluation, we manually validated 24 warnings out of 2,197 reported warnings on
10 randomly selected projects, 22 of which were confirmed by developers as real
bugs, demonstrating the practical usage of our tool.


  One of the ultimate goals in biology is to understand the design principles
of biological systems. Such principles, if they exist, can help us better
understand complex, natural biological systems and guide the engineering of de
novo ones. Towards deciphering design principles, in silico evolution of
biological systems with proper abstraction is a promising approach. Here, we
demonstrate the application of in silico evolution combined with rule-based
modelling for exploring design principles of cellular signaling networks. This
application is based on a computational platform, called BioJazz, which allows
in silico evolution of signaling networks with unbounded complexity. We provide
a detailed introduction to BioJazz architecture and implementation and describe
how it can be used to evolve and/or design signaling networks with defined
dynamics. For the latter, we evolve signaling networks with switch-like
response dynamics and demonstrate how BioJazz can result in new biological
insights on network structures that can endow bistable response dynamics. This
example also demonstrated both the power of BioJazz in evolving and designing
signaling networks and its limitations at the current stage of development.


  Twisted bilayer graphene (TwBLG) is one of the simplest van der Waals
heterostructures, yet it yields a complex electronic system with intricate
interplay between moir\'{e} physics and interlayer hybridization effects. We
report on electronic transport measurements of high mobility small angle TwBLG
devices showing clear evidence for insulating states at the superlattice band
edges, with thermal activation gaps several times larger than theoretically
predicted. Moreover, Shubnikov-de Haas oscillations and tight binding
calculations reveal that the band structure consists of two intersecting Fermi
contours whose crossing points are effectively unhybridized. We attribute this
to exponentially suppressed interlayer hopping amplitudes for momentum
transfers larger than the moir\'{e} wavevector.


  [Abridged] We carried out optical polarimetry of five dense cores, (IRAM
04191, L1521F, L328, L673-7, and L1014) which are found to harbour VeLLO. This
study was conducted mainly to understand the role played by the magnetic field
in the formation of very low and substellar mass range objects using optical
polarisation. The angular offsets between the envelope magnetic field direction
(inferred from optical polarisation measurements) and the outflow position
angles from the VeLLOs in IRAM 04191, L1521F, L328, L673-7, and L1014 are found
to be 84$^\circ$, 53$^\circ$, 24$^\circ$, 08$^\circ$, and 15$^\circ$,
respectively. The mean value of the offsets for all the five clouds is
$\sim37^\circ$. If we exclude IRAM 04191, the mean value reduces to become
$\sim25^\circ$. In IRAM 04191, the offset between the projected envelope and
the inner magnetic field (inferred from the submillimetre data from SCUPOL) is
found to be $\sim68^\circ$. The inner magnetic field, however, is found to be
nearly aligned with the projected position angles of the minor axis, the
rotation axis of the cloud, and the outflow from the IRAM 04191-IRS. We discuss
a possible explanation for the nearly perpendicular orientation between the
envelope and core scale magnetic fields in IRAM04191. The angular offset
between the envelope magnetic field direction and the minor axis of IRAM 04191,
L1521F, L673-7, and L1014 are 82$^\circ$, 60$^\circ$, 47$^\circ$, and
55$^\circ$, respectively. The mean value of the offsets between the envelope
magnetic field and the minor axis position angles for the four cores is found
to be $\sim60^\circ$. The results obtained from our study on the limited sample
of five cores with VeLLOs show that the outflows in three of them tend to
nearly align with the envelope magnetic field.


  Black hole feedback is now a standard component of galaxy formation models.
These models predict that the impact of black hole activity on its host galaxy
likely peaked at z=2-3, the epoch of strongest star formation activity and
black hole accretion activity in the Universe. We used XShooter on the Very
Large Telescope to measure rest-frame optical spectra of four z~2.5 extremely
red quasars with infrared luminosities ~10^47 erg/sec. We present the discovery
of very broad (full width at half max= 2600-5000 km/sec), strongly blue-shifted
(by up to 1500 km/sec) [OIII]5007A emission lines in these objects. In a large
sample of obscured and red quasars, [OIII] kinematics are positively correlated
with infrared luminosity, and the four objects in our sample are on the extreme
end both in [OIII] kinematics and infrared luminosity. We estimate that ~3% of
the bolometric luminosity in these objects is being converted into the kinetic
power of the observed wind. Photo-ionization estimates suggest that the [OIII]
emission might be extended on a few kpc scales, which would suggest that the
extreme outflow is affecting the entire host galaxy of the quasar. These
sources may be the signposts of the most extreme form of quasar feedback at the
peak epoch of galaxy formation, and may represent an active "blow-out" phase of
quasar evolution.


  We numerically study the origin of the multi-armed spiral structure observed
in the circumnuclear gaseous mini-disks of nearby galaxies. We show that the
presence of dust in such disks and its interaction with the gravitationally
stable gaseous component leads to the development of a multi-armed spiral
structure. As a particular example, we study the formation of the multi-armed
spiral pattern in the mini-disk of the galaxy NGC 4736, for which the
observational data for the rotation and the density distribution are available.
We find that the multi-armed spiral structure grows in the stable gaseous
mini-disk of NGC 4736 if the gas-to-dust ratio is about 5-20 percent. We also
demonstrate that together with the dust concentration, the important factor for
the development of instability is the size of the dust grains. A nonlinear
multi-armed spiral pattern develops in the stable gaseous disk with sizes of
grains larger than one micron. If future observations confirm the presence of a
large amount of dust in the mini-disks of galaxies, this will pinpoint the
mechanism of the formation of the multi-armed spiral structure in them.


  Large Language Models (LLMs) show promise in code generation tasks. However,
their code-writing abilities are often limited in scope: while they can
successfully implement simple functions, they struggle with more complex tasks.
A fundamental difference with how an LLM writes code, compared to a human
programmer, is that it cannot consistently spot and fix bugs. Debugging is a
crucial skill for programmers and it enables iterative code refinement towards
a correct implementation. In this work, we propose a novel algorithm to enable
LLMs to debug their code via self-reflection and search where a model attempts
to identify its previous mistakes. Our key contributions are 1) a best-first
tree search algorithm with self-reflections (BESTER) that achieves
state-of-the-art Pass@1 in three code generation benchmarks. BESTER maintains
its superiority when we measure pass rates taking into account additional
inference costs incurred by tree search. 2) A novel interpretability study on
what self-reflections attend to in buggy programs and how they impact bug
fixes, which provides a deeper understanding of the debugging process. 3) An
extensive study on when self-reflections are effective in finding bugs.


  We study a general framework for broadcast gossip algorithms which use
companion variables to solve the average consensus problem. Each node maintains
an initial state and a companion variable. Iterative updates are performed
asynchronously whereby one random node broadcasts its current state and
companion variable and all other nodes receiving the broadcast update their
state and companion variable. We provide conditions under which this scheme is
guaranteed to converge to a consensus solution, where all nodes have the same
limiting values, on any strongly connected directed graph. Under stronger
conditions, which are reasonable when the underlying communication graph is
undirected, we guarantee that the consensus value is equal to the average, both
in expectation and in the mean-squared sense. Our analysis uses tools from
non-negative matrix theory and perturbation theory. The perturbation results
rely on a parameter being sufficiently small. We characterize the allowable
upper bound as well as the optimal setting for the perturbation parameter as a
function of the network topology, and this allows us to characterize the
worst-case rate of convergence. Simulations illustrate that, in comparison to
existing broadcast gossip algorithms, the approaches proposed in this paper
have the advantage that they simultaneously can be guaranteed to converge to
the average consensus and they converge in a small number of broadcasts.


  We prove that a four-dimensional Lorentzian manifold that is curvature
homogeneous of order 3, or CH_3 for short, is necessarily locally homogeneous.
We also exhibit and classify four-dimensional Lorentzian, CH_2 manifolds that
are not homogeneous. The resulting metrics belong to the class of null
electromagnetic radiation, type N solutions on an anti-de Sitter background.
These findings prove that the four-dimensional Lorentzian Singer number
$k_{1,3}=3$, falsifying some recent conjectures by Gilkey. We also prove that
invariant classification for these proper CH_2 solutions requires
$\nabla^{(7)}R$, and that these are the unique metrics requiring the seventh
order.


  Let $(M,g)$ be a time oriented Lorentzian manifold and $d$ the Lorentzian
distance on $M$. The function $\tau(q):=\sup_{p< q} d(p,q)$ is the cosmological
time function of $M$, where as usual $p< q$ means that $p$ is in the causal
past of $q$. This function is called regular iff $\tau(q) < \infty$ for all $q$
and also $\tau \to 0$ along every past inextendible causal curve. If the
cosmological time function $\tau$ of a space time $(M,g)$ is regular it has
several pleasant consequences: (1) It forces $(M,g)$ to be globally hyperbolic,
(2) every point of $(M,g)$ can be connected to the initial singularity by a
rest curve (i.e., a timelike geodesic ray that maximizes the distance to the
singularity), (3) the function $\tau$ is a time function in the usual sense, in
particular (4) $\tau$ is continuous, in fact locally Lipschitz and the second
derivatives of $\tau$ exist almost everywhere.


  For $k\geq 3$, a k-rollercoaster is a sequence of numbers whose every maximal
contiguous subsequence, that is increasing or decreasing, has length at least
$k$; $3$-rollercoasters are called simply rollercoasters. Given a sequence of
distinct numbers, we are interested in computing its maximum-length (not
necessarily contiguous) subsequence that is a $k$-rollercoaster. Biedl et al.
[ICALP 2018] have shown that each sequence of $n$ distinct real numbers
contains a rollercoaster of length at least $\lceil n/2\rceil$ for $n>7$, and
that a longest rollercoaster contained in such a sequence can be computed in
$O(n\log n)$-time. They have also shown that every sequence of $n\geq
(k-1)^2+1$ distinct real numbers contains a $k$-rollercoaster of length at
least $\frac{n}{2(k-1)}-\frac{3k}{2}$, and gave an $O(nk\log n)$-time algorithm
computing a longest $k$-rollercoaster in a sequence of length $n$.
  In this paper, we give an $O(nk^2)$-time algorithm computing the length of a
longest $k$-rollercoaster contained in a sequence of $n$ distinct real numbers;
hence, for constant $k$, our algorithm computes the length of a longest
$k$-rollercoaster in optimal linear time. The algorithm can be easily adapted
to output the respective $k$-rollercoaster. In particular, this improves the
results of Biedl et al. [ICALP 2018], by showing that a longest rollercoaster
can be computed in optimal linear time. We also present an algorithm computing
the length of a longest $k$-rollercoaster in $O(n \log^2 n)$-time, that is,
subquadratic even for large values of $k\leq n$. Again, the rollercoaster can
be easily retrieved. Finally, we show an $\Omega(n \log k)$ lower bound for the
number of comparisons in any comparison-based algorithm computing the length of
a longest $k$-rollercoaster.


  A method is presented that, when used in conjunction with single molecule
experimental techniques, allows for the extraction of rates and mechanical
properties of a biomolecule undergoing transitions between mechanically
distinct states. This analysis enables the exploration of systems where the
lifetimes of survival are of order of the intrinsic time constant of the
experimental apparatus; permitting the study of kinetic events whose transition
rates are an order of magnitude (or two) larger than those that can be studied
with traditional averaging methods. Using current experimental techniques, this
allows for the study of biomolecules whose lifetime of survival in a given
state are as low as milliseconds down to microseconds. The relevant observable
is the auto-correlation function of the experimental probe that is attached to
the biomolecule of interest. General solutions are expressed in terms of a
series. Closed form solutions are found for two physically opposing limits:
where transitions between the mechanically distinct states of the biomolecule
occur on either much faster or much slower time scales than those governing the
motion of the experimental probe. Motivated by the derivation of these opposing
bounds, two series solutions for the general case are then presented. We
present an error analysis for truncating each series at arbitrary order and
obtain a range of parameters for which this method could be applicable to the
study of the two state biomolecular problem. Finally, both series (up to third
order) are expressed for the two state problem when the system obeys Markov
statistics. These solutions should be amiable to the analysis of experimental
data, expanding temporal analysis of data from single molecule experiments.


  Glaucoma is one of the ophthalmic diseases that may cause blindness, for
which early detection and treatment are very important. Fundus images and
optical coherence tomography (OCT) images are both widely-used modalities in
diagnosing glaucoma. However, existing glaucoma grading approaches mainly
utilize a single modality, ignoring the complementary information between
fundus and OCT. In this paper, we propose an efficient multi-modality
supervised contrastive learning framework, named COROLLA, for glaucoma grading.
Through layer segmentation as well as thickness calculation and projection,
retinal thickness maps are extracted from the original OCT volumes and used as
a replacing modality, resulting in more efficient calculations with less memory
usage. Given the high structure and distribution similarities across medical
image samples, we employ supervised contrastive learning to increase our
models' discriminative power with better convergence. Moreover, feature-level
fusion of paired fundus image and thickness map is conducted for enhanced
diagnosis accuracy. On the GAMMA dataset, our COROLLA framework achieves
overwhelming glaucoma grading performance compared to state-of-the-art methods.


  Let F_2 be the free group generated by x and y. In this article, we prove
that the commutator of x^m and y^n is a product of two squares if and only if
mn is even. We also show using topological methods that there are infinitely
many obstructions for an element in F_2 to be a product of two squares.


  We study the problem of change point detection for covariance matrices in
high dimensions. We assume that we observe a sequence {X_i}_{i=1,...,n} of
independent and centered p-dimensional sub-Gaussian random vectors whose
covariance matrices are piecewise constant. Our task is to recover with high
accuracy the number and locations of the change points, which are assumed
unknown. Our generic model setting allows for all the model parameters to
change with n, including the dimension p, the minimal spacing between
consecutive change points, the magnitude of smallest change size and the
maximal Orlicz- 2 norm of the covariance matrices of the sample points. Without
assuming any additional structural assumption, such as low rank matrices or
having sparse principle components, we set up a general framework and a
benchmark result for the covariance change point detection problem. We
introduce two procedures, one based on the binary segmentation algorithm (e.g.
Vostrikova, 1981) and the other on its extension known as wild binary
segmentation of Fryzlewicz (2014), and demonstrate that, under suitable
conditions, both procedures are able to consistently es- timate the number and
locations of change points. Our second algorithm, called Wild Binary
Segmentation through Independent Projection (WBSIP), is shown to be optimal in
the sense of allowing for the minimax scaling in all the relevant parameters.
Our minimax analysis reveals a phase transition effect based on the problem of
change point localization. To the best of our knowledge, this type of results
has not been established elsewhere in the high-dimensional change point
detection literature.


  A general overview of the results obtained by the ALICE experiment from the
analysis of the $\PbPb$ data sample collected at the end of 2010 during the
first heavy-ion run at the LHC is presented.


  The appearance of a geometric flow in the conservation law of particle number
in classical particle diffusion and in the conservation law of probability in
quantum mechanics is discussed in the geometrical environment of a
two-dimensional curved surface with thickness $\epsilon$ embedded in $R_3$.
  In such a system with a small thickness $\epsilon$, the usual two-dimensional
conservation law does not hold and we find an anomaly. The anomalous term is
obtained by the expansion of $\epsilon$. We find that this term has a Gaussian
and mean curvature dependence and can be written as the total divergence of
some geometric flow. We then have a new conservation law by adding the
geometric flow to the original one. This fact holds in both classical diffusion
and quantum mechanics when we confine particles to a curved surface with a
small thickness.


  Human keypoint detection from a single image is very challenging due to
occlusion, blur, illumination and scale variance of person instances. In this
paper, we find that context information plays an important role in addressing
these issues, and propose a novel method named progressive context refinement
(PCR) for human keypoint detection. First, we devise a simple but effective
context-aware module (CAM) that can efficiently integrate spatial and channel
context information to aid feature learning for locating hard keypoints. Then,
we construct the PCR model by stacking several CAMs sequentially with shortcuts
and employ multi-task learning to progressively refine the context information
and predictions. Besides, to maximize PCR's potential for the aforementioned
hard case inference, we propose a hard-negative person detection mining
strategy together with a joint-training strategy by exploiting the unlabeled
coco dataset and external dataset. Extensive experiments on the COCO keypoint
detection benchmark demonstrate the superiority of PCR over representative
state-of-the-art (SOTA) methods. Our single model achieves comparable
performance with the winner of the 2018 COCO Keypoint Detection Challenge. The
final ensemble model sets a new SOTA on this benchmark.


  The $\beta$-decay of neutron-rich $^{129}$In into $^{129}$Sn was studied
using the GRIFFIN spectrometer at the ISAC facility at TRIUMF. The study
observed the half-lives of the ground state and each of the $\beta$-decaying
isomers. The level scheme of $^{129}$Sn has been expanded with thirty-one new
$\gamma$-ray transitions and nine new excited levels, leading to a
re-evaluation of the $\beta$-branching ratios and level spin assignments. The
observation of the $\beta$-decay of the (29/2$^{+}$) 1911-keV isomeric state in
$^{129}$In is reported for the first time, with a branching ratio of
2.0(5)$\%$.


  In this work, a third-order Chapman-Enskog analysis of the
multiple-relaxation-time (MRT) pseudopotential lattice Boltzmann (LB) model for
multiphase flow is performed for the first time. The leading terms on the
interaction force, consisting of an anisotropic and an isotropic term, are
successfully identified in the third-order macroscopic equation recovered by
the lattice Boltzmann equation (LBE), and then new mathematical insights into
the pseudopotential LB model are provided. For the third-order anisotropic
term, numerical tests show that it can cause the stationary droplet to become
out-of-round, which suggests the isotropic property of the LBE needs to be
seriously considered in the pseudopotential LB model. By adopting the classical
equilibrium moment or setting the so-called "magic" parameter to 1/12, the
anisotropic term can be eliminated, which is found from the present third-order
analysis and also validated numerically. As for the third-order isotropic term,
when and only when it is considered, accurate continuum form pressure tensor
can be definitely obtained, by which the predicted coexistence densities always
agree well with the numerical results. Compared with this continuum form
pressure tensor, the classical discrete form pressure tensor is accurate only
when the isotropic term is a specific one. At last, in the framework of the
present third-order analysis, a consistent scheme for third-order additional
term is proposed, which can be used to independently adjust the coexistence
densities and surface tension. Numerical tests are subsequently carried out to
validate the present scheme.


  Type Ia and other peculiar supernovae (SNe) are thought to originate from the
thermonuclear explosions of white dwarfs (WDs). Some of the proposed channels
involve the ejection of a partly exploded WD (e.g. Iax SN remnant) or the
companion of an exploding WD at extremely high velocities ($>400$
km\,s$^{-1}$). Characterisation of such hyper-runaway/hypervelocity (HVS) WDs
might therefore shed light on the physics and origins of SNe. Here we analyse
the \textit{Gaia} DR3 data to search for HVS WDs candidates, and peculiar
sub-main-sequence (sub-MS) objects. We retrieve the previously identified HVSs,
and find 46 new HVS candidates. Among these we identify two new unbound WDs and
two new unbound sub-MS candidates. The remaining stars are hyper-runaway WDs
and hyper-runaway sub-MS stars. The numbers and properties of the HVS WD and
sub-MS candidates suggest that extreme velocity ejections ($>1000$
km\,s$^{-1}$) can accompany at most a small fraction of type Ia SNe,
disfavouring a significant contribution of the D6-scenario to the origin of Ia
SNe. The rate of HVS ejections following the hybrid WD reverse-detonation
channel could be consistent with the identified HVSs. The numbers of
lower-velocity HVS WDs could be consistent with type Iax SNe origin and/or
contribution from dynamical encounters. We also searched for HVS WDs related to
known SN remnants, but identified only one such candidate.


  Let $n\ge 1$ be an integer and $e_n(x)$ denote the truncated exponential
Taylor polynomial, i.e. $e_{n}(x)=\sum_{i=0}^n\frac{x^i}{i!}$. A well-known
theorem of Schur states that the Galois group of $e_n(x)$ over $\Q$ is the
alternating group $A_n$ if $n$ is divisible by 4 or the symmetric group $S_n$
otherwise. In this paper, we study algebraic properties of the summation of two
truncated exponential Taylor polynomials $\E_n(x):=e_n(x)+e_{n-1}(x)$. We show
that $\frac{x^n}{n!}+\sum_{i=0}^{n-1}c_i\frac{x^i}{i!}$ with all $c_i \ (0\le
i\le n-1)$ being integers is irreducible over $\Q$ if either $c_0=\pm 1$, or
$n$ is not a positive power of $2$ but $|c_0|$ is a positive power of 2. This
extends another theorem of Schur. We show also that $\E_n(x)$ is irreducible if
$n\not\in\{2,4\}$. Furthermore, we show that ${\rm Gal}_{\Q}(\E_n)$ contains
$A_{n}$ except for $n=4$, in which case, ${\rm Gal}_{\Q}(\E_4)=S_3$. Finally,
we show that the Galois group ${\rm Gal}_{\Q}(\E_n)$ is $S_n$ if $n\equiv 3
\pmod 4$, or if $n$ is even and $v_p(n!)$ is odd for a prime divisor of $n-1$,
or if $n\equiv 1\pmod 4$ and $n-2$ equals the product of an odd prime number
$p$ which is coprime to $\sum_{i=1}^{p-1}2^{p-1-i}i!$ and a positive integer
coprime to $p$.


  There is an increasing consensus that the design and optimization of low
light image enhancement methods need to be fully driven by perceptual quality.
With numerous approaches proposed to enhance low-light images, much less work
has been dedicated to quality assessment and quality optimization of low-light
enhancement. In this paper, to close the gap between enhancement and
assessment, we propose a loop enhancement framework that produces a clear
picture of how the enhancement of low-light images could be optimized towards
better visual quality. In particular, we create a large-scale database for
QUality assessment Of The Enhanced LOw-Light Image (QUOTE-LOL), which serves as
the foundation in studying and developing objective quality assessment
measures. The objective quality assessment measure plays a critical bridging
role between visual quality and enhancement and is further incorporated in the
optimization in learning the enhancement model towards perceptual optimally.
Finally, we iteratively perform the enhancement and optimization tasks,
enhancing the low-light images continuously. The superiority of the proposed
scheme is validated based on various low-light scenes. The database as well as
the code will be available.


  We address the problem of constructing elliptic polytopes in R^d, which are
convex hulls of finitely many two-dimensional ellipses with a common center.
Such sets arise in the study of spectral properties of matrices, asymptotics of
long matrix products, in the Lyapunov stability, etc.. The main issue in the
construction is to decide whether a given ellipse is in the convex hull of
others. The computational complexity of this problem is analysed by considering
an equivalent optimisation problem. We show that the number of local extrema of
that problem may grow exponentially in d. For d=2,3, it admits an explicit
solution for an arbitrary number of ellipses; for higher dimensions, several
geometric methods for approximate solutions are derived. Those methods are
analysed numerically and their efficiency is demonstrated in applications.


  Causal graphs, such as directed acyclic graphs (DAGs) and partial ancestral
graphs (PAGs), represent causal relationships among variables in a model.
Methods exist for learning DAGs and PAGs from data and for converting DAGs to
PAGs. However, these methods are significantly limited in that they only output
a single causal graph consistent with the independencies and dependencies (the
Markov equivalence class $M$) estimated from the data. This is problematic and
insufficient because many distinct graphs may be consistent with $M$. A data
modeler may wish to select among these numerous consistent graphs using domain
knowledge or other model selection algorithms. Enumeration of the set of
consistent graphs is the bottleneck. In this paper, we present a method that
makes this desired enumeration possible. We introduce PAG2ADMG, the first
algorithm for enumerating all causal graphs consistent with $M$. PAG2ADMG
converts a given PAG into the complete set of acyclic directed mixed graphs
(ADMGs) consistent with $M$. We prove the correctness of the approach and
demonstrate its efficiency relative to brute-force enumeration.


  Aizenbud, Gourevitch, Rallis and Schiffmann proves results of multicity one
in different cases, in particular for orthogonal groups. Using the same method,
we prove the same result for special orthogonal groups.


  In this talk, we study the impact of first order phase transitions with fast
bubble walls on mechanisms of leptogenesis and baryogenesis. We begin our
exploration with the usual leptogenesis where the breaking of $B-L$ occurs via
a PT with fast walls. Then we move to a more exotic case where the $B-L$
breaking phase transition creates heavy particles in the plasma and catalizes
the leptogenesis. Finally, we apply the same production mechanism to the EWPT
at low energy and build a new model of EWBG. Those models are all original and
contain crucial new phenomenological aspects like the emission of large amount
of Gravitational waves.


  Tutte founded the theory of enumeration of planar maps in a series of papers
in the 1960s. Rooted non-separable planar maps are in bijection with
West-2-stack-sortable permutations, beta(1,0)-trees introduced by Cori,
Jacquard and Schaeffer in 1997, as well as a family of permutations defined by
the avoidance of two four letter patterns. In this paper we give upper and
lower bounds on the number of multiple-edge-free rooted non-separable planar
maps. We also use the bijection between rooted non-separable planar maps and a
certain class of permutations, found by Claesson, Kitaev and Steingrimsson in
2009, to show that the number of 2-faces (excluding the root-face) in a map
equals the number of occurrences of a certain mesh pattern in the permutations.
We further show that this number is also the number of nodes in the
corresponding beta(1,0)-tree that are single children with maximum label.
Finally, we give asymptotics for some of our enumerative results.


  We are concerned about the barotropic compressible Navier-Stokes equations
with density-dependent viscosities which may degenerate in vacuum. We show that
any classical solution to barotropic compressible Navier-Stokes equations in
bounded domains will blow up, when the initial density admits an isolated mass
group and the viscousity coefficients satisfy some conditions. A new condition
on viscosities is first put forward in this paper.


  Human action recognition and performance assessment have been hot research
topics in recent years. Recognition problems have mature solutions in the field
of sign language, but past research in performance analysis has focused on
competitive sports and medical training, overlooking the scoring assessment
,which is an important part of sign language teaching digitalization. In this
paper, we analyze the existing technologies for performance assessment and
adopt methods that perform well in human pose reconstruction tasks combined
with motion rotation embedded expressions, proposing a two-stage sign language
performance evaluation pipeline. Our analysis shows that choosing
reconstruction tasks in the first stage can provide more expressive features,
and using smoothing methods can provide an effective reference for assessment.
Experiments show that our method provides good score feedback mechanisms and
high consistency with professional assessments compared to end-to-end
evaluations.


  In this work, we investigate the diversity-multiplexing tradeoff (DMT) of the
multiple-antenna (MIMO) static half-duplex relay channel. A general expression
is derived for the DMT upper bound, which can be achieved by a
compress-and-forward protocol at the relay, under certain assumptions. The DMT
expression is given as the solution of a minimization problem in general, and
an explicit expression is found when the relay channel is symmetric in terms of
number of antennas, i.e. the source and the destination have n antennas each,
and the relay has m antennas. It is observed that the static half-duplex DMT
matches the full-duplex DMT when the relay has a single antenna, and is
strictly below the full-duplex DMT when the relay has multiple antennas.
Besides, the derivation of the upper bound involves a new asymptotic study of
spherical integrals (that is, integrals with respect to the Haar measure on the
unitary group U(n)), which is a topic of mathematical interest in itself.


  Holomorphic chains on a Riemann surface arise naturally as fixed points of
the natural C*-action on the moduli space of Higgs bundles. In this paper we
associate a new quiver bundle to the Hom-complex of two chains, and prove that
stability of the chains implies stability of this new quiver bundle. Our
approach uses the Hitchin-Kobayashi correspondence for quiver bundles.
Moreover, we use our result to give a new proof of a key lemma on chains (due
to \'Alvarez-C\'onsul, Garc\'ia-Prada and Schmitt), which has been important in
the study of Higgs bundle moduli; this proof relies on stability and thus
avoids the direct use of the chain vortex equations.


  We develop a general theory of adiabatic output coupling from trapped atomic
Bose-Einstein Condensates at finite temperatures. For weak coupling, the output
rate from the condensate, and the excited levels in the trap, settles in a time
proportional to the inverse of the spectral width of the coupling to the output
modes. We discuss the properties of the output atoms in the quasi-steady-state
where the population in the trap is not appreciably depleted. We show how the
composition of the output beam, containing condensate and thermal component,
may be controlled by changing the frequency of the output coupler. This
composition determines the first and second order coherence of the output beam.
We discuss the changes in the composition of the bose gas left in the trap and
show how nonresonant output coupling can stimulate either the evaporation of
thermal excitations in the trap or the growth of non-thermal excitations, when
pairs of correlated atoms leave the condensate.


  A compact approach based on the folding model is suggested for the
determination of the isoscalar and isovector transition strengths of the
low-lying ($\Delta S=\Delta T=0$) excitations induced by inelastic proton
scattering measured with exotic beams. Our analysis of the recently measured
inelastic $^{18,20}$O+p scattering data at $E_{\rm lab}=30$ and 43 MeV/nucleon
has given for the first time an accurate estimate of the isoscalar $\beta_0$
and isovector $\beta_1$ deformation parameters (which cannot be determined from
the (p,p') data alone by standard methods) for 2$^+_1$ and $3^-_1$ excited
states in $^{18,20}$O. Quite strong isovector mixing was found in the 2$^+_1$
inelastic $^{20}$O+p scattering channel, where the strength of the isovector
form factor $F_1$ (prototype of the Lane potential) corresponds to a $\beta_1$
value almost 3 times larger than $\beta_0$ and a ratio of nuclear transition
matrix elements $M_n/M_p\simeq 4.2$.


  Background: Previous functional connectivity studies have found both hypo-
and hyper-connectivity in brains of individuals having autism spectrum disorder
(ASD). Here we studied abnormalities in functional brain subnetworks in
high-functioning individuals with ASD during free viewing of a movie containing
social cues and interactions. Methods: Thirteen subjects with ASD and 13
matched-pair controls watched a 68 minutes movie during functional magnetic
resonance imaging. For each subject, we computed Pearson`s correlation between
haemodynamic time-courses of each pair of 6-mm isotropic voxels. From the
whole-brain functional networks, we derived individual and group-level
subnetworks using graph theory. Scaled inclusivity was then calculated between
all subject pairs to estimate intersubject similarity of connectivity structure
of each subnetwork. Additional 27 individuals with ASD from the ABIDE
resting-state database were included to test the reproducibility of the
results. Results: Between-group differences were observed in the composition of
default-mode and a ventro-temporal-limbic (VTL) subnetwork. The VTL subnetwork
included amygdala, striatum, thalamus, parahippocampal, fusiform, and inferior
temporal gyri. Further, VTL subnetwork similarity between subject pairs
correlated significantly with similarity of symptom gravity measured with
autism quotient. This correlation was observed also within the controls, and in
the reproducibility dataset with ADI-R and ADOS scores. Conclusions:
Reorganization of functional subnetworks in individuals with ASD clarifies the
mixture of hypo- and hyper-connectivity findings. Importantly, only the
functional organization of the VTL subnetwork emerges as a marker of
inter-individual similarities that co-vary with behavioral measures across all
participants. These findings suggest a pivotal role of ventro-temporal and
limbic systems in autism.


  We present an isometric version of the complementably universal Banach space
$\mathbb{P}$ with a Schauder decomposition. The space $\mathbb{P}$ is
isomorphic to Pe{\l}czy\'nski's space with a universal basis as well as to
Kadec' complementably universal space with the bounded approximation property.


  The problems of Hadamard quantum coin flipping in n-trials and related
generalized Fibonacci sequences of numbers were introduced in [1]. It was shown
that for an arbitrary number of repeated consecutive states, probabilities are
determined by Fibonacci numbers for duplicated states, Tribonacci numbers for
triplicated states and N-Bonacci numbers for arbitrary N-plicated states. In
the present paper we generalize these results for direct product of multiple
qubit states and arbitrary position of repeated states. The calculations are
based on structure of Fibonacci trees in space of qubit states, growing in the
left and in the right directions, and number of branches and allowed paths on
the trees. By using $n$-qubit quantum coins as random n-qubit states with
maximal Shannon entropy, we show that quantum probabilities can be calculated
by means of geometric probabilities. It illustrates possible application of
geometric probabilities in quantum information theory. The Golden ratio of
probabilities and the limit of n going to infinity are discussed.


  Mathematical theory of an observer is elaborated upon the basis of
A.Poincare's ideas on the nature of geometry and the role of observer's
perceptive space. The said theory is generalizing reference frames theory in
GR. Physical structure (P-structure) and corresponding physical geometry
(P-geometry) notions, representing properties invariance of some physical
objects and their relations, are introduced. P-structure of classical physical
time and its corresponding chronogeometry is considered as an example. Some
quantitative characteristics of observer's visual space geometry are
experimentally determined. The affine model of visual geometry is offered to
interpret experimentally sampled data. The connection of the obtained results
with some problems of theoretical physics is being discussed.


  The rate of monopole decay into a dyon and an electron in an inhomogeneous
external electric field is calculated by semiclassical methods. Comparison is
made to an earlier result where this quantity was calculated for a constant
field. Experimental and cosmological tests are suggested.


  We consider the External Clock Synchronization problem in dynamic sensor
networks. Initially, sensors obtain inaccurate estimations of an external time
reference and subsequently collaborate in order to synchronize their internal
clocks with the external time. For simplicity, we adopt the drift-free
assumption, where internal clocks are assumed to tick at the same pace. Hence,
the problem is reduced to an estimation problem, in which the sensors need to
estimate the initial external time. This work is further relevant to the
problem of collective approximation of environmental values by biological
groups.
  Unlike most works on clock synchronization that assume static networks, this
paper focuses on an extreme case of highly dynamic networks. Specifically, we
assume a non-adaptive scheduler adversary that dictates in advance an
arbitrary, yet independent, meeting pattern. Such meeting patterns fit, for
example, with short-time scenarios in highly dynamic settings, where each
sensor interacts with only few other arbitrary sensors.
  We propose an extremely simple clock synchronization algorithm that is based
on weighted averages, and prove that its performance on any given independent
meeting pattern is highly competitive with that of the best possible algorithm,
which operates without any resource or computational restrictions, and knows
the meeting pattern in advance. In particular, when all distributions involved
are Gaussian, the performances of our scheme coincide with the optimal
performances. Our proofs rely on an extensive use of the concept of Fisher
information. We use the Cramer-Rao bound and our definition of a Fisher Channel
Capacity to quantify information flows and to obtain lower bounds on collective
performance. This opens the door for further rigorous quantifications of
information flows within collaborative sensors.


  We study the time-momentum representation of the kernel needed to compute
hadronic vacuum polarization contributions to the muon $g$-$2$ in the
space-like region at next-to-leading order. For small values of the time, we
present analytical series expansions; for large values of the time, we present
numerical series expansions which overcome the problems showed by na\"ive
asymptotic expansions. These results are to be employed in lattice QCD
determination of hadronic vacuum polarization contributions to the muon $g$-$2$
at next-to-leading order.


  Visual place recognition (VPR) is usually considered as a specific image
retrieval problem. Limited by existing training frameworks, most deep
learning-based works cannot extract sufficiently stable global features from
RGB images and rely on a time-consuming re-ranking step to exploit spatial
structural information for better performance. In this paper, we propose
StructVPR, a novel training architecture for VPR, to enhance structural
knowledge in RGB global features and thus improve feature stability in a
constantly changing environment. Specifically, StructVPR uses segmentation
images as a more definitive source of structural knowledge input into a CNN
network and applies knowledge distillation to avoid online segmentation and
inference of seg-branch in testing. Considering that not all samples contain
high-quality and helpful knowledge, and some even hurt the performance of
distillation, we partition samples and weigh each sample's distillation loss to
enhance the expected knowledge precisely. Finally, StructVPR achieves
impressive performance on several benchmarks using only global retrieval and
even outperforms many two-stage approaches by a large margin. After adding
additional re-ranking, ours achieves state-of-the-art performance while
maintaining a low computational cost.


  Dielectric loaded structures are promising candidates for use in the
structure wakefield acceleration (SWFA) technique, for both the collinear
wakefield and the two-beam acceleration (CWA and TBA respectively) approaches,
due to their low fabrication cost, low rf losses, and the potential to
withstand high gradient. A short pulse (<=20 ns) TBA program is under
development at the Argonne Wakefield Accelerator (AWA) facility where
dielectric loaded structures are being used for both the power
extractor/transfer structure (PETS) and the accelerator. In this study, an
X-band 11.7 GHz dielectric PETS was developed and tested at the AWA facility to
demonstrate high power wakefield generation. The PETS was driven by a train of
eight electron bunches separated by 769.2 ps (9 times of the X-band rf period)
in order to achieve coherent wakefield superposition. A total train charge of
360 nC was passed through the PETS structure to generate ~200 MW, ~3 ns
flat-top rf pulses without rf breakdown. A future experiment is being planned
to increase the generated rf power to approximately ~1 GW by optimizing the
structure design and improving the drive beam quality.


  If at least one of the members of a compact binary coalescence is charged,
the inspiral of the two members would generate a Poynting flux with an
increasing power, giving rise to a brief electromagnetic counterpart temporally
associated with the chirp signal of the merger (with possibly a small temporal
offset), which we term as the {\em charged Compact Binary Coalescence} (cCBC)
signal. We develop a general theory of cCBC for any mass and amount of charge
for each member. Neutron stars (NSs), as spinning magnets, are guaranteed to be
charged, so the cCBC signal should accompany all neutron star mergers. The cCBC
signal is clean in a BH-NS merger with a small mass ratio ($q \equiv m_2/m_1 <
0.2$), in which the NS plunges into the BH as a whole, and its
luminosity/energy can reach that of a fast radio burst if the NS is Crab-like.
The strength of the cCBC signal in Extreme Mass Ratio Inspiral Systems (EMRIs)
is also estimated.


  The properties of the massive neutron star PSR J0348+0432 is calculated in
the framework of the relativistic mean field theory by choosing the suitable
hyperon coupling constants. It is found that the central energy density
$\epsilon_{c}$ and the central pressure $p_{c}$ of the massive neutron star PSR
J0348+0432 respectively are 1.5 times larger and 3.6 times larger than those of
the canonical mass neutron star. It is also found that in the neutron star PSR
J0348+0432 there are five kinds of baryons appearing: n, p, $\Lambda$,
$\Xi^{-}$ and $\Xi^{0}$ but in the canonical mass neutron star there are only
three kinds of particles appearing: n, p and $\Lambda$. In our models, the
positive well depth $U_{\Sigma}^{(N)}$ will restrict the production of the
hyperons $\Sigma^{-}$, $\Sigma^{0}$ and $\Sigma^{+}$ and therefore either in
the neutron star PSR J0348+0432 or in the canonical mass neutron star the
hyperons $\Sigma^{-}$, $\Sigma^{0}$ and $\Sigma^{+}$ all do not appear. In
addition, our results also show that the radius $R$ of the massive neutron star
PSR J0348+0432 is less than that of the canonical mass neutron star while the
gravitational redshift of the former is larger than that of the latter.


  We investigate whether Jacobi preconditioning, accounting for the bootstrap
term in temporal difference (TD) learning, can help boost performance of
adaptive optimizers. Our method, TDprop, computes a per parameter learning rate
based on the diagonal preconditioning of the TD update rule. We show how this
can be used in both $n$-step returns and TD($\lambda$). Our theoretical
findings demonstrate that including this additional preconditioning information
is, surprisingly, comparable to normal semi-gradient TD if the optimal learning
rate is found for both via a hyperparameter search. In Deep RL experiments
using Expected SARSA, TDprop meets or exceeds the performance of Adam in all
tested games under near-optimal learning rates, but a well-tuned SGD can yield
similar improvements -- matching our theory. Our findings suggest that Jacobi
preconditioning may improve upon typical adaptive optimization methods in Deep
RL, but despite incorporating additional information from the TD bootstrap
term, may not always be better than SGD.


  Automatic text generation has received much attention owing to rapid
development of deep neural networks. In general, text generation systems based
on statistical language model will not consider anthropomorphic
characteristics, which results in machine-like generated texts. To fill the
gap, we propose a conditional language generation model with Big Five
Personality (BFP) feature vectors as input context, which writes human-like
short texts. The short text generator consists of a layer of long short memory
network (LSTM), where a BFP feature vector is concatenated as one part of input
for each cell. To enable supervised training generation model, a text
classification model based convolution neural network (CNN) has been used to
prepare BFP-tagged Chinese micro-blog corpora. Validated by a BFP linguistic
computational model, our generated Chinese short texts exhibit discriminative
personality styles, which are also syntactically correct and semantically
smooth with appropriate emoticons. With combination of natural language
generation with psychological linguistics, our proposed BFP-dependent text
generation model can be widely used for individualization in machine
translation, image caption, dialogue generation and so on.


  America has a massive railway system. As of 2006, U.S. freight railroads have
140,490 route- miles of standard gauge, but maintaining such a huge system and
eliminating any dangers, like reduced track stability and poor drainage, caused
by railway ballast degradation require huge amount of labor. The traditional
way to quantify the degradation of ballast is to use an index called Fouling
Index (FI) through ballast sampling and sieve analysis. However, determining
the FI values in lab is very time-consuming and laborious, but with the help of
recent development in the field of computer vision, a novel method for a
potential machine-vison based ballast inspection system can be employed that
can hopefully replace the traditional mechanical method. The new machine-vision
approach analyses the images of the in-service ballasts, and then utilizes
image segmentation algorithm to get ballast segments. By comparing the segment
results and their corresponding FI values, this novel method produces a
machine-vision-based index that has the best-fit relation with FI. The
implementation details of how this algorithm works are discussed in this
report.


  We prove that every non-degenerate minimal submanifold of codimension two can
be obtained as the energy concentration set of a family of critical maps for
the (rescaled) Ginzburg-Landau functional. The proof is purely variational, and
follows the strategy laid out by Jerrard and Sternberg, extending a recent
result for geodesics by Colinet-Jerrard-Sternberg. The same proof applies also
to the $U(1)$-Yang-Mills-Higgs and to the Allen-Cahn-Hilliard energies.


  We show that in a minimal extension of the MSSM by means of an extra U(1)
gauge group, the negative mass-squared problem characteristic of the Anomaly
Mediated Supersymmetry Breaking scenario is naturally solved by means of
Fayet-Iliopoulos D-terms. We derive a set of sum rules for the sparticle masses
which are consequences of the resulting framework.


  The issue of demographic disparities in face recognition accuracy has
attracted increasing attention in recent years. Various face image datasets
have been proposed as 'fair' or 'balanced' to assess the accuracy of face
recognition algorithms across demographics. These datasets typically balance
the number of identities and images across demographics. It is important to
note that the number of identities and images in an evaluation dataset are {\em
not} driving factors for 1-to-1 face matching accuracy. Moreover, balancing the
number of identities and images does not ensure balance in other factors known
to impact accuracy, such as head pose, brightness, and image quality. We
demonstrate these issues using several recently proposed datasets. To improve
the ability to perform less biased evaluations, we propose a bias-aware toolkit
that facilitates creation of cross-demographic evaluation datasets balanced on
factors mentioned in this paper.


  Define a ``truncation'' $r_{t}(p)$ of a polynomial $p$ in
$\{x_1,x_2,x_3,...\}$ as the polynomial with all but the first $t$ variables
set to zero. In certain good cases, the truncation of a Schubert or
Grothendieck polynomial may again be a Schubert or Grothendieck polynomial. We
use this phenomenon to give subtraction-free formulae for certain Schubert
structure constants in $K(Flags({\mathbb C}^n))$, in particular generalizing
those from [Kogan '00] in which only cohomology was treated, and from [Buch
`02] on the Grassmannian case. The terms of the answer are computed using
``marching'' operations on permutation diagrams.


  For the light relativistic dark matter (DM) boosted by high energy cosmic
ray, its scattering cross section with the nucleon is sensitively dependent on
the momentum-transfer and such an dependence is caused by the mediator in the
scattering. For puffy DM particle with a size, the momentum-transfer dependence
can also arise from the DM radius effect. All these momentum-transfer
dependences should be considered. In this note we study the direct detection
limits on the cosmic ray-boosted puffy DM for a simplified model with a light
mediator. For comparison, we first re-derive the direct detection limits on the
cosmic ray-boosted point-like DM. We display the limits on various planes of
parameters and find that the limits for the cosmic ray-boosted puffy DM are
stronger than for the point-like DM.


  Differential Privacy (DP) provides an elegant mathematical framework for
defining a provable disclosure risk in the presence of arbitrary adversaries;
it guarantees that whether an individual is in a database or not, the results
of a DP procedure should be similar in terms of their probability distribution.
While DP mechanisms are provably effective in protecting privacy, they often
negatively impact the utility of the query responses, statistics and/or
analyses that come as outputs from these mechanisms. To address this problem,
we use ideas from the area of robust statistics which aims at reducing the
influence of outlying observations on statistical inference. Based on the
preliminary known links between differential privacy and robust statistics, we
modify the objective perturbation mechanism by making use of a new bounded
function and define a bounded M-Estimator with adequate statistical properties.
The resulting privacy mechanism, named "Perturbed M-Estimation", shows
important potential in terms of improved statistical utility of its outputs as
suggested by some preliminary results. These results consequently support the
need to further investigate the use of robust statistical tools for
differential privacy.


  We study the periodic boundary value problem associated with the second order
nonlinear differential equation $$ u" + c u' + \left(a^{+}(t) - \mu \,
a^{-}(t)\right) g(u) = 0, $$ where $g(u)$ has superlinear growth at zero and at
infinity, $a(t)$ is a periodic sign-changing weight, $c\in\mathbb{R}$ and
$\mu>0$ is a real parameter. We prove the existence of $2^{m}-1$ positive
solutions when $a(t)$ has $m$ positive humps separated by $m$ negative ones (in
a periodicity interval) and $\mu$ is sufficiently large. The proof is based on
the extension of Mawhin's coincidence degree defined in open (possibly
unbounded) sets and applies also to Neumann boundary conditions. Our method
also provides a topological approach to detect subharmonic solutions.


  Newtonian gravitational noise from seismic fields will become a limiting
noise source at low frequency for second-generation, gravitational-wave
detectors. It is planned to use seismic sensors surrounding the detectors' test
masses to coherently subtract Newtonian noise using Wiener filters derived from
the correlations between the sensors and detector data. In this work, we use
data from a seismometer array deployed at the corner station of the LIGO
Hanford detector combined with a tiltmeter for a detailed characterization of
the seismic field and to predict achievable Newtonian-noise subtraction levels.
As was shown previously, cancellation of the tiltmeter signal using seismometer
data serves as the best available proxy of Newtonian-noise cancellation.
According to our results, a relatively small number of seismometers is likely
sufficient to perform the noise cancellation due to an almost ideal two-point
spatial correlation of seismic surface displacement at the corner station, or
alternatively, a tiltmeter deployed under each of the two test masses of the
corner station at Hanford will be able to efficiently cancel Newtonian noise.
Furthermore, we show that the ground tilt to differential arm-length coupling
observed during LIGO's second science run is consistent with gravitational
coupling.


  In this paper we use techniques first introduced by Florea to improve the
asymptotic formula for the first moment of the quadratic Dirichlet L-functions
over the rational function field, running over all monic, square-free
polynomials of even degree at the central point. With some extra technical
difficulties that doesn't appear in Florea's paper, we prove that there are
extra main terms of size $(2g+2)q^{\frac{2g+2}{3}},
q^{\frac{g}{6}+\left[\frac{g}{2}\right]}$ and
$q^{\frac{g}{6}+\left[\frac{g-1}{2}\right]}$, whilst bounding the error term by
$q^{\frac{g}{2}(1+\epsilon)}$.


  Open Quantum System (OQS) description of a many-body system involves
interaction of Shell Model (SM) states through the particle continuum. In
realistic nuclear applications, this interaction may lead to collective
phenomena in the ensemble of SM states. We claim that the nuclear clustering is
an emergent, near-threshold phenomenon, which cannot be elucidated within the
Closed Quantum System (CQS) framework. We approach this problem by
investigating the near-threshold behavior of Exceptional Points (EPs) in the
realistic Continuum Shell Model (CSM). The consequences for the
alpha-clustering phenomenon are discussed.


  Metals in amorphous state are promising for the use as structural materials
due to their superior properties related to the absence of grain boundaries and
dislocations.Obtaining the amorphous state requires quenching with a high
cooling rate.In conventional technologies,this is the reason for a considerable
size limitation hindering application of amorphous alloys.Additive
manufacturing (AM) is free of the size limitation.The so-called bulk metallic
glass (BMG) alloys have extremely low critical cooling rates and can be used in
AM. Recent studies on AM from Zr-based BMGs by selective laser melting(SLM)has
proved the possibility of attaining the amorphous state and revealed partial
crystallization to be the principal drawback of this process.The present work
aims to analyze the conditions for partial crystallization and try to control
it by optimizing the process parameters.A comprehensive parametric analysis is
accomplished in single-track SLM experiments with Zr-based BMG alloy Vit
106.The observed microstructures are related to the temperature fields and
thermal cycles estimated by an analytic heat-transfer model in the laser-impact
zone.In the cross section of a laser track,a central bright domain is
identified as the remelted zone.An annular darker crystallization zone
encircles the remelted zone.The model fits the experimentally obtained
dependencies of the remelted zone size versus laser power and scanning speed.It
seems that primary crystalline inclusions existing in the substrate before
laser processing dissolve at the laser melting.The mean cooling rate in the
remelted zone is much greater than the critical cooling
rate.Therefore,homogeneous nucleation isn't expected.Nevertheless,the
theoretically estimated crystallization times are sufficient for a considerable
crystal growth in the heat-affected zone where primary crystalline inclusions
and nuclei are not completely dissolved


  In this note, we study the effects of non-zero magnetic field on the fermion
spectral function coupled with a non-minimal coupling in the background of a
dyonic $AdS_4$ black hole. The system can be reduced to a non magnetic one with
the momentum being quantized into Landau levels $n$. By tuning the coupling
parameter, we study its effect on the Fermi level and the quasiparticle width.
We found an interesting scaling relation between the decay width and the
coupling parameter, with a universal scaling exponent which is independent of
the levels $n$.


  We present a review on the determination of the primordial helium abundance
Yp, based on the study of hydrogen and helium recombination lines in
extragalactic HII regions. We also discuss the observational determinations of
the increase of helium to the increase of oxygen by mass Delta Y / Delta O, and
compare them with predictions based on models of galactic chemical evolution.


  The intergalactic medium (IGM) at $z\sim$ 5 to 6 is largely ionized, and yet
the main source for the IGM ionization in the early universe is uncertain. Of
the possible contributors are faint quasars with $-26 \lesssim M_{\rm 1450}
\lesssim -23$, but their number density is poorly constrained at $z\sim5$. In
this paper, we present our survey of faint quasars at $z\sim5$ in the European
Large-Area {\it ISO} Survey-North 1 (ELAIS-N1) field over a survey area of 6.51
deg$^2$ and examine if such quasars can be the dominant source of the IGM
ionization. We use the deep optical/near-infrared data of the ELAIS-N1 field as
well as the additional medium-band observations to find $z \sim 5$ quasars
through a two-step approach using the broadband color selection, and SED
fitting with the medium-band information included. Adopting Bayesian
information criterion, we identify ten promising quasar candidates. Spectra of
three of the candidates are obtained, confirming all of them to be quasars at
$z\sim5$ and supporting the reliability of the quasar selection. Using the
promising candidates, we derive the $z\sim5$ quasar luminosity function at $-26
\lesssim M_{\rm 1450} \lesssim -23$. The number density of faint $z\sim5$
quasars in the ELAIS-N1 field is consistent with several previous results that
quasars are not the main contributors to the IGM-ionizing photons at $z\sim5$


  We have applied path integral simulations, in combination with new ab initio
based water potentials, to investigate nuclear quantum effects in liquid water.
Because direct ab initio path integral simulations are computationally
expensive, a flexible water model is parameterized by force-matching to density
functional theory-based molecular dynamics simulations. The resulting effective
potentials provide an inexpensive replacement for direct ab inito molecular
dynamics simulations and allow efficient simulation of nuclear quantum effects.
Static and dynamic properties of liquid water at ambient conditions are
presented and the role of nuclear quantum effects, exchange-correlation
functionals and dispersion corrections are discussed in regards to reproducing
the experimental properties of liquid water.


  A workshop sponsored by NSF C-CR and organized by the Center for Discrete
Math and Theoretical Computer Science (DIMACS) was held at Elmsford, New York,
January 17-18, 2002 where we had several discussions that gave structure to
this report. The workshop immediately followed the Fifth Annual Quantum
Information Processing Workshop that was held January 14-17 at IBM Yorktown.
  This is the report from that workshop. The report recommends that the NSF
Division of Computer-Communications Research (C-CR) develop a new initiative in
"Theory of Quantum Computing and Communication" and describes several research
directions that this initiative could support.


  The potential benefits of multiple-antenna systems may be limited by two
types of channel degradations rank deficiency and spatial fading correlation of
the channel. In this paper, we assess the effects of these degradations on the
diversity performance of multiple-input multiple-output (MIMO) systems, with an
emphasis on orthogonal space-time block codes, in terms of the symbol error
probability, the effective fading figure (EFF), and the capacity at low
signal-to-noise ratio (SNR). In particular, we consider a general family of
MIMO channels known as double-scattering channels, which encompasses a variety
of propagation environments from independent and identically distributed
Rayleigh to degenerate keyhole or pinhole cases by embracing both
rank-deficient and spatial correlation effects. It is shown that a MIMO system
with $n_T$ transmit and $n_R$ receive antennas achieves the diversity of order
$\frac{\n_T n_S n_R}{\max(n_T,n_S,n_R)}$ in a double-scattering channel with
$n_S$ effective scatterers. We also quantify the combined effect of the spatial
correlation and the lack of scattering richness on the EFF and the low-SNR
capacity in terms of the correlation figures of transmit, receive, and
scatterer correlation matrices. We further show the monotonicity properties of
these performance measures with respect to the strength of spatial correlation,
characterized by the eigenvalue majorization relations of the correlation
matrices.


  We investigate the fate of starlight in the Steady-State Cosmology. We
discover that it is largely unaffected by the presence of ions in intergalactic
space as it gets progressively red-shifted from the visible all the way down to
the plasma frequency of the intergalactic matter. At that point, after about
450 Gyr - and contrary to previously published claims - the radiation will be
thermalized. Under the assumptions adopted by Gold, Bondi, Hoyle, Narlikar,
Burbidge and others concerning the creation of matter in the Steady-State
Cosmology, and using reasonable estimates for the baryonic mass-density and
mass-fraction of 4He, the analysis predicts a universal radiation field
matching the CMB, i.e. having a black-body spectrum and temperature of about
2.7 K. The Steady-state Cosmology predicts that this radiation field will
appear to originate from the intergalactic plasma.


  A fast restoration of chiral symmetry in excited mesons is demonstrated. A
minimal "realistic" chirally symmetric confining model is used, where the only
interaction between quarks is the linear instantaneous Lorentz-vector confining
potential. Chiral symmetry breaking is generated via the nonperturbative
resummation of valence quarks self-energy loops and the meson bound states are
obtained from the Bethe-Salpeter equation. The excited mesons fall into
approximate chiral multiplets and lie on the approximately linear radial and
angular Regge trajectories, though a significant deviation from the linearity
of the angular trajectory is observed.


  The current work reports an efficient deep neural network (DNN) accelerator
where synaptic weight elements are controlled by ferroelectric domain dynamics.
An integrated device-to-algorithm framework for benchmarking novel synaptic
devices is used. In P(VDF-TrFE) based ferroelectric tunnel junctions, analog
conductance states are measured using a custom pulsing protocol and associated
custom circuits and array architectures for DNN training is simulated. Our
results show precise control of polarization switching dynamics in
multi-domain, polycrystalline ferroelectric thin films can produce considerable
weight update linearity in metal-ferroelectric-semiconductor (MFS) tunnel
junctions. Ultrafast switching and low junction current in these devices offer
extremely energy efficient operation. Through an integrated platform of
hardware development, characterization and modelling, we predict the available
conductance range where linearity is expected under identical potentiating and
depressing pulses for efficient DNN training and inference tasks. As an
example, an analog crossbar based DNN accelerator with MFS junctions as
synaptic weight elements showed ~ 93% training accuracy on large MNIST
handwritten digit dataset while for cropped images, a 95% accuracy is achieved.
One observed challenge is rather limited dynamic conductance range while
operating under identical potentiating and depressing pulses below 1V.
Investigation is underway for improving the dynamic conductance range without
losing the weight update linearity.


  In this paper we consider the topology optimization for a bipolar plate of a
hydrogen electrolysis cell. We use the Borvall-Petersson model to describe the
fluid flow and derive a criterion for a uniform flow distribution in the
bipolar plate. Furthermore, we introduce a novel deflation approach to compute
multiple local minimizers of topology optimization problems. The approach is
based on a penalty method that discourages convergence towards previously found
solutions. Finally, we demonstrate this technique on the topology optimization
for bipolar plates and show that multiple distinct local solutions can be
found.


  We demonstrated a simple technique for monitoring range variation with
millimeter-precision between two remote sites using off-the-shelf wireless
communication modules. The need for the flexible positioning of wireless
devices is significantly increasing as more devices are being connected and new
services are being developed that require devices to collaborate with one
another. We showed that one can monitor the distance variation by analyzing the
propagation delay of the wireless communication signal between devices. We
previously reported a technique for synchronizing clocks with picosecond
precision by monitoring the time variation of two rubidium clocks located at
remote sites. Precise measurement of the propagation time variation was
necessary for precise synchronization of the clocks, and we used this
information to estimate the distance with high precision. In a localized
situation, our technique makes it easy to implement a millimeter-precision
measurement system. Furthermore, it is less complex in terms of system design
and can be a low-cost alternative to existing systems that require precise
position measurement. We envision that this demonstrated protocol will be
implemented in wireless communication chips and microprocessing units.


  We study the localization in the one-dimensional trap model in terms of
statistical mechanics of trajectories. By numerically investigating overlap
between trajectories of two particles on a common disordered potential, we find
that there is a phase transition in the path ensemble. We characterize the low
temperature phase as a replica symmetry breaking phase in trajectory space.


  This chapter amalgamates some foundational developments and calculations in
factorization homology.


  The Gemini Planet Imager (GPI) is a next-generation, facility instrument
currently being commissioned at the Gemini South observatory. GPI combines an
extreme adaptive optics system and integral field spectrograph (IFS) with an
apodized-pupil Lyot coronagraph (APLC) producing an unprecedented capability
for directly imaging and spectroscopically characterizing extrasolar planets.
GPI's operating goal of $10^{-7}$ contrast requires very precise alignments
between the various elements of the coronagraph (two pupil masks and one focal
plane mask) and active control of the beam path throughout the instrument.
Here, we describe the techniques used to automatically align GPI and maintain
the alignment throughout the course of science observations. We discuss the
particular challenges of maintaining precision alignments on a Cassegrain
mounted instrument and strategies that we have developed that allow GPI to
achieve high contrast even in poor seeing conditions.


  We study the possibility of measuring T (time reversal) violation in a future
long baseline neutrino oscillation experiment. By assuming a neutrino factory
as a staging scenario of a muon collider at the J-PARC site, we find that the
${\nu}_e \to {\nu}_{\mu}$ oscillation probabilities can be measured with a good
accuracy at the Hyper-Kamiokande detector. By comparing with the probability of
the time-reversal process, ${\nu}_{\mu} \to {\nu}_e$, measured at the T2K/T2HK
experiments, one can determine the CP phase $\delta$ in the neutrino mixing
matrix if $| \sin(\delta)|$ is large enough. The determination of $\delta$ can
be made with poor knowledge of the matter density of the earth as T violation
is almost insensitive to the matter effects. The comparison of CP and
T-violation measurements, ${\it \`a\ la}$ the CPT theorem, provides us with a
non-trivial check of the three neutrino paradigm based on the quantum field
theory.


  Data quality monitoring is critical to all experiments impacting the quality
of any physics results. Traditionally, this is done through an alarm system,
which detects low level faults, leaving higher level monitoring to human crews.
Artificial Intelligence is beginning to find its way into scientific
applications, but comes with difficulties, relying on the acquisition of new
skill sets, either through education or acquisition, in data science. This
paper will discuss the development and deployment of the Hydra monitoring
system in production at Gluex. It will show how "off-the-shelf" technologies
can be rapidly developed, as well as discuss what sociological hurdles must be
overcome to successfully deploy such a system. Early results from production
running of Hydra will also be shared as well as a future outlook for
development of Hydra.


  Relativistic shocks are present in all high-energy astrophysical processes
involving relativistic plasma outflows interacting with their ambient medium.
While a well understood process in the context of relativistic hydrodynamics
and ideal magnetohydrodynamics, there is little to no understanding of their
propagation in media with a finite electrical conductivity. This work presents
a method for the derivation and solution of the jump conditions for
relativistic shocks propagating in MHD media with a finite electrical
conductivity. The covariant expressions of the jump conditions are derived and
the algebraic equations expressing the Rankine-Hugoniot conditions are solved
numerically. This method is employed for the solution of the Riemann problem
for the case of a forward and reverse shock which form during the interaction
of a gamma-ray burst ejecta with the circumburst medium in order to determine
the kinematics of the resulting blastwave and the dynamical conditions in its
interior. Our solutions clearly depict the impact of the plasma's electrical
conductivity in the properties of the post-shock medium. Two characteristic
regimes are identified with respect to the value of a dimensionless parameter
which has a linear dependence on the conductivity. For small values of this
parameter the shock affects only the hydrodynamic properties of the propagation
medium and leaves its electromagnetic field unaffected. No current layer forms
in the shock front; thus this is called the current-free regime. For large
values of this parameter the ideal MHD regime is retrieved. We also show that
the assumption of a finite electrical conductivity can lead to higher
efficiencies in the conversion of the ejecta energy into thermal energy of the
blastwave through the reverse shock. The theory developed in this work can be
applied to the construction of Riemann solvers for resistive relativistic MHD.


  In this proceeding, we study the dynamical evolution of the sigma field
within the framework of Langevin dynamics. We find that, as the system evolves
in the critical regime, the magnitudes and signs of the cumulants of sigma
field, $C_{3}$ and $C_{4}$, can be dramatically different from the equilibrated
ones due to the memory effects near $T_c$. For the dynamical evolution across
the 1st order phase transition boundary, the supercooling effect leads the
sigma field to be widely distributed in the thermodynamical potential, which
largely enhances the cumulants $C_3, \ C_4$, correspondingly.


  We compute the renormalisation factors (Z-matrices) of the $\Delta F=2$
four-quark operators needed for Beyond the Standard Model (BSM) kaon mixing. We
work with nf=2+1 flavours of Domain-Wall fermions whose chiral-flavour
properties are essential to maintain a continuum-like mixing pattern. We
introduce new RI-SMOM renormalisation schemes, which we argue are better
behaved compared to the commonly-used corresponding RI-MOM one. We find that,
once converted to MS, the Z-factors computed through these RI-SMOM schemes are
in good agreement but differ significantly from the ones computed through the
RI-MOM scheme. The RI-SMOM Z-factors presented here have been used to compute
the BSM neutral kaon mixing matrix elements in the companion paper [1]. We
argue that the renormalisation procedure is responsible for the discrepancies
observed by different collaborations, we will investigate and elucidate the
origin of these differences throughout this work.


  This work is devoted to the theoretical and numerical analysis of a
two-species chemotaxis- Navier-Stokes system with Lotka-Volterra competitive
kinetics in a bounded domain of Rd, d = 2, 3. First, we study the existence of
global weak solutions and establish a regularity criterion which provides
sufficient conditions to ensure the strong regularity of the weak solutions.
After, we propose a finite element numerical scheme in which we use a splitting
technique obtained by introducing an auxiliary variable given by the gradient
of the chemical concentration and applying an inductive strategy, in order to
deal with the chemoattraction terms in the two-species equations and prove
optimal error estimates. For this scheme, we study the well-posedness and
derive some uniform estimates for the discrete variables required in the
convergence analysis. Finally, we present some numerical simulations oriented
to verify the good behavior of our scheme, as well as to check numerically the
optimal error estimates proved in our theoretical analysis.


  Similar to the three-qubit Greenberger-Horne-Zeilinger (GHZ) symmetry we
explore the four-qubit GHZ symmetry group and its subgroup called restricted
GHZ symmetry group. While the set of symmetric states under the whole group
transformation is represented by three real parameters, the set of symmetric
states under the subgroup transformation is represented by two real parameters.
After comparing the symmetric states for whole and subgroup, the entanglement
is examined for the latter set. It is shown that the set has only two SLOCC
classes, $L_{abc_2}$ and $G_{abcd}$. Extension to the multi-qubit system is
briefly discussed.


  View planning for the acquisition of cardiac magnetic resonance imaging (CMR)
requires acquaintance with the cardiac anatomy and remains a challenging task
in clinical practice. Existing approaches to its automation relied either on an
additional volumetric image not typically acquired in clinic routine, or on
laborious manual annotations of cardiac structural landmarks. This work
presents a clinic-compatible and annotation-free system for automatic CMR view
planning. The system mines the spatial relationship -- more specifically,
locates and exploits the intersecting lines -- between the source and target
views, and trains deep networks to regress heatmaps defined by these
intersecting lines. As the spatial relationship is self-contained in properly
stored data, e.g., in the DICOM format, the need for manual annotation is
eliminated. Then, a multi-view planning strategy is proposed to aggregate
information from the predicted heatmaps for all the source views of a target
view, for a globally optimal prescription. The multi-view aggregation mimics
the similar strategy practiced by skilled human prescribers. Experimental
results on 181 clinical CMR exams show that our system achieves superior
accuracy to existing approaches including conventional atlas-based and newer
deep learning based ones, in prescribing four standard CMR views. The mean
angle difference and point-to-plane distance evaluated against the ground truth
planes are 5.98 degrees and 3.48 mm, respectively.


  We have exploited a variety of techniques to study the universality and
stability of the scaling properties of Harper's equation, the equation for a
particle moving on a tight-binding square lattice in the presence of a gauge
field, when coupling to next nearest sites is added. We find, from numerical
and analytical studies, that the scaling behavior of the total width of the
spectrum and the multifractal nature of the spectrum are unchanged, provided
the next nearest neighbor coupling terms are below a certain threshold value.
The full square symmetry of the Hamiltonian is not required for criticality,
but the square diagonals should remain as reflection lines. A bicritical line
is found at the boundary between the region in which the nearest neighbor terms
dominate and the region in which the next nearest neighbor terms dominate. On
the bicritical line a different critical exponent for the width of the spectrum
and different multifractal behavior are found. In the region in which the next
nearest neighbor terms dominate the behavior is still critical if the
Hamiltonian is invariant under reflection in the directions parallel to the
sides of the square, but a new length scale enters, and the behavior is no
longer universal but shows strongly oscillatory behavior. For a flux per unit
cell equal to $1/q$ the measure of the spectrum is proportional to $1/q$ in
this region, but if it is a ratio of Fibonacci numbers the measure decreases
with a rather higher inverse power of the denominator.


  This paper studies active learning in the context of robust statistics.
Specifically, we propose a variant of the Best Arm Identification problem for
\emph{contaminated bandits}, where each arm pull has probability $\varepsilon$
of generating a sample from an arbitrary contamination distribution instead of
the true underlying distribution. The goal is to identify the best (or
approximately best) true distribution with high probability, with a secondary
goal of providing guarantees on the quality of this distribution. The primary
challenge of the contaminated bandit setting is that the true distributions are
only partially identifiable, even with infinite samples. To address this, we
develop tight, non-asymptotic sample complexity bounds for high-probability
estimation of the first two robust moments (median and median absolute
deviation) from contaminated samples. These concentration inequalities are the
main technical contributions of the paper and may be of independent interest.
Using these results, we adapt several classical Best Arm Identification
algorithms to the contaminated bandit setting and derive sample complexity
upper bounds for our problem. Finally, we provide matching
information-theoretic lower bounds on the sample complexity (up to a small
logarithmic factor).


  Magnetic reconnection provides the primary source for explosive energy
release, plasma heating and particle acceleration in many astrophysical
environments. The last years witnessed a revival of interest in the MHD tearing
instability as a driver for efficient reconnection. It has been established
that, provided the current sheet aspect ratio becomes small enough ($a/L \sim
S^{-1/3}$ for a given Lundquist number $S\gg 1$), reconnection occurs on ideal
Alfv\'en timescales and becomes independent on $S$. Here we investigate, by
means of two-dimensional simulations, the \emph{ideal} tearing instability in
the Hall-MHD regime, which is appropriate when the width of the resistive layer
$\delta$ becomes comparable to the ion inertial length $d_i$. Moreover, we
study in detail the spontaneous development and reconnection of secondary
current sheets, which for high $S$ naturally adjust to the ideal aspect ratio
and hence their evolution proceeds very rapidly. For moderate low $S$, the
aspect ratio tends to the Sweet-Parker scaling ($a/L \sim S^{-1/2}$), in order
to fulfill the condition $\delta \ll a$ necessary for the onset of a tearing
instability. When the Hall term is included, the reconnection rate of this
secondary nonlinear phase is enhanced and, depending on the ratio $d_i/\delta$,
can be twice with respect to the pure MHD case, and up to ten times larger than
the linear phase. Therefore, the evolution of the tearing instability in thin
current sheets in the Hall-MHD regime naturally leads to an explosive
disruption of the reconnecting site and to energy release on super-Alfv\'enic
timescales, as required to explain astrophysical observations.


  Behavioral changes in animals and humans, as a consequence of an error or a
verbal instruction, can be extremely rapid. Improvement in behavioral
performances are usually associated in machine learning and reinforcement
learning to synaptic plasticity, and, in general, to changes and optimization
of network parameters. However, such rapid changes are not coherent with the
timescales of synaptic plasticity, suggesting that the mechanism responsible
for that could be a dynamical network reconfiguration. In the last few years,
similar capabilities have been observed in transformers, foundational
architecture in the field of machine learning that are widely used in
applications such as natural language and image processing. Transformers are
capable of in-context learning, the ability to adapt and acquire new
information dynamically within the context of the task or environment they are
currently engaged in, without the need for significant changes to their
underlying parameters. Building upon the notion of something unique within
transformers enabling the emergence of this property, we claim that it could
also be supported by input segregation and dendritic amplification, features
extensively observed in biological networks. We propose an architecture
composed of gain-modulated recurrent networks that excels at in-context
learning, showing abilities inaccessible to standard networks.


  The reconstruction loss and the Kullback-Leibler divergence (KLD) loss in a
variational autoencoder (VAE) often play antagonistic roles, and tuning the
weight of the KLD loss in $\beta$-VAE to achieve a balance between the two
losses is a tricky and dataset-specific task. As a result, current practices in
VAE training often result in a trade-off between the reconstruction fidelity
and the continuity$/$disentanglement of the latent space, if the weight $\beta$
is not carefully tuned. In this paper, we present intuitions and a careful
analysis of the antagonistic mechanism of the two losses, and propose, based on
the insights, a simple yet effective two-stage method for training a VAE.
Specifically, the method aggregates a learned Gaussian posterior $z \sim
q_{\theta} (z|x)$ with a decoder decoupled from the KLD loss, which is trained
to learn a new conditional distribution $p_{\phi} (x|z)$ of the input data $x$.
Experimentally, we show that the aggregated VAE maximally satisfies the
Gaussian assumption about the latent space, while still achieves a
reconstruction error comparable to when the latent space is only loosely
regularized by $\mathcal{N}(\mathbf{0},I)$. The proposed approach does not
require hyperparameter (i.e., the KLD weight $\beta$) tuning given a specific
dataset as required in common VAE training practices. We evaluate the method
using a medical dataset intended for 3D skull reconstruction and shape
completion, and the results indicate promising generative capabilities of the
VAE trained using the proposed method. Besides, through guided manipulation of
the latent variables, we establish a connection between existing autoencoder
(AE)-based approaches and generative approaches, such as VAE, for the shape
completion problem. Codes and pre-trained weights are available at
https://github.com/Jianningli/skullVAE


  The chemotaxis sensory system allows bacteria such as Escherichia coli to
swim towards nutrients and away from repellents. The underlying pathway is
remarkably sensitive in detecting chemical gradients over a wide range of
ambient concentrations. Interactions among receptors, which are predominantly
clustered at the cell poles, are crucial to this sensitivity. Although it has
been suggested that the kinase CheA and the adapter protein CheW are integral
for receptor connectivity, the exact coupling mechanism remains unclear. Here,
we present a statistical-mechanics approach to model the receptor linkage
mechanism itself, building on nanodisc and electron cryotomography experiments.
Specifically, we investigate how the sensing behavior of mixed receptor
clusters is affected by variations in the expression levels of CheA and CheW at
a constant receptor density in the membrane. Our model compares favorably with
dose-response curves from in vivo F\"orster resonance energy transfer (FRET)
measurements, demonstrating that the receptor-methylation level has only minor
effects on receptor cooperativity. Importantly, our model provides an
explanation for the non-intuitive conclusion that the receptor cooperativity
decreases with increasing levels of CheA, a core signaling protein associated
with the receptors, whereas the receptor cooperativity increases with
increasing levels of CheW, a key adapter protein. Finally, we propose an
evolutionary advantage as explanation for the recently suggested CheW-only
linker structures.


  The spin splitting of conduction band electrons in inversion-asymmetric
InGaAs/InP quantum wells is studied by Shubnikov-de Haas measurements combining
the analysis of beating patterns and coincidence measurements in doubly tilted
magnetic fields. The method allows us to determine the absolute values of the
Rashba and linear Dresselhaus spin-orbit interaction coefficients, their
relative sign and the full Land\'e g-tensor. This is achieved by analyzing the
anisotropy of the beat node positions with respect to both polar and azimuthal
angles between the magnetic field direction and the quantum well normal. We
show that the spin-orbit interaction is dominated by a large Rashba coefficient
together with a linear Dresselhaus coefficient that is 10 $\%$ of the Rashba
coefficient. Their relative sign is found to be positive. The g-tensor is found
to have a marked out-of-plane anisotropy and a smaller but distinct in-plane
anisotropy due to spin-orbit interaction.