  Retrieval-augmented generation has gained popularity as a framework to
enhance large language models with external knowledge. However, its
effectiveness hinges on the retrieval robustness of the model. If the model
lacks retrieval robustness, its performance is constrained by the accuracy of
the retriever, resulting in significant compromises when the retrieved context
is irrelevant. In this paper, we evaluate the "implicit" retrieval robustness
of various large language models, instructing them to directly output the final
answer without explicitly judging the relevance of the retrieved context. Our
findings reveal that fine-tuning on a mix of gold and distracting context
significantly enhances the model's robustness to retrieval inaccuracies, while
still maintaining its ability to extract correct answers when retrieval is
accurate. This suggests that large language models can implicitly handle
relevant or irrelevant retrieved context by learning solely from the
supervision of the final answer in an end-to-end manner. Introducing an
additional process for explicit relevance judgment can be unnecessary and
disrupts the end-to-end approach.


  When a fs duration and hundreds of kA peak current electron beam traverses
the vacuum and high-density plasma interface a new process, that we call
relativistic transition radiation (R-TR) generates an intense $\sim100$ as
pulse containing $\sim$ TW power of coherent VUV radiation accompanied by
several smaller fs duration satellite pulses. This pulse inherits the radial
polarization of the incident beam field and has a ring intensity distribution.
This R-TR is emitted when the beam density is comparable to the plasma density
and the spot size much larger than the plasma skin depth. Physically, it arises
from the return current or backward relativistic motion of electrons starting
just inside the plasma that Doppler up-shifts the emitted photons. The number
of R-TR pulses is determined by the number of groups of plasma electrons that
originate at different depths within the first plasma wake period and emit
coherently before phase mixing.


  In living matter, shape fluctuations induced by acto-myosin are usually
studied in vitro via reconstituted gels, whose properties are controlled by
changing the concentrations of actin, myosin and cross-linkers. Such an
approach deliberately avoids to consider the complexity of biochemical
signaling inherent to living systems. Acto-myosin activity inside living cells
is mainly regulated by the Rho signaling pathway which is composed of multiple
layers of coupled activators and inhibitors. We investigate how such a pathway
controls the dynamics of confluent epithelial tissues by tracking the
displacements of the junction points between cells. Using a phenomenological
model to analyze the vertex fluctuations, we rationalize the effects of
different Rho signaling targets on the emergent tissue activity by quantifying
the effective diffusion coefficient, the persistence time and persistence
length of the fluctuations. Our results reveal an unanticipated correlation
between layers of activation/inhibition and spatial fluctuations within
tissues. Overall, this work connects the regulation via biochemical signaling
with mesoscopic spatial fluctuations, with potential application to the study
of structural rearrangements in epithelial tissues.


  In this paper, we consider there exist two types of fundamental quasihole
excitation in the fractional quantum spin Hall state and investigate their
topological properties by both Chern-Simons field theory and Berry phase
technique. By the two different ways, we obtain the identical charge and
statistical angle for each type of quasihole, as well as the identical mutual
statistics between two different types of quasihole excitation.


  We extend the covariance-matrix description of atom--light quantum
interfaces, originally developed for real and effective spin-1/2 atoms, to
include "spin alignment" degrees of freedom. This allows accurate modeling of
optically-probed spin-1 ensembles in arbitrary magnetic fields. We also include
technical noise terms that are very common in experimental situations. These
include magnetic field noise, variable atom number and the effect of magnetic
field inhomogeneities. We demonstrate the validity of our extended model by
comparing numerical simulations to a free--induction decay (FID) measurement of
polarized $^{87}$Rb atoms in the $f = 1$ ground state. We qualitatively and
quantitatively reproduce experimental results with all free parameters of the
simulations fixed. The model can be easily extended to larger spin systems, and
adapted to more complicated experimental situations.


  Using 1533 type Ia supernovae (SNe Ia) from the five-year sample of the Dark
Energy Survey (DES), we investigate the effects of projected galactocentric
separation between the SNe and their host galaxies on their light curves and
standardization. We show, for the first time, that the difference in SN Ia
post-standardization brightnesses between high and low-mass hosts reduces from
$0.078\pm0.011$ mag in the full sample to $0.036 \pm 0.018$ mag for SNe Ia
located in the outer regions of their host galaxies, while increasing to $0.100
\pm 0.014$ mag for SNe in the inner regions. In these inner regions, the step
can be reduced (but not removed) using a model where the $R_V$ of dust along
the line-of-sight to the SN changes as a function of galaxy properties. To
explain the remaining difference, we use the distributions of the SN Ia stretch
parameter to test whether the inferred age of SN progenitors are more varied in
the inner regions of galaxies. We find that the proportion of high-stretch SNe
Ia in red (older) environments is more prominent in outer regions and that the
outer regions stretch distributions are overall more homogeneous compared to
inner regions, but conclude that this effect cannot explain the reduction in
significance of any Hubble residual step in outer regions. We conclude that the
standardized distances of SNe Ia located in the outer regions of galaxies are
less affected by their global host galaxy properties than those in the inner
regions.


  Human reconstruction and synthesis from monocular RGB videos is a challenging
problem due to clothing, occlusion, texture discontinuities and sharpness, and
framespecific pose changes. Many methods employ deferred rendering, NeRFs and
implicit methods to represent clothed humans, on the premise that mesh-based
representations cannot capture complex clothing and textures from RGB,
silhouettes, and keypoints alone. We provide a counter viewpoint to this
fundamental premise by optimizing a SMPL+D mesh and an efficient,
multi-resolution texture representation using only RGB images, binary
silhouettes and sparse 2D keypoints. Experimental results demonstrate that our
approach is more capable of capturing geometric details compared to visual
hull, mesh-based methods. We show competitive novel view synthesis and
improvements in novel pose synthesis compared to NeRF-based methods, which
introduce noticeable, unwanted artifacts. By restricting the solution space to
the SMPL+D model combined with differentiable rendering, we obtain dramatic
speedups in compute, training times (up to 24x) and inference times (up to
192x). Our method therefore can be used as is or as a fast initialization to
NeRF-based methods.


  The author has elsewhere given a complete classification of those compact
oriented Einstein 4-manifolds on which the self-dual Weyl curvature is
everywhere positive in the direction of some self-dual harmonic 2-form. In this
article, similar results are obtained when the self-dual Weyl curvature is
everywhere non-negative in the direction of a self-dual harmonic 2-form that is
transverse to the zero section of the bundle of self-dual 2-forms. However,
this transversality condition plays an essential role in the story; dropping it
leads one into wildly different territory where entirely different phenomena
predominate.


  This paper proposes an efficient method for computing selected generalized
eigenpairs of a sparse Hermitian definite matrix pencil $(A,B)$. Based on
Zolotarev's best rational function approximations of the signum function and
conformal mapping techniques, we construct the best rational function
approximation of a rectangular function supported on an arbitrary interval via
function compositions with partial fraction representations. This new best
rational function approximation can be applied to construct spectrum filters of
$(A,B)$ with a smaller number of poles than a direct construction without
function compositions. Combining fast direct solvers and the shift-invariant
generalized minimal residual method, a hybrid fast algorithm is proposed to
apply spectral filters efficiently. Compared to the state-of-the-art algorithm
FEAST, the proposed rational function approximation is more efficient when
sparse matrix factorizations are required to solve multi-shift linear systems
in the eigensolver, since the smaller number of matrix factorizations is needed
in our method. The efficiency and stability of the proposed method are
demonstrated by numerical examples from computational chemistry.


  We present an error bound for a least squares version of the kernel based
meshless finite difference method for elliptic differential equations on smooth
compact manifolds of arbitrary dimension without boundary. In particular, we
obtain sufficient conditions for the convergence of this method. Numerical
examples are provided for the equation $-\Delta_\mathcal{M} u + u = f$ on the
2- and 3-spheres, where $\Delta_\mathcal{M}$ is the Laplace-Beltrami operator.


  Hyperspherical partial wave approach has been applied here in the study of
double photoionization of the helium atom for equal energy sharing geometry at
20 eV excess energy. Calculations have been done both in length and velocity
gauges and are found to agree with each other, with the CCC results and with
experiments and exhibit some advantages of the corresponding three particle
wave function over other wave functions in use.


  Motivated by studying the power of randomness, certifying algorithms and
barriers for fine-grained reductions, we investigate the question whether the
multiplication of two $n\times n$ matrices can be performed in near-optimal
nondeterministic time $\tilde{O}(n^2)$. Since a classic algorithm due to
Freivalds verifies correctness of matrix products probabilistically in time
$O(n^2)$, our question is a relaxation of the open problem of derandomizing
Freivalds' algorithm.
  We discuss consequences of a positive or negative resolution of this problem
and provide potential avenues towards resolving it. Particularly, we show that
sufficiently fast deterministic verifiers for 3SUM or univariate polynomial
identity testing yield faster deterministic verifiers for matrix
multiplication. Furthermore, we present the partial algorithmic progress that
distinguishing whether an integer matrix product is correct or contains between
1 and $n$ erroneous entries can be performed in time $\tilde{O}(n^2)$ --
interestingly, the difficult case of deterministic matrix product verification
is not a problem of "finding a needle in the haystack", but rather cancellation
effects in the presence of many errors.
  Our main technical contribution is a deterministic algorithm that corrects an
integer matrix product containing at most $t$ errors in time
$\tilde{O}(\sqrt{t} n^2 + t^2)$. To obtain this result, we show how to compute
an integer matrix product with at most $t$ nonzeroes in the same running time.
This improves upon known deterministic output-sensitive integer matrix
multiplication algorithms for $t = \Omega(n^{2/3})$ nonzeroes, which is of
independent interest.


  The Casimir energy for a massless, neutral scalar field in presence of a
point interaction is analyzed using a general zeta-regularization approach
developed in earlier works. In addition to a regular bulk contribution, there
arises an anomalous boundary term which is infinite despite renormalization.
The intrinsic nature of this anomaly is briefly discussed.


  We propose novel charging protocols for quantum batteries based on quantum
superpositions of trajectories. Specifically, we consider that a qubit (the
battery) interacts with multiple cavities or a single cavity at various
positions, where the cavities act as chargers. Further, we introduce a quantum
control prepared in a quantum superposition state, allowing the battery to be
simultaneously charged by multiple cavities or a single cavity with different
entry positions. To assess the battery's performance, we evaluate the maximum
extractable work, referred to as ergotropy. Our main result is that the
proposed protocols can utilize quantum interference effects to speed up the
charging process. For the protocol involving multiple cavities, we observe a
substantial increase in ergotropy as the number of superposed trajectories
increases. In the case of the single-cavity protocol, we show that two
superposed trajectories (entry positions) are sufficient to achieve the upper
limit of the ergotropy throughout the entire charging process. Furthermore, we
propose circuit models for these charging protocols and conduct
proof-of-principle demonstrations on IBMQ and IonQ quantum processors. The
results validate our theoretical predictions, demonstrating a clear enhancement
in ergotropy.


  Results from the first two years of data from the Taiwanese-American
Occultation Survey (TAOS) are presented. Stars have been monitored
photometrically at 4 Hz or 5 Hz to search for occultations by small (~3 km)
Kuiper Belt Objects (KBOs). No statistically significant events were found,
allowing us to present an upper bound to the size distribution of KBOs with
diameters 0.5 km < D < 28 km.


  Charged colloidal particles - both on the nano and micron scales - have been
instrumental in enhancing our understanding of both atomic and colloidal
crystals. These systems can be straightforwardly realized in the lab, and tuned
to self-assemble into body-centered cubic (BCC) and face-centered cubic (FCC)
crystals. While these crystals will always exhibit a finite number of point
defects, including vacancies and interstitials - which can dramatically impact
their material properties - their existence is usually ignored in scientific
studies. Here, we use computer simulations and free-energy calculations to
characterize vacancies and interstitials in both FCC and BCC crystals of
point-Yukawa particles. We show that, in the BCC phase, defects are
surprisingly more common than in the FCC phase, and the interstitials manifest
as so-called crowdions: an exotic one-dimensional defect proposed to exist in
atomic BCC crystals. Our results open the door to directly observing these
elusive defects in the lab.


  The rim-hook rule for quantum cohomology of the Grassmannian allows one to
reduce quantum calculations to classical calculations in the cohomology of the
Grassmannian. We use the Abelian/non-Abelian correspondence for cohomology to
prove a rim-hook removal rule for the cohomology of quiver flag varieties.
Quiver flag varieties are generalisations of type A flag varieties; this result
is new even in the flag case. This gives an effective way of computing products
in their cohomology, reducing computations to that in the cohomology ring of
the Grassmannian. We then prove a quantum rim-hook rule for Fano quiver flag
varieties (including type A flag varieties). As a corollary, we see that the
Gu--Sharpe mirror to a Fano quiver flag variety computes its quantum
cohomology.


  A class of integral transforms, on the planar Gaussian Hilbert space with
range in the weighted Bergman space on the bi-disk, is defined as the dual
transforms of the 2d fractional Fourier transform associated with the Mehler
function for It\^o--Hermite polynomials. Some spectral properties of these
transforms are investigated. Namely, we study their boundedness and identify
their null spaces as well as their ranges. Such identification depends on the
zeros set of It\^o--Hermite polynomials. Moreover, the explicit expressions of
their singular values are given and compactness and membership in p-Schatten
class are studied. The relationship to specific fractional Hankel transforms is
also established


  We consider complete Riemannian manifolds which satisfy a weighted Poincar\`e
inequality and have the Ricci curvature bounded below in terms of the weight
function. When the weight function has a non-zero limit at infinity, the
structure of this class of manifolds at infinity are studied and certain
splitting result is obtained. Our result can be viewed as an improvement of
Li-Wang's result in \cite{LW3}.


  We present photoionization models of the high excitation gas in the Extended
Narrow Line Region (ENLR) of NGC1068. The ENLR line fluxes have been calculated
allowing for attenuation of the central-source ionizing continuum as a function
of distance from the centre. Diffuse continuum emission from low density ENLR
gas is included as an important secondary source of ionization. The observed
high excitation emission further than 25 arcsec from the centre of NGC1068 can
be fitted by photoionization models using a central-source luminosity of
3.6x10^44 erg/s between 10^14.6 and 10^18.4 Hz, with the continuum shape
attenuated by nuclear gas with an integrated column density of N_h=10^22 cm^-2.
The reflected soft X-ray continuum from the attenuating gas could be
responsible for about 10% of the observed, resolved circumnuclear soft X-ray
continuum extending out to 15 arcsec from the centre (Wilson et al 1992).


  The analysis of dynamical systems has been a topic of great interest for
researches mathematical sciences for a long times. The implementation of
several devices and tools have been useful in the finding of solutions as well
to describe common behaviors of parametric families of these systems. In this
paper we study deeply a particular parametric family of differential equations,
the so-called \emph{Linear Polyanin-Zaitsev Vector Field}, which has been
introduced in a general case, in the previous paper by the same authors, as a
correction of a family presented in the classical book of Polyanin and Zaitsev.
Linear Polyanin-Zaitsev Vector Field is transformed into a Li\'enard equation
and in particular we obtain the Van Der Pol equation. We present some algebraic
and qualitative results to illustrate some interactions between algebra and the
qualitative theory of differential equations in this parametric family.


  In order to help physicists to expand their knowledge of the climate in the
Lesser Antilles, we aim to identify the spatio-temporal configurations using
clustering analysis on wind speed and cumulative rainfall datasets. But we show
that using the L2 norm in conventional clustering methods as K-Means (KMS) and
Hierarchical Agglomerative Clustering (HAC) can induce undesirable effects. So,
we propose to replace Euclidean distance (L2) by a dissimilarity measure named
Expert Deviation (ED). Based on the symmetrized Kullback-Leibler divergence,
the ED integrates the properties of the observed physical parameters and
climate knowledge. This measure helps comparing histograms of four patches,
corresponding to geographical zones, that are influenced by atmospheric
structures. The combined evaluation of the internal homogeneity and the
separation of the clusters obtained using ED and L2 was performed. The results,
which are compared using the silhouette index, show five clusters with high
indexes. For the two available datasets one can see that, unlike KMS-L2, KMS-ED
discriminates the daily situations favorably, giving more physical meaning to
the clusters discovered by the algorithm. The effect of patches is observed in
the spatial analysis of representative elements for KMS-ED. The ED is able to
produce different configurations which makes the usual atmospheric structures
clearly identifiable. Atmospheric physicists can interpret the locations of the
impact of each cluster on a specific zone according to atmospheric structures.
KMS-L2 does not lead to such an interpretability, because the situations
represented are spatially quite smooth. This climatological study illustrates
the advantage of using ED as a new approach.


  Just-in-Time (JIT) compilers are used by many modern programming systems in
order to improve performance. Bugs in JIT compilers provide exploitable
security vulnerabilities and debugging them is difficult as they are large,
complex, and dynamic. Current debugging and visualization tools deal with
static code and are not suitable in this domain. We describe a new approach for
simplifying the large and complex intermediate representation, generated by a
JIT compiler and visualize it with a metro map metaphor to aid developers in
debugging. Experiments using our prototype implementation on Google's V8
JavaScript interpreter and TurboFan JIT compiler demonstrate that it can help
identify and localize buggy code.


  Keratin are among the most abundant proteins in epithelial cells. Functions
of the keratin network in cells are shaped by their dynamical organization.
Using a collection of experimentally-driven mathematical models, different
hypotheses for the turnover and transport of the keratin material in epithelial
cells are tested. The interplay between turnover and transport and their
effects on the keratin organization in cells are hence investigated by
combining mathematical modeling and experimental data. Amongst the collection
of mathematical models considered, a best model strongly supported by
experimental data is identified. Fundamental to this approach is the fact that
optimal parameter values associated with the best fit for each model are
established. The best candidate among the best fits is characterized by the
disassembly of the assembled keratin material in the perinuclear region and an
active transport of the assembled keratin. Our study shows that an active
transport of the assembled keratin is required to explain the experimentally
observed keratin organization.


  Vignetting in camera lenses is generally seen as something to avoid. For
spectral cameras with thin-film interference filters, however, we argue that
vignetting can be an advantage. When illuminated by focused light, the
bandwidth of interference filters increases with the chief-ray angle, causing
position-dependent smoothing of the spectra. We show that vignetting can be
used to reduce smoothing and preserve important spectral features. Furthermore,
we demonstrate that by adding additional vignetting to a lens, measurements can
be made more consistent across the scene. This makes vignetting a useful
parameter during spectral camera design.


  In this technical report, we present our solution to localize a
spatio-temporal person in an untrimmed video based on a sentence. We achieve
the second vIOU(0.30025) in the HC-STVG track of the 3rd Person in Context(PIC)
Challenge. Our solution contains three parts: 1) human attributes information
is extracted from the sentence, it is helpful to filter out tube proposals in
the testing phase and supervise our classifier to learn appearance information
in the training phase. 2) we detect humans with YoloV5 and track humans based
on the DeepSort framework but replace the original ReID network with FastReID.
3) a visual transformer is used to extract cross-modal representations for
localizing a spatio-temporal tube of the target person.


  We study the condensation transition of counterions on a charged cylinder via
Monte Carlo simulations. Varying the cylinder radius systematically in relation
to the system size, we find that all counterions are bound to the cylinder and
the heat capacity shows a drop at a finite Manning parameter. A finite-size
scaling analysis is carried out to confirm the criticality of the complete
condensation transition, yielding the same critical exponents with the Manning
transition. We show that the existence of the complete condensation is
essential to explain how the condensation nature alters from continuous to
discontinuous transition.


  We analyze the polarization observables of J/psi photoproduction at
next-to-leading order (NLO) within the factorization formalism of
nonrelativistic quantum chromodynamics (NRQCD). This is the first NLO study of
heavy-quarkonium polarization including the full relativistic corrections due
to the intermediate ^1S_0^{[8]}, ^3S_1^{[8]}, and ^3P_J^{[8]} color-octet (CO)
states in the worldwide endeavor to test NRQCD factorization at the quantum
level. We present theoretical predictions in the helicity, target, and
Collins-Soper frames of DESY HERA, evaluated using the CO long-distance matrix
elements previously extracted through a global fit to experimental data of
unpolarized J/psi production, and confront them with recent measurements by the
H1 and ZEUS Collaborations. We find the overall agreement to be satisfactory,
but the case for NRQCD to be not as strong as for the J/psi yield.


  We count numbers of tame frieze patterns with entries in a finite commutative
local ring. For the ring $\mathbb{Z}/p^r\mathbb{Z}$, $p$ a prime and
$r\in\mathbb{N}$ we obtain closed formulae for all heights. These may be
interpreted as formulae for the numbers of certain relations in quotients of
the modular group.


  On the basis of an idea of the electron-hole relation between $f^2$ and $f^4$
states in a $j$-$j$ coupling scheme, we point out a possibility that
two-channel Kondo phenomena can be observed even in cubic transuranium
compounds including Np and Pu ions with local $\Gamma_3$ non-Kramers doublet
ground state. For the purpose, we analyze a seven-orbital impurity Anderson
model hybridized with degenerate $\Gamma_8$ conduction electron bands by
employing a numerical renormalization group method. From the numerical results
for the case of four local $f$ electrons, corresponding to Np$^{3+}$ and
Pu$^{4+}$ ions, we confirm that a residual entropy of $0.5\log 2$, a
characteristic of two-channel Kondo phenomena, appears for the case with the
local $\Gamma_3$ doublet ground state.


  A new algebraic method to find two special types of exact traveling wave
solutions and the solitary type solutions to some conformable fractional
partial differential equations is proposed. The two special types of solutions
given by the product of exponential and Weierstrass elliptic functions, and the
product of exponential and Jacobi elliptic functions are new and they cannot be
obtained by using the existing algebraic methods.


  Air conditioning (AC) accounts for a critical portion of the global energy
consumption. To improve its energy performance, it is important to fairly
benchmark its energy performance and provide the evaluation feedback to users.
However, this task has not been well tackled in the residential sector. In this
paper, we propose a data-driven approach to fairly benchmark the AC energy
performance of residential rooms. First, regression model is built for each
benchmarked room so that its power consumption can be predicted given different
weather conditions and AC settings. Then, all the rooms are clustered based on
their areas and usual AC temperature set points. Lastly, within each cluster,
rooms are benchmarked based on their predicted power consumption under uniform
weather conditions and AC settings. A real-world case study was conducted with
data collected from 44 residential rooms. Results show that the constructed
regression models have an average prediction accuracy of 85.1% in
cross-validation tests, and support vector regression with Gaussian kernel is
the overall most suitable model structure for building the regression model. In
the clustering step, 44 rooms are successfully clustered into seven clusters.
By comparing the benchmarking scores generated by the proposed approach with
two sets of scores computed from historical power consumption data, we
demonstrate that the proposed approach is able to eliminate the influences of
room areas, weather conditions, and AC settings on the benchmarking results.
Therefore, the proposed benchmarking approach is valid and fair. As a
by-product, the approach is also shown to be useful to investigate how room
areas, weather conditions, and AC settings affect the AC power consumption of
rooms in real life.


  Searches for binary inspiral signals in data collected by interferometric
gravitational wave detectors utilize matched filtering techniques. Although
matched filtering is optimal in the case of stationary Gaussian noise, data
from real detectors often contains "glitches" and episodes of excess noise
which cause filter outputs to ring strongly. We review the standard \chi^2
statistic which is used to test whether the filter output has appropriate
contributions from several different frequency bands. We then propose a new
type of waveform consistency test which is based on the time history of the
filter output. We apply one such test to the data from the first LIGO science
run and show that it cleanly distinguishes between true inspiral waveforms and
large-amplitude false signals which managed to pass the standard \chi^2 test.


  Two-dimensional (2D) materials serve as exceptional platforms for controlled
second harmonic generation (SHG), an important nonlinear optical phenomenon
with diverse applications. Current approaches to SHG control often depend on
non-resonant conditions or symmetry breaking via single-gate control. Here, we
employ dual-gate bilayer WSe2 to demonstrate a new SHG enhancement concept that
leverages strong exciton resonance and layer-dependent exciton-polaron effect.
By selectively localizing injected holes within one layer, we induce
exciton-polaron states in the hole-filled layer while maintaining normal
exciton states in the charge-neutral layer. The distinct resonant conditions of
these layers effectively break interlayer inversion symmetry, thereby promoting
resonant SHG. Our method achieves a remarkable 40-fold enhancement of SHG at
minimal electric field, equivalent to conditions near the dielectric-breakdown
threshold but using only ~3% of the critical breakdown field. Our findings also
reveal significant sensitivity of resonant SHG to carrier density and carrier
type, with distinct enhancement and quenching observed across different gating
regimes. This advancement offers an innovative approach to manipulating SHG in
2D excitonic materials and provides a potent spectroscopic tool for probing
layer-dependent quantum states.


  Even though superconductivity has been studied intensively for more than a
century, the vast majority of superconductivity research today is carried out
in nearly the same manner as decades ago. That is, each study tends to focus on
only a single material or small subset of materials, and discoveries are made
more or less serendipitously. Recent increases in computing power, novel
machine learning algorithms, and improved experimental capabilities offer new
opportunities to revolutionize superconductor discovery. These will enable the
rapid prediction of structures and properties of novel materials in an
automated, high-throughput fashion and the efficient experimental testing of
these predictions. Here, we review efforts to use machine learning to attain
this goal.


  High-frequency trading (HFT) that executes algorithmic trading in short time
scales, has recently occupied the majority of cryptocurrency market. Besides
traditional quantitative trading methods, reinforcement learning (RL) has
become another appealing approach for HFT due to its terrific ability of
handling high-dimensional financial data and solving sophisticated sequential
decision-making problems, \emph{e.g.,} hierarchical reinforcement learning
(HRL) has shown its promising performance on second-level HFT by training a
router to select only one sub-agent from the agent pool to execute the current
transaction. However, existing RL methods for HFT still have some defects: 1)
standard RL-based trading agents suffer from the overfitting issue, preventing
them from making effective policy adjustments based on financial context; 2)
due to the rapid changes in market conditions, investment decisions made by an
individual agent are usually one-sided and highly biased, which might lead to
significant loss in extreme markets. To tackle these problems, we propose a
novel Memory Augmented Context-aware Reinforcement learning method On HFT,
\emph{a.k.a.} MacroHFT, which consists of two training phases: 1) we first
train multiple types of sub-agents with the market data decomposed according to
various financial indicators, specifically market trend and volatility, where
each agent owns a conditional adapter to adjust its trading policy according to
market conditions; 2) then we train a hyper-agent to mix the decisions from
these sub-agents and output a consistently profitable meta-policy to handle
rapid market fluctuations, equipped with a memory mechanism to enhance the
capability of decision-making. Extensive experiments on various cryptocurrency
markets demonstrate that MacroHFT can achieve state-of-the-art performance on
minute-level trading tasks.


  We demonstrate the effectiveness of one of the many multi-tracer analyses
enabled by Optimal Transport (OT) reconstruction. Leveraging a semi-discrete OT
algorithm, we determine the displacements between initial and observed
positions of biased tracers and the remaining matter field. With only
redshift-space distorted final positions of biased tracers and a simple premise
for the remaining mass distribution as input, OT solves the displacement field.
This extracted field, assuming asymptotically uniform density and a gradient
flow displacement, enables reconstruction of the initial overdensity
fluctuation field. We show that the divergence of the OT displacement field is
a good proxy of the linear density field, even though the method never assumes
the linear theory growth. Additionally, this divergence field can be combined
with the reconstructed protohalos to provide a higher signal-to-noise
measurement of the BAO standard ruler than was possible with either measurement
individually.


  Proliferative sickle cell retinopathy (PSCR) is the most important ocular
manifestation of sickle cell disease (SCD), but understanding of its
pathophysiology remains incomplete. Red blood cell (RBC) deformability has been
identified as a critical factor in SCD and is intrinsically related with cell
sphericity index (SI). The aim of this study was to develop an algorithm that
automatically analyzes defocusing microscopy (DM) images, providing
biomechanical parameters of individual RBCs, including cellular SI.
Furthermore, association of RBC SI with severity of PSCR in individuals with
HbSC-SCD was also investigated. We determined the SI of 255 RBCs from 17
individuals using DM. Nine individuals (53%) were healthy and eight (47%) had
HbSC-SCD. Mean SI was significantly lower in SCD than in control group (0.69
versus 0.73), and also in severe than in mild PSCR (0.67 versus 0.70). Lower SI
was also associated with more severe retinopathy (ROC AUC = 0.85) and the
proportion of participants with SI <= 0.69 was significantly greater in severe
than in mild PSCR (100% versus 25%). In conclusion, lower RBC SI determined by
DM was associated not only with the presence of SCD, but also with more severe
PSCR, possibly being a surrogate biomarker of disease severity.


  Let $G$ be a regular graph with $m$ edges, and let $\mu_1, \mu_2$ denote the
two largest eigenvalues of $A_G$, the adjacency matrix of $G$. We show that, if
$G$ is not complete, then
  $$\mu_1^2 + \mu_2^2 \leq \frac{2(\omega - 1)}{\omega} m$$
  where $\omega$ is the clique number of $G$. This confirms a conjecture of
Bollob\'{a}s and Nikiforov for regular graphs. We also show that equality holds
if and only if $G$ is either a balanced Tur\'{a}n graph or the disjoint union
of two balanced Tur\'{a}n graphs of the same size.


  We propose a Gaussian manifold variational auto-encoder (GM-VAE) whose latent
space consists of a set of Gaussian distributions. It is known that the set of
the univariate Gaussian distributions with the Fisher information metric form a
hyperbolic space, which we call a Gaussian manifold. To learn the VAE endowed
with the Gaussian manifolds, we propose a pseudo-Gaussian manifold normal
distribution based on the Kullback-Leibler divergence, a local approximation of
the squared Fisher-Rao distance, to define a density over the latent space. In
experiments, we demonstrate the efficacy of GM-VAE on two different tasks:
density estimation of image datasets and environment modeling in model-based
reinforcement learning. GM-VAE outperforms the other variants of hyperbolic-
and Euclidean-VAEs on density estimation tasks and shows competitive
performance in model-based reinforcement learning. We observe that our model
provides strong numerical stability, addressing a common limitation reported in
previous hyperbolic-VAEs.


  The mixed spin-1/2 and spin-3/2 Ising model on the union jack lattice is
solved by establishing a mapping correspondence with the eight-vertex model. It
is shown that the model under investigation becomes exactly soluble as a
free-fermion eight-vertex model when the parameter of uniaxial single-ion
anisotropy tends to infinity. Under this restriction, the critical points are
characterized by critical exponents from the standard Ising universality class.
In a certain subspace of interaction parameters, which corresponds to a
coexistence surface between two ordered phases, the model becomes exactly
soluble as a symmetric zero-field eight-vertex model. This surface is bounded
by a line of bicritical points having interaction-dependent critical exponents
that satisfy a weak universality hypothesis.


  Any Calderon-Zygmund operator T is pointwise dominated by a convergent sum of
positive dyadic operators. We give an elementary self-contained proof of this
fact, which is simpler than the probabilistic arguments used for all previous
results in this direction. Our argument also applies to the q-variation of
certain Calderon-Zygmund operators, a stronger nonlinearity than the maximal
truncations. As an application, we obtain new sharp weighted inequalities.


  We consider the framework of Document Modeling, which lays the formal basis
for representing the document lifecycle in Business Process Management systems.
We formulate document models in the scope of the logic-based Semantic Modeling
language and study the question whether transactions given by a document model
terminate on any input. We show that in general this problem is undecidable and
formulate sufficient conditions, which guarantee decidability and polynomial
boundedness of effects of transactions.


  Let $G$ be a graph of order $n$. A path decomposition $\mathcal{P}$ of $G$ is
a collection of edge-disjoint paths that covers all the edges of $G$. Let
$p(G)$ denote the minimum number of paths needed in a path decomposition of
$G$. Gallai conjectured that if $G$ is connected, then $p(G)\leq
\lceil\frac{n}{2}\rceil$. In this paper, we prove that Gallai's path
decomposition conjecture holds for the cartesian product $G\Box H$, where $H$
is any graph and $G$ is a unicyclic graph or a bicyclic graph.


  We propose a supersymmetric extension of the minimal $U(1)_X$ model, along
with a new $Z_2$-parity. One of the salient features of this model relates to
how both the $U(1)_X$ gauge symmetry and R-parity are broken radiatively at the
TeV scale by the VEV of a $Z_2$-even right handed neutrino. By assigning one
right-handed neutrino $Z_2$-odd parity, it can remain a viable dark matter (DM)
candidate, despite R-parity being broken. Furthermore, the DM relic abundance
receives an enhanced annihilation cross section due to the $U(1)_X$ gauge boson
($Z'$) resonance and is in agreement with the current observations. We have
also found a complementarity that exists between the observed DM relic
abundance and search results for the $Z^\prime$ boson resonance at the Large
Hadron Collider (LHC), which further constrains the parameter space of our
$U(1)_X$ model. Lastly, we consider a $SU(5)\times U(1)_x$ GUT extension and
investigate the complementarities mentioned previously.


  Normal forms of almost complex structures in a neighborhood of
pseudoholomorphic curve are considered. We define normal bundles of such curves
and study the properties of linear bundle almost complex structures. We
describe 1-jet of the almost complex structure along a curve in terms of its
Nijenhuis tensor. For pseudoholomorphic tori we investigate the problem of
pseudoholomorphic foliation of the neighborhood. We obtain some results on
nonexistence of the tori deformation.


  Gagie and Nekrich (2009) gave an algorithm for adaptive prefix-free coding
that, given a string $S [1..n]$ over the alphabet $\{1, \ldots, \sigma\}$ with
$\sigma = o (n / \log^{5 / 2} n)$, encodes $S$ in at most $n (H + 1) + o (n)$
bits, where $H$ is the empirical entropy of $S$, such that encoding and
decoding $S$ take $O (n)$ time. They also proved their bound on the encoding
length is optimal, even when the empirical entropy is high. Their algorithm is
impractical, however, because it uses complicated data structures. In this
paper we give an algorithm with the same bounds, except that we require $\sigma
= o (n^{1 / 2} / \log n)$, that uses no data structures more complicated than a
lookup table. Moreover, when Gagie and Nekrich's algorithm is used for optimal
adaptive alphabetic coding it takes $O (n \log \log n)$ time for decoding, but
ours still takes $O (n)$ time.


  Entanglement is assuming a central role in modern quantum many-body physics.
Yet, for lattice gauge theories its certification remains extremely
challenging. A key difficulty stems from the local gauge constraints underlying
the gauge theory, which separate the full Hilbert space into a direct sum of
subspaces characterized by different superselection rules. In this work, we
develop the theoretical framework of entanglement witnessing for lattice gauge
theories that takes this subtlety into account. We illustrate the concept at
the example of a $\mathrm{U}(1)$ lattice gauge theory in 2+1 dimensions,
without and with dynamical fermionic matter. As this framework circumvents
costly state tomography, it opens the door to resource-efficient certification
of entanglement in theoretical studies as well as in laboratory quantum
simulations of gauge theories.


  We compare dynamics and waveforms from binary neutron star coalescence as
computed by new long-term ($\sim 10 $ orbits) numerical relativity simulations
and by the tidal effective-one-body (EOB) model including analytical tidal
corrections up to second post-Newtonian order (2PN). The current analytical
knowledge encoded in the tidal EOB model is found to be sufficient to reproduce
the numerical data up to contact and within their uncertainties. Remarkably, no
calibration of any tidal EOB free parameters is required, beside those already
fitted to binary black holes data. The inclusion of 2PN tidal corrections
minimizes the differences with the numerical data, but it is not possible to
significantly distinguish them from the leading-order tidal contribution. The
presence of a relevant amplification of tidal effects is likely to be excluded,
although it can appear as a consequence of numerical inaccuracies. We conclude
that the tidally-completed effective-one-body model provides nowadays the most
advanced and accurate tool for modelling gravitational waveforms from binary
neutron star inspiral up to contact. This work also points out the importance
of extensive tests to assess the uncertainties of the numerical data, and the
potential need of new numerical strategies to perform accurate simulations.


  We study algebraic relations among postcritically finite (PCF) parameters in
the family $f_c(z) = z^2 + c$. Ghioca, Krieger, Nguyen and Ye proved that an
algebraic curve in $\mathbb{C}^2$ contains infinitely many PCF pairs $(c_1,
c_2)$ if and only if the curve is special (i.e., the curve is a vertical or
horizontal line through a PCF parameter, or the curve is the diagonal). Here we
extend this result to subvarieties of $\mathbb{C}^n$ for any $n\geq 2$.
Consequently, we obtain uniform bounds on the number of PCF pairs on
non-special curves in $\mathbb{C}^2$ and the number of PCF parameters in real
algebraic curves in $\mathbb{C}$, depending only on the degree of the curve. We
also compute the optimal bound for the general curve of degree $d$.


  Realising photonic analogues of the robust, unidirectional edge states of
electronic topological insulators would improve our control of light on the
nanoscale and revolutionise the performance of photonic devices. Here we show
that new symmetry protected topological phases can be detected by reformulating
energy eigenproblems as Berry curvature eigenproblems. The "Berry bands" span
the same eigenspace as the original valence energy bands, but separate into
pseudo-spinful and pseudo-spinless subspaces in
$\mathrm{C}_2\mathcal{T}$-symmetric crystals. We demonstrate the method on the
well-known case of Wu & Hu [Phys. Rev. Lett. 114, 223901 (2015)] and a recently
discovered fragilely topological crystal, and show that both crystals belong to
the same $\mathrm{C}_2\mathcal{T}$-protected $\mathbb{Z}_2$ topological phase.
This work helps unite theory and numerics, and is useful in defining and
identifying new symmetry-protected phases in photonics and electronics.


  There is a growing interest from both the academia and industry to employ
distributed ledger technology in the Internet-of-Things domain for addressing
security-related and performance challenges. Distributed ledger technology
enables non-trusted entities to communicate and reach consensus in a fully
distributed manner through a cryptographically secure and immutable ledger.
However, significant challenges arise mainly related to transaction processing
speed and user privacy. This work explores the interplay between
Internet-of-Things and distributed ledger technology, analysing the fundamental
characteristics of this technology and discussing the related benefits and
challenges.


  We present deep (9 hours) Gemini-N/GNIRS near-infrared spectroscopic
observations of ULAS J1342+0928, a luminous quasar at z=7.54. Various broad
emission lines were detected, as well as the underlying continuum and iron
forests over the rest-frame wavelength 970-2930A. There is a clear trend that
higher-ionization emission lines show larger blueshifts with CIV1549 exhibiting
5510^{+240}_{-110} km s-1 blueshift with respect to the systematic redshift
from the far-infrared [CII] 158um emission line. Those high ionization lines
have wide profiles with FWHM more than 10000 km s-1. A modest blueshift of
340^{+110}_{-80} km s-1 is also seen in MgII, the lowest ionization line
identified in the spectrum. The updated MgII-based black hole mass of
M_BH=9.1_{-1.3}^{+1.4} x 10^8 M_sun and the Eddington ratio of
L_bol/L_Edd=1.1_{-0.2}^{+0.2} confirm that ULAS J1342+0928 is powered by a
massive and actively accreting black hole. There is no significant difference
in the emission line ratios such as SiIV/CIV and AlIII/CIV when compared to
lower-redshift quasars in a similar luminosity range, which suggests early
metal pollution of the broad-line-region clouds. This trend also holds for the
FeII/MgII line ratio, known as a cosmic clock that traces the iron enrichment
in the early universe. Different iron templates and continuum fitting ranges
were used to explore how the FeII/MgII measurement changes as a function of
spectral modeling. Quasars at even higher redshift or at fainter luminosity
range (L_bol<10^46 erg s-1) are needed to probe the sites of early metal
enrichment and a corresponding change in the FeII/MgII ratio.


  Light intensity control of the orbital angular momentum of the fundamental
beam in a quadratic nonlinear process is theoretically and numerically
presented. In particular we analyzed a seeded second harmonic generation
process in presence of orbital angular momentum of the interacting beams due
both to on axis and off axis optical vortices. Examples are proposed and
discussed.


  Electron spin precession in nonuniform Rashba-Dresselhaus two-dimensional
electron systems along arbitrary continuous paths is investigated. We derive an
analytical formula to describe the spin vectors (expectation values of the
injected spin) in such conditions using a contour-integral method. The obtained
formalism is capable of dealing with the nonuniformity of the Rashba spin-orbit
field due to the inherent random distribution of the ionized dopants, and can
be applied to curved one-dimensional quantum wires. Interesting examples are
given, and the modification to the spin precession pattern in a
Rashba-Dresselhaus channel when taking the random Rashba field into account is
shown.


  Cosmological acceleration is difficult to accommodate in theories of
fundamental interactions involving supergravity and superstrings. An
alternative is that the acceleration is not universal but happens in a large
localized region, which is possible in theories admitting regular black holes
with de Sitter-like interiors. We considerably strengthen this scenario by
placing it in a global anti-de Sitter background, where the formation of 'de
Sitter bubbles' will be enhanced by mechanisms analogous to the
Bizon-Rostworowski instability in general relativity. This opens an arena for
discussing the production of multiple accelerating universes from anti-de
Sitter fluctuations. We demonstrate such collapse enhancement by explicit
numerical work in the context of a simple two-dimensional dilaton-gravity model
that mimics the spherically symmetric sector of higher-dimensional gravities.


  This work is concerned with existence of weak solutions to discon- tinuous
stochastic differential equations driven by multiplicative Gaus- sian noise and
sliding mode control dynamics generated by stochastic differential equations
with variable structure, that is with jump nonlin- earity. The treatment covers
the finite dimensional stochastic systems and the stochastic diffusion equation
with multiplicative noise.


  In this paper, we consider the broadcast channel with confidential messages
and external eavesdroppers (BCCE), where a multi-antenna base station
simultaneously communicates to multiple potentially malicious users, in the
presence of randomly located external eavesdroppers. Using the proposed model,
we study the secrecy rates achievable by regularized channel inversion (RCI)
precoding by performing a large-system analysis that combines tools from
stochastic geometry and random matrix theory. We obtain explicit expressions
for the probability of secrecy outage and an upper bound on the rate loss due
to the presence of external eavesdroppers. We show that both these quantities
scale as $\frac{\lambda_e}{\sqrt{N}}$, where $N$ is the number of transmit
antennas and $\lambda_e$ is the density of external eavesdroppers, irrespective
of their collusion strategy. Furthermore, we derive a practical rule for the
choice of the regularization parameter, which is agnostic of channel state
information and location of eavesdroppers, and yet provides close to optimal
performance.


  The verification of systems combining hard timing constraints with
concurrency is challenging. This challenge becomes even harder when some timing
constants are missing or unknown. Parametric timed formalisms, such as
parametric timed automata (PTAs), tackle the synthesis of such timing constants
(seen as parameters) for which a property holds. Such formalisms are highly
expressive, but also undecidable, and few decidable subclasses were proposed.
We propose here a syntactic restriction on PTAs consisting in removing guards
(constraints on transitions) to keep only invariants (constraints on
locations). While this restriction preserves the expressiveness of PTAs (and
therefore their undecidability), an additional restriction on the type of
constraints allows to not only prove decidability, but also to perform the
exact synthesis of parameter valuations satisfying reachability. This
formalism, that seems trivial at first sight as it benefits from the
decidability of the reachability problem with a better complexity than Timed
Automata (TAs), suffers from the undecidability of the whole TCTL logic that
TAs, on the contrary enjoy. We believe our formalism allows for an interesting
trade-off between decidability and practical expressiveness and is therefore
promising. We show its applicability in a small case study.


  This paper studies the dynamics of a network-based SIRS epidemic model with
vaccination and a nonmonotone incidence rate. This type of nonlinear incidence
can be used to describe the psychological or inhibitory effect from the
behavioral change of the susceptible individuals when the number of infective
individuals on heterogeneous networks is getting larger. Using the analytical
method, epidemic threshold $R_0$ is obtained. When $R_0$ is less than one, we
prove the disease-free equilibrium is globally asymptotically stable and the
disease dies out, while $R_0$ is greater than one, there exists a unique
endemic equilibrium. By constructing a suitable Lyapunov function, we also
prove the endemic equilibrium is globally asymptotically stable if the
inhibitory factor $\alpha$ is sufficiently large. Numerical experiments are
also given to support the theoretical results. It is shown both theoretically
and numerically a larger $\alpha$ can accelerate the extinction of the disease
and reduce the level of disease.


  Automatically detecting discourse segments is an important preliminary step
towards full discourse parsing. Previous research on discourse segmentation
have relied on the assumption that elementary discourse units (EDUs) in a
document always form a linear sequence (i.e., they can never be nested).
Unfortunately, this assumption turns out to be too strong, for some theories of
discourse like SDRT allows for nested discourse units. In this paper, we
present a simple approach to discourse segmentation that is able to produce
nested EDUs. Our approach builds on standard multi-class classification
techniques combined with a simple repairing heuristic that enforces global
coherence. Our system was developed and evaluated on the first round of
annotations provided by the French Annodis project (an ongoing effort to create
a discourse bank for French). Cross-validated on only 47 documents (1,445
EDUs), our system achieves encouraging performance results with an F-score of
73% for finding EDUs.


  We report on a VLBA imaging study of the nearby bright southern blazar PKS
1921 - 293 (OV - 236). High resolution VLBA observations, made at four
frequencies (5, 12, 15, and 43 GHz) over the period 1994 - 2000, have revealed
a strongly curved jet extending out to about 50 parsecs from the presumed
central engine. Two epoch VLBA observations, each simultaneously carried out at
both 5 and 43 GHz, show a large position angle difference of 51 - 67 degrees
between the jet emission at 5 and 43 GHz. Although the core of PKS 1921 - 293
has one of the highest brightness temperatures measured in any compact radio
source, unlike other bright blazars it is not a source of gamma-ray emission.
However, there is evidence in these images for superluminal motion within the
central region (a few parsecs from the core) and within the north-east diffuse
emission region. In all six-epoch 43 GHz images, two equally compact bright
components within the central parsec are seen.


  Low-resource extractive text summarization is a vital but heavily
underexplored area of research. Prior literature either focuses on abstractive
text summarization or prompts a large language model (LLM) like GPT-3 directly
to generate summaries. In this work, we propose MixSumm for low-resource
extractive text summarization. Specifically, MixSumm prompts an open-source
LLM, LLaMA-3-70b, to generate documents that mix information from multiple
topics as opposed to generating documents without mixup, and then trains a
summarization model on the generated dataset. We use ROUGE scores and L-Eval, a
reference-free LLaMA-3-based evaluation method to measure the quality of
generated summaries. We conduct extensive experiments on a challenging text
summarization benchmark comprising the TweetSumm, WikiHow, and ArXiv/PubMed
datasets and show that our LLM-based data augmentation framework outperforms
recent prompt-based approaches for low-resource extractive summarization.
Additionally, our results also demonstrate effective knowledge distillation
from LLaMA-3-70b to a small BERT-based extractive summarizer.


  The degree of dependencies among the modules of a software system is a key
attribute to characterize its design structure and its ability to evolve over
time. Several design problems are often correlated with undesired dependencies
among modules. Being able to anticipate those problems is important for
developers, so they can plan early for maintenance and refactoring efforts.
However, existing tools are limited to detecting undesired dependencies once
they appeared in the system. In this work, we investigate whether module
dependencies can be predicted (before they actually appear). Since the module
structure can be regarded as a network, i.e, a dependency graph, we leverage on
network features to analyze the dynamics of such a structure. In particular, we
apply link prediction techniques for this task. We conducted an evaluation on
two Java projects across several versions, using link prediction and machine
learning techniques, and assessed their performance for identifying new
dependencies from a project version to the next one. The results, although
preliminary, show that the link prediction approach is feasible for package
dependencies. Also, this work opens opportunities for further development of
software-specific strategies for dependency prediction.


  Integrative modeling enables structure determination for large macromolecular
assemblies by combining data from multiple sources of experiment data with
theoretical and computational predictions. Recent advancements in AI-based
structure prediction and electron cryo-microscopy have sparked renewed
enthusiasm for integrative modeling; structures from AI-based methods can be
integrated with in situ maps to characterize large assemblies. This approach
previously allowed us and others to determine the architectures of diverse
macromolecular assemblies, such as nuclear pore complexes, chromatin
remodelers, and cell-cell junctions. Experimental data spanning several scales
was used in these studies, ranging from high-resolution data, such as X-ray
crystallography and Alphafold structures, to low-resolution data, such as
cryo-electron tomography maps and data from co-immunoprecipitation experiments.
Two recurrent modeling challenges emerged across a range of studies. First,
modeling disordered regions, which constituted a significant portion of these
assemblies, necessitated the development of new methods. Second, methods needed
to be developed to utilize the information from cryo-electron tomography, a
timely challenge as structural biology is increasingly moving towards in situ
characterization. Here, we recapitulate recent developments in the modeling of
disordered proteins and the analysis of cryo-electron tomography data and
highlight opportunities for method development in the context of integrative
modeling.


  In this paper we deal with a weighted eigenvalue problem for the anisotropic
$(p,q)$-Laplacian with Dirichlet boundary conditions. We study the main
properties of the first eigenvalue and prove a reverse H\"older type inequality
for the corresponding eigenfunctions.


  This paper presents a simulation study of a permanent magnet electron
cyclotron resonance ion source (ECRIS) with a minimum-B quadrupole magnetic
field topology. The magnetic field is made to conform to conventional ECRIS
with $B_\textrm{min}/B_\textrm{ECR}$ of 0.67 and a last closed magnetic
isosurface of 1.86$B_\textrm{ECR}$ at 10 GHz. The distribution of magnetic
field gradients parallel to the field, affecting the electron heating
efficiency, cover a range from 0 to 13 T/m, being similar to conventional
ECRIS. Therefore it is expected that the novel ion source produces warm
electrons and high charge state ions in significant number. Single electron
tracking simulations are used to estimate plasma flux distribution on the
plasma chamber walls and to provide an estimate of the ion density profile at
the extraction slit then used in ion optical simulations demonstrating high
transmission through the low energy beam transport. The designed ion source is
intended to study if the quadrupole field topology could produce high charge
state beams in comparable intensities to conventional ECRIS and efficiently
transport them through a low energy beamline, thus paving the way for a
superconducting ARC-ECRIS using the same field topology. Furthermore, the
prospects of the presented ion source design as an injector of a single-ended
accelerator for ion beam analysis are discussed.


  We propose transferability from Large Geometric Vicinity (LGV), a new
technique to increase the transferability of black-box adversarial attacks. LGV
starts from a pretrained surrogate model and collects multiple weight sets from
a few additional training epochs with a constant and high learning rate. LGV
exploits two geometric properties that we relate to transferability. First,
models that belong to a wider weight optimum are better surrogates. Second, we
identify a subspace able to generate an effective surrogate ensemble among this
wider optimum. Through extensive experiments, we show that LGV alone
outperforms all (combinations of) four established test-time transformations by
1.8 to 59.9 percentage points. Our findings shed new light on the importance of
the geometry of the weight space to explain the transferability of adversarial
examples.


  The curvature of the noncommutative torus $T^2_\theta$ ($\theta$ irrational)
endowed with a noncommutative conformal metric has been the focus of attention
of several recent works. Continuing the approach taken in the paper [A. Connes
and H. Moscovici, http://arxiv.org/abs/1110.3500] we extend the study of the
curvature to twisted Dirac spectral triples constructed out of Heisenberg
bimodules that implement the Morita equivalence of the $C^*$-algebra $A_\theta
= C(T^2_\theta)$ with other toric algebras $A_{\theta'}$. In the enlarged
context the conformal metric on $T^2_\theta$ is exchanged with an arbitrary
Hermitian metric on the Heisenberg $(A_\theta, A_{\theta'})$-bimodule $E'$ for
which ${\rm End}_{A_{\theta'}}(E') = A_\theta $. We prove that the Ray-Singer
log-determinant of the corresponding Laplacian, viewed as a functional on the
space of all Hermitian metrics on $E'$, attains its extremum at the unique
Hermitian metric whose corresponding connection has constant curvature. The
gradient of the log-determinant functional gives rise to a noncommutative
analogue of the Gaussian curvature. The genuinely new outcome of this paper is
that the latter is shown to be independent of any Heisenberg bimodule $E'$ such
that $A_\theta = {\rm End}_{A_{\theta'}}(E')$, and in this sense it is Morita
invariant. To prove the above results we extend Connes' pseudodifferential
calculus to Heisenberg modules. The twisted version, which offers more
flexibility even in the case of trivial coefficients, could potentially be
applied to other problems in the elliptic theory on noncommutative tori. A
noteworthy technical feature is that we systematize the computation of the
resolvent expansion for elliptic differential operators on noncommutative tori
to an extent which makes the (previously employed) computer assistance
unnecessary.


  We discuss the rich phase diagram of doped AB2 $t-J$ chains by using data
from density matrix renormalization group and exact diagonalization techniques.
The $J$ vs $\delta$ (hole doping) phase diagram exhibits regions of itinerant
ferrimagnetism, incommensurate, resonating valence bond and Nagaoka states,
phase separation, and Luttinger liquid (LL) physics. Several features are
highlighted, such as the modulated ferrimagnetic structure, the occurrence of
Nagaoka spin polarons in the underdoped regime and small values of $J=4t^2/U$,
where $t$ is the first-neighbor hopping amplitude and $U$ is the on-site
repulsive Coulomb interaction, incommensurate structures with nonzero
magnetization, and strong-coupling LL physics in the high-doped regime. We also
verify that relevant findings are in agreement with the corresponding findings
in square and n-leg ladder lattices. In particular, we mention the instability
of Nagaoka ferromagnetism against $J$ and $\delta$.


  We compare the market quality of centralized crypto exchanges (CEXs) such as
Binance and Kraken to decentralized blockchain-based venues (DEXs) such as
Uniswap v2 and v3. After discussing the microstructure of such exchanges, we
analyze two key aspects of market quality: transaction costs and deviations
from the no-arbitrage condition. We find that CEXs and DEXs operate on roughly
equal footing in terms of transaction costs, particularly in light of recent
innovations in DEX protocols. Moreover, while CEXs provide superior price
efficiency, DEXs eliminate custodian risk. These complementary advantages may
explain why both market structures coexist.


  ITER's large and powerful neutral beam injection system is based on an ion
source utilizing a modular concept, where eight cylindrical drivers are
attached to one common expansion and extraction region. In each driver, a
plasma is sustained via inductive coupling with powers of up to 100 kW at a
driving radio frequency (RF) of 1 MHz to produce fusion-relevant hydrogen
beams. These high powers impose great stress on the electric system. Recent
measurements at the single-driver test bed BATMAN Upgrade showed that the RF
power transfer efficiency $\eta$, which measures the ratio of power absorbed by
plasma to total RF power, is only around 0.5, leaving room for optimization. In
multi-driver test beds such as ELISE with four drivers $\eta$ is found to be
even further decreased to around 0.4. To explain this difference, a previously
validated self-consistent 2D RF power coupling fluid model is applied. For the
same absorbed power per driver, the model shows virtually the same spatial
distributions of plasma parameters and power absorption in single- and
multi-driver sources. However, the coil current is slightly increased in the
multi-driver model due to a changed spatial distribution of the magnetic RF
field in the region surrounding the drivers. Typically, in multi-driver sources
conductive shields are applied to cancel the electromagnetic interference
between individual drivers. These shields are found to affect the spatial
distribution of the RF fields more severely, the effect being highly dependent
on the distance between the RF coil and the shield. In the case of the ELISE
ion source a further decrease of $\eta$ is calculated by the model being in
good agreement with experimental measurements.


  The Electric Autonomous Dial-A-Ride Problem (E-ADARP) consists in scheduling
a fleet of electric autonomous vehicles to provide ride-sharing services for
customers that specify their origins and destinations. The E-ADARP differs from
the classical DARP in two aspects: (i) a weighted-sum objective that minimizes
both total travel time and total excess user ride time; (ii) the employment of
electric autonomous vehicles and a partial recharging policy. This paper
presents a highly-efficient labeling algorithm, which is integrated into
Branch-and-Price (B&P) algorithms to solve the E-ADARP. To handle (i), we
introduce a fragment-based representation of paths. A novel approach is invoked
to abstract fragments to arcs while ensuring excess-user-ride-time optimality.
We then construct a new graph that preserves all feasible routes of the
original graph by enumerating all feasible fragments, abstracting them to arcs,
and connecting them with each other, depots, and recharging stations in a
feasible way. On the new graph, partial recharging (ii) is tackled exactly by
tailored Resource Extension Functions (REFs). We apply strong dominance rules
and constant-time feasibility checks to compute the shortest paths efficiently.
These methods construct the first labeling algorithm that can deal with
minimizing (excess) user ride time. In the computational experiments, the B&P
algorithm achieves optimality in 71 out of 84 instances. Remarkably, among
these instances, 50 were solved optimally at the root node without branching.
We identify 26 new best solutions, improve 30 previously reported lower bounds,
and provide 17 new lower bounds for large-scale instances with up to 8 vehicles
and 96 requests. In total 42 new best solutions are generated on previously
solved and unsolved instances.


  Homotopical geometry over differential operators is a convenient setting for
a coordinate-free investigation of nonlinear partial differential equations
modulo symmetries. One of the first issues one meets in the functor of points
approach to homotopical $\mathcal{D}$-geometry, is the question of a model
structure on the category $\tt DGAlg(\mathcal{D})$ of differential
non-negatively graded $\mathcal{O}$-quasi-coherent sheaves of commutative
algebras over the sheaf $\mathcal{D}$ of differential operators of an
appropriate underlying variety $(X,\mathcal{O})$. We define a cofibrantly
generated model structure on $\tt DGAlg(\mathcal{D})$ via the definition of its
weak equivalences and its fibrations, characterize the class of cofibrations,
and build an explicit functorial `cofibration - trivial fibration'
factorization. We then use the latter to get a functorial model categorical
Koszul-Tate resolution for $\mathcal{D}$-algebraic `on-shell function' algebras
(which contains the classical Koszul-Tate resolution). The paper is also the
starting point for a homotopical $\mathcal{D}$-geometric Batalin-Vilkovisky
formalism.


  The kinematic properties of the Scorpius-Centaurus association were studied
using spatial velocities of approximately 700 young T Tauri stars. Their proper
motions and trigonometric parallaxes were selected by Zari et al. from the Gaia
DR2 catalog, and radial velocities were taken from various sources. The linear
expansion coefficients new estimate of the association $K=39\pm2$ km/s/kpc is
obtained by considering the influence of the galactic spiral density wave with
an amplitude of radial disturbances $f_R=5$ km/s and solar phase in the wave
$-120^\circ$. The proper rotation of the association is shown to be small. The
residual velocity ellipsoid of these stars has semimajor axes
$\sigma_{1,2,3}=(7.72,1.87,1.74)\pm(0.56,0.37,0.22)$ km/s and is positioned at
an angle $12\pm2^\circ$ to the galactic plane.


  Gradient coding is a coding theoretic framework to provide robustness against
slow or unresponsive machines, known as stragglers, in distributed machine
learning applications. Recently, Kadhe et al. proposed a gradient code based on
a combinatorial design, called balanced incomplete block design (BIBD), which
is shown to outperform many existing gradient codes in worst-case adversarial
straggling scenarios. However, parameters for which such BIBD constructions
exist are very limited. In this paper, we aim to overcome such limitations and
construct gradient codes which exist for a wide range of system parameters
while retaining the superior performance of BIBD gradient codes. Two such
constructions are proposed, one based on a probabilistic construction that
relax the stringent BIBD gradient code constraints, and the other based on
taking the Kronecker product of existing gradient codes. The proposed gradient
codes allow flexible choices of system parameters while retaining comparable
error performance.


  We have investigated line profiles in a large sample of Cepheid spectra, and
found four stars that show unusual (for Cepheids) line profile structure (bumps
or/and asymmetries). The profiles can be phase dependent but the behavior
persists over many cycles. The asymmetries are unlikely to be due to the
spectroscopic binarity of these stars or the specific velocity field in their
atmospheres caused by shock waves. As a preliminary hypothesis, we suggest that
the observed features on the line profiles in the spectra of X Sgr, V1334 Cyg,
EV Sct and BG Cru can be caused by the non-radial oscillations. It is possible
that these non-radial oscillations are connected to resonances between the
radial modes (3.2, 7.5 or 10.0 days).


  Variational data assimilation technique applied to identification of optimal
approximations of derivatives near boundary is discussed in frames of
one-dimensional wave equation. Simplicity of the equation and of its numerical
scheme allows us to discuss in detail as the development of the adjoint model
and assimilation results. It is shown what kind of errors can be corrected by
this control and how these errors are corrected. This study is carried out in
view of using this control to identify optimal numerical schemes in coastal
regions of ocean models.


  We propose a new strategy of finding strongly-lensed supernovae (SNe) by
monitoring known galaxy-scale strong-lens systems. Strongly lensed SNe are
potentially powerful tools for the study of cosmology, galaxy evolution, and
stellar populations, but they are extremely rare. By targeting known strongly
lensed starforming galaxies, our strategy significantly boosts the detection
efficiency for lensed SNe compared to a blind search. As a reference sample, we
compile the 128 galaxy-galaxy strong-lens systems from the Sloan Lens ACS
Survey (SLACS), the SLACS for the Masses Survey, and the Baryon Oscillation
Spectroscopic Survey Emission-Line Lens Survey. Within this sample, we estimate
the rates of strongly-lensed Type Ia SN (SNIa) and core-collapse SN (CCSN) to
be $1.23 \pm 0.12$ and $10.4 \pm 1.1$ events per year, respectively. The lensed
SN images are expected to be widely separated with a median separation of 2
arcsec. Assuming a conservative fiducial lensing magnification factor of 5 for
the most highly magnified SN image, we forecast that a monitoring program with
a single-visit depth of 24.7 mag (5$\sigma$ point source, $r$ band) and a
cadence of 5 days can detect 0.49 strongly-lensed SNIa event and 2.1
strongly-lensed CCSN events per year within this sample. Our proposed
targeted-search strategy is particularly useful for prompt and efficient
identifications and follow-up observations of strongly-lensed SN candidates. It
also allows telescopes with small field of views and limited time to
efficiently discover strongly-lensed SNe with a pencil-beam scanning strategy.


  In this paper we are concerned with the approximation of functions by single
hidden layer neural networks with ReLU activation functions on the unit circle.
In particular, we are interested in the case when the number of data-points
exceeds the number of nodes. We first study the convergence to equilibrium of
the stochastic gradient flow associated with the cost function with a quadratic
penalization. Specifically, we prove a Poincar\'e inequality for a penalized
version of the cost function with explicit constants that are independent of
the data and of the number of nodes. As our penalization biases the weights to
be bounded, this leads us to study how well a network with bounded weights can
approximate a given function of bounded variation (BV).
  Our main contribution concerning approximation of BV functions, is a result
which we call the localization theorem. Specifically, it states that the
expected error of the constrained problem, where the length of the weights are
less than $R$, is of order $R^{-1/9}$ with respect to the unconstrained problem
(the global optimum). The proof is novel in this topic and is inspired by
techniques from regularity theory of elliptic partial differential equations.
Finally we quantify the expected value of the global optimum by proving a
quantitative version of the universal approximation theorem.


  The Lov\'{a}sz Local Lemma is a very powerful tool in probabilistic
combinatorics, that is often used to prove existence of combinatorial objects
satisfying certain constraints. Moser and Tardos have shown that the LLL gives
more than just pure existence results: there is an effective randomized
algorithm that can be used to find a desired object. In order to analyze this
algorithm Moser and Tardos developed the so-called entropy compression method.
It turned out that one could obtain better combinatorial results by a direct
application of the entropy compression method rather than simply appealing to
the LLL. We provide a general statement that implies both these new results and
the LLL itself.


  Scaling behaviour of dynamically driven vortex avalanches in superconducting
YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ films deposited on tilted crystalline
substrates has been observed using quantitative magneto-optical imaging. Two
films with different tilt angles are characterized by the probability
distributions of avalanche size in terms of the number of moving vortices. It
is found in both samples that these distributions follow power-laws over up to
three decades, and have exponents ranging between 1.0 and 1.4. The
distributions also show clear finite-size scaling, when the system size is
defined by the depth of the flux penetration front -- a signature of
self-organized criticality. A scaling relation between the avalanche size
exponent and the fractal dimension, previously derived theoretically from
conservation of the number of magnetic vortices in the stationary state and
shown in numerical simulations, is here shown to be satisfied also
experimentally.


  The Rezzolla-Zhidenko (RZ) framework provides an efficient approach to
characterize spherically symmetric black-hole spacetimes in arbitrary metric
theories of gravity using a small number of variables [L. Rezzolla and A.
Zhidenko, Phys. Rev. D. 90, 084009 (2014)]. These variables can be obtained in
principle from near-horizon measurements of various astrophysical processes,
thus potentially enabling efficient tests of both black-hole properties and the
theory of general relativity in the strong-field regime. Here, we extend this
framework to allow for the parametrization of arbitrary asymptotically-flat,
spherically symmetric metrics and introduce the notion of a 11-dimensional
(11D) parametrization space $\Pi$, on which each solution can be visualised as
a curve or surface. An $\mathscr{L}^2$ norm on this space is used to measure
the deviation of a particular compact object solution from the Schwarzschild
black-hole solution. We calculate various observables, related to particle and
photon orbits, within this framework and demonstrate that the relative errors
we obtain are low (about $10^{-6}$). In particular, we obtain the innermost
stable circular orbit (ISCO) frequency, the unstable photon-orbit impact
parameter (shadow radius), the entire orbital angular speed profile for
circular Kepler observers and the entire lensing deflection angle curve for
various types of compact objects, including non-singular and singular black
holes, boson stars and naked singularities, from various theories of gravity.
Finally, we provide in a tabular form the first 11 coefficients of the
fourth-order RZ parameterization needed to describe a variety of commonly used
black-hole spacetimes. When comparing with the first-order RZ parameterization
of astrophysical observables such as the ISCO frequency, the coefficients
provided here increase the accuracy of two orders of magnitude or more.


  Occupation of an interval by self-replicating initial pulses is studied
numerically. Two different approximates in different categories are proposed
for the numerical solutions of some initial-boundary value problems. The sinc
differential quadrature combined with third-fourth order implicit Rosenbrock
and exponential B-spline collocation methods are setup to obtain the numerical
solutions of the mentioned problems. The numerical simulations containing
occupation of single initial pulse, non or slow occupation model and covering
the domain with two initial pulses are demonstrated by using both proposed
methods.


  The birth and death of the first generation of stars have important
implications for the thermal state and chemical properties of the intergalactic
medium (IGM) in the early universe. Sometime after recombination, the neutral,
chemically pristine gas was reionized by ultraviolet photons emitted from the
first stars, but also enriched with heavy elements when these stars ended their
lives as energetic supernovae. Using the results from previous high-resolution
cosmological simulations of early structure formation that include radiative
transfer, we show that a significant volume fraction of the IGM can be
metal-polluted, as well as ionized, by massive Population III stars formed in
small-mass (10^6-10^7 Msun) halos early on. If most of the early generation
stars die as pair-instability supernovae with energies up to 10^{53} ergs, the
volume-averaged mean metallicity will quickly reach Z ~ 10^{-4}Zsun by a
redshift of 15-20, possibly causing a prompt transition to the formation of a
stellar population that is dominated by low-mass stars. In this scenario, the
early chemical enrichment history should closely trace the reionization history
of the IGM, and the end of the Population III era is marked by the completion
of reionization and pre-enrichment by z=15. We conclude that, while the
pre-enrichment may partially account for the ``metallicity-floor'' in
high-redshift Lyman-alpha clouds, it does not significantly affect the
elemental abundance in the intracluster medium.


  In this paper we study actions of reductive groups on affine spaces. We prove
that there is a fan structure on the space of characters of the group, which
parameterizes the possible invariant quotients. In the second half of the paper
we study various geometrical properties of the quotients: we compute their Chow
ring and the cohomology ring (in case we work over the complex numbers), both
with rational coefficients. Actually, the cycle map turns out to be an
isomorphism. Further, we construct families of such quotients over reduced base
schemes, and compute again the Chow and the cohomology rings. Finally, we prove
the vanishing of the higher cohomology groups of nef line bundles on the
geometric quotients that we obtain.


  The simulation of rarefied gas flow based on the Boltzmann equation is
challenging, especially when the gas mixtures have disparate molecular masses.
In this paper, a computationally tractable kinetic model is proposed for
monatomic gas mixtures, to mimic the Boltzmann collision operator as closely as
possible. The intra- and inter-collisions are modelled separately using
relaxation approximations, to correctly recover the relaxation timescales that
could span several orders of magnitude. The proposed kinetic model preserves
the accuracy of the Boltzmann equation in the continuum regime by recovering
the four critical transport properties of a gas mixture: the shear viscosity,
the thermal conductivity, the coefficients of diffusion and the thermal
diffusion. While in the rarefied flow regimes, the kinetic model is found to be
accurate when comparing its solutions with those from the direct simulation
Monte Carlo method in several representative cases (e.g. one-dimensional normal
shock wave, Fourier flow and Couette flow, two-dimensional supersonic flow
passing a cylinder and nozzle flow into a vacuum), for binary mixtures with a
wide range of mass ratios (up to 1000), species concentrations, and different
intermolecular potentials. Pronounced separations in species properties have
been observed, and the flow characteristics of gas mixtures in shock waves are
found to change as the mass difference increases from moderate to substantial.


  Machine learning algorithms have reached mainstream status and are widely
deployed in many applications. The accuracy of such algorithms depends
significantly on the size of the underlying training dataset; in reality a
small or medium sized organization often does not have the necessary data to
train a reasonably accurate model. For such organizations, a realistic solution
is to train their machine learning models based on their joint dataset (which
is a union of the individual ones). Unfortunately, privacy concerns prevent
them from straightforwardly doing so. While a number of privacy-preserving
solutions exist for collaborating organizations to securely aggregate the
parameters in the process of training the models, we are not aware of any work
that provides a rational framework for the participants to precisely balance
the privacy loss and accuracy gain in their collaboration. In this paper, by
focusing on a two-player setting, we model the collaborative training process
as a two-player game where each player aims to achieve higher accuracy while
preserving the privacy of its own dataset. We introduce the notion of Price of
Privacy, a novel approach for measuring the impact of privacy protection on the
accuracy in the proposed framework. Furthermore, we develop a game-theoretical
model for different player types, and then either find or prove the existence
of a Nash Equilibrium with regard to the strength of privacy protection for
each player. Using recommendation systems as our main use case, we demonstrate
how two players can make practical use of the proposed theoretical framework,
including setting up the parameters and approximating the non-trivial Nash
Equilibrium.


  In the manuscript, central black hole (BH) mass is estimated in the distant
TDE (tidal disruption event) of {\it Swift} J2058.4+0516 as the second
candidate of relativistic jet birth related to TDE. {\it Swift} J2058.4+0516
have quite different BH masses estimated through different indirect methods in
the literature. Therefore, it is necessary and interesting to determine the
central BH mass in {\it Swift} J2058.4+0516 by one another independent method.
Here, based on the theoretical TDE model applied to describe the long-term
time-dependent X-ray variabilities of {\it Swift} J2058.4+0516, the central BH
mass can be well determined to be around $1.05_{-0.29}^{+0.39}\times10^5{\rm
M_\odot}$, after kind considerations of suggested intrinsic beaming effects
from such relativistic jet tightly related to TDE. Moreover, the {\it Swift}
J2058.4+0516 is an unique object in the space of BH masses versus energy
transfer efficiencies of the reported TDE candidates, providing interesting
clues to detect and/or anticipate candidates of relativistic TDE to make the
birth of relativistic jets.


  We study a two-dimensional (2D) spin-half Heisenberg model related to the
quasi 2D antiferromagnets (Ba,Sr)2Cu3O4Cl2 by means of exact diagonalization
and spin-wave theory. The model consists of two inequivalent interpenetrating
square-lattice Heisenberg antiferromagnets A and B. While the antiferromagnetic
interaction JAA within the A subsystem is strong the coupling JBB within the B
subsystem is much weaker. The coupling JAB between A and B subsystems is
competing giving rise for interesting frustration effects. In dependence of the
strength of JAB we find a collinear Neel phase, non-collinear states with zero
magnetizations as well as canted and collinear ferrimagnetic phases with
non-zero magnetizations. For not too large values of frustration JAB, which
correpond to the situation in (Ba,Sr)2Cu3O4Cl2, we have Neel ordering in both
subsystems A and B. In the classical limit these two Neel states are decoupled.
Quantum fluctuations lead to a fluctuational coupling between both subsystems
('order from disorder') and select the collinear structure. For stronger JAB we
find evidence for a novel spin state with coexisting Neel ordering in the A
subsystem and disorder in the B subsystem.


  Stochastic entropy production, which quantifies the difference between the
probabilities of trajectories of a stochastic dynamics and its time reversals,
has a central role in nonequilibrium thermodynamics. In the theory of
probability, the change in the statistical properties of observables can be
represented by a change in the probability measure. We consider operators on
the space of probability measure that induce changes in the statistical
properties of a process, and formulate entropy productions in terms of these
change-of-probability-measure (CPM) operators. This mathematical underpinning
of the origin of entropy productions allows us to achieve an organization of
various forms of fluctuation relations: All entropy productions have a
non-negative mean value, admit the integral fluctuation theorem, and satisfy a
rather general fluctuation relation. Other results such as the transient
fluctuation theorem and detailed fluctuation theorems then are derived from the
general fluctuation relation with more constraints on the operator. We use a
discrete-time, discrete-state-space Markov process to draw the
contradistinction among three reversals of a process: time reversal, protocol
reversal and the dual process. The properties of their corresponding CPM
operators are examined, and the domains of validity of various fluctuation
relations for entropy productions in physics and chemistry are revealed. We
also show that our CPM operator formalism can help us rather easily extend
other fluctuations relations for excess work and heat, discuss the martingale
properties of entropy productions, and derive the stochastic integral formulas
for entropy productions in constant-noise diffusion process with Girsanov
theorem. Our formalism provides a general and concise way to study the
properties of entropy-related quantities in stochastic thermodynamics and
information theory.


  Starting from the Ginsparg-Wilson relation, a general construction of chiral
gauge theories on the lattice is described. Local and global anomalies are
easily discussed in this framework and a closed expression for the effective
action can be obtained. Particular attention is paid to the non-abelian gauge
anomaly, which is shown to be related to a local topological field on the
lattice representing the Chern character in 4+2 dimensions.


  Motion planning algorithms often leverage topological information about the
environment to improve planner performance. However, these methods often focus
only on the environment's connectivity while ignoring other properties such as
obstacle clearance, terrain conditions, and resource accessibility. We present
a method that augments a skeleton representing the workspace topology with such
information to guide a sampling-based motion planner to rapidly discover
regions most relevant to the problem at hand. Our approach decouples guidance
and planning, making it possible for basic planning algorithms to find desired
paths earlier in the planning process. We demonstrate the efficacy of our
approach in both robotics problems and applications in drug design. Our method
is able to produce desirable paths quickly with no change to the underlying
planner.


  We calculate the heat-kernel coefficients, up to $a_2$, for a U(1) bundle on
the 4-Ball for boundary conditions which are such that the normal derivative of
the field at the boundary is related to a first-order operator in boundary
derivatives acting on the field. The results are used to place restrictions on
the general forms of the coefficients. In the specific case considered, there
can be a breakdown of ellipticity.


  We point out a mistake in the statement of Corollary 2 in R. C. Alperin's
paper on Selberg's lemma.


  We present results from a new Keck spectroscopic survey of UV-faint LBGs in
the redshift range 3<z<7. Combined with earlier Keck and published ESO VLT
data, our sample contains more than 600 dropouts, offering new insight into the
nature of sub-L* sources typical of those likely to dominate the cosmic
reionisation process. Here we use this sample to characterise the fraction of
strong Lya emitters within the continuum-selected dropouts. By quantifying how
the "Lya fraction" varies with redshift, we seek to constrain changes in Lya
transmission associated with reionisation. In order to distinguish the effects
of reionisation from other factors which affect the Lya fraction (e.g. dust,
ISM kinematics), we study the luminosity and redshift-dependence of the Lya
fraction over 3<z<6, when the IGM is known to be ionised. These results reveal
that low luminosity galaxies show strong Lya emission much more frequently than
luminous systems, and that at fixed luminosity, the prevalence of strong Lya
emission increases moderately with redshift over 3 < z < 6. Based on the
correlation between blue UV slopes and strong Lya emitting galaxies in our
dataset, we argue that the Lya fraction trends are governed by redshift and
luminosity-dependent variations in the dust obscuration, with likely additional
contributions from trends in the kinematics and covering fraction of neutral
hydrogen. We find a tentative decrease in the Lya fraction at z~7 based on the
limited IR spectra for candidate z~7 lensed LBGs, a result which, if confirmed
with future surveys, would suggest an increase in the neutral fraction by this
epoch. Given the supply of z and Y-drops now available from Hubble WFC3/IR
surveys, we show it will soon be possible to significantly improve estimates of
the Lya fraction using optical and near-IR spectrographs, thereby extending the
study conducted in this paper to 7<z<8.


  Unsupervised disentanglement is a long-standing challenge in representation
learning. Recently, self-supervised techniques achieved impressive results in
the sequential setting, where data is time-dependent. However, the latter
methods employ modality-based data augmentations and random sampling or solve
auxiliary tasks. In this work, we propose to avoid that by generating,
sampling, and comparing empirical distributions from the underlying variational
model. Unlike existing work, we introduce a self-supervised sequential
disentanglement framework based on contrastive estimation with no external
signals, while using common batch sizes and samples from the latent space
itself. In practice, we propose a unified, efficient, and easy-to-code sampling
strategy for semantically similar and dissimilar views of the data. We evaluate
our approach on video, audio, and time series benchmarks. Our method presents
state-of-the-art results in comparison to existing techniques. The code is
available at https://github.com/azencot-group/SPYL.


  We prove that the Cuntz-Pimsner algebra O(E) of a vector bundle E over a
compact metrizable space X is determined up to an isomorphism of C(X)-algebras
by the ideal (1-[E])K(X) of the K-theory ring K(X). Moreover, if E and F are
vector bundles of rank >1, then a unital embedding of C(X)-algebras of O(E)
into O(F) exists if and only if 1-[E] is divisible by 1-[F] in the ring K(X).
We introduce related, but more computable K-theory and cohomology invariants
for O(E) and study their completeness. As an application we classify the unital
separable continuous fields with fibers isomorphic to the Cuntz algebra O(m+1)
over a finite connected CW complex X of dimension d< 2m+4 provided that the
cohomology of X has no m-torsion.


  Online traffic news web sites do not always announce traffic events in areas
in real-time. There is a capability to employ text mining and machine learning
techniques on the twitter stream to perform event detection, in order to
develop a real-time traffic detection system. In this present survey paper, we
will deliberate the current state-of-art techniques in detecting traffic events
in real-time focusing on five papers [1, 2, 3, 4, 5]. Lastly, applying text
mining techniques and SVM classifiers in paper [2] gave the best results (i.e.
95.75% accuracy and 95.8% F1-score).


  Services for Cyber-Physical Systems based on Artificial Intelligence and
Machine Learning require a virtual representation of the physical. To reduce
modeling efforts and to synchronize results, for each system, a common and
unique virtual representation used by all services during the whole system
life-cycle is needed, i.e. a DigitalTwin. In this paper such a DigitalTwin,
namely the AI reference model AITwin, is defined. This reference model is
verified by using a running example from process industry and by analyzing the
work done in recent projects.


  Designing control inputs for a system that involves dynamical responses in
multiple timescales is nontrivial. This paper proposes a parameterized
time-warping function to enable a non-uniformly sampling along a prediction
horizon given some parameters. The horizon should capture the responses under
faster dynamics in the near future and preview the impact from slower dynamics
in the distant future. Then a variable sampling MPC (VS-MPC) strategy is
proposed to jointly determine optimal control and sampling parameters at each
timestamp. VS-MPC adapts how it samples along the horizon and determines
optimal control accordingly at each timestamp without offline tuning or trial
and error. A numerical example of a wind farm battery energy storage system is
also provided to demonstrate that VS-MPC outperforms the uniform sampling MPC.


  In this paper, we first obtain some analogues of a formula of Zagier (1995)
and Stanley (2011). For instance, we prove that the number of pairs of
$n$-cycles whose product has $k$ cycles and has $m$ given elements contained in
distinct cycles (or separated) is given by $$ \frac{2 (n-1)!
C_m(n+1,k)}{(n+m)(n+1-m)} $$ when $n-k$ is even, where $C_m(n,k)$ is the number
of permutations of $n$ elements having $k$ cycles and separating $m$ given
elements. As consequences, we obtain the formulas for certain separation
probabilities due to Du and Stanley, answering a call of Stanley for simple
combinatorial proofs. Furthermore, we obtain the expectation and variance of
the number of fixed points in the product of two random $n$-cycles.


  In this paper, we consider privacy against hypothesis testing adversaries
within a non-stochastic framework. We develop a theory of non-stochastic
hypothesis testing by borrowing the notion of uncertain variables from
non-stochastic information theory. We define tests as binary-valued mappings on
uncertain variables and prove a fundamental bound on the best performance of
tests in non-stochastic hypothesis testing. We use this bound to develop a
measure of privacy. We then construct reporting policies with prescribed
privacy and utility guarantees. The utility of a reporting policy is measured
by the distance between the reported and original values. We illustrate the
effects of using such privacy-preserving reporting polices on a
publicly-available practical dataset of preferences and demographics of young
individuals, aged between 15-30, with Slovakian nationality.