  The goal of the YouMakeup VQA Challenge 2020 is to provide a common benchmark
for fine-grained action understanding in domain-specific videos e.g. makeup
instructional videos. We propose two novel question-answering tasks to evaluate
models' fine-grained action understanding abilities. The first task is
\textbf{Facial Image Ordering}, which aims to understand visual effects of
different actions expressed in natural language to the facial object. The
second task is \textbf{Step Ordering}, which aims to measure cross-modal
semantic alignments between untrimmed videos and multi-sentence texts. In this
paper, we present the challenge guidelines, the dataset used, and performances
of baseline models on the two proposed tasks. The baseline codes and models are
released at \url{https://github.com/AIM3-RUC/YouMakeup_Baseline}.


  In recent years, the notion of local robustness (or robustness for short) has
emerged as a desirable property of deep neural networks. Intuitively,
robustness means that small perturbations to an input do not cause the network
to perform misclassifications. In this paper, we present a novel algorithm for
verifying robustness properties of neural networks. Our method synergistically
combines gradient-based optimization methods for counterexample search with
abstraction-based proof search to obtain a sound and ({\delta}-)complete
decision procedure. Our method also employs a data-driven approach to learn a
verification policy that guides abstract interpretation during proof search. We
have implemented the proposed approach in a tool called Charon and
experimentally evaluated it on hundreds of benchmarks. Our experiments show
that the proposed approach significantly outperforms three state-of-the-art
tools, namely AI^2 , Reluplex, and Reluval.


  The realisation of sensing modalities based on the principles of compressed
sensing is often hindered by discrepancies between the mathematical model of
its sensing operator, which is necessary during signal recovery, and its actual
physical implementation, which can amply differ from the assumed model. In this
paper we tackle the bilinear inverse problem of recovering a sparse input
signal and some unknown, unstructured multiplicative factors affecting the
sensors that capture each compressive measurement. Our methodology relies on
collecting a few snapshots under new draws of the sensing operator, and
applying a greedy algorithm based on projected gradient descent and the
principles of iterative hard thresholding. We explore empirically the sample
complexity requirements of this algorithm by testing its phase transition, and
show in a practically relevant instance of this problem for compressive imaging
that the exact solution can be obtained with only a few snapshots.


  Physical phenomena in the real world are often described by energy-based
modeling theories, such as Hamiltonian mechanics or the Landau theory, which
yield various physical laws. Recent developments in neural networks have
enabled the mimicking of the energy conservation law by learning the underlying
continuous-time differential equations. However, this may not be possible in
discrete time, which is often the case in practical learning and computation.
Moreover, other physical laws have been overlooked in the previous neural
network models. In this study, we propose a deep energy-based physical model
that admits a specific differential geometric structure. From this structure,
the conservation or dissipation law of energy and the mass conservation law
follow naturally. To ensure the energetic behavior in discrete time, we also
propose an automatic discrete differential algorithm that enables neural
networks to employ the discrete gradient method.


  In [MzM] we defined a regularized analytic torsion for quotients of the
symmetric space $\mathrm{SL}(n,\mathbb{R})/\mathrm{SO}(n)$ by arithmetic
lattices. In this paper we study the limiting behaviour of the analytic torsion
as the lattices run through sequences of congruence subgroups of a fixed
arithmetic subgroup. Our main result states that for principal congruence
subgroups and strongly acyclic flat bundles, the logarithm of the analytic
torsion, divided by the index of the subgroup, converges to the $L^2$-analytic
torsion.


  With a weighting scheme proportional to t, a traditional stochastic gradient
descent (SGD) algorithm achieves a high probability convergence rate of
O({\kappa}/T) for strongly convex functions, instead of O({\kappa} ln(T)/T). We
also prove that an accelerated SGD algorithm also achieves a rate of
O({\kappa}/T).


  This paper considers a single-cell massive multiple-input multiple-output
(MIMO) system equipped with a base station (BS) that uses one-bit quantization
and investigates the energy efficiency (EE) and spectral efficiency (SE)
trade-off. We first propose a new precoding scheme and downlink power
allocation strategy that results in uplink-downlink SINR duality for one-bit
MIMO systems. Taking into account the effect of the imperfect channel state
information, we obtain approximate closed-form expressions for the uplink and
downlink achievable rates under duality with maximum ratio
combining/matched-filter and zero-forcing processing. We then focus on joint
optimization of the competing SE and EE objectives over the number of users,
pilot training duration and operating power, using the weighted product method
to obtain the EE/SE Pareto boundary. Numerical results are presented to verify
our analytical resultsand demonstrate the fundamental tradeoff between EE and
SE for different parameter settings.


  We have observed the phenomenon of stochastic resonance on the Brillouin
propagation modes of a dissipative optical lattice. Such a mode has been
excited by applying a moving potential modulation with phase velocity equal to
the velocity of the mode. Its amplitude has been characterized by the
center-of-mass (CM) velocity of the atomic cloud. At Brillouin resonance, we
studied the CM-velocity as a function of the optical pumping rate at a given
depth of the potential wells. We have observed a resonant dependence of the CM
velocity on the optical pumping rate, corresponding to the noise strength. This
corresponds to the experimental observation of stochastic resonance in a
periodic potential in the low-damping regime.


  Let $F$ be a field, $\ell$ a prime and $D$ a central division $F$-algebra of
$\ell$-power degree. By the Rost kernel of $D$ we mean the subgroup of $F^*$
consisting of elements $\lambda$ such that the cohomology class $(D)\cup
(\lambda)\in H^3(F,\,\mathbb{Q}_{\ell}/\mathbb{Z}_{\ell}(2))$ vanishes. In
1985, Suslin conjectured that the Rost kernel is generated by $i$-th powers of
reduced norms from $D^{\otimes i},\,\forall i\ge 1$. Despite of known
counterexamples, we prove some new cases of Suslin's conjecture. We assume $F$
is a henselian discrete valuation field with residue field $k$ of
characteristic different from $\ell$. When $D$ has period $\ell$, we show that
Suslin's conjecture holds if either $k$ is a $2$-local field or the
cohomological $\ell$-dimension $\mathrm{cd}_{\ell}(k)$ of $k$ is $\le 2$. When
the period is arbitrary, we prove the same result when $k$ itself is a
henselian discrete valuation field with $\mathrm{cd}_{\ell}(k)\le 2$. In the
case $\ell=\text{char}(k)$ an analog is obtained for tamely ramified algebras.
We conjecture that Suslin's conjecture holds for all fields of cohomological
dimension 3.


  Oscillation frequencies are the most accurate properties one can measure for
a star, potentially allowing detailed tests of stellar models and evolution
theories. We briefly review asteroseismology for two classes of stars. In delta
Scuti variables, the main problems are the identification of the observed modes
and the theoretical treatment of rotation. In solar-like stars the main
difficulty is the tiny amplitudes, but credible detections are now being made.
These confirm that stars are oscillating at the approximately the expected
levels, but suggest that amplitudes scale as 1/g rather than L/M. We also
stress the importance of multi-site campaigns. Several space missions will be
launched over the coming years, promising an exciting future for
asteroseismology.


  Solving the inverse kinematics problem is a fundamental challenge in motion
planning, control, and calibration for articulated robots. Kinematic models for
these robots are typically parametrized by joint angles, generating a
complicated mapping between the robot configuration and the end-effector pose.
Alternatively, the kinematic model and task constraints can be represented
using invariant distances between points attached to the robot. In this paper,
we formalize the equivalence of distance-based inverse kinematics and the
distance geometry problem for a large class of articulated robots and task
constraints. Unlike previous approaches, we use the connection between distance
geometry and low-rank matrix completion to find inverse kinematics solutions by
completing a partial Euclidean distance matrix through local optimization.
Furthermore, we parametrize the space of Euclidean distance matrices with the
Riemannian manifold of fixed-rank Gram matrices, allowing us to leverage a
variety of mature Riemannian optimization methods. Finally, we show that bound
smoothing can be used to generate informed initializations without significant
computational overhead, improving convergence. We demonstrate that our inverse
kinematics solver achieves higher success rates than traditional techniques,
and substantially outperforms them on problems that involve many workspace
constraints.


  We prove the vanishing of the space of 3-loop Jacobi diagrams of odd degree.
This implies that no 3-loop finite-type invariant can distinguish between a
knot and its inverse.


  Charge carrier dynamics essentially determine the performance of various
optoelectronic applications of colloidal semiconductor nanocrystals. Among
them, two-dimensional nanoplatelets provide new adjustment freedom for their
unique core/crown heterostructure. Herein, we demonstrate that by fine-tuning
the core size and the lateral quantum confinement, the charge carrier transfer
rate from the crown to the core can be varied by one order of magnitude in
CdSe/CdSeS core/alloy-crown nanoplatelets. In addition, the transfer can be
affected by a carrier blocking mechanism, i.e., the filled carriers hinder
further possible transfer. Furthermore, we found that the biexciton interaction
is oppositely affected by quantum confinement and electron delocalization,
resulting in a non-monotonic variation of the biexciton binding energy with the
emission wavelength. This work provides new observations and insights into the
charge carrier transfer dynamics and exciton interactions in colloidal
nanoplatelets and will promote their further applications in lasing, display,
sensing, etc.


  Folded linear molecular chains are ubiquitous in biology. Folding is mediated
by intra-chain interactions that "glue" two or more regions of a chain. The
resulting fold topology is widely believed to be a determinant of biomolecular
properties and function. Recently, knot theory has been extended to describe
the topology of folded linear chains such as proteins and nucleic acids. To
classify and distinguish chain topologies, algebraic structure of quandles has
been adapted and applied. However, the approach is limited as apparently
distinct topologies may end up having the same number of colorings. Here, we
enhance the resolving power of the quandle coloring approach by introducing
Boltzmann weights. We demonstrate that the enhanced coloring invariants can
distinguish fold topologies with an improved resolution.


  The efficient and economical exploitation of polymers with high thermal
conductivity is essential to solve the issue of heat dissipation in organic
devices. Currently, the experimental preparation of functional thermal
conductivity polymers remains a trial and error process due to the
multi-degrees of freedom during the synthesis and characterization process. In
this work, we have proposed a high-throughput screening framework for polymer
chains with high thermal conductivity via interpretable machine learning and
physical-feature engineering. The polymer thermal conductivity datasets for
training were first collected by molecular dynamics simulation. Inspired by the
drug-like small molecule representation and molecular force field, 320 polymer
monomer descriptors were calculated and the 20 optimized descriptors with
physical meaning were extracted by hierarchical down-selection. All the machine
learning models achieve a prediction accuracy R2 greater than 0.80, which is
superior to that of represented by traditional graph descriptors. Further, the
cross-sectional area and dihedral stiffness descriptors were identified for
positive/negative contribution to thermal conductivity, and 107 promising
polymer structures with thermal conductivity greater than 20.00 W/mK were
obtained. Mathematical formulas for predicting the polymer thermal conductivity
were also constructed by using symbolic regression. The high thermal
conductivity polymer structures are mostly {\pi}-conjugated, whose overlapping
p-orbitals enable easily to maintain strong chain stiffness and large group
velocities. The proposed data-driven framework should facilitate the
theoretical and experimental design of polymers with desirable properties.


  We explain how to derive largeness constraints in scalar curvature geometry
using some basic splitting results and the potential theory on singular area
minimizing hypersurfaces. This includes a variety of results like the
non-existence of positive scalar curvature metrics on enlargeable manifolds or
simplified proofs for positive mass theorems.


  Kinetic energy stored in ISM bulk/turbulent motions is a crucial ingredient
to properly describe most properties of observed galaxies. By using Monte Carlo
simulations, we investigate how this energy is injected by supernovae and
dissipated via cloud collisions and derive the corresponding ISM velocity
probability distribution function (PDF). The functional form of the PDF for the
modulus of the velocity dispersion is $$p(v) \propto v^2
\exp[-(v/\sigma)^\beta].$$ The power-law index of the PDF depends only on the
value of the average cloud collision elasticity < \epsilon > as \beta =
2\exp(<\epsilon > -1). If \beta and the gas velocity dispersion \sigma are
known, the specific kinetic energy dissipated by collisions is found to be
\propto \sigma^2 \ln (2 / \beta)/(\beta-0.947); in steady state, this is equal
to the energy input from SNe. We predict that in a multiphase, low metallicity
(Z \approx 5 \times 10^{-3} Z_\odot) ISM the PDF should be close to a
Maxwellian (\beta = 2) with velocity dispersion \sigma \simgt 11$ km s\m; in
more metal rich systems (Z \simgt 5 \times 10^{-2} Z_\odot), instead, we expect
to observe almost exponential PDFs. This is in good agreement with a number of
observations that we review and might explain the different star formation
modes seen in dwarfs and spiral galaxies.


  We study a variation of vanilla stochastic gradient descent where the
optimizer only has access to a Markovian sampling scheme. These schemes
encompass applications that range from decentralized optimization with a random
walker (token algorithms), to RL and online system identification problems. We
focus on obtaining rates of convergence under the least restrictive assumptions
possible on the underlying Markov chain and on the functions optimized. We
first unveil the theoretical lower bound for methods that sample stochastic
gradients along the path of a Markov chain, making appear a dependency in the
hitting time of the underlying Markov chain. We then study Markov chain SGD
(MC-SGD) under much milder regularity assumptions than prior works (e.g., no
bounded gradients or domain, and infinite state spaces). We finally introduce
MC-SAG, an alternative to MC-SGD with variance reduction, that only depends on
the hitting time of the Markov chain, therefore obtaining a
communication-efficient token algorithm.


  We give various examples of asymmetric orbifold models to possess
intertwining currents which convert untwisted string states to twisted ones,
and vice versa, and see that such asymmetric orbifold models are severely
restricted. The existence of the intertwining currents leads to the enhancement
of symmetries in asymmetric orbifold models.


  We demonstrate that there exists a continuum Hamiltonian $H(\bf{r},\bf{p})$
that is formally the operator equivalent of the general tight-binding method,
inheriting the associativity and Hermiticity of the latter operator. This
provides a powerful and controlled method of obtaining effective Hamiltonians
via Taylor expansion with respect to momentum and, optionally, deformation
fields. In particular, for fundamentally non-perturbative defects, such as
twist faults and partial dislocations, the method allows the deformation field
to be retained to all orders, providing an efficient scheme for the generation
of transparent and compact Hamiltonians for such defects. We apply the method
to a survey of incommensurate physics in twist bilayers of graphene,
graphdiyne, MoS$_2$, and phosphorene. For graphene we are able to reproduce the
`reflected Dirac cones' of the $30^\circ$ quasi-crystalline bilayer found in a
recent ARPES experiment, and show it is an example of a more general phenomena
of coupling by the moir\'e momentum. We show that incommensurate physics is
governed by the decay of the interlayer interaction on the scale of the single
layer reciprocal lattices, and demonstrate that if this is slow incommensurate
scattering effects lead to very rapid broadening of band manifolds as the twist
angle is tuned through commensurate values.


  Let $\overline{\mathcal{M}}_{g,A[n]}$ be the moduli stack parametrizing
weighted stable curves, and let $\overline{M}_{g,A[n]}$ be its coarse moduli
space. These spaces have been introduced by B. Hassett, as compactifications of
$\mathcal{M}_{g,n}$ and $M_{g,n}$ respectively, by assigning rational weights
$A = (a_{1},...,a_{n})$, $0< a_{i} \leq 1$ to the markings. In particular, the
classical Deligne-Mumford compactification arises for $a_1 = ... = a_n = 1$. In
genus zero some of these spaces appear as intermediate steps of the blow-up
construction of $\overline{M}_{0,n}$ developed by M. Kapranov, while in higher
genus they may be related to the LMMP on $\overline{M}_{g,n}$. We compute the
automorphism groups of most of the Hassett's spaces appearing in the Kapranov's
blow-up construction. Furthermore, if $g\geq 1$ we compute the automorphism
groups of all Hassett's spaces. In particular, we prove that if $g\geq 1$ and
$2g-2+n\geq 3$ then the automorphism groups of both
$\overline{\mathcal{M}}_{g,A[n]}$ and $\overline{M}_{g,A[n]}$ are isomorphic to
a subgroup of $S_{n}$ whose elements are permutations preserving the weight
data in a suitable sense.


  Heterogeneous hardware other than small-core CPU such as GPU, FPGA, or
many-core CPU is increasingly being used. However, heterogeneous hardware usage
presents high technical skill barriers such as familiarity with CUDA. To
overcome this challenge, I previously proposed environment-adaptive software
that enables automatic conversion, automatic configuration, and
high-performance and low-power operation of once-written code, in accordance
with the hardware to be placed. I also previously verified performance
improvement of automatic GPU and FPGA offloading. In this paper, I verify
low-power operation with environment adaptation by evaluating power utilization
after automatic offloading. I compare Watt*seconds of existing applications
after automatic offloading with the case of CPU-only processing.


  We consider two different quantizations of the character variety consisting
of all representations of surface groups in SL_2. One is the skein algebra
considered by Przytycki-Sikora and Turaev. The other is the quantum Teichmuller
space introduced by Chekhov-Fock and Kashaev. We construct a homomorphism from
the skein algebra to the quantum Teichmuller space which, when restricted the
classical case, corresponds to the equivalence between these two algebras
through trace functions.


  This short, self-contained article seeks to introduce and survey
continuous-time deep learning approaches that are based on neural ordinary
differential equations (neural ODEs). It primarily targets readers familiar
with ordinary and partial differential equations and their analysis who are
curious to see their role in machine learning. Using three examples from
machine learning and applied mathematics, we will see how neural ODEs can
provide new insights into deep learning and a foundation for more efficient
algorithms.


  We present empirical evidence that land values are scale-free and introduce a
network model that reproduces the observations. The network approach to urban
modelling is based on the assumption that the market dynamics that generates
land values can be represented as a growing scale-free network. Our results
suggest that the network properties of trade between specialized activities
causes land values, and likely also other observables such as population, to be
power law distributed. In addition to being an attractive avenue for further
analytical inquiry, the network representation is also applicable to empirical
data and is thereby attractive for predictive modelling.


  A short historical review is made of charged particle production at high
energy proton synchrotrons and at pp and {p}p colliders. The review concerns
mainly low p_t processes, including diffraction processes, and fragmentation of
nuclei in nucleus-nucleus collisions. A short recollection is made of the first
studies of high p_t processes. Conclusions and perspectives follow.


  Artificial intelligence (AI) is currently based largely on black-box machine
learning models which lack interpretability. The field of eXplainable AI (XAI)
strives to address this major concern, being critical in high-stakes areas such
as the finance, legal and health sectors.
  We present an approach to defining AI models and their interpretability based
on category theory. For this we employ the notion of a compositional model,
which sees a model in terms of formal string diagrams which capture its
abstract structure together with its concrete implementation. This
comprehensive view incorporates deterministic, probabilistic and quantum
models. We compare a wide range of AI models as compositional models, including
linear and rule-based models, (recurrent) neural networks, transformers, VAEs,
and causal and DisCoCirc models.
  Next we give a definition of interpretation of a model in terms of its
compositional structure, demonstrating how to analyse the interpretability of a
model, and using this to clarify common themes in XAI. We find that what makes
the standard 'intrinsically interpretable' models so transparent is brought out
most clearly diagrammatically. This leads us to the more general notion of
compositionally-interpretable (CI) models, which additionally include, for
instance, causal, conceptual space, and DisCoCirc models.
  We next demonstrate the explainability benefits of CI models. Firstly, their
compositional structure may allow the computation of other quantities of
interest, and may facilitate inference from the model to the modelled
phenomenon by matching its structure. Secondly, they allow for diagrammatic
explanations for their behaviour, based on influence constraints, diagram
surgery and rewrite explanations. Finally, we discuss many future directions
for the approach, raising the question of how to learn such meaningfully
structured models in practice.


  We numerically construct static localized black holes in ten spacetime
dimensions with one compact periodic dimension. In particular, we investigate
the critical regime in which the poles of the localized black hole are about to
merge. When approaching the critical region, the behavior of physical
quantities is described by a single real valued exponent giving rise to a
logarithmic scaling of the thermodynamic quantities, in agreement with the
theoretical prediction derived from the double-cone metric. As a peculiarity,
the localized black hole solution in ten dimensions can be related to the
spatially deconfined phase of two dimensional N=(8,8) super Yang-Mills theory
(SYM) on a spatial circle. We use the localized black hole solutions to
determine the SYM phase diagram. In particular, we compute the location of the
first order phase confinement/deconfinement transition and the related latent
heat to unprecedented accuracy.


  Capturing High Dynamic Range (HDR) scenery using 8-bit cameras often suffers
from over-/underexposure, loss of fine details due to low bit-depth
compression, skewed color distributions, and strong noise in dark areas.
Traditional LDR image enhancement methods primarily focus on color mapping,
which enhances the visual representation by expanding the image's color range
and adjusting the brightness. However, these approaches fail to effectively
restore content in dynamic range extremes, which are regions with pixel values
close to 0 or 255. To address the full scope of challenges in HDR imaging and
surpass the limitations of current models, we propose a novel two-stage
approach. The first stage maps the color and brightness to an appropriate range
while keeping the existing details, and the second stage utilizes a diffusion
prior to generate content in dynamic range extremes lost during capture. This
generative refinement module can also be used as a plug-and-play module to
enhance and complement existing LDR enhancement models. The proposed method
markedly improves the quality and details of LDR images, demonstrating superior
performance through rigorous experimental validation. The project page is at
https://sagiri0208.github.io


  A generic immersion of a circle into a $2$-sphere is often studied as a
projection of a knot; it is called a knot projection. A chord diagram is a
configuration of paired points on a circle; traditionally, the two points of
each pair are connected by a chord. A triple chord is a chord diagram
consisting of three chords, each of which intersects the other chords. Every
knot projection obtains a chord diagram in which every pair of points
corresponds to the inverse image of a double point. In this paper, we show that
for any knot projection $P$, if its chord diagram contains no triple chord,
then there exists a finite sequence from $P$ to a simple closed curve such that
the sequence consists of flat Reidemeister moves, each of which decreases
$1$-gons or strong $2$-gons, where a strong $2$-gon is a $2$-gon oriented by an
orientation of $P$.


  In this paper we present a connection between two dynamical systems arising
in entirely different contexts: one in signal processing and the other in
biology. The first is the famous Iteratively Reweighted Least Squares (IRLS)
algorithm used in compressed sensing and sparse recovery while the second is
the dynamics of a slime mold (Physarum polycephalum). Both of these dynamics
are geared towards finding a minimum l1-norm solution in an affine subspace.
Despite its simplicity the convergence of the IRLS method has been shown only
for a certain regularization of it and remains an important open problem. Our
first result shows that the two dynamics are projections of the same dynamical
system in higher dimensions. As a consequence, and building on the recent work
on Physarum dynamics, we are able to prove convergence and obtain complexity
bounds for a damped version of the IRLS algorithm.


  Multishot Magnetic Resonance Imaging (MRI) has recently gained popularity as
it accelerates the MRI data acquisition process without compromising the
quality of final MR image. However, it suffers from motion artifacts caused by
patient movements which may lead to misdiagnosis. Modern state-of-the-art
motion correction techniques are able to counter small degree motion, however,
their adoption is hindered by their time complexity. This paper proposes a
Generative Adversarial Network (GAN) for reconstructing motion free
high-fidelity images while reducing the image reconstruction time by an
impressive two orders of magnitude.


  We investigate the effect of modified gravity on the specific angular
momentum of galactic halos by analyzing the halo catalogs at z=0 from
high-resolution N-body simulations for a f(R) gravity model that meets the
solar-system constraint. It is shown that the galactic halos in the f(R)
gravity model tend to acquire significantly higher specific angular momentum
than those in the standard LCDM model. The largest difference in the specific
angular momentum distribution between these two models occurs for the case of
the isolated galactic halos with mass less than 10^{11}M_sun/h, which are
likely least shielded by the chameleon screening mechanism. As the specific
angular momentum of galactic halos is rather insensitive to the other
cosmological parameters, it can in principle be an independent discriminator of
modified gravity. We speculate a possibility of using the relative abundance of
the low surface brightness galaxies (LSBGs) as a test of GR given that the
formation of the LSBGs befalls in the fast spinning dark halos.


  The microscopic origins of Fourier's venerable law of thermal transport in
quantum electron systems has remained somewhat of a mystery, given that
previous derivations were forced to invoke intrinsic scattering rates far
exceeding those occurring in real systems. We propose an alternative
hypothesis, namely, that Fourier's law emerges naturally if many quantum states
participate in the transport of heat across the system. We test this hypothesis
systematically in a graphene flake junction, and show that the temperature
distribution becomes nearly classical when the broadening of the individual
quantum states of the flake exceeds their energetic separation. We develop a
thermal resistor network model to investigate the scaling of the sample and
contact thermal resistances, and show that the latter is consistent with
classical thermal transport theory in the limit of large level broadening.


  A recent laboratory experiment (Blaauwgeers et al. 2003) suggests that a
Kelvin-Helmholtz (KH) instability at the interface between two superfluids, one
rotating and anisotropic, the other stationary and isotropic, may trigger
sudden spin-up of the stationary superfluid. This result suggests that a KH
instability at the crust-core ($^1S_0$-$^3P_2$-superfluid) boundary of a
neutron star may provide a trigger mechanism for pulsar glitches. We calculate
the dispersion relation of the KH instability involving two different
superfluids including the normal fluid components and their effects on
stability, particularly entropy transport. We show that an entropy difference
between the core and crust superfluids reduces the threshold differential shear
velocity and threshold crust-core density ratio. We evaluate the wavelength of
maximum growth of the instability for neutron star parameters and find the
resultant circulation transfer to be within the range observed in pulsar
glitches.


  Extensive efforts in the past have been directed toward the development of
summarization datasets. However, a predominant number of these resources have
been (semi)-automatically generated, typically through web data crawling,
resulting in subpar resources for training and evaluating summarization
systems, a quality compromise that is arguably due to the substantial costs
associated with generating ground-truth summaries, particularly for diverse
languages and specialized domains. To address this issue, we present ACLSum, a
novel summarization dataset carefully crafted and evaluated by domain experts.
In contrast to previous datasets, ACLSum facilitates multi-aspect summarization
of scientific papers, covering challenges, approaches, and outcomes in depth.
Through extensive experiments, we evaluate the quality of our resource and the
performance of models based on pretrained language models and state-of-the-art
large language models (LLMs). Additionally, we explore the effectiveness of
extractive versus abstractive summarization within the scholarly domain on the
basis of automatically discovered aspects. Our results corroborate previous
findings in the general domain and indicate the general superiority of
end-to-end aspect-based summarization. Our data is released at
https://github.com/sobamchan/aclsum.


  Out-of-time-order correlation functions provide a proxy for diagnosing chaos
in quantum systems. We propose and analyze an interferometric scheme for their
measurement, using only local quantum control and no reverse time evolution.
Our approach utilizes a combination of Ramsey interferometry and the recently
demonstrated ability to directly measure Renyi entropies. To implement our
scheme, we present a pair of cold-atom-based experimental blueprints; moreover,
we demonstrate that within these systems, one can naturally realize the
transverse-field Sherrington-Kirkpatrick (TFSK) model, which exhibits certain
similarities with fast scrambling black holes. We perform a detailed numerical
study of scrambling in the TFSK model, observing an interesting interplay
between the fast scrambling bound and the onset of spin-glass order.


  We study the series s(n,x) which is the sum for k from 1 to n of the square
of the sine of the product x Gamma(k)/k, where x is a variable. By Wilson's
theorem we show that the integer part of s(n,x) for x = Pi/2 is the number of
primes less or equal to n and we get a similar formula for x a rational
multiple of Pi. We show that for almost all x in the Lebesgue measure s(n,x) is
equivalent to n/2 when n tends to infinity, while for almost all x in the Baire
sense, 1/2 is a limit point of the ratio of s(n,x) to the number of primes less
or equal to n.


  The magnetism of single atoms and molecules is governed by the atomic scale
environment. In general, the reduced symmetry of the surrounding splits the $d$
states and aligns the magnetic moment along certain favorable directions. Here,
we show that we can reversibly modify the magnetocrystalline anisotropy by
manipulating the environment of single iron(II) porphyrin molecules adsorbed on
Pb(111) with the tip of a scanning tunneling microscope. When we decrease the
tip--molecule distance, we first observe a small increase followed by an
exponential decrease of the axial anisotropy on the molecules. This is in
contrast to the monotonous increase observed earlier for the same molecule with
an additional axial Cl ligand. We ascribe the changes in the anisotropy of both
species to a deformation of the molecules in the presence of the attractive
force of the tip, which leads to a change in the $d$ level alignment. These
experiments demonstrate the feasibility of a precise tuning of the magnetic
anisotropy of an individual molecule by mechanical control.


  So far the spectra $E_n(N)$ of the paradigm model of complex
PT(Parity-Time)-symmetric potential $V_{BB}(x,N)=-(ix)^N$ is known to be
analytically continued for $N > 4$. Consequently, the well known eigenvalues of
the Hermitian cases ($N=6,10$) cannot be recovered. Here, we illustrate Kato's
theorem that even if a Hamiltonian $H(\lambda)$ is an analytic function of a
real parameter $\lambda$, its eigenvalues $E_n(\lambda)$ may not be analytic at
finite number of Isolated Points (IPs). In this light, we present the Dirichlet
spectra $E_n(N)$ of $V_{BB}(x,N)$ for $2\le N<12$ using the numerical
integration of Schr{\"o}dinger equation with $\psi(x=\pm \infty)=0$ and the
diagonalization of $H=p^2/2\mu+V_{BB}(x,N)$ in the harmonic oscillator basis.
We show that these real discrete spectra are consistent with the most simple
two-turning point CWKB (C refers to complex turning points) method provided we
choose the maximal turning points (MxTP) [$-a+ib,a+ib, a, b \in {\cal R}$] such
that $|a|$ is the largest for a given energy among all (multiple) turning
points. We find that $E_n(N)$ are continuous function of $N$ but non-analytic
(their first derivative is discontinuous) at IPs $N=4,8$; where the Dirichlet
spectrum is null (as $V_{BB}$ becomes a Hermitian flat-top potential barrier).
At $N=6$ and $10$, $V_{BB}(x,N)$ becomes a Hermitian well and we recover its
well known eigenvalues.


  In the field of Natural Language Processing (NLP), we revisit the well-known
word embedding algorithm word2vec. Word embeddings identify words by vectors
such that the words' distributional similarity is captured. Unexpectedly,
besides semantic similarity even relational similarity has been shown to be
captured in word embeddings generated by word2vec, whence two questions arise.
Firstly, which kind of relations are representable in continuous space and
secondly, how are relations built. In order to tackle these questions we
propose a bottom-up point of view. We call generating input text for which
word2vec outputs target relations solving the Corpus Replication Task. Deeming
generalizations of this approach to any set of relations possible, we expect
solving of the Corpus Replication Task to provide partial answers to the
questions.


  In this letter we study the asymptotic behavior of the free partition
function in the $t\rightarrow 0^+$ limit for a stochastic process which
consists of $d-$independent, one-dimensional, symmetric, $2s-$stable processes
in a hyperrectangular cavity $K \subset \mathbb {R}^d$ with an absorbing
boundary. Each term of the partition function for this polyhedron in
d-dimensions can be represented by a quermassintegral and the geometrical
information inherited by the eigenvalues for this solvable model is complete.
We also demonstrate the correctness of our result by applying the method of
images in one dimension.


  The review of current experiments on search and studying of double beta decay
processes is done. Results of the most sensitive experiments are discussed and
values of modern limits on effective Majorana neutrino mass ($<m_{\nu}>) are
given. New results on two neutrino double beta decay are presented. The special
attention is given to new current experiments with mass of studied isotopes
more than 100 kg, EXO--200 and KamLAND--Zen. These experiments open a new era
in research of double beta decay. In the second part of the review prospects of
search for neutrinoless double beta decay in new experiments with sensitivity
to $<m_{\nu}>$ at the level of $\sim 0.01-0.1$ eV are discussed. Parameters and
characteristics of the most perspective projects (CUORE, GERDA, MAJORANA,
SuperNEMO, EXO, KamLAND--Zen, SNO+) are given.


  SPIRou is a near-infrared (nIR) spectropolarimeter / velocimeter for the
Canada-France-Hawaii Telescope (CFHT), that will focus on two forefront science
topics, (i) the quest for habitable Earth-like planets around nearby M stars,
and (ii) the study of low-mass star/planet formation in the presence of
magnetic fields. SPIRou will also efficiently tackle many key programmes beyond
these two main goals, from weather patterns on brown dwarfs to Solar-System
planet and exoplanet atmospheres. SPIRou will cover a wide spectral domain in a
single exposure (0.98-2.44um at a resolving power of 70K, yielding unpolarized
and polarized spectra of low-mass stars with a 15% average throughput at a
radial velocity (RV) precision of 1 m/s. It consists of a Cassegrain unit
mounted at the Cassegrain focus of CFHT and featuring an achromatic
polarimeter, coupled to a cryogenic spectrograph cooled down at 80K through a
fluoride fiber link. SPIRou is currently integrated at IRAP/OMP and will be
mounted at CFHT in 2017 Q4 for a first light scheduled in late 2017. Science
operation is predicted to begin in 2018 S2, allowing many fruitful synergies
with major ground and space instruments such as the JWST, TESS, ALMA and
later-on PLATO and the ELT.


  The algebra of quasisymmetric functions QSym and the shuffle algebra of
compositions Sh are isomorphic as graded Hopf algebras (in characteristic
zero), and isomorphisms between them can be specified via shuffle bases of
QSym. We use the notion of infinitesimal characters to characterize shuffle
bases, and we establish a universal property for Sh in the category of
connected graded Hopf algebras equipped with an infinitesimal character,
analogous to the universal property of QSym as a combinatorial Hopf algebra
described by Aguiar, Bergeron, and Sottile. We then use these results to give
general constructions for quasisymmetric power sums, recovering four previous
constructions from the literature, and study their properties.


  In the field of quantum chaos, the study of energy levels plays an important
role. The aim of this review paper is to critically discuss some of the main
contributions regarding the connection between classical dynamics,
semi-classical quantization and spectral statistics of energy levels. In
particular, we analyze in detail degeneracies and quasi-crossings in the
eigenvalues of quantum Hamiltonians which are classically non-integrable.
Summary: 1. Introduction; 2. Quasi-Crossing and Chaos; 3. Molecular
Spectroscopy; 4. Nuclear Models; 4.1 Zirnbauer-Verbaashot-Weidenmuller Model;
4.2 Lipkin-Meshow-Glick Model; 5. Particle Physics and Field Theory; 6.
Conclusions.


  We investigate, using a first-principles density-functional methodology, the
nature of magnetism in monolayer $1T$-phase of tantalum disulfide ($1T$-TaS$_2$
). Magnetism in the insulating phase of TaS$_2$ is a longstanding puzzle and
has led to a variety of theoretical proposals including notably the realization
of a two-dimensional quantum-spin-liquid phase. By means of non-collinear spin
calculations, we derive $\textit{ab initio}$ spin Hamiltonians including
two-spin bilinear Heisenberg exchange, as well as biquadratic and four-spin
ring-exchange couplings. We find that both quadratic and quartic interactions
are consistently ferromagnetic, for all the functionals considered.
Relativistic calculations predict substantial magnetocrystalline anisotropy.
Altogether, our results suggest that this material may realize an easy-plane
XXZ quantum ferromagnet with large anisotropy.


  Let $A$ be an algebraically simple, separable, nuclear, $\mathcal{Z}$-stable
$C^*$-algebra for which the trace space $T(A)$ is a Bauer simplex and the
extremal boundary $\partial_e T(A)$ has finite covering dimension. We prove
that each automorphism $\alpha$ on $A$ is cocycle conjugate to its tensor
product with the trivial automorphism on the Jiang-Su algebra. At least for
single automorphisms this generalizes a recent result by
Gardella-Hirshberg-Vaccaro. If $\alpha$ is strongly outer as an action of
$\mathbb{Z}$, we prove it has finite Rokhlin dimension with commuting towers.
As a consequence it tensorially absorbs any automorphism on the Jiang-Su
algebra.


  The two- and three-dimensional classical Heisenberg spin XY (CHSXY) models,
with the spherical coordinates of spins taken as dynamic variables, are
numerically investigated. We allow the polar $\theta$ and azimuthal $\phi$
angles to have uniform values in $[0,\pi)$ and $[-\pi, \pi)$, respectively, and
the static universality class is shown to be identical to the classical XY
model with two-component spins, as well as the CHSXY model with a different
choice of dynamic variables, conventionally used in the literature. The
relaxational dynamic simulation reveals that the dynamic critical exponent $z$
is found to have the value $z \approx 2.0$ for both two and three dimensions,
in contrast to $z \approx d/2$ ($d=$ spatial dimension) found previously with
spin dynamics simulation of the conventional CHSXY model. Comparisons with the
usual two-component classical XY model are also made.


  The development of synchrotron radiation light sources has been going on for
decades. Recently, X-ray free-electron lasers as well as the fourth-generation
synchrotron radiation sources based on multiple bend achromat lattices are
commissioned and constructed. These advanced light source facilities result in
beam with superior performance, such as higher brilliance, higher degree of
coherence, smaller achievable focused size. To take full advantage of the
unique properties of the source, the superior benefits of synchrotron radiation
require high standards for the quality of optics used in beamline construction.
In this paper, we took nanoprobe beamline as an example and propose a method to
achieve pre-designed specifications of beamline by imposing restrictions on
certain parameters of the X-ray reflective mirrors. By using this method, one
can clearly illustrate the requirements of optical performance for the surface
accuracy of reflective mirrors and determine which specific requirement is more
stringent, which avoids procuring significantly more expensive mirrors than
necessary, the correspondence between spatial frequencies and statistical
parameters would also be understood. Furthermore, we have studied the problem
that power spectral density (PSD) function cannot guarantee an accurate
judgement of the mirror quality. This method can also be generalized to designs
of other beamlines.


  We introduce a new class of absorbing boundary conditions (ABCs) for the
Helmholtz equation. The proposed ABCs are obtained by using $L$ discrete layers
and the $Q_N$ Lagrange finite element in conjunction with the $N$-point
Gauss-Legendre quadrature reduced integration rule in a specific formulation of
perfectly matched layers. The proposed ABCs are classified by a tuple $(L,N)$,
and achieve reflection error of order $O(R^{2LN})$ for some $R<1$. The new ABCs
generalise the perfectly matched discrete layers proposed by Guddati and Lim
[Int. J. Numer. Meth. Engng 66 (6) (2006) 949-977], including them as type
$(L,1)$. An analysis of the proposed ABCs is performed motivated by the work of
Ainsworth [J. Comput. Phys. 198 (1) (2004) 106-130]. The new ABCs facilitate
numerical implementations of the Helmholtz problem with ABCs if $Q_N$ finite
elements are used in the physical domain as well as give more insight into this
field for the further advancement.


  In this article, we study the superradiance of charged scalar fields on the
sub-extremal Reissner-Nordstrom metric, a mechanism by which such fields can
extract energy from a static spherically symmetric charged black hole. A
geometrical way of measuring the amount of energy extracted is proposed. Then
we investigate the question numerically. The toy-model and the numerical
methods used in our simulations are presented and the problem of long time
measurement of the outgoing energy flux is discussed. We provide a numerical
example of a field exhibiting a behaviour analogous to the Penrose process: an
incoming wave packet which splits, as it approaches the black hole, into an
incoming part with negative energy and an outgoing part with more energy than
the initial incoming one. We also show another type of superradiant solution
for which the energy extraction is more important. Hyperradiant behaviour is
not observed, which is an indication that the Reissner-Nordstrom metric is
linearly stable in the sub-extremal case.


  In a dynamic nuclear polarization experiment on a 40 mM solution of
4-amino-TEMPO in a 40:60 water/glycerol mixture, we have observed that the bulk
dipolar reservoir is cooled to a spin temperature of 15.5 micro-K, following
microwave irradiation for 800 s. This is significantly cooler than the 35 mK
spin temperature of the Zeeman reservoir. Equilibration of the two reservoirs
results in a 50 % increase in the NMR signal intensity, corresponding to a
Zeeman spin temperature of 23 mK. In order to achieve this polarization
directly, it was necessary to irradiate the sample with microwaves for 1500 s.
Cooling of the dipolar reservoir occurs during polarization transport through
the magnetic field gradient around the paramagnetic impurity, and is rapidly
communicated to the bulk by dipolar spin diffusion. As dipolar spin diffusion
is significantly faster than Zeeman spin diffusion, the bulk dipolar reservoir
cools faster than the Zeeman reservoir. This process can be exploited to
rapidly polarize the nuclear spins, by repeatedly cooling the dipolar system
and transferring the polarization to the Zeeman reservoir.


  A particular form of the C-metric is investigated, giving it a non-standard
interpretation and removing any singularity at $r = 0$. In the weak field limit
of the accelerating black hole, the proper acceleration $A$ of a static
observer is constant and the geometry becomes conformally-flat (anti de
Sitter). The stress tensor is of $\Lambda$-type ($\Lambda = -3a^{2}/8\pi G$)
and its energy density is negative. We propose that $\Lambda$ is responsible of
inertial forces that appear in uniformly accelerated systems (far from the
accelerating source $m$ and for $r << 1/a$ the dominant term in the expression
of $a^{r}$ is $-a cos\theta$). The components of the stress tensor and all
invariants of the conformally-flat Schwarzschild spacetime are regulated by
means of the exponential factor $exp(-k/r), k > 0$.


  Theta functions were defined for varieties with effective anticanonical
divisor and are related to certain punctured Gromov-Witten invariants. In this
paper we show that in the case of a log Calabi-Yau surface (X,D) with smooth
very ample anticanonical divisor we can circumvent the notion of punctured
Gromov-Witten invariants and relate theta functions and their multiplicative
structure to certain 2-marked log Gromov-Witten invariants. This is a natural
extension of the correspondence between wall functions and 1-marked log
Gromov-Witten invariants.


  We analyze the stability and stabilizability properties of mixed
retarded-neutral type systems when the neutral term is allowed to be singular.
Considering an operator model of the system in a Hilbert space we are
interesting in the critical case when there exists a sequence of eigenvalues
with real parts approaching to zero. In this case the exponential stability is
not possible and we are studying the strong asymptotic stability property. The
behavior of spectra of mixed retarded-neutral type systems does not allow to
apply directly neither methods of retarded system nor the approach of neutral
type systems for analysis of stability. In this paper two technics are combined
to get the conditions of asymptotic non-exponential stability: the existence of
a Riesz basis of invariant finite-dimensional subspaces and the boundedness of
the resolvent in some subspaces of a special decomposition of the state space.
For unstable systems the technics introduced allow to analyze the concept of
regular strong stabilizability for mixed retarded-neutral type systems. The
present paper extends the results by R. Rabah, G.M. Sklyar, A.V. Rezounenko on
stability obtained in [J. Diff. Equat., 214(2005), No. 2, 391-428] and on
stabilizability from [J. Diff. Equat., 245(2008), No. 3, 569-593].


  In the context of altmetrics, tweets have been discussed as potential
indicators of immediate and broader societal impact of scientific documents.
However, it is not yet clear to what extent Twitter captures actual research
impact. A small case study (Thelwall et al., 2013b) suggests that tweets to
journal articles neither comment on nor express any sentiments towards the
publication, which suggests that tweets merely disseminate bibliographic
information, often even automatically. This study analyses the sentiments of
tweets for a large representative set of scientific papers by specifically
adapting different methods to academic articles distributed on Twitter. Results
will help to improve the understanding of Twitter's role in scholarly
communication and the meaning of tweets as impact metrics.


  The authors in this book introduce the notion of special set linear algebra
and special set fuzzy Linear algebra, which is an extension of the notion set
linear algebra and set fuzzy linear algebra. These concepts are best suited in
the application of multi expert models and cryptology. This book has five
chapters. In chapter one the basic concepts about set linear algebra is given
in order to make this book a self contained one. The notion of special set
linear algebra and their fuzzy analogue is introduced in chapter two. In
chapter three the notion of special set semigroup linear algebra is introduced.
The concept of special set n-vector spaces, n greater than or equal to three is
defined and their fuzzy analogue is their fuzzy analogue is given in chapter
four. The probable applications are also mentioned. The final chapter suggests
66 problems.


  In the real world, autonomous driving agents navigate in highly dynamic
environments full of unexpected situations where pre-trained models are
unreliable. In these situations, what is immediately available to vehicles is
often only human operators. Empowering autonomous driving agents with the
ability to navigate in a continuous and dynamic environment and to communicate
with humans through sensorimotor-grounded dialogue becomes critical. To this
end, we introduce Dialogue On the ROad To Handle Irregular Events (DOROTHIE), a
novel interactive simulation platform that enables the creation of unexpected
situations on the fly to support empirical studies on situated communication
with autonomous driving agents. Based on this platform, we created the Situated
Dialogue Navigation (SDN), a navigation benchmark of 183 trials with a total of
8415 utterances, around 18.7 hours of control streams, and 2.9 hours of trimmed
audio. SDN is developed to evaluate the agent's ability to predict dialogue
moves from humans as well as generate its own dialogue moves and physical
navigation actions. We further developed a transformer-based baseline model for
these SDN tasks. Our empirical results indicate that language guided-navigation
in a highly dynamic environment is an extremely difficult task for end-to-end
models. These results will provide insight towards future work on robust
autonomous driving agents. The DOROTHIE platform, SDN benchmark, and code for
the baseline model are available at https://github.com/sled-group/DOROTHIE.


  We use time-resolved direct frequency comb spectroscopy in the mid-infrared
to obtain high-resolution rovibrational spectra of products produced from the
OD+CO reaction. In this work, we present spectral analyses for isotopologues of
the transient DOCO radicals from this reaction in the OD stretch region. The
analyses were performed with aid of two different theoretical approaches based
on both perturbation theory and variational calculations used for prediction of
rovibrational spectra of polyatomic molecules. We discuss the advantages and
challenges of our current approach for studying spectroscopy and dynamics of
transient molecules.


  The extraplanar diffuse ionised gas is a key component for understanding the
feedback processes that connect galactic discs and their halos. In this paper,
we present the second study of the BETIS project, which aims to explore the
ionisation mechanisms of the eDIG. We use a sample of eight edge-on galaxies
observed with MUSE and apply the methodology developed in the first paper of
the BETIS project. We found that the vertical and radial profiles of the
[NII]/Ha, [SII]/Ha, [OIII]/Hb, and [OI]/Ha ratios depict a complex ionisation
structure within galactic halos, influenced by the spatial distribution of HII
regions across the galactic plane as observed from our line of sigh, with
photon leakage from OB associations constituting the main ionisation source.
Our analysis excludes low-mass, hot, and evolved stars as viable candidates for
secondary ionisation sources to elucidate the unusual behaviour of the line
ratios at greater distances from the galactic midplane. In contrast, we
ascertain that shocks induced in the interstellar medium by star formation
related feedback mechanisms represent a promising secondary ionisation source
of the eDIG. We present a suite of models integrating ionisation mechanisms
arising from fast shocks and photoionisation associated with star formation.
When applied to the classical BPT diagrams, these models reveal that the
ionisation budget of the eDIG ranges from 20% to 50% across our sample, with
local variations of up to 20% within individual galaxy halos. This correlates
with the presence of filaments and other structural components observed within
galaxy halos. The presence of shocks is additionally supported by the
observation of high-density, high [OI]/Ha ratios, characteristic of
shock-compressed ionised gas, likely induced by feedback from regions of
intense SF within the disk. These results are consistent across all galaxies
analysed in this sample.


  We introduce the coherent state mapping ring-polymer molecular dynamics
(CS-RPMD), a new method that accurately describes electronic non-adiabatic
dynamics with explicit nuclear quantization. This new approach is derived by
using coherent state mapping representation for the electronic degrees of
freedom (DOF) and the ring-polymer path-integral representation for the nuclear
DOF. CS-RPMD Hamiltonian does not contain any inter-bead coupling term in the
state-dependent potential, which is a key feature that ensures correct
electronic Rabi oscillations. Hamilton's equation of motion is used to sample
initial configurations and propagate the trajectories, preserving the
distribution with classical symplectic evolution. In the special one-bead limit
for mapping variables, CS-RPMD preserves the detailed balance. Numerical tests
of this method with a two-state model system show a very good agreement with
exact quantum results over a broad range of electronic couplings.


  Given arbitrary integers $d$ and $r$ with $d \geq 4$ and $1 \leq r \leq d +
1$, a reflexive polytope $\mathcal{P} \subset \mathbb{R}^d$ of dimension $d$
with ${\rm depth} K[\mathcal{P}] = r$ for which its dual polytope
$\mathcal{P}^\vee$ is normal will be constructed, where $K[\mathcal{P}]$ is the
toric ring of $\mathcal{P}$.


  Superpositioning of relaxation data as a function of the product variable
TV^{\gamma}, where T is temperature, V the specific volume, and {\gamma} a
material constant, is an experimental fact demonstrated for approximately 100
liquids and polymers. Such scaling behavior would result from the
intermolecular potential having the form of an inverse power law (IPL),
suggesting that an IPL is a good approximation for certain relaxation
properties over the relevant range of intermolecular distances. However, the
derivation of the scaling property of an IPL liquid is based on reduced
quantities, for example, the reduced relaxation time equal to T^1/2V^-1/3 times
the actual relaxation time. The difference between scaling using reduced rather
than unreduced units is negligible in the supercooled regime; however, at
higher temperature the difference can be substantial, accounting for the
purported breakdown of the scaling and giving rise to different values of the
scaling exponent. Only the {\gamma} obtained using reduced quantities can be
sensibly related to the intermolecular potential.


  Binospec is a high-throughput, 370 to 1000 nm, imaging spectrograph that
addresses two adjacent 8' by 15' fields of view. Binospec was commissioned in
late 2017 at the f/5 focus of the 6.5m MMT and is now available to all MMT
observers. Here we describe the Binospec software used for observation
planning, instrument control, and data reduction. The software and control
systems incorporate a high level of automation to minimize observer workload.
Instrument configuration and observation sequencing is implemented using a
database-driven approach to maximize observatory efficiency. A web-based
interface allows users to define observations, monitor status, and retrieve
data products.


  Out-of-home audience measurement aims to count and characterize the people
exposed to advertising content in the physical world. While audience
measurement solutions based on computer vision are of increasing interest, no
commonly accepted benchmark exists to evaluate and compare their performance.
In this paper, we propose the first benchmark for digital out-of-home audience
measurement that evaluates the vision-based tasks of audience localization and
counting, and audience demographics. The benchmark is composed of a novel,
dataset captured at multiple locations and a set of performance measures. Using
the benchmark, we present an in-depth comparison of eight open-source
algorithms on four hardware platforms with GPU and CPU-optimized inferences and
of two commercial off-the-shelf solutions for localization, count, age, and
gender estimation. This benchmark and related open-source codes are available
at http://ava.eecs.qmul.ac.uk.


  Beta decays of the isotones with N=126 are studied by shell model
calculations taking into account both the Gamow-Teller (GT) and first-forbidden
(FF) transitions. The FF transitions are found to be important to reduce the
half-lives, by nearly twice to several times, from those by the GT
contributions only. Possible implications of the short half-lives of the
waiting point nuclei on the r-process nucleosynthesis during the supernova
explosions are discussed. A slight shift of the third peak of the element
abundances in the r-process toward higher mass region is found.


  We study the microscopic time fluctuations of traffic-load and the global
statistical properties of a dense traffic of particles on scale-free cyclic
graphs. For a wide range of driving rates $R$ the traffic is stationary and the
load timeseries exhibit anti-persistence due to the regulatory role of the
super-structure associated with two hub nodes in the network. We discuss how
the super-structure effects the functioning of the network at high traffic
density and at the jamming threshold. The degree of correlations systematically
decreases with increasing traffic density and eventually disappears when
approaching a jamming density $R_c$. Already before jamming we observe
qualitative changes in the global network-load distributions and the particle
queuing-times. These changes are related to the occurrence of temporary crises
in which the network-load increases dramatically, and then slowly falls back to
a value characterizing free-flow.


  Unsupervised anomaly localization, which plays a critical role in industrial
manufacturing, aims to identify anomalous regions that deviate from normal
sample patterns. Most recent methods perform feature matching or reconstruction
for the target sample with pre-trained deep neural networks. However, they
still struggle to address challenging anomalies because the deep embeddings
stored in the memory bank can be less powerful and informative. More
specifically, prior methods often overly rely on the finite resources stored in
the memory bank, which leads to low robustness to unseen targets. In this
paper, we propose a novel subspace-guided feature reconstruction framework to
pursue adaptive feature approximation for anomaly localization. It first learns
to construct low-dimensional subspaces from the given nominal samples, and then
learns to reconstruct the given deep target embedding by linearly combining the
subspace basis vectors using the self-expressive model. Our core is that,
despite the limited resources in the memory bank, the out-of-bank features can
be alternatively ``mimicked'' under the self-expressive mechanism to adaptively
model the target. Eventually, the poorly reconstructed feature dimensions
indicate anomalies for localization. Moreover, we propose a sampling method
that leverages the sparsity of subspaces and allows the feature reconstruction
to depend only on a small resource subset, which contributes to less memory
overhead. Extensive experiments on three industrial benchmark datasets
demonstrate that our approach generally achieves state-of-the-art anomaly
localization performance.


  We report the discovery of a Milky Way satellite in the constellation of
Antlia. The Antlia 2 dwarf galaxy is located behind the Galactic disc at a
latitude of $b\sim 11^{\circ}$ and spans $1.26$ degrees, which corresponds to
$\sim2.9$ kpc at its distance of 130 kpc. While similar in spatial extent to
the Large Magellanic Cloud, Antlia 2 is orders of magnitude fainter at $M_V=-9$
mag, making it by far the lowest surface brightness system known (at $\sim31.9$
mag/arcsec$^2$), $\sim100$ times more diffuse than the so-called ultra diffuse
galaxies. The satellite was identified using a combination of astrometry,
photometry and variability data from \textit{Gaia} Data Release 2, and its
nature confirmed with deep archival DECam imaging, which revealed a conspicuous
BHB signal. We have also obtained follow-up spectroscopy using AAOmega on the
AAT, identifying 159 member stars, and we used them to measure the dwarf's
systemic velocity, $290.9\pm0.5$km/s, its velocity dispersion, $5.7\pm1.1$
km/s, and mean metallicity, [Fe/H]$=-1.4$. From these properties we conclude
that Antlia 2 inhabits one of the least dense Dark Matter (DM) halos probed to
date. Dynamical modelling and tidal-disruption simulations suggest that a
combination of a cored DM profile and strong tidal stripping may explain the
observed properties of this satellite. The origin of this core may be
consistent with aggressive feedback, or may even require alternatives to cold
dark matter (such as ultra-light bosons).


  Molecular junctions comprise small molecules on the order of one or a few
nanometers in length, chemically attached to two electrodes of metal or
semiconductors. They have recently been identified as promising candidates for
materials/devices for thermoelectric energy conversion. Molecules have the
potential to act as sharp energy filters for electrical currents and could
outperform other materials considered for thermoelectric energy conversion so
far, thereby providing a wide-spread technological relevance thermoelectrics
could not achieve to date. However, there is a clear gap between predictions
and demonstrations in the literature studying thermoelectric molecular
junctions. This opinionated review seeks to highlight necessary steps needed
for this approach to transition from fundamental research into a viable
technology. Some important conjectures, on which the study of molecular
junctions is based, are reviewed.


  Research in human-centered AI has shown the benefits of systems that can
explain their predictions. Methods that allow an AI to take advice from humans
in response to explanations are similarly useful. While both capabilities are
well-developed for transparent learning models (e.g., linear models and
GA$^2$Ms), and recent techniques (e.g., LIME and SHAP) can generate
explanations for opaque models, little attention has been given to advice
methods for opaque models. This paper introduces LIMEADE, the first general
framework that translates both positive and negative advice (expressed using
high-level vocabulary such as that employed by post-hoc explanations) into an
update to an arbitrary, underlying opaque model. We demonstrate the generality
of our approach with case studies on seventy real-world models across two broad
domains: image classification and text recommendation. We show our method
improves accuracy compared to a rigorous baseline on the image classification
domains. For the text modality, we apply our framework to a neural recommender
system for scientific papers on a public website; our user study shows that our
framework leads to significantly higher perceived user control, trust, and
satisfaction.


  Interlayer excitons, or bound electron-hole pairs whose constituent
quasiparticles are located in distinct stacked semiconducting layers, are being
intensively studied in heterobilayers of two dimensional semiconductors. They
owe their existence to an intrinsic type-II band alignment between both layers
that convert these into p-n junctions. Here, we unveil a pronounced interlayer
exciton (IX) in heterobilayers of metal monochalcogenides, namely gamma-InSe on
epsilon-GaSe, whose pronounced emission is adjustable just by varying their
thicknesses given their number of layers dependent direct bandgaps.
Time-dependent photoluminescense spectroscopy unveils considerably longer
interlayer exciton lifetimes with respect to intralayer ones, thus confirming
their nature. The linear Stark effect yields a bound electron-hole pair whose
separation d is just (3.6 \pm 0.1) {\AA} with d being very close to dSe = 3.4
{\AA} which is the calculated interfacial Se separation. The envelope of IX is
twist angle dependent and describable by superimposed emissions that are nearly
equally spaced in energy, as if quantized due to localization induced by the
small moir\'e periodicity. These heterostacks are characterized by extremely
flat interfacial valence bands making them prime candidates for the observation
of magnetism or other correlated electronic phases upon carrier doping.


  There is a growing interest in development of in-network dispersed computing
paradigms that leverage the computing capabilities of heterogeneous resources
dispersed across the network for processing massive amount of data is collected
at the edge of the network. We consider the problem of task scheduling for such
networks, in a dynamic setting in which arriving computation jobs are modeled
as chains, with nodes representing tasks, and edges representing precedence
constraints among tasks. In our proposed model, motivated by significant
communication costs in dispersed computing environments, the communication
times are taken into account. More specifically, we consider a network where
servers are capable of serving all task types, and sending the results of
processed tasks from one server to another server results in some communication
delay that makes the design of optimal scheduling policy significantly more
challenging than classical queueing networks. As the main contributions of the
paper, we first characterize the capacity region of the network, then propose a
novel virtual queueing network encoding the state of the network. Finally, we
propose a Max-Weight type scheduling policy, and considering the virtual
queueing network in the fluid limit, we use a Lyapunov argument to show that
the policy is throughput-optimal.


  We discuss gluon production by the Schwinger mechanism in collinear
color-electric and magnetic fields which may be realized in pre-equilibrium
stages of ultra-relativistic heavy-ion collisions. Fluctuations of non-Abelian
gauge fields around a purely color-magnetic field contain exponentially growing
unstable modes in a longitudinally soft momentum region, which is known as the
Nielsen--Olesen instability. With a color-electric field imposed parallelly to
the color-magnetic field, we can formulate this instability as the Schwinger
mechanism. This is because soft unstable modes are accelerated by the electric
fields to escape from the instability condition. Effects of instability remain
in the transverse spectrum of particle modes, leading to an anomalously intense
Schwinger particle production.


  The Light-Cone Distribution Amplitude (LCDA) encodes the non-perturbative
information of the leading Fock component of the hadron wave function,
therefore required for processes including exclusive hadron production. As the
pseudo-Nambu-Goldstone boson of QCD, the nonperturbative structure of the pion
is of particular interest. Progress on the Lattice QCD calculation of the pion
LCDA on ${\cal O}(a)$-improved Wilson fermion ensembles at several lattice
spacings is presented. Excited-state systematics are taken into account within
a Bayesian Model Averaging framework. A Renormalization-Group-Invariant (RGI)
ratio of matrix elements is formed for further extraction of the pion LCDA.


  We calculate the binding energy of two atoms interacting near a Feshbach
resonance in the presence of a 1D periodic potential. The critical value of the
scattering length needed to produce a molecule as well as the value of the
molecular binding energy in the unitarity limit of infinite scattering length
are calculated as a function of the intensity of the laser field generating the
periodic potential. The Bloch bandwidth and the effective mass of molecules are
shown to depend strongly on the value of the scattering length due to the
correlated motion of the two atoms.


  The emission region of $\rm \gamma$-ray bursts (GRBs) is poorly constrained.
The uncertainty on the size of the dissipation site spans over 4 orders of
magnitude ($\rm 10^{12}-10^{17}$ cm) depending on the unknown energy
composition of the GRB jets. The joint multi-band analysis from soft X-rays to
high energies (up to $\rm \sim$ 1 GeV) of one of the most energetic and distant
GRB 220101A (z = 4.618) allows us for an accurate distinction between prompt
and early afterglow emissions. The enormous amount of energy released by GRB
220101A ($\rm E_{iso} \approx 3 \times10^{54}$ erg) and the spectral cutoff at
$\rm E_{cutoff} = 85_{-26}^{+16}$ MeV observed in the prompt emission spectrum
constrains the parameter space of GRB dissipation site. We put stringent
constraints on the prompt emission site, requiring $\rm 700<\Gamma_0<1160 $ and
$\rm R_\gamma \sim 4.5 \times 10^{13}$ cm. Our findings further highlights the
difficulty of finding a simple self consistent picture in the
electron-synchrotron scenario, favoring instead a proton-synchrotron model,
which is also consistent with the observed spectral shape. Deeper measurements
of the time variability of GRBs together with accurate high-energy observations
(MeV-GeV) would unveil the nature of the prompt emission.


  Modern deep neural networks increasingly make use of features such as dynamic
control flow, data structures and dynamic tensor shapes. Existing deep learning
systems focus on optimizing and executing static neural networks which assume a
pre-determined model architecture and input data shapes--assumptions which are
violated by dynamic neural networks. Therefore, executing dynamic models with
deep learning systems is currently both inflexible and sub-optimal, if not
impossible. Optimizing dynamic neural networks is more challenging than static
neural networks; optimizations must consider all possible execution paths and
tensor shapes. This paper proposes Nimble, a high-performance and flexible
system to optimize, compile, and execute dynamic neural networks on multiple
platforms. Nimble handles model dynamism by introducing a dynamic type system,
a set of dynamism-oriented optimizations, and a light-weight virtual machine
runtime. Our evaluation demonstrates that Nimble outperforms state-of-the-art
deep learning frameworks and runtime systems for dynamic neural networks by up
to 20x on hardware platforms including Intel CPUs, ARM CPUs, and Nvidia GPUs.


  Motivated by the results of B. Berndtsson, in this memoir we use the new
estimates developed by W. He to extend a theorem of the second author on the
existence of weak $C^{1,1}$ geodesics between two smooth non-degenerate
K\"ahler potentials to the case where the metrics on the end points may have
singularities on some analytic set and may be positive semi-definite.


  When applying Machine Learning techniques to problems, one must select model
parameters to ensure that the system converges but also does not become stuck
at the objective function's local minimum. Tuning these parameters becomes a
non-trivial task for large models and it is not always apparent if the user has
found the optimal parameters. We aim to automate the process of tuning a Neural
Network, (where only a limited number of parameter search attempts are
available) by implementing Bayesian Optimization. In particular, by assigning
Gaussian Process Priors to the parameter space, we utilize Bayesian
Optimization to tune an Artificial Neural Network used to learn the XOR
function, with the result of achieving higher prediction accuracy.


  This thesis piles up the results of five works in the field of cosmological
inflation, inflationary cosmological perturbations, cosmic microwave
background(CMB) and weak gravitational lensing of cosmic microwave background.


  The 28 October 2003 flare gave us the unique opportunity to compare the
acceleration time of high-energy protons with the escaping time of those
particles which have been measured onboard spacecraft and by neutron monitors
network as GLE event. High-energy emission time scale and shock wave height and
velocity time dependencies were also studied.


  Magnetically ordered, electrically insulating materials pave the way towards
novel spintronic devices. In these materials the flow of magnetic excitations
such as magnons results in pure spin currents. These spin currents can be
driven by gradients of the spin chemical potential and/or temperature such that
they can play the same role in novel spintronic devices as charge currents in
traditional electronic circuits. Connecting spin current based and charge
current based devices requires spin to charge interconversion. This has been
achieved by the spin Hall effect with an efficiency of several 10%. The recent
progress in materials development and understanding of pure spin current
physics opens up a plethora of novel device concepts and opportunities for
fundamental studies.


  Jonathan M. Borwein (1951-2016) was a prolific mathematician whose career
spanned several countries (UK, Canada, USA, Australia) and whose many interests
included analysis, optimisation, number theory, special functions, experimental
mathematics, mathematical finance, mathematical education, and visualisation.
We describe his life and legacy, and give an annotated bibliography of some of
his most significant books and papers.


  We investigate early black hole (BH) growth through the methodical search for
$z\gtrsim5$ AGN in the $Chandra$ Deep Field South. We base our search on the
$Chandra$ 4-Ms data with flux limits of $9.1\times\ 10^{-18}$ (soft, 0.5 - 2
keV) and $5.5\times\ 10^{-17}\ \mathrm{erg}\ \mathrm{s}^{-1}\ \mathrm{cm}^{-2}$
(hard, 2 - 8 keV). At $z\sim5$ this corresponds to luminosities as low as
$\sim10^{42}$ ($\sim10^{43}$) $\mathrm{erg}\ \mathrm{s}^{-1}$ in the soft
(hard) band and should allow us to detect Compton-thin AGN with
$M_\mathrm{BH}>10^7 M_{\odot}$ and Eddington ratios > 0.1. Our field
($0.03~\mathrm{deg}^2$) contains over 600 $z\sim5$ Lyman Break Galaxies. Based
on lower redshift relations we would expect $\sim20$ of them to host AGN. After
combining the $Chandra$ data with GOODS/ACS, CANDELS/WFC3 and $Spitzer$/IRAC
data, the sample consists of 58 high-redshift candidates. We run a photometric
redshift code, stack the GOODS/ACS data, apply colour criteria and the Lyman
Break Technique and use the X-ray Hardness Ratio. We combine our tests and
using additional data find that all sources are most likely at low redshift. We
also find five X-ray sources without a counterpart in the optical or infrared
which might be spurious detections. We conclude that our field does not contain
any convincing $z\gtrsim5$ AGN. Explanations for this result include a low BH
occupation fraction, a low AGN fraction, short, super-Eddington growth modes,
BH growth through BH-BH mergers or in optically faint galaxies. By searching
for $z\gtrsim5$ AGN we are setting the foundation for constraining early BH
growth and seed formation scenarios.


  We present a calculation of the generalized parton distributions of the
photon using overlaps of photon light-front wave functions.


  Statistical analysis of bipartite networks frequently requires randomly
sampling from the set of all bipartite networks with the same degree sequence
as an observed network. Trade algorithms offer an efficient way to generate
samples of bipartite networks by incrementally `trading' the positions of some
of their edges. However, it is difficult to know how many such trades are
required to ensure that the sample is random. I propose a stopping rule that
focuses on the distance between sampled networks and the observed network, and
stops performing trades when this distribution stabilizes. Analyses demonstrate
that, for over 650 different degree sequences, using this stopping rule ensures
a random sample with a high probability, and that it is practical for use in
empirical applications.


  We have studied the rectified current in a geometrically symmetric
nano-electromechanical shuttle with periodic kicks and sinusoidal ac bias
voltages. The rectified current is exactly zero under the geometrical symmetry
which is generated by the electrons transferred from source to drain electrodes
through the movable shuttle. We investigate the nonzero rectified currents
through the symmetric shuttle with regular motion of which the
time-translational symmetry is broken. The motion of the shuttle, moreover,
becomes chaotic with the same mechanism of the kicked rotor and generates the
scattered current as increasing kick strength. We point out that the
time-translational-symmetry breaking of the instantaneous current is an
important role of manipulation of the rectified current.


  We introduce a new model for the generation of random satisfiability
problems. It is an extension of the hyper-SAT model of Ricci-Tersenghi, Weigt
and Zecchina, which is a variant of the famous K-SAT model: it is extended to
q-state variables and relates to a different choice of the statistical
ensemble. The model has an exactly solvable statistic: the critical exponents
and scaling functions of the SAT/UNSAT transition are calculable at zero
temperature, with no need of replicas, also with exact finite-size corrections.
We also introduce an exact duality of the model, and show an analogy of
thermodynamic properties with the Random Energy Model of disordered spin
systems theory. Relations with Error-Correcting Codes are also discussed.


  We have investigated the tunneling properties of an electron double quantum
well system where the lowest Landau level of each quantum well is half filled.
This system is expected to be a Bose condensate of excitons. Our four-terminal
dc measurements reveal a nearly vanishing interlayer voltage and the existence
of critical tunneling currents which depend on the strength of the condensate
state.


  We consider L-scheme and Newton based solvers for Biot model under small or
large deformation. The mechanical deformation follows the Saint Venant-Kirchoff
constitutive law. Further, the fluid compressibility is assumed to be
nonlinear. A Lagrangian frame of reference is used to keep track of the
deformation. We perform an implicit discretization in time (backward Euler) and
propose two linearization schemes for solving the nonlinear problems appearing
within each time step: Newton's method and L-scheme. The linearizations are
used monolithically or in combination with a splitting algorithm. The resulting
schemes can be applied for any spatial discretization. The convergences of all
schemes are shown analytically for cases under small deformation. Illustrative
numerical examples are presented to confirm the applicability of the schemes,
in particular, for large deformation.


  We have studied 23 long-lived G dwarfs that belong to the thin disk and thick
disk stellar populations. Abundances have been derived for 24 elements: O, Na,
Mg, Al, Si, Ca, Ti, Sc, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Sr, Y, Zr, Ba, La, Ce,
Nd, and Eu. We find that the behavior of [alpha/Fe] and [Eu/Fe] vs. [Fe/H] are
quite different for the two populations. As has long been known, the thin disk
O, Mg, Si, Ca, and Ti ratios are enhanced relative to iron at the lowest
metallicities, and decline toward solar values as [Fe/H] rises above -1.0. For
the thick disk, the decline in [alpha/Fe] and [Eu/Fe] does not begin at [Fe/H]
= -1.0, but at -0.4. Other elements share this behavior, including Sc, Co, and
Zn, suggesting that at least in the chemical enrichment history of the thick
disk, these elements were manufactured in similar-mass stars. Combining our
results for the oldest and longest-lived stars with prior work, we find clear
signs for an independent origin for the Galactic thick disk. (Abridged)


  We reformulate the covering and quantizer problems as the determination of
the ground states of interacting particles in $\mathbb{R}^d$ that generally
involve single-body, two-body, three-body, and higher-body interactions. This
is done by linking the covering and quantizer problems to certain optimization
problems involving the "void" nearest-neighbor functions that arise in the
theory of random media and statistical mechanics. These reformulations, which
again exemplifies the deep interplay between geometry and physics, allow one
now to employ theoretical and numerical optimization techniques to analyze and
solve these energy minimization problems. The covering and quantizer problems
have relevance in numerous applications, including wireless communication
network layouts, the search of high-dimensional data parameter spaces,
stereotactic radiation therapy, data compression, digital communications,
meshing of space for numerical analysis, and coding and cryptography, among
other examples. The connections between the covering and quantizer problems and
the sphere-packing and number-variance problems are discussed. We also show
that disordered saturated sphere packings provide relatively thin (economical)
coverings and may yield thinner coverings than the best known lattice coverings
in sufficiently large dimensions. In the case of the quantizer problem, we
derive improved upper bounds on the quantizer error using sphere-packing
solutions, which are generally substantially sharper than an existing upper
bound in low to moderately large dimensions. We also demonstrate that
disordered saturated sphere packings yield relatively good quantizers. Finally,
we remark on possible applications of our results for the detection of
gravitational waves.


  This is a survey of results obtained jointly with E. Aljadeff and published
in Adv. Math. 218 (2008), 1453-1495. We explain how to set up a theory of
polynomial identities for comodule algebras over a Hopf algebra, and
concentrate on the universal comodule algebra constructed from the identities
satisfied by a given comodule algebra. All concepts are illustrated with
various examples.


  This paper introduces noncommutative analogs of monomial symmetric functions
and fundamental noncommutative symmetric functions. The expansion of ribbon
Schur functions in both of these basis is nonnegative. With these functions at
hand, one can derive a noncommutative Cauchy identity as well as study a
noncommutative scalar product implied by Cauchy identity. This scalar product
seems be the noncommutative analog of Hall scalar product in the commutative
theory.


  In order to characterize the higher order moments of the particle
multiplicity, we implement the linear-sigma model with Polyakov-loop
correction. We first studied the critical phenomena and estimated some
thermodynamic quantities. Then, we compared all these results with the
first--principle lattice QCD calculations. Then, the extensive study of
non-normalized four moments is followed by investigating their thermal and
density dependence. We repeat this for moments normalized to temperature and
chemical potential. The fluctuations of the second order moment is used to
estimate the chiral phase--transition. Then, we implement all these in mapping
out the chiral phase transition, which shall be compared with the freeze-out
parameters estimated from the lattice QCD simulations and the thermal models
are compared with the chiral phase--diagram.


  We construct a function for almost-complex Riemannian manifolds.
Non-vanishing of the function for the almost-complex structure implies the
almost-complex structure is not integrable. Therefore the constructed function
is an obstruction for the existence of complex structures from the
almost-complex structure. It is a function, not a tensor, so it is easier to
work with.


  We derive the connection between the Cooperon problem in weak localization
theory and the random matrix description of type-II superconductors. As
magnetic field and disorder increase, an extreme type-II superconductor crosses
over from a state in which the low energy quasiparticles are primarily
localized and the density of states is determined by the electronic structure
of individual vortices, to a `chaotic' state, in which quasiparticles are
primarily extended and the density of states is determined by the random matrix
description.


  Normalizing flows map an independent set of latent variables to their samples
using a bijective transformation. Despite the exact correspondence between
samples and latent variables, their high level relationship is not well
understood. In this paper we characterize the geometric structure of flows
using principal manifolds and understand the relationship between latent
variables and samples using contours. We introduce a novel class of normalizing
flows, called principal manifold flows (PF), whose contours are its principal
manifolds, and a variant for injective flows (iPF) that is more efficient to
train than regular injective flows. PFs can be constructed using any flow
architecture, are trained with a regularized maximum likelihood objective and
can perform density estimation on all of their principal manifolds. In our
experiments we show that PFs and iPFs are able to learn the principal manifolds
over a variety of datasets. Additionally, we show that PFs can perform density
estimation on data that lie on a manifold with variable dimensionality, which
is not possible with existing normalizing flows.


  Numerical methods have become a powerful tool for research in astrophysics,
but their utility depends critically on the availability of suitable simulation
codes. This calls for continuous efforts in code development, which is
necessitated also by the rapidly evolving technology underlying today's
computing hardware. Here we discuss recent methodological progress in the
GADGET code, which has been widely applied in cosmic structure formation over
the past two decades. The new version offers improvements in force accuracy, in
time-stepping, in adaptivity to a large dynamic range in timescales, in
computational efficiency, and in parallel scalability through a special
MPI/shared-memory parallelization and communication strategy, and a
more-sophisticated domain decomposition algorithm. A manifestly momentum
conserving fast multipole method (FMM) can be employed as an alternative to the
one-sided TreePM gravity solver introduced in earlier versions. Two different
flavours of smoothed particle hydrodynamics, a classic entropy-conserving
formulation and a pressure-based approach, are supported for dealing with
gaseous flows. The code is able to cope with very large problem sizes, thus
allowing accurate predictions for cosmic structure formation in support of
future precision tests of cosmology, and at the same time is well adapted to
high dynamic range zoom-calculations with extreme variability of the particle
number density in the simulated volume. The GADGET-4 code is publicly released
to the community and contains infrastructure for on-the-fly group and
substructure finding and tracking, as well as merger tree building, a simple
model for radiative cooling and star formation, a high dynamic range power
spectrum estimator, and an initial conditions generator based on second-order
Lagrangian perturbation theory.


  In this paper we show two results. In the first result we consider
$\lambda_n-n=\frac{A}{n^\alpha}$ for $n\in\mathbb N$; if $\alpha>1/2$ and
$0<A<\frac{1}{\pi\sqrt{2 \sqrt{2}\zeta(2\alpha)}}$, the system
$\left\{\operatorname{sinc}( \lambda_n - t)\right\}_{n\in\mathbb N}$ is a Riesz
basis for $PW_{\pi}$. With the second result, we study the stability of
$\left\{\operatorname{sinc}( \lambda_n - t)\right\}_{n\in\mathbb Z}$ for
$\lambda_n\in\mathbb C$; if $|\lambda_n-n|\leqq L<\frac{1}{\pi}\,
\sqrt\frac{3\alpha}{8}$, for all $n\in\mathbb Z$, then
$\{\operatorname{sinc}(\lambda_n-t)\}_{n\in\mathbb Z}$ forms a Riesz basis for
$PW_{\pi}$. Here $\alpha$ is the Lamb-Oseen constant.


  We report measurements of the phase of the conductivity, $\phi_\sigma\equiv
arg(\sigma)$, in the normal state of a $Bi_{2}Sr_{2}CaCu_{2}O_{8+\delta}$
(BSCCO) thin film from 0.2-1.0 THz. From $\phi_\sigma$ we obtain the time delay
of the current response, $\tau_\sigma\equiv\phi_\sigma/\omega$. After
discovering a systematic error in the data analysis, the extracted
$\tau_\sigma$ has changed from that reported earlier. The revised data is shown
in the sole figure below. Analysis and discussion of these data will follow.


  In a backdoor attack, an adversary inserts maliciously constructed backdoor
examples into a training set to make the resulting model vulnerable to
manipulation. Defending against such attacks typically involves viewing these
inserted examples as outliers in the training set and using techniques from
robust statistics to detect and remove them.
  In this work, we present a different approach to the backdoor attack problem.
Specifically, we show that without structural information about the training
data distribution, backdoor attacks are indistinguishable from
naturally-occurring features in the data--and thus impossible to "detect" in a
general sense. Then, guided by this observation, we revisit existing defenses
against backdoor attacks and characterize the (often latent) assumptions they
make and on which they depend. Finally, we explore an alternative perspective
on backdoor attacks: one that assumes these attacks correspond to the strongest
feature in the training data. Under this assumption (which we make formal) we
develop a new primitive for detecting backdoor attacks. Our primitive naturally
gives rise to a detection algorithm that comes with theoretical guarantees and
is effective in practice.


  Space-based gravitational-wave observatories such as the Laser Interferometer
Space Antenna (LISA) use time-shifted and time-scaled linear combinations of
differential laser-phase beat signals to cancel the otherwise overwhelming
laser frequency noise. Nanosecond timing precision is needed to accurately form
these Time-Delay Interferometry (TDI) combinations which defines a ~1 meter
requirement on the inter-spacecraft ranging capability. The University of
Florida Hardware-in-the-loop LISA Interferometry Simulator (UFLIS) has been
used to test Time-Delay Interferometry in a configuration which incorporates
variable delays, realistic Doppler shifts, and simulated gravitational-wave
signals. The TDI 2.0 combinations are exploited to determine the time-changing
delays with nanosecond accuracy using a TDI-ranging reference tone. These
variable delays are used in forming the TDI combinations to achieve the LISA
interferometry sensitivity resulting from 10 orders of magnitude laser
frequency noise cancellation.


  The nature of the globule-coil transition of surface-confined polymers has
been an issue of debate. Here this 2D collapse transition is studied through a
partially directed lattice model. In the general case of polymers with positive
bending stiffness ($\Delta>0$), the collapse transition is {\em first-order};
it becomes {\em second-order} only in the limiting case of zero bending
stiffness ($\Delta\equiv 0$). These analytical results are confirmed by Monte
Carlo simulations. We also suggest some possible future experiments.


  A common misconception about laser interferometric detectors of gravitational
waves purports that, because the wavelength of laser light and the length of an
interferometer's arm are both stretched by a gravitational wave, no effect
should be visible, invoking an analogy with cosmological redshift in an
expanding universe. The issue is clarified with the help of a direct
calculation.


  Galactic neutron stars are a promising source of gravitational waves in the
analysis band of detectors such as LIGO and Virgo. Previous searches for
gravitational waves from neutron stars have focused on the detection of
individual neutron stars, which are either nearby or highly non-spherical. Here
we consider the stochastic gravitational-wave signal arising from the ensemble
of Galactic neutron stars. Using a population synthesis model, we estimate the
single-sigma sensitivity of current and planned gravitational-wave
observatories to average neutron star ellipticity $\epsilon$ as a function of
the number of in-band Galactic neutron stars $N_\text{tot}$. For the plausible
case of $N_\text{tot}\approx 53000$, and assuming one year of observation time
with colocated initial LIGO detectors, we find it to be
$\sigma_\epsilon=2.1\times10^{-7}$, which is comparable to current bounds on
some nearby neutron stars. (The current best $95\%$ upper limits are
$\epsilon\lesssim7\times10^{-8}.$) It is unclear if Advanced LIGO can
significantly improve on this sensitivity using spatially separated detectors.
For the proposed Einstein Telescope, we estimate that
$\sigma\epsilon=5.6\times10^{-10}$. Finally, we show that stochastic
measurements can be combined with measurements of individual neutron stars in
order to estimate the number of in-band Galactic neutron stars. In this way,
measurements of stochastic gravitational waves provide a complementary tool for
studying Galactic neutron stars.


  The Seemingly Unrelated Regressions (SUR) model is a wide used estimation
procedure in econometrics, insurance and finance, where very often, the
regression model contains more than one equation. Unknown parameters,
regression coefficients and covariances among the errors terms, are estimated
using algorithms based on Generalized Least Squares or Maximum Likelihood, and
the method, as a whole, is very sensitive to outliers. To overcome this problem
M-estimators and S-estimators are proposed in the literature together with fast
algorithms. However, these procedures are only able to cope with row-wise
outliers in the error terms, while their performance becomes very poor in the
presence of cell-wise outliers and as the number of equations increases. A new
robust approach is proposed which is able to perform well under both
contamination types as well as it is fast to compute. Illustrations based on
Monte Carlo simulations and a real data example are provided.


  An electronic nematic phase can be classified by a spontaneously broken
discrete rotational symmetry of a host lattice. In a square lattice, there are
two distinct nematic phases. The parallel nematic phase breaks $x$ and $y$
symmetry, while the diagonal nematic phase breaks the diagonal $(x+y)$ and
anti-diagonal $(x-y)$ symmetry. We investigate the interplay between the
parallel and diagonal nematic orders using mean field theory. We found that the
nematic phases compete with each other, while they coexist in a finite window
of parameter space. The quantum critical point between the diagonal nematic and
isotropic phases exists, and its location in a phase diagram depends on the
topology of the Fermi surface. We discuss the implication of our results in the
context of neutron scattering and Raman spectroscopy measurements on
La$_{2-x}$Sr$_x$CuO$_4$.